Finite Group Databasebeta

← #6393684

Subgroups — #6393684

Order 512.

3012 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×#3552C211yesmaximal, characteristic
2#34371C211yesmaximal, characteristic, complemented
3#34216C211yesmaximal, characteristic, complemented
4#22535C214yesmaximal, complemented
5#22534C214yesmaximal, complemented
6#22513C214yesmaximal, complemented
7Q8×#99C214yesmaximal, complemented
8#21877C214yesmaximal, complemented
9#21875C211yesmaximal, characteristic, complemented
10#21875C211yesmaximal, characteristic, complemented
11#21423C214yesmaximal, complemented
12#21421C211yesmaximal, characteristic, complemented
13#21421C211yesmaximal, characteristic, complemented
14#3552—22no—
15#3552—22no—
16#3552—22no—
17#3552—22no—
18#3552—22no—
19#3552—22no—
20#3552—22no—
21#3552—22no—
22C2×#563C414yescomplemented
23C2×#557C411yescharacteristic, complemented
24C2×#556C411yescharacteristic, complemented
25C2×#554C2212yes—
26C2×#553C2212yes—
27C2×D4×Q8C411yescharacteristic, complemented
28C2×D4×Q8C2212yes—
29C2×#548C2212yes—
30C2×#547C411yescharacteristic, complemented
31C2×#544C412yescomplemented
32C2×#542C412yescomplemented
33C2×#541C412yescomplemented
34C2×#539C2214yes—
35C2×#536C412yescomplemented
36C22×C4⋊Q8C2211yescharacteristic
37C2×#529C2211yescharacteristic
38C2×#529C2211yescharacteristic
39#2381—22no—
40#2369—22no—
41#2365—22no—
42#2365—22no—
43#2345C2214yes—
44#2345C2214yes—
45Q8×C22⋊C4C2214yes—
46Q8×C22⋊C4C2214yes—
47#2331—22no—
48#2331—22no—
49#2327—22no—
50#2316C2212yes—
51#2313C2214yes—
52C4×C4⋊Q8—22no—
53#2285C2211yescharacteristic
54#2283C2211yescharacteristic
55#2283C2211yescharacteristic
56#2274C2212yes—
57C4×#117C2211yescharacteristic
58#1996C2212yes—
59#1996C2212yes—
60#1996C2218yes—
61#1996C2212yes—
62#1996C2212yes—
63#1996C2218yes—
64#1964C2212yes—
65#1964C2212yes—
66#1964C2218yes—
67#1964C2218yes—
68#1964C2212yes—
69#1964C2212yes—
70#1899C2214yes—
71#1899C2214yes—
72#1899C2212yes—
73#1899C2212yes—
74#1899C2212yes—
75#1899C2212yes—
76#1799C2214yes—
77#1799C2218yes—
78#1799C2214yes—
79#1799C2218yes—
80C4×#99C2214yes—
81C4×#99C2218yes—
82C4×#99C2214yes—
83C4×#99C2218yes—
84C22×#41C2×C412yes—
85C23×Q8C2×C412yes—
86C23×Q8C2312yes—
87#563—28no—
88#563—28no—
89#563—28no—
90#563—28no—
91#557—22no—
92#557—22no—
93#557—22no—
94#557—22no—
95#556—22no—
96#556—22no—
97#556—22no—
98#556—22no—
99#554—24no—
100#554—24no—
101#554—24no—
102#554—24no—
103#553—24no—
104#553—24no—
105#553—24no—
106#553—24no—
107D4×Q8—24no—
108D4×Q8—24no—
109D4×Q8—24no—
110D4×Q8—24no—
111D4×Q8—22no—
112D4×Q8—22no—
113D4×Q8—22no—
114D4×Q8—22no—
115#548—24no—
116#548—24no—
117#548—24no—
118#548—24no—
119#547—22no—
120#547—22no—
121#547—22no—
122#547—22no—
123#544—24no—
124#544—24no—
125#544—24no—
126#544—24no—
127#542—24no—
128#542—24no—
129#542—24no—
130#542—24no—
131#541—24no—
132#541—24no—
133#541—24no—
134#541—24no—
135#539—28no—
136#539—28no—
137#539—28no—
138#539—28no—
139#536—24no—
140#536—24no—
141#536—24no—
142#536—24no—
143C2×C4⋊Q8C2×C412yes—
144C2×C4⋊Q8C2×C412yes—
145C2×C4⋊Q8C2×C414yes—
146C2×C4⋊Q8C2×C412yes—
147C2×C4⋊Q8C2×C412yes—
148C2×C4⋊Q8C2×C411yescharacteristic
149C2×C4⋊Q8C2×C411yescharacteristic
150C2×C4⋊Q8C2×C412yes—
151C2×C4⋊Q8D412yes—
152C2×C4⋊Q8D412yes—
153C2×C4⋊Q8D412yes—
154C2×C4⋊Q8D412yes—
155C2×C4⋊Q8D412yes—
156C2×C4⋊Q8D412yes—
157C2×C4⋊Q8D412yes—
158C2×C4⋊Q8D412yes—
159#529—21no—
160#529—21no—
161#529—21no—
162#529—21no—
163#529—21no—
164#529—21no—
165#529—21no—
166#529—21no—
167#529—21no—
168#529—21no—
169#529—21no—
170#529—21no—
171#529—21no—
172#529—21no—
173#529—21no—
174#529—21no—
175C2×#126C2×C412yes—
176C2×#126C2×C412yes—
177C2×#126C2×C414yes—
178C2×#126C2×C414yes—
179C2×#126C2×C414yes—
180C2×#125C2×C411yescharacteristic
181C2×#125C2×C411yescharacteristic
182C2×#125C2×C414yes—
183C2×#125C2×C414yes—
184C2×#125C2×C414yes—
185C2×#125C2×C412yes—
186C2×#124C2×C411yescharacteristic
187C2×#124C2×C411yescharacteristic
188C2×#124C2×C412yes—
189C2×#124C2×C414yes—
190C2×#123C2×C414yes—
191C2×#123C2×C414yes—
192C2×#123C2×C414yes—
193C2×#123C2312yes—
194C2×#123C2312yes—
195C2×C22⋊Q8C2×C414yes—
196C2×C22⋊Q8C2×C414yes—
197C2×C22⋊Q8C2×C414yes—
198C2×C22⋊Q8C2×C412yes—
199C2×C22⋊Q8C2×C412yes—
200C2×C22⋊Q8C2×C414yes—
201C2×C22⋊Q8C2×C412yes—
202C2×C22⋊Q8C2×C414yes—
203C2×C22⋊Q8C2311yescharacteristic
204C2×C22⋊Q8C2311yescharacteristic
205C2×C22⋊Q8C2314yes—
206C2×#121C2×C412yes—
207C2×#121C2311yescharacteristic
208C2×#121C2311yescharacteristic
209C2×#121C2314yes—
210C2×C4×Q8—24no—
211C2×C4×Q8—24no—
212C2×C4×Q8C2×C411yescharacteristic
213C2×C4×Q8C2×C411yescharacteristic
214C2×C4×Q8C2×C412yes—
215C2×C4×Q8C2×C412yes—
216C2×C4×Q8C2×C412yes—
217C2×C4×D4C2×C411yescharacteristic
218C2×C4×D4C2×C411yescharacteristic
219C2×C4×D4C2×C412yes—
220C2×C4×D4C2312yes—
221C2×C4×D4C2312yes—
222C2×C4×D4C2314yes—
223C2×C4×D4C2314yes—
224C2×#117C2×C412yes—
225C2×#117C2×C412yes—
226C2×#117C2×C412yes—
227C2×#117C2311yescharacteristic
228C2×#117C2311yescharacteristic
229C2×#117C2312yes—
230C22×C4⋊C4C2×C412yes—
231C22×C4⋊C4C2312yes—
232C22×C4⋊C4C2312yes—
233C22×C42C2311yescharacteristic
234C2×#99C2314yes—
235C2×#99C2314yes—
236C2×#99C2318yes—
237C2×#99C2314yes—
238C2×#99C2318yes—
239C2×#99C2314yes—
240#391—24no—
241#391—24no—
242#391—28no—
243#391—28no—
244#389—24no—
245#389—24no—
246#389—24no—
247#389—24no—
248#387—28no—
249#387—28no—
250#387—28no—
251#387—28no—
252#384—21no—
253#383—21no—
254#383—21no—
255#382—21no—
256#382—21no—
257#382—21no—
258#381C2312yes—
259#381C2312yes—
260#380C2318yes—
261#380C2318yes—
262#380C2312yes—
263#380C2312yes—
264#380C2312yes—
265#380C2312yes—
266C4×C4⋊C4—24no—
267C4×C4⋊C4—24no—
268C4×C4⋊C4—24no—
269C4×C4⋊C4—24no—
270C4×C4⋊C4—21no—
271C4×C4⋊C4—21no—
272C4×C4⋊C4—21no—
273C4×C4⋊C4—21no—
274C4×C4⋊C4—21no—
275C4×C4⋊C4—21no—
276C4×C22⋊C4C2318yes—
277C4×C22⋊C4C2312yes—
278C4×C22⋊C4C2312yes—
279C4×C22⋊C4C2318yes—
280C4×C22⋊C4C2312yes—
281C4×C22⋊C4C2312yes—
282#376—21no—
283#376—21no—
284#376—21no—
285C43—21no—
286#342C2318yes—
287#342C2314yes—
288#342C2318yes—
289#342C2314yes—
290#342C2314yes—
291#342C2314yes—
292C2×#41—24no—
293C2×#41—24no—
294C2×#41—84no—
295C22×Q8—24no—
296C22×Q8—24no—
297C22×Q8—84no—
298C22×Q8—84no—
299C22×Q8C22×C411yescharacteristic
300C22×Q8C22×C411yescharacteristic
301C22×Q8C22×C414yes—
302C22×Q8C22×C412yes—
303C22×Q8C22×C412yes—
304C22×Q8C22×C414yes—
305C22×Q8C2×D414yes—
306C22×Q8C2×D414yes—
307C22×Q8C2×D414yes—
308C22×Q8C2×D414yes—
309C22×D4C22×C411yescharacteristic
310C22×D4C22×C411yescharacteristic
311C22×D4C22×C414yes—
312C22×D4C2412yes—
313C22×D4C2412yes—
314C23×C4C22×C412yes—
315C23×C4C22×C412yes—
316C23×C4C22×C414yes—
317C23×C4C22×C414yes—
318C23×C4C2411yescharacteristic
319C23×C4C2411yescharacteristic
320C23×C4C2411yescharacteristic
321C23×C4C2414yes—
322C4⋊Q8—24no—
323C4⋊Q8—24no—
324C4⋊Q8—28no—
325C4⋊Q8—28no—
326C4⋊Q8—24no—
327C4⋊Q8—24no—
328C4⋊Q8C22⋊C414yes—
329C4⋊Q8C22⋊C414yes—
330C4⋊Q8C22⋊C414yes—
331C4⋊Q8C22⋊C414yes—
332C4⋊Q8C22⋊C414yes—
333C4⋊Q8C22⋊C414yes—
334C4⋊Q8C22⋊C414yes—
335C4⋊Q8C22⋊C414yes—
336C4⋊Q8C22⋊C412yes—
337C4⋊Q8C22⋊C412yes—
338C4⋊Q8C22⋊C412yes—
339C4⋊Q8C22⋊C412yes—
340C4⋊Q8C22⋊C412yes—
341C4⋊Q8C22⋊C412yes—
342C4⋊Q8C22⋊C412yes—
343C4⋊Q8C22⋊C412yes—
344C4⋊Q8C22⋊C414yes—
345C4⋊Q8C22⋊C414yes—
346C4⋊Q8C22⋊C414yes—
347C4⋊Q8C22⋊C414yes—
348#126—28no—
349#126—28no—
350#126—28no—
351#126—28no—
352#126—28no—
353#126—28no—
354#126—22no—
355#126—22no—
356#126—22no—
357#126—22no—
358#126—22no—
359#126—22no—
360#126—22no—
361#126—22no—
362#125—28no—
363#125—28no—
364#125—28no—
365#125—28no—
366#125—28no—
367#125—28no—
368#125—24no—
369#125—24no—
370#125—21no—
371#125—21no—
372#125—21no—
373#125—21no—
374#125—21no—
375#125—21no—
376#125—21no—
377#125—21no—
378#124—24no—
379#124—24no—
380#124—28no—
381#124—28no—
382#124—21no—
383#124—21no—
384#124—21no—
385#124—21no—
386#124—21no—
387#124—21no—
388#124—21no—
389#124—21no—
390#123—22no—
391#123—22no—
392#123—22no—
393#123—22no—
394#123—22no—
395#123—22no—
396#123—22no—
397#123—22no—
398#123—28no—
399#123—28no—
400#123—28no—
401#123—28no—
402#123—28no—
403#123—28no—
404C22⋊Q8—24no—
405C22⋊Q8—24no—
406C22⋊Q8—24no—
407C22⋊Q8—24no—
408C22⋊Q8—28no—
409C22⋊Q8—28no—
410C22⋊Q8—28no—
411C22⋊Q8—28no—
412C22⋊Q8—21no—
413C22⋊Q8—21no—
414C22⋊Q8—21no—
415C22⋊Q8—21no—
416C22⋊Q8—21no—
417C22⋊Q8—21no—
418C22⋊Q8—21no—
419C22⋊Q8—21no—
420C22⋊Q8—28no—
421C22⋊Q8—28no—
422C22⋊Q8—28no—
423C22⋊Q8—28no—
424C22⋊Q8—28no—
425C22⋊Q8—28no—
426C22⋊Q8—28no—
427C22⋊Q8—28no—
428C22⋊Q8—24no—
429C22⋊Q8—24no—
430#121—21no—
431#121—21no—
432#121—21no—
433#121—21no—
434#121—21no—
435#121—21no—
436#121—21no—
437#121—21no—
438#121—28no—
439#121—28no—
440#121—24no—
441#121—24no—
442C4×Q8—24no—
443C4×Q8—24no—
444C4×Q8—24no—
445C4×Q8—24no—
446C4×Q8—24no—
447C4×Q8—24no—
448C4×Q8—21no—
449C4×Q8—21no—
450C4×Q8—21no—
451C4×Q8—21no—
452C4×Q8—21no—
453C4×Q8—21no—
454C4×Q8—21no—
455C4×Q8—21no—
456C4×Q8—88no—
457C4×Q8—88no—
458C4×D4—22no—
459C4×D4—22no—
460C4×D4—22no—
461C4×D4—22no—
462C4×D4—22no—
463C4×D4—22no—
464C4×D4—22no—
465C4×D4—22no—
466C4×D4—28no—
467C4×D4—28no—
468C4×D4—28no—
469C4×D4—28no—
470C4×D4—24no—
471C4×D4—24no—
472C4×D4—21no—
473C4×D4—21no—
474C4×D4—21no—
475C4×D4—21no—
476C4×D4—21no—
477C4×D4—21no—
478C4×D4—21no—
479C4×D4—21no—
480#117—24no—
481#117—24no—
482#117—24no—
483#117—22no—
484#117—22no—
485#117—22no—
486#117—22no—
487#117—22no—
488#117—22no—
489#117—22no—
490#117—22no—
491#117—42no—
492#117—44no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—24no—
495C2×C4⋊C4—24no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—28no—
503C2×C4⋊C4—28no—
504C2×C4⋊C4C22×C411yescharacteristic
505C2×C4⋊C4C22×C414yes—
506C2×C4⋊C4C22×C411yescharacteristic
507C2×C4⋊C4C22×C412yes—
508C2×C4⋊C4C22×C412yes—
509C2×C4⋊C4C22×C412yes—
510C2×C4⋊C4C22×C412yes—
511C2×C4⋊C4C22×C411yescharacteristic
512C2×C4⋊C4C22×C414yes—
513C2×C4⋊C4C22×C412yes—
514C2×C4⋊C4C22×C414yes—
515C2×C4⋊C4C22×C412yes—
516C2×C4⋊C4C22×C411yescharacteristic
517C2×C4⋊C4C22×C414yes—
518C2×C4⋊C4C22×C414yes—
519C2×C4⋊C4C22×C414yes—
520C2×C4⋊C4C22×C412yes—
521C2×C4⋊C4C22×C412yes—
522C2×C4⋊C4C22×C412yes—
523C2×C4⋊C4C22×C412yes—
524C2×C4⋊C4C22×C412yes—
525C2×C4⋊C4C22×C414yes—
526C2×C4⋊C4C22×C414yes—
527C2×C4⋊C4C22×C412yes—
528C2×C4⋊C4C2×D414yes—
529C2×C4⋊C4C2×D414yes—
530C2×C4⋊C4C2×D414yes—
531C2×C4⋊C4C2×D414yes—
532C2×C4⋊C4C2×D414yes—
533C2×C4⋊C4C2×D414yes—
534C2×C4⋊C4C2×D414yes—
535C2×C4⋊C4C2×D414yes—
536C2×C22⋊C4C22×C414yes—
537C2×C22⋊C4C22×C412yes—
538C2×C22⋊C4C22×C412yes—
539C2×C22⋊C4C22×C412yes—
540C2×C22⋊C4C22×C412yes—
541C2×C22⋊C4C22×C414yes—
542C2×C22⋊C4C22×C412yes—
543C2×C22⋊C4C22×C412yes—
544C2×C22⋊C4C22×C414yes—
545C2×C22⋊C4C22×C412yes—
546C2×C22⋊C4C22×C414yes—
547C2×C22⋊C4C22×C412yes—
548C2×C22⋊C4C2412yes—
549C2×C22⋊C4C2414yes—
550C2×C22⋊C4C2414yes—
551C2×C22⋊C4C2414yes—
552C2×C22⋊C4C2412yes—
553C2×C22⋊C4C2412yes—
554C2×C22⋊C4C2412yes—
555C2×C42—21no—
556C2×C42—21no—
557C2×C42—22no—
558C2×C42—22no—
559C2×C42—22no—
560C2×C42—22no—
561C2×C42—22no—
562C2×C42—28no—
563C2×C42—28no—
564C2×C42C22×C412yes—
565C2×C42C22×C412yes—
566C2×C42C22×C414yes—
567C2×C42C22×C414yes—
568C2×C42C22×C411yescharacteristic
569C2×C42C22×C411yescharacteristic
570C2×C42C22×C411yescharacteristic
571C2×C42C22×C411yescharacteristic
572C2×C42C2×D411yescharacteristic
573C2×C42C2×D411yescharacteristic
574C2×C42C2×D411yescharacteristic
575C2×C42C2×D411yescharacteristic
576C2×C42C2×D411yescharacteristic
577C2×C42C2×D411yescharacteristic
578C2×C42C2×D411yescharacteristic
579C2×C42C2×D411yescharacteristic
580#99—28no—
581#99—28no—
582#99—48no—
583#99—44no—
584#99—48no—
585#99—44no—
586#95—22no—
587#95—22no—
588#95—22no—
589#95—22no—
590#95—22no—
591#95—22no—
592#95—28no—
593#95—22no—
594#95—22no—
595#95—28no—
596#95—22no—
597#95—22no—
598#95—28no—
599#95—28no—
600#95—22no—
601#95—22no—
602C24C23×C412yes—
603C24C23×C412yes—
604C24C2511yescharacteristic
605#41—88no—
606#41—88no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—21no—
611C2×Q8—28no—
612C2×Q8—48no—
613C2×Q8—48no—
614C2×Q8—44no—
615C2×Q8—44no—
616C2×Q8—42no—
617C2×Q8—42no—
618C2×Q8—84no—
619C2×Q8—84no—
620C2×Q8—84no—
621C2×Q8—84no—
622C2×Q8—88no—
623C2×Q8—88no—
624C2×Q8C2×C22⋊C414yes—
625C2×Q8C2×C22⋊C414yes—
626C2×Q8C2×C22⋊C414yes—
627C2×Q8C2×C22⋊C414yes—
628C2×Q8C2×C22⋊C418yes—
629C2×Q8C2×C22⋊C418yes—
630C2×D4—22no—
631C2×D4—22no—
632C2×D4—22no—
633C2×D4—22no—
634C2×D4—24no—
635C2×D4—24no—
636C2×D4—24no—
637C2×D4—24no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—28no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—84no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—28no—
654C22×C4—28no—
655C22×C4—24no—
656C22×C4—24no—
657C22×C4—22no—
658C22×C4—24no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—44no—
662C22×C4—44no—
663C22×C4—84no—
664C22×C4—84no—
665C22×C4—84no—
666C22×C4C23×C412yes—
667C22×C4C23×C412yes—
668C22×C4C23×C411yescharacteristic
669C22×C4C23×C411yescharacteristic
670C22×C4C23×C411yescharacteristic
671C22×C4C23×C411yescharacteristic
672C22×C4C23×C412yes—
673C22×C4C23×C412yes—
674C22×C4C23×C412yes—
675C22×C4C23×C412yes—
676C22×C4C23×C411yescharacteristic
677C22×C4C23×C411yescharacteristic
678C22×C4C23×C414yes—
679C22×C4C23×C414yes—
680C22×C4C22×D411yescharacteristic
681C22×C4C22×D411yescharacteristic
682C22×C4C22×D411yescharacteristic
683C22×C4C22×D411yescharacteristic
684C22×C4C22×D411yescharacteristic
685C22×C4C22×D411yescharacteristic
686C22×C4C22×D411yescharacteristic
687C22×C4C22×D411yescharacteristic
688C22×C4C22×D411yescharacteristic
689C22×C4C22×D411yescharacteristic
690C22×C4C22×D411yescharacteristic
691C22×C4C22×D411yescharacteristic
692C22×C4C22×D418yes—
693C22×C4C22×D418yes—
694C4⋊C4—24no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—28no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—22no—
701C4⋊C4—22no—
702C4⋊C4—22no—
703C4⋊C4—22no—
704C4⋊C4—22no—
705C4⋊C4—22no—
706C4⋊C4—22no—
707C4⋊C4—22no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—28no—
711C4⋊C4—22no—
712C4⋊C4—22no—
713C4⋊C4—28no—
714C4⋊C4—22no—
715C4⋊C4—22no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—28no—
719C4⋊C4—28no—
720C4⋊C4—28no—
721C4⋊C4—22no—
722C4⋊C4—22no—
723C4⋊C4—22no—
724C4⋊C4—22no—
725C4⋊C4—44no—
726C4⋊C4—44no—
727C4⋊C4—42no—
728C4⋊C4—44no—
729C4⋊C4—44no—
730C4⋊C4—44no—
731C4⋊C4—88no—
732C4⋊C4—88no—
733C4⋊C4C2×C22⋊C414yes—
734C4⋊C4C2×C22⋊C414yes—
735C4⋊C4C2×C22⋊C414yes—
736C4⋊C4C2×C22⋊C414yes—
737C4⋊C4C2×C22⋊C414yes—
738C4⋊C4C2×C22⋊C414yes—
739C4⋊C4C2×C22⋊C418yes—
740C4⋊C4C2×C22⋊C418yes—
741C4⋊C4C2×C22⋊C418yes—
742C4⋊C4C2×C22⋊C418yes—
743C4⋊C4C2×C22⋊C414yes—
744C4⋊C4C2×C22⋊C414yes—
745C22⋊C4—22no—
746C22⋊C4—22no—
747C22⋊C4—22no—
748C22⋊C4—22no—
749C22⋊C4—22no—
750C22⋊C4—28no—
751C22⋊C4—22no—
752C22⋊C4—22no—
753C22⋊C4—22no—
754C22⋊C4—22no—
755C22⋊C4—22no—
756C22⋊C4—22no—
757C22⋊C4—22no—
758C22⋊C4—22no—
759C22⋊C4—28no—
760C22⋊C4—28no—
761C22⋊C4—22no—
762C22⋊C4—22no—
763C22⋊C4—22no—
764C22⋊C4—22no—
765C22⋊C4—28no—
766C22⋊C4—22no—
767C22⋊C4—22no—
768C22⋊C4—22no—
769C22⋊C4—22no—
770C22⋊C4—24no—
771C22⋊C4—24no—
772C22⋊C4—24no—
773C22⋊C4—24no—
774C22⋊C4—22no—
775C22⋊C4—22no—
776C22⋊C4—28no—
777C22⋊C42−1+414yes—
778C42—24no—
779C42—22no—
780C42—22no—
781C42—22no—
782C42—22no—
783C42—28no—
784C42—28no—
785C42—44no—
786C42—44no—
787C42—44no—
788C42—42no—
789C42—44no—
790C42—44no—
791C42—88no—
792C42—88no—
793C42C2×C22⋊C411yescharacteristic
794C42C2×C22⋊C411yescharacteristic
795C42C2×C22⋊C411yescharacteristic
796C42C2×C22⋊C411yescharacteristic
797C42C2×C22⋊C411yescharacteristic
798C42C2×C22⋊C411yescharacteristic
799C42C2×C22⋊C411yescharacteristic
800C42C2×C22⋊C411yescharacteristic
801C42C2×C22⋊C411yescharacteristic
802C42C2×C22⋊C411yescharacteristic
803C42C2×C22⋊C411yescharacteristic
804C42C2×C22⋊C411yescharacteristic
805C42C2×C22⋊C411yescharacteristic
806C42C2×C22⋊C411yescharacteristic
807C42C2×C22⋊C411yescharacteristic
808C42C2×C22⋊C411yescharacteristic
809C23—22no—
810C23—22no—
811C23—24no—
812C23—24no—
813C23—41no—
814C23—41no—
815C23—42no—
816C23—42no—
817C23—42no—
818C23—42no—
819C23C24×C411yescharacteristic
820C23C23×D411yescharacteristic
821C23C23×D411yescharacteristic
822C23C2×2−1+412yes—
823C23#58512yes—
824Q8—28no—
825Q8—28no—
826Q8—44no—
827Q8—48no—
828Q8—48no—
829Q8—44no—
830Q8—42no—
831Q8—42no—
832Q8—42no—
833Q8—42no—
834Q8—88no—
835D4—42no—
836D4—42no—
837D4—42no—
838D4—42no—
839D4—42no—
840D4—42no—
841D4—44no—
842D4—44no—
843D4—42no—
844D4—42no—
845D4—88no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—24no—
867C2×C4—24no—
868C2×C4—24no—
869C2×C4—48no—
870C2×C4—48no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—44no—
878C2×C4—44no—
879C2×C4—44no—
880C2×C4—44no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—44no—
884C2×C4—44no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—44no—
890C2×C4—42no—
891C2×C4—44no—
892C2×C4—42no—
893C2×C4—44no—
894C2×C4—44no—
895C2×C4—44no—
896C2×C4—44no—
897C2×C4—42no—
898C2×C4—44no—
899C2×C4—44no—
900C2×C4—44no—
901C2×C4—88no—
902C2×C4—88no—
903C2×C4C22×C22⋊C411yescharacteristic
904C2×C4C22×C22⋊C411yescharacteristic
905C2×C4C22×C22⋊C418yes—
906C2×C4C22×C22⋊C418yes—
907C2×C4C22×C22⋊C411yescharacteristic
908C2×C4C22×C22⋊C411yescharacteristic
909C2×C4C22×C22⋊C411yescharacteristic
910C2×C4C22×C22⋊C411yescharacteristic
911C2×C4C22×C22⋊C411yescharacteristic
912C2×C4C22×C22⋊C411yescharacteristic
913C2×C4C22×C22⋊C411yescharacteristic
914C2×C4C22×C22⋊C411yescharacteristic
915C2×C4C22×C22⋊C411yescharacteristic
916C2×C4C22×C22⋊C411yescharacteristic
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—21no—
922C22—21no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—84no—
932C22—84no—
933C22C23×C22⋊C411yescharacteristic
934C22C4×2−1+412yes—
935C22#348611yescharacteristic
936C22#348711yescharacteristic
937C22#349712yes—
938C4—21no—
939C4—21no—
940C4—21no—
941C4—28no—
942C4—28no—
943C4—21no—
944C4—21no—
945C4—21no—
946C4—21no—
947C4—21no—
948C4—21no—
949C4—21no—
950C4—44no—
951C4—42no—
952C4—42no—
953C4—42no—
954C4—42no—
955C4—42no—
956C4—42no—
957C4—82no—
958C4—84no—
959C4—84no—
960C4—84no—
961C4#288312yes—
962C4#288412yes—
963C2—21no—
964C2—21no—
965C2—22no—
966C2—22no—
967C2—82no—
968C2—82no—
969C2#3425711yescharacteristic
970C2C2×#288311yescharacteristic
971C2C2×#288411yescharacteristic
subgroupG/H
center, socleC22C23×C22⋊C4
commutatorC23C24×C4
Frattini, cosocleC24C25
prime radicalC2×#3552C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4⋊Q8 ◁ G
LECSG ▷ C24 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34371C2semidirect
3. #34216C2semidirect
4. #22535C2semidirect
5. #22534C2semidirect
6. #22513C2semidirect
7. Q8×#99C2semidirect
8. #21877C2semidirect
9. #21875C2semidirect
10. #21875C2semidirect
11. #21423C2semidirect
12. #21421C2semidirect
13. #21421C2semidirect
22. C2×#563C4semidirect
23. C2×#557C4semidirect
24. C2×#556C4semidirect
27. C2×D4×Q8C4semidirect
30. C2×#547C4semidirect
31. C2×#544C4semidirect
32. C2×#542C4semidirect
33. C2×#541C4semidirect
35. C2×#536C4semidirect

Maximal subgroups

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

subgroupindex
C2×#35522
#343712
#342162
#225352
#225342
#225132
Q8×#992
#218772
#218752
#214232
#214212