Finite Group Databasebeta

← C2×#62952 #10586296

Subgroups — C2×#62952 #10586296

Order 512.

32030 conjugacy classes of subgroups.

The subgroup lattice has 1298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62952C2164yesmaximal, direct product factor
2C2×#3504C212yesmaximal, complemented
3C2×#3511C213yesmaximal, complemented
4C2×#3503C211yesmaximal, characteristic, complemented
5C2×#3524C212yesmaximal, complemented
6C2×#3524C212yesmaximal, complemented
7C2×#3517C212yesmaximal, complemented
8C2×#3517C211yesmaximal, characteristic, complemented
9C2×#3522C211yesmaximal, characteristic, complemented
10C2×#3522C213yesmaximal, complemented
11C2×#3502C211yesmaximal, characteristic, complemented
12C2×#3515C213yesmaximal, complemented
13C2×#3548C213yesmaximal, complemented
14C2×#3547C213yesmaximal, complemented
15C2×#3547C216yesmaximal, complemented
16C2×#3544C213yesmaximal, complemented
17C2×#3554C213yesmaximal, complemented
18C2×#3554C216yesmaximal, complemented
19C2×#3565C216yesmaximal, complemented
20C2×#3559C216yesmaximal, complemented
21C2×#3483C211yesmaximal, characteristic, complemented
22C2×Q8×#41C211yesmaximal, characteristic, complemented
23C2×#3480C211yesmaximal, characteristic, complemented
24C2×#3461C213yesmaximal, complemented
25#3565C221192yescomplemented
26#3559C221192yescomplemented
27#3554C22196yescomplemented
28#3554C221192yescomplemented
29#3548C22196yescomplemented
30#3547C22196yescomplemented
31#3547C221192yescomplemented
32#3544C22196yescomplemented
33C2×#563C22112yes—
34C2×#562C22112yes—
35C2×#562C22112yes—
36C2×#562C22112yes—
37#3524C22164yescomplemented
38#3524C22164yescomplemented
39#3522C22196yescomplemented
40#3522C22132yescomplemented
41#3517C22164yescomplemented
42#3517C22132yescomplemented
43#3515C22196yescomplemented
44#3511C22196yescomplemented
45#3504C22164yescomplemented
46#3503C22132yescomplemented
47#3502C22132yescomplemented
48#3483C22132yescomplemented
49#3480C22132yescomplemented
50C2×#559C2216yes—
51C2×#559C2213yes—
52C2×#559C2213yes—
53C2×#559C2216yes—
54Q8×#41C22132yescomplemented
55C2×Q82C2213yes—
56C2×Q82C2211yescharacteristic
57C2×Q82C2211yescharacteristic
58C2×#557C2216yes—
59C2×#557C2213yes—
60C2×#557C2212yes—
61C2×#557C2211yescharacteristic
62C2×#557C2212yes—
63C2×#557C2212yes—
64C2×#557C2211yescharacteristic
65C2×#556C2216yes—
66C2×#556C2213yes—
67C2×#555C2216yes—
68C2×#555C2213yes—
69C2×#555C2216yes—
70C2×#555C2216yes—
71C2×#554C2216yes—
72C2×#554C2216yes—
73C2×#554C2216yes—
74C2×#554C2216yes—
75C2×#554C2216yes—
76C2×#554C2213yes—
77C2×#554C2213yes—
78C2×#554C2213yes—
79C2×#554C2213yes—
80C2×#553C2213yes—
81C2×#553C2216yes—
82C2×#553C2216yes—
83C2×#553C2216yes—
84C2×#553C2216yes—
85C2×#553C2213yes—
86C2×#553C2216yes—
87C2×#552C2216yes—
88C2×#552C22112yes—
89C2×#552C2216yes—
90C2×#552C2216yes—
91C2×#550C2216yes—
92C2×#550C2213yes—
93C2×#550C2213yes—
94C2×#550C2211yescharacteristic
95C2×#550C2212yes—
96C2×#550C2211yescharacteristic
97C2×#550C2212yes—
98C2×D4×Q8C2216yes—
99C2×D4×Q8C2213yes—
100C2×#548C2216yes—
101C2×#548C2216yes—
102C2×#548C2216yes—
103C2×#548C2212yes—
104C2×#548C2211yescharacteristic
105C2×#548C2211yescharacteristic
106C2×#547C2216yes—
107C2×#547C22112yes—
108C2×#547C2216yes—
109C2×#547C2216yes—
110C2×#547C2216yes—
111C2×#547C2216yes—
112C2×#547C2213yes—
113#3461C22196yescomplemented
114C2×#544C2216yes—
115C2×#544C2216yes—
116C2×#544C2216yes—
117C2×#544C2213yes—
118C2×#544C2216yes—
119C2×#542C22112yes—
120C2×#542C2216yes—
121C2×#542C2216yes—
122C2×#542C22112yes—
123C2×#542C2216yes—
124C2×#542C2216yes—
125C2×#542C2216yes—
126C2×#542C2213yes—
127C2×#542C2213yes—
128C2×#541C2216yes—
129C2×#541C2213yes—
130C2×#541C2211yescharacteristic
131C2×#540C2216yes—
132C2×#540C2216yes—
133C2×#540C2216yes—
134C2×#540C2216yes—
135C2×#540C2216yes—
136C2×#539C2216yes—
137C2×#539C22112yes—
138C2×#539C22112yes—
139C2×#539C2216yes—
140C2×#537C22112yes—
141C2×#537C2216yes—
142C2×#537C2213yes—
143C2×#536C2213yes—
144C2×#536C22112yes—
145C2×#536C2213yes—
146C2×#533C2216yes—
147C2×#533C2213yes—
148C2×#533C2216yes—
149C2×#533C2213yes—
150C2×#533C2213yes—
151C2×#533C2213yes—
152C2×#532C2216yes—
153C2×#532C2213yes—
154C2×#532C2213yes—
155C2×#532C2216yes—
156C2×#532C2213yes—
157C2×#532C2213yes—
158C22×C4⋊Q8C2213yes—
159C2×#529C2216yes—
160C2×#529C2216yes—
161C2×#529C2216yes—
162C2×#529C2213yes—
163C2×#529C2216yes—
164C2×#529C2213yes—
165C2×#529C2213yes—
166C2×#529C2216yes—
167C2×#529C2213yes—
168C22×#125C2216yes—
169C2×#520C2216yes—
170C2×#520C2212yes—
171C2×#520C2212yes—
172C2×#520C2212yes—
173C2×#519C2212yes—
174C2×C4×#41C2213yes—
175C2×C4×#41C2212yes—
176C2×C4×#41C2211yescharacteristic
177C2×C4×#41C2212yes—
178C2×C4×#41C2213yes—
179C2×C4×#41C2211yescharacteristic
180C22×C4×Q8C2211yescharacteristic
181C22×C4×Q8C2213yes—
182C22×#41C2311yescharacteristic
183C22×#41C2311yescharacteristic
184C22×#41C2312yes—
185C22×#41C2313yes—
186C22×#41C2313yes—
187C22×#41C2316yes—
188C22×#41C2316yes—
189C22×#41C23112yes—
190C22×#41C2316yes—
191C23×Q8C2311yescharacteristic
192C23×Q8C2313yes—
193C23×Q8C2316yes—
194#563C231192yes—
195#562C231192yes—
196#562C231192yes—
197#562C231192yes—
198#559C23148yes—
199#559C23148yes—
200#559C23196yes—
201#559C23196yes—
202Q82C23116yes—
203Q82C23116yes—
204Q82C23148yes—
205#557C23116yes—
206#557C23132yes—
207#557C23116yes—
208#557C23132yes—
209#557C23148yes—
210#557C23196yes—
211#557C23132yes—
212#556C23148yes—
213#556C23196yes—
214#555C23148yes—
215#555C23196yes—
216#555C23196yes—
217#555C23196yes—
218#554C23148yes—
219#554C23196yes—
220#554C23148yes—
221#554C23148yes—
222#554C23196yes—
223#554C23196yes—
224#554C23196yes—
225#554C23196yes—
226#554C23148yes—
227#553C23148yes—
228#553C23148yes—
229#553C23196yes—
230#553C23196yes—
231#553C23196yes—
232#553C23196yes—
233#553C23196yes—
234#552C23196yes—
235#552C23196yes—
236#552C231192yes—
237#552C23196yes—
238#550C23116yes—
239#550C23116yes—
240#550C23132yes—
241#550C23148yes—
242#550C23132yes—
243#550C23148yes—
244#550C23196yes—
245D4×Q8C23148yes—
246D4×Q8C23196yes—
247#548C23116yes—
248#548C23116yes—
249#548C23196yes—
250#548C23196yes—
251#548C23132yes—
252#548C23196yes—
253#547C23196yes—
254#547C23148yes—
255#547C23196yes—
256#547C23196yes—
257#547C23196yes—
258#547C23196yes—
259#547C231192yes—
260#544C23148yes—
261#544C23196yes—
262#544C23196yes—
263#544C23196yes—
264#544C23196yes—
265#542C23148yes—
266#542C23148yes—
267#542C23196yes—
268#542C23196yes—
269#542C231192yes—
270#542C23196yes—
271#542C23196yes—
272#542C23196yes—
273#542C231192yes—
274#541C23116yes—
275#541C23148yes—
276#541C23196yes—
277#540C23196yes—
278#540C23196yes—
279#540C23196yes—
280#540C23196yes—
281#540C23196yes—
282#539C23196yes—
283#539C23196yes—
284#539C231192yes—
285#539C231192yes—
286#537C23148yes—
287#537C23196yes—
288#537C231192yes—
289#536C23148yes—
290#536C23148yes—
291#536C231192yes—
292#533C23148yes—
293#533C23148yes—
294#533C23196yes—
295#533C23148yes—
296#533C23196yes—
297#533C23148yes—
298#532C23148yes—
299#532C23148yes—
300#532C23196yes—
301#532C23148yes—
302#532C23148yes—
303#532C23196yes—
304C2×C4⋊Q8C2313yes—
305C2×C4⋊Q8C2313yes—
306C2×C4⋊Q8C2313yes—
307C2×C4⋊Q8C2316yes—
308C2×C4⋊Q8C2316yes—
309C2×C4⋊Q8C23148yes—
310C2×C4⋊Q8C2313yes—
311C2×C4⋊Q8C2316yes—
312C2×C4⋊Q8C2316yes—
313C2×C4⋊Q8C2313yes—
314C2×C4⋊Q8C2311yescharacteristic
315C2×C4⋊Q8C2316yes—
316C2×C4⋊Q8C2316yes—
317C2×C4⋊Q8C2313yes—
318C2×C4⋊Q8C2313yes—
319C2×C4⋊Q8C2316yes—
320C2×C4⋊Q8C2316yes—
321C2×C4⋊Q8C23112yes—
322C2×#127C2313yes—
323C2×#127C2316yes—
324C2×#127C2316yes—
325C2×#127C2313yes—
326#529C23148yes—
327#529C23196yes—
328#529C23148yes—
329#529C23196yes—
330#529C23196yes—
331#529C23148yes—
332#529C23148yes—
333#529C23196yes—
334#529C23196yes—
335C2×#126C2312yes—
336C2×#126C2316yes—
337C2×#126C2316yes—
338C2×#126C2312yes—
339C2×#126C2316yes—
340C2×#126C2316yes—
341C2×#126C2316yes—
342C2×#126C2316yes—
343C2×#126C2316yes—
344C2×#126C2316yes—
345C2×#126C23112yes—
346C2×#126C23112yes—
347C2×#125C2313yes—
348C2×#125C2316yes—
349C2×#125C2316yes—
350C2×#125C2316yes—
351C2×#125C2316yes—
352C2×#125C23112yes—
353C2×#125C23196yes—
354C2×#125C2312yes—
355C2×#125C2311yescharacteristic
356C2×#125C2316yes—
357C2×#125C2313yes—
358C2×#125C2316yes—
359C2×#125C2313yes—
360C2×#125C2316yes—
361C2×#125C2312yes—
362C2×#125C2316yes—
363C2×#125C2316yes—
364C2×#125C2316yes—
365C2×#125C2316yes—
366C2×#125C2316yes—
367C2×#125C23112yes—
368C2×#124C2313yes—
369C2×#124C2313yes—
370C2×#124C2316yes—
371C2×#124C2313yes—
372C2×#124C2316yes—
373C2×#124C2316yes—
374C2×#124C2316yes—
375C2×#124C2313yes—
376C2×#124C23112yes—
377C2×#124C2316yes—
378C2×#124C2316yes—
379C2×#124C2316yes—
380C2×#124C23112yes—
381C2×#124C23112yes—
382C2×#123C2316yes—
383C2×#123C2316yes—
384C2×#123C2316yes—
385C2×#123C2316yes—
386C2×#123C2316yes—
387C2×#123C2316yes—
388C2×#123C2316yes—
389C2×#123C2316yes—
390C2×#123C2316yes—
391C2×#123C2316yes—
392C2×#123C23112yes—
393C2×#123C23112yes—
394C2×#123C23112yes—
395C2×#123C23112yes—
396C2×#123C23112yes—
397C2×#123C23112yes—
398C2×#123C23112yes—
399C2×#123C23112yes—
400C2×C22⋊Q8C2311yescharacteristic
401C2×C22⋊Q8C2313yes—
402C2×C22⋊Q8C2316yes—
403C2×C22⋊Q8C2316yes—
404C2×C22⋊Q8C2313yes—
405C2×C22⋊Q8C2316yes—
406C2×C22⋊Q8C2316yes—
407C2×C22⋊Q8C2313yes—
408C2×C22⋊Q8C2313yes—
409C2×C22⋊Q8C2311yescharacteristic
410C2×C22⋊Q8C23112yes—
411C2×C22⋊Q8C2313yes—
412C2×C22⋊Q8C2316yes—
413C2×C22⋊Q8C2316yes—
414C2×C22⋊Q8C2313yes—
415C2×C22⋊Q8C2316yes—
416C2×C22⋊Q8C2316yes—
417C2×C22⋊Q8C2316yes—
418C2×C22⋊Q8C2316yes—
419C2×C22⋊Q8C2316yes—
420C2×C22⋊Q8C2316yes—
421C2×C22⋊Q8C23112yes—
422C2×C22⋊Q8C2316yes—
423C2×C22⋊Q8C23112yes—
424C2×C22⋊Q8C23112yes—
425C2×C22⋊Q8C23112yes—
426C2×C22⋊Q8C23112yes—
427C2×C22⋊Q8C23112yes—
428C2×C22⋊Q8C23112yes—
429C2×C22⋊Q8C23112yes—
430C2×#121C2313yes—
431C2×#121C2313yes—
432C2×#121C2316yes—
433C2×#121C2316yes—
434C2×#121C2316yes—
435C2×#121C2316yes—
436C2×#121C2313yes—
437C2×#121C2313yes—
438C2×#121C2316yes—
439C2×#121C2316yes—
440C2×#121C23112yes—
441C2×#121C2316yes—
442C2×#121C2316yes—
443C2×#121C23112yes—
444C2×#121C2316yes—
445C2×#121C2313yes—
446C2×#121C2313yes—
447C2×#121C2316yes—
448C2×#121C2316yes—
449C2×#121C2316yes—
450C2×#121C23112yes—
451C2×#121C23112yes—
452C2×#121C23112yes—
453C2×#121C23112yes—
454C2×#121C23112yes—
455#520C23132yes—
456#520C23132yes—
457#520C23132yes—
458#520C23196yes—
459#519C23132yes—
460C4×#41C23148yes—
461C4×#41C23148yes—
462C4×#41C23116yes—
463C4×#41C23132yes—
464C4×#41C23116yes—
465C4×#41C23132yes—
466C2×C4×Q8C2311yescharacteristic
467C2×C4×Q8C2311yescharacteristic
468C2×C4×Q8C2313yes—
469C2×C4×Q8C2311yescharacteristic
470C2×C4×Q8C2313yes—
471C2×C4×Q8C2313yes—
472C2×C4×Q8C2313yes—
473C2×C4×Q8C2316yes—
474C2×C4×Q8C2316yes—
475C2×C4×Q8C2313yes—
476C2×C4×Q8C23148yes—
477C2×C4×Q8C23116yes—
478C2×C4×Q8C2311yescharacteristic
479C2×C4×Q8C2311yescharacteristic
480C2×C4×Q8C2312yes—
481C2×C4×Q8C2312yes—
482C2×C4×Q8C2311yescharacteristic
483C2×C4×Q8C2312yes—
484C2×C4×Q8C2313yes—
485C2×C4×Q8C2313yes—
486C2×C4×Q8C2313yes—
487C2×C4×Q8C2316yes—
488C2×C4×Q8C2316yes—
489C2×C4×Q8C2316yes—
490C2×C4×Q8C2316yes—
491C2×C4×Q8C2316yes—
492C2×C4×Q8C2316yes—
493C2×C4×Q8C2316yes—
494C2×C4×D4C2313yes—
495C2×C4×D4C2313yes—
496C2×C4×D4C2313yes—
497C2×C4×D4C2313yes—
498C2×C4×D4C2316yes—
499C2×C4×D4C2313yes—
500C2×C4×D4C2313yes—
501C2×C4×D4C2313yes—
502C2×C4×D4C2316yes—
503C2×C4×D4C2316yes—
504C2×C4×D4C2313yes—
505C2×C4×D4C2313yes—
506C2×C4×D4C2313yes—
507C2×C4×D4C2313yes—
508C2×C4×D4C2316yes—
509C2×C4×D4C2316yes—
510C2×C4×D4C2316yes—
511C2×C4×D4C2313yes—
512C2×C4×D4C23112yes—
513C2×C4×D4C2316yes—
514C2×C4×D4C2316yes—
515C2×C4×D4C2316yes—
516C2×C4×D4C2316yes—
517C2×C4×D4C2316yes—
518C2×C4×D4C2316yes—
519C2×C4×D4C23112yes—
520C2×C4×D4C2316yes—
521C2×C4×D4C2316yes—
522C2×C4×D4C2316yes—
523C2×C4×D4C2316yes—
524C2×C4×D4C23112yes—
525C2×C4×D4C2316yes—
526C2×#117C2311yescharacteristic
527C2×#117C2313yes—
528C2×#117C2313yes—
529C2×#117C2316yes—
530C2×#117C2313yes—
531C2×#117C2313yes—
532C2×#117C2316yes—
533C2×#117C2316yes—
534C2×#117C2313yes—
535C2×#117C2316yes—
536C2×#117C2316yes—
537C2×#117C2316yes—
538C2×#117C2316yes—
539C2×#117C2316yes—
540C2×#117C23112yes—
541C2×#117C23112yes—
542C22×C4⋊C4C2313yes—
543C22×C4⋊C4C2316yes—
544C22×C4⋊C4C2313yes—
545C22×C4⋊C4C23112yes—
546C22×C4⋊C4C2316yes—
547C22×C4⋊C4C2316yes—
548C22×C4⋊C4C2316yes—
549C22×C4⋊C4C2316yes—
550C22×C4⋊C4C23112yes—
551C22×C42C2313yes—
552C22×C42C2316yes—
553C22×C42C2313yes—
554C22×C42C2316yes—
555C22×C42C2313yes—
556C2×#41—28no—
557C2×#41—28no—
558C2×#41—216no—
559C2×#41—412no—
560C2×#41—412no—
561C2×#41—424no—
562C2×#41—824no—
563C2×#41—812no—
564C2×#41—812no—
565C2×#41C2418yes—
566C2×#41C2418yes—
567C2×#41C24116yes—
568C2×#41C24124yes—
569C2×#41C24124yes—
570C2×#41C24148yes—
571C2×#41C24148yes—
572C2×#41C24196yes—
573C2×#41C24148yes—
574C22×Q8—28no—
575C22×Q8—412no—
576C22×Q8—812no—
577C22×Q8C2413yes—
578C22×Q8C2411yescharacteristic
579C22×Q8C2413yes—
580C22×Q8C2411yescharacteristic
581C22×Q8C2418yes—
582C22×Q8C2416yes—
583C22×Q8C2413yes—
584C22×Q8C24124yes—
585C22×Q8C2416yes—
586C22×Q8C2416yes—
587C22×Q8C2416yes—
588C22×Q8C2416yes—
589C22×Q8C24148yes—
590C22×Q8C2411yescharacteristic
591C22×D4C2413yes—
592C22×D4C2413yes—
593C22×D4C2416yes—
594C22×D4C2413yes—
595C22×D4C2413yes—
596C22×D4C2413yes—
597C22×D4C24112yes—
598C22×D4C2416yes—
599C22×D4C2413yes—
600C22×D4C2416yes—
601C22×D4C2416yes—
602C22×D4C24112yes—
603C22×D4C2416yes—
604C22×D4C2416yes—
605C23×C4C2416yes—
606C23×C4C2413yes—
607C23×C4C2413yes—
608C23×C4C2413yes—
609C23×C4C2413yes—
610C23×C4C2413yes—
611C23×C4C2411yescharacteristic
612C23×C4C24112yes—
613C23×C4C24112yes—
614C23×C4C24112yes—
615C23×C4C2416yes—
616C23×C4C2413yes—
617C23×C4C2416yes—
618C23×C4C2413yes—
619C23×C4C2416yes—
620C23×C4C2416yes—
621C23×C4C2413yes—
622C4⋊Q8C24124yes—
623C4⋊Q8C24124yes—
624C4⋊Q8C24124yes—
625C4⋊Q8C24148yes—
626C4⋊Q8C24148yes—
627C4⋊Q8C24124yes—
628C4⋊Q8C24148yes—
629C4⋊Q8C24148yes—
630C4⋊Q8C24124yes—
631C4⋊Q8C2418yes—
632C4⋊Q8C24148yes—
633C4⋊Q8C24148yes—
634C4⋊Q8C24124yes—
635C4⋊Q8C24124yes—
636C4⋊Q8C24148yes—
637C4⋊Q8C24148yes—
638C4⋊Q8C24196yes—
639#127C24124yes—
640#127C24148yes—
641#127C24148yes—
642#127C24124yes—
643#126C24116yes—
644#126C24148yes—
645#126C24148yes—
646#126C24116yes—
647#126C24148yes—
648#126C24148yes—
649#126C24148yes—
650#126C24148yes—
651#126C24148yes—
652#126C24148yes—
653#126C24196yes—
654#126C24196yes—
655#125C24124yes—
656#125C24148yes—
657#125C24148yes—
658#125C24148yes—
659#125C24148yes—
660#125C24196yes—
661#125C24116yes—
662#125C2418yes—
663#125C24148yes—
664#125C24124yes—
665#125C24148yes—
666#125C24124yes—
667#125C24148yes—
668#125C24116yes—
669#125C24148yes—
670#125C24148yes—
671#125C24148yes—
672#125C24148yes—
673#125C24148yes—
674#125C24196yes—
675#124C24124yes—
676#124C24124yes—
677#124C24148yes—
678#124C24124yes—
679#124C24148yes—
680#124C24148yes—
681#124C24148yes—
682#124C24124yes—
683#124C24196yes—
684#124C24148yes—
685#124C24148yes—
686#124C24148yes—
687#124C24196yes—
688#124C24196yes—
689#123C24148yes—
690#123C24148yes—
691#123C24148yes—
692#123C24148yes—
693#123C24148yes—
694#123C24148yes—
695#123C24148yes—
696#123C24148yes—
697#123C24148yes—
698#123C24148yes—
699#123C24196yes—
700#123C24196yes—
701#123C24196yes—
702#123C24196yes—
703#123C24196yes—
704#123C24196yes—
705#123C24196yes—
706#123C24196yes—
707C22⋊Q8C2418yes—
708C22⋊Q8C24124yes—
709C22⋊Q8C24148yes—
710C22⋊Q8C24148yes—
711C22⋊Q8C24124yes—
712C22⋊Q8C24148yes—
713C22⋊Q8C24148yes—
714C22⋊Q8C24124yes—
715C22⋊Q8C24124yes—
716C22⋊Q8C2418yes—
717C22⋊Q8C24196yes—
718C22⋊Q8C24124yes—
719C22⋊Q8C24148yes—
720C22⋊Q8C24148yes—
721C22⋊Q8C24124yes—
722C22⋊Q8C24148yes—
723C22⋊Q8C24148yes—
724C22⋊Q8C24148yes—
725C22⋊Q8C24148yes—
726C22⋊Q8C24148yes—
727C22⋊Q8C24148yes—
728C22⋊Q8C24196yes—
729C22⋊Q8C24148yes—
730C22⋊Q8C24196yes—
731C22⋊Q8C24196yes—
732C22⋊Q8C24196yes—
733C22⋊Q8C24196yes—
734C22⋊Q8C24196yes—
735C22⋊Q8C24196yes—
736C22⋊Q8C24196yes—
737#121C24124yes—
738#121C24124yes—
739#121C24148yes—
740#121C24148yes—
741#121C24148yes—
742#121C24148yes—
743#121C24124yes—
744#121C24124yes—
745#121C24148yes—
746#121C24148yes—
747#121C24196yes—
748#121C24148yes—
749#121C24148yes—
750#121C24196yes—
751#121C24148yes—
752#121C24124yes—
753#121C24124yes—
754#121C24148yes—
755#121C24148yes—
756#121C24148yes—
757#121C24196yes—
758#121C24196yes—
759#121C24196yes—
760#121C24196yes—
761#121C24196yes—
762C4×Q8C2418yes—
763C4×Q8C2418yes—
764C4×Q8C24124yes—
765C4×Q8C2418yes—
766C4×Q8C24124yes—
767C4×Q8C24124yes—
768C4×Q8C24124yes—
769C4×Q8C24148yes—
770C4×Q8C24148yes—
771C4×Q8C24124yes—
772C4×Q8C2418yes—
773C4×Q8C2418yes—
774C4×Q8C24116yes—
775C4×Q8C24116yes—
776C4×Q8C2418yes—
777C4×Q8C24116yes—
778C4×Q8C24124yes—
779C4×Q8C24124yes—
780C4×Q8C24124yes—
781C4×Q8C24148yes—
782C4×Q8C24148yes—
783C4×Q8C24148yes—
784C4×Q8C24148yes—
785C4×Q8C24148yes—
786C4×Q8C24148yes—
787C4×Q8C24148yes—
788C4×D4C24124yes—
789C4×D4C24124yes—
790C4×D4C24124yes—
791C4×D4C24124yes—
792C4×D4C24148yes—
793C4×D4C24124yes—
794C4×D4C24124yes—
795C4×D4C24124yes—
796C4×D4C24148yes—
797C4×D4C24124yes—
798C4×D4C24148yes—
799C4×D4C24124yes—
800C4×D4C24124yes—
801C4×D4C24124yes—
802C4×D4C24148yes—
803C4×D4C24148yes—
804C4×D4C24148yes—
805C4×D4C24124yes—
806C4×D4C24196yes—
807C4×D4C24148yes—
808C4×D4C24148yes—
809C4×D4C24148yes—
810C4×D4C24148yes—
811C4×D4C24148yes—
812C4×D4C24148yes—
813C4×D4C24196yes—
814C4×D4C24148yes—
815C4×D4C24148yes—
816C4×D4C24148yes—
817C4×D4C24148yes—
818C4×D4C24196yes—
819C4×D4C24148yes—
820#117C2418yes—
821#117C24124yes—
822#117C24124yes—
823#117C24148yes—
824#117C24124yes—
825#117C24124yes—
826#117C24148yes—
827#117C24148yes—
828#117C24124yes—
829#117C24148yes—
830#117C24148yes—
831#117C24148yes—
832#117C24148yes—
833#117C24148yes—
834#117C24196yes—
835#117C24196yes—
836C2×C4⋊C4C2413yes—
837C2×C4⋊C4C2413yes—
838C2×C4⋊C4C2413yes—
839C2×C4⋊C4C2416yes—
840C2×C4⋊C4C2411yescharacteristic
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2413yes—
843C2×C4⋊C4C2416yes—
844C2×C4⋊C4C2413yes—
845C2×C4⋊C4C24112yes—
846C2×C4⋊C4C2416yes—
847C2×C4⋊C4C2416yes—
848C2×C4⋊C4C2416yes—
849C2×C4⋊C4C2416yes—
850C2×C4⋊C4C2416yes—
851C2×C4⋊C4C2416yes—
852C2×C4⋊C4C2416yes—
853C2×C4⋊C4C2413yes—
854C2×C4⋊C4C2416yes—
855C2×C4⋊C4C24112yes—
856C2×C4⋊C4C24112yes—
857C2×C4⋊C4C2416yes—
858C2×C4⋊C4C2416yes—
859C2×C4⋊C4C2416yes—
860C2×C4⋊C4C2416yes—
861C2×C4⋊C4C24124yes—
862C2×C4⋊C4C24148yes—
863C2×C4⋊C4C24124yes—
864C2×C4⋊C4C24196yes—
865C2×C4⋊C4C24148yes—
866C2×C4⋊C4C24148yes—
867C2×C4⋊C4C24148yes—
868C2×C4⋊C4C24148yes—
869C2×C4⋊C4C24196yes—
870C2×C4⋊C4C2413yes—
871C2×C4⋊C4C2413yes—
872C2×C4⋊C4C2411yescharacteristic
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2416yes—
878C2×C4⋊C4C2411yescharacteristic
879C2×C4⋊C4C2411yescharacteristic
880C2×C4⋊C4C2416yes—
881C2×C4⋊C4C2413yes—
882C2×C4⋊C4C2413yes—
883C2×C4⋊C4C2416yes—
884C2×C4⋊C4C2416yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2416yes—
887C2×C4⋊C4C2416yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2416yes—
890C2×C4⋊C4C2412yes—
891C2×C22⋊C4C2416yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2416yes—
894C2×C22⋊C4C2416yes—
895C2×C22⋊C4C2416yes—
896C2×C22⋊C4C2413yes—
897C2×C22⋊C4C2411yescharacteristic
898C2×C22⋊C4C2413yes—
899C2×C22⋊C4C2411yescharacteristic
900C2×C22⋊C4C2416yes—
901C2×C22⋊C4C2416yes—
902C2×C22⋊C4C2416yes—
903C2×C22⋊C4C24112yes—
904C2×C22⋊C4C2416yes—
905C2×C22⋊C4C2416yes—
906C2×C22⋊C4C24112yes—
907C2×C22⋊C4C2416yes—
908C2×C22⋊C4C2416yes—
909C2×C22⋊C4C2416yes—
910C2×C22⋊C4C2413yes—
911C2×C22⋊C4C2416yes—
912C2×C22⋊C4C2416yes—
913C2×C22⋊C4C24112yes—
914C2×C22⋊C4C2413yes—
915C2×C22⋊C4C2416yes—
916C2×C22⋊C4C2416yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2416yes—
919C2×C42C2416yes—
920C2×C42C2411yescharacteristic
921C2×C42C2416yes—
922C2×C42C2413yes—
923C2×C42C2411yescharacteristic
924C2×C42C24112yes—
925C2×C42C2413yes—
926C2×C42C2416yes—
927C2×C42C2413yes—
928C2×C42C2413yes—
929C2×C42C2416yes—
930C2×C42C2416yes—
931C2×C42C2413yes—
932C2×C42C2413yes—
933C2×C42C2413yes—
934C2×C42C2412yes—
935C2×C42C2413yes—
936C2×C42C2412yes—
937C2×C42C24124yes—
938C2×C42C24148yes—
939C2×C42C24124yes—
940C2×C42C24148yes—
941C2×C42C24124yes—
942C24C2511yescharacteristic
943C24C2513yes—
944C24C2513yes—
945C24C2516yes—
946#41—232no—
947#41—232no—
948#41—264no—
949#41—448no—
950#41—448no—
951#41—496no—
952#41—896no—
953#41—848no—
954#41—848no—
955C2×Q8—232no—
956C2×Q8—212no—
957C2×Q8—24no—
958C2×Q8—212no—
959C2×Q8—24no—
960C2×Q8—412no—
961C2×Q8—412no—
962C2×Q8—412no—
963C2×Q8—412no—
964C2×Q8—46no—
965C2×Q8—412no—
966C2×Q8—448no—
967C2×Q8—848no—
968C2×Q82−1+418yes—
969C2×Q8C25112yes—
970C2×Q8C2514yes—
971C2×Q8C25112yes—
972C2×Q8C2514yes—
973C2×Q8C25124yes—
974C2×Q8C25112yes—
975C2×Q8C25124yes—
976C2×Q8C25124yes—
977C2×Q8C25124yes—
978C2×Q8C25124yes—
979C2×Q8C2514yes—
980C2×D4—212no—
981C2×D4—212no—
982C2×D4—224no—
983C2×D4—212no—
984C2×D4—46no—
985C2×D4—46no—
986C2×D4—46no—
987C2×D4—412no—
988C2×D4—424no—
989C2×D4—412no—
990C2×D4—412no—
991C2×D4—412no—
992C2×D4—412no—
993C2×D4—424no—
994C2×D4C25112yes—
995C2×D4C25112yes—
996C2×D4C25124yes—
997C2×D4C25112yes—
998C2×D4C25112yes—
999C2×D4C25112yes—
1000C2×D4C25148yes—
1001C2×D4C25124yes—
1002C2×D4C25112yes—
1003C2×D4C25124yes—
1004C2×D4C25124yes—
1005C2×D4C25148yes—
1006C2×D4C25124yes—
1007C2×D4C25124yes—
1008C22×C4—212no—
1009C22×C4—224no—
1010C22×C4—212no—
1011C22×C4—212no—
1012C22×C4—212no—
1013C22×C4—212no—
1014C22×C4—24no—
1015C22×C4—412no—
1016C22×C4—46no—
1017C22×C4—424no—
1018C22×C4—424no—
1019C22×C4—412no—
1020C22×C4—46no—
1021C22×C4—412no—
1022C22×C4—424no—
1023C22×C4—46no—
1024C22×C4—412no—
1025C22×C4C25112yes—
1026C22×C4C2514yes—
1027C22×C4C25124yes—
1028C22×C4C25112yes—
1029C22×C4C25112yes—
1030C22×C4C25112yes—
1031C22×C4C25112yes—
1032C22×C4C2511yescharacteristic
1033C22×C4C2513yes—
1034C22×C4C2511yescharacteristic
1035C22×C4C2511yescharacteristic
1036C22×C4C2512yes—
1037C22×C4C2511yescharacteristic
1038C22×C4C2512yes—
1039C22×C4C2511yescharacteristic
1040C22×C4C2513yes—
1041C22×C4C2516yes—
1042C22×C4C2516yes—
1043C22×C4C2513yes—
1044C22×C4C2512yes—
1045C22×C4C2512yes—
1046C22×C4C2513yes—
1047C22×C4C2516yes—
1048C22×C4C2513yes—
1049C22×C4C25124yes—
1050C22×C4C25112yes—
1051C22×C4C25124yes—
1052C22×C4C25112yes—
1053C22×C4C25124yes—
1054C22×C4C25124yes—
1055C22×C4C25112yes—
1056C22×C4C25148yes—
1057C22×C4C25148yes—
1058C22×C4C25148yes—
1059C22×C4C2513yes—
1060C22×C4C2511yescharacteristic
1061C4⋊C4C25112yes—
1062C4⋊C4C25112yes—
1063C4⋊C4C25112yes—
1064C4⋊C4C25124yes—
1065C4⋊C4C2514yes—
1066C4⋊C4C2518yes—
1067C4⋊C4C25112yes—
1068C4⋊C4C25124yes—
1069C4⋊C4C25112yes—
1070C4⋊C4C25148yes—
1071C4⋊C4C25124yes—
1072C4⋊C4C25124yes—
1073C4⋊C4C25124yes—
1074C4⋊C4C25124yes—
1075C4⋊C4C25124yes—
1076C4⋊C4C25124yes—
1077C4⋊C4C25124yes—
1078C4⋊C4C25112yes—
1079C4⋊C4C25124yes—
1080C4⋊C4C25148yes—
1081C4⋊C4C25148yes—
1082C4⋊C4C25124yes—
1083C4⋊C4C25124yes—
1084C4⋊C4C25124yes—
1085C4⋊C4C25124yes—
1086C4⋊C4C25112yes—
1087C4⋊C4C25112yes—
1088C4⋊C4C2514yes—
1089C4⋊C4C2518yes—
1090C4⋊C4C2518yes—
1091C4⋊C4C2518yes—
1092C4⋊C4C2518yes—
1093C4⋊C4C25124yes—
1094C4⋊C4C2514yes—
1095C4⋊C4C2514yes—
1096C4⋊C4C25124yes—
1097C4⋊C4C25112yes—
1098C4⋊C4C25112yes—
1099C4⋊C4C25124yes—
1100C4⋊C4C25124yes—
1101C4⋊C4C2518yes—
1102C4⋊C4C25124yes—
1103C4⋊C4C25124yes—
1104C4⋊C4C2518yes—
1105C4⋊C4C25124yes—
1106C4⋊C4C2518yes—
1107C22⋊C4C25124yes—
1108C22⋊C4C2518yes—
1109C22⋊C4C25124yes—
1110C22⋊C4C25124yes—
1111C22⋊C4C25124yes—
1112C22⋊C4C25112yes—
1113C22⋊C4C2514yes—
1114C22⋊C4C25112yes—
1115C22⋊C4C2514yes—
1116C22⋊C4C25124yes—
1117C22⋊C4C25124yes—
1118C22⋊C4C25124yes—
1119C22⋊C4C25148yes—
1120C22⋊C4C25124yes—
1121C22⋊C4C25124yes—
1122C22⋊C4C25148yes—
1123C22⋊C4C25124yes—
1124C22⋊C4C25124yes—
1125C22⋊C4C25124yes—
1126C22⋊C4C25112yes—
1127C22⋊C4C25124yes—
1128C22⋊C4C25124yes—
1129C22⋊C4C25148yes—
1130C22⋊C4C25112yes—
1131C22⋊C4C25124yes—
1132C22⋊C4C25124yes—
1133C22⋊C4C2518yes—
1134C22⋊C4C25124yes—
1135C42C2514yes—
1136C42C2514yes—
1137C42C25112yes—
1138C42C25112yes—
1139C42C2518yes—
1140C42C2518yes—
1141C42C25124yes—
1142C42C25124yes—
1143C42C25112yes—
1144C42C25112yes—
1145C42C25124yes—
1146C42C25112yes—
1147C42C25112yes—
1148C42C25124yes—
1149C42C25124yes—
1150C42C25112yes—
1151C42C25112yes—
1152C42C25148yes—
1153C23—22no—
1154C23—26no—
1155C23—26no—
1156C23—212no—
1157C23—26no—
1158C23—22no—
1159C23—26no—
1160C23—212no—
1161C23—26no—
1162C23—22no—
1163C23—26no—
1164C23—212no—
1165C23C2612yes—
1166C23C2616yes—
1167C23C2616yes—
1168C23C26112yes—
1169C23C2611yescharacteristic
1170Q8—224no—
1171Q8—28no—
1172Q8—224no—
1173Q8—28no—
1174Q8—424no—
1175Q8—424no—
1176Q8—424no—
1177Q8—424no—
1178Q8—412no—
1179Q8—424no—
1180Q8C2×2−1+4116yes—
1181D4—224no—
1182D4—224no—
1183D4—248no—
1184D4—224no—
1185D4—412no—
1186D4—412no—
1187D4—412no—
1188D4—424no—
1189D4—448no—
1190D4—424no—
1191D4—424no—
1192D4—424no—
1193D4—424no—
1194D4—448no—
1195C2×C4—22no—
1196C2×C4—24no—
1197C2×C4—22no—
1198C2×C4—26no—
1199C2×C4—26no—
1200C2×C4—26no—
1201C2×C4—22no—
1202C2×C4—24no—
1203C2×C4—212no—
1204C2×C4—24no—
1205C2×C4—22no—
1206C2×C4—26no—
1207C2×C4—212no—
1208C2×C4—24no—
1209C2×C4—26no—
1210C2×C4—212no—
1211C2×C4—22no—
1212C2×C4—224no—
1213C2×C4—224no—
1214C2×C4—248no—
1215C2×C4—224no—
1216C2×C4—224no—
1217C2×C4—224no—
1218C2×C4—28no—
1219C2×C4—424no—
1220C2×C4—412no—
1221C2×C4—448no—
1222C2×C4—448no—
1223C2×C4—424no—
1224C2×C4—412no—
1225C2×C4—424no—
1226C2×C4—448no—
1227C2×C4—412no—
1228C2×C4—424no—
1229C2×C4C2×2−1+4112yes—
1230C2×C4#58514yes—
1231C2×C4C2612yes—
1232C2×C4C2616yes—
1233C2×C4C2612yes—
1234C2×C4C2612yes—
1235C2×C4C2612yes—
1236C2×C4C2614yes—
1237C2×C4C2614yes—
1238C2×C4C2612yes—
1239C2×C4C2616yes—
1240C2×C4C26112yes—
1241C2×C4C2616yes—
1242C2×C4C26112yes—
1243C2×C4C2614yes—
1244C2×C4C2614yes—
1245C2×C4C2616yes—
1246C2×C4C26112yes—
1247C2×C4C2616yes—
1248C2×C4C2616yes—
1249C2×C4C2612yes—
1250C22—22no—
1251C22—26no—
1252C22—26no—
1253C22—212no—
1254C22—26no—
1255C22—22no—
1256C22—26no—
1257C22—212no—
1258C22—26no—
1259C22—22no—
1260C22—26no—
1261C22—212no—
1262C22—44no—
1263C22—412no—
1264C22—412no—
1265C22—424no—
1266C22C22×2−1+412yes—
1267C22C2×#58512yes—
1268C22H(7,𝔽2)12yes—
1269C22C2711yescharacteristic
1270C4—22no—
1271C4—22no—
1272C4—24no—
1273C4—26no—
1274C4—26no—
1275C4—26no—
1276C4—22no—
1277C4—24no—
1278C4—212no—
1279C4—24no—
1280C4—22no—
1281C4—26no—
1282C4—212no—
1283C4—24no—
1284C4—26no—
1285C4—212no—
1286C4—22no—
1287C4C22×2−1+4112yes—
1288C4C2×#58514yes—
1289C2—42no—
1290C2—46no—
1291C2—46no—
1292C2—412no—
1293C2#6295214yesdirect product factor
1294C2C23×2−1+411yescharacteristic
1295C2C22×#58511yescharacteristic
1296C2C2×H(7,𝔽2)11yescharacteristic
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. #62952C2direct (N × H)
2. C2×#3504C2semidirect
3. C2×#3511C2semidirect
4. C2×#3503C2semidirect
5. C2×#3524C2semidirect
6. C2×#3524C2semidirect
7. C2×#3517C2semidirect
8. C2×#3517C2semidirect
9. C2×#3522C2semidirect
10. C2×#3522C2semidirect
11. C2×#3502C2semidirect
12. C2×#3515C2semidirect
13. C2×#3548C2semidirect
14. C2×#3547C2semidirect
15. C2×#3547C2semidirect
16. C2×#3544C2semidirect
17. C2×#3554C2semidirect
18. C2×#3554C2semidirect
19. C2×#3565C2semidirect
20. C2×#3559C2semidirect
21. C2×#3483C2semidirect
22. C2×Q8×#41C2semidirect
23. C2×#3480C2semidirect
24. C2×#3461C2semidirect
25. #3565C22semidirect
26. #3559C22semidirect
27. #3554C22semidirect
28. #3554C22semidirect
29. #3548C22semidirect
30. #3547C22semidirect
31. #3547C22semidirect
32. #3544C22semidirect
37. #3524C22semidirect
38. #3524C22semidirect
39. #3522C22semidirect
40. #3522C22semidirect
41. #3517C22semidirect
42. #3517C22semidirect
43. #3515C22semidirect
44. #3511C22semidirect
45. #3504C22semidirect
46. #3503C22semidirect
47. #3502C22semidirect
48. #3483C22semidirect
49. #3480C22semidirect
54. Q8×#41C22semidirect
113. #3461C22semidirect
1293. C2#62952direct (N × H)

Maximal subgroups

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

subgroupindex
#629522
C2×#35042
C2×#35112
C2×#35032
C2×#35242
C2×#35172
C2×#35222
C2×#35022
C2×#35152
C2×#35482
C2×#35472
C2×#35442
C2×#35542
C2×#35652
C2×#35592
C2×#34832
C2×Q8×#412
C2×#34802
C2×#34612