Finite Group Databasebeta

← C2×#10594718 #11918763

Subgroups — C2×#10594718 #11918763

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
1C2×#64306C211yesmaximal, characteristic, complemented
2C22×#3796C211yesmaximal, characteristic, complemented
3C2×M16×C3⋊D3C211yesmaximal, characteristic, complemented
4C2×C3×#909C211yesmaximal, characteristic, complemented
5C2×C3×#908C211yesmaximal, characteristic, complemented
6C2×#63827C211yesmaximal, characteristic, complemented
7C2×#63823C211yesmaximal, characteristic, complemented
8#10594718C2116yesmaximal, direct product factor
9C2×#63811C212yesmaximal, complemented
10C2×#63810C212yesmaximal, complemented
11C2×#63809C212yesmaximal, complemented
12C2×#63798C212yesmaximal, complemented
13C2×#5777—31nomaximal
14C2×#5773—31nomaximal
15C22×C4×C3⋊D3C2211yescharacteristic
16C2×C3×#235C2211yescharacteristic
17C2×C3×#235C2211yescharacteristic
18C22×C3×D12C2211yescharacteristic, complemented
19C22×C3×Dic6C2211yescharacteristic, complemented
20C2×#3811—21no—
21C22×#626—21no—
22C2×#3805—21no—
23C22×D3×Dic3—21no—
24#64306—24no—
25#64306C2218yescomplemented
26C2×#3802C2211yescharacteristic, complemented
27C2×C4×D32—21no—
28C2×#3798—21no—
29C2×#3797C2211yescharacteristic, complemented
30C2×#3796—24no—
31C2×#3796—21no—
32C2×#3796—21no—
33C2×#3796C2212yes—
34C2×#3796C2218yescomplemented
35C2×#3796C2212yescomplemented
36C2×#3796C2211yescharacteristic, complemented
37C2×#3796C2211yescharacteristic, complemented
38C2×C32×M16C2211yescharacteristic, complemented
39C2×#3748C2211yescharacteristic, complemented
40M16×C3⋊D3C2218yescomplemented
41C2×#3743C2212yescomplemented
42C2×C8×C3⋊D3C2212yescomplemented
43C3×#909C2218yescomplemented
44C3×#908C2218yescomplemented
45C2×C3×Dic12C2212yescomplemented
46C2×C3×D24C2212yescomplemented
47C2×C3×#204C2212yescomplemented
48C2×C3×#204C2212yescomplemented
49C2×#3718C2212yescomplemented
50#63827C2218yescomplemented
51C2×#3715C2212yescomplemented
52C2×#3715C2212yescomplemented
53#63823C2218yescomplemented
54C2×#3713C2212yescomplemented
55#63811C22116yescomplemented
56#63810C22116yescomplemented
57#63809C22116yescomplemented
58#63798C22116yescomplemented
59C2×D3×#41—31no—
60C2×D3×#41—31no—
61C22×#239—31no—
62C22×#237—31no—
63C2×C3×#137—31no—
64C2×C3×AGL(1,ℤ/8)—31no—
65C2×#951—31no—
66C2×#949—31no—
67C2×#942—31no—
68C2×#932—31no—
69#5777—316no—
70#5773—316no—
71C2×#919—32no—
72C2×#918—32no—
73C2×#916—32no—
74C2×#916—32no—
75C2×#915—32no—
76C2×#914—32no—
77C2×#912—32no—
78C2×#911—32no—
79C2×#909D311yescharacteristic, complemented
80C2×#908D311yescharacteristic, complemented
81C2×D3×M16—31no—
82C2×D3×M16—31no—
83C2×D3×M16—61no—
84C23×C3⋊D3D411yescharacteristic
85C23×C3×D3—21no—
86C22×D32—21no—
87C22×C32×C4C2311yescharacteristic
88C22×C3⋊Dic3D411yescharacteristic
89C2×C4×C3⋊D3D411yescharacteristic
90C2×C4×C3⋊D3D411yescharacteristic
91C2×C4×C3⋊D3D414yes—
92C2×C4×C3⋊D3C2311yescharacteristic
93C2×C4×C3⋊D3C2311yescharacteristic
94C2×C4×C3⋊D3C2314yes—
95C2×C3×#67—21no—
96C2×C3×#67—21no—
97C22×C3×Dic3—21no—
98C3×#235—22no—
99C3×#235—22no—
100C3×#235C2314yes—
101C3×#235C2314yes—
102C2×C3×D12—22no—
103C2×C3×D12—21no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2312yes—
106C2×C3×D12C2311yescharacteristic
107C2×C3×D12C2314yescomplemented
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3—21no—
110C2×C3×Dic6—22no—
111C2×C3×Dic6—21no—
112C2×C3×Dic6C2311yescharacteristic
113C2×C3×Dic6C2312yes—
114C2×C3×Dic6C2311yescharacteristic
115C2×C3×Dic6C2314yescomplemented
116#3811—28no—
117C2×#627—21no—
118C2×#626—22no—
119C2×#626—28no—
120C2×#626—22no—
121C2×#626—21no—
122C2×#626—21no—
123C2×#625—21no—
124C2×#624—21no—
125#3805—28no—
126C2×D3×Dic3—22no—
127C2×D3×Dic3—28no—
128C2×D3×Dic3—22no—
129C2×D3×Dic3—21no—
130C2×D3×Dic3—21no—
131#3802—22no—
132#3802C2314yescomplemented
133C4×D32—28no—
134#3798—28no—
135#3797—22no—
136#3797C2314yescomplemented
137#3796—24no—
138#3796—28no—
139#3796—28no—
140#3796—24no—
141#3796—22no—
142#3796—22no—
143#3796C2318yes—
144#3796C2318yescomplemented
145#3796C2314yescomplemented
146#3796C2314yescomplemented
147C32×M16C2314yescomplemented
148C2×C32×C8C2312yes—
149#3748C2314yescomplemented
150C2×C3⋊(C3⋊C8)C2312yes—
151#3743C2318yescomplemented
152C8×C3⋊D3C2318yescomplemented
153C3×Dic12C2318yescomplemented
154C3×D24C2318yescomplemented
155C3×#204C2318yescomplemented
156C3×#204C2318yescomplemented
157#3718C2318yescomplemented
158#3715C2318yescomplemented
159#3715C2318yescomplemented
160#3713C2318yescomplemented
161C2×#575—91noSylow
162C2×C3×#41—31no—
163C2×C3×#41—31no—
164C22×C3×Q8—31no—
165C22×C3×D4—31no—
166C22×#67—61no—
167C23×Dic3—61no—
168D3×#41—38no—
169D3×#41—38no—
170D3×#41—64no—
171D3×#41—64no—
172C2×#239—32no—
173C2×#239—32no—
174C2×#239—31no—
175C2×#239—31no—
176C2×#239—38no—
177C2×#239—61no—
178C2×#239—61no—
179C2×#239—64no—
180C2×D3×Q8—31no—
181C2×D3×Q8—31no—
182C2×#237—32no—
183C2×#237—32no—
184C2×#237—31no—
185C2×#237—31no—
186C2×#237—38no—
187C2×#237—61no—
188C2×#237—61no—
189C2×#237—64no—
190C2×#237—61no—
191C2×#237—61no—
192C2×D3×D4—31no—
193C2×D3×D4—31no—
194C2×D3×D4—61no—
195C2×D3×D4—61no—
196C2×#235—61no—
197C2×#235—61no—
198C2×#235C2×D311yescharacteristic
199C2×#235C2×D311yescharacteristic
200C22×D12—61no—
201C22×D12C2×D311yescharacteristic, complemented
202C22×C4×D3—31no—
203C22×C4×D3—31no—
204C22×C4×D3—61no—
205C22×C4×D3—61no—
206C22×C4×D3—61no—
207C22×C4×D3—61no—
208C22×Dic6C2×D311yescharacteristic, complemented
209C3×#137—38no—
210C3×AGL(1,ℤ/8)—38no—
211C2×C3×Q16—32no—
212C2×C3×SD16—32no—
213C2×C3×SD16—32no—
214C2×C3×D8—32no—
215C2×C3×M16—21no—
216C2×C3×M16C2×D311yescharacteristic, complemented
217C2×C3×M16C2×D311yescharacteristic, complemented
218#951—38no—
219#949—38no—
220C2×#216—32no—
221C2×#216—32no—
222#942—38no—
223C2×#215—32no—
224C2×#215—32no—
225C2×#214—32no—
226C2×#214—32no—
227#932—38no—
228C2×#213—32no—
229C2×#213—32no—
230C2×#208—31no—
231C2×#208—31no—
232C2×#208—61no—
233#919—316no—
234#918—316no—
235#916—316no—
236#916—316no—
237#915—316no—
238#914—316no—
239#912—316no—
240#911—316no—
241#909C2×D318yescomplemented
242#908C2×D318yescomplemented
243D3×M16—38no—
244D3×M16—38no—
245D3×M16—68no—
246C2×Dic12C2×D312yescomplemented
247C2×D24C2×D312yescomplemented
248C2×#204C2×D312yescomplemented
249C2×#204C2×D312yescomplemented
250C2×ΓL(1,𝔽25)—32no—
251C2×ΓL(1,𝔽25)—32no—
252C2×ΓL(1,𝔽25)—62no—
253C2×D3×C8—32no—
254C2×D3×C8—32no—
255C2×D3×C8—62no—
256C23×C32C2×D411yescharacteristic
257C22×C3⋊D3—42no—
258C22×C3⋊D3C2×D411yescharacteristic
259C22×C3⋊D3C2×D411yescharacteristic
260C22×C3⋊D3C2×D414yes—
261C22×C3×D3—21no—
262C22×C3×D3—21no—
263C22×C3×D3—22no—
264C22×C3×D3—24no—
265C22×C3×D3—44no—
266C2×D32—24no—
267C2×D32—44no—
268C2×C32×C4C2×D411yescharacteristic
269C2×C32×C4C2×D412yes—
270C2×C32×C4C2411yescharacteristic
271C2×C32×C4C2412yes—
272C2×C3⋊Dic3C2×D411yescharacteristic
273C2×C3⋊Dic3C2×D414yes—
274C2×C3⋊Dic3C2×D411yescharacteristic
275C4×C3⋊D3C2×D412yes—
276C4×C3⋊D3C2×D412yes—
277C4×C3⋊D3C2×D414yes—
278C4×C3⋊D3C2×D414yes—
279C4×C3⋊D3C2412yes—
280C4×C3⋊D3C2412yes—
281C3×#67—24no—
282C3×#67—24no—
283C2×C3×Dic3—22no—
284C2×C3×Dic3—24no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—21no—
287C3×D12—22no—
288C3×D12—24no—
289C3×D12—21no—
290C3×D12—21no—
291C3×D12C2412yes—
292C3×D12C2414yes—
293C3×D12C2412yes—
294C3×C4×D3—24no—
295C3×C4×D3—24no—
296C3×Dic6—22no—
297C3×Dic6—24no—
298C3×Dic6—21no—
299C3×Dic6—21no—
300C3×Dic6C2412yes—
301C3×Dic6C2414yes—
302C3×Dic6C2412yes—
303#627—24no—
304#626—28no—
305#626—28no—
306#626—24no—
307#626—24no—
308#625—24no—
309#624—24no—
310D3×Dic3—28no—
311D3×Dic3—28no—
312D3×Dic3—24no—
313D3×Dic3—24no—
314C32×C8C2414yes—
315C3⋊(C3⋊C8)C2414yes—
316C22×#41—91no—
317C22×#41—91no—
318#575—916no—
319C2×#137—31no—
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—61no—
329C23×D3—21no—
330C23×D3—31no—
331C23×D3—31no—
332C23×D3—61no—
333C23×D3—61no—
334C23×D3—61no—
335C3×#41—34no—
336C3×#41—34no—
337C3×#41—62no—
338C3×#41—62no—
339C2×C3×Q8—31no—
340C2×C3×Q8—32no—
341C2×C3×Q8—34no—
342C2×C3×Q8—31no—
343C2×C3×Q8—61no—
344C2×C3×Q8—62no—
345C2×C3×D4—31no—
346C2×C3×D4—32no—
347C2×C3×D4—34no—
348C2×C3×D4—31no—
349C2×C3×D4—61no—
350C2×C3×D4—61no—
351C2×C3×D4—61no—
352C2×C3×D4—62no—
353C22×C3×C4—21no—
354C22×C3×C4—61no—
355C22×C3×C4—61no—
356C22×C3×C4—61no—
357C22×C3×C4C22×D311yescharacteristic
358C22×C3×C4C22×D311yescharacteristic
359C2×#67—21no—
360C2×#67—21no—
361C2×#67—61no—
362C2×#67—61no—
363C2×#67—62no—
364C2×#67—62no—
365C2×#67—68no—
366C2×#67—61no—
367C2×#67—61no—
368C22×Dic3—21no—
369C22×Dic3—31no—
370C22×Dic3—31no—
371C22×Dic3—61no—
372C22×Dic3—61no—
373C22×Dic3—61no—
374C22×Dic3—62no—
375C22×Dic3—62no—
376C22×Dic3—68no—
377#239—38no—
378#239—34no—
379#239—38no—
380#239—34no—
381#239—68no—
382#239—68no—
383#239—64no—
384#239—64no—
385#239—62no—
386#239—62no—
387D3×Q8—34no—
388D3×Q8—34no—
389D3×Q8—62no—
390D3×Q8—62no—
391#237—38no—
392#237—34no—
393#237—38no—
394#237—34no—
395#237—64no—
396#237—64no—
397#237—68no—
398#237—68no—
399#237—62no—
400#237—62no—
401#237—68no—
402#237—68no—
403D3×D4—34no—
404D3×D4—34no—
405D3×D4—62no—
406D3×D4—62no—
407D3×D4—68no—
408D3×D4—68no—
409#235—22no—
410#235—22no—
411#235—68no—
412#235—68no—
413#235C22×D314yes—
414#235C22×D314yes—
415C2×D12—22no—
416C2×D12—21no—
417C2×D12—62no—
418C2×D12—62no—
419C2×D12—68no—
420C2×D12—61no—
421C2×D12—61no—
422C2×D12C22×D311yescharacteristic
423C2×D12C22×D312yes—
424C2×D12C22×D311yescharacteristic
425C2×D12C22×D314yescomplemented
426C2×C4×D3—21no—
427C2×C4×D3—21no—
428C2×C4×D3—31no—
429C2×C4×D3—31no—
430C2×C4×D3—31no—
431C2×C4×D3—31no—
432C2×C4×D3—34no—
433C2×C4×D3—34no—
434C2×C4×D3—31no—
435C2×C4×D3—31no—
436C2×C4×D3—31no—
437C2×C4×D3—31no—
438C2×C4×D3—34no—
439C2×C4×D3—34no—
440C2×C4×D3—61no—
441C2×C4×D3—61no—
442C2×C4×D3—64no—
443C2×C4×D3—61no—
444C2×C4×D3—61no—
445C2×C4×D3—64no—
446C2×C4×D3—68no—
447C2×C4×D3—68no—
448C2×C4×D3—61no—
449C2×C4×D3—61no—
450C2×C4×D3—61no—
451C2×C4×D3—61no—
452C2×C4×D3—62no—
453C2×C4×D3—62no—
454C2×C4×D3—68no—
455C2×Dic6—22no—
456C2×Dic6—21no—
457C2×Dic6—61no—
458C2×Dic6—61no—
459C2×Dic6C22×D311yescharacteristic
460C2×Dic6C22×D312yes—
461C2×Dic6C22×D311yescharacteristic
462C2×Dic6C22×D314yescomplemented
463C3×Q16—38no—
464C3×SD16—38no—
465C3×SD16—38no—
466C3×D8—38no—
467C3×M16—24no—
468C3×M16C22×D314yescomplemented
469C3×M16C22×D314yescomplemented
470C2×C3×C8—22no—
471C2×C3×C8C22×D312yes—
472C2×C3×C8C22×D312yes—
473#216—38no—
474#216—38no—
475#215—38no—
476#215—38no—
477#214—38no—
478#214—38no—
479#213—38no—
480#213—38no—
481#208—34no—
482#208—34no—
483#208—64no—
484C2×C3⋊C8—32no—
485C2×C3⋊C8—32no—
486C2×C3⋊C8—62no—
487Dic12C22×D318yescomplemented
488D24C22×D318yescomplemented
489#204C22×D318yescomplemented
490#204C22×D318yescomplemented
491ΓL(1,𝔽25)—38no—
492ΓL(1,𝔽25)—38no—
493ΓL(1,𝔽25)—68no—
494D3×C8—38no—
495D3×C8—38no—
496D3×C8—68no—
497C22×C32—22no—
498C22×C32C22×D412yes—
499C22×C32C22×D411yescharacteristic
500C2×C3⋊D3—22no—
501C2×C3⋊D3—22no—
502C2×C3⋊D3—44no—
503C2×C3⋊D3C22×D412yes—
504C2×C3⋊D3C22×D412yes—
505C2×C3×D3—24no—
506C2×C3×D3—22no—
507C2×C3×D3—22no—
508C2×C3×D3—48no—
509C2×C3×D3—42no—
510C2×C3×D3—42no—
511C2×C3×D3—44no—
512D32—48no—
513C32×C4C22×D411yescharacteristic
514C32×C4C22×D412yes—
515C32×C4C2511yescharacteristic
516C3⋊Dic3C22×D412yes—
517C3⋊Dic3C22×D412yes—
518C3×Dic3—24no—
519C3×Dic3—22no—
520C3×Dic3—22no—
521C2×#41—31no—
522C2×#41—31no—
523C2×#41—91no—
524C2×#41—92no—
525C2×#41—91no—
526C2×#41—92no—
527C2×#41—98no—
528C2×#41—98no—
529C2×#41—181no—
530C2×#41—181no—
531C2×#41—181no—
532C2×#41—184no—
533C2×#41—181no—
534C2×#41—184no—
535C22×Q8—31no—
536C22×Q8—91no—
537C22×D4—31no—
538C22×D4—91no—
539C22×D4—181no—
540C22×D4—181no—
541C23×C4—91no—
542C23×C4—181no—
543C23×C4—181no—
544#137—38no—
545#137—916no—
546#137—98no—
547AGL(1,ℤ/8)—38no—
548AGL(1,ℤ/8)—916no—
549AGL(1,ℤ/8)—98no—
550#135—916no—
551#135—916no—
552C2×Q16—32no—
553C2×Q16—92no—
554C2×SD16—32no—
555C2×SD16—32no—
556C2×SD16—92no—
557C2×SD16—92no—
558C2×D8—32no—
559C2×D8—92no—
560C2×M16—91no—
561C2×M16—98no—
562C2×M16—92no—
563C2×M16D3211yescharacteristic, complemented
564C22×C8—92no—
565C23×C3—21no—
566C23×C3—64no—
567C23×C3—62no—
568C23×C3—61no—
569C23×C3—61no—
570C23×C3—124no—
571C23×C3D3×D411yescharacteristic
572C23×C3D3×D411yescharacteristic
573C22×D3—21no—
574C22×D3—21no—
575C22×D3—22no—
576C22×D3—24no—
577C22×D3—31no—
578C22×D3—31no—
579C22×D3—31no—
580C22×D3—31no—
581C22×D3—34no—
582C22×D3—34no—
583C22×D3—44no—
584C22×D3—61no—
585C22×D3—61no—
586C22×D3—64no—
587C22×D3—64no—
588C22×D3—64no—
589C22×D3—124no—
590C22×D3—124no—
591C22×D3—122no—
592C22×D3—122no—
593C22×D3—124no—
594C3×Q8—32no—
595C3×Q8—34no—
596C3×Q8—32no—
597C3×Q8—61no—
598C3×Q8—61no—
599C3×Q8—62no—
600C3×Q8—64no—
601C3×D4—32no—
602C3×D4—34no—
603C3×D4—32no—
604C3×D4—64no—
605C3×D4—64no—
606C3×D4—61no—
607C3×D4—61no—
608C3×D4—62no—
609C3×D4—64no—
610C2×C3×C4—21no—
611C2×C3×C4—22no—
612C2×C3×C4—22no—
613C2×C3×C4—21no—
614C2×C3×C4—61no—
615C2×C3×C4—61no—
616C2×C3×C4—64no—
617C2×C3×C4—62no—
618C2×C3×C4—64no—
619C2×C3×C4—64no—
620C2×C3×C4D3×D411yescharacteristic
621C2×C3×C4D3×D412yes—
622C2×C3×C4D3×D411yescharacteristic
623C2×C3×C4D3×D412yes—
624C2×C3×C4C23×D311yescharacteristic
625C2×C3×C4C23×D311yescharacteristic
626C2×C3×C4C23×D312yes—
627C2×C3×C4C23×D312yes—
628#67—24no—
629#67—24no—
630#67—64no—
631#67—64no—
632#67—68no—
633#67—68no—
634#67—64no—
635#67—64no—
636C2×Dic3—22no—
637C2×Dic3—24no—
638C2×Dic3—21no—
639C2×Dic3—21no—
640C2×Dic3—31no—
641C2×Dic3—31no—
642C2×Dic3—31no—
643C2×Dic3—34no—
644C2×Dic3—31no—
645C2×Dic3—34no—
646C2×Dic3—64no—
647C2×Dic3—61no—
648C2×Dic3—61no—
649C2×Dic3—64no—
650C2×Dic3—64no—
651C2×Dic3—68no—
652C2×Dic3—68no—
653D12—22no—
654D12—24no—
655D12—21no—
656D12—21no—
657D12—68no—
658D12—68no—
659D12—64no—
660D12—64no—
661D12C23×D312yes—
662D12C23×D314yes—
663D12C23×D312yes—
664C4×D3—24no—
665C4×D3—24no—
666C4×D3—34no—
667C4×D3—34no—
668C4×D3—34no—
669C4×D3—34no—
670C4×D3—32no—
671C4×D3—32no—
672C4×D3—32no—
673C4×D3—32no—
674C4×D3—32no—
675C4×D3—32no—
676C4×D3—32no—
677C4×D3—32no—
678C4×D3—64no—
679C4×D3—62no—
680C4×D3—62no—
681C4×D3—64no—
682C4×D3—62no—
683C4×D3—62no—
684C4×D3—64no—
685C4×D3—64no—
686C4×D3—64no—
687C4×D3—64no—
688C4×D3—68no—
689C4×D3—68no—
690Dic6—22no—
691Dic6—24no—
692Dic6—21no—
693Dic6—21no—
694Dic6—64no—
695Dic6—64no—
696Dic6C23×D312yes—
697Dic6C23×D314yes—
698Dic6C23×D312yes—
699C3×C8—24no—
700C3×C8C23×D314yes—
701C3×C8C23×D314yes—
702C3⋊C8—34no—
703C3⋊C8—34no—
704C3⋊C8—64no—
705C2×C32—22no—
706C2×C32#57512yescomplemented
707C2×C32C23×D411yescharacteristic
708C3⋊D3—22no—
709C3⋊D3—22no—
710C3×D3—42no—
711C3×D3—42no—
712C3×D3—44no—
713C24—61no—
714C24—91no—
715C24—181no—
716#41—34no—
717#41—34no—
718#41—62no—
719#41—62no—
720#41—94no—
721#41—98no—
722#41—94no—
723#41—98no—
724#41—188no—
725#41—188no—
726#41—188no—
727#41—184no—
728#41—184no—
729#41—188no—
730#41—182no—
731#41—182no—
732C2×Q8—31no—
733C2×Q8—32no—
734C2×Q8—31no—
735C2×Q8—34no—
736C2×Q8—62no—
737C2×Q8—61no—
738C2×Q8—94no—
739C2×Q8—181no—
740C2×Q8—182no—
741C2×D4—31no—
742C2×D4—32no—
743C2×D4—31no—
744C2×D4—34no—
745C2×D4—61no—
746C2×D4—61no—
747C2×D4—62no—
748C2×D4—61no—
749C2×D4—94no—
750C2×D4—188no—
751C2×D4—181no—
752C2×D4—181no—
753C2×D4—182no—
754C2×D4—182no—
755C2×D4—182no—
756C2×D4—181no—
757C2×D4—188no—
758C22×C4—61no—
759C22×C4—61no—
760C22×C4—61no—
761C22×C4—91no—
762C22×C4—91no—
763C22×C4—91no—
764C22×C4—94no—
765C22×C4—91no—
766C22×C4—94no—
767C22×C4—91no—
768C22×C4—188no—
769C22×C4—181no—
770C22×C4—188no—
771C22×C4—181no—
772C22×C4—181no—
773C22×C4—182no—
774C22×C4—182no—
775C22×C4C2×D3211yescharacteristic
776Q16—38no—
777Q16—98no—
778SD16—38no—
779SD16—38no—
780SD16—98no—
781SD16—98no—
782D8—38no—
783D8—98no—
784M16—94no—
785M16—98no—
786M16C2×D3214yescomplemented
787C2×C8—92no—
788C2×C8—98no—
789C2×C8C2×D3212yes—
790C22×C3—22no—
791C22×C3—22no—
792C22×C3—22no—
793C22×C3—21no—
794C22×C3—42no—
795C22×C3—64no—
796C22×C3—62no—
797C22×C3—62no—
798C22×C3—128no—
799C22×C3—122no—
800C22×C3—122no—
801C22×C3—124no—
802C22×C3C2×D3×D412yes—
803C22×C3C2×D3×D412yes—
804C22×C3C2×D3×D411yescharacteristic
805C22×C3C2×D3×D411yescharacteristic
806C2×D3—22no—
807C2×D3—22no—
808C2×D3—24no—
809C2×D3—32no—
810C2×D3—32no—
811C2×D3—32no—
812C2×D3—32no—
813C2×D3—48no—
814C2×D3—44no—
815C2×D3—42no—
816C2×D3—42no—
817C2×D3—62no—
818C2×D3—62no—
819C2×D3—64no—
820C2×D3—62no—
821C2×D3—62no—
822C2×D3—62no—
823C2×D3—62no—
824C2×D3—122no—
825C2×D3—128no—
826C2×D3—128no—
827C2×D3—124no—
828C2×D3—124no—
829C2×D3—128no—
830C3×C4—22no—
831C3×C4—21no—
832C3×C4—21no—
833C3×C4—62no—
834C3×C4—62no—
835C3×C4—64no—
836C3×C4C2×D3×D411yescharacteristic
837C3×C4C2×D3×D412yes—
838C3×C4C2×D3×D411yescharacteristic
839C3×C4C2×D3×D412yes—
840C3×C4C24×D311yescharacteristic
841C3×C4C24×D311yescharacteristic
842Dic3—24no—
843Dic3—22no—
844Dic3—22no—
845Dic3—32no—
846Dic3—32no—
847Dic3—32no—
848Dic3—32no—
849Dic3—62no—
850Dic3—62no—
851C32C2×#57511yescharacteristic, complemented, Sylow
852C23—64no—
853C23—61no—
854C23—61no—
855C23—62no—
856C23—91no—
857C23—91no—
858C23—94no—
859C23—124no—
860C23—184no—
861C23—362no—
862C23—364no—
863C23#380211yescharacteristic
864Q8—32no—
865Q8—34no—
866Q8—32no—
867Q8—64no—
868Q8—62no—
869Q8—61no—
870Q8—61no—
871Q8—184no—
872D4—32no—
873D4—34no—
874D4—32no—
875D4—64no—
876D4—64no—
877D4—64no—
878D4—62no—
879D4—61no—
880D4—61no—
881D4—184no—
882D4—184no—
883D4—188no—
884D4—188no—
885D4—184no—
886C2×C4—64no—
887C2×C4—61no—
888C2×C4—61no—
889C2×C4—62no—
890C2×C4—64no—
891C2×C4—64no—
892C2×C4—94no—
893C2×C4—91no—
894C2×C4—91no—
895C2×C4—94no—
896C2×C4—92no—
897C2×C4—92no—
898C2×C4—94no—
899C2×C4—92no—
900C2×C4—92no—
901C2×C4—184no—
902C2×C4—184no—
903C2×C4—184no—
904C2×C4—188no—
905C2×C4—188no—
906C2×C4#380212yes—
907C2×C4#380211yescharacteristic
908C2×C4C22×D3212yes—
909C2×C4C22×D3211yescharacteristic
910C8—94no—
911C8C22×D3214yes—
912C2×C3—22no—
913C2×C3—22no—
914C2×C3—21no—
915C2×C3—22no—
916C2×C3—42no—
917C2×C3—122no—
918C2×C3—122no—
919C2×C3—124no—
920C2×C3#577312yescomplemented
921C2×C3#577712yescomplemented
922C2×C3C22×D3×D411yescharacteristic
923C2×C3C22×D3×D411yescharacteristic
924D3—44no—
925D3—42no—
926D3—42no—
927D3—64no—
928D3—62no—
929D3—62no—
930D3—62no—
931D3—62no—
932D3—122no—
933C22—22no—
934C22—62no—
935C22—62no—
936C22—64no—
937C22—92no—
938C22—92no—
939C22—128no—
940C22—124no—
941C22—122no—
942C22—122no—
943C22—182no—
944C22—182no—
945C22—364no—
946C22—368no—
947C22C2×#380212yes—
948C22C2×#380211yescharacteristic
949C4—62no—
950C4—62no—
951C4—64no—
952C4—92no—
953C4—92no—
954C4C2×#380212yes—
955C4C2×#380211yescharacteristic
956C4C23×D3211yescharacteristic
957C3—21no—
958C3C2×#577311yescharacteristic, complemented
959C3C2×#577711yescharacteristic, complemented
960C2—22no—
961C2—124no—
962C2—122no—
963C2—122no—
964C2—182no—
965C2—182no—
966C2#1059471812yesdirect product factor
967C2C22×#380211yescharacteristic
subgroupG/H
centerC22C2×#3802
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×#64306C2semidirect
2. C22×#3796C2semidirect
3. C2×M16×C3⋊D3C2semidirect
4. C2×C3×#909C2semidirect
5. C2×C3×#908C2semidirect
6. C2×#63827C2semidirect
7. C2×#63823C2semidirect
8. #10594718C2direct (N × H)
9. C2×#63811C2semidirect
10. C2×#63810C2semidirect
11. C2×#63809C2semidirect
12. C2×#63798C2semidirect
18. C22×C3×D12C22semidirect
19. C22×C3×Dic6C22semidirect
25. #64306C22semidirect
26. C2×#3802C22semidirect
29. C2×#3797C22semidirect
34. C2×#3796C22semidirect
35. C2×#3796C22semidirect
36. C2×#3796C22semidirect
37. C2×#3796C22semidirect
38. C2×C32×M16C22semidirect
39. C2×#3748C22semidirect
40. M16×C3⋊D3C22semidirect
41. C2×#3743C22semidirect
42. C2×C8×C3⋊D3C22semidirect
43. C3×#909C22semidirect
44. C3×#908C22semidirect
45. C2×C3×Dic12C22semidirect
46. C2×C3×D24C22semidirect
47. C2×C3×#204C22semidirect
48. C2×C3×#204C22semidirect
49. C2×#3718C22semidirect
50. #63827C22semidirect
51. C2×#3715C22semidirect
52. C2×#3715C22semidirect
53. #63823C22semidirect
54. C2×#3713C22semidirect
55. #63811C22semidirect
56. #63810C22semidirect
57. #63809C22semidirect
58. #63798C22semidirect
79. C2×#909D3semidirect
80. C2×#908D3semidirect
107. C2×C3×D12C23semidirect
115. C2×C3×Dic6C23semidirect
132. #3802C23semidirect
136. #3797C23semidirect
144. #3796C23semidirect
145. #3796C23semidirect
146. #3796C23semidirect
147. C32×M16C23semidirect
149. #3748C23semidirect
151. #3743C23semidirect
152. C8×C3⋊D3C23semidirect
153. C3×Dic12C23semidirect
154. C3×D24C23semidirect
155. C3×#204C23semidirect
156. C3×#204C23semidirect
157. #3718C23semidirect
158. #3715C23semidirect
159. #3715C23semidirect
160. #3713C23semidirect
201. C22×D12C2×D3semidirect
208. C22×Dic6C2×D3semidirect
216. C2×C3×M16C2×D3semidirect
217. C2×C3×M16C2×D3semidirect
241. #909C2×D3semidirect
242. #908C2×D3semidirect
246. C2×Dic12C2×D3semidirect
247. C2×D24C2×D3semidirect
248. C2×#204C2×D3semidirect
249. C2×#204C2×D3semidirect
425. C2×D12C22×D3semidirect
462. C2×Dic6C22×D3semidirect
468. C3×M16C22×D3semidirect
469. C3×M16C22×D3semidirect
487. Dic12C22×D3semidirect
488. D24C22×D3semidirect
489. #204C22×D3semidirect
490. #204C22×D3semidirect
563. C2×M16D32semidirect
706. C2×C32#575semidirect
786. M16C2×D32semidirect
851. C32C2×#575semidirect
920. C2×C3#5773semidirect
921. C2×C3#5777semidirect
958. C3C2×#5773semidirect
959. C3C2×#5777semidirect
966. C2#10594718direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#643062
C22×#37962
C2×M16×C3⋊D32
C2×C3×#9092
C2×C3×#9082
C2×#638272
C2×#638232
#105947182
C2×#638112
C2×#638102
C2×#638092
C2×#637982
C2×#57773
C2×#57733