Finite Group Databasebeta

← C3×#80772 #11884524

Subgroups — C3×#80772 #11884524

Order 1152.

1013 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#918C211yesmaximal, characteristic, complemented
2C2×C3×#904C211yesmaximal, characteristic, complemented
3C3×#5633C211yesmaximal, characteristic, complemented
4C3×#5631C211yesmaximal, characteristic, complemented
5C32×#467C211yesmaximal, characteristic, complemented
6C3×#5190C211yesmaximal, characteristic, complemented
7C3×#5111C211yesmaximal, characteristic, complemented
8C3×#5047C211yesmaximal, characteristic, complemented
9C3×#5047C211yesmaximal, characteristic, complemented
10C3×#4889C211yesmaximal, characteristic, complemented
11C3×#4886C211yesmaximal, characteristic, complemented
12C3×#4819C211yesmaximal, characteristic, complemented
13C3×#4810C211yesmaximal, characteristic, complemented
14C3×#4809C211yesmaximal, characteristic, complemented
15C3×#4795C211yesmaximal, characteristic, complemented
16C3×#3269—31nomaximal
17#80772C311yesmaximal, characteristic, direct product factor
18C2×C3×#239C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic
21C2×C3×#235C2211yescharacteristic
22C2×C32×Q16C2211yescharacteristic
23C22×C32×C8C2211yescharacteristic
24C32×C22⋊Q8C2211yescharacteristic
25C32×C22⋊Q8C2211yescharacteristic
26C3×#947C2211yescharacteristic
27C3×#944C2211yescharacteristic
28C2×C3×#216C2211yescharacteristic
29C2×C3×#216C2211yescharacteristic
30C2×C3×#215C2211yescharacteristic
31C2×C3×#215C2211yescharacteristic
32C3×C4×#67C2211yescharacteristic
33C3×#918—24no—
34C2×C3×Dic12C2211yescharacteristic
35C3×#904—24no—
36C2×C3×D24C2211yescharacteristic
37C2×C3×#204C2211yescharacteristic
38C2×C3×#204C2211yescharacteristic
39C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
40C3×#897C2211yescharacteristic
41C3×#896—21no—
42C3×#895C2211yescharacteristic
43C3×#894—21no—
44C3×#893—21no—
45C3×#893C2211yescharacteristic
46C3×D3×C4⋊C4—21no—
47C3×#887C2211yescharacteristic
48C3×#885—21no—
49C3×#884—21no—
50C3×#884—21no—
51C3×#883—21no—
52C32×#107C2211yescharacteristic
53C32×#103C2211yescharacteristic
54C32×#103C2211yescharacteristic
55C3×#830C2211yescharacteristic
56C3×(C2×D3)⋊C8C2211yescharacteristic
57C3×#815C2211yescharacteristic
58C3×Dic3⋊C8C2211yescharacteristic
59C3×#810C2211yescharacteristic
60C3×#810C2211yescharacteristic
61C3×#809C2211yescharacteristic
62C3×#809C2211yescharacteristic
63C2×C3×#137—31no—
64C2×C3×#135—31no—
65C3×#548—31no—
66C3×#547—31no—
67C2×#918C2×C311yescharacteristic, complemented
68C2×#904C2×C311yescharacteristic, complemented
69#5633C2×C311yescharacteristic, complemented
70#5631C2×C311yescharacteristic, complemented
71C3×#497—31no—
72C3×#468—31no—
73C3×#467—21no—
74C3×#467D311yescharacteristic, complemented
75C3×#467C2×C311yescharacteristic, complemented
76C3×#463—31no—
77C3×#462—31no—
78C3×#452—31no—
79C3×#452—31no—
80C3×#451—31no—
81C3×#449—31no—
82C3×#440—31no—
83C3×#435—31no—
84#5190C2×C311yescharacteristic, complemented
85#5111C2×C311yescharacteristic, complemented
86#5047C2×C311yescharacteristic, complemented
87#5047C2×C311yescharacteristic, complemented
88#4889C2×C311yescharacteristic, complemented
89#4886C2×C311yescharacteristic, complemented
90#4819C2×C311yescharacteristic, complemented
91#4810C2×C311yescharacteristic, complemented
92#4809C2×C311yescharacteristic, complemented
93#4795C2×C311yescharacteristic, complemented
94C2×C32×Q8C2311yescharacteristic
95C2×C32×Q8C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C2×C3×#67D411yescharacteristic
100C3×#239—22no—
101C3×#239—41no—
102C3×D3×Q8—22no—
103C3×D3×Q8—41no—
104C3×#235—22no—
105C3×#235—22no—
106C3×#235—41no—
107C3×#235—41no—
108C2×C3×D12—21no—
109C2×C3×D12—21no—
110C2×C3×D12C2311yescharacteristic
111C2×C3×D12C2311yescharacteristic
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3—21no—
116C2×C3×C4×D3—21no—
117C2×C3×C4×D3C2311yescharacteristic
118C2×C3×Dic6—21no—
119C2×C3×Dic6C2311yescharacteristic
120C2×C3×Dic6C2311yescharacteristic
121C32×Q16—22no—
122C2×C32×C8—22no—
123C2×C32×C8C2311yescharacteristic
124C2×C32×C8C2311yescharacteristic
125C32×C4⋊C4—21no—
126C32×C4⋊C4—21no—
127C32×C4⋊C4C2311yescharacteristic
128C32×C4⋊C4C2311yescharacteristic
129C32×C22⋊C4—21no—
130C32×C22⋊C4—21no—
131C3×#217D411yescharacteristic
132C3×#216—22no—
133C3×#216—41no—
134C3×#215—22no—
135C3×#215—41no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4—21no—
140C3×(C2×D3)⋊C4—21no—
141C3×(C2×D3)⋊C4D411yescharacteristic
142C3×C4⋊Dic3—21no—
143C3×Dic3⋊C4—21no—
144C3×Dic3⋊C4—21no—
145C3×Dic3⋊C4—21no—
146C3×Dic3⋊C4D411yescharacteristic
147C3×C4×Dic3—21no—
148C3×C4×Dic3C2311yescharacteristic
149C2×C3×C3⋊C8C2311yescharacteristic
150C2×C3×C3⋊C8C2311yescharacteristic
151C3×Dic12—22no—
152C3×D24—22no—
153C3×#204—22no—
154C3×#204D414yescomplemented
155C3×ΓL(1,𝔽25)—22no—
156#3269—31noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C2×C3×#41—31no—
160C22×C3×Q8—31no—
161C2×#239C22×C311yescharacteristic
162C2×D3×Q8C22×C311yescharacteristic
163C2×#235C22×C311yescharacteristic
164C2×#235C22×C311yescharacteristic
165C3×#137—64no—
166C3×#135—64no—
167C2×C3×Q16—21no—
168C2×C3×Q16—31no—
169C2×C3×Q16—31no—
170C2×C3×Q16—31no—
171C2×C3×Q16C2×D311yescharacteristic
172C2×C3×Q16C22×C311yescharacteristic
173C2×C3×SD16—31no—
174C2×C3×SD16—31no—
175C2×C3×SD16—31no—
176C2×C3×SD16—31no—
177C2×C3×D8—31no—
178C2×C3×M16—31no—
179C22×C3×C8—21no—
180C22×C3×C8C2×D311yescharacteristic
181C22×C3×C8C22×C311yescharacteristic
182C3×C4⋊Q8—31no—
183C3×#124—31no—
184C3×#124—61no—
185C3×#123—61no—
186C3×#123—61no—
187C3×C22⋊Q8—21no—
188C3×C22⋊Q8—21no—
189C3×C22⋊Q8—31no—
190C3×C22⋊Q8—61no—
191C3×C22⋊Q8C2×D311yescharacteristic
192C3×C22⋊Q8C2×D311yescharacteristic
193C3×C22⋊Q8C22×C311yescharacteristic
194C3×C22⋊Q8C22×C311yescharacteristic
195C3×#121—31no—
196C3×#121—61no—
197C3×#121—61no—
198C3×C4×Q8—31no—
199C3×C4×D4—31no—
200C3×C4×D4—31no—
201C3×C4×D4—61no—
202C2×C3×C4⋊C4—61no—
203#947C22×C311yescharacteristic
204#944C22×C311yescharacteristic
205C2×#216C22×C311yescharacteristic
206C2×#216C22×C311yescharacteristic
207C2×#215C22×C311yescharacteristic
208C2×#215C22×C311yescharacteristic
209C4×#67C22×C311yescharacteristic
210#918—24no—
211C2×Dic12C22×C311yescharacteristic
212#904—24no—
213C2×D24C22×C311yescharacteristic
214C2×#204C22×C311yescharacteristic
215C2×#204C22×C311yescharacteristic
216C2×ΓL(1,𝔽25)C22×C311yescharacteristic
217#897C22×C311yescharacteristic
218#896—21no—
219#895C22×C311yescharacteristic
220#894—21no—
221#893—21no—
222#893C22×C311yescharacteristic
223D3×C4⋊C4—21no—
224#887C22×C311yescharacteristic
225#885—21no—
226#884—21no—
227#884—21no—
228#883—21no—
229C3×#107—21no—
230C3×#107C2×D311yescharacteristic
231C3×#107C22×C311yescharacteristic
232C3×C4⋊C8—31no—
233C3×#103—21no—
234C3×#103—21no—
235C3×#103—31no—
236C3×#103—31no—
237C3×#103C2×D311yescharacteristic
238C3×#103C2×D311yescharacteristic
239C3×#103C22×C311yescharacteristic
240C3×#103C22×C311yescharacteristic
241C3×#102—31no—
242C3×#102—31no—
243C3×C22⋊C8—31no—
244C3×C22⋊C8—31no—
245C3×#97—31no—
246#830C22×C311yescharacteristic
247(C2×D3)⋊C8C22×C311yescharacteristic
248#815C22×C311yescharacteristic
249Dic3⋊C8C22×C311yescharacteristic
250#810C22×C311yescharacteristic
251#810C22×C311yescharacteristic
252#809C22×C311yescharacteristic
253#809C22×C311yescharacteristic
254C23×C32C2×D411yescharacteristic
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3C2×D411yescharacteristic
258C32×Q8—21no—
259C32×Q8—21no—
260C32×Q8—21no—
261C32×Q8—21no—
262C2×C32×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4C2×D411yescharacteristic
269C2×C32×C4C2411yescharacteristic
270C3×#67—41no—
271C3×#67—42no—
272C3×#67—42no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3C2×D411yescharacteristic
276C2×C3×Dic3C2×D411yescharacteristic
277C2×C3×Dic3C2×D411yescharacteristic
278C3×D12—21no—
279C3×D12—21no—
280C3×D12—21no—
281C3×D12—42no—
282C3×D12—42no—
283C3×D12C2×D412yes—
284C3×C4×D3—21no—
285C3×C4×D3—21no—
286C3×C4×D3—42no—
287C3×C4×D3—42no—
288C3×C4×D3—42no—
289C3×C4×D3—42no—
290C3×C4×D3—42no—
291C3×Dic6—21no—
292C3×Dic6—21no—
293C3×Dic6—21no—
294C3×Dic6—42no—
295C3×Dic6C2×D412yes—
296C32×C8—21no—
297C32×C8C2×D412yes—
298C3×C3⋊C8—21no—
299C3×C3⋊C8—21no—
300C2×#137—31no—
301C2×#135—31no—
302#548—31no—
303#547—31no—
304#497—31no—
305#468—31no—
306#467C3×D311yescharacteristic, complemented
307#463—31no—
308#462—31no—
309#452—31no—
310#452—31no—
311#451—31no—
312#449—31no—
313#440—31no—
314#435—31no—
315C3×#41—62no—
316C3×#41—62no—
317C3×#41—62no—
318C3×#41—121no—
319C3×#41—121no—
320C3×#41—121no—
321C2×C3×Q8—21no—
322C2×C3×Q8—21no—
323C2×C3×Q8—31no—
324C2×C3×Q8—31no—
325C2×C3×Q8—61no—
326C2×C3×Q8—62no—
327C2×C3×Q8—121no—
328C2×C3×Q8C22×D311yescharacteristic
329C2×C3×Q8C22×D311yescharacteristic
330C2×C3×Q8C23×C311yescharacteristic
331C2×C3×Q8C23×C311yescharacteristic
332C2×C3×D4—31no—
333C2×C3×D4—31no—
334C2×C3×D4—31no—
335C2×C3×D4—61no—
336C2×C3×D4—61no—
337C2×C3×D4—61no—
338C2×C3×D4—61no—
339C22×C3×C4—21no—
340C22×C3×C4—31no—
341C22×C3×C4—61no—
342C22×C3×C4—61no—
343C22×C3×C4—61no—
344C22×C3×C4—61no—
345C22×C3×C4—61no—
346C22×C3×C4C22×D311yescharacteristic
347C22×C3×C4C23×C311yescharacteristic
348C2×#67—21no—
349C2×#67—21no—
350C2×#67C3×D411yescharacteristic
351#239—22no—
352#239—41no—
353D3×Q8—22no—
354D3×Q8—41no—
355#235—22no—
356#235—22no—
357#235—41no—
358#235—41no—
359C2×D12—21no—
360C2×D12—21no—
361C2×D12C23×C311yescharacteristic
362C2×D12C23×C311yescharacteristic
363C2×C4×D3—21no—
364C2×C4×D3—21no—
365C2×C4×D3—21no—
366C2×C4×D3—21no—
367C2×C4×D3—21no—
368C2×C4×D3C23×C311yescharacteristic
369C2×Dic6—21no—
370C2×Dic6C23×C311yescharacteristic
371C2×Dic6C23×C311yescharacteristic
372C3×Q16—22no—
373C3×Q16—22no—
374C3×Q16—42no—
375C3×Q16—62no—
376C3×Q16—62no—
377C3×Q16—121no—
378C3×SD16—34no—
379C3×SD16—62no—
380C3×SD16—62no—
381C3×SD16—121no—
382C3×D8—62no—
383C3×M16—62no—
384C2×C3×C8—22no—
385C2×C3×C8—22no—
386C2×C3×C8—21no—
387C2×C3×C8—21no—
388C2×C3×C8—31no—
389C2×C3×C8—31no—
390C2×C3×C8—42no—
391C2×C3×C8C22×D311yescharacteristic
392C2×C3×C8C22×D311yescharacteristic
393C2×C3×C8C23×C311yescharacteristic
394C2×C3×C8C23×C311yescharacteristic
395C3×C4⋊C4—21no—
396C3×C4⋊C4—21no—
397C3×C4⋊C4—21no—
398C3×C4⋊C4—21no—
399C3×C4⋊C4—21no—
400C3×C4⋊C4—21no—
401C3×C4⋊C4—31no—
402C3×C4⋊C4—41no—
403C3×C4⋊C4—41no—
404C3×C4⋊C4—61no—
405C3×C4⋊C4—61no—
406C3×C4⋊C4—61no—
407C3×C4⋊C4—61no—
408C3×C4⋊C4C22×D311yescharacteristic
409C3×C4⋊C4C22×D311yescharacteristic
410C3×C4⋊C4C23×C311yescharacteristic
411C3×C4⋊C4C23×C311yescharacteristic
412C3×C22⋊C4—21no—
413C3×C22⋊C4—21no—
414C3×C22⋊C4—21no—
415C3×C22⋊C4—21no—
416C3×C22⋊C4—31no—
417C3×C22⋊C4—31no—
418C3×C22⋊C4—41no—
419C3×C22⋊C4—41no—
420C3×C22⋊C4—61no—
421C3×C22⋊C4—61no—
422C3×C22⋊C4—61no—
423C3×C22⋊C4—61no—
424C3×C22⋊C4—61no—
425C3×C42—31no—
426C3×C42—61no—
427#217C3×D411yescharacteristic
428#216—22no—
429#216—41no—
430#215—22no—
431#215—41no—
432(C2×D3)⋊C4—21no—
433(C2×D3)⋊C4—21no—
434(C2×D3)⋊C4—21no—
435(C2×D3)⋊C4—21no—
436(C2×D3)⋊C4—21no—
437(C2×D3)⋊C4C3×D411yescharacteristic
438C4⋊Dic3—21no—
439Dic3⋊C4—21no—
440Dic3⋊C4—21no—
441Dic3⋊C4—21no—
442Dic3⋊C4C3×D411yescharacteristic
443C4×Dic3—21no—
444C4×Dic3C23×C311yescharacteristic
445C2×C3⋊C8C23×C311yescharacteristic
446C2×C3⋊C8C23×C311yescharacteristic
447Dic12—22no—
448D24—22no—
449#204—22no—
450#204C3×D414yescomplemented
451ΓL(1,𝔽25)—22no—
452C22×C32—21no—
453C22×C32—21no—
454C22×C32—21no—
455C22×C32C22×D411yescharacteristic
456C2×C3×D3—21no—
457C2×C3×D3—22no—
458C2×C3×D3—21no—
459C2×C3×D3—21no—
460C2×C3×D3—41no—
461C2×C3×D3—41no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C32×C4—21no—
466C32×C4—41no—
467C32×C4—41no—
468C32×C4—41no—
469C32×C4—41no—
470C32×C4C22×D411yescharacteristic
471C32×C4H(5,𝔽2)11yescharacteristic
472C3×Dic3—22no—
473C3×Dic3—21no—
474C3×Dic3—21no—
475C3×Dic3—21no—
476C3×Dic3—41no—
477C2×#41—31no—
478C2×#41—31no—
479C2×#41—31no—
480C22×Q8—31no—
481#137—64no—
482#135—64no—
483C2×Q16—31no—
484C2×Q16—31no—
485C2×Q16—31no—
486C2×Q16C2×C3×D311yescharacteristic
487C2×SD16—31no—
488C2×SD16—31no—
489C2×SD16—31no—
490C2×SD16—31no—
491C2×D8—31no—
492C2×M16—31no—
493C22×C8C2×C3×D311yescharacteristic
494C4⋊Q8—31no—
495#124—31no—
496#124—61no—
497#123—61no—
498#123—61no—
499C22⋊Q8—31no—
500C22⋊Q8—61no—
501C22⋊Q8C2×C3×D311yescharacteristic
502C22⋊Q8C2×C3×D311yescharacteristic
503#121—31no—
504#121—61no—
505#121—61no—
506C4×Q8—31no—
507C4×D4—31no—
508C4×D4—31no—
509C4×D4—61no—
510C2×C4⋊C4—61no—
511#107C2×C3×D311yescharacteristic
512C4⋊C8—31no—
513#103—31no—
514#103—31no—
515#103C2×C3×D311yescharacteristic
516#103C2×C3×D311yescharacteristic
517#102—31no—
518#102—31no—
519C22⋊C8—31no—
520C22⋊C8—31no—
521#97—31no—
522C23×C3—21no—
523C23×C3—31no—
524C23×C3—61no—
525C23×C3—61no—
526C23×C3D3×D411yescharacteristic
527C23×C3C2×C3×D411yescharacteristic
528C22×D3—21no—
529C22×D3—21no—
530C22×D3C2×C3×D411yescharacteristic
531C3×Q8—21no—
532C3×Q8—21no—
533C3×Q8—21no—
534C3×Q8—21no—
535C3×Q8—21no—
536C3×Q8—21no—
537C3×Q8—21no—
538C3×Q8—21no—
539C3×Q8—32no—
540C3×Q8—41no—
541C3×Q8—41no—
542C3×Q8—41no—
543C3×Q8—41no—
544C3×Q8—61no—
545C3×Q8—61no—
546C3×Q8—61no—
547C3×Q8—122no—
548C3×D4—32no—
549C3×D4—61no—
550C3×D4—61no—
551C3×D4—61no—
552C3×D4—122no—
553C3×D4—122no—
554C3×D4—121no—
555C3×D4—122no—
556C3×D4—122no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—31no—
572C2×C3×C4—31no—
573C2×C3×C4—31no—
574C2×C3×C4—41no—
575C2×C3×C4—41no—
576C2×C3×C4—41no—
577C2×C3×C4—41no—
578C2×C3×C4—41no—
579C2×C3×C4—41no—
580C2×C3×C4—61no—
581C2×C3×C4—61no—
582C2×C3×C4—61no—
583C2×C3×C4—61no—
584C2×C3×C4—122no—
585C2×C3×C4—122no—
586C2×C3×C4—122no—
587C2×C3×C4—122no—
588C2×C3×C4—122no—
589C2×C3×C4D3×D411yescharacteristic
590C2×C3×C4C2×C3×D411yescharacteristic
591C2×C3×C4C23×D311yescharacteristic
592C2×C3×C4C24×C311yescharacteristic
593#67—41no—
594#67—42no—
595#67—42no—
596C2×Dic3—21no—
597C2×Dic3—21no—
598C2×Dic3C2×C3×D411yescharacteristic
599C2×Dic3C2×C3×D411yescharacteristic
600C2×Dic3C2×C3×D411yescharacteristic
601D12—21no—
602D12—21no—
603D12—21no—
604D12—42no—
605D12—42no—
606D12C2×C3×D412yes—
607C4×D3—21no—
608C4×D3—21no—
609C4×D3—42no—
610C4×D3—42no—
611C4×D3—42no—
612C4×D3—42no—
613C4×D3—42no—
614Dic6—21no—
615Dic6—21no—
616Dic6—21no—
617Dic6—42no—
618Dic6C2×C3×D412yes—
619C3×C8—21no—
620C3×C8—21no—
621C3×C8—22no—
622C3×C8—41no—
623C3×C8—61no—
624C3×C8—61no—
625C3×C8D3×D412yes—
626C3×C8C2×C3×D412yes—
627C3⋊C8—21no—
628C3⋊C8—21no—
629C2×C32—41no—
630C2×C32D4211yescharacteristic
631C2×C32#57511yescharacteristic
632C2×C32#57811yescharacteristic
633C3×D3—41no—
634C3×D3—42no—
635C3×D3—81no—
636#41—62no—
637#41—62no—
638#41—62no—
639#41—121no—
640#41—121no—
641#41—121no—
642C2×Q8—31no—
643C2×Q8—31no—
644C2×Q8—61no—
645C2×Q8—62no—
646C2×Q8—121no—
647C2×Q8C22×C3×D311yescharacteristic
648C2×Q8C22×C3×D311yescharacteristic
649C2×D4—31no—
650C2×D4—31no—
651C2×D4—31no—
652C2×D4—61no—
653C2×D4—61no—
654C2×D4—61no—
655C2×D4—61no—
656C22×C4—31no—
657C22×C4—61no—
658C22×C4—61no—
659C22×C4—61no—
660C22×C4—61no—
661C22×C4—61no—
662C22×C4C22×C3×D311yescharacteristic
663Q16—22no—
664Q16—62no—
665Q16—62no—
666Q16—121no—
667SD16—34no—
668SD16—62no—
669SD16—62no—
670SD16—121no—
671D8—62no—
672M16—62no—
673C2×C8—22no—
674C2×C8—31no—
675C2×C8—31no—
676C2×C8C22×C3×D311yescharacteristic
677C2×C8C22×C3×D311yescharacteristic
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—31no—
681C4⋊C4—61no—
682C4⋊C4—61no—
683C4⋊C4—61no—
684C4⋊C4—61no—
685C4⋊C4C22×C3×D311yescharacteristic
686C4⋊C4C22×C3×D311yescharacteristic
687C22⋊C4—21no—
688C22⋊C4—21no—
689C22⋊C4—31no—
690C22⋊C4—31no—
691C22⋊C4—61no—
692C22⋊C4—61no—
693C22⋊C4—61no—
694C22⋊C4—61no—
695C22⋊C4—61no—
696C42—31no—
697C42—61no—
698C22×C3—22no—
699C22×C3—21no—
700C22×C3—21no—
701C22×C3—21no—
702C22×C3—21no—
703C22×C3—21no—
704C22×C3—21no—
705C22×C3—21no—
706C22×C3—41no—
707C22×C3—41no—
708C22×C3—61no—
709C22×C3—61no—
710C22×C3—61no—
711C22×C3—62no—
712C22×C3—121no—
713C22×C3—121no—
714C22×C3—121no—
715C22×C3—121no—
716C22×C3—121no—
717C22×C3C2×D3×D411yescharacteristic
718C22×C3C22×C3×D411yescharacteristic
719C2×D3—21no—
720C2×D3—21no—
721C2×D3—21no—
722C2×D3—22no—
723C2×D3—41no—
724C2×D3—41no—
725C2×D3—41no—
726C2×D3—41no—
727C2×D3—41no—
728C3×C4—21no—
729C3×C4—21no—
730C3×C4—21no—
731C3×C4—21no—
732C3×C4—41no—
733C3×C4—41no—
734C3×C4—41no—
735C3×C4—41no—
736C3×C4—41no—
737C3×C4—41no—
738C3×C4—41no—
739C3×C4—41no—
740C3×C4—41no—
741C3×C4—61no—
742C3×C4—61no—
743C3×C4—61no—
744C3×C4—62no—
745C3×C4—81no—
746C3×C4—81no—
747C3×C4—81no—
748C3×C4—81no—
749C3×C4—121no—
750C3×C4C2×D3×D411yescharacteristic
751C3×C4#100911yescharacteristic
752C3×C4C22×C3×D411yescharacteristic
753C3×C4C3×H(5,𝔽2)11yescharacteristic
754Dic3—21no—
755Dic3—21no—
756Dic3—22no—
757Dic3—21no—
758Dic3—41no—
759C32#326911yescharacteristic, complemented, Sylow
760C23—31no—
761C23—61no—
762C23—61no—
763C23C3×D3×D411yescharacteristic
764Q8—21no—
765Q8—21no—
766Q8—21no—
767Q8—21no—
768Q8—32no—
769Q8—61no—
770Q8—61no—
771Q8—61no—
772Q8—122no—
773D4—32no—
774D4—61no—
775D4—61no—
776D4—61no—
777D4—122no—
778D4—122no—
779D4—121no—
780D4—122no—
781D4—122no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—31no—
789C2×C4—31no—
790C2×C4—31no—
791C2×C4—61no—
792C2×C4—61no—
793C2×C4—61no—
794C2×C4—61no—
795C2×C4—122no—
796C2×C4—122no—
797C2×C4—122no—
798C2×C4—122no—
799C2×C4—122no—
800C2×C4C3×D3×D411yescharacteristic
801C2×C4C23×C3×D311yescharacteristic
802C8—21no—
803C8—61no—
804C8—61no—
805C8C3×D3×D412yes—
806C2×C3—21no—
807C2×C3—21no—
808C2×C3—21no—
809C2×C3—42no—
810C2×C3—41no—
811C2×C3—41no—
812C2×C3—121no—
813C2×C3—122no—
814C2×C3—241no—
815C2×C3#560911yescharacteristic
816C2×C3#576611yescharacteristic
817C2×C3#576811yescharacteristic
818C2×C3C3×D4211yescharacteristic
819C2×C3C3×#57511yescharacteristic
820C2×C3C3×#57811yescharacteristic
821D3—41no—
822D3—42no—
823D3—81no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—61no—
828C22—61no—
829C22—61no—
830C22—62no—
831C22—121no—
832C22—121no—
833C22—121no—
834C22—121no—
835C22—121no—
836C22C2×C3×D3×D411yescharacteristic
837C4—21no—
838C4—41no—
839C4—41no—
840C4—41no—
841C4—41no—
842C4—61no—
843C4—61no—
844C4—61no—
845C4—62no—
846C4—121no—
847C4C2×C3×D3×D411yescharacteristic
848C4C3×#100911yescharacteristic
849C3—21no—
850C3#8077211yescharacteristic, direct product factor
851C3C3×#326911yescharacteristic, complemented
852C2—41no—
853C2—121no—
854C2—122no—
855C2—241no—
856C2C3×#560911yescharacteristic
857C2C3×#576611yescharacteristic
858C2C3×#576811yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#467C2
socleC22×C32C22×D4
hypercenterC3×#467D3
hypocenterC3C3×#3269
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#467

Complements

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

NH ≅ G/Ntype
1. C2×C3×#918C2semidirect
2. C2×C3×#904C2semidirect
3. C3×#5633C2semidirect
4. C3×#5631C2semidirect
5. C32×#467C2semidirect
6. C3×#5190C2semidirect
7. C3×#5111C2semidirect
8. C3×#5047C2semidirect
9. C3×#5047C2semidirect
10. C3×#4889C2semidirect
11. C3×#4886C2semidirect
12. C3×#4819C2semidirect
13. C3×#4810C2semidirect
14. C3×#4809C2semidirect
15. C3×#4795C2semidirect
17. #80772C3direct (N × H)
67. C2×#918C2×C3semidirect
68. C2×#904C2×C3semidirect
69. #5633C2×C3semidirect
70. #5631C2×C3semidirect
74. C3×#467D3semidirect
75. C3×#467C2×C3semidirect
84. #5190C2×C3semidirect
85. #5111C2×C3semidirect
86. #5047C2×C3semidirect
87. #5047C2×C3semidirect
88. #4889C2×C3semidirect
89. #4886C2×C3semidirect
90. #4819C2×C3semidirect
91. #4810C2×C3semidirect
92. #4809C2×C3semidirect
93. #4795C2×C3semidirect
154. C3×#204D4semidirect
306. #467C3×D3semidirect
450. #204C3×D4semidirect
759. C32#3269semidirect
850. C3#80772direct (N × H)
851. C3C3×#3269semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9182
C2×C3×#9042
C3×#56332
C3×#56312
C32×#4672
C3×#51902
C3×#51112
C3×#50472
C3×#48892
C3×#48862
C3×#48192
C3×#48102
C3×#48092
C3×#47952
C3×#32693
#807723