Finite Group Databasebeta

← C2×#79667 #11664993

Subgroups — C2×#79667 #11664993

Order 768.

1970 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5583C211yesmaximal, characteristic, complemented
2C2×#5562C211yesmaximal, characteristic
3C2×C3×C4×SD16C211yesmaximal, characteristic, complemented
4C2×#5171C211yesmaximal, characteristic, complemented
5C2×#5175C211yesmaximal, characteristic, complemented
6C2×#5026C211yesmaximal, characteristic, complemented
7C2×#5018C211yesmaximal, characteristic, complemented
8#79667C2116yesmaximal, direct product factor
9C2×#4864C211yesmaximal, characteristic, complemented
10C2×#4858C211yesmaximal, characteristic, complemented
11C2×#4812C211yesmaximal, characteristic, complemented
12C2×#4797C211yesmaximal, characteristic, complemented
13C2×#4780C211yesmaximal, characteristic, complemented
14C2×#4764C211yesmaximal, characteristic, complemented
15C2×C4×#204C211yesmaximal, characteristic, complemented
16C2×#4689C211yesmaximal, characteristic, complemented
17C2×#3174—31nomaximal, Sylow
18C22×C3×SD16C2211yescharacteristic
19C2×C3×C4×Q8C2211yescharacteristic
20C2×C3×C4×D4C2211yescharacteristic
21C2×#946C2211yescharacteristic
22C2×#944C2211yescharacteristic
23C22×#215C2211yescharacteristic
24C2×#940C2211yescharacteristic
25C2×#938C2211yescharacteristic
26C22×#214C2211yescharacteristic
27C2×#930—21no—
28C2×#929—21no—
29C22×#204C2211yescharacteristic
30C22×ΓL(1,𝔽25)C2211yescharacteristic
31C22×D3×C8C2211yescharacteristic
32#5583—24no—
33#5583C2218yescomplemented
34#5562—24no—
35#5562C2218yes—
36C2×#898—21no—
37C2×#897C2211yescharacteristic
38C2×#895C2211yescharacteristic
39C2×#890C2211yescharacteristic
40C2×#890C2211yescharacteristic
41C2×#889—21no—
42C2×#884—21no—
43C2×#883—21no—
44C2×#876—21no—
45C2×C4×D12C2211yescharacteristic
46C2×#872C2211yescharacteristic
47C2×#870—21no—
48C2×C4×Dic6C2211yescharacteristic
49C3×C4×SD16C2218yescomplemented
50C2×C3×#106C2211yescharacteristic
51C2×C3×#103C2211yescharacteristic
52C2×C3×#102C2211yescharacteristic
53C2×C3×C4×C8C2211yescharacteristic
54C2×#835C2211yescharacteristic
55C2×#832C2211yescharacteristic
56#5175C2218yescomplemented
57#5171C2218yescomplemented
58C2×#821C2211yescharacteristic
59C2×#817C2211yescharacteristic
60C2×#816C2211yescharacteristic
61C2×#815C2211yescharacteristic
62C2×C8×Dic3C2211yescharacteristic
63#5026C2218yescomplemented
64#5018C2218yescomplemented
65C2×#810C2211yescharacteristic
66C2×#809C2211yescharacteristic
67C2×#807C2211yescharacteristic
68C2×#807C2211yescharacteristic
69C2×#803C2211yescharacteristic
70#4864C2218yescomplemented
71#4858C2218yescomplemented
72#4812C2218yescomplemented
73#4797C2218yescomplemented
74#4780C2218yescomplemented
75#4764C2218yescomplemented
76C4×#204C2218yescomplemented
77#4689C2218yescomplemented
78C2×#541—31no—
79C2×#540—31no—
80#3174—316no—
81C2×#499—31no—
82C2×#492—31no—
83C2×#491—31no—
84C2×#490—31no—
85C2×#468—31no—
86C2×#468—31no—
87C2×#465—31no—
88C2×#465—31no—
89C2×#440—31no—
90C2×#440—31no—
91C2×C4×SD16—31no—
92C2×C4×SD16D311yescharacteristic, complemented
93C2×#405—31no—
94C22×C3×Q8C2311yescharacteristic
95C22×C3×D4C2311yescharacteristic
96C23×C3×C4—21no—
97C22×#67—21no—
98C22×#67—21no—
99C22×#67—21no—
100C22×D12—21no—
101C22×D12C2311yescharacteristic
102C22×C4×D3—21no—
103C22×C4×D3C2311yescharacteristic
104C22×Dic6C2311yescharacteristic
105C2×C3×SD16—24no—
106C2×C3×SD16C2314yes—
107C22×C3×C8C2311yescharacteristic
108C22×C3×C8C2311yescharacteristic
109C3×C4×Q8—22no—
110C3×C4×Q8C2314yes—
111C3×C4×D4—22no—
112C3×C4×D4C2314yes—
113C2×C3×C4⋊C4—21no—
114C2×C3×C4⋊C4C2311yescharacteristic
115C2×C3×C4⋊C4C2311yescharacteristic
116C2×C3×C22⋊C4—21no—
117C2×C3×C42—21no—
118C2×C3×C42C2311yescharacteristic
119C2×#217—21no—
120#946—22no—
121#946C2314yes—
122#944—22no—
123#944C2314yes—
124C2×#215—24no—
125C2×#215C2314yes—
126#940—22no—
127#940C2314yes—
128#938—22no—
129#938C2314yes—
130C2×#214—24no—
131C2×#214C2314yes—
132#930—28no—
133#929—28no—
134C2×(C2×D3)⋊C4—21no—
135C2×(C2×D3)⋊C4—21no—
136C2×(C2×D3)⋊C4—21no—
137C2×(C2×D3)⋊C4—21no—
138C2×(C2×D3)⋊C4D411yescharacteristic
139C2×(C2×D3)⋊C4D411yescharacteristic
140C2×C4⋊Dic3—21no—
141C2×C4⋊Dic3—21no—
142C2×C4⋊Dic3—21no—
143C2×C4⋊Dic3C2311yescharacteristic
144C2×C4⋊Dic3C2311yescharacteristic
145C2×Dic3⋊C4—21no—
146C2×Dic3⋊C4—21no—
147C2×Dic3⋊C4—21no—
148C2×Dic3⋊C4—21no—
149C2×Dic3⋊C4—21no—
150C2×Dic3⋊C4—21no—
151C2×Dic3⋊C4D411yescharacteristic
152C2×Dic3⋊C4D411yescharacteristic
153C2×C4×Dic3—21no—
154C2×C4×Dic3C2311yescharacteristic
155C22×C3⋊C8C2311yescharacteristic
156C22×C3⋊C8C2311yescharacteristic
157C2×#204—24no—
158C2×#204C2314yes—
159C2×ΓL(1,𝔽25)—24no—
160C2×ΓL(1,𝔽25)C2314yes—
161C2×D3×C8—24no—
162C2×D3×C8C2314yes—
163#898—28no—
164#897—22no—
165#897C2314yes—
166#895—22no—
167#895C2314yes—
168#890—22no—
169#890—22no—
170#890C2314yes—
171#890C2314yes—
172#889—28no—
173#884—28no—
174#883—28no—
175#876—28no—
176C4×D12—22no—
177C4×D12C2314yes—
178#872D414yes—
179#872C2314yes—
180#870—28no—
181C4×Dic6—22no—
182C4×Dic6C2314yes—
183C3×#106C2314yes—
184C3×#103C2314yes—
185C3×#102C2314yes—
186C3×C4×C8C2314yes—
187#835C2314yes—
188#832C2314yes—
189#821C2314yes—
190#817C2314yes—
191#816C2314yes—
192#815C2314yes—
193C8×Dic3C2314yes—
194#810C2314yes—
195#809C2314yes—
196#807C2314yes—
197#807C2314yes—
198#803C2314yes—
199C22×SD16—31no—
200C22×SD16—31no—
201C22×SD16—31no—
202C22×SD16C2×D311yescharacteristic
203C22×M16—31no—
204C23×C8—31no—
205#541—38no—
206#541—64no—
207#540—38no—
208#540—64no—
209C2×C4⋊Q8—31no—
210C2×#127—31no—
211C2×#126—61no—
212C2×#126—61no—
213C2×#125—31no—
214C2×#125—31no—
215C2×#125—61no—
216C2×#125—61no—
217C2×#123—61no—
218C2×#123—61no—
219C2×C22⋊Q8—31no—
220C2×C22⋊Q8—31no—
221C2×#121—31no—
222C2×#121—31no—
223C2×#121—61no—
224C2×#121—61no—
225C2×C4×Q8—31no—
226C2×C4×Q8C2×D311yescharacteristic
227C2×C4×D4—31no—
228C2×C4×D4C2×D311yescharacteristic
229C2×#117—31no—
230#499—38no—
231#492—38no—
232#491—38no—
233#490—38no—
234#468—38no—
235#468—38no—
236#465—38no—
237#465—38no—
238#440—38no—
239#440—38no—
240C4×SD16—38no—
241C4×SD16C2×D318yescomplemented
242C2×#107—31no—
243C2×#107—31no—
244C2×#106—31no—
245C2×#106C2×D311yescharacteristic
246C2×#103—31no—
247C2×#103—31no—
248C2×#103—31no—
249C2×#103C2×D311yescharacteristic
250C2×#102—31no—
251C2×#102—31no—
252C2×#102—31no—
253C2×#102C2×D311yescharacteristic
254#405—38no—
255C2×#97—31no—
256C2×#97—31no—
257C2×C4×C8—31no—
258C2×C4×C8C2×D311yescharacteristic
259C24×C3—21no—
260C23×D3—21no—
261C23×D3C2×D411yescharacteristic
262C2×C3×Q8—21no—
263C2×C3×Q8—22no—
264C2×C3×Q8—22no—
265C2×C3×Q8C2412yes—
266C2×C3×D4—21no—
267C2×C3×D4—22no—
268C2×C3×D4—22no—
269C2×C3×D4C2412yes—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—24no—
274C22×C3×C4—82no—
275C22×C3×C4C2×D411yescharacteristic
276C22×C3×C4C2×D411yescharacteristic
277C22×C3×C4C2411yescharacteristic
278C2×#67—24no—
279C2×#67—24no—
280C2×#67—24no—
281C2×#67—82no—
282C2×#67—82no—
283C2×#67—82no—
284C22×Dic3—21no—
285C22×Dic3—21no—
286C22×Dic3—21no—
287C22×Dic3C2×D411yescharacteristic
288C22×Dic3C2×D411yescharacteristic
289C22×Dic3C2×D411yescharacteristic
290C2×D12—22no—
291C2×D12—22no—
292C2×D12—21no—
293C2×D12—24no—
294C2×D12—82no—
295C2×D12C2412yes—
296C2×C4×D3—22no—
297C2×C4×D3—22no—
298C2×C4×D3—24no—
299C2×C4×D3—82no—
300C2×C4×D3C2×D412yes—
301C2×C4×D3C2412yes—
302C2×Dic6—22no—
303C2×Dic6—22no—
304C2×Dic6—21no—
305C2×Dic6C2412yes—
306C3×SD16—28no—
307C2×C3×C8—22no—
308C2×C3×C8#4114yes—
309C2×C3×C8C2412yes—
310C2×C3×C8C2412yes—
311C3×C4⋊C4—24no—
312C3×C4⋊C4—21no—
313C3×C4⋊C4—21no—
314C3×C4⋊C4C2412yes—
315C3×C4⋊C4C2412yes—
316C3×C22⋊C4—24no—
317C3×C42—24no—
318C3×C42C2×D412yes—
319C3×C42C2412yes—
320#217—24no—
321#215—28no—
322#214—28no—
323(C2×D3)⋊C4—24no—
324(C2×D3)⋊C4—24no—
325(C2×D3)⋊C4—24no—
326(C2×D3)⋊C4—24no—
327(C2×D3)⋊C4C2×D414yes—
328(C2×D3)⋊C4C2×D414yes—
329C4⋊Dic3—21no—
330C4⋊Dic3—21no—
331C4⋊Dic3—24no—
332C4⋊Dic3—24no—
333C4⋊Dic3—24no—
334C4⋊Dic3C2412yes—
335C4⋊Dic3C2412yes—
336Dic3⋊C4—24no—
337Dic3⋊C4—24no—
338Dic3⋊C4—24no—
339Dic3⋊C4—24no—
340Dic3⋊C4—24no—
341Dic3⋊C4—24no—
342Dic3⋊C4C2×D414yes—
343Dic3⋊C4C2×D414yes—
344C4×Dic3—24no—
345C4×Dic3C2×D412yes—
346C4×Dic3C2412yes—
347C2×C3⋊C8—22no—
348C2×C3⋊C8#4114yes—
349C2×C3⋊C8C2412yes—
350C2×C3⋊C8C2412yes—
351#204—28no—
352ΓL(1,𝔽25)—28no—
353D3×C8—28no—
354C22×Q8—31no—
355C22×Q8C22×D311yescharacteristic
356C22×D4—31no—
357C22×D4—61no—
358C22×D4—61no—
359C22×D4—61no—
360C22×D4—61no—
361C22×D4C22×D311yescharacteristic
362C23×C4—21no—
363C23×C4—31no—
364C23×C4—61no—
365C2×SD16—24no—
366C2×SD16—34no—
367C2×SD16—34no—
368C2×SD16—34no—
369C2×SD16—64no—
370C2×SD16—64no—
371C2×SD16—64no—
372C2×SD16C22×D314yes—
373C2×M16—34no—
374C2×M16—64no—
375C22×C8—31no—
376C22×C8—31no—
377C22×C8—34no—
378C22×C8—64no—
379C22×C8C22×D311yescharacteristic
380C22×C8C22×D311yescharacteristic
381C4⋊Q8—34no—
382C4⋊Q8—62no—
383#127—34no—
384#127—62no—
385#126—68no—
386#126—68no—
387#125—34no—
388#125—34no—
389#125—68no—
390#125—62no—
391#125—62no—
392#125—68no—
393#123—68no—
394#123—68no—
395C22⋊Q8—34no—
396C22⋊Q8—34no—
397C22⋊Q8—62no—
398C22⋊Q8—62no—
399#121—34no—
400#121—34no—
401#121—68no—
402#121—68no—
403#121—62no—
404#121—62no—
405C4×Q8—22no—
406C4×Q8—34no—
407C4×Q8—62no—
408C4×Q8C22×D314yes—
409C4×D4—22no—
410C4×D4—34no—
411C4×D4—62no—
412C4×D4C22×D314yes—
413#117—34no—
414#117—34no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—31no—
417C2×C4⋊C4—31no—
418C2×C4⋊C4—31no—
419C2×C4⋊C4—31no—
420C2×C4⋊C4—61no—
421C2×C4⋊C4—61no—
422C2×C4⋊C4—61no—
423C2×C4⋊C4—61no—
424C2×C4⋊C4—61no—
425C2×C4⋊C4—61no—
426C2×C4⋊C4—61no—
427C2×C4⋊C4—61no—
428C2×C4⋊C4—61no—
429C2×C4⋊C4C22×D311yescharacteristic
430C2×C4⋊C4C22×D311yescharacteristic
431C2×C22⋊C4—21no—
432C2×C22⋊C4—31no—
433C2×C22⋊C4—31no—
434C2×C22⋊C4—61no—
435C2×C22⋊C4—61no—
436C2×C22⋊C4—61no—
437C2×C22⋊C4—61no—
438C2×C22⋊C4—61no—
439C2×C42—21no—
440C2×C42—31no—
441C2×C42—61no—
442C2×C42C22×D311yescharacteristic
443#107—34no—
444#107—34no—
445#106—34no—
446#106C22×D314yes—
447#103—34no—
448#103—34no—
449#103—34no—
450#103C22×D314yes—
451#102—34no—
452#102—34no—
453#102—34no—
454#102C22×D314yes—
455#97—34no—
456#97—34no—
457C4×C8—34no—
458C4×C8C22×D314yes—
459C23×C3—22no—
460C23×C3—42no—
461C23×C3—42no—
462C23×C3—42no—
463C23×C3C22×D411yescharacteristic
464C22×D3—22no—
465C22×D3—22no—
466C22×D3—22no—
467C22×D3—22no—
468C22×D3—42no—
469C22×D3—42no—
470C22×D3—42no—
471C22×D3C22×D412yes—
472C3×Q8—22no—
473C3×Q8—22no—
474C3×Q8—42no—
475C3×D4—22no—
476C3×D4—22no—
477C3×D4—42no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—42no—
484C2×C3×C4—42no—
485C2×C3×C4—42no—
486C2×C3×C4—84no—
487C2×C3×C4C22×D412yes—
488C2×C3×C4C22×D412yes—
489C2×C3×C4C22×D411yescharacteristic
490C2×C3×C4C2×#4112yes—
491C2×C3×C4C2×#4112yes—
492C2×C3×C4C2511yescharacteristic
493#67—84no—
494#67—84no—
495#67—84no—
496C2×Dic3—22no—
497C2×Dic3—22no—
498C2×Dic3—22no—
499C2×Dic3—22no—
500C2×Dic3—22no—
501C2×Dic3—22no—
502C2×Dic3—42no—
503C2×Dic3—42no—
504C2×Dic3—42no—
505C2×Dic3C22×D412yes—
506C2×Dic3C22×D412yes—
507C2×Dic3C22×D412yes—
508D12—22no—
509D12—22no—
510D12—42no—
511D12—84no—
512C4×D3—24no—
513C4×D3—22no—
514C4×D3—22no—
515C4×D3—84no—
516Dic6—22no—
517Dic6—22no—
518Dic6—42no—
519C3×C8—22no—
520C3×C8C2×#4114yes—
521C3⋊C8—22no—
522C3⋊C8C2×#4114yes—
523C24—21no—
524C24—31no—
525C24—61no—
526C2×Q8—21no—
527C2×Q8—22no—
528C2×Q8—22no—
529C2×Q8—32no—
530C2×Q8—61no—
531C2×Q8—62no—
532C2×Q8—62no—
533C2×Q8C23×D312yes—
534C2×D4—22no—
535C2×D4—21no—
536C2×D4—22no—
537C2×D4—32no—
538C2×D4—64no—
539C2×D4—64no—
540C2×D4—64no—
541C2×D4—64no—
542C2×D4—62no—
543C2×D4—61no—
544C2×D4—62no—
545C2×D4—242no—
546C2×D4—242no—
547C2×D4—242no—
548C2×D4—242no—
549C2×D4C23×D312yes—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—24no—
554C22×C4—31no—
555C22×C4—31no—
556C22×C4—31no—
557C22×C4—32no—
558C22×C4—32no—
559C22×C4—62no—
560C22×C4—62no—
561C22×C4—61no—
562C22×C4—61no—
563C22×C4—61no—
564C22×C4—64no—
565C22×C4—82no—
566C22×C4—242no—
567C22×C4D3×D411yescharacteristic
568C22×C4D3×D411yescharacteristic
569C22×C4C23×D311yescharacteristic
570SD16—28no—
571SD16—68no—
572SD16—68no—
573SD16—68no—
574M16—68no—
575C2×C8—22no—
576C2×C8—34no—
577C2×C8—32no—
578C2×C8—32no—
579C2×C8—62no—
580C2×C8—68no—
581C2×C8#23514yes—
582C2×C8C23×D312yes—
583C2×C8C23×D312yes—
584C4⋊C4—24no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—34no—
588C4⋊C4—34no—
589C4⋊C4—32no—
590C4⋊C4—32no—
591C4⋊C4—64no—
592C4⋊C4—64no—
593C4⋊C4—64no—
594C4⋊C4—64no—
595C4⋊C4—64no—
596C4⋊C4—64no—
597C4⋊C4—64no—
598C4⋊C4—64no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4—64no—
602C4⋊C4C23×D312yes—
603C4⋊C4C23×D312yes—
604C22⋊C4—24no—
605C22⋊C4—34no—
606C22⋊C4—34no—
607C22⋊C4—64no—
608C22⋊C4—64no—
609C22⋊C4—64no—
610C22⋊C4—64no—
611C22⋊C4—64no—
612C42—24no—
613C42—32no—
614C42—32no—
615C42—64no—
616C42D3×D412yes—
617C42C23×D312yes—
618C22×C3—42no—
619C22×C3—42no—
620C22×C3—42no—
621C22×C3—84no—
622C22×C3#53212yes—
623C22×C3#57712yes—
624C22×C3#57712yes—
625C22×C3C23×D411yescharacteristic
626C2×D3—22no—
627C2×D3—22no—
628C2×D3—22no—
629C2×D3—44no—
630C2×D3—42no—
631C2×D3—42no—
632C2×D3—42no—
633C2×D3—84no—
634C3×C4—22no—
635C3×C4—22no—
636C3×C4—42no—
637C3×C4—42no—
638C3×C4—42no—
639C3×C4#53212yes—
640C3×C4C22×#4111yescharacteristic
641C3×C4C22×#4111yescharacteristic
642Dic3—22no—
643Dic3—22no—
644Dic3—22no—
645Dic3—42no—
646Dic3—42no—
647Dic3—42no—
648C23—22no—
649C23—32no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—62no—
654C23—62no—
655C23—62no—
656C23—62no—
657C23—122no—
658C23—122no—
659C23—122no—
660C23C2×D3×D411yescharacteristic
661Q8—22no—
662Q8—22no—
663Q8—42no—
664Q8—62no—
665Q8—62no—
666Q8—122no—
667D4—22no—
668D4—22no—
669D4—42no—
670D4—62no—
671D4—62no—
672D4—122no—
673D4—244no—
674D4—244no—
675D4—244no—
676D4—244no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—32no—
683C2×C4—32no—
684C2×C4—32no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—62no—
689C2×C4—62no—
690C2×C4—62no—
691C2×C4—62no—
692C2×C4—62no—
693C2×C4—64no—
694C2×C4—62no—
695C2×C4—62no—
696C2×C4—62no—
697C2×C4—84no—
698C2×C4—122no—
699C2×C4—122no—
700C2×C4—122no—
701C2×C4—244no—
702C2×C4C2×#23512yes—
703C2×C4C2×D3×D412yes—
704C2×C4C2×D3×D412yes—
705C2×C4C2×D3×D411yescharacteristic
706C2×C4D3×#4112yes—
707C2×C4C24×D311yescharacteristic
708C8—22no—
709C8—34no—
710C8—62no—
711C8C2×#23514yes—
712C2×C3—82no—
713C2×C3#317414yescomplemented
714C2×C3C2×#53211yescharacteristic
715C2×C3C2×#57711yescharacteristic
716C2×C3C2×#57711yescharacteristic
717D3—42no—
718D3—82no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—62no—
723C22—62no—
724C22—62no—
725C22—84no—
726C22—124no—
727C22—122no—
728C22—122no—
729C22—122no—
730C22—244no—
731C22#554812yes—
732C22#576212yes—
733C22#577012yes—
734C22C22×D3×D411yescharacteristic
735C4—22no—
736C4—22no—
737C4—42no—
738C4—42no—
739C4—42no—
740C4—62no—
741C4—62no—
742C4—62no—
743C4—122no—
744C4—122no—
745C4—122no—
746C4#554812yes—
747C4C22×#23511yescharacteristic
748C4C2×D3×#4111yescharacteristic
749C3C2×#317411yescharacteristic, complemented, Sylow
750C2—82no—
751C2—122no—
752C2—242no—
753C2#7966714yesdirect product factor
754C2C2×#554811yescharacteristic
755C2C2×#576211yescharacteristic
756C2C2×#577011yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×C4×SD16C2
socleC23×C3C22×D4
prime radicalC2×#5562C2
hypercenterC2×C4×SD16D3
hypocenterC3C2×#3174
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#5583C2semidirect
3. C2×C3×C4×SD16C2semidirect
4. C2×#5171C2semidirect
5. C2×#5175C2semidirect
6. C2×#5026C2semidirect
7. C2×#5018C2semidirect
8. #79667C2direct (N × H)
9. C2×#4864C2semidirect
10. C2×#4858C2semidirect
11. C2×#4812C2semidirect
12. C2×#4797C2semidirect
13. C2×#4780C2semidirect
14. C2×#4764C2semidirect
15. C2×C4×#204C2semidirect
16. C2×#4689C2semidirect
33. #5583C22semidirect
49. C3×C4×SD16C22semidirect
56. #5175C22semidirect
57. #5171C22semidirect
63. #5026C22semidirect
64. #5018C22semidirect
70. #4864C22semidirect
71. #4858C22semidirect
72. #4812C22semidirect
73. #4797C22semidirect
74. #4780C22semidirect
75. #4764C22semidirect
76. C4×#204C22semidirect
77. #4689C22semidirect
92. C2×C4×SD16D3semidirect
241. C4×SD16C2×D3semidirect
713. C2×C3#3174semidirect
749. C3C2×#3174semidirect
753. C2#79667direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#55832
C2×#55622
C2×C3×C4×SD162
C2×#51712
C2×#51752
C2×#50262
C2×#50182
#796672
C2×#48642
C2×#48582
C2×#48122
C2×#47972
C2×#47802
C2×#47642
C2×C4×#2042
C2×#46892
C2×#31743