Finite Group Databasebeta

← #6344276

Subgroups — #6344276

Order 512.

2750 conjugacy classes of subgroups.

The subgroup lattice has 907 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62833C211yesmaximal, characteristic
2#60293C211yesmaximal, characteristic, complemented
3#60293C211yesmaximal, characteristic, complemented
4#17775C214yesmaximal, complemented
5#17774C214yesmaximal, complemented
6#17769C214yesmaximal, complemented
7#17767C214yesmaximal, complemented
8#17761C214yesmaximal, complemented
9#17759C214yesmaximal, complemented
10#17756C211yesmaximal, characteristic, complemented
11#17756C211yesmaximal, characteristic, complemented
12#17742C211yesmaximal, characteristic, complemented
13C2×#1556C211yesmaximal, characteristic, complemented
14#3552—22no—
15#3552—22no—
16#3552—22no—
17#3552C414yes—
18#3544—22no—
19#3544C414yes—
20#3511—21no—
21#3511C412yes—
22#3511C2212yes—
23#3511C2212yes—
24#3509—21no—
25#3509C2212yes—
26#3503—21no—
27#3503C412yes—
28#3503C2212yes—
29#3503C2212yes—
30#3499—21no—
31#3499C2212yes—
32#3492—22no—
33#3492C414yes—
34#3486—22no—
35#3444C2211yescharacteristic
36#3444C2211yescharacteristic
37C22×C4⋊Q8C2211yescharacteristic
38#2990C2214yes—
39#2990C2214yes—
40#2989C2214yes—
41#2989C2214yes—
42#2987—21no—
43#2987—21no—
44#2980—21no—
45#2980—21no—
46#2976—22no—
47#2976—22no—
48#2968—22no—
49#2968—22no—
50#2967—22no—
51#2967—22no—
52#2925C2214yes—
53#2925C2214yes—
54#2920C2211yescharacteristic
55#2920C2211yescharacteristic
56C2×#432C2211yescharacteristic
57C2×#432C2211yescharacteristic
58#1561C2214yescomplemented
59#1559C2212yes—
60#1559C2212yes—
61#1559C2214yescomplemented
62#1557C2212yes—
63#1557C2212yes—
64#1557C2214yescomplemented
65#1556C2214yes—
66#1556C2214yes—
67#1556C2214yes—
68#1556C2214yescomplemented
69#1554C2212yes—
70#1554C2212yes—
71#1554C2214yescomplemented
72#1553C2212yes—
73#1553C2212yes—
74#1553C2214yescomplemented
75#1552C2212yes—
76#1552C2212yes—
77#1552C2214yescomplemented
78#1552C2214yescomplemented
79#1551C2212yes—
80#1551C2212yes—
81#1550C2214yescomplemented
82#1549C2214yes—
83#1549C2214yescomplemented
84#1547C2214yescomplemented
85#1546C2214yes—
86#1546C2214yescomplemented
87#1544C2214yescomplemented
88#1542C2214yescomplemented
89#1540C2214yescomplemented
90C2×#332C2214yes—
91C2×#332C2214yescomplemented
92C2×2−1+4—22no—
93C23×Q8—21no—
94#563—28no—
95#563—28no—
96Q82—22no—
97Q82C2×C414yes—
98#557—22no—
99#557—22no—
100#557—22no—
101#557C2×C414yes—
102#556—22no—
103#556—22no—
104#556—22no—
105#556C2×C414yes—
106#555—22no—
107#555C2×C414yes—
108#554—24no—
109#554—24no—
110#554—22no—
111#554—24no—
112#554—22no—
113#554C2×C414yes—
114#554C2×C418yes—
115#554C2×C414yes—
116#553—24no—
117#553—24no—
118#553—24no—
119#553C2×C418yes—
120#552—24no—
121#552—24no—
122#552—24no—
123#552C2×C418yes—
124D4×Q8—24no—
125D4×Q8—24no—
126D4×Q8—22no—
127D4×Q8—24no—
128D4×Q8—24no—
129D4×Q8—22no—
130D4×Q8—22no—
131D4×Q8C2×C414yes—
132#548—24no—
133#548—24no—
134#548—24no—
135#548—24no—
136#547—24no—
137#547—24no—
138#547—24no—
139#547—22no—
140#547—22no—
141#547—22no—
142#547C2×C418yes—
143#547C2×C414yes—
144#544—24no—
145#544—24no—
146#544—22no—
147#544—24no—
148#544C2×C414yes—
149#544C2×C418yes—
150#542—24no—
151#542—24no—
152#542—24no—
153#542C2×C418yes—
154#541—24no—
155#541—24no—
156#539—28no—
157#539—28no—
158#537—22no—
159#537C2×C414yes—
160#536—22no—
161#536—24no—
162#536—28no—
163#536—22no—
164#536—24no—
165#533—22no—
166#533—22no—
167#533C2×C411yescharacteristic
168#533D411yescharacteristic
169#533D411yescharacteristic
170#533C2314yes—
171#533C2311yescharacteristic
172#533C2311yescharacteristic
173#533C2314yes—
174#533C2311yescharacteristic
175#532—22no—
176#532C2×C411yescharacteristic
177#532D411yescharacteristic
178#532D411yescharacteristic
179#532C2311yescharacteristic
180#532C2314yes—
181#532C2311yescharacteristic
182#532C2311yescharacteristic
183C2×C4⋊Q8—22no—
184C2×C4⋊Q8—21no—
185C2×C4⋊Q8—21no—
186C2×C4⋊Q8—21no—
187C2×C4⋊Q8—21no—
188C2×C4⋊Q8—21no—
189C2×C4⋊Q8—21no—
190C2×C4⋊Q8C2×C412yes—
191C2×C4⋊Q8C2×C412yes—
192C2×C4⋊Q8C2×C412yes—
193C2×C4⋊Q8C2312yes—
194C2×C4⋊Q8C2314yes—
195C2×C4⋊Q8C2312yes—
196C2×C4⋊Q8C2312yes—
197#529—21no—
198#529—21no—
199#529—21no—
200#529—21no—
201#529C2×C412yes—
202#529C2×C412yes—
203#529C2×C412yes—
204#529C2×C412yes—
205#529D412yes—
206#529D412yes—
207#529D412yes—
208#529D412yes—
209#525—21no—
210#525—21no—
211#525—28no—
212#525C2×C412yes—
213#525C2×C412yes—
214#525D412yes—
215#525D412yes—
216#520—22no—
217#520—22no—
218#520C2×C414yes—
219#520C2×C414yes—
220#519—22no—
221C4×#41—21no—
222C4×#41—21no—
223C4×#41C2×C412yes—
224C4×#41C2312yes—
225C4×#41C2312yes—
226C4×#41C2312yes—
227C22×C4⋊C4—21no—
228C22×C4⋊C4C2×C412yes—
229C22×C42C2311yescharacteristic
230#446—24no—
231#446—24no—
232#446—24no—
233#446—24no—
234#436—24no—
235#436—24no—
236#435—24no—
237#435—24no—
238#435—24no—
239#435—24no—
240#435—24no—
241#435—24no—
242#435—24no—
243#435—24no—
244C8×D4—24no—
245C8×D4—24no—
246#433—24no—
247#433—24no—
248#433—24no—
249#433—24no—
250#432—21no—
251#432—21no—
252#432—21no—
253#432—21no—
254#432—21no—
255#432—21no—
256#432C2312yes—
257#432C2312yes—
258#432C2314yes—
259#432C2314yes—
260#432C2312yes—
261#432C2312yes—
262#432C2312yes—
263#432C2312yes—
264#431—21no—
265#431—21no—
266#431C2314yes—
267#431C2314yes—
268#431C2312yes—
269#431C2312yes—
270#423C2312yes—
271#423C2314yes—
272#423C2312yes—
273#423C2314yes—
274C2×C4⋊C8C2312yes—
275C2×C4⋊C8C2312yes—
276C2×C4⋊C8C2314yes—
277C2×C4⋊C8C2314yes—
278#408—24no—
279#408—24no—
280#407—21no—
281#407—21no—
282C2×C22⋊C8—21no—
283C2×C22⋊C8—21no—
284#405—24no—
285#405—24no—
286C4×M16—21no—
287C4×M16—21no—
288C2×#97—21no—
289C2×#97—21no—
290#333C2314yes—
291#333C2314yes—
292#332C2314yes—
293#332C2314yes—
294#332C2314yes—
295#332C2314yes—
296#332C2314yes—
297#332C2314yes—
298#332C2314yes—
299#332C2314yes—
300#332C2314yes—
301#332C2314yes—
302#332C2314yes—
303#332C2314yes—
304#331C2314yes—
305#331C2314yes—
3062−1+4—84no—
3072−1+4—84no—
308C2×#41—28no—
309C2×#41—24no—
310C2×#41—21no—
311C2×#41—21no—
312C2×#41—24no—
313C2×#41C22×C412yes—
314C2×#41C22×C412yes—
315C2×#41C2×D412yes—
316C2×#41C2×D412yes—
317C22×Q8—24no—
318C22×Q8—22no—
319C22×Q8—22no—
320C22×Q8—22no—
321C22×Q8—22no—
322C22×Q8—22no—
323C22×Q8—22no—
324C22×Q8—24no—
325C22×Q8—84no—
326C23×C4—22no—
327C23×C4C22×C411yescharacteristic
328C23×C4C2×D411yescharacteristic
329C23×C4C2×D411yescharacteristic
330C2×M16—22no—
331C2×M16—22no—
332C2×M16—24no—
333C2×M16—24no—
334C22×C8—22no—
335C22×C8—22no—
336C22×C8—24no—
337C22×C8—24no—
338C4⋊Q8—24no—
339C4⋊Q8—24no—
340C4⋊Q8—24no—
341C4⋊Q8—28no—
342C4⋊Q8—28no—
343C4⋊Q8—22no—
344C4⋊Q8—22no—
345C4⋊Q8—22no—
346C4⋊Q8—22no—
347C4⋊Q8—22no—
348C4⋊Q8—22no—
349C4⋊Q8—22no—
350C4⋊Q8—22no—
351C4⋊Q8—22no—
352C4⋊Q8—22no—
353C4⋊Q8—22no—
354C4⋊Q8—22no—
355C4⋊Q8—24no—
356C4⋊Q8—24no—
357C4⋊Q8C22⋊C411yescharacteristic
358C4⋊Q8C22⋊C411yescharacteristic
359C4⋊Q8C22⋊C411yescharacteristic
360C4⋊Q8C22×C414yes—
361C4⋊Q8C22×C414yes—
362C4⋊Q8C22×C414yes—
363C4⋊Q8C22×C418yes—
364C4⋊Q8C2411yescharacteristic
365C4⋊Q8C2414yes—
366C4⋊Q8C2411yescharacteristic
367C4⋊Q8C2411yescharacteristic
368#127C22⋊C411yescharacteristic
369#127C2411yescharacteristic
370#126—28no—
371#126—28no—
372#126—28no—
373#126—28no—
374#126—22no—
375#126—22no—
376#126C22⋊C414yes—
377#126C22⋊C414yes—
378#125—24no—
379#125—24no—
380#125—28no—
381#125—28no—
382#125—28no—
383#125—28no—
384#125—21no—
385#125—21no—
386#125—24no—
387#125C22⋊C412yes—
388#125C22⋊C412yes—
389#125C22⋊C412yes—
390#125C22×C412yes—
391#125C22×C418yes—
392#124—24no—
393#124—28no—
394#124—28no—
395#124—21no—
396#124—21no—
397#124—24no—
398#124C22⋊C412yes—
399#124C22⋊C412yes—
400#124C22⋊C412yes—
401#124C22×C412yes—
402#123—28no—
403#123—22no—
404#123—22no—
405#123—22no—
406#123—28no—
407#123—28no—
408#123—28no—
409#123—28no—
410#123—28no—
411#123C22⋊C414yes—
412#123C22⋊C414yes—
413#123C22⋊C414yes—
414C22⋊Q8—24no—
415C22⋊Q8—24no—
416C22⋊Q8—21no—
417C22⋊Q8—21no—
418C22⋊Q8—21no—
419C22⋊Q8—21no—
420C22⋊Q8—24no—
421C22⋊Q8—24no—
422C22⋊Q8—24no—
423C22⋊Q8—24no—
424C22⋊Q8—24no—
425C22⋊Q8—28no—
426C22⋊Q8—28no—
427C22⋊Q8—28no—
428C22⋊Q8—28no—
429C22⋊Q8—28no—
430C22⋊Q8—28no—
431C22⋊Q8—28no—
432C22⋊Q8—28no—
433C22⋊Q8—28no—
434C22⋊Q8—28no—
435C22⋊Q8C22⋊C412yes—
436C22⋊Q8C22⋊C412yes—
437C22⋊Q8C22⋊C412yes—
438C22⋊Q8C22⋊C412yes—
439C22⋊Q8C22⋊C412yes—
440C22⋊Q8C22⋊C412yes—
441C22⋊Q8C22×C412yes—
442C22⋊Q8C22×C412yes—
443C22⋊Q8C22×C418yes—
444#121—28no—
445#121—28no—
446#121—24no—
447#121—24no—
448#121—21no—
449#121—21no—
450#121—21no—
451#121—21no—
452#121—24no—
453#121C22⋊C412yes—
454#121C22⋊C412yes—
455#121C22⋊C412yes—
456#121C22⋊C412yes—
457#121C22⋊C412yes—
458#121C22⋊C412yes—
459#121C22×C412yes—
460#121C22×C412yes—
461#121C22×C418yes—
462#120—22no—
463#120C22⋊C414yes—
464C4×Q8—24no—
465C4×Q8—24no—
466C4×Q8—24no—
467C4×Q8—24no—
468C4×Q8—21no—
469C4×Q8—21no—
470C4×Q8—21no—
471C4×Q8—21no—
472C4×Q8—24no—
473C4×Q8—24no—
474C4×Q8—24no—
475C4×Q8C22×C412yes—
476C4×Q8C22×C412yes—
477C4×Q8C22×C418yes—
478C4×Q8C22×C412yes—
479C4×Q8C22×C412yes—
480C4×Q8C2×D412yes—
481C4×Q8C2×D412yes—
482C4×Q8C2×D412yes—
483C4×Q8C2×D412yes—
484C4×D4—28no—
485C4×D4—24no—
486C4×D4—28no—
487C4×D4—24no—
488C4×D4—22no—
489C4×D4—22no—
490C4×D4—22no—
491C4×D4—22no—
492C4×D4—22no—
493C4×D4—22no—
494C4×D4—28no—
495C4×D4—28no—
496C4×D4—21no—
497C4×D4—21no—
498C4×D4—21no—
499C4×D4—21no—
500C4×D4—24no—
501C4×D4C22×C412yes—
502C4×D4C22×C412yes—
503C4×D4C22×C418yes—
504C4×D4C22×C414yes—
505C4×D4C22×C414yes—
506C4×D4C22×C412yes—
507C4×D4C22×C412yes—
508C4×D4C2×D414yes—
509C4×D4C2×D414yes—
510C4×D4C2×D414yes—
511C4×D4C2×D414yes—
512C4×D4C2×D412yes—
513C4×D4C2×D412yes—
514C4×D4C2×D412yes—
515C4×D4C2×D412yes—
516#117—21no—
517#117—21no—
518#117—24no—
519#117—24no—
520#117—24no—
521#117—28no—
522#117—22no—
523#117—22no—
524#117—22no—
525#117C22×C412yes—
526#117C22×C418yes—
527#117C22×C412yes—
528#117C22×C414yes—
529#117C2×D412yes—
530#117C2×D412yes—
531#117C2×D414yes—
532#117C2×D414yes—
533C2×C4⋊C4—22no—
534C2×C4⋊C4—22no—
535C2×C4⋊C4—22no—
536C2×C4⋊C4—22no—
537C2×C4⋊C4—22no—
538C2×C4⋊C4—22no—
539C2×C4⋊C4—22no—
540C2×C4⋊C4—22no—
541C2×C4⋊C4—22no—
542C2×C4⋊C4—24no—
543C2×C4⋊C4—24no—
544C2×C4⋊C4—24no—
545C2×C4⋊C4C22×C414yes—
546C2×C4⋊C4C22×C414yes—
547C2×C4⋊C4C22×C414yes—
548C2×C4⋊C4C22×C418yes—
549C2×C42—22no—
550C2×C42C22×C411yescharacteristic
551C2×C42C22×C411yescharacteristic
552C2×C42C22×C411yescharacteristic
553C2×C42C2×D411yescharacteristic
554C2×C42C2×D411yescharacteristic
555C2×C42C2×D411yescharacteristic
556C2×C42C2×D411yescharacteristic
557C2×C42C2×D411yescharacteristic
558C2×C42C2×D411yescharacteristic
559C2×C42C2414yes—
560C2×C42C2411yescharacteristic
561C2×C42C2411yescharacteristic
562C2×C42C2411yescharacteristic
563C4⋊C8—22no—
564C4⋊C8—22no—
565C4⋊C8—24no—
566C4⋊C8—24no—
567C4⋊C8—22no—
568C4⋊C8—22no—
569C4⋊C8—24no—
570C4⋊C8—24no—
571C4⋊C8C2414yes—
572C4⋊C8C2414yes—
573C4⋊C8C2414yes—
574C4⋊C8C2414yes—
575C22⋊C8—22no—
576C22⋊C8—22no—
577C22⋊C8—22no—
578C22⋊C8—22no—
579C22⋊C8—22no—
580C22⋊C8—22no—
581C22⋊C8—22no—
582C22⋊C8—22no—
583C22⋊C8—24no—
584C22⋊C8—24no—
585C22⋊C8—24no—
586C22⋊C8—24no—
587#97—22no—
588#97—22no—
589#97—22no—
590#97—22no—
591#97—22no—
592#97—22no—
593#97—24no—
594#97—24no—
595C4×C8—22no—
596C4×C8—22no—
597C4×C8—24no—
598C4×C8—24no—
599C24C2×C22⋊C411yescharacteristic
600#41—42no—
601#41—42no—
602#41—42no—
603#41—42no—
604#41—44no—
605#41—44no—
606#41—44no—
607#41—44no—
608#41—84no—
609#41—84no—
610#41—816no—
611#41—88no—
612C2×Q8—24no—
613C2×Q8—28no—
614C2×Q8—24no—
615C2×Q8—24no—
616C2×Q8—21no—
617C2×Q8—24no—
618C2×Q8—21no—
619C2×Q8—44no—
620C2×Q8—44no—
621C2×Q8—84no—
622C2×Q8—84no—
623C2×Q8—84no—
624C2×Q8—84no—
625C2×Q8—84no—
626C2×Q8—84no—
627C2×Q8—84no—
628C2×Q8—88no—
629C2×Q8C2×C22⋊C412yes—
630C2×Q8C2×C22⋊C412yes—
631C2×Q8C2×C22⋊C412yes—
632C2×Q8C23×C412yes—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—22no—
636C2×D4—28no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4C2×C22⋊C414yes—
640C2×D4C2×C22⋊C414yes—
641C2×D4C2×C22⋊C412yes—
642C2×D4C2×C22⋊C412yes—
643C2×D4C2×C22⋊C414yes—
644C2×D4C2×C22⋊C412yes—
645C2×D4C23×C412yes—
646C22×C4—24no—
647C22×C4—24no—
648C22×C4—24no—
649C22×C4—28no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—28no—
654C22×C4—42no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—84no—
658C22×C4C2×C22⋊C411yescharacteristic
659C22×C4C2×C22⋊C411yescharacteristic
660C22×C4C2×C22⋊C411yescharacteristic
661C22×C4C2×C22⋊C411yescharacteristic
662C22×C4C2×C22⋊C411yescharacteristic
663C22×C4C2×C22⋊C411yescharacteristic
664C22×C4C2×C22⋊C411yescharacteristic
665C22×C4C2×C22⋊C411yescharacteristic
666C22×C4C2×C22⋊C411yescharacteristic
667C22×C4C23×C411yescharacteristic
668C22×C4C23×C411yescharacteristic
669C22×C4C23×C411yescharacteristic
670C22×C4C23×C414yes—
671C22×C4C22×D411yescharacteristic
672C22×C4C22×D411yescharacteristic
673C22×C4C22×D411yescharacteristic
674C22×C4C22×D411yescharacteristic
675C22×C4C22×D411yescharacteristic
676C22×C4C22×D411yescharacteristic
677C22×C4C22×D414yes—
678C22×C4C22×D414yes—
679M16—84no—
680M16—82no—
681M16—84no—
682M16—82no—
683C2×C8—24no—
684C2×C8—24no—
685C2×C8—24no—
686C2×C8—24no—
687C2×C8—82no—
688C2×C8—84no—
689C2×C8—82no—
690C2×C8—84no—
691C4⋊C4—24no—
692C4⋊C4—24no—
693C4⋊C4—24no—
694C4⋊C4—24no—
695C4⋊C4—24no—
696C4⋊C4—24no—
697C4⋊C4—28no—
698C4⋊C4—28no—
699C4⋊C4—28no—
700C4⋊C4—28no—
701C4⋊C4—22no—
702C4⋊C4—22no—
703C4⋊C4—22no—
704C4⋊C4—22no—
705C4⋊C4—22no—
706C4⋊C4—22no—
707C4⋊C4—28no—
708C4⋊C4—28no—
709C4⋊C4—24no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4C2×C22⋊C412yes—
715C4⋊C4C2×C22⋊C412yes—
716C4⋊C4C2×C22⋊C412yes—
717C4⋊C4C2×C22⋊C412yes—
718C4⋊C4C2×C22⋊C414yes—
719C4⋊C4C2×C22⋊C414yes—
720C4⋊C4C2×C22⋊C412yes—
721C4⋊C4C2×C22⋊C414yes—
722C4⋊C4C2×C22⋊C414yes—
723C4⋊C4C2×C22⋊C412yes—
724C4⋊C4C2×C22⋊C414yes—
725C4⋊C4C2×C22⋊C414yes—
726C4⋊C4C23×C418yes—
727C4⋊C4C23×C412yes—
728C4⋊C4C23×C412yes—
729C22⋊C4—22no—
730C22⋊C4—22no—
731C22⋊C4—28no—
732C22⋊C4—22no—
733C22⋊C4—28no—
734C22⋊C4—28no—
735C22⋊C4—22no—
736C22⋊C4—22no—
737C22⋊C4—22no—
738C22⋊C4—22no—
739C22⋊C4—28no—
740C22⋊C4—22no—
741C22⋊C4—22no—
742C22⋊C4C2×C22⋊C414yes—
743C22⋊C4C2×C22⋊C414yes—
744C22⋊C4C2×C22⋊C414yes—
745C22⋊C4C2×C22⋊C414yes—
746C22⋊C4C2×C22⋊C414yes—
747C22⋊C4C2×C22⋊C414yes—
748C22⋊C4C2×C22⋊C414yes—
749C22⋊C4C2×C22⋊C414yes—
750C22⋊C4C2×C22⋊C414yes—
751C42—22no—
752C42—22no—
753C42—22no—
754C42—28no—
755C42—28no—
756C42C2×C22⋊C411yescharacteristic
757C42C2×C22⋊C411yescharacteristic
758C42C2×C22⋊C411yescharacteristic
759C42C2×C22⋊C411yescharacteristic
760C42C2×C22⋊C411yescharacteristic
761C42C2×C22⋊C411yescharacteristic
762C42C23×C411yescharacteristic
763C42C23×C411yescharacteristic
764C42C23×C411yescharacteristic
765C42C23×C414yes—
766C42C22×D411yescharacteristic
767C42C22×D411yescharacteristic
768C42C22×D414yes—
769C42C22×D414yes—
770C42C22×D411yescharacteristic
771C42C22×D411yescharacteristic
772C42C22×D411yescharacteristic
773C42C22×D411yescharacteristic
774C42C2511yescharacteristic
775C23—22no—
776C23—22no—
777C23—41no—
778C23—41no—
779C23C22×C22⋊C414yes—
780C23C22×C22⋊C411yescharacteristic
781C23C22×C22⋊C411yescharacteristic
782C23C22×C22⋊C411yescharacteristic
783Q8—42no—
784Q8—42no—
785Q8—42no—
786Q8—42no—
787Q8—48no—
788Q8—44no—
789Q8—44no—
790Q8—42no—
791Q8—42no—
792Q8—84no—
793Q8—84no—
794Q8—88no—
795D4—28no—
796D4—42no—
797D4—42no—
798D4—44no—
799D4—42no—
800D4—44no—
801D4—42no—
802D4—44no—
803D4—44no—
804D4—44no—
805D4—42no—
806D4—42no—
807D4—88no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—24no—
812C2×C4—22no—
813C2×C4—24no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—24no—
817C2×C4—22no—
818C2×C4—24no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—28no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—44no—
835C2×C4—44no—
836C2×C4—44no—
837C2×C4—44no—
838C2×C4—48no—
839C2×C4—88no—
840C2×C4—84no—
841C2×C4—84no—
842C2×C4—88no—
843C2×C4C22×C22⋊C411yescharacteristic
844C2×C4C22×C22⋊C411yescharacteristic
845C2×C4C22×C22⋊C411yescharacteristic
846C2×C4C22×C22⋊C414yes—
847C2×C4C22×C22⋊C414yes—
848C2×C4C22×C22⋊C411yescharacteristic
849C2×C4C22×C22⋊C411yescharacteristic
850C2×C4C22×C22⋊C411yescharacteristic
851C2×C4C22×C22⋊C411yescharacteristic
852C2×C4C22×C22⋊C411yescharacteristic
853C2×C4C22×C22⋊C411yescharacteristic
854C2×C4C22×C22⋊C414yes—
855C2×C4C24×C411yescharacteristic
856C2×C4C23×D411yescharacteristic
857C2×C4C23×D411yescharacteristic
858C8—44no—
859C8—44no—
860C8—44no—
861C8—44no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—24no—
867C22—21no—
868C22—21no—
869C22—24no—
870C22—21no—
871C22—21no—
872C22—24no—
873C22—44no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22#288912yes—
878C22C23×C22⋊C411yescharacteristic
879C4—21no—
880C4—21no—
881C4—21no—
882C4—21no—
883C4—24no—
884C4—21no—
885C4—21no—
886C4—21no—
887C4—24no—
888C4—21no—
889C4—21no—
890C4—21no—
891C4—24no—
892C4—42no—
893C4—42no—
894C4—48no—
895C4—42no—
896C4#358512yes—
897C4#358612yes—
898C2—22no—
899C2—44no—
900C2—41no—
901C2—41no—
902C2—82no—
903C2C2×#288911yescharacteristic
904C2#6008711yescharacteristic
905C2#6008811yescharacteristic
subgroupG/H
center, socleC22C23×C22⋊C4
commutatorC2×C4C24×C4
Frattini, cosocleC42C25
prime radical#62833C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ #3444 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60293C2semidirect
3. #60293C2semidirect
4. #17775C2semidirect
5. #17774C2semidirect
6. #17769C2semidirect
7. #17767C2semidirect
8. #17761C2semidirect
9. #17759C2semidirect
10. #17756C2semidirect
11. #17756C2semidirect
12. #17742C2semidirect
13. C2×#1556C2semidirect
58. #1561C22semidirect
61. #1559C22semidirect
64. #1557C22semidirect
68. #1556C22semidirect
71. #1554C22semidirect
74. #1553C22semidirect
77. #1552C22semidirect
78. #1552C22semidirect
81. #1550C22semidirect
83. #1549C22semidirect
84. #1547C22semidirect
86. #1546C22semidirect
87. #1544C22semidirect
88. #1542C22semidirect
89. #1540C22semidirect
91. C2×#332C22semidirect

Maximal subgroups

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

subgroupindex
#628332
#602932
#177752
#177742
#177692
#177672
#177612
#177592
#177562
#177422
C2×#15562