Finite Group Databasebeta

← C3×#81708 #11895714

Subgroups — C3×#81708 #11895714

Order 1152.

847 conjugacy classes of subgroups.

The subgroup lattice has 773 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5718C211yesmaximal, characteristic, complemented
2C3×#5690C211yesmaximal, characteristic, complemented
3C32×#490C211yesmaximal, characteristic, complemented
4C3×#5072C211yesmaximal, characteristic, complemented
5C3×#5066C211yesmaximal, characteristic, complemented
6C3×#4786C211yesmaximal, characteristic, complemented
7C3×#4786C211yesmaximal, characteristic, complemented
8C3×#4785C211yesmaximal, characteristic, complemented
9C3×#4764C211yesmaximal, characteristic, complemented
10C3×#4763C211yesmaximal, characteristic, complemented
11C3×#4761C211yesmaximal, characteristic, complemented
12C3×#4760C211yesmaximal, characteristic, complemented
13C3×#4756C211yesmaximal, characteristic, complemented
14C3×#4711C211yesmaximal, characteristic, complemented
15C3×#4701C211yesmaximal, characteristic, complemented
16C3×#3366—31nomaximal
17#81708C311yesmaximal, characteristic, direct product factor
18C2×C3×#237—21no—
19C32×#127C2211yescharacteristic
20C32×#125C2211yescharacteristic
21C3×#940C2211yescharacteristic
22C3×#940C2211yescharacteristic
23C3×#939—21no—
24C3×#939—21no—
25C3×#938—21no—
26C3×D4×Dic3C2211yescharacteristic
27C3×D4×Dic3C2211yescharacteristic
28C2×C3×#213C2211yescharacteristic
29C2×C3×#213C2211yescharacteristic
30C2×C3×D24C2211yescharacteristic
31C3×#897—21no—
32C3×#896—21no—
33C3×#896—21no—
34C3×#893C2211yescharacteristic
35C3×#893C2211yescharacteristic
36C3×D3×C4⋊C4—21no—
37C3×#890C2211yescharacteristic
38C3×#888C2211yescharacteristic
39C3×C4×D12C2211yescharacteristic
40C3×C4×D12C2211yescharacteristic
41C3×C4×Dic6C2211yescharacteristic
42C32×#102C2211yescharacteristic
43C32×#102C2211yescharacteristic
44C32×#102C2211yescharacteristic
45C32×#102C2211yescharacteristic
46C32×#97C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#817C2211yescharacteristic
52C3×#815C2211yescharacteristic
53C3×Dic3⋊C8C2211yescharacteristic
54C3×Dic3⋊C8C2211yescharacteristic
55C3×C8×Dic3C2211yescharacteristic
56C3×#809C2211yescharacteristic
57C3×#809C2211yescharacteristic
58C3×#808C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×C4⋊(C3⋊C8)C2211yescharacteristic
61C3×#554—31no—
62C3×#550—31no—
63#5718C2×C311yescharacteristic, complemented
64#5690C2×C311yescharacteristic, complemented
65C3×#490—21no—
66C3×#490—31no—
67C3×#490D311yescharacteristic, complemented
68C3×#490C2×C311yescharacteristic, complemented
69C3×#486—31no—
70C3×#478—31no—
71C3×#478—31no—
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#5072C2×C311yescharacteristic, complemented
81#5066C2×C311yescharacteristic, complemented
82#4786C2×C311yescharacteristic, complemented
83#4786C2×C311yescharacteristic, complemented
84#4785C2×C311yescharacteristic, complemented
85#4764C2×C311yescharacteristic, complemented
86#4763C2×C311yescharacteristic, complemented
87#4761C2×C311yescharacteristic, complemented
88#4760C2×C311yescharacteristic, complemented
89#4756C2×C311yescharacteristic, complemented
90#4711C2×C311yescharacteristic, complemented
91#4701C2×C311yescharacteristic, complemented
92C2×C32×D4—21no—
93C2×C32×D4—21no—
94C2×C32×D4C2311yescharacteristic
95C2×C32×D4C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C22×C3×Dic3—21no—
101C22×C3×Dic3—21no—
102C3×#237—44no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
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×C42C2311yescharacteristic
118C3×#217—21no—
119C3×#217—21no—
120C3×#213—22no—
121C3×#213—22no—
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×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4D411yescharacteristic
133C3×Dic3⋊C4D411yescharacteristic
134C3×C4×Dic3C2311yescharacteristic
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C3×D24—22no—
139#3366—31noSylow
140C2×C3×#41—61no—
141C2×#237—21no—
142C2×C3×D8—31no—
143C2×C3×D8—31no—
144C2×C3×D8—31no—
145C3×C4⋊Q8—31no—
146C3×#127—21no—
147C3×#127—31no—
148C3×#127—31no—
149C3×#127C2×D311yescharacteristic
150C3×#127C22×C311yescharacteristic
151C3×#125—21no—
152C3×#125—31no—
153C3×#125C2×D311yescharacteristic
154C3×#125C22×C311yescharacteristic
155C3×C22⋊Q8—61no—
156C3×C22⋊Q8—61no—
157C3×C22⋊Q8—61no—
158C3×#121—61no—
159C3×#121—61no—
160C3×#121—61no—
161C3×C4×Q8—31no—
162C3×C4×D4—31no—
163C3×C4×D4—31no—
164C3×C4×D4—31no—
165C3×C4×D4—31no—
166C3×C4×D4—31no—
167C3×C4×D4—31no—
168C2×C3×C4⋊C4—61no—
169#940C22×C311yescharacteristic
170#940C22×C311yescharacteristic
171#939—21no—
172#939—21no—
173#938—21no—
174D4×Dic3C22×C311yescharacteristic
175D4×Dic3C22×C311yescharacteristic
176C2×#213C22×C311yescharacteristic
177C2×#213C22×C311yescharacteristic
178C2×D24C22×C311yescharacteristic
179#897—21no—
180#896—21no—
181#896—21no—
182#893C22×C311yescharacteristic
183#893C22×C311yescharacteristic
184D3×C4⋊C4—21no—
185#890C22×C311yescharacteristic
186#888C22×C311yescharacteristic
187C4×D12C22×C311yescharacteristic
188C4×D12C22×C311yescharacteristic
189C4×Dic6C22×C311yescharacteristic
190C3×#107—31no—
191C3×#106—31no—
192C3×#106—31no—
193C3×C4⋊C8—31no—
194C3×C4⋊C8—31no—
195C3×C4⋊C8—31no—
196C3×#102—21no—
197C3×#102—21no—
198C3×#102—21no—
199C3×#102—21no—
200C3×#102—31no—
201C3×#102—31no—
202C3×#102—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102C2×D311yescharacteristic
207C3×#102C2×D311yescharacteristic
208C3×#102C2×D311yescharacteristic
209C3×#102C2×D311yescharacteristic
210C3×#102C22×C311yescharacteristic
211C3×#102C22×C311yescharacteristic
212C3×#102C22×C311yescharacteristic
213C3×#102C22×C311yescharacteristic
214C3×#97—21no—
215C3×#97—31no—
216C3×#97C2×D311yescharacteristic
217C3×#97C22×C311yescharacteristic
218C3×C4×C8—31no—
219#832C22×C311yescharacteristic
220#832C22×C311yescharacteristic
221#821C22×C311yescharacteristic
222#821C22×C311yescharacteristic
223#817C22×C311yescharacteristic
224#815C22×C311yescharacteristic
225Dic3⋊C8C22×C311yescharacteristic
226Dic3⋊C8C22×C311yescharacteristic
227C8×Dic3C22×C311yescharacteristic
228#809C22×C311yescharacteristic
229#809C22×C311yescharacteristic
230#808C22×C311yescharacteristic
231#807C22×C311yescharacteristic
232C4⋊(C3⋊C8)C22×C311yescharacteristic
233C23×C32—21no—
234C23×C32—21no—
235C22×C3×D3—21no—
236C22×C3×D3—21no—
237C32×D4—21no—
238C32×D4—21no—
239C32×D4—21no—
240C32×D4—21no—
241C32×D4—42no—
242C32×D4—81no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2411yescharacteristic
248C3×#67—42no—
249C3×#67—42no—
250C3×#67—81no—
251C3×#67—81no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—42no—
255C2×C3×Dic3—42no—
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C3×D12—21no—
261C3×D12—21no—
262C3×D12—21no—
263C3×D12#4112yescomplemented
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#490C3×D311yescharacteristic, complemented
278#486—31no—
279#478—31no—
280#478—31no—
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—21no—
294C2×C3×D4—21no—
295C2×C3×D4—21no—
296C2×C3×D4—21no—
297C2×C3×D4—21no—
298C2×C3×D4—31no—
299C2×C3×D4—31no—
300C2×C3×D4—41no—
301C2×C3×D4—41no—
302C2×C3×D4—61no—
303C2×C3×D4—61no—
304C2×C3×D4—61no—
305C2×C3×D4—61no—
306C2×C3×D4C22×D311yescharacteristic
307C2×C3×D4C22×D311yescharacteristic
308C2×C3×D4C23×C311yescharacteristic
309C2×C3×D4C23×C311yescharacteristic
310C22×C3×C4—61no—
311C22×C3×C4—61no—
312C22×C3×C4—61no—
313C22×C3×C4—61no—
314C22×C3×C4—61no—
315C22×C3×C4—61no—
316C2×#67—21no—
317C2×#67—21no—
318C2×#67—21no—
319C2×#67—21no—
320C22×Dic3—21no—
321C22×Dic3—21no—
322#237—44no—
323C2×D12C23×C311yescharacteristic
324C2×D12C23×C311yescharacteristic
325C2×C4×D3—21no—
326C2×C4×D3—21no—
327C2×C4×D3—21no—
328C2×C4×D3—21no—
329C2×Dic6—21no—
330C2×Dic6C3×D411yescharacteristic
331C3×D8—62no—
332C3×D8—62no—
333C3×D8—62no—
334C2×C3×C8—21no—
335C2×C3×C8—21no—
336C2×C3×C8—31no—
337C2×C3×C8—31no—
338C2×C3×C8C22×D311yescharacteristic
339C2×C3×C8C22×D311yescharacteristic
340C2×C3×C8C23×C311yescharacteristic
341C2×C3×C8C23×C311yescharacteristic
342C3×C4⋊C4—21no—
343C3×C4⋊C4—21no—
344C3×C4⋊C4—21no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—41no—
354C3×C4⋊C4—41no—
355C3×C4⋊C4—61no—
356C3×C4⋊C4—61no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4C22×D311yescharacteristic
359C3×C4⋊C4C22×D311yescharacteristic
360C3×C4⋊C4C23×C311yescharacteristic
361C3×C4⋊C4C23×C311yescharacteristic
362C3×C22⋊C4—61no—
363C3×C22⋊C4—61no—
364C3×C22⋊C4—61no—
365C3×C22⋊C4—61no—
366C3×C22⋊C4—61no—
367C3×C22⋊C4—61no—
368C3×C42—21no—
369C3×C42—31no—
370C3×C42—31no—
371C3×C42C22×D311yescharacteristic
372C3×C42C23×C311yescharacteristic
373#217—21no—
374#217—21no—
375#213—22no—
376#213—22no—
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
384C4⋊Dic3C23×C311yescharacteristic
385Dic3⋊C4—21no—
386Dic3⋊C4—21no—
387Dic3⋊C4C3×D411yescharacteristic
388Dic3⋊C4C3×D411yescharacteristic
389C4×Dic3C23×C311yescharacteristic
390C4×Dic3C23×C311yescharacteristic
391C2×C3⋊C8C23×C311yescharacteristic
392C2×C3⋊C8C23×C311yescharacteristic
393D24—22no—
394C22×C32—41no—
395C22×C32—41no—
396C22×C32—41no—
397C22×C32—41no—
398C22×C32—41no—
399C22×C32—41no—
400C22×C32C22×D411yescharacteristic
401C2×C3×D3—22no—
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×C4C2×#4111yescharacteristic
412C32×C42−1+411yescharacteristic
413C3×Dic3—21no—
414C3×Dic3—21no—
415C3×Dic3—21no—
416C3×Dic3—41no—
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#127C2×C3×D311yescharacteristic
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×D4—31no—
442C2×C4⋊C4—61no—
443#107—31no—
444#106—31no—
445#106—31no—
446C4⋊C8—31no—
447C4⋊C8—31no—
448C4⋊C8—31no—
449#102—31no—
450#102—31no—
451#102—31no—
452#102—31no—
453#102—31no—
454#102—31no—
455#102C2×C3×D311yescharacteristic
456#102C2×C3×D311yescharacteristic
457#102C2×C3×D311yescharacteristic
458#102C2×C3×D311yescharacteristic
459#97—31no—
460#97C2×C3×D311yescharacteristic
461C4×C8—31no—
462C23×C3—21no—
463C23×C3—21no—
464C23×C3—21no—
465C23×C3—21no—
466C23×C3—41no—
467C23×C3—41no—
468C23×C3—61no—
469C23×C3—61no—
470C22×D3—21no—
471C22×D3—21no—
472C3×Q8—62no—
473C3×Q8—241no—
474C3×D4—21no—
475C3×D4—21no—
476C3×D4—21no—
477C3×D4—21no—
478C3×D4—21no—
479C3×D4—21no—
480C3×D4—21no—
481C3×D4—21no—
482C3×D4—32no—
483C3×D4—41no—
484C3×D4—41no—
485C3×D4—41no—
486C3×D4—41no—
487C3×D4—42no—
488C3×D4—42no—
489C3×D4—61no—
490C3×D4—61no—
491C3×D4—61no—
492C3×D4—82no—
493C3×D4—81no—
494C3×D4—81no—
495C3×D4—82no—
496C3×D4—122no—
497C3×D4—122no—
498C3×D4—241no—
499C3×D4—241no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—31no—
508C2×C3×C4—31no—
509C2×C3×C4—31no—
510C2×C3×C4—31no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—122no—
516C2×C3×C4—122no—
517C2×C3×C4—122no—
518C2×C3×C4—122no—
519C2×C3×C4—241no—
520C2×C3×C4—241no—
521C2×C3×C4D3×D411yescharacteristic
522C2×C3×C4D3×D411yescharacteristic
523C2×C3×C4C2×C3×D411yescharacteristic
524C2×C3×C4C2×C3×D411yescharacteristic
525C2×C3×C4C23×D311yescharacteristic
526C2×C3×C4C24×C311yescharacteristic
527#67—42no—
528#67—42no—
529#67—81no—
530#67—81no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—42no—
534C2×Dic3—42no—
535C2×Dic3C2×C3×D411yescharacteristic
536C2×Dic3C2×C3×D411yescharacteristic
537C2×Dic3C2×C3×D411yescharacteristic
538C2×Dic3C2×C3×D411yescharacteristic
539D12—21no—
540D12—21no—
541D12—21no—
542D12C3×#4112yescomplemented
543C4×D3—42no—
544C4×D3—42no—
545C4×D3—81no—
546C4×D3—81no—
547Dic6—22no—
548Dic6—81no—
549C3×C8—21no—
550C3×C8—21no—
551C3×C8—21no—
552C3×C8—21no—
553C3×C8—41no—
554C3×C8—41no—
555C3×C8—61no—
556C3×C8—61no—
557C3⋊C8—21no—
558C3⋊C8—21no—
559C2×C32—81no—
560C2×C32—81no—
561C2×C32#54811yescharacteristic
562C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
563C2×C32#57611yescharacteristic
564C3×D3—42no—
565C3×D3—81no—
566#41—124no—
567C2×Q8—31no—
568C2×Q8—61no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—31no—
572C2×D4—31no—
573C2×D4—61no—
574C2×D4—61no—
575C2×D4—61no—
576C2×D4—61no—
577C2×D4C22×C3×D311yescharacteristic
578C2×D4C22×C3×D311yescharacteristic
579C22×C4—61no—
580C22×C4—61no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4—61no—
584C22×C4—61no—
585D8—62no—
586D8—62no—
587D8—62no—
588C2×C8—31no—
589C2×C8—31no—
590C2×C8C22×C3×D311yescharacteristic
591C2×C8C22×C3×D311yescharacteristic
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—31no—
595C4⋊C4—31no—
596C4⋊C4—31no—
597C4⋊C4—31no—
598C4⋊C4—31no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4C22×C3×D311yescharacteristic
603C4⋊C4C22×C3×D311yescharacteristic
604C22⋊C4—61no—
605C22⋊C4—61no—
606C22⋊C4—61no—
607C22⋊C4—61no—
608C22⋊C4—61no—
609C22⋊C4—61no—
610C42—31no—
611C42—31no—
612C42C22×C3×D311yescharacteristic
613C22×C3—21no—
614C22×C3—41no—
615C22×C3—41no—
616C22×C3—41no—
617C22×C3—41no—
618C22×C3—41no—
619C22×C3—41no—
620C22×C3—41no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—62no—
627C22×C3—81no—
628C22×C3—81no—
629C22×C3—81no—
630C22×C3—81no—
631C22×C3—81no—
632C22×C3—81no—
633C22×C3—121no—
634C22×C3—121no—
635C22×C3—121no—
636C22×C3—121no—
637C22×C3—121no—
638C22×C3C2×D3×D411yescharacteristic
639C22×C3C22×C3×D411yescharacteristic
640C2×D3—22no—
641C2×D3—41no—
642C2×D3—41no—
643C2×D3—41no—
644C2×D3—41no—
645C2×D3—41no—
646C3×C4—21no—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—21no—
652C3×C4—32no—
653C3×C4—41no—
654C3×C4—41no—
655C3×C4—41no—
656C3×C4—41no—
657C3×C4—41no—
658C3×C4—41no—
659C3×C4—61no—
660C3×C4—61no—
661C3×C4—61no—
662C3×C4—81no—
663C3×C4—81no—
664C3×C4—121no—
665C3×C4—121no—
666C3×C4D3×#4111yescharacteristic
667C3×C4#101011yescharacteristic
668C3×C4C2×C3×#4111yescharacteristic
669C3×C4C3×2−1+411yescharacteristic
670Dic3—21no—
671Dic3—21no—
672Dic3—21no—
673Dic3—41no—
674Dic3—41no—
675Dic3C3×AGL(1,ℤ/8)12yes—
676C32#336611yescharacteristic, complemented, Sylow
677C23—21no—
678C23—21no—
679C23—61no—
680C23—61no—
681Q8—62no—
682Q8—241no—
683D4—21no—
684D4—21no—
685D4—21no—
686D4—21no—
687D4—32no—
688D4—42no—
689D4—61no—
690D4—61no—
691D4—61no—
692D4—81no—
693D4—122no—
694D4—122no—
695D4—241no—
696D4—241no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—31no—
700C2×C4—31no—
701C2×C4—31no—
702C2×C4—31no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—122no—
706C2×C4—122no—
707C2×C4—122no—
708C2×C4—122no—
709C2×C4—241no—
710C2×C4—241no—
711C2×C4C3×D3×D411yescharacteristic
712C2×C4C3×D3×D411yescharacteristic
713C2×C4C23×C3×D311yescharacteristic
714C8—21no—
715C8—21no—
716C8—61no—
717C8—61no—
718C2×C3—21no—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—81no—
722C2×C3—81no—
723C2×C3—81no—
724C2×C3—81no—
725C2×C3—122no—
726C2×C3—161no—
727C2×C3—161no—
728C2×C3—241no—
729C2×C3#567711yescharacteristic
730C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
731C2×C3#577411yescharacteristic
732C2×C3C3×#54811yescharacteristic
733C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
734C2×C3C3×#57611yescharacteristic
735D3—42no—
736D3—81no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—62no—
744C22—121no—
745C22—121no—
746C22—121no—
747C22—121no—
748C22—121no—
749C22C2×C3×D3×D411yescharacteristic
750C4—21no—
751C4—21no—
752C4—32no—
753C4—41no—
754C4—41no—
755C4—61no—
756C4—61no—
757C4—61no—
758C4—121no—
759C4—121no—
760C4C3×D3×#4111yescharacteristic
761C4C3×#101011yescharacteristic
762C3—21no—
763C3#8170811yescharacteristic, direct product factor
764C3C3×#336611yescharacteristic, complemented
765C2—81no—
766C2—81no—
767C2—122no—
768C2—241no—
769C2C3×#567711yescharacteristic
770C2C3×D3×AGL(1,ℤ/8)11yescharacteristic
771C2C3×#577411yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#490C2
socleC22×C32C22×D4
hypercenterC3×#490D3
hypocenterC3C3×#3366
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#490

Complements

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

NH ≅ G/Ntype
1. C3×#5718C2semidirect
2. C3×#5690C2semidirect
3. C32×#490C2semidirect
4. C3×#5072C2semidirect
5. C3×#5066C2semidirect
6. C3×#4786C2semidirect
7. C3×#4786C2semidirect
8. C3×#4785C2semidirect
9. C3×#4764C2semidirect
10. C3×#4763C2semidirect
11. C3×#4761C2semidirect
12. C3×#4760C2semidirect
13. C3×#4756C2semidirect
14. C3×#4711C2semidirect
15. C3×#4701C2semidirect
17. #81708C3direct (N × H)
63. #5718C2×C3semidirect
64. #5690C2×C3semidirect
67. C3×#490D3semidirect
68. C3×#490C2×C3semidirect
80. #5072C2×C3semidirect
81. #5066C2×C3semidirect
82. #4786C2×C3semidirect
83. #4786C2×C3semidirect
84. #4785C2×C3semidirect
85. #4764C2×C3semidirect
86. #4763C2×C3semidirect
87. #4761C2×C3semidirect
88. #4760C2×C3semidirect
89. #4756C2×C3semidirect
90. #4711C2×C3semidirect
91. #4701C2×C3semidirect
263. C3×D12#41semidirect
277. #490C3×D3semidirect
542. D12C3×#41semidirect
676. C32#3366semidirect
763. C3#81708direct (N × H)
764. C3C3×#3366semidirect

Maximal subgroups

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

subgroupindex
C3×#57182
C3×#56902
C32×#4902
C3×#50722
C3×#50662
C3×#47862
C3×#47852
C3×#47642
C3×#47632
C3×#47612
C3×#47602
C3×#47562
C3×#47112
C3×#47012
C3×#33663
#817083