Finite Group Databasebeta

← C2×#61831 #10578225

Subgroups — C2×#61831 #10578225

Order 512.

6408 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×#3507C211yesmaximal, characteristic, complemented
2C22×#554C211yesmaximal, characteristic, complemented
3#61831C2132yesmaximal, direct product factor
4C2×#3389C214yesmaximal, complemented
5C2×#3388C214yesmaximal, complemented
6C2×#3376C214yesmaximal, complemented
7C2×#3370C214yesmaximal, complemented
8C2×#3239C212yesmaximal, complemented
9C2×#3236C211yesmaximal, characteristic, complemented
10C2×#3234C211yesmaximal, characteristic, complemented
11C2×#3232C212yesmaximal, complemented
12C2×#3110C211yesmaximal, characteristic, complemented
13C2×#3109C211yesmaximal, characteristic
14C2×#3114C212yesmaximal, complemented
15C2×#3105C212yesmaximal, complemented
16C2×#2983C211yesmaximal, characteristic, complemented
17#3507—28no—
18#3507C22116yescomplemented
19C2×#559C2212yescomplemented
20C2×#557C2212yescomplemented
21C2×#556—22no—
22C2×#556C2212yescomplemented
23C2×#554—22no—
24C2×#554—22no—
25C2×#554—28no—
26C2×#554C2214yes—
27C2×#554C2214yes—
28C2×#554C22116yescomplemented
29C2×#554C2212yescomplemented
30C2×#552—22no—
31C2×#539—21no—
32C2×#539—21no—
33C2×#536—21no—
34C2×#533C2211yescharacteristic
35C2×#532C2211yescharacteristic
36C22×C4⋊Q8C2211yescharacteristic
37C2×#529C2212yes—
38C2×#529C2212yes—
39C22×#125C2211yescharacteristic
40C22×#125C2211yescharacteristic
41C22×C22⋊Q8—21no—
42C22×C22⋊Q8—21no—
43C22×C22⋊Q8—21no—
44C2×#520—21no—
45C22×C4×Q8C2211yescharacteristic
46C22×C4×D4C2211yescharacteristic
47C22×C4×D4C2211yescharacteristic
48C22×C4×D4C2211yescharacteristic
49C23×C4⋊C4—21no—
50#3389C22164yescomplemented
51#3388C22164yescomplemented
52#3376C22164yescomplemented
53#3370C22164yescomplemented
54#3239C22132yescomplemented
55#3236C22116yescomplemented
56#3234C22116yescomplemented
57#3232C22132yescomplemented
58C2×#501C2212yescomplemented
59C2×#501C2212yescomplemented
60C2×#501C2214yescomplemented
61C2×#499C2214yescomplemented
62C2×#491C2212yescomplemented
63C2×#490C2212yescomplemented
64C2×#489C2214yescomplemented
65C2×#488C2214yescomplemented
66#3114C22132yescomplemented
67#3110C22116yescomplemented
68#3109C22116yes—
69#3105C22132yescomplemented
70C2×#484C2212yes—
71C2×#484C2212yes—
72C2×#481C2212yes—
73C2×#481C2212yes—
74C2×#483C2212yes—
75C2×#480C2212yes—
76C2×#479C2214yescomplemented
77C2×#479C2214yescomplemented
78C2×#475C2214yescomplemented
79C2×#478C2214yes—
80C2×#478C2214yes—
81C2×#478C2214yescomplemented
82C2×#478C2214yescomplemented
83C2×#476C2212yes—
84C2×#474C2212yes—
85C2×#474C2214yescomplemented
86C2×#463C2214yes—
87C2×#463C2214yes—
88C2×#461C2212yes—
89C2×#459C2212yes—
90C2×#450C2212yes—
91C2×#447C2212yes—
92#2983C22116yescomplemented
93C2×#446C2214yescomplemented
94C2×#446C2214yescomplemented
95C2×#442C2214yes—
96C2×#442C2214yes—
97C2×#440C2214yes—
98C2×#440C2214yes—
99C2×C4×SD16C2214yes—
100C2×C4×D8C2214yes—
101C2×#432C2212yes—
102C2×#432C2211yescharacteristic
103C2×#432C2211yescharacteristic
104C2×#431C2212yes—
105C22×#41—21no—
106C23×Q8—21no—
107C23×Q8D411yescharacteristic
108C23×D4C2311yescharacteristic
109C24×C4—21no—
110C24×C4—21no—
111C24×C4—21no—
112C22×SD16C2314yes—
113C22×D8C2314yes—
114#559—28no—
115#559C23116yescomplemented
116#557—28no—
117#557C23116yescomplemented
118#556—232no—
119#556—28no—
120#556C23116yescomplemented
121#554—216no—
122#554—216no—
123#554—232no—
124#554—232no—
125#554—28no—
126#554C23132yes—
127#554C23132yes—
128#554C23116yescomplemented
129#552—232no—
130#539—216no—
131#539—216no—
132#536—216no—
133#533—24no—
134#533C2318yes—
135#532—24no—
136#532C2318yes—
137C2×C4⋊Q8—22no—
138C2×C4⋊Q8—22no—
139C2×C4⋊Q8—24no—
140C2×C4⋊Q8C2311yescharacteristic
141C2×C4⋊Q8C2314yes—
142C2×C4⋊Q8C2311yescharacteristic
143C2×C4⋊Q8C2311yescharacteristic
144C2×C4⋊Q8C2318yes—
145C2×#127C2311yescharacteristic
146#529—28no—
147#529—28no—
148#529C23116yes—
149#529C23116yes—
150C2×#126—22no—
151C2×#126—22no—
152C2×#126—22no—
153C2×#126—22no—
154C2×#125—22no—
155C2×#125—22no—
156C2×#125—22no—
157C2×#125—21no—
158C2×#125—21no—
159C2×#125—24no—
160C2×#125—24no—
161C2×#125—21no—
162C2×#125C2312yes—
163C2×#125C2312yes—
164C2×#125C2312yes—
165C2×#125C2314yes—
166C2×#125C2312yes—
167C2×#125C2318yes—
168C2×#125C2318yes—
169C2×#124—22no—
170C2×#124—21no—
171C2×#124C2312yes—
172C2×#124C2312yes—
173C2×#123—22no—
174C2×#123—22no—
175C2×#123—22no—
176C2×#123—22no—
177C2×C22⋊Q8—24no—
178C2×C22⋊Q8—24no—
179C2×C22⋊Q8—216no—
180C2×C22⋊Q8—22no—
181C2×C22⋊Q8—22no—
182C2×C22⋊Q8—21no—
183C2×C22⋊Q8—24no—
184C2×C22⋊Q8—24no—
185C2×C22⋊Q8—24no—
186C2×C22⋊Q8—24no—
187C2×C22⋊Q8—216no—
188C2×C22⋊Q8—216no—
189C2×C22⋊Q8—22no—
190C2×C22⋊Q8—22no—
191C2×C22⋊Q8C2312yes—
192C2×#121—21no—
193C2×#121C2312yes—
194#520—216no—
195C2×C4×Q8—22no—
196C2×C4×Q8—21no—
197C2×C4×Q8D412yes—
198C2×C4×Q8D412yes—
199C2×C4×Q8D418yes—
200C2×C4×Q8C2312yes—
201C2×C4×Q8C2312yes—
202C2×C4×Q8C2312yes—
203C2×C4×Q8C2312yes—
204C2×C4×Q8C2312yes—
205C2×C4×Q8C2318yes—
206C2×C4×D4—22no—
207C2×C4×D4—22no—
208C2×C4×D4—22no—
209C2×C4×D4—22no—
210C2×C4×D4—22no—
211C2×C4×D4—21no—
212C2×C4×D4—21no—
213C2×C4×D4—24no—
214C2×C4×D4—24no—
215C2×C4×D4—24no—
216C2×C4×D4—21no—
217C2×C4×D4C2314yes—
218C2×C4×D4C2314yes—
219C2×C4×D4C2312yes—
220C2×C4×D4C2312yes—
221C2×C4×D4C2318yes—
222C2×C4×D4C2318yes—
223C2×C4×D4C2318yes—
224C2×C4×D4C2312yes—
225C2×C4×D4C2312yes—
226C2×C4×D4C2312yes—
227C2×#117—21no—
228C2×#117—22no—
229C2×#117—22no—
230C2×#117—22no—
231C22×C4⋊C4—21no—
232C22×C4⋊C4—21no—
233C22×C4⋊C4—21no—
234C22×C4⋊C4—21no—
235C22×C4⋊C4—21no—
236C22×C4⋊C4—24no—
237C22×C4⋊C4—24no—
238C22×C4⋊C4—216no—
239C22×C4⋊C4—22no—
240C22×C4⋊C4D411yescharacteristic
241C22×C4⋊C4D411yescharacteristic
242C22×C4⋊C4D411yescharacteristic
243C22×C4⋊C4C2311yescharacteristic
244C22×C4⋊C4C2311yescharacteristic
245C22×C4⋊C4C2311yescharacteristic
246C22×C22⋊C4—21no—
247C22×C22⋊C4—21no—
248C22×C22⋊C4—21no—
249C22×C42C2311yescharacteristic
250C22×C42C2311yescharacteristic
251C22×C42C2311yescharacteristic
252#501C23116yescomplemented
253#501C23132yescomplemented
254#501C23116yescomplemented
255#499C23132yescomplemented
256#491C23116yescomplemented
257#490C23116yescomplemented
258#489C23132yescomplemented
259#488C23132yescomplemented
260#484C23116yes—
261#484C23116yes—
262#483C23116yes—
263#481C23116yes—
264#481C23116yes—
265#480C23116yes—
266#479C23132yescomplemented
267#479C23132yescomplemented
268#478C23132yes—
269#478C23132yes—
270#478C23132yescomplemented
271#478C23132yescomplemented
272#476C23116yes—
273#475C23132yescomplemented
274#474C23116yes—
275#474C23132yescomplemented
276#463C23132yes—
277#463C23132yes—
278#461C23116yes—
279#459C23116yes—
280#450C23116yes—
281#447C23116yes—
282#446C23132yescomplemented
283#446C23132yescomplemented
284#442C23132yes—
285#442C23132yes—
286#440C23132yes—
287#440C23132yes—
288C4×SD16C23132yes—
289C4×D8C23132yes—
290#432C2318yes—
291#432C2318yes—
292#432C23116yes—
293#431C23116yes—
294C2×#107C2314yes—
295C2×#107C2314yes—
296C2×#107C2314yes—
297C2×#106C2314yes—
298C2×#106C2314yes—
299C2×#106C2314yes—
300C2×C4⋊C8C2314yes—
301C2×C4⋊C8C2314yes—
302C2×C4⋊C8C2312yes—
303C2×C4⋊C8C2312yes—
304C2×#103C2314yes—
305C2×#103C2314yes—
306C2×#103C2314yes—
307C2×#102C2314yes—
308C2×#102C2314yes—
309C2×#102C2314yes—
310C2×#102C2314yes—
311C2×#102C2314yes—
312C2×C22⋊C8C2312yes—
313C2×C22⋊C8C2312yes—
314C2×#97C2314yes—
315C2×#97C2312yes—
316C2×#97C2312yes—
317C2×C4×C8C2314yes—
318C25—21no—
319C2×#41—28no—
320C2×#41—48no—
321C22×Q8—21no—
322C22×Q8—21no—
323C22×Q8—28no—
324C22×Q8—24no—
325C22×Q8—44no—
326C22×Q8—84no—
327C22×Q8C2×D412yes—
328C22×Q8C2×D412yes—
329C22×Q8C2×D418yes—
330C22×Q8C2412yes—
331C22×D4—28no—
332C22×D4—22no—
333C22×D4—22no—
334C22×D4—21no—
335C22×D4—21no—
336C22×D4—21no—
337C22×D4C2414yes—
338C22×D4C2412yes—
339C22×D4C2412yes—
340C23×C4—21no—
341C23×C4—21no—
342C23×C4—21no—
343C23×C4—28no—
344C23×C4—24no—
345C23×C4—22no—
346C23×C4—28no—
347C23×C4—28no—
348C23×C4—24no—
349C23×C4—22no—
350C23×C4—22no—
351C23×C4—22no—
352C23×C4—22no—
353C23×C4—48no—
354C23×C4—84no—
355C23×C4—84no—
356C23×C4C2×D411yescharacteristic
357C23×C4C2×D411yescharacteristic
358C23×C4C2×D411yescharacteristic
359C23×C4C2×D411yescharacteristic
360C23×C4C2×D411yescharacteristic
361C23×C4C2×D411yescharacteristic
362C23×C4C2411yescharacteristic
363C2×SD16—216no—
364C2×SD16C24116yes—
365C2×D8—216no—
366C2×D8C24116yes—
367C22×C8C2414yes—
368C22×C8C2414yes—
369C4⋊Q8—216no—
370C4⋊Q8—216no—
371C4⋊Q8—28no—
372C4⋊Q8—22no—
373C4⋊Q8—22no—
374C4⋊Q8—22no—
375C4⋊Q8C2414yes—
376C4⋊Q8C24116yes—
377C4⋊Q8C2414yes—
378C4⋊Q8C2414yes—
379#127—22no—
380#127C2414yes—
381#126—216no—
382#126—216no—
383#126—216no—
384#126—216no—
385#125—216no—
386#125—216no—
387#125—216no—
388#125—28no—
389#125—24no—
390#125—28no—
391#125—28no—
392#125—24no—
393#125—28no—
394#125—24no—
395#125—24no—
396#125C2418yes—
397#125C24116yes—
398#125C2418yes—
399#125C2418yes—
400#125C2418yes—
401#124—216no—
402#124—28no—
403#124—24no—
404#124—24no—
405#124C2418yes—
406#124C2418yes—
407#123—216no—
408#123—216no—
409#123—216no—
410#123—216no—
411C22⋊Q8—232no—
412C22⋊Q8—232no—
413C22⋊Q8—216no—
414C22⋊Q8—216no—
415C22⋊Q8—28no—
416C22⋊Q8—24no—
417C22⋊Q8—232no—
418C22⋊Q8—232no—
419C22⋊Q8—232no—
420C22⋊Q8—232no—
421C22⋊Q8—216no—
422C22⋊Q8—216no—
423C22⋊Q8C2418yes—
424#121—28no—
425#121—24no—
426#121C2418yes—
427C4×Q8—216no—
428C4×Q8—28no—
429C4×Q8—24no—
430C4×Q8—24no—
431C4×Q8—24no—
432C4×Q8C2×D4116yes—
433C4×Q8C2×D418yes—
434C4×Q8C2×D4116yes—
435C4×Q8C2×D418yes—
436C4×Q8C2418yes—
437C4×Q8C2418yes—
438C4×Q8C2418yes—
439C4×Q8C2418yes—
440C4×Q8C2418yes—
441C4×D4—216no—
442C4×D4—216no—
443C4×D4—216no—
444C4×D4—216no—
445C4×D4—216no—
446C4×D4—28no—
447C4×D4—24no—
448C4×D4—28no—
449C4×D4—28no—
450C4×D4—28no—
451C4×D4—24no—
452C4×D4—28no—
453C4×D4—24no—
454C4×D4—24no—
455C4×D4—24no—
456C4×D4C24116yes—
457C4×D4C2418yes—
458C4×D4C24116yes—
459C4×D4C2418yes—
460C4×D4C2418yes—
461C4×D4C2418yes—
462C4×D4C2418yes—
463#117—28no—
464#117—216no—
465#117—216no—
466#117—216no—
467C2×C4⋊C4—28no—
468C2×C4⋊C4—28no—
469C2×C4⋊C4—24no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—28no—
473C2×C4⋊C4—24no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—28no—
478C2×C4⋊C4—28no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—24no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—22no—
491C2×C4⋊C4—22no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—22no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—232no—
498C2×C4⋊C4—232no—
499C2×C4⋊C4—216no—
500C2×C4⋊C4C2×D412yes—
501C2×C4⋊C4C2×D412yes—
502C2×C4⋊C4C2×D418yes—
503C2×C4⋊C4C2×D412yes—
504C2×C4⋊C4C2×D412yes—
505C2×C4⋊C4C2×D418yes—
506C2×C4⋊C4C2×D412yes—
507C2×C4⋊C4C2×D412yes—
508C2×C4⋊C4C2×D418yes—
509C2×C4⋊C4C2412yes—
510C2×C4⋊C4C2414yes—
511C2×C4⋊C4C2412yes—
512C2×C4⋊C4C2412yes—
513C2×C4⋊C4C2414yes—
514C2×C4⋊C4C2414yes—
515C2×C4⋊C4C2412yes—
516C2×C4⋊C4C2412yes—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—28no—
519C2×C22⋊C4—28no—
520C2×C22⋊C4—28no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—22no—
525C2×C22⋊C4—22no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—22no—
530C2×C22⋊C4—22no—
531C2×C22⋊C4—22no—
532C2×C22⋊C4—22no—
533C2×C42—22no—
534C2×C42—22no—
535C2×C42—22no—
536C2×C42C2×D412yes—
537C2×C42C2×D412yes—
538C2×C42C2×D411yescharacteristic
539C2×C42C2×D411yescharacteristic
540C2×C42C2×D414yes—
541C2×C42C2×D414yes—
542C2×C42C2×D414yes—
543C2×C42C2411yescharacteristic
544C2×C42C2412yes—
545C2×C42C2412yes—
546C2×C42C2411yescharacteristic
547C2×C42C2414yes—
548C2×C42C2414yes—
549C2×C42C2414yes—
550#107C24116yes—
551#107C24116yes—
552#107C24116yes—
553#106C24116yes—
554#106C24116yes—
555#106C24116yes—
556C4⋊C8C24116yes—
557C4⋊C8C2418yes—
558C4⋊C8C2418yes—
559C4⋊C8C24116yes—
560#103C24116yes—
561#103C24116yes—
562#103C24116yes—
563#102C24116yes—
564#102C24116yes—
565#102C24116yes—
566#102C24116yes—
567#102C24116yes—
568C22⋊C8C2418yes—
569C22⋊C8C2418yes—
570#97C2418yes—
571#97C24116yes—
572#97C2418yes—
573C4×C8C24116yes—
574C24—28no—
575C24—24no—
576C24—22no—
577C24—22no—
578C24—44no—
579C24—44no—
580C24C22×D411yescharacteristic
581#41—432no—
582C2×Q8—22no—
583C2×Q8—24no—
584C2×Q8—24no—
585C2×Q8—216no—
586C2×Q8—28no—
587C2×Q8—44no—
588C2×Q8—44no—
589C2×Q8—416no—
590C2×Q8—44no—
591C2×Q8—82no—
592C2×Q8—88no—
593C2×Q8—816no—
594C2×Q8C22×D418yes—
595C2×Q8C22×D418yes—
596C2×Q8C2514yes—
597C2×D4—28no—
598C2×D4—216no—
599C2×D4—216no—
600C2×D4—28no—
601C2×D4—24no—
602C2×D4—22no—
603C2×D4—22no—
604C2×D4—24no—
605C2×D4—24no—
606C2×D4—24no—
607C2×D4—28no—
608C2×D4—44no—
609C2×D4—48no—
610C2×D4—82no—
611C2×D42−1+418yes—
612C2×D4C2514yes—
613C2×D4C2514yes—
614C22×C4—24no—
615C22×C4—24no—
616C22×C4—24no—
617C22×C4—24no—
618C22×C4—24no—
619C22×C4—24no—
620C22×C4—24no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—216no—
628C22×C4—28no—
629C22×C4—216no—
630C22×C4—28no—
631C22×C4—28no—
632C22×C4—28no—
633C22×C4—28no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—432no—
638C22×C4—416no—
639C22×C4—48no—
640C22×C4—44no—
641C22×C4—44no—
642C22×C4—44no—
643C22×C4—84no—
644C22×C4—84no—
645C22×C4—88no—
646C22×C4—84no—
647C22×C4—84no—
648C22×C4—816no—
649C22×C4—816no—
650C22×C4C22×D412yes—
651C22×C4C22×D414yes—
652C22×C4C22×D414yes—
653C22×C4C22×D414yes—
654C22×C4C22×D411yescharacteristic
655C22×C4C22×D412yes—
656C22×C4C22×D412yes—
657C22×C4C22×D411yescharacteristic
658C22×C4C22×D412yes—
659C22×C4C22×D412yes—
660C22×C4C22×D411yescharacteristic
661C22×C4C22×D411yescharacteristic
662C22×C4C22×D411yescharacteristic
663C22×C4C22×D414yes—
664C22×C4C22×D414yes—
665C22×C4C22×D414yes—
666C22×C4C2512yes—
667C22×C4C2511yescharacteristic
668SD16—232no—
669D8—232no—
670C2×C8—28no—
671C2×C8—28no—
672C2×C8C2518yes—
673C2×C8C2518yes—
674C4⋊C4—216no—
675C4⋊C4—28no—
676C4⋊C4—28no—
677C4⋊C4—216no—
678C4⋊C4—24no—
679C4⋊C4—28no—
680C4⋊C4—28no—
681C4⋊C4—28no—
682C4⋊C4—216no—
683C4⋊C4—28no—
684C4⋊C4—24no—
685C4⋊C4—22no—
686C4⋊C4—24no—
687C4⋊C4—24no—
688C4⋊C4—22no—
689C4⋊C4—22no—
690C4⋊C4—24no—
691C4⋊C4—28no—
692C4⋊C4—28no—
693C4⋊C4—28no—
694C4⋊C4—24no—
695C4⋊C4—24no—
696C4⋊C4—28no—
697C4⋊C4—28no—
698C4⋊C4—28no—
699C4⋊C4—22no—
700C4⋊C4—22no—
701C4⋊C4C22×D418yes—
702C4⋊C4C22×D418yes—
703C4⋊C4C22×D418yes—
704C4⋊C4C22×D418yes—
705C4⋊C4C22×D418yes—
706C4⋊C4C22×D418yes—
707C4⋊C4C2514yes—
708C4⋊C4C2514yes—
709C4⋊C4C2514yes—
710C4⋊C4C2514yes—
711C4⋊C4C2514yes—
712C22⋊C4—28no—
713C22⋊C4—216no—
714C22⋊C4—28no—
715C22⋊C4—216no—
716C22⋊C4—28no—
717C22⋊C4—28no—
718C22⋊C4—28no—
719C22⋊C4—28no—
720C22⋊C4—28no—
721C22⋊C4—28no—
722C22⋊C4—28no—
723C22⋊C4—28no—
724C22⋊C4—28no—
725C42—28no—
726C42—28no—
727C42—28no—
728C42C22×D418yes—
729C42C22×D418yes—
730C42C22×D414yes—
731C42C22×D412yes—
732C42C22×D414yes—
733C42C22×D414yes—
734C42C22×D414yes—
735C42C22×D412yes—
736C42C2514yes—
737C42C2512yes—
738C42C2514yes—
739C42C2512yes—
740C23—22no—
741C23—22no—
742C23—216no—
743C23—24no—
744C23—28no—
745C23—24no—
746C23—48no—
747C23—432no—
748C23—44no—
749C23—48no—
750C23—44no—
751C23—44no—
752C23—44no—
753C23—44no—
754C23#57514yes—
755C23C23×D412yes—
756C23C23×D411yescharacteristic
757Q8—28no—
758Q8—48no—
759Q8—48no—
760Q8—48no—
761Q8—44no—
762Q8—84no—
763Q8—816no—
764D4—216no—
765D4—24no—
766D4—28no—
767D4—28no—
768D4—48no—
769D4—416no—
770D4—44no—
771D4—84no—
772D4C2×2−1+418yes—
773C2×C4—24no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—24no—
777C2×C4—22no—
778C2×C4—28no—
779C2×C4—24no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—28no—
783C2×C4—24no—
784C2×C4—28no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—432no—
797C2×C4—416no—
798C2×C4—48no—
799C2×C4—48no—
800C2×C4—44no—
801C2×C4—44no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—48no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—88no—
808C2×C4—88no—
809C2×C4—816no—
810C2×C4—88no—
811C2×C4—88no—
812C2×C4C23×D412yes—
813C2×C4C23×D414yes—
814C2×C4C23×D414yes—
815C2×C4C23×D412yes—
816C2×C4C23×D414yes—
817C2×C4C23×D414yes—
818C2×C4C23×D412yes—
819C2×C4C23×D412yes—
820C2×C4C23×D412yes—
821C2×C4C23×D411yescharacteristic
822C2×C4C2×2−1+414yes—
823C2×C4C2611yescharacteristic
824C8—28no—
825C8—28no—
826C22—22no—
827C22—22no—
828C22—28no—
829C22—28no—
830C22—432no—
831C22—44no—
832C22—44no—
833C22—416no—
834C22—44no—
835C22—44no—
836C22—44no—
837C22—88no—
838C22#348612yes—
839C22C2×#57514yes—
840C22C2×#57512yes—
841C22#358512yes—
842C22C24×D411yescharacteristic
843C4—22no—
844C4—24no—
845C4—22no—
846C4—22no—
847C4—24no—
848C4—24no—
849C4—22no—
850C4—22no—
851C4—24no—
852C4—44no—
853C4—44no—
854C4—44no—
855C4—44no—
856C4—44no—
857C4—44no—
858C4#348612yes—
859C4C22×2−1+412yes—
860C2—24no—
861C2—48no—
862C2—84no—
863C2#6183114yesdirect product factor
864C2C2×#348611yescharacteristic
865C2C22×#57511yescharacteristic
866C2C2×#358511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC2×C4C26
prime radicalC2×#3109C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×Q8 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3507C2semidirect
2. C22×#554C2semidirect
3. #61831C2direct (N × H)
4. C2×#3389C2semidirect
5. C2×#3388C2semidirect
6. C2×#3376C2semidirect
7. C2×#3370C2semidirect
8. C2×#3239C2semidirect
9. C2×#3236C2semidirect
10. C2×#3234C2semidirect
11. C2×#3232C2semidirect
12. C2×#3110C2semidirect
14. C2×#3114C2semidirect
15. C2×#3105C2semidirect
16. C2×#2983C2semidirect
18. #3507C22semidirect
19. C2×#559C22semidirect
20. C2×#557C22semidirect
22. C2×#556C22semidirect
28. C2×#554C22semidirect
29. C2×#554C22semidirect
50. #3389C22semidirect
51. #3388C22semidirect
52. #3376C22semidirect
53. #3370C22semidirect
54. #3239C22semidirect
55. #3236C22semidirect
56. #3234C22semidirect
57. #3232C22semidirect
58. C2×#501C22semidirect
59. C2×#501C22semidirect
60. C2×#501C22semidirect
61. C2×#499C22semidirect
62. C2×#491C22semidirect
63. C2×#490C22semidirect
64. C2×#489C22semidirect
65. C2×#488C22semidirect
66. #3114C22semidirect
67. #3110C22semidirect
69. #3105C22semidirect
76. C2×#479C22semidirect
77. C2×#479C22semidirect
78. C2×#475C22semidirect
81. C2×#478C22semidirect
82. C2×#478C22semidirect
85. C2×#474C22semidirect
92. #2983C22semidirect
93. C2×#446C22semidirect
94. C2×#446C22semidirect
115. #559C23semidirect
117. #557C23semidirect
120. #556C23semidirect
128. #554C23semidirect
252. #501C23semidirect
253. #501C23semidirect
254. #501C23semidirect
255. #499C23semidirect
256. #491C23semidirect
257. #490C23semidirect
258. #489C23semidirect
259. #488C23semidirect
266. #479C23semidirect
267. #479C23semidirect
270. #478C23semidirect
271. #478C23semidirect
273. #475C23semidirect
275. #474C23semidirect
282. #446C23semidirect
283. #446C23semidirect
863. C2#61831direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#35072
C22×#5542
#618312
C2×#33892
C2×#33882
C2×#33762
C2×#33702
C2×#32392
C2×#32362
C2×#32342
C2×#32322
C2×#31102
C2×#31092
C2×#31142
C2×#31052
C2×#29832