Finite Group Databasebeta

← #11883935

Subgroups — #11883935

Order 1152.

1171 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#914C211yesmaximal, characteristic, complemented
2#10595414C211yesmaximal, characteristic, complemented
3C2×#63940C211yesmaximal, characteristic, complemented
4#10595293C211yesmaximal, characteristic, complemented
5#10592869C211yesmaximal, characteristic, complemented
6C3×#5163C211yesmaximal, characteristic, complemented
7#10591586C211yesmaximal, characteristic, complemented
8#10591566C211yesmaximal, characteristic, complemented
9#10591469C211yesmaximal, characteristic, complemented
10#10591459C211yesmaximal, characteristic, complemented
11#10591455C211yesmaximal, characteristic, complemented
12#10590945C211yesmaximal, characteristic, complemented
13#10590828C211yesmaximal, characteristic, complemented
14#10590755C211yesmaximal, characteristic, complemented
15#10590738C211yesmaximal, characteristic, complemented
16#83953—31nomaximal
17#80404—31nomaximal
18C2×Q8×C3⋊D3C2211yescharacteristic, complemented
19C2×C3×#239C2211yescharacteristic, complemented
20C2×C3×D3×D4C2211yescharacteristic
21C2×D3×#67—21no—
22C2×#3802C2211yescharacteristic
23C2×C32×SD16C2211yescharacteristic, complemented
24#64147C2211yescharacteristic
25C2×#3754C2211yescharacteristic, complemented
26C3×Q8×Dic3C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic
28C2×C3×#215C2211yescharacteristic, complemented
29C3×#940C2211yescharacteristic
30C2×C3×#213C2211yescharacteristic, complemented
31C3×#914—24no—
32C2×C3×D24C2211yescharacteristic
33C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
34#63983—21no—
35#63976—21no—
36#63970—21no—
37#63940—24no—
38#63916—21no—
39#63916C2211yescharacteristic, complemented
40#63908C2211yescharacteristic
41C4×#626—21no—
42C4×#626C2211yescharacteristic
43Dic3×D12C2211yescharacteristic
44#63860—21no—
45#63860C2211yescharacteristic, complemented
46#63857—21no—
47#63857C2211yescharacteristic, complemented
48C2×#3716C2211yescharacteristic
49C2×#3716C2211yescharacteristic, complemented
50C2×#3713C2211yescharacteristic, complemented
51C2×#3710C2211yescharacteristic, complemented
52#63662C2211yescharacteristic, complemented
53#63647C2211yescharacteristic, complemented
54#63643C2211yescharacteristic, complemented
55C3×#832C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic, complemented
57C3×Dic3⋊C8C2211yescharacteristic, complemented
58#63575C2211yescharacteristic, complemented
59#63563C2211yescharacteristic, complemented
60#63562C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63C2×C3×AGL(1,ℤ/8)—31no—
64#5831—31no—
65D4×#67—31no—
66C2×#914D311yescharacteristic, complemented
67C2×D3×SD16—31no—
68C2×D3×SD16—31no—
69#5717—31no—
70#5576—31no—
71C3×#460—31no—
72#5238—31no—
73#5218—31no—
74#5172—31no—
75#5170—31no—
76#5170—31no—
77#5170—61no—
78#5164—31no—
79#5163D311yescharacteristic, complemented
80#5157—31no—
81#5156—31no—
82#5154—31no—
83#5153—31no—
84#5134—31no—
85#5127—31no—
86#5074—31no—
87#5026—31no—
88#4844—31no—
89#4836—31no—
90#4780—31no—
91#4776—31no—
92#4775—31no—
93#4773—31no—
94C23×C3×D3—21no—
95C22×D32—21no—
96C2×C32×Q8C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C2×#638—21no—
99Q8×C3⋊D3—22no—
100Q8×C3⋊D3—41no—
101C2×C4×C3⋊D3—21no—
102C2×C4×C3⋊D3C2311yescharacteristic
103C2×#634—21no—
104C2×#634C2311yescharacteristic
105C2×C3×#67—21no—
106C2×C3×#67—21no—
107C2×C3×#67—21no—
108C3×#239—22no—
109C3×#239—41no—
110C3×D3×D4—22no—
111C3×D3×D4—41no—
112C2×C3×D12—21no—
113C2×C3×D12C2311yescharacteristic
114C2×C3×D12C2311yescharacteristic
115C2×C3×D12C2311yescharacteristic
116C2×C3×C4×D3—21no—
117C2×C3×C4×D3C2311yescharacteristic
118D3×#67—44no—
119C2×#626—21no—
120C2×#626D411yescharacteristic
121C2×#625—21no—
122C2×#625—21no—
123C2×D3×Dic3—21no—
124#3802—22no—
125#3802—41no—
126C32×SD16—22no—
127C2×C32×C8C2311yescharacteristic
128#3757—21no—
129#3754—41no—
130C4⋊(C3⋊Dic3)C2311yescharacteristic
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132C3×#215—22no—
133C3×#215D414yescomplemented
134C3×#213—22no—
135C3×C4⋊Dic3—21no—
136C3×C4⋊Dic3C2311yescharacteristic
137C3×C4×Dic3—21no—
138C3×C4×Dic3C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C3×D24—22no—
142C3×ΓL(1,𝔽25)—22no—
143Dic3⋊Dic3—21no—
144Dic3⋊Dic3D411yescharacteristic
145#3722D411yescharacteristic
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3—21no—
152(C2×D3)⋊Dic3D411yescharacteristic
153#3716—22no—
154#3716—22no—
155#3713—41no—
156#3710—22no—
157#3265—91noSylow
158C2×C3×#41—31no—
159C22×C3×D4—31no—
160C22×#67—61no—
161C2×#239C2×D311yescharacteristic, complemented
162C2×D3×Q8—31no—
163C2×D3×Q8—31no—
164C2×D3×Q8—61no—
165C2×D3×D4—31no—
166C2×D3×D4—31no—
167C2×D3×D4—61no—
168C2×D3×D4C2×D311yescharacteristic
169C3×AGL(1,ℤ/8)—64no—
170C2×C3×SD16—21no—
171C2×C3×SD16—31no—
172C2×C3×SD16—31no—
173C2×C3×SD16C2×D311yescharacteristic, complemented
174C2×C3×SD16C2×D311yescharacteristic, complemented
175C2×C3×D8—31no—
176C2×C3×D8—31no—
177C2×C3×M16—31no—
178C3×#127—31no—
179C3×C4×Q8—31no—
180#953—61no—
181Q8×Dic3C2×D311yescharacteristic, complemented
182C2×#215C2×D311yescharacteristic
183C2×#215C2×D311yescharacteristic, complemented
184#940C2×D311yescharacteristic
185#939—61no—
186#938—31no—
187#938—31no—
188#938—31no—
189#938—31no—
190#938—61no—
191#938—61no—
192#938—61no—
193#937—61no—
194#937—61no—
195#937—61no—
196#936—31no—
197#936—61no—
198D4×Dic3—31no—
199C2×#214—31no—
200C2×#214—31no—
201C2×#214—31no—
202C2×#214—31no—
203C2×#214—61no—
204C2×#213—31no—
205C2×#213—31no—
206C2×#213C2×D311yescharacteristic, complemented
207#930—31no—
208C4×#67—31no—
209C4×#67—61no—
210#924—31no—
211#924—61no—
212#914—24no—
213D3×SD16—64no—
214D3×SD16—64no—
215C2×D24C2×D311yescharacteristic
216C2×#204—31no—
217C2×#204—31no—
218C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
219C2×D3×C8—31no—
220C2×D3×C8—31no—
221#897—31no—
222#897—61no—
223#895—31no—
224#895—61no—
225#875—31no—
226#875—61no—
227C4×D12—31no—
228C4×D12—31no—
229C4×D12—61no—
230C3×C4⋊C8—31no—
231C3×#102—31no—
232C3×#102—31no—
233#835—31no—
234#835—31no—
235#835—61no—
236#832—31no—
237#832—31no—
238#832C2×D311yescharacteristic, complemented
239#830—31no—
240#821—31no—
241#821C2×D311yescharacteristic, complemented
242(C2×D3)⋊C8—31no—
243(C2×D3)⋊C8—31no—
244(C2×D3)⋊C8—31no—
245(C2×D3)⋊C8—61no—
246#818—31no—
247#816—31no—
248#816—31no—
249#816—61no—
250#815—31no—
251Dic3⋊C8C2×D311yescharacteristic, complemented
252#809—31no—
253#807—31no—
254#803—31no—
255C23×C32—21no—
256C22×C3⋊D3C2×D411yescharacteristic
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—42no—
261C22×C3×D3—42no—
262C22×C3×D3—81no—
263C22×C3×D3C2×D411yescharacteristic
264C2×D32—42no—
265C2×D32—42no—
266C2×D32—81no—
267C32×Q8—21no—
268C32×Q8C2×D412yescomplemented
269C32×D4—21no—
270C32×D4—21no—
271C2×C32×C4—21no—
272C2×C32×C4C2411yescharacteristic
273#638—42no—
274C2×C3⋊Dic3—21no—
275C2×C3⋊Dic3—21no—
276C2×C3⋊Dic3C2×D411yescharacteristic
277C4×C3⋊D3—21no—
278C4×C3⋊D3—21no—
279C4×C3⋊D3—42no—
280#634—21no—
281#634—21no—
282#634—42no—
283C3×#67—42no—
284C3×#67—42no—
285C3×#67—81no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3C2×D411yescharacteristic
288C2×C3×Dic3C2×D411yescharacteristic
289C2×C3×Dic3C2×D411yescharacteristic
290C3×D12—21no—
291C3×D12—21no—
292C3×D12—21no—
293C3×D12—21no—
294C3×D12—21no—
295C3×D12—42no—
296C3×D12C2×D412yes—
297C3×C4×D3—21no—
298C3×C4×D3—21no—
299C3×C4×D3—42no—
300#626—22no—
301#626—42no—
302#625—42no—
303#625—42no—
304D3×Dic3—42no—
305C32×C8—21no—
306C3⋊(C3⋊C8)—21no—
307C3×C3⋊C8—21no—
308C3×C3⋊C8C2×D412yescomplemented
309C2×AGL(1,ℤ/8)—31no—
310C22×SD16—91no—
311#548—91no—
312D42—91no—
313#496—91no—
314#468—91no—
315#466—91no—
316#463—91no—
317#460—31no—
318#450—91no—
319#449—91no—
320#448—91no—
321#447—91no—
322#440—91no—
323#435—91no—
324C24×C3—61no—
325C23×D3—21no—
326C23×D3—61no—
327C23×D3—61no—
328C3×#41—62no—
329C3×#41—121no—
330C2×C3×Q8—21no—
331C2×C3×Q8C22×D311yescharacteristic
332C2×C3×Q8C22×D311yescharacteristic
333C2×C3×D4—21no—
334C2×C3×D4—31no—
335C2×C3×D4—31no—
336C2×C3×D4—31no—
337C2×C3×D4—61no—
338C2×C3×D4—61no—
339C2×C3×D4—61no—
340C2×C3×D4—61no—
341C2×C3×D4—62no—
342C2×C3×D4—121no—
343C2×C3×D4C22×D311yescharacteristic
344C2×C3×D4C22×D311yescharacteristic
345C22×C3×C4—31no—
346C22×C3×C4—61no—
347C2×#67—21no—
348C2×#67—21no—
349C2×#67—21no—
350C2×#67—31no—
351C2×#67—61no—
352C2×#67—61no—
353C2×#67—61no—
354C2×#67—61no—
355C2×#67—61no—
356C2×#67—61no—
357C2×#67—61no—
358C2×#67—121no—
359C2×#67—124no—
360C22×Dic3—61no—
361#239—22no—
362#239—41no—
363D3×Q8—62no—
364D3×Q8—62no—
365D3×Q8—122no—
366D3×Q8—121no—
367D3×Q8—121no—
368D3×Q8—122no—
369D3×D4—22no—
370D3×D4—41no—
371D3×D4—62no—
372D3×D4—62no—
373D3×D4—121no—
374D3×D4—121no—
375D3×D4—124no—
376C2×D12—21no—
377C2×D12—31no—
378C2×D12—61no—
379C2×D12C22×D311yescharacteristic
380C2×D12C22×D311yescharacteristic
381C2×D12C22×D311yescharacteristic
382C2×C4×D3—21no—
383C2×C4×D3—31no—
384C2×C4×D3—31no—
385C2×C4×D3—61no—
386C2×C4×D3—61no—
387C2×C4×D3—61no—
388C2×C4×D3—61no—
389C2×C4×D3—121no—
390C2×C4×D3C22×D311yescharacteristic
391C2×Dic6—31no—
392C2×Dic6—31no—
393C2×Dic6—61no—
394C2×Dic6—61no—
395C2×Dic6—61no—
396C2×Dic6—121no—
397C3×SD16—22no—
398C3×SD16—22no—
399C3×SD16—34no—
400C3×SD16—42no—
401C3×SD16—62no—
402C3×D8—62no—
403C3×D8—62no—
404C3×M16—62no—
405C2×C3×C8—21no—
406C2×C3×C8—31no—
407C2×C3×C8—31no—
408C2×C3×C8C22×D311yescharacteristic
409C2×C3×C8C22×D311yescharacteristic
410C3×C4⋊C4—31no—
411C3×C4⋊C4—61no—
412C3×C42—31no—
413C3×C42—61no—
414#217—31no—
415#217—61no—
416#217—61no—
417#217—61no—
418#217—61no—
419#217—61no—
420#217—61no—
421#217—61no—
422#217—61no—
423#217—121no—
424#215—22no—
425#215#6714yescomplemented
426#214—62no—
427#214—62no—
428#214—121no—
429#214—121no—
430#214—122no—
431#213—22no—
432#213—121no—
433#213—121no—
434(C2×D3)⋊C4—31no—
435(C2×D3)⋊C4—31no—
436(C2×D3)⋊C4—31no—
437(C2×D3)⋊C4—61no—
438(C2×D3)⋊C4—61no—
439(C2×D3)⋊C4—61no—
440(C2×D3)⋊C4—61no—
441(C2×D3)⋊C4—61no—
442(C2×D3)⋊C4—61no—
443C4⋊Dic3—21no—
444C4⋊Dic3—31no—
445C4⋊Dic3—31no—
446C4⋊Dic3—31no—
447C4⋊Dic3—61no—
448C4⋊Dic3—61no—
449C4⋊Dic3C22×D311yescharacteristic
450Dic3⋊C4—31no—
451Dic3⋊C4—61no—
452C4×Dic3—21no—
453C4×Dic3C22×D311yescharacteristic
454C2×C3⋊C8—31no—
455C2×C3⋊C8—31no—
456C2×C3⋊C8—61no—
457C2×C3⋊C8C22×D311yescharacteristic
458C2×C3⋊C8C22×D311yescharacteristic
459D24—22no—
460#204—62no—
461#204—62no—
462ΓL(1,𝔽25)—22no—
463D3×C8—62no—
464D3×C8—62no—
465C22×C32—41no—
466C22×C32—41no—
467C22×C32—41no—
468C22×C32C22×D411yescharacteristic
469C2×C3⋊D3—21no—
470C2×C3⋊D3—21no—
471C2×C3⋊D3AGL(1,ℤ/8)12yescomplemented
472C2×C3×D3—22no—
473C2×C3×D3—21no—
474C2×C3×D3—21no—
475C2×C3×D3—21no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3—41no—
482C2×C3×D3—41no—
483C2×C3×D3—41no—
484C2×C3×D3—84no—
485D32—84no—
486C32×C4—22no—
487C32×C4C22×D411yescharacteristic
488C32×C4H(5,𝔽2)11yescharacteristic
489C3⋊Dic3—21no—
490C3⋊Dic3—41no—
491C3⋊Dic3—41no—
492C3×Dic3—21no—
493C3×Dic3—21no—
494C3×Dic3—21no—
495C3×Dic3—41no—
496C2×#41—31no—
497C22×Q8—91no—
498C22×D4—31no—
499C22×D4—91no—
500C22×D4—181no—
501AGL(1,ℤ/8)—64no—
502C2×SD16—31no—
503C2×SD16—31no—
504C2×SD16—91no—
505C2×SD16—91no—
506C2×SD16—91no—
507C2×SD16—184no—
508C2×SD16D3211yescharacteristic, complemented
509C2×D8—31no—
510C2×D8—31no—
511C2×D8—91no—
512C2×M16—31no—
513C22×C8—91no—
514#127—31no—
515#124—91no—
516#124—181no—
517C22⋊Q8—91no—
518C22⋊Q8—181no—
519#121—91no—
520#121—91no—
521#121—91no—
522#121—181no—
523#121—181no—
524#120—181no—
525#120—181no—
526C4×Q8—31no—
527C4×D4—91no—
528C4×D4—91no—
529C4×D4—181no—
530#107—91no—
531C4⋊C8—31no—
532#103—91no—
533#103—91no—
534#102—31no—
535#102—31no—
536#102—91no—
537#102—91no—
538C22⋊C8—91no—
539C22⋊C8—91no—
540#97—91no—
541C23×C3—21no—
542C23×C3—21no—
543C23×C3—31no—
544C23×C3—41no—
545C23×C3—61no—
546C23×C3—61no—
547C23×C3—61no—
548C23×C3—122no—
549C23×C3—122no—
550C23×C3—241no—
551C22×D3—21no—
552C22×D3—21no—
553C22×D3—21no—
554C22×D3—31no—
555C22×D3—31no—
556C22×D3—42no—
557C22×D3—42no—
558C22×D3—61no—
559C22×D3—81no—
560C22×D3—122no—
561C22×D3—122no—
562C22×D3—122no—
563C22×D3—122no—
564C22×D3—241no—
565C22×D3—241no—
566C22×D3D3×D411yescharacteristic
567C3×Q8—21no—
568C3×Q8—21no—
569C3×Q8—22no—
570C3×Q8—41no—
571C3×Q8D3×D412yescomplemented
572C3×Q8C2×#6712yescomplemented
573C3×D4—21no—
574C3×D4—21no—
575C3×D4—21no—
576C3×D4—21no—
577C3×D4—32no—
578C3×D4—41no—
579C3×D4—41no—
580C3×D4—61no—
581C3×D4—61no—
582C3×D4—61no—
583C3×D4—61no—
584C3×D4—61no—
585C3×D4—122no—
586C3×D4—122no—
587C3×D4—122no—
588C3×D4—241no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—31no—
593C2×C3×C4—31no—
594C2×C3×C4—31no—
595C2×C3×C4—41no—
596C2×C3×C4—61no—
597C2×C3×C4—61no—
598C2×C3×C4—61no—
599C2×C3×C4—122no—
600C2×C3×C4C23×D311yescharacteristic
601C2×C3×C4C23×D311yescharacteristic
602#67—42no—
603#67—42no—
604#67—62no—
605#67—81no—
606#67—122no—
607#67—122no—
608#67—122no—
609#67—122no—
610#67—122no—
611#67—122no—
612#67—122no—
613#67—242no—
614C2×Dic3—21no—
615C2×Dic3—31no—
616C2×Dic3—31no—
617C2×Dic3—61no—
618C2×Dic3—61no—
619C2×Dic3—61no—
620C2×Dic3—61no—
621C2×Dic3—61no—
622C2×Dic3—121no—
623C2×Dic3—121no—
624C2×Dic3—122no—
625C2×Dic3D3×D411yescharacteristic
626C2×Dic3D3×D411yescharacteristic
627C2×Dic3D3×D411yescharacteristic
628D12—21no—
629D12—21no—
630D12—21no—
631D12—21no—
632D12—21no—
633D12—42no—
634D12—62no—
635D12—122no—
636D12C2×#6712yes—
637C4×D3—21no—
638C4×D3—21no—
639C4×D3—42no—
640C4×D3—61no—
641C4×D3—61no—
642C4×D3—61no—
643C4×D3—61no—
644C4×D3—121no—
645C4×D3—121no—
646C4×D3—122no—
647C4×D3—122no—
648C4×D3—124no—
649C4×D3—122no—
650Dic6—62no—
651Dic6—61no—
652Dic6—61no—
653Dic6—61no—
654Dic6—61no—
655Dic6—121no—
656Dic6—122no—
657Dic6—122no—
658Dic6—124no—
659C3×C8—21no—
660C3×C8—21no—
661C3×C8—32no—
662C3×C8—41no—
663C3×C8—61no—
664C3⋊C8—21no—
665C3⋊C8—61no—
666C3⋊C8—61no—
667C3⋊C8—121no—
668C3⋊C8C2×#6712yescomplemented
669C2×C32—81no—
670C2×C32D4211yescharacteristic
671C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
672C2×C32#57711yescharacteristic
673C3⋊D3—22no—
674C3×D3—42no—
675C3×D3—41no—
676C3×D3—81no—
677C3×D3—81no—
678C24—61no—
679C24—181no—
680#41—62no—
681#41—121no—
682C2×Q8—91no—
683C2×Q8—181no—
684C2×Q8—182no—
685C2×Q8—361no—
686C2×Q8C2×D3211yescharacteristic
687C2×D4—31no—
688C2×D4—31no—
689C2×D4—31no—
690C2×D4—61no—
691C2×D4—61no—
692C2×D4—61no—
693C2×D4—61no—
694C2×D4—62no—
695C2×D4—91no—
696C2×D4—121no—
697C2×D4—181no—
698C2×D4—181no—
699C2×D4—182no—
700C2×D4—181no—
701C2×D4—181no—
702C2×D4—361no—
703C2×D4—364no—
704C2×D4C2×D3211yescharacteristic
705C22×C4—31no—
706C22×C4—61no—
707C22×C4—91no—
708C22×C4—181no—
709C22×C4—181no—
710SD16—22no—
711SD16—34no—
712SD16—62no—
713SD16—182no—
714SD16—182no—
715SD16—361no—
716D8—62no—
717D8—62no—
718D8—361no—
719M16—62no—
720C2×C8—31no—
721C2×C8—31no—
722C2×C8—91no—
723C2×C8—182no—
724C2×C8C2×D3211yescharacteristic
725C4⋊C4—31no—
726C4⋊C4—61no—
727C4⋊C4—91no—
728C4⋊C4—91no—
729C4⋊C4—181no—
730C22⋊C4—91no—
731C22⋊C4—91no—
732C22⋊C4—181no—
733C22⋊C4—181no—
734C22⋊C4—181no—
735C22⋊C4—181no—
736C22⋊C4—181no—
737C22⋊C4—181no—
738C22⋊C4—181no—
739C42—31no—
740C42—61no—
741C22×C3—21no—
742C22×C3—41no—
743C22×C3—41no—
744C22×C3—41no—
745C22×C3—41no—
746C22×C3—41no—
747C22×C3—41no—
748C22×C3—61no—
749C22×C3—61no—
750C22×C3—62no—
751C22×C3—61no—
752C22×C3—81no—
753C22×C3—81no—
754C22×C3—81no—
755C22×C3—121no—
756C22×C3—121no—
757C22×C3—121no—
758C22×C3—121no—
759C22×C3—121no—
760C22×C3—121no—
761C22×C3—121no—
762C22×C3—121no—
763C22×C3—244no—
764C22×C3C2×D3×D411yescharacteristic
765C22×C3C2×D3×D411yescharacteristic
766C2×D3—21no—
767C2×D3—21no—
768C2×D3—21no—
769C2×D3—22no—
770C2×D3—32no—
771C2×D3—32no—
772C2×D3—41no—
773C2×D3—41no—
774C2×D3—41no—
775C2×D3—41no—
776C2×D3—41no—
777C2×D3—41no—
778C2×D3—41no—
779C2×D3—41no—
780C2×D3—62no—
781C2×D3—61no—
782C2×D3—61no—
783C2×D3—61no—
784C2×D3—61no—
785C2×D3—84no—
786C2×D3—121no—
787C2×D3—121no—
788C2×D3—244no—
789C2×D3—244no—
790C3×C4—22no—
791C3×C4—22no—
792C3×C4—21no—
793C3×C4—21no—
794C3×C4—42no—
795C3×C4—61no—
796C3×C4—61no—
797C3×C4—61no—
798C3×C4—121no—
799C3×C4C2×D3×D411yescharacteristic
800C3×C4#100411yescharacteristic
801C3×C4#100911yescharacteristic
802C3×C4C22×#6711yescharacteristic
803Dic3—21no—
804Dic3—21no—
805Dic3—21no—
806Dic3—41no—
807Dic3—61no—
808Dic3—61no—
809Dic3—121no—
810Dic3—122no—
811Dic3—121no—
812Dic3—121no—
813Dic3—121no—
814Dic3—121no—
815Dic3—241no—
816C32#326511yescharacteristic, complemented, Sylow
817C23—21no—
818C23—31no—
819C23—61no—
820C23—61no—
821C23—61no—
822C23—91no—
823C23—122no—
824C23—122no—
825C23—241no—
826C23—362no—
827C23—362no—
828C23—721no—
829Q8—21no—
830Q8—181no—
831Q8—181no—
832Q8—362no—
833Q8D3×#6712yescomplemented
834D4—21no—
835D4—21no—
836D4—32no—
837D4—61no—
838D4—61no—
839D4—61no—
840D4—61no—
841D4—61no—
842D4—122no—
843D4—122no—
844D4—122no—
845D4—182no—
846D4—241no—
847D4—362no—
848D4—362no—
849D4—362no—
850D4—362no—
851C2×C4—21no—
852C2×C4—31no—
853C2×C4—31no—
854C2×C4—31no—
855C2×C4—61no—
856C2×C4—61no—
857C2×C4—61no—
858C2×C4—91no—
859C2×C4—122no—
860C2×C4—181no—
861C2×C4—181no—
862C2×C4—181no—
863C2×C4—181no—
864C2×C4—362no—
865C2×C4—362no—
866C2×C4C22×D3211yescharacteristic
867C8—21no—
868C8—32no—
869C8—61no—
870C8—181no—
871C2×C3—21no—
872C2×C3—21no—
873C2×C3—21no—
874C2×C3—81no—
875C2×C3—81no—
876C2×C3—122no—
877C2×C3—121no—
878C2×C3—161no—
879C2×C3—241no—
880C2×C3—241no—
881C2×C3#560911yescharacteristic
882C2×C3#576211yescharacteristic
883C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
884C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
885C2×C3#577511yescharacteristic
886C2×C3D4×#6711yescharacteristic
887D3—41no—
888D3—42no—
889D3—62no—
890D3—62no—
891D3—81no—
892D3—81no—
893D3—122no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—61no—
898C22—61no—
899C22—61no—
900C22—62no—
901C22—92no—
902C22—121no—
903C22—121no—
904C22—121no—
905C22—121no—
906C22—121no—
907C22—121no—
908C22—121no—
909C22—121no—
910C22—181no—
911C22—181no—
912C22—244no—
913C22—724no—
914C22D32×D411yescharacteristic
915C4—22no—
916C4—61no—
917C4—61no—
918C4—61no—
919C4—121no—
920C4—181no—
921C4—361no—
922C4—361no—
923C4#6431411yescharacteristic
924C4C2×D3×#6711yescharacteristic
925C3—21no—
926C3#8040411yescharacteristic, complemented
927C3#8395311yescharacteristic, complemented
928C2—81no—
929C2—121no—
930C2—122no—
931C2—182no—
932C2—241no—
933C2—241no—
934C2#1059474011yescharacteristic
935C2#1059474911yescharacteristic
936C2#1059529111yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
hypercenterC2×SD16D32
hypocenterC32#3265
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×C3×#914C2semidirect
2. #10595414C2semidirect
3. C2×#63940C2semidirect
4. #10595293C2semidirect
5. #10592869C2semidirect
6. C3×#5163C2semidirect
7. #10591586C2semidirect
8. #10591566C2semidirect
9. #10591469C2semidirect
10. #10591459C2semidirect
11. #10591455C2semidirect
12. #10590945C2semidirect
13. #10590828C2semidirect
14. #10590755C2semidirect
15. #10590738C2semidirect
18. C2×Q8×C3⋊D3C22semidirect
19. C2×C3×#239C22semidirect
23. C2×C32×SD16C22semidirect
25. C2×#3754C22semidirect
26. C3×Q8×Dic3C22semidirect
28. C2×C3×#215C22semidirect
30. C2×C3×#213C22semidirect
33. C2×C3×ΓL(1,𝔽25)C22semidirect
39. #63916C22semidirect
45. #63860C22semidirect
47. #63857C22semidirect
49. C2×#3716C22semidirect
50. C2×#3713C22semidirect
51. C2×#3710C22semidirect
52. #63662C22semidirect
53. #63647C22semidirect
54. #63643C22semidirect
55. C3×#832C22semidirect
56. C3×#821C22semidirect
57. C3×Dic3⋊C8C22semidirect
58. #63575C22semidirect
59. #63563C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63554C22semidirect
66. C2×#914D3semidirect
79. #5163D3semidirect
133. C3×#215D4semidirect
161. C2×#239C2×D3semidirect
173. C2×C3×SD16C2×D3semidirect
174. C2×C3×SD16C2×D3semidirect
181. Q8×Dic3C2×D3semidirect
183. C2×#215C2×D3semidirect
206. C2×#213C2×D3semidirect
218. C2×ΓL(1,𝔽25)C2×D3semidirect
238. #832C2×D3semidirect
241. #821C2×D3semidirect
251. Dic3⋊C8C2×D3semidirect
268. C32×Q8C2×D4semidirect
308. C3×C3⋊C8C2×D4semidirect
425. #215#67semidirect
471. C2×C3⋊D3AGL(1,ℤ/8)semidirect
508. C2×SD16D32semidirect
571. C3×Q8D3×D4semidirect
572. C3×Q8C2×#67semidirect
668. C3⋊C8C2×#67semidirect
816. C32#3265semidirect
833. Q8D3×#67semidirect
926. C3#80404semidirect
927. C3#83953semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9142
#105954142
C2×#639402
#105952932
#105928692
C3×#51632
#105915862
#105915662
#105914692
#105914592
#105914552
#105909452
#105908282
#105907552
#105907382
#839533
#804043