Finite Group Databasebeta

← C2×#80688 #11670245

Subgroups — C2×#80688 #11670245

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×#915C211yesmaximal, characteristic, complemented
2C22×#904C211yesmaximal, characteristic, complemented
3C2×#5633C211yesmaximal, characteristic, complemented
4C2×#5599C211yesmaximal, characteristic, complemented
5C2×C3×#465C211yesmaximal, characteristic, complemented
6C2×#5176C211yesmaximal, characteristic, complemented
7C2×#5111C211yesmaximal, characteristic, complemented
8C2×#5047C211yesmaximal, characteristic, complemented
9C2×#5037C211yesmaximal, characteristic, complemented
10#80688C2116yesmaximal, direct product factor
11C2×#4865C211yesmaximal, characteristic, complemented
12C2×#4853C211yesmaximal, characteristic, complemented
13C2×#4798C211yesmaximal, characteristic, complemented
14C2×#4806C211yesmaximal, characteristic, complemented
15C2×#4762C211yesmaximal, characteristic, complemented
16C2×#4781C211yesmaximal, characteristic, complemented
17C2×#3271—31nomaximal, Sylow
18C22×D3×Q8C2211yescharacteristic
19C22×#237C2211yescharacteristic
20C22×#235C2211yescharacteristic
21C22×#235C2211yescharacteristic
22C22×C3×SD16C2211yescharacteristic
23C23×C3×C8C2211yescharacteristic
24C2×C3×C22⋊Q8C2211yescharacteristic
25C2×C3×#121C2211yescharacteristic
26C2×#947C2211yescharacteristic
27C22×#216C2211yescharacteristic
28C22×#215C2211yescharacteristic
29C2×#940—21no—
30C2×#940C2211yescharacteristic
31C2×#939—21no—
32C22×#214C2211yescharacteristic
33C22×#213C2211yescharacteristic
34C2×C4×#67C2211yescharacteristic
35C2×#915—28no—
36C2×#915C2218yescomplemented
37C22×Dic12C2211yescharacteristic
38C2×#904—28no—
39C2×#904C2218yescomplemented
40C22×D24C2211yescharacteristic
41C22×#204C2211yescharacteristic
42C22×#204C2211yescharacteristic
43C22×ΓL(1,𝔽25)C2211yescharacteristic
44#5633—24no—
45#5633C2218yescomplemented
46#5599—24no—
47#5599C2218yescomplemented
48C2×#896—21no—
49C2×#895C2211yescharacteristic
50C2×#895C2211yescharacteristic
51C2×#893—21no—
52C2×#887C2211yescharacteristic
53C2×#887C2211yescharacteristic
54C2×#885—21no—
55C2×#884—21no—
56C2×#884—21no—
57C2×#67⋊C4—21no—
58C3×#465C2218yescomplemented
59C2×C3×#106C2211yescharacteristic
60C2×C3×#103C2211yescharacteristic
61C2×C3×#102C2211yescharacteristic
62C2×#830C2211yescharacteristic
63#5176C2218yescomplemented
64#5111C2218yescomplemented
65C2×(C2×D3)⋊C8C2211yescharacteristic
66C2×#815C2211yescharacteristic
67C2×Dic3⋊C8C2211yescharacteristic
68#5047C2218yescomplemented
69#5037C2218yescomplemented
70C2×#810C2211yescharacteristic
71C2×#810C2211yescharacteristic
72C2×#809C2211yescharacteristic
73C2×#809C2211yescharacteristic
74#4865C2218yescomplemented
75#4853C2218yescomplemented
76#4806C2218yescomplemented
77#4798C2218yescomplemented
78#4781C2218yescomplemented
79#4762C2218yescomplemented
80C22×#137—31no—
81C22×#135—31no—
82C2×#550—31no—
83C2×#548—31no—
84#3271—316no—
85C2×#496—31no—
86C2×#469—31no—
87C2×#465D311yescharacteristic, complemented
88C2×#464—31no—
89C2×#460—31no—
90C2×#452—31no—
91C2×#449—31no—
92C2×#449—31no—
93C2×#448—31no—
94C2×#441—31no—
95C2×#435—31no—
96C22×C3×Q8C2311yescharacteristic
97C22×C3×D4—21no—
98C22×C3×D4C2311yescharacteristic
99C23×C3×C4C2311yescharacteristic
100C22×#67—21no—
101C22×#67—21no—
102C22×#67—21no—
103C22×#67—21no—
104C22×#67—21no—
105C22×#67D411yescharacteristic
106C23×Dic3—21no—
107C2×D3×Q8—22no—
108C2×D3×Q8—24no—
109C2×D3×Q8—42no—
110C2×D3×Q8C2314yes—
111C2×#237—22no—
112C2×#237—24no—
113C2×#237—42no—
114C2×#237C2314yes—
115C2×#235—22no—
116C2×#235—22no—
117C2×#235—24no—
118C2×#235—24no—
119C2×#235—42no—
120C2×#235—42no—
121C2×#235C2314yes—
122C2×#235C2314yes—
123C22×D12—21no—
124C22×D12—21no—
125C22×D12C2311yescharacteristic
126C22×D12C2311yescharacteristic
127C22×C4×D3—21no—
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—
136C22×C3×C8—24no—
137C22×C3×C8C2311yescharacteristic
138C22×C3×C8C2314yes—
139C22×C3×C8C2311yescharacteristic
140C3×C22⋊Q8—22no—
141C3×C22⋊Q8C2314yes—
142C3×#121—22no—
143C3×#121C2314yes—
144C2×C3×C4⋊C4—21no—
145C2×C3×C4⋊C4C2311yescharacteristic
146C2×C3×C4⋊C4C2311yescharacteristic
147C2×C3×C22⋊C4—21no—
148C2×C3×C22⋊C4—21no—
149C2×#217D411yescharacteristic
150#947—22no—
151#947C2314yes—
152C2×#216—24no—
153C2×#216C2314yes—
154C2×#215—42no—
155C2×#215C2314yes—
156#940—28no—
157#940—22no—
158#940C2314yes—
159#939—28no—
160C2×#214—24no—
161C2×#214C2314yes—
162C2×#213—42no—
163C2×#213C2314yes—
164C4×#67D414yes—
165C4×#67C2314yes—
166C2×(C2×D3)⋊C4—21no—
167C2×(C2×D3)⋊C4—21no—
168C2×(C2×D3)⋊C4—21no—
169C2×(C2×D3)⋊C4—21no—
170C2×(C2×D3)⋊C4D411yescharacteristic
171C2×Dic3⋊C4—21no—
172C2×Dic3⋊C4—21no—
173C2×Dic3⋊C4D411yescharacteristic
174C2×C4×Dic3—21no—
175C2×C4×Dic3—21no—
176C2×C4×Dic3C2311yescharacteristic
177C22×C3⋊C8C2311yescharacteristic
178C22×C3⋊C8C2311yescharacteristic
179#915—232no—
180C2×Dic12D418yescomplemented
181C2×Dic12C2314yes—
182#904—232no—
183C2×D24—24no—
184C2×D24C2314yes—
185C2×#204—24no—
186C2×#204—24no—
187C2×#204C2314yes—
188C2×#204C2314yes—
189C2×ΓL(1,𝔽25)—24no—
190C2×ΓL(1,𝔽25)C2314yes—
191#896—28no—
192#895—22no—
193#895—22no—
194#895C2314yes—
195#895C2314yes—
196#893—28no—
197#887—22no—
198#887—22no—
199#887C2314yes—
200#887C2314yes—
201#885—28no—
202#884—28no—
203#884—28no—
204#67⋊C4—28no—
205C3×#106C2314yes—
206C3×#103C2314yes—
207C3×#102C2314yes—
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×SD16—31no—
227C22×SD16—31no—
228C22×SD16—31no—
229C22×SD16—31no—
230C22×SD16C2×D311yescharacteristic
231C22×D8—31no—
232C22×D8—31no—
233C22×M16—31no—
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—61no—
244C2×C22⋊Q8C2×D311yescharacteristic
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#465C2×D318yescomplemented
259#464—38no—
260#460—38no—
261#452—38no—
262#449—38no—
263#449—38no—
264#448—38no—
265#441—38no—
266#435—38no—
267C2×#106C2×D311yescharacteristic
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⋊C8—31no—
277C2×#97—31no—
278C24×C3—21no—
279C24×C3C2×D411yescharacteristic
280C23×D3—21no—
281C23×D3—21no—
282C23×D3C2×D411yescharacteristic
283C2×C3×Q8—21no—
284C2×C3×Q8—22no—
285C2×C3×Q8—22no—
286C2×C3×Q8C2412yes—
287C2×C3×D4—24no—
288C2×C3×D4—22no—
289C2×C3×D4—21no—
290C2×C3×D4—22no—
291C2×C3×D4—82no—
292C2×C3×D4C2412yes—
293C22×C3×C4—22no—
294C22×C3×C4—22no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4C2×D411yescharacteristic
299C22×C3×C4C2×D412yes—
300C22×C3×C4C2412yes—
301C22×C3×C4C2411yescharacteristic
302C2×#67—24no—
303C2×#67—24no—
304C2×#67—24no—
305C2×#67—24no—
306C2×#67—24no—
307C2×#67—42no—
308C2×#67—44no—
309C2×#67—44no—
310C2×#67—44no—
311C2×#67—44no—
312C2×#67—82no—
313C2×#67C2×D414yes—
314C22×Dic3—21no—
315C22×Dic3—21no—
316C22×Dic3—24no—
317C22×Dic3—44no—
318C22×Dic3C2×D411yescharacteristic
319C22×Dic3C2×D411yescharacteristic
320C22×Dic3C2×D411yescharacteristic
321D3×Q8—28no—
322D3×Q8—44no—
323D3×Q8—48no—
324#237—28no—
325#237—44no—
326#237—48no—
327#235—28no—
328#235—28no—
329#235—44no—
330#235—44no—
331#235—48no—
332#235—48no—
333C2×D12—22no—
334C2×D12—22no—
335C2×D12—22no—
336C2×D12—22no—
337C2×D12—24no—
338C2×D12—21no—
339C2×D12—21no—
340C2×D12—24no—
341C2×D12—44no—
342C2×D12—82no—
343C2×D12C2412yes—
344C2×D12C2412yes—
345C2×C4×D3—22no—
346C2×C4×D3—22no—
347C2×C4×D3—24no—
348C2×C4×D3—24no—
349C2×C4×D3—24no—
350C2×C4×D3—44no—
351C2×C4×D3—44no—
352C2×C4×D3—44no—
353C2×C4×D3C2×D412yes—
354C2×C4×D3C2412yes—
355C2×Dic6—21no—
356C2×Dic6—21no—
357C2×Dic6—22no—
358C2×Dic6—22no—
359C2×Dic6—24no—
360C2×Dic6—44no—
361C2×Dic6C2×D414yes—
362C2×Dic6C2×D414yes—
363C2×Dic6C2412yes—
364C2×Dic6C2412yes—
365C3×SD16—28no—
366C2×C3×C8—22no—
367C2×C3×C8—28no—
368C2×C3×C8C2×D414yes—
369C2×C3×C8C2412yes—
370C2×C3×C8C2412yes—
371C3×C4⋊C4—21no—
372C3×C4⋊C4—21no—
373C3×C4⋊C4—24no—
374C3×C4⋊C4C2412yes—
375C3×C4⋊C4C2412yes—
376C3×C22⋊C4—24no—
377C3×C22⋊C4—24no—
378#217C2×D414yes—
379#216—28no—
380#215—44no—
381#214—28no—
382#213—44no—
383(C2×D3)⋊C4—24no—
384(C2×D3)⋊C4—24no—
385(C2×D3)⋊C4—24no—
386(C2×D3)⋊C4—24no—
387(C2×D3)⋊C4C2×D414yes—
388Dic3⋊C4—24no—
389Dic3⋊C4—24no—
390Dic3⋊C4C2×D414yes—
391C4×Dic3—24no—
392C4×Dic3—24no—
393C4×Dic3C2×D412yes—
394C4×Dic3C2412yes—
395C2×C3⋊C8—22no—
396C2×C3⋊C8—22no—
397C2×C3⋊C8C2412yes—
398C2×C3⋊C8C2412yes—
399Dic12C2×D4116yescomplemented
400D24—28no—
401#204—28no—
402#204—28no—
403ΓL(1,𝔽25)—28no—
404C2×#41—34no—
405C2×#41—34no—
406C2×#41—34no—
407C2×#41—64no—
408C2×#41—64no—
409C2×#41—62no—
410C2×#41—62no—
411C2×#41—62no—
412C2×#41—64no—
413C2×#41—122no—
414C2×#41—122no—
415C2×#41—122no—
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—31no—
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×D4—61no—
435C22×D4C22×D311yescharacteristic
436C23×C4—31no—
437C23×C4—61no—
438C23×C4—61no—
439C23×C4—61no—
440C23×C4—61no—
441C23×C4C22×D311yescharacteristic
442#137—632no—
443#135—632no—
444C2×Q16—34no—
445C2×Q16—38no—
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—34no—
460C2×D8—64no—
461C2×D8—122no—
462C2×M16—34no—
463C2×M16—64no—
464C22×C8—24no—
465C22×C8—31no—
466C22×C8—31no—
467C22×C8C22×D311yescharacteristic
468C22×C8C22×D314yes—
469C22×C8C22×D311yescharacteristic
470#127—34no—
471#127—62no—
472#127—68no—
473#124—34no—
474#124—62no—
475#124—68no—
476C22⋊Q8—22no—
477C22⋊Q8—68no—
478C22⋊Q8C22×D314yes—
479#121—22no—
480#121—34no—
481#121—34no—
482#121—68no—
483#121—68no—
484#121—68no—
485#121—62no—
486#121—62no—
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—21no—
497C2×C4⋊C4—31no—
498C2×C4⋊C4—61no—
499C2×C4⋊C4—61no—
500C2×C4⋊C4C22×D311yescharacteristic
501C2×C4⋊C4C22×D311yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—31no—
505C2×C22⋊C4—31no—
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#106C22×D314yes—
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⋊C8—34no—
523#97—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—22no—
535C22×D3—22no—
536C22×D3—22no—
537C22×D3—22no—
538C22×D3—42no—
539C22×D3—42no—
540C22×D3—42no—
541C22×D3—42no—
542C22×D3—42no—
543C22×D3—42no—
544C22×D3C22×D412yes—
545C3×Q8—22no—
546C3×Q8—22no—
547C3×Q8—42no—
548C3×D4—22no—
549C3×D4—22no—
550C3×D4—42no—
551C3×D4—84no—
552C2×C3×C4—22no—
553C2×C3×C4—24no—
554C2×C3×C4—22no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
558C2×C3×C4—22no—
559C2×C3×C4—42no—
560C2×C3×C4—42no—
561C2×C3×C4—42no—
562C2×C3×C4C22×D412yes—
563C2×C3×C4C22×D411yescharacteristic
564C2×C3×C4C22×D412yes—
565C2×C3×C4H(5,𝔽2)12yes—
566C2×C3×C4C2511yescharacteristic
567#67—44no—
568#67—48no—
569#67—48no—
570#67—48no—
571#67—48no—
572#67—84no—
573C2×Dic3—24no—
574C2×Dic3—24no—
575C2×Dic3—22no—
576C2×Dic3—22no—
577C2×Dic3—22no—
578C2×Dic3—22no—
579C2×Dic3—22no—
580C2×Dic3—48no—
581C2×Dic3C22×D412yes—
582C2×Dic3C22×D412yes—
583C2×Dic3C22×D412yes—
584D12—22no—
585D12—22no—
586D12—22no—
587D12—22no—
588D12—48no—
589D12—42no—
590D12—42no—
591D12—84no—
592C4×D3—24no—
593C4×D3—22no—
594C4×D3—22no—
595C4×D3—48no—
596C4×D3—48no—
597C4×D3—48no—
598Dic6—24no—
599Dic6—24no—
600Dic6—22no—
601Dic6—22no—
602Dic6—48no—
603Dic6C22×D414yes—
604Dic6C22×D414yes—
605C3×C8—22no—
606C3×C8C22×D414yes—
607C3⋊C8—22no—
608C3⋊C8—22no—
609C24—21no—
610C24—31no—
611C24—61no—
612C24—61no—
613C24D3×D411yescharacteristic
614#41—68no—
615#41—68no—
616#41—68no—
617#41—124no—
618#41—124no—
619#41—128no—
620#41—128no—
621#41—124no—
622#41—128no—
623C2×Q8—21no—
624C2×Q8—22no—
625C2×Q8—22no—
626C2×Q8—34no—
627C2×Q8—34no—
628C2×Q8—32no—
629C2×Q8—32no—
630C2×Q8—64no—
631C2×Q8—61no—
632C2×Q8—61no—
633C2×Q8—62no—
634C2×Q8—62no—
635C2×Q8—68no—
636C2×Q8—124no—
637C2×Q8—124no—
638C2×Q8—128no—
639C2×Q8C23×D312yes—
640C2×D4—24no—
641C2×D4—22no—
642C2×D4—21no—
643C2×D4—22no—
644C2×D4—34no—
645C2×D4—32no—
646C2×D4—32no—
647C2×D4—64no—
648C2×D4—64no—
649C2×D4—64no—
650C2×D4—64no—
651C2×D4—64no—
652C2×D4—64no—
653C2×D4—64no—
654C2×D4—62no—
655C2×D4—62no—
656C2×D4—61no—
657C2×D4—61no—
658C2×D4—62no—
659C2×D4—62no—
660C2×D4—82no—
661C2×D4—124no—
662C2×D4—122no—
663C2×D4—124no—
664C2×D4—124no—
665C2×D4—124no—
666C2×D4—124no—
667C2×D4—242no—
668C2×D4—242no—
669C2×D4C23×D312yes—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—31no—
676C22×C4—31no—
677C22×C4—31no—
678C22×C4—32no—
679C22×C4—32no—
680C22×C4—64no—
681C22×C4—64no—
682C22×C4—61no—
683C22×C4—61no—
684C22×C4—62no—
685C22×C4—62no—
686C22×C4—64no—
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—316no—
697Q16—68no—
698SD16—28no—
699SD16—68no—
700SD16—68no—
701SD16—68no—
702SD16—124no—
703D8—68no—
704D8—124no—
705M16—68no—
706C2×C8—22no—
707C2×C8—28no—
708C2×C8—32no—
709C2×C8—32no—
710C2×C8—62no—
711C2×C8—62no—
712C2×C8D3×D414yes—
713C2×C8C23×D312yes—
714C2×C8C23×D312yes—
715C4⋊C4—24no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—34no—
719C4⋊C4—64no—
720C4⋊C4—64no—
721C4⋊C4C23×D312yes—
722C4⋊C4C23×D312yes—
723C22⋊C4—24no—
724C22⋊C4—24no—
725C22⋊C4—34no—
726C22⋊C4—34no—
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—84no—
743C22×C3D4212yes—
744C22×C3#57512yes—
745C22×C3#57712yes—
746C22×C3C23×D411yescharacteristic
747C2×D3—22no—
748C2×D3—22no—
749C2×D3—22no—
750C2×D3—44no—
751C2×D3—42no—
752C2×D3—42no—
753C2×D3—42no—
754C2×D3—42no—
755C2×D3—42no—
756C2×D3—42no—
757C2×D3—84no—
758C2×D3—84no—
759C3×C4—22no—
760C3×C4—42no—
761C3×C4—42no—
762C3×C4—42no—
763C3×C4D4212yes—
764C3×C4C23×D411yescharacteristic
765C3×C4C2×H(5,𝔽2)11yescharacteristic
766Dic3—24no—
767Dic3—24no—
768Dic3—22no—
769Dic3—22no—
770Dic3—22no—
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—62no—
784C23—122no—
785C23—122no—
786C23—122no—
787C23—122no—
788C23—122no—
789C23—122no—
790C23C2×D3×D412yes—
791C23C2×D3×D411yescharacteristic
792Q8—22no—
793Q8—22no—
794Q8—34no—
795Q8—34no—
796Q8—42no—
797Q8—62no—
798Q8—62no—
799Q8—64no—
800Q8—64no—
801Q8—128no—
802D4—22no—
803D4—22no—
804D4—42no—
805D4—62no—
806D4—62no—
807D4—62no—
808D4—62no—
809D4—84no—
810D4—128no—
811D4—124no—
812D4—128no—
813D4—128no—
814D4—128no—
815D4—128no—
816D4—122no—
817D4—122no—
818D4—244no—
819D4—244no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—24no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—32no—
828C2×C4—32no—
829C2×C4—32no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—62no—
834C2×C4—62no—
835C2×C4—62no—
836C2×C4—62no—
837C2×C4—62no—
838C2×C4—64no—
839C2×C4—64no—
840C2×C4—62no—
841C2×C4—62no—
842C2×C4—64no—
843C2×C4—128no—
844C2×C4—128no—
845C2×C4—128no—
846C2×C4—128no—
847C2×C4C2×D3×D412yes—
848C2×C4C2×D3×D412yes—
849C2×C4C2×D3×D411yescharacteristic
850C2×C4#100912yes—
851C2×C4C24×D311yescharacteristic
852C8—22no—
853C8—62no—
854C8—62no—
855C8C2×D3×D414yes—
856C2×C3—42no—
857C2×C3—82no—
858C2×C3#327114yescomplemented
859C2×C3C2×D4211yescharacteristic
860C2×C3C2×#57511yescharacteristic
861C2×C3C2×#57711yescharacteristic
862D3—42no—
863D3—82no—
864D3—82no—
865C22—22no—
866C22—22no—
867C22—22no—
868C22—44no—
869C22—42no—
870C22—42no—
871C22—42no—
872C22—62no—
873C22—62no—
874C22—62no—
875C22—84no—
876C22—124no—
877C22—122no—
878C22—122no—
879C22—122no—
880C22—122no—
881C22—122no—
882C22—122no—
883C22—244no—
884C22—244no—
885C22#560912yes—
886C22#576212yes—
887C22#576812yes—
888C22C22×D3×D411yescharacteristic
889C4—22no—
890C4—42no—
891C4—42no—
892C4—42no—
893C4—62no—
894C4—62no—
895C4—62no—
896C4—64no—
897C4—64no—
898C4#560912yes—
899C4C22×D3×D411yescharacteristic
900C4C2×#100911yescharacteristic
901C3C2×#327111yescharacteristic, complemented, Sylow
902C2—42no—
903C2—82no—
904C2—122no—
905C2—242no—
906C2—242no—
907C2#8068814yesdirect product factor
908C2C2×#560911yescharacteristic
909C2C2×#576211yescharacteristic
910C2C2×#576811yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#465C2
socleC23×C3C22×D4
hypercenterC2×#465D3
hypocenterC3C2×#3271
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C22×#915C2semidirect
2. C22×#904C2semidirect
3. C2×#5633C2semidirect
4. C2×#5599C2semidirect
5. C2×C3×#465C2semidirect
6. C2×#5176C2semidirect
7. C2×#5111C2semidirect
8. C2×#5047C2semidirect
9. C2×#5037C2semidirect
10. #80688C2direct (N × H)
11. C2×#4865C2semidirect
12. C2×#4853C2semidirect
13. C2×#4798C2semidirect
14. C2×#4806C2semidirect
15. C2×#4762C2semidirect
16. C2×#4781C2semidirect
36. C2×#915C22semidirect
39. C2×#904C22semidirect
45. #5633C22semidirect
47. #5599C22semidirect
58. C3×#465C22semidirect
63. #5176C22semidirect
64. #5111C22semidirect
68. #5047C22semidirect
69. #5037C22semidirect
74. #4865C22semidirect
75. #4853C22semidirect
76. #4806C22semidirect
77. #4798C22semidirect
78. #4781C22semidirect
79. #4762C22semidirect
87. C2×#465D3semidirect
180. C2×Dic12D4semidirect
258. #465C2×D3semidirect
399. Dic12C2×D4semidirect
858. C2×C3#3271semidirect
901. C3C2×#3271semidirect
907. C2#80688direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#9152
C22×#9042
C2×#56332
C2×#55992
C2×C3×#4652
C2×#51762
C2×#51112
C2×#50472
C2×#50372
#806882
C2×#48652
C2×#48532
C2×#47982
C2×#48062
C2×#47622
C2×#47812
C2×#32713