Finite Group Databasebeta

← C3×#81635 #11895613

Subgroups — C3×#81635 #11895613

Order 1152.

744 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5685C211yesmaximal, characteristic, complemented
2C3×#5681C211yesmaximal, characteristic
3C32×#488C211yesmaximal, characteristic, complemented
4C3×#5066C211yesmaximal, characteristic, complemented
5C3×#5054C211yesmaximal, characteristic, complemented
6C3×#4800C211yesmaximal, characteristic, complemented
7C3×#4798C211yesmaximal, characteristic, complemented
8C3×#4791C211yesmaximal, characteristic, complemented
9C3×#4790C211yesmaximal, characteristic, complemented
10C3×#4763C211yesmaximal, characteristic, complemented
11C3×#4762C211yesmaximal, characteristic
12C3×#4760C211yesmaximal, characteristic
13C3×#4758C211yesmaximal, characteristic, complemented
14C3×C4×#204C211yesmaximal, characteristic, complemented
15C3×C8×Dic6C211yesmaximal, characteristic, complemented
16C3×#3365—31nomaximal
17#81635C311yesmaximal, characteristic, direct product factor
18C32×#125C2211yescharacteristic
19C32×#124C2211yescharacteristic
20C3×#947C2211yescharacteristic
21C3×Q8×Dic3C2211yescharacteristic
22C2×C3×#216C2211yescharacteristic
23C3×#940C2211yescharacteristic
24C3×D4×Dic3C2211yescharacteristic
25C2×C3×#214C2211yescharacteristic
26C2×C3×#204C2211yescharacteristic
27C3×#890C2211yescharacteristic
28C3×#889—21no—
29C3×#889—21no—
30C3×#888—21no—
31C3×#888C2211yescharacteristic
32C3×#887—21no—
33C3×#887C2211yescharacteristic
34C3×#887C2211yescharacteristic
35C3×#886—21no—
36C3×#885—21no—
37C3×#883—21no—
38C3×#67⋊C4—21no—
39C3×C4×D12C2211yescharacteristic
40C3×C4×Dic6C2211yescharacteristic
41C3×C4×Dic6C2211yescharacteristic
42C32×#103C2211yescharacteristic
43C32×#103C2211yescharacteristic
44C32×#102C2211yescharacteristic
45C32×#102C2211yescharacteristic
46C32×C4×C8C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#817C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×Dic3⋊C8C2211yescharacteristic
53C3×Dic3⋊C8C2211yescharacteristic
54C3×C8×Dic3C2211yescharacteristic
55C3×C8×Dic3C2211yescharacteristic
56C3×#809C2211yescharacteristic
57C3×#809C2211yescharacteristic
58C3×#808C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×C4⋊(C3⋊C8)C2211yescharacteristic
61C3×#559—31no—
62C3×#557—31no—
63#5685C2×C311yescharacteristic, complemented
64#5681C2×C311yescharacteristic
65C3×#488—21no—
66C3×#488—31no—
67C3×#488D311yescharacteristic, complemented
68C3×#488C2×C311yescharacteristic, complemented
69C3×#486—31no—
70C3×#478—31no—
71C3×#478—31no—
72C3×#475—31no—
73C3×#464—31no—
74C3×#464—31no—
75C3×#460—31no—
76C3×C8×Q8—31no—
77C3×C4×Q16—31no—
78C3×C4×SD16—31no—
79C3×C4×SD16—31no—
80#5066C2×C311yescharacteristic, complemented
81#5054C2×C311yescharacteristic, complemented
82#4800C2×C311yescharacteristic, complemented
83#4798C2×C311yescharacteristic, complemented
84#4791C2×C311yescharacteristic, complemented
85#4790C2×C311yescharacteristic, complemented
86#4763C2×C311yescharacteristic, complemented
87#4762C2×C311yescharacteristic
88#4760C2×C311yescharacteristic
89#4758C2×C311yescharacteristic, complemented
90C4×#204C2×C311yescharacteristic, complemented
91C8×Dic6C2×C311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93C2×C32×D4C2311yescharacteristic
94C2×C3×#67—21no—
95C2×C3×#67—21no—
96C22×C3×Dic3—21no—
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×Dic6—21no—
100C2×C3×Dic6D411yescharacteristic
101C2×C3×Dic6C2311yescharacteristic
102C2×C32×C8C2311yescharacteristic
103C2×C32×C8C2311yescharacteristic
104C32×C4⋊C4—21no—
105C32×C4⋊C4—21no—
106C32×C4⋊C4C2311yescharacteristic
107C32×C4⋊C4C2311yescharacteristic
108C32×C22⋊C4—21no—
109C32×C22⋊C4—21no—
110C32×C42C2311yescharacteristic
111C3×#217—21no—
112C3×#216—22no—
113C3×#214—22no—
114C3×(C2×D3)⋊C4—21no—
115C3×(C2×D3)⋊C4—21no—
116C3×(C2×D3)⋊C4—21no—
117C3×C4⋊Dic3—21no—
118C3×C4⋊Dic3—21no—
119C3×C4⋊Dic3D411yescharacteristic
120C3×C4⋊Dic3C2311yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×Dic3⋊C4—21no—
123C3×Dic3⋊C4—21no—
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4D411yescharacteristic
128C3×Dic3⋊C4D411yescharacteristic
129C3×C4×Dic3—21no—
130C3×C4×Dic3—21no—
131C3×C4×Dic3—21no—
132C3×C4×Dic3—21no—
133C3×C4×Dic3C2311yescharacteristic
134C3×C4×Dic3C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C3×#204—22no—
138#3365—31noSylow
139C2×C3×Q16—31no—
140C2×C3×SD16—31no—
141C2×C3×SD16—31no—
142C3×C4⋊Q8—31no—
143C3×C4⋊Q8—61no—
144C3×#127—31no—
145C3×#125—21no—
146C3×#125—31no—
147C3×#125—61no—
148C3×#125—61no—
149C3×#125C2×D311yescharacteristic
150C3×#125C22×C311yescharacteristic
151C3×#124—21no—
152C3×#124—31no—
153C3×#124—61no—
154C3×#124C2×D311yescharacteristic
155C3×#124C22×C311yescharacteristic
156C3×#123—61no—
157C3×#123—61no—
158C3×C4×Q8—31no—
159C3×C4×Q8—31no—
160C3×C4×Q8—31no—
161C3×C4×Q8—31no—
162C3×C4×Q8—31no—
163C3×C4×Q8—61no—
164C3×C4×D4—31no—
165C3×C4×D4—31no—
166C3×C4×D4—61no—
167#947C22×C311yescharacteristic
168Q8×Dic3C22×C311yescharacteristic
169C2×#216C22×C311yescharacteristic
170#940C22×C311yescharacteristic
171D4×Dic3C22×C311yescharacteristic
172C2×#214C22×C311yescharacteristic
173C2×#204C22×C311yescharacteristic
174#890C22×C311yescharacteristic
175#889—21no—
176#889—21no—
177#888—21no—
178#888C22×C311yescharacteristic
179#887—21no—
180#887C22×C311yescharacteristic
181#887C22×C311yescharacteristic
182#886—21no—
183#885—21no—
184#883—21no—
185#67⋊C4—21no—
186C4×D12C22×C311yescharacteristic
187C4×Dic6C22×C311yescharacteristic
188C4×Dic6C22×C311yescharacteristic
189C3×#107—31no—
190C3×#106—31no—
191C3×#106—31no—
192C3×C4⋊C8—31no—
193C3×C4⋊C8—31no—
194C3×C4⋊C8—31no—
195C3×#103—21no—
196C3×#103—21no—
197C3×#103—31no—
198C3×#103—31no—
199C3×#103C2×D311yescharacteristic
200C3×#103C2×D311yescharacteristic
201C3×#103C22×C311yescharacteristic
202C3×#103C22×C311yescharacteristic
203C3×#102—21no—
204C3×#102—21no—
205C3×#102—31no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102—31no—
209C3×#102C2×D311yescharacteristic
210C3×#102C2×D311yescharacteristic
211C3×#102C22×C311yescharacteristic
212C3×#102C22×C311yescharacteristic
213C3×C4×C8—21no—
214C3×C4×C8—31no—
215C3×C4×C8—31no—
216C3×C4×C8C2×D311yescharacteristic
217C3×C4×C8C22×C311yescharacteristic
218#835C22×C311yescharacteristic
219#832C22×C311yescharacteristic
220#821C22×C311yescharacteristic
221#817C22×C311yescharacteristic
222#816C22×C311yescharacteristic
223Dic3⋊C8C22×C311yescharacteristic
224Dic3⋊C8C22×C311yescharacteristic
225C8×Dic3C22×C311yescharacteristic
226C8×Dic3C22×C311yescharacteristic
227#809C22×C311yescharacteristic
228#809C22×C311yescharacteristic
229#808C22×C311yescharacteristic
230#807C22×C311yescharacteristic
231C4⋊(C3⋊C8)C22×C311yescharacteristic
232C23×C32—21no—
233C22×C3×D3—21no—
234C32×Q8—21no—
235C32×Q8—21no—
236C32×D4—21no—
237C32×D4—21no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
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×Dic3—21no—
249C2×C3×Dic3—81no—
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C3×D12—21no—
255C3×D12—21no—
256C3×C4×D3—81no—
257C3×Dic6—21no—
258C3×Dic6—22no—
259C3×Dic6—42no—
260C3×Dic6#4112yes—
261C32×C8—21no—
262C32×C8—21no—
263C3×C3⋊C8—21no—
264C3×C3⋊C8—21no—
265#559—31no—
266#557—31no—
267#488—31no—
268#488C3×D311yescharacteristic, complemented
269#486—31no—
270#478—31no—
271#478—31no—
272#475—31no—
273#464—31no—
274#464—31no—
275#460—31no—
276C8×Q8—31no—
277C4×Q16—31no—
278C4×SD16—31no—
279C4×SD16—31no—
280C2×C3×Q8—21no—
281C2×C3×Q8—31no—
282C2×C3×Q8—31no—
283C2×C3×Q8—61no—
284C2×C3×Q8C22×D311yescharacteristic
285C2×C3×Q8C23×C311yescharacteristic
286C2×C3×D4—21no—
287C2×C3×D4—31no—
288C2×C3×D4—61no—
289C2×C3×D4—61no—
290C2×C3×D4C22×D311yescharacteristic
291C2×C3×D4C23×C311yescharacteristic
292C22×C3×C4—61no—
293C22×C3×C4—61no—
294C2×#67—21no—
295C2×#67—21no—
296C22×Dic3—21no—
297C2×D12C23×C311yescharacteristic
298C2×C4×D3—21no—
299C2×Dic6—21no—
300C2×Dic6C3×D411yescharacteristic
301C2×Dic6C23×C311yescharacteristic
302C3×Q16—62no—
303C3×SD16—62no—
304C3×SD16—62no—
305C2×C3×C8—21no—
306C2×C3×C8—21no—
307C2×C3×C8—31no—
308C2×C3×C8—31no—
309C2×C3×C8C22×D311yescharacteristic
310C2×C3×C8C22×D311yescharacteristic
311C2×C3×C8C23×C311yescharacteristic
312C2×C3×C8C23×C311yescharacteristic
313C3×C4⋊C4—21no—
314C3×C4⋊C4—21no—
315C3×C4⋊C4—21no—
316C3×C4⋊C4—21no—
317C3×C4⋊C4—21no—
318C3×C4⋊C4—21no—
319C3×C4⋊C4—31no—
320C3×C4⋊C4—31no—
321C3×C4⋊C4—31no—
322C3×C4⋊C4—31no—
323C3×C4⋊C4—31no—
324C3×C4⋊C4—41no—
325C3×C4⋊C4—41no—
326C3×C4⋊C4—61no—
327C3×C4⋊C4—61no—
328C3×C4⋊C4—61no—
329C3×C4⋊C4—61no—
330C3×C4⋊C4—61no—
331C3×C4⋊C4—61no—
332C3×C4⋊C4—61no—
333C3×C4⋊C4C22×D311yescharacteristic
334C3×C4⋊C4C22×D311yescharacteristic
335C3×C4⋊C4C23×C311yescharacteristic
336C3×C4⋊C4C23×C311yescharacteristic
337C3×C22⋊C4—21no—
338C3×C22⋊C4—21no—
339C3×C22⋊C4—21no—
340C3×C22⋊C4—21no—
341C3×C22⋊C4—41no—
342C3×C22⋊C4—41no—
343C3×C22⋊C4—61no—
344C3×C22⋊C4—61no—
345C3×C22⋊C4—61no—
346C3×C22⋊C4—61no—
347C3×C42—21no—
348C3×C42—31no—
349C3×C42—31no—
350C3×C42—61no—
351C3×C42—61no—
352C3×C42—61no—
353C3×C42—61no—
354C3×C42C22×D311yescharacteristic
355C3×C42C23×C311yescharacteristic
356#217—21no—
357#216—22no—
358#214—22no—
359(C2×D3)⋊C4—21no—
360(C2×D3)⋊C4—21no—
361(C2×D3)⋊C4—21no—
362C4⋊Dic3—21no—
363C4⋊Dic3—21no—
364C4⋊Dic3C3×D411yescharacteristic
365C4⋊Dic3C23×C311yescharacteristic
366C4⋊Dic3C23×C311yescharacteristic
367Dic3⋊C4—21no—
368Dic3⋊C4—21no—
369Dic3⋊C4—21no—
370Dic3⋊C4—21no—
371Dic3⋊C4—21no—
372Dic3⋊C4C3×D411yescharacteristic
373Dic3⋊C4C3×D411yescharacteristic
374C4×Dic3—21no—
375C4×Dic3—21no—
376C4×Dic3—21no—
377C4×Dic3—21no—
378C4×Dic3C23×C311yescharacteristic
379C4×Dic3C23×C311yescharacteristic
380C2×C3⋊C8C23×C311yescharacteristic
381C2×C3⋊C8C23×C311yescharacteristic
382#204—22no—
383C22×C32—41no—
384C22×C32—41no—
385C22×C32—41no—
386C22×C32C22×D411yescharacteristic
387C2×C3×D3—41no—
388C2×C3×D3—41no—
389C2×C3×D3—41no—
390C32×C4—21no—
391C32×C4—21no—
392C32×C4—41no—
393C32×C4—41no—
394C32×C4—41no—
395C32×C4C2×#4111yescharacteristic
396C32×C42−1+411yescharacteristic
397C3×Dic3—22no—
398C3×Dic3—21no—
399C3×Dic3—21no—
400C3×Dic3—21no—
401C3×Dic3—41no—
402C3×Dic3—41no—
403C3×Dic3#13512yes—
404C2×Q16—31no—
405C2×SD16—31no—
406C2×SD16—31no—
407C4⋊Q8—31no—
408C4⋊Q8—61no—
409#127—31no—
410#125—31no—
411#125—61no—
412#125—61no—
413#125C2×C3×D311yescharacteristic
414#124—31no—
415#124—61no—
416#124C2×C3×D311yescharacteristic
417#123—61no—
418#123—61no—
419C4×Q8—31no—
420C4×Q8—31no—
421C4×Q8—31no—
422C4×Q8—31no—
423C4×Q8—31no—
424C4×Q8—61no—
425C4×D4—31no—
426C4×D4—31no—
427C4×D4—61no—
428#107—31no—
429#106—31no—
430#106—31no—
431C4⋊C8—31no—
432C4⋊C8—31no—
433C4⋊C8—31no—
434#103—31no—
435#103—31no—
436#103C2×C3×D311yescharacteristic
437#103C2×C3×D311yescharacteristic
438#102—31no—
439#102—31no—
440#102—31no—
441#102—31no—
442#102C2×C3×D311yescharacteristic
443#102C2×C3×D311yescharacteristic
444C4×C8—31no—
445C4×C8—31no—
446C4×C8C2×C3×D311yescharacteristic
447C23×C3—21no—
448C23×C3—21no—
449C23×C3—41no—
450C23×C3—61no—
451C22×D3—21no—
452C3×Q8—21no—
453C3×Q8—21no—
454C3×Q8—21no—
455C3×Q8—21no—
456C3×Q8—32no—
457C3×Q8—41no—
458C3×Q8—41no—
459C3×Q8—62no—
460C3×Q8—61no—
461C3×Q8—122no—
462C3×D4—21no—
463C3×D4—21no—
464C3×D4—21no—
465C3×D4—21no—
466C3×D4—41no—
467C3×D4—41no—
468C3×D4—61no—
469C3×D4—61no—
470C3×D4—122no—
471C3×D4—241no—
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—31no—
482C2×C3×C4—31no—
483C2×C3×C4—31no—
484C2×C3×C4—31no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—61no—
489C2×C3×C4—61no—
490C2×C3×C4—61no—
491C2×C3×C4—241no—
492C2×C3×C4—241no—
493C2×C3×C4D3×D411yescharacteristic
494C2×C3×C4D3×D411yescharacteristic
495C2×C3×C4C2×C3×D411yescharacteristic
496C2×C3×C4C2×C3×D411yescharacteristic
497C2×C3×C4C23×D311yescharacteristic
498C2×C3×C4C24×C311yescharacteristic
499#67—42no—
500#67—81no—
501C2×Dic3—21no—
502C2×Dic3—21no—
503C2×Dic3—21no—
504C2×Dic3—81no—
505C2×Dic3C2×C3×D411yescharacteristic
506C2×Dic3C2×C3×D411yescharacteristic
507C2×Dic3C2×C3×D411yescharacteristic
508C2×Dic3C2×C3×D411yescharacteristic
509D12—21no—
510D12—21no—
511C4×D3—81no—
512Dic6—21no—
513Dic6—22no—
514Dic6—42no—
515Dic6C3×#4112yes—
516C3×C8—21no—
517C3×C8—21no—
518C3×C8—21no—
519C3×C8—21no—
520C3×C8—41no—
521C3×C8—41no—
522C3×C8—61no—
523C3×C8—61no—
524C3⋊C8—21no—
525C3⋊C8—21no—
526C2×C32—81no—
527C2×C32#54811yescharacteristic
528C2×C32C2×#13511yescharacteristic
529C2×C32#57711yescharacteristic
530C3×D3—81no—
531C2×Q8—31no—
532C2×Q8—31no—
533C2×Q8—61no—
534C2×Q8C22×C3×D311yescharacteristic
535C2×D4—31no—
536C2×D4—61no—
537C2×D4—61no—
538C2×D4C22×C3×D311yescharacteristic
539C22×C4—61no—
540C22×C4—61no—
541Q16—62no—
542SD16—62no—
543SD16—62no—
544C2×C8—31no—
545C2×C8—31no—
546C2×C8C22×C3×D311yescharacteristic
547C2×C8C22×C3×D311yescharacteristic
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—31no—
551C4⋊C4—31no—
552C4⋊C4—31no—
553C4⋊C4—31no—
554C4⋊C4—31no—
555C4⋊C4—61no—
556C4⋊C4—61no—
557C4⋊C4—61no—
558C4⋊C4—61no—
559C4⋊C4—61no—
560C4⋊C4—61no—
561C4⋊C4—61no—
562C4⋊C4C22×C3×D311yescharacteristic
563C4⋊C4C22×C3×D311yescharacteristic
564C22⋊C4—21no—
565C22⋊C4—21no—
566C22⋊C4—61no—
567C22⋊C4—61no—
568C22⋊C4—61no—
569C22⋊C4—61no—
570C42—31no—
571C42—31no—
572C42—61no—
573C42—61no—
574C42—61no—
575C42—61no—
576C42C22×C3×D311yescharacteristic
577C22×C3—21no—
578C22×C3—41no—
579C22×C3—41no—
580C22×C3—41no—
581C22×C3—41no—
582C22×C3—41no—
583C22×C3—41no—
584C22×C3—81no—
585C22×C3—81no—
586C22×C3—81no—
587C22×C3—121no—
588C22×C3—121no—
589C22×C3—121no—
590C22×C3C2×D3×D411yescharacteristic
591C22×C3C22×C3×D411yescharacteristic
592C2×D3—41no—
593C2×D3—41no—
594C2×D3—41no—
595C3×C4—21no—
596C3×C4—21no—
597C3×C4—21no—
598C3×C4—21no—
599C3×C4—21no—
600C3×C4—21no—
601C3×C4—32no—
602C3×C4—41no—
603C3×C4—41no—
604C3×C4—41no—
605C3×C4—41no—
606C3×C4—41no—
607C3×C4—41no—
608C3×C4—41no—
609C3×C4—41no—
610C3×C4—62no—
611C3×C4—61no—
612C3×C4—61no—
613C3×C4—61no—
614C3×C4—81no—
615C3×C4—81no—
616C3×C4—81no—
617C3×C4—121no—
618C3×C4—121no—
619C3×C4D3×#4111yescharacteristic
620C3×C4#101011yescharacteristic
621C3×C4C2×C3×#4111yescharacteristic
622C3×C4C3×2−1+411yescharacteristic
623Dic3—21no—
624Dic3—21no—
625Dic3—21no—
626Dic3—22no—
627Dic3—41no—
628Dic3—41no—
629Dic3C3×#13512yes—
630C32#336511yescharacteristic, complemented, Sylow
631C23—21no—
632C23—61no—
633Q8—21no—
634Q8—21no—
635Q8—32no—
636Q8—62no—
637Q8—61no—
638Q8—122no—
639D4—21no—
640D4—21no—
641D4—61no—
642D4—61no—
643D4—122no—
644D4—241no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—31no—
649C2×C4—31no—
650C2×C4—31no—
651C2×C4—31no—
652C2×C4—61no—
653C2×C4—61no—
654C2×C4—61no—
655C2×C4—241no—
656C2×C4—241no—
657C2×C4C3×D3×D411yescharacteristic
658C2×C4C3×D3×D411yescharacteristic
659C2×C4C23×C3×D311yescharacteristic
660C8—21no—
661C8—21no—
662C8—61no—
663C8—61no—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—21no—
667C2×C3—81no—
668C2×C3—81no—
669C2×C3—161no—
670C2×C3—241no—
671C2×C3#567711yescharacteristic
672C2×C3D3×#13511yescharacteristic
673C2×C3#577011yescharacteristic
674C2×C3C3×#54811yescharacteristic
675C2×C3C2×C3×#13511yescharacteristic
676C2×C3C3×#57711yescharacteristic
677D3—81no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—121no—
682C22—121no—
683C22—121no—
684C22C2×C3×D3×D411yescharacteristic
685C4—21no—
686C4—21no—
687C4—32no—
688C4—41no—
689C4—41no—
690C4—41no—
691C4—61no—
692C4—61no—
693C4—61no—
694C4—62no—
695C4—121no—
696C4—121no—
697C4C3×D3×#4111yescharacteristic
698C4C3×#101011yescharacteristic
699C3—21no—
700C3#8163511yescharacteristic, direct product factor
701C3C3×#336511yescharacteristic, complemented
702C2—81no—
703C2—241no—
704C2C3×#567711yescharacteristic
705C2C3×D3×#13511yescharacteristic
706C2C3×#577011yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#488C2
socleC22×C32C22×D4
prime radicalC3×#940C22
hypercenterC3×#488D3
hypocenterC3C3×#3365
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#488

Complements

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

NH ≅ G/Ntype
1. C3×#5685C2semidirect
3. C32×#488C2semidirect
4. C3×#5066C2semidirect
5. C3×#5054C2semidirect
6. C3×#4800C2semidirect
7. C3×#4798C2semidirect
8. C3×#4791C2semidirect
9. C3×#4790C2semidirect
10. C3×#4763C2semidirect
13. C3×#4758C2semidirect
14. C3×C4×#204C2semidirect
15. C3×C8×Dic6C2semidirect
17. #81635C3direct (N × H)
63. #5685C2×C3semidirect
67. C3×#488D3semidirect
68. C3×#488C2×C3semidirect
80. #5066C2×C3semidirect
81. #5054C2×C3semidirect
82. #4800C2×C3semidirect
83. #4798C2×C3semidirect
84. #4791C2×C3semidirect
85. #4790C2×C3semidirect
86. #4763C2×C3semidirect
89. #4758C2×C3semidirect
90. C4×#204C2×C3semidirect
91. C8×Dic6C2×C3semidirect
268. #488C3×D3semidirect
630. C32#3365semidirect
700. C3#81635direct (N × H)
701. C3C3×#3365semidirect

Maximal subgroups

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

subgroupindex
C3×#56852
C3×#56812
C32×#4882
C3×#50662
C3×#50542
C3×#48002
C3×#47982
C3×#47912
C3×#47902
C3×#47632
C3×#47622
C3×#47602
C3×#47582
C3×C4×#2042
C3×C8×Dic62
C3×#33653
#816353