Finite Group Databasebeta

← C2×#10594679 #11918881

Subgroups — C2×#10594679 #11918881

Order 1152.

3069 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64308C211yesmaximal, characteristic, complemented
2C2×#64298C211yesmaximal, characteristic, complemented
3C22×#3744C211yesmaximal, characteristic, complemented
4C2×C3×#904C211yesmaximal, characteristic, complemented
5C2×C3×#901C211yesmaximal, characteristic, complemented
6C2×#63831C211yesmaximal, characteristic, complemented
7C2×#63825C211yesmaximal, characteristic, complemented
8C2×#63806C212yesmaximal, complemented
9C2×#63801C212yesmaximal, complemented
10#10594679C2116yesmaximal, direct product factor
11C2×#63795C212yesmaximal, complemented
12C2×D3×#204C212yesmaximal, complemented
13C2×#5770—31nomaximal
14C2×#5751—31nomaximal
15C22×C4⋊(C3⋊D3)C2211yescharacteristic
16C22×#634C2211yescharacteristic, complemented
17C2×C3×#235C2211yescharacteristic
18C2×C3×#235C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic, complemented
20C2×#3811—22no—
21C2×#3805—22no—
22#64308—24no—
23#64308C2218yescomplemented
24C2×D3×D12—21no—
25C2×D3×D12C2212yes—
26C2×#3799—21no—
27C2×#3799C2212yes—
28#64298—24no—
29#64298C2218yescomplemented
30C2×#3795—21no—
31C2×#3795C2212yescomplemented
32C2×D3×Dic6—21no—
33C2×D3×Dic6C2212yescomplemented
34C22×C32×C8C2211yescharacteristic, complemented
35C2×#3744C2212yescomplemented
36C2×#3744C2212yescomplemented
37C2×#3744C2218yescomplemented
38C2×C3×#208C2211yescharacteristic, complemented
39C2×C3×Dic12C2211yescharacteristic, complemented
40C3×#904C2218yescomplemented
41C2×C3×D24C2211yescharacteristic, complemented
42C2×C3×#204C2211yescharacteristic, complemented
43C2×C3×#204C2211yescharacteristic, complemented
44C3×#901C2218yescomplemented
45C2×C3×ΓL(1,𝔽25)C2212yescomplemented
46C2×C3×D3×C8C2212yescomplemented
47C2×#3719C2212yescomplemented
48C2×#3717C2212yescomplemented
49#63831C2218yescomplemented
50C2×#3716C2212yescomplemented
51#63825C2218yescomplemented
52C2×#3714C2212yescomplemented
53#63806C22116yescomplemented
54#63801C22116yescomplemented
55#63795C22116yescomplemented
56D3×#204C22116yescomplemented
57C2×#1010—31no—
58C2×#1010—31no—
59C2×#1009—31no—
60C2×#1009—31no—
61C2×C3×#135—31no—
62C2×C3×#131—31no—
63C2×#951—31no—
64C2×#949—31no—
65#5770—316no—
66C2×#918—32no—
67C2×#916—32no—
68C2×D3×SD16—32no—
69C2×#911—32no—
70#5751—316no—
71C2×#909—31no—
72C2×#909—32no—
73C2×#908—31no—
74C2×#908—32no—
75C2×#904—32no—
76C2×#904D311yescharacteristic, complemented
77C22×#204—31no—
78C22×#204—31no—
79C22×#204—32no—
80C22×#204—61no—
81C2×#901D311yescharacteristic, complemented
82C23×C3⋊D3—21no—
83C22×D32—22no—
84C22×C32×C4C2311yescharacteristic
85C22×C3⋊Dic3—21no—
86C2×C4⋊(C3⋊D3)—21no—
87C2×C4⋊(C3⋊D3)—22no—
88C2×C4⋊(C3⋊D3)C2312yes—
89C2×C4⋊(C3⋊D3)C2314yes—
90C2×#634—21no—
91C2×#634—22no—
92C2×#634C2312yes—
93C2×#634C2314yescomplemented
94C2×C3×#67—21no—
95C2×C3×#67—21no—
96C2×C3×#67D412yes—
97C3×#235—22no—
98C3×#235—22no—
99C3×#235D414yes—
100C3×#235C2314yes—
101C3×#235C2314yes—
102C3×#235C2314yescomplemented
103C2×C3×D12D411yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3C2312yes—
109C2×C3×Dic6D411yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111C2×C3×Dic6C2311yescharacteristic
112#3811—216no—
113C2×#627—22no—
114C2×#626—22no—
115C2×#626—22no—
116C2×#625—22no—
117C2×#624—22no—
118#3805—216no—
119C2×D3×Dic3—22no—
120C2×D3×Dic3—22no—
121D3×D12—28no—
122D3×D12—24no—
123D3×D12C2318yes—
124#3799—24no—
125#3799—28no—
126#3799C2318yes—
127#3795—28no—
128#3795—24no—
129#3795C2318yescomplemented
130D3×Dic6—24no—
131D3×Dic6—28no—
132D3×Dic6C2318yescomplemented
133C2×C32×C8C2311yescharacteristic
134C2×C32×C8C2311yescharacteristic
135C2×C32×C8C2314yescomplemented
136#3744C2318yescomplemented
137#3744C2318yescomplemented
138C3×#208C2314yescomplemented
139C2×C3×C3⋊C8C2312yes—
140C3×Dic12C2314yescomplemented
141C3×D24C2314yescomplemented
142C3×#204C2314yescomplemented
143C3×#204C2314yescomplemented
144C3×ΓL(1,𝔽25)C2318yescomplemented
145C3×D3×C8C2318yescomplemented
146#3719C2318yescomplemented
147#3717C2318yescomplemented
148#3716C2318yescomplemented
149#3714C2318yescomplemented
150C2×#577—91noSylow
151C2×C3×#41—31no—
152C2×C3×#41—31no—
153C2×C3×#41—31no—
154#1010—38no—
155#1010—38no—
156#1010—64no—
157#1010—64no—
158#1009—38no—
159#1009—38no—
160#1009—64no—
161#1009—64no—
162C2×#239—32no—
163C2×#239—61no—
164C2×D3×Q8—32no—
165C2×D3×Q8—61no—
166C2×#237—32no—
167C2×#237—61no—
168C2×#237—62no—
169C2×#237—62no—
170C2×D3×D4—32no—
171C2×D3×D4—61no—
172C2×D3×D4—62no—
173C2×D3×D4—62no—
174C2×#235—32no—
175C2×#235—32no—
176C2×#235—61no—
177C2×#235—61no—
178C2×#235C2×D311yescharacteristic
179C2×#235C2×D311yescharacteristic
180C2×#235C2×D311yescharacteristic, complemented
181C22×D12—31no—
182C22×D12—31no—
183C22×D12—32no—
184C22×D12—61no—
185C22×D12—61no—
186C22×Dic6—31no—
187C22×Dic6—31no—
188C22×Dic6—32no—
189C22×Dic6—61no—
190C22×Dic6—61no—
191C3×#135—38no—
192C2×C3×Q16—31no—
193C2×C3×SD16—31no—
194C2×C3×SD16—31no—
195C2×C3×D8—31no—
196C3×#131—38no—
197C2×C3×M16—31no—
198C2×C3×M16—32no—
199C22×C3×C8—21no—
200C22×C3×C8—32no—
201C22×C3×C8C2×D311yescharacteristic, complemented
202C22×C3×C8C2×D311yescharacteristic, complemented
203#951—38no—
204#949—38no—
205C2×#216—32no—
206C2×#215—32no—
207C2×#214—32no—
208C2×#213—32no—
209C2×#208C2×D311yescharacteristic, complemented
210#918—316no—
211#916—316no—
212D3×SD16—316no—
213#911—316no—
214#909—38no—
215#909—316no—
216#908—38no—
217#908—316no—
218C2×Dic12—32no—
219C2×Dic12C2×D311yescharacteristic, complemented
220#904—316no—
221#904C2×D318yescomplemented
222C2×D24—32no—
223C2×D24C2×D311yescharacteristic, complemented
224C2×#204—32no—
225C2×#204—32no—
226C2×#204—32no—
227C2×#204—32no—
228C2×#204—32no—
229C2×#204—32no—
230C2×#204—38no—
231C2×#204—38no—
232C2×#204—316no—
233C2×#204—62no—
234C2×#204—62no—
235C2×#204—68no—
236C2×#204C2×D311yescharacteristic, complemented
237C2×#204C2×D311yescharacteristic, complemented
238#901C2×D318yescomplemented
239C2×ΓL(1,𝔽25)C2×D312yescomplemented
240C2×D3×C8C2×D312yescomplemented
241C23×C32C2×D411yescharacteristic
242C22×C3⋊D3—22no—
243C22×C3⋊D3—24no—
244C22×C3⋊D3—82no—
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3C2×D412yes—
248C2×D32—28no—
249C2×D32—84no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2×D412yes—
252C2×C32×C4C2411yescharacteristic
253C2×C32×C4C2412yes—
254C2×C3⋊Dic3—22no—
255C2×C3⋊Dic3—24no—
256C4⋊(C3⋊D3)—24no—
257C4⋊(C3⋊D3)—22no—
258C4⋊(C3⋊D3)C2414yes—
259#634—22no—
260#634—24no—
261#634C2414yes—
262C3×#67—24no—
263C3×#67—24no—
264C3×#67C2×D418yes—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3C2×D412yes—
268C3×D12—21no—
269C3×D12—21no—
270C3×D12C2×D414yes—
271C3×D12C2412yes—
272C3×D12C2412yes—
273C3×C4×D3—24no—
274C3×C4×D3—24no—
275C3×C4×D3C2×D414yes—
276C3×C4×D3C2414yes—
277C3×Dic6—21no—
278C3×Dic6—21no—
279C3×Dic6C2×D414yes—
280C3×Dic6C2412yes—
281C3×Dic6C2412yes—
282#627—28no—
283#626—28no—
284#626—28no—
285#625—28no—
286#624—28no—
287D3×Dic3—28no—
288D3×Dic3—28no—
289C32×C8C2412yes—
290C32×C8C2412yes—
291C3×C3⋊C8C2414yes—
292C2×2−1+4—91no—
293C2×H(5,𝔽2)—91no—
294#577—916no—
295C2×#137—92no—
296C2×#137—91no—
297C2×AGL(1,ℤ/8)—92no—
298C2×AGL(1,ℤ/8)—91no—
299C2×#135—31no—
300C2×#135—92no—
301C22×SD16—92no—
302C22×SD16—91no—
303C2×#131—31no—
304C23×D3—62no—
305C23×D3—61no—
306C23×D3—61no—
307C23×D3—62no—
308C23×D3—121no—
309C3×#41—34no—
310C3×#41—34no—
311C3×#41—34no—
312C3×#41—34no—
313C3×#41—62no—
314C3×#41—62no—
315C2×C3×Q8—31no—
316C2×C3×Q8—31no—
317C2×C3×Q8—31no—
318C2×C3×D4—32no—
319C2×C3×D4—31no—
320C2×C3×D4—31no—
321C2×C3×D4—31no—
322C2×C3×D4—61no—
323C2×C3×D4—61no—
324C22×C3×C4—21no—
325C22×C3×C4—32no—
326C22×C3×C4—61no—
327C22×C3×C4—61no—
328C22×C3×C4C22×D311yescharacteristic
329C22×C3×C4C22×D311yescharacteristic
330C2×#67—21no—
331C2×#67—21no—
332C2×#67—62no—
333C2×#67—62no—
334C2×#67—62no—
335C2×#67—62no—
336C2×#67D1212yes—
337C22×Dic3—62no—
338C22×Dic3—61no—
339C22×Dic3—61no—
340C22×Dic3—62no—
341C22×Dic3—121no—
342#239—38no—
343#239—68no—
344#239—64no—
345D3×Q8—38no—
346D3×Q8—68no—
347D3×Q8—64no—
348#237—38no—
349#237—68no—
350#237—616no—
351#237—616no—
352#237—64no—
353D3×D4—38no—
354D3×D4—68no—
355D3×D4—616no—
356D3×D4—616no—
357D3×D4—64no—
358#235—22no—
359#235—22no—
360#235—38no—
361#235—38no—
362#235—64no—
363#235—64no—
364#235—68no—
365#235—68no—
366#235D1214yes—
367#235C22×D314yes—
368#235C22×D314yes—
369#235C22×D314yescomplemented
370C2×D12—32no—
371C2×D12—34no—
372C2×D12—32no—
373C2×D12—34no—
374C2×D12—38no—
375C2×D12—62no—
376C2×D12—64no—
377C2×D12—64no—
378C2×D12—62no—
379C2×D12—62no—
380C2×D12—61no—
381C2×D12—62no—
382C2×D12—61no—
383C2×D12—62no—
384C2×D12—68no—
385C2×D12—121no—
386C2×D12—122no—
387C2×D12D1211yescharacteristic
388C2×D12C22×D311yescharacteristic
389C2×D12C22×D311yescharacteristic
390C2×C4×D3—21no—
391C2×C4×D3—21no—
392C2×C4×D3—62no—
393C2×C4×D3—62no—
394C2×C4×D3—62no—
395C2×C4×D3—62no—
396C2×C4×D3C22×D312yes—
397C2×Dic6—32no—
398C2×Dic6—34no—
399C2×Dic6—32no—
400C2×Dic6—34no—
401C2×Dic6—38no—
402C2×Dic6—62no—
403C2×Dic6—64no—
404C2×Dic6—64no—
405C2×Dic6—62no—
406C2×Dic6—61no—
407C2×Dic6—62no—
408C2×Dic6—61no—
409C2×Dic6—62no—
410C2×Dic6—62no—
411C2×Dic6—68no—
412C2×Dic6—121no—
413C2×Dic6—122no—
414C2×Dic6D1211yescharacteristic
415C2×Dic6C22×D311yescharacteristic
416C2×Dic6C22×D311yescharacteristic
417C3×Q16—34no—
418C3×SD16—34no—
419C3×SD16—34no—
420C3×D8—34no—
421C3×M16—34no—
422C3×M16—38no—
423C2×C3×C8—21no—
424C2×C3×C8—21no—
425C2×C3×C8—24no—
426C2×C3×C8—32no—
427C2×C3×C8—38no—
428C2×C3×C8C22×D311yescharacteristic
429C2×C3×C8C22×D311yescharacteristic
430C2×C3×C8C22×D311yescharacteristic
431C2×C3×C8C22×D311yescharacteristic
432C2×C3×C8C22×D314yescomplemented
433C2×C3×C8C22×D314yescomplemented
434#216—38no—
435#215—38no—
436#214—38no—
437#213—38no—
438#208C22×D314yescomplemented
439C2×C3⋊C8C22×D312yes—
440Dic12—38no—
441Dic12C22×D314yescomplemented
442D24—38no—
443D24C22×D314yescomplemented
444#204—38no—
445#204—38no—
446#204—38no—
447#204—38no—
448#204—38no—
449#204—38no—
450#204—68no—
451#204—68no—
452#204C22×D314yescomplemented
453#204C22×D314yescomplemented
454ΓL(1,𝔽25)C22×D318yescomplemented
455D3×C8C22×D318yescomplemented
456C22×C32—22no—
457C22×C32C22×D412yes—
458C22×C32C22×D411yescharacteristic
459C2×C3⋊D3—24no—
460C2×C3⋊D3—44no—
461C2×C3⋊D3—84no—
462C2×C3×D3—24no—
463C2×C3×D3—22no—
464C2×C3×D3—22no—
465C2×C3×D3—42no—
466C2×C3×D3—42no—
467C2×C3×D3C22×D414yes—
468D32—88no—
469C32×C4C22×D411yescharacteristic
470C32×C4C22×D412yes—
471C32×C4C2511yescharacteristic
472C3⋊Dic3—24no—
473C3×Dic3—22no—
474C3×Dic3—22no—
475C3×Dic3C22×D414yes—
4762−1+4—98no—
4772−1+4—184no—
478H(5,𝔽2)—98no—
479H(5,𝔽2)—184no—
480C2×#41—31no—
481C2×#41—31no—
482C2×#41—31no—
483C2×#41—92no—
484C2×#41—92no—
485C2×#41—181no—
486C2×#41—181no—
487C2×#41—182no—
488C22×Q8—92no—
489C22×Q8—91no—
490C22×Q8—181no—
491C22×D4—92no—
492C22×D4—91no—
493C22×D4—181no—
494C22×D4—182no—
495#137—916no—
496#137—98no—
497AGL(1,ℤ/8)—916no—
498AGL(1,ℤ/8)—98no—
499#135—38no—
500#135—916no—
501C2×Q16—31no—
502C2×Q16—92no—
503C2×SD16—31no—
504C2×SD16—31no—
505C2×SD16—916no—
506C2×SD16—92no—
507C2×SD16—92no—
508C2×SD16—92no—
509C2×SD16—92no—
510C2×SD16—98no—
511C2×D8—31no—
512C2×D8—92no—
513#131—38no—
514C2×M16—31no—
515C2×M16—32no—
516C22×C8—32no—
517C22×C8D3211yescharacteristic, complemented
518C23×C3—21no—
519C23×C3—32no—
520C23×C3—61no—
521C23×C3—61no—
522C23×C3C2×D1211yescharacteristic
523C23×C3D3×D411yescharacteristic
524C22×D3—21no—
525C22×D3—21no—
526C22×D3—68no—
527C22×D3—62no—
528C22×D3—62no—
529C22×D3—64no—
530C22×D3—64no—
531C22×D3—68no—
532C22×D3—122no—
533C22×D3—124no—
534C22×D3—244no—
535C22×D3—244no—
536C22×D3—242no—
537C22×D3—242no—
538C22×D3—244no—
539C22×D3C2×D1212yes—
540C3×Q8—34no—
541C3×Q8—32no—
542C3×Q8—32no—
543C3×Q8—61no—
544C3×Q8—61no—
545C3×D4—38no—
546C3×D4—34no—
547C3×D4—32no—
548C3×D4—32no—
549C3×D4—64no—
550C3×D4—64no—
551C3×D4—61no—
552C3×D4—61no—
553C2×C3×C4—22no—
554C2×C3×C4—21no—
555C2×C3×C4—22no—
556C2×C3×C4—21no—
557C2×C3×C4—32no—
558C2×C3×C4—34no—
559C2×C3×C4—34no—
560C2×C3×C4—61no—
561C2×C3×C4—61no—
562C2×C3×C4—64no—
563C2×C3×C4—64no—
564C2×C3×C4C2×D1211yescharacteristic
565C2×C3×C4C2×D1212yes—
566C2×C3×C4D3×D411yescharacteristic
567C2×C3×C4D3×D412yes—
568C2×C3×C4C23×D311yescharacteristic
569C2×C3×C4C23×D312yes—
570C2×C3×C4C23×D311yescharacteristic
571C2×C3×C4C23×D312yes—
572#67—24no—
573#67—24no—
574#67—68no—
575#67—68no—
576#67—68no—
577#67—68no—
578#67C2×D1218yes—
579C2×Dic3—21no—
580C2×Dic3—21no—
581C2×Dic3—68no—
582C2×Dic3—62no—
583C2×Dic3—64no—
584C2×Dic3—62no—
585C2×Dic3—64no—
586C2×Dic3—68no—
587C2×Dic3—124no—
588C2×Dic3—122no—
589C2×Dic3C2×D1212yes—
590D12—21no—
591D12—21no—
592D12—34no—
593D12—34no—
594D12—64no—
595D12—68no—
596D12—68no—
597D12—64no—
598D12—62no—
599D12—62no—
600D12—64no—
601D12—122no—
602D12—124no—
603D12C2×D1214yes—
604D12C23×D312yes—
605D12C23×D312yes—
606C4×D3—24no—
607C4×D3—24no—
608C4×D3—68no—
609C4×D3—68no—
610C4×D3—68no—
611C4×D3—68no—
612C4×D3C2×D1214yes—
613C4×D3C23×D314yes—
614Dic6—21no—
615Dic6—21no—
616Dic6—34no—
617Dic6—34no—
618Dic6—64no—
619Dic6—68no—
620Dic6—64no—
621Dic6—62no—
622Dic6—62no—
623Dic6—64no—
624Dic6—68no—
625Dic6—122no—
626Dic6—124no—
627Dic6C2×D1214yes—
628Dic6C23×D312yes—
629Dic6C23×D312yes—
630C3×C8—22no—
631C3×C8—22no—
632C3×C8—34no—
633C3×C8C23×D312yes—
634C3×C8C23×D312yes—
635C3×C8C23×D312yes—
636C3×C8C23×D312yes—
637C3⋊C8C23×D314yes—
638C2×C32—22no—
639C2×C32#57712yescomplemented
640C2×C32C23×D411yescharacteristic
641C3⋊D3—44no—
642C3×D3—24no—
643C3×D3—42no—
644C3×D3—42no—
645C24—182no—
646C24—181no—
647#41—34no—
648#41—34no—
649#41—34no—
650#41—34no—
651#41—62no—
652#41—62no—
653#41—98no—
654#41—98no—
655#41—184no—
656#41—184no—
657#41—188no—
658#41—188no—
659#41—1816no—
660C2×Q8—31no—
661C2×Q8—31no—
662C2×Q8—31no—
663C2×Q8—98no—
664C2×Q8—92no—
665C2×Q8—94no—
666C2×Q8—182no—
667C2×Q8—184no—
668C2×Q8—188no—
669C2×Q8—181no—
670C2×Q8—182no—
671C2×D4—32no—
672C2×D4—31no—
673C2×D4—31no—
674C2×D4—31no—
675C2×D4—61no—
676C2×D4—61no—
677C2×D4—98no—
678C2×D4—92no—
679C2×D4—94no—
680C2×D4—184no—
681C2×D4—182no—
682C2×D4—188no—
683C2×D4—182no—
684C2×D4—1816no—
685C2×D4—182no—
686C2×D4—181no—
687C2×D4—182no—
688C22×C4—32no—
689C22×C4—61no—
690C22×C4—61no—
691C22×C4—182no—
692C22×C4—182no—
693C22×C4—182no—
694C22×C4—181no—
695C22×C4C2×D3211yescharacteristic
696Q16—34no—
697Q16—98no—
698SD16—34no—
699SD16—34no—
700SD16—98no—
701SD16—98no—
702SD16—98no—
703SD16—98no—
704D8—34no—
705D8—98no—
706M16—34no—
707M16—38no—
708C2×C8—32no—
709C2×C8—38no—
710C2×C8C2×D3211yescharacteristic
711C2×C8C2×D3211yescharacteristic
712C2×C8C2×D3214yescomplemented
713C22×C3—24no—
714C22×C3—22no—
715C22×C3—22no—
716C22×C3—22no—
717C22×C3—21no—
718C22×C3—34no—
719C22×C3—64no—
720C22×C3—62no—
721C22×C3—62no—
722C22×C3—122no—
723C22×C3—122no—
724C22×C3C22×D1212yes—
725C22×C3C22×D1211yescharacteristic
726C22×C3C2×D3×D412yes—
727C22×C3C2×D3×D411yescharacteristic
728C2×D3—24no—
729C2×D3—22no—
730C2×D3—22no—
731C2×D3—42no—
732C2×D3—42no—
733C2×D3—64no—
734C2×D3—64no—
735C2×D3—124no—
736C2×D3—124no—
737C2×D3—124no—
738C2×D3—244no—
739C2×D3—248no—
740C2×D3—248no—
741C2×D3—244no—
742C2×D3—244no—
743C2×D3—248no—
744C2×D3C22×D1214yes—
745C3×C4—21no—
746C3×C4—22no—
747C3×C4—21no—
748C3×C4—34no—
749C3×C4—62no—
750C3×C4—62no—
751C3×C4C22×D1212yes—
752C3×C4C22×D1211yescharacteristic
753C3×C4C2×D3×D411yescharacteristic
754C3×C4C2×D3×D412yes—
755C3×C4C24×D311yescharacteristic
756C3×C4C24×D311yescharacteristic
757Dic3—22no—
758Dic3—22no—
759Dic3—64no—
760Dic3—64no—
761Dic3—124no—
762Dic3C22×D1214yes—
763C32C2×#57711yescharacteristic, complemented, Sylow
764C23—32no—
765C23—61no—
766C23—61no—
767C23—188no—
768C23—182no—
769C23—184no—
770C23—722no—
771C23—724no—
772C23D3×D1211yescharacteristic
773Q8—34no—
774Q8—32no—
775Q8—32no—
776Q8—61no—
777Q8—61no—
778Q8—94no—
779Q8—188no—
780Q8—182no—
781Q8—184no—
782D4—38no—
783D4—34no—
784D4—32no—
785D4—32no—
786D4—64no—
787D4—64no—
788D4—61no—
789D4—61no—
790D4—94no—
791D4—188no—
792D4—188no—
793D4—188no—
794D4—182no—
795D4—184no—
796C2×C4—32no—
797C2×C4—34no—
798C2×C4—34no—
799C2×C4—61no—
800C2×C4—61no—
801C2×C4—64no—
802C2×C4—64no—
803C2×C4—188no—
804C2×C4—188no—
805C2×C4—188no—
806C2×C4—184no—
807C2×C4—182no—
808C2×C4D3×D1212yes—
809C2×C4D3×D1211yescharacteristic
810C2×C4C22×D3212yes—
811C2×C4C22×D3211yescharacteristic
812C8—34no—
813C8C22×D3212yes—
814C8C22×D3212yes—
815C2×C3—24no—
816C2×C3—22no—
817C2×C3—22no—
818C2×C3—21no—
819C2×C3—22no—
820C2×C3—64no—
821C2×C3—122no—
822C2×C3—122no—
823C2×C3#575112yescomplemented
824C2×C3#577012yescomplemented
825C2×C3C23×D1211yescharacteristic
826C2×C3C22×D3×D411yescharacteristic
827D3—24no—
828D3—42no—
829D3—42no—
830D3—124no—
831D3—124no—
832D3—244no—
833C22—22no—
834C22—34no—
835C22—64no—
836C22—62no—
837C22—62no—
838C22—122no—
839C22—122no—
840C22—184no—
841C22—364no—
842C22—724no—
843C22—728no—
844C22C2×D3×D1212yes—
845C22C2×D3×D1211yescharacteristic
846C4—34no—
847C4—62no—
848C4—62no—
849C4—184no—
850C4C2×D3×D1211yescharacteristic
851C4C2×D3×D1212yes—
852C4C23×D3211yescharacteristic
853C3—21no—
854C3C2×#575111yescharacteristic, complemented
855C3C2×#577011yescharacteristic, complemented
856C2—22no—
857C2—64no—
858C2—122no—
859C2—122no—
860C2—364no—
861C2#1059467912yesdirect product factor
862C2C22×D3×D1211yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
hypercenterC22×C8D32
hypocenterC32C2×#577
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C2×#64308C2semidirect
2. C2×#64298C2semidirect
3. C22×#3744C2semidirect
4. C2×C3×#904C2semidirect
5. C2×C3×#901C2semidirect
6. C2×#63831C2semidirect
7. C2×#63825C2semidirect
8. C2×#63806C2semidirect
9. C2×#63801C2semidirect
10. #10594679C2direct (N × H)
11. C2×#63795C2semidirect
12. C2×D3×#204C2semidirect
16. C22×#634C22semidirect
19. C2×C3×#235C22semidirect
23. #64308C22semidirect
29. #64298C22semidirect
31. C2×#3795C22semidirect
33. C2×D3×Dic6C22semidirect
34. C22×C32×C8C22semidirect
35. C2×#3744C22semidirect
36. C2×#3744C22semidirect
37. C2×#3744C22semidirect
38. C2×C3×#208C22semidirect
39. C2×C3×Dic12C22semidirect
40. C3×#904C22semidirect
41. C2×C3×D24C22semidirect
42. C2×C3×#204C22semidirect
43. C2×C3×#204C22semidirect
44. C3×#901C22semidirect
45. C2×C3×ΓL(1,𝔽25)C22semidirect
46. C2×C3×D3×C8C22semidirect
47. C2×#3719C22semidirect
48. C2×#3717C22semidirect
49. #63831C22semidirect
50. C2×#3716C22semidirect
51. #63825C22semidirect
52. C2×#3714C22semidirect
53. #63806C22semidirect
54. #63801C22semidirect
55. #63795C22semidirect
56. D3×#204C22semidirect
76. C2×#904D3semidirect
81. C2×#901D3semidirect
93. C2×#634C23semidirect
102. C3×#235C23semidirect
129. #3795C23semidirect
132. D3×Dic6C23semidirect
135. C2×C32×C8C23semidirect
136. #3744C23semidirect
137. #3744C23semidirect
138. C3×#208C23semidirect
140. C3×Dic12C23semidirect
141. C3×D24C23semidirect
142. C3×#204C23semidirect
143. C3×#204C23semidirect
144. C3×ΓL(1,𝔽25)C23semidirect
145. C3×D3×C8C23semidirect
146. #3719C23semidirect
147. #3717C23semidirect
148. #3716C23semidirect
149. #3714C23semidirect
180. C2×#235C2×D3semidirect
201. C22×C3×C8C2×D3semidirect
202. C22×C3×C8C2×D3semidirect
209. C2×#208C2×D3semidirect
219. C2×Dic12C2×D3semidirect
221. #904C2×D3semidirect
223. C2×D24C2×D3semidirect
236. C2×#204C2×D3semidirect
237. C2×#204C2×D3semidirect
238. #901C2×D3semidirect
239. C2×ΓL(1,𝔽25)C2×D3semidirect
240. C2×D3×C8C2×D3semidirect
369. #235C22×D3semidirect
432. C2×C3×C8C22×D3semidirect
433. C2×C3×C8C22×D3semidirect
438. #208C22×D3semidirect
441. Dic12C22×D3semidirect
443. D24C22×D3semidirect
452. #204C22×D3semidirect
453. #204C22×D3semidirect
454. ΓL(1,𝔽25)C22×D3semidirect
455. D3×C8C22×D3semidirect
517. C22×C8D32semidirect
639. C2×C32#577semidirect
712. C2×C8C2×D32semidirect
763. C32C2×#577semidirect
823. C2×C3#5751semidirect
824. C2×C3#5770semidirect
854. C3C2×#5751semidirect
855. C3C2×#5770semidirect
861. C2#10594679direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#643082
C2×#642982
C22×#37442
C2×C3×#9042
C2×C3×#9012
C2×#638312
C2×#638252
C2×#638062
C2×#638012
#105946792
C2×#637952
C2×D3×#2042
C2×#57703
C2×#57513