Finite Group Databasebeta

← C2×#80129 #11670241

Subgroups — C2×#80129 #11670241

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
1C2×#5831C211yesmaximal, characteristic, complemented
2C22×#950C211yesmaximal, characteristic, complemented
3C22×#915C211yesmaximal, characteristic, complemented
4C2×#5599C211yesmaximal, characteristic, complemented
5C2×C3×#449C211yesmaximal, characteristic, complemented
6C2×#5163C211yesmaximal, characteristic, complemented
7C2×#5158C211yesmaximal, characteristic, complemented
8C2×#5154C211yesmaximal, characteristic, complemented
9C2×#5041C211yesmaximal, characteristic, complemented
10#80129C2116yesmaximal, direct product factor
11C2×#4806C211yesmaximal, characteristic, complemented
12C2×#4789C211yesmaximal, characteristic, complemented
13C2×#4767C211yesmaximal, characteristic, complemented
14C2×#4782C211yesmaximal, characteristic, complemented
15C2×#4733C211yesmaximal, characteristic, complemented
16C2×#4730C211yesmaximal, characteristic, complemented
17C2×#3271—31nomaximal, Sylow
18C22×C3×#41C2211yescharacteristic
19C22×D3×Q8C2211yescharacteristic
20C22×#237C2211yescharacteristic
21C22×#235C2211yescharacteristic
22C22×C3×SD16C2211yescharacteristic
23C22×C3×D8C2211yescharacteristic
24C2×C3×#121C2211yescharacteristic
25#5831—24no—
26#5831C2218yescomplemented
27C2×#950—28no—
28C2×#950C2218yescomplemented
29C2×Q8×Dic3C2211yescharacteristic
30C22×#216C2211yescharacteristic
31C22×#215C2211yescharacteristic
32C2×#940—21no—
33C2×#940C2211yescharacteristic
34C2×#939—21no—
35C2×#938—21no—
36C2×#938C2211yescharacteristic
37C2×#936—21no—
38C2×#936C2211yescharacteristic
39C22×#214C2211yescharacteristic
40C22×#214C2211yescharacteristic
41C22×#213C2211yescharacteristic
42C2×C4×#67—21no—
43C2×C4×#67C2211yescharacteristic
44C2×#924—21no—
45C2×#924C2211yescharacteristic
46C23×C3⋊C8C2211yescharacteristic
47C2×#915—28no—
48C2×#915C2218yescomplemented
49C22×Dic12C2211yescharacteristic
50C22×#204C2211yescharacteristic
51C22×ΓL(1,𝔽25)C2211yescharacteristic
52#5599—24no—
53#5599C2218yescomplemented
54C2×#895C2211yescharacteristic
55C2×#887C2211yescharacteristic
56C2×#884—21no—
57C2×#67⋊C4—21no—
58C3×#449C2218yescomplemented
59C2×C3×#103C2211yescharacteristic
60C2×C3×#102C2211yescharacteristic
61C2×C3×C22⋊C8C2211yescharacteristic
62C2×#832C2211yescharacteristic
63#5163C2218yescomplemented
64#5158C2218yescomplemented
65#5154C2218yescomplemented
66C2×#821C2211yescharacteristic
67C2×(C2×D3)⋊C8C2211yescharacteristic
68C2×#816C2211yescharacteristic
69C2×#815C2211yescharacteristic
70C2×Dic3⋊C8C2211yescharacteristic
71#5041C2218yescomplemented
72C2×#810C2211yescharacteristic
73C2×#808C2211yescharacteristic
74#4806C2218yescomplemented
75#4789C2218yescomplemented
76#4782C2218yescomplemented
77#4767C2218yescomplemented
78#4733C2218yescomplemented
79#4730C2218yescomplemented
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×#449D311yescharacteristic, complemented
93C2×#448—31no—
94C2×#441—31no—
95C2×#435—31no—
96C2×C3×#41—22no—
97C2×C3×#41—24no—
98C2×C3×#41—42no—
99C2×C3×#41C2314yes—
100C22×C3×Q8C2311yescharacteristic
101C22×C3×D4—21no—
102C22×C3×D4—21no—
103C22×C3×D4C2311yescharacteristic
104C22×C3×D4C2311yescharacteristic
105C23×C3×C4—21no—
106C23×C3×C4C2311yescharacteristic
107C22×#67—21no—
108C22×#67—21no—
109C22×#67—21no—
110C22×#67—21no—
111C22×#67—21no—
112C22×#67D411yescharacteristic
113C23×Dic3—21no—
114C2×D3×Q8—22no—
115C2×D3×Q8—24no—
116C2×D3×Q8—42no—
117C2×D3×Q8C2314yes—
118C2×#237—22no—
119C2×#237—24no—
120C2×#237—42no—
121C2×#237C2314yes—
122C2×#235—22no—
123C2×#235—24no—
124C2×#235—42no—
125C2×#235C2314yes—
126C22×D12—21no—
127C22×D12C2311yescharacteristic
128C22×C4×D3—21no—
129C22×C4×D3—21no—
130C22×C4×D3C2311yescharacteristic
131C22×Dic6—21no—
132C22×Dic6C2311yescharacteristic
133C22×Dic6C2311yescharacteristic
134C2×C3×SD16—24no—
135C2×C3×SD16C2314yes—
136C2×C3×D8—42no—
137C2×C3×D8C2314yes—
138C22×C3×C8C2311yescharacteristic
139C22×C3×C8C2311yescharacteristic
140C3×#121—22no—
141C3×#121C2314yes—
142C2×C3×C4⋊C4C2311yescharacteristic
143C2×C3×C22⋊C4—21no—
144C2×#217—21no—
145C2×#217—21no—
146C2×#217—21no—
147C2×#217—21no—
148C2×#217D411yescharacteristic
149#950—232no—
150Q8×Dic3—22no—
151Q8×Dic3C2314yes—
152C2×#216D418yescomplemented
153C2×#216C2314yes—
154C2×#215—24no—
155C2×#215C2314yes—
156#940—28no—
157#940—22no—
158#940C2314yes—
159#939—28no—
160#938—28no—
161#938—22no—
162#938C2314yes—
163#936—28no—
164#936—22no—
165#936C2314yes—
166C2×#214—24no—
167C2×#214—24no—
168C2×#214C2314yes—
169C2×#214C2314yes—
170C2×#213—24no—
171C2×#213C2314yes—
172C4×#67—28no—
173C4×#67D414yes—
174C4×#67C2314yes—
175C2×(C2×D3)⋊C4—21no—
176C2×(C2×D3)⋊C4D411yescharacteristic
177C2×C4⋊Dic3—21no—
178C2×C4⋊Dic3C2311yescharacteristic
179#924—22no—
180#924—28no—
181#924C2314yes—
182C2×Dic3⋊C4—21no—
183C2×Dic3⋊C4—21no—
184C2×Dic3⋊C4D411yescharacteristic
185C2×C4×Dic3—21no—
186C2×C4×Dic3—21no—
187C2×C4×Dic3C2311yescharacteristic
188C22×C3⋊C8—24no—
189C22×C3⋊C8C2311yescharacteristic
190C22×C3⋊C8C2314yes—
191C22×C3⋊C8C2311yescharacteristic
192#915—232no—
193C2×Dic12—24no—
194C2×Dic12C2314yes—
195C2×#204—42no—
196C2×#204C2314yes—
197C2×ΓL(1,𝔽25)—24no—
198C2×ΓL(1,𝔽25)C2314yes—
199#895—22no—
200#895C2314yes—
201#887—22no—
202#887C2314yes—
203#884—28no—
204#67⋊C4—28no—
205C3×#103C2314yes—
206C3×#102C2314yes—
207C3×C22⋊C8C2314yes—
208#832C2314yes—
209#821C2314yes—
210(C2×D3)⋊C8C2314yes—
211#816C2314yes—
212#815C2314yes—
213Dic3⋊C8C2314yes—
214#810C2314yes—
215#808C2314yes—
216C22×#41—31no—
217C22×#41—31no—
218C22×#41C2×D311yescharacteristic
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×SD16C2×D311yescharacteristic
231C22×D8—31no—
232C22×D8C2×D311yescharacteristic
233C22×M16—31no—
234C23×C8—31no—
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—61no—
248C2×#121—61no—
249C2×#121—61no—
250C2×#121C2×D311yescharacteristic
251C2×C4×Q8—31no—
252C2×C4×Q8—31no—
253C2×C4×D4—31no—
254C2×C4×D4—61no—
255C2×C4×D4—61no—
256#496—38no—
257#469—38no—
258#465—38no—
259#464—38no—
260#460—38no—
261#452—38no—
262#449—38no—
263#449C2×D318yescomplemented
264#448—38no—
265#441—38no—
266#435—38no—
267C2×#106—31no—
268C2×C4⋊C8—31no—
269C2×#103—31no—
270C2×#103—31no—
271C2×#103C2×D311yescharacteristic
272C2×#102—31no—
273C2×#102—31no—
274C2×#102C2×D311yescharacteristic
275C2×C22⋊C8—31no—
276C2×C22⋊C8C2×D311yescharacteristic
277C2×#97—31no—
278C24×C3—21no—
279C24×C3—21no—
280C24×C3C2×D411yescharacteristic
281C23×D3—21no—
282C23×D3C2×D411yescharacteristic
283C3×#41—28no—
284C3×#41—44no—
285C3×#41—48no—
286C2×C3×Q8—21no—
287C2×C3×Q8—22no—
288C2×C3×Q8C2×D414yes—
289C2×C3×Q8C2412yes—
290C2×C3×D4—24no—
291C2×C3×D4—24no—
292C2×C3×D4—22no—
293C2×C3×D4—22no—
294C2×C3×D4—21no—
295C2×C3×D4—21no—
296C2×C3×D4—22no—
297C2×C3×D4—22no—
298C2×C3×D4—44no—
299C2×C3×D4—82no—
300C2×C3×D4C2412yes—
301C2×C3×D4C2412yes—
302C22×C3×C4—21no—
303C22×C3×C4—22no—
304C22×C3×C4—22no—
305C22×C3×C4—21no—
306C22×C3×C4—24no—
307C22×C3×C4—44no—
308C22×C3×C4C2×D411yescharacteristic
309C22×C3×C4C2×D412yes—
310C22×C3×C4C2412yes—
311C22×C3×C4C2411yescharacteristic
312C2×#67—24no—
313C2×#67—24no—
314C2×#67—24no—
315C2×#67—24no—
316C2×#67—24no—
317C2×#67—42no—
318C2×#67—44no—
319C2×#67—44no—
320C2×#67—44no—
321C2×#67—44no—
322C2×#67—82no—
323C2×#67C2×D414yes—
324C22×Dic3—21no—
325C22×Dic3—21no—
326C22×Dic3—21no—
327C22×Dic3—24no—
328C22×Dic3—44no—
329C22×Dic3C2×D411yescharacteristic
330C22×Dic3C2×D411yescharacteristic
331C22×Dic3C2×D411yescharacteristic
332D3×Q8—28no—
333D3×Q8—44no—
334D3×Q8—48no—
335#237—28no—
336#237—44no—
337#237—48no—
338#235—28no—
339#235—44no—
340#235—48no—
341C2×D12—22no—
342C2×D12—22no—
343C2×D12—21no—
344C2×D12—24no—
345C2×D12—82no—
346C2×D12C2412yes—
347C2×C4×D3—22no—
348C2×C4×D3—22no—
349C2×C4×D3—24no—
350C2×C4×D3—24no—
351C2×C4×D3—44no—
352C2×C4×D3—44no—
353C2×C4×D3C2×D412yes—
354C2×C4×D3C2412yes—
355C2×Dic6—21no—
356C2×Dic6—22no—
357C2×Dic6—22no—
358C2×Dic6—22no—
359C2×Dic6—21no—
360C2×Dic6—24no—
361C2×Dic6—44no—
362C2×Dic6C2×D414yes—
363C2×Dic6C2412yes—
364C2×Dic6C2412yes—
365C3×SD16—28no—
366C3×D8—44no—
367C2×C3×C8—22no—
368C2×C3×C8—22no—
369C2×C3×C8C2412yes—
370C2×C3×C8C2412yes—
371C3×C4⋊C4—21no—
372C3×C4⋊C4C2412yes—
373C3×C22⋊C4—24no—
374#217—24no—
375#217—24no—
376#217—24no—
377#217—24no—
378#217C2×D414yes—
379#216C2×D4116yescomplemented
380#215—28no—
381#214—28no—
382#214—28no—
383#213—28no—
384(C2×D3)⋊C4—24no—
385(C2×D3)⋊C4C2×D414yes—
386C4⋊Dic3—21no—
387C4⋊Dic3—24no—
388C4⋊Dic3C2412yes—
389Dic3⋊C4—24no—
390Dic3⋊C4—24no—
391Dic3⋊C4C2×D414yes—
392C4×Dic3—24no—
393C4×Dic3—24no—
394C4×Dic3C2×D412yes—
395C4×Dic3C2412yes—
396C2×C3⋊C8—22no—
397C2×C3⋊C8—28no—
398C2×C3⋊C8C2×D414yes—
399C2×C3⋊C8C2412yes—
400C2×C3⋊C8C2412yes—
401Dic12—28no—
402#204—44no—
403ΓL(1,𝔽25)—28no—
404C2×#41—22no—
405C2×#41—24no—
406C2×#41—34no—
407C2×#41—34no—
408C2×#41—42no—
409C2×#41—64no—
410C2×#41—62no—
411C2×#41—62no—
412C2×#41—64no—
413C2×#41—122no—
414C2×#41—122no—
415C2×#41C22×D314yes—
416C22×Q8—34no—
417C22×Q8—31no—
418C22×Q8—31no—
419C22×Q8—61no—
420C22×Q8—62no—
421C22×Q8—64no—
422C22×Q8—122no—
423C22×Q8C22×D311yescharacteristic
424C22×D4—21no—
425C22×D4—21no—
426C22×D4—31no—
427C22×D4—31no—
428C22×D4—61no—
429C22×D4—61no—
430C22×D4—61no—
431C22×D4—61no—
432C22×D4—61no—
433C22×D4—61no—
434C22×D4C22×D311yescharacteristic
435C22×D4C22×D311yescharacteristic
436C23×C4—21no—
437C23×C4—31no—
438C23×C4—61no—
439C23×C4—61no—
440C23×C4—61no—
441C23×C4C22×D311yescharacteristic
442#137—632no—
443#135—632no—
444C2×Q16—38no—
445C2×Q16—34no—
446C2×Q16—34no—
447C2×Q16—64no—
448C2×SD16—24no—
449C2×SD16—34no—
450C2×SD16—34no—
451C2×SD16—34no—
452C2×SD16—34no—
453C2×SD16—64no—
454C2×SD16—64no—
455C2×SD16—64no—
456C2×SD16—122no—
457C2×SD16C22×D314yes—
458C2×D8—34no—
459C2×D8—42no—
460C2×D8—64no—
461C2×D8C22×D314yes—
462C2×M16—34no—
463C2×M16—64no—
464C22×C8—31no—
465C22×C8—31no—
466C22×C8—34no—
467C22×C8—64no—
468C22×C8C22×D311yescharacteristic
469C22×C8C22×D311yescharacteristic
470#127—34no—
471#127—62no—
472#127—68no—
473#124—34no—
474#124—62no—
475#124—68no—
476C22⋊Q8—34no—
477C22⋊Q8—68no—
478C22⋊Q8—62no—
479#121—22no—
480#121—34no—
481#121—34no—
482#121—68no—
483#121—68no—
484#121—62no—
485#121—62no—
486#121—68no—
487#121C22×D314yes—
488C4×Q8—34no—
489C4×Q8—34no—
490C4×Q8—62no—
491C4×Q8—62no—
492C4×D4—34no—
493C4×D4—34no—
494C4×D4—68no—
495C4×D4—68no—
496C2×C4⋊C4—31no—
497C2×C4⋊C4—31no—
498C2×C4⋊C4—61no—
499C2×C4⋊C4—61no—
500C2×C4⋊C4—61no—
501C2×C4⋊C4C22×D311yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—31no—
504C2×C22⋊C4—31no—
505C2×C22⋊C4—61no—
506C2×C22⋊C4—61no—
507C2×C22⋊C4—61no—
508C2×C22⋊C4—61no—
509C2×C22⋊C4—61no—
510C2×C42—31no—
511C2×C42—61no—
512C2×C42—61no—
513#106—34no—
514C4⋊C8—34no—
515#103—34no—
516#103—34no—
517#103C22×D314yes—
518#102—34no—
519#102—34no—
520#102C22×D314yes—
521C22⋊C8—34no—
522C22⋊C8C22×D314yes—
523#97—34no—
524C23×C3—22no—
525C23×C3—22no—
526C23×C3—22no—
527C23×C3—22no—
528C23×C3—22no—
529C23×C3—42no—
530C23×C3—42no—
531C23×C3—42no—
532C23×C3—42no—
533C23×C3—42no—
534C23×C3—42no—
535C23×C3C22×D412yes—
536C23×C3C22×D411yescharacteristic
537C22×D3—22no—
538C22×D3—22no—
539C22×D3—22no—
540C22×D3—22no—
541C22×D3—42no—
542C22×D3—42no—
543C22×D3—42no—
544C22×D3C22×D412yes—
545C3×Q8—24no—
546C3×Q8—22no—
547C3×Q8C22×D414yes—
548C3×D4—22no—
549C3×D4—22no—
550C3×D4—22no—
551C3×D4—22no—
552C3×D4—48no—
553C3×D4—42no—
554C3×D4—42no—
555C3×D4—84no—
556C2×C3×C4—24no—
557C2×C3×C4—22no—
558C2×C3×C4—22no—
559C2×C3×C4—24no—
560C2×C3×C4—22no—
561C2×C3×C4—22no—
562C2×C3×C4—22no—
563C2×C3×C4—48no—
564C2×C3×C4—42no—
565C2×C3×C4C22×D412yes—
566C2×C3×C4C22×D411yescharacteristic
567C2×C3×C4C22×D412yes—
568C2×C3×C4H(5,𝔽2)12yes—
569C2×C3×C4C2511yescharacteristic
570#67—44no—
571#67—48no—
572#67—48no—
573#67—48no—
574#67—48no—
575#67—84no—
576C2×Dic3—24no—
577C2×Dic3—22no—
578C2×Dic3—22no—
579C2×Dic3—22no—
580C2×Dic3—22no—
581C2×Dic3—22no—
582C2×Dic3—22no—
583C2×Dic3—48no—
584C2×Dic3—42no—
585C2×Dic3—42no—
586C2×Dic3C22×D412yes—
587C2×Dic3C22×D412yes—
588C2×Dic3C22×D412yes—
589D12—22no—
590D12—22no—
591D12—42no—
592D12—84no—
593C4×D3—24no—
594C4×D3—22no—
595C4×D3—22no—
596C4×D3—48no—
597C4×D3—48no—
598Dic6—24no—
599Dic6—22no—
600Dic6—22no—
601Dic6—22no—
602Dic6—48no—
603Dic6—42no—
604Dic6C22×D414yes—
605C3×C8—22no—
606C3×C8—22no—
607C3⋊C8—22no—
608C3⋊C8C22×D414yes—
609C24—21no—
610C24—21no—
611C24—31no—
612C24—61no—
613C24D3×D411yescharacteristic
614#41—28no—
615#41—44no—
616#41—48no—
617#41—68no—
618#41—68no—
619#41—124no—
620#41—128no—
621#41—124no—
622#41—128no—
623C2×Q8—21no—
624C2×Q8—22no—
625C2×Q8—34no—
626C2×Q8—32no—
627C2×Q8—32no—
628C2×Q8—64no—
629C2×Q8—61no—
630C2×Q8—61no—
631C2×Q8—62no—
632C2×Q8—68no—
633C2×Q8—62no—
634C2×Q8—62no—
635C2×Q8—124no—
636C2×Q8—124no—
637C2×Q8—128no—
638C2×Q8D3×D414yes—
639C2×Q8C23×D312yes—
640C2×D4—24no—
641C2×D4—24no—
642C2×D4—22no—
643C2×D4—22no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—22no—
647C2×D4—22no—
648C2×D4—34no—
649C2×D4—32no—
650C2×D4—44no—
651C2×D4—64no—
652C2×D4—64no—
653C2×D4—64no—
654C2×D4—64no—
655C2×D4—64no—
656C2×D4—64no—
657C2×D4—62no—
658C2×D4—61no—
659C2×D4—62no—
660C2×D4—82no—
661C2×D4—122no—
662C2×D4—124no—
663C2×D4—124no—
664C2×D4—124no—
665C2×D4—124no—
666C2×D4—242no—
667C2×D4—242no—
668C2×D4C23×D312yes—
669C2×D4C23×D312yes—
670C22×C4—21no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—21no—
674C22×C4—24no—
675C22×C4—31no—
676C22×C4—31no—
677C22×C4—31no—
678C22×C4—32no—
679C22×C4—32no—
680C22×C4—44no—
681C22×C4—64no—
682C22×C4—64no—
683C22×C4—61no—
684C22×C4—62no—
685C22×C4—62no—
686C22×C4—61no—
687C22×C4—61no—
688C22×C4—64no—
689C22×C4—124no—
690C22×C4—124no—
691C22×C4—124no—
692C22×C4D3×D412yes—
693C22×C4D3×D411yescharacteristic
694C22×C4C23×D312yes—
695C22×C4C23×D311yescharacteristic
696Q16—316no—
697Q16—68no—
698SD16—28no—
699SD16—68no—
700SD16—68no—
701SD16—68no—
702SD16—124no—
703D8—44no—
704D8—68no—
705M16—68no—
706C2×C8—22no—
707C2×C8—22no—
708C2×C8—34no—
709C2×C8—32no—
710C2×C8—32no—
711C2×C8—68no—
712C2×C8—62no—
713C2×C8C23×D312yes—
714C2×C8C23×D312yes—
715C4⋊C4—21no—
716C4⋊C4—34no—
717C4⋊C4—32no—
718C4⋊C4—64no—
719C4⋊C4—64no—
720C4⋊C4—61no—
721C4⋊C4—64no—
722C4⋊C4C23×D312yes—
723C22⋊C4—24no—
724C22⋊C4—34no—
725C22⋊C4—34no—
726C22⋊C4—64no—
727C22⋊C4—64no—
728C22⋊C4—64no—
729C22⋊C4—64no—
730C22⋊C4—64no—
731C42—32no—
732C42—32no—
733C42—64no—
734C42—64no—
735C22×C3—22no—
736C22×C3—22no—
737C22×C3—22no—
738C22×C3—44no—
739C22×C3—42no—
740C22×C3—42no—
741C22×C3—42no—
742C22×C3—42no—
743C22×C3—42no—
744C22×C3—42no—
745C22×C3—84no—
746C22×C3—84no—
747C22×C3D4212yes—
748C22×C3#57512yes—
749C22×C3#57712yes—
750C22×C3C23×D411yescharacteristic
751C2×D3—22no—
752C2×D3—22no—
753C2×D3—22no—
754C2×D3—44no—
755C2×D3—42no—
756C2×D3—42no—
757C2×D3—42no—
758C2×D3—84no—
759C3×C4—24no—
760C3×C4—22no—
761C3×C4—42no—
762C3×C4D4212yes—
763C3×C4C23×D411yescharacteristic
764C3×C4C2×H(5,𝔽2)11yescharacteristic
765Dic3—24no—
766Dic3—22no—
767Dic3—22no—
768Dic3—22no—
769Dic3—42no—
770Dic3—42no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—32no—
777C23—42no—
778C23—42no—
779C23—42no—
780C23—42no—
781C23—42no—
782C23—42no—
783C23—62no—
784C23—62no—
785C23—62no—
786C23—62no—
787C23—122no—
788C23—122no—
789C23—122no—
790C23C2×D3×D412yes—
791C23C2×D3×D411yescharacteristic
792Q8—22no—
793Q8—24no—
794Q8—34no—
795Q8—62no—
796Q8—64no—
797Q8—62no—
798Q8—62no—
799Q8—128no—
800Q8—122no—
801Q8C2×D3×D414yes—
802D4—22no—
803D4—22no—
804D4—22no—
805D4—22no—
806D4—48no—
807D4—42no—
808D4—42no—
809D4—62no—
810D4—62no—
811D4—84no—
812D4—124no—
813D4—128no—
814D4—128no—
815D4—128no—
816D4—128no—
817D4—122no—
818D4—244no—
819D4—244no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—24no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—24no—
826C2×C4—22no—
827C2×C4—32no—
828C2×C4—32no—
829C2×C4—32no—
830C2×C4—48no—
831C2×C4—42no—
832C2×C4—62no—
833C2×C4—62no—
834C2×C4—62no—
835C2×C4—62no—
836C2×C4—64no—
837C2×C4—62no—
838C2×C4—62no—
839C2×C4—64no—
840C2×C4—62no—
841C2×C4—62no—
842C2×C4—128no—
843C2×C4—128no—
844C2×C4—128no—
845C2×C4—122no—
846C2×C4—122no—
847C2×C4C2×D3×D412yes—
848C2×C4C2×D3×D412yes—
849C2×C4C2×D3×D411yescharacteristic
850C2×C4#100412yes—
851C2×C4C24×D311yescharacteristic
852C8—22no—
853C8—22no—
854C8—34no—
855C8—62no—
856C2×C3—42no—
857C2×C3—82no—
858C2×C3—82no—
859C2×C3#327114yescomplemented
860C2×C3C2×D4211yescharacteristic
861C2×C3C2×#57511yescharacteristic
862C2×C3C2×#57711yescharacteristic
863D3—42no—
864D3—82no—
865C22—22no—
866C22—22no—
867C22—22no—
868C22—44no—
869C22—42no—
870C22—42no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—42no—
875C22—62no—
876C22—62no—
877C22—62no—
878C22—84no—
879C22—84no—
880C22—124no—
881C22—122no—
882C22—122no—
883C22—122no—
884C22—244no—
885C22#559012yes—
886C22#576812yes—
887C22#577512yes—
888C22C22×D3×D411yescharacteristic
889C4—22no—
890C4—24no—
891C4—42no—
892C4—62no—
893C4—62no—
894C4—62no—
895C4—64no—
896C4—122no—
897C4—122no—
898C4#559012yes—
899C4C22×D3×D411yescharacteristic
900C4C2×#100411yescharacteristic
901C3C2×#327111yescharacteristic, complemented, Sylow
902C2—42no—
903C2—82no—
904C2—82no—
905C2—122no—
906C2—242no—
907C2#8012914yesdirect product factor
908C2C2×#559011yescharacteristic
909C2C2×#576811yescharacteristic
910C2C2×#577511yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#449C2
socleC23×C3C22×D4
hypercenterC2×#449D3
hypocenterC3C2×#3271
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#5831C2semidirect
2. C22×#950C2semidirect
3. C22×#915C2semidirect
4. C2×#5599C2semidirect
5. C2×C3×#449C2semidirect
6. C2×#5163C2semidirect
7. C2×#5158C2semidirect
8. C2×#5154C2semidirect
9. C2×#5041C2semidirect
10. #80129C2direct (N × H)
11. C2×#4806C2semidirect
12. C2×#4789C2semidirect
13. C2×#4767C2semidirect
14. C2×#4782C2semidirect
15. C2×#4733C2semidirect
16. C2×#4730C2semidirect
26. #5831C22semidirect
28. C2×#950C22semidirect
48. C2×#915C22semidirect
53. #5599C22semidirect
58. C3×#449C22semidirect
63. #5163C22semidirect
64. #5158C22semidirect
65. #5154C22semidirect
71. #5041C22semidirect
74. #4806C22semidirect
75. #4789C22semidirect
76. #4782C22semidirect
77. #4767C22semidirect
78. #4733C22semidirect
79. #4730C22semidirect
92. C2×#449D3semidirect
152. C2×#216D4semidirect
263. #449C2×D3semidirect
379. #216C2×D4semidirect
859. C2×C3#3271semidirect
901. C3C2×#3271semidirect
907. C2#80129direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#58312
C22×#9502
C22×#9152
C2×#55992
C2×C3×#4492
C2×#51632
C2×#51582
C2×#51542
C2×#50412
#801292
C2×#48062
C2×#47892
C2×#47672
C2×#47822
C2×#47332
C2×#47302
C2×#32713