Finite Group Databasebeta

← C2×#83565 #11670233

Subgroups — C2×#83565 #11670233

Order 768.

2742 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×Q8C211yesmaximal, characteristic, complemented
2C23×#216C211yesmaximal, characteristic, complemented
3C22×#942C211yesmaximal, characteristic, complemented
4C2×#5552C211yesmaximal, characteristic
5C2×#5228C211yesmaximal, characteristic, complemented
6C2×#5227C211yesmaximal, characteristic, complemented
7#83565C2116yesmaximal, direct product factor
8C2×#5090C211yesmaximal, characteristic, complemented
9C2×#5086C211yesmaximal, characteristic, complemented
10C2×#5050C211yesmaximal, characteristic, complemented
11C2×#5047C211yesmaximal, characteristic, complemented
12C2×#5052C211yesmaximal, characteristic, complemented
13C2×#5048C211yesmaximal, characteristic, complemented
14C2×#5028C211yesmaximal, characteristic, complemented
15C2×#5030C211yesmaximal, characteristic, complemented
16C2×#5011C211yesmaximal, characteristic, complemented
17C2×#3270—31nomaximal, Sylow
18C23×C3×Q8C2211yescharacteristic
19C23×C3×Q8C2211yescharacteristic
20C22×#235C2211yescharacteristic
21C23×Dic6C2211yescharacteristic
22C3×D4×Q8—24no—
23C3×D4×Q8C2218yescomplemented
24C2×C3×C4⋊Q8—21no—
25C2×C3×C4⋊Q8C2211yescharacteristic
26C2×C3×C22⋊Q8—21no—
27C2×C3×C22⋊Q8—21no—
28C2×C3×C22⋊Q8C2211yescharacteristic
29C2×C3×C22⋊Q8C2211yescharacteristic
30C2×C3×C4×Q8C2211yescharacteristic
31C2×C3×C4×D4—21no—
32C2×C3×C4×D4C2211yescharacteristic
33C22×#216—28no—
34C22×#216C2211yescharacteristic
35C22×#216C2211yescharacteristic
36C22×#216C2211yescharacteristic
37C22×#216C2211yescharacteristic
38C22×#216C2211yescharacteristic
39C22×#216C2211yescharacteristic
40C22×#216C2218yescomplemented
41C2×#942—28no—
42C2×#942C2218yescomplemented
43C22×#215C2211yescharacteristic
44C22×#215C2211yescharacteristic
45C22×#215C2211yescharacteristic
46C2×#939—21no—
47C2×#930C2211yescharacteristic
48C2×#924C2211yescharacteristic
49C22×#208C2211yescharacteristic
50C23×C3⋊C8C2211yescharacteristic
51#5552—24no—
52#5552C2218yes—
53C2×#896—21no—
54C2×#885—21no—
55C2×#67⋊C4—21no—
56C2×#875C2211yescharacteristic
57C2×C4×Dic6C2211yescharacteristic
58#5228C2218yescomplemented
59#5227C2218yescomplemented
60C2×#835C2211yescharacteristic
61C2×#835C2211yescharacteristic
62C2×#835C2211yescharacteristic
63C2×#830C2211yescharacteristic
64C2×#830C2211yescharacteristic
65#5090C2218yescomplemented
66#5086C2218yescomplemented
67#5052C2218yescomplemented
68#5050C2218yescomplemented
69#5048C2218yescomplemented
70#5047C2218yescomplemented
71#5030C2218yescomplemented
72#5028C2218yescomplemented
73#5011C2218yescomplemented
74C2×#810C2211yescharacteristic
75C2×#810C2211yescharacteristic
76C2×#809C2211yescharacteristic
77C2×#808C2211yescharacteristic
78C2×C4⋊(C3⋊C8)C2211yescharacteristic
79C2×#803C2211yescharacteristic
80C22×#137—31no—
81C23×Q16—31no—
82C2×D4×Q8D311yescharacteristic, complemented
83C2×#548—31no—
84#3270—316no—
85C2×#497—31no—
86C2×#470—31no—
87C2×#465—31no—
88C2×#464—31no—
89C2×#462—31no—
90C2×#452—31no—
91C2×#451—31no—
92C2×#451—31no—
93C2×#448—31no—
94C2×#441—31no—
95C2×#435—31no—
96C22×C3×Q8—21no—
97C22×C3×Q8—21no—
98C22×C3×Q8—22no—
99C22×C3×Q8—22no—
100C22×C3×Q8—24no—
101C22×C3×Q8—24no—
102C22×C3×Q8—42no—
103C22×C3×Q8—42no—
104C22×C3×Q8C2311yescharacteristic
105C22×C3×Q8C2311yescharacteristic
106C22×C3×Q8C2314yes—
107C22×C3×Q8C2314yes—
108C22×C3×Q8C2311yescharacteristic
109C22×C3×D4D411yescharacteristic
110C23×C3×C4—21no—
111C23×C3×C4—21no—
112C23×C3×C4C2311yescharacteristic
113C23×C3×C4C2311yescharacteristic
114C22×#67—21no—
115C22×#67—21no—
116C23×Dic3—21no—
117C2×#235—22no—
118C2×#235—24no—
119C2×#235—42no—
120C2×#235C2314yes—
121C22×D12C2311yescharacteristic
122C22×C4×D3—21no—
123C22×Dic6—24no—
124C22×Dic6—21no—
125C22×Dic6—22no—
126C22×Dic6—42no—
127C22×Dic6C2311yescharacteristic
128C22×Dic6C2314yes—
129C22×Dic6C2311yescharacteristic
130C3×C4⋊Q8—28no—
131C3×C4⋊Q8—22no—
132C3×C4⋊Q8C2314yes—
133C3×C22⋊Q8—22no—
134C3×C22⋊Q8—22no—
135C3×C22⋊Q8—28no—
136C3×C22⋊Q8—28no—
137C3×C22⋊Q8C2314yes—
138C3×C22⋊Q8C2314yes—
139C3×C4×Q8—22no—
140C3×C4×Q8C2314yes—
141C3×C4×D4—28no—
142C3×C4×D4D414yes—
143C3×C4×D4C2314yes—
144C2×C3×C4⋊C4—21no—
145C2×C3×C4⋊C4—21no—
146C2×C3×C4⋊C4—21no—
147C2×C3×C4⋊C4—21no—
148C2×C3×C4⋊C4—21no—
149C2×C3×C4⋊C4D411yescharacteristic
150C2×C3×C4⋊C4C2311yescharacteristic
151C2×C3×C22⋊C4—21no—
152C2×C3×C22⋊C4—21no—
153C2×C3×C22⋊C4D411yescharacteristic
154C2×C3×C22⋊C4D411yescharacteristic
155C2×C3×C42—21no—
156C2×C3×C42C2311yescharacteristic
157C2×#217—21no—
158C2×#216—24no—
159C2×#216—24no—
160C2×#216—24no—
161C2×#216—232no—
162C2×#216—24no—
163C2×#216—42no—
164C2×#216D418yescomplemented
165C2×#216C2314yes—
166C2×#216C2314yes—
167C2×#216C2314yes—
168C2×#216C2314yes—
169C2×#216C2314yes—
170C2×#216C2314yes—
171#942—232no—
172C2×#215—24no—
173C2×#215—24no—
174C2×#215—42no—
175C2×#215C2314yes—
176C2×#215C2314yes—
177C2×#215C2314yes—
178#939—28no—
179#930—22no—
180#930C2314yes—
181C2×(C2×D3)⋊C4—21no—
182C2×(C2×D3)⋊C4—21no—
183C2×(C2×D3)⋊C4—21no—
184C2×C4⋊Dic3C2311yescharacteristic
185#924—22no—
186#924C2314yes—
187C2×Dic3⋊C4—21no—
188C2×Dic3⋊C4—21no—
189C2×C4×Dic3—21no—
190C2×#208—24no—
191C2×#208C2314yes—
192C22×C3⋊C8—24no—
193C22×C3⋊C8C2311yescharacteristic
194C22×C3⋊C8C2311yescharacteristic
195C22×C3⋊C8C2311yescharacteristic
196C22×C3⋊C8C2314yes—
197C22×C3⋊C8C2311yescharacteristic
198#896—28no—
199#885—28no—
200#67⋊C4—28no—
201#875—22no—
202#875C2314yes—
203C4×Dic6—22no—
204C4×Dic6C2314yes—
205#835C2314yes—
206#835C2314yes—
207#835C2314yes—
208#830C2314yes—
209#830C2314yes—
210#810C2314yes—
211#810C2314yes—
212#809C2314yes—
213#808C2314yes—
214C4⋊(C3⋊C8)C2314yes—
215#803C2314yes—
216C22×#41—31no—
217C23×Q8—31no—
218C23×Q8C2×D311yescharacteristic
219C23×Q8C2×D311yescharacteristic
220C2×#137—38no—
221C2×#137—68no—
222C22×Q16—31no—
223C22×Q16—31no—
224C22×Q16—31no—
225C22×Q16—31no—
226C22×Q16—31no—
227C22×Q16—38no—
228C22×Q16—31no—
229C22×Q16—68no—
230C22×SD16—31no—
231C22×SD16—31no—
232C22×SD16—31no—
233C22×M16—31no—
234C23×C8—31no—
235D4×Q8—24no—
236D4×Q8C2×D318yescomplemented
237#548—38no—
238#548—64no—
239C2×C4⋊Q8—21no—
240C2×C4⋊Q8C2×D311yescharacteristic
241C2×#124—31no—
242C2×#124—61no—
243C2×C22⋊Q8—21no—
244C2×C22⋊Q8—21no—
245C2×C22⋊Q8—31no—
246C2×C22⋊Q8—61no—
247C2×C22⋊Q8C2×D311yescharacteristic
248C2×C22⋊Q8C2×D311yescharacteristic
249C2×#121—31no—
250C2×#121—61no—
251C2×C4×Q8—31no—
252C2×C4×Q8C2×D311yescharacteristic
253C2×C4×D4—21no—
254C2×C4×D4—61no—
255C2×C4×D4C2×D311yescharacteristic
256#497—38no—
257#470—38no—
258#465—38no—
259#464—38no—
260#462—38no—
261#452—38no—
262#451—38no—
263#451—38no—
264#448—38no—
265#441—38no—
266#435—38no—
267C2×#106—31no—
268C2×C4⋊C8—31no—
269C2×#103—31no—
270C2×#103—31no—
271C2×#103—31no—
272C2×#103—31no—
273C2×#103—31no—
274C2×#102—31no—
275C2×C22⋊C8—31no—
276C2×C22⋊C8—31no—
277C2×#97—31no—
278C24×C3C2×D411yescharacteristic
279C24×C3C2×D411yescharacteristic
280C23×D3—21no—
281C2×C3×Q8—21no—
282C2×C3×Q8—24no—
283C2×C3×Q8—24no—
284C2×C3×Q8—21no—
285C2×C3×Q8—21no—
286C2×C3×Q8—22no—
287C2×C3×Q8—28no—
288C2×C3×Q8—28no—
289C2×C3×Q8—22no—
290C2×C3×Q8—22no—
291C2×C3×Q8—22no—
292C2×C3×Q8—22no—
293C2×C3×Q8—44no—
294C2×C3×Q8—44no—
295C2×C3×Q8—44no—
296C2×C3×Q8—44no—
297C2×C3×Q8—48no—
298C2×C3×Q8—48no—
299C2×C3×Q8C2×D414yes—
300C2×C3×Q8C2412yes—
301C2×C3×Q8C2412yes—
302C2×C3×Q8C2412yes—
303C2×C3×D4—24no—
304C2×C3×D4C2×D414yes—
305C22×C3×C4—21no—
306C22×C3×C4—22no—
307C22×C3×C4—22no—
308C22×C3×C4—22no—
309C22×C3×C4—22no—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—24no—
314C22×C3×C4—24no—
315C22×C3×C4—44no—
316C22×C3×C4—44no—
317C22×C3×C4C2×D411yescharacteristic
318C22×C3×C4C2×D411yescharacteristic
319C22×C3×C4C2×D411yescharacteristic
320C22×C3×C4C2×D412yes—
321C22×C3×C4C2×D411yescharacteristic
322C22×C3×C4C2×D412yes—
323C22×C3×C4C2412yes—
324C22×C3×C4C2412yes—
325C22×C3×C4C2411yescharacteristic
326C2×#67—24no—
327C2×#67—24no—
328C2×#67—44no—
329C2×#67—44no—
330C22×Dic3—21no—
331C22×Dic3—24no—
332C22×Dic3—21no—
333C22×Dic3—21no—
334C22×Dic3—44no—
335#235—28no—
336#235—44no—
337#235—48no—
338C2×D12—22no—
339C2×D12—22no—
340C2×D12—21no—
341C2×D12C2412yes—
342C2×C4×D3—24no—
343C2×C4×D3—44no—
344C2×Dic6—21no—
345C2×Dic6—22no—
346C2×Dic6—22no—
347C2×Dic6—22no—
348C2×Dic6—28no—
349C2×Dic6—21no—
350C2×Dic6—24no—
351C2×Dic6—44no—
352C2×Dic6—48no—
353C2×Dic6—44no—
354C2×Dic6C2×D414yes—
355C2×Dic6C2412yes—
356C2×Dic6C2412yes—
357C3×C4⋊C4—24no—
358C3×C4⋊C4—24no—
359C3×C4⋊C4—24no—
360C3×C4⋊C4—24no—
361C3×C4⋊C4—24no—
362C3×C4⋊C4—21no—
363C3×C4⋊C4C2×D414yes—
364C3×C4⋊C4C2412yes—
365C3×C22⋊C4—24no—
366C3×C22⋊C4—24no—
367C3×C22⋊C4C2×D414yes—
368C3×C22⋊C4C2×D414yes—
369C3×C42—24no—
370C3×C42C2×D412yes—
371C3×C42C2412yes—
372#217—24no—
373#216—28no—
374#216—28no—
375#216—28no—
376#216—28no—
377#216—44no—
378#216C2×D4116yescomplemented
379#215—28no—
380#215—28no—
381#215—44no—
382(C2×D3)⋊C4—24no—
383(C2×D3)⋊C4—24no—
384(C2×D3)⋊C4—24no—
385C4⋊Dic3—21no—
386C4⋊Dic3C2412yes—
387Dic3⋊C4—24no—
388Dic3⋊C4—24no—
389C4×Dic3—24no—
390#208—28no—
391C2×C3⋊C8—22no—
392C2×C3⋊C8—22no—
393C2×C3⋊C8—22no—
394C2×C3⋊C8—28no—
395C2×C3⋊C8C2×D414yes—
396C2×C3⋊C8C2412yes—
397C2×C3⋊C8C2412yes—
398C2×C3⋊C8C2412yes—
399C2×C3⋊C8C2412yes—
400C2×#41—34no—
401C2×#41—64no—
402C2×#41—62no—
403C2×#41—122no—
404C22×Q8—21no—
405C22×Q8—21no—
406C22×Q8—22no—
407C22×Q8—22no—
408C22×Q8—24no—
409C22×Q8—24no—
410C22×Q8—31no—
411C22×Q8—31no—
412C22×Q8—34no—
413C22×Q8—42no—
414C22×Q8—42no—
415C22×Q8—64no—
416C22×Q8—61no—
417C22×Q8—62no—
418C22×Q8—122no—
419C22×Q8C22×D311yescharacteristic
420C22×Q8C22×D311yescharacteristic
421C22×Q8C22×D314yes—
422C22×Q8C22×D314yes—
423C22×Q8C22×D311yescharacteristic
424C22×D4—31no—
425C22×D4—61no—
426C22×D4—61no—
427C22×D4#6711yescharacteristic
428C23×C4—21no—
429C23×C4—21no—
430C23×C4—61no—
431C23×C4—61no—
432C23×C4C22×D311yescharacteristic
433C23×C4C22×D311yescharacteristic
434#137—632no—
435C2×Q16—38no—
436C2×Q16—34no—
437C2×Q16—34no—
438C2×Q16—34no—
439C2×Q16—34no—
440C2×Q16—34no—
441C2×Q16—34no—
442C2×Q16—64no—
443C2×Q16—632no—
444C2×Q16—64no—
445C2×Q16—64no—
446C2×Q16—64no—
447C2×Q16—122no—
448C2×SD16—34no—
449C2×SD16—34no—
450C2×SD16—34no—
451C2×SD16—64no—
452C2×SD16—64no—
453C2×SD16—122no—
454C2×M16—34no—
455C2×M16—64no—
456C22×C8—31no—
457C22×C8—31no—
458C22×C8—34no—
459C22×C8—31no—
460C22×C8—31no—
461C22×C8—64no—
462C4⋊Q8—28no—
463C4⋊Q8—22no—
464C4⋊Q8C22×D314yes—
465#124—34no—
466#124—68no—
467#124—62no—
468C22⋊Q8—22no—
469C22⋊Q8—22no—
470C22⋊Q8—28no—
471C22⋊Q8—28no—
472C22⋊Q8—34no—
473C22⋊Q8—62no—
474C22⋊Q8—68no—
475C22⋊Q8C22×D314yes—
476C22⋊Q8C22×D314yes—
477#121—34no—
478#121—68no—
479#121—62no—
480C4×Q8—22no—
481C4×Q8—34no—
482C4×Q8—62no—
483C4×Q8C22×D314yes—
484C4×D4—28no—
485C4×D4—68no—
486C4×D4#6714yes—
487C4×D4C22×D314yes—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—31no—
494C2×C4⋊C4—61no—
495C2×C4⋊C4—61no—
496C2×C4⋊C4#6711yescharacteristic
497C2×C4⋊C4C22×D311yescharacteristic
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—61no—
501C2×C22⋊C4—61no—
502C2×C22⋊C4—61no—
503C2×C22⋊C4—61no—
504C2×C22⋊C4#6711yescharacteristic
505C2×C22⋊C4#6711yescharacteristic
506C2×C42—21no—
507C2×C42—61no—
508C2×C42C22×D311yescharacteristic
509#106—34no—
510C4⋊C8—34no—
511#103—34no—
512#103—34no—
513#103—34no—
514#103—34no—
515#103—34no—
516#102—34no—
517C22⋊C8—34no—
518C22⋊C8—34no—
519#97—34no—
520C23×C3—22no—
521C23×C3—22no—
522C23×C3—22no—
523C23×C3—22no—
524C23×C3—22no—
525C23×C3#13714yescomplemented
526C23×C3C22×D412yes—
527C23×C3C22×D412yes—
528C23×C3C22×D411yescharacteristic
529C22×D3—22no—
530C22×D3—42no—
531C22×D3—42no—
532C22×D3—42no—
533C3×Q8—24no—
534C3×Q8—22no—
535C3×Q8—22no—
536C3×Q8—22no—
537C3×Q8—22no—
538C3×Q8—22no—
539C3×Q8—48no—
540C3×Q8—48no—
541C3×Q8—42no—
542C3×Q8—42no—
543C3×Q8C22×D414yes—
544C3×D4—28no—
545C2×C3×C4—22no—
546C2×C3×C4—22no—
547C2×C3×C4—24no—
548C2×C3×C4—22no—
549C2×C3×C4—22no—
550C2×C3×C4—22no—
551C2×C3×C4—24no—
552C2×C3×C4—24no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
558C2×C3×C4—22no—
559C2×C3×C4—22no—
560C2×C3×C4—48no—
561C2×C3×C4—48no—
562C2×C3×C4—42no—
563C2×C3×C4—42no—
564C2×C3×C4—42no—
565C2×C3×C4C22×D412yes—
566C2×C3×C4C22×D412yes—
567C2×C3×C4C22×D412yes—
568C2×C3×C4C22×D412yes—
569C2×C3×C4C22×D412yes—
570C2×C3×C4C22×D411yescharacteristic
571C2×C3×C4H(5,𝔽2)12yes—
572C2×C3×C4C2511yescharacteristic
573#67—48no—
574#67—48no—
575C2×Dic3—24no—
576C2×Dic3—22no—
577C2×Dic3—22no—
578C2×Dic3—22no—
579C2×Dic3—48no—
580C2×Dic3—42no—
581C2×Dic3—42no—
582D12—22no—
583D12—22no—
584D12—42no—
585C4×D3—48no—
586Dic6—24no—
587Dic6—22no—
588Dic6—22no—
589Dic6—22no—
590Dic6—48no—
591Dic6—42no—
592Dic6C22×D414yes—
593C3⋊C8—22no—
594C3⋊C8—22no—
595C3⋊C8—22no—
596C3⋊C8C22×D414yes—
597C24—61no—
598C24C2×#6711yescharacteristic
599C24C2×#6711yescharacteristic
600#41—68no—
601#41—124no—
602#41—128no—
603C2×Q8—22no—
604C2×Q8—21no—
605C2×Q8—24no—
606C2×Q8—24no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—28no—
610C2×Q8—28no—
611C2×Q8—22no—
612C2×Q8—22no—
613C2×Q8—22no—
614C2×Q8—22no—
615C2×Q8—34no—
616C2×Q8—32no—
617C2×Q8—32no—
618C2×Q8—44no—
619C2×Q8—44no—
620C2×Q8—44no—
621C2×Q8—44no—
622C2×Q8—48no—
623C2×Q8—48no—
624C2×Q8—68no—
625C2×Q8—62no—
626C2×Q8—61no—
627C2×Q8—64no—
628C2×Q8—61no—
629C2×Q8—62no—
630C2×Q8—62no—
631C2×Q8—124no—
632C2×Q8—124no—
633C2×Q8—128no—
634C2×Q8D3×D414yes—
635C2×Q8C23×D312yes—
636C2×Q8C23×D312yes—
637C2×Q8C23×D312yes—
638C2×D4—24no—
639C2×D4—32no—
640C2×D4—64no—
641C2×D4—64no—
642C2×D4—62no—
643C2×D4—62no—
644C2×D4—61no—
645C2×D4—124no—
646C2×D4—124no—
647C2×D4C2×#6714yes—
648C22×C4—21no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—24no—
654C22×C4—24no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—44no—
659C22×C4—44no—
660C22×C4—61no—
661C22×C4—64no—
662C22×C4—61no—
663C22×C4—61no—
664C22×C4—64no—
665C22×C4—124no—
666C22×C4—124no—
667C22×C4C2×#6712yes—
668C22×C4C2×#6712yes—
669C22×C4C2×#6711yescharacteristic
670C22×C4C2×#6711yescharacteristic
671C22×C4C2×#6711yescharacteristic
672C22×C4C2×#6711yescharacteristic
673C22×C4C23×D312yes—
674C22×C4C23×D312yes—
675C22×C4C23×D311yescharacteristic
676Q16—316no—
677Q16—68no—
678Q16—68no—
679Q16—68no—
680Q16—68no—
681Q16—124no—
682SD16—68no—
683SD16—68no—
684SD16—124no—
685M16—68no—
686C2×C8—34no—
687C2×C8—32no—
688C2×C8—32no—
689C2×C8—32no—
690C2×C8—32no—
691C2×C8—68no—
692C2×C8—62no—
693C2×C8—62no—
694C2×C8—62no—
695C4⋊C4—24no—
696C4⋊C4—24no—
697C4⋊C4—24no—
698C4⋊C4—24no—
699C4⋊C4—24no—
700C4⋊C4—21no—
701C4⋊C4—32no—
702C4⋊C4—61no—
703C4⋊C4—64no—
704C4⋊C4—64no—
705C4⋊C4C2×#6714yes—
706C4⋊C4C23×D312yes—
707C22⋊C4—24no—
708C22⋊C4—24no—
709C22⋊C4—64no—
710C22⋊C4—64no—
711C22⋊C4—64no—
712C22⋊C4—64no—
713C22⋊C4C2×#6714yes—
714C22⋊C4C2×#6714yes—
715C42—24no—
716C42—64no—
717C42C2×#6712yes—
718C42C23×D312yes—
719C22×C3—22no—
720C22×C3—28no—
721C22×C3—22no—
722C22×C3—22no—
723C22×C3—22no—
724C22×C3—22no—
725C22×C3—44no—
726C22×C3D4212yes—
727C22×C3C2×#13712yes—
728C22×C3C2×#13714yescomplemented
729C22×C3#57812yes—
730C22×C3C23×D411yescharacteristic
731C2×D3—42no—
732C2×D3—42no—
733C2×D3—42no—
734C2×D3—84no—
735C3×C4—22no—
736C3×C4—22no—
737C3×C4—24no—
738C3×C4—22no—
739C3×C4—22no—
740C3×C4—42no—
741C3×C4—42no—
742C3×C4—42no—
743C3×C4D4212yes—
744C3×C4C23×D411yescharacteristic
745C3×C4C2×H(5,𝔽2)11yescharacteristic
746Dic3—24no—
747Dic3—42no—
748Dic3—42no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—62no—
755C23—122no—
756C23—122no—
757C23—122no—
758C23#94214yescomplemented
759C23C22×#6712yes—
760C23C22×#6712yes—
761C23C22×#6711yescharacteristic
762Q8—22no—
763Q8—24no—
764Q8—22no—
765Q8—22no—
766Q8—22no—
767Q8—22no—
768Q8—34no—
769Q8—48no—
770Q8—48no—
771Q8—42no—
772Q8—42no—
773Q8—62no—
774Q8—64no—
775Q8—62no—
776Q8—62no—
777Q8—128no—
778Q8—122no—
779Q8C2×D3×D414yes—
780D4—28no—
781D4—62no—
782D4—62no—
783D4—128no—
784D4—128no—
785D4—122no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—24no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—24no—
797C2×C4—24no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—48no—
802C2×C4—48no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—62no—
807C2×C4—64no—
808C2×C4—62no—
809C2×C4—62no—
810C2×C4—128no—
811C2×C4—128no—
812C2×C4—122no—
813C2×C4—122no—
814C2×C4C2×D3×D412yes—
815C2×C4#100412yes—
816C2×C4C22×#6712yes—
817C2×C4C22×#6712yes—
818C2×C4C22×#6712yes—
819C2×C4C22×#6712yes—
820C2×C4C22×#6711yescharacteristic
821C2×C4C24×D311yescharacteristic
822C8—34no—
823C8—62no—
824C8—62no—
825C8—62no—
826C2×C3—24no—
827C2×C3—42no—
828C2×C3#327014yescomplemented
829C2×C3C2×D4211yescharacteristic
830C2×C3C22×#13711yescharacteristic
831C2×C3C2×#57811yescharacteristic
832D3—82no—
833C22—28no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—44no—
840C22—122no—
841C22—122no—
842C22—122no—
843C22—244no—
844C22D4×#6712yes—
845C22C2×#94212yes—
846C22C2×#94214yescomplemented
847C22#583812yes—
848C22C23×#6711yescharacteristic
849C4—22no—
850C4—22no—
851C4—24no—
852C4—22no—
853C4—22no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—64no—
858C4—122no—
859C4—122no—
860C4D4×#6712yes—
861C4C22×D3×D411yescharacteristic
862C4C2×#100411yescharacteristic
863C3C2×#327011yescharacteristic, complemented, Sylow
864C2—24no—
865C2—42no—
866C2—242no—
867C2#8356514yesdirect product factor
868C2C2×D4×#6711yescharacteristic
869C2C22×#94211yescharacteristic
870C2C2×#583811yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×D4×Q8C2
socleC23×C3C22×D4
prime radicalC2×#5552C2
hypercenterC2×D4×Q8D3
hypocenterC3C2×#3270
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×D4×Q8C2semidirect
2. C23×#216C2semidirect
3. C22×#942C2semidirect
5. C2×#5228C2semidirect
6. C2×#5227C2semidirect
7. #83565C2direct (N × H)
8. C2×#5090C2semidirect
9. C2×#5086C2semidirect
10. C2×#5050C2semidirect
11. C2×#5047C2semidirect
12. C2×#5052C2semidirect
13. C2×#5048C2semidirect
14. C2×#5028C2semidirect
15. C2×#5030C2semidirect
16. C2×#5011C2semidirect
23. C3×D4×Q8C22semidirect
40. C22×#216C22semidirect
42. C2×#942C22semidirect
58. #5228C22semidirect
59. #5227C22semidirect
65. #5090C22semidirect
66. #5086C22semidirect
67. #5052C22semidirect
68. #5050C22semidirect
69. #5048C22semidirect
70. #5047C22semidirect
71. #5030C22semidirect
72. #5028C22semidirect
73. #5011C22semidirect
82. C2×D4×Q8D3semidirect
164. C2×#216D4semidirect
236. D4×Q8C2×D3semidirect
378. #216C2×D4semidirect
525. C23×C3#137semidirect
728. C22×C3C2×#137semidirect
758. C23#942semidirect
828. C2×C3#3270semidirect
846. C22C2×#942semidirect
863. C3C2×#3270semidirect
867. C2#83565direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D4×Q82
C23×#2162
C22×#9422
C2×#55522
C2×#52282
C2×#52272
#835652
C2×#50902
C2×#50862
C2×#50502
C2×#50472
C2×#50522
C2×#50482
C2×#50282
C2×#50302
C2×#50112
C2×#32703