Finite Group Databasebeta

← #11866295

Subgroups — #11866295

Order 1152.

1063 conjugacy classes of subgroups.

The subgroup lattice has 851 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595364C211yesmaximal, characteristic, complemented
2C2×#63940C211yesmaximal, characteristic, complemented
3C2×#63798C211yesmaximal, characteristic
4#10594606C211yesmaximal, characteristic, complemented
5#10592501C211yesmaximal, characteristic, complemented
6C3×#4819C211yesmaximal, characteristic, complemented
7C3×#4818C211yesmaximal, characteristic, complemented
8#10591567C211yesmaximal, characteristic, complemented
9#10591564C211yesmaximal, characteristic, complemented
10#10590755C211yesmaximal, characteristic, complemented
11#10590752C211yesmaximal, characteristic, complemented
12#10590702C211yesmaximal, characteristic, complemented
13#10590611C211yesmaximal, characteristic, complemented
14#10590559C211yesmaximal, characteristic, complemented
15#10590530C211yesmaximal, characteristic, complemented
16#80537—31nomaximal
17#80430—31nomaximal
18C2×Q8×C3⋊D3C2211yescharacteristic
19C2×#3802C2211yescharacteristic
20C2×#3796C2211yescharacteristic
21C2×#3743C2211yescharacteristic
22#64101C2211yescharacteristic
23C3×#947C2211yescharacteristic, complemented
24C3×#944C2211yescharacteristic, complemented
25C2×C3×#215C2211yescharacteristic
26C2×C3×#215C2211yescharacteristic
27C2×C3×D24C2211yescharacteristic
28C2×C3×#204C2211yescharacteristic
29C3×#893C2211yescharacteristic
30C3×#893C2211yescharacteristic
31#63940—24no—
32D3×(C2×D3)⋊C4—21no—
33D3×(C2×D3)⋊C4—21no—
34#63902—21no—
35C4×#625—21no—
36#63896—21no—
37#63896—21no—
38Dic3×D12C2211yescharacteristic
39Dic3×D12C2211yescharacteristic
40#63874C2211yescharacteristic
41#63866C2211yescharacteristic, complemented
42#63860C2211yescharacteristic, complemented
43#63853—21no—
44#63853—21no—
45C2×#3716C2211yescharacteristic
46C2×#3716C2211yescharacteristic
47C2×#3715C2211yescharacteristic
48C2×#3713C2211yescharacteristic
49C2×#3710C2211yescharacteristic
50#63798—24no—
51C32×#103C2211yescharacteristic, complemented
52#63662C2211yescharacteristic, complemented
53#63643C2211yescharacteristic, complemented
54#63637C2211yescharacteristic, complemented
55C3×Dic3⋊C8C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57C3×#810C2211yescharacteristic, complemented
58C3×#809C2211yescharacteristic, complemented
59Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
60Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
61#63566C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63C2×#914—31no—
64C2×D3×SD16—31no—
65C2×D3×SD16—31no—
66C2×#911—31no—
67#5724—31no—
68#5675—31no—
69#5545—31no—
70#5545—31no—
71C3×#463—31no—
72C3×#461—31no—
73#5165—31no—
74#5162—31no—
75#5162—31no—
76#5153—31no—
77#5083—31no—
78#5057—31no—
79#5019—31no—
80#5016—31no—
81#4844—31no—
82#4841—31no—
83#4839—31no—
84#4839—31no—
85#4819D311yescharacteristic, complemented
86#4818—31no—
87#4818D311yescharacteristic, complemented
88#4804—31no—
89#4802—31no—
90#4802—31no—
91#4802—61no—
92#4787—31no—
93#4772—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96Q8×C3⋊D3—22no—
97Q8×C3⋊D3—22no—
98C2×C4×C3⋊D3—21no—
99C2×C4×C3⋊D3C2311yescharacteristic
100C2×#634—21no—
101C2×#634C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—21no—
107C2×C3×Dic6C2311yescharacteristic
108C2×#626—21no—
109C2×#625—21no—
110C2×D3×Dic3—21no—
111C2×D3×Dic3—21no—
112C2×D3×Dic3—21no—
113#3802—22no—
114#3802D414yes—
115#3796—22no—
116#3796—22no—
117C2×C32×C8C2311yescharacteristic
118C32×C4⋊C4C2311yescharacteristic
119#3752—21no—
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121C4×C3⋊Dic3—21no—
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123#3743—22no—
124C3×#215—22no—
125C3×#215—22no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×C4×Dic3C2311yescharacteristic
133C3×C4×Dic3C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C3×D24—22no—
137C3×#204—22no—
138#3724D411yescharacteristic
139#3724D411yescharacteristic
140Dic3⋊Dic3—21no—
141Dic3⋊Dic3—21no—
142#3722D411yescharacteristic
143#3722D411yescharacteristic
144(C2×D3)⋊Dic3—21no—
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148#3716—22no—
149#3716—22no—
150#3715—22no—
151#3713—22no—
152#3710—22no—
153#3042—91noSylow
154C2×#239—31no—
155C2×D3×Q8—31no—
156C2×D3×Q8—31no—
157C2×D3×Q8—61no—
158C2×#237—31no—
159C2×D3×D4—31no—
160C2×D3×D4—31no—
161C2×C3×SD16—31no—
162C2×C3×SD16—31no—
163C2×C3×SD16—31no—
164C2×C3×D8—31no—
165C3×C4⋊Q8—31no—
166C3×#124—31no—
167C3×C4×D4—31no—
168C3×C4×D4—31no—
169#947C2×D311yescharacteristic, complemented
170#944—31no—
171#944C2×D311yescharacteristic, complemented
172C2×#215—31no—
173C2×#215C2×D311yescharacteristic
174C2×#215C2×D311yescharacteristic
175#936—31no—
176D4×Dic3—31no—
177D4×Dic3—31no—
178C2×#214—31no—
179C2×#214—31no—
180C2×#214—31no—
181C2×#213—31no—
182C2×#213—31no—
183C4×#67—61no—
184C4×#67—61no—
185C2×(C2×D3)⋊C4—61no—
186C2×(C2×D3)⋊C4—61no—
187#914—64no—
188D3×SD16—64no—
189D3×SD16—64no—
190#911—64no—
191C2×D24C2×D311yescharacteristic
192C2×#204—31no—
193C2×#204—31no—
194C2×#204C2×D311yescharacteristic
195C2×ΓL(1,𝔽25)—31no—
196C2×ΓL(1,𝔽25)—31no—
197C2×ΓL(1,𝔽25)—61no—
198C2×D3×C8—31no—
199C2×D3×C8—31no—
200#896—61no—
201#896—61no—
202#894—61no—
203#894—61no—
204#893C2×D311yescharacteristic
205#893C2×D311yescharacteristic
206#892—31no—
207#892—31no—
208#892—61no—
209#883—61no—
210#883—61no—
211#67⋊C4—61no—
212#67⋊C4—61no—
213D3×C22⋊C4—61no—
214D3×C22⋊C4—61no—
215#878—61no—
216#878—61no—
217#875—31no—
218C4×D12—31no—
219C4×D12—31no—
220#872—31no—
221#872—31no—
222#869—31no—
223C3×C4⋊C8—31no—
224C3×C4⋊C8—31no—
225C3×#103—21no—
226C3×#103—31no—
227C3×#103C2×D311yescharacteristic, complemented
228C3×#103C2×D311yescharacteristic, complemented
229C3×#102—31no—
230#835—31no—
231#835—31no—
232#835—31no—
233#835—61no—
234#832—31no—
235#821—31no—
236#816—31no—
237#816—31no—
238#816—31no—
239#816—61no—
240Dic3⋊C8—31no—
241Dic3⋊C8—31no—
242Dic3⋊C8C2×D311yescharacteristic, complemented
243Dic3⋊C8C2×D311yescharacteristic, complemented
244#810—31no—
245#810—31no—
246#810—61no—
247#810C2×D311yescharacteristic, complemented
248#809C2×D311yescharacteristic, complemented
249C4⋊(C3⋊C8)—31no—
250C4⋊(C3⋊C8)—31no—
251C22×C3⋊D3C2×D411yescharacteristic
252C22×C3×D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3—21no—
255C2×D32—24no—
256C2×D32—81no—
257C2×D32—81no—
258C32×Q8—21no—
259C32×Q8—21no—
260C2×C32×C4—21no—
261C2×C32×C4—21no—
262C2×C32×C4C2411yescharacteristic
263C2×C3⋊Dic3—21no—
264C2×C3⋊Dic3—21no—
265C2×C3⋊Dic3C2×D411yescharacteristic
266C4×C3⋊D3—42no—
267C4×C3⋊D3C2×D412yes—
268C4×C3⋊D3#4112yes—
269#634—21no—
270#634—21no—
271#634—42no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3C2×D411yescharacteristic
274C2×C3×Dic3C2×D411yescharacteristic
275C2×C3×Dic3C2×D411yescharacteristic
276C2×C3×Dic3C2×D411yescharacteristic
277C3×D12—21no—
278C3×D12—21no—
279C3×D12—21no—
280C3×D12—21no—
281C3×D12C2×D412yes—
282C3×D12C2×D412yes—
283C3×C4×D3—81no—
284C3×C4×D3—81no—
285C3×Dic6—21no—
286C3×Dic6—21no—
287#626—42no—
288#625—24no—
289D3×Dic3—42no—
290D3×Dic3—81no—
291D3×Dic3—81no—
292C32×C8—21no—
293C3⋊(C3⋊C8)—21no—
294C3×C3⋊C8—21no—
295C3×C3⋊C8—21no—
296C2×AGL(1,ℤ/8)—91no—
297C22×SD16—91no—
298#536—91no—
299#518—91no—
300#463—31no—
301#463—91no—
302#463—91no—
303#463—91no—
304#461—31no—
305#461—91no—
306#461—91no—
307#461—91no—
308#424—91no—
309#419—91no—
310#416—91no—
311C23×D3—61no—
312C23×D3—61no—
313C2×C3×Q8—21no—
314C2×C3×Q8—31no—
315C2×C3×Q8C22×D311yescharacteristic
316C2×C3×Q8C22×D311yescharacteristic
317C2×C3×D4—31no—
318C2×C3×D4—31no—
319C2×C3×D4—31no—
320C22×C3×C4—61no—
321C22×C3×C4—61no—
322C2×#67—61no—
323C2×#67—61no—
324C2×#67—61no—
325C22×Dic3—61no—
326C22×Dic3—61no—
327C22×Dic3—61no—
328#239—62no—
329#239—62no—
330D3×Q8—62no—
331D3×Q8—62no—
332D3×Q8—62no—
333D3×Q8—62no—
334D3×Q8—64no—
335D3×Q8—122no—
336#237—62no—
337#237—62no—
338D3×D4—34no—
339D3×D4—34no—
340D3×D4—62no—
341D3×D4—62no—
342C2×D12—61no—
343C2×D12C22×D311yescharacteristic
344C2×D12C22×D311yescharacteristic
345C2×D12C22×D311yescharacteristic
346C2×C4×D3—21no—
347C2×C4×D3—21no—
348C2×C4×D3—31no—
349C2×C4×D3—31no—
350C2×C4×D3—61no—
351C2×C4×D3—61no—
352C2×C4×D3—61no—
353C2×C4×D3—61no—
354C2×C4×D3—61no—
355C2×C4×D3—61no—
356C2×C4×D3—121no—
357C2×Dic6—31no—
358C2×Dic6—31no—
359C2×Dic6—61no—
360C2×Dic6—61no—
361C2×Dic6—61no—
362C2×Dic6—121no—
363C2×Dic6C22×D311yescharacteristic
364C3×SD16—62no—
365C3×SD16—62no—
366C3×SD16—62no—
367C3×D8—62no—
368C2×C3×C8—21no—
369C2×C3×C8—31no—
370C2×C3×C8—31no—
371C2×C3×C8C22×D311yescharacteristic
372C2×C3×C8C22×D311yescharacteristic
373C3×C4⋊C4—21no—
374C3×C4⋊C4—61no—
375C3×C4⋊C4—61no—
376C3×C4⋊C4C22×D311yescharacteristic
377C3×C4⋊C4C22×D311yescharacteristic
378C3×C22⋊C4—61no—
379C3×C22⋊C4—61no—
380C3×C22⋊C4—61no—
381C3×C22⋊C4—61no—
382C3×C42—31no—
383C3×C42—31no—
384#217—61no—
385#217—61no—
386#217—61no—
387#217—61no—
388#215—22no—
389#215—22no—
390#215—62no—
391#214—62no—
392#214—62no—
393#214—62no—
394#213—62no—
395#213—62no—
396(C2×D3)⋊C4—21no—
397(C2×D3)⋊C4—21no—
398(C2×D3)⋊C4—21no—
399(C2×D3)⋊C4—21no—
400(C2×D3)⋊C4—31no—
401(C2×D3)⋊C4—31no—
402(C2×D3)⋊C4—31no—
403(C2×D3)⋊C4—31no—
404(C2×D3)⋊C4—61no—
405(C2×D3)⋊C4—61no—
406(C2×D3)⋊C4—61no—
407(C2×D3)⋊C4—61no—
408(C2×D3)⋊C4—61no—
409(C2×D3)⋊C4—61no—
410(C2×D3)⋊C4—121no—
411C4⋊Dic3—31no—
412C4⋊Dic3—31no—
413C4⋊Dic3—61no—
414C4⋊Dic3—61no—
415C4⋊Dic3—61no—
416Dic3⋊C4—21no—
417Dic3⋊C4—21no—
418Dic3⋊C4—31no—
419Dic3⋊C4—31no—
420Dic3⋊C4—31no—
421Dic3⋊C4—31no—
422Dic3⋊C4—61no—
423Dic3⋊C4—61no—
424C4×Dic3—61no—
425C4×Dic3—61no—
426C4×Dic3—121no—
427C4×Dic3C22×D311yescharacteristic
428C4×Dic3C22×D311yescharacteristic
429C2×C3⋊C8—31no—
430C2×C3⋊C8—31no—
431C2×C3⋊C8—61no—
432C2×C3⋊C8C22×D311yescharacteristic
433C2×C3⋊C8C22×D311yescharacteristic
434D24—22no—
435#204—22no—
436#204—62no—
437#204—62no—
438ΓL(1,𝔽25)—62no—
439ΓL(1,𝔽25)—62no—
440ΓL(1,𝔽25)—122no—
441D3×C8—62no—
442D3×C8—62no—
443C22×C32C22×D411yescharacteristic
444C2×C3⋊D3—21no—
445C2×C3⋊D3—21no—
446C2×C3⋊D3#12112yes—
447C2×C3×D3—22no—
448C2×C3×D3—22no—
449C2×C3×D3—41no—
450C2×C3×D3—41no—
451C2×C3×D3—41no—
452C2×C3×D3—41no—
453C2×C3×D3—41no—
454C2×C3×D3—41no—
455C2×C3×D3—41no—
456D32—84no—
457C32×C4—41no—
458C32×C4—41no—
459C32×C4C22×D411yescharacteristic
460C32×C4C2×#4111yescharacteristic
461C3⋊Dic3—41no—
462C3⋊Dic3—41no—
463C3⋊Dic3#12112yes—
464C3×Dic3—21no—
465C3×Dic3—21no—
466C3×Dic3—21no—
467C3×Dic3—21no—
468C3×Dic3—41no—
469C2×#41—91no—
470C22×Q8—91no—
471C22×D4—91no—
472AGL(1,ℤ/8)—184no—
473C2×SD16—31no—
474C2×SD16—31no—
475C2×SD16—31no—
476C2×SD16—91no—
477C2×SD16—91no—
478C2×SD16—91no—
479C2×SD16—184no—
480C2×D8—31no—
481C2×D8—91no—
482C2×M16—91no—
483C22×C8—91no—
484C4⋊Q8—31no—
485C4⋊Q8—91no—
486#124—31no—
487#124—91no—
488#123—181no—
489#123—181no—
490C22⋊Q8—181no—
491C22⋊Q8—181no—
492C4×D4—31no—
493C4×D4—31no—
494C4×D4—91no—
495C4×D4—91no—
496C4×D4—181no—
497C4×D4—181no—
498#117—91no—
499#117—91no—
500C2×C22⋊C4—181no—
501C2×C22⋊C4—181no—
502C4⋊C8—31no—
503C4⋊C8—31no—
504C4⋊C8—91no—
505C4⋊C8—91no—
506#103—31no—
507#103—91no—
508#103—91no—
509#103—91no—
510#103—91no—
511#103D3211yescharacteristic, complemented
512#102—31no—
513#102—91no—
514C23×C3—61no—
515C23×C3—61no—
516C23×C3—61no—
517C22×D3—21no—
518C22×D3—21no—
519C22×D3—21no—
520C22×D3—31no—
521C22×D3—31no—
522C22×D3—61no—
523C22×D3—64no—
524C22×D3—64no—
525C22×D3—241no—
526C22×D3—241no—
527C22×D3—241no—
528C22×D3—241no—
529C3×Q8—22no—
530C3×Q8—21no—
531C3×Q8—21no—
532C3×Q8—21no—
533C3×Q8—21no—
534C3×Q8—41no—
535C3×Q8—61no—
536C3×Q8—61no—
537C3×D4—32no—
538C3×D4—32no—
539C3×D4—61no—
540C3×D4—61no—
541C3×D4—61no—
542C3×D4—61no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—31no—
549C2×C3×C4—31no—
550C2×C3×C4—31no—
551C2×C3×C4—31no—
552C2×C3×C4—41no—
553C2×C3×C4—41no—
554C2×C3×C4—61no—
555C2×C3×C4—241no—
556C2×C3×C4—241no—
557C2×C3×C4C23×D311yescharacteristic
558C2×C3×C4C23×D311yescharacteristic
559#67—64no—
560#67—64no—
561#67—122no—
562C2×Dic3—21no—
563C2×Dic3—31no—
564C2×Dic3—31no—
565C2×Dic3—61no—
566C2×Dic3—61no—
567C2×Dic3—61no—
568C2×Dic3—61no—
569C2×Dic3—61no—
570C2×Dic3—121no—
571C2×Dic3—121no—
572C2×Dic3—122no—
573C2×Dic3—241no—
574C2×Dic3—241no—
575C2×Dic3D3×D411yescharacteristic
576C2×Dic3D3×D411yescharacteristic
577C2×Dic3D3×D411yescharacteristic
578C2×Dic3D3×D411yescharacteristic
579D12—21no—
580D12—21no—
581D12—21no—
582D12—21no—
583D12—122no—
584D12D3×D412yes—
585D12D3×D412yes—
586C4×D3—32no—
587C4×D3—32no—
588C4×D3—32no—
589C4×D3—32no—
590C4×D3—62no—
591C4×D3—62no—
592C4×D3—81no—
593C4×D3—81no—
594C4×D3—122no—
595C4×D3—122no—
596C4×D3—122no—
597C4×D3—124no—
598C4×D3—241no—
599C4×D3—241no—
600Dic6—21no—
601Dic6—21no—
602Dic6—62no—
603Dic6—61no—
604Dic6—61no—
605Dic6—61no—
606Dic6—61no—
607Dic6—121no—
608Dic6—122no—
609Dic6—122no—
610Dic6—124no—
611C3×C8—21no—
612C3×C8—21no—
613C3×C8—41no—
614C3×C8—61no—
615C3×C8—61no—
616C3⋊C8—21no—
617C3⋊C8—21no—
618C3⋊C8—61no—
619C3⋊C8—61no—
620C3⋊C8—121no—
621C2×C32C2×#12111yescharacteristic
622C2×C32#57711yescharacteristic
623C2×C32#57711yescharacteristic
624C3⋊D3—22no—
625C3×D3—42no—
626C3×D3—42no—
627C3×D3—81no—
628C24—181no—
629#41—182no—
630#41—182no—
631C2×Q8—31no—
632C2×Q8—91no—
633C2×Q8—181no—
634C2×Q8—182no—
635C2×Q8—182no—
636C2×Q8C2×D3211yescharacteristic
637C2×D4—31no—
638C2×D4—31no—
639C2×D4—31no—
640C2×D4—94no—
641C2×D4—181no—
642C2×D4—182no—
643C2×D4—181no—
644C22×C4—61no—
645C22×C4—61no—
646C22×C4—91no—
647C22×C4—181no—
648C22×C4—181no—
649C22×C4—181no—
650C22×C4—181no—
651SD16—62no—
652SD16—62no—
653SD16—62no—
654SD16—182no—
655SD16—182no—
656SD16—182no—
657D8—62no—
658D8—182no—
659M16—182no—
660C2×C8—31no—
661C2×C8—31no—
662C2×C8—91no—
663C2×C8—182no—
664C2×C8C2×D3211yescharacteristic
665C4⋊C4—61no—
666C4⋊C4—61no—
667C4⋊C4—91no—
668C4⋊C4—91no—
669C4⋊C4—91no—
670C4⋊C4—181no—
671C4⋊C4—181no—
672C4⋊C4C2×D3211yescharacteristic
673C22⋊C4—61no—
674C22⋊C4—61no—
675C22⋊C4—61no—
676C22⋊C4—61no—
677C22⋊C4—91no—
678C22⋊C4—91no—
679C22⋊C4—181no—
680C22⋊C4—181no—
681C22⋊C4—181no—
682C22⋊C4—181no—
683C22⋊C4—181no—
684C42—31no—
685C42—31no—
686C42—181no—
687C22×C3—21no—
688C22×C3—62no—
689C22×C3—62no—
690C22×C3—121no—
691C22×C3—121no—
692C22×C3—121no—
693C22×C3—121no—
694C22×C3—121no—
695C22×C3—121no—
696C22×C3—121no—
697C22×C3C2×D3×D411yescharacteristic
698C22×C3C2×D3×D411yescharacteristic
699C2×D3—22no—
700C2×D3—22no—
701C2×D3—32no—
702C2×D3—32no—
703C2×D3—41no—
704C2×D3—41no—
705C2×D3—41no—
706C2×D3—41no—
707C2×D3—41no—
708C2×D3—41no—
709C2×D3—41no—
710C2×D3—62no—
711C2×D3—61no—
712C2×D3—61no—
713C2×D3—61no—
714C2×D3—61no—
715C2×D3—121no—
716C2×D3—121no—
717C2×D3—244no—
718C2×D3—244no—
719C3×C4—21no—
720C3×C4—21no—
721C3×C4—42no—
722C3×C4—41no—
723C3×C4—41no—
724C3×C4—41no—
725C3×C4—41no—
726C3×C4—61no—
727C3×C4—61no—
728C3×C4—61no—
729C3×C4—61no—
730C3×C4—81no—
731C3×C4—121no—
732C3×C4C2×D3×D411yescharacteristic
733C3×C4C2×D3×D411yescharacteristic
734C3×C4D3×#4111yescharacteristic
735C3×C4D3×#4111yescharacteristic
736Dic3—21no—
737Dic3—21no—
738Dic3—21no—
739Dic3—21no—
740Dic3—32no—
741Dic3—32no—
742Dic3—41no—
743Dic3—62no—
744Dic3—122no—
745Dic3—121no—
746Dic3—121no—
747Dic3—121no—
748Dic3—121no—
749Dic3—241no—
750C32#304211yescharacteristic, complemented, Sylow
751C23—61no—
752C23—61no—
753C23—61no—
754C23—91no—
755C23—184no—
756C23—721no—
757C23—721no—
758Q8—21no—
759Q8—21no—
760Q8—61no—
761Q8—61no—
762Q8—181no—
763Q8—181no—
764Q8—362no—
765D4—32no—
766D4—32no—
767D4—61no—
768D4—61no—
769D4—61no—
770D4—61no—
771D4—184no—
772D4—362no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—31no—
776C2×C4—31no—
777C2×C4—31no—
778C2×C4—31no—
779C2×C4—61no—
780C2×C4—91no—
781C2×C4—92no—
782C2×C4—92no—
783C2×C4—181no—
784C2×C4—181no—
785C2×C4—241no—
786C2×C4—241no—
787C2×C4—362no—
788C2×C4—362no—
789C2×C4—721no—
790C2×C4—721no—
791C2×C4C22×D3211yescharacteristic
792C8—21no—
793C8—61no—
794C8—61no—
795C8—181no—
796C2×C3—21no—
797C2×C3—21no—
798C2×C3—21no—
799C2×C3—122no—
800C2×C3—122no—
801C2×C3—241no—
802C2×C3D3×#12111yescharacteristic
803C2×C3D3×#12111yescharacteristic
804C2×C3#576211yescharacteristic
805C2×C3#577011yescharacteristic
806C2×C3#577511yescharacteristic
807C2×C3#577811yescharacteristic
808D3—42no—
809D3—42no—
810D3—62no—
811D3—62no—
812D3—81no—
813D3—122no—
814C22—62no—
815C22—62no—
816C22—92no—
817C22—121no—
818C22—121no—
819C22—121no—
820C22—121no—
821C22—121no—
822C22—121no—
823C22—121no—
824C22—181no—
825C22—181no—
826C22—724no—
827C22D32×D411yescharacteristic
828C4—41no—
829C4—41no—
830C4—61no—
831C4—61no—
832C4—61no—
833C4—61no—
834C4—92no—
835C4—121no—
836C4—361no—
837C4—361no—
838C4#6430611yescharacteristic
839C4D32×D411yescharacteristic
840C3—21no—
841C3#8043011yescharacteristic, complemented
842C3#8053711yescharacteristic, complemented
843C2—122no—
844C2—122no—
845C2—182no—
846C2—241no—
847C2#1059426511yescharacteristic
848C2#1059474911yescharacteristic
849C2#1059477011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×#63798C2
hypercenter#103D32
hypocenterC32#3042
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. #10595364C2semidirect
2. C2×#63940C2semidirect
4. #10594606C2semidirect
5. #10592501C2semidirect
6. C3×#4819C2semidirect
7. C3×#4818C2semidirect
8. #10591567C2semidirect
9. #10591564C2semidirect
10. #10590755C2semidirect
11. #10590752C2semidirect
12. #10590702C2semidirect
13. #10590611C2semidirect
14. #10590559C2semidirect
15. #10590530C2semidirect
23. C3×#947C22semidirect
24. C3×#944C22semidirect
41. #63866C22semidirect
42. #63860C22semidirect
51. C32×#103C22semidirect
52. #63662C22semidirect
53. #63643C22semidirect
54. #63637C22semidirect
55. C3×Dic3⋊C8C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. C3×#810C22semidirect
58. C3×#809C22semidirect
59. Dic3⋊(C3⋊C8)C22semidirect
60. Dic3⋊(C3⋊C8)C22semidirect
61. #63566C22semidirect
62. #63563C22semidirect
85. #4819D3semidirect
87. #4818D3semidirect
169. #947C2×D3semidirect
171. #944C2×D3semidirect
227. C3×#103C2×D3semidirect
228. C3×#103C2×D3semidirect
242. Dic3⋊C8C2×D3semidirect
243. Dic3⋊C8C2×D3semidirect
247. #810C2×D3semidirect
248. #809C2×D3semidirect
511. #103D32semidirect
750. C32#3042semidirect
841. C3#80430semidirect
842. C3#80537semidirect

Maximal subgroups

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

subgroupindex
#105953642
C2×#639402
C2×#637982
#105946062
#105925012
C3×#48192
C3×#48182
#105915672
#105915642
#105907552
#105907522
#105907022
#105906112
#105905592
#105905302
#805373
#804303