Finite Group Databasebeta

← C3×#81151 #11895631

Subgroups — C3×#81151 #11895631

Order 1152.

747 conjugacy classes of subgroups.

The subgroup lattice has 707 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5685C211yesmaximal, characteristic, complemented
2C3×#5559C211yesmaximal, characteristic
3C32×#478C211yesmaximal, characteristic, complemented
4C3×#5068C211yesmaximal, characteristic, complemented
5C3×C4×#214C211yesmaximal, characteristic, complemented
6C3×#4891C211yesmaximal, characteristic, complemented
7C3×#4873C211yesmaximal, characteristic, complemented
8C3×#4854C211yesmaximal, characteristic, complemented
9C3×#4852C211yesmaximal, characteristic, complemented
10C3×#4845C211yesmaximal, characteristic, complemented
11C3×#4830C211yesmaximal, characteristic, complemented
12C3×#4768C211yesmaximal, characteristic, complemented
13C3×#4767C211yesmaximal, characteristic, complemented
14C3×#4762C211yesmaximal, characteristic
15C3×#4760C211yesmaximal, characteristic
16C3×#3365—31nomaximal
17#81151C311yesmaximal, characteristic, direct product factor
18C32×#125C2211yescharacteristic
19C32×C4×D4C2211yescharacteristic
20C3×#940C2211yescharacteristic
21C3×#936C2211yescharacteristic
22C2×C3×#214C2211yescharacteristic
23C3×#929—21no—
24C3×C4×#67—21no—
25C2×C3×Dic12C2211yescharacteristic
26C2×C3×#204C2211yescharacteristic
27C3×#893C2211yescharacteristic
28C3×#890C2211yescharacteristic
29C3×#889—21no—
30C3×#889—21no—
31C3×#888—21no—
32C3×#888C2211yescharacteristic
33C3×#887—21no—
34C3×#887C2211yescharacteristic
35C3×#887C2211yescharacteristic
36C3×#887C2211yescharacteristic
37C3×#885—21no—
38C3×#883—21no—
39C3×#875C2211yescharacteristic
40C3×C4×Dic6C2211yescharacteristic
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×#810C2211yescharacteristic
57C3×#809C2211yescharacteristic
58C3×#809C2211yescharacteristic
59C3×#808C2211yescharacteristic
60C3×C4×C3⋊C8C2211yescharacteristic
61C3×#559—31no—
62C3×#557—31no—
63#5685C2×C311yescharacteristic, complemented
64#5559C2×C311yescharacteristic
65C3×#488—31no—
66C3×#488—31no—
67C3×#486—31no—
68C3×#478—21no—
69C3×#478—31no—
70C3×#478D311yescharacteristic, complemented
71C3×#478C2×C311yescharacteristic, complemented
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#5068C2×C311yescharacteristic, complemented
81C4×#214C2×C311yescharacteristic, complemented
82#4891C2×C311yescharacteristic, complemented
83#4873C2×C311yescharacteristic, complemented
84#4854C2×C311yescharacteristic, complemented
85#4852C2×C311yescharacteristic, complemented
86#4845C2×C311yescharacteristic, complemented
87#4830C2×C311yescharacteristic, complemented
88#4768C2×C311yescharacteristic, complemented
89#4767C2×C311yescharacteristic, complemented
90#4762C2×C311yescharacteristic
91#4760C2×C311yescharacteristic
92C2×C32×D4C2311yescharacteristic
93C22×C32×C4—21no—
94C2×C3×#67—21no—
95C2×C3×#67—21no—
96C2×C3×D12C2311yescharacteristic
97C2×C3×C4×D3—21no—
98C2×C3×Dic6—21no—
99C2×C3×Dic6D411yescharacteristic
100C2×C3×Dic6C2311yescharacteristic
101C2×C3×Dic6C2311yescharacteristic
102C2×C32×C8C2311yescharacteristic
103C2×C32×C8C2311yescharacteristic
104C32×C4⋊C4—21no—
105C32×C4⋊C4—21no—
106C32×C4⋊C4C2311yescharacteristic
107C32×C4⋊C4C2311yescharacteristic
108C32×C4⋊C4C2311yescharacteristic
109C32×C22⋊C4—21no—
110C32×C42C2311yescharacteristic
111C3×#217—21no—
112C3×#217—21no—
113C3×#214—22no—
114C3×(C2×D3)⋊C4—21no—
115C3×(C2×D3)⋊C4—21no—
116C3×(C2×D3)⋊C4—21no—
117C3×C4⋊Dic3—21no—
118C3×C4⋊Dic3D411yescharacteristic
119C3×C4⋊Dic3C2311yescharacteristic
120C3×Dic3⋊C4—21no—
121C3×Dic3⋊C4—21no—
122C3×Dic3⋊C4—21no—
123C3×Dic3⋊C4—21no—
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4D411yescharacteristic
127C3×Dic3⋊C4D411yescharacteristic
128C3×C4×Dic3—21no—
129C3×C4×Dic3—21no—
130C3×C4×Dic3—21no—
131C3×C4×Dic3—21no—
132C3×C4×Dic3C2311yescharacteristic
133C3×C4×Dic3C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C3×Dic12—22no—
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—31no—
152C3×#124—31no—
153C3×#124—61no—
154C3×#123—61no—
155C3×#123—61no—
156C3×C4×Q8—31no—
157C3×C4×Q8—31no—
158C3×C4×Q8—31no—
159C3×C4×Q8—31no—
160C3×C4×Q8—31no—
161C3×C4×Q8—61no—
162C3×C4×D4—21no—
163C3×C4×D4—31no—
164C3×C4×D4—61no—
165C3×C4×D4C2×D311yescharacteristic
166C3×C4×D4C22×C311yescharacteristic
167#940C22×C311yescharacteristic
168#936C22×C311yescharacteristic
169C2×#214C22×C311yescharacteristic
170#929—21no—
171C4×#67—21no—
172C2×Dic12C22×C311yescharacteristic
173C2×#204C22×C311yescharacteristic
174#893C22×C311yescharacteristic
175#890C22×C311yescharacteristic
176#889—21no—
177#889—21no—
178#888—21no—
179#888C22×C311yescharacteristic
180#887—21no—
181#887C22×C311yescharacteristic
182#887C22×C311yescharacteristic
183#887C22×C311yescharacteristic
184#885—21no—
185#883—21no—
186#875C22×C311yescharacteristic
187C4×Dic6C22×C311yescharacteristic
188C4×Dic6C22×C311yescharacteristic
189C3×#107—21no—
190C3×#107C2×D311yescharacteristic
191C3×#107C22×C311yescharacteristic
192C3×#106—21no—
193C3×#106—31no—
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×#103—31no—
205C3×#102—21no—
206C3×#102—21no—
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#810C22×C311yescharacteristic
228#809C22×C311yescharacteristic
229#809C22×C311yescharacteristic
230#808C22×C311yescharacteristic
231C4×C3⋊C8C22×C311yescharacteristic
232C23×C32—21no—
233C22×C3×D3—21no—
234C32×D4—21no—
235C32×D4—21no—
236C2×C32×C4—21no—
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4—81no—
240C2×C32×C4C2×D411yescharacteristic
241C2×C32×C4C2×D411yescharacteristic
242C2×C32×C4C2411yescharacteristic
243C3×#67—42no—
244C3×#67—81no—
245C2×C3×Dic3—21no—
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×C4×D3—81no—
255C3×Dic6—21no—
256C3×Dic6—22no—
257C3×Dic6—21no—
258C3×Dic6—21no—
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#488—31no—
269#486—31no—
270#478—31no—
271#478C3×D311yescharacteristic, complemented
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—31no—
281C2×C3×Q8—31no—
282C2×C3×Q8—31no—
283C2×C3×Q8—61no—
284C2×C3×D4—21no—
285C2×C3×D4—31no—
286C2×C3×D4—61no—
287C2×C3×D4—61no—
288C2×C3×D4C22×D311yescharacteristic
289C2×C3×D4C23×C311yescharacteristic
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—41no—
293C22×C3×C4—61no—
294C2×#67—21no—
295C2×#67—21no—
296C2×D12C23×C311yescharacteristic
297C2×C4×D3—21no—
298C2×Dic6—21no—
299C2×Dic6C3×D411yescharacteristic
300C2×Dic6C23×C311yescharacteristic
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—21no—
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⋊C4C22×D311yescharacteristic
336C3×C4⋊C4C23×C311yescharacteristic
337C3×C4⋊C4C23×C311yescharacteristic
338C3×C4⋊C4C23×C311yescharacteristic
339C3×C22⋊C4—21no—
340C3×C22⋊C4—21no—
341C3×C22⋊C4—41no—
342C3×C22⋊C4—61no—
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#217—21no—
358#214—22no—
359(C2×D3)⋊C4—21no—
360(C2×D3)⋊C4—21no—
361(C2×D3)⋊C4—21no—
362C4⋊Dic3—21no—
363C4⋊Dic3C3×D411yescharacteristic
364C4⋊Dic3C23×C311yescharacteristic
365Dic3⋊C4—21no—
366Dic3⋊C4—21no—
367Dic3⋊C4—21no—
368Dic3⋊C4—21no—
369Dic3⋊C4—21no—
370Dic3⋊C4—21no—
371Dic3⋊C4C3×D411yescharacteristic
372Dic3⋊C4C3×D411yescharacteristic
373C4×Dic3—21no—
374C4×Dic3—21no—
375C4×Dic3—21no—
376C4×Dic3—21no—
377C4×Dic3C23×C311yescharacteristic
378C4×Dic3C23×C311yescharacteristic
379C2×C3⋊C8C23×C311yescharacteristic
380C2×C3⋊C8C23×C311yescharacteristic
381Dic12—22no—
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—31no—
416#124—61no—
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—61no—
427C4×D4C2×C3×D311yescharacteristic
428#107C2×C3×D311yescharacteristic
429#106—31no—
430#106C2×C3×D311yescharacteristic
431C4⋊C8—31no—
432C4⋊C8—31no—
433C4⋊C8C2×C3×D311yescharacteristic
434#103—31no—
435#103—31no—
436#103—31no—
437#103—31no—
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×C8—31no—
447C23×C3—21no—
448C23×C3—21no—
449C23×C3—41no—
450C23×C3—61no—
451C22×D3—21no—
452C3×Q8—32no—
453C3×Q8—62no—
454C3×Q8—61no—
455C3×Q8—61no—
456C3×Q8—61no—
457C3×Q8—122no—
458C3×D4—22no—
459C3×D4—21no—
460C3×D4—21no—
461C3×D4—21no—
462C3×D4—21no—
463C3×D4—41no—
464C3×D4—61no—
465C3×D4—61no—
466C3×D4—122no—
467C3×D4—241no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
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—31no—
478C2×C3×C4—31no—
479C2×C3×C4—31no—
480C2×C3×C4—31no—
481C2×C3×C4—41no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4—61no—
485C2×C3×C4—61no—
486C2×C3×C4—61no—
487C2×C3×C4—81no—
488C2×C3×C4—81no—
489C2×C3×C4—82no—
490C2×C3×C4—241no—
491C2×C3×C4D3×D411yescharacteristic
492C2×C3×C4D3×D411yescharacteristic
493C2×C3×C4C2×C3×D411yescharacteristic
494C2×C3×C4C2×C3×D411yescharacteristic
495C2×C3×C4C23×D311yescharacteristic
496C2×C3×C4C24×C311yescharacteristic
497#67—42no—
498#67—81no—
499C2×Dic3—21no—
500C2×Dic3—21no—
501C2×Dic3—21no—
502C2×Dic3C2×C3×D411yescharacteristic
503C2×Dic3C2×C3×D411yescharacteristic
504C2×Dic3C2×C3×D411yescharacteristic
505C2×Dic3C2×C3×D411yescharacteristic
506D12—21no—
507D12—21no—
508C4×D3—81no—
509Dic6—21no—
510Dic6—22no—
511Dic6—21no—
512Dic6—21no—
513Dic6—42no—
514Dic6C3×#4112yes—
515C3×C8—21no—
516C3×C8—21no—
517C3×C8—21no—
518C3×C8—21no—
519C3×C8—41no—
520C3×C8—41no—
521C3×C8—61no—
522C3×C8—61no—
523C3⋊C8—21no—
524C3⋊C8—21no—
525C2×C32—81no—
526C2×C32#54811yescharacteristic
527C2×C32C2×#13511yescharacteristic
528C2×C32#57711yescharacteristic
529C3×D3—81no—
530C2×Q8—31no—
531C2×Q8—31no—
532C2×Q8—31no—
533C2×Q8—61no—
534C2×D4—31no—
535C2×D4—61no—
536C2×D4—61no—
537C2×D4C22×C3×D311yescharacteristic
538C22×C4—21no—
539C22×C4—61no—
540Q16—62no—
541SD16—62no—
542SD16—62no—
543C2×C8—31no—
544C2×C8—31no—
545C2×C8C22×C3×D311yescharacteristic
546C2×C8C22×C3×D311yescharacteristic
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—31no—
550C4⋊C4—31no—
551C4⋊C4—31no—
552C4⋊C4—31no—
553C4⋊C4—61no—
554C4⋊C4—61no—
555C4⋊C4—61no—
556C4⋊C4—61no—
557C4⋊C4—61no—
558C4⋊C4—61no—
559C4⋊C4—61no—
560C4⋊C4C22×C3×D311yescharacteristic
561C4⋊C4C22×C3×D311yescharacteristic
562C4⋊C4C22×C3×D311yescharacteristic
563C22⋊C4—21no—
564C22⋊C4—61no—
565C22⋊C4—61no—
566C22⋊C4—61no—
567C22⋊C4—61no—
568C22⋊C4—61no—
569C42—31no—
570C42—31no—
571C42—61no—
572C42—61no—
573C42—61no—
574C42—61no—
575C42C22×C3×D311yescharacteristic
576C22×C3—21no—
577C22×C3—42no—
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—121no—
587C22×C3—121no—
588C22×C3—121no—
589C22×C3C2×D3×D411yescharacteristic
590C22×C3C22×C3×D411yescharacteristic
591C2×D3—41no—
592C2×D3—41no—
593C2×D3—41no—
594C3×C4—21no—
595C3×C4—21no—
596C3×C4—21no—
597C3×C4—21no—
598C3×C4—21no—
599C3×C4—21no—
600C3×C4—32no—
601C3×C4—41no—
602C3×C4—41no—
603C3×C4—41no—
604C3×C4—41no—
605C3×C4—41no—
606C3×C4—41no—
607C3×C4—41no—
608C3×C4—41no—
609C3×C4—62no—
610C3×C4—61no—
611C3×C4—61no—
612C3×C4—61no—
613C3×C4—81no—
614C3×C4—81no—
615C3×C4—81no—
616C3×C4—121no—
617C3×C4—121no—
618C3×C4#100711yescharacteristic
619C3×C4D3×#4111yescharacteristic
620C3×C4C2×C3×#4111yescharacteristic
621C3×C4C3×2−1+411yescharacteristic
622Dic3—21no—
623Dic3—21no—
624Dic3—21no—
625Dic3—22no—
626Dic3—41no—
627Dic3—41no—
628Dic3C3×#13512yes—
629C32#336511yescharacteristic, complemented, Sylow
630C23—21no—
631C23—61no—
632Q8—32no—
633Q8—62no—
634Q8—61no—
635Q8—61no—
636Q8—61no—
637Q8—122no—
638D4—21no—
639D4—21no—
640D4—61no—
641D4—61no—
642D4—122no—
643D4—241no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—31no—
648C2×C4—31no—
649C2×C4—31no—
650C2×C4—31no—
651C2×C4—61no—
652C2×C4—61no—
653C2×C4—61no—
654C2×C4—81no—
655C2×C4—241no—
656C2×C4C3×D3×D411yescharacteristic
657C2×C4C3×D3×D411yescharacteristic
658C2×C4C23×C3×D311yescharacteristic
659C8—21no—
660C8—21no—
661C8—61no—
662C8—61no—
663C2×C3—21no—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—82no—
667C2×C3—81no—
668C2×C3—81no—
669C2×C3—241no—
670C2×C3#563311yescharacteristic
671C2×C3D3×#13511yescharacteristic
672C2×C3#577511yescharacteristic
673C2×C3C3×#54811yescharacteristic
674C2×C3C2×C3×#13511yescharacteristic
675C2×C3C3×#57711yescharacteristic
676D3—81no—
677C22—41no—
678C22—41no—
679C22—41no—
680C22—121no—
681C22—121no—
682C22—121no—
683C22C2×C3×D3×D411yescharacteristic
684C4—21no—
685C4—21no—
686C4—32no—
687C4—41no—
688C4—41no—
689C4—41no—
690C4—61no—
691C4—61no—
692C4—61no—
693C4—62no—
694C4—121no—
695C4—121no—
696C4C3×#100711yescharacteristic
697C4C3×D3×#4111yescharacteristic
698C3—21no—
699C3#8115111yescharacteristic, direct product factor
700C3C3×#336511yescharacteristic, complemented
701C2—81no—
702C2—241no—
703C2C3×#563311yescharacteristic
704C2C3×D3×#13511yescharacteristic
705C2C3×#577511yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#478C2
socleC22×C32C22×D4
prime radicalC3×#940C22
hypercenterC3×#478D3
hypocenterC3C3×#3365
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×#5685C2semidirect
3. C32×#478C2semidirect
4. C3×#5068C2semidirect
5. C3×C4×#214C2semidirect
6. C3×#4891C2semidirect
7. C3×#4873C2semidirect
8. C3×#4854C2semidirect
9. C3×#4852C2semidirect
10. C3×#4845C2semidirect
11. C3×#4830C2semidirect
12. C3×#4768C2semidirect
13. C3×#4767C2semidirect
17. #81151C3direct (N × H)
63. #5685C2×C3semidirect
70. C3×#478D3semidirect
71. C3×#478C2×C3semidirect
80. #5068C2×C3semidirect
81. C4×#214C2×C3semidirect
82. #4891C2×C3semidirect
83. #4873C2×C3semidirect
84. #4854C2×C3semidirect
85. #4852C2×C3semidirect
86. #4845C2×C3semidirect
87. #4830C2×C3semidirect
88. #4768C2×C3semidirect
89. #4767C2×C3semidirect
271. #478C3×D3semidirect
629. C32#3365semidirect
699. C3#81151direct (N × H)
700. 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×#55592
C32×#4782
C3×#50682
C3×C4×#2142
C3×#48912
C3×#48732
C3×#48542
C3×#48522
C3×#48452
C3×#48302
C3×#47682
C3×#47672
C3×#47622
C3×#47602
C3×#33653
#811513