Finite Group Databasebeta

← C3×#82528 #11870563

Subgroups — C3×#82528 #11870563

Order 1152.

947 conjugacy classes of subgroups.

The subgroup lattice has 783 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C4×#41C211yesmaximal, characteristic, complemented
2C3×#5479C211yesmaximal, characteristic, complemented
3C3×#5239C211yesmaximal, characteristic, complemented
4C3×#5238C211yesmaximal, characteristic
5C3×C4×#216C211yesmaximal, characteristic, complemented
6C3×#5028C211yesmaximal, characteristic, complemented
7C3×C4×#215C211yesmaximal, characteristic, complemented
8C3×#5022C211yesmaximal, characteristic, complemented
9C3×C4×#214C211yesmaximal, characteristic, complemented
10C3×#5016C211yesmaximal, characteristic, complemented
11C3×C4×#213C211yesmaximal, characteristic, complemented
12C3×#5009C211yesmaximal, characteristic, complemented
13C3×#5003C211yesmaximal, characteristic, complemented
14C3×#4996C211yesmaximal, characteristic, complemented
15C3×#4925C211yesmaximal, characteristic, complemented
16C3×#3102—31nomaximal
17#82528C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic
19C32×C4×Q8C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic
21C32×C4×D4—21no—
22C32×C4×D4—21no—
23C32×C4×D4C2211yescharacteristic
24C32×C4×D4C2211yescharacteristic
25C32×#117—21no—
26C32×#117C2211yescharacteristic
27C2×C32×C42—21no—
28C2×C32×C42C2211yescharacteristic
29C2×C3×#216C2211yescharacteristic
30C2×C3×#215C2211yescharacteristic
31C2×C3×#214C2211yescharacteristic
32C2×C3×#213C2211yescharacteristic
33C3×#930C2211yescharacteristic
34C3×#929—21no—
35C3×C4×#67—21no—
36C3×#924C2211yescharacteristic
37C3×#876—21no—
38C3×#875C2211yescharacteristic
39C3×C4×D12C2211yescharacteristic
40C3×#872—21no—
41C3×#870C2211yescharacteristic
42C3×C4×Dic6C2211yescharacteristic
43C3×#835C2211yescharacteristic
44C3×#835C2211yescharacteristic
45C3×#832C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#830C2211yescharacteristic
48C3×#830C2211yescharacteristic
49C3×#810C2211yescharacteristic
50C3×#810C2211yescharacteristic
51C3×#809C2211yescharacteristic
52C3×#809C2211yescharacteristic
53C3×#808C2211yescharacteristic
54C3×#808C2211yescharacteristic
55C3×#807C2211yescharacteristic
56C3×#807C2211yescharacteristic
57C3×C4⋊(C3⋊C8)C2211yescharacteristic
58C3×C4⋊(C3⋊C8)C2211yescharacteristic
59C3×C4×C3⋊C8C2211yescharacteristic
60C3×C4×C3⋊C8C2211yescharacteristic
61C3×#529—31no—
62C3×C4×#41—21no—
63C3×C4×#41D311yescharacteristic, complemented
64C3×C4×#41C2×C311yescharacteristic, complemented
65#5479C2×C311yescharacteristic, complemented
66C3×#485—31no—
67C3×#482—31no—
68C3×#479—31no—
69C3×#478—31no—
70C3×#464—31no—
71C3×#463—31no—
72C3×#452—31no—
73C3×#449—31no—
74C3×C4×Q16—31no—
75C3×C4×SD16—31no—
76C3×C4×SD16—31no—
77C3×C4×D8—31no—
78C3×#431—31no—
79#5239C2×C311yescharacteristic, complemented
80#5238C2×C311yescharacteristic
81C4×#216C2×C311yescharacteristic, complemented
82#5028C2×C311yescharacteristic, complemented
83C4×#215C2×C311yescharacteristic, complemented
84#5022C2×C311yescharacteristic, complemented
85C4×#214C2×C311yescharacteristic, complemented
86#5016C2×C311yescharacteristic, complemented
87C4×#213C2×C311yescharacteristic, complemented
88#5009C2×C311yescharacteristic, complemented
89#5003C2×C311yescharacteristic, complemented
90#4996C2×C311yescharacteristic, complemented
91#4925C2×C311yescharacteristic, complemented
92C32×#41—22no—
93C32×#41—22no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×D4—21no—
96C2×C32×D4C2311yescharacteristic
97C22×C32×C4—21no—
98C22×C32×C4—21no—
99C22×C32×C4—21no—
100C22×C32×C4D411yescharacteristic
101C22×C32×C4D411yescharacteristic
102C22×C32×C4C2311yescharacteristic
103C2×C3×#67—21no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×Dic6C2311yescharacteristic
107C32×C4⋊C4—21no—
108C32×C4⋊C4—21no—
109C32×C4⋊C4C2311yescharacteristic
110C32×C4⋊C4C2311yescharacteristic
111C32×C22⋊C4—21no—
112C32×C22⋊C4—21no—
113C32×C22⋊C4—21no—
114C32×C42—21no—
115C32×C42—21no—
116C32×C42—21no—
117C32×C42D411yescharacteristic
118C32×C42D411yescharacteristic
119C32×C42C2311yescharacteristic
120C32×C42C2311yescharacteristic
121C3×#217—21no—
122C3×#216—22no—
123C3×#215—22no—
124C3×#214—22no—
125C3×#213—22no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×C4×Dic3—21no—
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141#3102—31noSylow
142C2×C3×#41—21no—
143C2×C3×#41C2×D311yescharacteristic
144C2×C3×#41C22×C311yescharacteristic
145C2×C3×Q16—31no—
146C2×C3×SD16—31no—
147C2×C3×SD16—31no—
148C2×C3×D8—31no—
149C3×#126—61no—
150C3×#125—31no—
151C3×#124—31no—
152C3×#123—61no—
153C3×C22⋊Q8—31no—
154C3×#121—31no—
155C3×C4×Q8—21no—
156C3×C4×Q8—21no—
157C3×C4×Q8—31no—
158C3×C4×Q8C2×D311yescharacteristic
159C3×C4×Q8C2×D311yescharacteristic
160C3×C4×Q8C22×C311yescharacteristic
161C3×C4×Q8C22×C311yescharacteristic
162C3×C4×D4—22no—
163C3×C4×D4—22no—
164C3×C4×D4—21no—
165C3×C4×D4—21no—
166C3×C4×D4—21no—
167C3×C4×D4—21no—
168C3×C4×D4—21no—
169C3×C4×D4—21no—
170C3×C4×D4—31no—
171C3×C4×D4—61no—
172C3×C4×D4C2×D311yescharacteristic
173C3×C4×D4C2×D311yescharacteristic
174C3×C4×D4C22×C311yescharacteristic
175C3×C4×D4C22×C311yescharacteristic
176C3×#117—22no—
177C3×#117—21no—
178C3×#117—21no—
179C3×#117—21no—
180C3×#117—61no—
181C3×#117C2×D311yescharacteristic
182C3×#117C22×C311yescharacteristic
183C2×C3×C42—22no—
184C2×C3×C42—21no—
185C2×C3×C42—21no—
186C2×C3×C42—21no—
187C2×C3×C42C2×D311yescharacteristic
188C2×C3×C42C22×C311yescharacteristic
189C2×#216C22×C311yescharacteristic
190C2×#215C22×C311yescharacteristic
191C2×#214C22×C311yescharacteristic
192C2×#213C22×C311yescharacteristic
193#930C22×C311yescharacteristic
194#929—21no—
195C4×#67—21no—
196#924C22×C311yescharacteristic
197#876—21no—
198#875C22×C311yescharacteristic
199C4×D12C22×C311yescharacteristic
200#872—21no—
201#870C22×C311yescharacteristic
202C4×Dic6C22×C311yescharacteristic
203C3×#107—31no—
204C3×#107—31no—
205C3×#106—31no—
206C3×#106—31no—
207C3×C4⋊C8—31no—
208C3×C4⋊C8—31no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#103—31no—
212C3×#103—31no—
213C3×#102—31no—
214C3×#102—31no—
215C3×#102—31no—
216C3×#102—31no—
217C3×C22⋊C8—31no—
218C3×C22⋊C8—31no—
219C3×C4×C8—31no—
220C3×C4×C8—31no—
221#835C22×C311yescharacteristic
222#835C22×C311yescharacteristic
223#832C22×C311yescharacteristic
224#832C22×C311yescharacteristic
225#830C22×C311yescharacteristic
226#830C22×C311yescharacteristic
227#810C22×C311yescharacteristic
228#810C22×C311yescharacteristic
229#809C22×C311yescharacteristic
230#809C22×C311yescharacteristic
231#808C22×C311yescharacteristic
232#808C22×C311yescharacteristic
233#807C22×C311yescharacteristic
234#807C22×C311yescharacteristic
235C4⋊(C3⋊C8)C22×C311yescharacteristic
236C4⋊(C3⋊C8)C22×C311yescharacteristic
237C4×C3⋊C8C22×C311yescharacteristic
238C4×C3⋊C8C22×C311yescharacteristic
239C23×C32—21no—
240C23×C32C2×D411yescharacteristic
241C22×C3×D3—21no—
242C32×Q8—21no—
243C32×Q8#4112yes—
244C32×D4—24no—
245C32×D4—21no—
246C32×D4#4112yes—
247C2×C32×C4—24no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—22no—
254C2×C32×C4—41no—
255C2×C32×C4—42no—
256C2×C32×C4—42no—
257C2×C32×C4C2×D411yescharacteristic
258C2×C32×C4C2×D411yescharacteristic
259C2×C32×C4C2×D411yescharacteristic
260C2×C32×C4C2×D411yescharacteristic
261C2×C32×C4C2×D411yescharacteristic
262C2×C32×C4C2411yescharacteristic
263C3×#67—42no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C3×D12—21no—
268C3×D12—21no—
269C3×C4×D3—42no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272C3×C3⋊C8—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#529—31no—
277C4×#41C3×D311yescharacteristic, complemented
278#485—31no—
279#482—31no—
280#479—31no—
281#478—31no—
282#464—31no—
283#463—31no—
284#452—31no—
285#449—31no—
286C4×Q16—31no—
287C4×SD16—31no—
288C4×SD16—31no—
289C4×D8—31no—
290#431—31no—
291C3×#41—24no—
292C3×#41—24no—
293C3×#41—22no—
294C3×#41—22no—
295C3×#41—22no—
296C3×#41—22no—
297C2×C3×Q8—21no—
298C2×C3×Q8—31no—
299C2×C3×Q8C22×D311yescharacteristic
300C2×C3×Q8C23×C311yescharacteristic
301C2×C3×D4—22no—
302C2×C3×D4—21no—
303C2×C3×D4—21no—
304C2×C3×D4—21no—
305C2×C3×D4—31no—
306C2×C3×D4—61no—
307C2×C3×D4C22×D311yescharacteristic
308C2×C3×D4C23×C311yescharacteristic
309C22×C3×C4—22no—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—22no—
313C22×C3×C4—22no—
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4—61no—
322C22×C3×C4#6711yescharacteristic
323C22×C3×C4#6711yescharacteristic
324C22×C3×C4C3×D411yescharacteristic
325C22×C3×C4C3×D411yescharacteristic
326C22×C3×C4C22×D311yescharacteristic
327C22×C3×C4C23×C311yescharacteristic
328C2×#67—21no—
329C2×D12C23×C311yescharacteristic
330C2×C4×D3—21no—
331C2×Dic6C23×C311yescharacteristic
332C3×Q16—62no—
333C3×SD16—62no—
334C3×SD16—62no—
335C3×D8—62no—
336C2×C3×C8—31no—
337C2×C3×C8—31no—
338C2×C3×C8—31no—
339C2×C3×C8—31no—
340C3×C4⋊C4—22no—
341C3×C4⋊C4—22no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—21no—
344C3×C4⋊C4—21no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4C22×D311yescharacteristic
355C3×C4⋊C4C22×D311yescharacteristic
356C3×C4⋊C4C23×C311yescharacteristic
357C3×C4⋊C4C23×C311yescharacteristic
358C3×C22⋊C4—22no—
359C3×C22⋊C4—22no—
360C3×C22⋊C4—22no—
361C3×C22⋊C4—21no—
362C3×C22⋊C4—21no—
363C3×C22⋊C4—21no—
364C3×C22⋊C4—21no—
365C3×C22⋊C4—21no—
366C3×C22⋊C4—21no—
367C3×C22⋊C4—61no—
368C3×C22⋊C4—61no—
369C3×C22⋊C4—61no—
370C3×C22⋊C4—61no—
371C3×C22⋊C4—61no—
372C3×C42—22no—
373C3×C42—22no—
374C3×C42—22no—
375C3×C42—21no—
376C3×C42—21no—
377C3×C42—21no—
378C3×C42—21no—
379C3×C42—21no—
380C3×C42—21no—
381C3×C42—21no—
382C3×C42—21no—
383C3×C42—21no—
384C3×C42—21no—
385C3×C42—61no—
386C3×C42#6711yescharacteristic
387C3×C42#6711yescharacteristic
388C3×C42C3×D411yescharacteristic
389C3×C42C3×D411yescharacteristic
390C3×C42C22×D311yescharacteristic
391C3×C42C22×D311yescharacteristic
392C3×C42C23×C311yescharacteristic
393C3×C42C23×C311yescharacteristic
394#217—21no—
395#216—22no—
396#215—22no—
397#214—22no—
398#213—22no—
399(C2×D3)⋊C4—21no—
400(C2×D3)⋊C4—21no—
401(C2×D3)⋊C4—21no—
402(C2×D3)⋊C4—21no—
403C4⋊Dic3C23×C311yescharacteristic
404C4⋊Dic3C23×C311yescharacteristic
405Dic3⋊C4—21no—
406Dic3⋊C4—21no—
407Dic3⋊C4—21no—
408Dic3⋊C4—21no—
409C4×Dic3—21no—
410C2×C3⋊C8C23×C311yescharacteristic
411C2×C3⋊C8C23×C311yescharacteristic
412C2×C3⋊C8C23×C311yescharacteristic
413C2×C3⋊C8C23×C311yescharacteristic
414C22×C32—21no—
415C22×C32—22no—
416C22×C32—21no—
417C22×C32—21no—
418C22×C32—41no—
419C22×C32—41no—
420C22×C32C22×D411yescharacteristic
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C32×C4—21no—
425C32×C4—22no—
426C32×C4—21no—
427C32×C4—21no—
428C32×C4—21no—
429C32×C4—41no—
430C32×C4—41no—
431C32×C4#13512yes—
432C32×C4C2×#4111yescharacteristic
433C32×C4C2×#4111yescharacteristic
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C2×#41C2×C3×D311yescharacteristic
438C2×Q16—31no—
439C2×SD16—31no—
440C2×SD16—31no—
441C2×D8—31no—
442#126—61no—
443#125—31no—
444#124—31no—
445#123—61no—
446C22⋊Q8—31no—
447#121—31no—
448C4×Q8—31no—
449C4×Q8C2×C3×D311yescharacteristic
450C4×Q8C2×C3×D311yescharacteristic
451C4×D4—21no—
452C4×D4—21no—
453C4×D4—31no—
454C4×D4—61no—
455C4×D4C2×C3×D311yescharacteristic
456C4×D4C2×C3×D311yescharacteristic
457#117—21no—
458#117—61no—
459#117C2×C3×D311yescharacteristic
460C2×C42—21no—
461C2×C42C2×C3×D311yescharacteristic
462#107—31no—
463#107—31no—
464#106—31no—
465#106—31no—
466C4⋊C8—31no—
467C4⋊C8—31no—
468#103—31no—
469#103—31no—
470#103—31no—
471#103—31no—
472#102—31no—
473#102—31no—
474#102—31no—
475#102—31no—
476C22⋊C8—31no—
477C22⋊C8—31no—
478C4×C8—31no—
479C4×C8—31no—
480C23×C3—22no—
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—61no—
485C23×C3C2×#6711yescharacteristic
486C23×C3C2×C3×D411yescharacteristic
487C22×D3—21no—
488C3×Q8—22no—
489C3×Q8—21no—
490C3×Q8—21no—
491C3×Q8—22no—
492C3×Q8—61no—
493C3×Q8—61no—
494C3×Q8#23512yes—
495C3×Q8C3×#4112yes—
496C3×D4—28no—
497C3×D4—24no—
498C3×D4—24no—
499C3×D4—22no—
500C3×D4—21no—
501C3×D4—21no—
502C3×D4—22no—
503C3×D4—61no—
504C3×D4—61no—
505C3×D4—122no—
506C3×D4#23512yes—
507C3×D4C3×#4112yes—
508C2×C3×C4—22no—
509C2×C3×C4—28no—
510C2×C3×C4—24no—
511C2×C3×C4—24no—
512C2×C3×C4—22no—
513C2×C3×C4—22no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—22no—
517C2×C3×C4—22no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—22no—
523C2×C3×C4—22no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—42no—
535C2×C3×C4—41no—
536C2×C3×C4—41no—
537C2×C3×C4—42no—
538C2×C3×C4—44no—
539C2×C3×C4—42no—
540C2×C3×C4—42no—
541C2×C3×C4—44no—
542C2×C3×C4—42no—
543C2×C3×C4—42no—
544C2×C3×C4—61no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—122no—
548C2×C3×C4C2×#6711yescharacteristic
549C2×C3×C4C2×#6711yescharacteristic
550C2×C3×C4C2×#6711yescharacteristic
551C2×C3×C4C2×#6711yescharacteristic
552C2×C3×C4C2×#6711yescharacteristic
553C2×C3×C4C2×C3×D411yescharacteristic
554C2×C3×C4C2×C3×D411yescharacteristic
555C2×C3×C4C2×C3×D411yescharacteristic
556C2×C3×C4C2×C3×D411yescharacteristic
557C2×C3×C4C2×C3×D411yescharacteristic
558C2×C3×C4C23×D311yescharacteristic
559C2×C3×C4C24×C311yescharacteristic
560#67—42no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—21no—
564D12—21no—
565D12—21no—
566C4×D3—42no—
567Dic6—21no—
568Dic6—21no—
569C3×C8—61no—
570C3×C8—61no—
571C3×C8—61no—
572C3×C8—61no—
573C3⋊C8—21no—
574C3⋊C8—21no—
575C3⋊C8—21no—
576C3⋊C8—21no—
577C2×C32—41no—
578C2×C32—42no—
579C2×C32#52511yescharacteristic
580C2×C32C2×#13511yescharacteristic
581C2×C32#57511yescharacteristic
582C3×D3—81no—
583#41—22no—
584#41—22no—
585C2×Q8—31no—
586C2×Q8C22×C3×D311yescharacteristic
587C2×D4—21no—
588C2×D4—31no—
589C2×D4—61no—
590C2×D4C22×C3×D311yescharacteristic
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—61no—
595C22×C4C3×#6711yescharacteristic
596C22×C4C3×#6711yescharacteristic
597C22×C4C22×C3×D311yescharacteristic
598Q16—62no—
599SD16—62no—
600SD16—62no—
601D8—62no—
602C2×C8—31no—
603C2×C8—31no—
604C2×C8—31no—
605C2×C8—31no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—31no—
609C4⋊C4—31no—
610C4⋊C4—61no—
611C4⋊C4—61no—
612C4⋊C4—61no—
613C4⋊C4—61no—
614C4⋊C4C22×C3×D311yescharacteristic
615C4⋊C4C22×C3×D311yescharacteristic
616C22⋊C4—21no—
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—61no—
620C22⋊C4—61no—
621C22⋊C4—61no—
622C22⋊C4—61no—
623C22⋊C4—61no—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—61no—
628C42C3×#6711yescharacteristic
629C42C3×#6711yescharacteristic
630C42C22×C3×D311yescharacteristic
631C42C22×C3×D311yescharacteristic
632C22×C3—22no—
633C22×C3—24no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—22no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—22no—
642C22×C3—21no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—42no—
646C22×C3—42no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—121no—
652C22×C3—121no—
653C22×C3—121no—
654C22×C3C22×#6711yescharacteristic
655C22×C3C22×C3×D411yescharacteristic
656C2×D3—41no—
657C2×D3—41no—
658C2×D3—41no—
659C3×C4—22no—
660C3×C4—24no—
661C3×C4—22no—
662C3×C4—21no—
663C3×C4—21no—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—22no—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—22no—
672C3×C4—22no—
673C3×C4—21no—
674C3×C4—21no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—42no—
678C3×C4—42no—
679C3×C4—41no—
680C3×C4—41no—
681C3×C4—41no—
682C3×C4—41no—
683C3×C4—121no—
684C3×C4—121no—
685C3×C4—121no—
686C3×C4#95012yes—
687C3×C4C3×#13512yes—
688C3×C4C2×#23511yescharacteristic
689C3×C4C2×#23511yescharacteristic
690C3×C4C2×C3×#4111yescharacteristic
691C3×C4C2×C3×#4111yescharacteristic
692Dic3—41no—
693Dic3—41no—
694Dic3—41no—
695C32#310211yescharacteristic, complemented, Sylow
696C23—21no—
697C23—61no—
698C23C2×C3×#6711yescharacteristic
699Q8—21no—
700Q8—61no—
701Q8—61no—
702Q8C3×#23512yes—
703D4—24no—
704D4—21no—
705D4—61no—
706D4—61no—
707D4—122no—
708D4C3×#23512yes—
709C2×C4—24no—
710C2×C4—21no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—41no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—122no—
723C2×C4C2×C3×#6711yescharacteristic
724C2×C4C2×C3×#6711yescharacteristic
725C2×C4C2×C3×#6711yescharacteristic
726C2×C4C2×C3×#6711yescharacteristic
727C2×C4C2×C3×#6711yescharacteristic
728C2×C4C23×C3×D311yescharacteristic
729C8—61no—
730C8—61no—
731C8—61no—
732C8—61no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—42no—
737C2×C3—44no—
738C2×C3—41no—
739C2×C3—42no—
740C2×C3—41no—
741C2×C3—42no—
742C2×C3—241no—
743C2×C3#579111yescharacteristic
744C2×C3C2×#95011yescharacteristic
745C2×C3#582211yescharacteristic
746C2×C3C3×#52511yescharacteristic
747C2×C3C2×C3×#13511yescharacteristic
748C2×C3C3×#57511yescharacteristic
749D3—81no—
750C22—21no—
751C22—22no—
752C22—21no—
753C22—21no—
754C22—41no—
755C22—41no—
756C22—121no—
757C22—121no—
758C22—121no—
759C22C22×C3×#6711yescharacteristic
760C4—21no—
761C4—22no—
762C4—21no—
763C4—21no—
764C4—21no—
765C4—41no—
766C4—41no—
767C4—121no—
768C4—121no—
769C4—121no—
770C4C3×#95012yes—
771C4C2×C3×#23511yescharacteristic
772C4C2×C3×#23511yescharacteristic
773C3—21no—
774C3#8252811yescharacteristic, direct product factor
775C3C3×#310211yescharacteristic, complemented
776C2—41no—
777C2—42no—
778C2—241no—
779C2C3×#579111yescharacteristic
780C2C2×C3×#95011yescharacteristic
781C2C3×#582211yescharacteristic
subgroupG/H
centerC2×C3×C4C2×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×C4×#41C2
socleC22×C32C22×D4
prime radicalC3×#5238C2
hypercenterC3×C4×#41D3
hypocenterC3C3×#3102
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C42 ◁ C3×C4×#41

Complements

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

NH ≅ G/Ntype
1. C32×C4×#41C2semidirect
2. C3×#5479C2semidirect
3. C3×#5239C2semidirect
5. C3×C4×#216C2semidirect
6. C3×#5028C2semidirect
7. C3×C4×#215C2semidirect
8. C3×#5022C2semidirect
9. C3×C4×#214C2semidirect
10. C3×#5016C2semidirect
11. C3×C4×#213C2semidirect
12. C3×#5009C2semidirect
13. C3×#5003C2semidirect
14. C3×#4996C2semidirect
15. C3×#4925C2semidirect
17. #82528C3direct (N × H)
63. C3×C4×#41D3semidirect
64. C3×C4×#41C2×C3semidirect
65. #5479C2×C3semidirect
79. #5239C2×C3semidirect
81. C4×#216C2×C3semidirect
82. #5028C2×C3semidirect
83. C4×#215C2×C3semidirect
84. #5022C2×C3semidirect
85. C4×#214C2×C3semidirect
86. #5016C2×C3semidirect
87. C4×#213C2×C3semidirect
88. #5009C2×C3semidirect
89. #5003C2×C3semidirect
90. #4996C2×C3semidirect
91. #4925C2×C3semidirect
277. C4×#41C3×D3semidirect
695. C32#3102semidirect
774. C3#82528direct (N × H)
775. C3C3×#3102semidirect

Maximal subgroups

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

subgroupindex
C32×C4×#412
C3×#54792
C3×#52392
C3×#52382
C3×C4×#2162
C3×#50282
C3×C4×#2152
C3×#50222
C3×C4×#2142
C3×#50162
C3×C4×#2132
C3×#50092
C3×#50032
C3×#49962
C3×#49252
C3×#31023
#825283