Finite Group Databasebeta

← C2×#10594732 #11918810

Subgroups — C2×#10594732 #11918810

Order 1152.

3173 conjugacy classes of subgroups.

The subgroup lattice has 1254 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64314C211yesmaximal, characteristic, complemented
2C2×#64313C211yesmaximal, characteristic, complemented
3C2×#64120C211yesmaximal, characteristic, complemented
4C2×C3×#911C211yesmaximal, characteristic, complemented
5C2×C3×D3×D8C211yesmaximal, characteristic, complemented
6C2×#63936C211yesmaximal, characteristic, complemented
7C2×#63934C211yesmaximal, characteristic, complemented
8C2×#63933C211yesmaximal, characteristic, complemented
9C2×#63932C211yesmaximal, characteristic, complemented
10C2×#63926C211yesmaximal, characteristic, complemented
11C2×D3×#213C211yesmaximal, characteristic, complemented
12#10594732C2116yesmaximal, direct product factor
13C2×#63806C211yesmaximal, characteristic, complemented
14C2×#63804C211yesmaximal, characteristic, complemented
15C2×#63798C211yesmaximal, characteristic, complemented
16C2×#63795C211yesmaximal, characteristic, complemented
17C2×#5774—31nomaximal
18C2×#5757—31nomaximal
19C2×#3830C2211yescharacteristic, complemented
20C2×D4×C3⋊D3C2211yescharacteristic, complemented
21C2×C3×#237C2211yescharacteristic, complemented
22C2×C3×D3×D4C2211yescharacteristic, complemented
23C2×C3×D3×D4C2211yescharacteristic, complemented
24C2×C3×D3×D4C2211yescharacteristic, complemented
25C2×#3811—21no—
26C2×D3×#67—21no—
27C2×D3×#67—21no—
28C2×D3×#67—21no—
29C22×#626—21no—
30C22×#625—21no—
31C2×#3805—21no—
32C2×#3804—21no—
33#64314—24no—
34#64314C2218yescomplemented
35#64313—24no—
36#64313C2218yescomplemented
37C2×#3802C2211yescharacteristic, complemented
38C2×D3×D12C2211yescharacteristic, complemented
39C2×#3799C2211yescharacteristic, complemented
40C2×#3798C2211yescharacteristic
41C2×#3796C2211yescharacteristic, complemented
42C2×#3795C2211yescharacteristic, complemented
43C2×#3795C2211yescharacteristic, complemented
44C2×C32×D8C2211yescharacteristic, complemented
45C2×#3754C2211yescharacteristic, complemented
46C2×#3753C2211yescharacteristic, complemented
47#64120C2218yescomplemented
48C2×#3744C2211yescharacteristic, complemented
49C2×#3743C2211yescharacteristic, complemented
50C2×C3×#214C2211yescharacteristic, complemented
51C2×C3×#213C2211yescharacteristic, complemented
52C2×C3×#213C2211yescharacteristic, complemented
53C2×C3×#213C2211yescharacteristic, complemented
54C3×#911C2218yescomplemented
55C3×D3×D8C2218yescomplemented
56C2×C3×D24C2211yescharacteristic, complemented
57C2×C3×#204C2211yescharacteristic, complemented
58C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
59C2×C3×D3×C8C2211yescharacteristic, complemented
60#63936C2218yescomplemented
61#63934C2218yescomplemented
62#63933C2218yescomplemented
63#63932C2218yescomplemented
64#63926C2218yescomplemented
65D3×#213C2218yescomplemented
66C2×#3719C2211yescharacteristic, complemented
67C2×#3716C2211yescharacteristic, complemented
68C2×#3715C2211yescharacteristic, complemented
69C2×#3714C2211yescharacteristic, complemented
70C2×#3714C2211yescharacteristic, complemented
71C2×#3713C2211yescharacteristic, complemented
72C2×#3711C2211yescharacteristic, complemented
73C2×#3710C2211yescharacteristic, complemented
74C2×D3×C3⋊C8C2211yescharacteristic, complemented
75#63806C2218yescomplemented
76#63804C2218yescomplemented
77#63798C2218yescomplemented
78#63795C2218yescomplemented
79C2×#1009—31no—
80C2×#1004—31no—
81C2×#1004—31no—
82C2×#1004—31no—
83C2×C3×AGL(1,ℤ/8)—31no—
84C22×C3×D8—31no—
85C2×#950—31no—
86C2×#932—31no—
87C2×#932—31no—
88C22×#213—31no—
89#5774—316no—
90C2×#916—31no—
91C2×#916—31no—
92C2×#914—31no—
93C2×#914—31no—
94#5757—316no—
95C2×#912—31no—
96C2×#912—31no—
97C2×#911—31no—
98C2×#911—31no—
99C2×#911—31no—
100C2×#911—31no—
101C2×#911—31no—
102C2×#911—61no—
103C2×#911D311yescharacteristic, complemented
104C2×D3×D8—31no—
105C2×D3×D8—31no—
106C2×D3×D8—31no—
107C2×D3×D8D311yescharacteristic, complemented
108C2×#908—31no—
109C2×#907—31no—
110C2×#904—31no—
111C2×#901—31no—
112C23×C3⋊D3—21no—
113C23×C3×D3—21no—
114C23×C3×D3—21no—
115C23×C3×D3—21no—
116C22×D32—21no—
117C22×D32—21no—
118C2×C32×D4C2311yescharacteristic
119C2×C32×D4C2311yescharacteristic
120C2×#638—21no—
121C2×#638—21no—
122C22×C3⋊Dic3—21no—
123#3830—22no—
124#3830C2314yescomplemented
125D4×C3⋊D3—22no—
126D4×C3⋊D3C2314yescomplemented
127C2×C4⋊(C3⋊D3)C2311yescharacteristic
128C2×C4×C3⋊D3C2311yescharacteristic
129C2×#634C2311yescharacteristic
130C2×C3×#67—21no—
131C2×C3×#67—21no—
132C2×C3×#67—21no—
133C2×C3×#67—21no—
134C22×C3×Dic3—21no—
135C3×#237—22no—
136C3×#237C2314yescomplemented
137C3×D3×D4—22no—
138C3×D3×D4—22no—
139C3×D3×D4—22no—
140C3×D3×D4C2314yescomplemented
141C3×D3×D4C2314yescomplemented
142C3×D3×D4C2314yescomplemented
143C2×C3×D12C2311yescharacteristic
144C2×C3×D12C2311yescharacteristic
145C2×C3×D12C2311yescharacteristic
146C2×C3×C4×D3C2311yescharacteristic
147C2×C3×C4×D3C2311yescharacteristic
148C2×C3×Dic6C2311yescharacteristic
149#3811—28no—
150D3×#67—28no—
151D3×#67—28no—
152D3×#67—28no—
153C2×#627D411yescharacteristic
154C2×#626—21no—
155C2×#626—21no—
156C2×#626—21no—
157C2×#626—28no—
158C2×#626D411yescharacteristic
159C2×#626D411yescharacteristic
160C2×#625—21no—
161C2×#625—21no—
162C2×#625—21no—
163C2×#625—28no—
164C2×#625D411yescharacteristic
165C2×#624—21no—
166#3805—28no—
167#3804—28no—
168C2×D3×Dic3—21no—
169C2×D3×Dic3—21no—
170C2×D3×Dic3—21no—
171#3802—22no—
172#3802C2314yescomplemented
173D3×D12—22no—
174D3×D12C2314yescomplemented
175#3799—22no—
176#3799C2314yescomplemented
177#3798D414yes—
178#3798C2314yes—
179#3796—22no—
180#3796C2314yescomplemented
181#3795—22no—
182#3795—22no—
183#3795C2314yescomplemented
184#3795C2314yescomplemented
185C32×D8C2314yescomplemented
186C2×C32×C8C2311yescharacteristic
187#3754C2314yescomplemented
188#3753C2314yescomplemented
189C2×C3⋊(C3⋊C8)C2311yescharacteristic
190#3744C2314yescomplemented
191#3743C2314yescomplemented
192C3×#214C2314yescomplemented
193C3×#213C2314yescomplemented
194C3×#213C2314yescomplemented
195C3×#213C2314yescomplemented
196C2×C3×C3⋊C8C2311yescharacteristic
197C2×C3×C3⋊C8C2311yescharacteristic
198C3×D24C2314yescomplemented
199C3×#204C2314yescomplemented
200C3×ΓL(1,𝔽25)C2314yescomplemented
201C3×D3×C8C2314yescomplemented
202#3719C2314yescomplemented
203#3716C2314yescomplemented
204#3715C2314yescomplemented
205#3714C2314yescomplemented
206#3714C2314yescomplemented
207#3713C2314yescomplemented
208#3711C2314yescomplemented
209#3710C2314yescomplemented
210D3×C3⋊C8C2314yescomplemented
211C2×#576—91noSylow
212C2×C3×#41—31no—
213C22×C3×D4—31no—
214C22×C3×D4—31no—
215C22×C3×D4—31no—
216C22×#67—61no—
217C22×#67—61no—
218C22×#67—61no—
219C22×#67—61no—
220C22×#67—61no—
221C22×#67—61no—
222#1009—38no—
223#1009—64no—
224C2×#239—31no—
225C2×#239—31no—
226#1004—38no—
227#1004—38no—
228#1004—38no—
229#1004—64no—
230#1004—64no—
231#1004—64no—
232C2×#237—31no—
233C2×#237—31no—
234C2×#237—31no—
235C2×#237—31no—
236C2×#237—31no—
237C2×#237—61no—
238C2×#237—61no—
239C2×#237—61no—
240C2×#237—61no—
241C2×#237C2×D311yescharacteristic, complemented
242C2×D3×D4—31no—
243C2×D3×D4—31no—
244C2×D3×D4—31no—
245C2×D3×D4—31no—
246C2×D3×D4—31no—
247C2×D3×D4—61no—
248C2×D3×D4—61no—
249C2×D3×D4—61no—
250C2×D3×D4—61no—
251C2×D3×D4—61no—
252C2×D3×D4—61no—
253C2×D3×D4C2×D311yescharacteristic, complemented
254C2×D3×D4C2×D311yescharacteristic, complemented
255C2×D3×D4C2×D311yescharacteristic, complemented
256C2×#235—31no—
257C2×#235—31no—
258C2×#235—31no—
259C2×#235—31no—
260C2×#235—31no—
261C2×#235—61no—
262C22×D12—31no—
263C22×D12—61no—
264C3×AGL(1,ℤ/8)—38no—
265C2×C3×SD16—31no—
266C2×C3×SD16—31no—
267C2×C3×D8—21no—
268C2×C3×D8—31no—
269C2×C3×D8—31no—
270C2×C3×D8—31no—
271C2×C3×D8—38no—
272C2×C3×D8—31no—
273C2×C3×D8C2×D311yescharacteristic, complemented
274C2×C3×D8C2×D311yescharacteristic, complemented
275C2×C3×M16—31no—
276C22×C3×C8—31no—
277#950—38no—
278C2×#216—31no—
279C2×#215—31no—
280C2×#214—31no—
281C2×#214—31no—
282C2×#214—31no—
283C2×#214—31no—
284C2×#214—61no—
285C2×#214C2×D311yescharacteristic, complemented
286#932—38no—
287#932—38no—
288C2×#213—31no—
289C2×#213—31no—
290C2×#213—31no—
291C2×#213—31no—
292C2×#213—38no—
293C2×#213—31no—
294C2×#213—31no—
295C2×#213—61no—
296C2×#213C2×D311yescharacteristic, complemented
297C2×#213C2×D311yescharacteristic, complemented
298C2×#213C2×D311yescharacteristic, complemented
299C2×#208—31no—
300C22×C3⋊C8—31no—
301#916—38no—
302#916—38no—
303#914—38no—
304#914—38no—
305#912—38no—
306#912—38no—
307#911—38no—
308#911—38no—
309#911—38no—
310#911—38no—
311#911—38no—
312#911—68no—
313#911C2×D318yescomplemented
314D3×D8—38no—
315D3×D8—38no—
316D3×D8—38no—
317D3×D8C2×D318yescomplemented
318#908—38no—
319#907—38no—
320C2×Dic12—31no—
321#904—38no—
322C2×D24—31no—
323C2×D24—31no—
324C2×D24C2×D311yescharacteristic, complemented
325C2×#204—31no—
326C2×#204—31no—
327C2×#204—31no—
328C2×#204—61no—
329C2×#204C2×D311yescharacteristic, complemented
330#901—38no—
331C2×ΓL(1,𝔽25)—31no—
332C2×ΓL(1,𝔽25)—31no—
333C2×ΓL(1,𝔽25)—31no—
334C2×ΓL(1,𝔽25)—61no—
335C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
336C2×D3×C8—31no—
337C2×D3×C8—31no—
338C2×D3×C8—31no—
339C2×D3×C8C2×D311yescharacteristic, complemented
340C23×C32—21no—
341C23×C32—21no—
342C22×C3⋊D3—21no—
343C22×C3⋊D3—24no—
344C22×C3⋊D3—82no—
345C22×C3⋊D3C2×D411yescharacteristic
346C22×C3×D3—21no—
347C22×C3×D3—21no—
348C22×C3×D3—21no—
349C22×C3×D3—24no—
350C22×C3×D3—24no—
351C22×C3×D3—24no—
352C22×C3×D3—82no—
353C22×C3×D3—82no—
354C22×C3×D3—82no—
355C22×C3×D3C2×D411yescharacteristic
356C22×C3×D3C2×D411yescharacteristic
357C2×D32—24no—
358C2×D32—24no—
359C2×D32—82no—
360C2×D32—82no—
361C32×D4—21no—
362C32×D4—21no—
363C32×D4C2412yes—
364C32×D4C2412yes—
365C2×C32×C4C2411yescharacteristic
366#638—24no—
367#638—24no—
368C2×C3⋊Dic3—21no—
369C2×C3⋊Dic3—24no—
370C2×C3⋊Dic3C2×D411yescharacteristic
371C4⋊(C3⋊D3)—21no—
372C4⋊(C3⋊D3)C2412yes—
373C4×C3⋊D3C2×D412yes—
374C4×C3⋊D3C2412yes—
375#634—21no—
376#634C2412yes—
377C3×#67—24no—
378C3×#67—24no—
379C3×#67—24no—
380C3×#67—24no—
381C2×C3×Dic3—21no—
382C2×C3×Dic3—24no—
383C2×C3×Dic3C2×D411yescharacteristic
384C2×C3×Dic3C2×D411yescharacteristic
385C3×D12—21no—
386C3×D12—21no—
387C3×D12—21no—
388C3×D12C2412yes—
389C3×D12C2412yes—
390C3×D12C2412yes—
391C3×C4×D3C2×D412yes—
392C3×C4×D3C2×D412yes—
393C3×C4×D3C2412yes—
394C3×C4×D3C2412yes—
395C3×Dic6—21no—
396C3×Dic6C2412yes—
397#627C2×D414yes—
398#626—24no—
399#626—24no—
400#626—24no—
401#626C2×D414yes—
402#626C2×D414yes—
403#625—24no—
404#625—24no—
405#625—24no—
406#625C2×D414yes—
407#624—24no—
408D3×Dic3—24no—
409D3×Dic3—24no—
410D3×Dic3—24no—
411C32×C8C2412yes—
412C3⋊(C3⋊C8)C2412yes—
413C3×C3⋊C8C2412yes—
414C3×C3⋊C8C2412yes—
415C2×H(5,𝔽2)—91no—
416C2×H(5,𝔽2)—91no—
417#576—916no—
418C2×AGL(1,ℤ/8)—31no—
419C2×AGL(1,ℤ/8)—91no—
420C2×AGL(1,ℤ/8)—91no—
421C2×AGL(1,ℤ/8)—91no—
422C2×AGL(1,ℤ/8)—91no—
423C2×AGL(1,ℤ/8)—91no—
424C2×#135—91no—
425C2×#135—91no—
426C2×#135—91no—
427C22×D8—31no—
428C22×D8—91no—
429C22×D8—91no—
430C2×#131—91no—
431C24×C3—61no—
432C24×C3—61no—
433C24×C3—61no—
434C23×D3—21no—
435C23×D3—21no—
436C23×D3—21no—
437C23×D3—61no—
438C23×D3—61no—
439C23×D3—61no—
440C23×D3—61no—
441C23×D3—61no—
442C23×D3—61no—
443C23×D3—121no—
444C3×#41—34no—
445C3×#41—62no—
446C2×C3×Q8—31no—
447C2×C3×D4—21no—
448C2×C3×D4—21no—
449C2×C3×D4—34no—
450C2×C3×D4—34no—
451C2×C3×D4—34no—
452C2×C3×D4—31no—
453C2×C3×D4—31no—
454C2×C3×D4—31no—
455C2×C3×D4—62no—
456C2×C3×D4—62no—
457C2×C3×D4—62no—
458C2×C3×D4—61no—
459C2×C3×D4—61no—
460C2×C3×D4—61no—
461C2×C3×D4—61no—
462C2×C3×D4C22×D311yescharacteristic
463C2×C3×D4C22×D311yescharacteristic
464C2×C3×D4C22×D311yescharacteristic
465C2×C3×D4C22×D311yescharacteristic
466C22×C3×C4—31no—
467C22×C3×C4—31no—
468C22×C3×C4—61no—
469C2×#67—21no—
470C2×#67—21no—
471C2×#67—21no—
472C2×#67—21no—
473C2×#67—31no—
474C2×#67—31no—
475C2×#67—31no—
476C2×#67—31no—
477C2×#67—68no—
478C2×#67—61no—
479C2×#67—61no—
480C2×#67—61no—
481C2×#67—61no—
482C2×#67—61no—
483C2×#67—61no—
484C2×#67—68no—
485C2×#67—68no—
486C2×#67—68no—
487C2×#67—68no—
488C2×#67—68no—
489C2×#67—61no—
490C2×#67—61no—
491C2×#67—61no—
492C2×#67—61no—
493C2×#67—61no—
494C2×#67—61no—
495C2×#67—61no—
496C2×#67—121no—
497C2×#67—121no—
498C22×Dic3—21no—
499C22×Dic3—61no—
500C22×Dic3—61no—
501C22×Dic3—61no—
502C22×Dic3—61no—
503C22×Dic3—61no—
504C22×Dic3—121no—
505#239—34no—
506#239—34no—
507#239—62no—
508#239—62no—
509#237—22no—
510#237—34no—
511#237—34no—
512#237—34no—
513#237—34no—
514#237—34no—
515#237—64no—
516#237—62no—
517#237—68no—
518#237—68no—
519#237—68no—
520#237—62no—
521#237—62no—
522#237—62no—
523#237—62no—
524#237—122no—
525#237C22×D314yescomplemented
526D3×D4—22no—
527D3×D4—22no—
528D3×D4—22no—
529D3×D4—34no—
530D3×D4—34no—
531D3×D4—34no—
532D3×D4—34no—
533D3×D4—34no—
534D3×D4—64no—
535D3×D4—62no—
536D3×D4—62no—
537D3×D4—62no—
538D3×D4—62no—
539D3×D4—68no—
540D3×D4—68no—
541D3×D4—68no—
542D3×D4—68no—
543D3×D4—68no—
544D3×D4—62no—
545D3×D4—122no—
546D3×D4C22×D314yescomplemented
547D3×D4C22×D314yescomplemented
548D3×D4C22×D314yescomplemented
549#235—34no—
550#235—34no—
551#235—34no—
552#235—34no—
553#235—34no—
554#235—34no—
555#235—34no—
556#235—62no—
557#235—68no—
558#235—62no—
559#235—62no—
560C2×D12—31no—
561C2×D12—31no—
562C2×D12—31no—
563C2×D12—31no—
564C2×D12—34no—
565C2×D12—61no—
566C2×D12—62no—
567C2×D12—68no—
568C2×D12—61no—
569C2×D12—61no—
570C2×D12—61no—
571C2×D12C22×D311yescharacteristic
572C2×D12C22×D311yescharacteristic
573C2×D12C22×D311yescharacteristic
574C2×C4×D3—31no—
575C2×C4×D3—31no—
576C2×C4×D3—61no—
577C2×C4×D3—61no—
578C2×C4×D3—61no—
579C2×C4×D3—61no—
580C2×C4×D3—61no—
581C2×C4×D3—61no—
582C2×C4×D3C22×D311yescharacteristic
583C2×C4×D3C22×D311yescharacteristic
584C2×Dic6—31no—
585C2×Dic6—31no—
586C2×Dic6—31no—
587C2×Dic6—31no—
588C2×Dic6—61no—
589C2×Dic6C22×D311yescharacteristic
590C3×SD16—34no—
591C3×SD16—34no—
592C3×D8—24no—
593C3×D8—34no—
594C3×D8—34no—
595C3×D8—34no—
596C3×D8—34no—
597C3×D8C22×D314yescomplemented
598C3×D8C22×D314yescomplemented
599C3×M16—34no—
600C2×C3×C8—21no—
601C2×C3×C8—31no—
602C2×C3×C8—31no—
603C2×C3×C8—34no—
604C2×C3×C8C22×D311yescharacteristic
605C2×C3×C8C22×D311yescharacteristic
606#216—34no—
607#215—34no—
608#214—34no—
609#214—34no—
610#214—34no—
611#214—34no—
612#214—64no—
613#214C22×D314yescomplemented
614#213—34no—
615#213—34no—
616#213—34no—
617#213—34no—
618#213—34no—
619#213—34no—
620#213—64no—
621#213C22×D314yescomplemented
622#213C22×D314yescomplemented
623#213C22×D314yescomplemented
624#208—34no—
625C2×C3⋊C8—31no—
626C2×C3⋊C8—31no—
627C2×C3⋊C8—34no—
628C2×C3⋊C8—61no—
629C2×C3⋊C8C22×D311yescharacteristic
630C2×C3⋊C8C22×D311yescharacteristic
631Dic12—34no—
632D24—34no—
633D24—34no—
634D24C22×D314yescomplemented
635#204—34no—
636#204—34no—
637#204—34no—
638#204—64no—
639#204C22×D314yescomplemented
640ΓL(1,𝔽25)—34no—
641ΓL(1,𝔽25)—34no—
642ΓL(1,𝔽25)—34no—
643ΓL(1,𝔽25)—64no—
644ΓL(1,𝔽25)C22×D314yescomplemented
645D3×C8—34no—
646D3×C8—34no—
647D3×C8—34no—
648D3×C8C22×D314yescomplemented
649C22×C32—22no—
650C22×C32—22no—
651C22×C32—42no—
652C22×C32—42no—
653C22×C32C22×D411yescharacteristic
654C2×C3⋊D3—22no—
655C2×C3⋊D3—22no—
656C2×C3⋊D3—42no—
657C2×C3⋊D3—84no—
658C2×C3⋊D3C22×D412yes—
659C2×C3×D3—22no—
660C2×C3×D3—22no—
661C2×C3×D3—22no—
662C2×C3×D3—22no—
663C2×C3×D3—22no—
664C2×C3×D3—42no—
665C2×C3×D3—42no—
666C2×C3×D3—42no—
667C2×C3×D3—84no—
668C2×C3×D3—84no—
669C2×C3×D3—84no—
670C2×C3×D3C22×D412yes—
671C2×C3×D3C22×D412yes—
672D32—84no—
673D32—84no—
674C32×C4C22×D411yescharacteristic
675C32×C4C2511yescharacteristic
676C3⋊Dic3—22no—
677C3⋊Dic3C22×D412yes—
678C3×Dic3—22no—
679C3×Dic3C22×D412yes—
680C3×Dic3C22×D412yes—
681H(5,𝔽2)—98no—
682H(5,𝔽2)—98no—
683H(5,𝔽2)—184no—
684H(5,𝔽2)—184no—
685C2×#41—31no—
686C2×#41—91no—
687C2×#41—91no—
688C2×#41—91no—
689C2×#41—91no—
690C2×#41—91no—
691C2×#41—91no—
692C2×#41—181no—
693C2×#41—181no—
694C22×D4—31no—
695C22×D4—31no—
696C22×D4—31no—
697C22×D4—91no—
698C22×D4—91no—
699C22×D4—91no—
700C22×D4—181no—
701C22×D4—181no—
702C22×D4—181no—
703C22×D4—181no—
704C22×D4—181no—
705C22×D4—181no—
706AGL(1,ℤ/8)—38no—
707AGL(1,ℤ/8)—98no—
708AGL(1,ℤ/8)—98no—
709AGL(1,ℤ/8)—98no—
710AGL(1,ℤ/8)—98no—
711AGL(1,ℤ/8)—98no—
712#135—98no—
713#135—98no—
714#135—98no—
715C2×Q16—91no—
716C2×SD16—31no—
717C2×SD16—31no—
718C2×SD16—91no—
719C2×SD16—91no—
720C2×SD16—91no—
721C2×SD16—91no—
722C2×D8—31no—
723C2×D8—31no—
724C2×D8—31no—
725C2×D8—38no—
726C2×D8—31no—
727C2×D8—91no—
728C2×D8—91no—
729C2×D8—98no—
730C2×D8—98no—
731C2×D8—91no—
732C2×D8—91no—
733C2×D8D3211yescharacteristic, complemented
734#131—98no—
735C2×M16—31no—
736C2×M16—91no—
737C2×M16—91no—
738C22×C8—31no—
739C22×C8—91no—
740C22×C8—91no—
741C23×C3—21no—
742C23×C3—21no—
743C23×C3—21no—
744C23×C3—21no—
745C23×C3—31no—
746C23×C3—31no—
747C23×C3—41no—
748C23×C3—41no—
749C23×C3—64no—
750C23×C3—64no—
751C23×C3—64no—
752C23×C3—61no—
753C23×C3—61no—
754C23×C3—61no—
755C23×C3—242no—
756C23×C3—242no—
757C23×C3—242no—
758C22×D3—21no—
759C22×D3—21no—
760C22×D3—21no—
761C22×D3—24no—
762C22×D3—24no—
763C22×D3—24no—
764C22×D3—31no—
765C22×D3—31no—
766C22×D3—61no—
767C22×D3—64no—
768C22×D3—64no—
769C22×D3—64no—
770C22×D3—64no—
771C22×D3—64no—
772C22×D3—61no—
773C22×D3—61no—
774C22×D3—64no—
775C22×D3—82no—
776C22×D3—82no—
777C22×D3—82no—
778C22×D3—124no—
779C22×D3—121no—
780C22×D3—242no—
781C22×D3—242no—
782C22×D3—242no—
783C22×D3—242no—
784C22×D3—242no—
785C22×D3—242no—
786C22×D3—244no—
787C22×D3D3×D411yescharacteristic
788C22×D3D3×D411yescharacteristic
789C3×Q8—32no—
790C3×Q8—61no—
791C3×D4—21no—
792C3×D4—21no—
793C3×D4—21no—
794C3×D4—21no—
795C3×D4—22no—
796C3×D4—22no—
797C3×D4—32no—
798C3×D4—32no—
799C3×D4—32no—
800C3×D4—41no—
801C3×D4—41no—
802C3×D4—64no—
803C3×D4—64no—
804C3×D4—64no—
805C3×D4—64no—
806C3×D4—61no—
807C3×D4—61no—
808C3×D4—61no—
809C3×D4C23×D312yes—
810C3×D4C23×D312yes—
811C3×D4C23×D312yes—
812C3×D4C23×D312yes—
813C2×C3×C4—21no—
814C2×C3×C4—31no—
815C2×C3×C4—31no—
816C2×C3×C4—32no—
817C2×C3×C4—32no—
818C2×C3×C4—32no—
819C2×C3×C4—32no—
820C2×C3×C4—64no—
821C2×C3×C4—61no—
822C2×C3×C4C23×D311yescharacteristic
823C2×C3×C4C23×D311yescharacteristic
824#67—24no—
825#67—24no—
826#67—24no—
827#67—24no—
828#67—34no—
829#67—34no—
830#67—34no—
831#67—34no—
832#67—64no—
833#67—64no—
834#67—64no—
835#67—64no—
836#67—64no—
837#67—64no—
838#67—64no—
839#67—64no—
840#67—64no—
841#67—64no—
842#67—64no—
843#67—64no—
844#67—64no—
845#67—124no—
846#67—124no—
847C2×Dic3—21no—
848C2×Dic3—24no—
849C2×Dic3—31no—
850C2×Dic3—31no—
851C2×Dic3—61no—
852C2×Dic3—64no—
853C2×Dic3—64no—
854C2×Dic3—64no—
855C2×Dic3—61no—
856C2×Dic3—61no—
857C2×Dic3—64no—
858C2×Dic3—64no—
859C2×Dic3—124no—
860C2×Dic3—121no—
861C2×Dic3D3×D411yescharacteristic
862C2×Dic3D3×D411yescharacteristic
863D12—21no—
864D12—21no—
865D12—21no—
866D12—34no—
867D12—34no—
868D12—32no—
869D12—32no—
870D12—62no—
871D12—64no—
872D12—64no—
873D12—64no—
874D12—61no—
875D12—61no—
876D12—121no—
877D12C23×D312yes—
878D12C23×D312yes—
879D12C23×D312yes—
880C4×D3—32no—
881C4×D3—32no—
882C4×D3—32no—
883C4×D3—32no—
884C4×D3—62no—
885C4×D3—62no—
886C4×D3—64no—
887C4×D3—64no—
888C4×D3—64no—
889C4×D3—64no—
890C4×D3—64no—
891C4×D3D3×D412yes—
892C4×D3D3×D412yes—
893C4×D3C23×D312yes—
894C4×D3C23×D312yes—
895Dic6—21no—
896Dic6—34no—
897Dic6—34no—
898Dic6—32no—
899Dic6—32no—
900Dic6—62no—
901Dic6—61no—
902Dic6—61no—
903Dic6—121no—
904Dic6C23×D312yes—
905C3×C8—22no—
906C3×C8—32no—
907C3×C8—32no—
908C3×C8C23×D312yes—
909C3×C8C23×D312yes—
910C3⋊C8—32no—
911C3⋊C8—32no—
912C3⋊C8—62no—
913C3⋊C8C23×D312yes—
914C3⋊C8C23×D312yes—
915C2×C32—42no—
916C2×C32—42no—
917C2×C32#57612yescomplemented
918C2×C32C23×D411yescharacteristic
919C3⋊D3—22no—
920C3⋊D3—42no—
921C3×D3—22no—
922C3×D3—22no—
923C3×D3—42no—
924C3×D3—42no—
925C3×D3—42no—
926C24—61no—
927C24—61no—
928C24—61no—
929C24—181no—
930C24—181no—
931C24—181no—
932#41—34no—
933#41—62no—
934#41—94no—
935#41—94no—
936#41—94no—
937#41—94no—
938#41—94no—
939#41—94no—
940#41—94no—
941#41—182no—
942#41—182no—
943#41—182no—
944#41—188no—
945#41—182no—
946#41—182no—
947#41—188no—
948C2×Q8—31no—
949C2×Q8—91no—
950C2×Q8—91no—
951C2×D4—34no—
952C2×D4—34no—
953C2×D4—34no—
954C2×D4—31no—
955C2×D4—31no—
956C2×D4—31no—
957C2×D4—62no—
958C2×D4—62no—
959C2×D4—62no—
960C2×D4—61no—
961C2×D4—61no—
962C2×D4—61no—
963C2×D4—61no—
964C2×D4—94no—
965C2×D4—91no—
966C2×D4—91no—
967C2×D4—94no—
968C2×D4—91no—
969C2×D4—94no—
970C2×D4—91no—
971C2×D4—182no—
972C2×D4—181no—
973C2×D4—188no—
974C2×D4—181no—
975C2×D4—181no—
976C2×D4—182no—
977C2×D4—182no—
978C2×D4—181no—
979C2×D4—181no—
980C2×D4—188no—
981C2×D4—188no—
982C2×D4—188no—
983C2×D4—188no—
984C2×D4—188no—
985C2×D4—181no—
986C2×D4—181no—
987C2×D4—181no—
988C2×D4C2×D3211yescharacteristic
989C2×D4C2×D3211yescharacteristic
990C22×C4—31no—
991C22×C4—31no—
992C22×C4—61no—
993C22×C4—91no—
994C22×C4—181no—
995C22×C4—181no—
996C22×C4—181no—
997C22×C4—181no—
998C22×C4—181no—
999Q16—94no—
1000SD16—34no—
1001SD16—34no—
1002SD16—94no—
1003SD16—94no—
1004SD16—94no—
1005SD16—94no—
1006D8—34no—
1007D8—34no—
1008D8—34no—
1009D8—34no—
1010D8—94no—
1011D8—94no—
1012D8—94no—
1013D8—94no—
1014D8C2×D3214yescomplemented
1015M16—34no—
1016M16—94no—
1017M16—94no—
1018C2×C8—31no—
1019C2×C8—31no—
1020C2×C8—34no—
1021C2×C8—94no—
1022C2×C8—94no—
1023C2×C8—91no—
1024C2×C8C2×D3211yescharacteristic
1025C22×C3—22no—
1026C22×C3—22no—
1027C22×C3—22no—
1028C22×C3—22no—
1029C22×C3—21no—
1030C22×C3—32no—
1031C22×C3—32no—
1032C22×C3—42no—
1033C22×C3—42no—
1034C22×C3—42no—
1035C22×C3—42no—
1036C22×C3—42no—
1037C22×C3—42no—
1038C22×C3—62no—
1039C22×C3—62no—
1040C22×C3—62no—
1041C22×C3—62no—
1042C22×C3—62no—
1043C22×C3—82no—
1044C22×C3—82no—
1045C22×C3—122no—
1046C22×C3—122no—
1047C22×C3—122no—
1048C22×C3—244no—
1049C22×C3—244no—
1050C22×C3—244no—
1051C22×C3C2×D3×D411yescharacteristic
1052C22×C3C2×D3×D411yescharacteristic
1053C2×D3—22no—
1054C2×D3—22no—
1055C2×D3—22no—
1056C2×D3—22no—
1057C2×D3—22no—
1058C2×D3—32no—
1059C2×D3—32no—
1060C2×D3—42no—
1061C2×D3—42no—
1062C2×D3—42no—
1063C2×D3—62no—
1064C2×D3—62no—
1065C2×D3—62no—
1066C2×D3—62no—
1067C2×D3—62no—
1068C2×D3—84no—
1069C2×D3—84no—
1070C2×D3—84no—
1071C2×D3—122no—
1072C2×D3—122no—
1073C2×D3—122no—
1074C2×D3—122no—
1075C2×D3—242no—
1076C2×D3—244no—
1077C2×D3—244no—
1078C2×D3—244no—
1079C2×D3—244no—
1080C2×D3—244no—
1081C2×D3—244no—
1082C2×D3—248no—
1083C2×D3C2×D3×D412yes—
1084C2×D3C2×D3×D412yes—
1085C3×C4—21no—
1086C3×C4—21no—
1087C3×C4—32no—
1088C3×C4—32no—
1089C3×C4—62no—
1090C3×C4C2×D3×D411yescharacteristic
1091C3×C4C2×D3×D411yescharacteristic
1092C3×C4C24×D311yescharacteristic
1093C3×C4C24×D311yescharacteristic
1094Dic3—22no—
1095Dic3—32no—
1096Dic3—32no—
1097Dic3—62no—
1098Dic3—62no—
1099Dic3—62no—
1100Dic3—122no—
1101Dic3C2×D3×D412yes—
1102Dic3C2×D3×D412yes—
1103C32C2×#57611yescharacteristic, complemented, Sylow
1104C23—21no—
1105C23—21no—
1106C23—31no—
1107C23—31no—
1108C23—64no—
1109C23—64no—
1110C23—64no—
1111C23—61no—
1112C23—61no—
1113C23—61no—
1114C23—91no—
1115C23—184no—
1116C23—184no—
1117C23—184no—
1118C23—181no—
1119C23—242no—
1120C23—242no—
1121C23—242no—
1122C23—722no—
1123C23—722no—
1124C23—722no—
1125Q8—32no—
1126Q8—61no—
1127Q8—94no—
1128Q8—92no—
1129Q8—181no—
1130D4—21no—
1131D4—21no—
1132D4—32no—
1133D4—32no—
1134D4—32no—
1135D4—64no—
1136D4—64no—
1137D4—64no—
1138D4—64no—
1139D4—61no—
1140D4—61no—
1141D4—61no—
1142D4—94no—
1143D4—94no—
1144D4—94no—
1145D4—92no—
1146D4—184no—
1147D4—184no—
1148D4—184no—
1149D4—184no—
1150D4—184no—
1151D4—184no—
1152D4—184no—
1153D4—184no—
1154D4—181no—
1155D4C22×D3212yes—
1156D4C22×D3212yes—
1157C2×C4—31no—
1158C2×C4—31no—
1159C2×C4—32no—
1160C2×C4—32no—
1161C2×C4—32no—
1162C2×C4—32no—
1163C2×C4—64no—
1164C2×C4—61no—
1165C2×C4—91no—
1166C2×C4—92no—
1167C2×C4—92no—
1168C2×C4—184no—
1169C2×C4—184no—
1170C2×C4—184no—
1171C2×C4—184no—
1172C2×C4—184no—
1173C2×C4—181no—
1174C2×C4C22×D3211yescharacteristic
1175C8—32no—
1176C8—32no—
1177C8—92no—
1178C8C22×D3212yes—
1179C2×C3—21no—
1180C2×C3—22no—
1181C2×C3—42no—
1182C2×C3—42no—
1183C2×C3—42no—
1184C2×C3—42no—
1185C2×C3—62no—
1186C2×C3—62no—
1187C2×C3—82no—
1188C2×C3—82no—
1189C2×C3—122no—
1190C2×C3—122no—
1191C2×C3—122no—
1192C2×C3#575712yescomplemented
1193C2×C3#577412yescomplemented
1194C2×C3C22×D3×D411yescharacteristic
1195C2×C3C22×D3×D411yescharacteristic
1196D3—22no—
1197D3—22no—
1198D3—42no—
1199D3—42no—
1200D3—42no—
1201D3—62no—
1202D3—62no—
1203D3—122no—
1204D3—122no—
1205D3—122no—
1206D3—242no—
1207C22—22no—
1208C22—22no—
1209C22—32no—
1210C22—32no—
1211C22—42no—
1212C22—42no—
1213C22—62no—
1214C22—62no—
1215C22—62no—
1216C22—62no—
1217C22—62no—
1218C22—92no—
1219C22—122no—
1220C22—122no—
1221C22—122no—
1222C22—182no—
1223C22—182no—
1224C22—244no—
1225C22—244no—
1226C22—244no—
1227C22—362no—
1228C22—724no—
1229C22—724no—
1230C22—724no—
1231C22D32×D411yescharacteristic
1232C4—32no—
1233C4—32no—
1234C4—62no—
1235C4—92no—
1236C4—182no—
1237C4D32×D411yescharacteristic
1238C4C23×D3211yescharacteristic
1239C3—21no—
1240C3C2×#575711yescharacteristic, complemented
1241C3C2×#577411yescharacteristic, complemented
1242C2—42no—
1243C2—42no—
1244C2—62no—
1245C2—62no—
1246C2—122no—
1247C2—122no—
1248C2—122no—
1249C2—182no—
1250C2—362no—
1251C2#1059473212yesdirect product factor
1252C2C2×D32×D411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
hypercenterC2×D8D32
hypocenterC32C2×#576
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×#64314C2semidirect
2. C2×#64313C2semidirect
3. C2×#64120C2semidirect
4. C2×C3×#911C2semidirect
5. C2×C3×D3×D8C2semidirect
6. C2×#63936C2semidirect
7. C2×#63934C2semidirect
8. C2×#63933C2semidirect
9. C2×#63932C2semidirect
10. C2×#63926C2semidirect
11. C2×D3×#213C2semidirect
12. #10594732C2direct (N × H)
13. C2×#63806C2semidirect
14. C2×#63804C2semidirect
15. C2×#63798C2semidirect
16. C2×#63795C2semidirect
19. C2×#3830C22semidirect
20. C2×D4×C3⋊D3C22semidirect
21. C2×C3×#237C22semidirect
22. C2×C3×D3×D4C22semidirect
23. C2×C3×D3×D4C22semidirect
24. C2×C3×D3×D4C22semidirect
34. #64314C22semidirect
36. #64313C22semidirect
37. C2×#3802C22semidirect
38. C2×D3×D12C22semidirect
39. C2×#3799C22semidirect
41. C2×#3796C22semidirect
42. C2×#3795C22semidirect
43. C2×#3795C22semidirect
44. C2×C32×D8C22semidirect
45. C2×#3754C22semidirect
46. C2×#3753C22semidirect
47. #64120C22semidirect
48. C2×#3744C22semidirect
49. C2×#3743C22semidirect
50. C2×C3×#214C22semidirect
51. C2×C3×#213C22semidirect
52. C2×C3×#213C22semidirect
53. C2×C3×#213C22semidirect
54. C3×#911C22semidirect
55. C3×D3×D8C22semidirect
56. C2×C3×D24C22semidirect
57. C2×C3×#204C22semidirect
58. C2×C3×ΓL(1,𝔽25)C22semidirect
59. C2×C3×D3×C8C22semidirect
60. #63936C22semidirect
61. #63934C22semidirect
62. #63933C22semidirect
63. #63932C22semidirect
64. #63926C22semidirect
65. D3×#213C22semidirect
66. C2×#3719C22semidirect
67. C2×#3716C22semidirect
68. C2×#3715C22semidirect
69. C2×#3714C22semidirect
70. C2×#3714C22semidirect
71. C2×#3713C22semidirect
72. C2×#3711C22semidirect
73. C2×#3710C22semidirect
74. C2×D3×C3⋊C8C22semidirect
75. #63806C22semidirect
76. #63804C22semidirect
77. #63798C22semidirect
78. #63795C22semidirect
103. C2×#911D3semidirect
107. C2×D3×D8D3semidirect
124. #3830C23semidirect
126. D4×C3⋊D3C23semidirect
136. C3×#237C23semidirect
140. C3×D3×D4C23semidirect
141. C3×D3×D4C23semidirect
142. C3×D3×D4C23semidirect
172. #3802C23semidirect
174. D3×D12C23semidirect
176. #3799C23semidirect
180. #3796C23semidirect
183. #3795C23semidirect
184. #3795C23semidirect
185. C32×D8C23semidirect
187. #3754C23semidirect
188. #3753C23semidirect
190. #3744C23semidirect
191. #3743C23semidirect
192. C3×#214C23semidirect
193. C3×#213C23semidirect
194. C3×#213C23semidirect
195. C3×#213C23semidirect
198. C3×D24C23semidirect
199. C3×#204C23semidirect
200. C3×ΓL(1,𝔽25)C23semidirect
201. C3×D3×C8C23semidirect
202. #3719C23semidirect
203. #3716C23semidirect
204. #3715C23semidirect
205. #3714C23semidirect
206. #3714C23semidirect
207. #3713C23semidirect
208. #3711C23semidirect
209. #3710C23semidirect
210. D3×C3⋊C8C23semidirect
241. C2×#237C2×D3semidirect
253. C2×D3×D4C2×D3semidirect
254. C2×D3×D4C2×D3semidirect
255. C2×D3×D4C2×D3semidirect
273. C2×C3×D8C2×D3semidirect
274. C2×C3×D8C2×D3semidirect
285. C2×#214C2×D3semidirect
296. C2×#213C2×D3semidirect
297. C2×#213C2×D3semidirect
298. C2×#213C2×D3semidirect
313. #911C2×D3semidirect
317. D3×D8C2×D3semidirect
324. C2×D24C2×D3semidirect
329. C2×#204C2×D3semidirect
335. C2×ΓL(1,𝔽25)C2×D3semidirect
339. C2×D3×C8C2×D3semidirect
525. #237C22×D3semidirect
546. D3×D4C22×D3semidirect
547. D3×D4C22×D3semidirect
548. D3×D4C22×D3semidirect
597. C3×D8C22×D3semidirect
598. C3×D8C22×D3semidirect
613. #214C22×D3semidirect
621. #213C22×D3semidirect
622. #213C22×D3semidirect
623. #213C22×D3semidirect
634. D24C22×D3semidirect
639. #204C22×D3semidirect
644. ΓL(1,𝔽25)C22×D3semidirect
648. D3×C8C22×D3semidirect
733. C2×D8D32semidirect
917. C2×C32#576semidirect
1014. D8C2×D32semidirect
1103. C32C2×#576semidirect
1192. C2×C3#5757semidirect
1193. C2×C3#5774semidirect
1240. C3C2×#5757semidirect
1241. C3C2×#5774semidirect
1251. C2#10594732direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#643142
C2×#643132
C2×#641202
C2×C3×#9112
C2×C3×D3×D82
C2×#639362
C2×#639342
C2×#639332
C2×#639322
C2×#639262
C2×D3×#2132
#105947322
C2×#638062
C2×#638042
C2×#637982
C2×#637952
C2×#57743
C2×#57573