Finite Group Databasebeta

← #6394058

Subgroups — #6394058

Order 512.

2914 conjugacy classes of subgroups.

The subgroup lattice has 939 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3559C211yesmaximal, characteristic
2#60264C211yesmaximal, characteristic, complemented
3#60214C211yesmaximal, characteristic, complemented
4#22515C214yesmaximal, complemented
5#22482C214yesmaximal, complemented
6#22482C214yesmaximal, complemented
7#22479C214yesmaximal, complemented
8#21882C212yesmaximal, complemented
9#21878C211yesmaximal, characteristic, complemented
10#21832C212yesmaximal, complemented
11#21830C211yesmaximal, characteristic, complemented
12#21428C212yesmaximal, complemented
13#21424C211yesmaximal, characteristic, complemented
14#21338C212yesmaximal, complemented
15C2×#1998C211yesmaximal, characteristic, complemented
16#3559—22no—
17#3559—22no—
18#3559—22no—
19#3559—22no—
20#3559—22no—
21#3559—22no—
22#3559—22no—
23#3559—22no—
24C2×#563C412yes—
25C2×#562C412yes—
26C2×#554C2212yes—
27C2×#553C2212yes—
28C2×#553C2212yes—
29C2×#547C414yes—
30C2×#547C2212yes—
31C2×#544C2212yes—
32C2×#540C2212yes—
33C2×#539C412yes—
34C2×#539C414yes—
35C2×#537C412yes—
36C2×#532C2211yescharacteristic
37C2×#529C2211yescharacteristic
38C22×#125C2211yescharacteristic
39#2995—22no—
40#2994—22no—
41#2993—22no—
42#2992—22no—
43#2969—22no—
44#2968—22no—
45#2967—22no—
46#2966—22no—
47Q8×M16C2212yes—
48Q8×M16C2212yes—
49D4×M16C2214yes—
50D4×M16C2212yes—
51D4×M16C2214yes—
52D4×M16C2212yes—
53#2921C2212yes—
54#2921C2212yes—
55#2920C2211yescharacteristic
56#2920C2211yescharacteristic
57#2905C2212yes—
58C2×#423C2211yescharacteristic
59#2873C2212yes—
60C2×C4×M16C2211yescharacteristic
61#1998C2212yes—
62#1998C2212yes—
63#1998C2214yes—
64#1998C2212yes—
65#1998C2214yes—
66#1998C2212yes—
67#1998C2214yes—
68#1998C2214yes—
69#1997C2211yescharacteristic
70#1997C2212yes—
71#1997C2214yes—
72#1997C2211yescharacteristic
73#1997C2214yes—
74#1965C2212yes—
75#1965C2211yescharacteristic
76#1965C2211yescharacteristic
77#1900C2214yes—
78#1900C2214yes—
79#1900C2214yes—
80#1900C2214yes—
81#1900C2214yes—
82#1900C2214yes—
83#1822C2214yes—
84#1821C2212yes—
85#1821C2212yes—
86#1821C2214yes—
87#1800C2214yes—
88#1800C2214yes—
89#1800C2214yes—
90C4×#100C2214yes—
91C4×#100C2214yes—
92C4×#100C2214yes—
93#1742C2214yes—
94C2×#343C2212yes—
95C2×#343C2212yes—
96C2×#343C2214yes—
97C22×#41C2×C412yes—
98C22×#41C2×C414yes—
99C22×M16C2312yes—
100C22×M16C2314yes—
101C22×M16C2312yes—
102C22×M16C2314yes—
103#563—24no—
104#563—24no—
105#563—24no—
106#563—24no—
107#562—24no—
108#562—24no—
109#562—24no—
110#562—24no—
111#554—24no—
112#554—24no—
113#554—24no—
114#554—24no—
115#553—24no—
116#553—24no—
117#553—24no—
118#553—24no—
119#553—24no—
120#553—24no—
121#553—24no—
122#553—24no—
123#547—28no—
124#547—28no—
125#547—28no—
126#547—28no—
127#547—24no—
128#547—24no—
129#547—24no—
130#547—24no—
131#544—24no—
132#544—24no—
133#544—24no—
134#544—24no—
135#540—24no—
136#540—24no—
137#540—24no—
138#540—24no—
139#539—28no—
140#539—28no—
141#539—28no—
142#539—28no—
143#539—24no—
144#539—24no—
145#539—24no—
146#539—24no—
147#537—24no—
148#537—24no—
149#537—24no—
150#537—24no—
151#532—21no—
152#532—21no—
153#532—21no—
154#532—21no—
155#532—21no—
156#532—21no—
157#532—21no—
158#532—21no—
159C2×C4⋊Q8C2×C414yes—
160C2×C4⋊Q8C2311yescharacteristic
161C2×C4⋊Q8C2312yes—
162C2×#127C2311yescharacteristic
163#529D412yes—
164#529D412yes—
165#529D412yes—
166#529D412yes—
167#529D412yes—
168#529D412yes—
169#529D412yes—
170#529D412yes—
171C2×#126C2×C414yes—
172C2×#126C2×C414yes—
173C2×#126C2×C412yes—
174C2×#125—21no—
175C2×#125—21no—
176C2×#125—21no—
177C2×#125—21no—
178C2×#125—21no—
179C2×#125—21no—
180C2×#125—21no—
181C2×#125—21no—
182C2×#125C2×C412yes—
183C2×#125C2×C412yes—
184C2×#125C2×C414yes—
185C2×#125C2×C411yescharacteristic
186C2×#125C2312yes—
187C2×#125C2312yes—
188C2×#125C2312yes—
189C2×#124C2×C412yes—
190C2×#124C2×C411yescharacteristic
191C2×#123C2×C414yes—
192C2×#123C2×C414yes—
193C2×#123C2×C414yes—
194C2×#123C2×C414yes—
195C2×#123C2×C414yes—
196C2×#123C2×C414yes—
197C2×#123C2×C412yes—
198C2×C22⋊Q8C2×C414yes—
199C2×C22⋊Q8C2×C414yes—
200C2×C22⋊Q8C2×C414yes—
201C2×C22⋊Q8C2×C414yes—
202C2×C22⋊Q8C2×C414yes—
203C2×C22⋊Q8C2×C414yes—
204C2×C22⋊Q8C2×C411yescharacteristic
205C2×#121C2×C412yes—
206C2×#121C2×C414yes—
207C2×#121C2×C414yes—
208C2×#121C2×C414yes—
209C2×#121C2×C414yes—
210C2×#121C2×C411yescharacteristic
211C2×#121C2312yes—
212C2×#121C2312yes—
213C2×#121C2312yes—
214C2×C4×Q8C2311yescharacteristic
215C2×C4×D4C2×C412yes—
216C2×C4×D4C2×C414yes—
217C2×C4×D4C2×C414yes—
218C2×C4×D4C2312yes—
219C2×C4×D4C2311yescharacteristic
220C2×C4×D4C2312yes—
221C2×C4×D4C2312yes—
222C2×C4×D4C2312yes—
223C2×#117C2312yes—
224C2×#117C2312yes—
225C22×C4⋊C4C2×C412yes—
226C22×C4⋊C4C2×C412yes—
227C22×C4⋊C4C2×C414yes—
228C22×C4⋊C4C2311yescharacteristic
229C22×C4⋊C4C2311yescharacteristic
230C22×C4⋊C4C2312yes—
231C22×C42C2311yescharacteristic
232#446—22no—
233#446—24no—
234#446—24no—
235#446—22no—
236C8×Q8—22no—
237C8×Q8—22no—
238#436—22no—
239#436—24no—
240#436—22no—
241#436—24no—
242#435—24no—
243#435—24no—
244#435—24no—
245#435—24no—
246#435—24no—
247#435—24no—
248C8×D4—24no—
249C8×D4—22no—
250C8×D4—24no—
251C8×D4—22no—
252#433—24no—
253#433—24no—
254#433—24no—
255#433—24no—
256#432—21no—
257#432—21no—
258#432—21no—
259#432—21no—
260#431—21no—
261#431—21no—
262#431—21no—
263#431—21no—
264#424—24no—
265#424—24no—
266#423—21no—
267#423—21no—
268#423C2312yes—
269#423C2314yes—
270#423C2312yes—
271#423C2314yes—
272#423C2312yes—
273#423C2311yescharacteristic
274#423C2311yescharacteristic
275C2×C4⋊C8—21no—
276C2×C4⋊C8—21no—
277C2×#100C2314yes—
278C2×#100C2314yes—
279C2×#100C2314yes—
280C2×#100C2314yes—
281#407C2312yes—
282#407C2312yes—
283#407C2314yes—
284#407C2314yes—
285#405—24no—
286#405—24no—
287C4×M16—21no—
288C4×M16—21no—
289C4×M16C2311yescharacteristic
290C4×M16C2311yescharacteristic
291C4×M16C2312yes—
292C4×M16C2312yes—
293C4×M16C2314yes—
294C4×M16C2312yes—
295C4×M16C2314yes—
296C2×#97—21no—
297C2×C4×C8—21no—
298#343C2314yes—
299#343C2314yes—
300#343C2314yes—
301#343C2314yes—
302#343C2314yes—
303#343C2314yes—
304#343C2314yes—
305#343C2314yes—
306#343C2314yes—
307#343C2314yes—
308#343C2314yes—
309#343C2314yes—
310C2×#41—28no—
311C2×#41—28no—
312C2×#41—22no—
313C2×#41—22no—
314C2×#41—22no—
315C2×#41—22no—
316C2×#41—84no—
317C2×#41—88no—
318C22×Q8C22×C414yes—
319C22×Q8C22×C412yes—
320C22×Q8C22×C411yescharacteristic
321C22×D4C22×C414yes—
322C22×D4C22×C414yes—
323C22×D4C22×C412yes—
324C22×D4C22×C414yes—
325C22×D4C22×C412yes—
326C22×D4C22×C412yes—
327C22×D4C22×C411yescharacteristic
328C22×D4C2412yes—
329C23×C4C22×C412yes—
330C23×C4C22×C412yes—
331C23×C4C22×C414yes—
332C23×C4C22×C414yes—
333C23×C4C22×C414yes—
334C23×C4C22×C414yes—
335C23×C4C22×C411yescharacteristic
336C23×C4C22×C411yescharacteristic
337C23×C4C2411yescharacteristic
338C23×C4C2412yes—
339C2×M16—22no—
340C2×M16—24no—
341C2×M16—22no—
342C2×M16—24no—
343C2×M16—24no—
344C2×M16—28no—
345C2×M16—42no—
346C2×M16—44no—
347C2×M16—42no—
348C2×M16—42no—
349C2×M16—44no—
350C2×M16—44no—
351C2×M16C2414yes—
352C2×M16C2412yes—
353C2×M16C2412yes—
354C2×M16C2414yes—
355C2×M16C2412yes—
356C2×M16C2412yes—
357C22×C8—22no—
358C22×C8—24no—
359C22×C8—22no—
360C22×C8—24no—
361C4⋊Q8—28no—
362C4⋊Q8—28no—
363C4⋊Q8—21no—
364C4⋊Q8—21no—
365C4⋊Q8—21no—
366C4⋊Q8—21no—
367C4⋊Q8—24no—
368C4⋊Q8—24no—
369#127—21no—
370#127—21no—
371#127—21no—
372#127—21no—
373#126—28no—
374#126—28no—
375#126—28no—
376#126—28no—
377#126C22⋊C414yes—
378#126C22⋊C414yes—
379#126C22⋊C414yes—
380#126C22⋊C414yes—
381#125—28no—
382#125—28no—
383#125—22no—
384#125—22no—
385#125—22no—
386#125—22no—
387#125—22no—
388#125—22no—
389#125—22no—
390#125—22no—
391#125—22no—
392#125—22no—
393#125—22no—
394#125—22no—
395#125—22no—
396#125—22no—
397#125—22no—
398#125—22no—
399#125—24no—
400#125—24no—
401#125C22⋊C412yes—
402#125C22⋊C412yes—
403#125C22⋊C412yes—
404#125C22⋊C412yes—
405#124—22no—
406#124—22no—
407#124—22no—
408#124—22no—
409#124C22⋊C412yes—
410#124C22⋊C412yes—
411#124C22⋊C412yes—
412#124C22⋊C412yes—
413#123—28no—
414#123—28no—
415#123—28no—
416#123—28no—
417#123—28no—
418#123—28no—
419#123—28no—
420#123—28no—
421#123—28no—
422#123—28no—
423#123—28no—
424#123—28no—
425#123C22⋊C414yes—
426#123C22⋊C414yes—
427#123C22⋊C414yes—
428#123C22⋊C414yes—
429C22⋊Q8—28no—
430C22⋊Q8—28no—
431C22⋊Q8—28no—
432C22⋊Q8—28no—
433C22⋊Q8—28no—
434C22⋊Q8—28no—
435C22⋊Q8—28no—
436C22⋊Q8—28no—
437C22⋊Q8—28no—
438C22⋊Q8—28no—
439C22⋊Q8—28no—
440C22⋊Q8—28no—
441C22⋊Q8C22⋊C412yes—
442C22⋊Q8C22⋊C412yes—
443C22⋊Q8C22⋊C412yes—
444C22⋊Q8C22⋊C412yes—
445#121—28no—
446#121—28no—
447#121—28no—
448#121—28no—
449#121—22no—
450#121—22no—
451#121—22no—
452#121—22no—
453#121—22no—
454#121—22no—
455#121—22no—
456#121—22no—
457#121—24no—
458#121—24no—
459#121—24no—
460#121—24no—
461#121—28no—
462#121—28no—
463#121—28no—
464#121—28no—
465#121C22⋊C412yes—
466#121C22⋊C412yes—
467#121C22⋊C412yes—
468#121C22⋊C412yes—
469C4×Q8C2×D412yes—
470C4×Q8C2×D412yes—
471C4×Q8C2×D412yes—
472C4×Q8C2×D412yes—
473C4×D4—28no—
474C4×D4—28no—
475C4×D4—28no—
476C4×D4—28no—
477C4×D4—22no—
478C4×D4—22no—
479C4×D4—22no—
480C4×D4—22no—
481C4×D4—22no—
482C4×D4—22no—
483C4×D4—22no—
484C4×D4—22no—
485C4×D4—24no—
486C4×D4—24no—
487C4×D4—24no—
488C4×D4—24no—
489C4×D4C2×D414yes—
490C4×D4C2×D414yes—
491C4×D4C2×D414yes—
492C4×D4C2×D414yes—
493C4×D4C2×D412yes—
494C4×D4C2×D412yes—
495C4×D4C2×D412yes—
496C4×D4C2×D412yes—
497#117—24no—
498#117—24no—
499#117C2×D414yes—
500#117C2×D414yes—
501#117C2×D414yes—
502#117C2×D414yes—
503C2×C4⋊C4—22no—
504C2×C4⋊C4—22no—
505C2×C4⋊C4—22no—
506C2×C4⋊C4—22no—
507C2×C4⋊C4—22no—
508C2×C4⋊C4—22no—
509C2×C4⋊C4—22no—
510C2×C4⋊C4—22no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—24no—
520C2×C4⋊C4—24no—
521C2×C4⋊C4—28no—
522C2×C4⋊C4—28no—
523C2×C4⋊C4C22×C414yes—
524C2×C4⋊C4C22×C414yes—
525C2×C4⋊C4C22×C414yes—
526C2×C4⋊C4C22×C414yes—
527C2×C4⋊C4C22×C414yes—
528C2×C4⋊C4C22×C414yes—
529C2×C4⋊C4C22×C412yes—
530C2×C4⋊C4C22×C414yes—
531C2×C4⋊C4C22×C412yes—
532C2×C4⋊C4C22×C412yes—
533C2×C4⋊C4C22×C414yes—
534C2×C4⋊C4C22×C412yes—
535C2×C4⋊C4C22×C412yes—
536C2×C4⋊C4C22×C412yes—
537C2×C4⋊C4C22×C412yes—
538C2×C4⋊C4C22×C411yescharacteristic
539C2×C4⋊C4C22×C411yescharacteristic
540C2×C4⋊C4C2412yes—
541C2×C4⋊C4C2412yes—
542C2×C4⋊C4C2412yes—
543C2×C22⋊C4C22×C414yes—
544C2×C22⋊C4C22×C414yes—
545C2×C22⋊C4C22×C414yes—
546C2×C22⋊C4C22×C414yes—
547C2×C22⋊C4C22×C414yes—
548C2×C22⋊C4C22×C414yes—
549C2×C22⋊C4C22×C414yes—
550C2×C22⋊C4C22×C412yes—
551C2×C22⋊C4C22×C412yes—
552C2×C22⋊C4C22×C412yes—
553C2×C22⋊C4C22×C412yes—
554C2×C22⋊C4C22×C412yes—
555C2×C42C22×C414yes—
556C2×C42C22×C411yescharacteristic
557C2×C42C22×C411yescharacteristic
558C2×C42C2×D411yescharacteristic
559C2×C42C2×D411yescharacteristic
560C2×C42C2×D411yescharacteristic
561C2×C42C2×D411yescharacteristic
562C2×C42C2×D411yescharacteristic
563C2×C42C2×D411yescharacteristic
564C2×C42C2×D411yescharacteristic
565C2×C42C2×D411yescharacteristic
566C2×C42C2411yescharacteristic
567C2×C42C2412yes—
568C2×C42C2411yescharacteristic
569C4⋊C8—22no—
570C4⋊C8—22no—
571C4⋊C8—22no—
572C4⋊C8—22no—
573C4⋊C8—21no—
574C4⋊C8—21no—
575C4⋊C8—24no—
576C4⋊C8—24no—
577C4⋊C8—21no—
578C4⋊C8—21no—
579C4⋊C8—22no—
580C4⋊C8—22no—
581C4⋊C8—24no—
582C4⋊C8—24no—
583#100—28no—
584#100—44no—
585#100—44no—
586#100—44no—
587C22⋊C8—22no—
588C22⋊C8—22no—
589C22⋊C8—22no—
590C22⋊C8—22no—
591C22⋊C8—24no—
592C22⋊C8—24no—
593C22⋊C8—24no—
594C22⋊C8—24no—
595#97—21no—
596#97—21no—
597#97—22no—
598#97—22no—
599#97—24no—
600#97—22no—
601#97—24no—
602C4×C8—21no—
603C4×C8—21no—
604C4×C8—22no—
605C4×C8—22no—
606C4×C8—24no—
607C4×C8—22no—
608C4×C8—24no—
609C24C23×C411yescharacteristic
610C24C23×C414yes—
611C24C23×C412yes—
612#41—84no—
613#41—84no—
614#41—816no—
615#41—84no—
616#41—84no—
617#41—816no—
618C2×Q8—28no—
619C2×Q8—22no—
620C2×Q8—22no—
621C2×Q8—81no—
622C2×Q8—82no—
623C2×Q8—84no—
624C2×Q8C2×C22⋊C412yes—
625C2×Q8C2×C22⋊C412yes—
626C2×D4—24no—
627C2×D4—24no—
628C2×D4—28no—
629C2×D4—28no—
630C2×D4—22no—
631C2×D4—22no—
632C2×D4—22no—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—22no—
636C2×D4—24no—
637C2×D4—24no—
638C2×D4—44no—
639C2×D4—48no—
640C2×D4—81no—
641C2×D4—82no—
642C2×D4—84no—
643C2×D4—82no—
644C2×D4—84no—
645C2×D4C2×C22⋊C414yes—
646C2×D4C2×C22⋊C412yes—
647C2×D4C2×C22⋊C412yes—
648C2×D4C2×C22⋊C414yes—
649C22×C4—22no—
650C22×C4—24no—
651C22×C4—22no—
652C22×C4—24no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—28no—
658C22×C4—24no—
659C22×C4—24no—
660C22×C4—28no—
661C22×C4—28no—
662C22×C4—42no—
663C22×C4—44no—
664C22×C4—81no—
665C22×C4—84no—
666C22×C4—82no—
667C22×C4—84no—
668C22×C4—84no—
669C22×C4—84no—
670C22×C4C2×C22⋊C411yescharacteristic
671C22×C4C2×C22⋊C411yescharacteristic
672C22×C4C2×C22⋊C411yescharacteristic
673C22×C4C2×C22⋊C411yescharacteristic
674C22×C4C2×C22⋊C411yescharacteristic
675C22×C4C2×C22⋊C411yescharacteristic
676C22×C4C2×C22⋊C411yescharacteristic
677C22×C4C2×C22⋊C411yescharacteristic
678C22×C4C23×C412yes—
679C22×C4C23×C411yescharacteristic
680C22×C4C23×C414yes—
681C22×C4C23×C414yes—
682C22×C4C23×C414yes—
683C22×C4C23×C411yescharacteristic
684C22×C4C23×C411yescharacteristic
685C22×C4C23×C411yescharacteristic
686C22×C4C23×C411yescharacteristic
687C22×C4C23×C412yes—
688C22×C4C23×C412yes—
689C22×C4C22×D411yescharacteristic
690C22×C4C22×D411yescharacteristic
691C22×C4C22×D411yescharacteristic
692C22×C4C22×D411yescharacteristic
693C22×C4C22×D414yes—
694C22×C4C22×D414yes—
695C22×C4C2511yescharacteristic
696M16—22no—
697M16—24no—
698M16—22no—
699M16—24no—
700M16—22no—
701M16—24no—
702M16—24no—
703M16—24no—
704M16—24no—
705M16—44no—
706M16—48no—
707M16—84no—
708M16—82no—
709M162−1+414yes—
710C2×C8—22no—
711C2×C8—22no—
712C2×C8—22no—
713C2×C8—24no—
714C2×C8—22no—
715C2×C8—24no—
716C2×C8—44no—
717C2×C8—48no—
718C2×C8—82no—
719C2×C8—84no—
720C4⋊C4—24no—
721C4⋊C4—24no—
722C4⋊C4—24no—
723C4⋊C4—24no—
724C4⋊C4—28no—
725C4⋊C4—24no—
726C4⋊C4—24no—
727C4⋊C4—24no—
728C4⋊C4—24no—
729C4⋊C4—22no—
730C4⋊C4—22no—
731C4⋊C4—28no—
732C4⋊C4—28no—
733C4⋊C4—22no—
734C4⋊C4—22no—
735C4⋊C4—22no—
736C4⋊C4—22no—
737C4⋊C4—28no—
738C4⋊C4—22no—
739C4⋊C4—22no—
740C4⋊C4—22no—
741C4⋊C4—22no—
742C4⋊C4—22no—
743C4⋊C4—22no—
744C4⋊C4C2×C22⋊C414yes—
745C4⋊C4C2×C22⋊C414yes—
746C4⋊C4C2×C22⋊C414yes—
747C4⋊C4C2×C22⋊C414yes—
748C4⋊C4C2×C22⋊C414yes—
749C4⋊C4C2×C22⋊C414yes—
750C4⋊C4C2×C22⋊C414yes—
751C4⋊C4C2×C22⋊C414yes—
752C4⋊C4C2×C22⋊C412yes—
753C4⋊C4C2×C22⋊C412yes—
754C4⋊C4C2×C22⋊C412yes—
755C4⋊C4C2×C22⋊C412yes—
756C22⋊C4—28no—
757C22⋊C4—28no—
758C22⋊C4—24no—
759C22⋊C4—24no—
760C22⋊C4—28no—
761C22⋊C4—28no—
762C22⋊C4—24no—
763C22⋊C4—24no—
764C22⋊C4—28no—
765C22⋊C4C2×C22⋊C414yes—
766C22⋊C4C2×C22⋊C414yes—
767C22⋊C4C2×C22⋊C414yes—
768C22⋊C4C2×C22⋊C414yes—
769C22⋊C4C2×C22⋊C414yes—
770C22⋊C4C2×C22⋊C414yes—
771C22⋊C4C2×C22⋊C414yes—
772C22⋊C4C2×C22⋊C414yes—
773C22⋊C4C2×C22⋊C414yes—
774C22⋊C4C2×C22⋊C414yes—
775C42—28no—
776C42C2×C22⋊C411yescharacteristic
777C42C2×C22⋊C411yescharacteristic
778C42C2×C22⋊C411yescharacteristic
779C42C2×C22⋊C411yescharacteristic
780C42C2×C22⋊C411yescharacteristic
781C42C2×C22⋊C411yescharacteristic
782C42C2×C22⋊C411yescharacteristic
783C42C2×C22⋊C411yescharacteristic
784C42C22×D411yescharacteristic
785C42C22×D411yescharacteristic
786C42C22×D411yescharacteristic
787C42C22×D411yescharacteristic
788C42C22×D414yes—
789C42C22×D414yes—
790C42C22×D411yescharacteristic
791C42C22×D411yescharacteristic
792C42C22×D411yescharacteristic
793C42C22×D411yescharacteristic
794C23—22no—
795C23—22no—
796C23—24no—
797C23—24no—
798C23—28no—
799C23—41no—
800C23—42no—
801C23—42no—
802C23—44no—
803C23—44no—
804C23C22×C22⋊C414yes—
805C23C22×C22⋊C411yescharacteristic
806C23C22×C22⋊C411yescharacteristic
807C23C24×C411yescharacteristic
808Q8—42no—
809Q8—42no—
810Q8—82no—
811Q8—82no—
812Q8—88no—
813D4—28no—
814D4—44no—
815D4—42no—
816D4—42no—
817D4—48no—
818D4—48no—
819D4—44no—
820D4—42no—
821D4—42no—
822D4—82no—
823D4—82no—
824D4—82no—
825D4—82no—
826D4—88no—
827D4—88no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—24no—
832C2×C4—22no—
833C2×C4—24no—
834C2×C4—22no—
835C2×C4—24no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—24no—
839C2×C4—21no—
840C2×C4—24no—
841C2×C4—21no—
842C2×C4—24no—
843C2×C4—24no—
844C2×C4—24no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—44no—
858C2×C4—44no—
859C2×C4—44no—
860C2×C4—44no—
861C2×C4—44no—
862C2×C4—88no—
863C2×C4—84no—
864C2×C4—84no—
865C2×C4—88no—
866C2×C4—82no—
867C2×C4—82no—
868C2×C4—88no—
869C2×C4C22×C22⋊C414yes—
870C2×C4C22×C22⋊C411yescharacteristic
871C2×C4C22×C22⋊C411yescharacteristic
872C2×C4C22×C22⋊C411yescharacteristic
873C2×C4C22×C22⋊C411yescharacteristic
874C2×C4C22×C22⋊C411yescharacteristic
875C2×C4C22×C22⋊C411yescharacteristic
876C2×C4C22×C22⋊C411yescharacteristic
877C2×C4C22×C22⋊C411yescharacteristic
878C2×C4C22×C22⋊C411yescharacteristic
879C2×C4C22×C22⋊C411yescharacteristic
880C2×C4C22×C22⋊C414yes—
881C2×C4C22×C22⋊C414yes—
882C2×C4C23×D411yescharacteristic
883C2×C4C23×D411yescharacteristic
884C2×C4C2×2−1+412yes—
885C2×C4#58512yes—
886C8—24no—
887C8—42no—
888C8—44no—
889C8—42no—
890C8—42no—
891C8—44no—
892C22—21no—
893C22—21no—
894C22—21no—
895C22—21no—
896C22—21no—
897C22—24no—
898C22—21no—
899C22—24no—
900C22—21no—
901C22—24no—
902C22—44no—
903C22—44no—
904C22—44no—
905C22—44no—
906C22—84no—
907C22—88no—
908C22#288812yes—
909C22C23×C22⋊C411yescharacteristic
910C22C4×2−1+412yes—
911C4—21no—
912C4—21no—
913C4—21no—
914C4—21no—
915C4—24no—
916C4—21no—
917C4—21no—
918C4—21no—
919C4—21no—
920C4—24no—
921C4—21no—
922C4—24no—
923C4—21no—
924C4—44no—
925C4—44no—
926C4—44no—
927C4#348912yes—
928C4#349911yescharacteristic
929C4#350011yescharacteristic
930C2—22no—
931C2—22no—
932C2—41no—
933C2—44no—
934C2—84no—
935C2#3425911yescharacteristic
936C2C2×#288811yescharacteristic
937C2#6007611yescharacteristic
subgroupG/H
center, socleC22C23×C22⋊C4
commutatorC23C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#3559C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×#529 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60264C2semidirect
3. #60214C2semidirect
4. #22515C2semidirect
5. #22482C2semidirect
6. #22482C2semidirect
7. #22479C2semidirect
8. #21882C2semidirect
9. #21878C2semidirect
10. #21832C2semidirect
11. #21830C2semidirect
12. #21428C2semidirect
13. #21424C2semidirect
14. #21338C2semidirect
15. C2×#1998C2semidirect

Maximal subgroups

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

subgroupindex
C2×#35592
#602642
#602142
#225152
#224822
#224792
#218822
#218782
#218322
#218302
#214282
#214242
#213382
C2×#19982