Finite Group Databasebeta

← C2×C3×#5556 #11902883

Subgroups — C2×C3×#5556 #11902883

Order 1152.

2869 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×D4C211yesmaximal, characteristic, complemented
2C2×C3×#937C211yesmaximal, characteristic
3C2×C3×#935C211yesmaximal, characteristic, complemented
4C2×C3×#929C211yesmaximal, characteristic, complemented
5C2×C3×C4×#67C211yesmaximal, characteristic, complemented
6C22×C3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
7C2×C3×#924C211yesmaximal, characteristic, complemented
8C3×#5556C2116yesmaximal, direct product factor
9C2×C3×#898C211yesmaximal, characteristic, complemented
10C2×C3×#896C211yesmaximal, characteristic, complemented
11C2×C3×#885C211yesmaximal, characteristic, complemented
12C2×C3×#883C211yesmaximal, characteristic, complemented
13C2×C3×D3×C22⋊C4C211yesmaximal, characteristic, complemented
14C2×C3×#877C211yesmaximal, characteristic, complemented
15C2×C3×#876C211yesmaximal, characteristic, complemented
16C2×C3×#872C211yesmaximal, characteristic, complemented
17C2×C3×#551—31nomaximal
18C2×#5556C311yesmaximal, characteristic, direct product factor
19C24×C3×D3C2211yescharacteristic
20C22×C32×D4C2211yescharacteristic
21C23×C32×C4C2211yescharacteristic
22C23×C32×C4C2211yescharacteristic, complemented
23C22×C3×#67C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic
25C23×C3×Dic3C2211yescharacteristic
26C22×C3×C4×D3C2211yescharacteristic
27C22×C3×C4×D3C2211yescharacteristic
28C22×C3×Dic6C2211yescharacteristic, complemented
29C32×C4×D4C2218yescomplemented
30C2×C32×C4⋊C4C2211yescharacteristic, complemented
31C2×C32×C22⋊C4C2211yescharacteristic
32C2×C32×C22⋊C4C2211yescharacteristic, complemented
33C2×C32×C42C2211yescharacteristic, complemented
34C2×C3×#217C2211yescharacteristic
35C2×C3×#217C2211yescharacteristic
36C2×C3×#217C2211yescharacteristic, complemented
37C2×C3×#217C2211yescharacteristic, complemented
38C3×#937C2218yes—
39C3×#935C2218yescomplemented
40C3×#929C2218yescomplemented
41C3×C4×#67C2218yescomplemented
42C2×C3×(C2×D3)⋊C4C2211yescharacteristic
43C2×C3×(C2×D3)⋊C4C2211yescharacteristic
44C2×C3×(C2×D3)⋊C4C2211yescharacteristic
45C2×C3×(C2×D3)⋊C4C2211yescharacteristic
46C2×C3×(C2×D3)⋊C4C2211yescharacteristic
47C2×C3×(C2×D3)⋊C4C2211yescharacteristic
48C2×C3×(C2×D3)⋊C4C2211yescharacteristic
49C2×C3×(C2×D3)⋊C4C2211yescharacteristic
50C2×C3×(C2×D3)⋊C4C2218yescomplemented
51C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
52C3×#924C2218yescomplemented
53C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
54C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
55C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
56C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
57C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
58C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
59C2×C3×C4×Dic3C2211yescharacteristic, complemented
60C2×C3×C4×Dic3C2211yescharacteristic, complemented
61C3×#898C2218yescomplemented
62C3×#896C2218yescomplemented
63C3×#885C2218yescomplemented
64C3×#883C2218yescomplemented
65C3×D3×C22⋊C4C2218yescomplemented
66C3×#877C2218yescomplemented
67C3×#876C2218yescomplemented
68C3×#872C2218yescomplemented
69C3×#551—316no—
70C2×C3×#126—31no—
71C2×C3×#126—31no—
72C2×C3×#124—31no—
73C2×C3×#123—31no—
74C2×C3×#123—31no—
75C2×C3×#123—31no—
76C2×C3×C22⋊Q8—31no—
77C2×C3×C22⋊Q8—31no—
78C2×C3×#120—31no—
79C2×C3×C4×D4—21no—
80C2×C3×C4×D4—31no—
81C2×C3×C4×D4D311yescharacteristic, complemented
82C2×C3×C4×D4C2×C311yescharacteristic, complemented
83C2×C3×#117—31no—
84C2×C3×#117—31no—
85C22×C3×C22⋊C4—31no—
86C22×C3×C22⋊C4—31no—
87C2×#937C2×C311yescharacteristic
88C2×#935C2×C311yescharacteristic, complemented
89C2×#929C2×C311yescharacteristic, complemented
90C2×C4×#67C2×C311yescharacteristic, complemented
91C22×(C2×D3)⋊C4C2×C311yescharacteristic, complemented
92C2×#924C2×C311yescharacteristic, complemented
93#5556C2×C3116yesdirect product factor
94C2×#898C2×C311yescharacteristic, complemented
95C2×#896C2×C311yescharacteristic, complemented
96C2×#885C2×C311yescharacteristic, complemented
97C2×#883C2×C311yescharacteristic, complemented
98C2×D3×C22⋊C4C2×C311yescharacteristic, complemented
99C2×#877C2×C311yescharacteristic, complemented
100C2×#876C2×C311yescharacteristic, complemented
101C2×#872C2×C311yescharacteristic, complemented
102C24×C32C2311yescharacteristic
103C24×C32C2311yescharacteristic
104C23×C3×D3—24no—
105C23×C3×D3—24no—
106C23×C3×D3—42no—
107C23×C3×D3C2311yescharacteristic
108C23×C3×D3C2314yes—
109C23×C3×D3C2311yescharacteristic
110C2×C32×D4—24no—
111C2×C32×D4C2314yes—
112C22×C32×C4—42no—
113C22×C32×C4—42no—
114C22×C32×C4C2311yescharacteristic
115C22×C32×C4C2311yescharacteristic
116C22×C32×C4C2311yescharacteristic
117C22×C32×C4C2311yescharacteristic
118C22×C32×C4C2311yescharacteristic
119C22×C32×C4C2314yes—
120C22×C32×C4C2314yescomplemented
121C2×C3×#67—24no—
122C2×C3×#67—42no—
123C2×C3×#67C2314yes—
124C2×C3×#67C2314yes—
125C22×C3×Dic3—24no—
126C22×C3×Dic3C2314yes—
127C22×C3×Dic3C2311yescharacteristic
128C22×C3×Dic3C2311yescharacteristic
129C22×C3×Dic3C2311yescharacteristic
130C22×C3×Dic3C2311yescharacteristic
131C22×C3×Dic3C2311yescharacteristic
132C22×C3×Dic3C2311yescharacteristic
133C2×C3×C4×D3—24no—
134C2×C3×C4×D3—42no—
135C2×C3×C4×D3C2314yes—
136C2×C3×C4×D3C2314yes—
137C2×C3×Dic6—42no—
138C2×C3×Dic6C2314yescomplemented
139C32×C4⋊C4C2314yescomplemented
140C32×C22⋊C4C2314yes—
141C32×C22⋊C4C2314yescomplemented
142C32×C42C2314yescomplemented
143C3×#217C2314yes—
144C3×#217C2314yes—
145C3×#217C2314yescomplemented
146C3×#217C2314yescomplemented
147C3×(C2×D3)⋊C4C2314yes—
148C3×(C2×D3)⋊C4C2314yes—
149C3×(C2×D3)⋊C4C2314yes—
150C3×(C2×D3)⋊C4C2314yes—
151C3×(C2×D3)⋊C4C2314yes—
152C3×(C2×D3)⋊C4C2314yes—
153C3×(C2×D3)⋊C4C2314yes—
154C3×(C2×D3)⋊C4C2314yes—
155C3×C4⋊Dic3C2314yescomplemented
156C3×Dic3⋊C4C2314yescomplemented
157C3×Dic3⋊C4C2314yescomplemented
158C3×Dic3⋊C4C2314yescomplemented
159C3×Dic3⋊C4C2314yescomplemented
160C3×Dic3⋊C4C2314yescomplemented
161C3×Dic3⋊C4C2314yescomplemented
162C3×C4×Dic3C2314yescomplemented
163C3×C4×Dic3C2314yescomplemented
164C2×#551—31noSylow
165C25×C3—31no—
166C24×D3C22×C311yescharacteristic
167C22×C3×Q8—31no—
168C22×C3×D4—21no—
169C22×C3×D4—31no—
170C22×C3×D4—31no—
171C22×C3×D4C2×D311yescharacteristic
172C22×C3×D4C22×C311yescharacteristic
173C23×C3×C4—21no—
174C23×C3×C4—21no—
175C23×C3×C4—31no—
176C23×C3×C4—31no—
177C23×C3×C4—31no—
178C23×C3×C4C2×D311yescharacteristic
179C23×C3×C4C2×D311yescharacteristic, complemented
180C23×C3×C4C22×C311yescharacteristic
181C23×C3×C4C22×C311yescharacteristic, complemented
182C22×#67C22×C311yescharacteristic
183C22×#67C22×C311yescharacteristic
184C23×Dic3C22×C311yescharacteristic
185C22×C4×D3C22×C311yescharacteristic
186C22×C4×D3C22×C311yescharacteristic
187C22×Dic6C22×C311yescharacteristic, complemented
188C3×#126—38no—
189C3×#126—38no—
190C3×#124—38no—
191C3×#123—38no—
192C3×#123—38no—
193C3×#123—38no—
194C3×C22⋊Q8—38no—
195C3×C22⋊Q8—38no—
196C3×#120—38no—
197C3×C4×D4—28no—
198C3×C4×D4—38no—
199C3×C4×D4C2×D318yescomplemented
200C3×C4×D4C22×C318yescomplemented
201C3×#117—38no—
202C3×#117—38no—
203C2×C3×C4⋊C4—21no—
204C2×C3×C4⋊C4—31no—
205C2×C3×C4⋊C4—31no—
206C2×C3×C4⋊C4—31no—
207C2×C3×C4⋊C4—31no—
208C2×C3×C4⋊C4—31no—
209C2×C3×C4⋊C4—31no—
210C2×C3×C4⋊C4—31no—
211C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
212C2×C3×C4⋊C4C22×C311yescharacteristic, complemented
213C2×C3×C22⋊C4—21no—
214C2×C3×C22⋊C4—21no—
215C2×C3×C22⋊C4—31no—
216C2×C3×C22⋊C4—31no—
217C2×C3×C22⋊C4—31no—
218C2×C3×C22⋊C4—31no—
219C2×C3×C22⋊C4—31no—
220C2×C3×C22⋊C4—31no—
221C2×C3×C22⋊C4—31no—
222C2×C3×C22⋊C4—31no—
223C2×C3×C22⋊C4—31no—
224C2×C3×C22⋊C4—31no—
225C2×C3×C22⋊C4—31no—
226C2×C3×C22⋊C4—31no—
227C2×C3×C22⋊C4—38no—
228C2×C3×C22⋊C4—38no—
229C2×C3×C22⋊C4C2×D311yescharacteristic
230C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
231C2×C3×C22⋊C4C22×C311yescharacteristic
232C2×C3×C22⋊C4C22×C311yescharacteristic, complemented
233C2×C3×C42—21no—
234C2×C3×C42—31no—
235C2×C3×C42—31no—
236C2×C3×C42C2×D311yescharacteristic, complemented
237C2×C3×C42C22×C311yescharacteristic, complemented
238C2×#217C22×C311yescharacteristic
239C2×#217C22×C311yescharacteristic
240C2×#217C22×C311yescharacteristic, complemented
241C2×#217C22×C311yescharacteristic, complemented
242#937C22×C318yes—
243#935C22×C318yescomplemented
244#929C22×C318yescomplemented
245C4×#67C22×C318yescomplemented
246C2×(C2×D3)⋊C4C22×C311yescharacteristic
247C2×(C2×D3)⋊C4C22×C311yescharacteristic
248C2×(C2×D3)⋊C4C22×C311yescharacteristic
249C2×(C2×D3)⋊C4C22×C311yescharacteristic
250C2×(C2×D3)⋊C4C22×C311yescharacteristic
251C2×(C2×D3)⋊C4C22×C311yescharacteristic
252C2×(C2×D3)⋊C4C22×C311yescharacteristic
253C2×(C2×D3)⋊C4C22×C311yescharacteristic
254C2×(C2×D3)⋊C4C22×C318yescomplemented
255C2×C4⋊Dic3C22×C311yescharacteristic, complemented
256#924C22×C318yescomplemented
257C2×Dic3⋊C4C22×C311yescharacteristic, complemented
258C2×Dic3⋊C4C22×C311yescharacteristic, complemented
259C2×Dic3⋊C4C22×C311yescharacteristic, complemented
260C2×Dic3⋊C4C22×C311yescharacteristic, complemented
261C2×Dic3⋊C4C22×C311yescharacteristic, complemented
262C2×Dic3⋊C4C22×C311yescharacteristic, complemented
263C2×C4×Dic3C22×C311yescharacteristic, complemented
264C2×C4×Dic3C22×C311yescharacteristic, complemented
265#898C22×C318yescomplemented
266#896C22×C318yescomplemented
267#885C22×C318yescomplemented
268#883C22×C318yescomplemented
269D3×C22⋊C4C22×C318yescomplemented
270#877C22×C318yescomplemented
271#876C22×C318yescomplemented
272#872C22×C318yescomplemented
273C23×C32—22no—
274C23×C32—22no—
275C23×C32—22no—
276C23×C32—22no—
277C23×C32—22no—
278C23×C32#4114yes—
279C23×C32C2412yes—
280C23×C32C2412yes—
281C23×C32C2411yescharacteristic
282C22×C3×D3—22no—
283C22×C3×D3—22no—
284C22×C3×D3—28no—
285C22×C3×D3—22no—
286C22×C3×D3—22no—
287C22×C3×D3—22no—
288C22×C3×D3—28no—
289C22×C3×D3—44no—
290C22×C3×D3—416no—
291C22×C3×D3#4114yes—
292C22×C3×D3C2412yes—
293C22×C3×D3C2412yes—
294C32×D4—28no—
295C2×C32×C4—22no—
296C2×C32×C4—22no—
297C2×C32×C4—22no—
298C2×C32×C4—22no—
299C2×C32×C4—22no—
300C2×C32×C4—44no—
301C2×C32×C4—44no—
302C2×C32×C4C2412yes—
303C2×C32×C4C2412yes—
304C2×C32×C4C2412yes—
305C2×C32×C4C2412yes—
306C2×C32×C4C2412yes—
307C3×#67—28no—
308C3×#67—44no—
309C2×C3×Dic3—22no—
310C2×C3×Dic3—28no—
311C2×C3×Dic3—22no—
312C2×C3×Dic3—22no—
313C2×C3×Dic3—22no—
314C2×C3×Dic3—22no—
315C2×C3×Dic3—22no—
316C2×C3×Dic3C2412yes—
317C2×C3×Dic3C2412yes—
318C2×C3×Dic3C2412yes—
319C2×C3×Dic3C2412yes—
320C2×C3×Dic3C2412yes—
321C2×C3×Dic3C2412yes—
322C3×C4×D3—28no—
323C3×C4×D3—44no—
324C3×Dic6—44no—
325#551—316no—
326C2×#126—31no—
327C2×#126—31no—
328C2×#124—31no—
329C2×#123—31no—
330C2×#123—31no—
331C2×#123—31no—
332C2×C22⋊Q8—31no—
333C2×C22⋊Q8—31no—
334C2×#120—31no—
335C2×C4×D4—31no—
336C2×C4×D4C3×D311yescharacteristic, complemented
337C2×#117—31no—
338C2×#117—31no—
339C22×C22⋊C4—31no—
340C22×C22⋊C4—31no—
341C24×C3—21no—
342C24×C3—21no—
343C24×C3—31no—
344C24×C3—31no—
345C24×C3—34no—
346C24×C3—64no—
347C24×C3—64no—
348C24×C3—122no—
349C24×C3C22×D311yescharacteristic
350C24×C3C22×D311yescharacteristic
351C24×C3C23×C311yescharacteristic
352C24×C3C23×C311yescharacteristic
353C23×D3—24no—
354C23×D3—24no—
355C23×D3—42no—
356C23×D3C23×C311yescharacteristic
357C23×D3C23×C314yes—
358C23×D3C23×C311yescharacteristic
359C2×C3×Q8—34no—
360C2×C3×Q8—122no—
361C2×C3×D4—28no—
362C2×C3×D4—24no—
363C2×C3×D4—24no—
364C2×C3×D4—24no—
365C2×C3×D4—34no—
366C2×C3×D4—34no—
367C2×C3×D4—64no—
368C2×C3×D4—122no—
369C2×C3×D4C22×D314yes—
370C2×C3×D4C23×C314yes—
371C22×C3×C4—21no—
372C22×C3×C4—21no—
373C22×C3×C4—21no—
374C22×C3×C4—21no—
375C22×C3×C4—21no—
376C22×C3×C4—24no—
377C22×C3×C4—24no—
378C22×C3×C4—34no—
379C22×C3×C4—31no—
380C22×C3×C4—31no—
381C22×C3×C4—31no—
382C22×C3×C4—31no—
383C22×C3×C4—31no—
384C22×C3×C4—31no—
385C22×C3×C4—34no—
386C22×C3×C4—34no—
387C22×C3×C4—42no—
388C22×C3×C4—42no—
389C22×C3×C4—42no—
390C22×C3×C4—42no—
391C22×C3×C4—44no—
392C22×C3×C4—44no—
393C22×C3×C4—64no—
394C22×C3×C4—64no—
395C22×C3×C4—122no—
396C22×C3×C4C22×D311yescharacteristic
397C22×C3×C4C22×D311yescharacteristic
398C22×C3×C4C22×D311yescharacteristic
399C22×C3×C4C22×D311yescharacteristic
400C22×C3×C4C22×D311yescharacteristic
401C22×C3×C4C22×D314yes—
402C22×C3×C4C22×D314yescomplemented
403C22×C3×C4C23×C311yescharacteristic
404C22×C3×C4C23×C311yescharacteristic
405C22×C3×C4C23×C311yescharacteristic
406C22×C3×C4C23×C311yescharacteristic
407C22×C3×C4C23×C311yescharacteristic
408C22×C3×C4C23×C314yes—
409C22×C3×C4C23×C314yescomplemented
410C2×#67—24no—
411C2×#67—42no—
412C2×#67C23×C314yes—
413C2×#67C23×C314yes—
414C22×Dic3—24no—
415C22×Dic3C23×C314yes—
416C22×Dic3C23×C311yescharacteristic
417C22×Dic3C23×C311yescharacteristic
418C22×Dic3C23×C311yescharacteristic
419C22×Dic3C23×C311yescharacteristic
420C22×Dic3C23×C311yescharacteristic
421C22×Dic3C23×C311yescharacteristic
422C2×C4×D3—24no—
423C2×C4×D3—42no—
424C2×C4×D3C23×C314yes—
425C2×C4×D3C23×C314yes—
426C2×Dic6—42no—
427C2×Dic6C23×C314yescomplemented
428C3×C4⋊C4—24no—
429C3×C4⋊C4—34no—
430C3×C4⋊C4—34no—
431C3×C4⋊C4—34no—
432C3×C4⋊C4—34no—
433C3×C4⋊C4—34no—
434C3×C4⋊C4—34no—
435C3×C4⋊C4—34no—
436C3×C4⋊C4C22×D314yescomplemented
437C3×C4⋊C4C23×C314yescomplemented
438C3×C22⋊C4—24no—
439C3×C22⋊C4—24no—
440C3×C22⋊C4—34no—
441C3×C22⋊C4—34no—
442C3×C22⋊C4—34no—
443C3×C22⋊C4—34no—
444C3×C22⋊C4—34no—
445C3×C22⋊C4—34no—
446C3×C22⋊C4—34no—
447C3×C22⋊C4—34no—
448C3×C22⋊C4—34no—
449C3×C22⋊C4—34no—
450C3×C22⋊C4—34no—
451C3×C22⋊C4—34no—
452C3×C22⋊C4C22×D314yes—
453C3×C22⋊C4C22×D314yescomplemented
454C3×C22⋊C4C23×C314yes—
455C3×C22⋊C4C23×C314yescomplemented
456C3×C42—24no—
457C3×C42—34no—
458C3×C42—34no—
459C3×C42C22×D314yescomplemented
460C3×C42C23×C314yescomplemented
461#217C23×C314yes—
462#217C23×C314yes—
463#217C23×C314yescomplemented
464#217C23×C314yescomplemented
465(C2×D3)⋊C4C23×C314yes—
466(C2×D3)⋊C4C23×C314yes—
467(C2×D3)⋊C4C23×C314yes—
468(C2×D3)⋊C4C23×C314yes—
469(C2×D3)⋊C4C23×C314yes—
470(C2×D3)⋊C4C23×C314yes—
471(C2×D3)⋊C4C23×C314yes—
472(C2×D3)⋊C4C23×C314yes—
473C4⋊Dic3C23×C314yescomplemented
474Dic3⋊C4C23×C314yescomplemented
475Dic3⋊C4C23×C314yescomplemented
476Dic3⋊C4C23×C314yescomplemented
477Dic3⋊C4C23×C314yescomplemented
478Dic3⋊C4C23×C314yescomplemented
479Dic3⋊C4C23×C314yescomplemented
480C4×Dic3C23×C314yescomplemented
481C4×Dic3C23×C314yescomplemented
482C22×C32—22no—
483C22×C32—28no—
484C22×C32—22no—
485C22×C32—22no—
486C22×C32—22no—
487C22×C32—22no—
488C22×C32—44no—
489C22×C32C2×#4114yes—
490C22×C32C2×#4112yes—
491C22×C32C2×#4112yes—
492C22×C32H(5,𝔽2)12yes—
493C22×C32C2511yescharacteristic
494C2×C3×D3—28no—
495C2×C3×D3—22no—
496C2×C3×D3—22no—
497C2×C3×D3—22no—
498C2×C3×D3—22no—
499C2×C3×D3—22no—
500C2×C3×D3—416no—
501C2×C3×D3—44no—
502C2×C3×D3C2×#4114yes—
503C32×C4—22no—
504C32×C4—22no—
505C32×C4—22no—
506C32×C4—22no—
507C32×C4—22no—
508C3×Dic3—22no—
509C3×Dic3—22no—
510C3×Dic3—22no—
511C3×Dic3—22no—
512C3×Dic3—22no—
513C3×Dic3—22no—
514C25—31no—
515C22×Q8—31no—
516C22×D4—31no—
517C22×D4—31no—
518C22×D4C2×C3×D311yescharacteristic
519C23×C4—31no—
520C23×C4—31no—
521C23×C4—31no—
522C23×C4C2×C3×D311yescharacteristic
523C23×C4C2×C3×D311yescharacteristic, complemented
524#126—38no—
525#126—38no—
526#124—38no—
527#123—38no—
528#123—38no—
529#123—38no—
530C22⋊Q8—38no—
531C22⋊Q8—38no—
532#120—38no—
533C4×D4—38no—
534C4×D4C2×C3×D318yescomplemented
535#117—38no—
536#117—38no—
537C2×C4⋊C4—31no—
538C2×C4⋊C4—31no—
539C2×C4⋊C4—31no—
540C2×C4⋊C4—31no—
541C2×C4⋊C4—31no—
542C2×C4⋊C4—31no—
543C2×C4⋊C4—31no—
544C2×C4⋊C4C2×C3×D311yescharacteristic, complemented
545C2×C22⋊C4—31no—
546C2×C22⋊C4—31no—
547C2×C22⋊C4—31no—
548C2×C22⋊C4—31no—
549C2×C22⋊C4—31no—
550C2×C22⋊C4—31no—
551C2×C22⋊C4—31no—
552C2×C22⋊C4—31no—
553C2×C22⋊C4—31no—
554C2×C22⋊C4—31no—
555C2×C22⋊C4—38no—
556C2×C22⋊C4—31no—
557C2×C22⋊C4—31no—
558C2×C22⋊C4—38no—
559C2×C22⋊C4C2×C3×D311yescharacteristic
560C2×C22⋊C4C2×C3×D311yescharacteristic, complemented
561C2×C42—31no—
562C2×C42—31no—
563C2×C42C2×C3×D311yescharacteristic, complemented
564C23×C3—22no—
565C23×C3—22no—
566C23×C3—22no—
567C23×C3—22no—
568C23×C3—24no—
569C23×C3—22no—
570C23×C3—22no—
571C23×C3—22no—
572C23×C3—22no—
573C23×C3—22no—
574C23×C3—22no—
575C23×C3—21no—
576C23×C3—22no—
577C23×C3—22no—
578C23×C3—24no—
579C23×C3—34no—
580C23×C3—32no—
581C23×C3—32no—
582C23×C3—42no—
583C23×C3—42no—
584C23×C3—42no—
585C23×C3—42no—
586C23×C3—68no—
587C23×C3—62no—
588C23×C3—62no—
589C23×C3—68no—
590C23×C3—62no—
591C23×C3—62no—
592C23×C3—62no—
593C23×C3—124no—
594C23×C3—1216no—
595C23×C3#23514yes—
596C23×C3C3×#4114yes—
597C23×C3C23×D312yes—
598C23×C3C23×D312yes—
599C23×C3C23×D311yescharacteristic
600C23×C3C24×C312yes—
601C23×C3C24×C312yes—
602C23×C3C24×C311yescharacteristic
603C22×D3—22no—
604C22×D3—22no—
605C22×D3—28no—
606C22×D3—22no—
607C22×D3—22no—
608C22×D3—22no—
609C22×D3—28no—
610C22×D3—44no—
611C22×D3—416no—
612C22×D3C3×#4114yes—
613C22×D3C24×C312yes—
614C22×D3C24×C312yes—
615C3×Q8—124no—
616C3×D4—216no—
617C3×D4—28no—
618C3×D4—28no—
619C3×D4—68no—
620C3×D4—124no—
621C2×C3×C4—24no—
622C2×C3×C4—24no—
623C2×C3×C4—22no—
624C2×C3×C4—22no—
625C2×C3×C4—22no—
626C2×C3×C4—22no—
627C2×C3×C4—22no—
628C2×C3×C4—22no—
629C2×C3×C4—22no—
630C2×C3×C4—22no—
631C2×C3×C4—22no—
632C2×C3×C4—22no—
633C2×C3×C4—22no—
634C2×C3×C4—22no—
635C2×C3×C4—22no—
636C2×C3×C4—22no—
637C2×C3×C4—22no—
638C2×C3×C4—32no—
639C2×C3×C4—32no—
640C2×C3×C4—32no—
641C2×C3×C4—32no—
642C2×C3×C4—32no—
643C2×C3×C4—32no—
644C2×C3×C4—42no—
645C2×C3×C4—42no—
646C2×C3×C4—42no—
647C2×C3×C4—44no—
648C2×C3×C4—44no—
649C2×C3×C4—44no—
650C2×C3×C4—44no—
651C2×C3×C4—48no—
652C2×C3×C4—48no—
653C2×C3×C4—68no—
654C2×C3×C4—68no—
655C2×C3×C4—62no—
656C2×C3×C4—62no—
657C2×C3×C4—62no—
658C2×C3×C4—62no—
659C2×C3×C4—62no—
660C2×C3×C4—62no—
661C2×C3×C4—124no—
662C2×C3×C4C23×D312yes—
663C2×C3×C4C23×D312yes—
664C2×C3×C4C23×D312yes—
665C2×C3×C4C23×D312yes—
666C2×C3×C4C23×D312yes—
667C2×C3×C4C24×C312yes—
668C2×C3×C4C24×C312yes—
669C2×C3×C4C24×C312yes—
670C2×C3×C4C24×C312yes—
671C2×C3×C4C24×C312yes—
672#67—28no—
673#67—44no—
674C2×Dic3—22no—
675C2×Dic3—28no—
676C2×Dic3—22no—
677C2×Dic3—22no—
678C2×Dic3—22no—
679C2×Dic3—22no—
680C2×Dic3—22no—
681C2×Dic3C24×C312yes—
682C2×Dic3C24×C312yes—
683C2×Dic3C24×C312yes—
684C2×Dic3C24×C312yes—
685C2×Dic3C24×C312yes—
686C2×Dic3C24×C312yes—
687C4×D3—28no—
688C4×D3—44no—
689Dic6—44no—
690C2×C32—24no—
691C2×C32—42no—
692C2×C32#55114yescomplemented
693C2×C32C22×#4111yescharacteristic
694C2×C32C22×#4111yescharacteristic
695C2×C32C2×H(5,𝔽2)11yescharacteristic
696C3×D3—24no—
697C3×D3—42no—
698C24—31no—
699C24—31no—
700C24—34no—
701C24—64no—
702C24—64no—
703C24—122no—
704C24C22×C3×D311yescharacteristic
705C24C22×C3×D311yescharacteristic
706C2×Q8—34no—
707C2×Q8—122no—
708C2×D4—24no—
709C2×D4—34no—
710C2×D4—34no—
711C2×D4—64no—
712C2×D4—122no—
713C2×D4C22×C3×D314yes—
714C22×C4—31no—
715C22×C4—31no—
716C22×C4—31no—
717C22×C4—31no—
718C22×C4—31no—
719C22×C4—31no—
720C22×C4—34no—
721C22×C4—34no—
722C22×C4—34no—
723C22×C4—42no—
724C22×C4—42no—
725C22×C4—64no—
726C22×C4—64no—
727C22×C4—122no—
728C22×C4C22×C3×D311yescharacteristic
729C22×C4C22×C3×D311yescharacteristic
730C22×C4C22×C3×D311yescharacteristic
731C22×C4C22×C3×D311yescharacteristic
732C22×C4C22×C3×D311yescharacteristic
733C22×C4C22×C3×D314yes—
734C22×C4C22×C3×D314yescomplemented
735C4⋊C4—34no—
736C4⋊C4—34no—
737C4⋊C4—34no—
738C4⋊C4—34no—
739C4⋊C4—34no—
740C4⋊C4—34no—
741C4⋊C4—34no—
742C4⋊C4C22×C3×D314yescomplemented
743C22⋊C4—34no—
744C22⋊C4—34no—
745C22⋊C4—34no—
746C22⋊C4—34no—
747C22⋊C4—34no—
748C22⋊C4—34no—
749C22⋊C4—34no—
750C22⋊C4—34no—
751C22⋊C4—34no—
752C22⋊C4—34no—
753C22⋊C4—34no—
754C22⋊C4—34no—
755C22⋊C4C22×C3×D314yes—
756C22⋊C4C22×C3×D314yescomplemented
757C42—34no—
758C42—34no—
759C42C22×C3×D314yescomplemented
760C22×C3—22no—
761C22×C3—22no—
762C22×C3—22no—
763C22×C3—22no—
764C22×C3—28no—
765C22×C3—28no—
766C22×C3—24no—
767C22×C3—22no—
768C22×C3—22no—
769C22×C3—22no—
770C22×C3—22no—
771C22×C3—22no—
772C22×C3—22no—
773C22×C3—22no—
774C22×C3—24no—
775C22×C3—22no—
776C22×C3—22no—
777C22×C3—21no—
778C22×C3—34no—
779C22×C3—42no—
780C22×C3—42no—
781C22×C3—48no—
782C22×C3—42no—
783C22×C3—42no—
784C22×C3—48no—
785C22×C3—44no—
786C22×C3—44no—
787C22×C3—62no—
788C22×C3—62no—
789C22×C3—68no—
790C22×C3—62no—
791C22×C3—62no—
792C22×C3—62no—
793C22×C3—1216no—
794C22×C3—124no—
795C22×C3C2×#23514yes—
796C22×C3C2×#23512yes—
797C22×C3#100412yes—
798C22×C3D3×#4112yes—
799C22×C3C2×C3×#4114yes—
800C22×C3C2×C3×#4112yes—
801C22×C3C2×C3×#4112yes—
802C22×C3C3×H(5,𝔽2)12yes—
803C22×C3C24×D311yescharacteristic
804C22×C3C25×C311yescharacteristic
805C2×D3—22no—
806C2×D3—22no—
807C2×D3—28no—
808C2×D3—22no—
809C2×D3—22no—
810C2×D3—22no—
811C2×D3—416no—
812C2×D3—44no—
813C2×D3C2×C3×#4114yes—
814C3×C4—24no—
815C3×C4—24no—
816C3×C4—22no—
817C3×C4—22no—
818C3×C4—22no—
819C3×C4—22no—
820C3×C4—22no—
821C3×C4—22no—
822C3×C4—22no—
823C3×C4—22no—
824C3×C4—22no—
825C3×C4—22no—
826C3×C4—42no—
827C3×C4—42no—
828C3×C4—42no—
829C3×C4—62no—
830C3×C4—62no—
831C3×C4—62no—
832C3×C4—62no—
833C3×C4—62no—
834C3×C4—62no—
835Dic3—22no—
836Dic3—22no—
837Dic3—22no—
838Dic3—22no—
839Dic3—22no—
840Dic3—22no—
841C32C2×#55111yescharacteristic, complemented, Sylow
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—34no—
848C23—32no—
849C23—32no—
850C23—68no—
851C23—62no—
852C23—62no—
853C23—68no—
854C23—62no—
855C23—62no—
856C23—62no—
857C23—124no—
858C23—1216no—
859C23C3×#23514yes—
860C23C23×C3×D312yes—
861C23C23×C3×D312yes—
862C23C23×C3×D311yescharacteristic
863Q8—124no—
864D4—28no—
865D4—68no—
866D4—124no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—32no—
873C2×C4—32no—
874C2×C4—32no—
875C2×C4—32no—
876C2×C4—32no—
877C2×C4—32no—
878C2×C4—44no—
879C2×C4—44no—
880C2×C4—68no—
881C2×C4—68no—
882C2×C4—62no—
883C2×C4—62no—
884C2×C4—62no—
885C2×C4—62no—
886C2×C4—62no—
887C2×C4—62no—
888C2×C4—124no—
889C2×C4C23×C3×D312yes—
890C2×C4C23×C3×D312yes—
891C2×C4C23×C3×D312yes—
892C2×C4C23×C3×D312yes—
893C2×C4C23×C3×D312yes—
894C2×C3—24no—
895C2×C3—24no—
896C2×C3—24no—
897C2×C3—21no—
898C2×C3—21no—
899C2×C3—21no—
900C2×C3—44no—
901C2×C3—44no—
902C2×C3—42no—
903C2×C3—42no—
904C2×C3—64no—
905C2×C3—122no—
906C2×C3#555614yesdirect product factor
907C2×C3C3×#55114yescomplemented
908C2×C3C22×#23511yescharacteristic
909C2×C3C2×#100411yescharacteristic
910C2×C3C2×D3×#4111yescharacteristic
911C2×C3C22×C3×#4111yescharacteristic
912C2×C3C22×C3×#4111yescharacteristic
913C2×C3C2×C3×H(5,𝔽2)11yescharacteristic
914D3—24no—
915D3—42no—
916C22—28no—
917C22—22no—
918C22—22no—
919C22—22no—
920C22—22no—
921C22—22no—
922C22—34no—
923C22—44no—
924C22—68no—
925C22—62no—
926C22—62no—
927C22—62no—
928C22—62no—
929C22—62no—
930C22—1216no—
931C22—124no—
932C22C2×C3×#23514yes—
933C22C2×C3×#23512yes—
934C22C3×#100412yes—
935C22C3×D3×#4112yes—
936C22C24×C3×D311yescharacteristic
937C4—22no—
938C4—22no—
939C4—22no—
940C4—22no—
941C4—22no—
942C4—62no—
943C4—62no—
944C4—62no—
945C4—62no—
946C4—62no—
947C4—62no—
948C3—21no—
949C3C2×#555611yescharacteristic, direct product factor
950C3C2×C3×#55111yescharacteristic, complemented
951C2—24no—
952C2—42no—
953C2—64no—
954C2—122no—
955C2C3×#555614yesdirect product factor
956C2C22×C3×#23511yescharacteristic
957C2C2×C3×#100411yescharacteristic
958C2C2×C3×D3×#4111yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×C4×D4C2
socleC23×C32C24
prime radicalC2×C3×#937C2
hypercenterC2×C3×C4×D4D3
hypocenterC3C2×C3×#551
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×C4×D4C2semidirect
3. C2×C3×#935C2semidirect
4. C2×C3×#929C2semidirect
5. C2×C3×C4×#67C2semidirect
6. C22×C3×(C2×D3)⋊C4C2semidirect
7. C2×C3×#924C2semidirect
8. C3×#5556C2direct (N × H)
9. C2×C3×#898C2semidirect
10. C2×C3×#896C2semidirect
11. C2×C3×#885C2semidirect
12. C2×C3×#883C2semidirect
13. C2×C3×D3×C22⋊C4C2semidirect
14. C2×C3×#877C2semidirect
15. C2×C3×#876C2semidirect
16. C2×C3×#872C2semidirect
18. C2×#5556C3direct (N × H)
22. C23×C32×C4C22semidirect
28. C22×C3×Dic6C22semidirect
29. C32×C4×D4C22semidirect
30. C2×C32×C4⋊C4C22semidirect
32. C2×C32×C22⋊C4C22semidirect
33. C2×C32×C42C22semidirect
36. C2×C3×#217C22semidirect
37. C2×C3×#217C22semidirect
39. C3×#935C22semidirect
40. C3×#929C22semidirect
41. C3×C4×#67C22semidirect
50. C2×C3×(C2×D3)⋊C4C22semidirect
51. C2×C3×C4⋊Dic3C22semidirect
52. C3×#924C22semidirect
53. C2×C3×Dic3⋊C4C22semidirect
54. C2×C3×Dic3⋊C4C22semidirect
55. C2×C3×Dic3⋊C4C22semidirect
56. C2×C3×Dic3⋊C4C22semidirect
57. C2×C3×Dic3⋊C4C22semidirect
58. C2×C3×Dic3⋊C4C22semidirect
59. C2×C3×C4×Dic3C22semidirect
60. C2×C3×C4×Dic3C22semidirect
61. C3×#898C22semidirect
62. C3×#896C22semidirect
63. C3×#885C22semidirect
64. C3×#883C22semidirect
65. C3×D3×C22⋊C4C22semidirect
66. C3×#877C22semidirect
67. C3×#876C22semidirect
68. C3×#872C22semidirect
81. C2×C3×C4×D4D3semidirect
82. C2×C3×C4×D4C2×C3semidirect
88. C2×#935C2×C3semidirect
89. C2×#929C2×C3semidirect
90. C2×C4×#67C2×C3semidirect
91. C22×(C2×D3)⋊C4C2×C3semidirect
92. C2×#924C2×C3semidirect
93. #5556C2×C3direct (N × H)
94. C2×#898C2×C3semidirect
95. C2×#896C2×C3semidirect
96. C2×#885C2×C3semidirect
97. C2×#883C2×C3semidirect
98. C2×D3×C22⋊C4C2×C3semidirect
99. C2×#877C2×C3semidirect
100. C2×#876C2×C3semidirect
101. C2×#872C2×C3semidirect
120. C22×C32×C4C23semidirect
138. C2×C3×Dic6C23semidirect
139. C32×C4⋊C4C23semidirect
141. C32×C22⋊C4C23semidirect
142. C32×C42C23semidirect
145. C3×#217C23semidirect
146. C3×#217C23semidirect
155. C3×C4⋊Dic3C23semidirect
156. C3×Dic3⋊C4C23semidirect
157. C3×Dic3⋊C4C23semidirect
158. C3×Dic3⋊C4C23semidirect
159. C3×Dic3⋊C4C23semidirect
160. C3×Dic3⋊C4C23semidirect
161. C3×Dic3⋊C4C23semidirect
162. C3×C4×Dic3C23semidirect
163. C3×C4×Dic3C23semidirect
179. C23×C3×C4C2×D3semidirect
181. C23×C3×C4C22×C3semidirect
187. C22×Dic6C22×C3semidirect
199. C3×C4×D4C2×D3semidirect
200. C3×C4×D4C22×C3semidirect
211. C2×C3×C4⋊C4C2×D3semidirect
212. C2×C3×C4⋊C4C22×C3semidirect
230. C2×C3×C22⋊C4C2×D3semidirect
232. C2×C3×C22⋊C4C22×C3semidirect
236. C2×C3×C42C2×D3semidirect
237. C2×C3×C42C22×C3semidirect
240. C2×#217C22×C3semidirect
241. C2×#217C22×C3semidirect
243. #935C22×C3semidirect
244. #929C22×C3semidirect
245. C4×#67C22×C3semidirect
254. C2×(C2×D3)⋊C4C22×C3semidirect
255. C2×C4⋊Dic3C22×C3semidirect
256. #924C22×C3semidirect
257. C2×Dic3⋊C4C22×C3semidirect
258. C2×Dic3⋊C4C22×C3semidirect
259. C2×Dic3⋊C4C22×C3semidirect
260. C2×Dic3⋊C4C22×C3semidirect
261. C2×Dic3⋊C4C22×C3semidirect
262. C2×Dic3⋊C4C22×C3semidirect
263. C2×C4×Dic3C22×C3semidirect
264. C2×C4×Dic3C22×C3semidirect
265. #898C22×C3semidirect
266. #896C22×C3semidirect
267. #885C22×C3semidirect
268. #883C22×C3semidirect
269. D3×C22⋊C4C22×C3semidirect
270. #877C22×C3semidirect
271. #876C22×C3semidirect
272. #872C22×C3semidirect
336. C2×C4×D4C3×D3semidirect
402. C22×C3×C4C22×D3semidirect
409. C22×C3×C4C23×C3semidirect
427. C2×Dic6C23×C3semidirect
436. C3×C4⋊C4C22×D3semidirect
437. C3×C4⋊C4C23×C3semidirect
453. C3×C22⋊C4C22×D3semidirect
455. C3×C22⋊C4C23×C3semidirect
459. C3×C42C22×D3semidirect
460. C3×C42C23×C3semidirect
463. #217C23×C3semidirect
464. #217C23×C3semidirect
473. C4⋊Dic3C23×C3semidirect
474. Dic3⋊C4C23×C3semidirect
475. Dic3⋊C4C23×C3semidirect
476. Dic3⋊C4C23×C3semidirect
477. Dic3⋊C4C23×C3semidirect
478. Dic3⋊C4C23×C3semidirect
479. Dic3⋊C4C23×C3semidirect
480. C4×Dic3C23×C3semidirect
481. C4×Dic3C23×C3semidirect
523. C23×C4C2×C3×D3semidirect
534. C4×D4C2×C3×D3semidirect
544. C2×C4⋊C4C2×C3×D3semidirect
560. C2×C22⋊C4C2×C3×D3semidirect
563. C2×C42C2×C3×D3semidirect
692. C2×C32#551semidirect
734. C22×C4C22×C3×D3semidirect
742. C4⋊C4C22×C3×D3semidirect
756. C22⋊C4C22×C3×D3semidirect
759. C42C22×C3×D3semidirect
841. C32C2×#551semidirect
906. C2×C3#5556direct (N × H)
907. C2×C3C3×#551semidirect
949. C3C2×#5556direct (N × H)
950. C3C2×C3×#551semidirect
955. C2C3×#5556direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×C4×D42
C2×C3×#9372
C2×C3×#9352
C2×C3×#9292
C2×C3×C4×#672
C22×C3×(C2×D3)⋊C42
C2×C3×#9242
C3×#55562
C2×C3×#8982
C2×C3×#8962
C2×C3×#8852
C2×C3×#8832
C2×C3×D3×C22⋊C42
C2×C3×#8772
C2×C3×#8762
C2×C3×#8722
C2×C3×#5513
C2×#55563