Finite Group Databasebeta

← #6374636

Subgroups — #6374636

Order 512.

3042 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3511C211yesmaximal, characteristic
2#60125C211yesmaximal, characteristic, complemented
3#60123C211yesmaximal, characteristic, complemented
4#21881C214yesmaximal, complemented
5#21879C212yesmaximal, complemented
6#21878C212yesmaximal, complemented
7#21829C212yesmaximal, complemented
8#21800C212yesmaximal, complemented
9#21757C214yesmaximal, complemented
10#21427C214yesmaximal, complemented
11#21425C212yesmaximal, complemented
12#21424C212yesmaximal, complemented
13#20731C214yesmaximal, complemented
14#3511—24no—
15#3511—24no—
16#3511—24no—
17#3511—24no—
18C2×#556C412yes—
19C2×#555C412yes—
20C2×#554C412yes—
21C2×#553C412yes—
22C2×#553C412yes—
23C2×#548C412yes—
24C2×#548C412yes—
25C2×#547C412yes—
26C2×#542C2212yes—
27C2×#542C2212yes—
28C2×#537C2212yes—
29C2×#533C2211yescharacteristic
30C2×#533C2211yescharacteristic
31C2×#532C2211yescharacteristic
32C2×#532C2211yescharacteristic
33C2×#532C2211yescharacteristic
34C22×C4⋊Q8C2211yescharacteristic
35C2×#520C2212yes—
36C2×C4×#41C2211yescharacteristic
37#2925—24no—
38#2925—24no—
39#2923—24no—
40#2922—24no—
41#2921C2212yes—
42#2921C2212yes—
43#2921C2212yes—
44#2921C2212yes—
45#2920C2212yes—
46#2920C2212yes—
47#2920C2212yes—
48#2920C2212yes—
49#2905C2212yes—
50C2×#423C2212yes—
51#2879C2212yes—
52#2879C2212yes—
53#2873C2212yes—
54C2×C4×M16C2212yes—
55#1997C2214yes—
56#1997C2214yes—
57#1997C2218yes—
58#1967C2218yes—
59#1966C2214yes—
60#1965C2214yes—
61#1901C2218yes—
62#1901C2218yes—
63#1900C2218yes—
64#1900C2218yes—
65#1821C2218yes—
66#1801C2218yes—
67#1800C2218yes—
68#1785C2218yes—
69C4×#101C2218yes—
70C4×#100C2218yes—
71C22×#41C2×C412yes—
72C22×#41C2×C412yes—
73C22×#41C2312yes—
74C22×#41C2311yescharacteristic
75C23×Q8C2×C412yes—
76C22×M16C2314yes—
77C22×M16C2314yes—
78#556—28no—
79#556—28no—
80#555—28no—
81#555—28no—
82#554—28no—
83#554—28no—
84#553—28no—
85#553—28no—
86#553—28no—
87#553—28no—
88#548—28no—
89#548—28no—
90#548—28no—
91#548—28no—
92#547—28no—
93#547—28no—
94#542—28no—
95#542—28no—
96#542—28no—
97#542—28no—
98#537—28no—
99#537—28no—
100#533—22no—
101#533—22no—
102#533—22no—
103#533—22no—
104#533—22no—
105#533—22no—
106#533—22no—
107#533—22no—
108#532—22no—
109#532—22no—
110#532—22no—
111#532—22no—
112#532—22no—
113#532—22no—
114#532—22no—
115#532—22no—
116#532—22no—
117#532—22no—
118#532—22no—
119#532—22no—
120C2×C4⋊Q8—22no—
121C2×C4⋊Q8—22no—
122C2×C4⋊Q8—22no—
123C2×C4⋊Q8—22no—
124C2×C4⋊Q8C2×C412yes—
125C2×C4⋊Q8C2×C412yes—
126C2×C4⋊Q8C2311yescharacteristic
127C2×C4⋊Q8C2311yescharacteristic
128C2×C4⋊Q8C2311yescharacteristic
129C2×C4⋊Q8C2312yes—
130C2×#127C2311yescharacteristic
131C2×#126C2×C414yes—
132C2×#126C2×C414yes—
133C2×#125C2×C412yes—
134C2×#125C2×C412yes—
135C2×#124C2×C412yes—
136C2×#124C2×C412yes—
137C2×#124C2×C414yes—
138C2×#124C2×C414yes—
139C2×#124C2312yes—
140C2×#123C2×C414yes—
141C2×#123C2×C414yes—
142C2×C22⋊Q8C2×C412yes—
143C2×C22⋊Q8C2×C412yes—
144C2×C22⋊Q8C2×C414yes—
145C2×C22⋊Q8C2×C414yes—
146C2×C22⋊Q8C2×C414yes—
147C2×C22⋊Q8C2312yes—
148C2×C22⋊Q8C2312yes—
149C2×#121C2×C412yes—
150C2×#121C2×C412yes—
151C2×#121C2×C412yes—
152C2×#121C2×C412yes—
153C2×#121C2×C414yes—
154C2×#121C2×C414yes—
155C2×#121C2×C414yes—
156C2×#121C2312yes—
157C2×#121C2312yes—
158#520—28no—
159#520—28no—
160C4×#41D414yes—
161C4×#41D414yes—
162C4×#41D414yes—
163C4×#41D414yes—
164C2×C4×Q8C2×C412yes—
165C2×C4×Q8C2×C412yes—
166C2×C4×Q8C2×C411yescharacteristic
167C2×C4×Q8C2×C411yescharacteristic
168C2×C4×Q8C2312yes—
169C2×C4×Q8C2312yes—
170C2×C4×D4C2×C414yes—
171C2×C4×D4C2×C414yes—
172C2×C4×D4C2×C412yes—
173C2×C4×D4C2×C412yes—
174C2×C4×D4C2×C412yes—
175C2×C4×D4C2×C412yes—
176C2×C4×D4C2×C411yescharacteristic
177C2×C4×D4C2×C411yescharacteristic
178C2×C4×D4C2×C411yescharacteristic
179C2×C4×D4C2×C411yescharacteristic
180C2×C4×D4C2×C411yescharacteristic
181C2×C4×D4C2×C411yescharacteristic
182C2×C4×D4C2312yes—
183C2×C4×D4C2312yes—
184C2×#117C2×C414yes—
185C2×#117C2×C412yes—
186C2×#117C2×C412yes—
187C2×#117C2311yescharacteristic
188C2×#117C2311yescharacteristic
189C2×#117C2311yescharacteristic
190C22×C4⋊C4C2×C414yes—
191C22×C4⋊C4C2×C412yes—
192C22×C4⋊C4C2312yes—
193C22×C42C2311yescharacteristic
194C22×C42C2311yescharacteristic
195C22×C42C2311yescharacteristic
196#433—28no—
197#433—28no—
198#433—28no—
199#433—28no—
200#432—24no—
201#432—24no—
202#432—22no—
203#432—22no—
204#432—22no—
205#432—22no—
206#431—24no—
207#431—24no—
208#431—22no—
209#431—22no—
210#431—22no—
211#431—22no—
212#424—28no—
213#423—22no—
214#423—22no—
215#423C2314yes—
216#423C2314yes—
217#423C2314yes—
218#423C2314yes—
219C2×C4⋊C8—22no—
220C2×C4⋊C8—22no—
221C2×#101C23116yes—
222C2×#100C23116yes—
223#408—28no—
224#408—28no—
225#407C2314yes—
226#407C2314yes—
227#407C2314yes—
228#407C2314yes—
229#405—28no—
230C4×M16—22no—
231C4×M16—22no—
232C4×M16C2314yes—
233C4×M16C2314yes—
234C4×M16C2314yes—
235C4×M16C2314yes—
236C2×#97—22no—
237C2×C4×C8—22no—
238#343C23116yes—
239#343C23116yes—
240C2×#41—24no—
241C2×#41—24no—
242C2×#41—24no—
243C2×#41—24no—
244C2×#41—24no—
245C2×#41—24no—
246C2×#41—44no—
247C2×#41—48no—
248C2×#41—84no—
249C2×#41—84no—
250C2×#41C2×D414yes—
251C2×#41C2×D414yes—
252C22×Q8—24no—
253C22×Q8—24no—
254C22×Q8—84no—
255C22×Q8C22×C412yes—
256C22×Q8C22×C412yes—
257C22×Q8C22×C414yes—
258C22×Q8C22×C411yescharacteristic
259C22×Q8C2412yes—
260C22×D4C22×C412yes—
261C22×D4C22×C414yes—
262C22×D4C22×C412yes—
263C22×D4C22×C414yes—
264C22×D4C22×C414yes—
265C22×D4C22×C411yescharacteristic
266C22×D4C22×C411yescharacteristic
267C22×D4C22×C411yescharacteristic
268C22×D4C2412yes—
269C23×C4C22×C414yes—
270C23×C4C22×C414yes—
271C23×C4C22×C414yes—
272C23×C4C22×C414yes—
273C23×C4C22×C411yescharacteristic
274C23×C4C22×C411yescharacteristic
275C23×C4C22×C411yescharacteristic
276C23×C4C22×C411yescharacteristic
277C23×C4C22×C411yescharacteristic
278C23×C4C22×C411yescharacteristic
279C23×C4C2411yescharacteristic
280C23×C4C2411yescharacteristic
281C23×C4C2411yescharacteristic
282C2×M16—24no—
283C2×M16—24no—
284C2×M16—48no—
285C2×M16—48no—
286C2×M16C2418yes—
287C2×M16C2418yes—
288C22×C8—24no—
289C22×C8—24no—
290C4⋊Q8—24no—
291C4⋊Q8—24no—
292C4⋊Q8—24no—
293C4⋊Q8—24no—
294C4⋊Q8—21no—
295C4⋊Q8—21no—
296C4⋊Q8—21no—
297C4⋊Q8—21no—
298C4⋊Q8—21no—
299C4⋊Q8—21no—
300C4⋊Q8—21no—
301C4⋊Q8—21no—
302C4⋊Q8—24no—
303C4⋊Q8—24no—
304C4⋊Q8—21no—
305C4⋊Q8—21no—
306C4⋊Q8—21no—
307C4⋊Q8—21no—
308#127—21no—
309#127—21no—
310#127—21no—
311#127—21no—
312#126—216no—
313#126—216no—
314#125—24no—
315#125—24no—
316#125—24no—
317#125—24no—
318#124—216no—
319#124—216no—
320#124—24no—
321#124—24no—
322#124—24no—
323#124—24no—
324#124—24no—
325#124—24no—
326#123—216no—
327#123—216no—
328C22⋊Q8—216no—
329C22⋊Q8—24no—
330C22⋊Q8—24no—
331C22⋊Q8—24no—
332C22⋊Q8—24no—
333C22⋊Q8—24no—
334C22⋊Q8—24no—
335C22⋊Q8—24no—
336C22⋊Q8—24no—
337C22⋊Q8—216no—
338C22⋊Q8—216no—
339#121—216no—
340#121—216no—
341#121—216no—
342#121—24no—
343#121—24no—
344#121—24no—
345#121—24no—
346#121—24no—
347#121—24no—
348#121—24no—
349#121—24no—
350#121—24no—
351#121—24no—
352#121—24no—
353#121—24no—
354C4×Q8—24no—
355C4×Q8—24no—
356C4×Q8—24no—
357C4×Q8—24no—
358C4×Q8—24no—
359C4×Q8—24no—
360C4×Q8—24no—
361C4×Q8—24no—
362C4×Q8C22⋊C414yes—
363C4×Q8C22⋊C414yes—
364C4×Q8C22⋊C414yes—
365C4×Q8C22⋊C414yes—
366C4×D4—216no—
367C4×D4—216no—
368C4×D4—24no—
369C4×D4—24no—
370C4×D4—24no—
371C4×D4—24no—
372C4×D4—24no—
373C4×D4—24no—
374C4×D4—24no—
375C4×D4—24no—
376C4×D4—24no—
377C4×D4—24no—
378C4×D4—24no—
379C4×D4—24no—
380C4×D4C22⋊C414yes—
381C4×D4C22⋊C414yes—
382C4×D4C22⋊C414yes—
383C4×D4C22⋊C414yes—
384C4×D4C22⋊C414yes—
385C4×D4C22⋊C414yes—
386C4×D4C22⋊C414yes—
387C4×D4C22⋊C414yes—
388C4×D4C22⋊C414yes—
389C4×D4C22⋊C414yes—
390C4×D4C22⋊C414yes—
391C4×D4C22⋊C414yes—
392#117—24no—
393#117—24no—
394#117—24no—
395#117—24no—
396#117—216no—
397#117C2×D414yes—
398#117C2×D414yes—
399#117C2×D414yes—
400#117C2×D414yes—
401#117C2×D414yes—
402#117C2×D414yes—
403C2×C4⋊C4—24no—
404C2×C4⋊C4—24no—
405C2×C4⋊C4—24no—
406C2×C4⋊C4—24no—
407C2×C4⋊C4—216no—
408C2×C4⋊C4C22×C414yes—
409C2×C4⋊C4C22×C412yes—
410C2×C4⋊C4C22×C412yes—
411C2×C4⋊C4C22×C414yes—
412C2×C4⋊C4C22×C414yes—
413C2×C4⋊C4C22×C414yes—
414C2×C4⋊C4C22×C412yes—
415C2×C4⋊C4C22×C412yes—
416C2×C4⋊C4C22×C414yes—
417C2×C4⋊C4C22×C414yes—
418C2×C4⋊C4C22×C411yescharacteristic
419C2×C4⋊C4C22×C411yescharacteristic
420C2×C4⋊C4C22×C411yescharacteristic
421C2×C4⋊C4C22×C411yescharacteristic
422C2×C4⋊C4C22×C411yescharacteristic
423C2×C4⋊C4C22×C411yescharacteristic
424C2×C4⋊C4C2412yes—
425C2×C4⋊C4C2412yes—
426C2×C22⋊C4C22×C414yes—
427C2×C22⋊C4C22×C414yes—
428C2×C22⋊C4C22×C414yes—
429C2×C22⋊C4C22×C414yes—
430C2×C22⋊C4C22×C414yes—
431C2×C22⋊C4C22×C414yes—
432C2×C22⋊C4C22×C414yes—
433C2×C22⋊C4C22×C414yes—
434C2×C22⋊C4C22×C411yescharacteristic
435C2×C22⋊C4C22×C411yescharacteristic
436C2×C22⋊C4C22×C411yescharacteristic
437C2×C22⋊C4C22×C411yescharacteristic
438C2×C22⋊C4C22×C411yescharacteristic
439C2×C22⋊C4C22×C411yescharacteristic
440C2×C42C22×C414yes—
441C2×C42C22×C414yes—
442C2×C42C22×C411yescharacteristic
443C2×C42C22×C411yescharacteristic
444C2×C42C22×C411yescharacteristic
445C2×C42C22×C411yescharacteristic
446C2×C42C22×C411yescharacteristic
447C2×C42C22×C411yescharacteristic
448C2×C42C2×D412yes—
449C2×C42C2×D412yes—
450C2×C42C2×D412yes—
451C2×C42C2×D412yes—
452C2×C42C2×D412yes—
453C2×C42C2×D412yes—
454C2×C42C2×D412yes—
455C2×C42C2×D412yes—
456C2×C42C2×D412yes—
457C2×C42C2×D412yes—
458C2×C42C2×D412yes—
459C2×C42C2×D412yes—
460C2×C42C2411yescharacteristic
461C2×C42C2411yescharacteristic
462C2×C42C2411yescharacteristic
463C2×C42C2411yescharacteristic
464C4⋊C8—24no—
465C4⋊C8—24no—
466C4⋊C8—24no—
467C4⋊C8—24no—
468C4⋊C8—28no—
469C4⋊C8—28no—
470#101—416no—
471#100—416no—
472C22⋊C8—28no—
473C22⋊C8—24no—
474C22⋊C8—24no—
475C22⋊C8—28no—
476C22⋊C8—24no—
477C22⋊C8—24no—
478#97—24no—
479#97—24no—
480#97—24no—
481#97—24no—
482C4×C8—24no—
483C4×C8—24no—
484C4×C8—24no—
485C4×C8—24no—
486C24C23×C414yes—
487C24C23×C411yescharacteristic
488C24C23×C411yescharacteristic
489C24C23×C411yescharacteristic
490#41—44no—
491#41—48no—
492#41—44no—
493#41—416no—
494#41—416no—
495#41—88no—
496#41—88no—
497#41—88no—
498#41—88no—
499C2×Q8—22no—
500C2×Q8—22no—
501C2×Q8—22no—
502C2×Q8—22no—
503C2×Q8—28no—
504C2×Q8—22no—
505C2×Q8—22no—
506C2×Q8—28no—
507C2×Q8—42no—
508C2×Q8—44no—
509C2×Q8—44no—
510C2×Q8—88no—
511C2×Q8—84no—
512C2×Q8—88no—
513C2×Q8C2×C22⋊C414yes—
514C2×D4—28no—
515C2×D4—28no—
516C2×D4—28no—
517C2×D4—22no—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—28no—
524C2×D4—42no—
525C2×D4—42no—
526C2×D4—42no—
527C2×D4—48no—
528C2×D4—44no—
529C2×D4—44no—
530C2×D4—84no—
531C2×D4—84no—
532C2×D4C2×C22⋊C414yes—
533C2×D4C2×C22⋊C414yes—
534C2×D4C2×C22⋊C414yes—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—28no—
539C22×C4—28no—
540C22×C4—28no—
541C22×C4—28no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—48no—
549C22×C4—84no—
550C22×C4—84no—
551C22×C4—84no—
552C22×C4C2×C22⋊C412yes—
553C22×C4C2×C22⋊C412yes—
554C22×C4C2×C22⋊C412yes—
555C22×C4C2×C22⋊C412yes—
556C22×C4C2×C22⋊C412yes—
557C22×C4C2×C22⋊C412yes—
558C22×C4C2×C22⋊C412yes—
559C22×C4C2×C22⋊C412yes—
560C22×C4C2×C22⋊C412yes—
561C22×C4C2×C22⋊C412yes—
562C22×C4C2×C22⋊C412yes—
563C22×C4C2×C22⋊C412yes—
564C22×C4C23×C414yes—
565C22×C4C23×C411yescharacteristic
566C22×C4C23×C411yescharacteristic
567C22×C4C23×C411yescharacteristic
568C22×C4C23×C411yescharacteristic
569C22×C4C23×C411yescharacteristic
570C22×C4C23×C414yes—
571C22×C4C23×C414yes—
572C22×C4C23×C411yescharacteristic
573C22×C4C23×C411yescharacteristic
574C22×C4C23×C411yescharacteristic
575C22×C4C23×C411yescharacteristic
576C22×C4C23×C411yescharacteristic
577C22×C4C23×C411yescharacteristic
578C22×C4C22×D412yes—
579C22×C4C22×D412yes—
580C22×C4C22×D412yes—
581C22×C4C22×D412yes—
582C22×C4C22×D412yes—
583C22×C4C22×D412yes—
584C22×C4C2511yescharacteristic
585M16—28no—
586M16—216no—
587M16—28no—
588M16—48no—
589M16—48no—
590C2×C8—28no—
591C2×C8—28no—
592C2×C8—48no—
593C2×C8—48no—
594C4⋊C4—28no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—28no—
600C4⋊C4—28no—
601C4⋊C4—28no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—28no—
607C4⋊C4—28no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4C2×C22⋊C414yes—
613C4⋊C4C2×C22⋊C414yes—
614C4⋊C4C2×C22⋊C414yes—
615C4⋊C4C2×C22⋊C414yes—
616C4⋊C4C2×C22⋊C414yes—
617C4⋊C4C2×C22⋊C414yes—
618C22⋊C4—28no—
619C22⋊C4—28no—
620C22⋊C4—28no—
621C22⋊C4—28no—
622C22⋊C4—28no—
623C22⋊C4—28no—
624C22⋊C4—28no—
625C22⋊C4—28no—
626C22⋊C4C2×C22⋊C414yes—
627C22⋊C4C2×C22⋊C414yes—
628C22⋊C4C2×C22⋊C414yes—
629C22⋊C4C2×C22⋊C414yes—
630C22⋊C4C2×C22⋊C414yes—
631C22⋊C4C2×C22⋊C414yes—
632C42—28no—
633C42—28no—
634C42C2×C22⋊C412yes—
635C42C2×C22⋊C412yes—
636C42C2×C22⋊C412yes—
637C42C2×C22⋊C412yes—
638C42C2×C22⋊C412yes—
639C42C2×C22⋊C412yes—
640C42C2×C22⋊C412yes—
641C42C2×C22⋊C412yes—
642C42C2×C22⋊C412yes—
643C42C2×C22⋊C412yes—
644C42C2×C22⋊C412yes—
645C42C2×C22⋊C412yes—
646C42C22×D411yescharacteristic
647C42C22×D412yes—
648C42C22×D412yes—
649C42C22×D412yes—
650C42C22×D411yescharacteristic
651C42C22×D411yescharacteristic
652C42C22×D411yescharacteristic
653C42C22×D412yes—
654C42C22×D412yes—
655C42C22×D412yes—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—24no—
660C23—28no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—44no—
668C23—44no—
669C23C22×C22⋊C412yes—
670C23C22×C22⋊C412yes—
671C23C22×C22⋊C412yes—
672C23C24×C411yescharacteristic
673Q8—44no—
674Q8—44no—
675Q8—44no—
676Q8—44no—
677Q8—44no—
678Q8—44no—
679Q8—44no—
680Q8—88no—
681D4—44no—
682D4—44no—
683D4—44no—
684D4—44no—
685D4—44no—
686D4—416no—
687D4—44no—
688D4—44no—
689D4—44no—
690D4—44no—
691D4—88no—
692D4—88no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—28no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—416no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—88no—
731C2×C4—88no—
732C2×C4—88no—
733C2×C4C22×C22⋊C412yes—
734C2×C4C22×C22⋊C412yes—
735C2×C4C22×C22⋊C411yescharacteristic
736C2×C4C22×C22⋊C411yescharacteristic
737C2×C4C22×C22⋊C412yes—
738C2×C4C22×C22⋊C412yes—
739C2×C4C22×C22⋊C412yes—
740C2×C4C22×C22⋊C412yes—
741C2×C4C22×C22⋊C412yes—
742C2×C4C22×C22⋊C412yes—
743C2×C4C22×C22⋊C412yes—
744C2×C4C22×C22⋊C411yescharacteristic
745C2×C4C22×C22⋊C411yescharacteristic
746C2×C4C23×D411yescharacteristic
747C2×C4C23×D411yescharacteristic
748C2×C4#58514yes—
749C8—48no—
750C8—48no—
751C22—21no—
752C22—21no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—44no—
763C22—44no—
764C22—44no—
765C22—44no—
766C22—82no—
767C22—82no—
768C22—88no—
769C22C23×C22⋊C411yescharacteristic
770C22#342812yes—
771C4—21no—
772C4—22no—
773C4—22no—
774C4—22no—
775C4—21no—
776C4—22no—
777C4—22no—
778C4—22no—
779C4—22no—
780C4—22no—
781C4—22no—
782C4—44no—
783C4—44no—
784C4—44no—
785C4#288812yes—
786C4#288912yes—
787C4#344912yes—
788C4#344912yes—
789C2—22no—
790C2—42no—
791C2—42no—
792C2—42no—
793C2—84no—
794C2#3404411yescharacteristic
795C2C2×#288811yescharacteristic
796C2C2×#288911yescharacteristic
subgroupG/H
center, socleC22C23×C22⋊C4
commutatorC23C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#3511C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×C4×#41 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60125C2semidirect
3. #60123C2semidirect
4. #21881C2semidirect
5. #21879C2semidirect
6. #21878C2semidirect
7. #21829C2semidirect
8. #21800C2semidirect
9. #21757C2semidirect
10. #21427C2semidirect
11. #21425C2semidirect
12. #21424C2semidirect
13. #20731C2semidirect

Maximal subgroups

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

subgroupindex
C2×#35112
#601252
#601232
#218812
#218792
#218782
#218292
#218002
#217572
#214272
#214252
#214242
#207312