Finite Group Databasebeta

← C3×#81150 #11895320

Subgroups — C3×#81150 #11895320

Order 1152.

775 conjugacy classes of subgroups.

The subgroup lattice has 731 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5690C211yesmaximal, characteristic, complemented
2C3×#5559C211yesmaximal, characteristic, complemented
3C32×#478C211yesmaximal, characteristic, complemented
4C3×#5068C211yesmaximal, characteristic, complemented
5C3×C4×#213C211yesmaximal, characteristic, complemented
6C3×#4875C211yesmaximal, characteristic, complemented
7C3×#4872C211yesmaximal, characteristic, complemented
8C3×#4871C211yesmaximal, characteristic, complemented
9C3×#4852C211yesmaximal, characteristic, complemented
10C3×#4844C211yesmaximal, characteristic, complemented
11C3×#4830C211yesmaximal, characteristic, complemented
12C3×#4787C211yesmaximal, characteristic, complemented
13C3×#4786C211yesmaximal, characteristic
14C3×#4768C211yesmaximal, characteristic, complemented
15C3×#4760C211yesmaximal, characteristic, complemented
16C3×#3361—31nomaximal
17#81150C311yesmaximal, characteristic, direct product factor
18C32×#125C2211yescharacteristic
19C32×C4×D4C2211yescharacteristic
20C3×#940C2211yescharacteristic
21C3×#936C2211yescharacteristic
22C2×C3×#213C2211yescharacteristic
23C3×#929—21no—
24C3×C4×#67—21no—
25C2×C3×D24C2211yescharacteristic
26C2×C3×#204C2211yescharacteristic
27C3×#897—21no—
28C3×#896—21no—
29C3×#896—21no—
30C3×#893C2211yescharacteristic
31C3×#893C2211yescharacteristic
32C3×#893C2211yescharacteristic
33C3×D3×C4⋊C4—21no—
34C3×#890C2211yescharacteristic
35C3×#888C2211yescharacteristic
36C3×#887C2211yescharacteristic
37C3×#885—21no—
38C3×#883—21no—
39C3×#875C2211yescharacteristic
40C3×C4×D12C2211yescharacteristic
41C3×C4×Dic6C2211yescharacteristic
42C32×#107C2211yescharacteristic
43C32×#106C2211yescharacteristic
44C32×C4⋊C8C2211yescharacteristic
45C32×#102C2211yescharacteristic
46C32×#102C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×#816C2211yescharacteristic
50C3×Dic3⋊C8C2211yescharacteristic
51C3×Dic3⋊C8C2211yescharacteristic
52C3×C8×Dic3C2211yescharacteristic
53C3×C8×Dic3C2211yescharacteristic
54C3×#810C2211yescharacteristic
55C3×#810C2211yescharacteristic
56C3×#809C2211yescharacteristic
57C3×#809C2211yescharacteristic
58C3×#809C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×C4×C3⋊C8C2211yescharacteristic
61C3×#559—31no—
62C3×#554—31no—
63#5690C2×C311yescharacteristic, complemented
64#5559C2×C311yescharacteristic, complemented
65C3×#488—31no—
66C3×#488—31no—
67C3×#486—31no—
68C3×#478—21no—
69C3×#478—31no—
70C3×#478D311yescharacteristic, complemented
71C3×#478C2×C311yescharacteristic, complemented
72C3×#477—31no—
73C3×#463—31no—
74C3×#463—31no—
75C3×#459—31no—
76C3×C8×Q8—31no—
77C3×C4×SD16—31no—
78C3×C4×D8—31no—
79C3×C4×D8—31no—
80#5068C2×C311yescharacteristic, complemented
81C4×#213C2×C311yescharacteristic, complemented
82#4875C2×C311yescharacteristic, complemented
83#4872C2×C311yescharacteristic, complemented
84#4871C2×C311yescharacteristic, complemented
85#4852C2×C311yescharacteristic, complemented
86#4844C2×C311yescharacteristic, complemented
87#4830C2×C311yescharacteristic, complemented
88#4787C2×C311yescharacteristic, complemented
89#4786C2×C311yescharacteristic
90#4768C2×C311yescharacteristic, complemented
91#4760C2×C311yescharacteristic, complemented
92C2×C32×D4C2311yescharacteristic
93C22×C32×C4—21no—
94C2×C3×#67—21no—
95C2×C3×#67—21no—
96C2×C3×D12C2311yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×C3×Dic6—21no—
103C2×C3×Dic6D411yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×C32×C8C2311yescharacteristic
106C2×C32×C8C2311yescharacteristic
107C32×C4⋊C4—21no—
108C32×C4⋊C4—21no—
109C32×C4⋊C4C2311yescharacteristic
110C32×C4⋊C4C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112C32×C22⋊C4—21no—
113C32×C42C2311yescharacteristic
114C3×#217—21no—
115C3×#217—21no—
116C3×#213—22no—
117C3×(C2×D3)⋊C4—21no—
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3D411yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4D411yescharacteristic
130C3×Dic3⋊C4D411yescharacteristic
131C3×C4×Dic3—21no—
132C3×C4×Dic3C2311yescharacteristic
133C3×C4×Dic3C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C3×D24—22no—
137C3×#204—22no—
138#3361—31noSylow
139C2×C3×SD16—31no—
140C2×C3×D8—31no—
141C2×C3×D8—31no—
142C3×C4⋊Q8—31no—
143C3×#127—31no—
144C3×#125—21no—
145C3×#125—31no—
146C3×#125C2×D311yescharacteristic
147C3×#125C22×C311yescharacteristic
148C3×#124—31no—
149C3×#124—31no—
150C3×#124—61no—
151C3×#123—61no—
152C3×#123—61no—
153C3×C22⋊Q8—61no—
154C3×C22⋊Q8—61no—
155C3×C22⋊Q8—61no—
156C3×C4×Q8—31no—
157C3×C4×Q8—31no—
158C3×C4×D4—21no—
159C3×C4×D4—31no—
160C3×C4×D4—31no—
161C3×C4×D4—31no—
162C3×C4×D4—31no—
163C3×C4×D4—61no—
164C3×C4×D4C2×D311yescharacteristic
165C3×C4×D4C22×C311yescharacteristic
166C2×C3×C4⋊C4—61no—
167#940C22×C311yescharacteristic
168#936C22×C311yescharacteristic
169C2×#213C22×C311yescharacteristic
170#929—21no—
171C4×#67—21no—
172C2×D24C22×C311yescharacteristic
173C2×#204C22×C311yescharacteristic
174#897—21no—
175#896—21no—
176#896—21no—
177#893C22×C311yescharacteristic
178#893C22×C311yescharacteristic
179#893C22×C311yescharacteristic
180D3×C4⋊C4—21no—
181#890C22×C311yescharacteristic
182#888C22×C311yescharacteristic
183#887C22×C311yescharacteristic
184#885—21no—
185#883—21no—
186#875C22×C311yescharacteristic
187C4×D12C22×C311yescharacteristic
188C4×Dic6C22×C311yescharacteristic
189C3×#107—21no—
190C3×#107—31no—
191C3×#107C2×D311yescharacteristic
192C3×#107C22×C311yescharacteristic
193C3×#106—21no—
194C3×#106C2×D311yescharacteristic
195C3×#106C22×C311yescharacteristic
196C3×C4⋊C8—21no—
197C3×C4⋊C8—31no—
198C3×C4⋊C8—31no—
199C3×C4⋊C8C2×D311yescharacteristic
200C3×C4⋊C8C22×C311yescharacteristic
201C3×#103—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×#102—21no—
205C3×#102—21no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102—31no—
209C3×#102—31no—
210C3×#102—31no—
211C3×#102C2×D311yescharacteristic
212C3×#102C2×D311yescharacteristic
213C3×#102C22×C311yescharacteristic
214C3×#102C22×C311yescharacteristic
215C3×C4×C8—31no—
216C3×C4×C8—31no—
217C3×C4×C8—31no—
218#832C22×C311yescharacteristic
219#821C22×C311yescharacteristic
220#816C22×C311yescharacteristic
221Dic3⋊C8C22×C311yescharacteristic
222Dic3⋊C8C22×C311yescharacteristic
223C8×Dic3C22×C311yescharacteristic
224C8×Dic3C22×C311yescharacteristic
225#810C22×C311yescharacteristic
226#810C22×C311yescharacteristic
227#809C22×C311yescharacteristic
228#809C22×C311yescharacteristic
229#809C22×C311yescharacteristic
230#807C22×C311yescharacteristic
231C4×C3⋊C8C22×C311yescharacteristic
232C23×C32—21no—
233C22×C3×D3—21no—
234C22×C3×D3—21no—
235C32×D4—21no—
236C32×D4—21no—
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—81no—
241C2×C32×C4C2×D411yescharacteristic
242C2×C32×C4C2×D411yescharacteristic
243C2×C32×C4C2411yescharacteristic
244C3×#67—42no—
245C3×#67—81no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3C2×D411yescharacteristic
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C3×D12—21no—
253C3×D12—21no—
254C3×D12—21no—
255C3×D12#4112yes—
256C3×C4×D3—42no—
257C3×C4×D3—81no—
258C3×C4×D3—81no—
259C3×C4×D3—81no—
260C3×Dic6—22no—
261C3×Dic6—21no—
262C3×Dic6—21no—
263C3×Dic6—81no—
264C32×C8—21no—
265C32×C8—21no—
266C3×C3⋊C8—21no—
267C3×C3⋊C8—21no—
268#559—31no—
269#554—31no—
270#488—31no—
271#488—31no—
272#486—31no—
273#478—31no—
274#478C3×D311yescharacteristic, complemented
275#477—31no—
276#463—31no—
277#463—31no—
278#459—31no—
279C8×Q8—31no—
280C4×SD16—31no—
281C4×D8—31no—
282C4×D8—31no—
283C2×C3×Q8—31no—
284C2×C3×Q8—31no—
285C2×C3×Q8—61no—
286C2×C3×D4—21no—
287C2×C3×D4—31no—
288C2×C3×D4—31no—
289C2×C3×D4—61no—
290C2×C3×D4—61no—
291C2×C3×D4C22×D311yescharacteristic
292C2×C3×D4C23×C311yescharacteristic
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—41no—
296C22×C3×C4—61no—
297C22×C3×C4—61no—
298C22×C3×C4—61no—
299C22×C3×C4—61no—
300C2×#67—21no—
301C2×#67—21no—
302C2×D12C23×C311yescharacteristic
303C2×D12C23×C311yescharacteristic
304C2×C4×D3—21no—
305C2×C4×D3—21no—
306C2×C4×D3—21no—
307C2×C4×D3—21no—
308C2×Dic6—21no—
309C2×Dic6C3×D411yescharacteristic
310C2×Dic6C23×C311yescharacteristic
311C3×SD16—62no—
312C3×D8—62no—
313C3×D8—62no—
314C2×C3×C8—21no—
315C2×C3×C8—21no—
316C2×C3×C8—31no—
317C2×C3×C8—31no—
318C2×C3×C8C22×D311yescharacteristic
319C2×C3×C8C22×D311yescharacteristic
320C2×C3×C8C23×C311yescharacteristic
321C2×C3×C8C23×C311yescharacteristic
322C3×C4⋊C4—21no—
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—31no—
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⋊C4C22×D311yescharacteristic
340C3×C4⋊C4C22×D311yescharacteristic
341C3×C4⋊C4C22×D311yescharacteristic
342C3×C4⋊C4C23×C311yescharacteristic
343C3×C4⋊C4C23×C311yescharacteristic
344C3×C4⋊C4C23×C311yescharacteristic
345C3×C22⋊C4—21no—
346C3×C22⋊C4—21no—
347C3×C22⋊C4—41no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C42—21no—
357C3×C42—31no—
358C3×C42—31no—
359C3×C42—61no—
360C3×C42C22×D311yescharacteristic
361C3×C42C23×C311yescharacteristic
362#217—21no—
363#217—21no—
364#213—22no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4—21no—
367(C2×D3)⋊C4—21no—
368(C2×D3)⋊C4—21no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—21no—
371C4⋊Dic3—21no—
372C4⋊Dic3C3×D411yescharacteristic
373C4⋊Dic3C23×C311yescharacteristic
374Dic3⋊C4—21no—
375Dic3⋊C4—21no—
376Dic3⋊C4—21no—
377Dic3⋊C4C3×D411yescharacteristic
378Dic3⋊C4C3×D411yescharacteristic
379C4×Dic3—21no—
380C4×Dic3C23×C311yescharacteristic
381C4×Dic3C23×C311yescharacteristic
382C2×C3⋊C8C23×C311yescharacteristic
383C2×C3⋊C8C23×C311yescharacteristic
384D24—22no—
385#204—22no—
386C22×C32—41no—
387C22×C32—41no—
388C22×C32—41no—
389C22×C32C22×D411yescharacteristic
390C2×C3×D3—22no—
391C2×C3×D3—41no—
392C2×C3×D3—41no—
393C2×C3×D3—41no—
394C2×C3×D3—41no—
395C2×C3×D3—41no—
396C32×C4—21no—
397C32×C4—21no—
398C32×C4—41no—
399C32×C4—41no—
400C32×C4—41no—
401C32×C4C2×#4111yescharacteristic
402C32×C42−1+411yescharacteristic
403C3×Dic3—21no—
404C3×Dic3—21no—
405C3×Dic3—21no—
406C3×Dic3—41no—
407C3×Dic3—41no—
408C3×Dic3#13512yes—
409C2×SD16—31no—
410C2×D8—31no—
411C2×D8—31no—
412C4⋊Q8—31no—
413#127—31no—
414#125—31no—
415#125C2×C3×D311yescharacteristic
416#124—31no—
417#124—31no—
418#124—61no—
419#123—61no—
420#123—61no—
421C22⋊Q8—61no—
422C22⋊Q8—61no—
423C22⋊Q8—61no—
424C4×Q8—31no—
425C4×Q8—31no—
426C4×D4—31no—
427C4×D4—31no—
428C4×D4—31no—
429C4×D4—31no—
430C4×D4—61no—
431C4×D4C2×C3×D311yescharacteristic
432C2×C4⋊C4—61no—
433#107—31no—
434#107C2×C3×D311yescharacteristic
435#106C2×C3×D311yescharacteristic
436C4⋊C8—31no—
437C4⋊C8—31no—
438C4⋊C8C2×C3×D311yescharacteristic
439#103—31no—
440#103—31no—
441#103—31no—
442#102—31no—
443#102—31no—
444#102—31no—
445#102—31no—
446#102—31no—
447#102C2×C3×D311yescharacteristic
448#102C2×C3×D311yescharacteristic
449C4×C8—31no—
450C4×C8—31no—
451C4×C8—31no—
452C23×C3—21no—
453C23×C3—21no—
454C23×C3—41no—
455C23×C3—61no—
456C23×C3—61no—
457C22×D3—21no—
458C22×D3—21no—
459C3×Q8—62no—
460C3×Q8—61no—
461C3×Q8—61no—
462C3×Q8—241no—
463C3×D4—22no—
464C3×D4—21no—
465C3×D4—21no—
466C3×D4—21no—
467C3×D4—21no—
468C3×D4—32no—
469C3×D4—41no—
470C3×D4—61no—
471C3×D4—61no—
472C3×D4—61no—
473C3×D4—122no—
474C3×D4—241no—
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—31no—
485C2×C3×C4—31no—
486C2×C3×C4—31no—
487C2×C3×C4—31no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—61no—
492C2×C3×C4—61no—
493C2×C3×C4—81no—
494C2×C3×C4—81no—
495C2×C3×C4—82no—
496C2×C3×C4—122no—
497C2×C3×C4—241no—
498C2×C3×C4—241no—
499C2×C3×C4—241no—
500C2×C3×C4D3×D411yescharacteristic
501C2×C3×C4D3×D411yescharacteristic
502C2×C3×C4C2×C3×D411yescharacteristic
503C2×C3×C4C2×C3×D411yescharacteristic
504C2×C3×C4C23×D311yescharacteristic
505C2×C3×C4C24×C311yescharacteristic
506#67—42no—
507#67—81no—
508C2×Dic3—21no—
509C2×Dic3—21no—
510C2×Dic3C2×C3×D411yescharacteristic
511C2×Dic3C2×C3×D411yescharacteristic
512C2×Dic3C2×C3×D411yescharacteristic
513C2×Dic3C2×C3×D411yescharacteristic
514D12—21no—
515D12—21no—
516D12—21no—
517D12C3×#4112yes—
518C4×D3—42no—
519C4×D3—81no—
520C4×D3—81no—
521C4×D3—81no—
522Dic6—22no—
523Dic6—21no—
524Dic6—21no—
525Dic6—81no—
526C3×C8—21no—
527C3×C8—21no—
528C3×C8—21no—
529C3×C8—21no—
530C3×C8—41no—
531C3×C8—41no—
532C3×C8—61no—
533C3×C8—61no—
534C3⋊C8—21no—
535C3⋊C8—21no—
536C2×C32—81no—
537C2×C32#54811yescharacteristic
538C2×C32C2×#13511yescharacteristic
539C2×C32#57611yescharacteristic
540C3×D3—42no—
541C3×D3—81no—
542C2×Q8—31no—
543C2×Q8—31no—
544C2×Q8—61no—
545C2×D4—31no—
546C2×D4—31no—
547C2×D4—61no—
548C2×D4—61no—
549C2×D4C22×C3×D311yescharacteristic
550C22×C4—21no—
551C22×C4—61no—
552C22×C4—61no—
553C22×C4—61no—
554C22×C4—61no—
555SD16—62no—
556D8—62no—
557D8—62no—
558C2×C8—31no—
559C2×C8—31no—
560C2×C8C22×C3×D311yescharacteristic
561C2×C8C22×C3×D311yescharacteristic
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—31no—
565C4⋊C4—31no—
566C4⋊C4—31no—
567C4⋊C4—31no—
568C4⋊C4—61no—
569C4⋊C4—61no—
570C4⋊C4—61no—
571C4⋊C4—61no—
572C4⋊C4C22×C3×D311yescharacteristic
573C4⋊C4C22×C3×D311yescharacteristic
574C4⋊C4C22×C3×D311yescharacteristic
575C22⋊C4—21no—
576C22⋊C4—61no—
577C22⋊C4—61no—
578C22⋊C4—61no—
579C22⋊C4—61no—
580C22⋊C4—61no—
581C22⋊C4—61no—
582C22⋊C4—61no—
583C22⋊C4—61no—
584C42—31no—
585C42—31no—
586C42—61no—
587C42C22×C3×D311yescharacteristic
588C22×C3—21no—
589C22×C3—42no—
590C22×C3—41no—
591C22×C3—41no—
592C22×C3—41no—
593C22×C3—41no—
594C22×C3—41no—
595C22×C3—41no—
596C22×C3—62no—
597C22×C3—81no—
598C22×C3—81no—
599C22×C3—121no—
600C22×C3—121no—
601C22×C3—121no—
602C22×C3—121no—
603C22×C3—121no—
604C22×C3C2×D3×D411yescharacteristic
605C22×C3C22×C3×D411yescharacteristic
606C2×D3—22no—
607C2×D3—41no—
608C2×D3—41no—
609C2×D3—41no—
610C2×D3—41no—
611C2×D3—41no—
612C3×C4—21no—
613C3×C4—21no—
614C3×C4—21no—
615C3×C4—21no—
616C3×C4—21no—
617C3×C4—21no—
618C3×C4—32no—
619C3×C4—41no—
620C3×C4—41no—
621C3×C4—41no—
622C3×C4—41no—
623C3×C4—41no—
624C3×C4—41no—
625C3×C4—41no—
626C3×C4—41no—
627C3×C4—61no—
628C3×C4—61no—
629C3×C4—61no—
630C3×C4—81no—
631C3×C4—81no—
632C3×C4—81no—
633C3×C4—121no—
634C3×C4—121no—
635C3×C4#100711yescharacteristic
636C3×C4D3×#4111yescharacteristic
637C3×C4C2×C3×#4111yescharacteristic
638C3×C4C3×2−1+411yescharacteristic
639Dic3—21no—
640Dic3—21no—
641Dic3—21no—
642Dic3—41no—
643Dic3—41no—
644Dic3C3×#13512yes—
645C32#336111yescharacteristic, complemented, Sylow
646C23—21no—
647C23—61no—
648C23—61no—
649Q8—62no—
650Q8—61no—
651Q8—61no—
652Q8—241no—
653D4—21no—
654D4—21no—
655D4—32no—
656D4—61no—
657D4—61no—
658D4—61no—
659D4—122no—
660D4—241no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—31no—
665C2×C4—31no—
666C2×C4—31no—
667C2×C4—31no—
668C2×C4—61no—
669C2×C4—61no—
670C2×C4—81no—
671C2×C4—122no—
672C2×C4—241no—
673C2×C4—241no—
674C2×C4—241no—
675C2×C4C3×D3×D411yescharacteristic
676C2×C4C3×D3×D411yescharacteristic
677C2×C4C23×C3×D311yescharacteristic
678C8—21no—
679C8—21no—
680C8—61no—
681C8—61no—
682C2×C3—21no—
683C2×C3—21no—
684C2×C3—21no—
685C2×C3—82no—
686C2×C3—81no—
687C2×C3—81no—
688C2×C3—122no—
689C2×C3—241no—
690C2×C3#563311yescharacteristic
691C2×C3D3×#13511yescharacteristic
692C2×C3#577411yescharacteristic
693C2×C3C3×#54811yescharacteristic
694C2×C3C2×C3×#13511yescharacteristic
695C2×C3C3×#57611yescharacteristic
696D3—42no—
697D3—81no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—62no—
702C22—121no—
703C22—121no—
704C22—121no—
705C22—121no—
706C22—121no—
707C22C2×C3×D3×D411yescharacteristic
708C4—21no—
709C4—21no—
710C4—32no—
711C4—41no—
712C4—41no—
713C4—41no—
714C4—61no—
715C4—61no—
716C4—61no—
717C4—121no—
718C4—121no—
719C4C3×#100711yescharacteristic
720C4C3×D3×#4111yescharacteristic
721C3—21no—
722C3#8115011yescharacteristic, direct product factor
723C3C3×#336111yescharacteristic, complemented
724C2—81no—
725C2—122no—
726C2—241no—
727C2C3×#563311yescharacteristic
728C2C3×D3×#13511yescharacteristic
729C2C3×#577411yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#478C2
socleC22×C32C22×D4
prime radicalC3×#4786C2
hypercenterC3×#478D3
hypocenterC3C3×#3361
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#478

Complements

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

NH ≅ G/Ntype
1. C3×#5690C2semidirect
2. C3×#5559C2semidirect
3. C32×#478C2semidirect
4. C3×#5068C2semidirect
5. C3×C4×#213C2semidirect
6. C3×#4875C2semidirect
7. C3×#4872C2semidirect
8. C3×#4871C2semidirect
9. C3×#4852C2semidirect
10. C3×#4844C2semidirect
11. C3×#4830C2semidirect
12. C3×#4787C2semidirect
14. C3×#4768C2semidirect
15. C3×#4760C2semidirect
17. #81150C3direct (N × H)
63. #5690C2×C3semidirect
64. #5559C2×C3semidirect
70. C3×#478D3semidirect
71. C3×#478C2×C3semidirect
80. #5068C2×C3semidirect
81. C4×#213C2×C3semidirect
82. #4875C2×C3semidirect
83. #4872C2×C3semidirect
84. #4871C2×C3semidirect
85. #4852C2×C3semidirect
86. #4844C2×C3semidirect
87. #4830C2×C3semidirect
88. #4787C2×C3semidirect
90. #4768C2×C3semidirect
91. #4760C2×C3semidirect
274. #478C3×D3semidirect
645. C32#3361semidirect
722. C3#81150direct (N × H)
723. C3C3×#3361semidirect

Maximal subgroups

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

subgroupindex
C3×#56902
C3×#55592
C32×#4782
C3×#50682
C3×C4×#2132
C3×#48752
C3×#48722
C3×#48712
C3×#48522
C3×#48442
C3×#48302
C3×#47872
C3×#47862
C3×#47682
C3×#47602
C3×#33613
#811503