Finite Group Databasebeta

← C2×#10594712 #11918764

Subgroups — C2×#10594712 #11918764

Order 1152.

3097 conjugacy classes of subgroups.

The subgroup lattice has 965 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#235C211yesmaximal, characteristic, complemented
2C22×#3795C211yesmaximal, characteristic, complemented
3C2×#64118C211yesmaximal, characteristic, complemented
4C2×C3×#908C211yesmaximal, characteristic, complemented
5C2×C3×D3×M16C211yesmaximal, characteristic, complemented
6C2×#63831C211yesmaximal, characteristic, complemented
7C2×#63830C211yesmaximal, characteristic, complemented
8#10594712C2116yesmaximal, direct product factor
9C2×#63807C212yesmaximal, complemented
10C2×#63806C212yesmaximal, complemented
11C2×#63800C212yesmaximal, complemented
12C2×#63795C212yesmaximal, complemented
13C2×#5773—31nomaximal
14C2×#5748—31nomaximal
15C2×#3828C2211yescharacteristic
16C22×#634C2211yescharacteristic, complemented
17C2×C3×#235C2211yescharacteristic
18C22×C3×D12C2211yescharacteristic, complemented
19C22×C3×C4×D3C2211yescharacteristic
20C2×D3×#67—21no—
21C22×#625—21no—
22C2×#3804—21no—
23C22×D3×Dic3—21no—
24D3×#235—24no—
25D3×#235C2218yescomplemented
26C2×D3×D12C2211yescharacteristic, complemented
27C2×C4×D32—21no—
28C2×#3799C2211yescharacteristic, complemented
29C2×#3798—21no—
30C2×#3795—24no—
31C2×#3795—21no—
32C2×#3795—21no—
33C2×#3795C2212yes—
34C2×#3795C2218yescomplemented
35C2×#3795C2212yescomplemented
36C2×#3795C2211yescharacteristic, complemented
37C2×D3×Dic6C2211yescharacteristic, complemented
38C2×C32×M16C2211yescharacteristic, complemented
39#64118C2218yescomplemented
40C2×#3746C2212yescomplemented
41C2×#3744C2212yescomplemented
42C2×C3×#208C2211yescharacteristic, complemented
43C3×#908C2218yescomplemented
44C3×D3×M16C2218yescomplemented
45C2×C3×D24C2212yescomplemented
46C2×C3×#204C2212yescomplemented
47C2×C3×ΓL(1,𝔽25)C2212yescomplemented
48C2×C3×D3×C8C2212yescomplemented
49C2×#3719C2212yescomplemented
50#63831C2218yescomplemented
51#63830C2218yescomplemented
52C2×#3716C2212yescomplemented
53C2×#3716C2212yescomplemented
54C2×#3714C2212yescomplemented
55#63807C22116yescomplemented
56#63806C22116yescomplemented
57#63800C22116yescomplemented
58#63795C22116yescomplemented
59C2×D3×#41—31no—
60C22×#237—31no—
61C22×#235—31no—
62C22×#235—31no—
63C2×C3×AGL(1,ℤ/8)—31no—
64C22×C3×M16—31no—
65C2×#951—31no—
66C2×#932—31no—
67#5773—316no—
68C2×#916—32no—
69C2×#915—32no—
70C2×#912—32no—
71C2×#911—32no—
72#5748—316no—
73C2×#909—31no—
74C2×#909—31no—
75C2×#909—31no—
76C2×#909—32no—
77C2×#909—61no—
78C2×#908—31no—
79C2×#908—32no—
80C2×#908D311yescharacteristic, complemented
81C2×D3×M16D311yescharacteristic, complemented
82C2×#904—32no—
83C2×#904—32no—
84C23×C3×D3—21no—
85C23×C3×D3D411yescharacteristic
86C22×D32—21no—
87C22×C32×C4C2311yescharacteristic
88C2×#638—21no—
89C22×C3⋊Dic3—21no—
90#3828—22no—
91#3828C2314yes—
92C2×C4⋊(C3⋊D3)C2311yescharacteristic
93C2×C4×C3⋊D3—21no—
94C2×#634—22no—
95C2×#634—21no—
96C2×#634C2311yescharacteristic
97C2×#634C2312yes—
98C2×#634C2314yescomplemented
99C2×C3×#67—21no—
100C22×C3×Dic3D411yescharacteristic
101C3×#235—22no—
102C3×#235C2314yes—
103C2×C3×D12—22no—
104C2×C3×D12—21no—
105C2×C3×D12C2312yes—
106C2×C3×D12C2311yescharacteristic
107C2×C3×D12C2314yescomplemented
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3D411yescharacteristic
110C2×C3×C4×D3D411yescharacteristic
111C2×C3×C4×D3D414yes—
112C2×C3×C4×D3C2311yescharacteristic
113C2×C3×C4×D3C2311yescharacteristic
114C2×C3×C4×D3C2314yes—
115C2×C3×Dic6C2311yescharacteristic
116D3×#67—28no—
117C2×#627—21no—
118C2×#626—21no—
119C2×#626—21no—
120C2×#625—22no—
121C2×#625—28no—
122C2×#625—22no—
123C2×#625—21no—
124C2×#624—21no—
125#3804—28no—
126C2×D3×Dic3—21no—
127C2×D3×Dic3—22no—
128C2×D3×Dic3—28no—
129C2×D3×Dic3—22no—
130C2×D3×Dic3—21no—
131D3×D12—22no—
132D3×D12C2314yescomplemented
133C4×D32—28no—
134#3799—22no—
135#3799C2314yescomplemented
136#3798—28no—
137#3795—24no—
138#3795—28no—
139#3795—28no—
140#3795—24no—
141#3795—22no—
142#3795C2318yes—
143#3795C2318yescomplemented
144#3795C2314yescomplemented
145D3×Dic6—22no—
146D3×Dic6C2314yescomplemented
147C32×M16C2314yescomplemented
148C2×C32×C8C2312yes—
149#3746C2318yescomplemented
150#3744C2318yescomplemented
151C3×#208C2314yescomplemented
152C2×C3×C3⋊C8C2312yes—
153C3×D24C2318yescomplemented
154C3×#204C2318yescomplemented
155C3×ΓL(1,𝔽25)C2318yescomplemented
156C3×D3×C8C2318yescomplemented
157#3719C2318yescomplemented
158#3716C2318yescomplemented
159#3716C2318yescomplemented
160#3714C2318yescomplemented
161C2×#575—91noSylow
162C2×C3×#41—31no—
163C22×C3×D4—31no—
164C23×C3×C4—31no—
165C22×#67—61no—
166C22×#67—61no—
167C22×#67—61no—
168C23×Dic3—61no—
169D3×#41—38no—
170D3×#41—64no—
171C2×#239—31no—
172C2×D3×Q8—31no—
173C2×#237—32no—
174C2×#237—32no—
175C2×#237—38no—
176C2×#237—31no—
177C2×#237—61no—
178C2×#237—61no—
179C2×#237—61no—
180C2×#237—64no—
181C2×D3×D4—31no—
182C2×D3×D4—61no—
183C2×#235—31no—
184C2×#235—31no—
185C2×#235—38no—
186C2×#235—32no—
187C2×#235—31no—
188C2×#235—32no—
189C2×#235—38no—
190C2×#235—31no—
191C2×#235—61no—
192C2×#235—61no—
193C2×#235—61no—
194C2×#235—61no—
195C2×#235—64no—
196C2×#235—64no—
197C2×#235—61no—
198C2×#235—61no—
199C2×#235C2×D311yescharacteristic
200C22×D12—31no—
201C22×D12C2×D311yescharacteristic, complemented
202C22×C4×D3—61no—
203C22×C4×D3—61no—
204C22×C4×D3—61no—
205C22×C4×D3C2×D311yescharacteristic
206C22×Dic6—31no—
207C22×Dic6—31no—
208C22×Dic6—31no—
209C22×Dic6—61no—
210C3×AGL(1,ℤ/8)—38no—
211C2×C3×SD16—32no—
212C2×C3×D8—32no—
213C2×C3×M16—21no—
214C2×C3×M16—31no—
215C2×C3×M16—38no—
216C2×C3×M16—32no—
217C2×C3×M16C2×D311yescharacteristic, complemented
218C2×C3×M16C2×D311yescharacteristic, complemented
219C22×C3×C8—32no—
220#951—38no—
221C2×#216—32no—
222C2×#214—32no—
223C2×#214—32no—
224#932—38no—
225C2×#213—32no—
226C2×#208C2×D311yescharacteristic, complemented
227#916—316no—
228#915—316no—
229#912—316no—
230#911—316no—
231#909—38no—
232#909—38no—
233#909—38no—
234#909—316no—
235#909—68no—
236#908—38no—
237#908—316no—
238#908C2×D318yescomplemented
239D3×M16C2×D318yescomplemented
240C2×Dic12—32no—
241C2×Dic12—32no—
242C2×Dic12—32no—
243C2×Dic12—62no—
244#904—316no—
245#904—316no—
246C2×D24—32no—
247C2×D24C2×D312yescomplemented
248C2×#204—32no—
249C2×#204—32no—
250C2×#204—32no—
251C2×#204—32no—
252C2×#204—62no—
253C2×#204C2×D312yescomplemented
254C2×ΓL(1,𝔽25)C2×D312yescomplemented
255C2×D3×C8C2×D312yescomplemented
256C23×C32C2×D411yescharacteristic
257C22×C3⋊D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—22no—
260C22×C3×D3—24no—
261C22×C3×D3—42no—
262C22×C3×D3—44no—
263C22×C3×D3C2×D411yescharacteristic
264C22×C3×D3C2×D411yescharacteristic
265C22×C3×D3C2×D414yes—
266C2×D32—24no—
267C2×D32—44no—
268C2×C32×C4C2×D411yescharacteristic
269C2×C32×C4C2×D412yes—
270C2×C32×C4C2411yescharacteristic
271C2×C32×C4C2412yes—
272#638—24no—
273C2×C3⋊Dic3—22no—
274C2×C3⋊Dic3—24no—
275C2×C3⋊Dic3—21no—
276C4⋊(C3⋊D3)—21no—
277C4⋊(C3⋊D3)C2412yes—
278C4×C3⋊D3—24no—
279#634—21no—
280#634—22no—
281#634—24no—
282#634C2412yes—
283#634C2414yes—
284C3×#67—24no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3C2×D411yescharacteristic
287C2×C3×Dic3C2×D414yes—
288C2×C3×Dic3C2×D411yescharacteristic
289C3×D12—22no—
290C3×D12—24no—
291C3×D12—21no—
292C3×D12C2414yes—
293C3×D12C2412yes—
294C3×C4×D3—24no—
295C3×C4×D3C2×D412yes—
296C3×C4×D3C2×D412yes—
297C3×C4×D3C2×D414yes—
298C3×C4×D3C2×D414yes—
299C3×C4×D3C2412yes—
300C3×C4×D3C2412yes—
301C3×Dic6—21no—
302C3×Dic6C2412yes—
303#627—24no—
304#626—24no—
305#626—24no—
306#625—28no—
307#625—28no—
308#625—24no—
309#624—24no—
310D3×Dic3—24no—
311D3×Dic3—28no—
312D3×Dic3—28no—
313D3×Dic3—24no—
314C32×C8C2414yes—
315C3×C3⋊C8C2414yes—
316C22×#41—91no—
317C22×#41—91no—
318#575—916no—
319C2×#137—92no—
320C2×#137—91no—
321C2×#137—91no—
322C2×AGL(1,ℤ/8)—31no—
323C2×AGL(1,ℤ/8)—92no—
324C2×AGL(1,ℤ/8)—91no—
325C2×#135—92no—
326C2×#135—92no—
327C22×M16—31no—
328C24×C3—31no—
329C24×C3—61no—
330C23×D3—21no—
331C23×D3—61no—
332C23×D3—61no—
333C23×D3D1211yescharacteristic
334C3×#41—34no—
335C3×#41—62no—
336C2×C3×Q8—31no—
337C2×C3×D4—32no—
338C2×C3×D4—34no—
339C2×C3×D4—31no—
340C2×C3×D4—61no—
341C2×C3×D4—61no—
342C2×C3×D4—62no—
343C22×C3×C4—21no—
344C22×C3×C4—31no—
345C22×C3×C4—31no—
346C22×C3×C4—31no—
347C22×C3×C4—34no—
348C22×C3×C4—31no—
349C22×C3×C4—31no—
350C22×C3×C4—34no—
351C22×C3×C4—61no—
352C22×C3×C4C22×D311yescharacteristic
353C22×C3×C4C22×D311yescharacteristic
354C2×#67—21no—
355C2×#67—61no—
356C2×#67—68no—
357C2×#67—61no—
358C2×#67—62no—
359C2×#67—62no—
360C2×#67—68no—
361C2×#67—61no—
362C2×#67—61no—
363C2×#67—61no—
364C2×#67—62no—
365C2×#67—62no—
366C2×#67—68no—
367C2×#67—61no—
368C2×#67—121no—
369C22×Dic3—61no—
370C22×Dic3—61no—
371C22×Dic3—61no—
372C22×Dic3—61no—
373C22×Dic3—62no—
374C22×Dic3—62no—
375C22×Dic3—68no—
376C22×Dic3—121no—
377C22×Dic3D1211yescharacteristic
378#239—34no—
379#239—62no—
380D3×Q8—34no—
381D3×Q8—62no—
382#237—38no—
383#237—34no—
384#237—38no—
385#237—68no—
386#237—68no—
387#237—68no—
388#237—64no—
389#237—64no—
390#237—62no—
391D3×D4—34no—
392D3×D4—68no—
393D3×D4—62no—
394#235—22no—
395#235—34no—
396#235—34no—
397#235—34no—
398#235—38no—
399#235—38no—
400#235—34no—
401#235—64no—
402#235—62no—
403#235—68no—
404#235—64no—
405#235—64no—
406#235—68no—
407#235—68no—
408#235—62no—
409#235—68no—
410#235—62no—
411#235—62no—
412#235—68no—
413#235—122no—
414#235C22×D314yes—
415C2×D12—22no—
416C2×D12—21no—
417C2×D12—31no—
418C2×D12—31no—
419C2×D12—34no—
420C2×D12—61no—
421C2×D12—62no—
422C2×D12—61no—
423C2×D12—61no—
424C2×D12C22×D311yescharacteristic
425C2×D12C22×D312yes—
426C2×D12C22×D314yescomplemented
427C2×C4×D3—21no—
428C2×C4×D3—68no—
429C2×C4×D3—61no—
430C2×C4×D3—62no—
431C2×C4×D3—61no—
432C2×C4×D3—62no—
433C2×C4×D3—68no—
434C2×C4×D3—61no—
435C2×C4×D3—61no—
436C2×C4×D3—61no—
437C2×C4×D3—61no—
438C2×C4×D3—68no—
439C2×C4×D3—121no—
440C2×C4×D3D1211yescharacteristic
441C2×C4×D3D1211yescharacteristic
442C2×C4×D3D1214yes—
443C2×C4×D3C22×D311yescharacteristic
444C2×C4×D3C22×D311yescharacteristic
445C2×C4×D3C22×D314yes—
446C2×Dic6—31no—
447C2×Dic6—32no—
448C2×Dic6—32no—
449C2×Dic6—31no—
450C2×Dic6—34no—
451C2×Dic6—34no—
452C2×Dic6—34no—
453C2×Dic6—62no—
454C2×Dic6—61no—
455C2×Dic6—64no—
456C2×Dic6—62no—
457C2×Dic6—61no—
458C2×Dic6—61no—
459C2×Dic6—62no—
460C2×Dic6—61no—
461C2×Dic6—62no—
462C2×Dic6—61no—
463C2×Dic6—121no—
464C2×Dic6—122no—
465C2×Dic6C22×D311yescharacteristic
466C3×SD16—38no—
467C3×D8—38no—
468C3×M16—24no—
469C3×M16—34no—
470C3×M16—38no—
471C3×M16C22×D314yescomplemented
472C3×M16C22×D314yescomplemented
473C2×C3×C8—22no—
474C2×C3×C8—32no—
475C2×C3×C8—38no—
476C2×C3×C8C22×D312yes—
477C2×C3×C8C22×D312yes—
478#216—38no—
479#214—38no—
480#214—38no—
481#213—38no—
482#208C22×D314yescomplemented
483C2×C3⋊C8C22×D312yes—
484Dic12—38no—
485Dic12—38no—
486Dic12—38no—
487Dic12—68no—
488D24—38no—
489D24C22×D318yescomplemented
490#204—38no—
491#204—38no—
492#204—38no—
493#204—38no—
494#204—68no—
495#204C22×D318yescomplemented
496ΓL(1,𝔽25)C22×D318yescomplemented
497D3×C8C22×D318yescomplemented
498C22×C32—22no—
499C22×C32C22×D412yes—
500C22×C32C22×D411yescharacteristic
501C2×C3⋊D3—22no—
502C2×C3⋊D3—42no—
503C2×C3×D3—22no—
504C2×C3×D3—22no—
505C2×C3×D3—24no—
506C2×C3×D3—22no—
507C2×C3×D3—44no—
508C2×C3×D3—48no—
509C2×C3×D3—42no—
510C2×C3×D3—44no—
511C2×C3×D3C22×D412yes—
512C2×C3×D3C22×D412yes—
513D32—48no—
514C32×C4C22×D411yescharacteristic
515C32×C4C22×D412yes—
516C32×C4C2511yescharacteristic
517C3⋊Dic3—24no—
518C3⋊Dic3—22no—
519C3×Dic3—22no—
520C3×Dic3C22×D412yes—
521C3×Dic3C22×D412yes—
522C2×#41—31no—
523C2×#41—91no—
524C2×#41—92no—
525C2×#41—92no—
526C2×#41—98no—
527C2×#41—91no—
528C2×#41—98no—
529C2×#41—91no—
530C2×#41—181no—
531C2×#41—181no—
532C2×#41—181no—
533C2×#41—184no—
534C2×#41—181no—
535C2×#41—184no—
536C22×Q8—91no—
537C22×Q8—91no—
538C22×D4—31no—
539C22×D4—91no—
540C22×D4—181no—
541C22×D4—181no—
542C23×C4—31no—
543C23×C4—181no—
544C23×C4—181no—
545#137—916no—
546#137—98no—
547#137—98no—
548AGL(1,ℤ/8)—38no—
549AGL(1,ℤ/8)—916no—
550AGL(1,ℤ/8)—98no—
551#135—916no—
552#135—916no—
553C2×Q16—92no—
554C2×Q16—92no—
555C2×SD16—32no—
556C2×SD16—92no—
557C2×SD16—92no—
558C2×SD16—92no—
559C2×D8—32no—
560C2×D8—92no—
561C2×M16—31no—
562C2×M16—38no—
563C2×M16—32no—
564C2×M16D3211yescharacteristic, complemented
565C22×C8—32no—
566C23×C3—21no—
567C23×C3—31no—
568C23×C3—31no—
569C23×C3—34no—
570C23×C3—64no—
571C23×C3—62no—
572C23×C3—61no—
573C23×C3—122no—
574C23×C3—124no—
575C23×C3C2×D1211yescharacteristic
576C23×C3D3×D411yescharacteristic
577C22×D3—21no—
578C22×D3—22no—
579C22×D3—24no—
580C22×D3—42no—
581C22×D3—44no—
582C22×D3—64no—
583C22×D3—61no—
584C22×D3—61no—
585C22×D3—64no—
586C22×D3—121no—
587C22×D3—124no—
588C22×D3—124no—
589C22×D3C2×D1211yescharacteristic
590C22×D3C2×D1211yescharacteristic
591C22×D3C2×D1214yes—
592C3×Q8—32no—
593C3×Q8—61no—
594C3×D4—34no—
595C3×D4—32no—
596C3×D4—64no—
597C3×D4—61no—
598C3×D4—62no—
599C3×D4—64no—
600C2×C3×C4—21no—
601C2×C3×C4—22no—
602C2×C3×C4—21no—
603C2×C3×C4—22no—
604C2×C3×C4—31no—
605C2×C3×C4—31no—
606C2×C3×C4—34no—
607C2×C3×C4—32no—
608C2×C3×C4—34no—
609C2×C3×C4—34no—
610C2×C3×C4—32no—
611C2×C3×C4—32no—
612C2×C3×C4—32no—
613C2×C3×C4—61no—
614C2×C3×C4—64no—
615C2×C3×C4C2×D1211yescharacteristic
616C2×C3×C4C2×D1212yes—
617C2×C3×C4D3×D411yescharacteristic
618C2×C3×C4D3×D412yes—
619C2×C3×C4C23×D311yescharacteristic
620C2×C3×C4C23×D312yes—
621C2×C3×C4C23×D311yescharacteristic
622C2×C3×C4C23×D312yes—
623#67—24no—
624#67—64no—
625#67—64no—
626#67—68no—
627#67—68no—
628#67—64no—
629#67—64no—
630#67—64no—
631#67—68no—
632#67—68no—
633#67—64no—
634#67—124no—
635C2×Dic3—21no—
636C2×Dic3—64no—
637C2×Dic3—61no—
638C2×Dic3—64no—
639C2×Dic3—62no—
640C2×Dic3—64no—
641C2×Dic3—62no—
642C2×Dic3—61no—
643C2×Dic3—64no—
644C2×Dic3—68no—
645C2×Dic3—68no—
646C2×Dic3—124no—
647C2×Dic3—122no—
648C2×Dic3—121no—
649C2×Dic3C2×D1211yescharacteristic
650C2×Dic3C2×D1211yescharacteristic
651C2×Dic3C2×D1214yes—
652D12—22no—
653D12—24no—
654D12—21no—
655D12—32no—
656D12—32no—
657D12—62no—
658D12—64no—
659D12—64no—
660D12—61no—
661D12—61no—
662D12—121no—
663D12C23×D312yes—
664D12C23×D314yes—
665C4×D3—24no—
666C4×D3—64no—
667C4×D3—68no—
668C4×D3—64no—
669C4×D3—68no—
670C4×D3—64no—
671C4×D3—64no—
672C4×D3—64no—
673C4×D3—64no—
674C4×D3—124no—
675C4×D3C2×D1214yes—
676C4×D3C2×D1214yes—
677C4×D3C2×D1212yes—
678C4×D3C2×D1212yes—
679C4×D3C23×D312yes—
680C4×D3C23×D312yes—
681Dic6—21no—
682Dic6—32no—
683Dic6—34no—
684Dic6—34no—
685Dic6—32no—
686Dic6—64no—
687Dic6—62no—
688Dic6—64no—
689Dic6—62no—
690Dic6—64no—
691Dic6—61no—
692Dic6—61no—
693Dic6—62no—
694Dic6—64no—
695Dic6—64no—
696Dic6—122no—
697Dic6—124no—
698Dic6—121no—
699Dic6C23×D312yes—
700C3×C8—24no—
701C3×C8—34no—
702C3×C8C23×D314yes—
703C3×C8C23×D314yes—
704C3⋊C8C23×D314yes—
705C2×C32—22no—
706C2×C32#57512yescomplemented
707C2×C32C23×D411yescharacteristic
708C3⋊D3—42no—
709C3×D3—22no—
710C3×D3—22no—
711C3×D3—42no—
712C3×D3—44no—
713C24—31no—
714C24—61no—
715C24—181no—
716#41—34no—
717#41—62no—
718#41—94no—
719#41—98no—
720#41—98no—
721#41—94no—
722#41—94no—
723#41—188no—
724#41—188no—
725#41—188no—
726#41—184no—
727#41—184no—
728#41—188no—
729#41—182no—
730#41—182no—
731#41—182no—
732C2×Q8—31no—
733C2×Q8—94no—
734C2×Q8—91no—
735C2×Q8—92no—
736C2×Q8—94no—
737C2×Q8—181no—
738C2×Q8—182no—
739C2×Q8—182no—
740C2×Q8—181no—
741C2×D4—31no—
742C2×D4—32no—
743C2×D4—34no—
744C2×D4—61no—
745C2×D4—62no—
746C2×D4—61no—
747C2×D4—94no—
748C2×D4—91no—
749C2×D4—182no—
750C2×D4—181no—
751C2×D4—181no—
752C2×D4—188no—
753C2×D4—188no—
754C2×D4—182no—
755C2×D4—181no—
756C2×D4—182no—
757C2×D4—181no—
758C22×C4—31no—
759C22×C4—31no—
760C22×C4—31no—
761C22×C4—34no—
762C22×C4—31no—
763C22×C4—34no—
764C22×C4—31no—
765C22×C4—61no—
766C22×C4—181no—
767C22×C4—188no—
768C22×C4—188no—
769C22×C4—181no—
770C22×C4—182no—
771C22×C4—182no—
772C22×C4—181no—
773C22×C4—181no—
774C22×C4—181no—
775C22×C4C2×D3211yescharacteristic
776Q16—98no—
777Q16—98no—
778SD16—38no—
779SD16—98no—
780SD16—98no—
781SD16—98no—
782D8—38no—
783D8—98no—
784M16—34no—
785M16—38no—
786M16C2×D3214yescomplemented
787C2×C8—32no—
788C2×C8—38no—
789C2×C8C2×D3212yes—
790C22×C3—22no—
791C22×C3—22no—
792C22×C3—22no—
793C22×C3—21no—
794C22×C3—32no—
795C22×C3—32no—
796C22×C3—42no—
797C22×C3—62no—
798C22×C3—62no—
799C22×C3—64no—
800C22×C3—62no—
801C22×C3—124no—
802C22×C3—128no—
803C22×C3—122no—
804C22×C3—124no—
805C22×C3C22×D1212yes—
806C22×C3C22×D1211yescharacteristic
807C22×C3C2×D3×D412yes—
808C22×C3C2×D3×D411yescharacteristic
809C2×D3—22no—
810C2×D3—22no—
811C2×D3—22no—
812C2×D3—24no—
813C2×D3—44no—
814C2×D3—48no—
815C2×D3—44no—
816C2×D3—42no—
817C2×D3—62no—
818C2×D3—62no—
819C2×D3—122no—
820C2×D3—128no—
821C2×D3—128no—
822C2×D3—122no—
823C2×D3—122no—
824C2×D3—242no—
825C2×D3C22×D1212yes—
826C2×D3C22×D1212yes—
827C3×C4—21no—
828C3×C4—22no—
829C3×C4—21no—
830C3×C4—32no—
831C3×C4—32no—
832C3×C4—62no—
833C3×C4C22×D1211yescharacteristic
834C3×C4C22×D1212yes—
835C3×C4C2×D3×D411yescharacteristic
836C3×C4C2×D3×D412yes—
837C3×C4C24×D311yescharacteristic
838C3×C4C24×D311yescharacteristic
839Dic3—22no—
840Dic3—62no—
841Dic3—64no—
842Dic3—62no—
843Dic3—64no—
844Dic3—124no—
845Dic3—122no—
846Dic3C22×D1212yes—
847Dic3C22×D1212yes—
848C32C2×#57511yescharacteristic, complemented, Sylow
849C23—31no—
850C23—31no—
851C23—34no—
852C23—64no—
853C23—61no—
854C23—62no—
855C23—122no—
856C23—124no—
857C23—184no—
858C23—181no—
859C23—364no—
860C23D3×D1211yescharacteristic
861Q8—32no—
862Q8—61no—
863Q8—92no—
864Q8—94no—
865Q8—184no—
866Q8—184no—
867Q8—181no—
868Q8—182no—
869D4—32no—
870D4—34no—
871D4—64no—
872D4—64no—
873D4—62no—
874D4—61no—
875D4—92no—
876D4—184no—
877D4—184no—
878D4—188no—
879D4—184no—
880D4—188no—
881D4—184no—
882D4—181no—
883C2×C4—34no—
884C2×C4—31no—
885C2×C4—31no—
886C2×C4—34no—
887C2×C4—32no—
888C2×C4—32no—
889C2×C4—34no—
890C2×C4—32no—
891C2×C4—32no—
892C2×C4—61no—
893C2×C4—64no—
894C2×C4—184no—
895C2×C4—184no—
896C2×C4—188no—
897C2×C4—188no—
898C2×C4—184no—
899C2×C4—184no—
900C2×C4—182no—
901C2×C4—181no—
902C2×C4—184no—
903C2×C4D3×D1212yes—
904C2×C4D3×D1211yescharacteristic
905C2×C4C22×D3212yes—
906C2×C4C22×D3211yescharacteristic
907C8—34no—
908C8C22×D3214yes—
909C2×C3—22no—
910C2×C3—22no—
911C2×C3—21no—
912C2×C3—22no—
913C2×C3—42no—
914C2×C3—62no—
915C2×C3—62no—
916C2×C3—122no—
917C2×C3—124no—
918C2×C3#574812yescomplemented
919C2×C3#577312yescomplemented
920C2×C3C23×D1211yescharacteristic
921C2×C3C22×D3×D411yescharacteristic
922D3—22no—
923D3—22no—
924D3—44no—
925D3—42no—
926D3—122no—
927D3—122no—
928D3—242no—
929C22—22no—
930C22—32no—
931C22—32no—
932C22—62no—
933C22—62no—
934C22—62no—
935C22—64no—
936C22—124no—
937C22—128no—
938C22—124no—
939C22—122no—
940C22—182no—
941C22—368no—
942C22—362no—
943C22C2×D3×D1212yes—
944C22C2×D3×D1211yescharacteristic
945C4—32no—
946C4—32no—
947C4—62no—
948C4—184no—
949C4—182no—
950C4C2×D3×D1212yes—
951C4C2×D3×D1211yescharacteristic
952C4C23×D3211yescharacteristic
953C3—21no—
954C3C2×#574811yescharacteristic, complemented
955C3C2×#577311yescharacteristic, complemented
956C2—22no—
957C2—62no—
958C2—62no—
959C2—124no—
960C2—122no—
961C2—362no—
962C2#1059471212yesdirect product factor
963C2C22×D3×D1211yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
hypercenterC2×M16D32
hypocenterC32C2×#575
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×D3×#235C2semidirect
2. C22×#3795C2semidirect
3. C2×#64118C2semidirect
4. C2×C3×#908C2semidirect
5. C2×C3×D3×M16C2semidirect
6. C2×#63831C2semidirect
7. C2×#63830C2semidirect
8. #10594712C2direct (N × H)
9. C2×#63807C2semidirect
10. C2×#63806C2semidirect
11. C2×#63800C2semidirect
12. C2×#63795C2semidirect
16. C22×#634C22semidirect
18. C22×C3×D12C22semidirect
25. D3×#235C22semidirect
26. C2×D3×D12C22semidirect
28. C2×#3799C22semidirect
34. C2×#3795C22semidirect
35. C2×#3795C22semidirect
36. C2×#3795C22semidirect
37. C2×D3×Dic6C22semidirect
38. C2×C32×M16C22semidirect
39. #64118C22semidirect
40. C2×#3746C22semidirect
41. C2×#3744C22semidirect
42. C2×C3×#208C22semidirect
43. C3×#908C22semidirect
44. C3×D3×M16C22semidirect
45. C2×C3×D24C22semidirect
46. C2×C3×#204C22semidirect
47. C2×C3×ΓL(1,𝔽25)C22semidirect
48. C2×C3×D3×C8C22semidirect
49. C2×#3719C22semidirect
50. #63831C22semidirect
51. #63830C22semidirect
52. C2×#3716C22semidirect
53. C2×#3716C22semidirect
54. C2×#3714C22semidirect
55. #63807C22semidirect
56. #63806C22semidirect
57. #63800C22semidirect
58. #63795C22semidirect
80. C2×#908D3semidirect
81. C2×D3×M16D3semidirect
98. C2×#634C23semidirect
107. C2×C3×D12C23semidirect
132. D3×D12C23semidirect
135. #3799C23semidirect
143. #3795C23semidirect
144. #3795C23semidirect
146. D3×Dic6C23semidirect
147. C32×M16C23semidirect
149. #3746C23semidirect
150. #3744C23semidirect
151. C3×#208C23semidirect
153. C3×D24C23semidirect
154. C3×#204C23semidirect
155. C3×ΓL(1,𝔽25)C23semidirect
156. C3×D3×C8C23semidirect
157. #3719C23semidirect
158. #3716C23semidirect
159. #3716C23semidirect
160. #3714C23semidirect
201. C22×D12C2×D3semidirect
217. C2×C3×M16C2×D3semidirect
218. C2×C3×M16C2×D3semidirect
226. C2×#208C2×D3semidirect
238. #908C2×D3semidirect
239. D3×M16C2×D3semidirect
247. C2×D24C2×D3semidirect
253. C2×#204C2×D3semidirect
254. C2×ΓL(1,𝔽25)C2×D3semidirect
255. C2×D3×C8C2×D3semidirect
426. C2×D12C22×D3semidirect
471. C3×M16C22×D3semidirect
472. C3×M16C22×D3semidirect
482. #208C22×D3semidirect
489. D24C22×D3semidirect
495. #204C22×D3semidirect
496. ΓL(1,𝔽25)C22×D3semidirect
497. D3×C8C22×D3semidirect
564. C2×M16D32semidirect
706. C2×C32#575semidirect
786. M16C2×D32semidirect
848. C32C2×#575semidirect
918. C2×C3#5748semidirect
919. C2×C3#5773semidirect
954. C3C2×#5748semidirect
955. C3C2×#5773semidirect
962. C2#10594712direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D3×#2352
C22×#37952
C2×#641182
C2×C3×#9082
C2×C3×D3×M162
C2×#638312
C2×#638302
#105947122
C2×#638072
C2×#638062
C2×#638002
C2×#637952
C2×#57733
C2×#57483