Finite Group Databasebeta

← C2×#10595469 #11918759

Subgroups — C2×#10595469 #11918759

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×C3×D3×#41C211yesmaximal, characteristic, complemented
2C22×#3795C211yesmaximal, characteristic, complemented
3C2×#64160C211yesmaximal, characteristic, complemented
4C2×C3×#949C211yesmaximal, characteristic, complemented
5#10595469C2116yesmaximal, direct product factor
6C2×#63947C212yesmaximal, complemented
7C2×#63946C212yesmaximal, complemented
8C2×#63933C212yesmaximal, complemented
9C2×#63932C212yesmaximal, complemented
10C2×#63831C211yesmaximal, characteristic, complemented
11C2×#63823C211yesmaximal, characteristic, complemented
12C2×D3×#208C211yesmaximal, characteristic, complemented
13C2×#5822—31nomaximal
14C2×#5773—31nomaximal
15C2×C32×#41C2211yescharacteristic
16C22×#634C2211yescharacteristic, complemented
17C3×D3×#41—24no—
18C3×D3×#41C2218yescomplemented
19C2×C3×#239C2211yescharacteristic, complemented
20C2×C3×D3×Q8C2211yescharacteristic, complemented
21C2×C3×#237—21no—
22C2×C3×#237C2211yescharacteristic, complemented
23C2×C3×D3×D4—21no—
24C2×C3×D3×D4C2211yescharacteristic, complemented
25C2×C3×#235—21no—
26C2×C3×#235C2211yescharacteristic
27C22×C3×D12C2211yescharacteristic, complemented
28C22×C3×C4×D3—21no—
29C22×C3×C4×D3C2211yescharacteristic
30C22×#625—21no—
31C22×D3×Dic3—21no—
32C2×#3795—24no—
33C2×#3795—21no—
34C2×#3795—21no—
35C2×#3795C2212yes—
36C2×#3795C2218yescomplemented
37C2×#3795C2212yescomplemented
38#64160C2218yescomplemented
39C2×#3756C2212yescomplemented
40C2×#3754C2212yescomplemented
41C2×#3748C2211yescharacteristic, complemented
42C3×#949C2218yescomplemented
43C2×C3×#215C2212yescomplemented
44C2×C3×#213C2212yescomplemented
45C2×C3×#208C2211yescharacteristic, complemented
46#63947C22116yescomplemented
47#63946C22116yescomplemented
48#63933C22116yescomplemented
49#63932C22116yescomplemented
50C2×#3719C2212yescomplemented
51#63831C2218yescomplemented
52C2×#3716C2212yescomplemented
53C2×#3715C2212yescomplemented
54#63823C2218yescomplemented
55C2×#3713C2212yescomplemented
56C2×#3711C2212yescomplemented
57D3×#208C2218yescomplemented
58C2×D3×C3⋊C8C2212yescomplemented
59C22×C3×#41—31no—
60C2×D3×#41D311yescharacteristic, complemented
61C22×#237—31no—
62C22×#235—31no—
63C2×C3×AGL(1,ℤ/8)—31no—
64C2×#951—31no—
65C2×#951—31no—
66C2×#951—31no—
67C2×#951—61no—
68#5822—316no—
69C2×#950—32no—
70C2×#950—32no—
71C2×#949—31no—
72C2×#949D311yescharacteristic, complemented
73C2×#942—32no—
74C2×#932—31no—
75C2×#932—32no—
76C22×#208—31no—
77#5773—316no—
78C2×#916—32no—
79C2×#915—32no—
80C2×#912—32no—
81C2×#911—32no—
82C2×#909—31no—
83C2×D3×M16—31no—
84C23×C3×D3—21no—
85C23×C3×D3—21no—
86C23×C3×D3D411yescharacteristic
87C32×#41—22no—
88C32×#41C2314yes—
89C2×C32×Q8C2311yescharacteristic
90C2×C32×D4—21no—
91C2×C32×D4C2311yescharacteristic
92C22×C32×C4—21no—
93C22×C32×C4C2311yescharacteristic
94C22×C3⋊Dic3—21no—
95C2×#634—22no—
96C2×#634—21no—
97C2×#634C2312yes—
98C2×#634C2314yescomplemented
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C22×C3×Dic3—21no—
103C22×C3×Dic3D411yescharacteristic
104C3×#239—22no—
105C3×#239C2314yescomplemented
106C3×D3×Q8—22no—
107C3×D3×Q8C2314yescomplemented
108C3×#237—28no—
109C3×#237—22no—
110C3×#237C2314yescomplemented
111C3×D3×D4—28no—
112C3×D3×D4—22no—
113C3×D3×D4C2314yescomplemented
114C3×#235—22no—
115C3×#235—28no—
116C3×#235C2314yes—
117C2×C3×D12—21no—
118C2×C3×D12—22no—
119C2×C3×D12—21no—
120C2×C3×D12C2312yes—
121C2×C3×D12C2311yescharacteristic
122C2×C3×D12C2314yescomplemented
123C2×C3×C4×D3—21no—
124C2×C3×C4×D3—21no—
125C2×C3×C4×D3—21no—
126C2×C3×C4×D3—28no—
127C2×C3×C4×D3D411yescharacteristic
128C2×C3×C4×D3D411yescharacteristic
129C2×C3×C4×D3D414yes—
130C2×C3×C4×D3C2311yescharacteristic
131C2×C3×C4×D3C2311yescharacteristic
132C2×C3×C4×D3C2314yes—
133C2×C3×Dic6—21no—
134C2×C3×Dic6C2311yescharacteristic
135C2×#625—22no—
136C2×#625—28no—
137C2×#625—22no—
138C2×D3×Dic3—22no—
139C2×D3×Dic3—28no—
140C2×D3×Dic3—22no—
141#3795—24no—
142#3795—28no—
143#3795—28no—
144#3795—24no—
145#3795C2318yes—
146#3795C2318yescomplemented
147#3756C2318yescomplemented
148#3754C2318yescomplemented
149#3748C2314yescomplemented
150C2×C3⋊(C3⋊C8)C2312yes—
151C3×#215C2318yescomplemented
152C3×#213C2318yescomplemented
153C3×#208C2314yescomplemented
154C2×C3×C3⋊C8C2312yes—
155#3719C2318yescomplemented
156#3716C2318yescomplemented
157#3715C2318yescomplemented
158#3713C2318yescomplemented
159#3711C2318yescomplemented
160D3×C3⋊C8C2318yescomplemented
161C2×#575—91noSylow
162C2×C3×#41—21no—
163C2×C3×#41—38no—
164C2×C3×#41—31no—
165C2×C3×#41—31no—
166C2×C3×#41—31no—
167C2×C3×#41—61no—
168C2×C3×#41—61no—
169C2×C3×#41—64no—
170C2×C3×#41C2×D311yescharacteristic
171C2×C3×#41C2×D311yescharacteristic
172C22×C3×Q8—31no—
173C22×C3×D4—31no—
174C22×C3×D4—31no—
175C22×C3×D4—61no—
176C23×C3×C4—31no—
177C23×C3×C4—61no—
178C22×#67—61no—
179C22×#67—61no—
180C23×Dic3—61no—
181D3×#41—24no—
182D3×#41C2×D318yescomplemented
183C2×#239C2×D311yescharacteristic, complemented
184C2×D3×Q8C2×D311yescharacteristic, complemented
185C2×#237—21no—
186C2×#237—32no—
187C2×#237—32no—
188C2×#237—38no—
189C2×#237—61no—
190C2×#237—61no—
191C2×#237—64no—
192C2×#237C2×D311yescharacteristic, complemented
193C2×D3×D4—21no—
194C2×D3×D4C2×D311yescharacteristic, complemented
195C2×#235—21no—
196C2×#235—32no—
197C2×#235—32no—
198C2×#235—38no—
199C2×#235—61no—
200C2×#235—61no—
201C2×#235—64no—
202C2×#235C2×D311yescharacteristic
203C22×D12C2×D311yescharacteristic, complemented
204C22×C4×D3—21no—
205C22×C4×D3—61no—
206C22×C4×D3C2×D311yescharacteristic
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—31no—
214#951—38no—
215#951—38no—
216#951—38no—
217#951—68no—
218#950—316no—
219#950—316no—
220#949—38no—
221#949C2×D318yescomplemented
222C2×#216—32no—
223C2×#216—32no—
224C2×#216—32no—
225C2×#216—62no—
226#942—316no—
227C2×#215—32no—
228C2×#215C2×D312yescomplemented
229C2×#214—32no—
230C2×#214—32no—
231C2×#214—32no—
232C2×#214—32no—
233C2×#214—62no—
234#932—38no—
235#932—316no—
236C2×#213—32no—
237C2×#213—32no—
238C2×#213C2×D312yescomplemented
239C2×#208—31no—
240C2×#208—31no—
241C2×#208—38no—
242C2×#208—32no—
243C2×#208—61no—
244C2×#208C2×D311yescharacteristic, complemented
245C22×C3⋊C8—32no—
246#916—316no—
247#915—316no—
248#912—316no—
249#911—316no—
250#909—38no—
251D3×M16—38no—
252C2×Dic12—32no—
253C2×#204—32no—
254C2×ΓL(1,𝔽25)—32no—
255C2×D3×C8—32no—
256C23×C32—21no—
257C23×C32C2×D411yescharacteristic
258C22×C3×D3—22no—
259C22×C3×D3—24no—
260C22×C3×D3—21no—
261C22×C3×D3—24no—
262C22×C3×D3—42no—
263C22×C3×D3—44no—
264C22×C3×D3—44no—
265C22×C3×D3C2×D411yescharacteristic
266C22×C3×D3C2×D411yescharacteristic
267C22×C3×D3C2×D414yes—
268C32×Q8—21no—
269C32×Q8C2412yes—
270C32×D4—24no—
271C32×D4—21no—
272C32×D4C2412yes—
273C2×C32×C4—21no—
274C2×C32×C4—24no—
275C2×C32×C4C2×D411yescharacteristic
276C2×C32×C4C2×D412yes—
277C2×C32×C4C2411yescharacteristic
278C2×C32×C4C2412yes—
279C2×C3⋊Dic3—22no—
280C2×C3⋊Dic3—24no—
281#634—22no—
282#634—24no—
283#634C2414yes—
284C3×#67—24no—
285C3×#67—24no—
286C3×#67—24no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3—24no—
289C2×C3×Dic3C2×D411yescharacteristic
290C2×C3×Dic3C2×D411yescharacteristic
291C2×C3×Dic3C2×D414yes—
292C3×D12—24no—
293C3×D12—22no—
294C3×D12—24no—
295C3×D12—21no—
296C3×D12C2412yes—
297C3×D12C2414yes—
298C3×C4×D3—24no—
299C3×C4×D3—24no—
300C3×C4×D3—24no—
301C3×C4×D3C2×D414yes—
302C3×C4×D3C2×D414yes—
303C3×C4×D3C2×D412yes—
304C3×C4×D3C2×D412yes—
305C3×C4×D3C2412yes—
306C3×C4×D3C2412yes—
307C3×Dic6—21no—
308C3×Dic6—24no—
309C3×Dic6C2412yes—
310#625—28no—
311#625—28no—
312D3×Dic3—28no—
313D3×Dic3—28no—
314C3⋊(C3⋊C8)C2414yes—
315C3×C3⋊C8C2414yes—
316C22×#41—31no—
317C22×#41—91no—
318#575—916no—
319C2×#137—91no—
320C2×#137—92no—
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—91no—
328C24×C3—31no—
329C24×C3—61no—
330C24×C3—61no—
331C23×D3—21no—
332C23×D3—21no—
333C23×D3#6711yescharacteristic
334C3×#41—22no—
335C3×#41—22no—
336C3×#41—24no—
337C3×#41—34no—
338C3×#41—34no—
339C3×#41—34no—
340C3×#41—42no—
341C3×#41—68no—
342C3×#41—68no—
343C3×#41—62no—
344C3×#41—62no—
345C3×#41—62no—
346C3×#41C22×D314yes—
347C3×#41C22×D314yes—
348C2×C3×Q8—21no—
349C2×C3×Q8—34no—
350C2×C3×Q8—31no—
351C2×C3×Q8—61no—
352C2×C3×Q8—62no—
353C2×C3×Q8C22×D311yescharacteristic
354C2×C3×Q8C22×D311yescharacteristic
355C2×C3×D4—21no—
356C2×C3×D4—21no—
357C2×C3×D4—21no—
358C2×C3×D4—34no—
359C2×C3×D4—31no—
360C2×C3×D4—32no—
361C2×C3×D4—34no—
362C2×C3×D4—41no—
363C2×C3×D4—61no—
364C2×C3×D4—62no—
365C2×C3×D4—61no—
366C2×C3×D4—68no—
367C2×C3×D4—61no—
368C2×C3×D4—61no—
369C2×C3×D4—61no—
370C2×C3×D4—62no—
371C2×C3×D4C22×D311yescharacteristic
372C2×C3×D4C22×D311yescharacteristic
373C22×C3×C4—21no—
374C22×C3×C4—21no—
375C22×C3×C4—21no—
376C22×C3×C4—31no—
377C22×C3×C4—31no—
378C22×C3×C4—31no—
379C22×C3×C4—34no—
380C22×C3×C4—31no—
381C22×C3×C4—31no—
382C22×C3×C4—34no—
383C22×C3×C4—41no—
384C22×C3×C4—61no—
385C22×C3×C4—68no—
386C22×C3×C4—61no—
387C22×C3×C4—61no—
388C22×C3×C4—61no—
389C22×C3×C4C22×D311yescharacteristic
390C22×C3×C4C22×D311yescharacteristic
391C2×#67—21no—
392C2×#67—21no—
393C2×#67—21no—
394C2×#67—62no—
395C2×#67—62no—
396C2×#67—68no—
397C2×#67—62no—
398C2×#67—62no—
399C2×#67—68no—
400C22×Dic3—21no—
401C22×Dic3—61no—
402C22×Dic3—61no—
403C22×Dic3—62no—
404C22×Dic3—62no—
405C22×Dic3—68no—
406C22×Dic3—121no—
407C22×Dic3#6711yescharacteristic
408#239—22no—
409#239C22×D314yescomplemented
410D3×Q8—22no—
411D3×Q8C22×D314yescomplemented
412#237—28no—
413#237—22no—
414#237—38no—
415#237—38no—
416#237—68no—
417#237—68no—
418#237—64no—
419#237—64no—
420#237C22×D314yescomplemented
421D3×D4—28no—
422D3×D4—22no—
423D3×D4C22×D314yescomplemented
424#235—22no—
425#235—28no—
426#235—38no—
427#235—38no—
428#235—64no—
429#235—64no—
430#235—68no—
431#235—68no—
432#235C22×D314yes—
433C2×D12—21no—
434C2×D12—22no—
435C2×D12—21no—
436C2×D12C22×D311yescharacteristic
437C2×D12C22×D312yes—
438C2×D12C22×D314yescomplemented
439C2×C4×D3—21no—
440C2×C4×D3—21no—
441C2×C4×D3—21no—
442C2×C4×D3—28no—
443C2×C4×D3—62no—
444C2×C4×D3—62no—
445C2×C4×D3—68no—
446C2×C4×D3#6711yescharacteristic
447C2×C4×D3#6711yescharacteristic
448C2×C4×D3#6714yes—
449C2×C4×D3C22×D311yescharacteristic
450C2×C4×D3C22×D311yescharacteristic
451C2×C4×D3C22×D314yes—
452C2×Dic6—21no—
453C2×Dic6—32no—
454C2×Dic6—34no—
455C2×Dic6—32no—
456C2×Dic6—34no—
457C2×Dic6—62no—
458C2×Dic6—64no—
459C2×Dic6—61no—
460C2×Dic6—62no—
461C2×Dic6—61no—
462C2×Dic6—62no—
463C2×Dic6—121no—
464C2×Dic6—122no—
465C2×Dic6C22×D311yescharacteristic
466C3×SD16—38no—
467C3×D8—38no—
468C3×M16—34no—
469C2×C3×C8—32no—
470#216—38no—
471#216—38no—
472#216—38no—
473#216—68no—
474#215—38no—
475#215C22×D318yescomplemented
476#214—38no—
477#214—38no—
478#214—38no—
479#214—38no—
480#214—68no—
481#213—38no—
482#213—38no—
483#213C22×D318yescomplemented
484#208—34no—
485#208—34no—
486#208—38no—
487#208—64no—
488#208C22×D314yescomplemented
489C2×C3⋊C8—32no—
490C2×C3⋊C8—32no—
491C2×C3⋊C8—38no—
492C2×C3⋊C8—62no—
493C2×C3⋊C8C22×D312yes—
494Dic12—38no—
495#204—38no—
496ΓL(1,𝔽25)—38no—
497D3×C8—38no—
498C22×C32—22no—
499C22×C32—22no—
500C22×C32—42no—
501C22×C32C22×D412yes—
502C22×C32C22×D411yescharacteristic
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—48no—
510C2×C3×D3—44no—
511C2×C3×D3—42no—
512C2×C3×D3C22×D412yes—
513C2×C3×D3C22×D412yes—
514C32×C4—22no—
515C32×C4C22×D411yescharacteristic
516C32×C4C22×D412yes—
517C32×C4C2511yescharacteristic
518C3⋊Dic3—24no—
519C3×Dic3—22no—
520C3×Dic3C22×D412yes—
521C3×Dic3C22×D412yes—
522C2×#41—38no—
523C2×#41—31no—
524C2×#41—31no—
525C2×#41—31no—
526C2×#41—61no—
527C2×#41—61no—
528C2×#41—64no—
529C2×#41—92no—
530C2×#41—92no—
531C2×#41—98no—
532C2×#41—181no—
533C2×#41—184no—
534C2×#41—181no—
535C2×#41D3211yescharacteristic
536C22×Q8—31no—
537C22×Q8—91no—
538C22×D4—31no—
539C22×D4—31no—
540C22×D4—61no—
541C22×D4—181no—
542C23×C4—31no—
543C23×C4—61no—
544C23×C4—181no—
545#137—98no—
546#137—916no—
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—92no—
563C2×M16—98no—
564C2×M16—91no—
565C22×C8—92no—
566C23×C3—21no—
567C23×C3—21no—
568C23×C3—21no—
569C23×C3—31no—
570C23×C3—31no—
571C23×C3—34no—
572C23×C3—41no—
573C23×C3—64no—
574C23×C3—61no—
575C23×C3—64no—
576C23×C3—62no—
577C23×C3—122no—
578C23×C3—124no—
579C23×C3—124no—
580C23×C3D3×D411yescharacteristic
581C23×C3C2×#6711yescharacteristic
582C22×D3—22no—
583C22×D3—24no—
584C22×D3—21no—
585C22×D3—24no—
586C22×D3—42no—
587C22×D3—44no—
588C22×D3—44no—
589C22×D3C2×#6711yescharacteristic
590C22×D3C2×#6711yescharacteristic
591C22×D3C2×#6714yes—
592C3×Q8—21no—
593C3×Q8—21no—
594C3×Q8—22no—
595C3×Q8—32no—
596C3×Q8—41no—
597C3×Q8—64no—
598C3×Q8—61no—
599C3×Q8C23×D312yes—
600C3×Q8C23×D312yes—
601C3×D4—24no—
602C3×D4—24no—
603C3×D4—21no—
604C3×D4—21no—
605C3×D4—22no—
606C3×D4—32no—
607C3×D4—34no—
608C3×D4—41no—
609C3×D4—44no—
610C3×D4—64no—
611C3×D4—64no—
612C3×D4—64no—
613C3×D4—64no—
614C3×D4—61no—
615C3×D4—62no—
616C3×D4—64no—
617C3×D4C23×D312yes—
618C3×D4C23×D312yes—
619C2×C3×C4—21no—
620C2×C3×C4—21no—
621C2×C3×C4—24no—
622C2×C3×C4—24no—
623C2×C3×C4—21no—
624C2×C3×C4—22no—
625C2×C3×C4—21no—
626C2×C3×C4—22no—
627C2×C3×C4—31no—
628C2×C3×C4—31no—
629C2×C3×C4—34no—
630C2×C3×C4—34no—
631C2×C3×C4—32no—
632C2×C3×C4—32no—
633C2×C3×C4—34no—
634C2×C3×C4—32no—
635C2×C3×C4—32no—
636C2×C3×C4—44no—
637C2×C3×C4—41no—
638C2×C3×C4—64no—
639C2×C3×C4—64no—
640C2×C3×C4—64no—
641C2×C3×C4—61no—
642C2×C3×C4—64no—
643C2×C3×C4D3×D411yescharacteristic
644C2×C3×C4D3×D412yes—
645C2×C3×C4C2×#6711yescharacteristic
646C2×C3×C4C2×#6712yes—
647C2×C3×C4C23×D311yescharacteristic
648C2×C3×C4C23×D312yes—
649C2×C3×C4C23×D311yescharacteristic
650C2×C3×C4C23×D312yes—
651#67—24no—
652#67—24no—
653#67—24no—
654#67—68no—
655#67—68no—
656#67—68no—
657#67—68no—
658C2×Dic3—21no—
659C2×Dic3—24no—
660C2×Dic3—64no—
661C2×Dic3—62no—
662C2×Dic3—64no—
663C2×Dic3—62no—
664C2×Dic3—68no—
665C2×Dic3—68no—
666C2×Dic3—124no—
667C2×Dic3—122no—
668C2×Dic3C2×#6711yescharacteristic
669C2×Dic3C2×#6711yescharacteristic
670C2×Dic3C2×#6714yes—
671D12—24no—
672D12—22no—
673D12—24no—
674D12—21no—
675D12C23×D312yes—
676D12C23×D314yes—
677C4×D3—24no—
678C4×D3—24no—
679C4×D3—24no—
680C4×D3—68no—
681C4×D3—68no—
682C4×D3C2×#6714yes—
683C4×D3C2×#6714yes—
684C4×D3C2×#6712yes—
685C4×D3C2×#6712yes—
686C4×D3C23×D312yes—
687C4×D3C23×D312yes—
688Dic6—21no—
689Dic6—24no—
690Dic6—34no—
691Dic6—34no—
692Dic6—64no—
693Dic6—64no—
694Dic6—62no—
695Dic6—62no—
696Dic6—64no—
697Dic6—124no—
698Dic6—122no—
699Dic6C23×D312yes—
700C3×C8—34no—
701C3⋊C8—34no—
702C3⋊C8—34no—
703C3⋊C8—64no—
704C3⋊C8C23×D314yes—
705C2×C32—22no—
706C2×C32—42no—
707C2×C32#57512yescomplemented
708C2×C32C23×D411yescharacteristic
709C3×D3—22no—
710C3×D3—22no—
711C3×D3—44no—
712C3×D3—42no—
713C24—31no—
714C24—61no—
715C24—61no—
716#41—22no—
717#41—34no—
718#41—34no—
719#41—34no—
720#41—68no—
721#41—68no—
722#41—62no—
723#41—62no—
724#41—62no—
725#41—98no—
726#41—98no—
727#41—188no—
728#41—184no—
729#41—184no—
730#41—188no—
731#41C2×D3214yes—
732C2×Q8—34no—
733C2×Q8—31no—
734C2×Q8—61no—
735C2×Q8—62no—
736C2×Q8—92no—
737C2×Q8—94no—
738C2×Q8—182no—
739C2×Q8—181no—
740C2×Q8C2×D3211yescharacteristic
741C2×D4—21no—
742C2×D4—34no—
743C2×D4—32no—
744C2×D4—31no—
745C2×D4—34no—
746C2×D4—61no—
747C2×D4—62no—
748C2×D4—61no—
749C2×D4—68no—
750C2×D4—61no—
751C2×D4—61no—
752C2×D4—62no—
753C2×D4—61no—
754C2×D4—188no—
755C2×D4—182no—
756C2×D4—182no—
757C2×D4C2×D3211yescharacteristic
758C22×C4—21no—
759C22×C4—31no—
760C22×C4—31no—
761C22×C4—31no—
762C22×C4—34no—
763C22×C4—31no—
764C22×C4—34no—
765C22×C4—31no—
766C22×C4—61no—
767C22×C4—68no—
768C22×C4—61no—
769C22×C4—61no—
770C22×C4—61no—
771C22×C4—188no—
772C22×C4—182no—
773C22×C4—182no—
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—98no—
786M16—94no—
787C2×C8—32no—
788C2×C8—98no—
789C2×C8—92no—
790C22×C3—22no—
791C22×C3—22no—
792C22×C3—22no—
793C22×C3—22no—
794C22×C3—22no—
795C22×C3—21no—
796C22×C3—32no—
797C22×C3—32no—
798C22×C3—42no—
799C22×C3—42no—
800C22×C3—42no—
801C22×C3—42no—
802C22×C3—62no—
803C22×C3—62no—
804C22×C3—62no—
805C22×C3—64no—
806C22×C3—82no—
807C22×C3—124no—
808C22×C3—128no—
809C22×C3—128no—
810C22×C3—122no—
811C22×C3—124no—
812C22×C3C2×D3×D412yes—
813C22×C3C2×D3×D411yescharacteristic
814C22×C3C22×#6712yes—
815C22×C3C22×#6711yescharacteristic
816C2×D3—22no—
817C2×D3—22no—
818C2×D3—24no—
819C2×D3—22no—
820C2×D3—44no—
821C2×D3—48no—
822C2×D3—48no—
823C2×D3—44no—
824C2×D3—42no—
825C2×D3C22×#6712yes—
826C2×D3C22×#6712yes—
827C3×C4—22no—
828C3×C4—22no—
829C3×C4—22no—
830C3×C4—21no—
831C3×C4—21no—
832C3×C4—32no—
833C3×C4—32no—
834C3×C4—42no—
835C3×C4—62no—
836C3×C4C2×D3×D412yes—
837C3×C4C2×D3×D411yescharacteristic
838C3×C4C22×#6711yescharacteristic
839C3×C4C22×#6712yes—
840C3×C4C24×D311yescharacteristic
841C3×C4C24×D311yescharacteristic
842Dic3—22no—
843Dic3—64no—
844Dic3—64no—
845Dic3—124no—
846Dic3C22×#6712yes—
847Dic3C22×#6712yes—
848C32C2×#57511yescharacteristic, complemented, Sylow
849C23—21no—
850C23—31no—
851C23—31no—
852C23—34no—
853C23—64no—
854C23—64no—
855C23—61no—
856C23—62no—
857C23—122no—
858C23—124no—
859C23—124no—
860C23D3×#6711yescharacteristic
861Q8—21no—
862Q8—32no—
863Q8—64no—
864Q8—61no—
865Q8—94no—
866Q8—184no—
867Q8—182no—
868Q8C22×D3212yes—
869D4—24no—
870D4—21no—
871D4—34no—
872D4—32no—
873D4—64no—
874D4—64no—
875D4—64no—
876D4—64no—
877D4—61no—
878D4—64no—
879D4—62no—
880D4—188no—
881D4—188no—
882D4C22×D3212yes—
883C2×C4—21no—
884C2×C4—24no—
885C2×C4—34no—
886C2×C4—31no—
887C2×C4—31no—
888C2×C4—34no—
889C2×C4—32no—
890C2×C4—32no—
891C2×C4—34no—
892C2×C4—32no—
893C2×C4—32no—
894C2×C4—64no—
895C2×C4—64no—
896C2×C4—64no—
897C2×C4—61no—
898C2×C4—64no—
899C2×C4—188no—
900C2×C4—188no—
901C2×C4—184no—
902C2×C4—182no—
903C2×C4D3×#6712yes—
904C2×C4D3×#6711yescharacteristic
905C2×C4C22×D3212yes—
906C2×C4C22×D3211yescharacteristic
907C8—34no—
908C8—94no—
909C2×C3—22no—
910C2×C3—22no—
911C2×C3—21no—
912C2×C3—22no—
913C2×C3—42no—
914C2×C3—42no—
915C2×C3—42no—
916C2×C3—62no—
917C2×C3—62no—
918C2×C3—82no—
919C2×C3—122no—
920C2×C3—124no—
921C2×C3#577312yescomplemented
922C2×C3#582212yescomplemented
923C2×C3C22×D3×D411yescharacteristic
924C2×C3C23×#6711yescharacteristic
925D3—22no—
926D3—22no—
927D3—44no—
928D3—42no—
929C22—22no—
930C22—22no—
931C22—32no—
932C22—32no—
933C22—42no—
934C22—62no—
935C22—62no—
936C22—62no—
937C22—64no—
938C22—124no—
939C22—128no—
940C22—128no—
941C22—122no—
942C22—124no—
943C22C2×D3×#6712yes—
944C22C2×D3×#6711yescharacteristic
945C4—22no—
946C4—32no—
947C4—32no—
948C4—62no—
949C4—184no—
950C4C2×D3×#6712yes—
951C4C2×D3×#6711yescharacteristic
952C4C23×D3211yescharacteristic
953C3—21no—
954C3C2×#577311yescharacteristic, complemented
955C3C2×#582211yescharacteristic, complemented
956C2—22no—
957C2—42no—
958C2—62no—
959C2—62no—
960C2—122no—
961C2—124no—
962C2#1059546912yesdirect product factor
963C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32C2×#575
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×#41C2semidirect
2. C22×#3795C2semidirect
3. C2×#64160C2semidirect
4. C2×C3×#949C2semidirect
5. #10595469C2direct (N × H)
6. C2×#63947C2semidirect
7. C2×#63946C2semidirect
8. C2×#63933C2semidirect
9. C2×#63932C2semidirect
10. C2×#63831C2semidirect
11. C2×#63823C2semidirect
12. C2×D3×#208C2semidirect
16. C22×#634C22semidirect
18. C3×D3×#41C22semidirect
19. C2×C3×#239C22semidirect
20. C2×C3×D3×Q8C22semidirect
22. C2×C3×#237C22semidirect
24. C2×C3×D3×D4C22semidirect
27. C22×C3×D12C22semidirect
36. C2×#3795C22semidirect
37. C2×#3795C22semidirect
38. #64160C22semidirect
39. C2×#3756C22semidirect
40. C2×#3754C22semidirect
41. C2×#3748C22semidirect
42. C3×#949C22semidirect
43. C2×C3×#215C22semidirect
44. C2×C3×#213C22semidirect
45. C2×C3×#208C22semidirect
46. #63947C22semidirect
47. #63946C22semidirect
48. #63933C22semidirect
49. #63932C22semidirect
50. C2×#3719C22semidirect
51. #63831C22semidirect
52. C2×#3716C22semidirect
53. C2×#3715C22semidirect
54. #63823C22semidirect
55. C2×#3713C22semidirect
56. C2×#3711C22semidirect
57. D3×#208C22semidirect
58. C2×D3×C3⋊C8C22semidirect
60. C2×D3×#41D3semidirect
72. C2×#949D3semidirect
98. C2×#634C23semidirect
105. C3×#239C23semidirect
107. C3×D3×Q8C23semidirect
110. C3×#237C23semidirect
113. C3×D3×D4C23semidirect
122. C2×C3×D12C23semidirect
146. #3795C23semidirect
147. #3756C23semidirect
148. #3754C23semidirect
149. #3748C23semidirect
151. C3×#215C23semidirect
152. C3×#213C23semidirect
153. C3×#208C23semidirect
155. #3719C23semidirect
156. #3716C23semidirect
157. #3715C23semidirect
158. #3713C23semidirect
159. #3711C23semidirect
160. D3×C3⋊C8C23semidirect
182. D3×#41C2×D3semidirect
183. C2×#239C2×D3semidirect
184. C2×D3×Q8C2×D3semidirect
192. C2×#237C2×D3semidirect
194. C2×D3×D4C2×D3semidirect
203. C22×D12C2×D3semidirect
221. #949C2×D3semidirect
228. C2×#215C2×D3semidirect
238. C2×#213C2×D3semidirect
244. C2×#208C2×D3semidirect
409. #239C22×D3semidirect
411. D3×Q8C22×D3semidirect
420. #237C22×D3semidirect
423. D3×D4C22×D3semidirect
438. C2×D12C22×D3semidirect
475. #215C22×D3semidirect
483. #213C22×D3semidirect
488. #208C22×D3semidirect
707. C2×C32#575semidirect
848. C32C2×#575semidirect
921. C2×C3#5773semidirect
922. C2×C3#5822semidirect
954. C3C2×#5773semidirect
955. C3C2×#5822semidirect
962. C2#10595469direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D3×#412
C22×#37952
C2×#641602
C2×C3×#9492
#105954692
C2×#639472
C2×#639462
C2×#639332
C2×#639322
C2×#638312
C2×#638232
C2×D3×#2082
C2×#58223
C2×#57733