Finite Group Databasebeta

← C2×#80772 #11670213

Subgroups — C2×#80772 #11670213

Order 768.

2774 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#918C211yesmaximal, characteristic, complemented
2C22×#904C211yesmaximal, characteristic, complemented
3C2×#5633C211yesmaximal, characteristic, complemented
4C2×#5631C211yesmaximal, characteristic, complemented
5C2×C3×#467C211yesmaximal, characteristic, complemented
6C2×#5190C211yesmaximal, characteristic, complemented
7C2×#5111C211yesmaximal, characteristic, complemented
8C2×#5047C211yesmaximal, characteristic, complemented
9C2×#5047C211yesmaximal, characteristic, complemented
10#80772C2116yesmaximal, direct product factor
11C2×#4886C211yesmaximal, characteristic, complemented
12C2×#4889C211yesmaximal, characteristic, complemented
13C2×#4795C211yesmaximal, characteristic, complemented
14C2×#4819C211yesmaximal, characteristic, complemented
15C2×#4810C211yesmaximal, characteristic, complemented
16C2×#4809C211yesmaximal, characteristic, complemented
17C2×#3269—31nomaximal, Sylow
18C22×#239C2211yescharacteristic
19C22×D3×Q8C2211yescharacteristic
20C22×#235C2211yescharacteristic
21C22×#235C2211yescharacteristic
22C22×C3×Q16C2211yescharacteristic
23C23×C3×C8C2211yescharacteristic
24C2×C3×C22⋊Q8C2211yescharacteristic
25C2×C3×C22⋊Q8C2211yescharacteristic
26C2×#947C2211yescharacteristic
27C2×#944C2211yescharacteristic
28C22×#216C2211yescharacteristic
29C22×#216C2211yescharacteristic
30C22×#215C2211yescharacteristic
31C22×#215C2211yescharacteristic
32C2×C4×#67C2211yescharacteristic
33C2×#918—28no—
34C2×#918C2218yescomplemented
35C22×Dic12C2211yescharacteristic
36C2×#904—28no—
37C2×#904C2218yescomplemented
38C22×D24C2211yescharacteristic
39C22×#204C2211yescharacteristic
40C22×#204C2211yescharacteristic
41C22×ΓL(1,𝔽25)C2211yescharacteristic
42#5633—24no—
43#5633C2218yescomplemented
44#5631—24no—
45#5631C2218yescomplemented
46C2×#897C2211yescharacteristic
47C2×#896—21no—
48C2×#895C2211yescharacteristic
49C2×#894—21no—
50C2×#893—21no—
51C2×#893C2211yescharacteristic
52C2×D3×C4⋊C4—21no—
53C2×#887C2211yescharacteristic
54C2×#885—21no—
55C2×#884—21no—
56C2×#884—21no—
57C2×#883—21no—
58C3×#467C2218yescomplemented
59C2×C3×#107C2211yescharacteristic
60C2×C3×#103C2211yescharacteristic
61C2×C3×#103C2211yescharacteristic
62C2×#830C2211yescharacteristic
63#5190C2218yescomplemented
64#5111C2218yescomplemented
65C2×(C2×D3)⋊C8C2211yescharacteristic
66C2×#815C2211yescharacteristic
67C2×Dic3⋊C8C2211yescharacteristic
68#5047C2218yescomplemented
69#5047C2218yescomplemented
70C2×#810C2211yescharacteristic
71C2×#810C2211yescharacteristic
72C2×#809C2211yescharacteristic
73C2×#809C2211yescharacteristic
74#4889C2218yescomplemented
75#4886C2218yescomplemented
76#4819C2218yescomplemented
77#4810C2218yescomplemented
78#4809C2218yescomplemented
79#4795C2218yescomplemented
80C22×#137—31no—
81C22×#135—31no—
82C2×#548—31no—
83C2×#547—31no—
84#3269—316no—
85C2×#497—31no—
86C2×#468—31no—
87C2×#467D311yescharacteristic, complemented
88C2×#462—31no—
89C2×#463—31no—
90C2×#452—31no—
91C2×#452—31no—
92C2×#449—31no—
93C2×#451—31no—
94C2×#440—31no—
95C2×#435—31no—
96C22×C3×Q8C2311yescharacteristic
97C22×C3×Q8C2311yescharacteristic
98C23×C3×C4C2311yescharacteristic
99C22×#67—21no—
100C22×#67—21no—
101C22×#67D411yescharacteristic
102C2×#239—22no—
103C2×#239—24no—
104C2×#239—42no—
105C2×#239C2314yes—
106C2×D3×Q8—22no—
107C2×D3×Q8—24no—
108C2×D3×Q8—42no—
109C2×D3×Q8C2314yes—
110C2×#235—22no—
111C2×#235—22no—
112C2×#235—24no—
113C2×#235—24no—
114C2×#235—42no—
115C2×#235—42no—
116C2×#235C2314yes—
117C2×#235C2314yes—
118C22×D12—21no—
119C22×D12—21no—
120C22×D12C2311yescharacteristic
121C22×D12C2311yescharacteristic
122C22×C4×D3—21no—
123C22×C4×D3—21no—
124C22×C4×D3—21no—
125C22×C4×D3—21no—
126C22×C4×D3—21no—
127C22×C4×D3C2311yescharacteristic
128C22×Dic6—21no—
129C22×Dic6C2311yescharacteristic
130C22×Dic6C2311yescharacteristic
131C2×C3×Q16—24no—
132C2×C3×Q16C2314yes—
133C22×C3×C8—24no—
134C22×C3×C8C2311yescharacteristic
135C22×C3×C8C2314yes—
136C22×C3×C8C2311yescharacteristic
137C3×C22⋊Q8—22no—
138C3×C22⋊Q8—22no—
139C3×C22⋊Q8C2314yes—
140C3×C22⋊Q8C2314yes—
141C2×C3×C4⋊C4—21no—
142C2×C3×C4⋊C4—21no—
143C2×C3×C4⋊C4C2311yescharacteristic
144C2×C3×C4⋊C4C2311yescharacteristic
145C2×C3×C22⋊C4—21no—
146C2×C3×C22⋊C4—21no—
147C2×#217D411yescharacteristic
148#947—22no—
149#947C2314yes—
150#944—22no—
151#944C2314yes—
152C2×#216—24no—
153C2×#216—42no—
154C2×#216C2314yes—
155C2×#216C2314yes—
156C2×#215—24no—
157C2×#215—42no—
158C2×#215C2314yes—
159C2×#215C2314yes—
160C4×#67D414yes—
161C4×#67C2314yes—
162C2×(C2×D3)⋊C4—21no—
163C2×(C2×D3)⋊C4—21no—
164C2×(C2×D3)⋊C4—21no—
165C2×(C2×D3)⋊C4—21no—
166C2×(C2×D3)⋊C4—21no—
167C2×(C2×D3)⋊C4D411yescharacteristic
168C2×C4⋊Dic3—21no—
169C2×Dic3⋊C4—21no—
170C2×Dic3⋊C4—21no—
171C2×Dic3⋊C4—21no—
172C2×Dic3⋊C4D411yescharacteristic
173C2×C4×Dic3—21no—
174C2×C4×Dic3C2311yescharacteristic
175C22×C3⋊C8C2311yescharacteristic
176C22×C3⋊C8C2311yescharacteristic
177#918—232no—
178C2×Dic12—24no—
179C2×Dic12C2314yes—
180#904—232no—
181C2×D24—24no—
182C2×D24C2314yes—
183C2×#204—24no—
184C2×#204D418yescomplemented
185C2×#204C2314yes—
186C2×#204C2314yes—
187C2×ΓL(1,𝔽25)—24no—
188C2×ΓL(1,𝔽25)C2314yes—
189#897—22no—
190#897C2314yes—
191#896—28no—
192#895—22no—
193#895C2314yes—
194#894—28no—
195#893—28no—
196#893—22no—
197#893C2314yes—
198D3×C4⋊C4—28no—
199#887—22no—
200#887C2314yes—
201#885—28no—
202#884—28no—
203#884—28no—
204#883—28no—
205C3×#107C2314yes—
206C3×#103C2314yes—
207C3×#103C2314yes—
208#830C2314yes—
209(C2×D3)⋊C8C2314yes—
210#815C2314yes—
211Dic3⋊C8C2314yes—
212#810C2314yes—
213#810C2314yes—
214#809C2314yes—
215#809C2314yes—
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×Q16—31no—
227C22×Q16C2×D311yescharacteristic
228C22×SD16—31no—
229C22×SD16—31no—
230C22×SD16—31no—
231C22×SD16—31no—
232C22×D8—31no—
233C22×M16—31no—
234C23×C8C2×D311yescharacteristic
235#548—38no—
236#548—64no—
237#547—38no—
238#547—64no—
239C2×C4⋊Q8—31no—
240C2×#124—31no—
241C2×#124—61no—
242C2×#123—61no—
243C2×#123—61no—
244C2×C22⋊Q8—31no—
245C2×C22⋊Q8—61no—
246C2×C22⋊Q8C2×D311yescharacteristic
247C2×C22⋊Q8C2×D311yescharacteristic
248C2×#121—31no—
249C2×#121—61no—
250C2×#121—61no—
251C2×C4×Q8—31no—
252C2×C4×D4—31no—
253C2×C4×D4—31no—
254C2×C4×D4—61no—
255C22×C4⋊C4—61no—
256#497—38no—
257#468—38no—
258#467C2×D318yescomplemented
259#463—38no—
260#462—38no—
261#452—38no—
262#452—38no—
263#451—38no—
264#449—38no—
265#440—38no—
266#435—38no—
267C2×#107C2×D311yescharacteristic
268C2×C4⋊C8—31no—
269C2×#103—31no—
270C2×#103—31no—
271C2×#103C2×D311yescharacteristic
272C2×#103C2×D311yescharacteristic
273C2×#102—31no—
274C2×#102—31no—
275C2×C22⋊C8—31no—
276C2×C22⋊C8—31no—
277C2×#97—31no—
278C24×C3C2×D411yescharacteristic
279C23×D3—21no—
280C23×D3—21no—
281C23×D3C2×D411yescharacteristic
282C2×C3×Q8—21no—
283C2×C3×Q8—21no—
284C2×C3×Q8—22no—
285C2×C3×Q8—22no—
286C2×C3×Q8—22no—
287C2×C3×Q8—22no—
288C2×C3×Q8C2412yes—
289C2×C3×Q8C2412yes—
290C22×C3×C4—22no—
291C22×C3×C4—22no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4C2×D411yescharacteristic
297C22×C3×C4C2×D412yes—
298C22×C3×C4C2412yes—
299C22×C3×C4C2411yescharacteristic
300C2×#67—24no—
301C2×#67—24no—
302C2×#67—42no—
303C2×#67—44no—
304C2×#67—44no—
305C2×#67C2×D414yes—
306C22×Dic3—21no—
307C22×Dic3—21no—
308C22×Dic3C2×D411yescharacteristic
309C22×Dic3C2×D411yescharacteristic
310C22×Dic3C2×D411yescharacteristic
311#239—28no—
312#239—44no—
313#239—48no—
314D3×Q8—28no—
315D3×Q8—44no—
316D3×Q8—48no—
317#235—28no—
318#235—28no—
319#235—44no—
320#235—44no—
321#235—48no—
322#235—48no—
323C2×D12—21no—
324C2×D12—22no—
325C2×D12—22no—
326C2×D12—22no—
327C2×D12—24no—
328C2×D12—24no—
329C2×D12—21no—
330C2×D12—44no—
331C2×D12—44no—
332C2×D12C2×D414yes—
333C2×D12C2412yes—
334C2×D12C2412yes—
335C2×C4×D3—22no—
336C2×C4×D3—22no—
337C2×C4×D3—24no—
338C2×C4×D3—24no—
339C2×C4×D3—24no—
340C2×C4×D3—24no—
341C2×C4×D3—24no—
342C2×C4×D3—44no—
343C2×C4×D3—44no—
344C2×C4×D3—44no—
345C2×C4×D3—44no—
346C2×C4×D3—44no—
347C2×C4×D3C2×D412yes—
348C2×C4×D3C2412yes—
349C2×Dic6—21no—
350C2×Dic6—22no—
351C2×Dic6—22no—
352C2×Dic6—22no—
353C2×Dic6—21no—
354C2×Dic6—24no—
355C2×Dic6—44no—
356C2×Dic6C2×D414yes—
357C2×Dic6C2412yes—
358C2×Dic6C2412yes—
359C3×Q16—28no—
360C2×C3×C8—22no—
361C2×C3×C8—28no—
362C2×C3×C8C2×D414yes—
363C2×C3×C8C2412yes—
364C2×C3×C8C2412yes—
365C3×C4⋊C4—21no—
366C3×C4⋊C4—24no—
367C3×C4⋊C4—24no—
368C3×C4⋊C4—21no—
369C3×C4⋊C4C2412yes—
370C3×C4⋊C4C2412yes—
371C3×C22⋊C4—24no—
372C3×C22⋊C4—24no—
373#217C2×D414yes—
374#216—28no—
375#216—44no—
376#215—28no—
377#215—44no—
378(C2×D3)⋊C4—24no—
379(C2×D3)⋊C4—24no—
380(C2×D3)⋊C4—24no—
381(C2×D3)⋊C4—24no—
382(C2×D3)⋊C4—24no—
383(C2×D3)⋊C4C2×D414yes—
384C4⋊Dic3—24no—
385Dic3⋊C4—24no—
386Dic3⋊C4—24no—
387Dic3⋊C4—24no—
388Dic3⋊C4C2×D414yes—
389C4×Dic3—24no—
390C4×Dic3C2×D412yes—
391C4×Dic3C2412yes—
392C2×C3⋊C8—22no—
393C2×C3⋊C8—22no—
394C2×C3⋊C8C2412yes—
395C2×C3⋊C8C2412yes—
396Dic12—28no—
397D24—28no—
398#204—28no—
399#204C2×D4116yescomplemented
400ΓL(1,𝔽25)—28no—
401C2×#41—34no—
402C2×#41—34no—
403C2×#41—34no—
404C2×#41—64no—
405C2×#41—64no—
406C2×#41—62no—
407C2×#41—62no—
408C2×#41—62no—
409C2×#41—64no—
410C2×#41—122no—
411C2×#41—122no—
412C2×#41—122no—
413C22×Q8—34no—
414C22×Q8—31no—
415C22×Q8—31no—
416C22×Q8—61no—
417C22×Q8—62no—
418C22×Q8—64no—
419C22×Q8—122no—
420C22×Q8C22×D311yescharacteristic
421C22×Q8C22×D311yescharacteristic
422C22×D4—31no—
423C22×D4—31no—
424C22×D4—31no—
425C22×D4—61no—
426C22×D4—61no—
427C22×D4—61no—
428C22×D4—61no—
429C23×C4—31no—
430C23×C4—61no—
431C23×C4—61no—
432C23×C4—61no—
433C23×C4—61no—
434C23×C4—61no—
435C23×C4C22×D311yescharacteristic
436#137—632no—
437#135—632no—
438C2×Q16—24no—
439C2×Q16—34no—
440C2×Q16—34no—
441C2×Q16—34no—
442C2×Q16—64no—
443C2×Q16—64no—
444C2×Q16—122no—
445C2×Q16C22×D314yes—
446C2×SD16—34no—
447C2×SD16—34no—
448C2×SD16—38no—
449C2×SD16—34no—
450C2×SD16—34no—
451C2×SD16—64no—
452C2×SD16—64no—
453C2×SD16—122no—
454C2×D8—34no—
455C2×D8—64no—
456C2×M16—34no—
457C2×M16—64no—
458C22×C8—24no—
459C22×C8—31no—
460C22×C8—31no—
461C22×C8C22×D311yescharacteristic
462C22×C8C22×D314yes—
463C22×C8C22×D311yescharacteristic
464C4⋊Q8—34no—
465C4⋊Q8—62no—
466#124—34no—
467#124—62no—
468#124—68no—
469#123—68no—
470#123—68no—
471C22⋊Q8—22no—
472C22⋊Q8—22no—
473C22⋊Q8—34no—
474C22⋊Q8—68no—
475C22⋊Q8—62no—
476C22⋊Q8C22×D314yes—
477C22⋊Q8C22×D314yes—
478#121—34no—
479#121—68no—
480#121—68no—
481#121—62no—
482C4×Q8—34no—
483C4×Q8—62no—
484C4×D4—34no—
485C4×D4—34no—
486C4×D4—34no—
487C4×D4—62no—
488C4×D4—68no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—31no—
492C2×C4⋊C4—68no—
493C2×C4⋊C4—61no—
494C2×C4⋊C4—61no—
495C2×C4⋊C4—61no—
496C2×C4⋊C4—61no—
497C2×C4⋊C4C22×D311yescharacteristic
498C2×C4⋊C4C22×D311yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—31no—
502C2×C22⋊C4—31no—
503C2×C22⋊C4—61no—
504C2×C22⋊C4—61no—
505C2×C22⋊C4—61no—
506C2×C22⋊C4—61no—
507C2×C22⋊C4—61no—
508C2×C42—31no—
509C2×C42—61no—
510#107C22×D314yes—
511C4⋊C8—34no—
512#103—34no—
513#103—34no—
514#103C22×D314yes—
515#103C22×D314yes—
516#102—34no—
517#102—34no—
518C22⋊C8—34no—
519C22⋊C8—34no—
520#97—34no—
521C23×C3—22no—
522C23×C3—22no—
523C23×C3—22no—
524C23×C3C22×D412yes—
525C23×C3C22×D411yescharacteristic
526C22×D3—22no—
527C22×D3—24no—
528C22×D3—22no—
529C22×D3—22no—
530C22×D3—22no—
531C22×D3—22no—
532C22×D3—42no—
533C22×D3—42no—
534C22×D3—42no—
535C22×D3—42no—
536C22×D3—42no—
537C22×D3C22×D412yes—
538C3×Q8—22no—
539C3×Q8—22no—
540C3×Q8—22no—
541C3×Q8—22no—
542C3×Q8—42no—
543C3×Q8—42no—
544C2×C3×C4—22no—
545C2×C3×C4—24no—
546C2×C3×C4—22no—
547C2×C3×C4—22no—
548C2×C3×C4—22no—
549C2×C3×C4—22no—
550C2×C3×C4—22no—
551C2×C3×C4—22no—
552C2×C3×C4—42no—
553C2×C3×C4—42no—
554C2×C3×C4—42no—
555C2×C3×C4—42no—
556C2×C3×C4C22×D412yes—
557C2×C3×C4C22×D411yescharacteristic
558C2×C3×C4C22×D412yes—
559C2×C3×C4H(5,𝔽2)12yes—
560C2×C3×C4C2511yescharacteristic
561#67—44no—
562#67—48no—
563#67—48no—
564C2×Dic3—24no—
565C2×Dic3—22no—
566C2×Dic3—22no—
567C2×Dic3—22no—
568C2×Dic3—22no—
569C2×Dic3—22no—
570C2×Dic3—42no—
571C2×Dic3C22×D412yes—
572C2×Dic3C22×D412yes—
573C2×Dic3C22×D412yes—
574D12—24no—
575D12—22no—
576D12—22no—
577D12—22no—
578D12—48no—
579D12—48no—
580D12—42no—
581D12C22×D414yes—
582C4×D3—24no—
583C4×D3—22no—
584C4×D3—22no—
585C4×D3—48no—
586C4×D3—48no—
587C4×D3—48no—
588C4×D3—48no—
589C4×D3—48no—
590Dic6—24no—
591Dic6—22no—
592Dic6—22no—
593Dic6—22no—
594Dic6—48no—
595Dic6—42no—
596Dic6C22×D414yes—
597C3×C8—22no—
598C3×C8C22×D414yes—
599C3⋊C8—22no—
600C3⋊C8—22no—
601C24—31no—
602C24—61no—
603C24—61no—
604C24D3×D411yescharacteristic
605#41—68no—
606#41—68no—
607#41—68no—
608#41—124no—
609#41—124no—
610#41—128no—
611#41—128no—
612#41—124no—
613#41—128no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8—22no—
617C2×Q8—22no—
618C2×Q8—22no—
619C2×Q8—22no—
620C2×Q8—34no—
621C2×Q8—32no—
622C2×Q8—32no—
623C2×Q8—64no—
624C2×Q8—61no—
625C2×Q8—61no—
626C2×Q8—62no—
627C2×Q8—68no—
628C2×Q8—62no—
629C2×Q8—62no—
630C2×Q8—124no—
631C2×Q8—124no—
632C2×Q8—128no—
633C2×Q8C23×D312yes—
634C2×Q8C23×D312yes—
635C2×D4—34no—
636C2×D4—34no—
637C2×D4—32no—
638C2×D4—32no—
639C2×D4—64no—
640C2×D4—64no—
641C2×D4—64no—
642C2×D4—64no—
643C2×D4—61no—
644C2×D4—62no—
645C2×D4—61no—
646C2×D4—62no—
647C2×D4—62no—
648C2×D4—124no—
649C2×D4—124no—
650C2×D4—122no—
651C2×D4—124no—
652C2×D4—124no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—31no—
660C22×C4—31no—
661C22×C4—31no—
662C22×C4—32no—
663C22×C4—32no—
664C22×C4—64no—
665C22×C4—64no—
666C22×C4—64no—
667C22×C4—61no—
668C22×C4—62no—
669C22×C4—62no—
670C22×C4—61no—
671C22×C4—64no—
672C22×C4—64no—
673C22×C4—124no—
674C22×C4—124no—
675C22×C4—124no—
676C22×C4—124no—
677C22×C4—124no—
678C22×C4D3×D412yes—
679C22×C4D3×D411yescharacteristic
680C22×C4C23×D312yes—
681C22×C4C23×D311yescharacteristic
682Q16—28no—
683Q16—68no—
684Q16—68no—
685Q16—124no—
686SD16—316no—
687SD16—68no—
688SD16—68no—
689SD16—124no—
690D8—68no—
691M16—68no—
692C2×C8—22no—
693C2×C8—28no—
694C2×C8—32no—
695C2×C8—32no—
696C2×C8—62no—
697C2×C8—62no—
698C2×C8D3×D414yes—
699C2×C8C23×D312yes—
700C2×C8C23×D312yes—
701C4⋊C4—24no—
702C4⋊C4—24no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—34no—
706C4⋊C4—64no—
707C4⋊C4—64no—
708C4⋊C4—64no—
709C4⋊C4—64no—
710C4⋊C4C23×D312yes—
711C4⋊C4C23×D312yes—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—34no—
715C22⋊C4—34no—
716C22⋊C4—64no—
717C22⋊C4—64no—
718C22⋊C4—64no—
719C22⋊C4—64no—
720C22⋊C4—64no—
721C42—32no—
722C42—32no—
723C42—64no—
724C22×C3—22no—
725C22×C3—22no—
726C22×C3—22no—
727C22×C3—44no—
728C22×C3D4212yes—
729C22×C3#57512yes—
730C22×C3#57812yes—
731C22×C3C23×D411yescharacteristic
732C2×D3—22no—
733C2×D3—24no—
734C2×D3—22no—
735C2×D3—22no—
736C2×D3—44no—
737C2×D3—48no—
738C2×D3—42no—
739C2×D3—42no—
740C2×D3—42no—
741C2×D3—42no—
742C2×D3—42no—
743C2×D3—84no—
744C3×C4—22no—
745C3×C4—42no—
746C3×C4—42no—
747C3×C4—42no—
748C3×C4—42no—
749C3×C4D4212yes—
750C3×C4C23×D411yescharacteristic
751C3×C4C2×H(5,𝔽2)11yescharacteristic
752Dic3—24no—
753Dic3—22no—
754Dic3—22no—
755Dic3—22no—
756Dic3—42no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—32no—
761C23—62no—
762C23—62no—
763C23—62no—
764C23—62no—
765C23—64no—
766C23—62no—
767C23—122no—
768C23—122no—
769C23—122no—
770C23—122no—
771C23—122no—
772C23C2×D3×D412yes—
773C23C2×D3×D411yescharacteristic
774Q8—22no—
775Q8—22no—
776Q8—22no—
777Q8—22no—
778Q8—34no—
779Q8—42no—
780Q8—42no—
781Q8—62no—
782Q8—64no—
783Q8—62no—
784Q8—62no—
785Q8—128no—
786Q8—122no—
787D4—34no—
788D4—62no—
789D4—62no—
790D4—62no—
791D4—64no—
792D4—128no—
793D4—128no—
794D4—124no—
795D4—128no—
796D4—128no—
797D4—122no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—24no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—32no—
807C2×C4—32no—
808C2×C4—32no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—62no—
814C2×C4—62no—
815C2×C4—62no—
816C2×C4—62no—
817C2×C4—64no—
818C2×C4—62no—
819C2×C4—62no—
820C2×C4—64no—
821C2×C4—62no—
822C2×C4—128no—
823C2×C4—128no—
824C2×C4—128no—
825C2×C4—128no—
826C2×C4—128no—
827C2×C4—122no—
828C2×C4C2×D3×D412yes—
829C2×C4C2×D3×D412yes—
830C2×C4C2×D3×D411yescharacteristic
831C2×C4#100912yes—
832C2×C4C24×D311yescharacteristic
833C8—22no—
834C8—62no—
835C8—62no—
836C8C2×D3×D414yes—
837C2×C3—42no—
838C2×C3#326914yescomplemented
839C2×C3C2×D4211yescharacteristic
840C2×C3C2×#57511yescharacteristic
841C2×C3C2×#57811yescharacteristic
842D3—42no—
843D3—44no—
844D3—82no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—44no—
849C22—62no—
850C22—62no—
851C22—62no—
852C22—64no—
853C22—124no—
854C22—128no—
855C22—122no—
856C22—122no—
857C22—122no—
858C22—122no—
859C22—122no—
860C22—244no—
861C22#560912yes—
862C22#576612yes—
863C22#576812yes—
864C22C22×D3×D411yescharacteristic
865C4—22no—
866C4—42no—
867C4—42no—
868C4—42no—
869C4—42no—
870C4—62no—
871C4—62no—
872C4—62no—
873C4—64no—
874C4—122no—
875C4#560912yes—
876C4C22×D3×D411yescharacteristic
877C4C2×#100911yescharacteristic
878C3C2×#326911yescharacteristic, complemented, Sylow
879C2—42no—
880C2—122no—
881C2—124no—
882C2—242no—
883C2#8077214yesdirect product factor
884C2C2×#560911yescharacteristic
885C2C2×#576611yescharacteristic
886C2C2×#576811yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#467C2
socleC23×C3C22×D4
hypercenterC2×#467D3
hypocenterC3C2×#3269
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
1. C22×#918C2semidirect
2. C22×#904C2semidirect
3. C2×#5633C2semidirect
4. C2×#5631C2semidirect
5. C2×C3×#467C2semidirect
6. C2×#5190C2semidirect
7. C2×#5111C2semidirect
8. C2×#5047C2semidirect
9. C2×#5047C2semidirect
10. #80772C2direct (N × H)
11. C2×#4886C2semidirect
12. C2×#4889C2semidirect
13. C2×#4795C2semidirect
14. C2×#4819C2semidirect
15. C2×#4810C2semidirect
16. C2×#4809C2semidirect
34. C2×#918C22semidirect
37. C2×#904C22semidirect
43. #5633C22semidirect
45. #5631C22semidirect
58. C3×#467C22semidirect
63. #5190C22semidirect
64. #5111C22semidirect
68. #5047C22semidirect
69. #5047C22semidirect
74. #4889C22semidirect
75. #4886C22semidirect
76. #4819C22semidirect
77. #4810C22semidirect
78. #4809C22semidirect
79. #4795C22semidirect
87. C2×#467D3semidirect
184. C2×#204D4semidirect
258. #467C2×D3semidirect
399. #204C2×D4semidirect
838. C2×C3#3269semidirect
878. C3C2×#3269semidirect
883. C2#80772direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#9182
C22×#9042
C2×#56332
C2×#56312
C2×C3×#4672
C2×#51902
C2×#51112
C2×#50472
#807722
C2×#48862
C2×#48892
C2×#47952
C2×#48192
C2×#48102
C2×#48092
C2×#32693