Finite Group Databasebeta

← C2×#62949 #10586293

Subgroups — C2×#62949 #10586293

Order 512.

31320 conjugacy classes of subgroups.

The subgroup lattice has 1114 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62949C2164yesmaximal, direct product factor
2C2×#3504C212yesmaximal, complemented
3C2×#3524C212yesmaximal, complemented
4C2×#3523C211yesmaximal, characteristic, complemented
5C2×#3522C211yesmaximal, characteristic, complemented
6C2×#3516C212yesmaximal, complemented
7C2×#3516C212yesmaximal, complemented
8C2×#3502C212yesmaximal, complemented
9C2×#3515C216yesmaximal, complemented
10C2×#3507C213yesmaximal, complemented
11C2×#3555C216yesmaximal, complemented
12C2×#3544C216yesmaximal, complemented
13C2×#3565C216yesmaximal, complemented
14C2×#3557C216yesmaximal, complemented
15C2×#3563C213yesmaximal, complemented
16C2×#3563C216yesmaximal, complemented
17C2×#3559C213yesmaximal, complemented
18C2×#3482C212yesmaximal, complemented
19C22×#557C211yesmaximal, characteristic, complemented
20C2×#3461C213yesmaximal, complemented
21#3565C221192yescomplemented
22#3563C22196yescomplemented
23#3563C221192yescomplemented
24#3559C22196yescomplemented
25#3557C221192yescomplemented
26#3555C221192yescomplemented
27#3544C221192yescomplemented
28C2×#564C2216yes—
29C2×#563C2216yes—
30C2×#563C2216yes—
31C2×#563C22112yes—
32C2×#563C22112yes—
33C2×#562C2216yes—
34#3524C22164yescomplemented
35#3523C22132yescomplemented
36#3522C22132yescomplemented
37#3516C22164yescomplemented
38#3516C22164yescomplemented
39#3515C221192yescomplemented
40#3507C22196yescomplemented
41#3504C22164yescomplemented
42#3502C22164yescomplemented
43#3482C22164yescomplemented
44C2×#559C2213yes—
45C2×#559C2216yes—
46C2×Q82C2216yes—
47C2×Q82C2211yescharacteristic
48C2×#557C2216yes—
49C2×#557C2216yes—
50C2×#557C2216yes—
51C2×#557C2216yes—
52C2×#557C2213yes—
53C2×#557C2216yes—
54C2×#557C2212yes—
55C2×#557C2212yes—
56C2×#557C2212yes—
57C2×#557C2212yes—
58C2×#557C2211yescharacteristic
59C2×#557C22132yescomplemented
60C2×#556C2216yes—
61C2×#556C2216yes—
62C2×#556C2213yes—
63C2×#556C22112yes—
64C2×#556C2216yes—
65C2×#555C2216yes—
66C2×#554C2216yes—
67C2×#554C2213yes—
68C2×#554C2216yes—
69C2×#554C2216yes—
70C2×#554C2216yes—
71C2×#554C2216yes—
72C2×#554C2216yes—
73C2×#553C2216yes—
74C2×#553C2216yes—
75C2×#553C2216yes—
76C2×#552C2216yes—
77C2×#552C22112yes—
78C2×#552C22112yes—
79C2×#552C2216yes—
80C2×#552C2216yes—
81C2×#552C22112yes—
82C2×#552C2216yes—
83C2×#552C2216yes—
84C2×#552C22112yes—
85C2×#552C2216yes—
86C2×#550C2211yescharacteristic
87C2×D4×Q8C2211yescharacteristic
88C2×D4×Q8C2212yes—
89C2×#548C2212yes—
90C2×#548C2212yes—
91C2×#548C2212yes—
92C2×#547C22112yes—
93C2×#547C2216yes—
94C2×#547C2216yes—
95#3461C22196yescomplemented
96C2×#544C2216yes—
97C2×#544C2213yes—
98C2×#544C2216yes—
99C2×#544C22112yes—
100C2×#544C2216yes—
101C2×#544C2216yes—
102C2×#542C2216yes—
103C2×#542C22112yes—
104C2×#542C2216yes—
105C2×#542C2216yes—
106C2×#542C2216yes—
107C2×#542C2216yes—
108C2×#542C2216yes—
109C2×#541C2216yes—
110C2×#541C2216yes—
111C2×#541C22112yes—
112C2×#541C22112yes—
113C2×#541C2216yes—
114C2×#541C2216yes—
115C2×#541C2216yes—
116C2×#540C2216yes—
117C2×#539C22112yes—
118C2×#539C2216yes—
119C2×#539C22112yes—
120C2×#539C2213yes—
121C2×#539C2216yes—
122C2×#539C2211yescharacteristic
123C2×#537C2213yes—
124C2×#536C2216yes—
125C2×#536C2216yes—
126C2×#533C2216yes—
127C2×#533C2213yes—
128C2×#533C2216yes—
129C2×#533C2216yes—
130C2×#533C2216yes—
131C2×#532C2213yes—
132C22×C4⋊Q8C2213yes—
133C2×#529C2213yes—
134C2×#529C2213yes—
135C2×#529C2216yes—
136C2×#529C2216yes—
137C2×#529C2216yes—
138C2×#529C2216yes—
139C2×#529C2216yes—
140C2×#529C2216yes—
141C2×#529C2216yes—
142C2×#529C2216yes—
143C22×#125C2213yes—
144C22×#125C2216yes—
145C22×#125C2213yes—
146C2×#520C2216yes—
147C2×#520C2212yes—
148C2×#520C2212yes—
149C2×#519C2212yes—
150C2×#519C2212yes—
151C2×C4×#41C2216yes—
152C2×C4×#41C2212yes—
153C22×C4×Q8C2213yes—
154C22×C4×Q8C2212yes—
155C22×C4×Q8C2211yescharacteristic
156C22×C4×Q8C2211yescharacteristic
157C22×C4×Q8C2211yescharacteristic
158C22×#41C2312yes—
159C22×#41C2316yes—
160C22×#41C2316yes—
161C23×Q8C2311yescharacteristic
162C23×Q8C2312yes—
163C23×Q8C2313yes—
164#564C23196yes—
165#563C231192yes—
166#563C231192yes—
167#563C23196yes—
168#563C23196yes—
169#562C23196yes—
170#559C23196yes—
171#559C23148yes—
172Q82C23116yes—
173Q82C23196yes—
174#557C23132yes—
175#557C23132yes—
176#557C23196yes—
177#557C23196yes—
178#557C23132yes—
179#557C23132yes—
180#557C23196yes—
181#557C23196yes—
182#557C23196yes—
183#557C23116yes—
184#557C23148yes—
185#556C23196yes—
186#556C23196yes—
187#556C231192yes—
188#556C23196yes—
189#556C23148yes—
190#555C23196yes—
191#554C23196yes—
192#554C23196yes—
193#554C23196yes—
194#554C23196yes—
195#554C23196yes—
196#554C23196yes—
197#554C23148yes—
198#553C23196yes—
199#553C23196yes—
200#553C23196yes—
201#552C23196yes—
202#552C23196yes—
203#552C231192yes—
204#552C23196yes—
205#552C23196yes—
206#552C231192yes—
207#552C231192yes—
208#552C231192yes—
209#552C23196yes—
210#552C23196yes—
211#550C23116yes—
212D4×Q8C23132yes—
213D4×Q8C23116yes—
214#548C23132yes—
215#548C23132yes—
216#548C23132yes—
217#547C23196yes—
218#547C23196yes—
219#547C231192yes—
220#544C23148yes—
221#544C23196yes—
222#544C23196yes—
223#544C23196yes—
224#544C23196yes—
225#544C231192yes—
226#542C23196yes—
227#542C23196yes—
228#542C23196yes—
229#542C23196yes—
230#542C23196yes—
231#542C23196yes—
232#542C231192yes—
233#541C23196yes—
234#541C23196yes—
235#541C231192yes—
236#541C23196yes—
237#541C23196yes—
238#541C23196yes—
239#541C231192yes—
240#540C23196yes—
241#539C23116yes—
242#539C23148yes—
243#539C23196yes—
244#539C23196yes—
245#539C231192yes—
246#539C231192yes—
247#537C23148yes—
248#536C23196yes—
249#536C23196yes—
250#533C23196yes—
251#533C23196yes—
252#533C23196yes—
253#533C23196yes—
254#533C23148yes—
255#532C23148yes—
256C2×C4⋊Q8C2316yes—
257C2×C4⋊Q8C2316yes—
258C2×C4⋊Q8C23112yes—
259C2×C4⋊Q8C23148yes—
260C2×C4⋊Q8C2313yes—
261C2×C4⋊Q8C2316yes—
262C2×C4⋊Q8C2316yes—
263C2×C4⋊Q8C2316yes—
264C2×C4⋊Q8C2313yes—
265C2×C4⋊Q8C2316yes—
266C2×C4⋊Q8C2316yes—
267C2×C4⋊Q8C2316yes—
268C2×C4⋊Q8C2316yes—
269C2×C4⋊Q8C2316yes—
270C2×C4⋊Q8C2313yes—
271C2×C4⋊Q8C23112yes—
272C2×C4⋊Q8C23112yes—
273C2×#127C2313yes—
274#529C23196yes—
275#529C23196yes—
276#529C23148yes—
277#529C23148yes—
278#529C23196yes—
279#529C23196yes—
280#529C23196yes—
281#529C23196yes—
282#529C23196yes—
283#529C23196yes—
284C2×#126C2312yes—
285C2×#126C2316yes—
286C2×#126C2316yes—
287C2×#126C2316yes—
288C2×#126C23112yes—
289C2×#126C2316yes—
290C2×#126C2316yes—
291C2×#126C2316yes—
292C2×#126C23112yes—
293C2×#126C23112yes—
294C2×#126C23112yes—
295C2×#126C2316yes—
296C2×#126C23112yes—
297C2×#126C23112yes—
298C2×#126C23112yes—
299C2×#126C23112yes—
300C2×#125C2316yes—
301C2×#125C2316yes—
302C2×#125C2316yes—
303C2×#125C2316yes—
304C2×#125C2316yes—
305C2×#125C23112yes—
306C2×#125C2316yes—
307C2×#125C2316yes—
308C2×#125C2316yes—
309C2×#125C2316yes—
310C2×#125C2316yes—
311C2×#125C23112yes—
312C2×#125C23148yes—
313C2×#125C23148yes—
314C2×#125C23196yes—
315C2×#125C2316yes—
316C2×#125C2316yes—
317C2×#125C2313yes—
318C2×#125C2313yes—
319C2×#125C2316yes—
320C2×#125C2316yes—
321C2×#125C2316yes—
322C2×#125C2312yes—
323C2×#125C2316yes—
324C2×#125C2316yes—
325C2×#125C2316yes—
326C2×#125C23112yes—
327C2×#125C23112yes—
328C2×#125C23112yes—
329C2×#125C23112yes—
330C2×#125C23112yes—
331C2×#125C23112yes—
332C2×#124C2316yes—
333C2×#124C2316yes—
334C2×#124C2316yes—
335C2×#124C2316yes—
336C2×#124C2316yes—
337C2×#124C2316yes—
338C2×#124C2313yes—
339C2×#124C2313yes—
340C2×#124C2316yes—
341C2×#124C23112yes—
342C2×#123C2312yes—
343C2×#123C2316yes—
344C2×#123C2316yes—
345C2×#123C2312yes—
346C2×#123C2316yes—
347C2×#123C2316yes—
348C2×#123C23112yes—
349C2×#123C23112yes—
350C2×#123C2316yes—
351C2×#123C2316yes—
352C2×#123C23112yes—
353C2×#123C23112yes—
354C2×#123C23112yes—
355C2×#123C23112yes—
356C2×#123C23112yes—
357C2×C22⋊Q8C2311yescharacteristic
358C2×C22⋊Q8C2316yes—
359C2×C22⋊Q8C2313yes—
360C2×C22⋊Q8C2316yes—
361C2×C22⋊Q8C2316yes—
362C2×C22⋊Q8C2316yes—
363C2×C22⋊Q8C2316yes—
364C2×C22⋊Q8C2316yes—
365C2×C22⋊Q8C2316yes—
366C2×C22⋊Q8C2316yes—
367C2×C22⋊Q8C2312yes—
368C2×C22⋊Q8C2316yes—
369C2×C22⋊Q8C2316yes—
370C2×C22⋊Q8C2316yes—
371C2×C22⋊Q8C2316yes—
372C2×C22⋊Q8C2316yes—
373C2×C22⋊Q8C2316yes—
374C2×C22⋊Q8C23112yes—
375C2×C22⋊Q8C2316yes—
376C2×C22⋊Q8C2316yes—
377C2×C22⋊Q8C23112yes—
378C2×C22⋊Q8C23112yes—
379C2×C22⋊Q8C23112yes—
380C2×C22⋊Q8C23112yes—
381C2×C22⋊Q8C23112yes—
382C2×C22⋊Q8C23112yes—
383C2×C22⋊Q8C23112yes—
384C2×C22⋊Q8C23112yes—
385C2×#121C2311yescharacteristic
386C2×#121C2316yes—
387C2×#121C2313yes—
388C2×#121C2316yes—
389C2×#121C2316yes—
390C2×#121C2316yes—
391C2×#121C2316yes—
392C2×#121C2316yes—
393C2×#121C2316yes—
394C2×#121C23112yes—
395#520C23132yes—
396#520C23132yes—
397#520C23196yes—
398#519C23132yes—
399#519C23132yes—
400C4×#41C23196yes—
401C4×#41C23132yes—
402C2×C4×Q8C2312yes—
403C2×C4×Q8C2311yescharacteristic
404C2×C4×Q8C2312yes—
405C2×C4×Q8C2312yes—
406C2×C4×Q8C2311yescharacteristic
407C2×C4×Q8C2316yes—
408C2×C4×Q8C2316yes—
409C2×C4×Q8C2316yes—
410C2×C4×Q8C2316yes—
411C2×C4×Q8C2313yes—
412C2×C4×Q8C2316yes—
413C2×C4×Q8C2316yes—
414C2×C4×Q8C2316yes—
415C2×C4×Q8C2316yes—
416C2×C4×Q8C2313yes—
417C2×C4×Q8C23148yes—
418C2×C4×Q8C23116yes—
419C2×C4×Q8C23116yes—
420C2×C4×Q8C23116yes—
421C2×C4×Q8C23132yes—
422C2×C4×Q8C2312yes—
423C2×C4×Q8C2316yes—
424C2×C4×Q8C2316yes—
425C2×C4×Q8C2316yes—
426C2×C4×Q8C2316yes—
427C2×C4×Q8C2316yes—
428C2×C4×Q8C2316yes—
429C2×C4×Q8C23112yes—
430C2×C4×Q8C2313yes—
431C2×C4×Q8C2316yes—
432C2×C4×Q8C2313yes—
433C2×C4×Q8C2316yes—
434C2×C4×Q8C23112yes—
435C2×C4×D4C2312yes—
436C2×C4×D4C2316yes—
437C2×C4×D4C2316yes—
438C2×C4×D4C2316yes—
439C2×C4×D4C2316yes—
440C2×C4×D4C2316yes—
441C2×C4×D4C2316yes—
442C2×C4×D4C2316yes—
443C2×C4×D4C23112yes—
444C2×C4×D4C23112yes—
445C2×C4×D4C2316yes—
446C2×C4×D4C2316yes—
447C2×C4×D4C2316yes—
448C2×C4×D4C2316yes—
449C2×C4×D4C2316yes—
450C2×C4×D4C2313yes—
451C2×C4×D4C2313yes—
452C2×C4×D4C23112yes—
453C2×C4×D4C2316yes—
454C2×#117C2316yes—
455C2×#117C2316yes—
456C2×#117C2316yes—
457C2×#117C2316yes—
458C2×#117C2316yes—
459C2×#117C2316yes—
460C2×#117C2316yes—
461C2×#117C2316yes—
462C2×#117C2316yes—
463C2×#117C2316yes—
464C2×#117C23112yes—
465C2×#117C2316yes—
466C2×#117C23112yes—
467C2×#117C23112yes—
468C2×#117C23112yes—
469C22×C4⋊C4C2311yescharacteristic
470C22×C4⋊C4C2313yes—
471C22×C4⋊C4C2313yes—
472C22×C4⋊C4C2313yes—
473C22×C4⋊C4C2313yes—
474C22×C4⋊C4C2313yes—
475C22×C4⋊C4C2316yes—
476C22×C4⋊C4C23112yes—
477C22×C4⋊C4C2316yes—
478C22×C4⋊C4C2316yes—
479C22×C4⋊C4C2316yes—
480C22×C4⋊C4C23112yes—
481C22×C42C2313yes—
482C22×C42C2313yes—
483C22×C42C2313yes—
484C22×C42C2316yes—
485C22×C42C2316yes—
486C2×#41—216no—
487C2×#41—424no—
488C2×#41—424no—
489C2×#41C24116yes—
490C2×#41C24148yes—
491C2×#41C24148yes—
492C22×Q8—28no—
493C22×Q8—216no—
494C22×Q8—412no—
495C22×Q8C2413yes—
496C22×Q8C2416yes—
497C22×Q8C2418yes—
498C22×Q8C24116yes—
499C22×Q8C2416yes—
500C22×Q8C2413yes—
501C22×Q8C2411yescharacteristic
502C22×Q8C2416yes—
503C22×Q8C2416yes—
504C22×Q8C2416yes—
505C22×Q8C2416yes—
506C22×Q8C24124yes—
507C22×Q8C2411yescharacteristic
508C22×D4C2416yes—
509C22×D4C2412yes—
510C22×D4C2416yes—
511C22×D4C2416yes—
512C22×D4C2411yescharacteristic
513C22×D4C2413yes—
514C22×D4C2416yes—
515C22×D4C2416yes—
516C23×C4C2413yes—
517C23×C4C2413yes—
518C23×C4C2413yes—
519C23×C4C2416yes—
520C23×C4C2416yes—
521C23×C4C2411yescharacteristic
522C23×C4C2413yes—
523C23×C4C2411yescharacteristic
524C23×C4C2411yescharacteristic
525C23×C4C24112yes—
526C23×C4C24112yes—
527C23×C4C2416yes—
528C23×C4C2416yes—
529C23×C4C2416yes—
530C23×C4C2412yes—
531C4⋊Q8C24148yes—
532C4⋊Q8C24148yes—
533C4⋊Q8C24196yes—
534C4⋊Q8C24124yes—
535C4⋊Q8C24148yes—
536C4⋊Q8C24148yes—
537C4⋊Q8C24148yes—
538C4⋊Q8C24124yes—
539C4⋊Q8C24148yes—
540C4⋊Q8C24148yes—
541C4⋊Q8C24148yes—
542C4⋊Q8C24148yes—
543C4⋊Q8C24148yes—
544C4⋊Q8C24124yes—
545C4⋊Q8C24196yes—
546C4⋊Q8C24196yes—
547#127C24124yes—
548#126C24116yes—
549#126C24148yes—
550#126C24148yes—
551#126C24148yes—
552#126C24196yes—
553#126C24148yes—
554#126C24148yes—
555#126C24148yes—
556#126C24196yes—
557#126C24196yes—
558#126C24196yes—
559#126C24148yes—
560#126C24196yes—
561#126C24196yes—
562#126C24196yes—
563#126C24196yes—
564#125C24148yes—
565#125C24148yes—
566#125C24148yes—
567#125C24148yes—
568#125C24148yes—
569#125C24196yes—
570#125C24148yes—
571#125C24148yes—
572#125C24148yes—
573#125C24148yes—
574#125C24148yes—
575#125C24196yes—
576#125C24148yes—
577#125C24148yes—
578#125C24124yes—
579#125C24124yes—
580#125C24148yes—
581#125C24148yes—
582#125C24148yes—
583#125C24116yes—
584#125C24148yes—
585#125C24148yes—
586#125C24148yes—
587#125C24196yes—
588#125C24196yes—
589#125C24196yes—
590#125C24196yes—
591#125C24196yes—
592#125C24196yes—
593#124C24148yes—
594#124C24148yes—
595#124C24148yes—
596#124C24148yes—
597#124C24148yes—
598#124C24148yes—
599#124C24124yes—
600#124C24124yes—
601#124C24148yes—
602#124C24196yes—
603#123C24116yes—
604#123C24148yes—
605#123C24148yes—
606#123C24116yes—
607#123C24148yes—
608#123C24148yes—
609#123C24196yes—
610#123C24196yes—
611#123C24148yes—
612#123C24148yes—
613#123C24196yes—
614#123C24196yes—
615#123C24196yes—
616#123C24196yes—
617#123C24196yes—
618C22⋊Q8C2418yes—
619C22⋊Q8C24148yes—
620C22⋊Q8C24124yes—
621C22⋊Q8C24148yes—
622C22⋊Q8C24148yes—
623C22⋊Q8C24148yes—
624C22⋊Q8C24148yes—
625C22⋊Q8C24148yes—
626C22⋊Q8C24148yes—
627C22⋊Q8C24148yes—
628C22⋊Q8C24116yes—
629C22⋊Q8C24148yes—
630C22⋊Q8C24148yes—
631C22⋊Q8C24148yes—
632C22⋊Q8C24148yes—
633C22⋊Q8C24148yes—
634C22⋊Q8C24148yes—
635C22⋊Q8C24196yes—
636C22⋊Q8C24148yes—
637C22⋊Q8C24148yes—
638C22⋊Q8C24196yes—
639C22⋊Q8C24196yes—
640C22⋊Q8C24196yes—
641C22⋊Q8C24196yes—
642C22⋊Q8C24196yes—
643C22⋊Q8C24196yes—
644C22⋊Q8C24196yes—
645C22⋊Q8C24196yes—
646#121C2418yes—
647#121C24148yes—
648#121C24124yes—
649#121C24148yes—
650#121C24148yes—
651#121C24148yes—
652#121C24148yes—
653#121C24148yes—
654#121C24148yes—
655#121C24196yes—
656C4×Q8C24116yes—
657C4×Q8C2418yes—
658C4×Q8C24116yes—
659C4×Q8C24116yes—
660C4×Q8C2418yes—
661C4×Q8C24148yes—
662C4×Q8C24148yes—
663C4×Q8C24148yes—
664C4×Q8C24148yes—
665C4×Q8C24124yes—
666C4×Q8C24148yes—
667C4×Q8C24148yes—
668C4×Q8C24148yes—
669C4×Q8C24148yes—
670C4×Q8C24124yes—
671C4×Q8C24116yes—
672C4×Q8C24148yes—
673C4×Q8C24148yes—
674C4×Q8C24148yes—
675C4×Q8C24148yes—
676C4×Q8C24148yes—
677C4×Q8C24148yes—
678C4×Q8C24196yes—
679C4×Q8C24124yes—
680C4×Q8C24148yes—
681C4×Q8C24124yes—
682C4×Q8C24148yes—
683C4×Q8C24196yes—
684C4×D4C24116yes—
685C4×D4C24148yes—
686C4×D4C24148yes—
687C4×D4C24148yes—
688C4×D4C24148yes—
689C4×D4C24148yes—
690C4×D4C24148yes—
691C4×D4C24148yes—
692C4×D4C24196yes—
693C4×D4C24196yes—
694C4×D4C24148yes—
695C4×D4C24148yes—
696C4×D4C24148yes—
697C4×D4C24148yes—
698C4×D4C24148yes—
699C4×D4C24124yes—
700C4×D4C24124yes—
701C4×D4C24196yes—
702C4×D4C24148yes—
703#117C24148yes—
704#117C24148yes—
705#117C24148yes—
706#117C24148yes—
707#117C24148yes—
708#117C24148yes—
709#117C24148yes—
710#117C24148yes—
711#117C24148yes—
712#117C24148yes—
713#117C24196yes—
714#117C24148yes—
715#117C24196yes—
716#117C24196yes—
717#117C24196yes—
718C2×C4⋊C4C2416yes—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2416yes—
721C2×C4⋊C4C2416yes—
722C2×C4⋊C4C2416yes—
723C2×C4⋊C4C2416yes—
724C2×C4⋊C4C2416yes—
725C2×C4⋊C4C2416yes—
726C2×C4⋊C4C2416yes—
727C2×C4⋊C4C24112yes—
728C2×C4⋊C4C2416yes—
729C2×C4⋊C4C2416yes—
730C2×C4⋊C4C2416yes—
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C24112yes—
733C2×C4⋊C4C24112yes—
734C2×C4⋊C4C2416yes—
735C2×C4⋊C4C24112yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2418yes—
739C2×C4⋊C4C24124yes—
740C2×C4⋊C4C2416yes—
741C2×C4⋊C4C2416yes—
742C2×C4⋊C4C2416yes—
743C2×C4⋊C4C2416yes—
744C2×C4⋊C4C2416yes—
745C2×C4⋊C4C24112yes—
746C2×C4⋊C4C24124yes—
747C2×C4⋊C4C24124yes—
748C2×C4⋊C4C24124yes—
749C2×C4⋊C4C24124yes—
750C2×C4⋊C4C24148yes—
751C2×C4⋊C4C24196yes—
752C2×C4⋊C4C24148yes—
753C2×C4⋊C4C24148yes—
754C2×C4⋊C4C24148yes—
755C2×C4⋊C4C24196yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2416yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2416yes—
761C2×C4⋊C4C2416yes—
762C2×C4⋊C4C24112yes—
763C2×C4⋊C4C2416yes—
764C2×C4⋊C4C2416yes—
765C2×C4⋊C4C2416yes—
766C2×C4⋊C4C2416yes—
767C2×C4⋊C4C2416yes—
768C2×C4⋊C4C2416yes—
769C2×C4⋊C4C2416yes—
770C2×C4⋊C4C2416yes—
771C2×C4⋊C4C2411yescharacteristic
772C2×C4⋊C4C2413yes—
773C2×C4⋊C4C2413yes—
774C2×C4⋊C4C2411yescharacteristic
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2416yes—
777C2×C22⋊C4C2416yes—
778C2×C22⋊C4C2412yes—
779C2×C22⋊C4C2412yes—
780C2×C22⋊C4C2416yes—
781C2×C22⋊C4C2412yes—
782C2×C22⋊C4C2416yes—
783C2×C22⋊C4C2416yes—
784C2×C22⋊C4C2412yes—
785C2×C22⋊C4C2416yes—
786C2×C22⋊C4C24112yes—
787C2×C22⋊C4C24112yes—
788C2×C22⋊C4C2416yes—
789C2×C22⋊C4C2416yes—
790C2×C22⋊C4C2416yes—
791C2×C22⋊C4C24112yes—
792C2×C22⋊C4C24112yes—
793C2×C22⋊C4C2416yes—
794C2×C22⋊C4C2416yes—
795C2×C22⋊C4C2416yes—
796C2×C22⋊C4C2416yes—
797C2×C22⋊C4C2416yes—
798C2×C22⋊C4C2412yes—
799C2×C42C2416yes—
800C2×C42C2416yes—
801C2×C42C2416yes—
802C2×C42C24112yes—
803C2×C42C24112yes—
804C2×C42C2413yes—
805C2×C42C2416yes—
806C2×C42C2416yes—
807C2×C42C2416yes—
808C2×C42C2413yes—
809C2×C42C2416yes—
810C2×C42C2416yes—
811C2×C42C2416yes—
812C2×C42C2413yes—
813C2×C42C2412yes—
814C2×C42C2413yes—
815C2×C42C24124yes—
816C2×C42C24124yes—
817C2×C42C24124yes—
818C2×C42C24148yes—
819C2×C42C24148yes—
820C24C2512yes—
821C24C2516yes—
822C24C2511yescharacteristic
823#41—264no—
824#41—496no—
825#41—496no—
826C2×Q8—232no—
827C2×Q8—264no—
828C2×Q8—212no—
829C2×Q8—224no—
830C2×Q8—412no—
831C2×Q8—412no—
832C2×Q8—448no—
833C2×Q8—412no—
834C2×Q8—46no—
835C2×Q8—42no—
836C2×Q8—412no—
837C2×Q8—412no—
838C2×Q82−1+418yes—
839C2×Q8C25112yes—
840C2×Q8C25124yes—
841C2×Q8C25124yes—
842C2×Q8C25112yes—
843C2×Q8C2514yes—
844C2×Q8C25124yes—
845C2×Q8C25124yes—
846C2×Q8C25124yes—
847C2×Q8C25124yes—
848C2×Q8C2514yes—
849C2×D4—28no—
850C2×D4—224no—
851C2×D4—224no—
852C2×D4—412no—
853C2×D4—46no—
854C2×D4—42no—
855C2×D4—412no—
856C2×D4—412no—
857C2×D4C25124yes—
858C2×D4C2518yes—
859C2×D4C25124yes—
860C2×D4C25124yes—
861C2×D4C2514yes—
862C2×D4C25112yes—
863C2×D4C25124yes—
864C2×D4C25124yes—
865C22×C4—24no—
866C22×C4—212no—
867C22×C4—212no—
868C22×C4—212no—
869C22×C4—224no—
870C22×C4—224no—
871C22×C4—42no—
872C22×C4—412no—
873C22×C4—44no—
874C22×C4—46no—
875C22×C4—424no—
876C22×C4—42no—
877C22×C4—424no—
878C22×C4—412no—
879C22×C4—412no—
880C22×C4C25112yes—
881C22×C4C2514yes—
882C22×C4C25112yes—
883C22×C4C25112yes—
884C22×C4C25124yes—
885C22×C4C25124yes—
886C22×C4C2512yes—
887C22×C4C2513yes—
888C22×C4C2516yes—
889C22×C4C2512yes—
890C22×C4C2512yes—
891C22×C4C2511yescharacteristic
892C22×C4C2513yes—
893C22×C4C2511yescharacteristic
894C22×C4C2512yes—
895C22×C4C2516yes—
896C22×C4C2516yes—
897C22×C4C2516yes—
898C22×C4C2516yes—
899C22×C4C2512yes—
900C22×C4C2513yes—
901C22×C4C2514yes—
902C22×C4C2514yes—
903C22×C4C2518yes—
904C22×C4C25112yes—
905C22×C4C25124yes—
906C22×C4C25124yes—
907C22×C4C25124yes—
908C22×C4C25148yes—
909C22×C4C25148yes—
910C22×C4C2513yes—
911C4⋊C4C25124yes—
912C4⋊C4C25112yes—
913C4⋊C4C25124yes—
914C4⋊C4C25124yes—
915C4⋊C4C25124yes—
916C4⋊C4C25124yes—
917C4⋊C4C25124yes—
918C4⋊C4C25124yes—
919C4⋊C4C25124yes—
920C4⋊C4C25148yes—
921C4⋊C4C25124yes—
922C4⋊C4C25124yes—
923C4⋊C4C25124yes—
924C4⋊C4C25112yes—
925C4⋊C4C25148yes—
926C4⋊C4C25148yes—
927C4⋊C4C25124yes—
928C4⋊C4C25148yes—
929C4⋊C4C2518yes—
930C4⋊C4C2518yes—
931C4⋊C4C25124yes—
932C4⋊C4C25124yes—
933C4⋊C4C25124yes—
934C4⋊C4C25124yes—
935C4⋊C4C25124yes—
936C4⋊C4C25148yes—
937C4⋊C4C2518yes—
938C4⋊C4C25124yes—
939C4⋊C4C2518yes—
940C4⋊C4C2518yes—
941C4⋊C4C25124yes—
942C4⋊C4C25124yes—
943C4⋊C4C25148yes—
944C4⋊C4C25124yes—
945C4⋊C4C25124yes—
946C4⋊C4C25124yes—
947C4⋊C4C25124yes—
948C4⋊C4C25124yes—
949C4⋊C4C25124yes—
950C4⋊C4C25124yes—
951C4⋊C4C25124yes—
952C4⋊C4C2514yes—
953C4⋊C4C25112yes—
954C4⋊C4C25112yes—
955C4⋊C4C2514yes—
956C4⋊C4C2518yes—
957C4⋊C4C25124yes—
958C22⋊C4C25124yes—
959C22⋊C4C2518yes—
960C22⋊C4C2518yes—
961C22⋊C4C25124yes—
962C22⋊C4C2518yes—
963C22⋊C4C25124yes—
964C22⋊C4C25124yes—
965C22⋊C4C2518yes—
966C22⋊C4C25124yes—
967C22⋊C4C25148yes—
968C22⋊C4C25148yes—
969C22⋊C4C25124yes—
970C22⋊C4C25124yes—
971C22⋊C4C25124yes—
972C22⋊C4C25148yes—
973C22⋊C4C25148yes—
974C22⋊C4C25124yes—
975C22⋊C4C25124yes—
976C22⋊C4C25124yes—
977C22⋊C4C25124yes—
978C22⋊C4C25124yes—
979C22⋊C4C2518yes—
980C42C25124yes—
981C42C2518yes—
982C42C25124yes—
983C42C25124yes—
984C42C25124yes—
985C42C25112yes—
986C42C25124yes—
987C42C25124yes—
988C42C25124yes—
989C42C25112yes—
990C42C25124yes—
991C42C25124yes—
992C42C25112yes—
993C42C25112yes—
994C42C25148yes—
995C42C25148yes—
996C23—22no—
997C23—22no—
998C23—24no—
999C23—212no—
1000C23—24no—
1001C23—212no—
1002C23—212no—
1003C23—24no—
1004C23#58514yes—
1005C23C2614yes—
1006C23C26112yes—
1007C23C2612yes—
1008C23C2611yescharacteristic
1009Q8—224no—
1010Q8—248no—
1011Q8—424no—
1012Q8—424no—
1013Q8—424no—
1014Q8—412no—
1015Q8—44no—
1016Q8—424no—
1017Q8—424no—
1018Q8C2×2−1+4116yes—
1019D4—216no—
1020D4—248no—
1021D4—248no—
1022D4—424no—
1023D4—412no—
1024D4—44no—
1025D4—424no—
1026D4—424no—
1027C2×C4—24no—
1028C2×C4—26no—
1029C2×C4—212no—
1030C2×C4—26no—
1031C2×C4—212no—
1032C2×C4—26no—
1033C2×C4—28no—
1034C2×C4—24no—
1035C2×C4—224no—
1036C2×C4—224no—
1037C2×C4—212no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—212no—
1041C2×C4—212no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—24no—
1045C2×C4—224no—
1046C2×C4—248no—
1047C2×C4—248no—
1048C2×C4—44no—
1049C2×C4—424no—
1050C2×C4—48no—
1051C2×C4—412no—
1052C2×C4—448no—
1053C2×C4—44no—
1054C2×C4—448no—
1055C2×C4—424no—
1056C2×C4—424no—
1057C2×C4C2×2−1+4112yes—
1058C2×C4C2614yes—
1059C2×C4C2616yes—
1060C2×C4C26112yes—
1061C2×C4C2614yes—
1062C2×C4C2614yes—
1063C2×C4C2612yes—
1064C2×C4C2616yes—
1065C2×C4C2612yes—
1066C2×C4C2614yes—
1067C2×C4C26112yes—
1068C2×C4C26112yes—
1069C2×C4C26112yes—
1070C2×C4C2614yes—
1071C2×C4C26112yes—
1072C2×C4C2616yes—
1073C2×C4C2616yes—
1074C22—22no—
1075C22—22no—
1076C22—28no—
1077C22—24no—
1078C22—212no—
1079C22—24no—
1080C22—212no—
1081C22—212no—
1082C22—24no—
1083C22—48no—
1084C22—424no—
1085C22C22×2−1+412yes—
1086C22C2×#58514yes—
1087C22C2×#58512yes—
1088C222−1+612yes—
1089C22C2711yescharacteristic
1090C4—24no—
1091C4—26no—
1092C4—212no—
1093C4—26no—
1094C4—212no—
1095C4—26no—
1096C4—24no—
1097C4—212no—
1098C4—24no—
1099C4—24no—
1100C4—212no—
1101C4—212no—
1102C4—22no—
1103C4—22no—
1104C4—24no—
1105C4C22×2−1+4112yes—
1106C2—24no—
1107C2—44no—
1108C2—412no—
1109C2#6294914yesdirect product factor
1110C2C23×2−1+411yescharacteristic
1111C2C22×#58511yescharacteristic
1112C2C2×2−1+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. #62949C2direct (N × H)
2. C2×#3504C2semidirect
3. C2×#3524C2semidirect
4. C2×#3523C2semidirect
5. C2×#3522C2semidirect
6. C2×#3516C2semidirect
7. C2×#3516C2semidirect
8. C2×#3502C2semidirect
9. C2×#3515C2semidirect
10. C2×#3507C2semidirect
11. C2×#3555C2semidirect
12. C2×#3544C2semidirect
13. C2×#3565C2semidirect
14. C2×#3557C2semidirect
15. C2×#3563C2semidirect
16. C2×#3563C2semidirect
17. C2×#3559C2semidirect
18. C2×#3482C2semidirect
19. C22×#557C2semidirect
20. C2×#3461C2semidirect
21. #3565C22semidirect
22. #3563C22semidirect
23. #3563C22semidirect
24. #3559C22semidirect
25. #3557C22semidirect
26. #3555C22semidirect
27. #3544C22semidirect
34. #3524C22semidirect
35. #3523C22semidirect
36. #3522C22semidirect
37. #3516C22semidirect
38. #3516C22semidirect
39. #3515C22semidirect
40. #3507C22semidirect
41. #3504C22semidirect
42. #3502C22semidirect
43. #3482C22semidirect
59. C2×#557C22semidirect
95. #3461C22semidirect
1109. C2#62949direct (N × H)

Maximal subgroups

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

subgroupindex
#629492
C2×#35042
C2×#35242
C2×#35232
C2×#35222
C2×#35162
C2×#35022
C2×#35152
C2×#35072
C2×#35552
C2×#35442
C2×#35652
C2×#35572
C2×#35632
C2×#35592
C2×#34822
C22×#5572
C2×#34612