Finite Group Databasebeta

← C2×#62953 #10586297

Subgroups — C2×#62953 #10586297

Order 512.

31314 conjugacy classes of subgroups.

The subgroup lattice has 1280 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62953C2164yesmaximal, direct product factor
2C2×#3509C213yesmaximal, complemented
3C2×#3503C211yesmaximal, characteristic, complemented
4C2×#3524C212yesmaximal, complemented
5C2×#3518C212yesmaximal, complemented
6C2×#3518C211yesmaximal, characteristic, complemented
7C2×#3518C213yesmaximal, complemented
8C2×#3523C211yesmaximal, characteristic, complemented
9C2×#3523C213yesmaximal, complemented
10C2×#3516C212yesmaximal, complemented
11C2×#3502C212yesmaximal, complemented
12C2×#3502C211yesmaximal, characteristic, complemented
13C2×#3550C213yesmaximal, complemented
14C2×#3555C213yesmaximal, complemented
15C2×#3555C216yesmaximal, complemented
16C2×#3547C213yesmaximal, complemented
17C2×#3552C213yesmaximal, complemented
18C2×#3565C216yesmaximal, complemented
19C2×#3565C216yesmaximal, complemented
20C2×#3557C216yesmaximal, complemented
21C2×#3482C211yesmaximal, characteristic, complemented
22C2×Q8×#41C211yesmaximal, characteristic, complemented
23C2×#3480C211yesmaximal, characteristic, complemented
24C2×#3461C213yesmaximal, complemented
25#3565C221192yescomplemented
26#3565C221192yescomplemented
27#3557C221192yescomplemented
28#3555C221192yescomplemented
29#3555C22196yescomplemented
30#3552C22196yescomplemented
31#3550C22196yescomplemented
32#3547C22196yescomplemented
33C2×#563C22112yes—
34C2×#563C22112yes—
35C2×#563C22112yes—
36C2×#562C22112yes—
37#3524C22164yescomplemented
38#3523C22196yescomplemented
39#3523C22132yescomplemented
40#3518C22196yescomplemented
41#3518C22164yescomplemented
42#3518C22132yescomplemented
43#3516C22164yescomplemented
44#3509C22196yescomplemented
45#3503C22132yescomplemented
46#3502C22132yescomplemented
47#3502C22164yescomplemented
48#3482C22132yescomplemented
49#3480C22132yescomplemented
50C2×#559C2213yes—
51C2×#559C2216yes—
52Q8×#41C22132yescomplemented
53C2×Q82C2216yes—
54C2×Q82C2213yes—
55C2×Q82C2212yes—
56C2×Q82C2211yescharacteristic
57C2×#557C2216yes—
58C2×#557C2216yes—
59C2×#557C2216yes—
60C2×#557C2216yes—
61C2×#557C2213yes—
62C2×#557C2216yes—
63C2×#557C2213yes—
64C2×#557C2212yes—
65C2×#557C2211yescharacteristic
66C2×#557C2212yes—
67C2×#557C2211yescharacteristic
68C2×#557C2211yescharacteristic
69C2×#556C2216yes—
70C2×#556C2216yes—
71C2×#556C2216yes—
72C2×#556C22112yes—
73C2×#556C2216yes—
74C2×#556C2216yes—
75C2×#556C2213yes—
76C2×#556C2213yes—
77C2×#556C2216yes—
78C2×#556C2213yes—
79C2×#556C2216yes—
80C2×#556C2213yes—
81C2×#555C2216yes—
82C2×#555C2216yes—
83C2×#555C2213yes—
84C2×#554C2216yes—
85C2×#554C2216yes—
86C2×#554C2216yes—
87C2×#554C2213yes—
88C2×#553C2213yes—
89C2×#553C2213yes—
90C2×#553C2216yes—
91C2×#553C2216yes—
92C2×#552C2216yes—
93C2×#552C22112yes—
94C2×#552C2216yes—
95C2×#552C2216yes—
96C2×#552C2216yes—
97C2×#552C2216yes—
98C2×#552C2216yes—
99C2×#552C2216yes—
100C2×#550C2211yescharacteristic
101C2×D4×Q8C2216yes—
102C2×D4×Q8C2213yes—
103C2×D4×Q8C2213yes—
104C2×D4×Q8C2213yes—
105C2×D4×Q8C2212yes—
106C2×D4×Q8C2211yescharacteristic
107C2×#548C2216yes—
108C2×#548C2211yescharacteristic
109C2×#548C2212yes—
110C2×#548C2211yescharacteristic
111C2×#548C2212yes—
112C2×#547C2213yes—
113#3461C22196yescomplemented
114C2×#544C2216yes—
115C2×#544C2216yes—
116C2×#544C2216yes—
117C2×#544C2216yes—
118C2×#544C2213yes—
119C2×#542C2216yes—
120C2×#542C22112yes—
121C2×#542C2216yes—
122C2×#542C22112yes—
123C2×#542C22112yes—
124C2×#542C2216yes—
125C2×#542C2216yes—
126C2×#542C2216yes—
127C2×#542C2216yes—
128C2×#542C2213yes—
129C2×#542C2211yescharacteristic
130C2×#541C2216yes—
131C2×#541C22112yes—
132C2×#541C22112yes—
133C2×#541C2216yes—
134C2×#541C2216yes—
135C2×#541C2216yes—
136C2×#541C2213yes—
137C2×#541C2213yes—
138C2×#540C2216yes—
139C2×#539C2216yes—
140C2×#539C22112yes—
141C2×#539C2216yes—
142C2×#537C2213yes—
143C2×#536C2213yes—
144C2×#536C2216yes—
145C2×#536C2213yes—
146C2×#533C2216yes—
147C2×#533C2216yes—
148C2×#533C2216yes—
149C2×#533C2213yes—
150C2×#533C2216yes—
151C2×#533C2213yes—
152C2×#533C2213yes—
153C2×#533C2213yes—
154C2×#533C2213yes—
155C2×#533C2213yes—
156C2×#533C2213yes—
157C2×#532C2213yes—
158C22×C4⋊Q8C2213yes—
159C2×#529C2216yes—
160C2×#529C2216yes—
161C2×#529C2216yes—
162C2×#529C2216yes—
163C2×#529C2216yes—
164C2×#529C2213yes—
165C2×#529C2213yes—
166C2×#529C2213yes—
167C2×#529C2216yes—
168C2×#529C2213yes—
169C2×#520C2212yes—
170C2×#519C2212yes—
171C2×#519C2212yes—
172C2×#519C2212yes—
173C2×#519C2216yes—
174C2×C4×#41C2212yes—
175C2×C4×#41C2211yescharacteristic
176C2×C4×#41C2213yes—
177C2×C4×#41C2213yes—
178C2×C4×#41C2211yescharacteristic
179C22×C4×Q8C2212yes—
180C22×C4×Q8C2211yescharacteristic
181C22×C4×Q8C2213yes—
182C22×#41C2311yescharacteristic
183C22×#41C2311yescharacteristic
184C22×#41C2313yes—
185C22×#41C2313yes—
186C23×Q8C2312yes—
187C23×Q8C2311yescharacteristic
188C23×Q8C2313yes—
189C23×Q8C2316yes—
190#563C231192yes—
191#563C231192yes—
192#563C231192yes—
193#562C231192yes—
194#559C23148yes—
195#559C23196yes—
196Q82C23116yes—
197Q82C23132yes—
198Q82C23148yes—
199Q82C23196yes—
200#557C23132yes—
201#557C23116yes—
202#557C23116yes—
203#557C23116yes—
204#557C23132yes—
205#557C23196yes—
206#557C23148yes—
207#557C23196yes—
208#557C23196yes—
209#557C23196yes—
210#557C23196yes—
211#557C23148yes—
212#556C23148yes—
213#556C23148yes—
214#556C23196yes—
215#556C23196yes—
216#556C23196yes—
217#556C23196yes—
218#556C23148yes—
219#556C23148yes—
220#556C23196yes—
221#556C23196yes—
222#556C231192yes—
223#556C23196yes—
224#555C23148yes—
225#555C23196yes—
226#555C23196yes—
227#554C23148yes—
228#554C23196yes—
229#554C23196yes—
230#554C23196yes—
231#553C23148yes—
232#553C23148yes—
233#553C23196yes—
234#553C23196yes—
235#552C23196yes—
236#552C23196yes—
237#552C23196yes—
238#552C23196yes—
239#552C23196yes—
240#552C23196yes—
241#552C231192yes—
242#552C23196yes—
243#550C23116yes—
244D4×Q8C23148yes—
245D4×Q8C23116yes—
246D4×Q8C23148yes—
247D4×Q8C23148yes—
248D4×Q8C23132yes—
249D4×Q8C23196yes—
250#548C23116yes—
251#548C23116yes—
252#548C23132yes—
253#548C23132yes—
254#548C23196yes—
255#547C23148yes—
256#544C23148yes—
257#544C23196yes—
258#544C23196yes—
259#544C23196yes—
260#544C23196yes—
261#542C23116yes—
262#542C23148yes—
263#542C23196yes—
264#542C23196yes—
265#542C23196yes—
266#542C23196yes—
267#542C23196yes—
268#542C231192yes—
269#542C23196yes—
270#542C231192yes—
271#542C231192yes—
272#541C23148yes—
273#541C23148yes—
274#541C23196yes—
275#541C23196yes—
276#541C23196yes—
277#541C23196yes—
278#541C231192yes—
279#541C231192yes—
280#540C23196yes—
281#539C23196yes—
282#539C23196yes—
283#539C231192yes—
284#537C23148yes—
285#536C23148yes—
286#536C23148yes—
287#536C23196yes—
288#533C23148yes—
289#533C23196yes—
290#533C23148yes—
291#533C23148yes—
292#533C23196yes—
293#533C23148yes—
294#533C23148yes—
295#533C23196yes—
296#533C23148yes—
297#533C23148yes—
298#533C23196yes—
299#532C23148yes—
300C2×C4⋊Q8C2313yes—
301C2×C4⋊Q8C2313yes—
302C2×C4⋊Q8C2313yes—
303C2×C4⋊Q8C2316yes—
304C2×C4⋊Q8C2316yes—
305C2×C4⋊Q8C23148yes—
306C2×C4⋊Q8C2313yes—
307C2×C4⋊Q8C2311yescharacteristic
308C2×C4⋊Q8C2313yes—
309C2×C4⋊Q8C2313yes—
310C2×C4⋊Q8C2313yes—
311C2×C4⋊Q8C2316yes—
312C2×C4⋊Q8C2316yes—
313C2×C4⋊Q8C2316yes—
314C2×C4⋊Q8C2316yes—
315C2×C4⋊Q8C2316yes—
316C2×C4⋊Q8C2316yes—
317C2×C4⋊Q8C2313yes—
318C2×C4⋊Q8C2316yes—
319C2×C4⋊Q8C2316yes—
320C2×C4⋊Q8C23112yes—
321C2×C4⋊Q8C23112yes—
322C2×C4⋊Q8C23112yes—
323C2×#127C2313yes—
324#529C23196yes—
325#529C23148yes—
326#529C23196yes—
327#529C23148yes—
328#529C23196yes—
329#529C23148yes—
330#529C23148yes—
331#529C23196yes—
332#529C23196yes—
333#529C23196yes—
334C2×#126C2316yes—
335C2×#126C2312yes—
336C2×#126C2316yes—
337C2×#126C2316yes—
338C2×#126C2316yes—
339C2×#126C2316yes—
340C2×#126C2316yes—
341C2×#126C2316yes—
342C2×#126C2316yes—
343C2×#126C23112yes—
344C2×#126C2316yes—
345C2×#126C23112yes—
346C2×#126C23112yes—
347C2×#126C23112yes—
348C2×#126C23112yes—
349C2×#126C23112yes—
350C2×#126C23112yes—
351C2×#126C23112yes—
352C2×#125C2316yes—
353C2×#125C2313yes—
354C2×#125C2316yes—
355C2×#125C2313yes—
356C2×#125C2316yes—
357C2×#125C2316yes—
358C2×#125C2313yes—
359C2×#125C2316yes—
360C2×#125C2313yes—
361C2×#125C2316yes—
362C2×#125C2316yes—
363C2×#125C2316yes—
364C2×#125C2316yes—
365C2×#125C2316yes—
366C2×#125C2316yes—
367C2×#125C2316yes—
368C2×#125C2316yes—
369C2×#125C2316yes—
370C2×#125C2316yes—
371C2×#125C23112yes—
372C2×#125C23112yes—
373C2×#125C23112yes—
374C2×#125C23112yes—
375C2×#125C23112yes—
376C2×#124C2311yescharacteristic
377C2×#124C2312yes—
378C2×#124C2313yes—
379C2×#124C2316yes—
380C2×#124C2313yes—
381C2×#124C2316yes—
382C2×#124C2316yes—
383C2×#124C2313yes—
384C2×#124C2316yes—
385C2×#124C2316yes—
386C2×#124C23112yes—
387C2×#124C23112yes—
388C2×#124C23112yes—
389C2×#124C23112yes—
390C2×#123C2312yes—
391C2×#123C2316yes—
392C2×#123C2316yes—
393C2×#123C2316yes—
394C2×#123C2316yes—
395C2×#123C2316yes—
396C2×#123C2316yes—
397C2×#123C2316yes—
398C2×#123C23112yes—
399C2×#123C2316yes—
400C2×#123C23112yes—
401C2×#123C2316yes—
402C2×#123C23112yes—
403C2×#123C23112yes—
404C2×C22⋊Q8C2313yes—
405C2×C22⋊Q8C2316yes—
406C2×C22⋊Q8C2313yes—
407C2×C22⋊Q8C2313yes—
408C2×C22⋊Q8C2316yes—
409C2×C22⋊Q8C2316yes—
410C2×C22⋊Q8C2316yes—
411C2×C22⋊Q8C2313yes—
412C2×C22⋊Q8C2316yes—
413C2×C22⋊Q8C2316yes—
414C2×C22⋊Q8C2311yescharacteristic
415C2×C22⋊Q8C2313yes—
416C2×C22⋊Q8C2312yes—
417C2×C22⋊Q8C2316yes—
418C2×C22⋊Q8C2316yes—
419C2×C22⋊Q8C2316yes—
420C2×C22⋊Q8C2316yes—
421C2×C22⋊Q8C2313yes—
422C2×C22⋊Q8C2316yes—
423C2×C22⋊Q8C2313yes—
424C2×C22⋊Q8C2316yes—
425C2×C22⋊Q8C23112yes—
426C2×C22⋊Q8C2316yes—
427C2×C22⋊Q8C2316yes—
428C2×C22⋊Q8C23112yes—
429C2×C22⋊Q8C2316yes—
430C2×C22⋊Q8C23112yes—
431C2×C22⋊Q8C2316yes—
432C2×C22⋊Q8C2316yes—
433C2×C22⋊Q8C23112yes—
434C2×C22⋊Q8C2316yes—
435C2×C22⋊Q8C23112yes—
436C2×C22⋊Q8C23112yes—
437C2×C22⋊Q8C23112yes—
438C2×#121C2311yescharacteristic
439C2×#121C2313yes—
440C2×#121C2316yes—
441C2×#121C2316yes—
442C2×#121C2313yes—
443C2×#121C2316yes—
444C2×#121C2316yes—
445C2×#121C2316yes—
446C2×#121C2313yes—
447C2×#121C2313yes—
448C2×#121C2313yes—
449C2×#121C2316yes—
450C2×#121C23112yes—
451#520C23132yes—
452#519C23132yes—
453#519C23132yes—
454#519C23132yes—
455#519C23196yes—
456C4×#41C23148yes—
457C4×#41C23148yes—
458C4×#41C23116yes—
459C4×#41C23132yes—
460C4×#41C23116yes—
461C2×C4×Q8C2311yescharacteristic
462C2×C4×Q8C2311yescharacteristic
463C2×C4×Q8C2311yescharacteristic
464C2×C4×Q8C2313yes—
465C2×C4×Q8C2311yescharacteristic
466C2×C4×Q8C2312yes—
467C2×C4×Q8C2313yes—
468C2×C4×Q8C2313yes—
469C2×C4×Q8C2313yes—
470C2×C4×Q8C2316yes—
471C2×C4×Q8C2316yes—
472C2×C4×Q8C2316yes—
473C2×C4×Q8C2313yes—
474C2×C4×Q8C2316yes—
475C2×C4×Q8C23148yes—
476C2×C4×Q8C23116yes—
477C2×C4×Q8C23132yes—
478C2×C4×Q8C2313yes—
479C2×C4×Q8C2312yes—
480C2×C4×Q8C2311yescharacteristic
481C2×C4×Q8C2312yes—
482C2×C4×Q8C2313yes—
483C2×C4×Q8C2313yes—
484C2×C4×Q8C2313yes—
485C2×C4×Q8C2316yes—
486C2×C4×Q8C2316yes—
487C2×C4×Q8C2316yes—
488C2×C4×Q8C2316yes—
489C2×C4×Q8C2316yes—
490C2×C4×Q8C23112yes—
491C2×C4×Q8C23112yes—
492C2×C4×Q8C2316yes—
493C2×C4×Q8C2316yes—
494C2×C4×Q8C2316yes—
495C2×C4×Q8C2316yes—
496C2×C4×Q8C2316yes—
497C2×C4×Q8C2316yes—
498C2×C4×Q8C2316yes—
499C2×C4×Q8C23112yes—
500C2×C4×Q8C2316yes—
501C2×C4×D4C2311yescharacteristic
502C2×C4×D4C2316yes—
503C2×C4×D4C2313yes—
504C2×C4×D4C2313yes—
505C2×C4×D4C2316yes—
506C2×C4×D4C2313yes—
507C2×C4×D4C2313yes—
508C2×C4×D4C2313yes—
509C2×C4×D4C2313yes—
510C2×C4×D4C2313yes—
511C2×C4×D4C2313yes—
512C2×C4×D4C2313yes—
513C2×C4×D4C2316yes—
514C2×C4×D4C2316yes—
515C2×C4×D4C2313yes—
516C2×C4×D4C2313yes—
517C2×C4×D4C2316yes—
518C2×C4×D4C2316yes—
519C2×C4×D4C2316yes—
520C2×C4×D4C2316yes—
521C2×C4×D4C2316yes—
522C2×C4×D4C23112yes—
523C2×C4×D4C23112yes—
524C2×#117C2311yescharacteristic
525C2×#117C2313yes—
526C2×#117C2313yes—
527C2×#117C2313yes—
528C2×#117C2316yes—
529C2×#117C2313yes—
530C2×#117C2316yes—
531C2×#117C2313yes—
532C2×#117C2316yes—
533C2×#117C2316yes—
534C2×#117C2316yes—
535C2×#117C23112yes—
536C2×#117C23112yes—
537C2×#117C2316yes—
538C2×#117C2316yes—
539C2×#117C2316yes—
540C2×#117C2316yes—
541C2×#117C2316yes—
542C2×#117C2316yes—
543C2×#117C23112yes—
544C2×#117C2316yes—
545C22×C4⋊C4C2313yes—
546C22×C4⋊C4C2316yes—
547C22×C4⋊C4C2316yes—
548C22×C4⋊C4C2313yes—
549C22×C4⋊C4C2316yes—
550C22×C4⋊C4C2316yes—
551C22×C42C2313yes—
552C22×C42C2316yes—
553C22×C42C2316yes—
554C22×C42C2313yes—
555C22×C42C2313yes—
556C2×#41—28no—
557C2×#41—28no—
558C2×#41—412no—
559C2×#41—412no—
560C2×#41C2418yes—
561C2×#41C2418yes—
562C2×#41C24124yes—
563C2×#41C24124yes—
564C22×Q8—216no—
565C22×Q8—28no—
566C22×Q8—424no—
567C22×Q8—412no—
568C22×Q8C2413yes—
569C22×Q8C2416yes—
570C22×Q8C2411yescharacteristic
571C22×Q8C2413yes—
572C22×Q8C2413yes—
573C22×Q8C2418yes—
574C22×Q8C24116yes—
575C22×Q8C2412yes—
576C22×Q8C2416yes—
577C22×Q8C2416yes—
578C22×Q8C2416yes—
579C22×Q8C24112yes—
580C22×Q8C2413yes—
581C22×Q8C24124yes—
582C22×Q8C24148yes—
583C22×Q8C2411yescharacteristic
584C22×D4C2413yes—
585C22×D4C2413yes—
586C22×D4C2411yescharacteristic
587C22×D4C2412yes—
588C22×D4C2416yes—
589C22×D4C2416yes—
590C22×D4C2416yes—
591C22×D4C2413yes—
592C22×D4C2413yes—
593C22×D4C2413yes—
594C23×C4C2413yes—
595C23×C4C2416yes—
596C23×C4C2413yes—
597C23×C4C2413yes—
598C23×C4C2413yes—
599C23×C4C2413yes—
600C23×C4C2411yescharacteristic
601C23×C4C2413yes—
602C23×C4C24112yes—
603C23×C4C2416yes—
604C23×C4C2413yes—
605C23×C4C2416yes—
606C23×C4C2413yes—
607C23×C4C2416yes—
608C23×C4C2412yes—
609C4⋊Q8C24124yes—
610C4⋊Q8C24124yes—
611C4⋊Q8C24124yes—
612C4⋊Q8C24148yes—
613C4⋊Q8C24148yes—
614C4⋊Q8C24124yes—
615C4⋊Q8C2418yes—
616C4⋊Q8C24124yes—
617C4⋊Q8C24124yes—
618C4⋊Q8C24124yes—
619C4⋊Q8C24148yes—
620C4⋊Q8C24148yes—
621C4⋊Q8C24148yes—
622C4⋊Q8C24148yes—
623C4⋊Q8C24148yes—
624C4⋊Q8C24148yes—
625C4⋊Q8C24124yes—
626C4⋊Q8C24148yes—
627C4⋊Q8C24148yes—
628C4⋊Q8C24196yes—
629C4⋊Q8C24196yes—
630C4⋊Q8C24196yes—
631#127C24124yes—
632#126C24148yes—
633#126C24116yes—
634#126C24148yes—
635#126C24148yes—
636#126C24148yes—
637#126C24148yes—
638#126C24148yes—
639#126C24148yes—
640#126C24148yes—
641#126C24196yes—
642#126C24148yes—
643#126C24196yes—
644#126C24196yes—
645#126C24196yes—
646#126C24196yes—
647#126C24196yes—
648#126C24196yes—
649#126C24196yes—
650#125C24148yes—
651#125C24124yes—
652#125C24148yes—
653#125C24124yes—
654#125C24148yes—
655#125C24148yes—
656#125C24124yes—
657#125C24148yes—
658#125C24124yes—
659#125C24148yes—
660#125C24148yes—
661#125C24148yes—
662#125C24148yes—
663#125C24148yes—
664#125C24148yes—
665#125C24148yes—
666#125C24148yes—
667#125C24148yes—
668#125C24148yes—
669#125C24196yes—
670#125C24196yes—
671#125C24196yes—
672#125C24196yes—
673#125C24196yes—
674#124C2418yes—
675#124C24116yes—
676#124C24124yes—
677#124C24148yes—
678#124C24124yes—
679#124C24148yes—
680#124C24148yes—
681#124C24124yes—
682#124C24148yes—
683#124C24148yes—
684#124C24196yes—
685#124C24196yes—
686#124C24196yes—
687#124C24196yes—
688#123C24116yes—
689#123C24148yes—
690#123C24148yes—
691#123C24148yes—
692#123C24148yes—
693#123C24148yes—
694#123C24148yes—
695#123C24148yes—
696#123C24196yes—
697#123C24148yes—
698#123C24196yes—
699#123C24148yes—
700#123C24196yes—
701#123C24196yes—
702C22⋊Q8C24124yes—
703C22⋊Q8C24148yes—
704C22⋊Q8C24124yes—
705C22⋊Q8C24124yes—
706C22⋊Q8C24148yes—
707C22⋊Q8C24148yes—
708C22⋊Q8C24148yes—
709C22⋊Q8C24124yes—
710C22⋊Q8C24148yes—
711C22⋊Q8C24148yes—
712C22⋊Q8C2418yes—
713C22⋊Q8C24124yes—
714C22⋊Q8C24116yes—
715C22⋊Q8C24148yes—
716C22⋊Q8C24148yes—
717C22⋊Q8C24148yes—
718C22⋊Q8C24148yes—
719C22⋊Q8C24124yes—
720C22⋊Q8C24148yes—
721C22⋊Q8C24124yes—
722C22⋊Q8C24148yes—
723C22⋊Q8C24196yes—
724C22⋊Q8C24148yes—
725C22⋊Q8C24148yes—
726C22⋊Q8C24196yes—
727C22⋊Q8C24148yes—
728C22⋊Q8C24196yes—
729C22⋊Q8C24148yes—
730C22⋊Q8C24148yes—
731C22⋊Q8C24196yes—
732C22⋊Q8C24148yes—
733C22⋊Q8C24196yes—
734C22⋊Q8C24196yes—
735C22⋊Q8C24196yes—
736#121C2418yes—
737#121C24124yes—
738#121C24148yes—
739#121C24148yes—
740#121C24124yes—
741#121C24148yes—
742#121C24148yes—
743#121C24148yes—
744#121C24124yes—
745#121C24124yes—
746#121C24124yes—
747#121C24148yes—
748#121C24196yes—
749C4×Q8C2418yes—
750C4×Q8C2418yes—
751C4×Q8C2418yes—
752C4×Q8C24124yes—
753C4×Q8C2418yes—
754C4×Q8C24116yes—
755C4×Q8C24124yes—
756C4×Q8C24124yes—
757C4×Q8C24124yes—
758C4×Q8C24148yes—
759C4×Q8C24148yes—
760C4×Q8C24148yes—
761C4×Q8C24124yes—
762C4×Q8C24148yes—
763C4×Q8C24124yes—
764C4×Q8C24116yes—
765C4×Q8C2418yes—
766C4×Q8C24116yes—
767C4×Q8C24124yes—
768C4×Q8C24124yes—
769C4×Q8C24124yes—
770C4×Q8C24148yes—
771C4×Q8C24148yes—
772C4×Q8C24148yes—
773C4×Q8C24148yes—
774C4×Q8C24148yes—
775C4×Q8C24196yes—
776C4×Q8C24196yes—
777C4×Q8C24148yes—
778C4×Q8C24148yes—
779C4×Q8C24148yes—
780C4×Q8C24148yes—
781C4×Q8C24148yes—
782C4×Q8C24148yes—
783C4×Q8C24148yes—
784C4×Q8C24196yes—
785C4×Q8C24148yes—
786C4×D4C2418yes—
787C4×D4C24148yes—
788C4×D4C24124yes—
789C4×D4C24124yes—
790C4×D4C24148yes—
791C4×D4C24124yes—
792C4×D4C24124yes—
793C4×D4C24124yes—
794C4×D4C24124yes—
795C4×D4C24124yes—
796C4×D4C24124yes—
797C4×D4C24124yes—
798C4×D4C24148yes—
799C4×D4C24148yes—
800C4×D4C24124yes—
801C4×D4C24124yes—
802C4×D4C24148yes—
803C4×D4C24148yes—
804C4×D4C24148yes—
805C4×D4C24148yes—
806C4×D4C24148yes—
807C4×D4C24196yes—
808C4×D4C24196yes—
809#117C2418yes—
810#117C24124yes—
811#117C24124yes—
812#117C24124yes—
813#117C24148yes—
814#117C24124yes—
815#117C24148yes—
816#117C24124yes—
817#117C24148yes—
818#117C24148yes—
819#117C24148yes—
820#117C24196yes—
821#117C24196yes—
822#117C24148yes—
823#117C24148yes—
824#117C24148yes—
825#117C24148yes—
826#117C24148yes—
827#117C24148yes—
828#117C24196yes—
829#117C24148yes—
830C2×C4⋊C4C2411yescharacteristic
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2413yes—
833C2×C4⋊C4C2416yes—
834C2×C4⋊C4C2416yes—
835C2×C4⋊C4C2416yes—
836C2×C4⋊C4C2413yes—
837C2×C4⋊C4C2416yes—
838C2×C4⋊C4C2413yes—
839C2×C4⋊C4C2413yes—
840C2×C4⋊C4C2416yes—
841C2×C4⋊C4C2416yes—
842C2×C4⋊C4C2416yes—
843C2×C4⋊C4C2416yes—
844C2×C4⋊C4C2416yes—
845C2×C4⋊C4C2416yes—
846C2×C4⋊C4C24112yes—
847C2×C4⋊C4C2416yes—
848C2×C4⋊C4C24124yes—
849C2×C4⋊C4C24148yes—
850C2×C4⋊C4C24148yes—
851C2×C4⋊C4C24124yes—
852C2×C4⋊C4C24148yes—
853C2×C4⋊C4C24148yes—
854C2×C4⋊C4C2416yes—
855C2×C4⋊C4C2413yes—
856C2×C4⋊C4C2413yes—
857C2×C4⋊C4C2411yescharacteristic
858C2×C4⋊C4C2416yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2416yes—
861C2×C4⋊C4C2416yes—
862C2×C4⋊C4C2416yes—
863C2×C4⋊C4C2411yescharacteristic
864C2×C4⋊C4C2411yescharacteristic
865C2×C4⋊C4C2413yes—
866C2×C4⋊C4C2413yes—
867C2×C4⋊C4C2413yes—
868C2×C4⋊C4C2416yes—
869C2×C4⋊C4C2413yes—
870C2×C4⋊C4C24112yes—
871C2×C4⋊C4C2416yes—
872C2×C4⋊C4C24112yes—
873C2×C4⋊C4C2416yes—
874C2×C4⋊C4C2416yes—
875C2×C4⋊C4C2416yes—
876C2×C4⋊C4C2416yes—
877C2×C4⋊C4C2416yes—
878C2×C4⋊C4C2416yes—
879C2×C4⋊C4C2416yes—
880C2×C4⋊C4C24112yes—
881C2×C4⋊C4C2416yes—
882C2×C4⋊C4C2416yes—
883C2×C4⋊C4C2416yes—
884C2×C4⋊C4C2412yes—
885C2×C22⋊C4C2413yes—
886C2×C22⋊C4C2413yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2416yes—
890C2×C22⋊C4C2416yes—
891C2×C22⋊C4C2416yes—
892C2×C22⋊C4C24112yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C24112yes—
896C2×C22⋊C4C2416yes—
897C2×C22⋊C4C2416yes—
898C2×C22⋊C4C2411yescharacteristic
899C2×C22⋊C4C2411yescharacteristic
900C2×C22⋊C4C2416yes—
901C2×C22⋊C4C2413yes—
902C2×C22⋊C4C2416yes—
903C2×C22⋊C4C24112yes—
904C2×C22⋊C4C2416yes—
905C2×C22⋊C4C2416yes—
906C2×C22⋊C4C2413yes—
907C2×C22⋊C4C2416yes—
908C2×C22⋊C4C2416yes—
909C2×C22⋊C4C2416yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2416yes—
912C2×C22⋊C4C2416yes—
913C2×C42C2411yescharacteristic
914C2×C42C2413yes—
915C2×C42C2416yes—
916C2×C42C2416yes—
917C2×C42C2411yescharacteristic
918C2×C42C24112yes—
919C2×C42C24112yes—
920C2×C42C24112yes—
921C2×C42C2416yes—
922C2×C42C2413yes—
923C2×C42C2416yes—
924C2×C42C2416yes—
925C2×C42C2413yes—
926C2×C42C2413yes—
927C2×C42C2413yes—
928C2×C42C2416yes—
929C2×C42C2413yes—
930C2×C42C2413yes—
931C2×C42C2413yes—
932C2×C42C2412yes—
933C2×C42C24124yes—
934C2×C42C24148yes—
935C2×C42C24148yes—
936C2×C42C24124yes—
937C2×C42C24124yes—
938C24C2511yescharacteristic
939C24C2512yes—
940C24C2513yes—
941C24C2513yes—
942#41—232no—
943#41—232no—
944#41—448no—
945#41—448no—
946C2×Q8—232no—
947C2×Q8—264no—
948C2×Q8—212no—
949C2×Q8—224no—
950C2×Q8—212no—
951C2×Q8—24no—
952C2×Q8—212no—
953C2×Q8—412no—
954C2×Q8—424no—
955C2×Q8—44no—
956C2×Q8—412no—
957C2×Q8—412no—
958C2×Q8—46no—
959C2×Q8—496no—
960C2×Q8—448no—
961C2×Q82−1+418yes—
962C2×Q8C25112yes—
963C2×Q8C25124yes—
964C2×Q8C2514yes—
965C2×Q8C25112yes—
966C2×Q8C25112yes—
967C2×Q8C2518yes—
968C2×Q8C25124yes—
969C2×Q8C25124yes—
970C2×Q8C25124yes—
971C2×Q8C25148yes—
972C2×Q8C25112yes—
973C2×Q8C2514yes—
974C2×D4—212no—
975C2×D4—212no—
976C2×D4—24no—
977C2×D4—44no—
978C2×D4—412no—
979C2×D4—412no—
980C2×D4—46no—
981C2×D4—46no—
982C2×D4—46no—
983C2×D4—412no—
984C2×D4C25112yes—
985C2×D4C25112yes—
986C2×D4C2514yes—
987C2×D4C2518yes—
988C2×D4C25124yes—
989C2×D4C25124yes—
990C2×D4C25124yes—
991C2×D4C25112yes—
992C2×D4C25112yes—
993C2×D4C25112yes—
994C22×C4—224no—
995C22×C4—212no—
996C22×C4—212no—
997C22×C4—212no—
998C22×C4—212no—
999C22×C4—212no—
1000C22×C4—24no—
1001C22×C4—46no—
1002C22×C4—44no—
1003C22×C4—412no—
1004C22×C4—46no—
1005C22×C4—46no—
1006C22×C4—424no—
1007C22×C4—412no—
1008C22×C4—412no—
1009C22×C4C25112yes—
1010C22×C4C2514yes—
1011C22×C4C25112yes—
1012C22×C4C25124yes—
1013C22×C4C25112yes—
1014C22×C4C25112yes—
1015C22×C4C25112yes—
1016C22×C4C2511yescharacteristic
1017C22×C4C2511yescharacteristic
1018C22×C4C2516yes—
1019C22×C4C2513yes—
1020C22×C4C2512yes—
1021C22×C4C2516yes—
1022C22×C4C2513yes—
1023C22×C4C2513yes—
1024C22×C4C2511yescharacteristic
1025C22×C4C2511yescharacteristic
1026C22×C4C2513yes—
1027C22×C4C2511yescharacteristic
1028C22×C4C2516yes—
1029C22×C4C2512yes—
1030C22×C4C2512yes—
1031C22×C4C2513yes—
1032C22×C4C2516yes—
1033C22×C4C2518yes—
1034C22×C4C25112yes—
1035C22×C4C25124yes—
1036C22×C4C25112yes—
1037C22×C4C25124yes—
1038C22×C4C25112yes—
1039C22×C4C25124yes—
1040C22×C4C25148yes—
1041C22×C4C2513yes—
1042C22×C4C2511yescharacteristic
1043C4⋊C4C2514yes—
1044C4⋊C4C2518yes—
1045C4⋊C4C25112yes—
1046C4⋊C4C25124yes—
1047C4⋊C4C25124yes—
1048C4⋊C4C25124yes—
1049C4⋊C4C25112yes—
1050C4⋊C4C25124yes—
1051C4⋊C4C25112yes—
1052C4⋊C4C25112yes—
1053C4⋊C4C25124yes—
1054C4⋊C4C25124yes—
1055C4⋊C4C25124yes—
1056C4⋊C4C25124yes—
1057C4⋊C4C25124yes—
1058C4⋊C4C25124yes—
1059C4⋊C4C25148yes—
1060C4⋊C4C25124yes—
1061C4⋊C4C25124yes—
1062C4⋊C4C25112yes—
1063C4⋊C4C25112yes—
1064C4⋊C4C2514yes—
1065C4⋊C4C25124yes—
1066C4⋊C4C2518yes—
1067C4⋊C4C25124yes—
1068C4⋊C4C25124yes—
1069C4⋊C4C25124yes—
1070C4⋊C4C2514yes—
1071C4⋊C4C2514yes—
1072C4⋊C4C25112yes—
1073C4⋊C4C25112yes—
1074C4⋊C4C25112yes—
1075C4⋊C4C25124yes—
1076C4⋊C4C25112yes—
1077C4⋊C4C25148yes—
1078C4⋊C4C25124yes—
1079C4⋊C4C25148yes—
1080C4⋊C4C25124yes—
1081C4⋊C4C25124yes—
1082C4⋊C4C25124yes—
1083C4⋊C4C25124yes—
1084C4⋊C4C25124yes—
1085C4⋊C4C25124yes—
1086C4⋊C4C25124yes—
1087C4⋊C4C25148yes—
1088C4⋊C4C25124yes—
1089C4⋊C4C25124yes—
1090C4⋊C4C25124yes—
1091C4⋊C4C2518yes—
1092C22⋊C4C25112yes—
1093C22⋊C4C25112yes—
1094C22⋊C4C2518yes—
1095C22⋊C4C2518yes—
1096C22⋊C4C25124yes—
1097C22⋊C4C25124yes—
1098C22⋊C4C25124yes—
1099C22⋊C4C25148yes—
1100C22⋊C4C2518yes—
1101C22⋊C4C2518yes—
1102C22⋊C4C25148yes—
1103C22⋊C4C25124yes—
1104C22⋊C4C25124yes—
1105C22⋊C4C2514yes—
1106C22⋊C4C2514yes—
1107C22⋊C4C25124yes—
1108C22⋊C4C25112yes—
1109C22⋊C4C25124yes—
1110C22⋊C4C25148yes—
1111C22⋊C4C25124yes—
1112C22⋊C4C25124yes—
1113C22⋊C4C25112yes—
1114C22⋊C4C25124yes—
1115C22⋊C4C25124yes—
1116C22⋊C4C25124yes—
1117C22⋊C4C2518yes—
1118C22⋊C4C25124yes—
1119C22⋊C4C25124yes—
1120C42C2514yes—
1121C42C2514yes—
1122C42C25112yes—
1123C42C25112yes—
1124C42C2518yes—
1125C42C25112yes—
1126C42C25124yes—
1127C42C25124yes—
1128C42C25124yes—
1129C42C25112yes—
1130C42C25124yes—
1131C42C25124yes—
1132C42C25112yes—
1133C42C25112yes—
1134C42C25112yes—
1135C42C25124yes—
1136C42C25112yes—
1137C42C25148yes—
1138C42C25148yes—
1139C42C25148yes—
1140C23—22no—
1141C23—24no—
1142C23—26no—
1143C23—26no—
1144C23—26no—
1145C23—26no—
1146C23—22no—
1147C23—24no—
1148C23—22no—
1149C23—26no—
1150C23—24no—
1151C23—26no—
1152C23C2612yes—
1153C23C2614yes—
1154C23C2616yes—
1155C23C2616yes—
1156C23C2611yescharacteristic
1157Q8—224no—
1158Q8—248no—
1159Q8—224no—
1160Q8—28no—
1161Q8—224no—
1162Q8—424no—
1163Q8—448no—
1164Q8—48no—
1165Q8—424no—
1166Q8—424no—
1167Q8—412no—
1168Q8C2×2−1+4116yes—
1169D4—224no—
1170D4—224no—
1171D4—28no—
1172D4—48no—
1173D4—424no—
1174D4—424no—
1175D4—412no—
1176D4—412no—
1177D4—412no—
1178D4—424no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—212no—
1182C2×C4—26no—
1183C2×C4—26no—
1184C2×C4—22no—
1185C2×C4—26no—
1186C2×C4—212no—
1187C2×C4—212no—
1188C2×C4—24no—
1189C2×C4—22no—
1190C2×C4—24no—
1191C2×C4—26no—
1192C2×C4—22no—
1193C2×C4—26no—
1194C2×C4—212no—
1195C2×C4—24no—
1196C2×C4—248no—
1197C2×C4—224no—
1198C2×C4—224no—
1199C2×C4—224no—
1200C2×C4—224no—
1201C2×C4—224no—
1202C2×C4—28no—
1203C2×C4—412no—
1204C2×C4—48no—
1205C2×C4—424no—
1206C2×C4—412no—
1207C2×C4—412no—
1208C2×C4—448no—
1209C2×C4—424no—
1210C2×C4—424no—
1211C2×C4C2×2−1+4112yes—
1212C2×C4#58514yes—
1213C2×C4C2612yes—
1214C2×C4C2612yes—
1215C2×C4C26112yes—
1216C2×C4C2616yes—
1217C2×C4C2614yes—
1218C2×C4C26112yes—
1219C2×C4C2616yes—
1220C2×C4C2616yes—
1221C2×C4C2612yes—
1222C2×C4C2612yes—
1223C2×C4C2612yes—
1224C2×C4C2616yes—
1225C2×C4C2614yes—
1226C2×C4C26112yes—
1227C2×C4C2614yes—
1228C2×C4C2616yes—
1229C2×C4C26112yes—
1230C2×C4C2616yes—
1231C2×C4C2612yes—
1232C22—22no—
1233C22—24no—
1234C22—26no—
1235C22—26no—
1236C22—26no—
1237C22—26no—
1238C22—22no—
1239C22—24no—
1240C22—22no—
1241C22—26no—
1242C22—24no—
1243C22—26no—
1244C22—44no—
1245C22—48no—
1246C22—412no—
1247C22—412no—
1248C22C22×2−1+412yes—
1249C22C2×#58512yes—
1250C222−1+612yes—
1251C22C2711yescharacteristic
1252C4—22no—
1253C4—22no—
1254C4—212no—
1255C4—26no—
1256C4—26no—
1257C4—22no—
1258C4—26no—
1259C4—212no—
1260C4—212no—
1261C4—24no—
1262C4—22no—
1263C4—24no—
1264C4—26no—
1265C4—22no—
1266C4—26no—
1267C4—212no—
1268C4—24no—
1269C4C22×2−1+4112yes—
1270C4C2×#58514yes—
1271C2—42no—
1272C2—44no—
1273C2—46no—
1274C2—46no—
1275C2#6295314yesdirect product factor
1276C2C23×2−1+411yescharacteristic
1277C2C22×#58511yescharacteristic
1278C2C2×2−1+611yescharacteristic
subgroupG/H
center, socleC23C26
commutator, Frattini, cosocleC22C27
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62953C2direct (N × H)
2. C2×#3509C2semidirect
3. C2×#3503C2semidirect
4. C2×#3524C2semidirect
5. C2×#3518C2semidirect
6. C2×#3518C2semidirect
7. C2×#3518C2semidirect
8. C2×#3523C2semidirect
9. C2×#3523C2semidirect
10. C2×#3516C2semidirect
11. C2×#3502C2semidirect
12. C2×#3502C2semidirect
13. C2×#3550C2semidirect
14. C2×#3555C2semidirect
15. C2×#3555C2semidirect
16. C2×#3547C2semidirect
17. C2×#3552C2semidirect
18. C2×#3565C2semidirect
19. C2×#3565C2semidirect
20. C2×#3557C2semidirect
21. C2×#3482C2semidirect
22. C2×Q8×#41C2semidirect
23. C2×#3480C2semidirect
24. C2×#3461C2semidirect
25. #3565C22semidirect
26. #3565C22semidirect
27. #3557C22semidirect
28. #3555C22semidirect
29. #3555C22semidirect
30. #3552C22semidirect
31. #3550C22semidirect
32. #3547C22semidirect
37. #3524C22semidirect
38. #3523C22semidirect
39. #3523C22semidirect
40. #3518C22semidirect
41. #3518C22semidirect
42. #3518C22semidirect
43. #3516C22semidirect
44. #3509C22semidirect
45. #3503C22semidirect
46. #3502C22semidirect
47. #3502C22semidirect
48. #3482C22semidirect
49. #3480C22semidirect
52. Q8×#41C22semidirect
113. #3461C22semidirect
1275. C2#62953direct (N × H)

Maximal subgroups

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

subgroupindex
#629532
C2×#35092
C2×#35032
C2×#35242
C2×#35182
C2×#35232
C2×#35162
C2×#35022
C2×#35502
C2×#35552
C2×#35472
C2×#35522
C2×#35652
C2×#35572
C2×#34822
C2×Q8×#412
C2×#34802
C2×#34612