Finite Group Databasebeta

← C2×D3×#3711 #13170496

Subgroups — C2×D3×#3711 #13170496

Order 1728.

1426 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×D32C211yesmaximal, characteristic
2C2×#88809C211yesmaximal, characteristic, complemented
3C2×#88787C211yesmaximal, characteristic, complemented
4C2×#88786C211yesmaximal, characteristic, complemented
5C2×D3×C3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6C2×C3×#3711C211yesmaximal, characteristic, complemented
7C2×C3×D3×C3⋊C8C211yesmaximal, characteristic, complemented
8D3×#3711C218yesmaximal, direct product factor
9C22×#3711—31nomaximal
10C2×D3×#208—31nomaximal
11C2×D3×ΓL(1,𝔽25)—31nomaximal
12C22×C3×D32C411yescharacteristic
13C2×C3×C4×C3⋊D3C2211yescharacteristic
14C2×C32×C4×D3C2211yescharacteristic
15C2×C32×C4×D3C2211yescharacteristic
16C2×C3×#624C411yescharacteristic
17C2×C3×D3×Dic3C411yescharacteristic
18C2×C3×D3×Dic3C411yescharacteristic
19C3×C4×D32C414yes—
20C3×C4×D32C2214yes—
21C2×C3⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
22C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
23C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
24C2×C32×C3⋊C8C2211yescharacteristic, complemented
25#88809C2214yescomplemented
26#88787C2214yescomplemented
27#88786C2214yescomplemented
28D3×C3⋊(C3⋊C8)C2214yescomplemented
29C3×#3711C2214yescomplemented
30C3×D3×C3⋊C8C2214yescomplemented
31C22×C3×C4×D3—31no—
32C22×C3×C4×D3—31no—
33C2×C4×D32D311yescharacteristic
34C2×#3748—31no—
35C22×C3⋊(C3⋊C8)—31no—
36C2×#3743—31no—
37C2×C3×#208—31no—
38C22×C3×C3⋊C8—31no—
39C2×C3×ΓL(1,𝔽25)—31no—
40C2×C3×D3×C8—31no—
41C2×#3712—31no—
42C2×#3711—31no—
43C2×#3711—31no—
44C2×#3711—31no—
45C2×#3711—31no—
46C2×#3711—31no—
47C2×#3711—31no—
48C2×#3711—38no—
49C2×#3711—61no—
50C2×#3711—61no—
51C2×#3711D311yescharacteristic, direct product factor
52D3×#208—38no—
53C2×D3×C3⋊C8—31no—
54C2×D3×C3⋊C8—31no—
55C2×D3×C3⋊C8—61no—
56C2×D3×C3⋊C8D311yescharacteristic, complemented
57D3×ΓL(1,𝔽25)—38no—
58C22×C3×C3⋊D3C2×C411yescharacteristic
59C22×C32×D3C2×C411yescharacteristic
60C22×C32×D3C2×C411yescharacteristic
61C2×C3×D32—24no—
62C2×C3×D32C2×C414yes—
63C2×C33×C4C2311yescharacteristic
64C2×C3×C3⋊Dic3C2×C411yescharacteristic
65C3×C4×C3⋊D3C2×C412yes—
66C3×C4×C3⋊D3C2312yes—
67C2×C32×Dic3C2×C411yescharacteristic
68C2×C32×Dic3C2×C411yescharacteristic
69C32×C4×D3C2×C412yes—
70C32×C4×D3C2×C412yes—
71C32×C4×D3C2312yes—
72C32×C4×D3C2312yes—
73C3×#624C2×C414yes—
74C3×D3×Dic3C2×C414yes—
75C3×D3×Dic3C2×C414yes—
76C3⋊(C3⋊(C3⋊C8))C2312yescomplemented
77C3×C3⋊(C3⋊C8)C2312yescomplemented
78C3×C3⋊(C3⋊C8)C2312yescomplemented
79C32×C3⋊C8C2312yescomplemented
80C22×#208—91no—
81C2×D3×M16—91no—
82C22×ΓL(1,𝔽25)—91no—
83C23×C3×D3—31no—
84C23×C3×D3—31no—
85C22×D32Dic311yescharacteristic
86C22×C32×C4—31no—
87C22×C32×C4—31no—
88C2×C4×C3⋊D3C2×D311yescharacteristic
89C22×C3×Dic3—31no—
90C22×C3×Dic3—31no—
91C2×C3×C4×D3—21no—
92C2×C3×C4×D3—21no—
93C2×C3×C4×D3—31no—
94C2×C3×C4×D3—31no—
95C2×C3×C4×D3—31no—
96C2×C3×C4×D3—31no—
97C2×C3×C4×D3—31no—
98C2×C3×C4×D3—31no—
99C2×C3×C4×D3—34no—
100C2×C3×C4×D3—34no—
101C2×C3×C4×D3—34no—
102C2×C3×C4×D3—34no—
103C2×C3×C4×D3—61no—
104C2×C3×C4×D3C2×D311yescharacteristic
105C2×C3×C4×D3C2×D311yescharacteristic
106C2×C3×C4×D3C2×D311yescharacteristic
107C2×C3×C4×D3C2×D311yescharacteristic
108C2×#624Dic311yescharacteristic
109C2×D3×Dic3Dic311yescharacteristic
110C2×D3×Dic3Dic311yescharacteristic
111C4×D32Dic314yes—
112C4×D32C2×D314yes—
113C2×C32×C8—31no—
114#3748—34no—
115C2×C3⋊(C3⋊C8)—31no—
116C2×C3⋊(C3⋊C8)—31no—
117C2×C3⋊(C3⋊C8)—31no—
118C2×C3⋊(C3⋊C8)—34no—
119C2×C3⋊(C3⋊C8)—61no—
120C2×C3⋊(C3⋊C8)—61no—
121C2×C3⋊(C3⋊C8)—61no—
122C2×C3⋊(C3⋊C8)—121no—
123C2×C3⋊(C3⋊C8)C2×D311yescharacteristic, complemented
124C2×C3⋊(C3⋊C8)C2×D311yescharacteristic, complemented
125#3743—34no—
126C3×#208—34no—
127C2×C3×C3⋊C8—21no—
128C2×C3×C3⋊C8—31no—
129C2×C3×C3⋊C8—31no—
130C2×C3×C3⋊C8—31no—
131C2×C3×C3⋊C8—31no—
132C2×C3×C3⋊C8—34no—
133C2×C3×C3⋊C8—61no—
134C2×C3×C3⋊C8—61no—
135C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
136C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
137C3×ΓL(1,𝔽25)—34no—
138C3×D3×C8—34no—
139#3712—34no—
140#3711—34no—
141#3711—34no—
142#3711—34no—
143#3711—34no—
144#3711—34no—
145#3711—34no—
146#3711—64no—
147#3711—64no—
148#3711C2×D314yesdirect product factor
149D3×C3⋊C8—34no—
150D3×C3⋊C8—34no—
151D3×C3⋊C8—64no—
152D3×C3⋊C8C2×D314yescomplemented
153C22×C33C22×C411yescharacteristic
154C2×C3×C3⋊D3—22no—
155C2×C3×C3⋊D3C22×C412yes—
156C2×C32×D3—22no—
157C2×C32×D3M1614yescomplemented
158C2×C32×D3C22×C412yes—
159C2×C32×D3C22×C412yes—
160C3×D32—28no—
161C33×C4C22×C411yescharacteristic
162C33×C4C2411yescharacteristic
163C3×C3⋊Dic3C22×C412yes—
164C32×Dic3C22×C412yes—
165C32×Dic3C22×C412yes—
166C23×C3×C4—91no—
167C22×C4×D3—31no—
168C22×C4×D3—31no—
169C2×C3×M16—91no—
170C22×C3×C8—91no—
171C2×#208—31no—
172C2×#208—91no—
173C2×#208—98no—
174C2×#208—91no—
175C2×#208—91no—
176C2×#208—91no—
177C2×#208—181no—
178C22×C3⋊C8—31no—
179C22×C3⋊C8—91no—
180C22×C3⋊C8—91no—
181C22×C3⋊C8—181no—
182D3×M16—98no—
183C2×ΓL(1,𝔽25)—31no—
184C2×ΓL(1,𝔽25)—98no—
185C2×ΓL(1,𝔽25)—91no—
186C2×ΓL(1,𝔽25)—91no—
187C2×ΓL(1,𝔽25)—91no—
188C2×ΓL(1,𝔽25)—91no—
189C2×ΓL(1,𝔽25)—91no—
190C2×ΓL(1,𝔽25)—181no—
191C2×D3×C8—31no—
192C2×D3×C8—91no—
193C23×C32—31no—
194C23×C32—31no—
195C22×C3⋊D3C2×Dic311yescharacteristic
196C22×C3×D3—21no—
197C22×C3×D3—21no—
198C22×C3×D3—31no—
199C22×C3×D3—31no—
200C22×C3×D3—34no—
201C22×C3×D3—34no—
202C22×C3×D3—61no—
203C22×C3×D3—64no—
204C22×C3×D3—64no—
205C22×C3×D3C4×D311yescharacteristic
206C22×C3×D3C4×D311yescharacteristic
207C22×C3×D3C2×Dic311yescharacteristic
208C22×C3×D3C2×Dic311yescharacteristic
209C2×D32—24no—
210C2×D32C2×Dic314yes—
211C2×C32×C4—21no—
212C2×C32×C4—21no—
213C2×C32×C4—21no—
214C2×C32×C4—31no—
215C2×C32×C4—31no—
216C2×C32×C4—32no—
217C2×C32×C4—32no—
218C2×C32×C4—32no—
219C2×C32×C4—32no—
220C2×C32×C4—41no—
221C2×C32×C4C22×D311yescharacteristic
222C2×C32×C4C22×D311yescharacteristic
223C2×C32×C4C22×D311yescharacteristic
224C2×C3⋊Dic3C2×Dic311yescharacteristic
225C4×C3⋊D3C2×Dic312yes—
226C4×C3⋊D3C22×D312yes—
227C2×C3×Dic3—21no—
228C2×C3×Dic3—21no—
229C2×C3×Dic3—31no—
230C2×C3×Dic3—31no—
231C2×C3×Dic3—34no—
232C2×C3×Dic3—34no—
233C2×C3×Dic3—61no—
234C2×C3×Dic3C4×D311yescharacteristic
235C2×C3×Dic3C4×D311yescharacteristic
236C2×C3×Dic3C2×Dic311yescharacteristic
237C2×C3×Dic3C2×Dic311yescharacteristic
238C3×C4×D3—22no—
239C3×C4×D3—22no—
240C3×C4×D3—22no—
241C3×C4×D3—22no—
242C3×C4×D3—34no—
243C3×C4×D3—34no—
244C3×C4×D3—32no—
245C3×C4×D3—32no—
246C3×C4×D3—32no—
247C3×C4×D3—32no—
248C3×C4×D3—34no—
249C3×C4×D3—34no—
250C3×C4×D3—62no—
251C3×C4×D3—62no—
252C3×C4×D3C4×D312yes—
253C3×C4×D3C4×D312yes—
254C3×C4×D3C2×Dic312yes—
255C3×C4×D3C2×Dic312yes—
256C3×C4×D3C22×D312yes—
257C3×C4×D3C22×D312yes—
258C3×C4×D3C22×D312yes—
259C3×C4×D3C22×D312yes—
260#624C2×Dic314yes—
261D3×Dic3C2×Dic314yes—
262D3×Dic3C2×Dic314yes—
263C32×C8—32no—
264C3⋊(C3⋊C8)—32no—
265C3⋊(C3⋊C8)—32no—
266C3⋊(C3⋊C8)—32no—
267C3⋊(C3⋊C8)—62no—
268C3⋊(C3⋊C8)—62no—
269C3⋊(C3⋊C8)—62no—
270C3⋊(C3⋊C8)—122no—
271C3⋊(C3⋊C8)C22×D312yescomplemented
272C3⋊(C3⋊C8)C22×D312yescomplemented
273C3×C3⋊C8—22no—
274C3×C3⋊C8—32no—
275C3×C3⋊C8—32no—
276C3×C3⋊C8—32no—
277C3×C3⋊C8—32no—
278C3×C3⋊C8—62no—
279C3×C3⋊C8—62no—
280C3×C3⋊C8C22×D312yescomplemented
281C3×C3⋊C8C22×D312yescomplemented
282C22×M16—271noSylow
283C2×C33C2×M1612yescomplemented
284C2×C33C23×C411yescharacteristic
285C3×C3⋊D3—22no—
286C32×D3—22no—
287C32×D3C2×M1614yescomplemented
288C24×C3—91no—
289C23×D3—31no—
290C23×D3—31no—
291C22×C3×C4—31no—
292C22×C3×C4—31no—
293C22×C3×C4—31no—
294C22×C3×C4—31no—
295C22×C3×C4—61no—
296C22×C3×C4—61no—
297C22×C3×C4—94no—
298C22×C3×C4—91no—
299C22×C3×C4—94no—
300C22×C3×C4—91no—
301C22×C3×C4—91no—
302C22×C3×C4—91no—
303C22×Dic3—31no—
304C22×Dic3—31no—
305C2×C4×D3—31no—
306C2×C4×D3—31no—
307C2×C4×D3—31no—
308C2×C4×D3—31no—
309C2×C4×D3—31no—
310C2×C4×D3—31no—
311C2×C4×D3—34no—
312C2×C4×D3—34no—
313C2×C4×D3—34no—
314C2×C4×D3—34no—
315C2×C4×D3—61no—
316C2×C4×D3D3211yescharacteristic
317C2×C4×D3D3211yescharacteristic
318C3×M16—94no—
319C2×C3×C8—31no—
320C2×C3×C8—31no—
321C2×C3×C8—61no—
322C2×C3×C8—94no—
323C2×C3×C8—91no—
324C2×C3×C8—91no—
325#208—34no—
326#208—94no—
327#208—94no—
328#208—94no—
329#208—94no—
330#208—184no—
331C2×C3⋊C8—31no—
332C2×C3⋊C8—31no—
333C2×C3⋊C8—31no—
334C2×C3⋊C8—31no—
335C2×C3⋊C8—34no—
336C2×C3⋊C8—61no—
337C2×C3⋊C8—61no—
338C2×C3⋊C8—94no—
339C2×C3⋊C8—94no—
340C2×C3⋊C8—91no—
341C2×C3⋊C8—91no—
342C2×C3⋊C8—91no—
343C2×C3⋊C8—184no—
344C2×C3⋊C8—181no—
345C2×C3⋊C8—181no—
346C2×C3⋊C8—181no—
347C2×C3⋊C8—361no—
348C2×C3⋊C8D3211yescharacteristic, complemented
349ΓL(1,𝔽25)—34no—
350ΓL(1,𝔽25)—94no—
351ΓL(1,𝔽25)—94no—
352ΓL(1,𝔽25)—94no—
353ΓL(1,𝔽25)—94no—
354ΓL(1,𝔽25)—94no—
355ΓL(1,𝔽25)—184no—
356D3×C8—34no—
357D3×C8—94no—
358C22×C32—21no—
359C22×C32—21no—
360C22×C32—21no—
361C22×C32—34no—
362C22×C32—32no—
363C22×C32—32no—
364C22×C32—41no—
365C22×C32—62no—
366C22×C32C2×C4×D311yescharacteristic
367C22×C32C2×C4×D311yescharacteristic
368C22×C32C22×Dic311yescharacteristic
369C2×C3⋊D3—22no—
370C2×C3⋊D3C22×Dic312yes—
371C2×C3×D3—22no—
372C2×C3×D3—22no—
373C2×C3×D3—24no—
374C2×C3×D3—22no—
375C2×C3×D3—22no—
376C2×C3×D3—32no—
377C2×C3×D3—32no—
378C2×C3×D3—42no—
379C2×C3×D3—62no—
380C2×C3×D3—68no—
381C2×C3×D3—62no—
382C2×C3×D3—62no—
383C2×C3×D3—68no—
384C2×C3×D3—122no—
385C2×C3×D3ΓL(1,𝔽25)14yescomplemented
386C2×C3×D3#20814yescomplemented
387C2×C3×D3C2×C4×D312yes—
388C2×C3×D3C2×C4×D312yes—
389C2×C3×D3C22×Dic312yes—
390C2×C3×D3C22×Dic312yes—
391D32—28no—
392C32×C4—21no—
393C32×C4—21no—
394C32×C4—21no—
395C32×C4—21no—
396C32×C4—21no—
397C32×C4—21no—
398C32×C4—32no—
399C32×C4—32no—
400C32×C4—41no—
401C32×C4—41no—
402C32×C4C2×C4×D311yescharacteristic
403C32×C4C2×C4×D311yescharacteristic
404C32×C4C22×Dic311yescharacteristic
405C32×C4C23×D311yescharacteristic
406C32×C4C23×D311yescharacteristic
407C32×C4C23×D311yescharacteristic
408C3⋊Dic3C22×Dic312yes—
409C3×Dic3—22no—
410C3×Dic3—22no—
411C3×Dic3—32no—
412C3×Dic3—32no—
413C3×Dic3—62no—
414C3×Dic3C2×C4×D312yes—
415C3×Dic3C2×C4×D312yes—
416C3×Dic3C22×Dic312yes—
417C3×Dic3C22×Dic312yes—
418C23×C4—91no—
419C2×M16—91no—
420C2×M16—271no—
421C2×M16—271no—
422C2×M16—278no—
423C2×M16—271no—
424C22×C8—91no—
425C22×C8—271no—
426C33C22×M1611yescharacteristic, complemented, Sylow
427C23×C3—31no—
428C23×C3—31no—
429C23×C3—31no—
430C23×C3—31no—
431C23×C3—61no—
432C23×C3—61no—
433C23×C3—94no—
434C23×C3—91no—
435C23×C3—184no—
436C22×D3—31no—
437C22×D3—31no—
438C22×D3—34no—
439C22×D3—34no—
440C22×D3—61no—
441C22×D3—64no—
442C22×D3—64no—
443C22×D3D3×Dic311yescharacteristic
444C22×D3D3×Dic311yescharacteristic
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—31no—
449C2×C3×C4—31no—
450C2×C3×C4—31no—
451C2×C3×C4—31no—
452C2×C3×C4—32no—
453C2×C3×C4—32no—
454C2×C3×C4—32no—
455C2×C3×C4—32no—
456C2×C3×C4—32no—
457C2×C3×C4—32no—
458C2×C3×C4—32no—
459C2×C3×C4—32no—
460C2×C3×C4—41no—
461C2×C3×C4—62no—
462C2×C3×C4—62no—
463C2×C3×C4—62no—
464C2×C3×C4—62no—
465C2×C3×C4—61no—
466C2×C3×C4—61no—
467C2×C3×C4—94no—
468C2×C3×C4—94no—
469C2×C3×C4—94no—
470C2×C3×C4—91no—
471C2×C3×C4—92no—
472C2×C3×C4—92no—
473C2×C3×C4C2×D3211yescharacteristic
474C2×C3×C4C2×D3211yescharacteristic
475C2×C3×C4C2×D3211yescharacteristic
476C2×Dic3—31no—
477C2×Dic3—31no—
478C2×Dic3—34no—
479C2×Dic3—34no—
480C2×Dic3—61no—
481C2×Dic3D3×Dic311yescharacteristic
482C2×Dic3D3×Dic311yescharacteristic
483C4×D3—34no—
484C4×D3—34no—
485C4×D3—32no—
486C4×D3—32no—
487C4×D3—32no—
488C4×D3—32no—
489C4×D3—34no—
490C4×D3—34no—
491C4×D3—62no—
492C4×D3—62no—
493C4×D3D3×Dic312yes—
494C4×D3D3×Dic312yes—
495C4×D3C2×D3212yes—
496C4×D3C2×D3212yes—
497C3×C8—32no—
498C3×C8—32no—
499C3×C8—62no—
500C3×C8—92no—
501C3×C8—92no—
502C3⋊C8—32no—
503C3⋊C8—32no—
504C3⋊C8—32no—
505C3⋊C8—32no—
506C3⋊C8—62no—
507C3⋊C8—62no—
508C3⋊C8—92no—
509C3⋊C8—92no—
510C3⋊C8—92no—
511C3⋊C8—182no—
512C3⋊C8—182no—
513C3⋊C8—182no—
514C3⋊C8—362no—
515C3⋊C8C2×D3212yescomplemented
516C2×C32—22no—
517C2×C32—21no—
518C2×C32—21no—
519C2×C32—21no—
520C2×C32—22no—
521C2×C32—22no—
522C2×C32—34no—
523C2×C32—42no—
524C2×C32—41no—
525C2×C32—62no—
526C2×C32C2×ΓL(1,𝔽25)12yescomplemented
527C2×C32D3×M1612yescomplemented
528C2×C32C2×#20812yescomplemented
529C2×C32C22×C4×D311yescharacteristic
530C2×C32C22×C4×D311yescharacteristic
531C2×C32C23×Dic311yescharacteristic
532C3⋊D3—22no—
533C3×D3—22no—
534C3×D3—22no—
535C3×D3—24no—
536C3×D3—42no—
537C3×D3—62no—
538C3×D3—62no—
539C3×D3—122no—
540C3×D3C2×ΓL(1,𝔽25)14yescomplemented
541C3×D3C2×#20814yescomplemented
542C24—91no—
543C22×C4—31no—
544C22×C4—31no—
545C22×C4—94no—
546C22×C4—91no—
547C22×C4—94no—
548C22×C4—91no—
549C22×C4—91no—
550C22×C4—91no—
551M16—94no—
552M16—274no—
553M16—274no—
554M16—274no—
555C2×C8—31no—
556C2×C8—94no—
557C2×C8—91no—
558C2×C8—91no—
559C2×C8—274no—
560C2×C8—271no—
561C22×C3—21no—
562C22×C3—21no—
563C22×C3—21no—
564C22×C3—34no—
565C22×C3—32no—
566C22×C3—32no—
567C22×C3—34no—
568C22×C3—32no—
569C22×C3—32no—
570C22×C3—41no—
571C22×C3—62no—
572C22×C3—64no—
573C22×C3—62no—
574C22×C3—62no—
575C22×C3—62no—
576C22×C3—92no—
577C22×C3—122no—
578C22×C3—188no—
579C22×C3—182no—
580C22×C3C4×D3211yescharacteristic
581C22×C3C2×D3×Dic311yescharacteristic
582C22×C3C2×D3×Dic311yescharacteristic
583C2×D3—22no—
584C2×D3—32no—
585C2×D3—32no—
586C2×D3—62no—
587C2×D3—68no—
588C2×D3—62no—
589C2×D3—62no—
590C2×D3—68no—
591C2×D3—122no—
592C2×D3#371114yesdirect product factor
593C2×D3C2×D3×Dic312yes—
594C2×D3C2×D3×Dic312yes—
595C3×C4—21no—
596C3×C4—21no—
597C3×C4—21no—
598C3×C4—21no—
599C3×C4—21no—
600C3×C4—21no—
601C3×C4—32no—
602C3×C4—32no—
603C3×C4—32no—
604C3×C4—32no—
605C3×C4—41no—
606C3×C4—41no—
607C3×C4—62no—
608C3×C4—62no—
609C3×C4—92no—
610C3×C4C4×D3211yescharacteristic
611C3×C4C2×D3×Dic311yescharacteristic
612C3×C4C2×D3×Dic311yescharacteristic
613C3×C4C22×D3211yescharacteristic
614C3×C4C22×D3211yescharacteristic
615C3×C4C22×D3211yescharacteristic
616Dic3—32no—
617Dic3—32no—
618Dic3—62no—
619Dic3C2×D3×Dic312yes—
620Dic3C2×D3×Dic312yes—
621C32—21no—
622C32—21no—
623C32—21no—
624C32—41no—
625C32C22×ΓL(1,𝔽25)11yescharacteristic, complemented
626C32C2×D3×M1611yescharacteristic, complemented
627C32C22×#20811yescharacteristic, complemented
628C23—31no—
629C23—31no—
630C23—94no—
631C23—91no—
632C23—184no—
633C2×C4—31no—
634C2×C4—31no—
635C2×C4—32no—
636C2×C4—32no—
637C2×C4—32no—
638C2×C4—32no—
639C2×C4—94no—
640C2×C4—94no—
641C2×C4—94no—
642C2×C4—91no—
643C2×C4—92no—
644C2×C4—92no—
645C2×C4D3311yescharacteristic
646C8—32no—
647C8—92no—
648C8—92no—
649C8—272no—
650C2×C3—22no—
651C2×C3—22no—
652C2×C3—22no—
653C2×C3—21no—
654C2×C3—21no—
655C2×C3—21no—
656C2×C3—34no—
657C2×C3—34no—
658C2×C3—42no—
659C2×C3—41no—
660C2×C3—64no—
661C2×C3—62no—
662C2×C3—62no—
663C2×C3—122no—
664C2×C3—182no—
665C2×C3D3×ΓL(1,𝔽25)12yescomplemented
666C2×C3D3×#20812yescomplemented
667C2×C3C2×#371112yescomplemented
668C2×C3C2×C4×D3211yescharacteristic
669C2×C3C22×D3×Dic311yescharacteristic
670C2×C3C22×D3×Dic311yescharacteristic
671D3—22no—
672D3—62no—
673D3—62no—
674D3—122no—
675D3C2×#371114yesdirect product factor
676C22—34no—
677C22—32no—
678C22—32no—
679C22—62no—
680C22—92no—
681C22—188no—
682C22—182no—
683C22D32×Dic311yescharacteristic
684C4—32no—
685C4—32no—
686C4—92no—
687C4D32×Dic311yescharacteristic
688C4C2×D3311yescharacteristic
689C3—21no—
690C3—21no—
691C3—21no—
692C3—41no—
693C3C2×D3×ΓL(1,𝔽25)11yescharacteristic, complemented
694C3C2×D3×#20811yescharacteristic, complemented
695C3C22×#371111yescharacteristic, complemented
696C2—34no—
697C2—62no—
698C2—182no—
699C2D3×#371112yesdirect product factor
700C2C2×D32×Dic311yescharacteristic
subgroupG/H
center, hypercenterC2×C4D33
commutatorC2×C33C23×C4
FrattiniC4C2×D33
FittingC2×C33×C4C23
socleC22×C33C22×C4
prime radicalC22×C3×D32C4
cosocleC33×C4C24
hypocenterC33C22×M16
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×#88809C2semidirect
3. C2×#88787C2semidirect
4. C2×#88786C2semidirect
5. C2×D3×C3⋊(C3⋊C8)C2semidirect
6. C2×C3×#3711C2semidirect
7. C2×C3×D3×C3⋊C8C2semidirect
8. D3×#3711C2direct (N × H)
21. C2×C3⋊(C3⋊(C3⋊C8))C22semidirect
22. C2×C3×C3⋊(C3⋊C8)C22semidirect
23. C2×C3×C3⋊(C3⋊C8)C22semidirect
24. C2×C32×C3⋊C8C22semidirect
25. #88809C22semidirect
26. #88787C22semidirect
27. #88786C22semidirect
28. D3×C3⋊(C3⋊C8)C22semidirect
29. C3×#3711C22semidirect
30. C3×D3×C3⋊C8C22semidirect
51. C2×#3711D3direct (N × H)
56. C2×D3×C3⋊C8D3semidirect
76. C3⋊(C3⋊(C3⋊C8))C23semidirect
77. C3×C3⋊(C3⋊C8)C23semidirect
78. C3×C3⋊(C3⋊C8)C23semidirect
79. C32×C3⋊C8C23semidirect
123. C2×C3⋊(C3⋊C8)C2×D3semidirect
124. C2×C3⋊(C3⋊C8)C2×D3semidirect
135. C2×C3×C3⋊C8C2×D3semidirect
136. C2×C3×C3⋊C8C2×D3semidirect
148. #3711C2×D3direct (N × H)
152. D3×C3⋊C8C2×D3semidirect
157. C2×C32×D3M16semidirect
271. C3⋊(C3⋊C8)C22×D3semidirect
272. C3⋊(C3⋊C8)C22×D3semidirect
280. C3×C3⋊C8C22×D3semidirect
281. C3×C3⋊C8C22×D3semidirect
283. C2×C33C2×M16semidirect
287. C32×D3C2×M16semidirect
348. C2×C3⋊C8D32semidirect
385. C2×C3×D3ΓL(1,𝔽25)semidirect
386. C2×C3×D3#208semidirect
426. C33C22×M16semidirect
515. C3⋊C8C2×D32semidirect
526. C2×C32C2×ΓL(1,𝔽25)semidirect
527. C2×C32D3×M16semidirect
528. C2×C32C2×#208semidirect
540. C3×D3C2×ΓL(1,𝔽25)semidirect
541. C3×D3C2×#208semidirect
592. C2×D3#3711direct (N × H)
625. C32C22×ΓL(1,𝔽25)semidirect
626. C32C2×D3×M16semidirect
627. C32C22×#208semidirect
665. C2×C3D3×ΓL(1,𝔽25)semidirect
666. C2×C3D3×#208semidirect
667. C2×C3C2×#3711semidirect
675. D3C2×#3711direct (N × H)
693. C3C2×D3×ΓL(1,𝔽25)semidirect
694. C3C2×D3×#208semidirect
695. C3C22×#3711semidirect
699. C2D3×#3711direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C4×D322
C2×#888092
C2×#887872
C2×#887862
C2×D3×C3⋊(C3⋊C8)2
C2×C3×#37112
C2×C3×D3×C3⋊C82
D3×#37112
C22×#37113
C2×D3×#2083
C2×D3×ΓL(1,𝔽25)3