Finite Group Databasebeta

← #10574511

Subgroups — #10574511

Order 512.

6908 conjugacy classes of subgroups.

The subgroup lattice has 1043 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62773C211yesmaximal, characteristic
2#60312C212yesmaximal, complemented
3#60311C218yesmaximal, complemented
4#60310C214yesmaximal, complemented
5#60309C212yesmaximal, complemented
6#60306C212yesmaximal, complemented
7#60305C218yesmaximal, complemented
8#60304C214yesmaximal, complemented
9C8×H(5,𝔽2)C212yesmaximal, complemented
10#60271C214yesmaximal, complemented
11#60265C212yesmaximal, complemented
12#60239C214yesmaximal, complemented
13#60233C214yesmaximal, complemented
14#60230C211yesmaximal, characteristic, complemented
15#60215C214yesmaximal, complemented
16#60204C212yesmaximal, complemented
17D4×#131C214yesmaximal, complemented
18C2×#2929C214yesmaximal, complemented
19C22×C8×D4C211yesmaximal, characteristic, complemented
20C22×#131C2214yescomplemented
21C24×C8C2212yescomplemented
22#3520C414yes—
23#3519C414yes—
24#3513C418yes—
25#3506C412yes—
26#3505C414yes—
27#3501C411yescharacteristic
28#3496C411yescharacteristic
29#3492C412yes—
30#3490C414yes—
31#3484C412yes—
32#3481C2218yes—
33#3475C2214yes—
34D4×#41C2214yes—
35#3460C2212yes—
36#3459C2214yes—
37#3444C2212yes—
38C2×#525C2214yes—
39C4×H(5,𝔽2)C2212yes—
40C22×C4×D4C2211yescharacteristic
41#2994C2218yescomplemented
42#2994C22116yescomplemented
43#2994C2218yescomplemented
44#2993C2218yescomplemented
45#2992C2218yescomplemented
46#2992C22116yescomplemented
47#2990C2218yescomplemented
48#2990C2218yescomplemented
49#2989C2214yescomplemented
50#2988C2214yescomplemented
51#2988C2218yescomplemented
52#2981C2218yescomplemented
53#2979C2218yescomplemented
54#2977C22116yescomplemented
55#2977C22116yescomplemented
56#2976C2218yescomplemented
57#2976C2218yescomplemented
58#2976C22116yescomplemented
59#2975C2212yescomplemented
60#2974C2218yescomplemented
61#2974C22116yescomplemented
62#2974C2218yescomplemented
63#2973C2214yescomplemented
64#2973C2218yescomplemented
65#2972C2212yes—
66#2972C2218yescomplemented
67#2972C2218yescomplemented
68#2970C2218yescomplemented
69#2969C2218yescomplemented
70#2968C22116yescomplemented
71#2966C2214yescomplemented
72#2966C2214yescomplemented
73#2966C2214yescomplemented
74#2966C2214yescomplemented
75#2966C22116yescomplemented
76#2966C2218yescomplemented
77#2965C2214yescomplemented
78#2965C2214yescomplemented
79C8×#41C2214yescomplemented
80C8×#41C2214yescomplemented
81C8×#41C2218yescomplemented
82#2962C2214yescomplemented
83#2960C2212yescomplemented
84#2960C2212yescomplemented
85#2935C2214yescomplemented
86#2935C2218yescomplemented
87D4×M16C2214yescomplemented
88D4×M16C2214yescomplemented
89D4×M16C2218yescomplemented
90#2933C2218yescomplemented
91#2933C2218yescomplemented
92#2933C22116yescomplemented
93#2931C2212yescomplemented
94#2931C2212yescomplemented
95#2931C2218yescomplemented
96#2929C2214yescomplemented
97#2929C2214yescomplemented
98#2929C2218yescomplemented
99#2929C2218yescomplemented
100#2929C2218yescomplemented
101#2929C2218yescomplemented
102#2929C2218yescomplemented
103#2929C2218yescomplemented
104#2929C2218yescomplemented
105#2929C22116yescomplemented
106C2×#435C2218yescomplemented
107C2×#435C2218yescomplemented
108C2×C8×D4C2211yescharacteristic
109C2×C8×D4C2211yescharacteristic
110C2×C8×D4C2214yescomplemented
111C2×C8×D4C2214yescomplemented
112C2×C8×D4C2212yescomplemented
113C2×C8×D4C2214yescomplemented
114C2×C8×D4C2211yescharacteristic, complemented
115C2×C8×D4C2212yescomplemented
116C2×C8×D4C2214yescomplemented
117C2×C8×D4C2211yescharacteristic, complemented
118C2×C8×D4C2218yescomplemented
119C2×C8×D4C2218yescomplemented
120C2×C8×D4C2218yescomplemented
121#2925C2214yescomplemented
122#2924C2218yescomplemented
123#2922C2214yescomplemented
124#2920C2212yescomplemented
125#2906C2214yescomplemented
126C2×#424C2214yescomplemented
127C22×C4⋊C8C2211yescharacteristic, complemented
128#2880C2218yescomplemented
129C2×#408C2214yescomplemented
130C2×#407C2214yescomplemented
131C22×C22⋊C8C2212yescomplemented
132C4×#131C2214yescomplemented
133C2×#405C2214yescomplemented
134C22×C4×C8C2211yescharacteristic, complemented
135C2×H(5,𝔽2)C2×C412yes—
136C22×#41C2314yes—
137C23×D4C2×C411yescharacteristic
138C24×C4C2312yes—
139C2×#131—416no—
140C2×#131C2314yes—
141C2×#131C2314yes—
142C2×#131C2318yes—
143C2×#131C2318yescomplemented
144C2×#131C2318yescomplemented
145C22×M16C2314yes—
146C22×M16C2314yes—
147C22×M16C2318yescomplemented
148C23×C8—48no—
149C23×C8C2311yescharacteristic
150C23×C8C2314yes—
151C23×C8C2311yescharacteristic
152C23×C8C2312yes—
153C23×C8C2314yes—
154C23×C8C2312yes—
155C23×C8C2312yes—
156C23×C8C2314yes—
157C23×C8C2314yes—
158C23×C8C2312yes—
159C23×C8C2312yes—
160C23×C8C2318yescomplemented
161#559C2×C418yes—
162#556C2×C414yes—
163#555C2×C414yes—
164#554C2×C414yes—
165#554C2×C418yes—
166#554C2×C418yes—
167#553C2×C418yes—
168#553C2×C418yes—
169#553C2×C4116yes—
170#553C2×C418yes—
171#552C2×C418yes—
172#552C2×C418yes—
173#551C2×C4116yes—
174#551C2×C4116yes—
175#551C2×C4116yes—
176#550C2×C414yes—
177D4×Q8C2×C414yes—
178#548C2×C418yes—
179#547C2×C418yes—
180#547C2×C414yes—
181#547C2×C414yes—
182#546C2×C4116yes—
183#546C2×C418yes—
184#546C2×C418yes—
185#546C2×C418yes—
186#546C2×C4116yes—
187#546C2×C418yes—
188D42C2×C418yes—
189D42C2×C414yes—
190D42C2×C418yes—
191#544C2×C412yes—
192#543C2×C414yes—
193#542C2×C418yes—
194#540C2×C418yes—
195#539C2×C418yes—
196#539C2×C4116yes—
197#538C2×C418yes—
198#538C2×C4116yes—
199#538C2×C418yes—
200#537C2×C412yes—
201#535C2×C414yes—
202#534C2×C418yes—
203#534C2×C414yes—
204#533C2×C412yes—
205#533C2×C412yes—
206#533C2312yes—
207#532C2×C412yes—
208#532C2×C412yes—
209#532C2312yes—
210#532C2318yes—
211#529C2×C414yes—
212#529C2×C414yes—
213#529C2×C414yes—
214#529C2×C414yes—
215#529C2314yes—
216#529C2314yes—
217#529C23116yes—
218#529C2318yes—
219#525C2×C418yes—
220#525C2×C418yes—
221#525C2×C418yes—
222#525C2×C418yes—
223#525C2×C414yes—
224#525C2×C414yes—
225#525C2314yes—
226#525C2318yes—
227#525C2318yes—
228#525C2318yes—
229#525C23116yes—
230C2×#123C2×C418yes—
231C2×C22⋊Q8C2×C414yes—
232C2×C22⋊Q8C2×C414yes—
233C2×#121C2×C414yes—
234C2×#121C2×C414yes—
235C2×#120C2×C418yes—
236#520C2×C414yes—
237#520C2×C418yes—
238#518C2×C412yes—
239#518C2×C418yes—
240#518C2×C418yes—
241C4×#41C2314yes—
242C4×#41C2318yes—
243C4×#41C2314yes—
244C4×#41C2314yes—
245C2×C4×D4C2×C411yescharacteristic
246C2×C4×D4C2×C412yes—
247C2×C4×D4C2×C411yescharacteristic
248C2×C4×D4C2×C414yes—
249C2×C4×D4C2×C414yes—
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2314yes—
252C2×C4×D4C2312yes—
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2314yes—
255C2×C4×D4C2318yes—
256C2×C4×D4C2318yes—
257C2×C4×D4C2318yes—
258C2×#117C2314yes—
259C22×C4⋊C4C2×C411yescharacteristic
260C22×C22⋊C4C2×C412yes—
261C22×C42C2311yescharacteristic
262#446C2314yescomplemented
263#446C2314yescomplemented
264#446C2314yescomplemented
265#446C2314yescomplemented
266#446C23116yescomplemented
267#446C2318yescomplemented
268C8×Q8C2314yescomplemented
269C8×Q8C2314yescomplemented
270C8×Q8C2314yescomplemented
271C8×Q8C2314yescomplemented
272C8×Q8C2318yescomplemented
273#436C2318yes—
274#436C2318yes—
275#436C2314yescomplemented
276#436C23116yescomplemented
277#436C2314yescomplemented
278#436C2318yescomplemented
279#436C2314yescomplemented
280#436C2314yescomplemented
281#436C23116yescomplemented
282#435C2318yes—
283#435C2318yes—
284#435C23116yes—
285#435C23116yes—
286#435C23116yes—
287#435C2318yes—
288#435C2318yes—
289#435C23116yes—
290#435C23116yescomplemented
291#435C23116yescomplemented
292#435C23116yescomplemented
293#435C23116yescomplemented
294#435C23116yescomplemented
295#435C23116yescomplemented
296#435C23116yescomplemented
297#435C23116yescomplemented
298#435C23116yescomplemented
299C8×D4C2314yes—
300C8×D4C2314yes—
301C8×D4C2314yes—
302C8×D4C2314yes—
303C8×D4C2318yes—
304C8×D4C2314yes—
305C8×D4C2318yes—
306C8×D4C2314yes—
307C8×D4C2318yes—
308C8×D4C2318yes—
309C8×D4C2314yes—
310C8×D4C2314yes—
311C8×D4C2318yes—
312C8×D4C2318yes—
313C8×D4C23116yes—
314C8×D4C23116yes—
315C8×D4C2318yes—
316C8×D4C2318yes—
317C8×D4C2318yes—
318C8×D4C2318yes—
319C8×D4C23116yescomplemented
320C8×D4C2314yescomplemented
321C8×D4C23116yescomplemented
322C8×D4C23116yescomplemented
323C8×D4C23116yescomplemented
324C8×D4C23116yescomplemented
325C8×D4C2318yescomplemented
326C8×D4C2314yescomplemented
327C8×D4C2314yescomplemented
328C8×D4C2314yescomplemented
329C8×D4C23116yescomplemented
330#433C2318yescomplemented
331#433C2318yescomplemented
332#433C23116yescomplemented
333#433C23116yescomplemented
334#433C23116yescomplemented
335#432C2314yes—
336#432C2314yes—
337#432C23116yescomplemented
338#432C2318yescomplemented
339#431C2314yes—
340#431C2314yes—
341#431C2318yescomplemented
342#431C2318yescomplemented
343#431C23116yescomplemented
344#431C2318yescomplemented
345#424C2314yes—
346#424C2318yes—
347#424C2314yes—
348#424C2318yescomplemented
349#424C2318yescomplemented
350#424C23116yescomplemented
351#423C2312yes—
352#423C2312yes—
353#423C2318yescomplemented
354C2×C4⋊C8C2314yes—
355C2×C4⋊C8C2311yescharacteristic
356C2×C4⋊C8C2311yescharacteristic
357C2×C4⋊C8C2314yes—
358C2×C4⋊C8C2312yes—
359C2×C4⋊C8C2318yescomplemented
360C2×C4⋊C8C2318yescomplemented
361C2×C4⋊C8C2318yescomplemented
362#408C2314yes—
363#408C2318yes—
364#408C2314yes—
365#408C2318yescomplemented
366#408C2318yescomplemented
367#408C23116yescomplemented
368#408C23116yescomplemented
369#407C2314yes—
370#407C2318yes—
371#407C2318yes—
372#407C2318yes—
373#407C23116yescomplemented
374C2×C22⋊C8C2318yes—
375C2×C22⋊C8C2312yes—
376C2×C22⋊C8C2312yes—
377C2×C22⋊C8C2318yes—
378C2×C22⋊C8C2312yes—
379C2×C22⋊C8C2312yes—
380C2×C22⋊C8C2318yes—
381C2×C22⋊C8C2318yes—
382C2×C22⋊C8C2318yescomplemented
383C2×C22⋊C8C2318yescomplemented
384C2×C22⋊C8C23116yescomplemented
385#405C2314yes—
386#405C2318yes—
387#405C2314yes—
388#405C2318yescomplemented
389#405C2318yescomplemented
390#405C2318yescomplemented
391#405C2318yescomplemented
392C4×M16C2314yes—
393C4×M16C2318yescomplemented
394C2×#97C2318yescomplemented
395C2×C4×C8C2312yes—
396C2×C4×C8C2312yes—
397C2×C4×C8C2311yescharacteristic
398C2×C4×C8C2311yescharacteristic
399C2×C4×C8C2312yes—
400C2×C4×C8C2312yes—
401C2×C4×C8C2311yescharacteristic
402C2×C4×C8C2311yescharacteristic
403C2×C4×C8C2318yescomplemented
404C2×C4×C8C2318yescomplemented
405C25C22×C412yes—
406H(5,𝔽2)—216no—
407C2×#41—48no—
408C2×#41—48no—
409C2×#41C22×C414yes—
410C2×#41C22×C418yes—
411C2×#41C22×C414yes—
412C2×#41C22×C418yes—
413C2×#41C22×C418yes—
414C2×#41C2414yes—
415C2×#41C2418yes—
416C22×Q8C22×C414yes—
417C22×D4—28no—
418C22×D4C22×C412yes—
419C22×D4C22×C411yescharacteristic
420C22×D4C22×C414yes—
421C22×D4C22×C414yes—
422C22×D4C22×C418yes—
423C22×D4C22×C418yes—
424C22×D4C22×C418yes—
425C22×D4C22×C418yes—
426C22×D4C22×C414yes—
427C22×D4C22×C411yescharacteristic
428C23×C4—44no—
429C23×C4—44no—
430C23×C4C22×C411yescharacteristic
431C23×C4C22×C411yescharacteristic
432C23×C4C22×C412yes—
433C23×C4C22×C412yes—
434C23×C4C22×C414yes—
435C23×C4C22×C414yes—
436C23×C4C22×C412yes—
437C23×C4C2414yes—
438C23×C4C2411yescharacteristic
439C23×C4C2412yes—
440C23×C4C2414yes—
441C23×C4C2418yes—
442C23×C4C2412yes—
443#131—216no—
444#131—416no—
445#131—416no—
446#131—416no—
447#131—48no—
448C2×M16—416no—
449C2×M16—48no—
450C2×M16—48no—
451C2×M16C2414yes—
452C2×M16C2414yes—
453C2×M16C2418yes—
454C2×M16C2418yes—
455C2×M16C2418yes—
456C2×M16C24116yes—
457C2×M16C2418yes—
458C22×C8—24no—
459C22×C8—216no—
460C22×C8—44no—
461C22×C8—48no—
462C22×C8—44no—
463C22×C8—48no—
464C22×C8—44no—
465C22×C8—44no—
466C22×C8—416no—
467C22×C8—48no—
468C22×C8—44no—
469C22×C8—42no—
470C22×C8C2411yescharacteristic
471C22×C8C2411yescharacteristic
472C22×C8C2411yescharacteristic
473C22×C8C2414yes—
474C22×C8C2414yes—
475C22×C8C2414yes—
476C22×C8C2412yes—
477C22×C8C2411yescharacteristic
478C22×C8C2411yescharacteristic
479C22×C8C2414yes—
480C22×C8C2414yes—
481C22×C8C2418yes—
482C22×C8C2412yes—
483C22×C8C2414yes—
484C22×C8C2412yes—
485C22×C8C2414yes—
486C22×C8C2414yes—
487C22×C8C2414yes—
488C22×C8C2414yes—
489C22×C8C2411yescharacteristic
490C22×C8C2412yes—
491C22×C8C2411yescharacteristic
492C22×C8C2418yes—
493C22×C8C24116yes—
494C22×C8C2418yes—
495C22×C8C2418yes—
496C22×C8C2411yescharacteristic
497C4⋊Q8C22×C412yes—
498C4⋊Q8C22×C412yes—
499C4⋊Q8C22×C412yes—
500C4⋊Q8C22×C418yes—
501#127C22×C412yes—
502#127C22×C418yes—
503#126C22×C418yes—
504#126C22×C418yes—
505#126C22×C4116yes—
506#126C22×C4116yes—
507#126C22×C4116yes—
508#125C22×C414yes—
509#125C22×C414yes—
510#125C22×C414yes—
511#125C22×C4116yes—
512#125C22×C418yes—
513#124C22×C414yes—
514#124C22×C414yes—
515#124C22×C414yes—
516#124C22×C418yes—
517#124C22×C4116yes—
518#124C22×C4116yes—
519#123C22×C418yes—
520#123C22×C4116yes—
521#123C22×C4116yes—
522#123C22×C4116yes—
523#123C22×C418yes—
524#123C22×C418yes—
525#123C22×C4116yes—
526#123C22×C4116yes—
527#123C22×C4116yes—
528#123C22×C4116yes—
529#123C22×C4116yes—
530C22⋊Q8C22×C414yes—
531C22⋊Q8C22×C414yes—
532C22⋊Q8C22×C418yes—
533C22⋊Q8C22×C418yes—
534C22⋊Q8C22×C418yes—
535C22⋊Q8C22×C418yes—
536C22⋊Q8C22×C418yes—
537C22⋊Q8C22×C418yes—
538C22⋊Q8C22×C414yes—
539C22⋊Q8C22×C414yes—
540C22⋊Q8C22×C414yes—
541C22⋊Q8C22×C414yes—
542C22⋊Q8C22×C4116yes—
543C22⋊Q8C22×C4116yes—
544C22⋊Q8C22×C418yes—
545C22⋊Q8C22×C4116yes—
546#121C22×C414yes—
547#121C22×C414yes—
548#121C22×C418yes—
549#121C22×C418yes—
550#121C22×C418yes—
551#121C22×C418yes—
552#121C22×C418yes—
553#121C22×C418yes—
554#121C22×C414yes—
555#121C22×C414yes—
556#121C22×C414yes—
557#121C22×C414yes—
558#121C22×C4116yes—
559#121C22×C4116yes—
560#121C22×C4116yes—
561#121C22×C418yes—
562#121C22×C418yes—
563#121C22×C418yes—
564#121C22×C4116yes—
565#120C22×C418yes—
566#120C22×C4116yes—
567#120C22×C4116yes—
568#120C22×C4116yes—
569#120C22×C4116yes—
570#120C22×C4116yes—
571C4×Q8C22×C414yes—
572C4×Q8C22×C418yes—
573C4×Q8C22×C414yes—
574C4×Q8C22×C414yes—
575C4×Q8C22×C414yes—
576C4×Q8C2414yes—
577C4×Q8C2414yes—
578C4×D4C22×C414yes—
579C4×D4C22×C418yes—
580C4×D4C22×C414yes—
581C4×D4C22×C414yes—
582C4×D4C22×C414yes—
583C4×D4C22×C418yes—
584C4×D4C22×C414yes—
585C4×D4C22×C418yes—
586C4×D4C22×C414yes—
587C4×D4C22×C4116yes—
588C4×D4C22×C4116yes—
589C4×D4C22×C418yes—
590C4×D4C22×C4116yes—
591C4×D4C22×C418yes—
592C4×D4C22×C4116yes—
593C4×D4C22×C4116yes—
594C4×D4C22×C418yes—
595C4×D4C22×C414yes—
596C4×D4C22×C418yes—
597C4×D4C22×C4116yes—
598C4×D4C22×C418yes—
599C4×D4C22×C418yes—
600C4×D4C22×C418yes—
601C4×D4C22×C414yes—
602C4×D4C22×C414yes—
603C4×D4C22×C414yes—
604C4×D4C2414yes—
605C4×D4C2418yes—
606C4×D4C2414yes—
607C4×D4C2418yes—
608C4×D4C2418yes—
609C4×D4C24116yes—
610C4×D4C2414yes—
611C4×D4C24116yes—
612C4×D4C2414yes—
613#117C22×C418yes—
614#117C22×C418yes—
615#117C22×C414yes—
616#117C22×C418yes—
617#117C22×C4116yes—
618#117C22×C418yes—
619#117C22×C414yes—
620#117C22×C418yes—
621#117C2414yes—
622#117C2418yes—
623#117C2418yes—
624C2×C4⋊C4C22×C411yescharacteristic
625C2×C4⋊C4C22×C411yescharacteristic
626C2×C4⋊C4C22×C412yes—
627C2×C4⋊C4C22×C414yes—
628C2×C4⋊C4C22×C414yes—
629C2×C4⋊C4C22×C414yes—
630C2×C4⋊C4C22×C414yes—
631C2×C4⋊C4C22×C418yes—
632C2×C4⋊C4C22×C418yes—
633C2×C4⋊C4C22×C418yes—
634C2×C22⋊C4C22×C412yes—
635C2×C22⋊C4C22×C412yes—
636C2×C22⋊C4C22×C412yes—
637C2×C22⋊C4C22×C412yes—
638C2×C22⋊C4C22×C418yes—
639C2×C22⋊C4C22×C418yes—
640C2×C22⋊C4C22×C418yes—
641C2×C22⋊C4C22×C418yes—
642C2×C22⋊C4C22×C418yes—
643C2×C22⋊C4C22×C4116yes—
644C2×C22⋊C4C22×C418yes—
645C2×C22⋊C4C22×C418yes—
646C2×C42C22×C412yes—
647C2×C42C22×C411yescharacteristic
648C2×C42C22×C412yes—
649C2×C42C22×C411yescharacteristic
650C2×C42C2418yes—
651C2×C42C2411yescharacteristic
652C2×C42C2412yes—
653C2×C42C2412yes—
654C2×C42C2411yescharacteristic
655C2×C42C2418yes—
656C4⋊C8C2414yes—
657C4⋊C8C2414yes—
658C4⋊C8C2418yes—
659C4⋊C8C2414yes—
660C4⋊C8C2418yes—
661C4⋊C8C24116yes—
662C4⋊C8C2418yes—
663C4⋊C8C24116yes—
664C4⋊C8C2414yes—
665C4⋊C8C2414yes—
666C4⋊C8C2414yes—
667C4⋊C8C2418yes—
668C4⋊C8C2418yes—
669C22⋊C8C2418yes—
670C22⋊C8C2418yes—
671C22⋊C8C2418yes—
672C22⋊C8C2418yes—
673C22⋊C8C2418yes—
674C22⋊C8C2418yes—
675C22⋊C8C24116yes—
676C22⋊C8C24116yes—
677C22⋊C8C2418yes—
678C22⋊C8C24116yes—
679C22⋊C8C2418yes—
680C22⋊C8C2418yes—
681C22⋊C8C24116yes—
682C22⋊C8C2418yes—
683#97C2418yes—
684#97C24116yes—
685#97C2418yes—
686#97C2418yes—
687C4×C8C2412yes—
688C4×C8C2412yes—
689C4×C8C2412yes—
690C4×C8C2412yes—
691C4×C8C2412yes—
692C4×C8C2412yes—
693C4×C8C2418yes—
694C4×C8C24116yes—
695C4×C8C2418yes—
696C4×C8C2412yes—
697C4×C8C2412yes—
698C4×C8C2418yes—
699C24—28no—
700C24—44no—
701C24—44no—
702C24C23×C411yescharacteristic
703C24C23×C414yes—
704C24C23×C414yes—
705C24C23×C418yes—
706C24C23×C412yes—
707C24C23×C412yes—
708#41—232no—
709#41—216no—
710#41—28no—
711#41—28no—
712#41—48no—
713#41—48no—
714#41—416no—
715#41—48no—
716#41—416no—
717C2×Q8—48no—
718C2×Q8C23×C414yes—
719C2×Q8C23×C414yes—
720C2×Q8C23×C414yes—
721C2×Q8C23×C418yes—
722C2×D4—28no—
723C2×D4—232no—
724C2×D4—216no—
725C2×D4—216no—
726C2×D4—232no—
727C2×D4—24no—
728C2×D4—48no—
729C2×D4—416no—
730C2×D4—416no—
731C2×D4#13118yescomplemented
732C2×D4C23×C418yes—
733C2×D4C23×C4116yes—
734C2×D4C23×C418yes—
735C2×D4C23×C418yes—
736C2×D4C23×C414yes—
737C2×D4C23×C414yes—
738C2×D4C23×C418yes—
739C2×D4C23×C414yes—
740C2×D4C23×C414yes—
741C2×D4C23×C4116yes—
742C2×D4C23×C4116yes—
743C2×D4C23×C418yes—
744C2×D4C23×C414yes—
745C22×C4—24no—
746C22×C4—22no—
747C22×C4—28no—
748C22×C4—22no—
749C22×C4—28no—
750C22×C4—42no—
751C22×C4—44no—
752C22×C4—42no—
753C22×C4—48no—
754C22×C4—44no—
755C22×C4—48no—
756C22×C4—44no—
757C22×C4—42no—
758C22×C4—44no—
759C22×C4—42no—
760C22×C4—48no—
761C22×C4—48no—
762C22×C4—44no—
763C22×C4—42no—
764C22×C4C23×C411yescharacteristic
765C22×C4C23×C411yescharacteristic
766C22×C4C23×C411yescharacteristic
767C22×C4C23×C412yes—
768C22×C4C23×C412yes—
769C22×C4C23×C412yes—
770C22×C4C23×C411yescharacteristic
771C22×C4C23×C418yes—
772C22×C4C23×C418yes—
773C22×C4C23×C414yes—
774C22×C4C23×C414yes—
775C22×C4C23×C414yes—
776C22×C4C23×C411yescharacteristic
777C22×C4C23×C412yes—
778C22×C4C23×C411yescharacteristic
779C22×C4C23×C418yes—
780C22×C4C23×C418yes—
781C22×C4C23×C412yes—
782C22×C4C23×C414yes—
783C22×C4C23×C414yes—
784C22×C4C23×C414yes—
785C22×C4C23×C418yes—
786C22×C4C23×C412yes—
787C22×C4C23×C4116yes—
788C22×C4C23×C414yes—
789C22×C4C23×C414yes—
790C22×C4C23×C411yescharacteristic
791C22×C4C2514yes—
792C22×C4C2511yescharacteristic
793C22×C4C2511yescharacteristic
794C22×C4C2518yes—
795C22×C4C2514yes—
796C22×C4C2511yescharacteristic
797M16—28no—
798M16—28no—
799M16—216no—
800M16—48no—
801M16—416no—
802M16—48no—
803M16—48no—
804C2×C8—22no—
805C2×C8—28no—
806C2×C8—24no—
807C2×C8—22no—
808C2×C8—22no—
809C2×C8—28no—
810C2×C8—22no—
811C2×C8—22no—
812C2×C8—28no—
813C2×C8—28no—
814C2×C8—28no—
815C2×C8—216no—
816C2×C8—42no—
817C2×C8—44no—
818C2×C8—44no—
819C2×C8—44no—
820C2×C8—44no—
821C2×C8—44no—
822C2×C8—42no—
823C2×C8—41no—
824C2×C8—42no—
825C2×C8—41no—
826C2×C8—48no—
827C2×C8—416no—
828C2×C8—48no—
829C2×C8—48no—
830C2×C8H(5,𝔽2)14yescomplemented
831C2×C8C2512yes—
832C2×C8C2512yes—
833C2×C8C2518yes—
834C2×C8C2511yescharacteristic
835C2×C8C2511yescharacteristic
836C2×C8C2514yes—
837C2×C8C2518yes—
838C2×C8C2514yes—
839C2×C8C2511yescharacteristic
840C2×C8C2511yescharacteristic
841C4⋊C4C23×C414yes—
842C4⋊C4C23×C414yes—
843C4⋊C4C23×C418yes—
844C4⋊C4C23×C414yes—
845C4⋊C4C23×C414yes—
846C4⋊C4C23×C414yes—
847C4⋊C4C23×C418yes—
848C4⋊C4C23×C4116yes—
849C4⋊C4C23×C418yes—
850C4⋊C4C23×C418yes—
851C4⋊C4C23×C418yes—
852C4⋊C4C23×C4116yes—
853C4⋊C4C23×C414yes—
854C4⋊C4C23×C418yes—
855C4⋊C4C23×C418yes—
856C4⋊C4C23×C414yes—
857C4⋊C4C23×C414yes—
858C4⋊C4C23×C418yes—
859C4⋊C4C23×C418yes—
860C22⋊C4C23×C418yes—
861C22⋊C4C23×C418yes—
862C22⋊C4C23×C418yes—
863C22⋊C4C23×C418yes—
864C22⋊C4C23×C418yes—
865C22⋊C4C23×C418yes—
866C22⋊C4C23×C4116yes—
867C22⋊C4C23×C418yes—
868C22⋊C4C23×C418yes—
869C22⋊C4C23×C4116yes—
870C22⋊C4C23×C418yes—
871C22⋊C4C23×C418yes—
872C22⋊C4C23×C4116yes—
873C22⋊C4C23×C4116yes—
874C22⋊C4C23×C4116yes—
875C22⋊C4C23×C418yes—
876C22⋊C4C23×C418yes—
877C22⋊C4C23×C418yes—
878C42C23×C412yes—
879C42C23×C412yes—
880C42C23×C412yes—
881C42C23×C412yes—
882C42C23×C412yes—
883C42C23×C412yes—
884C42C23×C4116yes—
885C42C23×C418yes—
886C42C23×C418yes—
887C42C2512yes—
888C42C2512yes—
889C42C2518yes—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—28no—
894C23—28no—
895C23—28no—
896C23—24no—
897C23—28no—
898C23—216no—
899C23—42no—
900C23—44no—
901C23—42no—
902C23—42no—
903C23—44no—
904C23—42no—
905C23—48no—
906C23—48no—
907C23—432no—
908C23C2×#13118yescomplemented
909C23C24×C414yes—
910C23C24×C418yes—
911C23C24×C411yescharacteristic
912C23C24×C414yes—
913C23C24×C411yescharacteristic
914C23C24×C411yescharacteristic
915Q8—28no—
916Q8—28no—
917Q8—48no—
918Q8—44no—
919D4—216no—
920D4—216no—
921D4—232no—
922D4—216no—
923D4—216no—
924D4—28no—
925D4—28no—
926D4—28no—
927D4—416no—
928D4—48no—
929D4—416no—
930D4—44no—
931D4C2×#131116yescomplemented
932C2×C4—22no—
933C2×C4—28no—
934C2×C4—22no—
935C2×C4—216no—
936C2×C4—24no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—28no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—24no—
945C2×C4—28no—
946C2×C4—24no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—28no—
950C2×C4—28no—
951C2×C4—24no—
952C2×C4—24no—
953C2×C4—216no—
954C2×C4—44no—
955C2×C4—42no—
956C2×C4—44no—
957C2×C4—44no—
958C2×C4—44no—
959C2×C4—44no—
960C2×C4—42no—
961C2×C4—41no—
962C2×C4—42no—
963C2×C4—41no—
964C2×C4—48no—
965C2×C4—416no—
966C2×C4—48no—
967C2×C4—48no—
968C2×C4C2×#13114yescomplemented
969C2×C4C24×C412yes—
970C2×C4C24×C411yescharacteristic
971C2×C4C24×C411yescharacteristic
972C2×C4C24×C414yes—
973C2×C4C24×C412yes—
974C2×C4C24×C418yes—
975C2×C4C24×C418yes—
976C2×C4C24×C412yes—
977C2×C4C24×C418yes—
978C2×C4C24×C414yes—
979C2×C4C24×C411yescharacteristic
980C2×C4C24×C412yes—
981C2×C4C2×H(5,𝔽2)12yes—
982C2×C4#58512yes—
983C2×C4C2611yescharacteristic
984C8—21no—
985C8—21no—
986C8—24no—
987C8—24no—
988C8—28no—
989C8—22no—
990C8—22no—
991C8—28no—
992C8C2×H(5,𝔽2)12yes—
993C8C2×H(5,𝔽2)12yes—
994C22—28no—
995C22—21no—
996C22—21no—
997C22—21no—
998C22—21no—
999C22—24no—
1000C22—21no—
1001C22—21no—
1002C22—24no—
1003C22—28no—
1004C22—24no—
1005C22—28no—
1006C22—24no—
1007C22—24no—
1008C22—28no—
1009C22—48no—
1010C22—416no—
1011C22—416no—
1012C22—48no—
1013C22—816no—
1014C22C4×H(5,𝔽2)12yes—
1015C22C22×#13118yes—
1016C22C22×#13112yes—
1017C22#357312yes—
1018C22C25×C411yescharacteristic
1019C4—22no—
1020C4—28no—
1021C4—22no—
1022C4—22no—
1023C4—28no—
1024C4—21no—
1025C4—21no—
1026C4—24no—
1027C4—24no—
1028C4—28no—
1029C4C4×H(5,𝔽2)12yes—
1030C4C22×#13114yes—
1031C4C22×H(5,𝔽2)11yescharacteristic
1032C4C2×#58511yescharacteristic
1033C2—22no—
1034C2—22no—
1035C2—22no—
1036C2—28no—
1037C2—44no—
1038C2—48no—
1039C2C2×C4×H(5,𝔽2)11yescharacteristic
1040C2C23×#13111yescharacteristic
1041C2C2×#357311yescharacteristic
subgroupG/H
centerC2×C8C25
commutator, socleC22C25×C4
Frattini, cosocleC2×C4C26
prime radical#62773C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C8 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60312C2semidirect
3. #60311C2semidirect
4. #60310C2semidirect
5. #60309C2semidirect
6. #60306C2semidirect
7. #60305C2semidirect
8. #60304C2semidirect
9. C8×H(5,𝔽2)C2semidirect
10. #60271C2semidirect
11. #60265C2semidirect
12. #60239C2semidirect
13. #60233C2semidirect
14. #60230C2semidirect
15. #60215C2semidirect
16. #60204C2semidirect
17. D4×#131C2semidirect
18. C2×#2929C2semidirect
19. C22×C8×D4C2semidirect
20. C22×#131C22semidirect
21. C24×C8C22semidirect
41. #2994C22semidirect
42. #2994C22semidirect
43. #2994C22semidirect
44. #2993C22semidirect
45. #2992C22semidirect
46. #2992C22semidirect
47. #2990C22semidirect
48. #2990C22semidirect
49. #2989C22semidirect
50. #2988C22semidirect
51. #2988C22semidirect
52. #2981C22semidirect
53. #2979C22semidirect
54. #2977C22semidirect
55. #2977C22semidirect
56. #2976C22semidirect
57. #2976C22semidirect
58. #2976C22semidirect
59. #2975C22semidirect
60. #2974C22semidirect
61. #2974C22semidirect
62. #2974C22semidirect
63. #2973C22semidirect
64. #2973C22semidirect
66. #2972C22semidirect
67. #2972C22semidirect
68. #2970C22semidirect
69. #2969C22semidirect
70. #2968C22semidirect
71. #2966C22semidirect
72. #2966C22semidirect
73. #2966C22semidirect
74. #2966C22semidirect
75. #2966C22semidirect
76. #2966C22semidirect
77. #2965C22semidirect
78. #2965C22semidirect
79. C8×#41C22semidirect
80. C8×#41C22semidirect
81. C8×#41C22semidirect
82. #2962C22semidirect
83. #2960C22semidirect
84. #2960C22semidirect
85. #2935C22semidirect
86. #2935C22semidirect
87. D4×M16C22semidirect
88. D4×M16C22semidirect
89. D4×M16C22semidirect
90. #2933C22semidirect
91. #2933C22semidirect
92. #2933C22semidirect
93. #2931C22semidirect
94. #2931C22semidirect
95. #2931C22semidirect
96. #2929C22semidirect
97. #2929C22semidirect
98. #2929C22semidirect
99. #2929C22semidirect
100. #2929C22semidirect
101. #2929C22semidirect
102. #2929C22semidirect
103. #2929C22semidirect
104. #2929C22semidirect
105. #2929C22semidirect
106. C2×#435C22semidirect
107. C2×#435C22semidirect
110. C2×C8×D4C22semidirect
111. C2×C8×D4C22semidirect
112. C2×C8×D4C22semidirect
113. C2×C8×D4C22semidirect
114. C2×C8×D4C22semidirect
115. C2×C8×D4C22semidirect
116. C2×C8×D4C22semidirect
117. C2×C8×D4C22semidirect
118. C2×C8×D4C22semidirect
119. C2×C8×D4C22semidirect
120. C2×C8×D4C22semidirect
121. #2925C22semidirect
122. #2924C22semidirect
123. #2922C22semidirect
124. #2920C22semidirect
125. #2906C22semidirect
126. C2×#424C22semidirect
127. C22×C4⋊C8C22semidirect
128. #2880C22semidirect
129. C2×#408C22semidirect
130. C2×#407C22semidirect
131. C22×C22⋊C8C22semidirect
132. C4×#131C22semidirect
133. C2×#405C22semidirect
134. C22×C4×C8C22semidirect
143. C2×#131C23semidirect
144. C2×#131C23semidirect
147. C22×M16C23semidirect
160. C23×C8C23semidirect
262. #446C23semidirect
263. #446C23semidirect
264. #446C23semidirect
265. #446C23semidirect
266. #446C23semidirect
267. #446C23semidirect
268. C8×Q8C23semidirect
269. C8×Q8C23semidirect
270. C8×Q8C23semidirect
271. C8×Q8C23semidirect
272. C8×Q8C23semidirect
275. #436C23semidirect
276. #436C23semidirect
277. #436C23semidirect
278. #436C23semidirect
279. #436C23semidirect
280. #436C23semidirect
281. #436C23semidirect
290. #435C23semidirect
291. #435C23semidirect
292. #435C23semidirect
293. #435C23semidirect
294. #435C23semidirect
295. #435C23semidirect
296. #435C23semidirect
297. #435C23semidirect
298. #435C23semidirect
319. C8×D4C23semidirect
320. C8×D4C23semidirect
321. C8×D4C23semidirect
322. C8×D4C23semidirect
323. C8×D4C23semidirect
324. C8×D4C23semidirect
325. C8×D4C23semidirect
326. C8×D4C23semidirect
327. C8×D4C23semidirect
328. C8×D4C23semidirect
329. C8×D4C23semidirect
330. #433C23semidirect
331. #433C23semidirect
332. #433C23semidirect
333. #433C23semidirect
334. #433C23semidirect
337. #432C23semidirect
338. #432C23semidirect
341. #431C23semidirect
342. #431C23semidirect
343. #431C23semidirect
344. #431C23semidirect
348. #424C23semidirect
349. #424C23semidirect
350. #424C23semidirect
353. #423C23semidirect
359. C2×C4⋊C8C23semidirect
360. C2×C4⋊C8C23semidirect
361. C2×C4⋊C8C23semidirect
365. #408C23semidirect
366. #408C23semidirect
367. #408C23semidirect
368. #408C23semidirect
373. #407C23semidirect
382. C2×C22⋊C8C23semidirect
383. C2×C22⋊C8C23semidirect
384. C2×C22⋊C8C23semidirect
388. #405C23semidirect
389. #405C23semidirect
390. #405C23semidirect
391. #405C23semidirect
393. C4×M16C23semidirect
394. C2×#97C23semidirect
403. C2×C4×C8C23semidirect
404. C2×C4×C8C23semidirect
731. C2×D4#131semidirect
830. C2×C8H(5,𝔽2)semidirect
908. C23C2×#131semidirect
931. D4C2×#131semidirect
968. C2×C4C2×#131semidirect

Maximal subgroups

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

subgroupindex
#627732
#603122
#603112
#603102
#603092
#603062
#603052
#603042
C8×H(5,𝔽2)2
#602712
#602652
#602392
#602332
#602302
#602152
#602042
D4×#1312
C2×#29292
C22×C8×D42