Finite Group Databasebeta

← #11865884

Subgroups — #11865884

Order 1152.

1177 conjugacy classes of subgroups.

The subgroup lattice has 891 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595167C211yesmaximal, characteristic, complemented
2C2×#63927C211yesmaximal, characteristic, complemented
3C2×#63798C211yesmaximal, characteristic, complemented
4#10594605C211yesmaximal, characteristic, complemented
5#10592470C211yesmaximal, characteristic, complemented
6C3×#4787C211yesmaximal, characteristic, complemented
7C3×#4786C211yesmaximal, characteristic, complemented
8#10591431C211yesmaximal, characteristic, complemented
9#10591428C211yesmaximal, characteristic, complemented
10#10590755C211yesmaximal, characteristic, complemented
11#10590752C211yesmaximal, characteristic, complemented
12#10590666C211yesmaximal, characteristic, complemented
13#10590612C211yesmaximal, characteristic, complemented
14#10590559C211yesmaximal, characteristic, complemented
15#10590530C211yesmaximal, characteristic, complemented
16#80534—31nomaximal
17#80332—31nomaximal
18C2×#3830C2211yescharacteristic
19C2×#3802C2211yescharacteristic
20C2×C4×D32—21no—
21C2×#3796C2211yescharacteristic
22C2×#3743C2211yescharacteristic
23C4⋊C4×C3⋊D3C2211yescharacteristic
24C3×#940C2211yescharacteristic, complemented
25C3×#936C2211yescharacteristic, complemented
26C2×C3×#213C2211yescharacteristic
27C2×C3×#213C2211yescharacteristic
28C2×C3×D24C2211yescharacteristic
29C2×C3×#204C2211yescharacteristic
30C3×#893C2211yescharacteristic
31C3×#893C2211yescharacteristic
32#67⋊Dic3—21no—
33#67⋊Dic3—21no—
34#63958—21no—
35#63958—21no—
36#63927—24no—
37#63921—21no—
38Dic3×D12C2211yescharacteristic
39Dic3×D12C2211yescharacteristic
40C4×#624C2211yescharacteristic
41#63879—21no—
42#63879—21no—
43#63866C2211yescharacteristic, complemented
44#63860C2211yescharacteristic, complemented
45C2×#3716C2211yescharacteristic
46C2×#3716C2211yescharacteristic
47C2×#3715C2211yescharacteristic
48C2×#3713C2211yescharacteristic
49C2×#3712C2211yescharacteristic
50#63798—24no—
51C32×#102C2211yescharacteristic, complemented
52#63659C2211yescharacteristic, 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×#911—31no—
65C2×#911—31no—
66C2×#911—31no—
67#5716—31no—
68#5668—31no—
69C4×D3×D4—31no—
70C4×D3×D4—31no—
71C3×#463—31no—
72C3×#459—31no—
73#5162—31no—
74#5153—31no—
75#5153—31no—
76#5150—31no—
77#5072—31no—
78#5057—31no—
79#5019—31no—
80#5016—31no—
81#4844—31no—
82#4841—31no—
83#4837—31no—
84#4837—31no—
85#4818—31no—
86#4803—31no—
87#4787—31no—
88#4787D311yescharacteristic, complemented
89#4786D311yescharacteristic, complemented
90#4771—31no—
91#4771—31no—
92#4771—31no—
93#4771—61no—
94C22×D32—21no—
95C2×C32×D4C2311yescharacteristic
96C2×#638—21no—
97C22×C3⋊Dic3—21no—
98#3830—22no—
99#3830—22no—
100C2×C4×C3⋊D3—21no—
101C2×C4×C3⋊D3C2311yescharacteristic
102C2×#634C2311yescharacteristic
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×D12C2311yescharacteristic
107C2×C3×D12C2311yescharacteristic
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3—21no—
110C2×C3×Dic6C2311yescharacteristic
111C2×#626—21no—
112C2×#625—21no—
113C2×#624D411yescharacteristic
114C2×#624D411yescharacteristic
115C2×D3×Dic3—21no—
116C2×D3×Dic3—21no—
117C2×D3×Dic3—21no—
118#3802—22no—
119#3802D414yescomplemented
120C4×D32—44no—
121#3796—22no—
122#3796—22no—
123C2×C32×C8C2311yescharacteristic
124C32×C4⋊C4C2311yescharacteristic
125C4⋊(C3⋊Dic3)C2311yescharacteristic
126#3750—21no—
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128#3743—22no—
129C3×#217—21no—
130C3×#217—21no—
131C3×#213—22no—
132C3×#213—22no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×C4×Dic3C2311yescharacteristic
136C3×C4×Dic3C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C3×D24—22no—
140C3×#204—22no—
141Dic3⋊Dic3—21no—
142Dic3⋊Dic3—21no—
143(C2×D3)⋊Dic3—21no—
144(C2×D3)⋊Dic3—21no—
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147Dic32D411yescharacteristic
148Dic32D411yescharacteristic
149#3716—22no—
150#3716—22no—
151#3715—22no—
152#3713—22no—
153#3712—22no—
154#3036—91noSylow
155C2×#239—31no—
156C2×#237—31no—
157C2×#237—31no—
158C2×#237—31no—
159C2×#237—61no—
160C2×D3×D4—31no—
161C2×D3×D4—31no—
162C22×C4×D3—61no—
163C22×C4×D3—61no—
164C2×C3×SD16—31no—
165C2×C3×D8—31no—
166C2×C3×D8—31no—
167C2×C3×D8—31no—
168C3×#127—31no—
169C3×#124—31no—
170C3×C4×D4—31no—
171C3×C4×D4—31no—
172#944—31no—
173C2×#215—31no—
174#940C2×D311yescharacteristic, complemented
175#938—61no—
176#938—61no—
177#936—31no—
178#936C2×D311yescharacteristic, complemented
179D4×Dic3—31no—
180D4×Dic3—31no—
181D4×Dic3—61no—
182D4×Dic3—61no—
183C2×#214—31no—
184C2×#214—31no—
185C2×#214—31no—
186C2×#213—31no—
187C2×#213—31no—
188C2×#213C2×D311yescharacteristic
189C2×#213C2×D311yescharacteristic
190C4×#67—61no—
191C4×#67—61no—
192#914—64no—
193#911—64no—
194#911—64no—
195#911—64no—
196C2×D24C2×D311yescharacteristic
197C2×#204—31no—
198C2×#204—31no—
199C2×#204C2×D311yescharacteristic
200C2×ΓL(1,𝔽25)—31no—
201C2×ΓL(1,𝔽25)—31no—
202C2×ΓL(1,𝔽25)—31no—
203C2×ΓL(1,𝔽25)—31no—
204C2×ΓL(1,𝔽25)—61no—
205#893C2×D311yescharacteristic
206#893C2×D311yescharacteristic
207D3×C4⋊C4—31no—
208D3×C4⋊C4—31no—
209D3×C4⋊C4—61no—
210#884—61no—
211#884—61no—
212#67⋊C4—61no—
213#67⋊C4—61no—
214#67⋊C4—61no—
215#67⋊C4—61no—
216D3×C22⋊C4—61no—
217D3×C22⋊C4—61no—
218#875—31no—
219C4×D12—31no—
220C4×D12—31no—
221C42×D3—31no—
222C42×D3—31no—
223#869—31no—
224C3×C4⋊C8—31no—
225C3×C4⋊C8—31no—
226C3×#103—31no—
227C3×#102—21no—
228C3×#102—31no—
229C3×#102C2×D311yescharacteristic, complemented
230C3×#102C2×D311yescharacteristic, complemented
231#835—31no—
232#832—31no—
233#832—31no—
234#832—31no—
235#832—61no—
236#821—31no—
237#816—31no—
238#816—31no—
239#816—31no—
240#816—61no—
241Dic3⋊C8—31no—
242Dic3⋊C8—31no—
243Dic3⋊C8C2×D311yescharacteristic, complemented
244Dic3⋊C8C2×D311yescharacteristic, complemented
245#810—31no—
246#810—31no—
247#810—61no—
248#810C2×D311yescharacteristic, complemented
249#809C2×D311yescharacteristic, complemented
250C4⋊(C3⋊C8)—31no—
251C4⋊(C3⋊C8)—31no—
252C23×C32—21no—
253C22×C3⋊D3C2×D411yescharacteristic
254C22×C3×D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C2×D32—24no—
258C2×D32—42no—
259C2×D32—42no—
260C32×D4—21no—
261C32×D4—21no—
262C2×C32×C4—21no—
263C2×C32×C4C2411yescharacteristic
264#638—42no—
265C2×C3⋊Dic3—21no—
266C2×C3⋊Dic3—21no—
267C2×C3⋊Dic3—42no—
268C2×C3⋊Dic3C2×D411yescharacteristic
269C4×C3⋊D3—42no—
270C4×C3⋊D3C2×D412yes—
271C4×C3⋊D3#4112yes—
272#634—21no—
273#634—21no—
274C3×#67—42no—
275C3×#67—42no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3C2×D411yescharacteristic
278C2×C3×Dic3C2×D411yescharacteristic
279C2×C3×Dic3C2×D411yescharacteristic
280C2×C3×Dic3C2×D411yescharacteristic
281C3×D12—21no—
282C3×D12—21no—
283C3×D12—21no—
284C3×D12—21no—
285C3×D12C2×D412yes—
286C3×D12C2×D412yes—
287C3×C4×D3—42no—
288C3×C4×D3—42no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291#626—42no—
292#625—24no—
293#624—22no—
294#624—41no—
295D3×Dic3—42no—
296D3×Dic3—42no—
297D3×Dic3—42no—
298C32×C8—21no—
299C3⋊(C3⋊C8)—21no—
300C3×C3⋊C8—21no—
301C3×C3⋊C8—21no—
302C2×AGL(1,ℤ/8)—91no—
303C2×AGL(1,ℤ/8)—91no—
304#532—91no—
305C2×C4×D4—91no—
306#463—31no—
307#463—91no—
308#463—91no—
309#463—91no—
310#461—91no—
311#461—91no—
312#459—31no—
313#459—91no—
314#423—91no—
315#417—91no—
316#417—91no—
317C23×D3—61no—
318C23×D3—61no—
319C2×C3×Q8—31no—
320C2×C3×D4—21no—
321C2×C3×D4—31no—
322C2×C3×D4—31no—
323C2×C3×D4—31no—
324C2×C3×D4—61no—
325C2×C3×D4—61no—
326C2×C3×D4C22×D311yescharacteristic
327C2×C3×D4C22×D311yescharacteristic
328C22×C3×C4—61no—
329C22×C3×C4—61no—
330C2×#67—21no—
331C2×#67—21no—
332C2×#67—61no—
333C2×#67—61no—
334C2×#67—61no—
335C2×#67—61no—
336C2×#67—61no—
337C2×#67—121no—
338C22×Dic3—61no—
339C22×Dic3—61no—
340C22×Dic3—61no—
341C22×Dic3—61no—
342C22×Dic3—61no—
343C22×Dic3—121no—
344#239—62no—
345#239—62no—
346#237—62no—
347#237—62no—
348#237—62no—
349#237—62no—
350#237—62no—
351#237—62no—
352#237—64no—
353#237—122no—
354D3×D4—34no—
355D3×D4—34no—
356D3×D4—62no—
357D3×D4—62no—
358C2×D12—61no—
359C2×D12C22×D311yescharacteristic
360C2×D12C22×D311yescharacteristic
361C2×D12C22×D311yescharacteristic
362C2×C4×D3—21no—
363C2×C4×D3—21no—
364C2×C4×D3—31no—
365C2×C4×D3—31no—
366C2×C4×D3—31no—
367C2×C4×D3—31no—
368C2×C4×D3—31no—
369C2×C4×D3—31no—
370C2×C4×D3—61no—
371C2×C4×D3—61no—
372C2×C4×D3—61no—
373C2×C4×D3—61no—
374C2×C4×D3—61no—
375C2×C4×D3—61no—
376C2×C4×D3—121no—
377C2×C4×D3—124no—
378C2×C4×D3—124no—
379C2×Dic6—31no—
380C2×Dic6—31no—
381C2×Dic6—61no—
382C2×Dic6C22×D311yescharacteristic
383C3×SD16—62no—
384C3×D8—62no—
385C3×D8—62no—
386C3×D8—62no—
387C2×C3×C8—21no—
388C2×C3×C8—31no—
389C2×C3×C8—31no—
390C2×C3×C8C22×D311yescharacteristic
391C2×C3×C8C22×D311yescharacteristic
392C3×C4⋊C4—21no—
393C3×C4⋊C4C22×D311yescharacteristic
394C3×C4⋊C4C22×D311yescharacteristic
395C3×C22⋊C4—61no—
396C3×C22⋊C4—61no—
397C3×C22⋊C4—61no—
398C3×C22⋊C4—61no—
399C3×C42—31no—
400C3×C42—31no—
401#217—21no—
402#217—21no—
403#217—61no—
404#217—61no—
405#217—61no—
406#217—61no—
407#215—62no—
408#214—62no—
409#214—62no—
410#214—62no—
411#213—22no—
412#213—22no—
413#213—62no—
414#213—62no—
415(C2×D3)⋊C4—21no—
416(C2×D3)⋊C4—21no—
417(C2×D3)⋊C4—61no—
418(C2×D3)⋊C4—61no—
419(C2×D3)⋊C4—61no—
420(C2×D3)⋊C4—61no—
421C4⋊Dic3—31no—
422C4⋊Dic3—31no—
423C4⋊Dic3—61no—
424C4⋊Dic3—61no—
425C4⋊Dic3—61no—
426Dic3⋊C4—61no—
427Dic3⋊C4—61no—
428Dic3⋊C4—61no—
429Dic3⋊C4—61no—
430Dic3⋊C4—121no—
431C4×Dic3—31no—
432C4×Dic3—31no—
433C4×Dic3—31no—
434C4×Dic3—31no—
435C4×Dic3C22×D311yescharacteristic
436C4×Dic3C22×D311yescharacteristic
437C2×C3⋊C8—31no—
438C2×C3⋊C8—31no—
439C2×C3⋊C8—61no—
440C2×C3⋊C8C22×D311yescharacteristic
441C2×C3⋊C8C22×D311yescharacteristic
442D24—22no—
443#204—22no—
444#204—62no—
445#204—62no—
446ΓL(1,𝔽25)—62no—
447ΓL(1,𝔽25)—62no—
448ΓL(1,𝔽25)—62no—
449ΓL(1,𝔽25)—62no—
450ΓL(1,𝔽25)—122no—
451C22×C32—41no—
452C22×C32—41no—
453C22×C32—41no—
454C22×C32C22×D411yescharacteristic
455C2×C3⋊D3—21no—
456C2×C3⋊D3—21no—
457C2×C3⋊D3#12112yes—
458C2×C3×D3—22no—
459C2×C3×D3—22no—
460C2×C3×D3—41no—
461C2×C3×D3—41no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467D32—48no—
468C32×C4—41no—
469C32×C4C22×D411yescharacteristic
470C32×C4C2×#4111yescharacteristic
471C3⋊Dic3—41no—
472C3⋊Dic3—41no—
473C3⋊Dic3#12112yes—
474C3×Dic3—21no—
475C3×Dic3—21no—
476C3×Dic3—21no—
477C3×Dic3—41no—
478C3×Dic3AGL(1,ℤ/8)12yescomplemented
479C2×#41—91no—
480C2×#41—91no—
481C22×D4—91no—
482C23×C4—181no—
483AGL(1,ℤ/8)—184no—
484AGL(1,ℤ/8)—184no—
485C2×SD16—31no—
486C2×SD16—91no—
487C2×SD16—91no—
488C2×SD16—91no—
489C2×D8—31no—
490C2×D8—31no—
491C2×D8—31no—
492C2×D8—91no—
493C2×M16—91no—
494C2×M16—91no—
495C4⋊Q8—91no—
496#127—31no—
497#124—31no—
498#124—91no—
499#121—181no—
500#121—181no—
501C4×D4—31no—
502C4×D4—31no—
503C4×D4—91no—
504C4×D4—91no—
505C4×D4—181no—
506C4×D4—181no—
507C4×D4—181no—
508C4×D4—181no—
509C2×C4⋊C4—91no—
510C2×C22⋊C4—181no—
511C2×C42—91no—
512C4⋊C8—31no—
513C4⋊C8—31no—
514C4⋊C8—91no—
515C4⋊C8—91no—
516#103—31no—
517#103—91no—
518#103—91no—
519#103—91no—
520#102—31no—
521#102—91no—
522#102—91no—
523#102D3211yescharacteristic, complemented
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—41no—
527C23×C3—61no—
528C23×C3—61no—
529C23×C3—61no—
530C22×D3—21no—
531C22×D3—21no—
532C22×D3—21no—
533C22×D3—31no—
534C22×D3—31no—
535C22×D3—61no—
536C22×D3—64no—
537C22×D3—64no—
538C22×D3—122no—
539C22×D3—122no—
540C22×D3—122no—
541C22×D3—122no—
542C3×Q8—61no—
543C3×Q8—61no—
544C3×D4—22no—
545C3×D4—21no—
546C3×D4—21no—
547C3×D4—21no—
548C3×D4—21no—
549C3×D4—32no—
550C3×D4—32no—
551C3×D4—41no—
552C3×D4—61no—
553C3×D4—61no—
554C3×D4—61no—
555C3×D4—61no—
556C3×D4—122no—
557C3×D4—122no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—31no—
562C2×C3×C4—31no—
563C2×C3×C4—31no—
564C2×C3×C4—31no—
565C2×C3×C4—41no—
566C2×C3×C4—61no—
567C2×C3×C4—122no—
568C2×C3×C4—122no—
569C2×C3×C4C23×D311yescharacteristic
570C2×C3×C4C23×D311yescharacteristic
571#67—42no—
572#67—42no—
573#67—64no—
574#67—64no—
575#67—122no—
576#67—122no—
577#67—122no—
578#67—124no—
579C2×Dic3—21no—
580C2×Dic3—31no—
581C2×Dic3—31no—
582C2×Dic3—61no—
583C2×Dic3—61no—
584C2×Dic3—61no—
585C2×Dic3—61no—
586C2×Dic3—61no—
587C2×Dic3—121no—
588C2×Dic3—121no—
589C2×Dic3—122no—
590C2×Dic3—122no—
591C2×Dic3—122no—
592C2×Dic3—122no—
593C2×Dic3—124no—
594C2×Dic3—122no—
595C2×Dic3D3×D411yescharacteristic
596C2×Dic3D3×D411yescharacteristic
597C2×Dic3D3×D411yescharacteristic
598C2×Dic3D3×D411yescharacteristic
599D12—21no—
600D12—21no—
601D12—21no—
602D12—21no—
603D12—122no—
604D12D3×D412yes—
605D12D3×D412yes—
606C4×D3—32no—
607C4×D3—32no—
608C4×D3—32no—
609C4×D3—32no—
610C4×D3—42no—
611C4×D3—42no—
612C4×D3—62no—
613C4×D3—62no—
614C4×D3—62no—
615C4×D3—62no—
616C4×D3—121no—
617C4×D3—121no—
618C4×D3—122no—
619C4×D3—122no—
620C4×D3—122no—
621C4×D3—122no—
622C4×D3—122no—
623C4×D3—242no—
624Dic6—21no—
625Dic6—21no—
626Dic6—62no—
627Dic6—61no—
628Dic6—61no—
629Dic6—61no—
630Dic6—61no—
631Dic6—121no—
632C3×C8—21no—
633C3×C8—21no—
634C3×C8—41no—
635C3×C8—61no—
636C3×C8—61no—
637C3⋊C8—21no—
638C3⋊C8—21no—
639C3⋊C8—61no—
640C3⋊C8—61no—
641C3⋊C8—121no—
642C2×C32—81no—
643C2×C32C2×#12111yescharacteristic
644C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
645C2×C32#57511yescharacteristic
646C3⋊D3—22no—
647C3×D3—42no—
648C3×D3—42no—
649C3×D3—81no—
650C24—181no—
651#41—182no—
652#41—182no—
653#41—182no—
654#41—182no—
655C2×Q8—31no—
656C2×Q8—91no—
657C2×D4—31no—
658C2×D4—31no—
659C2×D4—31no—
660C2×D4—61no—
661C2×D4—61no—
662C2×D4—94no—
663C2×D4—181no—
664C2×D4—182no—
665C2×D4—181no—
666C2×D4—181no—
667C2×D4C2×D3211yescharacteristic
668C22×C4—61no—
669C22×C4—61no—
670C22×C4—91no—
671C22×C4—91no—
672C22×C4—91no—
673C22×C4—181no—
674C22×C4—181no—
675C22×C4—181no—
676C22×C4—181no—
677C22×C4—181no—
678C22×C4—364no—
679SD16—62no—
680SD16—182no—
681SD16—182no—
682SD16—182no—
683D8—62no—
684D8—62no—
685D8—62no—
686D8—182no—
687M16—182no—
688M16—182no—
689C2×C8—31no—
690C2×C8—31no—
691C2×C8—91no—
692C2×C8C2×D3211yescharacteristic
693C4⋊C4—91no—
694C4⋊C4—181no—
695C4⋊C4—181no—
696C4⋊C4—181no—
697C4⋊C4C2×D3211yescharacteristic
698C22⋊C4—61no—
699C22⋊C4—61no—
700C22⋊C4—61no—
701C22⋊C4—61no—
702C22⋊C4—181no—
703C22⋊C4—181no—
704C22⋊C4—181no—
705C22⋊C4—181no—
706C42—31no—
707C42—31no—
708C42—91no—
709C42—91no—
710C22×C3—21no—
711C22×C3—42no—
712C22×C3—41no—
713C22×C3—41no—
714C22×C3—41no—
715C22×C3—41no—
716C22×C3—41no—
717C22×C3—41no—
718C22×C3—62no—
719C22×C3—62no—
720C22×C3—81no—
721C22×C3—81no—
722C22×C3—121no—
723C22×C3—121no—
724C22×C3—121no—
725C22×C3—121no—
726C22×C3—121no—
727C22×C3—121no—
728C22×C3—121no—
729C22×C3C2×D3×D411yescharacteristic
730C22×C3C2×D3×D411yescharacteristic
731C2×D3—22no—
732C2×D3—22no—
733C2×D3—32no—
734C2×D3—32no—
735C2×D3—41no—
736C2×D3—41no—
737C2×D3—41no—
738C2×D3—41no—
739C2×D3—41no—
740C2×D3—41no—
741C2×D3—41no—
742C2×D3—62no—
743C2×D3—61no—
744C2×D3—61no—
745C2×D3—61no—
746C2×D3—61no—
747C2×D3—121no—
748C2×D3—121no—
749C2×D3—128no—
750C2×D3—128no—
751C3×C4—21no—
752C3×C4—21no—
753C3×C4—32no—
754C3×C4—41no—
755C3×C4—41no—
756C3×C4—61no—
757C3×C4—61no—
758C3×C4—61no—
759C3×C4—81no—
760C3×C4—121no—
761C3×C4C2×D3×D411yescharacteristic
762C3×C4C2×D3×D411yescharacteristic
763C3×C4D3×#4111yescharacteristic
764C3×C4D3×#4111yescharacteristic
765Dic3—21no—
766Dic3—21no—
767Dic3—21no—
768Dic3—32no—
769Dic3—32no—
770Dic3—41no—
771Dic3—62no—
772Dic3—122no—
773Dic3—121no—
774Dic3—121no—
775Dic3—121no—
776Dic3—121no—
777Dic3—241no—
778Dic3#91112yescomplemented
779C32#303611yescharacteristic, complemented, Sylow
780C23—21no—
781C23—61no—
782C23—61no—
783C23—61no—
784C23—91no—
785C23—184no—
786C23—362no—
787C23—362no—
788Q8—61no—
789Q8—61no—
790Q8—181no—
791Q8—181no—
792D4—21no—
793D4—21no—
794D4—32no—
795D4—32no—
796D4—61no—
797D4—61no—
798D4—61no—
799D4—61no—
800D4—122no—
801D4—122no—
802D4—184no—
803D4—362no—
804D4—362no—
805C2×C4—21no—
806C2×C4—31no—
807C2×C4—31no—
808C2×C4—31no—
809C2×C4—31no—
810C2×C4—61no—
811C2×C4—91no—
812C2×C4—92no—
813C2×C4—92no—
814C2×C4—122no—
815C2×C4—122no—
816C2×C4—182no—
817C2×C4—181no—
818C2×C4—181no—
819C2×C4—362no—
820C2×C4—362no—
821C2×C4—361no—
822C2×C4—362no—
823C2×C4—362no—
824C2×C4—362no—
825C2×C4C22×D3211yescharacteristic
826C8—21no—
827C8—61no—
828C8—61no—
829C8—181no—
830C2×C3—21no—
831C2×C3—21no—
832C2×C3—21no—
833C2×C3—82no—
834C2×C3—81no—
835C2×C3—81no—
836C2×C3—122no—
837C2×C3—122no—
838C2×C3—241no—
839C2×C3D3×#12111yescharacteristic
840C2×C3D3×#12111yescharacteristic
841C2×C3C2×#91111yescharacteristic
842C2×C3#576811yescharacteristic
843C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
844C2×C3#577311yescharacteristic
845D3—42no—
846D3—42no—
847D3—62no—
848D3—62no—
849D3—81no—
850D3—122no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—62no—
855C22—62no—
856C22—92no—
857C22—121no—
858C22—121no—
859C22—121no—
860C22—121no—
861C22—121no—
862C22—121no—
863C22—121no—
864C22—181no—
865C22—181no—
866C22—368no—
867C22D32×D411yescharacteristic
868C4—32no—
869C4—41no—
870C4—61no—
871C4—61no—
872C4—61no—
873C4—92no—
874C4—121no—
875C4—361no—
876C4—361no—
877C4#6430611yescharacteristic
878C4D32×D411yescharacteristic
879C3—21no—
880C3#8033211yescharacteristic, complemented
881C3#8053411yescharacteristic, complemented
882C2—81no—
883C2—122no—
884C2—122no—
885C2—182no—
886C2—241no—
887C2#1059426511yescharacteristic
888C2D3×#91111yescharacteristic
889C2#1059474511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3036
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. #10595167C2semidirect
2. C2×#63927C2semidirect
3. C2×#63798C2semidirect
4. #10594605C2semidirect
5. #10592470C2semidirect
6. C3×#4787C2semidirect
7. C3×#4786C2semidirect
8. #10591431C2semidirect
9. #10591428C2semidirect
10. #10590755C2semidirect
11. #10590752C2semidirect
12. #10590666C2semidirect
13. #10590612C2semidirect
14. #10590559C2semidirect
15. #10590530C2semidirect
24. C3×#940C22semidirect
25. C3×#936C22semidirect
43. #63866C22semidirect
44. #63860C22semidirect
51. C32×#102C22semidirect
52. #63659C22semidirect
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
88. #4787D3semidirect
89. #4786D3semidirect
119. #3802D4semidirect
174. #940C2×D3semidirect
178. #936C2×D3semidirect
229. C3×#102C2×D3semidirect
230. C3×#102C2×D3semidirect
243. Dic3⋊C8C2×D3semidirect
244. Dic3⋊C8C2×D3semidirect
248. #810C2×D3semidirect
249. #809C2×D3semidirect
478. C3×Dic3AGL(1,ℤ/8)semidirect
523. #102D32semidirect
778. Dic3#911semidirect
779. C32#3036semidirect
880. C3#80332semidirect
881. C3#80534semidirect

Maximal subgroups

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

subgroupindex
#105951672
C2×#639272
C2×#637982
#105946052
#105924702
C3×#47872
C3×#47862
#105914312
#105914282
#105907552
#105907522
#105906662
#105906122
#105905592
#105905302
#805343
#803323