Finite Group Databasebeta

← #11883946

Subgroups — #11883946

Order 1152.

1156 conjugacy classes of subgroups.

The subgroup lattice has 933 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5576C211yesmaximal, characteristic, complemented
2C2×#63939C211yesmaximal, characteristic, complemented
3C2×D3×#215C211yesmaximal, characteristic, complemented
4D122C211yesmaximal, characteristic, complemented
5#10592726C211yesmaximal, characteristic, complemented
6C3×#5026C211yesmaximal, characteristic, complemented
7#10591588C211yesmaximal, characteristic, complemented
8#10591584C211yesmaximal, characteristic, complemented
9#10590596C211yesmaximal, characteristic, complemented
10#10590595C211yesmaximal, characteristic, complemented
11#10590585C211yesmaximal, characteristic, complemented
12#10590576C211yesmaximal, characteristic, complemented
13#10590351C211yesmaximal, characteristic, complemented
14#10590348C211yesmaximal, characteristic, complemented
15#10590326C211yesmaximal, characteristic, complemented
16#83542—31nomaximal
17#79794—31nomaximal
18C2×C3×#239C2211yescharacteristic, complemented
19C2×C3×D3×Q8C2211yescharacteristic, complemented
20C2×D3×D12—21no—
21C2×D3×D12C2211yescharacteristic
22C2×D3×D12C2211yescharacteristic
23C32×C4×Q8C2211yescharacteristic, complemented
24C2×#3755C2211yescharacteristic, complemented
25C2×#3755C2211yescharacteristic, complemented
26#64083C2211yescharacteristic
27C2×C3×#215C2211yescharacteristic
28C3×#897—21no—
29C3×#897C2211yescharacteristic, complemented
30C3×#895—21no—
31C3×#895C2211yescharacteristic, complemented
32C3×#875—21no—
33C3×#875C2211yescharacteristic, complemented
34C3×C4×D12—21no—
35C3×C4×D12C2211yescharacteristic
36C3×C4×D12C2211yescharacteristic
37#63939—24no—
38D3×#215—24no—
39#63923—21no—
40#63923—21no—
41#63909—21no—
42#63909C2211yescharacteristic
43#63909C2211yescharacteristic
44C2×#3717C2211yescharacteristic, complemented
45C2×#3717C2211yescharacteristic, complemented
46C2×#3715C2211yescharacteristic
47C2×#3714C2211yescharacteristic, complemented
48C2×#3714C2211yescharacteristic, complemented
49C2×#3713C2211yescharacteristic
50C2×#3711C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63636C2211yescharacteristic, complemented
53#63636C2211yescharacteristic, complemented
54C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
55C3×#835C2211yescharacteristic, complemented
56C3×#809C2211yescharacteristic
57C3×#807C2211yescharacteristic, complemented
58C3×#803C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63562C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
63C3×#548—31no—
64C2×#949—31no—
65C22×#215—31no—
66C2×#914—31no—
67C2×D3×SD16—31no—
68#5576D311yescharacteristic, complemented
69D4×D12—31no—
70D4×D12—31no—
71C3×#440—31no—
72#5238—31no—
73#5227—31no—
74#5058—31no—
75#5057—31no—
76#5049—31no—
77#5046—31no—
78#5038—31no—
79#5036—31no—
80#5027—31no—
81#5027—31no—
82#5027—61no—
83#5026D311yescharacteristic, complemented
84#5016—31no—
85#5011—31no—
86#4886—31no—
87#4883—31no—
88#4810—31no—
89#4806—31no—
90#4776—31no—
91#4773—31no—
92#4712—31no—
93#4706—31no—
94C22×D32—21no—
95C22×D32—21no—
96C2×C32×Q8C2311yescharacteristic
97C2×C4⋊(C3⋊D3)—21no—
98C2×C4⋊(C3⋊D3)—21no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C3×#239—22no—
102C3×#239—41no—
103C3×D3×Q8—22no—
104C3×D3×Q8—41no—
105C2×C3×D12—21no—
106C2×C3×D12—21no—
107C2×C3×D12D411yescharacteristic
108C2×C3×D12C2311yescharacteristic
109C2×C3×D12C2311yescharacteristic
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3C2311yescharacteristic
114C2×C3×C4×D3C2311yescharacteristic
115C2×C3×Dic6—21no—
116C2×C3×Dic6C2311yescharacteristic
117C2×#626—21no—
118C2×#626—21no—
119C2×#626—21no—
120C2×#626—21no—
121D3×D12—22no—
122D3×D12—22no—
123D3×D12—41no—
124D3×D12—41no—
125D3×D12—44no—
126C32×C4⋊C4—21no—
127C32×C4⋊C4C2311yescharacteristic
128C32×C42—21no—
129C32×C42C2311yescharacteristic
130#3755—22no—
131#3755—22no—
132C2×C3⋊(C3⋊C8)C2311yescharacteristic
133C2×C3⋊(C3⋊C8)C2311yescharacteristic
134C3×#215D414yescomplemented
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4—21no—
140C3×(C2×D3)⋊C4D411yescharacteristic
141C3×(C2×D3)⋊C4D411yescharacteristic
142C3×C4⋊Dic3—21no—
143C3×C4⋊Dic3D411yescharacteristic
144C3×C4⋊Dic3C2311yescharacteristic
145C2×C3×C3⋊C8C2311yescharacteristic
146C2×C3×C3⋊C8C2311yescharacteristic
147#3722—21no—
148#3722—21no—
149#3717—22no—
150#3717—41no—
151#3715—22no—
152#3714—22no—
153#3714—41no—
154#3713—22no—
155#3711—22no—
156D3×C3⋊C8—22no—
157#3265—91noSylow
158C2×C3×#41—31no—
159C22×C3×Q8—31no—
160C2×#239C2×D311yescharacteristic, complemented
161C2×D3×Q8C2×D311yescharacteristic, complemented
162C2×D3×D4—31no—
163C2×D3×D4—31no—
164C2×D3×D4—61no—
165C22×D12—31no—
166C22×D12—31no—
167C22×D12—61no—
168C2×C3×SD16—31no—
169C3×#124—31no—
170C3×#124—61no—
171C3×C22⋊Q8—31no—
172C3×C22⋊Q8—61no—
173C3×#121—31no—
174C3×#121—61no—
175C3×C4×Q8—21no—
176C3×C4×Q8C2×D311yescharacteristic, complemented
177C3×C4×Q8C2×D311yescharacteristic, complemented
178C3×C4×D4—31no—
179C3×C4×D4—31no—
180C3×C4×D4—61no—
181#949—64no—
182C2×#215—31no—
183C2×#215—31no—
184C2×#215—31no—
185C2×#215—31no—
186C2×#215—31no—
187C2×#215—31no—
188C2×#215—31no—
189C2×#215—61no—
190C2×#215—61no—
191C2×#215—64no—
192C2×#215C2×D311yescharacteristic
193C2×#214—31no—
194C2×#213—31no—
195C2×#213—31no—
196C2×#213—31no—
197C2×#213—31no—
198#930—31no—
199#930—31no—
200#930—61no—
201C2×#208—31no—
202C22×C3⋊C8—31no—
203#914—64no—
204D3×SD16—64no—
205C2×D24—31no—
206C2×D24—31no—
207C2×#204—31no—
208C2×#204—31no—
209C2×ΓL(1,𝔽25)—31no—
210C2×D3×C8—31no—
211#897—21no—
212#897C2×D311yescharacteristic, complemented
213#895—21no—
214#895—31no—
215#895—31no—
216#895—61no—
217#895C2×D311yescharacteristic, complemented
218#882—61no—
219#882—61no—
220#882—61no—
221#882—61no—
222#875—21no—
223#875C2×D311yescharacteristic, complemented
224#874—31no—
225#874—31no—
226#874—61no—
227C4×D12—21no—
228C4×D12C2×D311yescharacteristic
229C4×D12C2×D311yescharacteristic
230C3×#107—31no—
231C3×#103—31no—
232C3×#102—31no—
233C3×#97—31no—
234#835—31no—
235#835C2×D311yescharacteristic, complemented
236#832—31no—
237#830—31no—
238#830—31no—
239(C2×D3)⋊C8—31no—
240(C2×D3)⋊C8—31no—
241#810—31no—
242#809—31no—
243#809—31no—
244#809—31no—
245#809—31no—
246#809—31no—
247#809—61no—
248#809—61no—
249#809C2×D311yescharacteristic
250#807C2×D311yescharacteristic, complemented
251C4⋊(C3⋊C8)—31no—
252C4⋊(C3⋊C8)—31no—
253C4⋊(C3⋊C8)—61no—
254#803C2×D311yescharacteristic, complemented
255C22×C3⋊D3—21no—
256C22×C3⋊D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3C2×D411yescharacteristic
260C22×C3×D3C2×D411yescharacteristic
261C2×D32—42no—
262C2×D32—42no—
263C2×D32—42no—
264C2×D32—42no—
265C2×D32—81no—
266C2×D32—81no—
267C32×Q8—21no—
268C32×Q8C2×D412yescomplemented
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4C2×D411yescharacteristic
272C2×C32×C4C2×D411yescharacteristic
273C2×C32×C4C2411yescharacteristic
274C4⋊(C3⋊D3)—21no—
275C4⋊(C3⋊D3)—21no—
276C4⋊(C3⋊D3)—21no—
277C4⋊(C3⋊D3)—21no—
278C4⋊(C3⋊D3)—42no—
279C4⋊(C3⋊D3)—81no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3C2×D411yescharacteristic
283C2×C3×Dic3C2×D411yescharacteristic
284C3×D12—22no—
285C3×D12—21no—
286C3×D12—21no—
287C3×D12—21no—
288C3×D12—42no—
289C3×D12—42no—
290C3×D12C2×D412yes—
291C3×C4×D3—21no—
292C3×C4×D3—21no—
293C3×C4×D3—21no—
294C3×C4×D3—21no—
295C3×C4×D3—42no—
296C3×C4×D3—42no—
297C3×C4×D3—42no—
298C3×Dic6—21no—
299C3×Dic6—21no—
300C3×Dic6—42no—
301#626—42no—
302#626—42no—
303#626—42no—
304#626—42no—
305C3⋊(C3⋊C8)—21no—
306C3⋊(C3⋊C8)—21no—
307C3×C3⋊C8—21no—
308C3×C3⋊C8C2×D412yescomplemented
309C2×AGL(1,ℤ/8)—91no—
310C22×SD16—91no—
311#548—31no—
312D42—91no—
313#496—91no—
314#468—91no—
315#466—91no—
316#463—91no—
317#460—91no—
318#450—91no—
319#449—91no—
320#448—91no—
321#447—91no—
322#440—31no—
323#435—91no—
324C23×D3—61no—
325C23×D3—61no—
326C23×D3—61no—
327C23×D3—61no—
328C3×#41—62no—
329C3×#41—121no—
330C2×C3×Q8—21no—
331C2×C3×Q8—31no—
332C2×C3×Q8—61no—
333C2×C3×Q8—62no—
334C2×C3×Q8—121no—
335C2×C3×Q8C22×D311yescharacteristic
336C2×C3×Q8C22×D311yescharacteristic
337C2×C3×D4—31no—
338C2×C3×D4—31no—
339C2×C3×D4—31no—
340C2×C3×D4—61no—
341C2×C3×D4—61no—
342C22×C3×C4—31no—
343C22×C3×C4—31no—
344C22×C3×C4—61no—
345C22×C3×C4—61no—
346C22×C3×C4—61no—
347C2×#67—61no—
348C2×#67—61no—
349C2×#67—61no—
350C2×#67—61no—
351#239—22no—
352#239—41no—
353D3×Q8—22no—
354D3×Q8—41no—
355D3×D4—62no—
356D3×D4—62no—
357D3×D4—121no—
358D3×D4—121no—
359D3×D4—124no—
360C2×D12—21no—
361C2×D12—21no—
362C2×D12—31no—
363C2×D12—31no—
364C2×D12—31no—
365C2×D12—31no—
366C2×D12—61no—
367C2×D12—61no—
368C2×D12—62no—
369C2×D12—62no—
370C2×D12—61no—
371C2×D12—61no—
372C2×D12—61no—
373C2×D12—61no—
374C2×D12—61no—
375C2×D12—61no—
376C2×D12—61no—
377C2×D12—61no—
378C2×D12—121no—
379C2×D12—121no—
380C2×D12—121no—
381C2×D12—121no—
382C2×D12—124no—
383C2×D12#6711yescharacteristic
384C2×D12C22×D311yescharacteristic
385C2×D12C22×D311yescharacteristic
386C2×C4×D3—21no—
387C2×C4×D3—21no—
388C2×C4×D3—21no—
389C2×C4×D3C22×D311yescharacteristic
390C2×C4×D3C22×D311yescharacteristic
391C2×Dic6—21no—
392C2×Dic6C22×D311yescharacteristic
393C3×SD16—34no—
394C2×C3×C8—31no—
395C2×C3×C8—31no—
396C3×C4⋊C4—21no—
397C3×C4⋊C4—21no—
398C3×C4⋊C4—21no—
399C3×C4⋊C4—31no—
400C3×C4⋊C4—31no—
401C3×C4⋊C4—41no—
402C3×C4⋊C4—61no—
403C3×C4⋊C4C22×D311yescharacteristic
404C3×C4⋊C4C22×D311yescharacteristic
405C3×C22⋊C4—31no—
406C3×C22⋊C4—31no—
407C3×C22⋊C4—61no—
408C3×C22⋊C4—61no—
409C3×C22⋊C4—61no—
410C3×C22⋊C4—61no—
411C3×C22⋊C4—61no—
412C3×C42—21no—
413C3×C42—21no—
414C3×C42—21no—
415C3×C42—41no—
416C3×C42C22×D311yescharacteristic
417C3×C42C22×D311yescharacteristic
418#215—62no—
419#215—62no—
420#215—62no—
421#215—62no—
422#215—62no—
423#215—62no—
424#215—122no—
425#215—122no—
426#215—121no—
427#215D1214yescomplemented
428#214—62no—
429#213—62no—
430#213—62no—
431#213—62no—
432#213—121no—
433(C2×D3)⋊C4—21no—
434(C2×D3)⋊C4—21no—
435(C2×D3)⋊C4—21no—
436(C2×D3)⋊C4—21no—
437(C2×D3)⋊C4—21no—
438(C2×D3)⋊C4—61no—
439(C2×D3)⋊C4—61no—
440(C2×D3)⋊C4—61no—
441(C2×D3)⋊C4—61no—
442(C2×D3)⋊C4#6711yescharacteristic
443(C2×D3)⋊C4#6711yescharacteristic
444C4⋊Dic3—21no—
445C4⋊Dic3#6711yescharacteristic
446C4⋊Dic3C22×D311yescharacteristic
447#208—62no—
448C2×C3⋊C8—31no—
449C2×C3⋊C8—31no—
450C2×C3⋊C8—31no—
451C2×C3⋊C8—31no—
452C2×C3⋊C8—61no—
453C2×C3⋊C8—61no—
454C2×C3⋊C8—62no—
455C2×C3⋊C8C22×D311yescharacteristic
456C2×C3⋊C8C22×D311yescharacteristic
457D24—62no—
458D24—121no—
459#204—62no—
460#204—121no—
461ΓL(1,𝔽25)—62no—
462D3×C8—62no—
463C22×C32C22×D411yescharacteristic
464C2×C3⋊D3—41no—
465C2×C3⋊D3—41no—
466C2×C3⋊D3—41no—
467C2×C3⋊D3—41no—
468C2×C3⋊D3—41no—
469C2×C3⋊D3—41no—
470C2×C3×D3—21no—
471C2×C3×D3—21no—
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×D3AGL(1,ℤ/8)12yescomplemented
482D32—84no—
483D32—84no—
484C32×C4—21no—
485C32×C4—22no—
486C32×C4—21no—
487C32×C4—41no—
488C32×C4C22×D411yescharacteristic
489C32×C4H(5,𝔽2)11yescharacteristic
490C3×Dic3—21no—
491C3×Dic3—21no—
492C3×Dic3—41no—
493C3×Dic3—41no—
494C2×#41—31no—
495C22×Q8—31no—
496C22×D4—91no—
497C22×D4—91no—
498C22×D4—181no—
499AGL(1,ℤ/8)—184no—
500C2×SD16—31no—
501C2×SD16—91no—
502C2×SD16—91no—
503C2×SD16—91no—
504C2×SD16—91no—
505C2×SD16—91no—
506C2×SD16—184no—
507C2×D8—91no—
508C2×D8—91no—
509C2×D8—91no—
510C2×M16—91no—
511C22×C8—91no—
512#127—91no—
513#124—31no—
514#124—61no—
515C22⋊Q8—31no—
516C22⋊Q8—61no—
517#121—31no—
518#121—61no—
519#121—91no—
520#121—91no—
521#121—181no—
522#120—181no—
523#120—181no—
524C4×Q8D3211yescharacteristic, complemented
525C4×D4—31no—
526C4×D4—31no—
527C4×D4—61no—
528#107—31no—
529C4⋊C8—91no—
530#103—31no—
531#103—91no—
532#102—31no—
533#102—91no—
534#102—91no—
535#102—91no—
536C22⋊C8—91no—
537C22⋊C8—91no—
538#97—31no—
539C23×C3—31no—
540C23×C3—31no—
541C23×C3—61no—
542C23×C3—61no—
543C22×D3—21no—
544C22×D3—21no—
545C22×D3—61no—
546C22×D3—61no—
547C22×D3—61no—
548C22×D3—61no—
549C22×D3—121no—
550C22×D3—121no—
551C22×D3—122no—
552C22×D3—122no—
553C22×D3—122no—
554C22×D3—122no—
555C22×D3—122no—
556C22×D3—122no—
557C22×D3—122no—
558C22×D3—122no—
559C22×D3—241no—
560C22×D3—241no—
561C22×D3—241no—
562C22×D3—241no—
563C22×D3C2×#6711yescharacteristic
564C22×D3C2×#6711yescharacteristic
565C3×Q8—21no—
566C3×Q8—21no—
567C3×Q8—22no—
568C3×Q8—41no—
569C3×Q8—61no—
570C3×Q8—61no—
571C3×Q8—122no—
572C3×Q8C2×D1212yescomplemented
573C3×Q8D3×D412yescomplemented
574C3×D4—32no—
575C3×D4—62no—
576C3×D4—61no—
577C3×D4—61no—
578C3×D4—61no—
579C3×D4—122no—
580C3×D4—122no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—31no—
589C2×C3×C4—31no—
590C2×C3×C4—41no—
591C2×C3×C4—41no—
592C2×C3×C4—61no—
593C2×C3×C4—61no—
594C2×C3×C4—61no—
595C2×C3×C4—61no—
596C2×C3×C4—61no—
597C2×C3×C4—61no—
598C2×C3×C4—122no—
599C2×C3×C4—122no—
600C2×C3×C4—122no—
601C2×C3×C4D3×D411yescharacteristic
602C2×C3×C4D3×D411yescharacteristic
603C2×C3×C4C2×#6711yescharacteristic
604C2×C3×C4C2×#6711yescharacteristic
605C2×C3×C4C23×D311yescharacteristic
606C2×C3×C4C23×D311yescharacteristic
607#67—122no—
608#67—122no—
609#67—122no—
610#67—122no—
611C2×Dic3—21no—
612C2×Dic3—21no—
613C2×Dic3C2×#6711yescharacteristic
614C2×Dic3C2×#6711yescharacteristic
615D12—22no—
616D12—21no—
617D12—21no—
618D12—21no—
619D12—42no—
620D12—42no—
621D12—61no—
622D12—61no—
623D12—61no—
624D12—61no—
625D12—61no—
626D12—61no—
627D12—61no—
628D12—61no—
629D12—121no—
630D12—121no—
631D12—121no—
632D12—121no—
633D12—122no—
634D12—122no—
635D12—122no—
636D12—122no—
637D12—122no—
638D12—122no—
639D12—242no—
640D12—241no—
641D12—241no—
642D12—242no—
643D12C2×D1212yes—
644C4×D3—21no—
645C4×D3—21no—
646C4×D3—21no—
647C4×D3—21no—
648C4×D3—42no—
649C4×D3—42no—
650C4×D3—42no—
651Dic6—21no—
652Dic6—21no—
653Dic6—42no—
654C3×C8—32no—
655C3×C8—61no—
656C3⋊C8—21no—
657C3⋊C8—61no—
658C3⋊C8—61no—
659C3⋊C8—61no—
660C3⋊C8—61no—
661C3⋊C8—121no—
662C3⋊C8—121no—
663C3⋊C8C2×D1212yescomplemented
664C2×C32D4211yescharacteristic
665C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
666C2×C32#57711yescharacteristic
667C3⋊D3—81no—
668C3⋊D3—81no—
669C3×D3—22no—
670C3×D3—41no—
671C3×D3—42no—
672C3×D3—81no—
673C24—181no—
674C24—181no—
675#41—62no—
676#41—121no—
677C2×Q8—31no—
678C2×Q8—61no—
679C2×Q8—62no—
680C2×Q8—121no—
681C2×Q8C2×D3211yescharacteristic
682C2×D4—31no—
683C2×D4—31no—
684C2×D4—31no—
685C2×D4—61no—
686C2×D4—61no—
687C2×D4—91no—
688C2×D4—91no—
689C2×D4—181no—
690C2×D4—181no—
691C2×D4—182no—
692C2×D4—182no—
693C2×D4—181no—
694C2×D4—181no—
695C2×D4—181no—
696C2×D4—181no—
697C2×D4—361no—
698C2×D4—361no—
699C2×D4—364no—
700C22×C4—31no—
701C22×C4—31no—
702C22×C4—61no—
703C22×C4—61no—
704C22×C4—61no—
705SD16—34no—
706SD16—182no—
707SD16—182no—
708SD16—182no—
709SD16—182no—
710SD16—361no—
711D8—182no—
712D8—182no—
713D8—361no—
714M16—182no—
715C2×C8—31no—
716C2×C8—31no—
717C2×C8—91no—
718C2×C8—91no—
719C2×C8—182no—
720C4⋊C4—21no—
721C4⋊C4—31no—
722C4⋊C4—31no—
723C4⋊C4—61no—
724C4⋊C4C2×D3211yescharacteristic
725C22⋊C4—31no—
726C22⋊C4—31no—
727C22⋊C4—61no—
728C22⋊C4—61no—
729C22⋊C4—61no—
730C22⋊C4—61no—
731C22⋊C4—61no—
732C22⋊C4—181no—
733C22⋊C4—181no—
734C42—21no—
735C42C2×D3211yescharacteristic
736C22×C3—21no—
737C22×C3—32no—
738C22×C3—61no—
739C22×C3—61no—
740C22×C3—61no—
741C22×C3—61no—
742C22×C3—62no—
743C22×C3—61no—
744C22×C3—121no—
745C22×C3—121no—
746C22×C3—121no—
747C22×C3—121no—
748C22×C3—121no—
749C22×C3C2×D3×D411yescharacteristic
750C22×C3C22×#6711yescharacteristic
751C2×D3—21no—
752C2×D3—21no—
753C2×D3—21no—
754C2×D3—22no—
755C2×D3—21no—
756C2×D3—21no—
757C2×D3—41no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—41no—
762C2×D3—121no—
763C2×D3—121no—
764C2×D3—121no—
765C2×D3—121no—
766C2×D3—121no—
767C2×D3—121no—
768C2×D3—121no—
769C2×D3—121no—
770C2×D3—121no—
771C2×D3—121no—
772C2×D3—121no—
773C2×D3—121no—
774C2×D3—241no—
775C2×D3—241no—
776C2×D3—241no—
777C2×D3—241no—
778C2×D3—241no—
779C2×D3—241no—
780C2×D3—244no—
781C2×D3—244no—
782C2×D3—244no—
783C2×D3—244no—
784C2×D3#94912yescomplemented
785C3×C4—22no—
786C3×C4—21no—
787C3×C4—21no—
788C3×C4—22no—
789C3×C4—22no—
790C3×C4—21no—
791C3×C4—21no—
792C3×C4—21no—
793C3×C4—21no—
794C3×C4—41no—
795C3×C4—42no—
796C3×C4—41no—
797C3×C4—41no—
798C3×C4—61no—
799C3×C4—61no—
800C3×C4—81no—
801C3×C4—121no—
802C3×C4—121no—
803C3×C4C22×D1211yescharacteristic
804C3×C4C2×D3×D411yescharacteristic
805C3×C4#100411yescharacteristic
806C3×C4#100911yescharacteristic
807Dic3—21no—
808Dic3—21no—
809Dic3—41no—
810Dic3—41no—
811C32#326511yescharacteristic, complemented, Sylow
812C23—31no—
813C23—31no—
814C23—61no—
815C23—61no—
816C23—181no—
817C23—181no—
818C23—362no—
819C23—362no—
820C23—362no—
821C23—362no—
822C23—721no—
823C23—721no—
824Q8—21no—
825Q8—61no—
826Q8—61no—
827Q8—122no—
828Q8D3×D1212yescomplemented
829D4—32no—
830D4—62no—
831D4—61no—
832D4—61no—
833D4—61no—
834D4—122no—
835D4—122no—
836D4—181no—
837D4—181no—
838D4—181no—
839D4—181no—
840D4—362no—
841D4—362no—
842D4—362no—
843D4—362no—
844D4—362no—
845D4—721no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—31no—
849C2×C4—31no—
850C2×C4—61no—
851C2×C4—61no—
852C2×C4—61no—
853C2×C4—61no—
854C2×C4—61no—
855C2×C4—61no—
856C2×C4—122no—
857C2×C4—122no—
858C2×C4—122no—
859C2×C4D3×#6711yescharacteristic
860C2×C4D3×#6711yescharacteristic
861C2×C4C22×D3211yescharacteristic
862C8—32no—
863C8—61no—
864C8—181no—
865C8—181no—
866C2×C3—21no—
867C2×C3—21no—
868C2×C3—21no—
869C2×C3—62no—
870C2×C3—122no—
871C2×C3—121no—
872C2×C3—241no—
873C2×C3D4×D1211yescharacteristic
874C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
875C2×C3#577811yescharacteristic
876C2×C3D4×#6711yescharacteristic
877C2×C3C2×#94911yescharacteristic
878C2×C3#583711yescharacteristic
879D3—22no—
880D3—41no—
881D3—42no—
882D3—81no—
883D3—241no—
884D3—241no—
885D3—241no—
886D3—241no—
887D3—481no—
888D3—481no—
889C22—32no—
890C22—61no—
891C22—61no—
892C22—61no—
893C22—61no—
894C22—61no—
895C22—62no—
896C22—121no—
897C22—121no—
898C22—121no—
899C22—121no—
900C22—121no—
901C22—361no—
902C22—361no—
903C22—361no—
904C22—361no—
905C22—361no—
906C22—361no—
907C22—724no—
908C22—724no—
909C22C2×D3×#6711yescharacteristic
910C4—21no—
911C4—21no—
912C4—22no—
913C4—41no—
914C4—61no—
915C4—61no—
916C4—121no—
917C4—121no—
918C4C2×D3×D1211yescharacteristic
919C4#6430711yescharacteristic
920C3—21no—
921C3#7979411yescharacteristic, complemented
922C3#8354211yescharacteristic, complemented
923C2—62no—
924C2—121no—
925C2—122no—
926C2—241no—
927C2—721no—
928C2—721no—
929C2D12×#6711yescharacteristic
930C2#1059531911yescharacteristic
931C2D3×#94911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
hypercenterC4×Q8D32
hypocenterC32#3265
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×#5576C2semidirect
2. C2×#63939C2semidirect
3. C2×D3×#215C2semidirect
4. D122C2semidirect
5. #10592726C2semidirect
6. C3×#5026C2semidirect
7. #10591588C2semidirect
8. #10591584C2semidirect
9. #10590596C2semidirect
10. #10590595C2semidirect
11. #10590585C2semidirect
12. #10590576C2semidirect
13. #10590351C2semidirect
14. #10590348C2semidirect
15. #10590326C2semidirect
18. C2×C3×#239C22semidirect
19. C2×C3×D3×Q8C22semidirect
23. C32×C4×Q8C22semidirect
24. C2×#3755C22semidirect
25. C2×#3755C22semidirect
29. C3×#897C22semidirect
31. C3×#895C22semidirect
33. C3×#875C22semidirect
44. C2×#3717C22semidirect
45. C2×#3717C22semidirect
47. C2×#3714C22semidirect
48. C2×#3714C22semidirect
50. C2×#3711C22semidirect
51. C2×D3×C3⋊C8C22semidirect
52. #63636C22semidirect
53. #63636C22semidirect
54. C4⋊(C3⋊(C3⋊C8))C22semidirect
55. C3×#835C22semidirect
57. C3×#807C22semidirect
58. C3×#803C22semidirect
59. #63565C22semidirect
60. #63562C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. (C2×D3)⋊(C3⋊C8)C22semidirect
68. #5576D3semidirect
83. #5026D3semidirect
134. C3×#215D4semidirect
160. C2×#239C2×D3semidirect
161. C2×D3×Q8C2×D3semidirect
176. C3×C4×Q8C2×D3semidirect
177. C3×C4×Q8C2×D3semidirect
212. #897C2×D3semidirect
217. #895C2×D3semidirect
223. #875C2×D3semidirect
235. #835C2×D3semidirect
250. #807C2×D3semidirect
254. #803C2×D3semidirect
268. C32×Q8C2×D4semidirect
308. C3×C3⋊C8C2×D4semidirect
427. #215D12semidirect
481. C2×C3×D3AGL(1,ℤ/8)semidirect
524. C4×Q8D32semidirect
572. C3×Q8C2×D12semidirect
573. C3×Q8D3×D4semidirect
663. C3⋊C8C2×D12semidirect
784. C2×D3#949semidirect
811. C32#3265semidirect
828. Q8D3×D12semidirect
921. C3#79794semidirect
922. C3#83542semidirect

Maximal subgroups

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

subgroupindex
C3×#55762
C2×#639392
C2×D3×#2152
D1222
#105927262
C3×#50262
#105915882
#105915842
#105905962
#105905952
#105905852
#105905762
#105903512
#105903482
#105903262
#835423
#797943