Finite Group Databasebeta

← C3×#81456 #11872395

Subgroups — C3×#81456 #11872395

Order 1152.

796 conjugacy classes of subgroups.

The subgroup lattice has 725 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5625C211yesmaximal, characteristic, complemented
2C3×#5504C211yesmaximal, characteristic
3C32×#484C211yesmaximal, characteristic, complemented
4C3×#5047C211yesmaximal, characteristic
5C3×#4971C211yesmaximal, characteristic, complemented
6C3×#4891C211yesmaximal, characteristic, complemented
7C3×#4889C211yesmaximal, characteristic, complemented
8C3×#4877C211yesmaximal, characteristic, complemented
9C3×#4873C211yesmaximal, characteristic, complemented
10C3×#4818C211yesmaximal, characteristic, complemented
11C3×#4795C211yesmaximal, characteristic, complemented
12C3×#4789C211yesmaximal, characteristic, complemented
13C3×#4788C211yesmaximal, characteristic, complemented
14C3×#4733C211yesmaximal, characteristic
15C3×#4720C211yesmaximal, characteristic, complemented
16C3×#3120—31nomaximal
17#81456C311yesmaximal, characteristic, direct product factor
18C2×C3×#235C2211yescharacteristic
19C32×C22⋊Q8C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C3×Q8×Dic3C2211yescharacteristic
22C3×#944C2211yescharacteristic
23C2×C3×#216C2211yescharacteristic
24C2×C3×#215C2211yescharacteristic
25C3×C4×#67—21no—
26C3×C4×#67—21no—
27C3×#926C2211yescharacteristic
28C3×#924C2211yescharacteristic
29C2×C3×Dic12C2211yescharacteristic
30C2×C3×#204C2211yescharacteristic
31C3×#893C2211yescharacteristic
32C3×#893C2211yescharacteristic
33C3×#892—21no—
34C3×D3×C4⋊C4—21no—
35C3×#890—21no—
36C3×#890C2211yescharacteristic
37C3×#889—21no—
38C3×#887C2211yescharacteristic
39C3×#887C2211yescharacteristic
40C3×#887C2211yescharacteristic
41C3×#879—21no—
42C3×#879—21no—
43C32×#107C2211yescharacteristic
44C32×#107C2211yescharacteristic
45C32×#103C2211yescharacteristic
46C32×#103C2211yescharacteristic
47C32×C22⋊C8C2211yescharacteristic
48C3×#830C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#816C2211yescharacteristic
51C3×#815C2211yescharacteristic
52C3×Dic3⋊C8C2211yescharacteristic
53C3×Dic3⋊C8C2211yescharacteristic
54C3×C8×Dic3C2211yescharacteristic
55C3×#810C2211yescharacteristic
56C3×#810C2211yescharacteristic
57C3×#810C2211yescharacteristic
58C3×#809C2211yescharacteristic
59C3×#808C2211yescharacteristic
60C3×#808C2211yescharacteristic
61C3×#541—31no—
62C3×#520—31no—
63#5625C2×C311yescharacteristic, complemented
64#5504C2×C311yescharacteristic
65C3×#484—21no—
66C3×#484D311yescharacteristic, complemented
67C3×#484C2×C311yescharacteristic, complemented
68C3×#483—31no—
69C3×#479—31no—
70C3×#478—31no—
71C3×#462—31no—
72C3×#461—31no—
73C3×#452—31no—
74C3×#452—31no—
75C3×#441—31no—
76C3×#440—31no—
77C3×C4×Q16—31no—
78C3×C4×SD16—31no—
79C3×#433—31no—
80#5047C2×C311yescharacteristic
81#4971C2×C311yescharacteristic, complemented
82#4891C2×C311yescharacteristic, complemented
83#4889C2×C311yescharacteristic, complemented
84#4877C2×C311yescharacteristic, complemented
85#4873C2×C311yescharacteristic, complemented
86#4818C2×C311yescharacteristic, complemented
87#4795C2×C311yescharacteristic, complemented
88#4789C2×C311yescharacteristic, complemented
89#4788C2×C311yescharacteristic, complemented
90#4733C2×C311yescharacteristic
91#4720C2×C311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93C22×C32×C4—21no—
94C22×C32×C4C2311yescharacteristic
95C2×C3×#67—21no—
96C3×#235—22no—
97C3×#235—22no—
98C2×C3×D12C2311yescharacteristic
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×C3×Dic6C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×C32×C8C2311yescharacteristic
105C2×C32×C8C2311yescharacteristic
106C32×C4⋊C4—21no—
107C32×C4⋊C4—21no—
108C32×C4⋊C4C2311yescharacteristic
109C32×C4⋊C4C2311yescharacteristic
110C32×C4⋊C4C2311yescharacteristic
111C32×C22⋊C4—21no—
112C3×#217—21no—
113C3×#217D411yescharacteristic
114C3×#217D411yescharacteristic
115C3×#216—22no—
116C3×#215—22no—
117C3×(C2×D3)⋊C4—21no—
118C3×(C2×D3)⋊C4—21no—
119C3×C4⋊Dic3—21no—
120C3×C4⋊Dic3—21no—
121C3×C4⋊Dic3D411yescharacteristic
122C3×C4⋊Dic3D411yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
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×C4×Dic3—21no—
132C3×C4×Dic3—21no—
133C3×C4×Dic3—21no—
134C3×C4×Dic3—21no—
135C3×C4×Dic3C2311yescharacteristic
136C3×C4×Dic3C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C3×Dic12—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—21no—
155C3×C22⋊Q8—31no—
156C3×C22⋊Q8C2×D311yescharacteristic
157C3×C22⋊Q8C22×C311yescharacteristic
158C3×C4×Q8—31no—
159C3×C4×Q8—31no—
160C3×C4×Q8—31no—
161C3×C4×Q8—31no—
162C3×C4×D4—31no—
163C3×C4×D4—31no—
164C3×C4×D4—61no—
165C3×C4×D4—61no—
166C3×#117—31no—
167C3×#117—61no—
168C2×C3×C4⋊C4—21no—
169C2×C3×C4⋊C4—61no—
170C2×C3×C4⋊C4C2×D311yescharacteristic
171C2×C3×C4⋊C4C22×C311yescharacteristic
172Q8×Dic3C22×C311yescharacteristic
173#944C22×C311yescharacteristic
174C2×#216C22×C311yescharacteristic
175C2×#215C22×C311yescharacteristic
176C4×#67—21no—
177C4×#67—21no—
178#926C22×C311yescharacteristic
179#924C22×C311yescharacteristic
180C2×Dic12C22×C311yescharacteristic
181C2×#204C22×C311yescharacteristic
182#893C22×C311yescharacteristic
183#893C22×C311yescharacteristic
184#892—21no—
185D3×C4⋊C4—21no—
186#890—21no—
187#890C22×C311yescharacteristic
188#889—21no—
189#887C22×C311yescharacteristic
190#887C22×C311yescharacteristic
191#887C22×C311yescharacteristic
192#879—21no—
193#879—21no—
194C3×#107—21no—
195C3×#107—21no—
196C3×#107C2×D311yescharacteristic
197C3×#107C2×D311yescharacteristic
198C3×#107C22×C311yescharacteristic
199C3×#107C22×C311yescharacteristic
200C3×#106—31no—
201C3×#106—31no—
202C3×C4⋊C8—31no—
203C3×C4⋊C8—31no—
204C3×#103—21no—
205C3×#103—21no—
206C3×#103—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#103C2×D311yescharacteristic
211C3×#103C2×D311yescharacteristic
212C3×#103C22×C311yescharacteristic
213C3×#103C22×C311yescharacteristic
214C3×#102—31no—
215C3×#102—31no—
216C3×C22⋊C8—21no—
217C3×C22⋊C8—31no—
218C3×C22⋊C8C2×D311yescharacteristic
219C3×C22⋊C8C22×C311yescharacteristic
220C3×#97—31no—
221C3×C4×C8—31no—
222#830C22×C311yescharacteristic
223#821C22×C311yescharacteristic
224#816C22×C311yescharacteristic
225#815C22×C311yescharacteristic
226Dic3⋊C8C22×C311yescharacteristic
227Dic3⋊C8C22×C311yescharacteristic
228C8×Dic3C22×C311yescharacteristic
229#810C22×C311yescharacteristic
230#810C22×C311yescharacteristic
231#810C22×C311yescharacteristic
232#809C22×C311yescharacteristic
233#808C22×C311yescharacteristic
234#808C22×C311yescharacteristic
235C23×C32C2×D411yescharacteristic
236C22×C3×D3—21no—
237C32×Q8—21no—
238C32×Q8—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—81no—
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2411yescharacteristic
248C3×#67—24no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C3×D12—21no—
257C3×D12#4112yes—
258C3×C4×D3—24no—
259C3×C4×D3—81no—
260C3×C4×D3—81no—
261C3×Dic6—21no—
262C3×Dic6—21no—
263C3×Dic6—21no—
264C3×Dic6#4112yes—
265C32×C8—21no—
266C32×C8—21no—
267C3×C3⋊C8—21no—
268C3×C3⋊C8—21no—
269#541—31no—
270#520—31no—
271#484C3×D311yescharacteristic, complemented
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#433—31no—
284C3×#41—62no—
285C3×#41—62no—
286C2×C3×Q8—21no—
287C2×C3×Q8—31no—
288C2×C3×Q8—31no—
289C2×C3×Q8C22×D311yescharacteristic
290C2×C3×Q8C23×C311yescharacteristic
291C2×C3×D4—31no—
292C2×C3×D4—61no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—41no—
297C22×C3×C4—61no—
298C22×C3×C4—61no—
299C22×C3×C4—61no—
300C22×C3×C4C22×D311yescharacteristic
301C22×C3×C4C23×C311yescharacteristic
302C2×#67—21no—
303#235—22no—
304#235—22no—
305C2×D12C23×C311yescharacteristic
306C2×C4×D3—21no—
307C2×C4×D3—21no—
308C2×C4×D3—21no—
309C2×Dic6C23×C311yescharacteristic
310C2×Dic6C23×C311yescharacteristic
311C3×Q16—62no—
312C3×Q16—62no—
313C3×SD16—62no—
314C3×SD16—62no—
315C2×C3×C8—21no—
316C2×C3×C8—21no—
317C2×C3×C8—31no—
318C2×C3×C8—31no—
319C2×C3×C8C22×D311yescharacteristic
320C2×C3×C8C22×D311yescharacteristic
321C2×C3×C8C23×C311yescharacteristic
322C2×C3×C8C23×C311yescharacteristic
323C3×C4⋊C4—21no—
324C3×C4⋊C4—21no—
325C3×C4⋊C4—21no—
326C3×C4⋊C4—21no—
327C3×C4⋊C4—21no—
328C3×C4⋊C4—21no—
329C3×C4⋊C4—21no—
330C3×C4⋊C4—31no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—41no—
334C3×C4⋊C4—41no—
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⋊C4—61no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C4⋊C4C23×C311yescharacteristic
348C3×C4⋊C4C23×C311yescharacteristic
349C3×C4⋊C4C23×C311yescharacteristic
350C3×C22⋊C4—21no—
351C3×C22⋊C4—21no—
352C3×C22⋊C4—31no—
353C3×C22⋊C4—31no—
354C3×C22⋊C4—41no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C42—31no—
359C3×C42—31no—
360C3×C42—61no—
361C3×C42—61no—
362C3×C42—61no—
363C3×C42—61no—
364#217—21no—
365#217C3×D411yescharacteristic
366#217C3×D411yescharacteristic
367#216—22no—
368#215—22no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—21no—
371C4⋊Dic3—21no—
372C4⋊Dic3—21no—
373C4⋊Dic3C3×D411yescharacteristic
374C4⋊Dic3C3×D411yescharacteristic
375C4⋊Dic3C23×C311yescharacteristic
376Dic3⋊C4—21no—
377Dic3⋊C4—21no—
378Dic3⋊C4—21no—
379Dic3⋊C4—21no—
380Dic3⋊C4—21no—
381Dic3⋊C4—21no—
382Dic3⋊C4—21no—
383C4×Dic3—21no—
384C4×Dic3—21no—
385C4×Dic3—21no—
386C4×Dic3—21no—
387C4×Dic3C23×C311yescharacteristic
388C4×Dic3C23×C311yescharacteristic
389C2×C3⋊C8C23×C311yescharacteristic
390C2×C3⋊C8C23×C311yescharacteristic
391Dic12—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—41no—
402C32×C4—41no—
403C32×C4—41no—
404C32×C4—41no—
405C32×C4C2×#4111yescharacteristic
406C32×C4C2×#4111yescharacteristic
407C3×Dic3—22no—
408C3×Dic3—21no—
409C3×Dic3—21no—
410C3×Dic3—21no—
411C3×Dic3—21no—
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⋊Q8C2×C3×D311yescharacteristic
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—31no—
436#117—61no—
437C2×C4⋊C4—61no—
438C2×C4⋊C4C2×C3×D311yescharacteristic
439#107C2×C3×D311yescharacteristic
440#107C2×C3×D311yescharacteristic
441#106—31no—
442#106—31no—
443C4⋊C8—31no—
444C4⋊C8—31no—
445#103—31no—
446#103—31no—
447#103—31no—
448#103—31no—
449#103C2×C3×D311yescharacteristic
450#103C2×C3×D311yescharacteristic
451#102—31no—
452#102—31no—
453C22⋊C8—31no—
454C22⋊C8C2×C3×D311yescharacteristic
455#97—31no—
456C4×C8—31no—
457C23×C3—21no—
458C23×C3—61no—
459C23×C3D3×D411yescharacteristic
460C23×C3C2×C3×D411yescharacteristic
461C22×D3—21no—
462C3×Q8—21no—
463C3×Q8—21no—
464C3×Q8—21no—
465C3×Q8—21no—
466C3×Q8—32no—
467C3×Q8—41no—
468C3×Q8—41no—
469C3×Q8—61no—
470C3×Q8—61no—
471C3×Q8—61no—
472C3×D4—32no—
473C3×D4—64no—
474C3×D4—61no—
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—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—31no—
490C2×C3×C4—31no—
491C2×C3×C4—31no—
492C2×C3×C4—31no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—64no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—81no—
504C2×C3×C4—81no—
505C2×C3×C4—82no—
506C2×C3×C4—241no—
507C2×C3×C4—241no—
508C2×C3×C4D3×D411yescharacteristic
509C2×C3×C4C2×C3×D411yescharacteristic
510C2×C3×C4C23×D311yescharacteristic
511C2×C3×C4C24×C311yescharacteristic
512#67—24no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3C2×C3×D411yescharacteristic
517C2×Dic3C2×C3×D411yescharacteristic
518C2×Dic3C2×C3×D411yescharacteristic
519C2×Dic3C2×C3×D411yescharacteristic
520D12—21no—
521D12C3×#4112yes—
522C4×D3—24no—
523C4×D3—81no—
524C4×D3—81no—
525Dic6—21no—
526Dic6—21no—
527Dic6—21no—
528Dic6C3×#4112yes—
529C3×C8—21no—
530C3×C8—21no—
531C3×C8—21no—
532C3×C8—21no—
533C3×C8—41no—
534C3×C8—41no—
535C3×C8—61no—
536C3×C8—61no—
537C3⋊C8—21no—
538C3⋊C8—21no—
539C2×C32—41no—
540C2×C32#52511yescharacteristic
541C2×C32#57711yescharacteristic
542C2×C32#57811yescharacteristic
543C3×D3—42no—
544#41—62no—
545#41—62no—
546C2×Q8—31no—
547C2×Q8—31no—
548C2×Q8C22×C3×D311yescharacteristic
549C2×D4—31no—
550C2×D4—61no—
551C22×C4—21no—
552C22×C4—61no—
553C22×C4—61no—
554C22×C4—61no—
555C22×C4C22×C3×D311yescharacteristic
556Q16—62no—
557Q16—62no—
558SD16—62no—
559SD16—62no—
560C2×C8—31no—
561C2×C8—31no—
562C2×C8C22×C3×D311yescharacteristic
563C2×C8C22×C3×D311yescharacteristic
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—31no—
567C4⋊C4—31no—
568C4⋊C4—31no—
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⋊C4C22×C3×D311yescharacteristic
579C4⋊C4C22×C3×D311yescharacteristic
580C4⋊C4C22×C3×D311yescharacteristic
581C22⋊C4—21no—
582C22⋊C4—31no—
583C22⋊C4—31no—
584C22⋊C4—61no—
585C22⋊C4—61no—
586C22⋊C4—61no—
587C42—31no—
588C42—31no—
589C42—61no—
590C42—61no—
591C42—61no—
592C42—61no—
593C22×C3—22no—
594C22×C3—21no—
595C22×C3—21no—
596C22×C3—21no—
597C22×C3—21no—
598C22×C3—21no—
599C22×C3—21no—
600C22×C3—21no—
601C22×C3—41no—
602C22×C3—41no—
603C22×C3—62no—
604C22×C3—121no—
605C22×C3—121no—
606C22×C3C2×D3×D411yescharacteristic
607C22×C3C22×C3×D411yescharacteristic
608C2×D3—22no—
609C2×D3—41no—
610C2×D3—41no—
611C3×C4—21no—
612C3×C4—21no—
613C3×C4—21no—
614C3×C4—21no—
615C3×C4—41no—
616C3×C4—41no—
617C3×C4—41no—
618C3×C4—41no—
619C3×C4—41no—
620C3×C4—41no—
621C3×C4—41no—
622C3×C4—41no—
623C3×C4—41no—
624C3×C4—62no—
625C3×C4—61no—
626C3×C4—61no—
627C3×C4—61no—
628C3×C4—61no—
629C3×C4—81no—
630C3×C4—81no—
631C3×C4—81no—
632C3×C4—81no—
633C3×C4—121no—
634C3×C4—121no—
635C3×C4D3×#4111yescharacteristic
636C3×C4D3×#4111yescharacteristic
637C3×C4C2×C3×#4111yescharacteristic
638C3×C4C2×C3×#4111yescharacteristic
639Dic3—21no—
640Dic3—21no—
641Dic3—21no—
642Dic3—21no—
643Dic3—22no—
644Dic3—41no—
645Dic3—41no—
646C32#312011yescharacteristic, complemented, Sylow
647C23—61no—
648C23C3×D3×D411yescharacteristic
649Q8—21no—
650Q8—21no—
651Q8—32no—
652Q8—61no—
653Q8—61no—
654Q8—61no—
655D4—32no—
656D4—64no—
657D4—61no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—31no—
665C2×C4—31no—
666C2×C4—31no—
667C2×C4—31no—
668C2×C4—64no—
669C2×C4—61no—
670C2×C4—61no—
671C2×C4—61no—
672C2×C4—81no—
673C2×C4—241no—
674C2×C4—241no—
675C2×C4C3×D3×D411yescharacteristic
676C2×C4C23×C3×D311yescharacteristic
677C8—21no—
678C8—21no—
679C8—61no—
680C8—61no—
681C2×C3—21no—
682C2×C3—21no—
683C2×C3—21no—
684C2×C3—42no—
685C2×C3—41no—
686C2×C3—41no—
687C2×C3—122no—
688C2×C3#565611yescharacteristic
689C2×C3#576611yescharacteristic
690C2×C3#577511yescharacteristic
691C2×C3C3×#52511yescharacteristic
692C2×C3C3×#57711yescharacteristic
693C2×C3C3×#57811yescharacteristic
694D3—42no—
695C22—21no—
696C22—21no—
697C22—21no—
698C22—62no—
699C22—121no—
700C22—121no—
701C22C2×C3×D3×D411yescharacteristic
702C4—21no—
703C4—41no—
704C4—41no—
705C4—41no—
706C4—41no—
707C4—61no—
708C4—61no—
709C4—61no—
710C4—61no—
711C4—62no—
712C4—121no—
713C4—121no—
714C4C3×D3×#4111yescharacteristic
715C4C3×D3×#4111yescharacteristic
716C3—21no—
717C3#8145611yescharacteristic, direct product factor
718C3C3×#312011yescharacteristic, complemented
719C2—41no—
720C2—122no—
721C2C3×#565611yescharacteristic
722C2C3×#576611yescharacteristic
723C2C3×#577511yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#484C2
socleC22×C32C22×D4
prime radicalC2×C3×#235C22
hypercenterC3×#484D3
hypocenterC3C3×#3120
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#484

Complements

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

NH ≅ G/Ntype
1. C3×#5625C2semidirect
3. C32×#484C2semidirect
5. C3×#4971C2semidirect
6. C3×#4891C2semidirect
7. C3×#4889C2semidirect
8. C3×#4877C2semidirect
9. C3×#4873C2semidirect
10. C3×#4818C2semidirect
11. C3×#4795C2semidirect
12. C3×#4789C2semidirect
13. C3×#4788C2semidirect
15. C3×#4720C2semidirect
17. #81456C3direct (N × H)
63. #5625C2×C3semidirect
66. C3×#484D3semidirect
67. C3×#484C2×C3semidirect
81. #4971C2×C3semidirect
82. #4891C2×C3semidirect
83. #4889C2×C3semidirect
84. #4877C2×C3semidirect
85. #4873C2×C3semidirect
86. #4818C2×C3semidirect
87. #4795C2×C3semidirect
88. #4789C2×C3semidirect
89. #4788C2×C3semidirect
91. #4720C2×C3semidirect
271. #484C3×D3semidirect
646. C32#3120semidirect
717. C3#81456direct (N × H)
718. C3C3×#3120semidirect

Maximal subgroups

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

subgroupindex
C3×#56252
C3×#55042
C32×#4842
C3×#50472
C3×#49712
C3×#48912
C3×#48892
C3×#48772
C3×#48732
C3×#48182
C3×#47952
C3×#47892
C3×#47882
C3×#47332
C3×#47202
C3×#31203
#814563