Finite Group Databasebeta

← #11858040

Subgroups — #11858040

Order 1152.

1637 conjugacy classes of subgroups.

The subgroup lattice has 975 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64320C211yesmaximal, characteristic
2C2×#63804C211yesmaximal, characteristic, complemented
3#10594510C211yesmaximal, characteristic, complemented
4#10592502C211yesmaximal, characteristic, complemented
5C3×#4804C211yesmaximal, characteristic, complemented
6C3×#4803C211yesmaximal, characteristic, complemented
7#10591560C211yesmaximal, characteristic, complemented
8#10591556C211yesmaximal, characteristic, complemented
9#10591550C211yesmaximal, characteristic, complemented
10#10590941C211yesmaximal, characteristic, complemented
11#10590939C211yesmaximal, characteristic, complemented
12D3×#821C211yesmaximal, characteristic, complemented
13#10590593C211yesmaximal, characteristic, complemented
14#10590592C211yesmaximal, characteristic, complemented
15D3×#809C211yesmaximal, characteristic, complemented
16#78882—31nomaximal
17#78831—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×#239C2211yescharacteristic
21#64320—24no—
22#64320C418yescomplemented
23C2×#3802—21no—
24C2×#3802C2211yescharacteristic
25C2×D3×D12—21no—
26C2×D3×D12—21no—
27C2×D3×D12C2211yescharacteristic
28C2×D3×D12C2211yescharacteristic
29C2×#3798—21no—
30C2×#3798C2211yescharacteristic
31C2×#3743C2211yescharacteristic, complemented
32C4⋊C4×C3⋊D3C2211yescharacteristic, complemented
33C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
34C2×C3×D3×C8C2211yescharacteristic, complemented
35C3×#892C2211yescharacteristic, complemented
36C3×D3×C4⋊C4C2211yescharacteristic, complemented
37C4×#626—21no—
38D3×C4⋊Dic3C2211yescharacteristic, complemented
39#63881—21no—
40#63879—21no—
41#63849C2211yescharacteristic, complemented
42#63841C2211yescharacteristic, complemented
43#63837—21no—
44C2×#3711C2211yescharacteristic, complemented
45C2×#3710C2211yescharacteristic, complemented
46C2×D3×C3⋊C8C2211yescharacteristic, complemented
47#63804—24no—
48C32×#103C2211yescharacteristic, complemented
49#63662C2211yescharacteristic, complemented
50#63648C2211yescharacteristic, complemented
51#63636C2211yescharacteristic, complemented
52C3×#835C2211yescharacteristic, complemented
53C3×#835C2211yescharacteristic, complemented
54C3×#821C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×#809C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic, complemented
58#63564C2211yescharacteristic, complemented
59#63564C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61#63563C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63#63562C2211yescharacteristic, complemented
64C2×#1009—31no—
65C2×#1009—31no—
66C2×#907—31no—
67C2×#901—31no—
68#5523—31no—
69#5504—31no—
70C3×#417—31no—
71C3×#416—31no—
72#5233—31no—
73#5232—31no—
74#5131—31no—
75C2×#821—31no—
76#5001—31no—
77C2×#809—31no—
78#4804—31no—
79#4804—31no—
80#4804—31no—
81#4804D311yescharacteristic, complemented
82#4803—31no—
83#4803—31no—
84#4803—31no—
85#4803—61no—
86#4803D311yescharacteristic, complemented
87#4770—31no—
88#4770—31no—
89#4770—31no—
90#4770—31no—
91D3×#102—31no—
92D3×#102—31no—
93D3×#102—31no—
94D3×#102—31no—
95C22×D32—21no—
96C22×D32—21no—
97C22×D32—21no—
98C2×C32×Q8C2311yescharacteristic
99#3832—22no—
100#3832C2×C414yescomplemented
101C2×C4⋊(C3⋊D3)—21no—
102C2×C4⋊(C3⋊D3)C2311yescharacteristic
103C2×C4×C3⋊D3—21no—
104C2×C4×C3⋊D3—21no—
105C2×C4×C3⋊D3C2311yescharacteristic
106C3×#239—22no—
107C3×#239—22no—
108C3×#239C2×C414yescomplemented
109C3×#239C2×C414yescomplemented
110C2×C3×D12—21no—
111C2×C3×D12—21no—
112C2×C3×D12C2311yescharacteristic
113C2×C3×D12C2311yescharacteristic
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3—21no—
116C2×C3×C4×D3—21no—
117C2×C3×C4×D3C2311yescharacteristic
118C2×C3×C4×D3C2311yescharacteristic
119C2×#627D411yescharacteristic
120C2×#626—21no—
121C2×#626—21no—
122C2×#626D411yescharacteristic
123C2×#626D411yescharacteristic
124C2×#625—21no—
125C2×#625D411yescharacteristic
126C2×D3×Dic3—21no—
127#3802—22no—
128#3802—28no—
129#3802C2×C414yescomplemented
130D3×D12—22no—
131D3×D12—22no—
132D3×D12—28no—
133D3×D12—28no—
134D3×D12C2×C414yescomplemented
135D3×D12C2×C414yescomplemented
136#3798—28no—
137#3798C2×C414yes—
138#3798D414yes—
139C2×C32×C8C2311yescharacteristic
140C32×C4⋊C4C2311yescharacteristic
141C4⋊(C3⋊Dic3)C2311yescharacteristic
142#3750—21no—
143C2×C3⋊(C3⋊C8)C2311yescharacteristic
144#3743—22no—
145C3×(C2×D3)⋊C4—21no—
146C3×C4⋊Dic3C2311yescharacteristic
147C3×C4⋊Dic3C2311yescharacteristic
148C3×Dic3⋊C4—21no—
149C3×C4×Dic3—21no—
150C2×C3×C3⋊C8C2311yescharacteristic
151C2×C3×C3⋊C8C2311yescharacteristic
152C3×ΓL(1,𝔽25)—22no—
153C3×D3×C8—22no—
154Dic3⋊Dic3—21no—
155#3722—21no—
156(C2×D3)⋊Dic3—21no—
157Dic32—21no—
158Dic32—21no—
159#3711—22no—
160#3710—22no—
161D3×C3⋊C8—22no—
162#2897—91noSylow
163C2×C3×#41—31no—
164C2×C3×#41—31no—
165#1009—38no—
166#1009—38no—
167#1009—64no—
168#1009—64no—
169C2×#239—31no—
170C2×#239—31no—
171C2×#239—61no—
172C2×#239C2×D311yescharacteristic
173C2×#239C2×D311yescharacteristic
174C2×D3×D4—31no—
175C2×D3×D4—31no—
176C2×D3×D4—31no—
177C2×D3×D4—31no—
178C2×D3×D4—61no—
179C2×D3×D4—61no—
180C2×D3×D4—61no—
181C2×D3×D4—61no—
182C2×#235—31no—
183C2×#235—31no—
184C2×#235—61no—
185C2×#235—61no—
186C22×D12—31no—
187C22×D12—31no—
188C22×D12—61no—
189C22×D12—61no—
190C2×C3×M16—31no—
191C22×C3×C8—31no—
192C3×#117—31no—
193C2×C3×C4⋊C4—31no—
194C4×#67—61no—
195C4×#67—61no—
196#926—31no—
197C2×C4⋊Dic3—31no—
198C2×#208—31no—
199C22×C3⋊C8—31no—
200#907—64no—
201#901—64no—
202C2×ΓL(1,𝔽25)—31no—
203C2×ΓL(1,𝔽25)—31no—
204C2×ΓL(1,𝔽25)—31no—
205C2×ΓL(1,𝔽25)—61no—
206C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
207C2×D3×C8—31no—
208C2×D3×C8—31no—
209C2×D3×C8—31no—
210C2×D3×C8C2×D311yescharacteristic, complemented
211#893—61no—
212#892—31no—
213#892—31no—
214#892—31no—
215#892C2×D311yescharacteristic, complemented
216D3×C4⋊C4—31no—
217D3×C4⋊C4—31no—
218D3×C4⋊C4—31no—
219D3×C4⋊C4—61no—
220D3×C4⋊C4C2×D311yescharacteristic, complemented
221#887—61no—
222#67⋊C4—61no—
223#67⋊C4—61no—
224C4×D12—61no—
225C4×Dic6—61no—
226C3×#103—21no—
227C3×#103—31no—
228C3×#103—31no—
229C3×#103C2×D311yescharacteristic, complemented
230C3×#103C2×D311yescharacteristic, complemented
231C3×#102—31no—
232C3×#102—31no—
233C3×#102—31no—
234C3×#102—31no—
235#835—31no—
236#835—31no—
237#835—61no—
238#835C2×D311yescharacteristic, complemented
239#835C2×D311yescharacteristic, complemented
240#832—31no—
241#832—31no—
242#832—31no—
243#832—31no—
244#821—31no—
245#821—31no—
246#821—31no—
247#821—31no—
248#821—31no—
249#821—31no—
250#821—61no—
251#821C2×D311yescharacteristic, complemented
252#821C2×D311yescharacteristic, complemented
253#809—31no—
254#809—31no—
255#809—31no—
256#809—31no—
257#809—31no—
258#809—31no—
259#809—61no—
260#809C2×D311yescharacteristic, complemented
261#809C2×D311yescharacteristic, complemented
262C22×C3⋊D3—21no—
263C22×C3⋊D3C2×D411yescharacteristic
264C22×C3×D3—21no—
265C22×C3×D3—21no—
266C22×C3×D3C2×D411yescharacteristic
267C22×C3×D3C2×D411yescharacteristic
268C2×D32—24no—
269C2×D32—24no—
270C2×D32—24no—
271C2×D32—81no—
272C2×D32—81no—
273C2×D32—81no—
274C2×D32—81no—
275C2×D32—81no—
276C2×D32—81no—
277C32×Q8—21no—
278C32×Q8C22×C412yes—
279C2×C32×C4—21no—
280C2×C32×C4—21no—
281C2×C32×C4C2411yescharacteristic
282C2×C3⋊Dic3—21no—
283C2×C3⋊Dic3C2×D411yescharacteristic
284C4⋊(C3⋊D3)—24no—
285C4⋊(C3⋊D3)—21no—
286C4⋊(C3⋊D3)C22×C412yes—
287C4×C3⋊D3—24no—
288C4×C3⋊D3—81no—
289C4×C3⋊D3C22×C412yes—
290C4×C3⋊D3C2×D412yes—
291C2×C3×Dic3—21no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3C2×D411yescharacteristic
294C2×C3×Dic3C2×D411yescharacteristic
295C3×D12—24no—
296C3×D12—24no—
297C3×D12—21no—
298C3×D12—21no—
299C3×D12C22×C412yes—
300C3×D12C22×C412yes—
301C3×C4×D3—24no—
302C3×C4×D3—24no—
303C3×C4×D3—81no—
304C3×C4×D3C22×C412yes—
305C3×C4×D3C22×C412yes—
306C3×C4×D3C2×D412yes—
307C3×C4×D3C2×D412yes—
308#627C22⋊C414yes—
309#626—24no—
310#626—24no—
311#626C22⋊C414yes—
312#626C22⋊C414yes—
313#625—24no—
314#625C22⋊C414yes—
315D3×Dic3—81no—
316C32×C8—21no—
317C3⋊(C3⋊C8)—21no—
318C3×C3⋊C8—21no—
319C3×C3⋊C8—21no—
320C2×H(5,𝔽2)—91no—
321C2×#131—91no—
322#520—91no—
323#418—91no—
324#418—91no—
325#418—91no—
326#417—31no—
327#417—91no—
328#417—91no—
329#416—31no—
330#416—91no—
331#416—91no—
332C2×#102—91no—
333C2×#102—91no—
334C2×#102—91no—
335C23×D3—61no—
336C23×D3—61no—
337C23×D3—61no—
338C23×D3—61no—
339C23×D3—61no—
340C23×D3—61no—
341C3×#41—34no—
342C3×#41—34no—
343C3×#41—62no—
344C3×#41—62no—
345C2×C3×Q8—21no—
346C2×C3×Q8C22×D311yescharacteristic
347C2×C3×Q8C22×D311yescharacteristic
348C2×C3×D4—31no—
349C2×C3×D4—31no—
350C2×C3×D4—61no—
351C2×C3×D4—61no—
352C22×C3×C4—31no—
353C22×C3×C4—31no—
354C22×C3×C4—61no—
355C22×C3×C4—61no—
356C22×C3×C4—61no—
357C2×#67—31no—
358C2×#67—31no—
359C2×#67—31no—
360C2×#67—31no—
361C2×#67—61no—
362C2×#67—61no—
363C2×#67—61no—
364C2×#67—61no—
365C22×Dic3—61no—
366#239—22no—
367#239—22no—
368#239—34no—
369#239—34no—
370#239—64no—
371#239—62no—
372#239—62no—
373#239—122no—
374#239C4×D314yescomplemented
375#239C4×D314yescomplemented
376D3×D4—34no—
377D3×D4—34no—
378D3×D4—34no—
379D3×D4—34no—
380D3×D4—68no—
381D3×D4—68no—
382D3×D4—62no—
383D3×D4—62no—
384D3×D4—68no—
385D3×D4—68no—
386D3×D4—62no—
387D3×D4—62no—
388#235—34no—
389#235—34no—
390#235—34no—
391#235—34no—
392#235—68no—
393#235—68no—
394C2×D12—21no—
395C2×D12—21no—
396C2×D12—31no—
397C2×D12—31no—
398C2×D12—31no—
399C2×D12—31no—
400C2×D12—34no—
401C2×D12—34no—
402C2×D12—61no—
403C2×D12—68no—
404C2×D12—68no—
405C2×D12—62no—
406C2×D12—62no—
407C2×D12—61no—
408C2×D12—61no—
409C2×D12—61no—
410C2×D12—61no—
411C2×D12—121no—
412C2×D12C22×D311yescharacteristic
413C2×D12C22×D311yescharacteristic
414C2×C4×D3—21no—
415C2×C4×D3—21no—
416C2×C4×D3—21no—
417C2×C4×D3—31no—
418C2×C4×D3—31no—
419C2×C4×D3—61no—
420C2×C4×D3—61no—
421C2×C4×D3—61no—
422C2×C4×D3—61no—
423C2×C4×D3—61no—
424C2×C4×D3—61no—
425C2×C4×D3—121no—
426C2×C4×D3—121no—
427C2×C4×D3C22×D311yescharacteristic
428C2×C4×D3C22×D311yescharacteristic
429C2×Dic6—31no—
430C2×Dic6—31no—
431C3×M16—62no—
432C2×C3×C8—21no—
433C2×C3×C8—31no—
434C2×C3×C8—31no—
435C2×C3×C8—62no—
436C2×C3×C8C22×D311yescharacteristic
437C2×C3×C8C22×D311yescharacteristic
438C3×C4⋊C4—21no—
439C3×C4⋊C4—31no—
440C3×C4⋊C4—31no—
441C3×C4⋊C4—61no—
442C3×C4⋊C4C22×D311yescharacteristic
443C3×C4⋊C4C22×D311yescharacteristic
444C3×C22⋊C4—61no—
445C3×C42—61no—
446#217—61no—
447(C2×D3)⋊C4—21no—
448(C2×D3)⋊C4—61no—
449(C2×D3)⋊C4—61no—
450(C2×D3)⋊C4—61no—
451C4⋊Dic3—31no—
452C4⋊Dic3—31no—
453C4⋊Dic3—61no—
454C4⋊Dic3—61no—
455C4⋊Dic3C22×D311yescharacteristic
456C4⋊Dic3C22×D311yescharacteristic
457Dic3⋊C4—21no—
458Dic3⋊C4—61no—
459Dic3⋊C4—61no—
460Dic3⋊C4—61no—
461Dic3⋊C4—121no—
462C4×Dic3—21no—
463C4×Dic3—61no—
464C4×Dic3—61no—
465C4×Dic3—61no—
466C4×Dic3—61no—
467#208—62no—
468C2×C3⋊C8—31no—
469C2×C3⋊C8—31no—
470C2×C3⋊C8—61no—
471C2×C3⋊C8—62no—
472C2×C3⋊C8C22×D311yescharacteristic
473C2×C3⋊C8C22×D311yescharacteristic
474ΓL(1,𝔽25)—22no—
475ΓL(1,𝔽25)—62no—
476ΓL(1,𝔽25)—62no—
477ΓL(1,𝔽25)—62no—
478ΓL(1,𝔽25)—122no—
479D3×C8—22no—
480D3×C8—62no—
481D3×C8—62no—
482D3×C8—62no—
483C22×C32C22×D411yescharacteristic
484C2×C3⋊D3—21no—
485C2×C3⋊D3—21no—
486C2×C3⋊D3—22no—
487C2×C3⋊D3—41no—
488C2×C3⋊D3—41no—
489C2×C3⋊D3C2×C22⋊C412yes—
490C2×C3×D3—21no—
491C2×C3×D3—21no—
492C2×C3×D3—21no—
493C2×C3×D3—21no—
494C2×C3×D3—22no—
495C2×C3×D3—22no—
496C2×C3×D3—41no—
497C2×C3×D3—41no—
498C2×C3×D3—41no—
499C2×C3×D3—41no—
500C2×C3×D3C2×C22⋊C412yes—
501C2×C3×D3C2×C22⋊C412yes—
502D32—84no—
503D32—84no—
504D32—84no—
505C32×C4—22no—
506C32×C4—41no—
507C32×C4C23×C411yescharacteristic
508C32×C4C22×D411yescharacteristic
509C3⋊Dic3—41no—
510C3⋊Dic3C2×C22⋊C412yes—
511C3×Dic3—41no—
512C3×Dic3—41no—
513C3×Dic3C2×C22⋊C412yes—
514C3×Dic3C2×C22⋊C412yes—
515H(5,𝔽2)—98no—
516H(5,𝔽2)—184no—
517C2×#41—31no—
518C2×#41—31no—
519C2×#41—91no—
520C2×#41—91no—
521C2×#41—181no—
522C22×D4—91no—
523C22×D4—91no—
524C22×D4—91no—
525C22×D4—181no—
526C22×D4—181no—
527C22×D4—181no—
528#131—184no—
529C2×M16—31no—
530C2×M16—91no—
531C2×M16—91no—
532C22×C8—31no—
533C22×C8—91no—
534C22×C8—91no—
535C4×Q8—181no—
536C4×D4—181no—
537C4×D4—181no—
538C4×D4—181no—
539#117—31no—
540#117—91no—
541#117—91no—
542C2×C4⋊C4—31no—
543C2×C4⋊C4—91no—
544C2×C4⋊C4—91no—
545#103—31no—
546#103—31no—
547#103—91no—
548#103D3211yescharacteristic, complemented
549#102—31no—
550#102—31no—
551#102—31no—
552#102—31no—
553#102—91no—
554#102—91no—
555#102—91no—
556#102—91no—
557#102—91no—
558#102—91no—
559#102—91no—
560#102—91no—
561C23×C3—31no—
562C23×C3—31no—
563C23×C3—61no—
564C23×C3—61no—
565C22×D3—21no—
566C22×D3—21no—
567C22×D3—31no—
568C22×D3—31no—
569C22×D3—61no—
570C22×D3—64no—
571C22×D3—64no—
572C22×D3—64no—
573C22×D3—64no—
574C22×D3—61no—
575C22×D3—61no—
576C22×D3—64no—
577C22×D3—64no—
578C22×D3—121no—
579C22×D3—241no—
580C22×D3—241no—
581C22×D3—241no—
582C22×D3—241no—
583C22×D3—241no—
584C22×D3—241no—
585C22×D3—241no—
586C22×D3—241no—
587C22×D3—241no—
588C22×D3—241no—
589C22×D3—241no—
590C22×D3—241no—
591C22×D3D3×D411yescharacteristic
592C22×D3D3×D411yescharacteristic
593C3×Q8—21no—
594C3×Q8—21no—
595C3×Q8—22no—
596C3×Q8—41no—
597C3×Q8C2×C4×D312yes—
598C3×Q8C2×C4×D312yes—
599C3×D4—32no—
600C3×D4—32no—
601C3×D4—64no—
602C3×D4—64no—
603C3×D4—61no—
604C3×D4—61no—
605C2×C3×C4—21no—
606C2×C3×C4—21no—
607C2×C3×C4—21no—
608C2×C3×C4—21no—
609C2×C3×C4—21no—
610C2×C3×C4—31no—
611C2×C3×C4—31no—
612C2×C3×C4—32no—
613C2×C3×C4—32no—
614C2×C3×C4—32no—
615C2×C3×C4—32no—
616C2×C3×C4—41no—
617C2×C3×C4—41no—
618C2×C3×C4—64no—
619C2×C3×C4—64no—
620C2×C3×C4—61no—
621C2×C3×C4—61no—
622C2×C3×C4—241no—
623C2×C3×C4C23×D311yescharacteristic
624C2×C3×C4C23×D311yescharacteristic
625#67—34no—
626#67—34no—
627#67—34no—
628#67—34no—
629#67—64no—
630#67—64no—
631#67—64no—
632#67—64no—
633C2×Dic3—21no—
634C2×Dic3—21no—
635C2×Dic3—31no—
636C2×Dic3—31no—
637C2×Dic3—61no—
638C2×Dic3—61no—
639C2×Dic3—61no—
640C2×Dic3—121no—
641C2×Dic3—241no—
642C2×Dic3D3×D411yescharacteristic
643C2×Dic3D3×D411yescharacteristic
644D12—24no—
645D12—24no—
646D12—21no—
647D12—21no—
648D12—34no—
649D12—34no—
650D12—32no—
651D12—32no—
652D12—62no—
653D12—64no—
654D12—64no—
655D12—64no—
656D12—64no—
657D12—61no—
658D12—61no—
659D12—121no—
660D12—124no—
661D12C2×C4×D312yes—
662D12C2×C4×D312yes—
663C4×D3—24no—
664C4×D3—24no—
665C4×D3—32no—
666C4×D3—32no—
667C4×D3—32no—
668C4×D3—32no—
669C4×D3—62no—
670C4×D3—62no—
671C4×D3—64no—
672C4×D3—64no—
673C4×D3—81no—
674C4×D3—124no—
675C4×D3—241no—
676C4×D3—241no—
677C4×D3—241no—
678C4×D3—242no—
679C4×D3C2×C4×D312yes—
680C4×D3C2×C4×D312yes—
681C4×D3D3×D412yes—
682C4×D3D3×D412yes—
683Dic6—34no—
684Dic6—34no—
685C3×C8—21no—
686C3×C8—21no—
687C3×C8—41no—
688C3×C8—61no—
689C3×C8—61no—
690C3⋊C8—21no—
691C3⋊C8—21no—
692C3⋊C8—61no—
693C3⋊C8—61no—
694C3⋊C8—121no—
695C2×C32C22×C22⋊C411yescharacteristic
696C2×C32#57611yescharacteristic
697C2×C32#57711yescharacteristic
698C3⋊D3—22no—
699C3⋊D3—42no—
700C3×D3—22no—
701C3×D3—22no—
702C3×D3—42no—
703C3×D3—42no—
704C24—181no—
705C24—181no—
706C24—181no—
707#41—34no—
708#41—34no—
709#41—62no—
710#41—62no—
711#41—94no—
712#41—94no—
713#41—94no—
714#41—188no—
715#41—182no—
716C2×Q8—91no—
717C2×Q8C2×D3211yescharacteristic
718C2×D4—31no—
719C2×D4—31no—
720C2×D4—61no—
721C2×D4—61no—
722C2×D4—94no—
723C2×D4—94no—
724C2×D4—91no—
725C2×D4—91no—
726C2×D4—94no—
727C2×D4—91no—
728C2×D4—91no—
729C2×D4—181no—
730C2×D4—182no—
731C2×D4—182no—
732C2×D4—181no—
733C2×D4—181no—
734C2×D4—188no—
735C2×D4—188no—
736C2×D4—182no—
737C2×D4—181no—
738C2×D4—188no—
739C22×C4—31no—
740C22×C4—31no—
741C22×C4—61no—
742C22×C4—61no—
743C22×C4—61no—
744C22×C4—91no—
745C22×C4—181no—
746C22×C4—181no—
747C22×C4—181no—
748M16—62no—
749M16—182no—
750M16—182no—
751C2×C8—31no—
752C2×C8—31no—
753C2×C8—62no—
754C2×C8—91no—
755C2×C8—182no—
756C2×C8—182no—
757C2×C8C2×D3211yescharacteristic
758C4⋊C4—31no—
759C4⋊C4—31no—
760C4⋊C4—61no—
761C4⋊C4—91no—
762C4⋊C4—181no—
763C4⋊C4—181no—
764C4⋊C4C2×D3211yescharacteristic
765C22⋊C4—61no—
766C22⋊C4—181no—
767C22⋊C4—181no—
768C42—61no—
769C42—181no—
770C42—181no—
771C22×C3—21no—
772C22×C3—32no—
773C22×C3—32no—
774C22×C3—61no—
775C22×C3—61no—
776C22×C3—61no—
777C22×C3—61no—
778C22×C3—62no—
779C22×C3—62no—
780C22×C3—121no—
781C22×C3—121no—
782C22×C3—121no—
783C22×C3—121no—
784C22×C3C2×D3×D411yescharacteristic
785C22×C3C2×D3×D411yescharacteristic
786C2×D3—21no—
787C2×D3—21no—
788C2×D3—21no—
789C2×D3—21no—
790C2×D3—22no—
791C2×D3—22no—
792C2×D3—32no—
793C2×D3—32no—
794C2×D3—41no—
795C2×D3—41no—
796C2×D3—41no—
797C2×D3—41no—
798C2×D3—62no—
799C2×D3—61no—
800C2×D3—61no—
801C2×D3—61no—
802C2×D3—61no—
803C2×D3—62no—
804C2×D3—62no—
805C2×D3—121no—
806C2×D3—121no—
807C2×D3—122no—
808C2×D3—121no—
809C2×D3—121no—
810C2×D3—121no—
811C2×D3—121no—
812C2×D3—241no—
813C2×D3—241no—
814C2×D3—244no—
815C2×D3—244no—
816C2×D3—244no—
817C2×D3—244no—
818C2×D3—244no—
819C2×D3—244no—
820C2×D3D3×C22⋊C412yes—
821C2×D3D3×C22⋊C412yes—
822C3×C4—22no—
823C3×C4—22no—
824C3×C4—21no—
825C3×C4—21no—
826C3×C4—32no—
827C3×C4—32no—
828C3×C4—42no—
829C3×C4—41no—
830C3×C4—41no—
831C3×C4—81no—
832C3×C4—121no—
833C3×C4—121no—
834C3×C4C22×C4×D311yescharacteristic
835C3×C4C22×C4×D311yescharacteristic
836C3×C4C2×D3×D411yescharacteristic
837C3×C4C2×D3×D411yescharacteristic
838Dic3—32no—
839Dic3—32no—
840Dic3—41no—
841Dic3—41no—
842Dic3—62no—
843Dic3—121no—
844Dic3—121no—
845Dic3—241no—
846Dic3D3×C22⋊C412yes—
847Dic3D3×C22⋊C412yes—
848C32#289711yescharacteristic, complemented, Sylow
849C23—31no—
850C23—31no—
851C23—61no—
852C23—61no—
853C23—91no—
854C23—184no—
855C23—184no—
856C23—184no—
857C23—181no—
858C23—721no—
859C23—721no—
860C23—721no—
861C23—721no—
862C23—721no—
863C23—721no—
864Q8—21no—
865Q8—94no—
866Q8C4×D3212yes—
867D4—32no—
868D4—32no—
869D4—64no—
870D4—64no—
871D4—61no—
872D4—61no—
873D4—94no—
874D4—94no—
875D4—94no—
876D4—92no—
877D4—184no—
878D4—184no—
879D4—184no—
880D4—184no—
881D4—181no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—31no—
885C2×C4—31no—
886C2×C4—32no—
887C2×C4—32no—
888C2×C4—32no—
889C2×C4—32no—
890C2×C4—64no—
891C2×C4—64no—
892C2×C4—61no—
893C2×C4—61no—
894C2×C4—91no—
895C2×C4—92no—
896C2×C4—92no—
897C2×C4—184no—
898C2×C4—181no—
899C2×C4—241no—
900C2×C4—721no—
901C2×C4—721no—
902C2×C4C22×D3211yescharacteristic
903C8—21no—
904C8—61no—
905C8—61no—
906C8—181no—
907C2×C3—21no—
908C2×C3—21no—
909C2×C3—21no—
910C2×C3—62no—
911C2×C3—62no—
912C2×C3—122no—
913C2×C3—122no—
914C2×C3C2×D3×C22⋊C411yescharacteristic
915C2×C3C2×D3×C22⋊C411yescharacteristic
916C2×C3#576911yescharacteristic
917C2×C3#577011yescharacteristic
918C2×C3#577411yescharacteristic
919C2×C3#577811yescharacteristic
920D3—22no—
921D3—22no—
922D3—42no—
923D3—42no—
924D3—62no—
925D3—62no—
926D3—122no—
927D3—122no—
928D3—122no—
929D3—242no—
930C22—32no—
931C22—32no—
932C22—61no—
933C22—61no—
934C22—61no—
935C22—61no—
936C22—62no—
937C22—62no—
938C22—92no—
939C22—121no—
940C22—121no—
941C22—121no—
942C22—121no—
943C22—181no—
944C22—181no—
945C22—182no—
946C22—361no—
947C22—361no—
948C22—724no—
949C22—724no—
950C22—724no—
951C22D32×D411yescharacteristic
952C4—22no—
953C4—32no—
954C4—32no—
955C4—41no—
956C4—92no—
957C4—121no—
958C4—121no—
959C4—361no—
960C4C2×C4×D3211yescharacteristic
961C4D32×D411yescharacteristic
962C3—21no—
963C3#7883111yescharacteristic, complemented
964C3#7888211yescharacteristic, complemented
965C2—62no—
966C2—62no—
967C2—122no—
968C2—122no—
969C2—182no—
970C2—362no—
971C2D32×C22⋊C411yescharacteristic
972C2#1059475511yescharacteristic
973C2#1059477011yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×#64320C2
cosocleC2×C32×C4C24
hypercenter#103D32
hypocenterC32#2897
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
2. C2×#63804C2semidirect
3. #10594510C2semidirect
4. #10592502C2semidirect
5. C3×#4804C2semidirect
6. C3×#4803C2semidirect
7. #10591560C2semidirect
8. #10591556C2semidirect
9. #10591550C2semidirect
10. #10590941C2semidirect
11. #10590939C2semidirect
12. D3×#821C2semidirect
13. #10590593C2semidirect
14. #10590592C2semidirect
15. D3×#809C2semidirect
22. #64320C4semidirect
31. C2×#3743C22semidirect
32. C4⋊C4×C3⋊D3C22semidirect
33. C2×C3×ΓL(1,𝔽25)C22semidirect
34. C2×C3×D3×C8C22semidirect
35. C3×#892C22semidirect
36. C3×D3×C4⋊C4C22semidirect
38. D3×C4⋊Dic3C22semidirect
41. #63849C22semidirect
42. #63841C22semidirect
44. C2×#3711C22semidirect
45. C2×#3710C22semidirect
46. C2×D3×C3⋊C8C22semidirect
48. C32×#103C22semidirect
49. #63662C22semidirect
50. #63648C22semidirect
51. #63636C22semidirect
52. C3×#835C22semidirect
53. C3×#835C22semidirect
54. C3×#821C22semidirect
55. C3×#821C22semidirect
56. C3×#809C22semidirect
57. C3×#809C22semidirect
58. #63564C22semidirect
59. #63564C22semidirect
60. #63563C22semidirect
61. #63563C22semidirect
62. #63562C22semidirect
63. #63562C22semidirect
81. #4804D3semidirect
86. #4803D3semidirect
100. #3832C2×C4semidirect
108. C3×#239C2×C4semidirect
109. C3×#239C2×C4semidirect
129. #3802C2×C4semidirect
134. D3×D12C2×C4semidirect
135. D3×D12C2×C4semidirect
206. C2×ΓL(1,𝔽25)C2×D3semidirect
210. C2×D3×C8C2×D3semidirect
215. #892C2×D3semidirect
220. D3×C4⋊C4C2×D3semidirect
229. C3×#103C2×D3semidirect
230. C3×#103C2×D3semidirect
238. #835C2×D3semidirect
239. #835C2×D3semidirect
251. #821C2×D3semidirect
252. #821C2×D3semidirect
260. #809C2×D3semidirect
261. #809C2×D3semidirect
374. #239C4×D3semidirect
375. #239C4×D3semidirect
548. #103D32semidirect
848. C32#2897semidirect
963. C3#78831semidirect
964. C3#78882semidirect

Maximal subgroups

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

subgroupindex
C2×#643202
C2×#638042
#105945102
#105925022
C3×#48042
C3×#48032
#105915602
#105915562
#105915502
#105909412
#105909392
D3×#8212
#105905932
#105905922
D3×#8092
#788823
#788313