Finite Group Databasebeta

← C2×D3×M16×C3⋊D3 #72243322

Subgroups — C2×D3×M16×C3⋊D3 #72243322

Order 3456.

11512 conjugacy classes of subgroups.

The subgroup lattice has 1586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D3×C3⋊D3C211yesmaximal, characteristic
2C2×M16×C3⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
3C2×C3×M16×C3⋊D3C211yesmaximal, characteristic, complemented
4C2×C32×D3×M16C211yesmaximal, characteristic, complemented
5C2×#11723358C211yesmaximal, characteristic, complemented
6C2×D3×#3748C211yesmaximal, characteristic, complemented
7C2×C3⋊D3×#208C211yesmaximal, characteristic, complemented
8D3×M16×C3⋊D3C2116yesmaximal, direct product factor
9C2×#11723312C212yesmaximal, complemented
10C2×D3×#3743C212yesmaximal, complemented
11C2×C3⋊D3×ΓL(1,𝔽25)C212yesmaximal, complemented
12C2×D3×C8×C3⋊D3C212yesmaximal, complemented
13C2×D32×M16—34nomaximal
14C22×M16×C3⋊D3—31nomaximal
15C23×D3×C3⋊D3C411yescharacteristic
16C22×C4×C3⋊(C3⋊D3)C2211yescharacteristic
17C22×C3×C4×C3⋊D3C2211yescharacteristic
18C22×C32×C4×D3C2211yescharacteristic
19C22×#6289C411yescharacteristic
20C22×Dic3×C3⋊D3C411yescharacteristic
21C22×D3×C3⋊Dic3C411yescharacteristic
22C2×C4×D3×C3⋊D3C411yescharacteristic
23C2×C4×D3×C3⋊D3C411yescharacteristic
24C2×C4×D3×C3⋊D3C411yescharacteristic
25C2×C4×D3×C3⋊D3C418yes—
26C2×C4×D3×C3⋊D3C411yescharacteristic
27C2×C4×D3×C3⋊D3C2211yescharacteristic
28C2×C4×D3×C3⋊D3C2211yescharacteristic
29C2×C4×D3×C3⋊D3C2211yescharacteristic
30C2×C4×D3×C3⋊D3C2211yescharacteristic
31C2×C4×D3×C3⋊D3C2218yes—
32C2×C33×M16C2211yescharacteristic, complemented
33C2×#88855C2211yescharacteristic, complemented
34M16×C3⋊(C3⋊D3)C2218yescomplemented
35C2×#88850C2212yescomplemented
36C2×C8×C3⋊(C3⋊D3)C2212yescomplemented
37C2×C3×#3748C2211yescharacteristic, complemented
38C3×M16×C3⋊D3C2218yescomplemented
39C2×C3×#3743C2212yescomplemented
40C2×C3×C8×C3⋊D3C2212yescomplemented
41C2×C32×#208C2211yescharacteristic, complemented
42C32×D3×M16C2218yescomplemented
43C2×C32×ΓL(1,𝔽25)C2212yescomplemented
44C2×C32×D3×C8C2212yescomplemented
45C2×#88788C2212yescomplemented
46C2×#88787C2212yescomplemented
47C2×#88786C2212yescomplemented
48#11723358C2218yescomplemented
49C2×#88785C2212yescomplemented
50C3⋊D3×#208C2218yescomplemented
51C2×C3⋊D3×C3⋊C8C2212yescomplemented
52D3×#3748C2218yescomplemented
53C2×D3×C3⋊(C3⋊C8)C2212yescomplemented
54#11723312C22116yescomplemented
55C3⋊D3×ΓL(1,𝔽25)C22116yescomplemented
56D3×#3743C22116yescomplemented
57D3×C8×C3⋊D3C22116yescomplemented
58C23×C4×C3⋊D3—31no—
59C22×C4×D32—34no—
60C22×C32×M16—31no—
61C22×#3748—31no—
62C2×M16×C3⋊D3—31no—
63C2×M16×C3⋊D3—31no—
64C2×M16×C3⋊D3—316no—
65C2×M16×C3⋊D3—34no—
66C2×M16×C3⋊D3—32no—
67C2×M16×C3⋊D3—32no—
68C2×M16×C3⋊D3—31no—
69C2×M16×C3⋊D3—64no—
70C2×M16×C3⋊D3D311yescharacteristic, direct product factor
71C22×#3743—32no—
72C22×C8×C3⋊D3—32no—
73C2×C3×D3×M16—34no—
74C2×C3×D3×M16D314yescomplemented
75C2×#63818—34no—
76C2×D3×#208—34no—
77C2×D3×#208—34no—
78D32×M16—364no—
79C2×#63791—38no—
80C2×D3×ΓL(1,𝔽25)—38no—
81C2×D3×ΓL(1,𝔽25)—38no—
82C2×D32×C8—38no—
83C23×C3⋊(C3⋊D3)C2×C411yescharacteristic
84C23×C3×C3⋊D3C2×C411yescharacteristic
85C23×C32×D3C2×C411yescharacteristic
86C22×D3×C3⋊D3—28no—
87C22×D3×C3⋊D3C2×C411yescharacteristic
88C22×D3×C3⋊D3C2×C411yescharacteristic
89C22×D3×C3⋊D3C2×C411yescharacteristic
90C22×D3×C3⋊D3C2×C418yes—
91C22×D3×C3⋊D3C2×C411yescharacteristic
92C22×C33×C4C2311yescharacteristic
93C22×C3⋊(C3⋊Dic3)C2×C411yescharacteristic
94C2×C4×C3⋊(C3⋊D3)C2×C411yescharacteristic
95C2×C4×C3⋊(C3⋊D3)C2×C414yes—
96C2×C4×C3⋊(C3⋊D3)C2×C411yescharacteristic
97C2×C4×C3⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊(C3⋊D3)C2314yes—
99C2×C4×C3⋊(C3⋊D3)C2311yescharacteristic
100C22×C3×C3⋊Dic3C2×C411yescharacteristic
101C2×C3×C4×C3⋊D3C2×C414yes—
102C2×C3×C4×C3⋊D3C2×C411yescharacteristic
103C2×C3×C4×C3⋊D3C2×C411yescharacteristic
104C2×C3×C4×C3⋊D3C2311yescharacteristic
105C2×C3×C4×C3⋊D3C2311yescharacteristic
106C2×C3×C4×C3⋊D3C2314yes—
107C22×C32×Dic3C2×C411yescharacteristic
108C2×C32×C4×D3C2×C411yescharacteristic
109C2×C32×C4×D3C2×C414yes—
110C2×C32×C4×D3C2×C411yescharacteristic
111C2×C32×C4×D3C2311yescharacteristic
112C2×C32×C4×D3C2314yes—
113C2×C32×C4×D3C2311yescharacteristic
114C2×#6289C2×C411yescharacteristic
115C2×#6289C2×C411yescharacteristic
116C2×#6289C2×C418yes—
117C2×#6289C2×C411yescharacteristic
118C2×#6289C2×C411yescharacteristic
119C2×Dic3×C3⋊D3C2×C411yescharacteristic
120C2×Dic3×C3⋊D3C2×C411yescharacteristic
121C2×Dic3×C3⋊D3C2×C418yes—
122C2×Dic3×C3⋊D3C2×C411yescharacteristic
123C2×Dic3×C3⋊D3C2×C411yescharacteristic
124C2×D3×C3⋊Dic3C2×C411yescharacteristic
125C2×D3×C3⋊Dic3C2×C411yescharacteristic
126C2×D3×C3⋊Dic3C2×C418yes—
127C2×D3×C3⋊Dic3C2×C411yescharacteristic
128C2×D3×C3⋊Dic3C2×C411yescharacteristic
129C4×D3×C3⋊D3C2×C414yes—
130C4×D3×C3⋊D3C2×C414yes—
131C4×D3×C3⋊D3C2×C414yes—
132C4×D3×C3⋊D3C2×C418yes—
133C4×D3×C3⋊D3C2×C418yes—
134C4×D3×C3⋊D3C2×C418yes—
135C4×D3×C3⋊D3C2×C414yes—
136C4×D3×C3⋊D3C2×C418yes—
137C4×D3×C3⋊D3C2314yes—
138C4×D3×C3⋊D3C2314yes—
139C4×D3×C3⋊D3C2314yes—
140C4×D3×C3⋊D3C2314yes—
141C33×M16C2314yescomplemented
142C2×C33×C8C2312yescomplemented
143#88855C2314yescomplemented
144C2×C3⋊(C3⋊(C3⋊C8))C2312yescomplemented
145#88850C2318yescomplemented
146C8×C3⋊(C3⋊D3)C2318yescomplemented
147C3×#3748C2314yescomplemented
148C2×C3×C3⋊(C3⋊C8)C2312yescomplemented
149C3×#3743C2318yescomplemented
150C3×C8×C3⋊D3C2318yescomplemented
151C32×#208C2314yescomplemented
152C2×C32×C3⋊C8C2312yescomplemented
153C32×ΓL(1,𝔽25)C2318yescomplemented
154C32×D3×C8C2318yescomplemented
155#88788C2318yescomplemented
156#88787C2318yescomplemented
157#88786C2318yescomplemented
158#88785C2318yescomplemented
159C3⋊D3×C3⋊C8C2318yescomplemented
160D3×C3⋊(C3⋊C8)C2318yescomplemented
161C22×D3×M16—94no—
162C22×D3×M16—91no—
163C24×C3⋊D3—31no—
164C23×D32—34no—
165C23×C32×C4—31no—
166C23×C3⋊Dic3—31no—
167C22×C4×C3⋊D3—31no—
168C22×C4×C3⋊D3—31no—
169C22×C4×C3⋊D3—31no—
170C22×C4×C3⋊D3—31no—
171C22×C4×C3⋊D3—38no—
172C22×C4×C3⋊D3—31no—
173C22×C4×C3⋊D3—31no—
174C22×C4×C3⋊D3—31no—
175C22×C4×C3⋊D3—31no—
176C22×C4×C3⋊D3—31no—
177C22×C4×C3⋊D3—31no—
178C22×C4×C3⋊D3—38no—
179C22×C4×C3⋊D3—34no—
180C22×C4×C3⋊D3—31no—
181C22×C4×C3⋊D3—64no—
182C22×C4×C3⋊D3C2×D311yescharacteristic
183C22×C3×C4×D3—34no—
184C22×C3×C4×D3C2×D314yes—
185C22×#624—34no—
186C22×D3×Dic3—34no—
187C22×D3×Dic3—34no—
188C2×C4×D32—34no—
189C2×C4×D32—332no—
190C2×C4×D32—34no—
191C2×C4×D32—34no—
192C2×C4×D32—34no—
193C2×C4×D32—34no—
194C2×C4×D32—34no—
195C2×C4×D32—34no—
196C2×C4×D32—34no—
197C2×C4×D32—332no—
198C2×C32×M16—24no—
199C2×C32×M16—31no—
200C2×C32×M16—38no—
201C2×C32×M16—32no—
202C2×C32×M16C2×D314yescomplemented
203C2×C32×M16C2×D311yescharacteristic, complemented
204C22×C32×C8—32no—
205C2×#3748—31no—
206C2×#3748—38no—
207C2×#3748—32no—
208C2×#3748—34no—
209C2×#3748—64no—
210C2×#3748C2×D311yescharacteristic, complemented
211C22×C3⋊(C3⋊C8)—32no—
212M16×C3⋊D3—38no—
213M16×C3⋊D3—38no—
214M16×C3⋊D3—38no—
215M16×C3⋊D3—316no—
216M16×C3⋊D3—316no—
217M16×C3⋊D3—332no—
218M16×C3⋊D3—632no—
219M16×C3⋊D3C2×D318yesdirect product factor
220C2×#3743—32no—
221C2×#3743—32no—
222C2×#3743—32no—
223C2×#3743—316no—
224C2×#3743—38no—
225C2×#3743—68no—
226C2×#3743C2×D312yescomplemented
227C2×C8×C3⋊D3—32no—
228C2×C8×C3⋊D3—32no—
229C2×C8×C3⋊D3—32no—
230C2×C8×C3⋊D3—316no—
231C2×C8×C3⋊D3—38no—
232C2×C8×C3⋊D3—68no—
233C2×C8×C3⋊D3C2×D312yescomplemented
234C2×C3×#208—34no—
235C2×C3×#208C2×D314yescomplemented
236C3×D3×M16—332no—
237C3×D3×M16C2×D3132yescomplemented
238C2×C3×ΓL(1,𝔽25)—38no—
239C2×C3×ΓL(1,𝔽25)C2×D318yescomplemented
240C2×C3×D3×C8—38no—
241C2×C3×D3×C8C2×D318yescomplemented
242C2×#3712—38no—
243C2×#3711—38no—
244C2×#3711—38no—
245#63818—332no—
246C2×#3710—38no—
247D3×#208—332no—
248D3×#208—332no—
249C2×D3×C3⋊C8—38no—
250C2×D3×C3⋊C8—38no—
251#63791—364no—
252D3×ΓL(1,𝔽25)—364no—
253D3×ΓL(1,𝔽25)—364no—
254D32×C8—364no—
255C23×C33C22×C411yescharacteristic
256C22×C3⋊(C3⋊D3)—24no—
257C22×C3⋊(C3⋊D3)C22×C411yescharacteristic
258C22×C3⋊(C3⋊D3)C22×C414yes—
259C22×C3⋊(C3⋊D3)C22×C411yescharacteristic
260C22×C3×C3⋊D3—24no—
261C22×C3×C3⋊D3C22×C411yescharacteristic
262C22×C3×C3⋊D3C22×C414yes—
263C22×C3×C3⋊D3C22×C411yescharacteristic
264C22×C32×D3—24no—
265C22×C32×D3C22×C411yescharacteristic
266C22×C32×D3C22×C414yes—
267C22×C32×D3C22×C411yescharacteristic
268C2×D3×C3⋊D3—24no—
269C2×D3×C3⋊D3—24no—
270C2×D3×C3⋊D3—24no—
271C2×D3×C3⋊D3—232no—
272C2×D3×C3⋊D3M1618yesdirect product factor
273C2×D3×C3⋊D3C22×C414yes—
274C2×D3×C3⋊D3C22×C414yes—
275C2×D3×C3⋊D3C22×C414yes—
276C2×D3×C3⋊D3C22×C414yes—
277C2×C33×C4C22×C412yes—
278C2×C33×C4C22×C411yescharacteristic
279C2×C33×C4C2411yescharacteristic
280C2×C33×C4C2412yes—
281C2×C3⋊(C3⋊Dic3)C22×C414yes—
282C2×C3⋊(C3⋊Dic3)C22×C411yescharacteristic
283C2×C3⋊(C3⋊Dic3)C22×C411yescharacteristic
284C4×C3⋊(C3⋊D3)C22×C414yes—
285C4×C3⋊(C3⋊D3)C22×C412yes—
286C4×C3⋊(C3⋊D3)C22×C412yes—
287C4×C3⋊(C3⋊D3)C22×C414yes—
288C4×C3⋊(C3⋊D3)C2412yes—
289C4×C3⋊(C3⋊D3)C2412yes—
290C2×C3×C3⋊Dic3C22×C414yes—
291C2×C3×C3⋊Dic3C22×C411yescharacteristic
292C2×C3×C3⋊Dic3C22×C411yescharacteristic
293C3×C4×C3⋊D3C22×C412yes—
294C3×C4×C3⋊D3C22×C414yes—
295C3×C4×C3⋊D3C22×C412yes—
296C3×C4×C3⋊D3C22×C414yes—
297C3×C4×C3⋊D3C2412yes—
298C3×C4×C3⋊D3C2412yes—
299C2×C32×Dic3C22×C414yes—
300C2×C32×Dic3C22×C411yescharacteristic
301C2×C32×Dic3C22×C411yescharacteristic
302C32×C4×D3C22×C414yes—
303C32×C4×D3C22×C412yes—
304C32×C4×D3C22×C412yes—
305C32×C4×D3C22×C414yes—
306C32×C4×D3C2412yes—
307C32×C4×D3C2412yes—
308#6289C22×C414yes—
309#6289C22×C414yes—
310#6289C22×C414yes—
311#6289C22×C414yes—
312Dic3×C3⋊D3C22×C414yes—
313Dic3×C3⋊D3C22×C414yes—
314Dic3×C3⋊D3C22×C414yes—
315Dic3×C3⋊D3C22×C414yes—
316D3×C3⋊Dic3C22×C414yes—
317D3×C3⋊Dic3C22×C414yes—
318D3×C3⋊Dic3C22×C414yes—
319D3×C3⋊Dic3C22×C414yes—
320C33×C8C2414yescomplemented
321C3⋊(C3⋊(C3⋊C8))C2414yescomplemented
322C3×C3⋊(C3⋊C8)C2414yescomplemented
323C32×C3⋊C8C2414yescomplemented
324C23×C4×D3—94no—
325C23×C4×D3—91no—
326C22×C3×M16—34no—
327C22×C3×M16—91no—
328C22×#208—94no—
329C22×#208—91no—
330C2×D3×M16—34no—
331C2×D3×M16—98no—
332C2×D3×M16—98no—
333C2×D3×M16—964no—
334C2×D3×M16—94no—
335C2×D3×M16—94no—
336C2×D3×M16—91no—
337C2×D3×M16—94no—
338C2×D3×M16—91no—
339C2×D3×M16—91no—
340C2×D3×M16—916no—
341C2×D3×M16—92no—
342C2×D3×M16—92no—
343C2×D3×M16—184no—
344C2×D3×M16C3⋊D311yescharacteristic, direct product factor
345C22×ΓL(1,𝔽25)—98no—
346C22×ΓL(1,𝔽25)—92no—
347C22×D3×C8—98no—
348C22×D3×C8—92no—
349C24×C32—31no—
350C23×C3⋊D3—31no—
351C23×C3⋊D3—31no—
352C23×C3⋊D3—34no—
353C23×C3⋊D3—31no—
354C23×C3⋊D3—38no—
355C23×C3⋊D3—31no—
356C23×C3⋊D3—31no—
357C23×C3⋊D3—68no—
358C23×C3⋊D3—64no—
359C23×C3⋊D3C4×D311yescharacteristic
360C23×C3×D3—34no—
361C23×C3×D3C4×D314yes—
362C22×D32—34no—
363C22×D32—332no—
364C22×D32—34no—
365C22×D32—34no—
366C22×D32—34no—
367C22×D32—632no—
368C22×C32×C4—24no—
369C22×C32×C4—31no—
370C22×C32×C4—31no—
371C22×C32×C4—34no—
372C22×C32×C4—31no—
373C22×C32×C4—31no—
374C22×C32×C4—34no—
375C22×C32×C4—31no—
376C22×C32×C4C22×D314yes—
377C22×C32×C4C22×D311yescharacteristic
378C22×C3⋊Dic3—31no—
379C22×C3⋊Dic3—34no—
380C22×C3⋊Dic3—31no—
381C22×C3⋊Dic3—31no—
382C22×C3⋊Dic3—38no—
383C22×C3⋊Dic3—31no—
384C22×C3⋊Dic3—31no—
385C22×C3⋊Dic3—64no—
386C22×C3⋊Dic3C4×D311yescharacteristic
387C2×C4×C3⋊D3—31no—
388C2×C4×C3⋊D3—38no—
389C2×C4×C3⋊D3—31no—
390C2×C4×C3⋊D3—31no—
391C2×C4×C3⋊D3—31no—
392C2×C4×C3⋊D3—31no—
393C2×C4×C3⋊D3—34no—
394C2×C4×C3⋊D3—31no—
395C2×C4×C3⋊D3—34no—
396C2×C4×C3⋊D3—316no—
397C2×C4×C3⋊D3—34no—
398C2×C4×C3⋊D3—31no—
399C2×C4×C3⋊D3—31no—
400C2×C4×C3⋊D3—34no—
401C2×C4×C3⋊D3—34no—
402C2×C4×C3⋊D3—316no—
403C2×C4×C3⋊D3—34no—
404C2×C4×C3⋊D3—31no—
405C2×C4×C3⋊D3—31no—
406C2×C4×C3⋊D3—31no—
407C2×C4×C3⋊D3—38no—
408C2×C4×C3⋊D3—31no—
409C2×C4×C3⋊D3—34no—
410C2×C4×C3⋊D3—38no—
411C2×C4×C3⋊D3—34no—
412C2×C4×C3⋊D3—38no—
413C2×C4×C3⋊D3—34no—
414C2×C4×C3⋊D3—38no—
415C2×C4×C3⋊D3—38no—
416C2×C4×C3⋊D3—34no—
417C2×C4×C3⋊D3—34no—
418C2×C4×C3⋊D3—34no—
419C2×C4×C3⋊D3—34no—
420C2×C4×C3⋊D3—34no—
421C2×C4×C3⋊D3—64no—
422C2×C4×C3⋊D3—64no—
423C2×C4×C3⋊D3—616no—
424C2×C4×C3⋊D3—64no—
425C2×C4×C3⋊D3—616no—
426C2×C4×C3⋊D3—64no—
427C2×C4×C3⋊D3C4×D314yes—
428C2×C4×C3⋊D3C4×D311yescharacteristic
429C2×C4×C3⋊D3C4×D311yescharacteristic
430C2×C4×C3⋊D3C22×D311yescharacteristic
431C2×C4×C3⋊D3C22×D311yescharacteristic
432C2×C4×C3⋊D3C22×D314yes—
433C22×C3×Dic3—34no—
434C22×C3×Dic3C4×D314yes—
435C2×C3×C4×D3—34no—
436C2×C3×C4×D3—316no—
437C2×C3×C4×D3—34no—
438C2×C3×C4×D3—34no—
439C2×C3×C4×D3—34no—
440C2×C3×C4×D3—316no—
441C2×C3×C4×D3C4×D3116yes—
442C2×C3×C4×D3C4×D314yes—
443C2×C3×C4×D3C4×D314yes—
444C2×C3×C4×D3C22×D314yes—
445C2×C3×C4×D3C22×D314yes—
446C2×C3×C4×D3C22×D3116yes—
447C2×#624—34no—
448C2×#624—34no—
449C2×#624—34no—
450C2×#624—34no—
451C2×#624—332no—
452C2×D3×Dic3—34no—
453C2×D3×Dic3—34no—
454C2×D3×Dic3—332no—
455C2×D3×Dic3—34no—
456C2×D3×Dic3—34no—
457C2×D3×Dic3—34no—
458C2×D3×Dic3—34no—
459C2×D3×Dic3—34no—
460C2×D3×Dic3—34no—
461C2×D3×Dic3—332no—
462C4×D32—316no—
463C4×D32—332no—
464C4×D32—316no—
465C4×D32—316no—
466C4×D32—316no—
467C4×D32—332no—
468C4×D32—332no—
469C4×D32—332no—
470C4×D32—316no—
471C4×D32—316no—
472C4×D32—316no—
473C4×D32—316no—
474C32×M16—216no—
475C32×M16—34no—
476C32×M16—38no—
477C32×M16C22×D3116yescomplemented
478C32×M16C22×D314yescomplemented
479C2×C32×C8—28no—
480C2×C32×C8—32no—
481C2×C32×C8—38no—
482C2×C32×C8C22×D318yescomplemented
483C2×C32×C8C22×D312yescomplemented
484#3748—34no—
485#3748—316no—
486#3748—38no—
487#3748—616no—
488#3748C22×D314yescomplemented
489C2×C3⋊(C3⋊C8)—32no—
490C2×C3⋊(C3⋊C8)—38no—
491C2×C3⋊(C3⋊C8)—38no—
492C2×C3⋊(C3⋊C8)—68no—
493C2×C3⋊(C3⋊C8)C22×D312yescomplemented
494#3743—38no—
495#3743—38no—
496#3743—332no—
497#3743—38no—
498#3743—632no—
499#3743C22×D318yescomplemented
500C8×C3⋊D3—38no—
501C8×C3⋊D3—38no—
502C8×C3⋊D3—332no—
503C8×C3⋊D3—38no—
504C8×C3⋊D3—632no—
505C8×C3⋊D3C22×D318yescomplemented
506C3×#208—316no—
507C3×#208C22×D3116yescomplemented
508C2×C3×C3⋊C8—38no—
509C2×C3×C3⋊C8C22×D318yescomplemented
510C3×ΓL(1,𝔽25)—332no—
511C3×ΓL(1,𝔽25)C22×D3132yescomplemented
512C3×D3×C8—332no—
513C3×D3×C8C22×D3132yescomplemented
514#3712—332no—
515#3711—332no—
516#3711—332no—
517#3710—332no—
518D3×C3⋊C8—332no—
519D3×C3⋊C8—332no—
520C23×M16—271noSylow
521C22×C33—22no—
522C22×C33C23×C412yes—
523C22×C33C23×C411yescharacteristic
524C2×C3⋊(C3⋊D3)—22no—
525C2×C3⋊(C3⋊D3)—28no—
526C2×C3⋊(C3⋊D3)C2×M1614yescomplemented
527C2×C3⋊(C3⋊D3)C23×C412yes—
528C2×C3⋊(C3⋊D3)C23×C412yes—
529C2×C3×C3⋊D3—22no—
530C2×C3×C3⋊D3—28no—
531C2×C3×C3⋊D3C2×M1614yescomplemented
532C2×C3×C3⋊D3C23×C412yes—
533C2×C3×C3⋊D3C23×C412yes—
534C2×C32×D3—22no—
535C2×C32×D3—28no—
536C2×C32×D3C2×M1614yescomplemented
537C2×C32×D3C23×C412yes—
538C2×C32×D3C23×C412yes—
539D3×C3⋊D3—28no—
540D3×C3⋊D3—28no—
541D3×C3⋊D3—28no—
542D3×C3⋊D3C2×M16116yesdirect product factor
543C33×C4C23×C411yescharacteristic
544C33×C4C23×C412yes—
545C33×C4C2511yescharacteristic
546C3⋊(C3⋊Dic3)C23×C412yes—
547C3⋊(C3⋊Dic3)C23×C412yes—
548C3×C3⋊Dic3C23×C412yes—
549C3×C3⋊Dic3C23×C412yes—
550C32×Dic3C23×C412yes—
551C32×Dic3C23×C412yes—
552C24×D3—94no—
553C24×D3—91no—
554C23×C3×C4—34no—
555C23×C3×C4—91no—
556C23×Dic3—94no—
557C23×Dic3—91no—
558C22×C4×D3—34no—
559C22×C4×D3—94no—
560C22×C4×D3—94no—
561C22×C4×D3—932no—
562C22×C4×D3—94no—
563C22×C4×D3—94no—
564C22×C4×D3—94no—
565C22×C4×D3—94no—
566C22×C4×D3—94no—
567C22×C4×D3—94no—
568C22×C4×D3—932no—
569C22×C4×D3—94no—
570C22×C4×D3—94no—
571C22×C4×D3—91no—
572C22×C4×D3—94no—
573C22×C4×D3—91no—
574C22×C4×D3—91no—
575C22×C4×D3—91no—
576C22×C4×D3—91no—
577C22×C4×D3—98no—
578C22×C4×D3—91no—
579C22×C4×D3—91no—
580C22×C4×D3—91no—
581C22×C4×D3—91no—
582C22×C4×D3—91no—
583C22×C4×D3—91no—
584C22×C4×D3—98no—
585C22×C4×D3—184no—
586C22×C4×D3C2×C3⋊D311yescharacteristic
587C2×C3×M16—24no—
588C2×C3×M16—34no—
589C2×C3×M16—332no—
590C2×C3×M16—38no—
591C2×C3×M16—91no—
592C2×C3×M16—98no—
593C2×C3×M16—92no—
594C2×C3×M16D3214yescomplemented
595C2×C3×M16C2×C3⋊D311yescharacteristic, complemented
596C22×C3×C8—38no—
597C22×C3×C8—92no—
598C2×#208—34no—
599C2×#208—98no—
600C2×#208—932no—
601C2×#208—94no—
602C2×#208—91no—
603C2×#208—98no—
604C2×#208—92no—
605C2×#208—184no—
606C2×#208C2×C3⋊D311yescharacteristic, complemented
607C22×C3⋊C8—98no—
608C22×C3⋊C8—92no—
609D3×M16—332no—
610D3×M16—964no—
611D3×M16—964no—
612D3×M16—932no—
613D3×M16—932no—
614D3×M16—98no—
615D3×M16—932no—
616D3×M16—98no—
617D3×M16—98no—
618D3×M16—916no—
619D3×M16—916no—
620D3×M16—1832no—
621D3×M16C2×C3⋊D318yesdirect product factor
622C2×ΓL(1,𝔽25)—38no—
623C2×ΓL(1,𝔽25)—964no—
624C2×ΓL(1,𝔽25)—98no—
625C2×ΓL(1,𝔽25)—98no—
626C2×ΓL(1,𝔽25)—92no—
627C2×ΓL(1,𝔽25)—98no—
628C2×ΓL(1,𝔽25)—92no—
629C2×ΓL(1,𝔽25)—92no—
630C2×ΓL(1,𝔽25)—916no—
631C2×ΓL(1,𝔽25)—188no—
632C2×ΓL(1,𝔽25)C2×C3⋊D312yescomplemented
633C2×D3×C8—38no—
634C2×D3×C8—964no—
635C2×D3×C8—98no—
636C2×D3×C8—98no—
637C2×D3×C8—92no—
638C2×D3×C8—98no—
639C2×D3×C8—92no—
640C2×D3×C8—92no—
641C2×D3×C8—916no—
642C2×D3×C8—188no—
643C2×D3×C8C2×C3⋊D312yescomplemented
644C23×C32—24no—
645C23×C32—31no—
646C23×C32—34no—
647C23×C32—31no—
648C23×C32—64no—
649C23×C32C2×C4×D314yes—
650C23×C32C2×C4×D311yescharacteristic
651C22×C3⋊D3—24no—
652C22×C3⋊D3—31no—
653C22×C3⋊D3—38no—
654C22×C3⋊D3—34no—
655C22×C3⋊D3—34no—
656C22×C3⋊D3—31no—
657C22×C3⋊D3—34no—
658C22×C3⋊D3—34no—
659C22×C3⋊D3—34no—
660C22×C3⋊D3—34no—
661C22×C3⋊D3—316no—
662C22×C3⋊D3—34no—
663C22×C3⋊D3—64no—
664C22×C3⋊D3—616no—
665C22×C3⋊D3—64no—
666C22×C3⋊D3—64no—
667C22×C3⋊D3—632no—
668C22×C3⋊D3—64no—
669C22×C3⋊D3—64no—
670C22×C3⋊D3—64no—
671C22×C3⋊D3—616no—
672C22×C3⋊D3—1216no—
673C22×C3⋊D3C2×C4×D311yescharacteristic
674C22×C3⋊D3C2×C4×D314yes—
675C22×C3⋊D3C2×C4×D311yescharacteristic
676C22×C3×D3—216no—
677C22×C3×D3—34no—
678C22×C3×D3—316no—
679C22×C3×D3—34no—
680C22×C3×D3—616no—
681C22×C3×D3C2×C4×D314yes—
682C22×C3×D3C2×C4×D3116yes—
683C22×C3×D3C2×C4×D314yes—
684C2×D32—332no—
685C2×D32—316no—
686C2×D32—316no—
687C2×D32—316no—
688C2×D32—316no—
689C2×D32—6128no—
690C2×D32—616no—
691C2×D32—616no—
692C2×D32—616no—
693C2×C32×C4—24no—
694C2×C32×C4—28no—
695C2×C32×C4—24no—
696C2×C32×C4—28no—
697C2×C32×C4—34no—
698C2×C32×C4—31no—
699C2×C32×C4—31no—
700C2×C32×C4—32no—
701C2×C32×C4—34no—
702C2×C32×C4—34no—
703C2×C32×C4—32no—
704C2×C32×C4—32no—
705C2×C32×C4—32no—
706C2×C32×C4C2×C4×D318yes—
707C2×C32×C4C2×C4×D314yes—
708C2×C32×C4C2×C4×D312yes—
709C2×C32×C4C2×C4×D311yescharacteristic
710C2×C32×C4C23×D314yes—
711C2×C32×C4C23×D318yes—
712C2×C32×C4C23×D311yescharacteristic
713C2×C32×C4C23×D312yes—
714C2×C3⋊Dic3—34no—
715C2×C3⋊Dic3—31no—
716C2×C3⋊Dic3—31no—
717C2×C3⋊Dic3—34no—
718C2×C3⋊Dic3—34no—
719C2×C3⋊Dic3—34no—
720C2×C3⋊Dic3—34no—
721C2×C3⋊Dic3—316no—
722C2×C3⋊Dic3—34no—
723C2×C3⋊Dic3—34no—
724C2×C3⋊Dic3—64no—
725C2×C3⋊Dic3—64no—
726C2×C3⋊Dic3—616no—
727C2×C3⋊Dic3C2×C4×D314yes—
728C2×C3⋊Dic3C2×C4×D311yescharacteristic
729C2×C3⋊Dic3C2×C4×D311yescharacteristic
730C4×C3⋊D3—34no—
731C4×C3⋊D3—34no—
732C4×C3⋊D3—34no—
733C4×C3⋊D3—34no—
734C4×C3⋊D3—32no—
735C4×C3⋊D3—34no—
736C4×C3⋊D3—32no—
737C4×C3⋊D3—34no—
738C4×C3⋊D3—32no—
739C4×C3⋊D3—32no—
740C4×C3⋊D3—34no—
741C4×C3⋊D3—34no—
742C4×C3⋊D3—34no—
743C4×C3⋊D3—34no—
744C4×C3⋊D3—38no—
745C4×C3⋊D3—316no—
746C4×C3⋊D3—316no—
747C4×C3⋊D3—38no—
748C4×C3⋊D3—38no—
749C4×C3⋊D3—38no—
750C4×C3⋊D3—68no—
751C4×C3⋊D3—68no—
752C4×C3⋊D3—68no—
753C4×C3⋊D3—616no—
754C4×C3⋊D3—68no—
755C4×C3⋊D3—616no—
756C4×C3⋊D3C2×C4×D312yes—
757C4×C3⋊D3C2×C4×D314yes—
758C4×C3⋊D3C2×C4×D312yes—
759C4×C3⋊D3C2×C4×D314yes—
760C4×C3⋊D3C23×D312yes—
761C4×C3⋊D3C23×D312yes—
762C2×C3×Dic3—316no—
763C2×C3×Dic3—34no—
764C2×C3×Dic3—34no—
765C2×C3×Dic3C2×C4×D3116yes—
766C2×C3×Dic3C2×C4×D314yes—
767C2×C3×Dic3C2×C4×D314yes—
768C3×C4×D3—38no—
769C3×C4×D3—316no—
770C3×C4×D3—38no—
771C3×C4×D3—316no—
772C3×C4×D3—38no—
773C3×C4×D3—38no—
774C3×C4×D3C2×C4×D318yes—
775C3×C4×D3C2×C4×D3116yes—
776C3×C4×D3C2×C4×D318yes—
777C3×C4×D3C2×C4×D3116yes—
778C3×C4×D3C23×D318yes—
779C3×C4×D3C23×D318yes—
780#624—316no—
781#624—316no—
782#624—316no—
783#624—316no—
784D3×Dic3—316no—
785D3×Dic3—316no—
786D3×Dic3—316no—
787D3×Dic3—316no—
788D3×Dic3—316no—
789D3×Dic3—316no—
790D3×Dic3—316no—
791D3×Dic3—316no—
792C32×C8—216no—
793C32×C8—34no—
794C32×C8C23×D3116yescomplemented
795C32×C8C23×D314yescomplemented
796C3⋊(C3⋊C8)—34no—
797C3⋊(C3⋊C8)—316no—
798C3⋊(C3⋊C8)—616no—
799C3⋊(C3⋊C8)C23×D314yescomplemented
800C3×C3⋊C8—316no—
801C3×C3⋊C8C23×D3116yescomplemented
802C24×C4—271no—
803C22×M16—31no—
804C22×M16—91no—
805C22×M16—272no—
806C22×M16—272no—
807C22×M16—271no—
808C22×M16—2716no—
809C22×M16—272no—
810C22×M16—271no—
811C22×M16—271no—
812C22×M16—271no—
813C23×C8—272no—
814C2×C33—22no—
815C2×C33C22×M1612yescomplemented
816C2×C33C24×C411yescharacteristic
817C3⋊(C3⋊D3)—22no—
818C3⋊(C3⋊D3)C22×M1614yescomplemented
819C3×C3⋊D3—22no—
820C3×C3⋊D3C22×M1614yescomplemented
821C32×D3—22no—
822C32×D3C22×M1614yescomplemented
823C24×C3—34no—
824C24×C3—91no—
825C23×D3—34no—
826C23×D3—94no—
827C23×D3—94no—
828C23×D3—932no—
829C23×D3—94no—
830C23×D3—94no—
831C23×D3—91no—
832C23×D3—94no—
833C23×D3—91no—
834C23×D3—91no—
835C23×D3—98no—
836C23×D3—91no—
837C23×D3—91no—
838C23×D3—184no—
839C23×D3—188no—
840C23×D3—1832no—
841C23×D3C4×C3⋊D311yescharacteristic
842C22×C3×C4—24no—
843C22×C3×C4—34no—
844C22×C3×C4—34no—
845C22×C3×C4—316no—
846C22×C3×C4—34no—
847C22×C3×C4—34no—
848C22×C3×C4—316no—
849C22×C3×C4—34no—
850C22×C3×C4—91no—
851C22×C3×C4—91no—
852C22×C3×C4—94no—
853C22×C3×C4—91no—
854C22×C3×C4—91no—
855C22×C3×C4—94no—
856C22×C3×C4—91no—
857C22×C3×C4C2×D3214yes—
858C22×C3×C4C22×C3⋊D311yescharacteristic
859C22×Dic3—34no—
860C22×Dic3—94no—
861C22×Dic3—94no—
862C22×Dic3—932no—
863C22×Dic3—94no—
864C22×Dic3—94no—
865C22×Dic3—94no—
866C22×Dic3—91no—
867C22×Dic3—91no—
868C22×Dic3—91no—
869C22×Dic3—98no—
870C22×Dic3—91no—
871C22×Dic3—91no—
872C22×Dic3—184no—
873C22×Dic3C4×C3⋊D311yescharacteristic
874C2×C4×D3—34no—
875C2×C4×D3—34no—
876C2×C4×D3—316no—
877C2×C4×D3—34no—
878C2×C4×D3—316no—
879C2×C4×D3—34no—
880C2×C4×D3—916no—
881C2×C4×D3—916no—
882C2×C4×D3—916no—
883C2×C4×D3—916no—
884C2×C4×D3—916no—
885C2×C4×D3—932no—
886C2×C4×D3—916no—
887C2×C4×D3—916no—
888C2×C4×D3—932no—
889C2×C4×D3—916no—
890C2×C4×D3—932no—
891C2×C4×D3—932no—
892C2×C4×D3—94no—
893C2×C4×D3—94no—
894C2×C4×D3—94no—
895C2×C4×D3—932no—
896C2×C4×D3—94no—
897C2×C4×D3—94no—
898C2×C4×D3—94no—
899C2×C4×D3—94no—
900C2×C4×D3—932no—
901C2×C4×D3—94no—
902C2×C4×D3—91no—
903C2×C4×D3—98no—
904C2×C4×D3—91no—
905C2×C4×D3—91no—
906C2×C4×D3—91no—
907C2×C4×D3—94no—
908C2×C4×D3—94no—
909C2×C4×D3—916no—
910C2×C4×D3—91no—
911C2×C4×D3—91no—
912C2×C4×D3—94no—
913C2×C4×D3—94no—
914C2×C4×D3—916no—
915C2×C4×D3—94no—
916C2×C4×D3—91no—
917C2×C4×D3—94no—
918C2×C4×D3—91no—
919C2×C4×D3—91no—
920C2×C4×D3—91no—
921C2×C4×D3—91no—
922C2×C4×D3—98no—
923C2×C4×D3—91no—
924C2×C4×D3—94no—
925C2×C4×D3—94no—
926C2×C4×D3—94no—
927C2×C4×D3—94no—
928C2×C4×D3—94no—
929C2×C4×D3—98no—
930C2×C4×D3—94no—
931C2×C4×D3—98no—
932C2×C4×D3—94no—
933C2×C4×D3—98no—
934C2×C4×D3—98no—
935C2×C4×D3—94no—
936C2×C4×D3—184no—
937C2×C4×D3—184no—
938C2×C4×D3—1816no—
939C2×C4×D3—184no—
940C2×C4×D3—1816no—
941C2×C4×D3—184no—
942C2×C4×D3C4×C3⋊D314yes—
943C2×C4×D3C4×C3⋊D311yescharacteristic
944C2×C4×D3C4×C3⋊D311yescharacteristic
945C2×C4×D3C22×C3⋊D311yescharacteristic
946C2×C4×D3C22×C3⋊D311yescharacteristic
947C2×C4×D3C22×C3⋊D314yes—
948C3×M16—216no—
949C3×M16—316no—
950C3×M16—332no—
951C3×M16—94no—
952C3×M16—98no—
953C3×M16C2×D32116yescomplemented
954C3×M16C22×C3⋊D314yescomplemented
955C2×C3×C8—28no—
956C2×C3×C8—38no—
957C2×C3×C8—332no—
958C2×C3×C8—92no—
959C2×C3×C8—98no—
960C2×C3×C8C2×D3218yescomplemented
961C2×C3×C8C22×C3⋊D312yescomplemented
962#208—316no—
963#208—932no—
964#208—916no—
965#208—94no—
966#208—98no—
967#208—1816no—
968#208C22×C3⋊D314yescomplemented
969C2×C3⋊C8—38no—
970C2×C3⋊C8—932no—
971C2×C3⋊C8—98no—
972C2×C3⋊C8—92no—
973C2×C3⋊C8—98no—
974C2×C3⋊C8—188no—
975C2×C3⋊C8C22×C3⋊D312yescomplemented
976ΓL(1,𝔽25)—332no—
977ΓL(1,𝔽25)—932no—
978ΓL(1,𝔽25)—932no—
979ΓL(1,𝔽25)—98no—
980ΓL(1,𝔽25)—932no—
981ΓL(1,𝔽25)—98no—
982ΓL(1,𝔽25)—98no—
983ΓL(1,𝔽25)—1832no—
984ΓL(1,𝔽25)C22×C3⋊D318yescomplemented
985D3×C8—332no—
986D3×C8—932no—
987D3×C8—932no—
988D3×C8—98no—
989D3×C8—932no—
990D3×C8—98no—
991D3×C8—98no—
992D3×C8—1832no—
993D3×C8C22×C3⋊D318yescomplemented
994C22×C32—22no—
995C22×C32—24no—
996C22×C32—28no—
997C22×C32—28no—
998C22×C32—32no—
999C22×C32—34no—
1000C22×C32—32no—
1001C22×C32—48no—
1002C22×C32—68no—
1003C22×C32—62no—
1004C22×C32C22×C4×D318yes—
1005C22×C32C22×C4×D314yes—
1006C22×C32C22×C4×D312yes—
1007C22×C32C22×C4×D311yescharacteristic
1008C2×C3⋊D3—22no—
1009C2×C3⋊D3—28no—
1010C2×C3⋊D3—32no—
1011C2×C3⋊D3—34no—
1012C2×C3⋊D3—316no—
1013C2×C3⋊D3—32no—
1014C2×C3⋊D3—38no—
1015C2×C3⋊D3—316no—
1016C2×C3⋊D3—38no—
1017C2×C3⋊D3—616no—
1018C2×C3⋊D3—68no—
1019C2×C3⋊D3—68no—
1020C2×C3⋊D3—68no—
1021C2×C3⋊D3—68no—
1022C2×C3⋊D3—68no—
1023C2×C3⋊D3—62no—
1024C2×C3⋊D3—68no—
1025C2×C3⋊D3—632no—
1026C2×C3⋊D3—68no—
1027C2×C3⋊D3—1232no—
1028C2×C3⋊D3—128no—
1029C2×C3⋊D3D3×M1614yesdirect product factor
1030C2×C3⋊D3C22×C4×D312yes—
1031C2×C3⋊D3C22×C4×D312yes—
1032C2×C3×D3—28no—
1033C2×C3×D3—232no—
1034C2×C3×D3—38no—
1035C2×C3×D3—316no—
1036C2×C3×D3—38no—
1037C2×C3×D3—632no—
1038C2×C3×D3—68no—
1039C2×C3×D3D3×M16116yescomplemented
1040C2×C3×D3C22×C4×D318yes—
1041C2×C3×D3C22×C4×D318yes—
1042D32—364no—
1043D32—632no—
1044D32—632no—
1045D32—632no—
1046C32×C4—24no—
1047C32×C4—28no—
1048C32×C4—24no—
1049C32×C4—32no—
1050C32×C4—32no—
1051C32×C4C22×C4×D314yes—
1052C32×C4C22×C4×D318yes—
1053C32×C4C22×C4×D311yescharacteristic
1054C32×C4C22×C4×D312yes—
1055C32×C4C24×D314yes—
1056C32×C4C24×D311yescharacteristic
1057C3⋊Dic3—32no—
1058C3⋊Dic3—32no—
1059C3⋊Dic3—38no—
1060C3⋊Dic3—38no—
1061C3⋊Dic3—68no—
1062C3⋊Dic3—68no—
1063C3⋊Dic3C22×C4×D312yes—
1064C3⋊Dic3C22×C4×D312yes—
1065C3×Dic3—38no—
1066C3×Dic3—38no—
1067C3×Dic3C22×C4×D318yes—
1068C3×Dic3C22×C4×D318yes—
1069C25—271no—
1070C23×C4—31no—
1071C23×C4—91no—
1072C23×C4—271no—
1073C23×C4—278no—
1074C23×C4—271no—
1075C23×C4—271no—
1076C23×C4—271no—
1077C23×C4—271no—
1078C23×C4—271no—
1079C23×C4—271no—
1080C23×C4—271no—
1081C23×C4—271no—
1082C23×C4—278no—
1083C23×C4—271no—
1084C23×C4—271no—
1085C23×C4—271no—
1086C2×M16—31no—
1087C2×M16—38no—
1088C2×M16—32no—
1089C2×M16—91no—
1090C2×M16—98no—
1091C2×M16—92no—
1092C2×M16—272no—
1093C2×M16—2716no—
1094C2×M16—272no—
1095C2×M16—2716no—
1096C2×M16—272no—
1097C2×M16—278no—
1098C2×M16—2716no—
1099C2×M16—278no—
1100C2×M16—278no—
1101C2×M16—271no—
1102C2×M16—278no—
1103C2×M16—272no—
1104C2×M16D3×C3⋊D311yescharacteristic, direct product factor
1105C22×C8—32no—
1106C22×C8—92no—
1107C22×C8—272no—
1108C22×C8—2716no—
1109C22×C8—272no—
1110C22×C8—272no—
1111C22×C8—272no—
1112C33C23×M1611yescharacteristic, complemented, Sylow
1113C23×C3—24no—
1114C23×C3—34no—
1115C23×C3—316no—
1116C23×C3—34no—
1117C23×C3—616no—
1118C23×C3—91no—
1119C23×C3—94no—
1120C23×C3—91no—
1121C23×C3—184no—
1122C23×C3C4×D3214yes—
1123C23×C3C2×C4×C3⋊D311yescharacteristic
1124C22×D3—24no—
1125C22×D3—34no—
1126C22×D3—316no—
1127C22×D3—34no—
1128C22×D3—616no—
1129C22×D3—916no—
1130C22×D3—932no—
1131C22×D3—916no—
1132C22×D3—916no—
1133C22×D3—916no—
1134C22×D3—94no—
1135C22×D3—91no—
1136C22×D3—94no—
1137C22×D3—98no—
1138C22×D3—916no—
1139C22×D3—94no—
1140C22×D3—94no—
1141C22×D3—91no—
1142C22×D3—94no—
1143C22×D3—94no—
1144C22×D3—94no—
1145C22×D3—184no—
1146C22×D3—1816no—
1147C22×D3—184no—
1148C22×D3—184no—
1149C22×D3—1832no—
1150C22×D3—184no—
1151C22×D3—1816no—
1152C22×D3—18128no—
1153C22×D3—1816no—
1154C22×D3—1816no—
1155C22×D3—184no—
1156C22×D3—1816no—
1157C22×D3—184no—
1158C22×D3—3616no—
1159C22×D3C2×C4×C3⋊D311yescharacteristic
1160C22×D3C2×C4×C3⋊D314yes—
1161C22×D3C2×C4×C3⋊D311yescharacteristic
1162C2×C3×C4—28no—
1163C2×C3×C4—24no—
1164C2×C3×C4—24no—
1165C2×C3×C4—28no—
1166C2×C3×C4—316no—
1167C2×C3×C4—34no—
1168C2×C3×C4—34no—
1169C2×C3×C4—38no—
1170C2×C3×C4—316no—
1171C2×C3×C4—316no—
1172C2×C3×C4—38no—
1173C2×C3×C4—38no—
1174C2×C3×C4—38no—
1175C2×C3×C4—94no—
1176C2×C3×C4—91no—
1177C2×C3×C4—91no—
1178C2×C3×C4—92no—
1179C2×C3×C4—94no—
1180C2×C3×C4—94no—
1181C2×C3×C4—92no—
1182C2×C3×C4—92no—
1183C2×C3×C4—92no—
1184C2×C3×C4C4×D3218yes—
1185C2×C3×C4C4×D3214yes—
1186C2×C3×C4C2×C4×C3⋊D312yes—
1187C2×C3×C4C2×C4×C3⋊D311yescharacteristic
1188C2×C3×C4C22×D3218yes—
1189C2×C3×C4C22×D3214yes—
1190C2×C3×C4C23×C3⋊D312yes—
1191C2×C3×C4C23×C3⋊D311yescharacteristic
1192C2×Dic3—316no—
1193C2×Dic3—34no—
1194C2×Dic3—34no—
1195C2×Dic3—916no—
1196C2×Dic3—916no—
1197C2×Dic3—916no—
1198C2×Dic3—916no—
1199C2×Dic3—916no—
1200C2×Dic3—94no—
1201C2×Dic3—94no—
1202C2×Dic3—94no—
1203C2×Dic3—91no—
1204C2×Dic3—91no—
1205C2×Dic3—94no—
1206C2×Dic3—94no—
1207C2×Dic3—94no—
1208C2×Dic3—94no—
1209C2×Dic3—184no—
1210C2×Dic3—184no—
1211C2×Dic3—1816no—
1212C2×Dic3C2×C4×C3⋊D314yes—
1213C2×Dic3C2×C4×C3⋊D311yescharacteristic
1214C2×Dic3C2×C4×C3⋊D311yescharacteristic
1215C4×D3—38no—
1216C4×D3—316no—
1217C4×D3—38no—
1218C4×D3—316no—
1219C4×D3—38no—
1220C4×D3—38no—
1221C4×D3—916no—
1222C4×D3—916no—
1223C4×D3—916no—
1224C4×D3—916no—
1225C4×D3—916no—
1226C4×D3—916no—
1227C4×D3—916no—
1228C4×D3—916no—
1229C4×D3—94no—
1230C4×D3—94no—
1231C4×D3—94no—
1232C4×D3—94no—
1233C4×D3—98no—
1234C4×D3—916no—
1235C4×D3—98no—
1236C4×D3—916no—
1237C4×D3—92no—
1238C4×D3—94no—
1239C4×D3—92no—
1240C4×D3—94no—
1241C4×D3—98no—
1242C4×D3—98no—
1243C4×D3—92no—
1244C4×D3—92no—
1245C4×D3—94no—
1246C4×D3—94no—
1247C4×D3—94no—
1248C4×D3—94no—
1249C4×D3—188no—
1250C4×D3—188no—
1251C4×D3—188no—
1252C4×D3—1816no—
1253C4×D3—188no—
1254C4×D3—1816no—
1255C4×D3C2×C4×C3⋊D312yes—
1256C4×D3C2×C4×C3⋊D314yes—
1257C4×D3C2×C4×C3⋊D312yes—
1258C4×D3C2×C4×C3⋊D314yes—
1259C4×D3C23×C3⋊D312yes—
1260C4×D3C23×C3⋊D312yes—
1261C3×C8—216no—
1262C3×C8—316no—
1263C3×C8—94no—
1264C3×C8C22×D32116yescomplemented
1265C3×C8C23×C3⋊D314yescomplemented
1266C3⋊C8—316no—
1267C3⋊C8—916no—
1268C3⋊C8—94no—
1269C3⋊C8—1816no—
1270C3⋊C8C23×C3⋊D314yescomplemented
1271C2×C32—22no—
1272C2×C32—24no—
1273C2×C32—28no—
1274C2×C32—28no—
1275C2×C32—34no—
1276C2×C32—48no—
1277C2×C32—62no—
1278C2×C32C2×D3×M1618yescomplemented
1279C2×C32C2×D3×M1612yescomplemented
1280C2×C32C23×C4×D314yes—
1281C2×C32C23×C4×D311yescharacteristic
1282C3⋊D3—22no—
1283C3⋊D3—34no—
1284C3⋊D3—316no—
1285C3⋊D3—616no—
1286C3⋊D3—62no—
1287C3⋊D3—68no—
1288C3⋊D3—128no—
1289C3⋊D3C2×D3×M1614yesdirect product factor
1290C3×D3—28no—
1291C3×D3—316no—
1292C3×D3—68no—
1293C3×D3C2×D3×M16116yescomplemented
1294C24—31no—
1295C24—91no—
1296C24—271no—
1297C24—271no—
1298C24—271no—
1299C24—278no—
1300C24—271no—
1301C24—271no—
1302C24—548no—
1303C22×C4—31no—
1304C22×C4—34no—
1305C22×C4—31no—
1306C22×C4—31no—
1307C22×C4—31no—
1308C22×C4—34no—
1309C22×C4—31no—
1310C22×C4—91no—
1311C22×C4—94no—
1312C22×C4—91no—
1313C22×C4—91no—
1314C22×C4—91no—
1315C22×C4—94no—
1316C22×C4—91no—
1317C22×C4—274no—
1318C22×C4—274no—
1319C22×C4—274no—
1320C22×C4—274no—
1321C22×C4—271no—
1322C22×C4—271no—
1323C22×C4—278no—
1324C22×C4—271no—
1325C22×C4—271no—
1326C22×C4—274no—
1327C22×C4—278no—
1328C22×C4—278no—
1329C22×C4—278no—
1330C22×C4—278no—
1331C22×C4—274no—
1332C22×C4—274no—
1333C22×C4—274no—
1334C22×C4—271no—
1335C22×C4—271no—
1336C22×C4—278no—
1337C22×C4—271no—
1338C22×C4—271no—
1339C22×C4—271no—
1340C22×C4—271no—
1341C22×C4—278no—
1342C22×C4—271no—
1343C22×C4—271no—
1344C22×C4—271no—
1345C22×C4—274no—
1346C22×C4—271no—
1347C22×C4—271no—
1348C22×C4—271no—
1349C22×C4—274no—
1350C22×C4—271no—
1351C22×C4C2×D3×C3⋊D311yescharacteristic
1352M16—34no—
1353M16—38no—
1354M16—94no—
1355M16—98no—
1356M16—278no—
1357M16—278no—
1358M16—278no—
1359M16—274no—
1360M16—278no—
1361M16C2×D3×C3⋊D314yesdirect product factor
1362C2×C8—32no—
1363C2×C8—38no—
1364C2×C8—92no—
1365C2×C8—98no—
1366C2×C8—278no—
1367C2×C8—278no—
1368C2×C8—278no—
1369C2×C8—272no—
1370C2×C8—278no—
1371C2×C8C2×D3×C3⋊D312yescomplemented
1372C22×C3—22no—
1373C22×C3—28no—
1374C22×C3—24no—
1375C22×C3—28no—
1376C22×C3—38no—
1377C22×C3—316no—
1378C22×C3—38no—
1379C22×C3—48no—
1380C22×C3—632no—
1381C22×C3—68no—
1382C22×C3—94no—
1383C22×C3—92no—
1384C22×C3—92no—
1385C22×C3—188no—
1386C22×C3—182no—
1387C22×C3C2×C4×D3218yes—
1388C22×C3C2×C4×D3214yes—
1389C22×C3C22×C4×C3⋊D312yes—
1390C22×C3C22×C4×C3⋊D311yescharacteristic
1391C2×D3—22no—
1392C2×D3—28no—
1393C2×D3—38no—
1394C2×D3—316no—
1395C2×D3—38no—
1396C2×D3—632no—
1397C2×D3—68no—
1398C2×D3—964no—
1399C2×D3—98no—
1400C2×D3—94no—
1401C2×D3—92no—
1402C2×D3—916no—
1403C2×D3—916no—
1404C2×D3—98no—
1405C2×D3—92no—
1406C2×D3—188no—
1407C2×D3—1816no—
1408C2×D3—188no—
1409C2×D3—188no—
1410C2×D3—188no—
1411C2×D3—1832no—
1412C2×D3—1832no—
1413C2×D3—1832no—
1414C2×D3—188no—
1415C2×D3—1832no—
1416C2×D3—182no—
1417C2×D3—188no—
1418C2×D3—188no—
1419C2×D3—3632no—
1420C2×D3—368no—
1421C2×D3M16×C3⋊D314yesdirect product factor
1422C2×D3C22×C4×C3⋊D312yes—
1423C2×D3C22×C4×C3⋊D312yes—
1424C3×C4—28no—
1425C3×C4—24no—
1426C3×C4—24no—
1427C3×C4—38no—
1428C3×C4—38no—
1429C3×C4—92no—
1430C3×C4—92no—
1431C3×C4C2×C4×D3218yes—
1432C3×C4C2×C4×D3214yes—
1433C3×C4C22×C4×C3⋊D312yes—
1434C3×C4C22×C4×C3⋊D311yescharacteristic
1435C3×C4C23×D3214yes—
1436C3×C4C24×C3⋊D311yescharacteristic
1437Dic3—38no—
1438Dic3—38no—
1439Dic3—98no—
1440Dic3—98no—
1441Dic3—92no—
1442Dic3—92no—
1443Dic3—188no—
1444Dic3—188no—
1445Dic3C22×C4×C3⋊D312yes—
1446Dic3C22×C4×C3⋊D312yes—
1447C32—24no—
1448C32C22×D3×M1614yescomplemented
1449C32C22×D3×M1611yescharacteristic, complemented
1450C23—31no—
1451C23—34no—
1452C23—31no—
1453C23—64no—
1454C23—91no—
1455C23—94no—
1456C23—91no—
1457C23—184no—
1458C23—274no—
1459C23—278no—
1460C23—274no—
1461C23—274no—
1462C23—274no—
1463C23—271no—
1464C23—274no—
1465C23—271no—
1466C23—544no—
1467C23—544no—
1468C23—544no—
1469C23—5432no—
1470C23—544no—
1471C23C4×D3×C3⋊D311yescharacteristic
1472C2×C4—34no—
1473C2×C4—31no—
1474C2×C4—31no—
1475C2×C4—34no—
1476C2×C4—34no—
1477C2×C4—32no—
1478C2×C4—32no—
1479C2×C4—32no—
1480C2×C4—32no—
1481C2×C4—94no—
1482C2×C4—91no—
1483C2×C4—91no—
1484C2×C4—94no—
1485C2×C4—94no—
1486C2×C4—92no—
1487C2×C4—92no—
1488C2×C4—92no—
1489C2×C4—92no—
1490C2×C4—274no—
1491C2×C4—274no—
1492C2×C4—274no—
1493C2×C4—274no—
1494C2×C4—274no—
1495C2×C4—274no—
1496C2×C4—274no—
1497C2×C4—274no—
1498C2×C4—274no—
1499C2×C4—274no—
1500C2×C4—274no—
1501C2×C4—274no—
1502C2×C4—274no—
1503C2×C4—271no—
1504C2×C4—271no—
1505C2×C4—274no—
1506C2×C4—274no—
1507C2×C4—272no—
1508C2×C4—272no—
1509C2×C4—272no—
1510C2×C4—272no—
1511C2×C4C4×D3×C3⋊D311yescharacteristic
1512C2×C4C4×D3×C3⋊D312yes—
1513C2×C4C22×D3×C3⋊D312yes—
1514C2×C4C22×D3×C3⋊D311yescharacteristic
1515C8—34no—
1516C8—94no—
1517C8—274no—
1518C8C22×D3×C3⋊D314yescomplemented
1519C2×C3—22no—
1520C2×C3—28no—
1521C2×C3—28no—
1522C2×C3—24no—
1523C2×C3—316no—
1524C2×C3—48no—
1525C2×C3—68no—
1526C2×C3—94no—
1527C2×C3—182no—
1528C2×C3D32×M1618yescomplemented
1529C2×C3C2×M16×C3⋊D312yescomplemented
1530C2×C3C22×C4×D3214yes—
1531C2×C3C23×C4×C3⋊D311yescharacteristic
1532D3—22no—
1533D3—316no—
1534D3—68no—
1535D3—94no—
1536D3—916no—
1537D3—1816no—
1538D3—182no—
1539D3—188no—
1540D3—368no—
1541D3C2×M16×C3⋊D314yesdirect product factor
1542C22—22no—
1543C22—34no—
1544C22—32no—
1545C22—32no—
1546C22—68no—
1547C22—62no—
1548C22—94no—
1549C22—92no—
1550C22—92no—
1551C22—188no—
1552C22—182no—
1553C22—2716no—
1554C22—274no—
1555C22—272no—
1556C22—272no—
1557C22—548no—
1558C22—548no—
1559C22—548no—
1560C22—548no—
1561C22—542no—
1562C22C2×C4×D3×C3⋊D312yes—
1563C22C2×C4×D3×C3⋊D311yescharacteristic
1564C4—32no—
1565C4—32no—
1566C4—92no—
1567C4—92no—
1568C4—272no—
1569C4—272no—
1570C4C2×C4×D3×C3⋊D312yes—
1571C4C2×C4×D3×C3⋊D311yescharacteristic
1572C4C23×D3×C3⋊D311yescharacteristic
1573C3—24no—
1574C3C22×M16×C3⋊D311yescharacteristic, complemented
1575C3C2×D32×M1614yescomplemented
1576C2—22no—
1577C2—34no—
1578C2—62no—
1579C2—94no—
1580C2—182no—
1581C2—274no—
1582C2—542no—
1583C2D3×M16×C3⋊D312yesdirect product factor
1584C2C22×C4×D3×C3⋊D311yescharacteristic
subgroupG/H
centerC2×C4C22×D3×C3⋊D3
commutatorC2×C33C24×C4
FrattiniC4C23×D3×C3⋊D3
FittingC2×C33×M16C22
socleC22×C33C23×C4
prime radicalC23×D3×C3⋊D3C4
cosocleC33×C4C25
hypercenterC2×M16D3×C3⋊D3
hypocenterC33C23×M16
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C2×C4 ◁ C2×M16

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×M16×C3⋊(C3⋊D3)C2semidirect
3. C2×C3×M16×C3⋊D3C2semidirect
4. C2×C32×D3×M16C2semidirect
5. C2×#11723358C2semidirect
6. C2×D3×#3748C2semidirect
7. C2×C3⋊D3×#208C2semidirect
8. D3×M16×C3⋊D3C2direct (N × H)
9. C2×#11723312C2semidirect
10. C2×D3×#3743C2semidirect
11. C2×C3⋊D3×ΓL(1,𝔽25)C2semidirect
12. C2×D3×C8×C3⋊D3C2semidirect
32. C2×C33×M16C22semidirect
33. C2×#88855C22semidirect
34. M16×C3⋊(C3⋊D3)C22semidirect
35. C2×#88850C22semidirect
36. C2×C8×C3⋊(C3⋊D3)C22semidirect
37. C2×C3×#3748C22semidirect
38. C3×M16×C3⋊D3C22semidirect
39. C2×C3×#3743C22semidirect
40. C2×C3×C8×C3⋊D3C22semidirect
41. C2×C32×#208C22semidirect
42. C32×D3×M16C22semidirect
43. C2×C32×ΓL(1,𝔽25)C22semidirect
44. C2×C32×D3×C8C22semidirect
45. C2×#88788C22semidirect
46. C2×#88787C22semidirect
47. C2×#88786C22semidirect
48. #11723358C22semidirect
49. C2×#88785C22semidirect
50. C3⋊D3×#208C22semidirect
51. C2×C3⋊D3×C3⋊C8C22semidirect
52. D3×#3748C22semidirect
53. C2×D3×C3⋊(C3⋊C8)C22semidirect
54. #11723312C22semidirect
55. C3⋊D3×ΓL(1,𝔽25)C22semidirect
56. D3×#3743C22semidirect
57. D3×C8×C3⋊D3C22semidirect
70. C2×M16×C3⋊D3D3direct (N × H)
74. C2×C3×D3×M16D3semidirect
141. C33×M16C23semidirect
142. C2×C33×C8C23semidirect
143. #88855C23semidirect
144. C2×C3⋊(C3⋊(C3⋊C8))C23semidirect
145. #88850C23semidirect
146. C8×C3⋊(C3⋊D3)C23semidirect
147. C3×#3748C23semidirect
148. C2×C3×C3⋊(C3⋊C8)C23semidirect
149. C3×#3743C23semidirect
150. C3×C8×C3⋊D3C23semidirect
151. C32×#208C23semidirect
152. C2×C32×C3⋊C8C23semidirect
153. C32×ΓL(1,𝔽25)C23semidirect
154. C32×D3×C8C23semidirect
155. #88788C23semidirect
156. #88787C23semidirect
157. #88786C23semidirect
158. #88785C23semidirect
159. C3⋊D3×C3⋊C8C23semidirect
160. D3×C3⋊(C3⋊C8)C23semidirect
202. C2×C32×M16C2×D3semidirect
203. C2×C32×M16C2×D3semidirect
210. C2×#3748C2×D3semidirect
219. M16×C3⋊D3C2×D3direct (N × H)
226. C2×#3743C2×D3semidirect
233. C2×C8×C3⋊D3C2×D3semidirect
235. C2×C3×#208C2×D3semidirect
237. C3×D3×M16C2×D3semidirect
239. C2×C3×ΓL(1,𝔽25)C2×D3semidirect
241. C2×C3×D3×C8C2×D3semidirect
272. C2×D3×C3⋊D3M16direct (N × H)
320. C33×C8C24semidirect
321. C3⋊(C3⋊(C3⋊C8))C24semidirect
322. C3×C3⋊(C3⋊C8)C24semidirect
323. C32×C3⋊C8C24semidirect
344. C2×D3×M16C3⋊D3direct (N × H)
477. C32×M16C22×D3semidirect
478. C32×M16C22×D3semidirect
482. C2×C32×C8C22×D3semidirect
483. C2×C32×C8C22×D3semidirect
488. #3748C22×D3semidirect
493. C2×C3⋊(C3⋊C8)C22×D3semidirect
499. #3743C22×D3semidirect
505. C8×C3⋊D3C22×D3semidirect
507. C3×#208C22×D3semidirect
509. C2×C3×C3⋊C8C22×D3semidirect
511. C3×ΓL(1,𝔽25)C22×D3semidirect
513. C3×D3×C8C22×D3semidirect
526. C2×C3⋊(C3⋊D3)C2×M16semidirect
531. C2×C3×C3⋊D3C2×M16semidirect
536. C2×C32×D3C2×M16semidirect
542. D3×C3⋊D3C2×M16direct (N × H)
594. C2×C3×M16D32semidirect
595. C2×C3×M16C2×C3⋊D3semidirect
606. C2×#208C2×C3⋊D3semidirect
621. D3×M16C2×C3⋊D3direct (N × H)
632. C2×ΓL(1,𝔽25)C2×C3⋊D3semidirect
643. C2×D3×C8C2×C3⋊D3semidirect
794. C32×C8C23×D3semidirect
795. C32×C8C23×D3semidirect
799. C3⋊(C3⋊C8)C23×D3semidirect
801. C3×C3⋊C8C23×D3semidirect
815. C2×C33C22×M16semidirect
818. C3⋊(C3⋊D3)C22×M16semidirect
820. C3×C3⋊D3C22×M16semidirect
822. C32×D3C22×M16semidirect
953. C3×M16C2×D32semidirect
954. C3×M16C22×C3⋊D3semidirect
960. C2×C3×C8C2×D32semidirect
961. C2×C3×C8C22×C3⋊D3semidirect
968. #208C22×C3⋊D3semidirect
975. C2×C3⋊C8C22×C3⋊D3semidirect
984. ΓL(1,𝔽25)C22×C3⋊D3semidirect
993. D3×C8C22×C3⋊D3semidirect
1029. C2×C3⋊D3D3×M16direct (N × H)
1039. C2×C3×D3D3×M16semidirect
1104. C2×M16D3×C3⋊D3direct (N × H)
1112. C33C23×M16semidirect
1264. C3×C8C22×D32semidirect
1265. C3×C8C23×C3⋊D3semidirect
1270. C3⋊C8C23×C3⋊D3semidirect
1278. C2×C32C2×D3×M16semidirect
1279. C2×C32C2×D3×M16semidirect
1289. C3⋊D3C2×D3×M16direct (N × H)
1293. C3×D3C2×D3×M16semidirect
1361. M16C2×D3×C3⋊D3direct (N × H)
1371. C2×C8C2×D3×C3⋊D3semidirect
1421. C2×D3M16×C3⋊D3direct (N × H)
1448. C32C22×D3×M16semidirect
1449. C32C22×D3×M16semidirect
1518. C8C22×D3×C3⋊D3semidirect
1528. C2×C3D32×M16semidirect
1529. C2×C3C2×M16×C3⋊D3semidirect
1541. D3C2×M16×C3⋊D3direct (N × H)
1574. C3C22×M16×C3⋊D3semidirect
1575. C3C2×D32×M16semidirect
1583. C2D3×M16×C3⋊D3direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×C4×D3×C3⋊D32
C2×M16×C3⋊(C3⋊D3)2
C2×C3×M16×C3⋊D32
C2×C32×D3×M162
C2×#117233582
C2×D3×#37482
C2×C3⋊D3×#2082
D3×M16×C3⋊D32
C2×#117233122
C2×D3×#37432
C2×C3⋊D3×ΓL(1,𝔽25)2
C2×D3×C8×C3⋊D32
C2×D32×M163
C22×M16×C3⋊D33