Finite Group Databasebeta

← #10574369

Subgroups — #10574369

Order 512.

6449 conjugacy classes of subgroups.

The subgroup lattice has 1157 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62815C211yesmaximal, characteristic
2#60275C218yesmaximal, complemented
3#60275C214yesmaximal, complemented
4#60274C214yesmaximal, complemented
5#60273C214yesmaximal, complemented
6#60272C218yesmaximal, complemented
7#60271C214yesmaximal, complemented
8#60267C218yesmaximal, complemented
9#60266C214yesmaximal, complemented
10#60265C214yesmaximal, complemented
11#60192C211yesmaximal, characteristic, complemented
12C2×#2962C211yesmaximal, characteristic, complemented
13#60144C211yesmaximal, characteristic, complemented
14#60142C212yesmaximal, complemented
15#60140C212yesmaximal, complemented
16C2×#2935C211yesmaximal, characteristic, complemented
17#60126C212yesmaximal, complemented
18#60123C211yesmaximal, characteristic, complemented
19#60100C212yesmaximal, complemented
20C2×#2906C211yesmaximal, characteristic, complemented
21C2×#568C2212yes—
22C22×#131C2212yes—
23C22×#131C2212yes—
24#3512C414yes—
25#3511C412yes—
26#3511C412yes—
27#3510C414yes—
28#3509C412yes—
29#3508C412yes—
30#3507C412yes—
31#3507C412yes—
32#3506C412yes—
33#3506C412yes—
34#3505C414yes—
35#3505C414yes—
36#3480C2214yes—
37#3480C2214yes—
38#3475C2214yes—
39#3475C2214yes—
40#3455C2214yes—
41#3449C2212yes—
42#3444C2214yes—
43C2×#533C2211yescharacteristic
44C2×#532C2211yescharacteristic
45#3428C2212yes—
46C2×C4×#41C2211yescharacteristic
47#2995C22116yescomplemented
48#2995C22116yescomplemented
49#2995C22116yescomplemented
50#2994C2218yescomplemented
51#2994C2218yescomplemented
52#2994C22116yescomplemented
53#2994C22116yescomplemented
54#2993C2218yescomplemented
55#2993C2218yescomplemented
56#2993C22116yescomplemented
57#2993C22116yescomplemented
58#2992C22116yescomplemented
59#2992C22116yescomplemented
60#2992C22116yescomplemented
61#2991C2218yescomplemented
62#2990C22116yescomplemented
63#2990C2218yescomplemented
64#2989C2218yescomplemented
65#2989C22116yescomplemented
66#2988C2218yescomplemented
67Q8×M16C2214yescomplemented
68Q8×M16C2214yescomplemented
69#2962C2212yescomplemented
70#2962C2212yescomplemented
71#2962C2214yescomplemented
72#2962C2212yescomplemented
73#2962C2214yescomplemented
74#2962C2212yescomplemented
75#2962C2214yescomplemented
76#2962C2214yescomplemented
77#2961C2214yescomplemented
78#2960C2214yescomplemented
79C2×#446C2212yescomplemented
80C2×#446C2214yescomplemented
81C2×C8×Q8C2212yescomplemented
82#2935C2212yes—
83#2935C2214yes—
84#2935C2212yes—
85#2935C2214yes—
86#2935C2214yes—
87#2935C2212yescomplemented
88#2935C2218yescomplemented
89#2935C2212yescomplemented
90#2935C2214yescomplemented
91#2935C2218yescomplemented
92D4×M16C2214yescomplemented
93D4×M16C2214yescomplemented
94#2933C2218yes—
95#2933C2218yes—
96#2932C2218yescomplemented
97#2932C2214yescomplemented
98#2931C2218yescomplemented
99#2931C2214yescomplemented
100#2930C2218yes—
101#2930C2218yescomplemented
102#2930C2218yescomplemented
103#2929C2218yes—
104#2929C2218yescomplemented
105#2929C2218yescomplemented
106C2×#436C2212yescomplemented
107C2×#435C2214yescomplemented
108C2×C8×D4C2212yescomplemented
109#2925C2218yescomplemented
110#2925C2218yescomplemented
111#2924C2218yescomplemented
112#2924C2218yescomplemented
113#2923C2214yes—
114#2923C2214yescomplemented
115#2923C2218yescomplemented
116#2922C2214yes—
117#2922C2214yescomplemented
118#2922C2218yescomplemented
119#2921C2214yescomplemented
120#2920C2214yescomplemented
121#2906C2212yes—
122#2906C2214yes—
123#2906C2212yes—
124#2906C2218yescomplemented
125#2906C2218yescomplemented
126#2906C2212yescomplemented
127#2906C2218yescomplemented
128#2906C2212yescomplemented
129#2906C2214yescomplemented
130#2906C2218yescomplemented
131#2905C2212yes—
132#2905C2211yescharacteristic
133#2905C2211yescharacteristic
134#2905C2218yescomplemented
135C2×#424C2212yes—
136C2×#424C2212yes—
137C2×#424C2214yescomplemented
138C2×#424C2218yescomplemented
139C2×#423C2211yescharacteristic
140C2×#423C2212yescomplemented
141C22×C4⋊C8C2211yescharacteristic
142C22×C4⋊C8C2212yescomplemented
143#2879C2211yescharacteristic
144#2879C2211yescharacteristic
145#2879C2212yes—
146C2×#408C2212yes—
147#2873C2212yes—
148C2×#405C2212yes—
149C2×C4×M16C2211yescharacteristic
150C2×C4×M16C2211yescharacteristic
151C22×#41C2312yes—
152C22×#41C2311yescharacteristic
153#568—48no—
154C2×#131—48no—
155C2×#131—48no—
156C2×#131C2314yes—
157C2×#131C2314yes—
158C2×#131C2314yes—
159C2×#131C2318yes—
160C2×#131C2314yes—
161C2×#131C2314yes—
162C2×#131C2314yes—
163C2×#131C2318yes—
164C2×#131C2314yes—
165C2×#131C2314yes—
166C22×M16C2311yescharacteristic
167C22×M16C2311yescharacteristic
168C22×M16C2311yescharacteristic
169C22×M16C2311yescharacteristic
170C22×M16C2312yes—
171C22×M16C2314yes—
172C22×M16C2318yes—
173C22×M16C2314yes—
174C23×C8C2312yes—
175C23×C8C2314yes—
176C23×C8C2314yes—
177#559C2×C418yes—
178#559C2×C418yes—
179#559C2×C414yes—
180#559C2×C414yes—
181#557C2×C414yes—
182#557C2×C414yes—
183#556C2×C414yes—
184#556C2×C414yes—
185#556C2×C414yes—
186#556C2×C414yes—
187#556C2×C418yes—
188#556C2×C418yes—
189#555C2×C414yes—
190#555C2×C414yes—
191#554C2×C414yes—
192#554C2×C414yes—
193#553C2×C418yes—
194#553C2×C418yes—
195#553C2×C418yes—
196#553C2×C418yes—
197#553C2×C4116yes—
198#553C2×C4116yes—
199#552C2×C418yes—
200#552C2×C418yes—
201#552C2×C418yes—
202#552C2×C418yes—
203#551C2×C4116yes—
204#551C2×C4116yes—
205#550C2×C414yes—
206#550C2×C414yes—
207#548C2×C418yes—
208#548C2×C418yes—
209#547C2×C414yes—
210#547C2×C414yes—
211#546C2×C418yes—
212#546C2×C418yes—
213#542C2×C418yes—
214#542C2×C418yes—
215#541C2×C418yes—
216#540C2×C418yes—
217#539C2×C418yes—
218#539C2×C418yes—
219#538C2×C418yes—
220#538C2×C418yes—
221#537C2×C414yes—
222#537C2×C414yes—
223#536C2×C414yes—
224#536C2×C414yes—
225#535C2×C414yes—
226#535C2×C414yes—
227#534C2×C418yes—
228#533C2×C412yes—
229#533C2×C412yes—
230#533C2×C412yes—
231#533C2×C412yes—
232#533C2×C414yes—
233#533C2×C414yes—
234#533C2312yes—
235#533C2312yes—
236#533C2312yes—
237#533C2312yes—
238#532C2×C412yes—
239#532C2×C412yes—
240#532C2×C412yes—
241#532C2×C412yes—
242#532C2×C414yes—
243#532C2×C414yes—
244#532C2312yes—
245#532C2312yes—
246#532C2312yes—
247#532C2312yes—
248#532C2318yes—
249C2×C4⋊Q8C2×C411yescharacteristic
250C2×C4⋊Q8C2×C411yescharacteristic
251C2×C4⋊Q8C2×C411yescharacteristic
252C2×#127C2×C411yescharacteristic
253#529C2×C418yes—
254#529C2×C418yes—
255#529C2×C418yes—
256#529C2×C418yes—
257#529C2318yes—
258#529C2318yes—
259#529C23116yes—
260#529C23116yes—
261C2×#125C2×C412yes—
262C2×#124C2×C412yes—
263#525C2×C418yes—
264#525C2×C418yes—
265#525C2318yes—
266#525C2318yes—
267C2×C22⋊Q8C2×C412yes—
268C2×C22⋊Q8C2×C412yes—
269C2×#121C2×C412yes—
270C2×#121C2×C412yes—
271#520C2×C414yes—
272#520C2×C414yes—
273#520C2×C414yes—
274#520C2×C414yes—
275#519C2×C414yes—
276#518C2×C418yes—
277#518C2×C414yes—
278C4×#41C2×C412yes—
279C4×#41C2×C412yes—
280C4×#41C2×C412yes—
281C4×#41C2×C412yes—
282C4×#41C2318yes—
283C4×#41C2318yes—
284C4×#41C2312yes—
285C4×#41C2312yes—
286C4×#41C2312yes—
287C4×#41C2312yes—
288C4×#41C2318yes—
289C4×#41C2318yes—
290C2×C4×Q8C2×C411yescharacteristic
291C2×C4×Q8C2×C411yescharacteristic
292C2×C4×Q8C2312yes—
293C2×C4×Q8C2312yes—
294C2×C4×D4C2×C412yes—
295C2×C4×D4C2×C412yes—
296C2×C4×D4C2×C411yescharacteristic
297C2×C4×D4C2×C411yescharacteristic
298C2×C4×D4C2312yes—
299C2×C4×D4C2312yes—
300C2×#117C2312yes—
301C2×#117C2311yescharacteristic
302C2×#117C2312yes—
303C2×#117C2318yes—
304C22×C42C2311yescharacteristic
305C22×C42C2312yes—
306#446C2314yes—
307#446C2318yes—
308#446C2318yes—
309#446C2314yes—
310#446C2318yes—
311#446C2318yes—
312#446C2318yes—
313#446C2318yes—
314#446C2318yes—
315#446C23116yes—
316#446C23116yes—
317C8×Q8C2314yes—
318C8×Q8C2314yes—
319C8×Q8C2318yes—
320C8×Q8C2318yes—
321C8×Q8C2318yes—
322#436C2314yes—
323#436C2314yes—
324#436C2318yes—
325#436C23116yes—
326#436C23116yes—
327#436C23116yes—
328#436C23116yes—
329#436C2318yes—
330#436C2318yes—
331#435C2318yes—
332#435C2318yes—
333#435C2318yes—
334#435C2318yes—
335#435C23116yes—
336#435C23116yes—
337#435C23116yes—
338#435C23116yes—
339#435C23116yes—
340#435C23116yes—
341#435C23116yes—
342#435C23116yes—
343#435C23116yes—
344#435C23116yes—
345C8×D4C2314yes—
346C8×D4C2314yes—
347C8×D4C2318yes—
348C8×D4C23116yes—
349C8×D4C23116yes—
350C8×D4C23116yes—
351C8×D4C23116yes—
352C8×D4C2318yes—
353C8×D4C2318yes—
354#433C2318yes—
355#433C2318yes—
356#433C2318yes—
357#433C2318yes—
358#433C23116yes—
359#433C23116yes—
360#433C23116yes—
361#433C23116yes—
362#432C2318yes—
363#432C2318yes—
364#432C23116yes—
365#432C23116yes—
366#431C2318yes—
367#431C2318yes—
368#431C23116yes—
369#431C23116yes—
370#424C2314yes—
371#424C2314yes—
372#424C2314yes—
373#424C2314yes—
374#424C2314yes—
375#424C2314yes—
376#424C2314yes—
377#424C2314yes—
378#424C2314yes—
379#424C2318yes—
380#424C2318yes—
381#424C2318yes—
382#424C2318yes—
383#424C2318yes—
384#424C23116yes—
385#424C23116yes—
386#424C2314yes—
387#424C2318yes—
388#424C2314yes—
389#424C2314yes—
390#424C23116yes—
391#424C23116yes—
392#423C2312yes—
393#423C2312yes—
394#423C2312yes—
395#423C2312yes—
396#423C2318yes—
397#423C2314yes—
398#423C2314yes—
399#423C2314yes—
400#423C2318yes—
401#423C2314yes—
402#423C23116yes—
403#423C23116yes—
404C2×C4⋊C8C2311yescharacteristic
405C2×C4⋊C8C2311yescharacteristic
406C2×C4⋊C8C2312yes—
407C2×C4⋊C8C2311yescharacteristic
408C2×C4⋊C8C2312yes—
409C2×C4⋊C8C2311yescharacteristic
410C2×C4⋊C8C2311yescharacteristic
411C2×C4⋊C8C2312yes—
412C2×C4⋊C8C2311yescharacteristic
413C2×C4⋊C8C2312yes—
414C2×C4⋊C8C2314yes—
415C2×C4⋊C8C2314yes—
416C2×C4⋊C8C2314yes—
417C2×C4⋊C8C2318yes—
418C2×C4⋊C8C2312yes—
419C2×C4⋊C8C2314yes—
420C2×C4⋊C8C2314yes—
421C2×C4⋊C8C2314yes—
422C2×C4⋊C8C23116yes—
423C2×C4⋊C8C23116yes—
424#408C2314yes—
425#408C2314yes—
426#408C2314yes—
427#408C2314yes—
428#408C2314yes—
429#408C2314yes—
430#408C2314yes—
431#408C2318yes—
432#408C2314yes—
433#408C2318yes—
434#407C2314yes—
435#407C2314yes—
436#407C2318yes—
437C2×C22⋊C8C2314yes—
438C2×C22⋊C8C2314yes—
439#405C2314yes—
440#405C2314yes—
441#405C2314yes—
442#405C2314yes—
443#405C2318yes—
444#405C2318yes—
445C4×M16C2312yes—
446C4×M16C2312yes—
447C4×M16C2312yes—
448C4×M16C2312yes—
449C4×M16C2312yes—
450C4×M16C2312yes—
451C4×M16C2312yes—
452C4×M16C2312yes—
453C4×M16C2318yes—
454C2×#97C2312yes—
455C2×#97C2312yes—
456C2×#97C2314yes—
457C2×C4×C8C2312yes—
458C2×C4×C8C2312yes—
459C2×C4×C8C2314yes—
460C2×#41—24no—
461C2×#41—28no—
462C2×#41—28no—
463C2×#41—24no—
464C2×#41C22×C412yes—
465C2×#41C22×C412yes—
466C2×#41C22×C414yes—
467C2×#41C22×C414yes—
468C2×#41C22×C418yes—
469C2×#41C22×C418yes—
470C2×#41C2412yes—
471C2×#41C2414yes—
472C2×#41C2412yes—
473C2×#41C2414yes—
474C22×Q8C22×C411yescharacteristic
475C22×Q8C22×C412yes—
476C22×Q8C22×C412yes—
477C22×Q8C22×C412yes—
478C22×D4C22×C412yes—
479C22×D4C22×C411yescharacteristic
480C22×D4C22×C414yes—
481C22×D4C22×C412yes—
482C22×D4C22×C412yes—
483C22×D4C22×C412yes—
484C23×C4C22×C411yescharacteristic
485C23×C4C22×C412yes—
486C23×C4C22×C411yescharacteristic
487C23×C4C22×C412yes—
488C23×C4C2414yes—
489C23×C4C2412yes—
490C23×C4C2411yescharacteristic
491#131—48no—
492#131—48no—
493#131—48no—
494#131—48no—
495#131—48no—
496#131—48no—
497#131—48no—
498#131—48no—
499#131—416no—
500#131—416no—
501C2×M16—24no—
502C2×M16—28no—
503C2×M16—24no—
504C2×M16—24no—
505C2×M16—24no—
506C2×M16—48no—
507C2×M16—48no—
508C2×M16—416no—
509C2×M16C2412yes—
510C2×M16C2414yes—
511C2×M16C2412yes—
512C2×M16C2412yes—
513C2×M16C2412yes—
514C2×M16C2414yes—
515C2×M16C2412yes—
516C2×M16C2412yes—
517C2×M16C2412yes—
518C2×M16C2412yes—
519C2×M16C2418yes—
520C2×M16C2418yes—
521C2×M16C24116yes—
522C2×M16C2418yes—
523C2×M16C2418yes—
524C22×C8—28no—
525C22×C8—48no—
526C22×C8—48no—
527C22×C8C2412yes—
528C22×C8C2412yes—
529C22×C8C2412yes—
530C22×C8C2412yes—
531C22×C8C2412yes—
532C22×C8C2414yes—
533C22×C8C2412yes—
534C22×C8C2412yes—
535C22×C8C2412yes—
536C22×C8C2412yes—
537C22×C8C2412yes—
538C22×C8C2418yes—
539C22×C8C2418yes—
540C22×C8C2418yes—
541C22×C8C2418yes—
542C22×C8C24116yes—
543C4⋊Q8C22×C412yes—
544C4⋊Q8C22×C412yes—
545C4⋊Q8C22×C412yes—
546C4⋊Q8C22×C412yes—
547C4⋊Q8C22×C412yes—
548C4⋊Q8C22×C412yes—
549C4⋊Q8C22×C412yes—
550C4⋊Q8C22×C412yes—
551C4⋊Q8C22×C412yes—
552C4⋊Q8C22×C412yes—
553C4⋊Q8C22×C412yes—
554C4⋊Q8C22×C412yes—
555C4⋊Q8C22×C418yes—
556#127C22×C412yes—
557#127C22×C412yes—
558#127C22×C412yes—
559#127C22×C412yes—
560#127C22×C418yes—
561#126C22×C4116yes—
562#126C22×C4116yes—
563#126C22×C4116yes—
564#126C22×C4116yes—
565#126C22×C4116yes—
566#126C22×C4116yes—
567#125C22×C414yes—
568#125C22×C414yes—
569#125C22×C414yes—
570#125C22×C414yes—
571#125C22×C418yes—
572#125C22×C418yes—
573#125C22×C4116yes—
574#125C22×C4116yes—
575#124C22×C414yes—
576#124C22×C414yes—
577#124C22×C414yes—
578#124C22×C414yes—
579#124C22×C418yes—
580#124C22×C418yes—
581#124C22×C4116yes—
582#124C22×C4116yes—
583#124C22×C418yes—
584#124C22×C418yes—
585#123C22×C4116yes—
586#123C22×C4116yes—
587#123C22×C4116yes—
588#123C22×C4116yes—
589#123C22×C4116yes—
590#123C22×C4116yes—
591#123C22×C4116yes—
592#123C22×C4116yes—
593C22⋊Q8C22×C414yes—
594C22⋊Q8C22×C414yes—
595C22⋊Q8C22×C414yes—
596C22⋊Q8C22×C414yes—
597C22⋊Q8C22×C414yes—
598C22⋊Q8C22×C414yes—
599C22⋊Q8C22×C414yes—
600C22⋊Q8C22×C414yes—
601C22⋊Q8C22×C418yes—
602C22⋊Q8C22×C418yes—
603C22⋊Q8C22×C418yes—
604C22⋊Q8C22×C418yes—
605C22⋊Q8C22×C418yes—
606C22⋊Q8C22×C418yes—
607C22⋊Q8C22×C4116yes—
608C22⋊Q8C22×C4116yes—
609#121C22×C414yes—
610#121C22×C414yes—
611#121C22×C414yes—
612#121C22×C414yes—
613#121C22×C414yes—
614#121C22×C414yes—
615#121C22×C414yes—
616#121C22×C414yes—
617#121C22×C418yes—
618#121C22×C418yes—
619#121C22×C418yes—
620#121C22×C418yes—
621#121C22×C418yes—
622#121C22×C418yes—
623#121C22×C4116yes—
624#121C22×C4116yes—
625#121C22×C4116yes—
626#121C22×C4116yes—
627#120C22×C4116yes—
628#120C22×C4116yes—
629C4×Q8C22×C412yes—
630C4×Q8C22×C412yes—
631C4×Q8C22×C412yes—
632C4×Q8C22×C412yes—
633C4×Q8C22×C412yes—
634C4×Q8C22×C412yes—
635C4×Q8C22×C412yes—
636C4×Q8C22×C412yes—
637C4×Q8C22×C414yes—
638C4×Q8C22×C414yes—
639C4×Q8C22×C414yes—
640C4×Q8C22×C414yes—
641C4×Q8C22×C418yes—
642C4×Q8C22×C418yes—
643C4×Q8C22×C418yes—
644C4×Q8C22×C418yes—
645C4×Q8C22×C418yes—
646C4×Q8C22×C418yes—
647C4×Q8C2414yes—
648C4×Q8C2414yes—
649C4×Q8C2414yes—
650C4×Q8C2414yes—
651C4×D4C22×C414yes—
652C4×D4C22×C414yes—
653C4×D4C22×C412yes—
654C4×D4C22×C412yes—
655C4×D4C22×C414yes—
656C4×D4C22×C414yes—
657C4×D4C22×C412yes—
658C4×D4C22×C412yes—
659C4×D4C22×C414yes—
660C4×D4C22×C414yes—
661C4×D4C22×C414yes—
662C4×D4C22×C414yes—
663C4×D4C22×C412yes—
664C4×D4C22×C412yes—
665C4×D4C22×C412yes—
666C4×D4C22×C412yes—
667C4×D4C22×C414yes—
668C4×D4C22×C414yes—
669C4×D4C22×C414yes—
670C4×D4C22×C414yes—
671C4×D4C22×C4116yes—
672C4×D4C22×C4116yes—
673C4×D4C22×C418yes—
674C4×D4C22×C418yes—
675C4×D4C22×C4116yes—
676C4×D4C22×C4116yes—
677C4×D4C22×C418yes—
678C4×D4C22×C418yes—
679C4×D4C22×C4116yes—
680C4×D4C22×C4116yes—
681C4×D4C22×C418yes—
682C4×D4C22×C418yes—
683C4×D4C2414yes—
684C4×D4C2414yes—
685C4×D4C2414yes—
686C4×D4C2414yes—
687C4×D4C24116yes—
688C4×D4C24116yes—
689#117C22×C412yes—
690#117C22×C412yes—
691#117C22×C414yes—
692#117C22×C414yes—
693#117C22×C414yes—
694#117C22×C4116yes—
695#117C22×C414yes—
696#117C22×C418yes—
697#117C22×C418yes—
698#117C22×C418yes—
699#117C22×C418yes—
700#117C22×C4116yes—
701#117C22×C4116yes—
702#117C2412yes—
703#117C2414yes—
704#117C2412yes—
705#117C2414yes—
706#117C2414yes—
707#117C2414yes—
708#117C24116yes—
709C2×C4⋊C4C22×C411yescharacteristic
710C2×C4⋊C4C22×C411yescharacteristic
711C2×C4⋊C4C22×C412yes—
712C2×C4⋊C4C22×C412yes—
713C2×C4⋊C4C22×C412yes—
714C2×C4⋊C4C22×C412yes—
715C2×C4⋊C4C22×C418yes—
716C2×C4⋊C4C22×C418yes—
717C2×C4⋊C4C22×C412yes—
718C2×C4⋊C4C22×C412yes—
719C2×C4⋊C4C22×C414yes—
720C2×C4⋊C4C22×C414yes—
721C2×C4⋊C4C22×C412yes—
722C2×C4⋊C4C22×C412yes—
723C2×C22⋊C4C22×C412yes—
724C2×C22⋊C4C22×C412yes—
725C2×C22⋊C4C22×C412yes—
726C2×C22⋊C4C22×C414yes—
727C2×C22⋊C4C22×C4116yes—
728C2×C22⋊C4C22×C414yes—
729C2×C22⋊C4C22×C414yes—
730C2×C42C22×C412yes—
731C2×C42C22×C412yes—
732C2×C42C22×C411yescharacteristic
733C2×C42C22×C411yescharacteristic
734C2×C42C22×C411yescharacteristic
735C2×C42C22×C411yescharacteristic
736C2×C42C22×C414yes—
737C2×C42C22×C411yescharacteristic
738C2×C42C22×C411yescharacteristic
739C2×C42C22×C414yes—
740C2×C42C2412yes—
741C2×C42C2411yescharacteristic
742C2×C42C2414yes—
743C2×C42C24116yes—
744C2×C42C2411yescharacteristic
745C2×C42C2411yescharacteristic
746C2×C42C2411yescharacteristic
747C2×C42C2411yescharacteristic
748C2×C42C2414yes—
749C2×C42C2414yes—
750C2×C42C2411yescharacteristic
751C4⋊C8C2411yescharacteristic
752C4⋊C8C2412yes—
753C4⋊C8C2411yescharacteristic
754C4⋊C8C2418yes—
755C4⋊C8C2411yescharacteristic
756C4⋊C8C2414yes—
757C4⋊C8C2412yes—
758C4⋊C8C2414yes—
759C4⋊C8C2411yescharacteristic
760C4⋊C8C2418yes—
761C4⋊C8C2418yes—
762C4⋊C8C2412yes—
763C4⋊C8C2418yes—
764C4⋊C8C2412yes—
765C4⋊C8C2412yes—
766C4⋊C8C2418yes—
767C4⋊C8C2412yes—
768C4⋊C8C2418yes—
769C4⋊C8C2418yes—
770C4⋊C8C2418yes—
771C4⋊C8C2418yes—
772C4⋊C8C2414yes—
773C4⋊C8C24116yes—
774C4⋊C8C24116yes—
775C4⋊C8C2414yes—
776C4⋊C8C2418yes—
777C4⋊C8C2418yes—
778C4⋊C8C2418yes—
779C22⋊C8C2418yes—
780C22⋊C8C2418yes—
781C22⋊C8C2418yes—
782C22⋊C8C2418yes—
783C22⋊C8C2418yes—
784C22⋊C8C2418yes—
785C22⋊C8C2418yes—
786C22⋊C8C2418yes—
787C22⋊C8C24116yes—
788C22⋊C8C24116yes—
789#97C2414yes—
790#97C2414yes—
791#97C2414yes—
792#97C2414yes—
793#97C2418yes—
794#97C2418yes—
795#97C24116yes—
796C4×C8C2414yes—
797C4×C8C2414yes—
798C4×C8C2414yes—
799C4×C8C2414yes—
800C4×C8C2418yes—
801C4×C8C2418yes—
802C4×C8C24116yes—
803C24C23×C414yes—
804C24C23×C412yes—
805C24C23×C411yescharacteristic
806#41—28no—
807#41—216no—
808#41—28no—
809#41—216no—
810#41—28no—
811#41—24no—
812#41—24no—
813#41—28no—
814#41—24no—
815#41—28no—
816#41—24no—
817#41—28no—
818#41—416no—
819#41—88no—
820C2×Q8—28no—
821C2×Q8—24no—
822C2×Q8—44no—
823C2×Q8—82no—
824C2×Q8C23×C412yes—
825C2×Q8C23×C414yes—
826C2×Q8C23×C412yes—
827C2×Q8C23×C414yes—
828C2×Q8C23×C414yes—
829C2×Q8C23×C414yes—
830C2×Q8C23×C414yes—
831C2×Q8C23×C414yes—
832C2×D4—28no—
833C2×D4—216no—
834C2×D4—28no—
835C2×D4—24no—
836C2×D4—44no—
837C2×D4—82no—
838C2×D4C23×C414yes—
839C2×D4C23×C418yes—
840C2×D4C23×C414yes—
841C2×D4C23×C418yes—
842C2×D4C23×C412yes—
843C2×D4C23×C414yes—
844C2×D4C23×C412yes—
845C2×D4C23×C414yes—
846C2×D4C23×C414yes—
847C2×D4C23×C414yes—
848C2×D4C23×C4116yes—
849C2×D4C23×C4116yes—
850C2×D4C23×C414yes—
851C2×D4C23×C414yes—
852C22×C4—24no—
853C22×C4—28no—
854C22×C4—28no—
855C22×C4—24no—
856C22×C4—42no—
857C22×C4—44no—
858C22×C4—81no—
859C22×C4—82no—
860C22×C4C23×C411yescharacteristic
861C22×C4C23×C412yes—
862C22×C4C23×C414yes—
863C22×C4C23×C411yescharacteristic
864C22×C4C23×C411yescharacteristic
865C22×C4C23×C414yes—
866C22×C4C23×C414yes—
867C22×C4C23×C418yes—
868C22×C4C23×C411yescharacteristic
869C22×C4C23×C411yescharacteristic
870C22×C4C23×C411yescharacteristic
871C22×C4C23×C412yes—
872C22×C4C23×C412yes—
873C22×C4C23×C411yescharacteristic
874C22×C4C23×C411yescharacteristic
875C22×C4C23×C411yescharacteristic
876C22×C4C23×C411yescharacteristic
877C22×C4C23×C411yescharacteristic
878C22×C4C23×C411yescharacteristic
879C22×C4C23×C414yes—
880C22×C4C23×C414yes—
881C22×C4C23×C414yes—
882C22×C4C23×C414yes—
883C22×C4C23×C414yes—
884C22×C4C23×C4116yes—
885C22×C4C23×C4116yes—
886C22×C4C23×C411yescharacteristic
887C22×C4C23×C411yescharacteristic
888C22×C4C23×C411yescharacteristic
889C22×C4H(5,𝔽2)14yes—
890C22×C42−1+414yes—
891C22×C4C2518yes—
892C22×C4C2514yes—
893C22×C4C2511yescharacteristic
894C22×C4C2511yescharacteristic
895C22×C4C2511yescharacteristic
896M16—24no—
897M16—28no—
898M16—24no—
899M16—24no—
900M16—24no—
901M16—28no—
902M16—24no—
903M16—24no—
904M16—24no—
905M16—24no—
906M16—48no—
907M16—48no—
908M16—48no—
909M16—48no—
910M16—416no—
911C2×C8—24no—
912C2×C8—24no—
913C2×C8—24no—
914C2×C8—24no—
915C2×C8—24no—
916C2×C8—24no—
917C2×C8—24no—
918C2×C8—28no—
919C2×C8—24no—
920C2×C8—24no—
921C2×C8—24no—
922C2×C8—48no—
923C2×C8—48no—
924C2×C8—48no—
925C2×C8—48no—
926C2×C8—416no—
927C2×C8C2514yes—
928C2×C8C2514yes—
929C2×C8C2512yes—
930C2×C8C2512yes—
931C2×C8C2514yes—
932C2×C8C2514yes—
933C2×C8C2518yes—
934C2×C8C2512yes—
935C2×C8C2512yes—
936C4⋊C4C23×C412yes—
937C4⋊C4C23×C412yes—
938C4⋊C4C23×C414yes—
939C4⋊C4C23×C414yes—
940C4⋊C4C23×C414yes—
941C4⋊C4C23×C414yes—
942C4⋊C4C23×C418yes—
943C4⋊C4C23×C418yes—
944C4⋊C4C23×C414yes—
945C4⋊C4C23×C414yes—
946C4⋊C4C23×C412yes—
947C4⋊C4C23×C412yes—
948C4⋊C4C23×C414yes—
949C4⋊C4C23×C414yes—
950C4⋊C4C23×C414yes—
951C4⋊C4C23×C414yes—
952C4⋊C4C23×C4116yes—
953C4⋊C4C23×C4116yes—
954C4⋊C4C23×C414yes—
955C4⋊C4C23×C414yes—
956C4⋊C4C23×C414yes—
957C4⋊C4C23×C414yes—
958C4⋊C4C23×C418yes—
959C4⋊C4C23×C418yes—
960C4⋊C4C23×C414yes—
961C4⋊C4C23×C414yes—
962C4⋊C4C23×C4116yes—
963C4⋊C4C23×C4116yes—
964C22⋊C4C23×C414yes—
965C22⋊C4C23×C418yes—
966C22⋊C4C23×C418yes—
967C22⋊C4C23×C418yes—
968C22⋊C4C23×C414yes—
969C22⋊C4C23×C418yes—
970C22⋊C4C23×C414yes—
971C22⋊C4C23×C414yes—
972C22⋊C4C23×C4116yes—
973C22⋊C4C23×C4116yes—
974C22⋊C4C23×C414yes—
975C22⋊C4C23×C414yes—
976C22⋊C4C23×C418yes—
977C22⋊C4C23×C418yes—
978C22⋊C4C23×C4116yes—
979C22⋊C4C23×C4116yes—
980C22⋊C4C23×C4116yes—
981C22⋊C4C23×C4116yes—
982C42C23×C411yescharacteristic
983C42C23×C411yescharacteristic
984C42C23×C414yes—
985C42C23×C414yes—
986C42C23×C414yes—
987C42C23×C411yescharacteristic
988C42C23×C411yescharacteristic
989C42C23×C411yescharacteristic
990C42C23×C411yescharacteristic
991C42C23×C411yescharacteristic
992C42C23×C411yescharacteristic
993C42C23×C414yes—
994C42C23×C414yes—
995C42C23×C411yescharacteristic
996C42C23×C411yescharacteristic
997C42C23×C411yescharacteristic
998C42C23×C411yescharacteristic
999C42C23×C4116yes—
1000C42C23×C4116yes—
1001C42C23×C418yes—
1002C42C2511yescharacteristic
1003C42C2511yescharacteristic
1004C42C2511yescharacteristic
1005C42C2518yes—
1006C42C2511yescharacteristic
1007C42C2514yes—
1008C23—24no—
1009C23—28no—
1010C23—41no—
1011C23—42no—
1012C23—41no—
1013C23—42no—
1014C23—44no—
1015C23—44no—
1016C23#52014yes—
1017C23C24×C414yes—
1018C23C24×C418yes—
1019C23C24×C411yescharacteristic
1020C23C24×C411yescharacteristic
1021C23C24×C411yescharacteristic
1022Q8—24no—
1023Q8—28no—
1024Q8—28no—
1025Q8—24no—
1026Q8—28no—
1027Q8—44no—
1028Q8—44no—
1029Q8—44no—
1030D4—28no—
1031D4—216no—
1032D4—28no—
1033D4—216no—
1034D4—24no—
1035D4—28no—
1036D4—24no—
1037D4—28no—
1038D4—28no—
1039D4—44no—
1040D4—44no—
1041D4—44no—
1042D4—416no—
1043D4—416no—
1044C2×C4—28no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—28no—
1048C2×C4—24no—
1049C2×C4—28no—
1050C2×C4—216no—
1051C2×C4—28no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—28no—
1056C2×C4—42no—
1057C2×C4—44no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—42no—
1063C2×C4—44no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—44no—
1070C2×C4—44no—
1071C2×C4—44no—
1072C2×C4—416no—
1073C2×C4—416no—
1074C2×C4#52014yes—
1075C2×C4#52014yes—
1076C2×C4#52014yes—
1077C2×C4C24×C411yescharacteristic
1078C2×C4C24×C414yes—
1079C2×C4C24×C411yescharacteristic
1080C2×C4C24×C414yes—
1081C2×C4C24×C411yescharacteristic
1082C2×C4C24×C414yes—
1083C2×C4C24×C418yes—
1084C2×C4C24×C411yescharacteristic
1085C2×C4C24×C411yescharacteristic
1086C2×C4C24×C418yes—
1087C2×C4C24×C418yes—
1088C2×C4C24×C411yescharacteristic
1089C2×C4C24×C411yescharacteristic
1090C2×C4C24×C411yescharacteristic
1091C2×C4C24×C411yescharacteristic
1092C2×C4C24×C411yescharacteristic
1093C2×C4C24×C411yescharacteristic
1094C2×C4C2×H(5,𝔽2)12yes—
1095C2×C4C2×H(5,𝔽2)12yes—
1096C2×C4C2×H(5,𝔽2)12yes—
1097C2×C4C2×2−1+412yes—
1098C2×C4C2×2−1+412yes—
1099C2×C4C2×2−1+412yes—
1100C2×C4C2611yescharacteristic
1101C8—22no—
1102C8—22no—
1103C8—22no—
1104C8—22no—
1105C8—24no—
1106C8—28no—
1107C8—24no—
1108C8—24no—
1109C8—24no—
1110C22—21no—
1111C22—21no—
1112C22—21no—
1113C22—21no—
1114C22—21no—
1115C22—21no—
1116C22—24no—
1117C22—28no—
1118C22—24no—
1119C22—28no—
1120C22—24no—
1121C22—28no—
1122C22—44no—
1123C22—48no—
1124C22—88no—
1125C22C2×#52012yes—
1126C22C2×#52012yes—
1127C22C2×#52012yes—
1128C22C25×C411yescharacteristic
1129C4—21no—
1130C4—24no—
1131C4—21no—
1132C4—21no—
1133C4—28no—
1134C4—21no—
1135C4—24no—
1136C4—21no—
1137C4—21no—
1138C4—28no—
1139C4—21no—
1140C4—28no—
1141C4—24no—
1142C4C2×#52012yes—
1143C4C2×#52012yes—
1144C4C2×#52012yes—
1145C4#357312yes—
1146C4C22×H(5,𝔽2)11yescharacteristic
1147C4C22×2−1+411yescharacteristic
1148C2—22no—
1149C2—22no—
1150C2—22no—
1151C2—44no—
1152C2—48no—
1153C2C22×#52011yescharacteristic
1154C2C2×#357311yescharacteristic
1155C2#6307611yescharacteristic
subgroupG/H
center, Frattini, cosocleC2×C4C26
commutator, socleC22C25×C4
prime radical#62815C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60275C2semidirect
3. #60275C2semidirect
4. #60274C2semidirect
5. #60273C2semidirect
6. #60272C2semidirect
7. #60271C2semidirect
8. #60267C2semidirect
9. #60266C2semidirect
10. #60265C2semidirect
11. #60192C2semidirect
12. C2×#2962C2semidirect
13. #60144C2semidirect
14. #60142C2semidirect
15. #60140C2semidirect
16. C2×#2935C2semidirect
17. #60126C2semidirect
18. #60123C2semidirect
19. #60100C2semidirect
20. C2×#2906C2semidirect
47. #2995C22semidirect
48. #2995C22semidirect
49. #2995C22semidirect
50. #2994C22semidirect
51. #2994C22semidirect
52. #2994C22semidirect
53. #2994C22semidirect
54. #2993C22semidirect
55. #2993C22semidirect
56. #2993C22semidirect
57. #2993C22semidirect
58. #2992C22semidirect
59. #2992C22semidirect
60. #2992C22semidirect
61. #2991C22semidirect
62. #2990C22semidirect
63. #2990C22semidirect
64. #2989C22semidirect
65. #2989C22semidirect
66. #2988C22semidirect
67. Q8×M16C22semidirect
68. Q8×M16C22semidirect
69. #2962C22semidirect
70. #2962C22semidirect
71. #2962C22semidirect
72. #2962C22semidirect
73. #2962C22semidirect
74. #2962C22semidirect
75. #2962C22semidirect
76. #2962C22semidirect
77. #2961C22semidirect
78. #2960C22semidirect
79. C2×#446C22semidirect
80. C2×#446C22semidirect
81. C2×C8×Q8C22semidirect
87. #2935C22semidirect
88. #2935C22semidirect
89. #2935C22semidirect
90. #2935C22semidirect
91. #2935C22semidirect
92. D4×M16C22semidirect
93. D4×M16C22semidirect
96. #2932C22semidirect
97. #2932C22semidirect
98. #2931C22semidirect
99. #2931C22semidirect
101. #2930C22semidirect
102. #2930C22semidirect
104. #2929C22semidirect
105. #2929C22semidirect
106. C2×#436C22semidirect
107. C2×#435C22semidirect
108. C2×C8×D4C22semidirect
109. #2925C22semidirect
110. #2925C22semidirect
111. #2924C22semidirect
112. #2924C22semidirect
114. #2923C22semidirect
115. #2923C22semidirect
117. #2922C22semidirect
118. #2922C22semidirect
119. #2921C22semidirect
120. #2920C22semidirect
124. #2906C22semidirect
125. #2906C22semidirect
126. #2906C22semidirect
127. #2906C22semidirect
128. #2906C22semidirect
129. #2906C22semidirect
130. #2906C22semidirect
134. #2905C22semidirect
137. C2×#424C22semidirect
138. C2×#424C22semidirect
140. C2×#423C22semidirect
142. C22×C4⋊C8C22semidirect

Maximal subgroups

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

subgroupindex
#628152
#602752
#602742
#602732
#602722
#602712
#602672
#602662
#602652
#601922
C2×#29622
#601442
#601422
#601402
C2×#29352
#601262
#601232
#601002
C2×#29062