Finite Group Databasebeta

← C2×#10595095 #11918760

Subgroups — C2×#10595095 #11918760

Order 1152.

3117 conjugacy classes of subgroups.

The subgroup lattice has 969 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#237C211yesmaximal, characteristic, complemented
2C2×D3×#235C211yesmaximal, characteristic, complemented
3C2×#64141C211yesmaximal, characteristic, complemented
4C2×C3×#932C211yesmaximal, characteristic, complemented
5C2×#63935C212yesmaximal, complemented
6C2×#63933C212yesmaximal, complemented
7C2×#63929C212yesmaximal, complemented
8#10595095C2116yesmaximal, direct product factor
9C2×#63925C212yesmaximal, complemented
10C2×#63833C211yesmaximal, characteristic, complemented
11C2×#63827C211yesmaximal, characteristic, complemented
12C2×D3×#208C211yesmaximal, characteristic, complemented
13C2×#5822—31nomaximal
14C2×#5773—31nomaximal
15C22×C32×D4C2211yescharacteristic, complemented
16C2×#3828C2211yescharacteristic
17C22×C3×#67—21no—
18C23×C3×Dic3—21no—
19C2×C3×#237—21no—
20C2×C3×#237—21no—
21C2×C3×#237—24no—
22C2×C3×#237C2212yes—
23C2×C3×#237C2212yescomplemented
24C2×C3×#237C2218yescomplemented
25C2×C3×#235C2211yescharacteristic
26C22×C3×C4×D3C2211yescharacteristic
27C22×C3×Dic6C2211yescharacteristic, complemented
28C2×D3×#67—21no—
29C2×#3804—21no—
30D3×#235—24no—
31D3×#235C2218yescomplemented
32C2×D3×D12C2211yescharacteristic, complemented
33C2×C4×D32—21no—
34C2×#3799C2211yescharacteristic, complemented
35C2×#3798—21no—
36C2×#3795C2211yescharacteristic, complemented
37C2×D3×Dic6C2211yescharacteristic, complemented
38C2×#3754C2212yescomplemented
39#64141C2218yescomplemented
40C2×#3753C2212yescomplemented
41C2×#3748C2211yescharacteristic, complemented
42C2×C3×#214C2212yescomplemented
43C3×#932C2218yescomplemented
44C2×C3×#213C2212yescomplemented
45C2×C3×#208C2211yescharacteristic, complemented
46#63935C22116yescomplemented
47#63933C22116yescomplemented
48#63929C22116yescomplemented
49#63925C22116yescomplemented
50C2×#3719C2212yescomplemented
51C2×#3718C2212yescomplemented
52#63833C2218yescomplemented
53C2×#3717C2212yescomplemented
54#63827C2218yescomplemented
55C2×#3715C2212yescomplemented
56C2×#3711C2212yescomplemented
57D3×#208C2218yescomplemented
58C2×D3×C3⋊C8C2212yescomplemented
59C22×C3×#41—31no—
60C2×D3×#41—31no—
61C22×#237D311yescharacteristic, complemented
62C22×#235—31no—
63C2×C3×AGL(1,ℤ/8)—31no—
64C2×#951—31no—
65C2×#951—32no—
66#5822—316no—
67C2×#950—32no—
68C2×#950—32no—
69C2×#949—32no—
70C2×#942—31no—
71C2×#942—31no—
72C2×#932—31no—
73C2×#932—31no—
74C2×#932—61no—
75C2×#932D311yescharacteristic, complemented
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—
84C24×C32—21no—
85C23×C3×D3D411yescharacteristic
86C22×D32—21no—
87C2×C32×D4—21no—
88C2×C32×D4—22no—
89C2×C32×D4C2312yes—
90C2×C32×D4C2314yescomplemented
91C22×C32×C4C2311yescharacteristic
92C2×#638—21no—
93#3828—22no—
94#3828C2314yes—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4×C3⋊D3—21no—
97C2×#634C2311yescharacteristic
98C2×C3×#67—21no—
99C2×C3×#67—22no—
100C2×C3×#67—22no—
101C2×C3×#67—28no—
102C22×C3×Dic3—21no—
103C22×C3×Dic3—22no—
104C22×C3×Dic3—22no—
105C22×C3×Dic3—28no—
106C22×C3×Dic3D411yescharacteristic
107C3×#237—24no—
108C3×#237—24no—
109C3×#237—28no—
110C3×#237—28no—
111C3×#237C2318yes—
112C3×#237C2318yescomplemented
113C3×#235—22no—
114C3×#235C2314yes—
115C2×C3×D12C2311yescharacteristic
116C2×C3×C4×D3—21no—
117C2×C3×C4×D3D411yescharacteristic
118C2×C3×C4×D3D411yescharacteristic
119C2×C3×C4×D3D414yes—
120C2×C3×C4×D3C2311yescharacteristic
121C2×C3×C4×D3C2311yescharacteristic
122C2×C3×C4×D3C2314yes—
123C2×C3×Dic6—22no—
124C2×C3×Dic6—21no—
125C2×C3×Dic6C2311yescharacteristic
126C2×C3×Dic6C2312yes—
127C2×C3×Dic6C2314yescomplemented
128D3×#67—28no—
129C2×#627—21no—
130C2×#626—21no—
131C2×#626—21no—
132C2×#625—21no—
133C2×#624—21no—
134#3804—28no—
135C2×D3×Dic3—21no—
136C2×D3×Dic3—21no—
137D3×D12—22no—
138D3×D12C2314yescomplemented
139C4×D32—28no—
140#3799—22no—
141#3799C2314yescomplemented
142#3798—28no—
143#3795—22no—
144#3795C2314yescomplemented
145D3×Dic6—22no—
146D3×Dic6C2314yescomplemented
147#3754C2318yescomplemented
148#3753C2318yescomplemented
149#3748C2314yescomplemented
150C2×C3⋊(C3⋊C8)C2312yes—
151C3×#214C2318yescomplemented
152C3×#213C2318yescomplemented
153C3×#208C2314yescomplemented
154C2×C3×C3⋊C8C2312yes—
155#3719C2318yescomplemented
156#3718C2318yescomplemented
157#3717C2318yescomplemented
158#3715C2318yescomplemented
159#3711C2318yescomplemented
160D3×C3⋊C8C2318yescomplemented
161C2×#575—91noSylow
162C2×C3×#41—32no—
163C2×C3×#41—32no—
164C2×C3×#41—38no—
165C2×C3×#41—31no—
166C2×C3×#41—61no—
167C2×C3×#41—61no—
168C2×C3×#41—64no—
169C22×C3×Q8—31no—
170C22×C3×D4—21no—
171C22×C3×D4—61no—
172C22×C3×D4C2×D311yescharacteristic, complemented
173C22×C3×D4C2×D311yescharacteristic, complemented
174C23×C3×C4—31no—
175C23×C3×C4—61no—
176C22×#67—21no—
177C22×#67—61no—
178C23×Dic3—21no—
179D3×#41—38no—
180D3×#41—64no—
181C2×#239—31no—
182C2×D3×Q8—31no—
183C2×#237—21no—
184C2×#237—21no—
185C2×#237—24no—
186C2×#237—31no—
187C2×#237—61no—
188C2×#237C2×D312yes—
189C2×#237C2×D312yescomplemented
190C2×#237C2×D318yescomplemented
191C2×D3×D4—31no—
192C2×D3×D4—61no—
193C2×#235—31no—
194C2×#235—31no—
195C2×#235—38no—
196C2×#235—31no—
197C2×#235—31no—
198C2×#235—61no—
199C2×#235—61no—
200C2×#235—64no—
201C2×#235—61no—
202C2×#235—61no—
203C2×#235C2×D311yescharacteristic
204C22×D12—31no—
205C22×C4×D3—61no—
206C22×C4×D3—61no—
207C22×C4×D3C2×D311yescharacteristic
208C22×Dic6—31no—
209C22×Dic6C2×D311yescharacteristic, complemented
210C3×AGL(1,ℤ/8)—38no—
211C2×C3×SD16—32no—
212C2×C3×D8—32no—
213C2×C3×M16—31no—
214#951—38no—
215#951—316no—
216#950—316no—
217#950—316no—
218#949—316no—
219C2×#216—32no—
220C2×#216—32no—
221C2×#216—32no—
222#942—38no—
223#942—38no—
224C2×#215—32no—
225C2×#215—32no—
226C2×#214—32no—
227C2×#214—32no—
228C2×#214—32no—
229C2×#214—62no—
230C2×#214C2×D312yescomplemented
231#932—38no—
232#932—38no—
233#932—68no—
234#932C2×D318yescomplemented
235C2×#213—32no—
236C2×#213—32no—
237C2×#213—62no—
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—22no—
257C23×C32—24no—
258C23×C32—44no—
259C23×C32C2×D411yescharacteristic
260C22×C3⋊D3—21no—
261C22×C3×D3—21no—
262C22×C3×D3—42no—
263C22×C3×D3C2×D411yescharacteristic
264C22×C3×D3C2×D411yescharacteristic
265C22×C3×D3C2×D414yes—
266C2×D32—24no—
267C2×D32—44no—
268C32×D4—22no—
269C32×D4—24no—
270C32×D4C2414yes—
271C2×C32×C4C2×D411yescharacteristic
272C2×C32×C4C2×D412yes—
273C2×C32×C4C2411yescharacteristic
274C2×C32×C4C2412yes—
275#638—24no—
276C2×C3⋊Dic3—21no—
277C4⋊(C3⋊D3)—21no—
278C4⋊(C3⋊D3)C2412yes—
279C4×C3⋊D3—24no—
280#634—21no—
281#634C2412yes—
282C3×#67—24no—
283C3×#67—28no—
284C3×#67—28no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—22no—
287C2×C3×Dic3—24no—
288C2×C3×Dic3—28no—
289C2×C3×Dic3—28no—
290C2×C3×Dic3C2×D411yescharacteristic
291C2×C3×Dic3C2×D414yes—
292C2×C3×Dic3C2×D411yescharacteristic
293C3×D12—21no—
294C3×D12C2412yes—
295C3×C4×D3—24no—
296C3×C4×D3C2×D412yes—
297C3×C4×D3C2×D412yes—
298C3×C4×D3C2×D414yes—
299C3×C4×D3C2×D414yes—
300C3×C4×D3C2412yes—
301C3×C4×D3C2412yes—
302C3×Dic6—21no—
303C3×Dic6—22no—
304C3×Dic6—24no—
305C3×Dic6C2414yes—
306C3×Dic6C2412yes—
307#627—24no—
308#626—24no—
309#626—24no—
310#625—24no—
311#624—24no—
312D3×Dic3—24no—
313D3×Dic3—24no—
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—21no—
329C24×C3—21no—
330C24×C3—31no—
331C24×C3—41no—
332C23×D3—61no—
333C23×D3—61no—
334C23×D3#6711yescharacteristic
335C3×#41—38no—
336C3×#41—38no—
337C3×#41—34no—
338C3×#41—64no—
339C3×#41—68no—
340C3×#41—64no—
341C3×#41—68no—
342C3×#41—62no—
343C2×C3×Q8—32no—
344C2×C3×Q8—34no—
345C2×C3×Q8—31no—
346C2×C3×Q8—61no—
347C2×C3×Q8—62no—
348C2×C3×D4—21no—
349C2×C3×D4—22no—
350C2×C3×D4—21no—
351C2×C3×D4—22no—
352C2×C3×D4—22no—
353C2×C3×D4—24no—
354C2×C3×D4—31no—
355C2×C3×D4—41no—
356C2×C3×D4—42no—
357C2×C3×D4—62no—
358C2×C3×D4—62no—
359C2×C3×D4—68no—
360C2×C3×D4—61no—
361C2×C3×D4C22×D312yes—
362C2×C3×D4C22×D312yes—
363C2×C3×D4C22×D314yescomplemented
364C2×C3×D4C22×D314yescomplemented
365C22×C3×C4—21no—
366C22×C3×C4—31no—
367C22×C3×C4—31no—
368C22×C3×C4—31no—
369C22×C3×C4—34no—
370C22×C3×C4—31no—
371C22×C3×C4—31no—
372C22×C3×C4—34no—
373C22×C3×C4—62no—
374C22×C3×C4—62no—
375C22×C3×C4—68no—
376C22×C3×C4—61no—
377C22×C3×C4—61no—
378C22×C3×C4C22×D311yescharacteristic
379C22×C3×C4C22×D311yescharacteristic
380C2×#67—21no—
381C2×#67—22no—
382C2×#67—22no—
383C2×#67—28no—
384C2×#67—61no—
385C2×#67—68no—
386C2×#67—61no—
387C2×#67—61no—
388C2×#67—61no—
389C2×#67—61no—
390C2×#67—61no—
391C2×#67—121no—
392C22×Dic3—21no—
393C22×Dic3—22no—
394C22×Dic3—22no—
395C22×Dic3—28no—
396C22×Dic3—61no—
397C22×Dic3—61no—
398C22×Dic3#6711yescharacteristic
399#239—34no—
400#239—62no—
401D3×Q8—34no—
402D3×Q8—62no—
403#237—24no—
404#237—24no—
405#237—28no—
406#237—28no—
407#237—34no—
408#237—68no—
409#237—62no—
410#237C22×D318yes—
411#237C22×D318yescomplemented
412D3×D4—34no—
413D3×D4—68no—
414D3×D4—62no—
415#235—22no—
416#235—34no—
417#235—34no—
418#235—34no—
419#235—34no—
420#235—64no—
421#235—62no—
422#235—68no—
423#235—62no—
424#235—68no—
425#235—62no—
426#235—62no—
427#235—68no—
428#235—122no—
429#235C22×D314yes—
430C2×D12—31no—
431C2×D12—31no—
432C2×D12—34no—
433C2×D12—61no—
434C2×D12—62no—
435C2×D12—61no—
436C2×D12—61no—
437C2×D12C22×D311yescharacteristic
438C2×C4×D3—21no—
439C2×C4×D3—68no—
440C2×C4×D3—61no—
441C2×C4×D3—61no—
442C2×C4×D3—61no—
443C2×C4×D3—61no—
444C2×C4×D3—61no—
445C2×C4×D3—61no—
446C2×C4×D3—68no—
447C2×C4×D3—121no—
448C2×C4×D3#6711yescharacteristic
449C2×C4×D3#6711yescharacteristic
450C2×C4×D3#6714yes—
451C2×C4×D3C22×D311yescharacteristic
452C2×C4×D3C22×D311yescharacteristic
453C2×C4×D3C22×D314yes—
454C2×Dic6—22no—
455C2×Dic6—21no—
456C2×Dic6—31no—
457C2×Dic6—31no—
458C2×Dic6—34no—
459C2×Dic6—61no—
460C2×Dic6—62no—
461C2×Dic6—61no—
462C2×Dic6—61no—
463C2×Dic6C22×D312yes—
464C2×Dic6C22×D311yescharacteristic
465C2×Dic6C22×D314yescomplemented
466C3×SD16—38no—
467C3×D8—38no—
468C3×M16—34no—
469C2×C3×C8—32no—
470#216—38no—
471#216—38no—
472#216—38no—
473#215—38no—
474#215—38no—
475#214—38no—
476#214—38no—
477#214—38no—
478#214—68no—
479#214C22×D318yescomplemented
480#213—38no—
481#213—38no—
482#213—68no—
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—24no—
500C22×C32—48no—
501C22×C32—44no—
502C22×C32C22×D412yes—
503C22×C32C22×D411yescharacteristic
504C2×C3⋊D3—22no—
505C2×C3⋊D3—42no—
506C2×C3×D3—22no—
507C2×C3×D3—22no—
508C2×C3×D3—22no—
509C2×C3×D3—44no—
510C2×C3×D3—42no—
511C2×C3×D3C22×D412yes—
512C2×C3×D3C22×D412yes—
513D32—48no—
514C32×C4C22×D411yescharacteristic
515C32×C4C22×D412yes—
516C32×C4C2511yescharacteristic
517C3⋊Dic3—22no—
518C3×Dic3—22no—
519C3×Dic3—24no—
520C3×Dic3C22×D412yes—
521C3×Dic3C22×D412yes—
522C2×#41—32no—
523C2×#41—32no—
524C2×#41—38no—
525C2×#41—31no—
526C2×#41—61no—
527C2×#41—64no—
528C2×#41—61no—
529C2×#41—91no—
530C2×#41—91no—
531C2×#41—98no—
532C2×#41—91no—
533C2×#41—181no—
534C2×#41—181no—
535C2×#41—184no—
536C22×Q8—31no—
537C22×Q8—91no—
538C22×D4—61no—
539C22×D4—91no—
540C22×D4—181no—
541C22×D4D3211yescharacteristic, complemented
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—22no—
567C23×C3—24no—
568C23×C3—22no—
569C23×C3—24no—
570C23×C3—21no—
571C23×C3—31no—
572C23×C3—31no—
573C23×C3—34no—
574C23×C3—44no—
575C23×C3—42no—
576C23×C3—44no—
577C23×C3—44no—
578C23×C3—61no—
579C23×C3—84no—
580C23×C3—122no—
581C23×C3D3×D411yescharacteristic
582C23×C3C2×#6711yescharacteristic
583C22×D3—21no—
584C22×D3—42no—
585C22×D3—64no—
586C22×D3—61no—
587C22×D3—61no—
588C22×D3—64no—
589C22×D3—121no—
590C22×D3—124no—
591C22×D3—124no—
592C22×D3C2×#6711yescharacteristic
593C22×D3C2×#6711yescharacteristic
594C22×D3C2×#6714yes—
595C3×Q8—34no—
596C3×Q8—32no—
597C3×Q8—62no—
598C3×Q8—64no—
599C3×Q8—61no—
600C3×D4—22no—
601C3×D4—24no—
602C3×D4—22no—
603C3×D4—24no—
604C3×D4—24no—
605C3×D4—32no—
606C3×D4—42no—
607C3×D4—44no—
608C3×D4—68no—
609C3×D4—68no—
610C3×D4—64no—
611C3×D4—61no—
612C3×D4C23×D314yes—
613C3×D4C23×D314yes—
614C2×C3×C4—21no—
615C2×C3×C4—22no—
616C2×C3×C4—21no—
617C2×C3×C4—22no—
618C2×C3×C4—31no—
619C2×C3×C4—31no—
620C2×C3×C4—34no—
621C2×C3×C4—32no—
622C2×C3×C4—34no—
623C2×C3×C4—34no—
624C2×C3×C4—32no—
625C2×C3×C4—32no—
626C2×C3×C4—32no—
627C2×C3×C4—68no—
628C2×C3×C4—68no—
629C2×C3×C4—64no—
630C2×C3×C4—62no—
631C2×C3×C4—61no—
632C2×C3×C4—64no—
633C2×C3×C4D3×D411yescharacteristic
634C2×C3×C4D3×D412yes—
635C2×C3×C4C2×#6711yescharacteristic
636C2×C3×C4C2×#6712yes—
637C2×C3×C4C23×D311yescharacteristic
638C2×C3×C4C23×D312yes—
639C2×C3×C4C23×D311yescharacteristic
640C2×C3×C4C23×D312yes—
641#67—24no—
642#67—28no—
643#67—28no—
644#67—64no—
645#67—64no—
646#67—64no—
647#67—64no—
648#67—64no—
649#67—64no—
650#67—124no—
651C2×Dic3—21no—
652C2×Dic3—22no—
653C2×Dic3—24no—
654C2×Dic3—28no—
655C2×Dic3—28no—
656C2×Dic3—64no—
657C2×Dic3—61no—
658C2×Dic3—61no—
659C2×Dic3—64no—
660C2×Dic3—121no—
661C2×Dic3C2×#6711yescharacteristic
662C2×Dic3C2×#6711yescharacteristic
663C2×Dic3C2×#6714yes—
664D12—21no—
665D12—32no—
666D12—32no—
667D12—62no—
668D12—64no—
669D12—64no—
670D12—61no—
671D12—61no—
672D12—121no—
673D12C23×D312yes—
674C4×D3—24no—
675C4×D3—64no—
676C4×D3—64no—
677C4×D3—64no—
678C4×D3—64no—
679C4×D3—64no—
680C4×D3—64no—
681C4×D3—124no—
682C4×D3C2×#6714yes—
683C4×D3C2×#6714yes—
684C4×D3C2×#6712yes—
685C4×D3C2×#6712yes—
686C4×D3C23×D312yes—
687C4×D3C23×D312yes—
688Dic6—21no—
689Dic6—22no—
690Dic6—24no—
691Dic6—32no—
692Dic6—32no—
693Dic6—62no—
694Dic6—64no—
695Dic6—61no—
696Dic6—61no—
697Dic6—64no—
698Dic6—121no—
699Dic6C23×D314yes—
700Dic6C23×D312yes—
701C3×C8—34no—
702C3⋊C8—34no—
703C3⋊C8—34no—
704C3⋊C8—64no—
705C3⋊C8C23×D314yes—
706C2×C32—22no—
707C2×C32—44no—
708C2×C32#57512yescomplemented
709C2×C32C23×D411yescharacteristic
710C3⋊D3—42no—
711C3×D3—22no—
712C3×D3—22no—
713C3×D3—42no—
714C24—21no—
715C24—31no—
716C24—181no—
717#41—38no—
718#41—38no—
719#41—34no—
720#41—68no—
721#41—64no—
722#41—64no—
723#41—68no—
724#41—62no—
725#41—94no—
726#41—94no—
727#41—94no—
728#41—188no—
729#41—188no—
730#41—182no—
731#41—182no—
732#41—182no—
733C2×Q8—31no—
734C2×Q8—32no—
735C2×Q8—34no—
736C2×Q8—62no—
737C2×Q8—61no—
738C2×Q8—94no—
739C2×Q8—91no—
740C2×Q8—181no—
741C2×Q8—182no—
742C2×D4—22no—
743C2×D4—21no—
744C2×D4—31no—
745C2×D4—68no—
746C2×D4—62no—
747C2×D4—62no—
748C2×D4—61no—
749C2×D4—94no—
750C2×D4—91no—
751C2×D4—182no—
752C2×D4—181no—
753C2×D4—181no—
754C2×D4—188no—
755C2×D4—181no—
756C2×D4—181no—
757C2×D4C2×D3212yes—
758C2×D4C2×D3214yescomplemented
759C22×C4—31no—
760C22×C4—31no—
761C22×C4—31no—
762C22×C4—34no—
763C22×C4—31no—
764C22×C4—34no—
765C22×C4—31no—
766C22×C4—68no—
767C22×C4—62no—
768C22×C4—62no—
769C22×C4—61no—
770C22×C4—61no—
771C22×C4—181no—
772C22×C4—188no—
773C22×C4—181no—
774C22×C4—181no—
775C22×C4—181no—
776C22×C4C2×D3211yescharacteristic
777Q16—98no—
778Q16—98no—
779SD16—38no—
780SD16—98no—
781SD16—98no—
782SD16—98no—
783D8—38no—
784D8—98no—
785M16—34no—
786M16—98no—
787M16—94no—
788C2×C8—32no—
789C2×C8—98no—
790C2×C8—92no—
791C22×C3—22no—
792C22×C3—22no—
793C22×C3—24no—
794C22×C3—24no—
795C22×C3—22no—
796C22×C3—21no—
797C22×C3—32no—
798C22×C3—32no—
799C22×C3—42no—
800C22×C3—44no—
801C22×C3—48no—
802C22×C3—48no—
803C22×C3—44no—
804C22×C3—44no—
805C22×C3—62no—
806C22×C3—62no—
807C22×C3—62no—
808C22×C3—84no—
809C22×C3—88no—
810C22×C3—124no—
811C22×C3—122no—
812C22×C3C2×D3×D412yes—
813C22×C3C2×D3×D411yescharacteristic
814C22×C3C22×#6712yes—
815C22×C3C22×#6711yescharacteristic
816C2×D3—22no—
817C2×D3—22no—
818C2×D3—22no—
819C2×D3—44no—
820C2×D3—42no—
821C2×D3—62no—
822C2×D3—62no—
823C2×D3—122no—
824C2×D3—128no—
825C2×D3—128no—
826C2×D3—122no—
827C2×D3—122no—
828C2×D3—242no—
829C2×D3C22×#6712yes—
830C2×D3C22×#6712yes—
831C3×C4—21no—
832C3×C4—22no—
833C3×C4—21no—
834C3×C4—32no—
835C3×C4—32no—
836C3×C4—64no—
837C3×C4—62no—
838C3×C4C2×D3×D411yescharacteristic
839C3×C4C2×D3×D412yes—
840C3×C4C22×#6711yescharacteristic
841C3×C4C22×#6712yes—
842C3×C4C24×D311yescharacteristic
843C3×C4C24×D311yescharacteristic
844Dic3—22no—
845Dic3—24no—
846Dic3—62no—
847Dic3—62no—
848Dic3—122no—
849Dic3C22×#6712yes—
850Dic3C22×#6712yes—
851C32C2×#57511yescharacteristic, complemented, Sylow
852C23—24no—
853C23—22no—
854C23—31no—
855C23—31no—
856C23—34no—
857C23—44no—
858C23—61no—
859C23—122no—
860C23—184no—
861C23—181no—
862C23—364no—
863C23D3×#6711yescharacteristic
864Q8—32no—
865Q8—34no—
866Q8—64no—
867Q8—62no—
868Q8—61no—
869Q8—92no—
870Q8—184no—
871Q8—181no—
872D4—22no—
873D4—24no—
874D4—32no—
875D4—68no—
876D4—68no—
877D4—64no—
878D4—61no—
879D4—92no—
880D4—184no—
881D4—184no—
882D4—184no—
883D4—184no—
884D4—181no—
885D4C22×D3214yes—
886C2×C4—34no—
887C2×C4—31no—
888C2×C4—31no—
889C2×C4—34no—
890C2×C4—32no—
891C2×C4—32no—
892C2×C4—34no—
893C2×C4—32no—
894C2×C4—32no—
895C2×C4—68no—
896C2×C4—68no—
897C2×C4—64no—
898C2×C4—62no—
899C2×C4—61no—
900C2×C4—64no—
901C2×C4—184no—
902C2×C4—184no—
903C2×C4—184no—
904C2×C4—181no—
905C2×C4—184no—
906C2×C4D3×#6712yes—
907C2×C4D3×#6711yescharacteristic
908C2×C4C22×D3212yes—
909C2×C4C22×D3211yescharacteristic
910C8—34no—
911C8—94no—
912C2×C3—22no—
913C2×C3—22no—
914C2×C3—22no—
915C2×C3—21no—
916C2×C3—42no—
917C2×C3—44no—
918C2×C3—44no—
919C2×C3—62no—
920C2×C3—62no—
921C2×C3—84no—
922C2×C3—122no—
923C2×C3#577312yescomplemented
924C2×C3#582212yescomplemented
925C2×C3C22×D3×D411yescharacteristic
926C2×C3C23×#6711yescharacteristic
927D3—22no—
928D3—22no—
929D3—42no—
930D3—122no—
931D3—122no—
932D3—242no—
933C22—22no—
934C22—24no—
935C22—32no—
936C22—32no—
937C22—48no—
938C22—44no—
939C22—62no—
940C22—62no—
941C22—62no—
942C22—124no—
943C22—122no—
944C22—182no—
945C22—368no—
946C22—362no—
947C22C2×D3×#6712yes—
948C22C2×D3×#6711yescharacteristic
949C4—32no—
950C4—32no—
951C4—64no—
952C4—62no—
953C4—182no—
954C4C2×D3×#6712yes—
955C4C2×D3×#6711yescharacteristic
956C4C23×D3211yescharacteristic
957C3—21no—
958C3C2×#577311yescharacteristic, complemented
959C3C2×#582211yescharacteristic, complemented
960C2—22no—
961C2—44no—
962C2—62no—
963C2—62no—
964C2—122no—
965C2—362no—
966C2#1059509512yesdirect product factor
967C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32C2×#575
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×C3×#237C2semidirect
2. C2×D3×#235C2semidirect
3. C2×#64141C2semidirect
4. C2×C3×#932C2semidirect
5. C2×#63935C2semidirect
6. C2×#63933C2semidirect
7. C2×#63929C2semidirect
8. #10595095C2direct (N × H)
9. C2×#63925C2semidirect
10. C2×#63833C2semidirect
11. C2×#63827C2semidirect
12. C2×D3×#208C2semidirect
15. C22×C32×D4C22semidirect
23. C2×C3×#237C22semidirect
24. C2×C3×#237C22semidirect
27. C22×C3×Dic6C22semidirect
31. D3×#235C22semidirect
32. C2×D3×D12C22semidirect
34. C2×#3799C22semidirect
36. C2×#3795C22semidirect
37. C2×D3×Dic6C22semidirect
38. C2×#3754C22semidirect
39. #64141C22semidirect
40. C2×#3753C22semidirect
41. C2×#3748C22semidirect
42. C2×C3×#214C22semidirect
43. C3×#932C22semidirect
44. C2×C3×#213C22semidirect
45. C2×C3×#208C22semidirect
46. #63935C22semidirect
47. #63933C22semidirect
48. #63929C22semidirect
49. #63925C22semidirect
50. C2×#3719C22semidirect
51. C2×#3718C22semidirect
52. #63833C22semidirect
53. C2×#3717C22semidirect
54. #63827C22semidirect
55. C2×#3715C22semidirect
56. C2×#3711C22semidirect
57. D3×#208C22semidirect
58. C2×D3×C3⋊C8C22semidirect
61. C22×#237D3semidirect
75. C2×#932D3semidirect
90. C2×C32×D4C23semidirect
112. C3×#237C23semidirect
127. C2×C3×Dic6C23semidirect
138. D3×D12C23semidirect
141. #3799C23semidirect
144. #3795C23semidirect
146. D3×Dic6C23semidirect
147. #3754C23semidirect
148. #3753C23semidirect
149. #3748C23semidirect
151. C3×#214C23semidirect
152. C3×#213C23semidirect
153. C3×#208C23semidirect
155. #3719C23semidirect
156. #3718C23semidirect
157. #3717C23semidirect
158. #3715C23semidirect
159. #3711C23semidirect
160. D3×C3⋊C8C23semidirect
172. C22×C3×D4C2×D3semidirect
173. C22×C3×D4C2×D3semidirect
189. C2×#237C2×D3semidirect
190. C2×#237C2×D3semidirect
209. C22×Dic6C2×D3semidirect
230. C2×#214C2×D3semidirect
234. #932C2×D3semidirect
238. C2×#213C2×D3semidirect
244. C2×#208C2×D3semidirect
363. C2×C3×D4C22×D3semidirect
364. C2×C3×D4C22×D3semidirect
411. #237C22×D3semidirect
465. C2×Dic6C22×D3semidirect
479. #214C22×D3semidirect
483. #213C22×D3semidirect
488. #208C22×D3semidirect
541. C22×D4D32semidirect
708. C2×C32#575semidirect
758. C2×D4C2×D32semidirect
851. C32C2×#575semidirect
923. C2×C3#5773semidirect
924. C2×C3#5822semidirect
958. C3C2×#5773semidirect
959. C3C2×#5822semidirect
966. C2#10595095direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2372
C2×D3×#2352
C2×#641412
C2×C3×#9322
C2×#639352
C2×#639332
C2×#639292
#105950952
C2×#639252
C2×#638332
C2×#638272
C2×D3×#2082
C2×#58223
C2×#57733