Finite Group Databasebeta

← C2×#80270 #11670433

Subgroups — C2×#80270 #11670433

Order 768.

2858 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×#5834C211yesmaximal, characteristic, complemented
2C22×#950C211yesmaximal, characteristic, complemented
3C22×#919C211yesmaximal, characteristic, complemented
4C2×#5631C211yesmaximal, characteristic, complemented
5C2×C3×#452C211yesmaximal, characteristic, complemented
6C2×#5182C211yesmaximal, characteristic, complemented
7C2×#5172C211yesmaximal, characteristic, complemented
8C2×#5175C211yesmaximal, characteristic, complemented
9C2×#5048C211yesmaximal, characteristic, complemented
10#80270C2116yesmaximal, direct product factor
11C2×#4808C211yesmaximal, characteristic, complemented
12C2×#4788C211yesmaximal, characteristic, complemented
13C2×#4786C211yesmaximal, characteristic, complemented
14C2×#4778C211yesmaximal, characteristic, complemented
15C2×#4734C211yesmaximal, characteristic, complemented
16C2×#67⋊C8C211yesmaximal, characteristic, complemented
17C2×#3284—31nomaximal, Sylow
18C22×C3×#41C2211yescharacteristic
19C22×#239C2211yescharacteristic
20C22×#239C2211yescharacteristic
21C22×#235C2211yescharacteristic
22C22×C3×Q16C2211yescharacteristic
23C22×C3×SD16C2211yescharacteristic
24C2×C3×C22⋊Q8C2211yescharacteristic
25#5834—24no—
26#5834C2218yescomplemented
27C2×#950—28no—
28C2×#950C2218yescomplemented
29C2×Q8×Dic3C2211yescharacteristic
30C2×#944C2211yescharacteristic
31C22×#216C2211yescharacteristic
32C22×#215C2211yescharacteristic
33C22×#215C2211yescharacteristic
34C2×#940—21no—
35C2×#940C2211yescharacteristic
36C2×#938—21no—
37C2×#938C2211yescharacteristic
38C22×#214C2211yescharacteristic
39C22×#213C2211yescharacteristic
40C2×#930—21no—
41C2×#930C2211yescharacteristic
42C2×C4×#67—21no—
43C2×C4×#67C2211yescharacteristic
44C23×C3⋊C8C2211yescharacteristic
45C2×#919—28no—
46C2×#919C2218yescomplemented
47C22×D24C2211yescharacteristic
48C22×#204C2211yescharacteristic
49C22×D3×C8C2211yescharacteristic
50#5631—24no—
51#5631C2218yescomplemented
52C2×#897C2211yescharacteristic
53C2×#894—21no—
54C2×#893C2211yescharacteristic
55C2×D3×C4⋊C4—21no—
56C2×#884—21no—
57C2×#883—21no—
58C3×#452C2218yescomplemented
59C2×C3×#103C2211yescharacteristic
60C2×C3×#102C2211yescharacteristic
61C2×C3×C22⋊C8C2211yescharacteristic
62C2×#835C2211yescharacteristic
63#5182C2218yescomplemented
64#5175C2218yescomplemented
65#5172C2218yescomplemented
66C2×#821C2211yescharacteristic
67C2×(C2×D3)⋊C8C2211yescharacteristic
68C2×#816C2211yescharacteristic
69C2×Dic3⋊C8C2211yescharacteristic
70C2×C8×Dic3C2211yescharacteristic
71#5048C2218yescomplemented
72C2×#809C2211yescharacteristic
73C2×#808C2211yescharacteristic
74#4808C2218yescomplemented
75#4788C2218yescomplemented
76#4786C2218yescomplemented
77#4778C2218yescomplemented
78#4734C2218yescomplemented
79#67⋊C8C2218yescomplemented
80C22×#135—31no—
81C22×#135—31no—
82C2×#550—31no—
83C2×#547—31no—
84#3284—316no—
85C2×#492—31no—
86C2×#465—31no—
87C2×#465—31no—
88C2×#462—31no—
89C2×#459—31no—
90C2×#452—31no—
91C2×#452D311yescharacteristic, complemented
92C2×#449—31no—
93C2×#449—31no—
94C2×C4×SD16—31no—
95C2×C8×D4—31no—
96C2×C3×#41—22no—
97C2×C3×#41—24no—
98C2×C3×#41—42no—
99C2×C3×#41C2314yes—
100C22×C3×Q8C2311yescharacteristic
101C22×C3×Q8C2311yescharacteristic
102C22×C3×D4—21no—
103C22×C3×D4C2311yescharacteristic
104C23×C3×C4—21no—
105C23×C3×C4C2311yescharacteristic
106C22×#67—21no—
107C22×#67—21no—
108C22×#67—21no—
109C22×#67—21no—
110C22×#67—21no—
111C22×#67D411yescharacteristic
112C2×#239—22no—
113C2×#239—22no—
114C2×#239—24no—
115C2×#239—24no—
116C2×#239—42no—
117C2×#239—42no—
118C2×#239C2314yes—
119C2×#239C2314yes—
120C2×#235—22no—
121C2×#235—24no—
122C2×#235—42no—
123C2×#235C2314yes—
124C22×D12—21no—
125C22×D12—21no—
126C22×D12C2311yescharacteristic
127C22×D12C2311yescharacteristic
128C22×C4×D3—21no—
129C22×C4×D3—21no—
130C22×C4×D3—21no—
131C22×C4×D3—21no—
132C22×C4×D3C2311yescharacteristic
133C22×Dic6C2311yescharacteristic
134C2×C3×Q16—24no—
135C2×C3×Q16C2314yes—
136C2×C3×SD16—42no—
137C2×C3×SD16C2314yes—
138C22×C3×C8C2311yescharacteristic
139C22×C3×C8C2311yescharacteristic
140C3×C22⋊Q8—22no—
141C3×C22⋊Q8C2314yes—
142C2×C3×C4⋊C4—21no—
143C2×C3×C4⋊C4C2311yescharacteristic
144C2×C3×C22⋊C4—21no—
145C2×#217—21no—
146C2×#217D411yescharacteristic
147#950—232no—
148Q8×Dic3—22no—
149Q8×Dic3C2314yes—
150#944—22no—
151#944C2314yes—
152C2×#216—24no—
153C2×#216C2314yes—
154C2×#215—24no—
155C2×#215D418yescomplemented
156C2×#215C2314yes—
157C2×#215C2314yes—
158#940—28no—
159#940—22no—
160#940C2314yes—
161#938—22no—
162#938—28no—
163#938C2314yes—
164C2×#214—24no—
165C2×#214C2314yes—
166C2×#213—24no—
167C2×#213C2314yes—
168#930—22no—
169#930—28no—
170#930C2314yes—
171C4×#67—28no—
172C4×#67D414yes—
173C4×#67C2314yes—
174C2×(C2×D3)⋊C4—21no—
175C2×(C2×D3)⋊C4—21no—
176C2×(C2×D3)⋊C4—21no—
177C2×(C2×D3)⋊C4D411yescharacteristic
178C2×C4⋊Dic3—21no—
179C2×C4⋊Dic3—21no—
180C2×C4⋊Dic3C2311yescharacteristic
181C2×Dic3⋊C4—21no—
182C2×Dic3⋊C4—21no—
183C2×Dic3⋊C4D411yescharacteristic
184C2×C4×Dic3—21no—
185C2×C4×Dic3C2311yescharacteristic
186C22×C3⋊C8—24no—
187C22×C3⋊C8C2311yescharacteristic
188C22×C3⋊C8C2314yes—
189C22×C3⋊C8C2311yescharacteristic
190#919—232no—
191C2×D24—24no—
192C2×D24C2314yes—
193C2×#204—42no—
194C2×#204C2314yes—
195C2×D3×C8—24no—
196C2×D3×C8C2314yes—
197#897—22no—
198#897C2314yes—
199#894—28no—
200#893—22no—
201#893C2314yes—
202D3×C4⋊C4—28no—
203#884—28no—
204#883—28no—
205C3×#103C2314yes—
206C3×#102C2314yes—
207C3×C22⋊C8C2314yes—
208#835C2314yes—
209#821C2314yes—
210(C2×D3)⋊C8C2314yes—
211#816C2314yes—
212Dic3⋊C8C2314yes—
213C8×Dic3C2314yes—
214#809C2314yes—
215#808C2314yes—
216C22×#41—31no—
217C22×#41—31no—
218C22×#41—31no—
219C22×#41C2×D311yescharacteristic
220C2×#135—38no—
221C2×#135—38no—
222C2×#135—68no—
223C2×#135—68no—
224C22×Q16—31no—
225C22×Q16C2×D311yescharacteristic
226C22×SD16—31no—
227C22×SD16—31no—
228C22×SD16—31no—
229C22×SD16—31no—
230C22×SD16C2×D311yescharacteristic
231C22×D8—31no—
232C22×D8—31no—
233C23×C8—31no—
234C23×C8—31no—
235#550—38no—
236#550—64no—
237#547—38no—
238#547—64no—
239C2×C4⋊Q8—31no—
240C2×#127—31no—
241C2×#127—61no—
242C2×#123—61no—
243C2×#123—61no—
244C2×C22⋊Q8—31no—
245C2×C22⋊Q8C2×D311yescharacteristic
246C2×#121—31no—
247C2×#121—31no—
248C2×#121—61no—
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#492—38no—
257#465—38no—
258#465—38no—
259#462—38no—
260#459—38no—
261#452—38no—
262#452C2×D318yescomplemented
263#449—38no—
264#449—38no—
265C4×SD16—38no—
266C8×D4—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×C4×C8—31no—
278C24×C3—21no—
279C24×C3C2×D411yescharacteristic
280C23×D3—21no—
281C23×D3—21no—
282C23×D3C2×D411yescharacteristic
283C3×#41—28no—
284C3×#41—44no—
285C3×#41—48no—
286C2×C3×Q8—21no—
287C2×C3×Q8—21no—
288C2×C3×Q8—22no—
289C2×C3×Q8—22no—
290C2×C3×Q8—22no—
291C2×C3×Q8C2×D414yes—
292C2×C3×Q8C2412yes—
293C2×C3×Q8C2412yes—
294C2×C3×D4—24no—
295C2×C3×D4—22no—
296C2×C3×D4—21no—
297C2×C3×D4—22no—
298C2×C3×D4—44no—
299C2×C3×D4C2412yes—
300C22×C3×C4—21no—
301C22×C3×C4—22no—
302C22×C3×C4—22no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—24no—
306C22×C3×C4—44no—
307C22×C3×C4C2×D411yescharacteristic
308C22×C3×C4C2×D412yes—
309C22×C3×C4C2412yes—
310C22×C3×C4C2411yescharacteristic
311C2×#67—24no—
312C2×#67—24no—
313C2×#67—24no—
314C2×#67—24no—
315C2×#67—24no—
316C2×#67—24no—
317C2×#67—44no—
318C2×#67—44no—
319C2×#67—82no—
320C2×#67—82no—
321C2×#67—82no—
322C2×#67C2×D414yes—
323C22×Dic3—21no—
324C22×Dic3—21no—
325C22×Dic3C2×D411yescharacteristic
326C22×Dic3C2×D411yescharacteristic
327C22×Dic3C2×D411yescharacteristic
328#239—28no—
329#239—28no—
330#239—44no—
331#239—44no—
332#239—48no—
333#239—48no—
334#235—28no—
335#235—44no—
336#235—48no—
337C2×D12—21no—
338C2×D12—22no—
339C2×D12—22no—
340C2×D12—22no—
341C2×D12—24no—
342C2×D12—24no—
343C2×D12—21no—
344C2×D12—44no—
345C2×D12—44no—
346C2×D12C2×D414yes—
347C2×D12C2412yes—
348C2×D12C2412yes—
349C2×C4×D3—22no—
350C2×C4×D3—22no—
351C2×C4×D3—24no—
352C2×C4×D3—24no—
353C2×C4×D3—24no—
354C2×C4×D3—24no—
355C2×C4×D3—44no—
356C2×C4×D3—44no—
357C2×C4×D3—44no—
358C2×C4×D3—44no—
359C2×C4×D3C2×D412yes—
360C2×C4×D3C2412yes—
361C2×Dic6—22no—
362C2×Dic6—22no—
363C2×Dic6—21no—
364C2×Dic6C2412yes—
365C3×Q16—28no—
366C3×SD16—44no—
367C2×C3×C8—22no—
368C2×C3×C8—22no—
369C2×C3×C8C2412yes—
370C2×C3×C8C2412yes—
371C3×C4⋊C4—24no—
372C3×C4⋊C4—21no—
373C3×C4⋊C4C2412yes—
374C3×C22⋊C4—24no—
375#217—24no—
376#217C2×D414yes—
377#216—28no—
378#215—28no—
379#215C2×D4116yescomplemented
380#214—28no—
381#213—28no—
382(C2×D3)⋊C4—24no—
383(C2×D3)⋊C4—24no—
384(C2×D3)⋊C4—24no—
385(C2×D3)⋊C4C2×D414yes—
386C4⋊Dic3—21no—
387C4⋊Dic3—24no—
388C4⋊Dic3—24no—
389C4⋊Dic3C2412yes—
390Dic3⋊C4—24no—
391Dic3⋊C4—24no—
392Dic3⋊C4C2×D414yes—
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—
401D24—28no—
402#204—44no—
403D3×C8—28no—
404C2×#41—22no—
405C2×#41—24no—
406C2×#41—34no—
407C2×#41—34no—
408C2×#41—34no—
409C2×#41—42no—
410C2×#41—64no—
411C2×#41—62no—
412C2×#41—62no—
413C2×#41—62no—
414C2×#41—64no—
415C2×#41—64no—
416C2×#41—122no—
417C2×#41—122no—
418C2×#41—122no—
419C2×#41C22×D314yes—
420C22×Q8—31no—
421C22×Q8C22×D311yescharacteristic
422C22×Q8C22×D311yescharacteristic
423C22×D4—21no—
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×D4C22×D311yescharacteristic
435C23×C4—21no—
436C23×C4—31no—
437C23×C4—61no—
438C23×C4—61no—
439C23×C4—61no—
440C23×C4—61no—
441C23×C4C22×D311yescharacteristic
442#135—632no—
443#135—632no—
444C2×Q16—24no—
445C2×Q16—34no—
446C2×Q16—64no—
447C2×Q16C22×D314yes—
448C2×SD16—38no—
449C2×SD16—34no—
450C2×SD16—34no—
451C2×SD16—34no—
452C2×SD16—34no—
453C2×SD16—42no—
454C2×SD16—64no—
455C2×SD16—64no—
456C2×SD16—122no—
457C2×SD16C22×D314yes—
458C2×D8—34no—
459C2×D8—34no—
460C2×D8—64no—
461C2×D8—64no—
462C22×C8—31no—
463C22×C8—31no—
464C22×C8—34no—
465C22×C8—34no—
466C22×C8—64no—
467C22×C8—64no—
468C22×C8C22×D311yescharacteristic
469C22×C8C22×D311yescharacteristic
470C4⋊Q8—34no—
471C4⋊Q8—62no—
472#127—34no—
473#127—62no—
474#127—68no—
475#123—68no—
476#123—68no—
477C22⋊Q8—22no—
478C22⋊Q8—34no—
479C22⋊Q8—62no—
480C22⋊Q8C22×D314yes—
481#121—34no—
482#121—34no—
483#121—68no—
484#121—68no—
485#121—68no—
486#121—62no—
487#121—62no—
488C4×Q8—34no—
489C4×Q8—62no—
490C4×D4—34no—
491C4×D4—34no—
492C4×D4—34no—
493C4×D4—62no—
494C4×D4—68no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—31no—
497C2×C4⋊C4—31no—
498C2×C4⋊C4—68no—
499C2×C4⋊C4—61no—
500C2×C4⋊C4—61no—
501C2×C4⋊C4—61no—
502C2×C4⋊C4—61no—
503C2×C4⋊C4C22×D311yescharacteristic
504C2×C22⋊C4—21no—
505C2×C22⋊C4—31no—
506C2×C22⋊C4—31no—
507C2×C22⋊C4—61no—
508C2×C22⋊C4—61no—
509C2×C22⋊C4—61no—
510C2×C22⋊C4—61no—
511C2×C42—31no—
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—
523C4×C8—34no—
524C23×C3—22no—
525C23×C3—22no—
526C23×C3—22no—
527C23×C3—22no—
528C23×C3—42no—
529C23×C3—42no—
530C23×C3—42no—
531C23×C3C22×D412yes—
532C23×C3C22×D411yescharacteristic
533C22×D3—22no—
534C22×D3—24no—
535C22×D3—22no—
536C22×D3—22no—
537C22×D3—22no—
538C22×D3—22no—
539C22×D3—42no—
540C22×D3—42no—
541C22×D3—42no—
542C22×D3—42no—
543C22×D3—42no—
544C22×D3C22×D412yes—
545C3×Q8—24no—
546C3×Q8—22no—
547C3×Q8—22no—
548C3×Q8—22no—
549C3×Q8—42no—
550C3×Q8C22×D414yes—
551C3×D4—22no—
552C3×D4—22no—
553C3×D4—48no—
554C3×D4—42no—
555C2×C3×C4—22no—
556C2×C3×C4—24no—
557C2×C3×C4—22no—
558C2×C3×C4—24no—
559C2×C3×C4—22no—
560C2×C3×C4—22no—
561C2×C3×C4—22no—
562C2×C3×C4—22no—
563C2×C3×C4—48no—
564C2×C3×C4—42no—
565C2×C3×C4—42no—
566C2×C3×C4C22×D412yes—
567C2×C3×C4C22×D411yescharacteristic
568C2×C3×C4C22×D412yes—
569C2×C3×C4H(5,𝔽2)12yes—
570C2×C3×C4C2511yescharacteristic
571#67—28no—
572#67—48no—
573#67—48no—
574#67—84no—
575#67—84no—
576#67—84no—
577C2×Dic3—22no—
578C2×Dic3—22no—
579C2×Dic3—22no—
580C2×Dic3—22no—
581C2×Dic3—42no—
582C2×Dic3—42no—
583C2×Dic3#13514yescomplemented
584C2×Dic3C22×D412yes—
585C2×Dic3C22×D412yes—
586C2×Dic3C22×D412yes—
587D12—24no—
588D12—22no—
589D12—22no—
590D12—22no—
591D12—48no—
592D12—48no—
593D12—42no—
594D12C22×D414yes—
595C4×D3—24no—
596C4×D3—22no—
597C4×D3—22no—
598C4×D3—48no—
599C4×D3—48no—
600C4×D3—48no—
601C4×D3—48no—
602Dic6—22no—
603Dic6—22no—
604Dic6—42no—
605C3×C8—22no—
606C3×C8—22no—
607C3⋊C8—22no—
608C3⋊C8C22×D414yes—
609C24—21no—
610C24—31no—
611C24—61no—
612C24—61no—
613C24D3×D411yescharacteristic
614#41—28no—
615#41—44no—
616#41—48no—
617#41—68no—
618#41—68no—
619#41—68no—
620#41—124no—
621#41—128no—
622#41—124no—
623#41—124no—
624#41—128no—
625#41—128no—
626C2×Q8—21no—
627C2×Q8—21no—
628C2×Q8—22no—
629C2×Q8—22no—
630C2×Q8—22no—
631C2×Q8—32no—
632C2×Q8—61no—
633C2×Q8—62no—
634C2×Q8—62no—
635C2×Q8D3×D414yes—
636C2×Q8C23×D312yes—
637C2×Q8C23×D312yes—
638C2×D4—24no—
639C2×D4—22no—
640C2×D4—21no—
641C2×D4—22no—
642C2×D4—34no—
643C2×D4—34no—
644C2×D4—32no—
645C2×D4—32no—
646C2×D4—44no—
647C2×D4—64no—
648C2×D4—64no—
649C2×D4—64no—
650C2×D4—64no—
651C2×D4—64no—
652C2×D4—64no—
653C2×D4—64no—
654C2×D4—64no—
655C2×D4—61no—
656C2×D4—62no—
657C2×D4—61no—
658C2×D4—62no—
659C2×D4—62no—
660C2×D4—124no—
661C2×D4—124no—
662C2×D4—124no—
663C2×D4—124no—
664C2×D4—242no—
665C2×D4—242no—
666C2×D4—242no—
667C2×D4C23×D312yes—
668C22×C4—21no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—24no—
674C22×C4—31no—
675C22×C4—31no—
676C22×C4—31no—
677C22×C4—32no—
678C22×C4—32no—
679C22×C4—44no—
680C22×C4—64no—
681C22×C4—64no—
682C22×C4—64no—
683C22×C4—62no—
684C22×C4—62no—
685C22×C4—61no—
686C22×C4—61no—
687C22×C4—64no—
688C22×C4—124no—
689C22×C4—124no—
690C22×C4—124no—
691C22×C4—124no—
692C22×C4D3×D412yes—
693C22×C4D3×D411yescharacteristic
694C22×C4C23×D312yes—
695C22×C4C23×D311yescharacteristic
696Q16—28no—
697Q16—68no—
698SD16—316no—
699SD16—44no—
700SD16—68no—
701SD16—68no—
702SD16—124no—
703D8—68no—
704D8—68no—
705C2×C8—22no—
706C2×C8—22no—
707C2×C8—34no—
708C2×C8—32no—
709C2×C8—32no—
710C2×C8—68no—
711C2×C8—68no—
712C2×C8—62no—
713C2×C8C23×D312yes—
714C2×C8C23×D312yes—
715C4⋊C4—24no—
716C4⋊C4—21no—
717C4⋊C4—34no—
718C4⋊C4—32no—
719C4⋊C4—64no—
720C4⋊C4—64no—
721C4⋊C4—64no—
722C4⋊C4—64no—
723C4⋊C4—61no—
724C4⋊C4C23×D312yes—
725C22⋊C4—24no—
726C22⋊C4—34no—
727C22⋊C4—34no—
728C22⋊C4—64no—
729C22⋊C4—64no—
730C22⋊C4—64no—
731C22⋊C4—64no—
732C42—32no—
733C42—32no—
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—84no—
743C22×C3D4212yes—
744C22×C3C2×#13512yes—
745C22×C3#57712yes—
746C22×C3C23×D411yescharacteristic
747C2×D3—22no—
748C2×D3—24no—
749C2×D3—22no—
750C2×D3—22no—
751C2×D3—44no—
752C2×D3—48no—
753C2×D3—42no—
754C2×D3—42no—
755C2×D3—42no—
756C2×D3—42no—
757C2×D3—42no—
758C2×D3—84no—
759C3×C4—22no—
760C3×C4—24no—
761C3×C4—42no—
762C3×C4—42no—
763C3×C4D4212yes—
764C3×C4C23×D411yescharacteristic
765C3×C4C2×H(5,𝔽2)11yescharacteristic
766Dic3—22no—
767Dic3—22no—
768Dic3—42no—
769Dic3—42no—
770Dic3C2×#13514yescomplemented
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—32no—
776C23—42no—
777C23—42no—
778C23—42no—
779C23—62no—
780C23—62no—
781C23—62no—
782C23—62no—
783C23—64no—
784C23—62no—
785C23—122no—
786C23—122no—
787C23—122no—
788C23—122no—
789C23—122no—
790C23C2×D3×D412yes—
791C23C2×D3×D411yescharacteristic
792Q8—22no—
793Q8—24no—
794Q8—22no—
795Q8—22no—
796Q8—42no—
797Q8—62no—
798Q8—62no—
799Q8—122no—
800Q8C2×D3×D414yes—
801D4—22no—
802D4—22no—
803D4—34no—
804D4—48no—
805D4—42no—
806D4—68no—
807D4—62no—
808D4—62no—
809D4—62no—
810D4—64no—
811D4—128no—
812D4—128no—
813D4—128no—
814D4—128no—
815D4—122no—
816D4—244no—
817D4—244no—
818D4—244no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—24no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—24no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—32no—
828C2×C4—34no—
829C2×C4—32no—
830C2×C4—32no—
831C2×C4—48no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—62no—
835C2×C4—62no—
836C2×C4—62no—
837C2×C4—62no—
838C2×C4—64no—
839C2×C4—62no—
840C2×C4—62no—
841C2×C4—128no—
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#328414yescomplemented
859C2×C3C2×D4211yescharacteristic
860C2×C3C22×#13511yescharacteristic
861C2×C3C2×#57711yescharacteristic
862D3—42no—
863D3—44no—
864D3—82no—
865C22—22no—
866C22—22no—
867C22—22no—
868C22—44no—
869C22—42no—
870C22—42no—
871C22—42no—
872C22—62no—
873C22—62no—
874C22—62no—
875C22—64no—
876C22—84no—
877C22—124no—
878C22—128no—
879C22—122no—
880C22—122no—
881C22—122no—
882C22—122no—
883C22—122no—
884C22—244no—
885C22#559012yes—
886C22D3×#13512yes—
887C22#577812yes—
888C22C22×D3×D411yescharacteristic
889C4—22no—
890C4—24no—
891C4—34no—
892C4—42no—
893C4—42no—
894C4—62no—
895C4—62no—
896C4—122no—
897C4—122no—
898C4#559012yes—
899C4C22×D3×D411yescharacteristic
900C4C2×#100411yescharacteristic
901C3C2×#328411yescharacteristic, complemented, Sylow
902C2—42no—
903C2—82no—
904C2—122no—
905C2—124no—
906C2—242no—
907C2#8027014yesdirect product factor
908C2C2×#559011yescharacteristic
909C2C2×D3×#13511yescharacteristic
910C2C2×#577811yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#452C2
socleC23×C3C22×D4
hypercenterC2×#452D3
hypocenterC3C2×#3284
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#5834C2semidirect
2. C22×#950C2semidirect
3. C22×#919C2semidirect
4. C2×#5631C2semidirect
5. C2×C3×#452C2semidirect
6. C2×#5182C2semidirect
7. C2×#5172C2semidirect
8. C2×#5175C2semidirect
9. C2×#5048C2semidirect
10. #80270C2direct (N × H)
11. C2×#4808C2semidirect
12. C2×#4788C2semidirect
13. C2×#4786C2semidirect
14. C2×#4778C2semidirect
15. C2×#4734C2semidirect
16. C2×#67⋊C8C2semidirect
26. #5834C22semidirect
28. C2×#950C22semidirect
46. C2×#919C22semidirect
51. #5631C22semidirect
58. C3×#452C22semidirect
63. #5182C22semidirect
64. #5175C22semidirect
65. #5172C22semidirect
71. #5048C22semidirect
74. #4808C22semidirect
75. #4788C22semidirect
76. #4786C22semidirect
77. #4778C22semidirect
78. #4734C22semidirect
79. #67⋊C8C22semidirect
91. C2×#452D3semidirect
155. C2×#215D4semidirect
262. #452C2×D3semidirect
379. #215C2×D4semidirect
583. C2×Dic3#135semidirect
770. Dic3C2×#135semidirect
858. C2×C3#3284semidirect
901. C3C2×#3284semidirect
907. C2#80270direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#58342
C22×#9502
C22×#9192
C2×#56312
C2×C3×#4522
C2×#51822
C2×#51722
C2×#51752
C2×#50482
#802702
C2×#48082
C2×#47882
C2×#47862
C2×#47782
C2×#47342
C2×#67⋊C82
C2×#32843