Finite Group Databasebeta

← #6343394

Subgroups — #6343394

Order 512.

3355 conjugacy classes of subgroups.

The subgroup lattice has 1100 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3519C211yesmaximal, characteristic
2#60230C211yesmaximal, characteristic, complemented
3#34057C211yesmaximal, characteristic, complemented
4#17597C2116yesmaximal, complemented
5#17583C212yesmaximal, complemented
6#17582C212yesmaximal, complemented
7#17579C212yesmaximal, complemented
8#17577C212yesmaximal, complemented
9#17542C212yesmaximal, complemented
10C2×#1507C212yesmaximal, complemented
11#3519—24no—
12#3519—24no—
13#3519C418yescomplemented
14#3519C2218yes—
15C2×#555C411yescharacteristic, complemented
16C2×#554C411yescharacteristic, complemented
17C2×#553—21no—
18C2×#553C411yescharacteristic, complemented
19C2×#553C411yescharacteristic, complemented
20C2×#550C411yescharacteristic, complemented
21C2×#546—21no—
22C2×#546—21no—
23C2×#546C411yescharacteristic, complemented
24C2×#546C411yescharacteristic, complemented
25C2×D42—21no—
26C2×D42C411yescharacteristic, complemented
27C2×#540—21no—
28C2×#538—21no—
29C2×#538—21no—
30C2×#532C2211yescharacteristic
31C2×#529C2211yescharacteristic
32C2×#525C2211yescharacteristic
33C2×#525C2211yescharacteristic
34C22×#121C2211yescharacteristic
35C22×#121C2211yescharacteristic
36C2×#518—21no—
37C22×C4×D4C2211yescharacteristic
38#2975—21no—
39#2974C2218yescomplemented
40#2973—21no—
41#2973—21no—
42#2972—21no—
43D4×M16—24no—
44#2920C2212yescomplemented
45C2×#407C2212yescomplemented
46C2×#407C2212yescomplemented
47#2318C2218yescomplemented
48#2315—21no—
49#2313—21no—
50#2312—21no—
51#2308—21no—
52#2290—24no—
53#2283C2212yescomplemented
54#2280C2212yescomplemented
55C2×C4×C22⋊C4C2212yescomplemented
56#1521C2218yescomplemented
57#1519C2218yescomplemented
58#1517C2218yescomplemented
59#1516C2218yescomplemented
60#1514C2218yescomplemented
61#1513C2218yescomplemented
62#1512C2218yescomplemented
63#1510C2218yescomplemented
64#1508C2214yescomplemented
65#1507C2214yes—
66#1507C2218yescomplemented
67#1507C2214yescomplemented
68#1507C2214yescomplemented
69#1504C2218yescomplemented
70#1501C2218yescomplemented
71C2×#327C2218yescomplemented
72C22×#41—21no—
73C22×#41C2×C411yescharacteristic
74C22×#41C2×C411yescharacteristic, complemented
75C23×D4—21no—
76C23×D4—21no—
77C23×D4—21no—
78C23×D4C2×C411yescharacteristic
79C23×D4C2×C411yescharacteristic, complemented
80C23×D4D411yescharacteristic
81C24×C4C2311yescharacteristic
82C24×C4C2311yescharacteristic
83C22×M16—22no—
84C22×M16—22no—
85#555—24no—
86#555C2×C418yescomplemented
87#554—24no—
88#554C2×C418yescomplemented
89#553—24no—
90#553—24no—
91#553—28no—
92#553—28no—
93#553C2×C418yescomplemented
94#553C2×C418yescomplemented
95#550—24no—
96#550C2×C418yescomplemented
97#546—24no—
98#546—24no—
99#546—28no—
100#546—28no—
101#546—28no—
102#546—28no—
103#546C2×C418yescomplemented
104#546C2×C418yescomplemented
105D42—28no—
106D42—28no—
107D42—24no—
108D42C2×C418yescomplemented
109#540—28no—
110#540—28no—
111#538—28no—
112#538—28no—
113#538—28no—
114#538—28no—
115#532—22no—
116#532—22no—
117#532C2×C414yescomplemented
118#532C2314yes—
119C2×C4⋊Q8C2×C411yescharacteristic, complemented
120C2×#127—21no—
121C2×#127C2×C411yescharacteristic, complemented
122#529—22no—
123#529—22no—
124#529C2×C414yescomplemented
125#529C2314yes—
126C2×#126—21no—
127C2×#126—21no—
128C2×#126—21no—
129C2×#125—21no—
130C2×#125C2×C411yescharacteristic, complemented
131C2×#124—21no—
132C2×#124—21no—
133C2×#124—21no—
134C2×#124C2×C411yescharacteristic, complemented
135#525—22no—
136#525—22no—
137#525—22no—
138#525—22no—
139#525C2×C414yes—
140#525C2×C414yescomplemented
141#525C2314yes—
142#525C2314yes—
143C2×#123—21no—
144C2×#123—21no—
145C2×#123—21no—
146C2×#123—21no—
147C2×#123—21no—
148C2×#123—21no—
149C2×#123—21no—
150C2×C22⋊Q8—21no—
151C2×C22⋊Q8—21no—
152C2×C22⋊Q8C2×C411yescharacteristic
153C2×C22⋊Q8C2×C411yescharacteristic, complemented
154C2×C22⋊Q8C2311yescharacteristic
155C2×#121—21no—
156C2×#121—21no—
157C2×#121—21no—
158C2×#121—21no—
159C2×#121—21no—
160C2×#121—21no—
161C2×#121—21no—
162C2×#121—22no—
163C2×#121—22no—
164C2×#121—22no—
165C2×#121—22no—
166C2×#121—21no—
167C2×#121—21no—
168C2×#121—21no—
169C2×#121—21no—
170C2×#121—21no—
171C2×#121—21no—
172C2×#121C2×C411yescharacteristic
173C2×#121C2×C411yescharacteristic
174C2×#121C2×C414yes—
175C2×#121C2×C411yescharacteristic
176C2×#121C2×C411yescharacteristic, complemented
177C2×#121C2×C411yescharacteristic, complemented
178C2×#121C2×C414yescomplemented
179C2×#121C2×C411yescharacteristic, complemented
180C2×#121C2311yescharacteristic
181C2×#121C2311yescharacteristic
182C2×#121C2311yescharacteristic
183C2×#121C2314yes—
184C2×#121C2314yes—
185C2×#120—21no—
186C2×#120—21no—
187C2×#120—21no—
188C2×#120—21no—
189C2×#120—21no—
190C2×#120—21no—
191#518—28no—
192#518—28no—
193C2×C4×Q8C2×C411yescharacteristic, complemented
194C2×C4×D4—21no—
195C2×C4×D4—21no—
196C2×C4×D4—21no—
197C2×C4×D4—21no—
198C2×C4×D4—21no—
199C2×C4×D4—21no—
200C2×C4×D4—21no—
201C2×C4×D4—21no—
202C2×C4×D4—21no—
203C2×C4×D4—21no—
204C2×C4×D4C2×C411yescharacteristic
205C2×C4×D4C2×C411yescharacteristic
206C2×C4×D4C2×C411yescharacteristic
207C2×C4×D4C2×C411yescharacteristic
208C2×C4×D4C2×C414yes—
209C2×C4×D4C2×C411yescharacteristic, complemented
210C2×C4×D4C2×C411yescharacteristic, complemented
211C2×C4×D4C2×C411yescharacteristic, complemented
212C2×C4×D4D411yescharacteristic
213C2×C4×D4D414yes—
214C2×C4×D4D411yescharacteristic
215C2×C4×D4D411yescharacteristic
216C2×C4×D4D411yescharacteristic
217C2×C4×D4D414yes—
218C2×C4×D4C2314yes—
219C2×#117—22no—
220C2×#117—21no—
221C2×#117—21no—
222C2×#117C2×C411yescharacteristic
223C2×#117C2×C411yescharacteristic, complemented
224C22×C4⋊C4C2×C411yescharacteristic
225C22×C4⋊C4C2×C411yescharacteristic, complemented
226C22×C4⋊C4D411yescharacteristic
227C22×C22⋊C4—21no—
228C22×C22⋊C4—21no—
229C22×C22⋊C4—21no—
230C22×C22⋊C4—21no—
231C22×C22⋊C4—22no—
232C22×C22⋊C4D411yescharacteristic
233C22×C22⋊C4D411yescharacteristic
234C22×C42—22no—
235C22×C42C2311yescharacteristic
236#436—28no—
237#435—28no—
238#435—28no—
239C8×D4—28no—
240#432—22no—
241#432C2314yescomplemented
242#431—22no—
243#431C2314yescomplemented
244#423—22no—
245#407—22no—
246#407—22no—
247#407—22no—
248#407—22no—
249#407C2314yes—
250#407C2314yescomplemented
251#407C2314yescomplemented
252C2×C22⋊C8—22no—
253C2×C22⋊C8—22no—
254C2×C22⋊C8C2314yescomplemented
255C2×C22⋊C8C2314yescomplemented
256C4×M16—22no—
257#388—28no—
258#387—28no—
259#386—28no—
260#385—28no—
261#383C2314yescomplemented
262#382C2314yescomplemented
263#381—22no—
264#381C2314yescomplemented
265#380—22no—
266#380—22no—
267#380C2314yescomplemented
268#379—22no—
269C4×C4⋊C4—22no—
270C4×C22⋊C4—22no—
271C4×C22⋊C4—22no—
272C4×C22⋊C4—22no—
273C4×C22⋊C4C2314yes—
274C4×C22⋊C4C2314yescomplemented
275#376—22no—
276C2×#95C2314yescomplemented
277#328C23116yescomplemented
278#327C23116yes—
279#327C23116yescomplemented
280#327C23116yescomplemented
281C25—21no—
282C25—21no—
283C25C2×D411yescharacteristic
284C25C2×D411yescharacteristic
285C2×#41—22no—
286C2×#41—22no—
287C2×#41—24no—
288C2×#41—24no—
289C2×#41—84no—
290C2×#41—82no—
291C2×#41—82no—
292C2×#41C22×C414yes—
293C2×#41C22×C414yes—
294C22×Q8—21no—
295C22×Q8C22×C411yescharacteristic
296C22×D4—21no—
297C22×D4—21no—
298C22×D4—21no—
299C22×D4—21no—
300C22×D4—21no—
301C22×D4—21no—
302C22×D4—21no—
303C22×D4—21no—
304C22×D4—21no—
305C22×D4—21no—
306C22×D4—21no—
307C22×D4—24no—
308C22×D4—24no—
309C22×D4—24no—
310C22×D4—24no—
311C22×D4—28no—
312C22×D4—21no—
313C22×D4—21no—
314C22×D4—21no—
315C22×D4—21no—
316C22×D4—22no—
317C22×D4—22no—
318C22×D4—44no—
319C22×D4—48no—
320C22×D4—82no—
321C22×D4—82no—
322C22×D4—84no—
323C22×D4—84no—
324C22×D4C22⋊C411yescharacteristic
325C22×D4C22⋊C411yescharacteristic
326C22×D4C22⋊C411yescharacteristic
327C22×D4C22⋊C411yescharacteristic
328C22×D4C22⋊C414yes—
329C22×D4C22×C411yescharacteristic
330C22×D4C22×C411yescharacteristic
331C22×D4C22×C411yescharacteristic
332C22×D4C22×C414yes—
333C22×D4C22×C414yes—
334C22×D4C2×D414yes—
335C23×C4—21no—
336C23×C4—21no—
337C23×C4—21no—
338C23×C4—21no—
339C23×C4—21no—
340C23×C4—21no—
341C23×C4—21no—
342C23×C4—24no—
343C23×C4—82no—
344C23×C4—82no—
345C23×C4C22×C411yescharacteristic
346C23×C4C22×C411yescharacteristic
347C23×C4C22×C411yescharacteristic
348C23×C4C22×C411yescharacteristic
349C23×C4C22×C412yes—
350C23×C4C22×C412yes—
351C23×C4C2×D411yescharacteristic
352C23×C4C2×D411yescharacteristic
353C23×C4C2×D412yes—
354C23×C4C2×D412yes—
355C23×C4C2×D412yes—
356C23×C4C2×D412yes—
357C23×C4C2×D411yescharacteristic
358C23×C4C2×D411yescharacteristic
359C23×C4C2×D411yescharacteristic
360C23×C4C2×D411yescharacteristic
361C23×C4C2×D411yescharacteristic
362C23×C4C2×D411yescharacteristic
363C23×C4C2411yescharacteristic
364C23×C4C2412yes—
365C23×C4C2412yes—
366C2×M16—24no—
367C2×M16—24no—
368C2×M16—24no—
369C2×M16—84no—
370C2×M16—84no—
371C22×C8—24no—
372C22×C8—24no—
373C4⋊Q8—22no—
374C4⋊Q8C22×C414yes—
375#127—28no—
376#127—22no—
377#127C22×C414yes—
378#126—28no—
379#126—28no—
380#126—24no—
381#126—24no—
382#125—28no—
383#125—22no—
384#125C22×C414yes—
385#124—28no—
386#124—28no—
387#124—24no—
388#124—22no—
389#124—24no—
390#124C22×C414yes—
391#123—24no—
392#123—24no—
393#123—24no—
394#123—24no—
395#123—24no—
396#123—24no—
397#123—28no—
398#123—28no—
399#123—28no—
400#123—28no—
401C22⋊Q8—22no—
402C22⋊Q8—22no—
403C22⋊Q8—21no—
404C22⋊Q8—21no—
405C22⋊Q8—28no—
406C22⋊Q8—28no—
407C22⋊Q8C22×C414yes—
408C22⋊Q8C22×C414yes—
409C22⋊Q8C22×C412yes—
410C22⋊Q8C2412yes—
411#121—28no—
412#121—28no—
413#121—28no—
414#121—24no—
415#121—24no—
416#121—22no—
417#121—22no—
418#121—24no—
419#121—24no—
420#121—22no—
421#121—22no—
422#121—24no—
423#121—22no—
424#121—22no—
425#121—21no—
426#121—21no—
427#121—21no—
428#121—21no—
429#121—21no—
430#121—21no—
431#121—24no—
432#121—24no—
433#121—24no—
434#121—24no—
435#121—24no—
436#121—28no—
437#121—28no—
438#121—28no—
439#121—28no—
440#121—28no—
441#121C22×C412yes—
442#121C22×C412yes—
443#121C22×C414yes—
444#121C22×C414yes—
445#121C22×C414yes—
446#121C22×C412yes—
447#121C22×C414yes—
448#121C22×C414yes—
449#121C22×C414yes—
450#121C2412yes—
451#121C2412yes—
452#121C2412yes—
453#120—24no—
454#120—24no—
455#120—24no—
456#120—24no—
457#120—28no—
458#120—28no—
459#120—28no—
460#120—28no—
461C4×Q8—22no—
462C4×Q8C22×C414yes—
463C4×D4—28no—
464C4×D4—24no—
465C4×D4—24no—
466C4×D4—24no—
467C4×D4—24no—
468C4×D4—24no—
469C4×D4—24no—
470C4×D4—24no—
471C4×D4—24no—
472C4×D4—24no—
473C4×D4—24no—
474C4×D4—28no—
475C4×D4—28no—
476C4×D4—28no—
477C4×D4—24no—
478C4×D4—22no—
479C4×D4—22no—
480C4×D4—22no—
481C4×D4—24no—
482C4×D4C22⋊C414yes—
483C4×D4C22⋊C414yes—
484C4×D4C22⋊C414yes—
485C4×D4C22⋊C414yes—
486C4×D4C22⋊C414yes—
487C4×D4C22⋊C414yes—
488C4×D4C22⋊C414yes—
489C4×D4C22⋊C414yes—
490C4×D4C22×C414yes—
491C4×D4C22×C414yes—
492C4×D4C22×C414yes—
493C4×D4C22×C414yes—
494C4×D4C22×C414yes—
495C4×D4C22×C414yes—
496C4×D4C22×C414yes—
497C4×D4C2×D414yes—
498C4×D4C2×D414yes—
499C4×D4C2×D414yes—
500C4×D4C2×D414yes—
501#117—22no—
502#117—22no—
503#117—28no—
504#117—24no—
505#117—24no—
506#117—84no—
507#117C22×C414yes—
508#117C22×C414yes—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—22no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—22no—
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—21no—
520C2×C4⋊C4—24no—
521C2×C4⋊C4—24no—
522C2×C4⋊C4C22⋊C411yescharacteristic
523C2×C4⋊C4C22⋊C411yescharacteristic
524C2×C4⋊C4C22⋊C411yescharacteristic
525C2×C4⋊C4C22⋊C411yescharacteristic
526C2×C4⋊C4C22⋊C414yes—
527C2×C4⋊C4C22×C411yescharacteristic
528C2×C4⋊C4C22×C411yescharacteristic
529C2×C4⋊C4C22×C414yes—
530C2×C4⋊C4C22×C411yescharacteristic
531C2×C4⋊C4C22×C414yes—
532C2×C4⋊C4C22×C411yescharacteristic
533C2×C4⋊C4C2×D414yes—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—24no—
545C2×C22⋊C4—24no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—24no—
556C2×C22⋊C4—24no—
557C2×C22⋊C4—28no—
558C2×C22⋊C4—28no—
559C2×C22⋊C4—24no—
560C2×C22⋊C4—24no—
561C2×C22⋊C4—24no—
562C2×C22⋊C4—24no—
563C2×C22⋊C4—48no—
564C2×C22⋊C4C22⋊C411yescharacteristic
565C2×C22⋊C4C22⋊C411yescharacteristic
566C2×C22⋊C4C22⋊C411yescharacteristic
567C2×C22⋊C4C22⋊C411yescharacteristic
568C2×C22⋊C4C22⋊C411yescharacteristic
569C2×C22⋊C4C22⋊C411yescharacteristic
570C2×C22⋊C4C22⋊C411yescharacteristic
571C2×C22⋊C4C22⋊C411yescharacteristic
572C2×C22⋊C4C22⋊C414yes—
573C2×C22⋊C4C22⋊C414yes—
574C2×C22⋊C4C2×D414yes—
575C2×C22⋊C4C2×D414yes—
576C2×C42—21no—
577C2×C42—21no—
578C2×C42—21no—
579C2×C42—24no—
580C2×C42—24no—
581C2×C42—84no—
582C2×C42C22×C411yescharacteristic
583C2×C42C22×C411yescharacteristic
584C2×C42C22×C412yes—
585C2×C42C2×D412yes—
586C2×C42C2×D411yescharacteristic
587C2×C42C2×D411yescharacteristic
588C2×C42C2×D412yes—
589C2×C42C2412yes—
590C4⋊C8—24no—
591C4⋊C8—24no—
592C22⋊C8—24no—
593C22⋊C8—24no—
594C22⋊C8—24no—
595C22⋊C8—24no—
596C22⋊C8—24no—
597C22⋊C8C2418yes—
598#97—24no—
599C4×C8—24no—
600#95—24no—
601#95—24no—
602#95—24no—
603#95—24no—
604#95—24no—
605#95C2418yes—
606C24—24no—
607C24—21no—
608C24—21no—
609C24—21no—
610C24—24no—
611C24—24no—
612C24—42no—
613C24—42no—
614C24—42no—
615C24—44no—
616C24—44no—
617C24—81no—
618C24—81no—
619C24—82no—
620C24—82no—
621C24—82no—
622C24—82no—
623C24C2×C22⋊C411yescharacteristic
624C24C2×C22⋊C411yescharacteristic
625C24C2×C22⋊C411yescharacteristic
626C24C2×C22⋊C412yes—
627C24C2×C22⋊C412yes—
628C24C2×C22⋊C411yescharacteristic
629C24C22×D411yescharacteristic
630C24C22×D412yes—
631C24C22×D412yes—
632#41—88no—
633#41—84no—
634#41—84no—
635#41—88no—
636#41—84no—
637#41—84no—
638C2×Q8—21no—
639C2×Q8—24no—
640C2×Q8—42no—
641C2×Q8—82no—
642C2×Q8C23×C412yes—
643C2×D4—24no—
644C2×D4—24no—
645C2×D4—24no—
646C2×D4—24no—
647C2×D4—22no—
648C2×D4—22no—
649C2×D4—22no—
650C2×D4—22no—
651C2×D4—22no—
652C2×D4—22no—
653C2×D4—24no—
654C2×D4—24no—
655C2×D4—24no—
656C2×D4—24no—
657C2×D4—24no—
658C2×D4—24no—
659C2×D4—24no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—24no—
664C2×D4—24no—
665C2×D4—24no—
666C2×D4—42no—
667C2×D4—42no—
668C2×D4—44no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—42no—
672C2×D4—48no—
673C2×D4—48no—
674C2×D4—432no—
675C2×D4—44no—
676C2×D4—44no—
677C2×D4—44no—
678C2×D4—44no—
679C2×D4—44no—
680C2×D4—84no—
681C2×D4—84no—
682C2×D4—84no—
683C2×D4—84no—
684C2×D4—82no—
685C2×D4—82no—
686C2×D4—82no—
687C2×D4—82no—
688C2×D4—82no—
689C2×D4—82no—
690C2×D4—82no—
691C2×D4—82no—
692C2×D4—82no—
693C2×D4—88no—
694C2×D4—88no—
695C2×D4—88no—
696C2×D4—88no—
697C2×D4C2×C22⋊C414yes—
698C2×D4C2×C22⋊C414yes—
699C2×D4C2×C22⋊C414yes—
700C2×D4C2×C22⋊C414yes—
701C2×D4C23×C412yes—
702C2×D4C23×C412yes—
703C2×D4C23×C412yes—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—24no—
710C22×C4—24no—
711C22×C4—24no—
712C22×C4—24no—
713C22×C4—24no—
714C22×C4—24no—
715C22×C4—24no—
716C22×C4—28no—
717C22×C4—44no—
718C22×C4—44no—
719C22×C4—44no—
720C22×C4—44no—
721C22×C4—42no—
722C22×C4—42no—
723C22×C4—42no—
724C22×C4—42no—
725C22×C4—42no—
726C22×C4—42no—
727C22×C4—42no—
728C22×C4—44no—
729C22×C4—48no—
730C22×C4—82no—
731C22×C4—82no—
732C22×C4—81no—
733C22×C4—81no—
734C22×C4—81no—
735C22×C4—81no—
736C22×C4—81no—
737C22×C4—81no—
738C22×C4—82no—
739C22×C4—82no—
740C22×C4—84no—
741C22×C4—84no—
742C22×C4—82no—
743C22×C4—82no—
744C22×C4—82no—
745C22×C4—82no—
746C22×C4—82no—
747C22×C4—82no—
748C22×C4C2×C22⋊C411yescharacteristic
749C22×C4C2×C22⋊C411yescharacteristic
750C22×C4C2×C22⋊C412yes—
751C22×C4C2×C22⋊C412yes—
752C22×C4C2×C22⋊C412yes—
753C22×C4C2×C22⋊C412yes—
754C22×C4C2×C22⋊C411yescharacteristic
755C22×C4C2×C22⋊C411yescharacteristic
756C22×C4C2×C22⋊C411yescharacteristic
757C22×C4C2×C22⋊C411yescharacteristic
758C22×C4C2×C22⋊C412yes—
759C22×C4C2×C22⋊C412yes—
760C22×C4C2×C22⋊C412yes—
761C22×C4C2×C22⋊C412yes—
762C22×C4C2×C22⋊C411yescharacteristic
763C22×C4C2×C22⋊C411yescharacteristic
764C22×C4C2×C22⋊C412yes—
765C22×C4C2×C22⋊C412yes—
766C22×C4C2×C22⋊C412yes—
767C22×C4C2×C22⋊C412yes—
768C22×C4C23×C411yescharacteristic
769C22×C4C23×C411yescharacteristic
770C22×C4C23×C412yes—
771C22×C4C23×C412yes—
772C22×C4C23×C412yes—
773C22×C4C23×C412yes—
774C22×C4C22×D412yes—
775C22×C4C22×D411yescharacteristic
776C22×C4C22×D411yescharacteristic
777C22×C4C22×D412yes—
778C22×C4C22×D412yes—
779C22×C4C22×D412yes—
780C22×C4C22×D411yescharacteristic
781C22×C4C22×D412yes—
782C22×C4C22×D412yes—
783C22×C4C22×D412yes—
784C22×C4C22×D412yes—
785C22×C4C2511yescharacteristic
786M16—48no—
787M16—84no—
788M16—84no—
789C2×C8—28no—
790C2×C8—84no—
791C2×C8—84no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—24no—
796C4⋊C4—24no—
797C4⋊C4—24no—
798C4⋊C4—22no—
799C4⋊C4—24no—
800C4⋊C4—24no—
801C4⋊C4—24no—
802C4⋊C4—24no—
803C4⋊C4—24no—
804C4⋊C4—21no—
805C4⋊C4—22no—
806C4⋊C4—84no—
807C4⋊C4—84no—
808C4⋊C4C2×C22⋊C414yes—
809C4⋊C4C2×C22⋊C414yes—
810C4⋊C4C2×C22⋊C414yes—
811C4⋊C4C2×C22⋊C414yes—
812C4⋊C4C23×C412yes—
813C4⋊C4C23×C412yes—
814C4⋊C4C23×C412yes—
815C4⋊C4C23×C412yes—
816C22⋊C4—24no—
817C22⋊C4—24no—
818C22⋊C4—24no—
819C22⋊C4—24no—
820C22⋊C4—22no—
821C22⋊C4—22no—
822C22⋊C4—22no—
823C22⋊C4—24no—
824C22⋊C4—24no—
825C22⋊C4—24no—
826C22⋊C4—24no—
827C22⋊C4—24no—
828C22⋊C4—22no—
829C22⋊C4—22no—
830C22⋊C4—24no—
831C22⋊C4—24no—
832C22⋊C4—24no—
833C22⋊C4—24no—
834C22⋊C4—24no—
835C22⋊C4—24no—
836C22⋊C4—22no—
837C22⋊C4—22no—
838C22⋊C4—22no—
839C22⋊C4—48no—
840C22⋊C4—48no—
841C22⋊C4—84no—
842C22⋊C4—84no—
843C22⋊C4C2×C22⋊C414yes—
844C22⋊C4C2×C22⋊C414yes—
845C22⋊C4C2×C22⋊C414yes—
846C22⋊C4C2×C22⋊C414yes—
847C22⋊C4C2×C22⋊C414yes—
848C22⋊C4C2×C22⋊C414yes—
849C22⋊C4C2×C22⋊C414yes—
850C22⋊C4C2×C22⋊C414yes—
851C42—24no—
852C42—24no—
853C42—24no—
854C42—48no—
855C42—84no—
856C42C2×C22⋊C412yes—
857C42C2×C22⋊C412yes—
858C42C2×C22⋊C412yes—
859C42C2×C22⋊C412yes—
860C42C23×C412yes—
861C42C23×C412yes—
862C42C22×D412yes—
863C42C22×D412yes—
864C23—22no—
865C23—24no—
866C23—22no—
867C23—24no—
868C23—22no—
869C23—24no—
870C23—22no—
871C23—24no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—42no—
877C23—41no—
878C23—41no—
879C23—41no—
880C23—41no—
881C23—41no—
882C23—42no—
883C23—41no—
884C23—41no—
885C23—42no—
886C23—42no—
887C23—42no—
888C23—42no—
889C23—41no—
890C23—41no—
891C23—42no—
892C23—42no—
893C23—42no—
894C23—42no—
895C23—42no—
896C23—42no—
897C23—42no—
898C23—42no—
899C23—48no—
900C23—42no—
901C23—42no—
902C23—42no—
903C23—48no—
904C23—84no—
905C23—84no—
906C23—84no—
907C23—84no—
908C23—88no—
909C23—88no—
910C23—168no—
911C23—168no—
912C23#42114yes—
913C23C22×C22⋊C412yes—
914C23C22×C22⋊C412yes—
915C23C22×C22⋊C412yes—
916C23C22×C22⋊C411yescharacteristic
917C23C22×C22⋊C412yes—
918C23C22×C22⋊C411yescharacteristic
919C23C23×D411yescharacteristic
920Q8—42no—
921Q8—42no—
922Q8—84no—
923D4—28no—
924D4—28no—
925D4—44no—
926D4—44no—
927D4—42no—
928D4—42no—
929D4—42no—
930D4—48no—
931D4—48no—
932D4—44no—
933D4—44no—
934D4—44no—
935D4—44no—
936D4—44no—
937D4—44no—
938D4—48no—
939D4—42no—
940D4—42no—
941D4—42no—
942D4—84no—
943D4—84no—
944D4—84no—
945D4—84no—
946D4—84no—
947D4—84no—
948D4—84no—
949D4—84no—
950D4—84no—
951C2×C4—24no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—24no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—42no—
967C2×C4—42no—
968C2×C4—42no—
969C2×C4—42no—
970C2×C4—42no—
971C2×C4—42no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—42no—
979C2×C4—42no—
980C2×C4—42no—
981C2×C4—42no—
982C2×C4—42no—
983C2×C4—42no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—42no—
987C2×C4—42no—
988C2×C4—42no—
989C2×C4—42no—
990C2×C4—42no—
991C2×C4—41no—
992C2×C4—42no—
993C2×C4—42no—
994C2×C4—48no—
995C2×C4—42no—
996C2×C4—42no—
997C2×C4—42no—
998C2×C4—42no—
999C2×C4—42no—
1000C2×C4—48no—
1001C2×C4—48no—
1002C2×C4—48no—
1003C2×C4—84no—
1004C2×C4—84no—
1005C2×C4—84no—
1006C2×C4—84no—
1007C2×C4—84no—
1008C2×C4—84no—
1009C2×C4—816no—
1010C2×C4C22×C22⋊C412yes—
1011C2×C4C22×C22⋊C412yes—
1012C2×C4C22×C22⋊C412yes—
1013C2×C4C22×C22⋊C411yescharacteristic
1014C2×C4C22×C22⋊C412yes—
1015C2×C4C22×C22⋊C412yes—
1016C2×C4C22×C22⋊C412yes—
1017C2×C4C22×C22⋊C412yes—
1018C2×C4C22×C22⋊C412yes—
1019C2×C4C22×C22⋊C411yescharacteristic
1020C2×C4C24×C411yescharacteristic
1021C2×C4C23×D411yescharacteristic
1022C8—48no—
1023C22—21no—
1024C22—21no—
1025C22—22no—
1026C22—21no—
1027C22—22no—
1028C22—21no—
1029C22—21no—
1030C22—22no—
1031C22—22no—
1032C22—22no—
1033C22—21no—
1034C22—22no—
1035C22—22no—
1036C22—22no—
1037C22—21no—
1038C22—22no—
1039C22—22no—
1040C22—22no—
1041C22—44no—
1042C22—48no—
1043C22—44no—
1044C22—44no—
1045C22—42no—
1046C22—42no—
1047C22—42no—
1048C22—42no—
1049C22—42no—
1050C22—42no—
1051C22—42no—
1052C22—42no—
1053C22—42no—
1054C22—84no—
1055C22—82no—
1056C22—82no—
1057C22—84no—
1058C22—84no—
1059C22—84no—
1060C22—84no—
1061C22—84no—
1062C22—168no—
1063C22—168no—
1064C22C2×#42112yes—
1065C22C2×#42114yes—
1066C22C23×C22⋊C411yescharacteristic
1067C22#358512yes—
1068C4—21no—
1069C4—21no—
1070C4—21no—
1071C4—22no—
1072C4—22no—
1073C4—22no—
1074C4—22no—
1075C4—22no—
1076C4—22no—
1077C4—22no—
1078C4—22no—
1079C4—42no—
1080C4—42no—
1081C4—42no—
1082C4—42no—
1083C4—42no—
1084C4—88no—
1085C4#288312yes—
1086C2—22no—
1087C2—22no—
1088C2—24no—
1089C2—42no—
1090C2—41no—
1091C2—42no—
1092C2—42no—
1093C2—82no—
1094C2—82no—
1095C2—82no—
1096C2C2×#288311yescharacteristic
1097C2#6008711yescharacteristic
1098C2C22×#42111yescharacteristic
subgroupG/H
center, socleC22C23×C22⋊C4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#3519C2
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. #34057C2semidirect
4. #17597C2semidirect
5. #17583C2semidirect
6. #17582C2semidirect
7. #17579C2semidirect
8. #17577C2semidirect
9. #17542C2semidirect
10. C2×#1507C2semidirect
13. #3519C4semidirect
15. C2×#555C4semidirect
16. C2×#554C4semidirect
18. C2×#553C4semidirect
19. C2×#553C4semidirect
20. C2×#550C4semidirect
23. C2×#546C4semidirect
24. C2×#546C4semidirect
26. C2×D42C4semidirect
39. #2974C22semidirect
44. #2920C22semidirect
45. C2×#407C22semidirect
46. C2×#407C22semidirect
47. #2318C22semidirect
53. #2283C22semidirect
54. #2280C22semidirect
55. C2×C4×C22⋊C4C22semidirect
56. #1521C22semidirect
57. #1519C22semidirect
58. #1517C22semidirect
59. #1516C22semidirect
60. #1514C22semidirect
61. #1513C22semidirect
62. #1512C22semidirect
63. #1510C22semidirect
64. #1508C22semidirect
66. #1507C22semidirect
67. #1507C22semidirect
68. #1507C22semidirect
69. #1504C22semidirect
70. #1501C22semidirect
71. C2×#327C22semidirect
74. C22×#41C2×C4semidirect
79. C23×D4C2×C4semidirect
86. #555C2×C4semidirect
88. #554C2×C4semidirect
93. #553C2×C4semidirect
94. #553C2×C4semidirect
96. #550C2×C4semidirect
103. #546C2×C4semidirect
104. #546C2×C4semidirect
108. D42C2×C4semidirect
117. #532C2×C4semidirect
119. C2×C4⋊Q8C2×C4semidirect
121. C2×#127C2×C4semidirect
124. #529C2×C4semidirect
130. C2×#125C2×C4semidirect
134. C2×#124C2×C4semidirect
140. #525C2×C4semidirect
153. C2×C22⋊Q8C2×C4semidirect
176. C2×#121C2×C4semidirect
177. C2×#121C2×C4semidirect
178. C2×#121C2×C4semidirect
179. C2×#121C2×C4semidirect
193. C2×C4×Q8C2×C4semidirect
209. C2×C4×D4C2×C4semidirect
210. C2×C4×D4C2×C4semidirect
211. C2×C4×D4C2×C4semidirect
223. C2×#117C2×C4semidirect
225. C22×C4⋊C4C2×C4semidirect
241. #432C23semidirect
243. #431C23semidirect
250. #407C23semidirect
251. #407C23semidirect
254. C2×C22⋊C8C23semidirect
255. C2×C22⋊C8C23semidirect
261. #383C23semidirect
262. #382C23semidirect
264. #381C23semidirect
267. #380C23semidirect
274. C4×C22⋊C4C23semidirect
276. C2×#95C23semidirect
277. #328C23semidirect
279. #327C23semidirect
280. #327C23semidirect

Maximal subgroups

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

subgroupindex
C2×#35192
#602302
#340572
#175972
#175832
#175822
#175792
#175772
#175422
C2×#15072