Finite Group Databasebeta

← C3×#79385 #11872416

Subgroups — C3×#79385 #11872416

Order 1152.

792 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5523C211yesmaximal, characteristic
2C3×#5518C211yesmaximal, characteristic, complemented
3C32×#433C211yesmaximal, characteristic, complemented
4C3×#4849C211yesmaximal, characteristic, complemented
5C3×#4847C211yesmaximal, characteristic, complemented
6C3×#4841C211yesmaximal, characteristic, complemented
7C3×#4829C211yesmaximal, characteristic, complemented
8C3×#4733C211yesmaximal, characteristic
9C3×#4733C211yesmaximal, characteristic
10C3×#4722C211yesmaximal, characteristic, complemented
11C3×#4721C211yesmaximal, characteristic, complemented
12C3×#4716C211yesmaximal, characteristic, complemented
13C3×#4710C211yesmaximal, characteristic, complemented
14C3×C4×Dic12C211yesmaximal, characteristic, complemented
15C3×C4×#204C211yesmaximal, characteristic, complemented
16C3×#3120—31nomaximal
17#79385C311yesmaximal, characteristic, direct product factor
18C2×C3×#235C2211yescharacteristic
19C32×#117C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C3×#924C2211yescharacteristic
22C3×#924C2211yescharacteristic
23C2×C3×Dic12C2211yescharacteristic
24C2×C3×Dic12C2211yescharacteristic
25C2×C3×#204C2211yescharacteristic
26C2×C3×#204C2211yescharacteristic
27C3×#892—21no—
28C3×D3×C4⋊C4—21no—
29C3×#889—21no—
30C3×#889—21no—
31C3×#67⋊C4—21no—
32C3×#67⋊C4—21no—
33C3×#879—21no—
34C3×#879—21no—
35C3×C4×D12C2211yescharacteristic
36C3×C4×D12C2211yescharacteristic
37C3×#870C2211yescharacteristic
38C3×#869C2211yescharacteristic
39C3×C4×Dic6C2211yescharacteristic
40C3×C4×Dic6C2211yescharacteristic
41C3×C4×Dic6C2211yescharacteristic
42C3×C4×Dic6C2211yescharacteristic
43C32×C4⋊C8C2211yescharacteristic
44C32×C4⋊C8C2211yescharacteristic
45C32×C22⋊C8C2211yescharacteristic
46C32×C22⋊C8C2211yescharacteristic
47C32×#97C2211yescharacteristic
48C32×C4×C8C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#818C2211yescharacteristic
52C3×#818C2211yescharacteristic
53C3×#817C2211yescharacteristic
54C3×#817C2211yescharacteristic
55C3×#816C2211yescharacteristic
56C3×#816C2211yescharacteristic
57C3×#816C2211yescharacteristic
58C3×#816C2211yescharacteristic
59C3×#816C2211yescharacteristic
60C3×#816C2211yescharacteristic
61C3×#541—31no—
62C3×#520—31no—
63#5523C2×C311yescharacteristic
64#5518C2×C311yescharacteristic, complemented
65C3×#484—31no—
66C3×#483—31no—
67C3×#479—31no—
68C3×#478—31no—
69C3×#462—31no—
70C3×#461—31no—
71C3×#452—31no—
72C3×#452—31no—
73C3×#441—31no—
74C3×#440—31no—
75C3×C4×Q16—31no—
76C3×C4×SD16—31no—
77C3×#433—21no—
78C3×#433D311yescharacteristic, complemented
79C3×#433C2×C311yescharacteristic, complemented
80#4849C2×C311yescharacteristic, complemented
81#4847C2×C311yescharacteristic, complemented
82#4841C2×C311yescharacteristic, complemented
83#4829C2×C311yescharacteristic, complemented
84#4733C2×C311yescharacteristic
85#4733C2×C311yescharacteristic
86#4722C2×C311yescharacteristic, complemented
87#4721C2×C311yescharacteristic, complemented
88#4716C2×C311yescharacteristic, complemented
89#4710C2×C311yescharacteristic, complemented
90C4×Dic12C2×C311yescharacteristic, complemented
91C4×#204C2×C311yescharacteristic, complemented
92C22×C32×C4C2311yescharacteristic
93C2×C3×#67—21no—
94C22×C3×Dic3—21no—
95C3×#235—22no—
96C3×#235—22no—
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3—21no—
101C2×C3×Dic6C2311yescharacteristic
102C2×C3×Dic6C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×C32×C8C2311yescharacteristic
105C2×C32×C8C2311yescharacteristic
106C2×C32×C8C2311yescharacteristic
107C2×C32×C8C2311yescharacteristic
108C32×C4⋊C4D411yescharacteristic
109C32×C4⋊C4D411yescharacteristic
110C32×C22⋊C4D411yescharacteristic
111C32×C22⋊C4D411yescharacteristic
112C32×C42C2311yescharacteristic
113C32×C42C2311yescharacteristic
114C3×#217—21no—
115C3×#217—21no—
116C3×(C2×D3)⋊C4—21no—
117C3×(C2×D3)⋊C4—21no—
118C3×C4⋊Dic3—21no—
119C3×C4⋊Dic3—21no—
120C3×C4⋊Dic3—21no—
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×C4×Dic3—21no—
134C3×C4×Dic3—21no—
135C3×C4×Dic3—21no—
136C3×C4×Dic3—21no—
137C3×Dic12—22no—
138C3×Dic12—22no—
139C3×#204—22no—
140C3×#204—22no—
141#3120—31noSylow
142C2×C3×#41—31no—
143C2×#235C22×C311yescharacteristic
144C2×C3×Q16—31no—
145C2×C3×Q16—31no—
146C2×C3×SD16—31no—
147C2×C3×SD16—31no—
148C3×C4⋊Q8—31no—
149C3×#126—61no—
150C3×#126—61no—
151C3×#125—31no—
152C3×#125—61no—
153C3×#125—61no—
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8—31no—
156C3×C4×Q8—31no—
157C3×C4×Q8—31no—
158C3×C4×Q8—31no—
159C3×C4×Q8—31no—
160C3×C4×D4—31no—
161C3×C4×D4—31no—
162C3×C4×D4—61no—
163C3×C4×D4—61no—
164C3×#117—21no—
165C3×#117—61no—
166C3×#117C2×D311yescharacteristic
167C3×#117C22×C311yescharacteristic
168C2×C3×C4⋊C4—31no—
169C2×C3×C4⋊C4—61no—
170C2×C4⋊Dic3C22×C311yescharacteristic
171#924C22×C311yescharacteristic
172#924C22×C311yescharacteristic
173C2×Dic12C22×C311yescharacteristic
174C2×Dic12C22×C311yescharacteristic
175C2×#204C22×C311yescharacteristic
176C2×#204C22×C311yescharacteristic
177#892—21no—
178D3×C4⋊C4—21no—
179#889—21no—
180#889—21no—
181#67⋊C4—21no—
182#67⋊C4—21no—
183#879—21no—
184#879—21no—
185C4×D12C22×C311yescharacteristic
186C4×D12C22×C311yescharacteristic
187#870C22×C311yescharacteristic
188#869C22×C311yescharacteristic
189C4×Dic6C22×C311yescharacteristic
190C4×Dic6C22×C311yescharacteristic
191C4×Dic6C22×C311yescharacteristic
192C4×Dic6C22×C311yescharacteristic
193C3×#107—31no—
194C3×#107—31no—
195C3×#106—31no—
196C3×#106—31no—
197C3×C4⋊C8—21no—
198C3×C4⋊C8—21no—
199C3×C4⋊C8C2×D311yescharacteristic
200C3×C4⋊C8C2×D311yescharacteristic
201C3×C4⋊C8C22×C311yescharacteristic
202C3×C4⋊C8C22×C311yescharacteristic
203C3×#103—31no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#103—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#102—31no—
210C3×#102—31no—
211C3×C22⋊C8—21no—
212C3×C22⋊C8—21no—
213C3×C22⋊C8C2×D311yescharacteristic
214C3×C22⋊C8C2×D311yescharacteristic
215C3×C22⋊C8C22×C311yescharacteristic
216C3×C22⋊C8C22×C311yescharacteristic
217C3×#97—21no—
218C3×#97C2×D311yescharacteristic
219C3×#97C22×C311yescharacteristic
220C3×C4×C8—21no—
221C3×C4×C8C2×D311yescharacteristic
222C3×C4×C8C22×C311yescharacteristic
223#821C22×C311yescharacteristic
224#821C22×C311yescharacteristic
225#818C22×C311yescharacteristic
226#818C22×C311yescharacteristic
227#817C22×C311yescharacteristic
228#817C22×C311yescharacteristic
229#816C22×C311yescharacteristic
230#816C22×C311yescharacteristic
231#816C22×C311yescharacteristic
232#816C22×C311yescharacteristic
233#816C22×C311yescharacteristic
234#816C22×C311yescharacteristic
235C23×C32C2×D411yescharacteristic
236C22×C3×D3—21no—
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4C2×D411yescharacteristic
240C2×C32×C4C2×D411yescharacteristic
241C2×C32×C4C2×D411yescharacteristic
242C2×C32×C4C2×D411yescharacteristic
243C2×C32×C4C2×D411yescharacteristic
244C2×C32×C4C2411yescharacteristic
245C3×#67—24no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—81no—
254C3×D12—21no—
255C3×D12#4112yes—
256C3×C4×D3—24no—
257C3×C4×D3—81no—
258C3×C4×D3—81no—
259C3×Dic6—21no—
260C3×Dic6—21no—
261C3×Dic6—21no—
262C3×Dic6—21no—
263C3×Dic6—21no—
264C3×Dic6#4112yes—
265C32×C8—21no—
266C32×C8—21no—
267C32×C8—21no—
268C32×C8—21no—
269#541—31no—
270#520—31no—
271#484—31no—
272#483—31no—
273#479—31no—
274#478—31no—
275#462—31no—
276#461—31no—
277#452—31no—
278#452—31no—
279#441—31no—
280#440—31no—
281C4×Q16—31no—
282C4×SD16—31no—
283#433C3×D311yescharacteristic, complemented
284C3×#41—62no—
285C3×#41—62no—
286C2×C3×Q8—31no—
287C2×C3×Q8—31no—
288C2×C3×Q8—31no—
289C2×C3×D4—31no—
290C2×C3×D4—61no—
291C22×C3×C4—21no—
292C22×C3×C4—61no—
293C22×C3×C4—61no—
294C22×C3×C4—61no—
295C22×C3×C4—61no—
296C22×C3×C4C22×D311yescharacteristic
297C22×C3×C4C23×C311yescharacteristic
298C2×#67—21no—
299C22×Dic3—21no—
300#235—22no—
301#235—22no—
302C2×D12C23×C311yescharacteristic
303C2×C4×D3—21no—
304C2×C4×D3—21no—
305C2×C4×D3—21no—
306C2×Dic6C23×C311yescharacteristic
307C2×Dic6C23×C311yescharacteristic
308C2×Dic6C23×C311yescharacteristic
309C3×Q16—62no—
310C3×Q16—62no—
311C3×SD16—62no—
312C3×SD16—62no—
313C2×C3×C8—21no—
314C2×C3×C8—21no—
315C2×C3×C8—21no—
316C2×C3×C8—21no—
317C2×C3×C8C22×D311yescharacteristic
318C2×C3×C8C22×D311yescharacteristic
319C2×C3×C8C22×D311yescharacteristic
320C2×C3×C8C22×D311yescharacteristic
321C2×C3×C8C23×C311yescharacteristic
322C2×C3×C8C23×C311yescharacteristic
323C2×C3×C8C23×C311yescharacteristic
324C2×C3×C8C23×C311yescharacteristic
325C3×C4⋊C4—21no—
326C3×C4⋊C4—21no—
327C3×C4⋊C4—31no—
328C3×C4⋊C4—31no—
329C3×C4⋊C4—31no—
330C3×C4⋊C4—31no—
331C3×C4⋊C4—61no—
332C3×C4⋊C4—61no—
333C3×C4⋊C4—61no—
334C3×C4⋊C4—61no—
335C3×C4⋊C4—61no—
336C3×C4⋊C4—61no—
337C3×C4⋊C4—61no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4D1211yescharacteristic
343C3×C4⋊C4D1211yescharacteristic
344C3×C4⋊C4C3×D411yescharacteristic
345C3×C4⋊C4C3×D411yescharacteristic
346C3×C22⋊C4—21no—
347C3×C22⋊C4—21no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C22⋊C4D1211yescharacteristic
353C3×C22⋊C4D1211yescharacteristic
354C3×C22⋊C4C3×D411yescharacteristic
355C3×C22⋊C4C3×D411yescharacteristic
356C3×C42—21no—
357C3×C42—21no—
358C3×C42—61no—
359C3×C42—61no—
360C3×C42—61no—
361C3×C42—61no—
362C3×C42C22×D311yescharacteristic
363C3×C42C22×D311yescharacteristic
364C3×C42C23×C311yescharacteristic
365C3×C42C23×C311yescharacteristic
366#217—21no—
367#217—21no—
368(C2×D3)⋊C4—21no—
369(C2×D3)⋊C4—21no—
370C4⋊Dic3—21no—
371C4⋊Dic3—21no—
372C4⋊Dic3—21no—
373C4⋊Dic3C23×C311yescharacteristic
374C4⋊Dic3C23×C311yescharacteristic
375C4⋊Dic3C23×C311yescharacteristic
376C4⋊Dic3C23×C311yescharacteristic
377Dic3⋊C4—21no—
378Dic3⋊C4—21no—
379Dic3⋊C4—21no—
380Dic3⋊C4—21no—
381Dic3⋊C4—21no—
382Dic3⋊C4—21no—
383Dic3⋊C4—21no—
384Dic3⋊C4—21no—
385C4×Dic3—21no—
386C4×Dic3—21no—
387C4×Dic3—21no—
388C4×Dic3—21no—
389Dic12—22no—
390Dic12—22no—
391#204—22no—
392#204—22no—
393C22×C32—21no—
394C22×C32—21no—
395C22×C32—21no—
396C22×C32C22×D411yescharacteristic
397C2×C3×D3—22no—
398C2×C3×D3—41no—
399C2×C3×D3—41no—
400C32×C4—21no—
401C32×C4—21no—
402C32×C4—21no—
403C32×C4—21no—
404C32×C4—21no—
405C32×C4C2×#4111yescharacteristic
406C32×C4C2×#4111yescharacteristic
407C3×Dic3—22no—
408C3×Dic3—41no—
409C3×Dic3—41no—
410C3×Dic3—41no—
411C3×Dic3—41no—
412C3×Dic3—41no—
413C3×Dic3—41no—
414C2×#41—31no—
415C2×Q16—31no—
416C2×Q16—31no—
417C2×SD16—31no—
418C2×SD16—31no—
419C4⋊Q8—31no—
420#126—61no—
421#126—61no—
422#125—31no—
423#125—61no—
424#125—61no—
425C22⋊Q8—31no—
426C22⋊Q8—31no—
427C4×Q8—31no—
428C4×Q8—31no—
429C4×Q8—31no—
430C4×Q8—31no—
431C4×D4—31no—
432C4×D4—31no—
433C4×D4—61no—
434C4×D4—61no—
435#117—61no—
436#117C2×C3×D311yescharacteristic
437C2×C4⋊C4—31no—
438C2×C4⋊C4—61no—
439#107—31no—
440#107—31no—
441#106—31no—
442#106—31no—
443C4⋊C8C2×C3×D311yescharacteristic
444C4⋊C8C2×C3×D311yescharacteristic
445#103—31no—
446#103—31no—
447#103—31no—
448#103—31no—
449#103—31no—
450#103—31no—
451#102—31no—
452#102—31no—
453C22⋊C8C2×C3×D311yescharacteristic
454C22⋊C8C2×C3×D311yescharacteristic
455#97C2×C3×D311yescharacteristic
456C4×C8C2×C3×D311yescharacteristic
457C23×C3—21no—
458C23×C3—61no—
459C23×C3C2×D1211yescharacteristic
460C23×C3C2×C3×D411yescharacteristic
461C22×D3—21no—
462C3×Q8—32no—
463C3×Q8—61no—
464C3×Q8—61no—
465C3×Q8—61no—
466C3×Q8—61no—
467C3×Q8—61no—
468C3×D4—32no—
469C3×D4—64no—
470C3×D4—61no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—41no—
482C2×C3×C4—41no—
483C2×C3×C4—64no—
484C2×C3×C4—61no—
485C2×C3×C4—61no—
486C2×C3×C4—61no—
487C2×C3×C4—61no—
488C2×C3×C4—61no—
489C2×C3×C4—61no—
490C2×C3×C4—61no—
491C2×C3×C4—241no—
492C2×C3×C4—241no—
493C2×C3×C4—241no—
494C2×C3×C4C2×D1211yescharacteristic
495C2×C3×C4C2×D1211yescharacteristic
496C2×C3×C4C2×D1211yescharacteristic
497C2×C3×C4C2×D1211yescharacteristic
498C2×C3×C4C2×D1211yescharacteristic
499C2×C3×C4C2×C3×D411yescharacteristic
500C2×C3×C4C2×C3×D411yescharacteristic
501C2×C3×C4C2×C3×D411yescharacteristic
502C2×C3×C4C2×C3×D411yescharacteristic
503C2×C3×C4C2×C3×D411yescharacteristic
504C2×C3×C4C23×D311yescharacteristic
505C2×C3×C4C24×C311yescharacteristic
506#67—24no—
507C2×Dic3—21no—
508C2×Dic3—21no—
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—81no—
515D12—21no—
516D12C3×#4112yes—
517C4×D3—24no—
518C4×D3—81no—
519C4×D3—81no—
520Dic6—21no—
521Dic6—21no—
522Dic6—21no—
523Dic6—21no—
524Dic6—21no—
525Dic6C3×#4112yes—
526C3×C8—21no—
527C3×C8—21no—
528C3×C8—21no—
529C3×C8—21no—
530C3×C8—21no—
531C3×C8—21no—
532C3×C8—21no—
533C3×C8—21no—
534C3×C8—41no—
535C3×C8—41no—
536C3×C8—41no—
537C3×C8—41no—
538C2×C32—41no—
539C2×C32#52511yescharacteristic
540C2×C32#57711yescharacteristic
541C2×C32#57811yescharacteristic
542C3×D3—42no—
543#41—62no—
544#41—62no—
545C2×Q8—31no—
546C2×Q8—31no—
547C2×Q8—31no—
548C2×D4—31no—
549C2×D4—61no—
550C22×C4—61no—
551C22×C4—61no—
552C22×C4—61no—
553C22×C4—61no—
554C22×C4C22×C3×D311yescharacteristic
555Q16—62no—
556Q16—62no—
557SD16—62no—
558SD16—62no—
559C2×C8C22×C3×D311yescharacteristic
560C2×C8C22×C3×D311yescharacteristic
561C2×C8C22×C3×D311yescharacteristic
562C2×C8C22×C3×D311yescharacteristic
563C4⋊C4—31no—
564C4⋊C4—31no—
565C4⋊C4—31no—
566C4⋊C4—31no—
567C4⋊C4—61no—
568C4⋊C4—61no—
569C4⋊C4—61no—
570C4⋊C4—61no—
571C4⋊C4—61no—
572C4⋊C4—61no—
573C4⋊C4—61no—
574C4⋊C4—61no—
575C4⋊C4—61no—
576C4⋊C4—61no—
577C4⋊C4—61no—
578C4⋊C4C3×D1211yescharacteristic
579C4⋊C4C3×D1211yescharacteristic
580C22⋊C4—61no—
581C22⋊C4—61no—
582C22⋊C4—61no—
583C22⋊C4—61no—
584C22⋊C4C3×D1211yescharacteristic
585C22⋊C4C3×D1211yescharacteristic
586C42—61no—
587C42—61no—
588C42—61no—
589C42—61no—
590C42C22×C3×D311yescharacteristic
591C42C22×C3×D311yescharacteristic
592C22×C3—21no—
593C22×C3—21no—
594C22×C3—21no—
595C22×C3—21no—
596C22×C3—21no—
597C22×C3—21no—
598C22×C3—21no—
599C22×C3—41no—
600C22×C3—41no—
601C22×C3—41no—
602C22×C3—62no—
603C22×C3—121no—
604C22×C3—121no—
605C22×C3C22×D1211yescharacteristic
606C22×C3C22×C3×D411yescharacteristic
607C2×D3—22no—
608C2×D3—41no—
609C2×D3—41no—
610C3×C4—21no—
611C3×C4—21no—
612C3×C4—21no—
613C3×C4—21no—
614C3×C4—21no—
615C3×C4—21no—
616C3×C4—21no—
617C3×C4—21no—
618C3×C4—21no—
619C3×C4—21no—
620C3×C4—21no—
621C3×C4—21no—
622C3×C4—41no—
623C3×C4—41no—
624C3×C4—41no—
625C3×C4—41no—
626C3×C4—41no—
627C3×C4—62no—
628C3×C4—121no—
629C3×C4—121no—
630C3×C4—121no—
631C3×C4—121no—
632C3×C4—121no—
633C3×C4—121no—
634C3×C4D3×#4111yescharacteristic
635C3×C4D3×#4111yescharacteristic
636C3×C4C2×C3×#4111yescharacteristic
637C3×C4C2×C3×#4111yescharacteristic
638Dic3—22no—
639Dic3—41no—
640Dic3—41no—
641Dic3—41no—
642Dic3—41no—
643Dic3—41no—
644Dic3—41no—
645C32#312011yescharacteristic, complemented, Sylow
646C23—61no—
647C23C2×C3×D1211yescharacteristic
648Q8—32no—
649Q8—61no—
650Q8—61no—
651Q8—61no—
652Q8—61no—
653Q8—61no—
654D4—32no—
655D4—64no—
656D4—61no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—64no—
660C2×C4—61no—
661C2×C4—61no—
662C2×C4—61no—
663C2×C4—61no—
664C2×C4—61no—
665C2×C4—61no—
666C2×C4—61no—
667C2×C4—241no—
668C2×C4—241no—
669C2×C4—241no—
670C2×C4C2×C3×D1211yescharacteristic
671C2×C4C2×C3×D1211yescharacteristic
672C2×C4C2×C3×D1211yescharacteristic
673C2×C4C2×C3×D1211yescharacteristic
674C2×C4C2×C3×D1211yescharacteristic
675C2×C4C23×C3×D311yescharacteristic
676C8—21no—
677C8—21no—
678C8—21no—
679C8—21no—
680C2×C3—21no—
681C2×C3—21no—
682C2×C3—21no—
683C2×C3—41no—
684C2×C3—41no—
685C2×C3—81no—
686C2×C3—122no—
687C2×C3#552411yescharacteristic
688C2×C3#575111yescharacteristic
689C2×C3#575311yescharacteristic
690C2×C3C3×#52511yescharacteristic
691C2×C3C3×#57711yescharacteristic
692C2×C3C3×#57811yescharacteristic
693D3—42no—
694C22—21no—
695C22—21no—
696C22—21no—
697C22—62no—
698C22—121no—
699C22—121no—
700C22C22×C3×D1211yescharacteristic
701C4—21no—
702C4—21no—
703C4—21no—
704C4—21no—
705C4—21no—
706C4—62no—
707C4—121no—
708C4—121no—
709C4—121no—
710C4—121no—
711C4—121no—
712C4—121no—
713C4C3×D3×#4111yescharacteristic
714C4C3×D3×#4111yescharacteristic
715C3—21no—
716C3#7938511yescharacteristic, direct product factor
717C3C3×#312011yescharacteristic, complemented
718C2—41no—
719C2—122no—
720C2C3×#552411yescharacteristic
721C2C3×#575111yescharacteristic
722C2C3×#575311yescharacteristic
subgroupG/H
centerC22×C3C22×D12
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#433C2
socleC22×C32C22×D4
prime radicalC2×C3×#235C22
hypercenterC3×#433D3
hypocenterC3C3×#3120
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×#117 ◁ C3×#433

Complements

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

NH ≅ G/Ntype
2. C3×#5518C2semidirect
3. C32×#433C2semidirect
4. C3×#4849C2semidirect
5. C3×#4847C2semidirect
6. C3×#4841C2semidirect
7. C3×#4829C2semidirect
10. C3×#4722C2semidirect
11. C3×#4721C2semidirect
12. C3×#4716C2semidirect
13. C3×#4710C2semidirect
14. C3×C4×Dic12C2semidirect
15. C3×C4×#204C2semidirect
17. #79385C3direct (N × H)
64. #5518C2×C3semidirect
78. C3×#433D3semidirect
79. C3×#433C2×C3semidirect
80. #4849C2×C3semidirect
81. #4847C2×C3semidirect
82. #4841C2×C3semidirect
83. #4829C2×C3semidirect
86. #4722C2×C3semidirect
87. #4721C2×C3semidirect
88. #4716C2×C3semidirect
89. #4710C2×C3semidirect
90. C4×Dic12C2×C3semidirect
91. C4×#204C2×C3semidirect
283. #433C3×D3semidirect
645. C32#3120semidirect
716. C3#79385direct (N × H)
717. C3C3×#3120semidirect

Maximal subgroups

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

subgroupindex
C3×#55232
C3×#55182
C32×#4332
C3×#48492
C3×#48472
C3×#48412
C3×#48292
C3×#47332
C3×#47222
C3×#47212
C3×#47162
C3×#47102
C3×C4×Dic122
C3×C4×#2042
C3×#31203
#793853