Finite Group Databasebeta

← C3×#81673 #11896284

Subgroups — C3×#81673 #11896284

Order 1152.

738 conjugacy classes of subgroups.

The subgroup lattice has 709 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5721C211yesmaximal, characteristic, complemented
2C3×#5681C211yesmaximal, characteristic
3C32×#489C211yesmaximal, characteristic, complemented
4C3×#5084C211yesmaximal, characteristic, complemented
5C3×#5054C211yesmaximal, characteristic, complemented
6C3×#4800C211yesmaximal, characteristic, complemented
7C3×#4798C211yesmaximal, characteristic, complemented
8C3×#4796C211yesmaximal, characteristic, complemented
9C3×#4789C211yesmaximal, characteristic, complemented
10C3×#4766C211yesmaximal, characteristic, complemented
11C3×#4764C211yesmaximal, characteristic
12C3×#4762C211yesmaximal, characteristic
13C3×#4758C211yesmaximal, characteristic, complemented
14C3×#4710C211yesmaximal, characteristic, complemented
15C3×#4701C211yesmaximal, characteristic, complemented
16C3×#3371—31nomaximal
17#81673C311yesmaximal, characteristic, direct product factor
18C32×C4⋊Q8C2211yescharacteristic
19C32×#124C2211yescharacteristic
20C3×#947C2211yescharacteristic
21C3×Q8×Dic3—21no—
22C3×Q8×Dic3C2211yescharacteristic
23C3×#944—21no—
24C2×C3×#216C2211yescharacteristic
25C3×#940C2211yescharacteristic
26C3×D4×Dic3C2211yescharacteristic
27C2×C3×#214C2211yescharacteristic
28C2×C3×#204C2211yescharacteristic
29C3×#890C2211yescharacteristic
30C3×#890C2211yescharacteristic
31C3×#889—21no—
32C3×#889—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×#97C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#818C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#815C2211yescharacteristic
53C3×Dic3⋊C8C2211yescharacteristic
54C3×Dic3⋊C8C2211yescharacteristic
55C3×C8×Dic3C2211yescharacteristic
56C3×#809C2211yescharacteristic
57C3×#809C2211yescharacteristic
58C3×#808C2211yescharacteristic
59C3×#808C2211yescharacteristic
60C3×C4⋊(C3⋊C8)C2211yescharacteristic
61C3×#559—31no—
62C3×#557—31no—
63#5721C2×C311yescharacteristic, complemented
64#5681C2×C311yescharacteristic
65C3×#490—31no—
66C3×#489—21no—
67C3×#489D311yescharacteristic, complemented
68C3×#489C2×C311yescharacteristic, complemented
69C3×#488—31no—
70C3×#479—31no—
71C3×#478—31no—
72C3×#476—31no—
73C3×#464—31no—
74C3×#464—31no—
75C3×#460—31no—
76C3×#446—31no—
77C3×#441—31no—
78C3×#440—31no—
79C3×C4×SD16—31no—
80#5084C2×C311yescharacteristic, complemented
81#5054C2×C311yescharacteristic, complemented
82#4800C2×C311yescharacteristic, complemented
83#4798C2×C311yescharacteristic, complemented
84#4796C2×C311yescharacteristic, complemented
85#4789C2×C311yescharacteristic, complemented
86#4766C2×C311yescharacteristic, complemented
87#4764C2×C311yescharacteristic
88#4762C2×C311yescharacteristic
89#4758C2×C311yescharacteristic, complemented
90#4710C2×C311yescharacteristic, complemented
91#4701C2×C311yescharacteristic, complemented
92C2×C32×Q8—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C2×C3×#67—21no—
96C2×C3×#67—21no—
97C22×C3×Dic3—21no—
98C2×C3×D12C2311yescharacteristic
99C2×C3×C4×D3—21no—
100C2×C3×Dic6D411yescharacteristic
101C2×C3×Dic6C2311yescharacteristic
102C2×C32×C8C2311yescharacteristic
103C2×C32×C8C2311yescharacteristic
104C32×C4⋊C4—21no—
105C32×C4⋊C4C2311yescharacteristic
106C32×C4⋊C4C2311yescharacteristic
107C32×C22⋊C4—21no—
108C32×C22⋊C4—21no—
109C32×C42C2311yescharacteristic
110C3×#217—21no—
111C3×#216—22no—
112C3×#214—22no—
113C3×(C2×D3)⋊C4—21no—
114C3×(C2×D3)⋊C4—21no—
115C3×(C2×D3)⋊C4—21no—
116C3×C4⋊Dic3—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#3371—31noSylow
139C2×C3×Q16—31no—
140C2×C3×SD16—31no—
141C2×C3×SD16—31no—
142C3×C4⋊Q8—21no—
143C3×C4⋊Q8—61no—
144C3×C4⋊Q8C2×D311yescharacteristic
145C3×C4⋊Q8C22×C311yescharacteristic
146C3×#127—31no—
147C3×#125—31no—
148C3×#125—31no—
149C3×#125—61no—
150C3×#125—61no—
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×Dic3—21no—
169Q8×Dic3C22×C311yescharacteristic
170#944—21no—
171C2×#216C22×C311yescharacteristic
172#940C22×C311yescharacteristic
173D4×Dic3C22×C311yescharacteristic
174C2×#214C22×C311yescharacteristic
175C2×#204C22×C311yescharacteristic
176#890C22×C311yescharacteristic
177#890C22×C311yescharacteristic
178#889—21no—
179#889—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×#97—21no—
214C3×#97—31no—
215C3×#97C2×D311yescharacteristic
216C3×#97C22×C311yescharacteristic
217C3×C4×C8—31no—
218#835C22×C311yescharacteristic
219#832C22×C311yescharacteristic
220#821C22×C311yescharacteristic
221#818C22×C311yescharacteristic
222#816C22×C311yescharacteristic
223#815C22×C311yescharacteristic
224Dic3⋊C8C22×C311yescharacteristic
225Dic3⋊C8C22×C311yescharacteristic
226C8×Dic3C22×C311yescharacteristic
227#809C22×C311yescharacteristic
228#809C22×C311yescharacteristic
229#808C22×C311yescharacteristic
230#808C22×C311yescharacteristic
231C4⋊(C3⋊C8)C22×C311yescharacteristic
232C23×C32—21no—
233C22×C3×D3—21no—
234C32×Q8—21no—
235C32×Q8—21no—
236C32×Q8—42no—
237C32×D4—21no—
238C32×D4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4C2×D411yescharacteristic
243C2×C32×C4C2×D411yescharacteristic
244C2×C32×C4C2411yescharacteristic
245C3×#67—42no—
246C3×#67—81no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—81no—
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C3×D12—21no—
256C3×D12—21no—
257C3×C4×D3—81no—
258C3×Dic6—21no—
259C3×Dic6—41no—
260C3×Dic6#4112yes—
261C32×C8—21no—
262C32×C8—21no—
263C3×C3⋊C8—21no—
264C3×C3⋊C8—21no—
265#559—31no—
266#557—31no—
267#490—31no—
268#489C3×D311yescharacteristic, complemented
269#488—31no—
270#479—31no—
271#478—31no—
272#476—31no—
273#464—31no—
274#464—31no—
275#460—31no—
276#446—31no—
277#441—31no—
278#440—31no—
279C4×SD16—31no—
280C2×C3×Q8—21no—
281C2×C3×Q8—21no—
282C2×C3×Q8—21no—
283C2×C3×Q8—31no—
284C2×C3×Q8—31no—
285C2×C3×Q8—41no—
286C2×C3×Q8C22×D311yescharacteristic
287C2×C3×Q8C23×C311yescharacteristic
288C2×C3×D4—21no—
289C2×C3×D4—31no—
290C2×C3×D4—61no—
291C2×C3×D4—61no—
292C2×C3×D4C22×D311yescharacteristic
293C2×C3×D4C23×C311yescharacteristic
294C22×C3×C4—61no—
295C22×C3×C4—61no—
296C2×#67—21no—
297C2×#67—21no—
298C22×Dic3—21no—
299C2×D12C23×C311yescharacteristic
300C2×C4×D3—21no—
301C2×Dic6C3×D411yescharacteristic
302C2×Dic6C23×C311yescharacteristic
303C3×Q16—62no—
304C3×SD16—62no—
305C3×SD16—62no—
306C2×C3×C8—21no—
307C2×C3×C8—21no—
308C2×C3×C8—31no—
309C2×C3×C8—31no—
310C2×C3×C8C22×D311yescharacteristic
311C2×C3×C8C22×D311yescharacteristic
312C2×C3×C8C23×C311yescharacteristic
313C2×C3×C8C23×C311yescharacteristic
314C3×C4⋊C4—21no—
315C3×C4⋊C4—21no—
316C3×C4⋊C4—21no—
317C3×C4⋊C4—21no—
318C3×C4⋊C4—31no—
319C3×C4⋊C4—31no—
320C3×C4⋊C4—31no—
321C3×C4⋊C4—31no—
322C3×C4⋊C4—31no—
323C3×C4⋊C4—41no—
324C3×C4⋊C4—61no—
325C3×C4⋊C4—61no—
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⋊C4C22×D311yescharacteristic
333C3×C4⋊C4C22×D311yescharacteristic
334C3×C4⋊C4C23×C311yescharacteristic
335C3×C4⋊C4C23×C311yescharacteristic
336C3×C22⋊C4—21no—
337C3×C22⋊C4—21no—
338C3×C22⋊C4—21no—
339C3×C22⋊C4—21no—
340C3×C22⋊C4—41no—
341C3×C22⋊C4—41no—
342C3×C22⋊C4—61no—
343C3×C22⋊C4—61no—
344C3×C22⋊C4—61no—
345C3×C22⋊C4—61no—
346C3×C42—21no—
347C3×C42—31no—
348C3×C42—31no—
349C3×C42—61no—
350C3×C42—61no—
351C3×C42—61no—
352C3×C42—61no—
353C3×C42C22×D311yescharacteristic
354C3×C42C23×C311yescharacteristic
355#217—21no—
356#216—22no—
357#214—22no—
358(C2×D3)⋊C4—21no—
359(C2×D3)⋊C4—21no—
360(C2×D3)⋊C4—21no—
361C4⋊Dic3—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—21no—
402C3×Dic3—41no—
403C3×Dic3—41no—
404C2×Q16—31no—
405C2×SD16—31no—
406C2×SD16—31no—
407C4⋊Q8—61no—
408C4⋊Q8C2×C3×D311yescharacteristic
409#127—31no—
410#125—31no—
411#125—31no—
412#125—61no—
413#125—61no—
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
444#97—31no—
445#97C2×C3×D311yescharacteristic
446C4×C8—31no—
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—42no—
460C3×Q8—42no—
461C3×Q8—61no—
462C3×Q8—82no—
463C3×Q8—121no—
464C3×D4—21no—
465C3×D4—21no—
466C3×D4—21no—
467C3×D4—21no—
468C3×D4—41no—
469C3×D4—41no—
470C3×D4—61no—
471C3×D4—61no—
472C3×D4—122no—
473C3×D4—241no—
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—21no—
482C2×C3×C4—21no—
483C2×C3×C4—31no—
484C2×C3×C4—31no—
485C2×C3×C4—31no—
486C2×C3×C4—31no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—61no—
491C2×C3×C4—61no—
492C2×C3×C4—61no—
493C2×C3×C4—241no—
494C2×C3×C4—241no—
495C2×C3×C4D3×D411yescharacteristic
496C2×C3×C4D3×D411yescharacteristic
497C2×C3×C4C2×C3×D411yescharacteristic
498C2×C3×C4C2×C3×D411yescharacteristic
499C2×C3×C4C23×D311yescharacteristic
500C2×C3×C4C24×C311yescharacteristic
501#67—42no—
502#67—81no—
503C2×Dic3—21no—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—81no—
507C2×Dic3C2×C3×D411yescharacteristic
508C2×Dic3C2×C3×D411yescharacteristic
509C2×Dic3C2×C3×D411yescharacteristic
510C2×Dic3C2×C3×D411yescharacteristic
511D12—21no—
512D12—21no—
513C4×D3—81no—
514Dic6—21no—
515Dic6—41no—
516Dic6C3×#4112yes—
517C3×C8—21no—
518C3×C8—21no—
519C3×C8—21no—
520C3×C8—21no—
521C3×C8—41no—
522C3×C8—41no—
523C3×C8—61no—
524C3×C8—61no—
525C3⋊C8—21no—
526C3⋊C8—21no—
527C2×C32—81no—
528C2×C32#54811yescharacteristic
529C2×C32#57511yescharacteristic
530C2×C32#57711yescharacteristic
531C3×D3—81no—
532C2×Q8—21no—
533C2×Q8—31no—
534C2×Q8—31no—
535C2×Q8C22×C3×D311yescharacteristic
536C2×D4—31no—
537C2×D4—61no—
538C2×D4—61no—
539C2×D4C22×C3×D311yescharacteristic
540C22×C4—61no—
541C22×C4—61no—
542Q16—62no—
543SD16—62no—
544SD16—62no—
545C2×C8—31no—
546C2×C8—31no—
547C2×C8C22×C3×D311yescharacteristic
548C2×C8C22×C3×D311yescharacteristic
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⋊C4—61no—
563C4⋊C4C22×C3×D311yescharacteristic
564C4⋊C4C22×C3×D311yescharacteristic
565C22⋊C4—21no—
566C22⋊C4—21no—
567C22⋊C4—61no—
568C22⋊C4—61no—
569C22⋊C4—61no—
570C22⋊C4—61no—
571C42—31no—
572C42—31no—
573C42—61no—
574C42—61no—
575C42—61no—
576C42—61no—
577C42C22×C3×D311yescharacteristic
578C22×C3—21no—
579C22×C3—41no—
580C22×C3—41no—
581C22×C3—41no—
582C22×C3—41no—
583C22×C3—41no—
584C22×C3—41no—
585C22×C3—81no—
586C22×C3—81no—
587C22×C3—81no—
588C22×C3—121no—
589C22×C3—121no—
590C22×C3—121no—
591C22×C3C2×D3×D411yescharacteristic
592C22×C3C22×C3×D411yescharacteristic
593C2×D3—41no—
594C2×D3—41no—
595C2×D3—41no—
596C3×C4—21no—
597C3×C4—21no—
598C3×C4—21no—
599C3×C4—21no—
600C3×C4—21no—
601C3×C4—21no—
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—61no—
615C3×C4—81no—
616C3×C4—81no—
617C3×C4—81no—
618C3×C4—121no—
619C3×C4—121no—
620C3×C4D3×#4111yescharacteristic
621C3×C4#101011yescharacteristic
622C3×C4C2×C3×#4111yescharacteristic
623C3×C4C3×2−1+411yescharacteristic
624Dic3—21no—
625Dic3—21no—
626Dic3—21no—
627Dic3—21no—
628Dic3—22no—
629Dic3—41no—
630Dic3—41no—
631C32#337111yescharacteristic, complemented, Sylow
632C23—21no—
633C23—61no—
634Q8—21no—
635Q8—21no—
636Q8—32no—
637Q8—42no—
638Q8—61no—
639Q8—121no—
640D4—21no—
641D4—21no—
642D4—61no—
643D4—61no—
644D4—122no—
645D4—241no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—31no—
650C2×C4—31no—
651C2×C4—31no—
652C2×C4—31no—
653C2×C4—61no—
654C2×C4—61no—
655C2×C4—61no—
656C2×C4—241no—
657C2×C4—241no—
658C2×C4C3×D3×D411yescharacteristic
659C2×C4C3×D3×D411yescharacteristic
660C2×C4C23×C3×D311yescharacteristic
661C8—21no—
662C8—21no—
663C8—61no—
664C8—61no—
665C2×C3—21no—
666C2×C3—21no—
667C2×C3—21no—
668C2×C3—81no—
669C2×C3—81no—
670C2×C3—161no—
671C2×C3—241no—
672C2×C3#567711yescharacteristic
673C2×C3#577311yescharacteristic
674C2×C3#577811yescharacteristic
675C2×C3C3×#54811yescharacteristic
676C2×C3C3×#57511yescharacteristic
677C2×C3C3×#57711yescharacteristic
678D3—81no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—121no—
683C22—121no—
684C22—121no—
685C22C2×C3×D3×D411yescharacteristic
686C4—21no—
687C4—21no—
688C4—41no—
689C4—41no—
690C4—41no—
691C4—61no—
692C4—61no—
693C4—61no—
694C4—61no—
695C4—62no—
696C4—121no—
697C4—121no—
698C4C3×D3×#4111yescharacteristic
699C4C3×#101011yescharacteristic
700C3—21no—
701C3#8167311yescharacteristic, direct product factor
702C3C3×#337111yescharacteristic, complemented
703C2—81no—
704C2—241no—
705C2C3×#567711yescharacteristic
706C2C3×#577311yescharacteristic
707C2C3×#577811yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#489C2
socleC22×C32C22×D4
prime radicalC3×#940C22
hypercenterC3×#489D3
hypocenterC3C3×#3371
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#489

Complements

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

NH ≅ G/Ntype
1. C3×#5721C2semidirect
3. C32×#489C2semidirect
4. C3×#5084C2semidirect
5. C3×#5054C2semidirect
6. C3×#4800C2semidirect
7. C3×#4798C2semidirect
8. C3×#4796C2semidirect
9. C3×#4789C2semidirect
10. C3×#4766C2semidirect
13. C3×#4758C2semidirect
14. C3×#4710C2semidirect
15. C3×#4701C2semidirect
17. #81673C3direct (N × H)
63. #5721C2×C3semidirect
67. C3×#489D3semidirect
68. C3×#489C2×C3semidirect
80. #5084C2×C3semidirect
81. #5054C2×C3semidirect
82. #4800C2×C3semidirect
83. #4798C2×C3semidirect
84. #4796C2×C3semidirect
85. #4789C2×C3semidirect
86. #4766C2×C3semidirect
89. #4758C2×C3semidirect
90. #4710C2×C3semidirect
91. #4701C2×C3semidirect
268. #489C3×D3semidirect
631. C32#3371semidirect
701. C3#81673direct (N × H)
702. C3C3×#3371semidirect

Maximal subgroups

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

subgroupindex
C3×#57212
C3×#56812
C32×#4892
C3×#50842
C3×#50542
C3×#48002
C3×#47982
C3×#47962
C3×#47892
C3×#47662
C3×#47642
C3×#47622
C3×#47582
C3×#47102
C3×#47012
C3×#33713
#816733