Finite Group Databasebeta

← #10768613

Subgroups — #10768613

Order 768.

992 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3560C211yesmaximal, characteristic, complemented
2#83300C211yesmaximal, characteristic, complemented
3#83141C211yesmaximal, characteristic, complemented
4#83112C211yesmaximal, characteristic, complemented
5#71888C211yesmaximal, characteristic, complemented
6#71887C211yesmaximal, characteristic, complemented
7#71884C211yesmaximal, characteristic, complemented
8#71883C211yesmaximal, characteristic, complemented
9#71878C211yesmaximal, characteristic, complemented
10#71875C211yesmaximal, characteristic, complemented
11#71845C211yesmaximal, characteristic, complemented
12#71844C211yesmaximal, characteristic, complemented
13#71814C211yesmaximal, characteristic, complemented
14#71756C211yesmaximal, characteristic, complemented
15#71745C211yesmaximal, characteristic, complemented
16#18248—31nomaximal, Sylow
17C3×#563—21no—
18C3×#560—21no—
19C3×#553—21no—
20C3×#553—21no—
21C3×#551—21no—
22C3×#547—21no—
23C3×#546—21no—
24C3×#546—21no—
25C3×#542—21no—
26C3×#539—21no—
27C3×#539C2211yescharacteristic
28C3×#538—21no—
29C3×#538—21no—
30C3×#538C2211yescharacteristic
31C3×#537C2211yescharacteristic
32C3×#534C2211yescharacteristic
33C3×#532C2211yescharacteristic
34C3×#529C2211yescharacteristic
35C2×C3×#126C2211yescharacteristic
36C2×C4×D12C2211yescharacteristic, complemented
37#5084—21no—
38#5072—21no—
39#5066—21no—
40#5057—21no—
41#5046C2211yescharacteristic, complemented
42#5044C2211yescharacteristic, complemented
43#5036C2211yescharacteristic
44#5036C2211yescharacteristic
45#5036C2211yescharacteristic, complemented
46#5034C2211yescharacteristic
47#5034C2211yescharacteristic
48#5034C2211yescharacteristic, complemented
49C4×#215—21no—
50#5014—21no—
51#5014—21no—
52C4×#213—21no—
53#4994—21no—
54#4991C2211yescharacteristic, complemented
55#4989—21no—
56#4986C2211yescharacteristic, complemented
57#4961—21no—
58#4960C2211yescharacteristic
59#4956—21no—
60#4949C2211yescharacteristic
61#4936C2211yescharacteristic, complemented
62#4926C2211yescharacteristic, complemented
63#4925C2211yescharacteristic, complemented
64#4538C2211yescharacteristic, complemented
65#4538C2211yescharacteristic, complemented
66#4537C2211yescharacteristic
67#4537C2211yescharacteristic
68#4537C2211yescharacteristic
69#4537C2211yescharacteristic
70#4537C2211yescharacteristic, complemented
71#4537C2211yescharacteristic, complemented
72#4528C2211yescharacteristic, complemented
73#4528C2211yescharacteristic, complemented
74#4525C2211yescharacteristic
75#4525C2211yescharacteristic
76#3560D311yescharacteristic, complemented
77#3109—31no—
78#3105—31no—
79#2636—31no—
80#1618—31no—
81#1616—31no—
82#1615—31no—
83#1613—31no—
84#1600—31no—
85#1598—31no—
86#1597—31no—
87#1595—31no—
88#1517—31no—
89#1512—31no—
90#1473—31no—
91C2×C3×#41—21no—
92C2×C3×#41—21no—
93C22×C3×D4—21no—
94C22×#67—21no—
95C22×D12C2311yescharacteristic
96C22×C4×D3—21no—
97C3×C4⋊Q8—21no—
98C3×C4⋊Q8D411yescharacteristic, complemented
99C3×#127D411yescharacteristic, complemented
100C3×#126—21no—
101C3×#126—21no—
102C3×#126—21no—
103C3×#126—21no—
104C3×#126—21no—
105C3×#126—21no—
106C3×#126—21no—
107C3×#126—21no—
108C3×#126—21no—
109C3×#125—21no—
110C3×#125—21no—
111C3×#125D411yescharacteristic, complemented
112C3×#124—21no—
113C3×#124—21no—
114C3×#124—21no—
115C3×#124—21no—
116C3×#124D411yescharacteristic, complemented
117C3×#123—21no—
118C3×#123—21no—
119C3×#123—21no—
120C3×#123—21no—
121C3×#123—21no—
122C3×#123—21no—
123C3×#123—21no—
124C3×#123—21no—
125C3×#123—21no—
126C3×#123—21no—
127C3×#123—21no—
128C3×#123—21no—
129C3×C22⋊Q8—21no—
130C3×C22⋊Q8—21no—
131C3×C22⋊Q8—21no—
132C3×C22⋊Q8—21no—
133C3×C22⋊Q8—21no—
134C3×C22⋊Q8—21no—
135C3×C22⋊Q8—21no—
136C3×C22⋊Q8C2311yescharacteristic
137C3×#121—21no—
138C3×#121—21no—
139C3×#121—21no—
140C3×#121—21no—
141C3×#121—21no—
142C3×#121—21no—
143C3×#121—21no—
144C3×#121—21no—
145C3×#121—21no—
146C3×#121—21no—
147C3×#121—21no—
148C3×#121—21no—
149C3×#121C2311yescharacteristic
150C3×#121C2311yescharacteristic
151C3×#121C2311yescharacteristic
152C3×#120—21no—
153C3×#120—21no—
154C3×#120—21no—
155C3×#120—21no—
156C3×#120—21no—
157C3×C4×Q8D411yescharacteristic, complemented
158C3×C4×D4—21no—
159C3×C4×D4—21no—
160C3×C4×D4—21no—
161C3×C4×D4—21no—
162C3×C4×D4—21no—
163C3×C4×D4—21no—
164C3×C4×D4—21no—
165C3×C4×D4—21no—
166C3×C4×D4D411yescharacteristic, complemented
167C3×C4×D4D411yescharacteristic, complemented
168C3×C4×D4D411yescharacteristic, complemented
169C3×#117—21no—
170C3×#117—21no—
171C2×C3×C4⋊C4—21no—
172C2×C3×C4⋊C4D411yescharacteristic
173C2×C3×C4⋊C4D411yescharacteristic
174C2×C3×C4⋊C4C2311yescharacteristic
175C2×C3×C22⋊C4—21no—
176C2×C3×C22⋊C4—21no—
177C2×C3×C22⋊C4D411yescharacteristic
178C2×C3×C22⋊C4D411yescharacteristic
179C2×C3×C22⋊C4C2311yescharacteristic
180C2×C3×C42C2311yescharacteristic
181C2×#217—21no—
182C2×#215—21no—
183C2×#213—21no—
184C2×#213—21no—
185C2×#213—21no—
186C2×(C2×D3)⋊C4—21no—
187C2×(C2×D3)⋊C4—21no—
188C2×(C2×D3)⋊C4—21no—
189C2×(C2×D3)⋊C4—21no—
190C2×C4⋊Dic3—21no—
191C2×C4⋊Dic3C2311yescharacteristic
192C2×Dic3⋊C4—21no—
193C4×D12—21no—
194C4×D12—21no—
195C4×D12—21no—
196C4×D12—21no—
197#835—21no—
198#832—21no—
199#832—21no—
200#832—21no—
201C3⋊#95—21no—
202C3⋊#95—21no—
203C3⋊#95—21no—
204C3⋊#95C2311yescharacteristic
205C3⋊#95C2311yescharacteristic
206#830C2311yescharacteristic
207#830C2311yescharacteristic
208#830C2311yescharacteristic
209#830C2311yescharacteristic
210#809—21no—
211#809—21no—
212#809—21no—
213#809—21no—
214#808—21no—
215#808—21no—
216#808—21no—
217#807—21no—
218C4⋊(C3⋊C8)—21no—
219C4⋊(C3⋊C8)—21no—
220#803—21no—
221C4×C3⋊C8—21no—
222#563—21no—
223#560—21no—
224#553—21no—
225#553—21no—
226#551—21no—
227#547—21no—
228#546—21no—
229#546—21no—
230#542—21no—
231#539—21no—
232#539C2×D311yescharacteristic
233#538—21no—
234#538—21no—
235#538C2×D311yescharacteristic
236#537C2×D311yescharacteristic
237#534C2×D311yescharacteristic
238#532C2×D311yescharacteristic
239#529C2×D311yescharacteristic
240C2×#126C2×D311yescharacteristic
241C2×C4×D4—31no—
242#484—31no—
243#481—31no—
244#481—31no—
245#481—31no—
246#478—61no—
247#476—61no—
248#463—61no—
249#459—61no—
250#450—31no—
251#447—31no—
252#447—31no—
253#447—31no—
254#442—61no—
255#442—61no—
256C4×SD16—61no—
257C4×D8—61no—
258#432—31no—
259#431—31no—
260#400—31no—
261#399—31no—
262#396—61no—
263#394—31no—
264#394—61no—
265#392—31no—
266#386—61no—
267#385—61no—
268#382—31no—
269#328—31no—
270#328—31no—
271#327—31no—
272#327—31no—
273#327—31no—
274#327—31no—
275#327—31no—
276#327—31no—
277#324—31no—
278#324—31no—
279#323—31no—
280#323—31no—
281C24×C3—21no—
282C24×C3C2×D411yescharacteristic
283C23×D3—21no—
284C3×#41—81no—
285C3×#41—81no—
286C3×#41—81no—
287C3×#41—81no—
288C2×C3×Q8—21no—
289C2×C3×Q8—21no—
290C2×C3×Q8C2×D411yescharacteristic
291C2×C3×D4—21no—
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—21no—
299C2×C3×D4—21no—
300C2×C3×D4—21no—
301C2×C3×D4—21no—
302C2×C3×D4—21no—
303C2×C3×D4—81no—
304C2×C3×D4—81no—
305C2×C3×D4C2×D411yescharacteristic
306C2×C3×D4C2×D411yescharacteristic
307C2×C3×D4C2×D411yescharacteristic
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4C2×D411yescharacteristic
317C22×C3×C4C2×D411yescharacteristic
318C22×C3×C4C2×D411yescharacteristic
319C22×C3×C4C2×D411yescharacteristic
320C22×C3×C4C2×D411yescharacteristic
321C22×C3×C4C2411yescharacteristic
322C2×#67—42no—
323C2×#67—81no—
324C2×#67—81no—
325C22×Dic3—21no—
326C22×Dic3—21no—
327C22×Dic3—21no—
328C2×D12—21no—
329C2×D12—21no—
330C2×D12—42no—
331C2×C4×D3—41no—
332C2×C4×D3—41no—
333C2×C4×D3—81no—
334C2×C4×D3—81no—
335C3×C4⋊C4—21no—
336C3×C4⋊C4—21no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—21no—
339C3×C4⋊C4—21no—
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—21no—
348C3×C4⋊C4—21no—
349C3×C4⋊C4—21no—
350C3×C4⋊C4—21no—
351C3×C4⋊C4—21no—
352C3×C4⋊C4C2×D411yescharacteristic
353C3×C4⋊C4C2×D411yescharacteristic
354C3×C4⋊C4C2×D411yescharacteristic
355C3×C4⋊C4C2×D411yescharacteristic
356C3×C22⋊C4—21no—
357C3×C22⋊C4—21no—
358C3×C22⋊C4—21no—
359C3×C22⋊C4—21no—
360C3×C22⋊C4—21no—
361C3×C22⋊C4—21no—
362C3×C22⋊C4—21no—
363C3×C22⋊C4—21no—
364C3×C22⋊C4—21no—
365C3×C22⋊C4—21no—
366C3×C22⋊C4—21no—
367C3×C22⋊C4—21no—
368C3×C22⋊C4—21no—
369C3×C22⋊C4—21no—
370C3×C22⋊C4—21no—
371C3×C22⋊C4—21no—
372C3×C22⋊C4—21no—
373C3×C22⋊C4—21no—
374C3×C22⋊C4—21no—
375C3×C22⋊C4—21no—
376C3×C22⋊C4—21no—
377C3×C22⋊C4—21no—
378C3×C22⋊C4—21no—
379C3×C22⋊C4—21no—
380C3×C22⋊C4—21no—
381C3×C42—21no—
382C3×C42—21no—
383C3×C42—21no—
384C3×C42C2×D411yescharacteristic
385C3×C42C2×D411yescharacteristic
386C3×C42C2×D411yescharacteristic
387C3×C42C2×D411yescharacteristic
388#217—81no—
389#215—42no—
390#213—42no—
391#213—42no—
392#213—42no—
393(C2×D3)⋊C4—42no—
394(C2×D3)⋊C4—41no—
395(C2×D3)⋊C4—41no—
396(C2×D3)⋊C4—81no—
397(C2×D3)⋊C4—81no—
398C4⋊Dic3—21no—
399C4⋊Dic3—21no—
400C4⋊Dic3—81no—
401Dic3⋊C4—81no—
402C2×C3⋊C8—21no—
403C2×C3⋊C8—21no—
404C2×C3⋊C8—21no—
405C2×C3⋊C8—21no—
406C2×#41—21no—
407C2×#41—21no—
408C22×D4—21no—
409C22×D4—31no—
410C22×D4—61no—
411C23×C4—61no—
412C2×SD16—61no—
413C2×D8—61no—
414C2×D8—61no—
415C2×D8—61no—
416C4⋊Q8—21no—
417C4⋊Q8#6711yescharacteristic, complemented
418#127#6711yescharacteristic, complemented
419#126—21no—
420#126—21no—
421#126—21no—
422#126—21no—
423#126—21no—
424#126—21no—
425#126—21no—
426#126—21no—
427#126—21no—
428#125—21no—
429#125—21no—
430#125#6711yescharacteristic, complemented
431#124—21no—
432#124—21no—
433#124—21no—
434#124—21no—
435#124#6711yescharacteristic, complemented
436#123—21no—
437#123—21no—
438#123—21no—
439#123—21no—
440#123—21no—
441#123—21no—
442#123—21no—
443#123—21no—
444#123—21no—
445#123—21no—
446#123—21no—
447#123—21no—
448C22⋊Q8—21no—
449C22⋊Q8—21no—
450C22⋊Q8—21no—
451C22⋊Q8—21no—
452C22⋊Q8—21no—
453C22⋊Q8—21no—
454C22⋊Q8—21no—
455C22⋊Q8C22×D311yescharacteristic
456#121—21no—
457#121—21no—
458#121—21no—
459#121—21no—
460#121—21no—
461#121—21no—
462#121—21no—
463#121—21no—
464#121—21no—
465#121—21no—
466#121—21no—
467#121—21no—
468#121C22×D311yescharacteristic
469#121C22×D311yescharacteristic
470#121C22×D311yescharacteristic
471#120—21no—
472#120—21no—
473#120—21no—
474#120—21no—
475#120—21no—
476C4×Q8#6711yescharacteristic, complemented
477C4×D4—21no—
478C4×D4—21no—
479C4×D4—21no—
480C4×D4—21no—
481C4×D4—21no—
482C4×D4—21no—
483C4×D4—21no—
484C4×D4—21no—
485C4×D4—61no—
486C4×D4—61no—
487C4×D4—61no—
488C4×D4—61no—
489C4×D4#6711yescharacteristic, complemented
490C4×D4#6711yescharacteristic, complemented
491C4×D4#6711yescharacteristic, complemented
492#117—21no—
493#117—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—31no—
496C2×C4⋊C4—61no—
497C2×C4⋊C4—61no—
498C2×C4⋊C4#6711yescharacteristic
499C2×C4⋊C4#6711yescharacteristic
500C2×C4⋊C4C22×D311yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—61no—
504C2×C22⋊C4—61no—
505C2×C22⋊C4—61no—
506C2×C22⋊C4—61no—
507C2×C22⋊C4—61no—
508C2×C22⋊C4#6711yescharacteristic
509C2×C22⋊C4#6711yescharacteristic
510C2×C22⋊C4C22×D311yescharacteristic
511C2×C42C22×D311yescharacteristic
512#107—61no—
513#106—61no—
514#106—61no—
515#106—61no—
516C4⋊C8—61no—
517C4⋊C8—61no—
518#103—61no—
519#102—61no—
520#102—61no—
521#102—61no—
522#102—61no—
523#102—61no—
524#102—61no—
525#102—61no—
526C22⋊C8—31no—
527C22⋊C8—31no—
528C22⋊C8—31no—
529C22⋊C8—31no—
530#97—61no—
531C4×C8—61no—
532#95—31no—
533#95—31no—
534#95—61no—
535#95—61no—
536#95—61no—
537C23×C3—21no—
538C23×C3—21no—
539C23×C3—21no—
540C23×C3—21no—
541C23×C3—21no—
542C23×C3—21no—
543C23×C3—41no—
544C23×C3—41no—
545C23×C3—81no—
546C23×C3—81no—
547C23×C3—81no—
548C23×C3C22×D411yescharacteristic
549C22×D3—22no—
550C22×D3—41no—
551C22×D3—41no—
552C22×D3—41no—
553C22×D3—41no—
554C22×D3—41no—
555C22×D3—41no—
556C3×Q8—41no—
557C3×Q8—81no—
558C3×Q8—81no—
559C3×D4—41no—
560C3×D4—41no—
561C3×D4—41no—
562C3×D4—41no—
563C3×D4—41no—
564C3×D4—41no—
565C3×D4—41no—
566C3×D4—41no—
567C3×D4—41no—
568C3×D4—81no—
569C3×D4—81no—
570C3×D4—81no—
571C3×D4—81no—
572C3×D4—81no—
573C3×D4—81no—
574C3×D4—81no—
575C3×D4—81no—
576C3×D4—81no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—41no—
590C2×C3×C4—41no—
591C2×C3×C4—41no—
592C2×C3×C4—41no—
593C2×C3×C4—81no—
594C2×C3×C4—81no—
595C2×C3×C4—81no—
596C2×C3×C4—81no—
597C2×C3×C4—81no—
598C2×C3×C4—81no—
599C2×C3×C4—81no—
600C2×C3×C4—81no—
601C2×C3×C4#12011yescharacteristic
602C2×C3×C4#12011yescharacteristic
603C2×C3×C4#12011yescharacteristic
604C2×C3×C4#12011yescharacteristic
605C2×C3×C4C22×D411yescharacteristic
606C2×C3×C4C22×D411yescharacteristic
607#67—84no—
608C2×Dic3—41no—
609C2×Dic3—41no—
610C2×Dic3—41no—
611C2×Dic3—41no—
612C2×Dic3—41no—
613C2×Dic3—41no—
614C2×Dic3—41no—
615C2×Dic3—41no—
616C2×Dic3—41no—
617D12—22no—
618D12—22no—
619D12—41no—
620D12—41no—
621C4×D3—82no—
622C4×D3—82no—
623C3⋊C8—41no—
624C3⋊C8—41no—
625C3⋊C8—41no—
626C3⋊C8—41no—
627C24—21no—
628C24—61no—
629C24C2×#6711yescharacteristic
630#41—81no—
631#41—81no—
632#41—81no—
633#41—81no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8C2×#6711yescharacteristic
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—61no—
650C2×D4—61no—
651C2×D4—81no—
652C2×D4—81no—
653C2×D4—122no—
654C2×D4—122no—
655C2×D4—241no—
656C2×D4—241no—
657C2×D4C2×#6711yescharacteristic
658C2×D4C2×#6711yescharacteristic
659C2×D4C2×#6711yescharacteristic
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—61no—
669C22×C4—61no—
670C22×C4—61no—
671C22×C4—121no—
672C22×C4—121no—
673C22×C4—241no—
674C22×C4—241no—
675C22×C4C2×#6711yescharacteristic
676C22×C4C2×#6711yescharacteristic
677C22×C4C2×#6711yescharacteristic
678C22×C4C2×#6711yescharacteristic
679C22×C4C2×#6711yescharacteristic
680C22×C4C23×D311yescharacteristic
681SD16—122no—
682D8—122no—
683D8—122no—
684D8—122no—
685C2×C8—61no—
686C2×C8—61no—
687C2×C8—61no—
688C2×C8—61no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—61no—
707C4⋊C4—61no—
708C4⋊C4—241no—
709C4⋊C4—241no—
710C4⋊C4C2×#6711yescharacteristic
711C4⋊C4C2×#6711yescharacteristic
712C4⋊C4C2×#6711yescharacteristic
713C4⋊C4C2×#6711yescharacteristic
714C22⋊C4—21no—
715C22⋊C4—21no—
716C22⋊C4—21no—
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—21no—
723C22⋊C4—21no—
724C22⋊C4—21no—
725C22⋊C4—21no—
726C22⋊C4—21no—
727C22⋊C4—21no—
728C22⋊C4—21no—
729C22⋊C4—21no—
730C22⋊C4—21no—
731C22⋊C4—21no—
732C22⋊C4—21no—
733C22⋊C4—21no—
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—122no—
740C22⋊C4—121no—
741C22⋊C4—121no—
742C22⋊C4—241no—
743C22⋊C4—241no—
744C22⋊C4—241no—
745C42—21no—
746C42—21no—
747C42—21no—
748C42C2×#6711yescharacteristic
749C42C2×#6711yescharacteristic
750C42C2×#6711yescharacteristic
751C42C2×#6711yescharacteristic
752C22×C3—21no—
753C22×C3—21no—
754C22×C3—41no—
755C22×C3—41no—
756C22×C3—41no—
757C22×C3—41no—
758C22×C3—41no—
759C22×C3—41no—
760C22×C3—41no—
761C22×C3—41no—
762C22×C3—41no—
763C22×C3—41no—
764C22×C3—41no—
765C22×C3—41no—
766C22×C3—81no—
767C22×C3—81no—
768C22×C3—162no—
769C22×C3C2×#12011yescharacteristic
770C22×C3#57611yescharacteristic
771C22×C3#57711yescharacteristic
772C2×D3—42no—
773C2×D3—42no—
774C2×D3—42no—
775C2×D3—81no—
776C2×D3—81no—
777C2×D3—81no—
778C2×D3—81no—
779C3×C4—21no—
780C3×C4—21no—
781C3×C4—21no—
782C3×C4—21no—
783C3×C4—21no—
784C3×C4—21no—
785C3×C4—41no—
786C3×C4—41no—
787C3×C4—41no—
788C3×C4—41no—
789C3×C4—41no—
790C3×C4—41no—
791C3×C4—41no—
792C3×C4—41no—
793Dic3—81no—
794Dic3—81no—
795Dic3—81no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—41no—
803C23—41no—
804C23—62no—
805C23—81no—
806C23—81no—
807C23—81no—
808C23—121no—
809C23—121no—
810C23—121no—
811C23—121no—
812C23—121no—
813C23—121no—
814C23C22×#6711yescharacteristic
815Q8—41no—
816Q8—81no—
817Q8—81no—
818D4—41no—
819D4—41no—
820D4—41no—
821D4—41no—
822D4—41no—
823D4—41no—
824D4—41no—
825D4—41no—
826D4—41no—
827D4—62no—
828D4—62no—
829D4—81no—
830D4—81no—
831D4—81no—
832D4—81no—
833D4—81no—
834D4—81no—
835D4—81no—
836D4—81no—
837D4—81no—
838D4—121no—
839D4—121no—
840D4—244no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—81no—
858C2×C4—81no—
859C2×C4—81no—
860C2×C4—81no—
861C2×C4—81no—
862C2×C4—81no—
863C2×C4—81no—
864C2×C4—81no—
865C2×C4—121no—
866C2×C4—121no—
867C2×C4—121no—
868C2×C4—121no—
869C2×C4—121no—
870C2×C4—121no—
871C2×C4—121no—
872C2×C4—121no—
873C2×C4—121no—
874C2×C4—242no—
875C2×C4—242no—
876C2×C4#95311yescharacteristic
877C2×C4#95311yescharacteristic
878C2×C4#95311yescharacteristic
879C2×C4#95311yescharacteristic
880C2×C4C22×#6711yescharacteristic
881C2×C4C22×#6711yescharacteristic
882C8—121no—
883C8—121no—
884C8—121no—
885C8—121no—
886C2×C3—21no—
887C2×C3—21no—
888C2×C3—81no—
889C2×C3—81no—
890C2×C3—81no—
891C2×C3—81no—
892C2×C3#301211yescharacteristic
893C2×C3#302111yescharacteristic
894C2×C3#302511yescharacteristic
895D3—82no—
896C22—21no—
897C22—21no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—81no—
911C22—81no—
912C22—122no—
913C22—122no—
914C22—122no—
915C22—162no—
916C22—241no—
917C22—241no—
918C22—241no—
919C22—241no—
920C22#583511yescharacteristic
921C22#583611yescharacteristic
922C22C2×#95311yescharacteristic
923C4—21no—
924C4—21no—
925C4—21no—
926C4—21no—
927C4—21no—
928C4—21no—
929C4—41no—
930C4—41no—
931C4—41no—
932C4—41no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—241no—
938C4—241no—
939C4—241no—
940C3#1824811yescharacteristic, complemented, Sylow
941C2—21no—
942C2—21no—
943C2—81no—
944C2—81no—
945C2—81no—
946C2—81no—
947C2—242no—
948C2#8410211yescharacteristic
949C2#8412211yescharacteristic
950C2#8412511yescharacteristic
subgroupG/H
centerC22C2×#953
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#3560C2
socleC22×C3C2×#120
hypercenter#3560D3
hypocenterC3#18248
LCSG ▷ C22×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3560

Complements

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

NH ≅ G/Ntype
1. C3×#3560C2semidirect
2. #83300C2semidirect
3. #83141C2semidirect
4. #83112C2semidirect
5. #71888C2semidirect
6. #71887C2semidirect
7. #71884C2semidirect
8. #71883C2semidirect
9. #71878C2semidirect
10. #71875C2semidirect
11. #71845C2semidirect
12. #71844C2semidirect
13. #71814C2semidirect
14. #71756C2semidirect
15. #71745C2semidirect
36. C2×C4×D12C22semidirect
41. #5046C22semidirect
42. #5044C22semidirect
45. #5036C22semidirect
48. #5034C22semidirect
54. #4991C22semidirect
56. #4986C22semidirect
61. #4936C22semidirect
62. #4926C22semidirect
63. #4925C22semidirect
64. #4538C22semidirect
65. #4538C22semidirect
70. #4537C22semidirect
71. #4537C22semidirect
72. #4528C22semidirect
73. #4528C22semidirect
76. #3560D3semidirect
98. C3×C4⋊Q8D4semidirect
99. C3×#127D4semidirect
111. C3×#125D4semidirect
116. C3×#124D4semidirect
157. C3×C4×Q8D4semidirect
166. C3×C4×D4D4semidirect
167. C3×C4×D4D4semidirect
168. C3×C4×D4D4semidirect
417. C4⋊Q8#67semidirect
418. #127#67semidirect
430. #125#67semidirect
435. #124#67semidirect
476. C4×Q8#67semidirect
489. C4×D4#67semidirect
490. C4×D4#67semidirect
491. C4×D4#67semidirect
940. C3#18248semidirect

Maximal subgroups

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

subgroupindex
C3×#35602
#833002
#831412
#831122
#718882
#718872
#718842
#718832
#718782
#718752
#718452
#718442
#718142
#717562
#717452
#182483