Finite Group Databasebeta

← #6343507

Subgroups — #6343507

Order 512.

3209 conjugacy classes of subgroups.

The subgroup lattice has 934 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3506C211yesmaximal, characteristic
2#60230C211yesmaximal, characteristic, complemented
3#34126C211yesmaximal, characteristic, complemented
4#17630C214yesmaximal, complemented
5#17629C218yesmaximal, complemented
6#17617C214yesmaximal, complemented
7#17584C211yesmaximal, characteristic, complemented
8#17583C211yesmaximal, characteristic, complemented
9#17582C214yesmaximal, complemented
10#17545C211yesmaximal, characteristic, complemented
11#17544C211yesmaximal, characteristic, complemented
12#17542C214yesmaximal, complemented
13#3506—22no—
14#3506—22no—
15#3506—21no—
16#3506—22no—
17#3506—21no—
18#3506C414yescomplemented
19#3506C414yescomplemented
20#3506C2212yes—
21#3506C2212yes—
22#3506C2214yes—
23C2×#559—22no—
24C2×#556C412yescomplemented
25C2×#555C412yescomplemented
26C2×#553—22no—
27C2×#550C412yescomplemented
28C2×#547C412yescomplemented
29C2×#538—22no—
30C2×#535—21no—
31C2×#533C2211yescharacteristic
32C2×#532C2211yescharacteristic
33C2×#525C2214yes—
34C2×#520—21no—
35C22×C4×D4C2211yescharacteristic
36#2975C2212yescomplemented
37#2974—22no—
38#2974—22no—
39#2973C2214yescomplemented
40#2972C2212yescomplemented
41D4×M16—22no—
42D4×M16—22no—
43#2920C2211yescharacteristic
44#2920C2211yescharacteristic
45C2×#407C2214yes—
46#2357C2212yescomplemented
47#2353C2214yescomplemented
48#2349C2212yescomplemented
49#2345—21no—
50#2342—22no—
51D4×C22⋊C4—21no—
52#2293—21no—
53#2290—22no—
54#2283C2211yescharacteristic
55#2280C2212yes—
56C42×D4—21no—
57C4×#117C2211yescharacteristic
58C2×C4×C22⋊C4C2212yes—
59#1518C2214yescomplemented
60#1517C2214yescomplemented
61#1516C22116yescomplemented
62#1515C2214yescomplemented
63#1514C2214yescomplemented
64#1513C22116yescomplemented
65#1508C2212yes—
66#1508C2214yes—
67#1508C2212yes—
68#1507C2212yes—
69#1507C2214yes—
70#1507C2212yes—
71#1506C2214yescomplemented
72#1505C2214yescomplemented
73#1504C22116yescomplemented
74#1503C2214yescomplemented
75#1502C2214yescomplemented
76#1501C22116yescomplemented
77C22×#41—21no—
78C22×#41C2×C414yescomplemented
79C23×D4D411yescharacteristic
80C24×C4C2312yes—
81C22×M16—24no—
82#559—24no—
83#559—28no—
84#559—24no—
85#559—24no—
86#559—24no—
87#559—28no—
88#556—22no—
89#556—22no—
90#556—24no—
91#556C2×C414yes—
92#556C2×C418yescomplemented
93#556C2×C414yescomplemented
94#555—22no—
95#555—22no—
96#555—24no—
97#555C2×C414yes—
98#555C2×C418yescomplemented
99#555C2×C414yescomplemented
100#553—24no—
101#553—24no—
102#553—28no—
103#553—24no—
104#553—24no—
105#553—28no—
106#550—22no—
107#550—24no—
108#550—22no—
109#550C2×C414yes—
110#550C2×C414yescomplemented
111#550C2×C418yescomplemented
112#547—22no—
113#547—22no—
114#547—24no—
115#547C2×C414yes—
116#547C2×C414yescomplemented
117#547C2×C418yescomplemented
118#538—28no—
119#538—28no—
120#538—24no—
121#538—24no—
122#538—24no—
123#538—24no—
124#535—24no—
125#535—24no—
126#535—22no—
127#535—22no—
128#535—24no—
129#533—21no—
130#533—21no—
131#533—21no—
132#533—21no—
133#533C2×C412yescomplemented
134#533C2×C412yescomplemented
135#533C2312yes—
136#533C2312yes—
137#532—21no—
138#532—21no—
139#532—21no—
140#532—21no—
141#532C2×C412yescomplemented
142#532C2×C412yescomplemented
143#532C2312yes—
144#532C2312yes—
145C2×C4⋊Q8C2×C411yescharacteristic, complemented
146C2×C4⋊Q8C2×C411yescharacteristic, complemented
147C2×C4⋊Q8C2×C411yescharacteristic, complemented
148C2×#127—22no—
149C2×#127C2×C411yescharacteristic, complemented
150C2×#126—24no—
151C2×#125—21no—
152C2×#124—22no—
153C2×#124—24no—
154C2×#124—21no—
155#525—24no—
156#525—24no—
157#525—24no—
158#525—24no—
159#525C2×C418yescomplemented
160#525C2×C418yescomplemented
161#525C2318yes—
162#525C2318yes—
163C2×#123—24no—
164C2×#123—24no—
165C2×C22⋊Q8—21no—
166C2×C22⋊Q8C2×C414yescomplemented
167C2×C22⋊Q8C2312yes—
168C2×#121—22no—
169C2×#121—22no—
170C2×#121—21no—
171C2×#121—24no—
172C2×#121C2×C414yescomplemented
173C2×#121C2312yes—
174C2×#120—24no—
175#520—24no—
176#520—24no—
177#520—22no—
178#520—22no—
179#520—24no—
180C2×C4×Q8—22no—
181C2×C4×Q8—21no—
182C2×C4×Q8C2×C412yescomplemented
183C2×C4×D4—24no—
184C2×C4×D4—24no—
185C2×C4×D4—22no—
186C2×C4×D4—22no—
187C2×C4×D4—21no—
188C2×C4×D4C2×C412yes—
189C2×C4×D4C2×C412yes—
190C2×C4×D4C2×C412yes—
191C2×C4×D4C2×C412yes—
192C2×C4×D4C2×C412yescomplemented
193C2×C4×D4D412yes—
194C2×C4×D4D412yes—
195C2×C4×D4D412yes—
196C2×C4×D4D412yes—
197C2×C4×D4D411yescharacteristic
198C2×C4×D4D412yes—
199C2×C4×D4D411yescharacteristic
200C2×C4×D4C2311yescharacteristic
201C2×C4×D4C2312yes—
202C2×C4×D4C2311yescharacteristic
203C2×#117—21no—
204C2×#117—21no—
205C2×#117—22no—
206C2×#117—22no—
207C2×#117C2×C414yescomplemented
208C22×C4⋊C4—22no—
209C22×C4⋊C4D411yescharacteristic
210C22×C22⋊C4—22no—
211C22×C22⋊C4D412yes—
212C22×C42—22no—
213C22×C42C2311yescharacteristic
214#436—24no—
215#436—24no—
216#435—28no—
217#435—28no—
218C8×D4—24no—
219C8×D4—24no—
220#432—21no—
221#432—21no—
222#432C2312yes—
223#432C2312yes—
224#431—21no—
225#431—21no—
226#431C2312yes—
227#431C2312yes—
228#423—21no—
229#423—21no—
230#407—24no—
231#407—24no—
232#407C2312yes—
233#407C2312yes—
234#407C2318yes—
235C2×C22⋊C8—24no—
236C2×C22⋊C8C2318yes—
237C4×M16—21no—
238C4×M16—21no—
239#390—22no—
240#389—22no—
241#388—24no—
242#388—24no—
243#387—24no—
244#386—24no—
245#385—24no—
246#383C2312yes—
247#382C2312yes—
248#381—21no—
249#381C2314yes—
250#380—21no—
251#380—22no—
252#380C2314yes—
253#379—22no—
254C4×C4⋊C4—22no—
255C4×C4⋊C4—21no—
256C4×C4⋊C4—21no—
257C4×C4⋊C4C2312yes—
258C4×C22⋊C4—21no—
259C4×C22⋊C4—22no—
260C4×C22⋊C4—22no—
261C4×C22⋊C4—22no—
262C4×C22⋊C4—24no—
263C4×C22⋊C4C2314yes—
264C4×C22⋊C4C2311yescharacteristic
265C4×C22⋊C4C2312yes—
266C4×C22⋊C4C2311yescharacteristic
267#376—21no—
268#376C2312yes—
269C2×#95C2314yes—
270C43—21no—
271#328C2318yes—
272#328C23116yes—
273#328C2318yes—
274#327C2318yes—
275#327C23116yes—
276#327C2318yes—
277C25C2×D412yes—
278C2×#41—22no—
279C2×#41—22no—
280C2×#41—24no—
281C2×#41—24no—
282C2×#41—22no—
283C2×#41—22no—
284C2×#41—48no—
285C2×#41—88no—
286C2×#41C22×C418yes—
287C2×#41C22×C418yes—
288C22×Q8—21no—
289C22×Q8—21no—
290C22×Q8C22×C412yes—
291C22×D4—22no—
292C22×D4—24no—
293C22×D4—24no—
294C22×D4—21no—
295C22×D4—21no—
296C22×D4—44no—
297C22×D4C22⋊C412yes—
298C22×D4C22⋊C412yes—
299C22×D4C22⋊C412yes—
300C22×D4C22⋊C412yes—
301C22×D4C22×C412yes—
302C22×D4C2×D411yescharacteristic
303C22×D4C2×D411yescharacteristic
304C22×D4C2×D412yes—
305C23×C4—22no—
306C23×C4—24no—
307C23×C4—24no—
308C23×C4—84no—
309C23×C4C22×C414yes—
310C23×C4C22×C414yes—
311C23×C4C2×D411yescharacteristic
312C23×C4C2×D411yescharacteristic
313C23×C4C2×D412yes—
314C23×C4C2×D412yes—
315C23×C4C2×D414yes—
316C23×C4C2×D412yes—
317C23×C4C2×D414yes—
318C23×C4C2411yescharacteristic
319C23×C4C2412yes—
320C23×C4C2412yes—
321C2×M16—22no—
322C2×M16—22no—
323C2×M16—28no—
324C2×M16—88no—
325C22×C8—28no—
326C4⋊Q8—21no—
327C4⋊Q8—21no—
328C4⋊Q8—21no—
329C4⋊Q8—21no—
330C4⋊Q8—21no—
331C4⋊Q8—21no—
332C4⋊Q8C22×C412yes—
333C4⋊Q8C22×C412yes—
334C4⋊Q8C22×C412yes—
335C4⋊Q8C22×C412yes—
336C4⋊Q8C22×C412yes—
337C4⋊Q8C22×C412yes—
338#127—24no—
339#127—24no—
340#127—28no—
341#127—21no—
342#127—21no—
343#127C22×C412yes—
344#127C22×C412yes—
345#126—28no—
346#126—28no—
347#126—28no—
348#126—28no—
349#125—22no—
350#125—22no—
351#125—22no—
352#125—22no—
353#124—24no—
354#124—24no—
355#124—28no—
356#124—28no—
357#124—28no—
358#124—28no—
359#124—28no—
360#124—22no—
361#124—22no—
362#124—22no—
363#124—22no—
364#123—28no—
365#123—28no—
366#123—28no—
367#123—28no—
368#123—28no—
369#123—28no—
370#123—28no—
371#123—28no—
372C22⋊Q8—22no—
373C22⋊Q8—22no—
374C22⋊Q8—24no—
375C22⋊Q8—24no—
376C22⋊Q8—22no—
377C22⋊Q8—22no—
378C22⋊Q8—22no—
379C22⋊Q8—22no—
380C22⋊Q8C22×C418yes—
381C22⋊Q8C22×C418yes—
382C22⋊Q8C22×C414yes—
383C22⋊Q8C2414yes—
384#121—24no—
385#121—24no—
386#121—28no—
387#121—24no—
388#121—24no—
389#121—28no—
390#121—22no—
391#121—22no—
392#121—24no—
393#121—24no—
394#121—22no—
395#121—22no—
396#121—22no—
397#121—22no—
398#121—28no—
399#121—28no—
400#121—28no—
401#121—28no—
402#121C22×C418yes—
403#121C22×C418yes—
404#121C22×C414yes—
405#121C2414yes—
406#120—28no—
407#120—28no—
408#120—28no—
409#120—28no—
410C4×Q8—24no—
411C4×Q8—28no—
412C4×Q8—24no—
413C4×Q8—22no—
414C4×Q8—22no—
415C4×Q8—22no—
416C4×Q8—22no—
417C4×Q8—22no—
418C4×Q8—22no—
419C4×Q8C22×C414yes—
420C4×Q8C22×C414yes—
421C4×D4—28no—
422C4×D4—28no—
423C4×D4—28no—
424C4×D4—28no—
425C4×D4—28no—
426C4×D4—28no—
427C4×D4—28no—
428C4×D4—28no—
429C4×D4—24no—
430C4×D4—28no—
431C4×D4—24no—
432C4×D4—22no—
433C4×D4—22no—
434C4×D4—22no—
435C4×D4—22no—
436C4×D4—22no—
437C4×D4—22no—
438C4×D4—48no—
439C4×D4C22⋊C412yes—
440C4×D4C22⋊C412yes—
441C4×D4C22⋊C414yes—
442C4×D4C22⋊C412yes—
443C4×D4C22⋊C412yes—
444C4×D4C22⋊C414yes—
445C4×D4C22⋊C412yes—
446C4×D4C22⋊C412yes—
447C4×D4C22⋊C414yes—
448C4×D4C22⋊C412yes—
449C4×D4C22⋊C412yes—
450C4×D4C22⋊C414yes—
451C4×D4C22×C414yes—
452C4×D4C22×C414yes—
453C4×D4C22×C412yes—
454C4×D4C22×C412yes—
455C4×D4C22×C414yes—
456C4×D4C22×C412yes—
457C4×D4C22×C412yes—
458C4×D4C22×C414yes—
459C4×D4C2×D412yes—
460C4×D4C2×D414yes—
461C4×D4C2×D412yes—
462C4×D4C2×D412yes—
463C4×D4C2×D414yes—
464C4×D4C2×D412yes—
465#117—22no—
466#117—22no—
467#117—24no—
468#117—24no—
469#117—22no—
470#117—22no—
471#117—24no—
472#117—28no—
473#117—24no—
474#117—44no—
475#117—84no—
476#117C22×C418yes—
477#117C22×C418yes—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—24no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—24no—
486C2×C4⋊C4—28no—
487C2×C4⋊C4—24no—
488C2×C4⋊C4—22no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—24no—
491C2×C4⋊C4C22⋊C412yes—
492C2×C4⋊C4C22⋊C412yes—
493C2×C4⋊C4C22⋊C412yes—
494C2×C4⋊C4C22⋊C412yes—
495C2×C4⋊C4C22×C412yes—
496C2×C4⋊C4C22×C412yes—
497C2×C4⋊C4C2×D411yescharacteristic
498C2×C4⋊C4C2×D412yes—
499C2×C4⋊C4C2×D411yescharacteristic
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—48no—
513C2×C22⋊C4C22⋊C414yes—
514C2×C22⋊C4C22⋊C414yes—
515C2×C22⋊C4C22⋊C414yes—
516C2×C22⋊C4C22⋊C414yes—
517C2×C22⋊C4C2×D412yes—
518C2×C22⋊C4C2×D412yes—
519C2×C22⋊C4C2×D412yes—
520C2×C22⋊C4C2×D412yes—
521C2×C42—24no—
522C2×C42—22no—
523C2×C42—21no—
524C2×C42—22no—
525C2×C42—22no—
526C2×C42—22no—
527C2×C42—21no—
528C2×C42—24no—
529C2×C42—84no—
530C2×C42C22×C411yescharacteristic
531C2×C42C22×C411yescharacteristic
532C2×C42C22×C411yescharacteristic
533C2×C42C22×C411yescharacteristic
534C2×C42C2×D411yescharacteristic
535C2×C42C2×D411yescharacteristic
536C2×C42C2×D411yescharacteristic
537C2×C42C2×D411yescharacteristic
538C2×C42C2×D411yescharacteristic
539C2×C42C2×D411yescharacteristic
540C2×C42C2411yescharacteristic
541C2×C42C2411yescharacteristic
542C4⋊C8—22no—
543C4⋊C8—22no—
544C4⋊C8—22no—
545C4⋊C8—22no—
546C22⋊C8—22no—
547C22⋊C8—22no—
548C22⋊C8—28no—
549C22⋊C8—28no—
550C22⋊C8C2414yes—
551C22⋊C8C2414yes—
552#97—22no—
553#97—22no—
554C4×C8—22no—
555C4×C8—22no—
556#95—24no—
557#95—22no—
558#95—22no—
559#95—22no—
560#95—24no—
561#95—22no—
562#95C2412yes—
563#95C2414yes—
564#95C2412yes—
565C24—22no—
566C24—44no—
567C24—44no—
568C24—82no—
569C24C2×C22⋊C414yes—
570C24C2×C22⋊C414yes—
571C24C22×D411yescharacteristic
572C24C22×D412yes—
573C24C22×D412yes—
574#41—48no—
575#41—48no—
576#41—48no—
577#41—48no—
578#41—88no—
579#41—88no—
580#41—88no—
581#41—88no—
582C2×Q8—22no—
583C2×Q8—22no—
584C2×Q8—22no—
585C2×Q8—22no—
586C2×Q8—22no—
587C2×Q8—44no—
588C2×Q8—44no—
589C2×Q8—82no—
590C2×Q8C23×C414yes—
591C2×D4—24no—
592C2×D4—24no—
593C2×D4—28no—
594C2×D4—28no—
595C2×D4—28no—
596C2×D4—28no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—24no—
603C2×D4—24no—
604C2×D4—44no—
605C2×D4—44no—
606C2×D4—44no—
607C2×D4—44no—
608C2×D4—44no—
609C2×D4—44no—
610C2×D4—44no—
611C2×D4—48no—
612C2×D4—82no—
613C2×D4—88no—
614C2×D4—88no—
615C2×D4C2×C22⋊C412yes—
616C2×D4C2×C22⋊C412yes—
617C2×D4C2×C22⋊C412yes—
618C2×D4C2×C22⋊C412yes—
619C2×D4C2×C22⋊C414yes—
620C2×D4C2×C22⋊C414yes—
621C2×D4C23×C414yes—
622C22×C4—24no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—24no—
628C22×C4—24no—
629C22×C4—28no—
630C22×C4—28no—
631C22×C4—24no—
632C22×C4—22no—
633C22×C4—44no—
634C22×C4—44no—
635C22×C4—48no—
636C22×C4—42no—
637C22×C4—48no—
638C22×C4—42no—
639C22×C4—48no—
640C22×C4—48no—
641C22×C4—48no—
642C22×C4—84no—
643C22×C4—82no—
644C22×C4—84no—
645C22×C4—82no—
646C22×C4—82no—
647C22×C4—84no—
648C22×C4—88no—
649C22×C4C2×C22⋊C411yescharacteristic
650C22×C4C2×C22⋊C411yescharacteristic
651C22×C4C2×C22⋊C411yescharacteristic
652C22×C4C2×C22⋊C411yescharacteristic
653C22×C4C2×C22⋊C411yescharacteristic
654C22×C4C2×C22⋊C411yescharacteristic
655C22×C4C2×C22⋊C414yes—
656C22×C4C2×C22⋊C414yes—
657C22×C4C2×C22⋊C414yes—
658C22×C4C2×C22⋊C411yescharacteristic
659C22×C4C2×C22⋊C411yescharacteristic
660C22×C4C2×C22⋊C414yes—
661C22×C4C2×C22⋊C414yes—
662C22×C4C2×C22⋊C414yes—
663C22×C4C23×C411yescharacteristic
664C22×C4C23×C411yescharacteristic
665C22×C4C23×C414yes—
666C22×C4C23×C414yes—
667C22×C4C22×D411yescharacteristic
668C22×C4C22×D411yescharacteristic
669C22×C4C22×D411yescharacteristic
670C22×C4C22×D411yescharacteristic
671C22×C4C22×D412yes—
672C22×C4C22×D411yescharacteristic
673C22×C4C22×D412yes—
674C22×C4C22×D411yescharacteristic
675C22×C4C22×D414yes—
676C22×C4C22×D414yes—
677C22×C4C22×D411yescharacteristic
678C22×C4C2511yescharacteristic
679M16—44no—
680M16—44no—
681M16—88no—
682C2×C8—24no—
683C2×C8—24no—
684C2×C8—88no—
685C4⋊C4—22no—
686C4⋊C4—22no—
687C4⋊C4—28no—
688C4⋊C4—28no—
689C4⋊C4—22no—
690C4⋊C4—22no—
691C4⋊C4—24no—
692C4⋊C4—22no—
693C4⋊C4—22no—
694C4⋊C4—22no—
695C4⋊C4—22no—
696C4⋊C4—24no—
697C4⋊C4—24no—
698C4⋊C4—22no—
699C4⋊C4—22no—
700C4⋊C4—24no—
701C4⋊C4—44no—
702C4⋊C4—44no—
703C4⋊C4—84no—
704C4⋊C4C2×C22⋊C414yes—
705C4⋊C4C2×C22⋊C412yes—
706C4⋊C4C2×C22⋊C412yes—
707C4⋊C4C2×C22⋊C414yes—
708C4⋊C4C2×C22⋊C412yes—
709C4⋊C4C2×C22⋊C412yes—
710C4⋊C4C23×C414yes—
711C4⋊C4C23×C414yes—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—28no—
715C22⋊C4—28no—
716C22⋊C4—28no—
717C22⋊C4—28no—
718C22⋊C4—24no—
719C22⋊C4—28no—
720C22⋊C4—28no—
721C22⋊C4—24no—
722C22⋊C4—24no—
723C22⋊C4—24no—
724C22⋊C4—24no—
725C22⋊C4—48no—
726C22⋊C4—44no—
727C22⋊C4—42no—
728C22⋊C4—48no—
729C22⋊C4—84no—
730C22⋊C4C2×C22⋊C414yes—
731C22⋊C4C2×C22⋊C414yes—
732C22⋊C4C2×C22⋊C414yes—
733C22⋊C4C2×C22⋊C414yes—
734C22⋊C4C2×C22⋊C414yes—
735C22⋊C4C2×C22⋊C414yes—
736C22⋊C4C2×C22⋊C414yes—
737C22⋊C4C2×C22⋊C414yes—
738C42—28no—
739C42—28no—
740C42—24no—
741C42—24no—
742C42—42no—
743C42—44no—
744C42—44no—
745C42—42no—
746C42—44no—
747C42—84no—
748C42C2×C22⋊C411yescharacteristic
749C42C2×C22⋊C411yescharacteristic
750C42C2×C22⋊C411yescharacteristic
751C42C2×C22⋊C411yescharacteristic
752C42C2×C22⋊C411yescharacteristic
753C42C2×C22⋊C411yescharacteristic
754C42C2×C22⋊C411yescharacteristic
755C42C2×C22⋊C411yescharacteristic
756C42C23×C411yescharacteristic
757C42C23×C411yescharacteristic
758C42C23×C411yescharacteristic
759C42C23×C411yescharacteristic
760C42C22×D411yescharacteristic
761C42C22×D411yescharacteristic
762C42C22×D411yescharacteristic
763C42C22×D411yescharacteristic
764C23—22no—
765C23—24no—
766C23—22no—
767C23—28no—
768C23—24no—
769C23—24no—
770C23—42no—
771C23—42no—
772C23—41no—
773C23—42no—
774C23—42no—
775C23—44no—
776C23—44no—
777C23—44no—
778C23—44no—
779C23—44no—
780C23—44no—
781C23—44no—
782C23—44no—
783C23—816no—
784C23C22×C22⋊C414yes—
785C23C22×C22⋊C414yes—
786C23C22×C22⋊C411yescharacteristic
787C23C22×C22⋊C411yescharacteristic
788C23C23×D411yescharacteristic
789Q8—44no—
790Q8—44no—
791Q8—44no—
792Q8—44no—
793Q8—82no—
794Q8—82no—
795D4—24no—
796D4—24no—
797D4—24no—
798D4—24no—
799D4—44no—
800D4—44no—
801D4—44no—
802D4—44no—
803D4—48no—
804D4—48no—
805D4—44no—
806D4—44no—
807D4—82no—
808D4—82no—
809D4—88no—
810D4—88no—
811D4—88no—
812D4—88no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—28no—
820C2×C4—28no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—24no—
829C2×C4—41no—
830C2×C4—42no—
831C2×C4—41no—
832C2×C4—42no—
833C2×C4—44no—
834C2×C4—44no—
835C2×C4—44no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—44no—
840C2×C4—44no—
841C2×C4—44no—
842C2×C4—44no—
843C2×C4—44no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—48no—
847C2×C4—42no—
848C2×C4—44no—
849C2×C4—44no—
850C2×C4—44no—
851C2×C4—42no—
852C2×C4—48no—
853C2×C4—44no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—44no—
857C2×C4—42no—
858C2×C4—44no—
859C2×C4—88no—
860C2×C4—88no—
861C2×C4—816no—
862C2×C4C22×C22⋊C411yescharacteristic
863C2×C4C22×C22⋊C414yes—
864C2×C4C22×C22⋊C414yes—
865C2×C4C22×C22⋊C411yescharacteristic
866C2×C4C22×C22⋊C411yescharacteristic
867C2×C4C22×C22⋊C411yescharacteristic
868C2×C4C22×C22⋊C411yescharacteristic
869C2×C4C22×C22⋊C411yescharacteristic
870C2×C4C22×C22⋊C411yescharacteristic
871C2×C4C22×C22⋊C411yescharacteristic
872C2×C4C22×C22⋊C411yescharacteristic
873C2×C4C22×C22⋊C411yescharacteristic
874C2×C4#57514yes—
875C2×C4C24×C411yescharacteristic
876C2×C4C23×D411yescharacteristic
877C8—44no—
878C8—44no—
879C22—21no—
880C22—21no—
881C22—21no—
882C22—21no—
883C22—21no—
884C22—24no—
885C22—24no—
886C22—21no—
887C22—24no—
888C22—24no—
889C22—21no—
890C22—24no—
891C22—24no—
892C22—44no—
893C22—48no—
894C22—44no—
895C22—44no—
896C22—44no—
897C22—84no—
898C22—88no—
899C22—88no—
900C22—88no—
901C22#290112yes—
902C22C23×C22⋊C411yescharacteristic
903C22C2×#57512yes—
904C4—21no—
905C4—21no—
906C4—21no—
907C4—24no—
908C4—24no—
909C4—21no—
910C4—21no—
911C4—21no—
912C4—21no—
913C4—21no—
914C4—21no—
915C4—44no—
916C4—44no—
917C4—44no—
918C4—44no—
919C4—82no—
920C4—84no—
921C4#288312yes—
922C4#289612yes—
923C4#289612yes—
924C2—22no—
925C2—22no—
926C2—44no—
927C2—41no—
928C2—44no—
929C2—84no—
930C2C2×#288311yescharacteristic
931C2C2×#289611yescharacteristic
932C2C2×#290111yescharacteristic
subgroupG/H
center, socleC22C23×C22⋊C4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#3506C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60230C2semidirect
3. #34126C2semidirect
4. #17630C2semidirect
5. #17629C2semidirect
6. #17617C2semidirect
7. #17584C2semidirect
8. #17583C2semidirect
9. #17582C2semidirect
10. #17545C2semidirect
11. #17544C2semidirect
12. #17542C2semidirect
18. #3506C4semidirect
19. #3506C4semidirect
24. C2×#556C4semidirect
25. C2×#555C4semidirect
27. C2×#550C4semidirect
28. C2×#547C4semidirect
36. #2975C22semidirect
39. #2973C22semidirect
40. #2972C22semidirect
46. #2357C22semidirect
47. #2353C22semidirect
48. #2349C22semidirect
59. #1518C22semidirect
60. #1517C22semidirect
61. #1516C22semidirect
62. #1515C22semidirect
63. #1514C22semidirect
64. #1513C22semidirect
71. #1506C22semidirect
72. #1505C22semidirect
73. #1504C22semidirect
74. #1503C22semidirect
75. #1502C22semidirect
76. #1501C22semidirect
78. C22×#41C2×C4semidirect
92. #556C2×C4semidirect
93. #556C2×C4semidirect
98. #555C2×C4semidirect
99. #555C2×C4semidirect
110. #550C2×C4semidirect
111. #550C2×C4semidirect
116. #547C2×C4semidirect
117. #547C2×C4semidirect
133. #533C2×C4semidirect
134. #533C2×C4semidirect
141. #532C2×C4semidirect
142. #532C2×C4semidirect
145. C2×C4⋊Q8C2×C4semidirect
146. C2×C4⋊Q8C2×C4semidirect
147. C2×C4⋊Q8C2×C4semidirect
149. C2×#127C2×C4semidirect
159. #525C2×C4semidirect
160. #525C2×C4semidirect
166. C2×C22⋊Q8C2×C4semidirect
172. C2×#121C2×C4semidirect
182. C2×C4×Q8C2×C4semidirect
192. C2×C4×D4C2×C4semidirect
207. C2×#117C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#35062
#602302
#341262
#176302
#176292
#176172
#175842
#175832
#175822
#175452
#175442
#175422