Finite Group Databasebeta

← C2×#10595471 #11918758

Subgroups — C2×#10595471 #11918758

Order 1152.

3413 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×C3⋊D3C211yesmaximal, characteristic, complemented
2C22×#3796C211yesmaximal, characteristic, complemented
3C2×C3×#951C211yesmaximal, characteristic, complemented
4C2×C3×#949C211yesmaximal, characteristic, complemented
5#10595471C2116yesmaximal, direct product factor
6C2×#63951C212yesmaximal, complemented
7C2×#63950C212yesmaximal, complemented
8C2×#63937C212yesmaximal, complemented
9C2×#63936C212yesmaximal, complemented
10C2×#63833C211yesmaximal, characteristic, complemented
11C2×#63830C211yesmaximal, characteristic, complemented
12C2×#63818C211yesmaximal, characteristic, complemented
13C2×#5777—31nomaximal
14C2×#5773—31nomaximal
15C2×C32×#41C2211yescharacteristic
16#41×C3⋊D3—24no—
17#41×C3⋊D3C2218yescomplemented
18C2×#3832C2211yescharacteristic, complemented
19C2×Q8×C3⋊D3C2211yescharacteristic, complemented
20C2×#3830—21no—
21C2×#3830C2211yescharacteristic, complemented
22C2×D4×C3⋊D3—21no—
23C2×D4×C3⋊D3C2211yescharacteristic, complemented
24C2×#3828—21no—
25C2×#3828C2211yescharacteristic
26C22×C4×C3⋊D3—21no—
27C22×C4×C3⋊D3C2211yescharacteristic
28C22×C3×D12C2211yescharacteristic, complemented
29C22×C3×Dic6C2211yescharacteristic, complemented
30C22×#626—21no—
31C22×D3×Dic3—21no—
32C2×#3796—24no—
33C2×#3796—21no—
34C2×#3796—21no—
35C2×#3796C2212yes—
36C2×#3796C2218yescomplemented
37C2×#3796C2212yescomplemented
38C3×#951C2218yescomplemented
39C3×#949C2218yescomplemented
40C2×C3×#216C2212yescomplemented
41C2×C3×#215C2212yescomplemented
42C2×C3×#214C2212yescomplemented
43C2×C3×#213C2212yescomplemented
44C2×C3×#208C2211yescharacteristic, complemented
45C2×C3×#208C2211yescharacteristic, complemented
46#63951C22116yescomplemented
47#63950C22116yescomplemented
48#63937C22116yescomplemented
49#63936C22116yescomplemented
50C2×#3719C2212yescomplemented
51#63833C2218yescomplemented
52C2×#3717C2212yescomplemented
53#63830C2218yescomplemented
54C2×#3716C2212yescomplemented
55C2×#3714C2212yescomplemented
56C2×#3712C2212yescomplemented
57#63818C2218yescomplemented
58C2×#3710C2212yescomplemented
59C2×D3×#41—31no—
60C2×D3×#41—31no—
61C2×D3×#41—61no—
62C22×#239—31no—
63C22×#237—31no—
64C2×C3×#137—31no—
65C2×C3×AGL(1,ℤ/8)—31no—
66C2×#951D311yescharacteristic, complemented
67C2×#949D311yescharacteristic, complemented
68C2×#942—31no—
69C2×#932—31no—
70#5777—316no—
71#5773—316no—
72C2×#919—32no—
73C2×#918—32no—
74C2×#916—32no—
75C2×#916—32no—
76C2×#915—32no—
77C2×#914—32no—
78C2×#912—32no—
79C2×#911—32no—
80C2×#909—31no—
81C2×#908—31no—
82C2×D3×M16—31no—
83C2×D3×M16—31no—
84C23×C3⋊D3—21no—
85C23×C3⋊D3D411yescharacteristic
86C23×C3×D3—21no—
87C32×#41—22no—
88C32×#41C2314yes—
89C2×C32×Q8C2311yescharacteristic
90C2×C32×D4—21no—
91C2×C32×D4C2311yescharacteristic
92C22×C32×C4—21no—
93C22×C32×C4C2311yescharacteristic
94C2×#638—21no—
95C2×#638—21no—
96C2×#638—21no—
97C22×C3⋊Dic3—21no—
98C22×C3⋊Dic3D411yescharacteristic
99#3832—22no—
100#3832C2314yescomplemented
101Q8×C3⋊D3—22no—
102Q8×C3⋊D3C2314yescomplemented
103#3830—28no—
104#3830—22no—
105#3830C2314yescomplemented
106D4×C3⋊D3—28no—
107D4×C3⋊D3—22no—
108D4×C3⋊D3C2314yescomplemented
109#3828—22no—
110#3828—28no—
111#3828C2314yes—
112C2×C4⋊(C3⋊D3)—21no—
113C2×C4⋊(C3⋊D3)C2311yescharacteristic
114C2×C4×C3⋊D3—21no—
115C2×C4×C3⋊D3—21no—
116C2×C4×C3⋊D3—21no—
117C2×C4×C3⋊D3—28no—
118C2×C4×C3⋊D3D411yescharacteristic
119C2×C4×C3⋊D3D411yescharacteristic
120C2×C4×C3⋊D3D414yes—
121C2×C4×C3⋊D3C2311yescharacteristic
122C2×C4×C3⋊D3C2311yescharacteristic
123C2×C4×C3⋊D3C2314yes—
124C2×#634—21no—
125C2×#634C2311yescharacteristic
126C22×C3×Dic3—21no—
127C2×C3×D12—22no—
128C2×C3×D12—21no—
129C2×C3×D12C2312yes—
130C2×C3×D12C2314yescomplemented
131C2×C3×Dic6—22no—
132C2×C3×Dic6—21no—
133C2×C3×Dic6C2312yes—
134C2×C3×Dic6C2314yescomplemented
135C2×#626—22no—
136C2×#626—28no—
137C2×#626—22no—
138C2×D3×Dic3—22no—
139C2×D3×Dic3—28no—
140C2×D3×Dic3—22no—
141#3796—24no—
142#3796—28no—
143#3796—28no—
144#3796—24no—
145#3796C2318yes—
146#3796C2318yescomplemented
147C3×#216C2318yescomplemented
148C3×#215C2318yescomplemented
149C3×#214C2318yescomplemented
150C3×#213C2318yescomplemented
151C3×#208C2314yescomplemented
152C3×#208C2314yescomplemented
153C2×C3×C3⋊C8C2312yes—
154C2×C3×C3⋊C8C2312yes—
155#3719C2318yescomplemented
156#3717C2318yescomplemented
157#3716C2318yescomplemented
158#3714C2318yescomplemented
159#3712C2318yescomplemented
160#3710C2318yescomplemented
161C2×#575—91noSylow
162C2×C3×#41—21no—
163C2×C3×#41C2×D311yescharacteristic
164C2×C3×#41C2×D311yescharacteristic
165C22×C3×Q8—31no—
166C22×C3×D4—31no—
167C22×#67—61no—
168C23×Dic3—61no—
169D3×#41—38no—
170D3×#41—38no—
171D3×#41—68no—
172D3×#41—64no—
173D3×#41—64no—
174D3×#41—68no—
175C2×#239—31no—
176C2×#239—31no—
177C2×#239—32no—
178C2×#239—32no—
179C2×#239—38no—
180C2×#239—61no—
181C2×#239—61no—
182C2×#239—61no—
183C2×#239—64no—
184C2×D3×Q8—31no—
185C2×D3×Q8—31no—
186C2×D3×Q8—61no—
187C2×#237—31no—
188C2×#237—31no—
189C2×#237—32no—
190C2×#237—32no—
191C2×#237—38no—
192C2×#237—61no—
193C2×#237—61no—
194C2×#237—61no—
195C2×#237—64no—
196C2×#237—61no—
197C2×#237—61no—
198C2×#237—62no—
199C2×D3×D4—31no—
200C2×D3×D4—31no—
201C2×D3×D4—61no—
202C2×D3×D4—61no—
203C2×D3×D4—61no—
204C2×D3×D4—62no—
205C2×#235—31no—
206C2×#235—31no—
207C2×#235—61no—
208C2×#235—61no—
209C2×#235—61no—
210C2×#235—62no—
211C22×D12—61no—
212C22×D12C2×D311yescharacteristic, complemented
213C22×C4×D3—31no—
214C22×C4×D3—31no—
215C22×C4×D3—61no—
216C22×C4×D3—61no—
217C22×C4×D3—61no—
218C22×C4×D3—61no—
219C22×C4×D3—62no—
220C22×Dic6C2×D311yescharacteristic, complemented
221C3×#137—38no—
222C3×AGL(1,ℤ/8)—38no—
223C2×C3×Q16—32no—
224C2×C3×SD16—32no—
225C2×C3×SD16—32no—
226C2×C3×D8—32no—
227C2×C3×M16—31no—
228C2×C3×M16—31no—
229#951C2×D318yescomplemented
230#949C2×D318yescomplemented
231C2×#216—32no—
232C2×#216C2×D312yescomplemented
233#942—38no—
234C2×#215—32no—
235C2×#215C2×D312yescomplemented
236C2×#214—32no—
237C2×#214C2×D312yescomplemented
238#932—38no—
239C2×#213—32no—
240C2×#213C2×D312yescomplemented
241C2×#208C2×D311yescharacteristic, complemented
242C2×#208C2×D311yescharacteristic, complemented
243#919—316no—
244#918—316no—
245#916—316no—
246#916—316no—
247#915—316no—
248#914—316no—
249#912—316no—
250#911—316no—
251#909—38no—
252#908—38no—
253D3×M16—38no—
254D3×M16—38no—
255C2×Dic12—32no—
256C2×D24—32no—
257C2×#204—32no—
258C2×#204—32no—
259C2×ΓL(1,𝔽25)—32no—
260C2×ΓL(1,𝔽25)—32no—
261C2×D3×C8—32no—
262C2×D3×C8—32no—
263C23×C32—21no—
264C23×C32C2×D411yescharacteristic
265C22×C3⋊D3—21no—
266C22×C3⋊D3—24no—
267C22×C3⋊D3—42no—
268C22×C3⋊D3—44no—
269C22×C3⋊D3C2×D411yescharacteristic
270C22×C3⋊D3C2×D411yescharacteristic
271C22×C3⋊D3C2×D414yes—
272C22×C3×D3—22no—
273C22×C3×D3—24no—
274C22×C3×D3—44no—
275C32×Q8—21no—
276C32×Q8C2412yes—
277C32×D4—24no—
278C32×D4—21no—
279C32×D4C2412yes—
280C2×C32×C4—21no—
281C2×C32×C4—24no—
282C2×C32×C4C2×D411yescharacteristic
283C2×C32×C4C2×D412yes—
284C2×C32×C4C2411yescharacteristic
285C2×C32×C4C2412yes—
286#638—24no—
287#638—24no—
288#638—24no—
289C2×C3⋊Dic3—21no—
290C2×C3⋊Dic3—24no—
291C2×C3⋊Dic3C2×D411yescharacteristic
292C2×C3⋊Dic3C2×D411yescharacteristic
293C2×C3⋊Dic3C2×D414yes—
294C4⋊(C3⋊D3)—24no—
295C4⋊(C3⋊D3)—21no—
296C4⋊(C3⋊D3)C2412yes—
297C4×C3⋊D3—24no—
298C4×C3⋊D3—24no—
299C4×C3⋊D3—24no—
300C4×C3⋊D3C2×D414yes—
301C4×C3⋊D3C2×D414yes—
302C4×C3⋊D3C2×D412yes—
303C4×C3⋊D3C2×D412yes—
304C4×C3⋊D3C2412yes—
305C4×C3⋊D3C2412yes—
306#634—21no—
307#634—24no—
308#634C2412yes—
309C2×C3×Dic3—22no—
310C2×C3×Dic3—24no—
311C3×D12—22no—
312C3×D12—24no—
313C3×D12C2414yes—
314C3×Dic6—22no—
315C3×Dic6—24no—
316C3×Dic6C2414yes—
317#626—28no—
318#626—28no—
319D3×Dic3—28no—
320D3×Dic3—28no—
321C3×C3⋊C8C2414yes—
322C3×C3⋊C8C2414yes—
323C22×#41—91no—
324C22×#41—91no—
325#575—916no—
326C2×#137—31no—
327C2×#137—91no—
328C2×#137—92no—
329C2×AGL(1,ℤ/8)—31no—
330C2×AGL(1,ℤ/8)—91no—
331C2×AGL(1,ℤ/8)—92no—
332C2×#135—92no—
333C2×#135—92no—
334C22×M16—91no—
335C24×C3—61no—
336C23×D3—21no—
337C23×D3—31no—
338C23×D3—31no—
339C23×D3—61no—
340C23×D3—61no—
341C23×D3—61no—
342C23×D3—62no—
343C3×#41—24no—
344C3×#41—22no—
345C3×#41—22no—
346C3×#41—24no—
347C3×#41C22×D314yes—
348C3×#41C22×D314yes—
349C2×C3×Q8—21no—
350C2×C3×Q8—32no—
351C2×C3×Q8—34no—
352C2×C3×Q8—61no—
353C2×C3×Q8—62no—
354C2×C3×Q8C22×D311yescharacteristic
355C2×C3×Q8C22×D311yescharacteristic
356C2×C3×D4—22no—
357C2×C3×D4—21no—
358C2×C3×D4—21no—
359C2×C3×D4—21no—
360C2×C3×D4—32no—
361C2×C3×D4—34no—
362C2×C3×D4—61no—
363C2×C3×D4—62no—
364C2×C3×D4C22×D311yescharacteristic
365C2×C3×D4C22×D311yescharacteristic
366C22×C3×C4—22no—
367C22×C3×C4—21no—
368C22×C3×C4—21no—
369C22×C3×C4—21no—
370C22×C3×C4—61no—
371C22×C3×C4C22×D311yescharacteristic
372C22×C3×C4C22×D311yescharacteristic
373C2×#67—62no—
374C2×#67—62no—
375C2×#67—68no—
376C2×#67—61no—
377C2×#67—61no—
378C2×#67—61no—
379C2×#67—61no—
380C2×#67—62no—
381C2×#67—62no—
382C2×#67—62no—
383C2×#67—61no—
384C2×#67—61no—
385C22×Dic3—21no—
386C22×Dic3—31no—
387C22×Dic3—31no—
388C22×Dic3—61no—
389C22×Dic3—62no—
390C22×Dic3—62no—
391C22×Dic3—68no—
392C22×Dic3—61no—
393C22×Dic3—61no—
394C22×Dic3—62no—
395#239—34no—
396#239—34no—
397#239—38no—
398#239—38no—
399#239—64no—
400#239—68no—
401#239—68no—
402#239—64no—
403#239—64no—
404#239—62no—
405#239—62no—
406#239—64no—
407D3×Q8—34no—
408D3×Q8—34no—
409D3×Q8—64no—
410D3×Q8—62no—
411D3×Q8—62no—
412D3×Q8—64no—
413#237—34no—
414#237—34no—
415#237—38no—
416#237—38no—
417#237—64no—
418#237—64no—
419#237—64no—
420#237—68no—
421#237—68no—
422#237—62no—
423#237—62no—
424#237—68no—
425#237—68no—
426#237—64no—
427#237—616no—
428D3×D4—34no—
429D3×D4—34no—
430D3×D4—64no—
431D3×D4—62no—
432D3×D4—62no—
433D3×D4—68no—
434D3×D4—68no—
435D3×D4—64no—
436D3×D4—616no—
437#235—34no—
438#235—34no—
439#235—64no—
440#235—68no—
441#235—68no—
442#235—616no—
443#235—64no—
444#235—62no—
445#235—62no—
446C2×D12—22no—
447C2×D12—21no—
448C2×D12—31no—
449C2×D12—31no—
450C2×D12—61no—
451C2×D12—61no—
452C2×D12—61no—
453C2×D12—62no—
454C2×D12—62no—
455C2×D12—62no—
456C2×D12—68no—
457C2×D12C22×D312yes—
458C2×D12C22×D314yescomplemented
459C2×C4×D3—31no—
460C2×C4×D3—31no—
461C2×C4×D3—31no—
462C2×C4×D3—31no—
463C2×C4×D3—34no—
464C2×C4×D3—34no—
465C2×C4×D3—31no—
466C2×C4×D3—31no—
467C2×C4×D3—31no—
468C2×C4×D3—31no—
469C2×C4×D3—34no—
470C2×C4×D3—34no—
471C2×C4×D3—61no—
472C2×C4×D3—61no—
473C2×C4×D3—61no—
474C2×C4×D3—61no—
475C2×C4×D3—64no—
476C2×C4×D3—64no—
477C2×C4×D3—68no—
478C2×C4×D3—68no—
479C2×C4×D3—61no—
480C2×C4×D3—61no—
481C2×C4×D3—62no—
482C2×C4×D3—62no—
483C2×C4×D3—68no—
484C2×C4×D3—61no—
485C2×C4×D3—61no—
486C2×C4×D3—62no—
487C2×C4×D3—62no—
488C2×C4×D3—62no—
489C2×C4×D3—616no—
490C2×C4×D3—61no—
491C2×C4×D3—61no—
492C2×Dic6—22no—
493C2×Dic6—21no—
494C2×Dic6—31no—
495C2×Dic6—31no—
496C2×Dic6—61no—
497C2×Dic6—61no—
498C2×Dic6—61no—
499C2×Dic6—62no—
500C2×Dic6C22×D312yes—
501C2×Dic6C22×D314yescomplemented
502C3×Q16—38no—
503C3×SD16—38no—
504C3×SD16—38no—
505C3×D8—38no—
506C3×M16—34no—
507C3×M16—34no—
508C2×C3×C8—32no—
509C2×C3×C8—32no—
510#216—38no—
511#216C22×D318yescomplemented
512#215—38no—
513#215C22×D318yescomplemented
514#214—38no—
515#214C22×D318yescomplemented
516#213—38no—
517#213C22×D318yescomplemented
518#208C22×D314yescomplemented
519#208C22×D314yescomplemented
520C2×C3⋊C8C22×D312yes—
521C2×C3⋊C8C22×D312yes—
522Dic12—38no—
523D24—38no—
524#204—38no—
525#204—38no—
526ΓL(1,𝔽25)—38no—
527ΓL(1,𝔽25)—38no—
528D3×C8—38no—
529D3×C8—38no—
530C22×C32—22no—
531C22×C32—22no—
532C22×C32—42no—
533C22×C32C22×D412yes—
534C22×C32C22×D411yescharacteristic
535C2×C3⋊D3—22no—
536C2×C3⋊D3—22no—
537C2×C3⋊D3—22no—
538C2×C3⋊D3—44no—
539C2×C3⋊D3—48no—
540C2×C3⋊D3—42no—
541C2×C3⋊D3C22×D412yes—
542C2×C3⋊D3C22×D412yes—
543C2×C3×D3—24no—
544C2×C3×D3—48no—
545C2×C3×D3—44no—
546C32×C4—22no—
547C32×C4C22×D411yescharacteristic
548C32×C4C22×D412yes—
549C32×C4C2511yescharacteristic
550C3⋊Dic3—22no—
551C3⋊Dic3C22×D412yes—
552C3⋊Dic3C22×D412yes—
553C3×Dic3—24no—
554C2×#41—92no—
555C2×#41—92no—
556C2×#41—98no—
557C2×#41—98no—
558C2×#41—91no—
559C2×#41—91no—
560C2×#41—91no—
561C2×#41—181no—
562C2×#41—181no—
563C2×#41—181no—
564C2×#41—184no—
565C2×#41—181no—
566C2×#41—184no—
567C2×#41D3211yescharacteristic
568C22×Q8—31no—
569C22×Q8—91no—
570C22×D4—31no—
571C22×D4—91no—
572C22×D4—181no—
573C22×D4—181no—
574C23×C4—91no—
575C23×C4—181no—
576C23×C4—181no—
577#137—38no—
578#137—98no—
579#137—916no—
580AGL(1,ℤ/8)—38no—
581AGL(1,ℤ/8)—98no—
582AGL(1,ℤ/8)—916no—
583#135—916no—
584#135—916no—
585C2×Q16—32no—
586C2×Q16—92no—
587C2×SD16—32no—
588C2×SD16—32no—
589C2×SD16—92no—
590C2×SD16—92no—
591C2×D8—32no—
592C2×D8—92no—
593C2×M16—31no—
594C2×M16—31no—
595C2×M16—92no—
596C2×M16—98no—
597C22×C8—92no—
598C23×C3—22no—
599C23×C3—21no—
600C23×C3—21no—
601C23×C3—21no—
602C23×C3—64no—
603C23×C3—62no—
604C23×C3—124no—
605C23×C3D3×D411yescharacteristic
606C23×C3D3×D411yescharacteristic
607C22×D3—22no—
608C22×D3—24no—
609C22×D3—31no—
610C22×D3—31no—
611C22×D3—31no—
612C22×D3—31no—
613C22×D3—34no—
614C22×D3—34no—
615C22×D3—44no—
616C22×D3—61no—
617C22×D3—61no—
618C22×D3—64no—
619C22×D3—64no—
620C22×D3—64no—
621C22×D3—62no—
622C22×D3—68no—
623C22×D3—61no—
624C22×D3—61no—
625C22×D3—122no—
626C22×D3—122no—
627C22×D3—124no—
628C22×D3—128no—
629C22×D3—124no—
630C22×D3—124no—
631C3×Q8—22no—
632C3×Q8—21no—
633C3×Q8—21no—
634C3×Q8—22no—
635C3×Q8—34no—
636C3×Q8—62no—
637C3×Q8—64no—
638C3×Q8C23×D312yes—
639C3×Q8C23×D312yes—
640C3×D4—28no—
641C3×D4—22no—
642C3×D4—24no—
643C3×D4—24no—
644C3×D4—21no—
645C3×D4—21no—
646C3×D4—22no—
647C3×D4—34no—
648C3×D4—62no—
649C3×D4—64no—
650C3×D4C23×D312yes—
651C3×D4C23×D312yes—
652C2×C3×C4—22no—
653C2×C3×C4—28no—
654C2×C3×C4—21no—
655C2×C3×C4—21no—
656C2×C3×C4—24no—
657C2×C3×C4—24no—
658C2×C3×C4—21no—
659C2×C3×C4—22no—
660C2×C3×C4—21no—
661C2×C3×C4—22no—
662C2×C3×C4—64no—
663C2×C3×C4—62no—
664C2×C3×C4D3×D411yescharacteristic
665C2×C3×C4D3×D412yes—
666C2×C3×C4D3×D411yescharacteristic
667C2×C3×C4D3×D412yes—
668C2×C3×C4C23×D311yescharacteristic
669C2×C3×C4C23×D311yescharacteristic
670C2×C3×C4C23×D312yes—
671C2×C3×C4C23×D312yes—
672#67—68no—
673#67—68no—
674#67—64no—
675#67—64no—
676#67—64no—
677#67—64no—
678#67—68no—
679#67—68no—
680#67—68no—
681#67—64no—
682#67—64no—
683C2×Dic3—22no—
684C2×Dic3—24no—
685C2×Dic3—31no—
686C2×Dic3—31no—
687C2×Dic3—31no—
688C2×Dic3—34no—
689C2×Dic3—31no—
690C2×Dic3—34no—
691C2×Dic3—61no—
692C2×Dic3—61no—
693C2×Dic3—64no—
694C2×Dic3—68no—
695C2×Dic3—68no—
696C2×Dic3—64no—
697C2×Dic3—64no—
698C2×Dic3—62no—
699C2×Dic3—68no—
700C2×Dic3—61no—
701C2×Dic3—61no—
702D12—22no—
703D12—24no—
704D12—32no—
705D12—32no—
706D12—62no—
707D12—64no—
708D12—64no—
709D12—68no—
710D12—62no—
711D12—68no—
712D12—68no—
713D12—61no—
714D12—61no—
715D12C23×D314yes—
716C4×D3—34no—
717C4×D3—34no—
718C4×D3—34no—
719C4×D3—34no—
720C4×D3—32no—
721C4×D3—32no—
722C4×D3—32no—
723C4×D3—32no—
724C4×D3—32no—
725C4×D3—32no—
726C4×D3—32no—
727C4×D3—32no—
728C4×D3—64no—
729C4×D3—64no—
730C4×D3—62no—
731C4×D3—62no—
732C4×D3—62no—
733C4×D3—62no—
734C4×D3—64no—
735C4×D3—64no—
736C4×D3—68no—
737C4×D3—68no—
738C4×D3—64no—
739C4×D3—64no—
740C4×D3—68no—
741C4×D3—68no—
742C4×D3—68no—
743C4×D3—64no—
744C4×D3—64no—
745Dic6—22no—
746Dic6—24no—
747Dic6—32no—
748Dic6—32no—
749Dic6—62no—
750Dic6—64no—
751Dic6—64no—
752Dic6—68no—
753Dic6—62no—
754Dic6—61no—
755Dic6—61no—
756Dic6C23×D314yes—
757C3×C8—34no—
758C3×C8—34no—
759C3⋊C8C23×D314yes—
760C3⋊C8C23×D314yes—
761C2×C32—22no—
762C2×C32—42no—
763C2×C32#57512yescomplemented
764C2×C32C23×D411yescharacteristic
765C3⋊D3—22no—
766C3⋊D3—22no—
767C3⋊D3—42no—
768C3×D3—44no—
769C24—61no—
770C24—91no—
771C24—181no—
772#41—22no—
773#41—98no—
774#41—98no—
775#41—94no—
776#41—94no—
777#41—94no—
778#41—188no—
779#41—188no—
780#41—182no—
781#41—188no—
782#41—184no—
783#41—184no—
784#41—188no—
785#41—182no—
786#41—182no—
787#41C2×D3214yes—
788C2×Q8—32no—
789C2×Q8—34no—
790C2×Q8—62no—
791C2×Q8—61no—
792C2×Q8—94no—
793C2×Q8—91no—
794C2×Q8—181no—
795C2×Q8—182no—
796C2×Q8C2×D3211yescharacteristic
797C2×D4—21no—
798C2×D4—32no—
799C2×D4—34no—
800C2×D4—62no—
801C2×D4—61no—
802C2×D4—94no—
803C2×D4—91no—
804C2×D4—181no—
805C2×D4—188no—
806C2×D4—182no—
807C2×D4—182no—
808C2×D4—182no—
809C2×D4—181no—
810C2×D4—188no—
811C2×D4—181no—
812C2×D4—181no—
813C2×D4C2×D3211yescharacteristic
814C22×C4—21no—
815C22×C4—61no—
816C22×C4—91no—
817C22×C4—91no—
818C22×C4—91no—
819C22×C4—94no—
820C22×C4—91no—
821C22×C4—94no—
822C22×C4—91no—
823C22×C4—181no—
824C22×C4—188no—
825C22×C4—181no—
826C22×C4—188no—
827C22×C4—182no—
828C22×C4—182no—
829C22×C4—181no—
830C22×C4—181no—
831C22×C4C2×D3211yescharacteristic
832Q16—38no—
833Q16—98no—
834SD16—38no—
835SD16—38no—
836SD16—98no—
837SD16—98no—
838D8—38no—
839D8—98no—
840M16—34no—
841M16—34no—
842M16—98no—
843C2×C8—32no—
844C2×C8—32no—
845C2×C8—98no—
846C22×C3—22no—
847C22×C3—22no—
848C22×C3—24no—
849C22×C3—22no—
850C22×C3—22no—
851C22×C3—22no—
852C22×C3—21no—
853C22×C3—42no—
854C22×C3—44no—
855C22×C3—42no—
856C22×C3—42no—
857C22×C3—64no—
858C22×C3—128no—
859C22×C3—124no—
860C22×C3C2×D3×D412yes—
861C22×C3C2×D3×D412yes—
862C22×C3C2×D3×D411yescharacteristic
863C22×C3C2×D3×D411yescharacteristic
864C2×D3—24no—
865C2×D3—32no—
866C2×D3—32no—
867C2×D3—32no—
868C2×D3—32no—
869C2×D3—48no—
870C2×D3—44no—
871C2×D3—62no—
872C2×D3—62no—
873C2×D3—64no—
874C2×D3—62no—
875C2×D3—62no—
876C2×D3—62no—
877C2×D3—62no—
878C2×D3—64no—
879C2×D3—62no—
880C2×D3—62no—
881C2×D3—122no—
882C2×D3—124no—
883C2×D3—124no—
884C2×D3—128no—
885C2×D3—1216no—
886C2×D3—128no—
887C2×D3—128no—
888C2×D3—124no—
889C2×D3—122no—
890C2×D3—122no—
891C3×C4—24no—
892C3×C4—22no—
893C3×C4—22no—
894C3×C4—21no—
895C3×C4—22no—
896C3×C4—21no—
897C3×C4—64no—
898C3×C4C2×D3×D411yescharacteristic
899C3×C4C2×D3×D412yes—
900C3×C4C2×D3×D411yescharacteristic
901C3×C4C2×D3×D412yes—
902C3×C4C24×D311yescharacteristic
903C3×C4C24×D311yescharacteristic
904Dic3—24no—
905Dic3—32no—
906Dic3—32no—
907Dic3—32no—
908Dic3—32no—
909Dic3—62no—
910Dic3—62no—
911Dic3—64no—
912Dic3—62no—
913Dic3—62no—
914C32C2×#57511yescharacteristic, complemented, Sylow
915C23—21no—
916C23—64no—
917C23—62no—
918C23—91no—
919C23—91no—
920C23—94no—
921C23—124no—
922C23—184no—
923C23—181no—
924C23—362no—
925C23—364no—
926C23#381111yescharacteristic
927Q8—21no—
928Q8—34no—
929Q8—64no—
930Q8—62no—
931Q8—92no—
932Q8—184no—
933Q8—181no—
934Q8C22×D3212yes—
935D4—24no—
936D4—21no—
937D4—34no—
938D4—64no—
939D4—62no—
940D4—92no—
941D4—184no—
942D4—188no—
943D4—188no—
944D4—184no—
945D4—184no—
946D4—184no—
947D4—181no—
948D4C22×D3212yes—
949C2×C4—21no—
950C2×C4—24no—
951C2×C4—64no—
952C2×C4—62no—
953C2×C4—94no—
954C2×C4—91no—
955C2×C4—91no—
956C2×C4—94no—
957C2×C4—92no—
958C2×C4—92no—
959C2×C4—94no—
960C2×C4—92no—
961C2×C4—92no—
962C2×C4—184no—
963C2×C4—184no—
964C2×C4—188no—
965C2×C4—188no—
966C2×C4—184no—
967C2×C4—181no—
968C2×C4—184no—
969C2×C4#381112yes—
970C2×C4#381111yescharacteristic
971C2×C4C22×D3212yes—
972C2×C4C22×D3211yescharacteristic
973C8—34no—
974C8—34no—
975C2×C3—22no—
976C2×C3—22no—
977C2×C3—21no—
978C2×C3—22no—
979C2×C3—42no—
980C2×C3—44no—
981C2×C3—42no—
982C2×C3—42no—
983C2×C3—124no—
984C2×C3#577312yescomplemented
985C2×C3#577712yescomplemented
986C2×C3C22×D3×D411yescharacteristic
987C2×C3C22×D3×D411yescharacteristic
988D3—44no—
989D3—64no—
990D3—62no—
991D3—62no—
992D3—62no—
993D3—62no—
994D3—122no—
995D3—124no—
996D3—122no—
997D3—122no—
998C22—22no—
999C22—22no—
1000C22—42no—
1001C22—64no—
1002C22—92no—
1003C22—92no—
1004C22—128no—
1005C22—124no—
1006C22—182no—
1007C22—182no—
1008C22—182no—
1009C22—364no—
1010C22—368no—
1011C22—362no—
1012C22C2×#381112yes—
1013C22C2×#381111yescharacteristic
1014C4—22no—
1015C4—64no—
1016C4—92no—
1017C4—92no—
1018C4—182no—
1019C4C2×#381112yes—
1020C4C2×#381111yescharacteristic
1021C4C23×D3211yescharacteristic
1022C3—21no—
1023C3C2×#577311yescharacteristic, complemented
1024C3C2×#577711yescharacteristic, complemented
1025C2—22no—
1026C2—42no—
1027C2—124no—
1028C2—182no—
1029C2—182no—
1030C2—362no—
1031C2#1059547112yesdirect product factor
1032C2C22×#381111yescharacteristic
subgroupG/H
centerC22C2×#3811
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×#41×C3⋊D3C2semidirect
2. C22×#3796C2semidirect
3. C2×C3×#951C2semidirect
4. C2×C3×#949C2semidirect
5. #10595471C2direct (N × H)
6. C2×#63951C2semidirect
7. C2×#63950C2semidirect
8. C2×#63937C2semidirect
9. C2×#63936C2semidirect
10. C2×#63833C2semidirect
11. C2×#63830C2semidirect
12. C2×#63818C2semidirect
17. #41×C3⋊D3C22semidirect
18. C2×#3832C22semidirect
19. C2×Q8×C3⋊D3C22semidirect
21. C2×#3830C22semidirect
23. C2×D4×C3⋊D3C22semidirect
28. C22×C3×D12C22semidirect
29. C22×C3×Dic6C22semidirect
36. C2×#3796C22semidirect
37. C2×#3796C22semidirect
38. C3×#951C22semidirect
39. C3×#949C22semidirect
40. C2×C3×#216C22semidirect
41. C2×C3×#215C22semidirect
42. C2×C3×#214C22semidirect
43. C2×C3×#213C22semidirect
44. C2×C3×#208C22semidirect
45. C2×C3×#208C22semidirect
46. #63951C22semidirect
47. #63950C22semidirect
48. #63937C22semidirect
49. #63936C22semidirect
50. C2×#3719C22semidirect
51. #63833C22semidirect
52. C2×#3717C22semidirect
53. #63830C22semidirect
54. C2×#3716C22semidirect
55. C2×#3714C22semidirect
56. C2×#3712C22semidirect
57. #63818C22semidirect
58. C2×#3710C22semidirect
66. C2×#951D3semidirect
67. C2×#949D3semidirect
100. #3832C23semidirect
102. Q8×C3⋊D3C23semidirect
105. #3830C23semidirect
108. D4×C3⋊D3C23semidirect
130. C2×C3×D12C23semidirect
134. C2×C3×Dic6C23semidirect
146. #3796C23semidirect
147. C3×#216C23semidirect
148. C3×#215C23semidirect
149. C3×#214C23semidirect
150. C3×#213C23semidirect
151. C3×#208C23semidirect
152. C3×#208C23semidirect
155. #3719C23semidirect
156. #3717C23semidirect
157. #3716C23semidirect
158. #3714C23semidirect
159. #3712C23semidirect
160. #3710C23semidirect
212. C22×D12C2×D3semidirect
220. C22×Dic6C2×D3semidirect
229. #951C2×D3semidirect
230. #949C2×D3semidirect
232. C2×#216C2×D3semidirect
235. C2×#215C2×D3semidirect
237. C2×#214C2×D3semidirect
240. C2×#213C2×D3semidirect
241. C2×#208C2×D3semidirect
242. C2×#208C2×D3semidirect
458. C2×D12C22×D3semidirect
501. C2×Dic6C22×D3semidirect
511. #216C22×D3semidirect
513. #215C22×D3semidirect
515. #214C22×D3semidirect
517. #213C22×D3semidirect
518. #208C22×D3semidirect
519. #208C22×D3semidirect
763. C2×C32#575semidirect
914. C32C2×#575semidirect
984. C2×C3#5773semidirect
985. C2×C3#5777semidirect
1023. C3C2×#5773semidirect
1024. C3C2×#5777semidirect
1031. C2#10595471direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#41×C3⋊D32
C22×#37962
C2×C3×#9512
C2×C3×#9492
#105954712
C2×#639512
C2×#639502
C2×#639372
C2×#639362
C2×#638332
C2×#638302
C2×#638182
C2×#57773
C2×#57733