Finite Group Databasebeta

← C3×#81152 #11895732

Subgroups — C3×#81152 #11895732

Order 1152.

843 conjugacy classes of subgroups.

The subgroup lattice has 767 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5690C211yesmaximal, characteristic, complemented
2C3×#5553C211yesmaximal, characteristic, complemented
3C32×#478C211yesmaximal, characteristic, complemented
4C3×#5067C211yesmaximal, characteristic, complemented
5C3×#5014C211yesmaximal, characteristic, complemented
6C3×#4891C211yesmaximal, characteristic, complemented
7C3×#4872C211yesmaximal, characteristic, complemented
8C3×#4870C211yesmaximal, characteristic, complemented
9C3×#4869C211yesmaximal, characteristic, complemented
10C3×#4843C211yesmaximal, characteristic, complemented
11C3×#4828C211yesmaximal, characteristic, complemented
12C3×#4786C211yesmaximal, characteristic, complemented
13C3×#4786C211yesmaximal, characteristic, complemented
14C3×#4764C211yesmaximal, characteristic, complemented
15C3×#4760C211yesmaximal, characteristic, complemented
16C3×#3366—31nomaximal
17#81152C311yesmaximal, characteristic, direct product factor
18C2×C3×#235—21no—
19C32×#125C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21C3×#940C2211yescharacteristic
22C3×#940C2211yescharacteristic
23C2×C3×#213C2211yescharacteristic
24C3×#930—21no—
25C2×C3×D24C2211yescharacteristic
26C2×C3×D24C2211yescharacteristic
27C3×#897—21no—
28C3×#896—21no—
29C3×#896—21no—
30C3×#893C2211yescharacteristic
31C3×#893C2211yescharacteristic
32C3×#893C2211yescharacteristic
33C3×#893C2211yescharacteristic
34C3×D3×C4⋊C4—21no—
35C3×#890C2211yescharacteristic
36C3×#888C2211yescharacteristic
37C3×#884—21no—
38C3×#884—21no—
39C3×#874C2211yescharacteristic
40C3×C4×D12C2211yescharacteristic
41C3×C4×Dic6C2211yescharacteristic
42C32×#107C2211yescharacteristic
43C32×#106C2211yescharacteristic
44C32×C4⋊C8C2211yescharacteristic
45C32×#102C2211yescharacteristic
46C32×#102C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#815C2211yescharacteristic
51C3×Dic3⋊C8C2211yescharacteristic
52C3×Dic3⋊C8C2211yescharacteristic
53C3×C8×Dic3C2211yescharacteristic
54C3×#809C2211yescharacteristic
55C3×#809C2211yescharacteristic
56C3×#809C2211yescharacteristic
57C3×#809C2211yescharacteristic
58C3×#809C2211yescharacteristic
59C3×#808C2211yescharacteristic
60C3×#803C2211yescharacteristic
61C3×#554—31no—
62C3×#550—31no—
63#5690C2×C311yescharacteristic, complemented
64#5553C2×C311yescharacteristic, complemented
65C3×#490—31no—
66C3×#490—31no—
67C3×#486—31no—
68C3×#478—21no—
69C3×#478—31no—
70C3×#478D311yescharacteristic, complemented
71C3×#478C2×C311yescharacteristic, complemented
72C3×#476—31no—
73C3×#459—31no—
74C3×#459—31no—
75C3×#459—31no—
76C3×#446—31no—
77C3×#442—31no—
78C3×#442—31no—
79C3×C4×D8—31no—
80#5067C2×C311yescharacteristic, complemented
81#5014C2×C311yescharacteristic, complemented
82#4891C2×C311yescharacteristic, complemented
83#4872C2×C311yescharacteristic, complemented
84#4870C2×C311yescharacteristic, complemented
85#4869C2×C311yescharacteristic, complemented
86#4843C2×C311yescharacteristic, complemented
87#4828C2×C311yescharacteristic, complemented
88#4786C2×C311yescharacteristic, complemented
89#4786C2×C311yescharacteristic, complemented
90#4764C2×C311yescharacteristic, complemented
91#4760C2×C311yescharacteristic, complemented
92C2×C32×D4C2311yescharacteristic
93C22×C32×C4—21no—
94C2×C3×#67—21no—
95C2×C3×#67—21no—
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C3×#235—44no—
99C2×C3×D12—21no—
100C2×C3×D12—21no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3—21no—
109C2×C3×Dic6—21no—
110C2×C3×Dic6D411yescharacteristic
111C2×C32×C8C2311yescharacteristic
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4—21no—
114C32×C4⋊C4—21no—
115C32×C4⋊C4C2311yescharacteristic
116C32×C4⋊C4C2311yescharacteristic
117C32×C4⋊C4C2311yescharacteristic
118C32×C22⋊C4—21no—
119C32×C42C2311yescharacteristic
120C3×#213—22no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3D411yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4D411yescharacteristic
132C3×Dic3⋊C4D411yescharacteristic
133C3×C4×Dic3C2311yescharacteristic
134C3×C4×Dic3C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C3×D24—22no—
138C3×D24—22no—
139#3366—31noSylow
140C2×C3×#41—61no—
141C2×#235—21no—
142C2×C3×D8—31no—
143C2×C3×D8—31no—
144C2×C3×D8—31no—
145C3×C4⋊Q8—31no—
146C3×#127—31no—
147C3×#127—31no—
148C3×#127—31no—
149C3×#125—21no—
150C3×#125—31no—
151C3×#125C2×D311yescharacteristic
152C3×#125C22×C311yescharacteristic
153C3×C22⋊Q8—61no—
154C3×C22⋊Q8—61no—
155C3×C22⋊Q8—61no—
156C3×#121—61no—
157C3×#121—61no—
158C3×#121—61no—
159C3×C4×Q8—31no—
160C3×C4×D4—21no—
161C3×C4×D4—31no—
162C3×C4×D4—31no—
163C3×C4×D4—31no—
164C3×C4×D4—31no—
165C3×C4×D4—31no—
166C3×C4×D4C2×D311yescharacteristic
167C3×C4×D4C22×C311yescharacteristic
168C2×C3×C4⋊C4—61no—
169#940C22×C311yescharacteristic
170#940C22×C311yescharacteristic
171C2×#213C22×C311yescharacteristic
172#930—21no—
173C2×D24C22×C311yescharacteristic
174C2×D24C22×C311yescharacteristic
175#897—21no—
176#896—21no—
177#896—21no—
178#893C22×C311yescharacteristic
179#893C22×C311yescharacteristic
180#893C22×C311yescharacteristic
181#893C22×C311yescharacteristic
182D3×C4⋊C4—21no—
183#890C22×C311yescharacteristic
184#888C22×C311yescharacteristic
185#884—21no—
186#884—21no—
187#874C22×C311yescharacteristic
188C4×D12C22×C311yescharacteristic
189C4×Dic6C22×C311yescharacteristic
190C3×#107—21no—
191C3×#107C2×D311yescharacteristic
192C3×#107C22×C311yescharacteristic
193C3×#106—21no—
194C3×#106—31no—
195C3×#106C2×D311yescharacteristic
196C3×#106C22×C311yescharacteristic
197C3×C4⋊C8—21no—
198C3×C4⋊C8—31no—
199C3×C4⋊C8—31no—
200C3×C4⋊C8C2×D311yescharacteristic
201C3×C4⋊C8C22×C311yescharacteristic
202C3×#102—21no—
203C3×#102—21no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102—31no—
209C3×#102—31no—
210C3×#102—31no—
211C3×#102—31no—
212C3×#102C2×D311yescharacteristic
213C3×#102C2×D311yescharacteristic
214C3×#102C22×C311yescharacteristic
215C3×#102C22×C311yescharacteristic
216C3×#97—31no—
217C3×#97—31no—
218C3×C4×C8—31no—
219#832C22×C311yescharacteristic
220#821C22×C311yescharacteristic
221#821C22×C311yescharacteristic
222#815C22×C311yescharacteristic
223Dic3⋊C8C22×C311yescharacteristic
224Dic3⋊C8C22×C311yescharacteristic
225C8×Dic3C22×C311yescharacteristic
226#809C22×C311yescharacteristic
227#809C22×C311yescharacteristic
228#809C22×C311yescharacteristic
229#809C22×C311yescharacteristic
230#809C22×C311yescharacteristic
231#808C22×C311yescharacteristic
232#803C22×C311yescharacteristic
233C23×C32—21no—
234C22×C3×D3—21no—
235C22×C3×D3—21no—
236C22×C3×D3—21no—
237C32×D4—21no—
238C32×D4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—42no—
243C2×C32×C4C2×D411yescharacteristic
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2411yescharacteristic
246C3×#67—42no—
247C3×#67—42no—
248C3×#67—81no—
249C3×#67—81no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C3×D12—21no—
256C3×D12—21no—
257C3×D12—21no—
258C3×D12—21no—
259C3×D12—21no—
260C3×D12—42no—
261C3×D12—81no—
262C3×D12#4112yescomplemented
263C3×C4×D3—42no—
264C3×C4×D3—42no—
265C3×C4×D3—42no—
266C3×C4×D3—81no—
267C3×C4×D3—81no—
268C3×Dic6—22no—
269C3×Dic6—81no—
270C32×C8—21no—
271C32×C8—21no—
272C3×C3⋊C8—21no—
273C3×C3⋊C8—21no—
274#554—31no—
275#550—31no—
276#490—31no—
277#490—31no—
278#486—31no—
279#478—31no—
280#478C3×D311yescharacteristic, complemented
281#476—31no—
282#459—31no—
283#459—31no—
284#459—31no—
285#446—31no—
286#442—31no—
287#442—31no—
288C4×D8—31no—
289C3×#41—124no—
290C2×C3×Q8—31no—
291C2×C3×Q8—61no—
292C2×C3×D4—21no—
293C2×C3×D4—31no—
294C2×C3×D4—31no—
295C2×C3×D4—31no—
296C2×C3×D4—61no—
297C2×C3×D4—61no—
298C2×C3×D4—61no—
299C2×C3×D4—61no—
300C2×C3×D4—61no—
301C2×C3×D4—61no—
302C2×C3×D4C22×D311yescharacteristic
303C2×C3×D4C23×C311yescharacteristic
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—41no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C22×C3×C4—61no—
310C22×C3×C4—61no—
311C22×C3×C4—61no—
312C2×#67—21no—
313C2×#67—21no—
314C2×#67—21no—
315C2×#67—21no—
316#235—44no—
317C2×D12—21no—
318C2×D12—21no—
319C2×D12C23×C311yescharacteristic
320C2×D12C23×C311yescharacteristic
321C2×D12C23×C311yescharacteristic
322C2×C4×D3—21no—
323C2×C4×D3—21no—
324C2×C4×D3—21no—
325C2×C4×D3—21no—
326C2×C4×D3—21no—
327C2×Dic6—21no—
328C2×Dic6C3×D411yescharacteristic
329C3×D8—62no—
330C3×D8—62no—
331C3×D8—62no—
332C2×C3×C8—21no—
333C2×C3×C8—21no—
334C2×C3×C8—31no—
335C2×C3×C8—31no—
336C2×C3×C8C22×D311yescharacteristic
337C2×C3×C8C22×D311yescharacteristic
338C2×C3×C8C23×C311yescharacteristic
339C2×C3×C8C23×C311yescharacteristic
340C3×C4⋊C4—21no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—21no—
344C3×C4⋊C4—21no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—41no—
352C3×C4⋊C4—41no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4—61no—
356C3×C4⋊C4C22×D311yescharacteristic
357C3×C4⋊C4C22×D311yescharacteristic
358C3×C4⋊C4C22×D311yescharacteristic
359C3×C4⋊C4C23×C311yescharacteristic
360C3×C4⋊C4C23×C311yescharacteristic
361C3×C4⋊C4C23×C311yescharacteristic
362C3×C22⋊C4—21no—
363C3×C22⋊C4—21no—
364C3×C22⋊C4—41no—
365C3×C22⋊C4—61no—
366C3×C22⋊C4—61no—
367C3×C22⋊C4—61no—
368C3×C22⋊C4—61no—
369C3×C22⋊C4—61no—
370C3×C42—21no—
371C3×C42—31no—
372C3×C42—31no—
373C3×C42C22×D311yescharacteristic
374C3×C42C23×C311yescharacteristic
375#213—22no—
376(C2×D3)⋊C4—21no—
377(C2×D3)⋊C4—21no—
378(C2×D3)⋊C4—21no—
379(C2×D3)⋊C4—21no—
380(C2×D3)⋊C4—21no—
381C4⋊Dic3—21no—
382C4⋊Dic3C3×D411yescharacteristic
383C4⋊Dic3C23×C311yescharacteristic
384Dic3⋊C4—21no—
385Dic3⋊C4—21no—
386Dic3⋊C4C3×D411yescharacteristic
387Dic3⋊C4C3×D411yescharacteristic
388C4×Dic3C23×C311yescharacteristic
389C4×Dic3C23×C311yescharacteristic
390C2×C3⋊C8C23×C311yescharacteristic
391C2×C3⋊C8C23×C311yescharacteristic
392D24—22no—
393D24—22no—
394C22×C32—41no—
395C22×C32—41no—
396C22×C32—41no—
397C22×C32C22×D411yescharacteristic
398C2×C3×D3—22no—
399C2×C3×D3—41no—
400C2×C3×D3—41no—
401C2×C3×D3—41no—
402C2×C3×D3—41no—
403C2×C3×D3—41no—
404C2×C3×D3—41no—
405C2×C3×D3—41no—
406C2×C3×D3—41no—
407C32×C4—21no—
408C32×C4—21no—
409C32×C4—41no—
410C32×C4—41no—
411C32×C4—41no—
412C32×C4C2×#4111yescharacteristic
413C32×C42−1+411yescharacteristic
414C3×Dic3—21no—
415C3×Dic3—21no—
416C3×Dic3—21no—
417C3×Dic3—41no—
418C3×Dic3AGL(1,ℤ/8)12yes—
419C2×#41—61no—
420C2×D8—31no—
421C2×D8—31no—
422C2×D8—31no—
423C4⋊Q8—31no—
424#127—31no—
425#127—31no—
426#127—31no—
427#125—31no—
428#125C2×C3×D311yescharacteristic
429C22⋊Q8—61no—
430C22⋊Q8—61no—
431C22⋊Q8—61no—
432#121—61no—
433#121—61no—
434#121—61no—
435C4×Q8—31no—
436C4×D4—31no—
437C4×D4—31no—
438C4×D4—31no—
439C4×D4—31no—
440C4×D4—31no—
441C4×D4C2×C3×D311yescharacteristic
442C2×C4⋊C4—61no—
443#107C2×C3×D311yescharacteristic
444#106—31no—
445#106C2×C3×D311yescharacteristic
446C4⋊C8—31no—
447C4⋊C8—31no—
448C4⋊C8C2×C3×D311yescharacteristic
449#102—31no—
450#102—31no—
451#102—31no—
452#102—31no—
453#102—31no—
454#102—31no—
455#102—31no—
456#102—31no—
457#102C2×C3×D311yescharacteristic
458#102C2×C3×D311yescharacteristic
459#97—31no—
460#97—31no—
461C4×C8—31no—
462C23×C3—21no—
463C23×C3—21no—
464C23×C3—41no—
465C23×C3—61no—
466C23×C3—61no—
467C23×C3—61no—
468C22×D3—21no—
469C22×D3—21no—
470C22×D3—21no—
471C3×Q8—62no—
472C3×Q8—241no—
473C3×D4—22no—
474C3×D4—21no—
475C3×D4—21no—
476C3×D4—21no—
477C3×D4—21no—
478C3×D4—32no—
479C3×D4—41no—
480C3×D4—61no—
481C3×D4—61no—
482C3×D4—61no—
483C3×D4—61no—
484C3×D4—61no—
485C3×D4—122no—
486C3×D4—122no—
487C3×D4—122no—
488C3×D4—241no—
489C3×D4—241no—
490C3×D4—241no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—31no—
501C2×C3×C4—31no—
502C2×C3×C4—31no—
503C2×C3×C4—31no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—42no—
508C2×C3×C4—42no—
509C2×C3×C4—61no—
510C2×C3×C4—82no—
511C2×C3×C4—122no—
512C2×C3×C4—122no—
513C2×C3×C4—122no—
514C2×C3×C4—241no—
515C2×C3×C4—241no—
516C2×C3×C4D3×D411yescharacteristic
517C2×C3×C4D3×D411yescharacteristic
518C2×C3×C4C2×C3×D411yescharacteristic
519C2×C3×C4C2×C3×D411yescharacteristic
520C2×C3×C4C23×D311yescharacteristic
521C2×C3×C4C24×C311yescharacteristic
522#67—42no—
523#67—42no—
524#67—81no—
525#67—81no—
526C2×Dic3—21no—
527C2×Dic3C2×C3×D411yescharacteristic
528C2×Dic3C2×C3×D411yescharacteristic
529C2×Dic3C2×C3×D411yescharacteristic
530C2×Dic3C2×C3×D411yescharacteristic
531D12—21no—
532D12—21no—
533D12—21no—
534D12—21no—
535D12—21no—
536D12—42no—
537D12—81no—
538D12C3×#4112yescomplemented
539C4×D3—42no—
540C4×D3—42no—
541C4×D3—42no—
542C4×D3—81no—
543C4×D3—81no—
544Dic6—22no—
545Dic6—81no—
546C3×C8—21no—
547C3×C8—21no—
548C3×C8—21no—
549C3×C8—21no—
550C3×C8—41no—
551C3×C8—41no—
552C3×C8—61no—
553C3×C8—61no—
554C3⋊C8—21no—
555C3⋊C8—21no—
556C2×C32—81no—
557C2×C32#54811yescharacteristic
558C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
559C2×C32#57611yescharacteristic
560C3×D3—42no—
561C3×D3—81no—
562C3×D3—81no—
563#41—124no—
564C2×Q8—31no—
565C2×Q8—61no—
566C2×D4—31no—
567C2×D4—31no—
568C2×D4—31no—
569C2×D4—61no—
570C2×D4—61no—
571C2×D4—61no—
572C2×D4—61no—
573C2×D4—61no—
574C2×D4—61no—
575C2×D4C22×C3×D311yescharacteristic
576C22×C4—21no—
577C22×C4—61no—
578C22×C4—61no—
579C22×C4—61no—
580C22×C4—61no—
581C22×C4—61no—
582D8—62no—
583D8—62no—
584D8—62no—
585C2×C8—31no—
586C2×C8—31no—
587C2×C8C22×C3×D311yescharacteristic
588C2×C8C22×C3×D311yescharacteristic
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—31no—
592C4⋊C4—31no—
593C4⋊C4—31no—
594C4⋊C4—31no—
595C4⋊C4—61no—
596C4⋊C4—61no—
597C4⋊C4—61no—
598C4⋊C4C22×C3×D311yescharacteristic
599C4⋊C4C22×C3×D311yescharacteristic
600C4⋊C4C22×C3×D311yescharacteristic
601C22⋊C4—21no—
602C22⋊C4—61no—
603C22⋊C4—61no—
604C22⋊C4—61no—
605C22⋊C4—61no—
606C22⋊C4—61no—
607C42—31no—
608C42—31no—
609C42C22×C3×D311yescharacteristic
610C22×C3—21no—
611C22×C3—42no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3—41no—
615C22×C3—41no—
616C22×C3—41no—
617C22×C3—41no—
618C22×C3—62no—
619C22×C3—81no—
620C22×C3—81no—
621C22×C3—121no—
622C22×C3—121no—
623C22×C3—121no—
624C22×C3—121no—
625C22×C3—121no—
626C22×C3—121no—
627C22×C3—121no—
628C22×C3—121no—
629C22×C3C2×D3×D411yescharacteristic
630C22×C3C22×C3×D411yescharacteristic
631C2×D3—22no—
632C2×D3—41no—
633C2×D3—41no—
634C2×D3—41no—
635C2×D3—41no—
636C2×D3—41no—
637C2×D3—41no—
638C2×D3—41no—
639C2×D3—41no—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—21no—
644C3×C4—21no—
645C3×C4—21no—
646C3×C4—32no—
647C3×C4—41no—
648C3×C4—41no—
649C3×C4—41no—
650C3×C4—41no—
651C3×C4—41no—
652C3×C4—41no—
653C3×C4—41no—
654C3×C4—41no—
655C3×C4—61no—
656C3×C4—61no—
657C3×C4—61no—
658C3×C4—81no—
659C3×C4—81no—
660C3×C4—81no—
661C3×C4—121no—
662C3×C4#100711yescharacteristic
663C3×C4D3×#4111yescharacteristic
664C3×C4C2×C3×#4111yescharacteristic
665C3×C4C3×2−1+411yescharacteristic
666Dic3—21no—
667Dic3—21no—
668Dic3—21no—
669Dic3—41no—
670Dic3C3×AGL(1,ℤ/8)12yes—
671C32#336611yescharacteristic, complemented, Sylow
672C23—21no—
673C23—61no—
674C23—61no—
675C23—61no—
676Q8—62no—
677Q8—241no—
678D4—21no—
679D4—21no—
680D4—32no—
681D4—61no—
682D4—61no—
683D4—61no—
684D4—61no—
685D4—61no—
686D4—122no—
687D4—122no—
688D4—122no—
689D4—241no—
690D4—241no—
691D4—241no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—31no—
696C2×C4—31no—
697C2×C4—31no—
698C2×C4—31no—
699C2×C4—42no—
700C2×C4—61no—
701C2×C4—122no—
702C2×C4—122no—
703C2×C4—122no—
704C2×C4—241no—
705C2×C4—241no—
706C2×C4C3×D3×D411yescharacteristic
707C2×C4C3×D3×D411yescharacteristic
708C2×C4C23×C3×D311yescharacteristic
709C8—21no—
710C8—21no—
711C8—61no—
712C8—61no—
713C2×C3—21no—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—82no—
717C2×C3—81no—
718C2×C3—81no—
719C2×C3—122no—
720C2×C3—241no—
721C2×C3—241no—
722C2×C3#563311yescharacteristic
723C2×C3#576911yescharacteristic
724C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
725C2×C3C3×#54811yescharacteristic
726C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
727C2×C3C3×#57611yescharacteristic
728D3—42no—
729D3—81no—
730D3—81no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—62no—
735C22—121no—
736C22—121no—
737C22—121no—
738C22—121no—
739C22—121no—
740C22—121no—
741C22—121no—
742C22—121no—
743C22C2×C3×D3×D411yescharacteristic
744C4—21no—
745C4—21no—
746C4—32no—
747C4—41no—
748C4—41no—
749C4—41no—
750C4—61no—
751C4—61no—
752C4—61no—
753C4—121no—
754C4C3×#100711yescharacteristic
755C4C3×D3×#4111yescharacteristic
756C3—21no—
757C3#8115211yescharacteristic, direct product factor
758C3C3×#336611yescharacteristic, complemented
759C2—81no—
760C2—122no—
761C2—241no—
762C2—241no—
763C2C3×#563311yescharacteristic
764C2C3×#576911yescharacteristic
765C2C3×D3×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#478C2
socleC22×C32C22×D4
hypercenterC3×#478D3
hypocenterC3C3×#3366
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×#5553C2semidirect
3. C32×#478C2semidirect
4. C3×#5067C2semidirect
5. C3×#5014C2semidirect
6. C3×#4891C2semidirect
7. C3×#4872C2semidirect
8. C3×#4870C2semidirect
9. C3×#4869C2semidirect
10. C3×#4843C2semidirect
11. C3×#4828C2semidirect
12. C3×#4786C2semidirect
13. C3×#4786C2semidirect
14. C3×#4764C2semidirect
15. C3×#4760C2semidirect
17. #81152C3direct (N × H)
63. #5690C2×C3semidirect
64. #5553C2×C3semidirect
70. C3×#478D3semidirect
71. C3×#478C2×C3semidirect
80. #5067C2×C3semidirect
81. #5014C2×C3semidirect
82. #4891C2×C3semidirect
83. #4872C2×C3semidirect
84. #4870C2×C3semidirect
85. #4869C2×C3semidirect
86. #4843C2×C3semidirect
87. #4828C2×C3semidirect
88. #4786C2×C3semidirect
89. #4786C2×C3semidirect
90. #4764C2×C3semidirect
91. #4760C2×C3semidirect
262. C3×D12#41semidirect
280. #478C3×D3semidirect
538. D12C3×#41semidirect
671. C32#3366semidirect
757. C3#81152direct (N × H)
758. C3C3×#3366semidirect

Maximal subgroups

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

subgroupindex
C3×#56902
C3×#55532
C32×#4782
C3×#50672
C3×#50142
C3×#48912
C3×#48722
C3×#48702
C3×#48692
C3×#48432
C3×#48282
C3×#47862
C3×#47642
C3×#47602
C3×#33663
#811523