Finite Group Databasebeta

← #11884484

Subgroups — #11884484

Order 1152.

1096 conjugacy classes of subgroups.

The subgroup lattice has 921 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5630C211yesmaximal, characteristic, complemented
2C2×#63947C211yesmaximal, characteristic, complemented
3#10594919C211yesmaximal, characteristic, complemented
4C2×#63830C211yesmaximal, characteristic, complemented
5#10592746C211yesmaximal, characteristic, complemented
6C3×#5049C211yesmaximal, characteristic, complemented
7#10591619C211yesmaximal, characteristic, complemented
8#10591588C211yesmaximal, characteristic, complemented
9#10591577C211yesmaximal, characteristic, complemented
10#10591160C211yesmaximal, characteristic, complemented
11#10591147C211yesmaximal, characteristic, complemented
12#10590613C211yesmaximal, characteristic, complemented
13#10590590C211yesmaximal, characteristic, complemented
14#10590576C211yesmaximal, characteristic, complemented
15#10590547C211yesmaximal, characteristic, complemented
16#83507—31nomaximal
17#80836—31nomaximal
18C2×#3828C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C2×#3795C2211yescharacteristic, complemented
22C32×C22⋊Q8C2211yescharacteristic
23C2×#3756C2211yescharacteristic, complemented
24C2×#3755C2211yescharacteristic, complemented
25C3×#947C2211yescharacteristic
26C2×C3×#215C2211yescharacteristic, complemented
27C3×#930C2211yescharacteristic
28C3×C4×#67C2211yescharacteristic
29C2×C3×#208C2211yescharacteristic
30C3×#895—21no—
31C3×#895C2211yescharacteristic
32C3×#894—21no—
33C3×#893C2211yescharacteristic
34C3×#882—21no—
35C3×D3×C22⋊C4—21no—
36#63979—21no—
37#63971—21no—
38#63947—24no—
39#63912—21no—
40#63911C2211yescharacteristic, complemented
41#63909C2211yescharacteristic, complemented
42#63881—21no—
43#63844C2211yescharacteristic, complemented
44#63830—24no—
45C2×#3716C2211yescharacteristic
46C2×#3716C2211yescharacteristic
47C2×#3714C2211yescharacteristic
48C2×#3714C2211yescharacteristic
49C2×#3713C2211yescharacteristic
50C2×#3713C2211yescharacteristic
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63657C2211yescharacteristic
53#63637C2211yescharacteristic, complemented
54#63636C2211yescharacteristic, complemented
55C3×#835C2211yescharacteristic, complemented
56C3×#809C2211yescharacteristic, complemented
57C3×#807C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63562C2211yescharacteristic
60#63562C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63C3×#546—31no—
64C2×#950—31no—
65C2×#932—31no—
66C2×#916—31no—
67C2×#908—31no—
68#5630D311yescharacteristic, complemented
69#5599—31no—
70#5553—31no—
71C3×#468—31no—
72#5238—31no—
73#5217—31no—
74#5176—31no—
75#5127—31no—
76#5058—31no—
77#5054—31no—
78#5049D311yescharacteristic, complemented
79#5047—31no—
80#5047—31no—
81#5047—61no—
82#5038—31no—
83#5037—31no—
84#5036—31no—
85#5018—31no—
86#5015—31no—
87#5011—31no—
88#4889—31no—
89#4883—31no—
90#4810—31no—
91#4798—31no—
92#4786—31no—
93#4781—31no—
94C23×C3×D3—21no—
95C2×C32×Q8C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C2×#638—21no—
98#3828—22no—
99#3828—41no—
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C4×C3⋊D3—21no—
102C2×#634C2311yescharacteristic
103C2×C3×#67—21no—
104C2×C3×#67D411yescharacteristic
105C3×#239—22no—
106C3×#239—41no—
107C2×C3×D12—22no—
108C2×C3×D12—21no—
109C2×C3×D12—21no—
110C2×C3×D12—21no—
111C2×C3×D12—41no—
112C2×C3×D12C2311yescharacteristic
113C2×C3×D12C2311yescharacteristic
114C2×C3×D12C2311yescharacteristic
115C2×C3×C4×D3—21no—
116C2×C3×C4×D3—21no—
117C2×C3×C4×D3C2311yescharacteristic
118C2×#626—21no—
119C2×#626—21no—
120C2×#626—21no—
121C2×#625—21no—
122C2×D3×Dic3—21no—
123#3795—22no—
124#3795—41no—
125C32×C4⋊C4—21no—
126C32×C4⋊C4C2311yescharacteristic
127C32×C22⋊C4—21no—
128#3756—22no—
129#3755—41no—
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132C3×#217D411yescharacteristic
133C3×#215—22no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4D411yescharacteristic
140C3×C4⋊Dic3C2311yescharacteristic
141C3×Dic3⋊C4D411yescharacteristic
142C3×C4×Dic3C2311yescharacteristic
143C3×#208—22no—
144C2×C3×C3⋊C8C2311yescharacteristic
145C2×C3×C3⋊C8C2311yescharacteristic
146#3724—21no—
147#3722—21no—
148Dic32—21no—
149#3716—22no—
150#3716D414yescomplemented
151#3714—22no—
152#3714—22no—
153#3713—22no—
154#3713—41no—
155D3×C3⋊C8—22no—
156#3268—91noSylow
157C2×C3×#41—31no—
158C22×C3×D4—31no—
159C2×#239C2×D311yescharacteristic
160C2×#237—31no—
161C2×#235—31no—
162C2×#235—31no—
163C2×#235—31no—
164C2×#235—61no—
165C22×D12C2×D311yescharacteristic
166C2×C3×SD16—31no—
167C2×C3×M16—31no—
168C3×#124—31no—
169C3×#123—61no—
170C3×C22⋊Q8—21no—
171C3×C22⋊Q8C2×D311yescharacteristic
172C3×C22⋊Q8C2×D311yescharacteristic
173C3×#121—31no—
174C3×#121—31no—
175C3×#121—61no—
176C3×#120—61no—
177C3×C4×D4—31no—
178C3×C4×D4—31no—
179C2×C3×C22⋊C4—61no—
180#950—64no—
181#947C2×D311yescharacteristic
182C2×#216—31no—
183C2×#216—31no—
184C2×#216—61no—
185C2×#215—31no—
186C2×#215—31no—
187C2×#215—61no—
188C2×#215C2×D311yescharacteristic, complemented
189#940—31no—
190#940—61no—
191#940—61no—
192#939—61no—
193C2×#214—31no—
194C2×#214—31no—
195#932—64no—
196C2×#213—31no—
197C2×#213—31no—
198C2×#213—31no—
199C2×#213—31no—
200C2×#213—31no—
201C2×#213—31no—
202#930—31no—
203#930C2×D311yescharacteristic
204C4×#67C2×D311yescharacteristic
205C2×#208C2×D311yescharacteristic
206C22×C3⋊C8—31no—
207#916—64no—
208#908—64no—
209C2×D24—31no—
210C2×D24—31no—
211C2×#204—31no—
212C2×#204—31no—
213C2×D3×C8—31no—
214#895—21no—
215#895—31no—
216#895C2×D311yescharacteristic
217#894—21no—
218#893—61no—
219#893C2×D311yescharacteristic
220#887—31no—
221#884—61no—
222#884—61no—
223#884—61no—
224#882—21no—
225#67⋊C4—61no—
226D3×C22⋊C4—21no—
227#874—31no—
228C4×Dic6—31no—
229C3×#107—31no—
230C3×#103—31no—
231C3×#102—31no—
232#835C2×D311yescharacteristic, complemented
233#832—31no—
234#832—31no—
235#830—31no—
236#830—31no—
237#830—31no—
238#830—61no—
239(C2×D3)⋊C8—31no—
240#815—31no—
241Dic3⋊C8—31no—
242#810—31no—
243#810—31no—
244#810—61no—
245#809—31no—
246#809—31no—
247#809—31no—
248#809—31no—
249#809—61no—
250#809C2×D311yescharacteristic, complemented
251#807C2×D311yescharacteristic, complemented
252C4⋊(C3⋊C8)—31no—
253#803—31no—
254C23×C32C2×D411yescharacteristic
255C22×C3⋊D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—42no—
260C22×C3×D3—42no—
261C22×C3×D3—81no—
262C22×C3×D3C2×D411yescharacteristic
263C32×Q8—21no—
264C32×Q8—21no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4C2×D411yescharacteristic
270C2×C32×C4C2411yescharacteristic
271#638—42no—
272C2×C3⋊Dic3—21no—
273C4⋊(C3⋊D3)—21no—
274C4⋊(C3⋊D3)—21no—
275C4×C3⋊D3—42no—
276#634—21no—
277#634C2×D412yes—
278C3×#67—41no—
279C3×#67—81no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3C2×D411yescharacteristic
282C2×C3×Dic3C2×D411yescharacteristic
283C2×C3×Dic3C2×D411yescharacteristic
284C3×D12—21no—
285C3×D12—21no—
286C3×D12—21no—
287C3×D12—21no—
288C3×D12—21no—
289C3×D12—42no—
290C3×D12—42no—
291C3×D12—81no—
292C3×D12C2×D412yes—
293C3×C4×D3—21no—
294C3×C4×D3—21no—
295C3×C4×D3—42no—
296C3×C4×D3—81no—
297#626—42no—
298#626—81no—
299#626—81no—
300#625—42no—
301D3×Dic3—42no—
302C3⋊(C3⋊C8)—21no—
303C3⋊(C3⋊C8)—21no—
304C3×C3⋊C8—21no—
305C3×C3⋊C8C2×D412yes—
306C2×AGL(1,ℤ/8)—91no—
307C2×#135—91no—
308#550—91no—
309#546—31no—
310#496—91no—
311#468—31no—
312#466—91no—
313#464—91no—
314#459—91no—
315#452—91no—
316#449—91no—
317#449—91no—
318#447—91no—
319#440—91no—
320#435—91no—
321C24×C3—61no—
322C23×D3—21no—
323C3×#41—62no—
324C3×#41—121no—
325C2×C3×Q8—21no—
326C2×C3×Q8C22×D311yescharacteristic
327C2×C3×Q8C22×D311yescharacteristic
328C2×C3×D4—31no—
329C2×C3×D4—31no—
330C2×C3×D4—31no—
331C2×C3×D4—31no—
332C2×C3×D4—62no—
333C2×C3×D4—61no—
334C2×C3×D4—61no—
335C2×C3×D4—61no—
336C2×C3×D4—61no—
337C2×C3×D4—121no—
338C22×C3×C4—21no—
339C22×C3×C4—31no—
340C22×C3×C4—61no—
341C22×C3×C4—61no—
342C22×C3×C4C22×D311yescharacteristic
343C22×C3×C4C22×D311yescharacteristic
344C2×#67—21no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67—61no—
349C2×#67—61no—
350C2×#67—61no—
351C2×#67—61no—
352C2×#67—121no—
353C2×#67#6711yescharacteristic
354C22×Dic3—61no—
355#239—22no—
356#239—41no—
357#237—62no—
358#237—121no—
359#235—62no—
360#235—62no—
361#235—62no—
362#235—122no—
363#235—121no—
364#235—121no—
365#235—121no—
366#235—122no—
367C2×D12—22no—
368C2×D12—21no—
369C2×D12—21no—
370C2×D12—21no—
371C2×D12—31no—
372C2×D12—31no—
373C2×D12—41no—
374C2×D12—61no—
375C2×D12—61no—
376C2×D12—61no—
377C2×D12—61no—
378C2×D12C22×D311yescharacteristic
379C2×D12C22×D311yescharacteristic
380C2×D12C22×D311yescharacteristic
381C2×C4×D3—21no—
382C2×C4×D3—21no—
383C2×C4×D3—61no—
384C2×C4×D3—61no—
385C2×C4×D3—61no—
386C2×C4×D3—121no—
387C2×C4×D3C22×D311yescharacteristic
388C2×Dic6—31no—
389C2×Dic6—31no—
390C2×Dic6—61no—
391C3×SD16—62no—
392C3×M16—62no—
393C2×C3×C8—31no—
394C2×C3×C8—31no—
395C3×C4⋊C4—21no—
396C3×C4⋊C4—21no—
397C3×C4⋊C4—21no—
398C3×C4⋊C4—31no—
399C3×C4⋊C4—31no—
400C3×C4⋊C4—41no—
401C3×C4⋊C4C22×D311yescharacteristic
402C3×C4⋊C4C22×D311yescharacteristic
403C3×C22⋊C4—21no—
404C3×C22⋊C4—21no—
405C3×C22⋊C4—31no—
406C3×C22⋊C4—31no—
407C3×C22⋊C4—41no—
408C3×C22⋊C4—61no—
409C3×C22⋊C4—61no—
410C3×C22⋊C4—61no—
411C3×C22⋊C4—61no—
412C3×C22⋊C4—61no—
413C3×C42—31no—
414#217#6711yescharacteristic
415#216—62no—
416#216—62no—
417#216—122no—
418#215—22no—
419#215—121no—
420#215—121no—
421#215—122no—
422#214—34no—
423#214—62no—
424#213—62no—
425#213—62no—
426#213—62no—
427#213—62no—
428#213—121no—
429#213—121no—
430(C2×D3)⋊C4—21no—
431(C2×D3)⋊C4—21no—
432(C2×D3)⋊C4—21no—
433(C2×D3)⋊C4—21no—
434(C2×D3)⋊C4—21no—
435(C2×D3)⋊C4—61no—
436(C2×D3)⋊C4—61no—
437(C2×D3)⋊C4#6711yescharacteristic
438C4⋊Dic3C22×D311yescharacteristic
439Dic3⋊C4—61no—
440Dic3⋊C4—61no—
441Dic3⋊C4#6711yescharacteristic
442C4×Dic3—61no—
443C4×Dic3—61no—
444C4×Dic3C22×D311yescharacteristic
445#208—22no—
446C2×C3⋊C8—31no—
447C2×C3⋊C8—31no—
448C2×C3⋊C8—31no—
449C2×C3⋊C8—31no—
450C2×C3⋊C8—61no—
451C2×C3⋊C8—61no—
452C2×C3⋊C8—62no—
453C2×C3⋊C8C22×D311yescharacteristic
454C2×C3⋊C8C22×D311yescharacteristic
455D24—62no—
456D24—62no—
457#204—34no—
458#204—62no—
459D3×C8—62no—
460C22×C32—21no—
461C22×C32—21no—
462C22×C32—21no—
463C22×C32C22×D411yescharacteristic
464C2×C3⋊D3—41no—
465C2×C3⋊D3—41no—
466C2×C3⋊D3—41no—
467C2×C3×D3—21no—
468C2×C3×D3—22no—
469C2×C3×D3—21no—
470C2×C3×D3—21no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C2×C3×D3—84no—
480C32×C4—21no—
481C32×C4—41no—
482C32×C4—41no—
483C32×C4C22×D411yescharacteristic
484C32×C4H(5,𝔽2)11yescharacteristic
485C3⋊Dic3—22no—
486C3×Dic3—21no—
487C3×Dic3—21no—
488C3×Dic3—21no—
489C3×Dic3—41no—
490C2×#41—31no—
491C2×#41—91no—
492C2×#41—91no—
493C22×D4—31no—
494AGL(1,ℤ/8)—184no—
495#135—184no—
496C2×Q16—91no—
497C2×SD16—31no—
498C2×SD16—91no—
499C2×SD16—91no—
500C2×SD16—91no—
501C2×D8—91no—
502C2×D8—91no—
503C2×D8—91no—
504C2×D8—91no—
505C2×M16—31no—
506C22×C8—91no—
507#127—91no—
508#127—181no—
509#124—31no—
510#123—61no—
511C22⋊Q8D3211yescharacteristic
512#121—31no—
513#121—31no—
514#121—61no—
515#121—91no—
516#121—181no—
517#121—181no—
518#120—61no—
519C4×Q8—91no—
520C4×D4—31no—
521C4×D4—31no—
522C4×D4—181no—
523C2×C22⋊C4—61no—
524#107—31no—
525C4⋊C8—91no—
526#103—31no—
527#103—91no—
528#102—31no—
529#102—91no—
530#102—91no—
531#102—91no—
532C22⋊C8—91no—
533C22⋊C8—91no—
534#97—91no—
535C23×C3—21no—
536C23×C3—31no—
537C23×C3—61no—
538C23×C3—61no—
539C23×C3—61no—
540C23×C3—122no—
541C23×C3—122no—
542C23×C3—241no—
543C23×C3D3×D411yescharacteristic
544C23×C3C2×#6711yescharacteristic
545C22×D3—21no—
546C22×D3—21no—
547C22×D3—21no—
548C22×D3—42no—
549C22×D3—42no—
550C22×D3—61no—
551C22×D3—61no—
552C22×D3—81no—
553C22×D3—121no—
554C22×D3C2×#6711yescharacteristic
555C3×Q8—21no—
556C3×Q8—21no—
557C3×Q8—21no—
558C3×Q8—21no—
559C3×Q8—41no—
560C3×Q8—41no—
561C3×D4—32no—
562C3×D4—61no—
563C3×D4—61no—
564C3×D4—61no—
565C3×D4—61no—
566C3×D4—61no—
567C3×D4—122no—
568C3×D4—122no—
569C3×D4—121no—
570C3×D4—241no—
571C3×D4—241no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—31no—
583C2×C3×C4—31no—
584C2×C3×C4—31no—
585C2×C3×C4—41no—
586C2×C3×C4—41no—
587C2×C3×C4—41no—
588C2×C3×C4—41no—
589C2×C3×C4—61no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—122no—
593C2×C3×C4—241no—
594C2×C3×C4D3×D411yescharacteristic
595C2×C3×C4C2×#6711yescharacteristic
596C2×C3×C4C23×D311yescharacteristic
597C2×C3×C4C23×D311yescharacteristic
598#67—41no—
599#67—81no—
600#67—122no—
601#67—122no—
602#67—122no—
603#67—122no—
604#67—122no—
605#67—124no—
606#67—241no—
607#67—241no—
608C2×Dic3—21no—
609C2×Dic3—61no—
610C2×Dic3—61no—
611C2×Dic3—121no—
612C2×Dic3—122no—
613C2×Dic3C2×#6711yescharacteristic
614C2×Dic3C2×#6711yescharacteristic
615C2×Dic3C2×#6711yescharacteristic
616D12—21no—
617D12—21no—
618D12—21no—
619D12—21no—
620D12—21no—
621D12—42no—
622D12—42no—
623D12—62no—
624D12—61no—
625D12—61no—
626D12—61no—
627D12—61no—
628D12—81no—
629D12—121no—
630D12—122no—
631D12—241no—
632D12—241no—
633D12D3×D412yes—
634C4×D3—21no—
635C4×D3—21no—
636C4×D3—42no—
637C4×D3—81no—
638C4×D3—122no—
639C4×D3—122no—
640C4×D3—122no—
641C4×D3—124no—
642Dic6—32no—
643Dic6—32no—
644Dic6—62no—
645Dic6—61no—
646Dic6—61no—
647Dic6—121no—
648C3×C8—32no—
649C3×C8—61no—
650C3⋊C8—21no—
651C3⋊C8—61no—
652C3⋊C8—61no—
653C3⋊C8—61no—
654C3⋊C8—61no—
655C3⋊C8—121no—
656C3⋊C8—121no—
657C3⋊C8D3×D412yes—
658C2×C32—41no—
659C2×C32D4211yescharacteristic
660C2×C32#57511yescharacteristic
661C2×C32#57611yescharacteristic
662C3⋊D3—81no—
663C3×D3—41no—
664C3×D3—42no—
665C3×D3—81no—
666C3×D3—81no—
667C24—61no—
668#41—62no—
669#41—121no—
670#41—182no—
671#41—182no—
672#41—361no—
673#41—361no—
674C2×Q8—91no—
675C2×Q8C2×D3211yescharacteristic
676C2×D4—31no—
677C2×D4—31no—
678C2×D4—31no—
679C2×D4—31no—
680C2×D4—62no—
681C2×D4—61no—
682C2×D4—61no—
683C2×D4—61no—
684C2×D4—61no—
685C2×D4—91no—
686C2×D4—121no—
687C2×D4—181no—
688C2×D4—181no—
689C2×D4—181no—
690C2×D4—181no—
691C2×D4—181no—
692C22×C4—31no—
693C22×C4—61no—
694C22×C4—61no—
695C22×C4—181no—
696C22×C4—181no—
697C22×C4C2×D3211yescharacteristic
698Q16—182no—
699SD16—62no—
700SD16—94no—
701SD16—182no—
702SD16—361no—
703D8—182no—
704D8—182no—
705D8—182no—
706D8—361no—
707M16—62no—
708C2×C8—31no—
709C2×C8—31no—
710C2×C8—91no—
711C2×C8—91no—
712C2×C8—182no—
713C4⋊C4—21no—
714C4⋊C4—31no—
715C4⋊C4—31no—
716C4⋊C4—181no—
717C4⋊C4C2×D3211yescharacteristic
718C22⋊C4—21no—
719C22⋊C4—31no—
720C22⋊C4—31no—
721C22⋊C4—61no—
722C22⋊C4—61no—
723C22⋊C4—61no—
724C22⋊C4—61no—
725C22⋊C4—61no—
726C22⋊C4—181no—
727C42—31no—
728C42—181no—
729C22×C3—21no—
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—21no—
734C22×C3—21no—
735C22×C3—21no—
736C22×C3—41no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—61no—
740C22×C3—61no—
741C22×C3—61no—
742C22×C3—62no—
743C22×C3—121no—
744C22×C3—121no—
745C22×C3—121no—
746C22×C3—121no—
747C22×C3—121no—
748C22×C3—121no—
749C22×C3—121no—
750C22×C3—121no—
751C22×C3—244no—
752C22×C3C2×D3×D411yescharacteristic
753C22×C3C22×#6711yescharacteristic
754C2×D3—21no—
755C2×D3—22no—
756C2×D3—21no—
757C2×D3—21no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—41no—
762C2×D3—41no—
763C2×D3—41no—
764C2×D3—41no—
765C2×D3—41no—
766C2×D3—84no—
767C2×D3—122no—
768C2×D3—121no—
769C2×D3—121no—
770C2×D3—121no—
771C2×D3—121no—
772C2×D3—121no—
773C2×D3—121no—
774C2×D3—241no—
775C2×D3—241no—
776C3×C4—21no—
777C3×C4—21no—
778C3×C4—21no—
779C3×C4—21no—
780C3×C4—41no—
781C3×C4—41no—
782C3×C4—41no—
783C3×C4—41no—
784C3×C4—41no—
785C3×C4—61no—
786C3×C4—61no—
787C3×C4—61no—
788C3×C4—81no—
789C3×C4—81no—
790C3×C4—121no—
791C3×C4C2×D3×D411yescharacteristic
792C3×C4C2×D3×D411yescharacteristic
793C3×C4#100411yescharacteristic
794C3×C4#100911yescharacteristic
795Dic3—21no—
796Dic3—21no—
797Dic3—21no—
798Dic3—41no—
799Dic3—62no—
800Dic3—62no—
801Dic3—122no—
802C32#326811yescharacteristic, complemented, Sylow
803C23—31no—
804C23—61no—
805C23—61no—
806C23—61no—
807C23—122no—
808C23—122no—
809C23—181no—
810C23—241no—
811C23D3×#6711yescharacteristic
812Q8—21no—
813Q8—21no—
814Q8—92no—
815Q8—181no—
816D4—32no—
817D4—61no—
818D4—61no—
819D4—61no—
820D4—61no—
821D4—61no—
822D4—122no—
823D4—122no—
824D4—121no—
825D4—181no—
826D4—181no—
827D4—241no—
828D4—241no—
829D4—362no—
830D4—362no—
831D4—362no—
832D4—721no—
833D4—721no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—31no—
839C2×C4—31no—
840C2×C4—31no—
841C2×C4—61no—
842C2×C4—61no—
843C2×C4—61no—
844C2×C4—122no—
845C2×C4—181no—
846C2×C4—241no—
847C2×C4—362no—
848C2×C4—362no—
849C2×C4D3×#6711yescharacteristic
850C2×C4C22×D3211yescharacteristic
851C8—32no—
852C8—61no—
853C8—181no—
854C8—181no—
855C2×C3—21no—
856C2×C3—21no—
857C2×C3—21no—
858C2×C3—41no—
859C2×C3—41no—
860C2×C3—81no—
861C2×C3—121no—
862C2×C3—122no—
863C2×C3—241no—
864C2×C3—241no—
865C2×C3#560911yescharacteristic
866C2×C3#577411yescharacteristic
867C2×C3#577711yescharacteristic
868C2×C3D4×#6711yescharacteristic
869C2×C3#582211yescharacteristic
870C2×C3#583511yescharacteristic
871D3—41no—
872D3—42no—
873D3—81no—
874D3—81no—
875D3—242no—
876D3—241no—
877D3—241no—
878C22—21no—
879C22—21no—
880C22—21no—
881C22—61no—
882C22—61no—
883C22—62no—
884C22—61no—
885C22—121no—
886C22—121no—
887C22—121no—
888C22—121no—
889C22—121no—
890C22—121no—
891C22—121no—
892C22—121no—
893C22—244no—
894C22—361no—
895C22—361no—
896C22—361no—
897C22C2×D3×#6711yescharacteristic
898C4—21no—
899C4—41no—
900C4—41no—
901C4—61no—
902C4—61no—
903C4—61no—
904C4—121no—
905C4—182no—
906C4D32×D411yescharacteristic
907C4#6431411yescharacteristic
908C3—21no—
909C3#8083611yescharacteristic, complemented
910C3#8350711yescharacteristic, complemented
911C2—41no—
912C2—121no—
913C2—122no—
914C2—241no—
915C2—241no—
916C2—721no—
917C2#1059529111yescharacteristic
918C2#1059531711yescharacteristic
919C2#1059545411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
hypercenterC22⋊Q8D32
hypocenterC32#3268
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5630C2semidirect
2. C2×#63947C2semidirect
3. #10594919C2semidirect
4. C2×#63830C2semidirect
5. #10592746C2semidirect
6. C3×#5049C2semidirect
7. #10591619C2semidirect
8. #10591588C2semidirect
9. #10591577C2semidirect
10. #10591160C2semidirect
11. #10591147C2semidirect
12. #10590613C2semidirect
13. #10590590C2semidirect
14. #10590576C2semidirect
15. #10590547C2semidirect
21. C2×#3795C22semidirect
23. C2×#3756C22semidirect
24. C2×#3755C22semidirect
26. C2×C3×#215C22semidirect
40. #63911C22semidirect
41. #63909C22semidirect
43. #63844C22semidirect
51. C2×D3×C3⋊C8C22semidirect
53. #63637C22semidirect
54. #63636C22semidirect
55. C3×#835C22semidirect
56. C3×#809C22semidirect
57. C3×#807C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63554C22semidirect
68. #5630D3semidirect
78. #5049D3semidirect
150. #3716D4semidirect
188. C2×#215C2×D3semidirect
232. #835C2×D3semidirect
250. #809C2×D3semidirect
251. #807C2×D3semidirect
802. C32#3268semidirect
909. C3#80836semidirect
910. C3#83507semidirect

Maximal subgroups

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

subgroupindex
C3×#56302
C2×#639472
#105949192
C2×#638302
#105927462
C3×#50492
#105916192
#105915882
#105915772
#105911602
#105911472
#105906132
#105905902
#105905762
#105905472
#835073
#808363