Finite Group Databasebeta

← #11884632

Subgroups — #11884632

Order 1152.

1018 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5726C211yesmaximal, characteristic, complemented
2C2×#63949C211yesmaximal, characteristic, complemented
3C2×#63943C211yesmaximal, characteristic, complemented
4#10593899C211yesmaximal, characteristic, complemented
5#10592785C211yesmaximal, characteristic, complemented
6C3×#5090C211yesmaximal, characteristic, complemented
7#10591657C211yesmaximal, characteristic, complemented
8#10591653C211yesmaximal, characteristic, complemented
9#10591599C211yesmaximal, characteristic, complemented
10#10591596C211yesmaximal, characteristic, complemented
11#10591589C211yesmaximal, characteristic, complemented
12#10591588C211yesmaximal, characteristic, complemented
13#10590366C211yesmaximal, characteristic, complemented
14#10590358C211yesmaximal, characteristic, complemented
15#10590330C211yesmaximal, characteristic, complemented
16#83528—31nomaximal
17#80500—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×#3799C2211yescharacteristic
21C2×D3×Dic6C2211yescharacteristic
22C32×C4⋊Q8C2211yescharacteristic
23C2×#3756C2211yescharacteristic
24C2×#3756C2211yescharacteristic
25C2×#3755C2211yescharacteristic
26C2×#3755C2211yescharacteristic
27#64084C2211yescharacteristic
28C3×#946C2211yescharacteristic
29C3×#946C2211yescharacteristic
30C2×C3×#216C2211yescharacteristic
31C2×C3×#216C2211yescharacteristic
32C3×#895—21no—
33C3×#894—21no—
34C3×#894—21no—
35C3×D3×C4⋊C4—21no—
36C3×C4×D12C2211yescharacteristic
37C3×C4×D12C2211yescharacteristic
38C3×C4×Dic6C2211yescharacteristic
39#63949—24no—
40#63943—24no—
41#63909C2211yescharacteristic
42#63895—21no—
43#63886—21no—
44#63880—21no—
45#63857C2211yescharacteristic
46#63852—21no—
47C2×#3716C2211yescharacteristic
48C2×#3715C2211yescharacteristic
49C2×#3714C2211yescharacteristic
50C2×#3711C2211yescharacteristic
51C2×D3×C3⋊C8C2211yescharacteristic
52#63630C2211yescharacteristic
53C3×#835C2211yescharacteristic
54C3×#835C2211yescharacteristic
55C3×C4⋊(C3⋊C8)C2211yescharacteristic
56#63576C2211yescharacteristic
57#63567C2211yescharacteristic
58#63565C2211yescharacteristic
59#63564C2211yescharacteristic
60#63562C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
63C3×#547—31no—
64C2×#951—31no—
65C2×#950—31no—
66C2×#919—31no—
67C2×#918—31no—
68#5726D311yescharacteristic, complemented
69#5576—31no—
70#5552—31no—
71C3×#462—31no—
72#5239—31no—
73#5238—31no—
74#5187—31no—
75#5186—31no—
76#5090D311yescharacteristic, complemented
77#5086—31no—
78#5086—31no—
79#5086—61no—
80#5051—31no—
81#5050—31no—
82#5049—31no—
83#5047—31no—
84#5026—31no—
85#5018—31no—
86#5016—31no—
87#5011—31no—
88#4844—31no—
89#4836—31no—
90#4813—31no—
91#4812—31no—
92#4810—31no—
93#4808—31no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×Q8C2311yescharacteristic
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×#634C2311yescharacteristic
98C3×#239—22no—
99C3×#239—22no—
100C3×#239—41no—
101C3×#239—41no—
102C2×C3×D12—21no—
103C2×C3×D12—21no—
104C2×C3×D12D411yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×Dic6C2311yescharacteristic
112C2×#627—21no—
113C2×#626—21no—
114C2×#626—21no—
115C2×#624—21no—
116C2×D3×Dic3—21no—
117#3799—22no—
118#3799—41no—
119D3×Dic6—22no—
120D3×Dic6—41no—
121C32×C4⋊C4—21no—
122C32×C4⋊C4—21no—
123C32×C42C2311yescharacteristic
124#3756—22no—
125#3756—41no—
126#3755—22no—
127#3755—41no—
128#3752—21no—
129#3752—21no—
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132C3×#216—22no—
133C3×#216—22no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4D411yescharacteristic
138C3×(C2×D3)⋊C4D411yescharacteristic
139C3×C4⋊Dic3D411yescharacteristic
140C3×C4⋊Dic3C2311yescharacteristic
141C3×C4⋊Dic3C2311yescharacteristic
142C3×Dic3⋊C4—21no—
143C3×Dic3⋊C4—21no—
144C3×Dic3⋊C4—21no—
145C3×C4×Dic3—21no—
146C2×C3×C3⋊C8C2311yescharacteristic
147C2×C3×C3⋊C8C2311yescharacteristic
148Dic3⋊Dic3—21no—
149#3722—21no—
150(C2×D3)⋊Dic3—21no—
151#3716—22no—
152#3715D414yescomplemented
153#3714—22no—
154#3711—22no—
155D3×C3⋊C8—22no—
156#3269—91noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C2×#239—31no—
160C2×#239C2×D311yescharacteristic
161C2×#239C2×D311yescharacteristic
162C2×D3×Q8—31no—
163C2×#235—31no—
164C22×Dic6—31no—
165C2×C3×Q16—31no—
166C2×C3×Q16—31no—
167C3×C4⋊Q8—21no—
168C3×C4⋊Q8C2×D311yescharacteristic
169C3×C4⋊Q8C2×D311yescharacteristic
170C3×#123—61no—
171C3×#123—61no—
172C3×C22⋊Q8—31no—
173C3×C22⋊Q8—31no—
174C3×#121—61no—
175C3×C4×Q8—31no—
176C3×C4×D4—31no—
177C3×C4×D4—31no—
178C2×C3×C4⋊C4—61no—
179#951—64no—
180#950—64no—
181#946C2×D311yescharacteristic
182#946C2×D311yescharacteristic
183C2×#216—31no—
184C2×#216—31no—
185C2×#216—31no—
186C2×#216—31no—
187C2×#216—61no—
188C2×#216—61no—
189C2×#216C2×D311yescharacteristic
190C2×#216C2×D311yescharacteristic
191C2×#215—31no—
192C2×#215—31no—
193C2×#215—31no—
194C2×#215—31no—
195C2×#215—31no—
196C2×#215—61no—
197C2×#215—61no—
198#939—61no—
199C2×#214—31no—
200C2×#214—31no—
201C2×#213—31no—
202#930—31no—
203#924—31no—
204C2×#208—31no—
205C22×C3⋊C8—31no—
206#919—64no—
207#918—64no—
208C2×D24—31no—
209C2×#204—31no—
210C2×ΓL(1,𝔽25)—31no—
211C2×D3×C8—31no—
212#897—31no—
213#897—61no—
214#896—61no—
215#895—21no—
216#895—31no—
217#895—61no—
218#894—21no—
219#894—21no—
220D3×C4⋊C4—21no—
221#885—61no—
222#67⋊C4—61no—
223#875—31no—
224#875—31no—
225#875—61no—
226#875—61no—
227C4×D12—61no—
228C4×D12C2×D311yescharacteristic
229C4×D12C2×D311yescharacteristic
230C4×Dic6C2×D311yescharacteristic
231C3×C4⋊C8—31no—
232C3×#103—31no—
233C3×#103—31no—
234#835—31no—
235#835C2×D311yescharacteristic
236#835C2×D311yescharacteristic
237#832—31no—
238#830—31no—
239#830—31no—
240#821—31no—
241(C2×D3)⋊C8—31no—
242(C2×D3)⋊C8—31no—
243#816—31no—
244#810—31no—
245#810—31no—
246#809—31no—
247#809—31no—
248#807—31no—
249#807—31no—
250C4⋊(C3⋊C8)C2×D311yescharacteristic
251#803—31no—
252#803—31no—
253#803—61no—
254C22×C3⋊D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3C2×D411yescharacteristic
257C22×C3×D3C2×D411yescharacteristic
258C32×Q8—21no—
259C32×Q8—21no—
260C32×Q8—21no—
261C32×Q8—21no—
262C2×C32×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4C2×D411yescharacteristic
265C2×C32×C4C2×D411yescharacteristic
266C2×C32×C4C2411yescharacteristic
267C2×C3⋊Dic3—21no—
268C4⋊(C3⋊D3)—21no—
269C4⋊(C3⋊D3)—21no—
270#634—21no—
271#634—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3C2×D411yescharacteristic
276C2×C3×Dic3C2×D411yescharacteristic
277C3×D12—21no—
278C3×D12—41no—
279C3×D12—42no—
280C3×D12—42no—
281C3×D12C2×D412yes—
282C3×C4×D3—21no—
283C3×C4×D3—21no—
284C3×C4×D3—21no—
285C3×C4×D3—21no—
286C3×C4×D3—42no—
287C3×C4×D3—42no—
288C3×C4×D3—42no—
289C3×Dic6—21no—
290C3×Dic6C2×D412yes—
291#627—42no—
292#626—42no—
293#626—42no—
294#624—42no—
295D3×Dic3—42no—
296C3⋊(C3⋊C8)—21no—
297C3⋊(C3⋊C8)C2×D412yes—
298C3×C3⋊C8—21no—
299C3×C3⋊C8—21no—
300C2×#137—91no—
301C2×#135—91no—
302#548—91no—
303#547—31no—
304#497—91no—
305#468—91no—
306#467—91no—
307#463—91no—
308#462—31no—
309#452—91no—
310#452—91no—
311#451—91no—
312#449—91no—
313#440—91no—
314#435—91no—
315C3×#41—62no—
316C3×#41—62no—
317C3×#41—121no—
318C3×#41—121no—
319C2×C3×Q8—21no—
320C2×C3×Q8—21no—
321C2×C3×Q8—31no—
322C2×C3×Q8C22×D311yescharacteristic
323C2×C3×Q8C22×D311yescharacteristic
324C2×C3×Q8C22×D311yescharacteristic
325C2×C3×Q8C22×D311yescharacteristic
326C2×C3×D4—31no—
327C2×C3×D4—31no—
328C2×C3×D4—61no—
329C2×C3×D4—61no—
330C22×C3×C4—31no—
331C22×C3×C4—31no—
332C22×C3×C4—61no—
333C22×C3×C4—61no—
334C22×C3×C4—61no—
335C2×#67—61no—
336C2×#67—61no—
337C22×Dic3—61no—
338#239—22no—
339#239—22no—
340#239—41no—
341#239—41no—
342#239—62no—
343#239—121no—
344D3×Q8—62no—
345D3×Q8—121no—
346#235—62no—
347#235—121no—
348C2×D12—21no—
349C2×D12—21no—
350C2×D12—31no—
351C2×D12—31no—
352C2×D12—61no—
353C2×D12—61no—
354C2×D12—61no—
355C2×D12#6711yescharacteristic
356C2×D12C22×D311yescharacteristic
357C2×C4×D3—21no—
358C2×C4×D3—21no—
359C2×C4×D3—21no—
360C2×C4×D3—61no—
361C2×C4×D3—61no—
362C2×C4×D3—61no—
363C2×C4×D3C22×D311yescharacteristic
364C2×C4×D3C22×D311yescharacteristic
365C2×Dic6—31no—
366C2×Dic6—31no—
367C2×Dic6—61no—
368C2×Dic6—62no—
369C2×Dic6—61no—
370C2×Dic6—61no—
371C2×Dic6—121no—
372C2×Dic6C22×D311yescharacteristic
373C3×Q16—62no—
374C3×Q16—62no—
375C2×C3×C8—31no—
376C2×C3×C8—31no—
377C3×C4⋊C4—21no—
378C3×C4⋊C4—21no—
379C3×C4⋊C4—21no—
380C3×C4⋊C4—21no—
381C3×C4⋊C4—31no—
382C3×C4⋊C4—31no—
383C3×C4⋊C4—31no—
384C3×C4⋊C4—41no—
385C3×C4⋊C4—41no—
386C3×C4⋊C4—61no—
387C3×C4⋊C4—61no—
388C3×C4⋊C4—61no—
389C3×C22⋊C4—31no—
390C3×C22⋊C4—31no—
391C3×C22⋊C4—61no—
392C3×C22⋊C4—61no—
393C3×C22⋊C4—61no—
394C3×C42—21no—
395C3×C42—61no—
396C3×C42C22×D311yescharacteristic
397C3×C42C22×D311yescharacteristic
398#217—61no—
399#216—22no—
400#216—22no—
401#216—62no—
402#216—62no—
403#216—122no—
404#216—121no—
405#216—121no—
406#216—122no—
407#215—34no—
408#215—62no—
409#215—62no—
410#215—122no—
411#215—121no—
412#215—121no—
413#215—122no—
414#214—34no—
415#214—62no—
416#213—62no—
417(C2×D3)⋊C4—21no—
418(C2×D3)⋊C4—21no—
419(C2×D3)⋊C4—21no—
420(C2×D3)⋊C4—61no—
421(C2×D3)⋊C4—61no—
422(C2×D3)⋊C4—61no—
423(C2×D3)⋊C4—61no—
424(C2×D3)⋊C4—61no—
425(C2×D3)⋊C4—61no—
426(C2×D3)⋊C4—61no—
427(C2×D3)⋊C4—121no—
428(C2×D3)⋊C4—121no—
429(C2×D3)⋊C4#6711yescharacteristic
430(C2×D3)⋊C4#6711yescharacteristic
431C4⋊Dic3—61no—
432C4⋊Dic3#6711yescharacteristic
433C4⋊Dic3C22×D311yescharacteristic
434C4⋊Dic3C22×D311yescharacteristic
435Dic3⋊C4—21no—
436Dic3⋊C4—21no—
437Dic3⋊C4—21no—
438Dic3⋊C4—61no—
439C4×Dic3—21no—
440#208—62no—
441C2×C3⋊C8—31no—
442C2×C3⋊C8—31no—
443C2×C3⋊C8—31no—
444C2×C3⋊C8—31no—
445C2×C3⋊C8—61no—
446C2×C3⋊C8—61no—
447C2×C3⋊C8—62no—
448C2×C3⋊C8C22×D311yescharacteristic
449C2×C3⋊C8C22×D311yescharacteristic
450D24—62no—
451#204—62no—
452ΓL(1,𝔽25)—62no—
453D3×C8—62no—
454C22×C32C22×D411yescharacteristic
455C2×C3⋊D3—41no—
456C2×C3⋊D3—41no—
457C2×C3⋊D3—41no—
458C2×C3×D3—21no—
459C2×C3×D3—21no—
460C2×C3×D3—22no—
461C2×C3×D3—21no—
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—21no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C32×C4—21no—
468C32×C4—21no—
469C32×C4—41no—
470C32×C4—41no—
471C32×C4C22×D411yescharacteristic
472C32×C4H(5,𝔽2)11yescharacteristic
473C3⋊Dic3—41no—
474C3×Dic3—22no—
475C3×Dic3—21no—
476C3×Dic3—21no—
477C3×Dic3—41no—
478C3×Dic3—41no—
479C2×#41—31no—
480C2×#41—31no—
481C2×#41—91no—
482C22×Q8—91no—
483#137—184no—
484#135—184no—
485C2×Q16—31no—
486C2×Q16—31no—
487C2×Q16—91no—
488C2×Q16—91no—
489C2×SD16—91no—
490C2×SD16—91no—
491C2×SD16—91no—
492C2×SD16—91no—
493C2×D8—91no—
494C2×M16—91no—
495C22×C8—91no—
496C4⋊Q8D3211yescharacteristic
497#124—91no—
498#124—181no—
499#123—61no—
500#123—61no—
501C22⋊Q8—31no—
502C22⋊Q8—31no—
503C22⋊Q8—91no—
504C22⋊Q8—181no—
505#121—61no—
506#121—91no—
507#121—181no—
508C4×Q8—31no—
509C4×D4—31no—
510C4×D4—31no—
511C4×D4—181no—
512C2×C4⋊C4—61no—
513#107—91no—
514C4⋊C8—31no—
515#103—31no—
516#103—31no—
517#103—91no—
518#103—91no—
519#102—91no—
520#102—91no—
521C22⋊C8—91no—
522C22⋊C8—91no—
523#97—91no—
524C23×C3—31no—
525C23×C3—31no—
526C23×C3—61no—
527C22×D3—21no—
528C22×D3—61no—
529C22×D3—61no—
530C22×D3—121no—
531C22×D3C2×#6711yescharacteristic
532C22×D3C2×#6711yescharacteristic
533C3×Q8—21no—
534C3×Q8—21no—
535C3×Q8—21no—
536C3×Q8—21no—
537C3×Q8—21no—
538C3×Q8—21no—
539C3×Q8—21no—
540C3×Q8—21no—
541C3×Q8—32no—
542C3×Q8—41no—
543C3×Q8—41no—
544C3×Q8—41no—
545C3×Q8—41no—
546C3×Q8—61no—
547C3×D4—32no—
548C3×D4—61no—
549C3×D4—121no—
550C3×D4—122no—
551C3×D4—122no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—31no—
560C2×C3×C4—31no—
561C2×C3×C4—41no—
562C2×C3×C4—41no—
563C2×C3×C4—61no—
564C2×C3×C4—61no—
565C2×C3×C4—61no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—61no—
569C2×C3×C4—61no—
570C2×C3×C4—122no—
571C2×C3×C4—122no—
572C2×C3×C4—122no—
573C2×C3×C4D3×D411yescharacteristic
574C2×C3×C4D3×D411yescharacteristic
575C2×C3×C4C2×#6711yescharacteristic
576C2×C3×C4C2×#6711yescharacteristic
577C2×C3×C4C23×D311yescharacteristic
578C2×C3×C4C23×D311yescharacteristic
579#67—122no—
580#67—122no—
581C2×Dic3—21no—
582C2×Dic3—21no—
583C2×Dic3—21no—
584C2×Dic3—61no—
585C2×Dic3—61no—
586C2×Dic3—121no—
587C2×Dic3—122no—
588C2×Dic3C2×#6711yescharacteristic
589C2×Dic3C2×#6711yescharacteristic
590D12—21no—
591D12—41no—
592D12—42no—
593D12—42no—
594D12—61no—
595D12—61no—
596D12—61no—
597D12—61no—
598D12—121no—
599D12—121no—
600D12—122no—
601D12—122no—
602D12D3×D412yes—
603C4×D3—21no—
604C4×D3—21no—
605C4×D3—21no—
606C4×D3—21no—
607C4×D3—42no—
608C4×D3—42no—
609C4×D3—42no—
610C4×D3—122no—
611C4×D3—122no—
612C4×D3—122no—
613Dic6—21no—
614Dic6—61no—
615Dic6—61no—
616Dic6—61no—
617Dic6—61no—
618Dic6—121no—
619Dic6—121no—
620Dic6—122no—
621Dic6—122no—
622Dic6D3×D412yes—
623C3×C8—61no—
624C3×C8—61no—
625C3⋊C8—21no—
626C3⋊C8—21no—
627C3⋊C8—32no—
628C3⋊C8—32no—
629C3⋊C8—62no—
630C3⋊C8—62no—
631C3⋊C8—61no—
632C3⋊C8—61no—
633C2×C32D4211yescharacteristic
634C2×C32#57511yescharacteristic
635C2×C32#57811yescharacteristic
636C3⋊D3—81no—
637C3×D3—41no—
638C3×D3—41no—
639C3×D3—42no—
640#41—62no—
641#41—62no—
642#41—121no—
643#41—121no—
644#41—182no—
645#41—361no—
646C2×Q8—31no—
647C2×Q8—91no—
648C2×Q8—181no—
649C2×Q8—182no—
650C2×Q8—361no—
651C2×Q8C2×D3211yescharacteristic
652C2×Q8C2×D3211yescharacteristic
653C2×D4—31no—
654C2×D4—31no—
655C2×D4—61no—
656C2×D4—61no—
657C2×D4—91no—
658C2×D4—181no—
659C2×D4—181no—
660C22×C4—31no—
661C22×C4—31no—
662C22×C4—61no—
663C22×C4—61no—
664C22×C4—61no—
665C22×C4—181no—
666C22×C4—181no—
667Q16—62no—
668Q16—62no—
669Q16—182no—
670Q16—361no—
671SD16—94no—
672SD16—182no—
673SD16—182no—
674SD16—361no—
675D8—182no—
676M16—182no—
677C2×C8—31no—
678C2×C8—31no—
679C2×C8—91no—
680C2×C8—91no—
681C2×C8—182no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—31no—
685C4⋊C4—31no—
686C4⋊C4—31no—
687C4⋊C4—61no—
688C4⋊C4—61no—
689C4⋊C4—61no—
690C4⋊C4—181no—
691C22⋊C4—31no—
692C22⋊C4—31no—
693C22⋊C4—61no—
694C22⋊C4—61no—
695C22⋊C4—61no—
696C22⋊C4—181no—
697C22⋊C4—181no—
698C22⋊C4—181no—
699C22⋊C4—181no—
700C42—61no—
701C42C2×D3211yescharacteristic
702C22×C3—21no—
703C22×C3—61no—
704C22×C3—61no—
705C22×C3—61no—
706C22×C3—61no—
707C22×C3—61no—
708C22×C3—61no—
709C22×C3—62no—
710C22×C3—121no—
711C22×C3—121no—
712C22×C3C2×D3×D411yescharacteristic
713C22×C3C22×#6711yescharacteristic
714C2×D3—21no—
715C2×D3—21no—
716C2×D3—22no—
717C2×D3—21no—
718C2×D3—21no—
719C2×D3—21no—
720C2×D3—21no—
721C2×D3—41no—
722C2×D3—41no—
723C2×D3—121no—
724C2×D3—121no—
725C2×D3—121no—
726C2×D3—121no—
727C2×D3—121no—
728C2×D3—121no—
729C2×D3—241no—
730C2×D3—241no—
731C2×D3—241no—
732C3×C4—21no—
733C3×C4—21no—
734C3×C4—21no—
735C3×C4—21no—
736C3×C4—21no—
737C3×C4—21no—
738C3×C4—41no—
739C3×C4—41no—
740C3×C4—41no—
741C3×C4—41no—
742C3×C4—41no—
743C3×C4—41no—
744C3×C4—62no—
745C3×C4—61no—
746C3×C4—61no—
747C3×C4—81no—
748C3×C4—81no—
749C3×C4—121no—
750C3×C4—121no—
751C3×C4C2×D3×D411yescharacteristic
752C3×C4C2×D3×D411yescharacteristic
753C3×C4#100411yescharacteristic
754C3×C4#100911yescharacteristic
755Dic3—21no—
756Dic3—21no—
757Dic3—22no—
758Dic3—41no—
759Dic3—41no—
760Dic3—121no—
761Dic3—121no—
762Dic3—241no—
763C32#326911yescharacteristic, complemented, Sylow
764C23—31no—
765C23—31no—
766C23—61no—
767C23—181no—
768Q8—21no—
769Q8—21no—
770Q8—21no—
771Q8—21no—
772Q8—32no—
773Q8—61no—
774Q8—181no—
775Q8—181no—
776Q8—362no—
777D4—32no—
778D4—61no—
779D4—121no—
780D4—122no—
781D4—122no—
782D4—181no—
783D4—181no—
784D4—362no—
785D4—362no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—31no—
789C2×C4—31no—
790C2×C4—61no—
791C2×C4—61no—
792C2×C4—61no—
793C2×C4—61no—
794C2×C4—61no—
795C2×C4—61no—
796C2×C4—61no—
797C2×C4—122no—
798C2×C4—122no—
799C2×C4—122no—
800C2×C4—181no—
801C2×C4—362no—
802C2×C4—362no—
803C2×C4D3×#6711yescharacteristic
804C2×C4D3×#6711yescharacteristic
805C2×C4C22×D3211yescharacteristic
806C8—61no—
807C8—61no—
808C8—92no—
809C8—181no—
810C2×C3—21no—
811C2×C3—21no—
812C2×C3—21no—
813C2×C3—121no—
814C2×C3—121no—
815C2×C3—122no—
816C2×C3#560911yescharacteristic
817C2×C3#576611yescharacteristic
818C2×C3#577711yescharacteristic
819C2×C3D4×#6711yescharacteristic
820C2×C3#582211yescharacteristic
821C2×C3#583811yescharacteristic
822D3—41no—
823D3—41no—
824D3—42no—
825D3—241no—
826D3—241no—
827D3—481no—
828C22—61no—
829C22—61no—
830C22—62no—
831C22—61no—
832C22—61no—
833C22—61no—
834C22—61no—
835C22—121no—
836C22—121no—
837C22—361no—
838C22—361no—
839C22—361no—
840C22C2×D3×#6711yescharacteristic
841C4—21no—
842C4—21no—
843C4—41no—
844C4—41no—
845C4—61no—
846C4—61no—
847C4—62no—
848C4—121no—
849C4—121no—
850C4—361no—
851C4D32×D411yescharacteristic
852C4#6431411yescharacteristic
853C3—21no—
854C3#8050011yescharacteristic, complemented
855C3#8352811yescharacteristic, complemented
856C2—121no—
857C2—121no—
858C2—122no—
859C2—721no—
860C2#1059528811yescharacteristic
861C2#1059531711yescharacteristic
862C2#1059532711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
hypercenterC4⋊Q8D32
hypocenterC32#3269
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5726C2semidirect
2. C2×#63949C2semidirect
3. C2×#63943C2semidirect
4. #10593899C2semidirect
5. #10592785C2semidirect
6. C3×#5090C2semidirect
7. #10591657C2semidirect
8. #10591653C2semidirect
9. #10591599C2semidirect
10. #10591596C2semidirect
11. #10591589C2semidirect
12. #10591588C2semidirect
13. #10590366C2semidirect
14. #10590358C2semidirect
15. #10590330C2semidirect
68. #5726D3semidirect
76. #5090D3semidirect
152. #3715D4semidirect
763. C32#3269semidirect
854. C3#80500semidirect
855. C3#83528semidirect

Maximal subgroups

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

subgroupindex
C3×#57262
C2×#639492
C2×#639432
#105938992
#105927852
C3×#50902
#105916572
#105916532
#105915992
#105915962
#105915892
#105915882
#105903662
#105903582
#105903302
#835283
#805003