Finite Group Databasebeta

← C2×#79508 #11670253

Subgroups — C2×#79508 #11670253

Order 768.

2826 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#909C211yesmaximal, characteristic, complemented
2C22×#904C211yesmaximal, characteristic, complemented
3C2×#5553C211yesmaximal, characteristic, complemented
4C2×#5552C211yesmaximal, characteristic, complemented
5C2×C3×#435C211yesmaximal, characteristic, complemented
6C2×#5135C211yesmaximal, characteristic, complemented
7C2×#5114C211yesmaximal, characteristic, complemented
8#79508C2116yesmaximal, direct product factor
9C2×#4845C211yesmaximal, characteristic, complemented
10C2×#4848C211yesmaximal, characteristic, complemented
11C2×#4738C211yesmaximal, characteristic, complemented
12C2×#4733C211yesmaximal, characteristic, complemented
13C2×#4734C211yesmaximal, characteristic, complemented
14C2×#4734C211yesmaximal, characteristic, complemented
15C2×#4716C211yesmaximal, characteristic, complemented
16C2×#4712C211yesmaximal, characteristic, complemented
17C2×#3271—31nomaximal, Sylow
18C22×#235C2211yescharacteristic
19C22×#235C2211yescharacteristic
20C22×#235C2211yescharacteristic
21C23×Dic6C2211yescharacteristic
22C22×C3×M16C2211yescharacteristic
23C23×C3×C8C2211yescharacteristic
24C2×C3×C4×D4C2211yescharacteristic
25C2×#940—21no—
26C2×#939—21no—
27C2×#930C2211yescharacteristic
28C2×#930C2211yescharacteristic
29C2×#930C2211yescharacteristic
30C2×#924C2211yescharacteristic
31C2×#909—28no—
32C2×#909C2218yescomplemented
33C22×Dic12C2211yescharacteristic
34C22×Dic12C2211yescharacteristic
35C2×#904—28no—
36C2×#904C2218yescomplemented
37C22×D24C2211yescharacteristic
38C22×D24C2211yescharacteristic
39C22×#204C2211yescharacteristic
40C22×#204C2211yescharacteristic
41C22×#204C2211yescharacteristic
42C22×#204C2211yescharacteristic
43C22×#204C2211yescharacteristic
44#5553—24no—
45#5553C2218yescomplemented
46#5552—24no—
47#5552C2218yescomplemented
48C2×#896—21no—
49C2×#893—21no—
50C2×#885—21no—
51C2×#884—21no—
52C2×#884—21no—
53C2×#67⋊C4—21no—
54C2×#875C2211yescharacteristic
55C2×#874C2211yescharacteristic
56C2×C4×Dic6C2211yescharacteristic
57C2×C4×Dic6C2211yescharacteristic
58C3×#435C2218yescomplemented
59C2×C3×C4⋊C8C2211yescharacteristic
60C2×C3×C22⋊C8C2211yescharacteristic
61C2×C3×C22⋊C8C2211yescharacteristic
62C2×C3×#97C2211yescharacteristic
63#5135C2218yescomplemented
64#5114C2218yescomplemented
65C2×#821C2211yescharacteristic
66C2×#821C2211yescharacteristic
67C2×#821C2211yescharacteristic
68C2×#817C2211yescharacteristic
69C2×#816C2211yescharacteristic
70C2×#816C2211yescharacteristic
71C2×#816C2211yescharacteristic
72#4848C2218yescomplemented
73#4845C2218yescomplemented
74#4738C2218yescomplemented
75#4734C2218yescomplemented
76#4734C2218yescomplemented
77#4733C2218yescomplemented
78#4716C2218yescomplemented
79#4712C2218yescomplemented
80C22×#137—31no—
81C22×#135—31no—
82C2×#550—31no—
83C2×#548—31no—
84#3271—316no—
85C2×#496—31no—
86C2×#469—31no—
87C2×#465—31no—
88C2×#464—31no—
89C2×#460—31no—
90C2×#452—31no—
91C2×#449—31no—
92C2×#449—31no—
93C2×#448—31no—
94C2×#441—31no—
95C2×#435D311yescharacteristic, complemented
96C22×C3×D4D411yescharacteristic
97C23×C3×C4C2311yescharacteristic
98C23×C3×C4C2311yescharacteristic
99C22×#67—21no—
100C22×#67—21no—
101C22×#67—21no—
102C22×#67—21no—
103C22×#67—21no—
104C22×#67—21no—
105C23×Dic3—21no—
106C2×#235—22no—
107C2×#235—22no—
108C2×#235—22no—
109C2×#235—24no—
110C2×#235—24no—
111C2×#235—24no—
112C2×#235—42no—
113C2×#235—42no—
114C2×#235—42no—
115C2×#235C2314yes—
116C2×#235C2314yes—
117C2×#235C2314yes—
118C22×D12—21no—
119C22×D12—21no—
120C22×D12C2311yescharacteristic
121C22×D12C2311yescharacteristic
122C22×D12C2311yescharacteristic
123C22×C4×D3—21no—
124C22×C4×D3—21no—
125C22×C4×D3—21no—
126C22×Dic6—24no—
127C22×Dic6—21no—
128C22×Dic6—22no—
129C22×Dic6—42no—
130C22×Dic6C2311yescharacteristic
131C22×Dic6C2314yes—
132C22×Dic6C2311yescharacteristic
133C22×Dic6C2311yescharacteristic
134C2×C3×M16—24no—
135C2×C3×M16C2314yes—
136C22×C3×C8—24no—
137C22×C3×C8C2311yescharacteristic
138C22×C3×C8C2314yes—
139C22×C3×C8C2311yescharacteristic
140C22×C3×C8C2311yescharacteristic
141C22×C3×C8C2311yescharacteristic
142C3×C4×D4D414yes—
143C3×C4×D4C2314yes—
144C2×C3×C4⋊C4D411yescharacteristic
145C2×C3×C22⋊C4D411yescharacteristic
146C2×C3×C22⋊C4D411yescharacteristic
147C2×C3×C42C2311yescharacteristic
148C2×#217—21no—
149#940—28no—
150#939—28no—
151#930—22no—
152#930—22no—
153#930—22no—
154#930C2314yes—
155#930C2314yes—
156#930C2314yes—
157C2×(C2×D3)⋊C4—21no—
158C2×(C2×D3)⋊C4—21no—
159C2×(C2×D3)⋊C4—21no—
160C2×(C2×D3)⋊C4—21no—
161C2×(C2×D3)⋊C4—21no—
162C2×C4⋊Dic3C2311yescharacteristic
163C2×C4⋊Dic3C2311yescharacteristic
164#924—22no—
165#924C2314yes—
166C2×Dic3⋊C4—21no—
167C2×Dic3⋊C4—21no—
168C2×Dic3⋊C4—21no—
169C2×C4×Dic3—21no—
170C2×C4×Dic3—21no—
171#909—232no—
172C2×Dic12—24no—
173C2×Dic12D418yescomplemented
174C2×Dic12C2314yes—
175C2×Dic12C2314yes—
176#904—232no—
177C2×D24—24no—
178C2×D24—42no—
179C2×D24C2314yes—
180C2×D24C2314yes—
181C2×#204—24no—
182C2×#204—24no—
183C2×#204—24no—
184C2×#204—24no—
185C2×#204—42no—
186C2×#204C2314yes—
187C2×#204C2314yes—
188C2×#204C2314yes—
189C2×#204C2314yes—
190C2×#204C2314yes—
191#896—28no—
192#893—28no—
193#885—28no—
194#884—28no—
195#884—28no—
196#67⋊C4—28no—
197#875—22no—
198#875C2314yes—
199#874—22no—
200#874C2314yes—
201C4×Dic6—22no—
202C4×Dic6—22no—
203C4×Dic6C2314yes—
204C4×Dic6C2314yes—
205C3×C4⋊C8C2314yes—
206C3×C22⋊C8C2314yes—
207C3×C22⋊C8C2314yes—
208C3×#97C2314yes—
209#821C2314yes—
210#821C2314yes—
211#821C2314yes—
212#817C2314yes—
213#816C2314yes—
214#816C2314yes—
215#816C2314yes—
216C22×#41—31no—
217C22×#41—31no—
218C22×#41—31no—
219C23×Q8—31no—
220C2×#137—38no—
221C2×#137—68no—
222C2×#135—38no—
223C2×#135—68no—
224C22×Q16—31no—
225C22×Q16—31no—
226C22×SD16—31no—
227C22×SD16—31no—
228C22×SD16—31no—
229C22×SD16—31no—
230C22×SD16—31no—
231C22×D8—31no—
232C22×D8—31no—
233C22×M16C2×D311yescharacteristic
234C23×C8C2×D311yescharacteristic
235#550—38no—
236#550—64no—
237#548—38no—
238#548—64no—
239C2×#127—31no—
240C2×#127—61no—
241C2×#124—31no—
242C2×#124—61no—
243C2×C22⋊Q8—31no—
244C2×C22⋊Q8—61no—
245C2×#121—31no—
246C2×#121—31no—
247C2×#121—31no—
248C2×#121—61no—
249C2×#121—61no—
250C2×#121—61no—
251C2×C4×Q8—31no—
252C2×C4×Q8—31no—
253C2×C4×D4—61no—
254C2×C4×D4—61no—
255C2×C4×D4C2×D311yescharacteristic
256#496—38no—
257#469—38no—
258#465—38no—
259#464—38no—
260#460—38no—
261#452—38no—
262#449—38no—
263#449—38no—
264#448—38no—
265#441—38no—
266#435C2×D318yescomplemented
267C2×#106—31no—
268C2×C4⋊C8C2×D311yescharacteristic
269C2×#103—31no—
270C2×#103—31no—
271C2×#103—31no—
272C2×#102—31no—
273C2×#102—31no—
274C2×#102—31no—
275C2×C22⋊C8C2×D311yescharacteristic
276C2×C22⋊C8C2×D311yescharacteristic
277C2×#97C2×D311yescharacteristic
278C24×C3C2×D411yescharacteristic
279C24×C3C2×D411yescharacteristic
280C23×D3—21no—
281C23×D3—21no—
282C23×D3—21no—
283C2×C3×D4—42no—
284C2×C3×D4C2×D414yes—
285C22×C3×C4—22no—
286C22×C3×C4—22no—
287C22×C3×C4—22no—
288C22×C3×C4—22no—
289C22×C3×C4C2×D411yescharacteristic
290C22×C3×C4C2×D411yescharacteristic
291C22×C3×C4C2×D411yescharacteristic
292C22×C3×C4C2×D412yes—
293C22×C3×C4C2×D411yescharacteristic
294C22×C3×C4C2×D412yes—
295C22×C3×C4C2412yes—
296C22×C3×C4C2412yes—
297C22×C3×C4C2411yescharacteristic
298C2×#67—24no—
299C2×#67—24no—
300C2×#67—24no—
301C2×#67—24no—
302C2×#67—24no—
303C2×#67—24no—
304C2×#67—44no—
305C2×#67—44no—
306C2×#67—44no—
307C2×#67—44no—
308C2×#67—82no—
309C2×#67—82no—
310C22×Dic3—21no—
311C22×Dic3—21no—
312C22×Dic3—24no—
313C22×Dic3—21no—
314C22×Dic3—21no—
315C22×Dic3—21no—
316C22×Dic3—44no—
317#235—28no—
318#235—28no—
319#235—28no—
320#235—44no—
321#235—44no—
322#235—44no—
323#235—48no—
324#235—48no—
325#235—48no—
326C2×D12—22no—
327C2×D12—22no—
328C2×D12—22no—
329C2×D12—22no—
330C2×D12—22no—
331C2×D12—22no—
332C2×D12—21no—
333C2×D12—21no—
334C2×D12—24no—
335C2×D12—21no—
336C2×D12—24no—
337C2×D12—44no—
338C2×D12—82no—
339C2×D12C2412yes—
340C2×D12C2412yes—
341C2×D12C2412yes—
342C2×C4×D3—24no—
343C2×C4×D3—24no—
344C2×C4×D3—24no—
345C2×C4×D3—44no—
346C2×C4×D3—44no—
347C2×C4×D3—44no—
348C2×Dic6—21no—
349C2×Dic6—21no—
350C2×Dic6—22no—
351C2×Dic6—22no—
352C2×Dic6—22no—
353C2×Dic6—22no—
354C2×Dic6—28no—
355C2×Dic6—21no—
356C2×Dic6—24no—
357C2×Dic6—44no—
358C2×Dic6—48no—
359C2×Dic6—44no—
360C2×Dic6C2×D414yes—
361C2×Dic6C2×D414yes—
362C2×Dic6C2412yes—
363C2×Dic6C2412yes—
364C2×Dic6C2412yes—
365C3×M16—28no—
366C2×C3×C8—22no—
367C2×C3×C8—22no—
368C2×C3×C8—22no—
369C2×C3×C8—28no—
370C2×C3×C8C2×D414yes—
371C2×C3×C8C2412yes—
372C2×C3×C8C2412yes—
373C2×C3×C8C2412yes—
374C2×C3×C8C2412yes—
375C3×C4⋊C4C2×D414yes—
376C3×C22⋊C4C2×D414yes—
377C3×C22⋊C4C2×D414yes—
378C3×C42C2×D412yes—
379C3×C42C2412yes—
380#217—24no—
381(C2×D3)⋊C4—24no—
382(C2×D3)⋊C4—24no—
383(C2×D3)⋊C4—24no—
384(C2×D3)⋊C4—24no—
385(C2×D3)⋊C4—24no—
386C4⋊Dic3—21no—
387C4⋊Dic3—21no—
388C4⋊Dic3C2412yes—
389C4⋊Dic3C2412yes—
390Dic3⋊C4—24no—
391Dic3⋊C4—24no—
392Dic3⋊C4—24no—
393C4×Dic3—24no—
394C4×Dic3—24no—
395Dic12—28no—
396Dic12C2×D4116yescomplemented
397D24—28no—
398D24—44no—
399#204—28no—
400#204—28no—
401#204—28no—
402#204—28no—
403#204—44no—
404C2×#41—34no—
405C2×#41—34no—
406C2×#41—34no—
407C2×#41—64no—
408C2×#41—64no—
409C2×#41—64no—
410C2×#41—62no—
411C2×#41—62no—
412C2×#41—62no—
413C2×#41—122no—
414C2×#41—122no—
415C2×#41—122no—
416C22×Q8—31no—
417C22×Q8—31no—
418C22×Q8—31no—
419C22×Q8—34no—
420C22×Q8—64no—
421C22×Q8—61no—
422C22×Q8—62no—
423C22×Q8—122no—
424C22×D4—31no—
425C22×D4—31no—
426C22×D4—31no—
427C22×D4—61no—
428C22×D4—61no—
429C22×D4—61no—
430C22×D4—61no—
431C22×D4—61no—
432C22×D4—61no—
433C22×D4—61no—
434C22×D4—61no—
435C22×D4D1211yescharacteristic
436C23×C4—61no—
437C23×C4—61no—
438C23×C4—61no—
439C23×C4—61no—
440C23×C4C22×D311yescharacteristic
441C23×C4C22×D311yescharacteristic
442#137—632no—
443#135—632no—
444C2×Q16—38no—
445C2×Q16—34no—
446C2×Q16—34no—
447C2×Q16—64no—
448C2×SD16—34no—
449C2×SD16—34no—
450C2×SD16—34no—
451C2×SD16—34no—
452C2×SD16—34no—
453C2×SD16—64no—
454C2×SD16—64no—
455C2×SD16—64no—
456C2×SD16—64no—
457C2×SD16—122no—
458C2×D8—34no—
459C2×D8—34no—
460C2×D8—64no—
461C2×D8—122no—
462C2×M16—24no—
463C2×M16C22×D314yes—
464C22×C8—24no—
465C22×C8C22×D311yescharacteristic
466C22×C8C22×D314yes—
467C22×C8C22×D311yescharacteristic
468C22×C8C22×D311yescharacteristic
469C22×C8C22×D311yescharacteristic
470#127—34no—
471#127—68no—
472#127—62no—
473#124—34no—
474#124—68no—
475#124—62no—
476C22⋊Q8—34no—
477C22⋊Q8—62no—
478C22⋊Q8—68no—
479#121—34no—
480#121—34no—
481#121—34no—
482#121—68no—
483#121—62no—
484#121—62no—
485#121—62no—
486#121—68no—
487#121—68no—
488C4×Q8—34no—
489C4×Q8—34no—
490C4×Q8—62no—
491C4×Q8—62no—
492C4×D4—68no—
493C4×D4—68no—
494C4×D4D1214yes—
495C4×D4C22×D314yes—
496C2×C4⋊C4—31no—
497C2×C4⋊C4—31no—
498C2×C4⋊C4—61no—
499C2×C4⋊C4—61no—
500C2×C4⋊C4—61no—
501C2×C4⋊C4D1211yescharacteristic
502C2×C22⋊C4—61no—
503C2×C22⋊C4—61no—
504C2×C22⋊C4—61no—
505C2×C22⋊C4—61no—
506C2×C22⋊C4—61no—
507C2×C22⋊C4—61no—
508C2×C22⋊C4D1211yescharacteristic
509C2×C22⋊C4D1211yescharacteristic
510C2×C42—61no—
511C2×C42—61no—
512C2×C42C22×D311yescharacteristic
513#106—34no—
514C4⋊C8C22×D314yes—
515#103—34no—
516#103—34no—
517#103—34no—
518#102—34no—
519#102—34no—
520#102—34no—
521C22⋊C8C22×D314yes—
522C22⋊C8C22×D314yes—
523#97C22×D314yes—
524C23×C3—22no—
525C23×C3—22no—
526C23×C3—22no—
527C23×C3—22no—
528C23×C3—22no—
529C23×C3—22no—
530C23×C3C22×D412yes—
531C23×C3C22×D412yes—
532C23×C3C22×D411yescharacteristic
533C22×D3—22no—
534C22×D3—22no—
535C22×D3—22no—
536C22×D3—42no—
537C22×D3—42no—
538C22×D3—42no—
539C22×D3—42no—
540C22×D3—42no—
541C22×D3—42no—
542C22×D3—42no—
543C22×D3—42no—
544C22×D3—42no—
545C3×D4—44no—
546C2×C3×C4—22no—
547C2×C3×C4—22no—
548C2×C3×C4—22no—
549C2×C3×C4—22no—
550C2×C3×C4—24no—
551C2×C3×C4—24no—
552C2×C3×C4—22no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—22no—
556C2×C3×C4C22×D412yes—
557C2×C3×C4C22×D412yes—
558C2×C3×C4C22×D412yes—
559C2×C3×C4C22×D412yes—
560C2×C3×C4C22×D411yescharacteristic
561C2×C3×C4C22×D412yes—
562C2×C3×C4H(5,𝔽2)12yes—
563C2×C3×C4C2511yescharacteristic
564#67—48no—
565#67—48no—
566#67—48no—
567#67—48no—
568#67—84no—
569#67—84no—
570C2×Dic3—24no—
571C2×Dic3—24no—
572C2×Dic3—22no—
573C2×Dic3—22no—
574C2×Dic3—22no—
575C2×Dic3—22no—
576C2×Dic3—22no—
577C2×Dic3—48no—
578C2×Dic3—42no—
579C2×Dic3—42no—
580C2×Dic3—42no—
581D12—22no—
582D12—22no—
583D12—22no—
584D12—22no—
585D12—22no—
586D12—22no—
587D12—48no—
588D12—42no—
589D12—42no—
590D12—42no—
591D12—84no—
592C4×D3—48no—
593C4×D3—48no—
594C4×D3—48no—
595Dic6—24no—
596Dic6—24no—
597Dic6—22no—
598Dic6—22no—
599Dic6—22no—
600Dic6—22no—
601Dic6—48no—
602Dic6—42no—
603Dic6C22×D414yes—
604Dic6C22×D414yes—
605C3×C8—22no—
606C3×C8—22no—
607C3×C8—22no—
608C3×C8C22×D414yes—
609C24—61no—
610C24—61no—
611C24—61no—
612C24C2×D1211yescharacteristic
613C24C2×D1211yescharacteristic
614#41—68no—
615#41—68no—
616#41—68no—
617#41—124no—
618#41—124no—
619#41—124no—
620#41—128no—
621#41—128no—
622#41—128no—
623C2×Q8—34no—
624C2×Q8—34no—
625C2×Q8—32no—
626C2×Q8—32no—
627C2×Q8—32no—
628C2×Q8—68no—
629C2×Q8—61no—
630C2×Q8—61no—
631C2×Q8—64no—
632C2×Q8—61no—
633C2×Q8—62no—
634C2×Q8—62no—
635C2×Q8—62no—
636C2×Q8—62no—
637C2×Q8—124no—
638C2×Q8—124no—
639C2×Q8—128no—
640C2×D4—32no—
641C2×D4—32no—
642C2×D4—32no—
643C2×D4—42no—
644C2×D4—64no—
645C2×D4—64no—
646C2×D4—64no—
647C2×D4—64no—
648C2×D4—64no—
649C2×D4—64no—
650C2×D4—64no—
651C2×D4—61no—
652C2×D4—61no—
653C2×D4—61no—
654C2×D4—64no—
655C2×D4—62no—
656C2×D4—62no—
657C2×D4—62no—
658C2×D4—62no—
659C2×D4—62no—
660C2×D4—62no—
661C2×D4—124no—
662C2×D4—124no—
663C2×D4—124no—
664C2×D4—124no—
665C2×D4—124no—
666C2×D4—242no—
667C2×D4—242no—
668C2×D4—242no—
669C2×D4C2×D1214yes—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—61no—
675C22×C4—61no—
676C22×C4—64no—
677C22×C4—61no—
678C22×C4—61no—
679C22×C4—61no—
680C22×C4—64no—
681C22×C4—64no—
682C22×C4—64no—
683C22×C4—124no—
684C22×C4—124no—
685C22×C4—124no—
686C22×C4—124no—
687C22×C4C2×D1212yes—
688C22×C4C2×D1212yes—
689C22×C4C2×D1211yescharacteristic
690C22×C4C2×D1211yescharacteristic
691C22×C4C2×D1211yescharacteristic
692C22×C4C2×D1211yescharacteristic
693C22×C4C23×D312yes—
694C22×C4C23×D312yes—
695C22×C4C23×D311yescharacteristic
696Q16—316no—
697Q16—68no—
698SD16—68no—
699SD16—68no—
700SD16—68no—
701SD16—68no—
702SD16—124no—
703D8—68no—
704D8—124no—
705M16—28no—
706C2×C8—22no—
707C2×C8—22no—
708C2×C8—22no—
709C2×C8—28no—
710C2×C8D3×D414yes—
711C2×C8C23×D312yes—
712C2×C8C23×D312yes—
713C2×C8C23×D312yes—
714C2×C8C23×D312yes—
715C4⋊C4—32no—
716C4⋊C4—32no—
717C4⋊C4—61no—
718C4⋊C4—61no—
719C4⋊C4—64no—
720C4⋊C4—64no—
721C4⋊C4—64no—
722C4⋊C4C2×D1214yes—
723C22⋊C4—64no—
724C22⋊C4—64no—
725C22⋊C4—64no—
726C22⋊C4—64no—
727C22⋊C4—64no—
728C22⋊C4—64no—
729C22⋊C4C2×D1214yes—
730C22⋊C4C2×D1214yes—
731C42—64no—
732C42—64no—
733C42C2×D1212yes—
734C42C23×D312yes—
735C22×C3—22no—
736C22×C3—22no—
737C22×C3—22no—
738C22×C3—22no—
739C22×C3—22no—
740C22×C3—22no—
741C22×C3—44no—
742C22×C3—44no—
743C22×C3D4212yes—
744C22×C3#57512yes—
745C22×C3#57712yes—
746C22×C3C23×D411yescharacteristic
747C2×D3—42no—
748C2×D3—42no—
749C2×D3—42no—
750C2×D3—42no—
751C2×D3—42no—
752C2×D3—42no—
753C2×D3—42no—
754C2×D3—42no—
755C2×D3—42no—
756C2×D3—84no—
757C2×D3—84no—
758C2×D3—84no—
759C3×C4—22no—
760C3×C4—22no—
761C3×C4—22no—
762C3×C4—22no—
763C3×C4D4212yes—
764C3×C4C23×D411yescharacteristic
765C3×C4C2×H(5,𝔽2)11yescharacteristic
766Dic3—24no—
767Dic3—24no—
768Dic3—42no—
769Dic3—42no—
770Dic3—42no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—62no—
778C23—62no—
779C23—62no—
780C23—122no—
781C23—122no—
782C23—122no—
783C23—122no—
784C23—122no—
785C23—122no—
786C23—122no—
787C23—122no—
788C23—122no—
789C23C22×D1212yes—
790C23C22×D1212yes—
791C23C22×D1211yescharacteristic
792Q8—34no—
793Q8—34no—
794Q8—62no—
795Q8—62no—
796Q8—64no—
797Q8—64no—
798Q8—62no—
799Q8—62no—
800Q8—128no—
801Q8—122no—
802D4—44no—
803D4—62no—
804D4—62no—
805D4—62no—
806D4—62no—
807D4—62no—
808D4—62no—
809D4—128no—
810D4—128no—
811D4—128no—
812D4—128no—
813D4—128no—
814D4—122no—
815D4—122no—
816D4—122no—
817D4—244no—
818D4—244no—
819D4—244no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—24no—
829C2×C4—24no—
830C2×C4—62no—
831C2×C4—62no—
832C2×C4—64no—
833C2×C4—64no—
834C2×C4—62no—
835C2×C4—62no—
836C2×C4—62no—
837C2×C4—128no—
838C2×C4—128no—
839C2×C4—128no—
840C2×C4—128no—
841C2×C4—122no—
842C2×C4—122no—
843C2×C4—122no—
844C2×C4C22×D1212yes—
845C2×C4C22×D1212yes—
846C2×C4C22×D1212yes—
847C2×C4C22×D1212yes—
848C2×C4C22×D1211yescharacteristic
849C2×C4C2×D3×D412yes—
850C2×C4#100912yes—
851C2×C4C24×D311yescharacteristic
852C8—22no—
853C8—22no—
854C8—22no—
855C8C2×D3×D414yes—
856C2×C3—42no—
857C2×C3—42no—
858C2×C3#327114yescomplemented
859C2×C3C2×D4211yescharacteristic
860C2×C3C2×#57511yescharacteristic
861C2×C3C2×#57711yescharacteristic
862D3—82no—
863D3—82no—
864D3—82no—
865C22—22no—
866C22—22no—
867C22—22no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—44no—
872C22—44no—
873C22—122no—
874C22—122no—
875C22—122no—
876C22—122no—
877C22—122no—
878C22—122no—
879C22—122no—
880C22—122no—
881C22—122no—
882C22—244no—
883C22—244no—
884C22—244no—
885C22D4×D1212yes—
886C22#574812yes—
887C22#575112yes—
888C22C23×D1211yescharacteristic
889C4—22no—
890C4—22no—
891C4—22no—
892C4—22no—
893C4—64no—
894C4—64no—
895C4—122no—
896C4—122no—
897C4—122no—
898C4D4×D1212yes—
899C4C22×D3×D411yescharacteristic
900C4C2×#100911yescharacteristic
901C3C2×#327111yescharacteristic, complemented, Sylow
902C2—42no—
903C2—42no—
904C2—242no—
905C2—242no—
906C2—242no—
907C2#7950814yesdirect product factor
908C2C2×D4×D1211yescharacteristic
909C2C2×#574811yescharacteristic
910C2C2×#575111yescharacteristic
subgroupG/H
centerC23C22×D12
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#435C2
socleC23×C3C22×D4
hypercenterC2×#435D3
hypocenterC3C2×#3271
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C22×#909C2semidirect
2. C22×#904C2semidirect
3. C2×#5553C2semidirect
4. C2×#5552C2semidirect
5. C2×C3×#435C2semidirect
6. C2×#5135C2semidirect
7. C2×#5114C2semidirect
8. #79508C2direct (N × H)
9. C2×#4845C2semidirect
10. C2×#4848C2semidirect
11. C2×#4738C2semidirect
12. C2×#4733C2semidirect
13. C2×#4734C2semidirect
14. C2×#4734C2semidirect
15. C2×#4716C2semidirect
16. C2×#4712C2semidirect
32. C2×#909C22semidirect
36. C2×#904C22semidirect
45. #5553C22semidirect
47. #5552C22semidirect
58. C3×#435C22semidirect
63. #5135C22semidirect
64. #5114C22semidirect
72. #4848C22semidirect
73. #4845C22semidirect
74. #4738C22semidirect
75. #4734C22semidirect
76. #4734C22semidirect
77. #4733C22semidirect
78. #4716C22semidirect
79. #4712C22semidirect
95. C2×#435D3semidirect
173. C2×Dic12D4semidirect
266. #435C2×D3semidirect
396. Dic12C2×D4semidirect
858. C2×C3#3271semidirect
901. C3C2×#3271semidirect
907. C2#79508direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#9092
C22×#9042
C2×#55532
C2×#55522
C2×C3×#4352
C2×#51352
C2×#51142
#795082
C2×#48452
C2×#48482
C2×#47382
C2×#47332
C2×#47342
C2×#47162
C2×#47122
C2×#32713