Finite Group Databasebeta

← #6343587

Subgroups — #6343587

Order 512.

2902 conjugacy classes of subgroups.

The subgroup lattice has 973 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3495C211yesmaximal, characteristic
2#60124C211yesmaximal, characteristic, complemented
3#34177C211yesmaximal, characteristic, complemented
4#17609C2116yesmaximal, complemented
5#17590C212yesmaximal, complemented
6#17587C212yesmaximal
7#17580C212yesmaximal, complemented
8#17562C212yesmaximal, complemented
9#17554C212yesmaximal, complemented
10C2×#1511C212yesmaximal, complemented
11#3495—24no—
12#3495—24no—
13#3495C418yescomplemented
14#3495C2218yes—
15C2×#556—21no—
16C2×#554—21no—
17C2×#552—21no—
18C2×#552—21no—
19C2×#552—21no—
20C2×#552—21no—
21C2×#551—21no—
22C2×#551—21no—
23C2×#544C411yescharacteristic, complemented
24C2×#542C411yescharacteristic, complemented
25C2×#542C411yescharacteristic, complemented
26C2×#541C411yescharacteristic, complemented
27C2×#541C411yescharacteristic, complemented
28C2×#536C411yescharacteristic, complemented
29C2×#533C2211yescharacteristic
30C2×#533C2211yescharacteristic
31C2×#529C2211yescharacteristic
32C2×#529C2211yescharacteristic
33C2×#525C2211yescharacteristic
34C22×C22⋊Q8C2211yescharacteristic
35C2×#520C411yescharacteristic, complemented
36C2×#519C411yescharacteristic, complemented
37C22×#117C2211yescharacteristic
38#2924—24no—
39#2924C2218yescomplemented
40#2921—21no—
41#2921—21no—
42#2920C2212yes—
43#2920C2212yes—
44#2905—21no—
45C2×#407C2212yes—
46#2873—21no—
47#2343—24no—
48#2343C2218yescomplemented
49#2315—21no—
50#2313—21no—
51#2313—21no—
52#2283C2212yes—
53#2283C2212yes—
54C2×#381C2212yes—
55#2273—21no—
56#1521C2218yescomplemented
57#1518C2218yescomplemented
58#1516C2218yes—
59#1515C2218yescomplemented
60#1512C2218yescomplemented
61#1511C2214yes—
62#1511C2214yes—
63#1511C2214yes—
64#1511C2218yescomplemented
65#1510C2214yes—
66#1509C2218yescomplemented
67#1506C2218yescomplemented
68#1504C2218yes—
69#1503C2218yescomplemented
70#1500C2218yescomplemented
71C2×#328C2218yescomplemented
72C22×#41C2×C411yescharacteristic
73C23×Q8C2×C411yescharacteristic
74C24×C4C2311yescharacteristic
75C22×M16—22no—
76#556—28no—
77#556—28no—
78#554—28no—
79#554—28no—
80#552—28no—
81#552—28no—
82#552—28no—
83#552—28no—
84#552—28no—
85#552—28no—
86#552—28no—
87#552—28no—
88#551—28no—
89#551—28no—
90#551—28no—
91#551—28no—
92#544—24no—
93#544C2×C418yescomplemented
94#542—24no—
95#542—24no—
96#542C2×C418yescomplemented
97#542C2×C418yescomplemented
98#541—24no—
99#541—24no—
100#541C2×C418yescomplemented
101#541C2×C418yescomplemented
102#536—24no—
103#536C2×C418yescomplemented
104#533—22no—
105#533—22no—
106#533—22no—
107#533—22no—
108#533C2×C414yescomplemented
109#533C2×C414yescomplemented
110#533C2314yes—
111#533C2314yes—
112C2×C4⋊Q8—21no—
113C2×C4⋊Q8C2×C411yescharacteristic, complemented
114C2×C4⋊Q8C2×C411yescharacteristic, complemented
115C2×C4⋊Q8C2×C411yescharacteristic, complemented
116C2×C4⋊Q8C2×C411yescharacteristic, complemented
117#529—22no—
118#529—22no—
119#529—22no—
120#529—22no—
121#529C2×C414yescomplemented
122#529C2×C414yescomplemented
123#529C2314yes—
124#529C2314yes—
125C2×#126—21no—
126C2×#126—21no—
127C2×#126—21no—
128C2×#126—21no—
129C2×#126—21no—
130C2×#126—21no—
131C2×#126—21no—
132C2×#126—21no—
133C2×#125—21no—
134C2×#125—21no—
135C2×#125—21no—
136C2×#125—21no—
137C2×#125—21no—
138C2×#125—21no—
139C2×#125—21no—
140C2×#125C2×C411yescharacteristic, complemented
141C2×#125C2×C411yescharacteristic, complemented
142C2×#124—21no—
143C2×#124—21no—
144C2×#124C2×C411yescharacteristic, complemented
145C2×#124C2×C411yescharacteristic, complemented
146#525—22no—
147#525—22no—
148#525C2×C414yes—
149#525C2314yes—
150C2×#123—21no—
151C2×#123—21no—
152C2×#123—21no—
153C2×#123—21no—
154C2×#123—21no—
155C2×#123—21no—
156C2×#123—21no—
157C2×C22⋊Q8—21no—
158C2×C22⋊Q8—21no—
159C2×C22⋊Q8—22no—
160C2×C22⋊Q8—22no—
161C2×C22⋊Q8—21no—
162C2×C22⋊Q8—21no—
163C2×C22⋊Q8—21no—
164C2×C22⋊Q8—21no—
165C2×C22⋊Q8—21no—
166C2×C22⋊Q8—21no—
167C2×C22⋊Q8—21no—
168C2×C22⋊Q8—21no—
169C2×C22⋊Q8C2×C411yescharacteristic
170C2×C22⋊Q8C2×C411yescharacteristic
171C2×C22⋊Q8C2×C414yes—
172C2×C22⋊Q8C2×C411yescharacteristic
173C2×C22⋊Q8C2311yescharacteristic
174C2×C22⋊Q8C2311yescharacteristic
175C2×C22⋊Q8C2314yes—
176C2×C22⋊Q8C2311yescharacteristic
177C2×#121C2×C411yescharacteristic
178C2×#121C2311yescharacteristic
179C2×#120—21no—
180#520—24no—
181#520C2×C418yescomplemented
182#519—24no—
183#519C2×C418yescomplemented
184C2×C4×Q8—21no—
185C2×C4×Q8—21no—
186C2×C4×Q8—21no—
187C2×C4×Q8—21no—
188C2×C4×Q8C2×C411yescharacteristic, complemented
189C2×C4×Q8C2×C411yescharacteristic, complemented
190C2×C4×Q8C2×C411yescharacteristic, complemented
191C2×C4×Q8C2×C411yescharacteristic, complemented
192C2×C4×Q8C2×C411yescharacteristic, complemented
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×D4C2×C411yescharacteristic, complemented
201C2×C4×D4C2×C411yescharacteristic, complemented
202C2×#117—21no—
203C2×#117—21no—
204C2×#117—21no—
205C2×#117—21no—
206C2×#117—21no—
207C2×#117—21no—
208C2×#117—21no—
209C2×#117C2×C411yescharacteristic
210C2×#117C2×C411yescharacteristic
211C2×#117C2×C411yescharacteristic
212C2×#117C2×C411yescharacteristic
213C2×#117C2×C411yescharacteristic
214C2×#117C2×C414yes—
215C2×#117D411yescharacteristic
216C2×#117D411yescharacteristic
217C2×#117D411yescharacteristic
218C2×#117D411yescharacteristic
219C2×#117D414yes—
220C2×#117D414yes—
221C2×#117C2314yes—
222C22×C4⋊C4—21no—
223C22×C4⋊C4—21no—
224C22×C4⋊C4C2×C411yescharacteristic
225C22×C4⋊C4D411yescharacteristic
226C22×C4⋊C4D411yescharacteristic
227C22×C22⋊C4—21no—
228C22×C22⋊C4—22no—
229C22×C22⋊C4D411yescharacteristic
230C22×C22⋊C4D411yescharacteristic
231C22×C42C2311yescharacteristic
232C22×C42C2311yescharacteristic
233#433—28no—
234#433—28no—
235#432—22no—
236#432—22no—
237#432C2314yes—
238#432C2314yes—
239#431—22no—
240#431—22no—
241#431C2314yes—
242#431C2314yes—
243#424—28no—
244#423—22no—
245#423—22no—
246#407—22no—
247#407—22no—
248#407C2314yes—
249#407C2314yes—
250C2×C22⋊C8—22no—
251C2×C22⋊C8C2314yes—
252#405—28no—
253C4×M16—22no—
254C4×M16—22no—
255#387—28no—
256#387—28no—
257#385—28no—
258#383—22no—
259#383C2314yes—
260#382—22no—
261#382C2314yes—
262#381—22no—
263#381—22no—
264#381C2314yes—
265#381C2314yes—
266#380—22no—
267#380—22no—
268C4×C4⋊C4—22no—
269C4×C4⋊C4C2314yes—
270C4×C22⋊C4—22no—
271C4×C22⋊C4—22no—
272C4×C22⋊C4—28no—
273#376—22no—
274#376C2314yes—
275C2×#95—22no—
276C2×#95C2314yes—
277#328C23116yes—
278#328C23116yes—
279#328C23116yes—
280#327C23116yes—
281C25C2×D411yescharacteristic
282C2×#41—22no—
283C2×#41—44no—
284C2×#41C22×C414yes—
285C22×Q8—21no—
286C22×Q8—22no—
287C22×Q8—21no—
288C22×Q8—21no—
289C22×Q8—44no—
290C22×Q8C22×C411yescharacteristic
291C22×Q8C22×C411yescharacteristic
292C22×Q8C22×C411yescharacteristic
293C22×Q8C22×C414yes—
294C22×D4—21no—
295C22×D4—21no—
296C22×D4—21no—
297C22×D4C22×C411yescharacteristic
298C23×C4—21no—
299C23×C4—21no—
300C23×C4—21no—
301C23×C4—21no—
302C23×C4—21no—
303C23×C4—24no—
304C23×C4—44no—
305C23×C4C22×C411yescharacteristic
306C23×C4C22×C411yescharacteristic
307C23×C4C22×C412yes—
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2×D411yescharacteristic
311C23×C4C2×D411yescharacteristic
312C23×C4C2×D412yes—
313C23×C4C2×D411yescharacteristic
314C23×C4C2×D412yes—
315C23×C4C2×D411yescharacteristic
316C23×C4C2×D411yescharacteristic
317C23×C4C2412yes—
318C23×C4C2411yescharacteristic
319C2×M16—24no—
320C2×M16—24no—
321C2×M16—48no—
322C22×C8—24no—
323C4⋊Q8—28no—
324C4⋊Q8—22no—
325C4⋊Q8—22no—
326C4⋊Q8—22no—
327C4⋊Q8—22no—
328C4⋊Q8C22×C414yes—
329C4⋊Q8C22×C414yes—
330C4⋊Q8C22×C414yes—
331C4⋊Q8C22×C414yes—
332#126—28no—
333#126—28no—
334#126—28no—
335#126—28no—
336#126—28no—
337#126—28no—
338#126—24no—
339#126—24no—
340#126—24no—
341#126—24no—
342#125—28no—
343#125—28no—
344#125—28no—
345#125—28no—
346#125—28no—
347#125—24no—
348#125—24no—
349#125—22no—
350#125—22no—
351#125—24no—
352#125—24no—
353#125C22×C414yes—
354#125C22×C414yes—
355#124—28no—
356#124—28no—
357#124—22no—
358#124—22no—
359#124C22×C414yes—
360#124C22×C414yes—
361#123—24no—
362#123—24no—
363#123—24no—
364#123—24no—
365#123—24no—
366#123—24no—
367#123—28no—
368#123—28no—
369#123—28no—
370#123—28no—
371C22⋊Q8—22no—
372C22⋊Q8—22no—
373C22⋊Q8—24no—
374C22⋊Q8—24no—
375C22⋊Q8—24no—
376C22⋊Q8—24no—
377C22⋊Q8—22no—
378C22⋊Q8—21no—
379C22⋊Q8—21no—
380C22⋊Q8—21no—
381C22⋊Q8—21no—
382C22⋊Q8—24no—
383C22⋊Q8—24no—
384C22⋊Q8—24no—
385C22⋊Q8—24no—
386C22⋊Q8—21no—
387C22⋊Q8—21no—
388C22⋊Q8—28no—
389C22⋊Q8—28no—
390C22⋊Q8—28no—
391C22⋊Q8—28no—
392C22⋊Q8—28no—
393C22⋊Q8—28no—
394C22⋊Q8C22×C412yes—
395C22⋊Q8C22×C412yes—
396C22⋊Q8C22×C414yes—
397C22⋊Q8C22×C414yes—
398C22⋊Q8C22×C414yes—
399C22⋊Q8C22×C412yes—
400C22⋊Q8C2412yes—
401C22⋊Q8C2412yes—
402C22⋊Q8C2412yes—
403#121—22no—
404#121—21no—
405#121—21no—
406#121C22×C414yes—
407#121C22×C412yes—
408#121C2412yes—
409#120—24no—
410#120—24no—
411C4×Q8—28no—
412C4×Q8—28no—
413C4×Q8—24no—
414C4×Q8—24no—
415C4×Q8—22no—
416C4×Q8—22no—
417C4×Q8—22no—
418C4×Q8—22no—
419C4×Q8—22no—
420C4×Q8—22no—
421C4×Q8—24no—
422C4×Q8—24no—
423C4×Q8C22×C414yes—
424C4×Q8C22×C414yes—
425C4×Q8C22×C414yes—
426C4×Q8C22×C414yes—
427C4×Q8C22×C414yes—
428C4×Q8C22×C414yes—
429C4×D4—24no—
430C4×D4—24no—
431C4×D4—24no—
432C4×D4—24no—
433C4×D4—24no—
434C4×D4—24no—
435C4×D4—24no—
436C4×D4—24no—
437C4×D4—28no—
438C4×D4—28no—
439C4×D4—22no—
440C4×D4—22no—
441C4×D4C22×C414yes—
442C4×D4C22×C414yes—
443#117—24no—
444#117—24no—
445#117—22no—
446#117—24no—
447#117—24no—
448#117—28no—
449#117—28no—
450#117—28no—
451#117—24no—
452#117—24no—
453#117—24no—
454#117—24no—
455#117C22⋊C414yes—
456#117C22⋊C414yes—
457#117C22⋊C414yes—
458#117C22⋊C414yes—
459#117C22⋊C414yes—
460#117C22⋊C414yes—
461#117C22⋊C414yes—
462#117C22⋊C414yes—
463#117C22×C414yes—
464#117C22×C414yes—
465#117C22×C414yes—
466#117C22×C414yes—
467#117C22×C414yes—
468#117C2×D414yes—
469#117C2×D414yes—
470#117C2×D414yes—
471#117C2×D414yes—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—24no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—24no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—28no—
499C2×C4⋊C4—24no—
500C2×C4⋊C4—24no—
501C2×C4⋊C4C22⋊C411yescharacteristic
502C2×C4⋊C4C22⋊C411yescharacteristic
503C2×C4⋊C4C22⋊C411yescharacteristic
504C2×C4⋊C4C22⋊C411yescharacteristic
505C2×C4⋊C4C22⋊C411yescharacteristic
506C2×C4⋊C4C22⋊C411yescharacteristic
507C2×C4⋊C4C22⋊C411yescharacteristic
508C2×C4⋊C4C22⋊C411yescharacteristic
509C2×C4⋊C4C22⋊C414yes—
510C2×C4⋊C4C22⋊C414yes—
511C2×C4⋊C4C22×C411yescharacteristic
512C2×C4⋊C4C22×C411yescharacteristic
513C2×C4⋊C4C22×C414yes—
514C2×C4⋊C4C22×C411yescharacteristic
515C2×C4⋊C4C22×C411yescharacteristic
516C2×C4⋊C4C2×D414yes—
517C2×C4⋊C4C2×D414yes—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—24no—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—48no—
538C2×C22⋊C4C22⋊C411yescharacteristic
539C2×C22⋊C4C22⋊C411yescharacteristic
540C2×C22⋊C4C22⋊C411yescharacteristic
541C2×C22⋊C4C22⋊C411yescharacteristic
542C2×C22⋊C4C22⋊C411yescharacteristic
543C2×C22⋊C4C22⋊C411yescharacteristic
544C2×C22⋊C4C22⋊C411yescharacteristic
545C2×C22⋊C4C22⋊C411yescharacteristic
546C2×C22⋊C4C22⋊C414yes—
547C2×C22⋊C4C22⋊C414yes—
548C2×C22⋊C4C2×D414yes—
549C2×C22⋊C4C2×D414yes—
550C2×C42—21no—
551C2×C42—21no—
552C2×C42—21no—
553C2×C42—21no—
554C2×C42—21no—
555C2×C42—21no—
556C2×C42—21no—
557C2×C42—24no—
558C2×C42—24no—
559C2×C42C22×C411yescharacteristic
560C2×C42C22×C411yescharacteristic
561C2×C42C22×C411yescharacteristic
562C2×C42C22×C411yescharacteristic
563C2×C42C22×C412yes—
564C2×C42C22×C412yes—
565C2×C42C2×D412yes—
566C2×C42C2×D412yes—
567C2×C42C2×D411yescharacteristic
568C2×C42C2×D411yescharacteristic
569C2×C42C2×D411yescharacteristic
570C2×C42C2×D411yescharacteristic
571C2×C42C2×D412yes—
572C2×C42C2×D412yes—
573C2×C42C2412yes—
574C2×C42C2412yes—
575C4⋊C8—24no—
576C4⋊C8—24no—
577C4⋊C8—24no—
578C4⋊C8—24no—
579C22⋊C8—24no—
580C22⋊C8—24no—
581C22⋊C8—24no—
582C22⋊C8C2418yes—
583#97—24no—
584#97—24no—
585C4×C8—24no—
586C4×C8—24no—
587#95—24no—
588#95—24no—
589#95—24no—
590#95—24no—
591#95—24no—
592#95—24no—
593#95—24no—
594#95C2418yes—
595C24—24no—
596C24—21no—
597C24—42no—
598C24—81no—
599C24C2×C22⋊C411yescharacteristic
600C24C2×C22⋊C412yes—
601C24C2×C22⋊C411yescharacteristic
602C24C22×D411yescharacteristic
603C24C22×D412yes—
604#41—48no—
605#41—48no—
606C2×Q8—24no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—24no—
611C2×Q8—24no—
612C2×Q8—44no—
613C2×Q8—48no—
614C2×Q8—42no—
615C2×Q8—42no—
616C2×Q8—48no—
617C2×Q8—42no—
618C2×Q8—82no—
619C2×Q8—82no—
620C2×Q8C23×C412yes—
621C2×Q8C23×C412yes—
622C2×Q8C23×C412yes—
623C2×D4—22no—
624C2×D4—24no—
625C2×D4—22no—
626C2×D4—24no—
627C2×D4—21no—
628C2×D4—42no—
629C2×D4—44no—
630C2×D4—44no—
631C2×D4—82no—
632C2×D4C23×C412yes—
633C22×C4—24no—
634C22×C4—24no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—24no—
643C22×C4—24no—
644C22×C4—24no—
645C22×C4—24no—
646C22×C4—24no—
647C22×C4—28no—
648C22×C4—42no—
649C22×C4—44no—
650C22×C4—44no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4—44no—
654C22×C4—44no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—44no—
659C22×C4—44no—
660C22×C4—48no—
661C22×C4—81no—
662C22×C4—81no—
663C22×C4—82no—
664C22×C4—82no—
665C22×C4—82no—
666C22×C4—84no—
667C22×C4—84no—
668C22×C4C2×C22⋊C411yescharacteristic
669C22×C4C2×C22⋊C411yescharacteristic
670C22×C4C2×C22⋊C412yes—
671C22×C4C2×C22⋊C412yes—
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×C4C2×C22⋊C411yescharacteristic
679C22×C4C2×C22⋊C411yescharacteristic
680C22×C4C2×C22⋊C412yes—
681C22×C4C2×C22⋊C412yes—
682C22×C4C2×C22⋊C412yes—
683C22×C4C2×C22⋊C412yes—
684C22×C4C2×C22⋊C412yes—
685C22×C4C2×C22⋊C412yes—
686C22×C4C2×C22⋊C412yes—
687C22×C4C23×C411yescharacteristic
688C22×C4C23×C412yes—
689C22×C4C23×C411yescharacteristic
690C22×C4C23×C412yes—
691C22×C4C22×D412yes—
692C22×C4C22×D412yes—
693C22×C4C22×D411yescharacteristic
694C22×C4C22×D412yes—
695C22×C4C22×D411yescharacteristic
696C22×C4C22×D412yes—
697C22×C4C22×D412yes—
698C22×C4C22×D412yes—
699C22×C4C22×D411yescharacteristic
700C22×C4C22×D412yes—
701C22×C4C2511yescharacteristic
702M16—48no—
703M16—48no—
704C2×C8—28no—
705C2×C8—48no—
706C4⋊C4—24no—
707C4⋊C4—22no—
708C4⋊C4—22no—
709C4⋊C4—24no—
710C4⋊C4—24no—
711C4⋊C4—24no—
712C4⋊C4—24no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—24no—
716C4⋊C4—24no—
717C4⋊C4—24no—
718C4⋊C4—24no—
719C4⋊C4—24no—
720C4⋊C4—24no—
721C4⋊C4—24no—
722C4⋊C4—24no—
723C4⋊C4—24no—
724C4⋊C4—24no—
725C4⋊C4—22no—
726C4⋊C4—24no—
727C4⋊C4—24no—
728C4⋊C4—24no—
729C4⋊C4—24no—
730C4⋊C4—24no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—22no—
734C4⋊C4—22no—
735C4⋊C4—22no—
736C4⋊C4—84no—
737C4⋊C4—84no—
738C4⋊C4C2×C22⋊C414yes—
739C4⋊C4C2×C22⋊C414yes—
740C4⋊C4C2×C22⋊C414yes—
741C4⋊C4C2×C22⋊C414yes—
742C4⋊C4C2×C22⋊C414yes—
743C4⋊C4C2×C22⋊C414yes—
744C4⋊C4C2×C22⋊C414yes—
745C4⋊C4C2×C22⋊C414yes—
746C4⋊C4C23×C412yes—
747C4⋊C4C23×C412yes—
748C4⋊C4C23×C412yes—
749C4⋊C4C23×C412yes—
750C22⋊C4—22no—
751C22⋊C4—22no—
752C22⋊C4—24no—
753C22⋊C4—24no—
754C22⋊C4—24no—
755C22⋊C4—22no—
756C22⋊C4—24no—
757C22⋊C4—22no—
758C22⋊C4—22no—
759C22⋊C4—22no—
760C22⋊C4—22no—
761C22⋊C4—24no—
762C22⋊C4—24no—
763C22⋊C4—24no—
764C22⋊C4—24no—
765C22⋊C4—24no—
766C22⋊C4—24no—
767C22⋊C4—24no—
768C22⋊C4—22no—
769C22⋊C4—48no—
770C22⋊C4—48no—
771C22⋊C4C2×C22⋊C414yes—
772C22⋊C4C2×C22⋊C414yes—
773C22⋊C4C2×C22⋊C414yes—
774C22⋊C4C2×C22⋊C414yes—
775C22⋊C4C2×C22⋊C414yes—
776C22⋊C4C2×C22⋊C414yes—
777C22⋊C4C2×C22⋊C414yes—
778C22⋊C4C2×C22⋊C414yes—
779C42—24no—
780C42—24no—
781C42—24no—
782C42—24no—
783C42—24no—
784C42—24no—
785C42—24no—
786C42—84no—
787C42—84no—
788C42C2×C22⋊C412yes—
789C42C2×C22⋊C412yes—
790C42C2×C22⋊C412yes—
791C42C2×C22⋊C412yes—
792C42C2×C22⋊C412yes—
793C42C2×C22⋊C412yes—
794C42C2×C22⋊C412yes—
795C42C2×C22⋊C412yes—
796C42C23×C412yes—
797C42C23×C412yes—
798C42C23×C412yes—
799C42C23×C412yes—
800C42C22×D412yes—
801C42C22×D412yes—
802C42C22×D412yes—
803C42C22×D412yes—
804C23—22no—
805C23—24no—
806C23—22no—
807C23—24no—
808C23—22no—
809C23—24no—
810C23—22no—
811C23—41no—
812C23—41no—
813C23—42no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—42no—
818C23—42no—
819C23—42no—
820C23—42no—
821C23—42no—
822C23—88no—
823C23#41014yes—
824C23C22×C22⋊C412yes—
825C23C22×C22⋊C411yescharacteristic
826C23C22×C22⋊C412yes—
827C23C22×C22⋊C411yescharacteristic
828C23C23×D411yescharacteristic
829Q8—42no—
830Q8—42no—
831Q8—42no—
832Q8—48no—
833Q8—42no—
834Q8—42no—
835Q8—42no—
836Q8—84no—
837Q8—84no—
838D4—42no—
839D4—42no—
840D4—44no—
841D4—44no—
842D4—48no—
843D4—84no—
844C2×C4—24no—
845C2×C4—24no—
846C2×C4—24no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—24no—
851C2×C4—24no—
852C2×C4—22no—
853C2×C4—24no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—41no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—41no—
870C2×C4—42no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—48no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—48no—
894C2×C4—48no—
895C2×C4—48no—
896C2×C4—48no—
897C2×C4—84no—
898C2×C4—84no—
899C2×C4—84no—
900C2×C4—168no—
901C2×C4C22×C22⋊C412yes—
902C2×C4C22×C22⋊C412yes—
903C2×C4C22×C22⋊C412yes—
904C2×C4C22×C22⋊C412yes—
905C2×C4C22×C22⋊C412yes—
906C2×C4C22×C22⋊C411yescharacteristic
907C2×C4C22×C22⋊C411yescharacteristic
908C2×C4C22×C22⋊C412yes—
909C2×C4C22×C22⋊C412yes—
910C2×C4C22×C22⋊C412yes—
911C2×C4C22×C22⋊C412yes—
912C2×C4C22×C22⋊C412yes—
913C2×C4C24×C411yescharacteristic
914C2×C4C23×D411yescharacteristic
915C8—48no—
916C22—21no—
917C22—21no—
918C22—22no—
919C22—21no—
920C22—21no—
921C22—22no—
922C22—21no—
923C22—22no—
924C22—21no—
925C22—22no—
926C22—21no—
927C22—22no—
928C22—44no—
929C22—48no—
930C22—44no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—82no—
935C22—84no—
936C22—84no—
937C22C2×#41012yes—
938C22C2×#41014yes—
939C22C23×C22⋊C411yescharacteristic
940C22#358612yes—
941C4—21no—
942C4—22no—
943C4—22no—
944C4—21no—
945C4—21no—
946C4—21no—
947C4—22no—
948C4—22no—
949C4—22no—
950C4—22no—
951C4—22no—
952C4—22no—
953C4—22no—
954C4—22no—
955C4—42no—
956C4—42no—
957C4—42no—
958C4—42no—
959C4—42no—
960C4—42no—
961C4—42no—
962C4—88no—
963C2—22no—
964C2—22no—
965C2—24no—
966C2—41no—
967C2—42no—
968C2—82no—
969C2C22×#41011yescharacteristic
970C2#6008811yescharacteristic
971C2#6009311yescharacteristic
subgroupG/H
center, socleC22C23×C22⋊C4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#525C22
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C22×#117 ◁ G
LECSG ▷ C22×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60124C2semidirect
3. #34177C2semidirect
4. #17609C2semidirect
5. #17590C2semidirect
7. #17580C2semidirect
8. #17562C2semidirect
9. #17554C2semidirect
10. C2×#1511C2semidirect
13. #3495C4semidirect
23. C2×#544C4semidirect
24. C2×#542C4semidirect
25. C2×#542C4semidirect
26. C2×#541C4semidirect
27. C2×#541C4semidirect
28. C2×#536C4semidirect
35. C2×#520C4semidirect
36. C2×#519C4semidirect
39. #2924C22semidirect
48. #2343C22semidirect
56. #1521C22semidirect
57. #1518C22semidirect
59. #1515C22semidirect
60. #1512C22semidirect
64. #1511C22semidirect
66. #1509C22semidirect
67. #1506C22semidirect
69. #1503C22semidirect
70. #1500C22semidirect
71. C2×#328C22semidirect
93. #544C2×C4semidirect
96. #542C2×C4semidirect
97. #542C2×C4semidirect
100. #541C2×C4semidirect
101. #541C2×C4semidirect
103. #536C2×C4semidirect
108. #533C2×C4semidirect
109. #533C2×C4semidirect
113. C2×C4⋊Q8C2×C4semidirect
114. C2×C4⋊Q8C2×C4semidirect
115. C2×C4⋊Q8C2×C4semidirect
116. C2×C4⋊Q8C2×C4semidirect
121. #529C2×C4semidirect
122. #529C2×C4semidirect
140. C2×#125C2×C4semidirect
141. C2×#125C2×C4semidirect
144. C2×#124C2×C4semidirect
145. C2×#124C2×C4semidirect
181. #520C2×C4semidirect
183. #519C2×C4semidirect
188. C2×C4×Q8C2×C4semidirect
189. C2×C4×Q8C2×C4semidirect
190. C2×C4×Q8C2×C4semidirect
191. C2×C4×Q8C2×C4semidirect
192. C2×C4×Q8C2×C4semidirect
193. C2×C4×Q8C2×C4semidirect
200. C2×C4×D4C2×C4semidirect
201. C2×C4×D4C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#34952
#601242
#341772
#176092
#175902
#175872
#175802
#175622
#175542
C2×#15112