Finite Group Databasebeta

← C2×#86747 #11703511

Subgroups — C2×#86747 #11703511

Order 768.

7478 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×Q8C211yesmaximal, characteristic, complemented
2C2×Q8×#67C212yesmaximal, complemented
3C22×#944C212yesmaximal, complemented
4#86747C2132yesmaximal, direct product factor
5C2×#5729C212yesmaximal, complemented
6C2×D3×C4⋊Q8C211yesmaximal, characteristic, complemented
7C2×#5722C212yesmaximal, complemented
8C2×#5721C211yesmaximal, characteristic, complemented
9C2×#5636C214yesmaximal, complemented
10C2×#5632C212yesmaximal, complemented
11C2×#5623C214yesmaximal, complemented
12C2×#5622C212yesmaximal, complemented
13C2×#5578C211yesmaximal, characteristic, complemented
14C2×#5567C211yesmaximal, characteristic, complemented
15C2×#5539C212yesmaximal, complemented
16C2×D4×Dic6C211yesmaximal, characteristic, complemented
17C2×#5546C212yesmaximal
18C2×C4×#237C211yesmaximal, characteristic
19C2×#3503—31nomaximal, Sylow
20C23×C3×Q8C2212yes—
21C22×D3×Q8C2212yes—
22C22×#237C2211yescharacteristic
23C23×Dic6C2212yes—
24C3×D4×Q8C22116yescomplemented
25C2×C3×C4⋊Q8C2211yescharacteristic
26C2×C3×C4⋊Q8C2212yes—
27C2×C3×C22⋊Q8C2212yes—
28C2×C3×C22⋊Q8C2214yes—
29C2×C3×C4×Q8C2211yescharacteristic
30C2×C3×C4×D4C2212yes—
31C2×C3×C4×D4C2211yescharacteristic
32Q8×#67C22132yescomplemented
33C2×#946C2211yescharacteristic
34C2×#946C2214yes—
35C2×Q8×Dic3C2212yes—
36C2×#944C2212yes—
37C2×#944C2211yescharacteristic
38C2×#944C2212yes—
39C2×#944C2214yes—
40C2×#944C2214yes—
41C2×#944C2212yes—
42C2×#944C2214yes—
43C2×#944C22132yescomplemented
44C2×D4×Dic3C2211yescharacteristic
45C2×D4×Dic3C2212yes—
46C2×C4×#67C2212yes—
47C2×C4×#67C2214yes—
48C2×#924C2214yes—
49C2×#924C2212yes—
50C22×Dic3⋊C4C2214yes—
51C22×Dic3⋊C4C2214yes—
52C22×C4×Dic3C2212yes—
53#5729C22132yescomplemented
54D3×C4⋊Q8C22116yescomplemented
55#5722C22132yescomplemented
56#5721C22116yescomplemented
57#5636C22164yescomplemented
58#5632C22132yescomplemented
59#5623C22164yescomplemented
60#5622C22132yescomplemented
61#5578C22116yescomplemented
62#5567C22116yescomplemented
63#5546C22132yes—
64#5539C22132yescomplemented
65D4×Dic6C22116yescomplemented
66C4×#237C22116yes—
67C2×#897C2211yescharacteristic
68C2×#896C2212yes—
69C2×#896C2214yes—
70C2×#892C2211yescharacteristic
71C2×D3×C4⋊C4C2212yes—
72C2×D3×C4⋊C4C2212yes—
73C2×#890C2212yes—
74C2×#889C2214yes—
75C2×#889C2212yes—
76C2×#889C2214yes—
77C2×#889C2214yes—
78C2×#888C2212yes—
79C2×#888C2211yescharacteristic
80C2×#888C2212yes—
81C2×#888C2214yes—
82C2×#888C2212yes—
83C2×#887C2212yes—
84C2×#887C2212yes—
85C2×#887C2211yescharacteristic
86C2×#887C2214yes—
87C2×#67⋊C4C2214yes—
88C2×#67⋊C4C2212yes—
89C2×#878C2214yes—
90C2×#878C2214yes—
91C2×#878C2214yes—
92C2×#877C2214yes—
93C2×#877C2212yes—
94C2×#872C2212yes—
95C2×C42×D3C2211yescharacteristic
96C2×#870C2212yes—
97C2×#869C2211yescharacteristic
98C2×C4×Dic6C2212yes—
99C2×C4×Dic6C2211yescharacteristic
100C2×C4×Dic6C2212yes—
101C2×C4×Dic6C2211yescharacteristic
102#3503—332no—
103C2×Q82—32no—
104C2×#557—31no—
105C2×#557—31no—
106C2×#554—34no—
107C2×#554—32no—
108C2×D4×Q8—32no—
109C2×D4×Q8—32no—
110C2×D4×Q8—31no—
111C2×D4×Q8D311yescharacteristic, complemented
112C2×#544—32no—
113C2×#544—34no—
114C2×#533—32no—
115C2×#533—31no—
116C22×C4⋊Q8—32no—
117C22×C4⋊Q8—31no—
118C2×#520—32no—
119C2×C4×#41—31no—
120C22×C3×Q8—48no—
121C22×C3×Q8C2312yes—
122C22×C3×Q8C2311yescharacteristic
123C22×C3×Q8C2314yes—
124C22×C3×Q8C23116yes—
125C22×C3×D4C2311yescharacteristic
126C23×C3×C4C2312yes—
127C23×C3×C4C2314yes—
128C22×#67C2312yes—
129C23×Dic3C2312yes—
130C23×Dic3C2314yes—
131C23×Dic3C2312yes—
132C2×D3×Q8—48no—
133C2×D3×Q8C23116yes—
134C2×#237Q8116yescomplemented
135C2×#237C2318yes—
136C22×C4×D3C2311yescharacteristic
137C22×C4×D3C2311yescharacteristic
138C22×C4×D3C2314yes—
139C22×C4×D3C2311yescharacteristic
140C22×Dic6—48no—
141C22×Dic6C2311yescharacteristic
142C22×Dic6C2312yes—
143C22×Dic6C2312yes—
144C22×Dic6C23116yes—
145C22×Dic6C2314yes—
146C22×Dic6C2314yes—
147C22×Dic6C2311yescharacteristic
148C3×C4⋊Q8C2318yes—
149C3×C4⋊Q8C23116yes—
150C3×C22⋊Q8C23116yes—
151C3×C22⋊Q8C23132yes—
152C3×C4×Q8C2318yes—
153C3×C4×D4C2318yes—
154C3×C4×D4C23116yes—
155C2×C3×C4⋊C4C2311yescharacteristic
156C2×C3×C4⋊C4C2311yescharacteristic
157C2×C3×C4⋊C4C2314yes—
158C2×C3×C4⋊C4C2312yes—
159C2×C3×C4⋊C4C2312yes—
160C2×C3×C4⋊C4C2312yes—
161C2×C3×C22⋊C4C2314yes—
162C2×C3×C22⋊C4C2312yes—
163C2×C3×C42C2311yescharacteristic
164C2×C3×C42C2312yes—
165C2×#217C2314yes—
166C2×#217C2312yes—
167#946C23132yes—
168#946C2318yes—
169Q8×Dic3C23116yes—
170#944C23116yes—
171#944C23132yes—
172#944C23132yes—
173#944C23116yes—
174#944C23132yes—
175#944C2318yes—
176#944C23116yes—
177D4×Dic3C2318yes—
178D4×Dic3C23116yes—
179C4×#67C23116yes—
180C4×#67C23132yes—
181C2×(C2×D3)⋊C4C2312yes—
182C2×(C2×D3)⋊C4C2312yes—
183C2×(C2×D3)⋊C4C2312yes—
184C2×C4⋊Dic3C2312yes—
185C2×C4⋊Dic3C2311yescharacteristic
186C2×C4⋊Dic3C2312yes—
187C2×C4⋊Dic3C2311yescharacteristic
188C2×C4⋊Dic3C2312yes—
189C2×C4⋊Dic3C2314yes—
190#924C23116yes—
191#924C23132yes—
192C2×Dic3⋊C4C23132yes—
193C2×Dic3⋊C4C2312yes—
194C2×Dic3⋊C4C2312yes—
195C2×Dic3⋊C4C2314yes—
196C2×Dic3⋊C4C2312yes—
197C2×Dic3⋊C4C2312yes—
198C2×Dic3⋊C4C2314yes—
199C2×Dic3⋊C4C2314yes—
200C2×Dic3⋊C4C2312yes—
201C2×Dic3⋊C4C2312yes—
202C2×Dic3⋊C4C2312yes—
203C2×Dic3⋊C4C2314yes—
204C2×Dic3⋊C4C2314yes—
205C2×Dic3⋊C4C2314yes—
206C2×Dic3⋊C4C2314yes—
207C2×Dic3⋊C4C2314yes—
208C2×Dic3⋊C4C23132yes—
209C2×C4×Dic3C2311yescharacteristic
210C2×C4×Dic3C2312yes—
211C2×C4×Dic3C2314yes—
212C2×C4×Dic3C2312yes—
213C2×C4×Dic3C2311yescharacteristic
214C2×C4×Dic3C2311yescharacteristic
215C2×C4×Dic3C2314yes—
216C2×C4×Dic3C2312yes—
217C2×C4×Dic3C2312yes—
218C2×C4×Dic3C23116yes—
219#897C2318yes—
220#896C23132yes—
221#896C23116yes—
222#892C2318yes—
223D3×C4⋊C4C23116yes—
224D3×C4⋊C4C23116yes—
225#890C23116yes—
226#889C23132yes—
227#889C23132yes—
228#889C23132yes—
229#889C23116yes—
230#888C23132yes—
231#888C23116yes—
232#888C23116yes—
233#888C23116yes—
234#888C2318yes—
235#887C23116yes—
236#887C23132yes—
237#887C23116yes—
238#887C2318yes—
239#67⋊C4C23132yes—
240#67⋊C4C23116yes—
241#878C23132yes—
242#878C23132yes—
243#878C23132yes—
244#877C23116yes—
245#877C23132yes—
246#872C23116yes—
247C42×D3C2318yes—
248#870C23116yes—
249#869C2318yes—
250C4×Dic6C2318yes—
251C4×Dic6C2318yes—
252C4×Dic6C23116yes—
253C4×Dic6C23116yes—
254C22×#41—31no—
255C23×Q8—32no—
256C23×Q8—32no—
257C23×Q8C2×D312yes—
258Q82—332no—
259#557—316no—
260#557—316no—
261#554—364no—
262#554—332no—
263D4×Q8—332no—
264D4×Q8—332no—
265D4×Q8—316no—
266D4×Q8C2×D3116yescomplemented
267#544—332no—
268#544—364no—
269#533—332no—
270#533—316no—
271C2×C4⋊Q8—32no—
272C2×C4⋊Q8—31no—
273C2×C4⋊Q8—34no—
274C2×C4⋊Q8—32no—
275C2×C4⋊Q8—32no—
276C2×C4⋊Q8—34no—
277C2×C4⋊Q8—332no—
278C2×C4⋊Q8—34no—
279C2×C4⋊Q8—316no—
280C2×C4⋊Q8—32no—
281C2×C4⋊Q8—32no—
282C2×C4⋊Q8—31no—
283C2×C4⋊Q8—34no—
284C2×C4⋊Q8—32no—
285C2×C4⋊Q8—31no—
286C2×C4⋊Q8C2×D311yescharacteristic
287C2×C4⋊Q8C2×D312yes—
288C2×#125—34no—
289C2×#125—32no—
290C2×#125—34no—
291C2×#125—34no—
292C2×#125—32no—
293C2×#125—32no—
294C2×C22⋊Q8—31no—
295C2×C22⋊Q8—34no—
296C2×C22⋊Q8—32no—
297C2×C22⋊Q8—34no—
298C2×C22⋊Q8—32no—
299C2×C22⋊Q8—31no—
300C2×C22⋊Q8—34no—
301C2×C22⋊Q8—34no—
302C2×C22⋊Q8—34no—
303C2×C22⋊Q8—34no—
304C2×C22⋊Q8C2×D312yes—
305C2×C22⋊Q8C2×D314yes—
306#520—332no—
307C4×#41—316no—
308C2×C4×Q8—32no—
309C2×C4×Q8—31no—
310C2×C4×Q8—32no—
311C2×C4×Q8—32no—
312C2×C4×Q8—34no—
313C2×C4×Q8—31no—
314C2×C4×Q8—32no—
315C2×C4×Q8—31no—
316C2×C4×Q8—32no—
317C2×C4×Q8C2×D311yescharacteristic
318C2×C4×D4—31no—
319C2×C4×D4—32no—
320C2×C4×D4—32no—
321C2×C4×D4—34no—
322C2×C4×D4—32no—
323C2×C4×D4—34no—
324C2×C4×D4C2×D311yescharacteristic
325C2×C4×D4C2×D312yes—
326C2×#117—31no—
327C2×#117—32no—
328C2×#117—34no—
329C2×#117—32no—
330C22×C4⋊C4—34no—
331C22×C4⋊C4—34no—
332C22×C4⋊C4—32no—
333C22×C4⋊C4—32no—
334C22×C42—32no—
335C22×C42—31no—
336C24×C3C2412yes—
337C23×D3C2411yescharacteristic
338C2×C3×Q8—28no—
339C2×C3×Q8—24no—
340C2×C3×Q8—48no—
341C2×C3×Q8—432no—
342C2×C3×Q8C2414yes—
343C2×C3×Q8C2418yes—
344C2×C3×Q8C24116yes—
345C2×C3×D4C2×Q818yescomplemented
346C2×C3×D4C2414yes—
347C22×C3×C4—28no—
348C22×C3×C4—48no—
349C22×C3×C4C2412yes—
350C22×C3×C4C2412yes—
351C22×C3×C4C2418yes—
352C22×C3×C4C2411yescharacteristic
353C22×C3×C4C2414yes—
354C22×C3×C4C2412yes—
355C22×C3×C4C24116yes—
356C22×C3×C4C2411yescharacteristic
357C22×C3×C4C2411yescharacteristic
358C2×#67C2×Q8116yescomplemented
359C2×#67C2418yes—
360C22×Dic3—28no—
361C22×Dic3—48no—
362C22×Dic3C2×Q8116yescomplemented
363C22×Dic3C2418yes—
364C22×Dic3C2412yes—
365C22×Dic3C2412yes—
366C22×Dic3C2411yescharacteristic
367C22×Dic3C2412yes—
368C22×Dic3C2414yes—
369C22×Dic3C24116yes—
370C22×Dic3C2412yes—
371C22×Dic3C2411yescharacteristic
372C22×Dic3C2418yes—
373C22×Dic3C2411yescharacteristic
374D3×Q8—432no—
375#237C2×Q8164yescomplemented
376C2×C4×D3—24no—
377C2×C4×D3—24no—
378C2×C4×D3—48no—
379C2×C4×D3C2×Q818yescomplemented
380C2×C4×D3C2414yes—
381C2×C4×D3C2414yes—
382C2×C4×D3C24116yes—
383C2×C4×D3C2414yes—
384C2×Dic6—24no—
385C2×Dic6—28no—
386C2×Dic6—28no—
387C2×Dic6—432no—
388C2×Dic6—48no—
389C2×Dic6—48no—
390C2×Dic6C2×Q818yescomplemented
391C2×Dic6C2418yes—
392C2×Dic6C2414yes—
393C2×Dic6C2418yes—
394C2×Dic6C24116yes—
395C2×Dic6C24116yes—
396C2×Dic6C2414yes—
397C3×C4⋊C4C2414yes—
398C3×C4⋊C4C2414yes—
399C3×C4⋊C4C24116yes—
400C3×C4⋊C4C2418yes—
401C3×C4⋊C4C2418yes—
402C3×C4⋊C4C2418yes—
403C3×C22⋊C4C24116yes—
404C3×C22⋊C4C2418yes—
405C3×C42C2414yes—
406C3×C42C2418yes—
407#217C24116yes—
408#217C2418yes—
409(C2×D3)⋊C4C2418yes—
410(C2×D3)⋊C4C2418yes—
411(C2×D3)⋊C4C2418yes—
412C4⋊Dic3C2418yes—
413C4⋊Dic3C2414yes—
414C4⋊Dic3C2418yes—
415C4⋊Dic3C2414yes—
416C4⋊Dic3C2418yes—
417C4⋊Dic3C24116yes—
418Dic3⋊C4C2418yes—
419Dic3⋊C4C2418yes—
420Dic3⋊C4C24116yes—
421Dic3⋊C4C2418yes—
422Dic3⋊C4C2418yes—
423Dic3⋊C4C24116yes—
424Dic3⋊C4C24116yes—
425Dic3⋊C4C2418yes—
426Dic3⋊C4C2418yes—
427Dic3⋊C4C2418yes—
428Dic3⋊C4C24116yes—
429Dic3⋊C4C24116yes—
430Dic3⋊C4C24116yes—
431Dic3⋊C4C24116yes—
432Dic3⋊C4C24116yes—
433C4×Dic3C2414yes—
434C4×Dic3C2418yes—
435C4×Dic3C24116yes—
436C4×Dic3C2418yes—
437C4×Dic3C2414yes—
438C4×Dic3C2414yes—
439C4×Dic3C24116yes—
440C4×Dic3C2418yes—
441C4×Dic3C2418yes—
442C2×#41—316no—
443C2×#41—38no—
444C22×Q8—316no—
445C22×Q8—31no—
446C22×Q8—32no—
447C22×Q8—32no—
448C22×Q8—31no—
449C22×Q8—34no—
450C22×Q8—34no—
451C22×Q8—316no—
452C22×Q8—48no—
453C22×Q8—128no—
454C22×Q8—128no—
455C22×Q8C22×D312yes—
456C22×Q8C22×D311yescharacteristic
457C22×Q8C22×D314yes—
458C22×Q8C22×D3116yes—
459C22×D4—32no—
460C22×D4C22×D311yescharacteristic
461C23×C4—32no—
462C23×C4—31no—
463C23×C4—32no—
464C23×C4—34no—
465C23×C4—31no—
466C23×C4—31no—
467C23×C4—34no—
468C23×C4C22×D312yes—
469C23×C4C22×D314yes—
470C4⋊Q8—316no—
471C4⋊Q8—38no—
472C4⋊Q8—332no—
473C4⋊Q8—316no—
474C4⋊Q8—316no—
475C4⋊Q8—332no—
476C4⋊Q8—332no—
477C4⋊Q8—316no—
478C4⋊Q8—316no—
479C4⋊Q8—38no—
480C4⋊Q8—332no—
481C4⋊Q8—316no—
482C4⋊Q8—38no—
483C4⋊Q8C22×D318yes—
484C4⋊Q8C22×D3116yes—
485#125—332no—
486#125—316no—
487#125—332no—
488#125—332no—
489#125—316no—
490#125—316no—
491C22⋊Q8—38no—
492C22⋊Q8—332no—
493C22⋊Q8—316no—
494C22⋊Q8—332no—
495C22⋊Q8—38no—
496C22⋊Q8—316no—
497C22⋊Q8—332no—
498C22⋊Q8—332no—
499C22⋊Q8—332no—
500C22⋊Q8—332no—
501C22⋊Q8C22×D3116yes—
502C22⋊Q8C22×D3132yes—
503C4×Q8—316no—
504C4×Q8—38no—
505C4×Q8—316no—
506C4×Q8—316no—
507C4×Q8—332no—
508C4×Q8—38no—
509C4×Q8—316no—
510C4×Q8—38no—
511C4×Q8—316no—
512C4×Q8C22×D318yes—
513C4×D4—38no—
514C4×D4—316no—
515C4×D4—316no—
516C4×D4—332no—
517C4×D4—316no—
518C4×D4—332no—
519C4×D4C22×D318yes—
520C4×D4C22×D3116yes—
521#117—38no—
522#117—316no—
523#117—332no—
524#117—316no—
525C2×C4⋊C4—34no—
526C2×C4⋊C4—32no—
527C2×C4⋊C4—34no—
528C2×C4⋊C4—32no—
529C2×C4⋊C4—34no—
530C2×C4⋊C4—34no—
531C2×C4⋊C4—32no—
532C2×C4⋊C4—332no—
533C2×C4⋊C4—34no—
534C2×C4⋊C4—34no—
535C2×C4⋊C4—32no—
536C2×C4⋊C4—332no—
537C2×C4⋊C4—32no—
538C2×C4⋊C4—32no—
539C2×C4⋊C4—31no—
540C2×C4⋊C4—32no—
541C2×C4⋊C4—31no—
542C2×C4⋊C4—32no—
543C2×C4⋊C4—34no—
544C2×C4⋊C4—34no—
545C2×C4⋊C4—32no—
546C2×C4⋊C4—34no—
547C2×C4⋊C4—32no—
548C2×C4⋊C4—316no—
549C2×C4⋊C4—316no—
550C2×C4⋊C4C22×D312yes—
551C2×C4⋊C4C22×D312yes—
552C2×C4⋊C4C22×D311yescharacteristic
553C2×C4⋊C4C22×D311yescharacteristic
554C2×C4⋊C4C22×D314yes—
555C2×C4⋊C4C22×D312yes—
556C2×C22⋊C4—34no—
557C2×C22⋊C4—32no—
558C2×C22⋊C4—32no—
559C2×C22⋊C4—32no—
560C2×C22⋊C4—32no—
561C2×C22⋊C4C22×D314yes—
562C2×C22⋊C4C22×D312yes—
563C2×C42—32no—
564C2×C42—31no—
565C2×C42—34no—
566C2×C42—34no—
567C2×C42—32no—
568C2×C42—32no—
569C2×C42—32no—
570C2×C42—31no—
571C2×C42—316no—
572C2×C42—31no—
573C2×C42—38no—
574C2×C42C22×D312yes—
575C2×C42C22×D311yescharacteristic
576C23×C3—24no—
577C23×C3—24no—
578C23×C3C22×Q818yes—
579C23×C3C2514yes—
580C23×C3C2511yescharacteristic
581C22×D3—22no—
582C22×D3—22no—
583C22×D3C22×Q814yes—
584C22×D3C2512yes—
585C3×Q8—216no—
586C3×Q8—28no—
587C3×Q8—416no—
588C3×D4C22×Q8116yescomplemented
589C2×C3×C4—24no—
590C2×C3×C4—28no—
591C2×C3×C4—24no—
592C2×C3×C4—24no—
593C2×C3×C4—22no—
594C2×C3×C4—216no—
595C2×C3×C4—416no—
596C2×C3×C4C22×Q814yes—
597C2×C3×C4H(5,𝔽2)14yes—
598C2×C3×C4C2514yes—
599C2×C3×C4C2514yes—
600C2×C3×C4C2512yes—
601C2×C3×C4C2518yes—
602C2×C3×C4C2514yes—
603C2×C3×C4C2512yes—
604C2×C3×C4C2512yes—
605#67C22×Q8132yescomplemented
606C2×Dic3—28no—
607C2×Dic3—24no—
608C2×Dic3—22no—
609C2×Dic3—24no—
610C2×Dic3—24no—
611C2×Dic3—216no—
612C2×Dic3—416no—
613C2×Dic3C22×Q818yes—
614C2×Dic3C22×Q814yes—
615C2×Dic3C22×Q8132yescomplemented
616C2×Dic32−1+414yes—
617C2×Dic3C2514yes—
618C2×Dic3C2514yes—
619C2×Dic3C2512yes—
620C2×Dic3C2514yes—
621C2×Dic3C2518yes—
622C2×Dic3C2514yes—
623C2×Dic3C2512yes—
624C2×Dic3C2512yes—
625C4×D3—28no—
626C4×D3—28no—
627C4×D3—416no—
628C4×D3C22×Q8116yescomplemented
629Dic6—28no—
630Dic6—216no—
631Dic6—216no—
632Dic6—416no—
633Dic6—416no—
634Dic6C22×Q8116yescomplemented
635C24—31no—
636C24C23×D312yes—
637#41—364no—
638C2×Q8—24no—
639C2×Q8—28no—
640C2×Q8—38no—
641C2×Q8—34no—
642C2×Q8—38no—
643C2×Q8—38no—
644C2×Q8—34no—
645C2×Q8—316no—
646C2×Q8—316no—
647C2×Q8—48no—
648C2×Q8—432no—
649C2×Q8—68no—
650C2×Q8—64no—
651C2×Q8—68no—
652C2×Q8—128no—
653C2×Q8—128no—
654C2×Q8—1232no—
655C2×Q8—1232no—
656C2×Q8C23×D318yes—
657C2×Q8C23×D314yes—
658C2×Q8C23×D3116yes—
659C2×D4—316no—
660C2×D4—38no—
661C2×D4D3×Q818yescomplemented
662C2×D4C23×D314yes—
663C22×C4—28no—
664C22×C4—316no—
665C22×C4—38no—
666C22×C4—32no—
667C22×C4—31no—
668C22×C4—31no—
669C22×C4—38no—
670C22×C4—34no—
671C22×C4—38no—
672C22×C4—32no—
673C22×C4—32no—
674C22×C4—31no—
675C22×C4—34no—
676C22×C4—32no—
677C22×C4—316no—
678C22×C4—34no—
679C22×C4—34no—
680C22×C4—316no—
681C22×C4—48no—
682C22×C4—64no—
683C22×C4—68no—
684C22×C4—64no—
685C22×C4—128no—
686C22×C4—128no—
687C22×C4C23×D318yes—
688C22×C4C23×D312yes—
689C22×C4C23×D312yes—
690C22×C4C23×D311yescharacteristic
691C22×C4C23×D314yes—
692C22×C4C23×D312yes—
693C22×C4C23×D3116yes—
694C22×C4C23×D311yescharacteristic
695C22×C4C23×D311yescharacteristic
696C4⋊C4—316no—
697C4⋊C4—38no—
698C4⋊C4—316no—
699C4⋊C4—38no—
700C4⋊C4—316no—
701C4⋊C4—316no—
702C4⋊C4—38no—
703C4⋊C4—316no—
704C4⋊C4—316no—
705C4⋊C4—38no—
706C4⋊C4—38no—
707C4⋊C4—38no—
708C4⋊C4—34no—
709C4⋊C4—38no—
710C4⋊C4—34no—
711C4⋊C4—38no—
712C4⋊C4—316no—
713C4⋊C4—316no—
714C4⋊C4—38no—
715C4⋊C4—316no—
716C4⋊C4—38no—
717C4⋊C4C23×D318yes—
718C4⋊C4C23×D318yes—
719C4⋊C4C23×D314yes—
720C4⋊C4C23×D314yes—
721C4⋊C4C23×D3116yes—
722C4⋊C4C23×D318yes—
723C22⋊C4—316no—
724C22⋊C4—38no—
725C22⋊C4—38no—
726C22⋊C4—38no—
727C22⋊C4—38no—
728C22⋊C4C23×D3116yes—
729C22⋊C4C23×D318yes—
730C42—34no—
731C42—38no—
732C42—34no—
733C42—38no—
734C42—38no—
735C42—34no—
736C42—316no—
737C42—316no—
738C42—38no—
739C42C23×D314yes—
740C42C23×D318yes—
741C22×C3—24no—
742C22×C3—24no—
743C22×C3—216no—
744C22×C3C23×Q818yes—
745C22×C3C23×Q812yes—
746C22×C3C2×H(5,𝔽2)12yes—
747C22×C3C2×2−1+412yes—
748C22×C3C2611yescharacteristic
749C2×D3—22no—
750C2×D3—22no—
751C2×D3—28no—
752C2×D3C23×Q814yes—
753C3×C4—24no—
754C3×C4—28no—
755C3×C4—24no—
756C3×C4—24no—
757C3×C4—22no—
758C3×C4C23×Q814yes—
759C3×C4C2×H(5,𝔽2)14yes—
760Dic3—28no—
761Dic3—24no—
762Dic3—22no—
763Dic3—24no—
764Dic3—24no—
765Dic3C23×Q818yes—
766Dic3C23×Q814yes—
767Dic3C2×2−1+414yes—
768C23—24no—
769C23—24no—
770C23—34no—
771C23—32no—
772C23—62no—
773C23—62no—
774C23C2×D3×Q818yes—
775C23C24×D314yes—
776C23C24×D311yescharacteristic
777Q8—28no—
778Q8—216no—
779Q8—316no—
780Q8—416no—
781Q8—616no—
782Q8—68no—
783Q8—616no—
784Q8—1216no—
785Q8—1216no—
786D4—332no—
787D4C2×D3×Q8116yescomplemented
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—28no—
791C2×C4—22no—
792C2×C4—24no—
793C2×C4—216no—
794C2×C4—34no—
795C2×C4—38no—
796C2×C4—332no—
797C2×C4—34no—
798C2×C4—34no—
799C2×C4—32no—
800C2×C4—32no—
801C2×C4—316no—
802C2×C4—34no—
803C2×C4—34no—
804C2×C4—32no—
805C2×C4—38no—
806C2×C4—34no—
807C2×C4—416no—
808C2×C4—68no—
809C2×C4—616no—
810C2×C4—62no—
811C2×C4—68no—
812C2×C4—64no—
813C2×C4—64no—
814C2×C4—64no—
815C2×C4—68no—
816C2×C4—1216no—
817C2×C4—1216no—
818C2×C4#100414yes—
819C2×C4C2×D3×Q814yes—
820C2×C4C24×D314yes—
821C2×C4C24×D314yes—
822C2×C4C24×D312yes—
823C2×C4C24×D318yes—
824C2×C4C24×D314yes—
825C2×C4C24×D312yes—
826C2×C4C24×D312yes—
827C2×C3—28no—
828C2×C3#350314yescomplemented
829C2×C3C24×Q811yescharacteristic
830C2×C3C22×H(5,𝔽2)11yescharacteristic
831C2×C3C22×2−1+411yescharacteristic
832D3—24no—
833C22—24no—
834C22—24no—
835C22—216no—
836C22—34no—
837C22—62no—
838C22—62no—
839C22—68no—
840C22C2×#100412yes—
841C22C22×D3×Q818yes—
842C22C22×D3×Q812yes—
843C22D3×2−1+412yes—
844C22C25×D311yescharacteristic
845C4—24no—
846C4—24no—
847C4—28no—
848C4—22no—
849C4—24no—
850C4—34no—
851C4—38no—
852C4—34no—
853C4—62no—
854C4—68no—
855C4—64no—
856C4—64no—
857C4—64no—
858C4C2×#100414yes—
859C4C22×D3×Q814yes—
860C3C2×#350311yescharacteristic, complemented, Sylow
861C2—28no—
862C2—64no—
863C2#8674714yesdirect product factor
864C2C22×#100411yescharacteristic
865C2C23×D3×Q811yescharacteristic
866C2C2×D3×2−1+411yescharacteristic
subgroupG/H
centerC23C24×D3
commutator, cosocleC22×C3C26
FrattiniC22C25×D3
FittingC2×C3×D4×Q8C2
socleC23×C3C25
prime radicalC22×#237C22
hypercenterC2×D4×Q8D3
hypocenterC3C2×#3503
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×D4×Q8C2semidirect
2. C2×Q8×#67C2semidirect
3. C22×#944C2semidirect
4. #86747C2direct (N × H)
5. C2×#5729C2semidirect
6. C2×D3×C4⋊Q8C2semidirect
7. C2×#5722C2semidirect
8. C2×#5721C2semidirect
9. C2×#5636C2semidirect
10. C2×#5632C2semidirect
11. C2×#5623C2semidirect
12. C2×#5622C2semidirect
13. C2×#5578C2semidirect
14. C2×#5567C2semidirect
15. C2×#5539C2semidirect
16. C2×D4×Dic6C2semidirect
24. C3×D4×Q8C22semidirect
32. Q8×#67C22semidirect
43. C2×#944C22semidirect
53. #5729C22semidirect
54. D3×C4⋊Q8C22semidirect
55. #5722C22semidirect
56. #5721C22semidirect
57. #5636C22semidirect
58. #5632C22semidirect
59. #5623C22semidirect
60. #5622C22semidirect
61. #5578C22semidirect
62. #5567C22semidirect
64. #5539C22semidirect
65. D4×Dic6C22semidirect
111. C2×D4×Q8D3semidirect
134. C2×#237Q8semidirect
266. D4×Q8C2×D3semidirect
345. C2×C3×D4C2×Q8semidirect
358. C2×#67C2×Q8semidirect
362. C22×Dic3C2×Q8semidirect
375. #237C2×Q8semidirect
379. C2×C4×D3C2×Q8semidirect
390. C2×Dic6C2×Q8semidirect
588. C3×D4C22×Q8semidirect
605. #67C22×Q8semidirect
615. C2×Dic3C22×Q8semidirect
628. C4×D3C22×Q8semidirect
634. Dic6C22×Q8semidirect
661. C2×D4D3×Q8semidirect
787. D4C2×D3×Q8semidirect
828. C2×C3#3503semidirect
860. C3C2×#3503semidirect
863. C2#86747direct (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
C2×Q8×#672
C22×#9442
#867472
C2×#57292
C2×D3×C4⋊Q82
C2×#57222
C2×#57212
C2×#56362
C2×#56322
C2×#56232
C2×#56222
C2×#55782
C2×#55672
C2×#55392
C2×D4×Dic62
C2×#55462
C2×C4×#2372
C2×#35033