Finite Group Databasebeta

← #11884409

Subgroups — #11884409

Order 1152.

1176 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596048C211yesmaximal, characteristic, complemented
2C2×#63950C211yesmaximal, characteristic, complemented
3C2×#63941C211yesmaximal, characteristic, complemented
4#10594005C211yesmaximal, characteristic, complemented
5C3×#5028C211yesmaximal, characteristic, complemented
6C3×#5026C211yesmaximal, characteristic, complemented
7#10591602C211yesmaximal, characteristic, complemented
8#10591593C211yesmaximal, characteristic, complemented
9#10590617C211yesmaximal, characteristic, complemented
10#10590598C211yesmaximal, characteristic, complemented
11#10590522C211yesmaximal, characteristic, complemented
12#10590509C211yesmaximal, characteristic, complemented
13#10590351C211yesmaximal, characteristic, complemented
14#10590349C211yesmaximal, characteristic, complemented
15#10590328C211yesmaximal, characteristic, complemented
16#80628—31nomaximal
17#79796—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×#3832C2211yescharacteristic, complemented
20C2×#3802C2211yescharacteristic
21C2×#3796C2211yescharacteristic
22C32×C4×Q8C2211yescharacteristic, complemented
23#64104—21no—
24#64104—21no—
25#64104C2211yescharacteristic
26#64104C2211yescharacteristic, complemented
27#64083—21no—
28#64083C2211yescharacteristic, complemented
29C4×C4⋊(C3⋊D3)—21no—
30C4×C4⋊(C3⋊D3)C2211yescharacteristic
31C2×C3×#216C2211yescharacteristic, complemented
32C2×C3×#215C2211yescharacteristic
33C2×C3×#215C2211yescharacteristic
34C3×#875C2211yescharacteristic
35C3×C4×D12C2211yescharacteristic
36#63950—24no—
37#63941—24no—
38#63923—21no—
39D3×(C2×D3)⋊C4—21no—
40#63916C2211yescharacteristic
41#63906—21no—
42#63891—21no—
43#63871C2211yescharacteristic
44C2×#3717C2211yescharacteristic, complemented
45C2×#3717C2211yescharacteristic, complemented
46C2×#3714C2211yescharacteristic
47C2×#3714C2211yescharacteristic
48C2×#3714C2211yescharacteristic
49C2×#3714C2211yescharacteristic
50C2×#3712C2211yescharacteristic
51C2×#3710C2211yescharacteristic, complemented
52C3×#835C2211yescharacteristic, complemented
53C3×#810C2211yescharacteristic, complemented
54C3×#809C2211yescharacteristic
55C3×#809C2211yescharacteristic
56C3×#807C2211yescharacteristic, complemented
57C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
58C3×#803C2211yescharacteristic, complemented
59#63564C2211yescharacteristic, complemented
60#63564C2211yescharacteristic, complemented
61#63557C2211yescharacteristic
62#63557C2211yescharacteristic, complemented
63C2×#919—31no—
64C2×#916—31no—
65C2×#914—31no—
66C2×#914—31no—
67#5676—31no—
68#5577—31no—
69#5577—31no—
70#5577—61no—
71#5554—31no—
72C3×#464—31no—
73C3×#440—31no—
74#5187—31no—
75#5172—31no—
76#5058—31no—
77#5028D311yescharacteristic, complemented
78#5026D311yescharacteristic, complemented
79#5015—31no—
80#4886—31no—
81#4883—31no—
82#4843—31no—
83#4836—31no—
84#4812—31no—
85#4810—31no—
86#4810—31no—
87#4808—31no—
88#4781—31no—
89#4775—31no—
90#4773—31no—
91#4773—31no—
92#4712—31no—
93#4706—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96#3832—22no—
97#3832—22no—
98#3832—41no—
99#3832—41no—
100C2×C4⋊(C3⋊D3)—21no—
101C2×C4⋊(C3⋊D3)—21no—
102C2×C4⋊(C3⋊D3)—21no—
103C2×C4⋊(C3⋊D3)—21no—
104C2×C4⋊(C3⋊D3)—21no—
105C2×C4⋊(C3⋊D3)—21no—
106C2×C4⋊(C3⋊D3)D411yescharacteristic
107C2×C4⋊(C3⋊D3)C2311yescharacteristic
108C2×C4⋊(C3⋊D3)C2311yescharacteristic
109C2×C4×C3⋊D3—21no—
110C2×C4×C3⋊D3—21no—
111C2×C4×C3⋊D3C2311yescharacteristic
112C2×C4×C3⋊D3C2311yescharacteristic
113C2×C3×D12C2311yescharacteristic
114C2×C3×D12C2311yescharacteristic
115C2×C3×C4×D3—21no—
116C2×C3×Dic6C2311yescharacteristic
117C2×#626—21no—
118C2×#626—21no—
119C2×#625—21no—
120C2×D3×Dic3—21no—
121#3802—22no—
122#3802—41no—
123#3796—22no—
124#3796—41no—
125C32×C4⋊C4—21no—
126C32×C4⋊C4C2311yescharacteristic
127C32×C42—21no—
128C32×C42C2311yescharacteristic
129#3752—21no—
130#3752—21no—
131#3752D411yescharacteristic
132#3752D411yescharacteristic
133C4⋊(C3⋊Dic3)D411yescharacteristic
134C3×#216—22no—
135C3×#215—22no—
136C3×#215D414yescomplemented
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4—21no—
140C3×C4⋊Dic3C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145Dic3⋊Dic3—21no—
146#3722—21no—
147(C2×D3)⋊Dic3—21no—
148#3717—22no—
149#3717—41no—
150#3714—22no—
151#3714—22no—
152#3714—22no—
153#3714—41no—
154#3712—22no—
155#3710—22no—
156#3268—91noSylow
157C2×#239—31no—
158C2×#239—31no—
159C2×#239—31no—
160C2×#239—31no—
161C2×#239—31no—
162C2×#239—61no—
163C2×#239—61no—
164C2×#237—31no—
165C2×D3×D4—31no—
166C2×D3×D4—31no—
167C2×C3×Q16—31no—
168C2×C3×SD16—31no—
169C2×C3×SD16—31no—
170C3×#124—31no—
171C3×C4×Q8—21no—
172C3×C4×Q8C2×D311yescharacteristic, complemented
173C3×C4×Q8C2×D311yescharacteristic, complemented
174C3×C4×D4—31no—
175#946—31no—
176C2×#216C2×D311yescharacteristic, complemented
177C2×#215—31no—
178C2×#215—31no—
179C2×#215C2×D311yescharacteristic
180C2×#215C2×D311yescharacteristic
181#938—31no—
182C2×#213—31no—
183C2×#213—31no—
184C2×#213—31no—
185C2×#213—31no—
186#930—61no—
187C2×(C2×D3)⋊C4—61no—
188#919—64no—
189#916—64no—
190#914—64no—
191#914—64no—
192C2×D24—31no—
193C2×D24—31no—
194C2×D24—31no—
195C2×D24—31no—
196C2×#204—31no—
197C2×#204—31no—
198C2×ΓL(1,𝔽25)—31no—
199C2×ΓL(1,𝔽25)—31no—
200C2×D3×C8—31no—
201C2×D3×C8—31no—
202#897—31no—
203#895—31no—
204#895—31no—
205#895—31no—
206#895—31no—
207#895—31no—
208#895—61no—
209#895—61no—
210#895—61no—
211#895—61no—
212#895—61no—
213#895—61no—
214#895—62no—
215#895—62no—
216#886—61no—
217#884—61no—
218#883—61no—
219#882—61no—
220#882—61no—
221D3×C22⋊C4—61no—
222#875C2×D311yescharacteristic
223#874—31no—
224#874—31no—
225#874—61no—
226#874—61no—
227#874—61no—
228#874—62no—
229C4×D12—31no—
230C4×D12—31no—
231C4×D12—61no—
232C4×D12—61no—
233C4×D12—61no—
234C4×D12—62no—
235C4×D12C2×D311yescharacteristic
236C3×#107—31no—
237C3×C4⋊C8—31no—
238C3×#103—31no—
239C3×#103—31no—
240C3×#102—31no—
241C3×#102—31no—
242C3×#97—31no—
243#835C2×D311yescharacteristic, complemented
244#821—31no—
245#821—31no—
246(C2×D3)⋊C8—31no—
247(C2×D3)⋊C8—31no—
248(C2×D3)⋊C8—31no—
249(C2×D3)⋊C8—31no—
250#810C2×D311yescharacteristic, complemented
251#809—31no—
252#809—31no—
253#809C2×D311yescharacteristic
254#809C2×D311yescharacteristic
255#807C2×D311yescharacteristic, complemented
256C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
257#803C2×D311yescharacteristic, complemented
258C22×C3⋊D3—21no—
259C22×C3⋊D3—21no—
260C22×C3⋊D3C2×D411yescharacteristic
261C22×C3⋊D3C2×D411yescharacteristic
262C22×C3×D3—21no—
263C22×C3×D3—21no—
264C2×D32—42no—
265C2×D32—42no—
266C2×D32—81no—
267C32×Q8—21no—
268C32×Q8C2×D412yes—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4C2×D411yescharacteristic
272C2×C32×C4C2×D411yescharacteristic
273C2×C32×C4C2411yescharacteristic
274C2×C3⋊Dic3C2×D411yescharacteristic
275C2×C3⋊Dic3C2×D411yescharacteristic
276C4⋊(C3⋊D3)—21no—
277C4⋊(C3⋊D3)—21no—
278C4⋊(C3⋊D3)—21no—
279C4⋊(C3⋊D3)—21no—
280C4⋊(C3⋊D3)—41no—
281C4⋊(C3⋊D3)—42no—
282C4⋊(C3⋊D3)—42no—
283C4⋊(C3⋊D3)—42no—
284C4⋊(C3⋊D3)—81no—
285C4⋊(C3⋊D3)—81no—
286C4⋊(C3⋊D3)—81no—
287C4×C3⋊D3—21no—
288C4×C3⋊D3—21no—
289C4×C3⋊D3—21no—
290C4×C3⋊D3—21no—
291C4×C3⋊D3—42no—
292C4×C3⋊D3—42no—
293C2×C3×Dic3—21no—
294C2×C3×Dic3—21no—
295C3×D12—21no—
296C3×D12—21no—
297C3×D12—21no—
298C3×D12C2×D412yes—
299C3×C4×D3—81no—
300C3×Dic6—21no—
301C3×Dic6—21no—
302#626—42no—
303#626—81no—
304#625—42no—
305D3×Dic3—42no—
306C3×C3⋊C8—21no—
307C3×C3⋊C8—21no—
308C3×C3⋊C8—21no—
309C3×C3⋊C8C2×D412yes—
310C2×AGL(1,ℤ/8)—91no—
311C2×#135—91no—
312#550—91no—
313#546—91no—
314#496—91no—
315#468—91no—
316#466—91no—
317#464—31no—
318#459—91no—
319#452—91no—
320#449—91no—
321#449—91no—
322#447—91no—
323#440—31no—
324#435—91no—
325C23×D3—61no—
326C23×D3—61no—
327C2×C3×Q8—21no—
328C2×C3×Q8—31no—
329C2×C3×Q8C22×D311yescharacteristic
330C2×C3×Q8C22×D311yescharacteristic
331C2×C3×D4—31no—
332C2×C3×D4—31no—
333C22×C3×C4—61no—
334C2×#67—61no—
335C2×#67—61no—
336C2×#67—61no—
337C2×#67—61no—
338C22×Dic3—61no—
339#239—62no—
340#239—62no—
341#239—62no—
342#239—62no—
343#239—62no—
344#239—122no—
345#239—122no—
346#239—121no—
347#239—121no—
348#239—121no—
349#239—121no—
350#239—121no—
351#239—122no—
352#239—122no—
353#237—62no—
354#237—121no—
355D3×D4—62no—
356D3×D4—62no—
357D3×D4—121no—
358D3×D4—121no—
359C2×D12—31no—
360C2×D12—31no—
361C2×D12—31no—
362C2×D12—31no—
363C2×D12—31no—
364C2×D12—31no—
365C2×D12—61no—
366C2×D12—61no—
367C2×D12—61no—
368C2×D12—61no—
369C2×D12—61no—
370C2×D12—61no—
371C2×D12—61no—
372C2×D12—62no—
373C2×D12—62no—
374C2×D12—62no—
375C2×D12—61no—
376C2×D12—61no—
377C2×D12—61no—
378C2×D12—61no—
379C2×D12—61no—
380C2×D12—61no—
381C2×D12—61no—
382C2×D12—62no—
383C2×D12—62no—
384C2×D12—62no—
385C2×D12—61no—
386C2×D12—61no—
387C2×D12—61no—
388C2×D12C22×D311yescharacteristic
389C2×D12C22×D311yescharacteristic
390C2×C4×D3—21no—
391C2×C4×D3—31no—
392C2×C4×D3—31no—
393C2×C4×D3—31no—
394C2×C4×D3—31no—
395C2×C4×D3—61no—
396C2×C4×D3—61no—
397C2×C4×D3—61no—
398C2×C4×D3—61no—
399C2×C4×D3—61no—
400C2×C4×D3—61no—
401C2×C4×D3—61no—
402C2×C4×D3—62no—
403C2×C4×D3—62no—
404C2×Dic6C22×D311yescharacteristic
405C3×Q16—62no—
406C3×SD16—34no—
407C3×SD16—62no—
408C2×C3×C8—31no—
409C2×C3×C8—31no—
410C2×C3×C8—31no—
411C2×C3×C8—31no—
412C3×C4⋊C4—22no—
413C3×C4⋊C4—21no—
414C3×C4⋊C4—21no—
415C3×C4⋊C4—21no—
416C3×C4⋊C4—31no—
417C3×C4⋊C4C22×D311yescharacteristic
418C3×C4⋊C4C22×D311yescharacteristic
419C3×C22⋊C4—61no—
420C3×C22⋊C4—61no—
421C3×C22⋊C4—61no—
422C3×C42—22no—
423C3×C42—21no—
424C3×C42—21no—
425C3×C42—21no—
426C3×C42C22×D311yescharacteristic
427C3×C42C22×D311yescharacteristic
428#217—61no—
429#216—22no—
430#215—22no—
431#215—62no—
432#215—121no—
433#215D1214yescomplemented
434#213—62no—
435#213—62no—
436#213—62no—
437#213—121no—
438(C2×D3)⋊C4—21no—
439(C2×D3)⋊C4—21no—
440(C2×D3)⋊C4—21no—
441(C2×D3)⋊C4—31no—
442(C2×D3)⋊C4—31no—
443(C2×D3)⋊C4—31no—
444(C2×D3)⋊C4—31no—
445(C2×D3)⋊C4—61no—
446(C2×D3)⋊C4—61no—
447(C2×D3)⋊C4—61no—
448(C2×D3)⋊C4—61no—
449(C2×D3)⋊C4—61no—
450(C2×D3)⋊C4—61no—
451(C2×D3)⋊C4—61no—
452(C2×D3)⋊C4—61no—
453(C2×D3)⋊C4—61no—
454(C2×D3)⋊C4—62no—
455(C2×D3)⋊C4—62no—
456C4⋊Dic3—31no—
457C4⋊Dic3—31no—
458C4⋊Dic3—61no—
459C4⋊Dic3—61no—
460C4⋊Dic3C22×D311yescharacteristic
461Dic3⋊C4—61no—
462C2×C3⋊C8C22×D311yescharacteristic
463C2×C3⋊C8C22×D311yescharacteristic
464C2×C3⋊C8C22×D311yescharacteristic
465C2×C3⋊C8C22×D311yescharacteristic
466D24—62no—
467D24—62no—
468D24—62no—
469D24—121no—
470#204—62no—
471#204—121no—
472ΓL(1,𝔽25)—62no—
473ΓL(1,𝔽25)—62no—
474D3×C8—62no—
475D3×C8—62no—
476C22×C32C22×D411yescharacteristic
477C2×C3⋊D3—21no—
478C2×C3⋊D3—21no—
479C2×C3⋊D3—21no—
480C2×C3⋊D3—21no—
481C2×C3⋊D3—21no—
482C2×C3⋊D3—21no—
483C2×C3⋊D3—41no—
484C2×C3⋊D3—41no—
485C2×C3⋊D3—41no—
486C2×C3⋊D3—41no—
487C2×C3⋊D3—41no—
488C2×C3⋊D3—41no—
489C2×C3×D3—22no—
490C2×C3×D3—41no—
491C2×C3×D3—41no—
492C2×C3×D3—41no—
493C2×C3×D3—41no—
494C2×C3×D3—41no—
495D32—84no—
496C32×C4—22no—
497C32×C4—21no—
498C32×C4—21no—
499C32×C4—41no—
500C32×C4C22×D411yescharacteristic
501C32×C4H(5,𝔽2)11yescharacteristic
502C3⋊Dic3—21no—
503C3⋊Dic3—21no—
504C3×Dic3—41no—
505C3×Dic3—41no—
506C2×#41—91no—
507C2×#41—91no—
508C2×#41—91no—
509C22×D4—91no—
510AGL(1,ℤ/8)—184no—
511#135—184no—
512C2×Q16—31no—
513C2×SD16—31no—
514C2×SD16—31no—
515C2×SD16—91no—
516C2×SD16—91no—
517C2×D8—91no—
518C2×D8—91no—
519C2×D8—91no—
520C2×D8—91no—
521C2×M16—91no—
522C22×C8—91no—
523#127—91no—
524#127—181no—
525#124—31no—
526#123—181no—
527C22⋊Q8—91no—
528#121—91no—
529#121—91no—
530#121—91no—
531#121—181no—
532#121—181no—
533#121—181no—
534#120—181no—
535C4×Q8D3211yescharacteristic, complemented
536C4×D4—31no—
537C4×D4—91no—
538C4×D4—181no—
539C2×C22⋊C4—181no—
540#107—31no—
541C4⋊C8—31no—
542#103—31no—
543#103—31no—
544#102—31no—
545#102—31no—
546#102—91no—
547#102—91no—
548C22⋊C8—91no—
549C22⋊C8—91no—
550#97—31no—
551C23×C3—61no—
552C23×C3—61no—
553C22×D3—21no—
554C22×D3—21no—
555C22×D3—31no—
556C22×D3—31no—
557C22×D3—31no—
558C22×D3—31no—
559C22×D3—61no—
560C22×D3—61no—
561C22×D3—62no—
562C22×D3—62no—
563C22×D3—61no—
564C22×D3—61no—
565C22×D3—61no—
566C22×D3—61no—
567C22×D3—122no—
568C22×D3—122no—
569C22×D3—122no—
570C22×D3—122no—
571C22×D3—241no—
572C22×D3—241no—
573C3×Q8—22no—
574C3×Q8—21no—
575C3×Q8—21no—
576C3×Q8—22no—
577C3×Q8—61no—
578C3×Q8—61no—
579C3×Q8C2×D1212yes—
580C3×Q8D3×D412yes—
581C3×D4—32no—
582C3×D4—61no—
583C3×D4—61no—
584C3×D4—61no—
585C2×C3×C4—22no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—22no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—61no—
595C2×C3×C4—61no—
596C2×C3×C4—241no—
597C2×C3×C4D3×D411yescharacteristic
598C2×C3×C4D3×D411yescharacteristic
599C2×C3×C4D3×D411yescharacteristic
600C2×C3×C4D3×D411yescharacteristic
601C2×C3×C4C23×D311yescharacteristic
602C2×C3×C4C23×D311yescharacteristic
603#67—122no—
604#67—122no—
605#67—122no—
606#67—241no—
607C2×Dic3—21no—
608C2×Dic3—21no—
609C2×Dic3—31no—
610C2×Dic3—31no—
611C2×Dic3—31no—
612C2×Dic3—31no—
613C2×Dic3—61no—
614C2×Dic3—61no—
615C2×Dic3—122no—
616D12—21no—
617D12—21no—
618D12—21no—
619D12—61no—
620D12—61no—
621D12—61no—
622D12—61no—
623D12—61no—
624D12—61no—
625D12—61no—
626D12—61no—
627D12—121no—
628D12—121no—
629D12—121no—
630D12—121no—
631D12—121no—
632D12—121no—
633D12—122no—
634D12—122no—
635D12—122no—
636D12—122no—
637D12—122no—
638D12—124no—
639D12—122no—
640D12—122no—
641D12—124no—
642D12—124no—
643D12—122no—
644D12—241no—
645D12—241no—
646D12—241no—
647D12—241no—
648D12—241no—
649D12—241no—
650D12—242no—
651D12—242no—
652D12—242no—
653D12—241no—
654D12C2×D1212yes—
655C4×D3—61no—
656C4×D3—61no—
657C4×D3—61no—
658C4×D3—61no—
659C4×D3—61no—
660C4×D3—61no—
661C4×D3—61no—
662C4×D3—61no—
663C4×D3—81no—
664C4×D3—121no—
665C4×D3—121no—
666C4×D3—121no—
667C4×D3—121no—
668C4×D3—122no—
669C4×D3—122no—
670C4×D3—122no—
671C4×D3—122no—
672C4×D3—122no—
673C4×D3—124no—
674C4×D3—124no—
675Dic6—21no—
676Dic6—21no—
677C3×C8—32no—
678C3×C8—61no—
679C3×C8—61no—
680C3×C8—61no—
681C3⋊C8—21no—
682C3⋊C8—21no—
683C3⋊C8—21no—
684C3⋊C8C2×D1212yes—
685C2×C32D4211yescharacteristic
686C2×C32#57511yescharacteristic
687C2×C32#57611yescharacteristic
688C3⋊D3—41no—
689C3⋊D3—41no—
690C3⋊D3—81no—
691C3⋊D3—81no—
692C3×D3—42no—
693C3×D3—81no—
694C24—181no—
695#41—182no—
696#41—182no—
697#41—182no—
698#41—361no—
699#41—361no—
700#41—361no—
701C2×Q8—31no—
702C2×Q8C2×D3211yescharacteristic
703C2×D4—31no—
704C2×D4—31no—
705C2×D4—91no—
706C2×D4—91no—
707C2×D4—91no—
708C2×D4—181no—
709C2×D4—181no—
710C2×D4—181no—
711C2×D4—181no—
712C2×D4—181no—
713C2×D4—181no—
714C2×D4—181no—
715C2×D4—182no—
716C2×D4—181no—
717C2×D4—181no—
718C2×D4—361no—
719C22×C4—61no—
720C22×C4—91no—
721C22×C4—91no—
722C22×C4—181no—
723C22×C4—181no—
724C22×C4—181no—
725Q16—62no—
726SD16—34no—
727SD16—62no—
728SD16—182no—
729SD16—361no—
730D8—182no—
731D8—182no—
732D8—182no—
733D8—361no—
734M16—182no—
735C2×C8—31no—
736C2×C8—31no—
737C2×C8—31no—
738C2×C8—31no—
739C2×C8—182no—
740C4⋊C4—21no—
741C4⋊C4—31no—
742C4⋊C4—91no—
743C4⋊C4—181no—
744C4⋊C4C2×D3211yescharacteristic
745C22⋊C4—61no—
746C22⋊C4—61no—
747C22⋊C4—61no—
748C22⋊C4—91no—
749C22⋊C4—91no—
750C22⋊C4—181no—
751C22⋊C4—181no—
752C22⋊C4—181no—
753C22⋊C4—181no—
754C42—21no—
755C42C2×D3211yescharacteristic
756C22×C3—21no—
757C22×C3—62no—
758C22×C3—121no—
759C22×C3—121no—
760C22×C3—121no—
761C22×C3—121no—
762C22×C3—121no—
763C22×C3C2×D3×D411yescharacteristic
764C22×C3C2×D3×D411yescharacteristic
765C2×D3—22no—
766C2×D3—41no—
767C2×D3—41no—
768C2×D3—41no—
769C2×D3—41no—
770C2×D3—41no—
771C2×D3—61no—
772C2×D3—61no—
773C2×D3—61no—
774C2×D3—61no—
775C2×D3—61no—
776C2×D3—61no—
777C2×D3—61no—
778C2×D3—61no—
779C2×D3—61no—
780C2×D3—61no—
781C2×D3—61no—
782C2×D3—61no—
783C2×D3—121no—
784C2×D3—121no—
785C2×D3—121no—
786C2×D3—121no—
787C2×D3—121no—
788C2×D3—121no—
789C2×D3—122no—
790C2×D3—122no—
791C2×D3—122no—
792C2×D3—122no—
793C2×D3—122no—
794C2×D3—122no—
795C2×D3—121no—
796C2×D3—121no—
797C2×D3—121no—
798C2×D3—121no—
799C2×D3—121no—
800C2×D3—121no—
801C2×D3—121no—
802C2×D3—121no—
803C2×D3—121no—
804C2×D3—121no—
805C2×D3—121no—
806C2×D3—121no—
807C2×D3—244no—
808C2×D3—244no—
809C3×C4—24no—
810C3×C4—22no—
811C3×C4—21no—
812C3×C4—21no—
813C3×C4—21no—
814C3×C4—21no—
815C3×C4—22no—
816C3×C4—22no—
817C3×C4—21no—
818C3×C4—21no—
819C3×C4—41no—
820C3×C4—42no—
821C3×C4—41no—
822C3×C4—41no—
823C3×C4—121no—
824C3×C4—121no—
825C3×C4C22×D1211yescharacteristic
826C3×C4C2×D3×D411yescharacteristic
827C3×C4#100911yescharacteristic
828C3×C4#100911yescharacteristic
829Dic3—41no—
830Dic3—41no—
831Dic3—61no—
832Dic3—61no—
833Dic3—61no—
834Dic3—61no—
835Dic3—121no—
836Dic3—121no—
837C32#326811yescharacteristic, complemented, Sylow
838C23—61no—
839C23—61no—
840C23—91no—
841C23—91no—
842C23—181no—
843C23—181no—
844C23—362no—
845C23—362no—
846C23—721no—
847Q8—21no—
848Q8—61no—
849Q8—61no—
850Q8D3×D1212yes—
851D4—32no—
852D4—61no—
853D4—61no—
854D4—61no—
855D4—181no—
856D4—181no—
857D4—181no—
858D4—181no—
859D4—361no—
860D4—362no—
861D4—362no—
862D4—362no—
863D4—362no—
864D4—362no—
865D4—721no—
866D4—721no—
867D4—721no—
868D4—721no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—61no—
872C2×C4—61no—
873C2×C4—91no—
874C2×C4—91no—
875C2×C4—181no—
876C2×C4—181no—
877C2×C4—181no—
878C2×C4—181no—
879C2×C4—241no—
880C2×C4—362no—
881C2×C4—362no—
882C2×C4—362no—
883C2×C4#381111yescharacteristic
884C2×C4#381111yescharacteristic
885C2×C4C22×D3211yescharacteristic
886C8—32no—
887C8—61no—
888C8—61no—
889C8—61no—
890C2×C3—21no—
891C2×C3—21no—
892C2×C3—21no—
893C2×C3—122no—
894C2×C3—241no—
895C2×C3D4×D1211yescharacteristic
896C2×C3#560911yescharacteristic
897C2×C3#576911yescharacteristic
898C2×C3#577411yescharacteristic
899C2×C3#577711yescharacteristic
900C2×C3#577711yescharacteristic
901D3—42no—
902D3—81no—
903D3—121no—
904D3—121no—
905D3—121no—
906D3—121no—
907D3—241no—
908D3—241no—
909D3—242no—
910D3—242no—
911D3—241no—
912D3—241no—
913D3—241no—
914D3—241no—
915C22—62no—
916C22—121no—
917C22—121no—
918C22—121no—
919C22—121no—
920C22—121no—
921C22—181no—
922C22—181no—
923C22—181no—
924C22—181no—
925C22—181no—
926C22—181no—
927C22—361no—
928C22—361no—
929C22—361no—
930C22—361no—
931C22—361no—
932C22—361no—
933C22—724no—
934C22C2×#381111yescharacteristic
935C4—22no—
936C4—21no—
937C4—21no—
938C4—41no—
939C4—121no—
940C4—121no—
941C4—181no—
942C4—181no—
943C4C2×D3×D1211yescharacteristic
944C4#6430811yescharacteristic
945C3—21no—
946C3#7979611yescharacteristic, complemented
947C3#8062811yescharacteristic, complemented
948C2—122no—
949C2—241no—
950C2—361no—
951C2—361no—
952C2—721no—
953C2—721no—
954C2#1059507411yescharacteristic
955C2#1059532311yescharacteristic
956C2#1059546111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
hypercenterC4×Q8D32
hypocenterC32#3268
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. #10596048C2semidirect
2. C2×#63950C2semidirect
3. C2×#63941C2semidirect
4. #10594005C2semidirect
5. C3×#5028C2semidirect
6. C3×#5026C2semidirect
7. #10591602C2semidirect
8. #10591593C2semidirect
9. #10590617C2semidirect
10. #10590598C2semidirect
11. #10590522C2semidirect
12. #10590509C2semidirect
13. #10590351C2semidirect
14. #10590349C2semidirect
15. #10590328C2semidirect
19. C2×#3832C22semidirect
22. C32×C4×Q8C22semidirect
26. #64104C22semidirect
28. #64083C22semidirect
31. C2×C3×#216C22semidirect
44. C2×#3717C22semidirect
45. C2×#3717C22semidirect
51. C2×#3710C22semidirect
52. C3×#835C22semidirect
53. C3×#810C22semidirect
56. C3×#807C22semidirect
57. C3×C4⋊(C3⋊C8)C22semidirect
58. C3×#803C22semidirect
59. #63564C22semidirect
60. #63564C22semidirect
62. #63557C22semidirect
77. #5028D3semidirect
78. #5026D3semidirect
136. C3×#215D4semidirect
172. C3×C4×Q8C2×D3semidirect
173. C3×C4×Q8C2×D3semidirect
176. C2×#216C2×D3semidirect
243. #835C2×D3semidirect
250. #810C2×D3semidirect
255. #807C2×D3semidirect
256. C4⋊(C3⋊C8)C2×D3semidirect
257. #803C2×D3semidirect
433. #215D12semidirect
535. C4×Q8D32semidirect
837. C32#3268semidirect
946. C3#79796semidirect
947. C3#80628semidirect

Maximal subgroups

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

subgroupindex
#105960482
C2×#639502
C2×#639412
#105940052
C3×#50282
C3×#50262
#105916022
#105915932
#105906172
#105905982
#105905222
#105905092
#105903512
#105903492
#105903282
#806283
#797963