Finite Group Databasebeta

← #11633924

Subgroups — #11633924

Order 768.

2534 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#547C211yesmaximal, characteristic, complemented
2C2×#5728C211yesmaximal, characteristic, complemented
3#84097C212yesmaximal, complemented
4#84089C212yesmaximal, complemented
5#83229C211yesmaximal, characteristic, complemented
6#82876C214yesmaximal, complemented
7#82855C214yesmaximal, complemented
8#82778C212yesmaximal, complemented
9#82754C212yesmaximal, complemented
10#82668C212yesmaximal, complemented
11#82646C212yesmaximal, complemented
12C4×#938C211yesmaximal, characteristic, complemented
13C4×#938C211yesmaximal, characteristic, complemented
14#82382C211yesmaximal, characteristic, complemented
15#82379C211yesmaximal, characteristic, complemented
16#82194C212yesmaximal, complemented
17#82162C212yesmaximal, complemented
18#59040—31nomaximal, Sylow
19C22×C3×#41C2212yes—
20C3×#547—28no—
21C2×C3×C4⋊Q8C2211yescharacteristic
22C2×C3×#123C2214yes—
23C2×C3×C22⋊Q8C2212yes—
24C2×C3×#121C2212yes—
25C2×C3×C4×D4C2211yescharacteristic
26C2×C3×C4×D4C2211yescharacteristic
27C22×C3×C4⋊C4C2212yes—
28C2×#946C2212yes—
29C2×Q8×Dic3C2212yes—
30C2×Q8×Dic3C2212yes—
31C2×#938C2211yescharacteristic
32C2×#938C2211yescharacteristic
33C2×#936C2212yes—
34C2×C4×#67C2212yes—
35C2×C4×#67C2212yes—
36C2×#924C2212yes—
37C2×#924C2212yes—
38#5728—28no—
39C2×#897C2212yes—
40C2×#892C2212yes—
41C2×#890C2212yes—
42C2×#887C2212yes—
43C2×C42×D3C2211yescharacteristic
44C2×#869C2211yescharacteristic
45#5229C2212yes—
46#5223C2214yes—
47#5222C2214yes—
48#5221C2211yescharacteristic
49#5221C2212yes—
50#5221C2214yes—
51#5221C2214yes—
52#5221C2211yescharacteristic
53#5213C2214yes—
54#5212C2214yes—
55#5212C2212yes—
56#5212C2212yes—
57#5210C2214yes—
58C4×#217C2212yes—
59C4×#217C2214yes—
60C4×#217C2212yes—
61#4994C2214yes—
62#4987C2211yescharacteristic
63#4987C2211yescharacteristic
64#4984C2212yes—
65#4981C2214yes—
66#4980C2214yes—
67#4978C2214yes—
68#4976C2214yes—
69#4975C2212yes—
70Dic3×C4⋊C4C2212yes—
71#4973C2212yes—
72#4972C2211yescharacteristic
73#4972C2211yescharacteristic
74#4957C2214yes—
75#4956C2212yes—
76#4956C2212yes—
77#4953C2214yes—
78#4949C2214yes—
79#4949C2214yes—
80#4948C2214yes—
81#4944C2214yes—
82#4944C2212yes—
83#4944C2212yes—
84C4×C4⋊Dic3C2211yescharacteristic
85C4×C4⋊Dic3C2211yescharacteristic
86C2×#547D311yescharacteristic, complemented
87C2×#533—31no—
88#2694—34no—
89#2547—31no—
90#2542—31no—
91#2540—32no—
92#2538—32no—
93#2471—34no—
94#2426—32no—
95#2423—32no—
96#2417—32no—
97#2407—32no—
98#2365—31no—
99#2360—32no—
100#2341—32no—
101C4×#121—31no—
102C4×#121—31no—
103C2×C3×#41—28no—
104C2×C3×#41—28no—
105C2×C3×#41—44no—
106C22×C3×Q8C2312yes—
107C22×C3×D4C2311yescharacteristic
108C22×C3×D4C2314yes—
109C22×C3×D4C2311yescharacteristic
110C23×C3×C4C2312yes—
111C23×C3×C4C2312yes—
112C23×C3×C4C2314yes—
113C22×#67C2312yes—
114C22×#67C2312yes—
115C22×C4×D3C2311yescharacteristic
116C22×C4×D3C2311yescharacteristic
117C22×C4×D3C2311yescharacteristic
118C22×Dic6C2312yes—
119C3×C4⋊Q8D418yescomplemented
120C3×#123—216no—
121C3×C22⋊Q8—28no—
122C3×#121—28no—
123C3×C4×D4—24no—
124C3×C4×D4—24no—
125C2×C3×C4⋊C4—28no—
126C2×C3×C4⋊C4C2311yescharacteristic
127C2×C3×C4⋊C4C2311yescharacteristic
128C2×C3×C4⋊C4C2314yes—
129C2×C3×C4⋊C4C2312yes—
130C2×C3×C4⋊C4C2312yes—
131C2×C3×C22⋊C4C2314yes—
132C2×C3×C22⋊C4C2312yes—
133C2×C3×C22⋊C4C2312yes—
134C2×C3×C42C2311yescharacteristic
135C2×#217C2312yes—
136C2×#217C2312yes—
137C2×#217C2312yes—
138C2×#217C2314yes—
139C2×#217C2312yes—
140C2×#217C2312yes—
141C2×#217C2314yes—
142C2×#217C2312yes—
143C2×#217C2314yes—
144C2×#217C2314yes—
145#946—28no—
146Q8×Dic3—28no—
147Q8×Dic3—44no—
148#938—24no—
149#938—24no—
150#936—44no—
151C4×#67—44no—
152C4×#67—44no—
153C2×(C2×D3)⋊C4C2314yes—
154C2×(C2×D3)⋊C4C2312yes—
155C2×(C2×D3)⋊C4C2312yes—
156C2×C4⋊Dic3C2311yescharacteristic
157C2×C4⋊Dic3C2311yescharacteristic
158C2×C4⋊Dic3C2311yescharacteristic
159C2×C4⋊Dic3C2312yes—
160C2×C4⋊Dic3C2314yes—
161C2×C4⋊Dic3C2312yes—
162C2×C4⋊Dic3C2314yes—
163C2×C4⋊Dic3C2311yescharacteristic
164#924—28no—
165#924—44no—
166C2×Dic3⋊C4C2314yes—
167C2×Dic3⋊C4C2314yes—
168C2×Dic3⋊C4C2314yes—
169C2×Dic3⋊C4C2312yes—
170C2×Dic3⋊C4C2312yes—
171C2×C4×Dic3C2312yes—
172C2×C4×Dic3C2312yes—
173C2×C4×Dic3C2311yescharacteristic
174C2×C4×Dic3C2314yes—
175C2×C4×Dic3C2311yescharacteristic
176C2×C4×Dic3C2311yescharacteristic
177C2×C4×Dic3C2314yes—
178#897—28no—
179#892—28no—
180#890—28no—
181#887—28no—
182C42×D3—24no—
183#869—24no—
184C3⋊#95C2312yes—
185C3⋊#95C2312yes—
186C3⋊#95C2312yes—
187C3⋊#95C2312yes—
188C3⋊#95C2312yes—
189C3⋊#95C2314yes—
190C3⋊#95C2314yes—
191C3⋊#95C2314yes—
192C3⋊#95C2314yes—
193C3⋊#95C2312yes—
194C22×#41C2×D312yes—
195#547—28no—
196#533—68no—
197C2×C4⋊Q8—31no—
198C2×C4⋊Q8C2×D311yescharacteristic
199C2×#125—32no—
200C2×#124—32no—
201C2×#123C2×D314yes—
202C2×C22⋊Q8—32no—
203C2×C22⋊Q8—32no—
204C2×C22⋊Q8—32no—
205C2×C22⋊Q8—32no—
206C2×C22⋊Q8C2×D312yes—
207C2×#121—31no—
208C2×#121—31no—
209C2×#121C2×D312yes—
210C2×C4×Q8—32no—
211C2×C4×Q8—32no—
212C2×C4×Q8—32no—
213C2×C4×D4—32no—
214C2×C4×D4—32no—
215C2×C4×D4C2×D311yescharacteristic
216C2×C4×D4C2×D311yescharacteristic
217C2×#117—32no—
218C22×C4⋊C4C2×D312yes—
219C22×C42—31no—
220#399—34no—
221#399—34no—
222#398—34no—
223#397—34no—
224#396—34no—
225#396—34no—
226#394—34no—
227#392—34no—
228#391—32no—
229#391—32no—
230#390—31no—
231#390—32no—
232#390—34no—
233#390—34no—
234#390—31no—
235#390—34no—
236#389—31no—
237#389—34no—
238#389—32no—
239#389—31no—
240#388—34no—
241#388—32no—
242#388—32no—
243#387—34no—
244#387—34no—
245#386—34no—
246#386—32no—
247#386—32no—
248#385—34no—
249#384—32no—
250#380—34no—
251#380—32no—
252#380—32no—
253#380—31no—
254#380—31no—
255C4×C4⋊C4—32no—
256C4×C4⋊C4—31no—
257C4×C4⋊C4—31no—
258C4×C22⋊C4—34no—
259C4×C22⋊C4—32no—
260C4×C22⋊C4—32no—
261C24×C3C2412yes—
262C24×C3C2412yes—
263C23×D3C2411yescharacteristic
264C3×#41—432no—
265C2×C3×Q8—24no—
266C2×C3×Q8—24no—
267C2×C3×Q8C2×D418yes—
268C2×C3×D4—28no—
269C2×C3×D4—22no—
270C2×C3×D4—22no—
271C2×C3×D4—28no—
272C2×C3×D4—22no—
273C2×C3×D4—22no—
274C2×C3×D4—22no—
275C2×C3×D4—44no—
276C2×C3×D4#4114yes—
277C22×C3×C4—28no—
278C22×C3×C4—24no—
279C22×C3×C4—28no—
280C22×C3×C4—24no—
281C22×C3×C4—24no—
282C22×C3×C4—24no—
283C22×C3×C4—24no—
284C22×C3×C4—24no—
285C22×C3×C4—44no—
286C22×C3×C4C2412yes—
287C22×C3×C4C2412yes—
288C22×C3×C4C2411yescharacteristic
289C22×C3×C4C2414yes—
290C22×C3×C4C2411yescharacteristic
291C22×C3×C4C2411yescharacteristic
292C2×#67—24no—
293C2×#67—24no—
294C2×#67—24no—
295C2×#67—24no—
296C2×#67—42no—
297C2×#67—42no—
298C22×Dic3C2412yes—
299C22×Dic3C2412yes—
300C22×Dic3C2412yes—
301C22×Dic3C2411yescharacteristic
302C22×Dic3C2411yescharacteristic
303C22×Dic3C2414yes—
304C22×Dic3C2412yes—
305C22×Dic3C2411yescharacteristic
306C2×C4×D3—22no—
307C2×C4×D3—22no—
308C2×C4×D3—22no—
309C2×C4×D3—22no—
310C2×C4×D3—22no—
311C2×C4×D3—22no—
312C2×C4×D3—22no—
313C2×C4×D3—22no—
314C2×C4×D3—22no—
315C2×Dic6—24no—
316C2×Dic6—24no—
317C2×Dic6—24no—
318C3×C4⋊C4—22no—
319C3×C4⋊C4—28no—
320C3×C4⋊C4—22no—
321C3×C4⋊C4C2×D418yes—
322C3×C4⋊C4C2×D418yes—
323C3×C22⋊C4—24no—
324C3×C22⋊C4—24no—
325C3×C22⋊C4—28no—
326C3×C42C2×D414yes—
327#217—24no—
328#217—28no—
329#217—24no—
330#217—24no—
331#217—24no—
332#217—44no—
333#217—42no—
334#217—42no—
335#217—44no—
336#217—44no—
337(C2×D3)⋊C4—28no—
338(C2×D3)⋊C4—42no—
339(C2×D3)⋊C4—42no—
340C4⋊Dic3—24no—
341C4⋊Dic3—24no—
342C4⋊Dic3—28no—
343C4⋊Dic3—22no—
344C4⋊Dic3—22no—
345C4⋊Dic3—22no—
346C4⋊Dic3—44no—
347C4⋊Dic3#4114yescomplemented
348Dic3⋊C4—28no—
349Dic3⋊C4—28no—
350Dic3⋊C4—44no—
351Dic3⋊C4—42no—
352Dic3⋊C4—42no—
353C4×Dic3—22no—
354C4×Dic3—22no—
355C4×Dic3—22no—
356C4×Dic3—28no—
357C4×Dic3—24no—
358C4×Dic3—24no—
359C4×Dic3—44no—
360C2×#41—28no—
361C2×#41—28no—
362C2×#41—44no—
363C22×Q8—32no—
364C22×Q8C22×D312yes—
365C22×D4—32no—
366C22×D4—32no—
367C22×D4C22×D311yescharacteristic
368C22×D4C22×D314yes—
369C22×D4C22×D311yescharacteristic
370C23×C4—31no—
371C23×C4—31no—
372C23×C4—31no—
373C23×C4C22×D312yes—
374C23×C4C22×D312yes—
375C23×C4C22×D314yes—
376C4⋊Q8—64no—
377C4⋊Q8#6718yescomplemented
378#125—68no—
379#124—124no—
380#123—216no—
381C22⋊Q8—28no—
382C22⋊Q8—68no—
383C22⋊Q8—68no—
384C22⋊Q8—68no—
385C22⋊Q8—124no—
386#121—28no—
387#121—64no—
388#121—64no—
389C4×Q8—68no—
390C4×Q8—68no—
391C4×Q8—124no—
392C4×D4—24no—
393C4×D4—24no—
394C4×D4—124no—
395C4×D4—124no—
396#117—68no—
397C2×C4⋊C4—28no—
398C2×C4⋊C4—31no—
399C2×C4⋊C4—32no—
400C2×C4⋊C4—31no—
401C2×C4⋊C4—34no—
402C2×C4⋊C4—34no—
403C2×C4⋊C4—32no—
404C2×C4⋊C4—31no—
405C2×C4⋊C4—31no—
406C2×C4⋊C4—34no—
407C2×C4⋊C4—32no—
408C2×C4⋊C4—32no—
409C2×C4⋊C4—34no—
410C2×C4⋊C4—34no—
411C2×C4⋊C4C22×D311yescharacteristic
412C2×C4⋊C4C22×D314yes—
413C2×C4⋊C4C22×D311yescharacteristic
414C2×C4⋊C4C22×D312yes—
415C2×C4⋊C4C22×D312yes—
416C2×C22⋊C4—32no—
417C2×C22⋊C4—32no—
418C2×C22⋊C4—34no—
419C2×C22⋊C4—32no—
420C2×C22⋊C4—32no—
421C2×C22⋊C4—34no—
422C2×C22⋊C4—32no—
423C2×C22⋊C4—32no—
424C2×C22⋊C4—34no—
425C2×C22⋊C4—34no—
426C2×C22⋊C4—34no—
427C2×C22⋊C4—32no—
428C2×C22⋊C4—32no—
429C2×C22⋊C4C22×D312yes—
430C2×C22⋊C4C22×D312yes—
431C2×C22⋊C4C22×D314yes—
432C2×C42—34no—
433C2×C42—32no—
434C2×C42—32no—
435C2×C42—31no—
436C2×C42—31no—
437C2×C42—31no—
438C2×C42—34no—
439C2×C42—64no—
440C2×C42C22×D311yescharacteristic
441#95—32no—
442#95—32no—
443#95—34no—
444#95—32no—
445#95—32no—
446#95—34no—
447#95—32no—
448#95—32no—
449#95—34no—
450#95—34no—
451C23×C3—22no—
452C23×C3—22no—
453C23×C3—22no—
454C23×C3—22no—
455C23×C3—22no—
456C23×C3—22no—
457C23×C3—22no—
458C23×C3—22no—
459C23×C3—22no—
460C23×C3—22no—
461C23×C3—22no—
462C23×C3—22no—
463C23×C3—22no—
464C23×C3C2×#4114yes—
465C23×C3C2511yescharacteristic
466C22×D3—21no—
467C22×D3—21no—
468C22×D3—21no—
469C22×D3—21no—
470C22×D3—21no—
471C22×D3—21no—
472C22×D32−1+412yes—
473C3×Q8—216no—
474C3×D4—28no—
475C3×D4—416no—
476C3×D4—44no—
477C2×C3×C4—24no—
478C2×C3×C4—24no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—22no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
487C2×C3×C4—416no—
488C2×C3×C4—48no—
489C2×C3×C4—48no—
490C2×C3×C4C22×D418yes—
491C2×C3×C4C22×D412yes—
492C2×C3×C4C22×D412yes—
493C2×C3×C4C22×D412yes—
494C2×C3×C4C2×#4112yes—
495C2×C3×C4C2×#4112yes—
496C2×C3×C4H(5,𝔽2)12yes—
497C2×C3×C4H(5,𝔽2)12yes—
498#67—48no—
499#67—48no—
500C2×Dic3—21no—
501C2×Dic3—22no—
502C2×Dic3—21no—
503C2×Dic3—22no—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—24no—
507C2×Dic3—24no—
508C2×Dic3—22no—
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—22no—
512C2×Dic3—22no—
513C2×Dic3—22no—
514C2×Dic3—22no—
515C2×Dic3—22no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—24no—
519C2×Dic3—22no—
520C2×Dic3—22no—
521C2×Dic3—22no—
522C2×Dic3C2×#4114yes—
523C2×Dic32−1+412yes—
524C4×D3—28no—
525C4×D3—44no—
526C4×D3—44no—
527Dic6—48no—
528C24—31no—
529C24C23×D312yes—
530C24C23×D312yes—
531#41—432no—
532C2×Q8—24no—
533C2×Q8—24no—
534C2×Q8—64no—
535C2×Q8—64no—
536C2×Q8—64no—
537C2×Q8C2×#6718yes—
538C2×D4—28no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—28no—
545C2×D4—44no—
546C2×D4—64no—
547C2×D4—64no—
548C2×D4—64no—
549C2×D4—64no—
550C2×D4—122no—
551C2×D4—122no—
552C2×D4#23714yes—
553C22×C4—28no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—28no—
560C22×C4—24no—
561C22×C4—31no—
562C22×C4—32no—
563C22×C4—32no—
564C22×C4—32no—
565C22×C4—32no—
566C22×C4—31no—
567C22×C4—31no—
568C22×C4—34no—
569C22×C4—44no—
570C22×C4—62no—
571C22×C4—62no—
572C22×C4—62no—
573C22×C4—62no—
574C22×C4—62no—
575C22×C4—62no—
576C22×C4—62no—
577C22×C4—62no—
578C22×C4—62no—
579C22×C4C23×D312yes—
580C22×C4C23×D312yes—
581C22×C4C23×D311yescharacteristic
582C22×C4C23×D314yes—
583C22×C4C23×D311yescharacteristic
584C22×C4C23×D311yescharacteristic
585C4⋊C4—22no—
586C4⋊C4—28no—
587C4⋊C4—22no—
588C4⋊C4—34no—
589C4⋊C4—68no—
590C4⋊C4—62no—
591C4⋊C4—62no—
592C4⋊C4—62no—
593C4⋊C4—64no—
594C4⋊C4—68no—
595C4⋊C4—68no—
596C4⋊C4—64no—
597C4⋊C4—122no—
598C4⋊C4—122no—
599C4⋊C4—124no—
600C4⋊C4—124no—
601C4⋊C4C2×#6718yes—
602C4⋊C4C2×#6718yes—
603C22⋊C4—24no—
604C22⋊C4—24no—
605C22⋊C4—28no—
606C22⋊C4—64no—
607C22⋊C4—68no—
608C22⋊C4—64no—
609C22⋊C4—64no—
610C22⋊C4—64no—
611C22⋊C4—68no—
612C22⋊C4—122no—
613C22⋊C4—122no—
614C22⋊C4—122no—
615C22⋊C4—122no—
616C22⋊C4—124no—
617C22⋊C4—124no—
618C22⋊C4—124no—
619C42—64no—
620C42—64no—
621C42—62no—
622C42—62no—
623C42—62no—
624C42—68no—
625C42—124no—
626C42C2×#6714yes—
627C22×C3—24no—
628C22×C3—24no—
629C22×C3—24no—
630C22×C3—42no—
631C22×C3—42no—
632C22×C3—42no—
633C22×C3—42no—
634C22×C3—42no—
635C22×C3—42no—
636C22×C3—42no—
637C22×C3—42no—
638C22×C3—42no—
639C22×C3—42no—
640C22×C3—42no—
641C22×C3C23×D411yescharacteristic
642C22×C3C22×#4111yescharacteristic
643C22×C3C22×#4111yescharacteristic
644C22×C3C2×H(5,𝔽2)11yescharacteristic
645C22×C3C2×H(5,𝔽2)11yescharacteristic
646C22×C3C2×2−1+411yescharacteristic
647C22×C3C2×2−1+411yescharacteristic
648C2×D3—22no—
649C2×D3—22no—
650C2×D3—22no—
651C2×D3—41no—
652C2×D3—41no—
653C2×D3—41no—
654C2×D3—41no—
655C3×C4—28no—
656C3×C4—22no—
657C3×C4—42no—
658C3×C4—42no—
659C3×C4#54614yes—
660C3×C4#55014yes—
661Dic3—22no—
662Dic3—24no—
663Dic3—41no—
664Dic3—44no—
665Dic3—41no—
666Dic3—42no—
667Dic3—42no—
668Dic3—42no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—32no—
683C23—61no—
684C23—61no—
685C23—61no—
686C23—61no—
687C23—61no—
688C23—61no—
689C23C2×#23714yes—
690C23C24×D311yescharacteristic
691Q8—216no—
692Q8—128no—
693D4—28no—
694D4—416no—
695D4—44no—
696D4—128no—
697D4—128no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—34no—
709C2×C4—32no—
710C2×C4—416no—
711C2×C4—48no—
712C2×C4—48no—
713C2×C4—68no—
714C2×C4—62no—
715C2×C4—61no—
716C2×C4—62no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—62no—
720C2×C4—62no—
721C2×C4—62no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—64no—
725C2×C4—62no—
726C2×C4—62no—
727C2×C4—64no—
728C2×C4—62no—
729C2×C4—61no—
730C2×C4—62no—
731C2×C4—62no—
732C2×C4—62no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—64no—
736C2×C4—124no—
737C2×C4—124no—
738C2×C4C2×#23712yes—
739C2×C4#100412yes—
740C2×C4D3×#4112yes—
741C2×C4#100912yes—
742C2×C4C22×#6712yes—
743C2×C4C22×#6718yes—
744C2×C4C22×#6712yes—
745C2×C4C22×#6712yes—
746C2×C3—44no—
747C2×C3—82no—
748C2×C3C2×#54611yescharacteristic
749C2×C3C2×#55011yescharacteristic
750C2×C3#348211yescharacteristic
751C2×C3#348611yescharacteristic
752C2×C3#352011yescharacteristic
753C2×C3#352011yescharacteristic
754C2×C3#354811yescharacteristic
755D3—42no—
756C22—24no—
757C22—24no—
758C22—24no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—62no—
771C22—62no—
772C22—62no—
773C22—121no—
774C22—121no—
775C22—121no—
776C22—121no—
777C22C22×#23711yescharacteristic
778C22C2×#100411yescharacteristic
779C22C2×D3×#4111yescharacteristic
780C22C2×#100911yescharacteristic
781C22D3×2−1+411yescharacteristic
782C22D3×2−1+411yescharacteristic
783C22C23×#6711yescharacteristic
784C4—28no—
785C4—22no—
786C4—42no—
787C4—42no—
788C4—64no—
789C4—62no—
790C4—122no—
791C4—122no—
792C4—122no—
793C4—121no—
794C4—121no—
795C4—124no—
796C4#580614yes—
797C4#583414yes—
798C3#5904011yescharacteristic, complemented, Sylow
799C2—44no—
800C2—82no—
801C2—122no—
802C2#8667611yescharacteristic
803C2#8668511yescharacteristic
804C2#8668611yescharacteristic
805C2#8669311yescharacteristic
806C2C2×#580611yescharacteristic
807C2C2×#583411yescharacteristic
808C2#8729411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC2×C3×#547C2
hypercenterC2×#547D3
hypocenterC3#59040
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×C3×#547C2semidirect
2. C2×#5728C2semidirect
3. #84097C2semidirect
4. #84089C2semidirect
5. #83229C2semidirect
6. #82876C2semidirect
7. #82855C2semidirect
8. #82778C2semidirect
9. #82754C2semidirect
10. #82668C2semidirect
11. #82646C2semidirect
12. C4×#938C2semidirect
13. C4×#938C2semidirect
14. #82382C2semidirect
15. #82379C2semidirect
16. #82194C2semidirect
17. #82162C2semidirect
86. C2×#547D3semidirect
119. C3×C4⋊Q8D4semidirect
347. C4⋊Dic3#41semidirect
377. C4⋊Q8#67semidirect
798. C3#59040semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5472
C2×#57282
#840972
#840892
#832292
#828762
#828552
#827782
#827542
#826682
#826462
C4×#9382
#823822
#823792
#821942
#821622
#590403