Finite Group Databasebeta

← #10574607

Subgroups — #10574607

Order 512.

6148 conjugacy classes of subgroups.

The subgroup lattice has 1282 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62781C211yesmaximal, characteristic
2#60342C214yesmaximal, complemented
3#60340C214yesmaximal, complemented
4#60335C214yesmaximal, complemented
5#60324C214yesmaximal, complemented
6#60322C214yesmaximal, complemented
7#60311C214yesmaximal, complemented
8#60310C214yesmaximal, complemented
9#60309C214yesmaximal, complemented
10#60299C218yesmaximal, complemented
11#60294C212yesmaximal, complemented
12#60290C212yesmaximal, complemented
13#60288C212yesmaximal, complemented
14#60282C211yesmaximal, characteristic, complemented
15#60216C218yesmaximal, complemented
16#60214C212yesmaximal, complemented
17#60211C212yesmaximal, complemented
18C2×#2966C212yesmaximal, complemented
19C2×#2965C211yesmaximal, characteristic, complemented
20#3521C418yes—
21#3515C414yes—
22#3514C414yes—
23#3507C412yes—
24#3505C412yes—
25#3505C412yes—
26#3501C411yescharacteristic
27#3496C411yescharacteristic
28#3493C412yes—
29#3491C412yes—
30#3491C412yes—
31#3485C412yes—
32#3482C2214yes—
33#3481C2214yes—
34#3475C2218yes—
35#3461C2212yes—
36#3459C2212yes—
37#3459C2212yes—
38#3444C2212yes—
39C2×#529C2212yes—
40C2×#529C2212yes—
41C4×H(5,𝔽2)C2212yes—
42C2×C4×#41C2211yescharacteristic
43#2995C2218yescomplemented
44#2995C2218yescomplemented
45#2994C2214yescomplemented
46#2994C2214yescomplemented
47#2994C2218yescomplemented
48#2994C2218yescomplemented
49#2993C2214yescomplemented
50#2993C2214yescomplemented
51#2993C2218yescomplemented
52#2992C2214yescomplemented
53#2992C2214yescomplemented
54#2992C2218yescomplemented
55#2992C2218yescomplemented
56#2990C2214yescomplemented
57#2990C2214yescomplemented
58#2990C2218yescomplemented
59#2990C2218yescomplemented
60#2989C2214yescomplemented
61#2989C2218yescomplemented
62#2988C2214yescomplemented
63#2987C2218yescomplemented
64#2985C2212yescomplemented
65#2985C2212yescomplemented
66#2985C2218yescomplemented
67#2984C2214yescomplemented
68#2983C2212yescomplemented
69#2983C2212yescomplemented
70#2982C2212yescomplemented
71#2981C2212yescomplemented
72#2981C2212yescomplemented
73#2978C2218yescomplemented
74#2977C2218yescomplemented
75#2977C2218yescomplemented
76#2976C2218yescomplemented
77#2976C2218yescomplemented
78#2975C2212yescomplemented
79#2974C2214yescomplemented
80#2974C2218yescomplemented
81#2974C2218yescomplemented
82#2973C2212yes—
83#2973C2212yescomplemented
84#2973C2214yescomplemented
85#2973C2218yescomplemented
86#2972C2212yescomplemented
87#2972C2214yescomplemented
88#2972C2212yescomplemented
89#2971C2214yescomplemented
90#2970C2218yescomplemented
91#2970C2214yescomplemented
92#2970C2218yescomplemented
93#2970C2218yescomplemented
94#2969C2214yescomplemented
95#2969C2214yescomplemented
96#2969C2218yescomplemented
97#2969C2218yescomplemented
98#2968C2218yescomplemented
99#2968C2218yescomplemented
100#2968C2218yescomplemented
101#2968C2218yescomplemented
102#2968C2218yescomplemented
103#2967C2214yescomplemented
104#2967C2214yescomplemented
105#2967C2214yescomplemented
106#2967C2214yescomplemented
107#2967C2218yescomplemented
108#2967C2218yescomplemented
109#2966C2214yescomplemented
110#2966C2214yescomplemented
111#2966C2214yescomplemented
112#2966C2214yescomplemented
113#2966C2214yescomplemented
114#2966C2214yescomplemented
115#2966C2214yescomplemented
116#2966C2214yescomplemented
117#2966C2214yescomplemented
118#2966C2214yescomplemented
119#2966C2218yescomplemented
120#2965C2214yescomplemented
121#2965C2214yescomplemented
122#2965C2214yescomplemented
123#2965C2214yescomplemented
124#2965C2218yescomplemented
125Q8×M16C2214yescomplemented
126#2962C2214yescomplemented
127#2962C2218yescomplemented
128#2961C2218yescomplemented
129C2×#446C2212yescomplemented
130C2×#446C2212yescomplemented
131C2×C8×Q8C2212yescomplemented
132#2935C2214yescomplemented
133D4×M16C2218yescomplemented
134D4×M16C2214yescomplemented
135D4×M16C2218yescomplemented
136#2933C2218yescomplemented
137#2933C2218yescomplemented
138#2933C2218yescomplemented
139#2930C2218yescomplemented
140#2929C2218yescomplemented
141C2×#436C2212yescomplemented
142C2×#436C2212yescomplemented
143C2×#435C2212yes—
144C2×#435C2212yescomplemented
145C2×#435C2214yescomplemented
146C2×#435C2218yescomplemented
147C2×C8×D4C2214yescomplemented
148C2×C8×D4C2212yescomplemented
149#2925C2218yescomplemented
150#2924C2218yescomplemented
151#2924C2218yescomplemented
152#2923C2214yescomplemented
153#2921C2214yescomplemented
154#2920C2212yescomplemented
155C2×#433C2214yescomplemented
156C2×#432C2212yescomplemented
157C2×#432C2212yescomplemented
158C2×#431C2211yescharacteristic, complemented
159C2×#431C2211yescharacteristic, complemented
160C2×#431C2211yescharacteristic, complemented
161#2875C2214yescomplemented
162#2873C2214yescomplemented
163C2×#405C2214yescomplemented
164C2×C4×M16C2211yescharacteristic, complemented
165C2×C4×M16C2211yescharacteristic, complemented
166C22×C4×C8C2211yescharacteristic, complemented
167C2×H(5,𝔽2)C2×C412yes—
168C22×#41C2×C411yescharacteristic
169C2×#131C2318yes—
170C22×M16C2312yes—
171C22×M16C2312yes—
172C22×M16C2314yes—
173C22×M16C2318yes—
174C23×C8C2312yes—
175C23×C8C2314yes—
176#559C2×C414yes—
177#557C2×C414yes—
178#556C2×C418yes—
179#556C2×C418yes—
180#556C2×C414yes—
181#555C2×C418yes—
182#554C2×C418yes—
183#554C2×C414yes—
184#554C2×C414yes—
185#553C2×C418yes—
186#553C2×C418yes—
187#553C2×C418yes—
188#553C2×C414yes—
189#553C2×C414yes—
190#552C2×C418yes—
191#552C2×C418yes—
192#552C2×C418yes—
193#552C2×C418yes—
194#552C2×C418yes—
195#552C2×C418yes—
196#552C2×C414yes—
197#552C2×C414yes—
198#551C2×C418yes—
199#551C2×C418yes—
200#551C2×C418yes—
201#551C2×C418yes—
202#551C2×C418yes—
203#551C2×C418yes—
204D4×Q8C2×C414yes—
205#548C2×C414yes—
206#548C2×C414yes—
207#547C2×C418yes—
208#547C2×C418yes—
209#547C2×C414yes—
210#546C2×C418yes—
211#546C2×C418yes—
212#546C2×C418yes—
213#546C2×C414yes—
214#546C2×C414yes—
215D42C2×C414yes—
216#544C2×C412yes—
217#543C2×C412yes—
218#543C2×C412yes—
219#542C2×C418yes—
220#541C2×C418yes—
221#539C2×C414yes—
222#539C2×C414yes—
223#539C2×C418yes—
224#539C2×C418yes—
225#539C2×C414yes—
226#539C2×C414yes—
227#538C2×C414yes—
228#538C2×C414yes—
229#538C2×C418yes—
230#538C2×C418yes—
231#537C2×C412yes—
232#536C2×C414yes—
233#534C2×C414yes—
234#534C2×C414yes—
235#534C2×C412yes—
236#534C2×C412yes—
237#533C2×C412yes—
238#533C2×C412yes—
239#533C2312yes—
240#533C2318yes—
241#532C2×C412yes—
242#532C2×C412yes—
243#532C2312yes—
244#529C2×C414yes—
245#529C2×C414yes—
246#529C2×C414yes—
247#529C2×C414yes—
248#529C2×C414yes—
249#529C2×C414yes—
250#529C2×C414yes—
251#529C2×C414yes—
252#529C2×C414yes—
253#529C2×C414yes—
254#529C2×C414yes—
255#529C2×C414yes—
256#529C2314yes—
257#529C2314yes—
258#529C2314yes—
259#529C2314yes—
260#529C2314yes—
261#529C2314yes—
262#529C2314yes—
263#529C2314yes—
264#529C2318yes—
265#529C2318yes—
266#529C2318yes—
267C2×#126C2×C414yes—
268C2×#126C2×C414yes—
269C2×#125C2×C412yes—
270C2×#125C2×C412yes—
271C2×#124C2×C412yes—
272C2×#124C2×C412yes—
273#525C2×C414yes—
274#525C2×C414yes—
275#525C2318yes—
276#525C2318yes—
277#525C2314yes—
278C2×#123C2×C414yes—
279C2×#123C2×C414yes—
280C2×C22⋊Q8C2×C412yes—
281C2×C22⋊Q8C2×C412yes—
282C2×#121C2×C412yes—
283C2×#121C2×C412yes—
284#520C2×C414yes—
285#520C2×C418yes—
286#518C2×C412yes—
287#518C2×C414yes—
288#518C2×C414yes—
289#518C2×C418yes—
290C4×#41C2×C414yes—
291C4×#41C2×C414yes—
292C4×#41C2314yes—
293C4×#41C2314yes—
294C4×#41C2314yes—
295C4×#41C2318yes—
296C4×#41C2314yes—
297C4×#41C2314yes—
298C2×C4×Q8C2×C411yescharacteristic
299C2×C4×Q8C2311yescharacteristic
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2312yes—
302C2×C4×D4C2×C411yescharacteristic
303C2×C4×D4C2×C411yescharacteristic
304C2×C4×D4C2×C411yescharacteristic
305C2×C4×D4C2311yescharacteristic
306C2×C4×D4C2311yescharacteristic
307C2×C4×D4C2311yescharacteristic
308C2×C4×D4C2314yes—
309C2×C4×D4C2318yes—
310C2×C4×D4C2314yes—
311C2×C4×D4C2312yes—
312C2×C4×D4C2312yes—
313C2×#117C2×C411yescharacteristic
314C2×#117C2×C411yescharacteristic
315C2×#117C2×C411yescharacteristic
316C2×#117C2314yes—
317C2×#117C2314yes—
318C22×C42C2311yescharacteristic
319C22×C42C2311yescharacteristic
320C22×C42C2311yescharacteristic
321#446C2314yes—
322#446C2314yes—
323#446C2314yes—
324#446C2314yes—
325#446C2314yes—
326#446C2314yes—
327#446C2314yes—
328#446C2314yes—
329#446C2318yes—
330#446C2318yes—
331#446C2318yes—
332#446C2318yes—
333#446C2318yes—
334#446C2318yes—
335#446C2318yes—
336#446C2314yes—
337#446C2318yes—
338#446C2318yes—
339#446C2318yes—
340#446C2314yes—
341#446C2318yes—
342C8×Q8C2314yes—
343C8×Q8C2314yes—
344C8×Q8C2314yes—
345C8×Q8C2314yes—
346C8×Q8C2318yes—
347C8×Q8C2314yes—
348C8×Q8C2314yes—
349#436C2314yes—
350#436C2314yes—
351#436C2314yes—
352#436C2314yes—
353#436C2314yes—
354#436C2314yes—
355#436C2314yes—
356#436C2314yes—
357#436C2318yes—
358#436C2318yes—
359#436C2318yes—
360#436C2318yes—
361#436C2318yes—
362#436C2314yes—
363#436C2318yes—
364#436C2318yes—
365#436C2314yes—
366#435C2314yes—
367#435C2314yes—
368#435C2314yes—
369#435C2314yes—
370#435C2318yes—
371#435C2314yes—
372#435C2314yes—
373#435C2318yes—
374#435C2318yes—
375#435C2318yes—
376#435C2314yes—
377#435C2314yes—
378#435C2318yes—
379#435C2318yes—
380#435C2318yes—
381#435C2318yes—
382#435C2318yes—
383#435C2318yes—
384#435C2318yes—
385#435C2318yes—
386#435C2318yes—
387#435C2318yes—
388#435C2318yes—
389#435C2318yes—
390#435C2318yes—
391#435C2318yes—
392#435C2318yes—
393#435C2318yes—
394#435C2318yes—
395#435C2318yes—
396#435C2318yes—
397#435C2318yes—
398#435C2318yes—
399#435C2318yes—
400#435C2318yes—
401#435C2318yes—
402C8×D4C2314yes—
403C8×D4C2318yes—
404C8×D4C2318yes—
405C8×D4C2314yes—
406C8×D4C2314yes—
407C8×D4C2318yes—
408C8×D4C2318yes—
409C8×D4C2314yes—
410C8×D4C2318yes—
411C8×D4C2318yes—
412C8×D4C2318yes—
413C8×D4C2318yes—
414C8×D4C2318yes—
415C8×D4C2318yes—
416C8×D4C2318yes—
417C8×D4C2318yes—
418C8×D4C2318yes—
419C8×D4C2314yes—
420C8×D4C2314yes—
421#433C2318yes—
422#433C2318yes—
423#433C2318yes—
424#433C2318yes—
425#433C2318yes—
426#433C2318yes—
427#433C2318yes—
428#433C2318yes—
429#433C2318yes—
430#433C2318yes—
431#433C2318yes—
432#433C2318yes—
433#433C2318yes—
434#433C2318yes—
435#432C2314yes—
436#432C2314yes—
437#432C2314yes—
438#432C2314yes—
439#432C2314yes—
440#432C2314yes—
441#432C2312yes—
442#432C2312yes—
443#432C2314yes—
444#432C2318yes—
445#432C2318yes—
446#432C2318yes—
447#432C2318yes—
448#432C2318yes—
449#431C2314yes—
450#431C2314yes—
451#431C2314yes—
452#431C2312yes—
453#431C2314yes—
454#431C2312yes—
455#431C2312yes—
456#431C2312yes—
457#431C2314yes—
458#431C2312yes—
459#431C2312yes—
460#431C2318yes—
461#431C2318yes—
462#431C2318yes—
463#424C2318yes—
464#424C2318yes—
465#424C2318yes—
466#424C2318yes—
467#424C2318yes—
468#423C2314yes—
469#423C2318yes—
470#423C2318yes—
471C2×C4⋊C8C2312yes—
472C2×C4⋊C8C2312yes—
473C2×C4⋊C8C2312yes—
474C2×C4⋊C8C2312yes—
475C2×C4⋊C8C2312yes—
476C2×C4⋊C8C2314yes—
477C2×C4⋊C8C2314yes—
478C2×C4⋊C8C2314yes—
479C2×C4⋊C8C2318yes—
480#408C2318yes—
481#408C2318yes—
482#408C2318yes—
483#407C2314yes—
484#407C2318yes—
485#407C2318yes—
486#407C2318yes—
487C2×C22⋊C8C2312yes—
488C2×C22⋊C8C2312yes—
489C2×C22⋊C8C2312yes—
490C2×C22⋊C8C2314yes—
491C2×C22⋊C8C2314yes—
492C2×C22⋊C8C2314yes—
493C2×C22⋊C8C2314yes—
494C2×C22⋊C8C2318yes—
495C2×C22⋊C8C2318yes—
496#405C2318yes—
497#405C2318yes—
498#405C2318yes—
499#405C2318yes—
500#405C2318yes—
501#405C2318yes—
502#405C2318yes—
503#405C2318yes—
504#405C2318yes—
505C4×M16C2312yes—
506C4×M16C2312yes—
507C4×M16C2312yes—
508C4×M16C2312yes—
509C4×M16C2314yes—
510C4×M16C2314yes—
511C4×M16C2314yes—
512C4×M16C2318yes—
513C4×M16C2318yes—
514C2×#97C2312yes—
515C2×#97C2312yes—
516C2×#97C2314yes—
517C2×#97C2314yes—
518C2×#97C2314yes—
519C2×#97C2318yes—
520C2×C4×C8C2311yescharacteristic
521C2×C4×C8C2312yes—
522C2×C4×C8C2311yescharacteristic
523C2×C4×C8C2312yes—
524C2×C4×C8C2312yes—
525C2×C4×C8C2312yes—
526C2×C4×C8C2312yes—
527C2×C4×C8C2311yescharacteristic
528C2×C4×C8C2311yescharacteristic
529C2×C4×C8C2314yes—
530H(5,𝔽2)—48no—
531C2×#41—44no—
532C2×#41C22×C414yes—
533C2×#41C22×C414yes—
534C2×#41C22×C414yes—
535C2×#41C22×C418yes—
536C2×#41C22×C414yes—
537C2×#41C2414yes—
538C22×Q8C22×C411yescharacteristic
539C22×Q8C22×C412yes—
540C22×Q8C22×C412yes—
541C22×D4C22×C411yescharacteristic
542C22×D4C22×C411yescharacteristic
543C22×D4C22×C414yes—
544C22×D4C22×C411yescharacteristic
545C22×D4C22×C414yes—
546C22×D4C22×C418yes—
547C22×D4C22×C412yes—
548C22×D4C22×C412yes—
549C23×C4C22×C411yescharacteristic
550C23×C4C22×C411yescharacteristic
551C23×C4C22×C411yescharacteristic
552C23×C4C22×C411yescharacteristic
553C23×C4C22×C411yescharacteristic
554C23×C4C22×C411yescharacteristic
555C23×C4C2414yes—
556C23×C4C2414yes—
557C23×C4C2411yescharacteristic
558C23×C4C2411yescharacteristic
559C23×C4C2411yescharacteristic
560#131—416no—
561C2×M16—44no—
562C2×M16—48no—
563C2×M16—44no—
564C2×M16—416no—
565C2×M16C2414yes—
566C2×M16C2418yes—
567C2×M16C2414yes—
568C2×M16C2418yes—
569C2×M16C2414yes—
570C2×M16C2414yes—
571C2×M16C2418yes—
572C2×M16C2418yes—
573C2×M16C2418yes—
574C22×C8—44no—
575C22×C8—48no—
576C22×C8C2412yes—
577C22×C8C2412yes—
578C22×C8C2412yes—
579C22×C8C2418yes—
580C22×C8C2412yes—
581C22×C8C2412yes—
582C22×C8C2412yes—
583C22×C8C2414yes—
584C22×C8C2418yes—
585C22×C8C2412yes—
586C22×C8C2412yes—
587C22×C8C2414yes—
588C22×C8C2418yes—
589C22×C8C2418yes—
590C22×C8C2418yes—
591C4⋊Q8C22×C412yes—
592C4⋊Q8C22×C412yes—
593C4⋊Q8C22×C412yes—
594C4⋊Q8C22×C418yes—
595C4⋊Q8C22×C418yes—
596#127C22×C412yes—
597#126C22×C418yes—
598#126C22×C418yes—
599#126C22×C418yes—
600#126C22×C418yes—
601#126C22×C418yes—
602#126C22×C418yes—
603#126C22×C418yes—
604#126C22×C418yes—
605#126C22×C418yes—
606#126C22×C418yes—
607#126C22×C418yes—
608#126C22×C418yes—
609#126C22×C418yes—
610#126C22×C418yes—
611#125C22×C414yes—
612#125C22×C414yes—
613#125C22×C414yes—
614#125C22×C414yes—
615#125C22×C414yes—
616#125C22×C414yes—
617#125C22×C414yes—
618#125C22×C414yes—
619#125C22×C414yes—
620#125C22×C418yes—
621#125C22×C418yes—
622#125C22×C418yes—
623#125C22×C418yes—
624#125C22×C418yes—
625#124C22×C414yes—
626#124C22×C414yes—
627#124C22×C414yes—
628#124C22×C414yes—
629#124C22×C414yes—
630#124C22×C414yes—
631#124C22×C414yes—
632#124C22×C414yes—
633#124C22×C414yes—
634#124C22×C418yes—
635#124C22×C418yes—
636#124C22×C418yes—
637#123C22×C418yes—
638#123C22×C418yes—
639#123C22×C418yes—
640#123C22×C418yes—
641#123C22×C418yes—
642#123C22×C418yes—
643#123C22×C418yes—
644#123C22×C418yes—
645#123C22×C418yes—
646#123C22×C418yes—
647#123C22×C418yes—
648#123C22×C418yes—
649#123C22×C418yes—
650#123C22×C418yes—
651#123C22×C418yes—
652#123C22×C418yes—
653#123C22×C418yes—
654#123C22×C418yes—
655#123C22×C418yes—
656C22⋊Q8C22×C414yes—
657C22⋊Q8C22×C414yes—
658C22⋊Q8C22×C414yes—
659C22⋊Q8C22×C414yes—
660C22⋊Q8C22×C414yes—
661C22⋊Q8C22×C414yes—
662C22⋊Q8C22×C414yes—
663C22⋊Q8C22×C414yes—
664C22⋊Q8C22×C414yes—
665C22⋊Q8C22×C414yes—
666C22⋊Q8C22×C414yes—
667C22⋊Q8C22×C414yes—
668C22⋊Q8C22×C418yes—
669C22⋊Q8C22×C418yes—
670C22⋊Q8C22×C418yes—
671C22⋊Q8C22×C418yes—
672C22⋊Q8C22×C418yes—
673C22⋊Q8C22×C418yes—
674C22⋊Q8C22×C418yes—
675C22⋊Q8C22×C418yes—
676C22⋊Q8C22×C418yes—
677C22⋊Q8C22×C418yes—
678C22⋊Q8C22×C418yes—
679#121C22×C414yes—
680#121C22×C414yes—
681#121C22×C414yes—
682#121C22×C414yes—
683#121C22×C414yes—
684#121C22×C414yes—
685#121C22×C414yes—
686#121C22×C414yes—
687#121C22×C414yes—
688#121C22×C414yes—
689#121C22×C414yes—
690#121C22×C414yes—
691#121C22×C418yes—
692#121C22×C418yes—
693#121C22×C418yes—
694#121C22×C418yes—
695#121C22×C418yes—
696#121C22×C418yes—
697#121C22×C418yes—
698#120C22×C418yes—
699#120C22×C418yes—
700#120C22×C418yes—
701#120C22×C418yes—
702#120C22×C418yes—
703C4×Q8C22×C414yes—
704C4×Q8C22×C414yes—
705C4×Q8C22×C414yes—
706C4×Q8C22×C414yes—
707C4×Q8C22×C414yes—
708C4×Q8C22×C414yes—
709C4×Q8C22×C414yes—
710C4×Q8C22×C414yes—
711C4×Q8C22×C418yes—
712C4×Q8C22×C414yes—
713C4×Q8C22×C414yes—
714C4×Q8C22×C414yes—
715C4×Q8C2414yes—
716C4×Q8C2414yes—
717C4×Q8C2414yes—
718C4×Q8C2414yes—
719C4×Q8C2414yes—
720C4×D4C22×C414yes—
721C4×D4C22×C414yes—
722C4×D4C22×C414yes—
723C4×D4C22×C414yes—
724C4×D4C22×C414yes—
725C4×D4C22×C414yes—
726C4×D4C22×C414yes—
727C4×D4C22×C414yes—
728C4×D4C22×C414yes—
729C4×D4C22×C418yes—
730C4×D4C22×C418yes—
731C4×D4C22×C418yes—
732C4×D4C22×C418yes—
733C4×D4C22×C418yes—
734C4×D4C22×C418yes—
735C4×D4C22×C418yes—
736C4×D4C22×C418yes—
737C4×D4C22×C414yes—
738C4×D4C22×C414yes—
739C4×D4C22×C414yes—
740C4×D4C22×C414yes—
741C4×D4C22×C418yes—
742C4×D4C22×C414yes—
743C4×D4C22×C418yes—
744C4×D4C22×C418yes—
745C4×D4C22×C418yes—
746C4×D4C22×C418yes—
747C4×D4C22×C418yes—
748C4×D4C22×C418yes—
749C4×D4C22×C414yes—
750C4×D4C22×C414yes—
751C4×D4C22×C414yes—
752C4×D4C2414yes—
753C4×D4C2418yes—
754C4×D4C2418yes—
755C4×D4C2418yes—
756C4×D4C2414yes—
757C4×D4C2414yes—
758C4×D4C2414yes—
759C4×D4C2414yes—
760C4×D4C2414yes—
761C4×D4C2414yes—
762C4×D4C2418yes—
763#117C22×C414yes—
764#117C22×C414yes—
765#117C22×C414yes—
766#117C22×C414yes—
767#117C22×C414yes—
768#117C22×C414yes—
769#117C22×C418yes—
770#117C22×C418yes—
771#117C22×C418yes—
772#117C22×C418yes—
773#117C22×C414yes—
774#117C22×C418yes—
775#117C22×C418yes—
776#117C22×C418yes—
777#117C22×C418yes—
778#117C22×C414yes—
779#117C22×C418yes—
780#117C2418yes—
781#117C2418yes—
782#117C2418yes—
783#117C2414yes—
784C2×C4⋊C4C22×C411yescharacteristic
785C2×C4⋊C4C22×C411yescharacteristic
786C2×C4⋊C4C22×C411yescharacteristic
787C2×C4⋊C4C22×C411yescharacteristic
788C2×C4⋊C4C22×C411yescharacteristic
789C2×C4⋊C4C22×C411yescharacteristic
790C2×C4⋊C4C22×C414yes—
791C2×C4⋊C4C22×C414yes—
792C2×C4⋊C4C22×C414yes—
793C2×C4⋊C4C22×C414yes—
794C2×C4⋊C4C22×C414yes—
795C2×C4⋊C4C22×C414yes—
796C2×C4⋊C4C22×C418yes—
797C2×C4⋊C4C22×C412yes—
798C2×C4⋊C4C22×C412yes—
799C2×C4⋊C4C22×C412yes—
800C2×C4⋊C4C22×C412yes—
801C2×C4⋊C4C22×C414yes—
802C2×C4⋊C4C22×C414yes—
803C2×C22⋊C4C22×C411yescharacteristic
804C2×C22⋊C4C22×C411yescharacteristic
805C2×C22⋊C4C22×C411yescharacteristic
806C2×C22⋊C4C22×C411yescharacteristic
807C2×C22⋊C4C22×C411yescharacteristic
808C2×C22⋊C4C22×C411yescharacteristic
809C2×C22⋊C4C22×C414yes—
810C2×C22⋊C4C22×C414yes—
811C2×C22⋊C4C22×C414yes—
812C2×C22⋊C4C22×C414yes—
813C2×C22⋊C4C22×C414yes—
814C2×C22⋊C4C22×C414yes—
815C2×C22⋊C4C22×C414yes—
816C2×C22⋊C4C22×C414yes—
817C2×C22⋊C4C22×C418yes—
818C2×C22⋊C4C22×C418yes—
819C2×C22⋊C4C22×C414yes—
820C2×C22⋊C4C22×C414yes—
821C2×C42C22×C411yescharacteristic
822C2×C42C22×C411yescharacteristic
823C2×C42C22×C411yescharacteristic
824C2×C42C22×C411yescharacteristic
825C2×C42C22×C411yescharacteristic
826C2×C42C22×C411yescharacteristic
827C2×C42C22×C412yes—
828C2×C42C22×C412yes—
829C2×C42C22×C412yes—
830C2×C42C22×C412yes—
831C2×C42C22×C412yes—
832C2×C42C22×C412yes—
833C2×C42C2412yes—
834C2×C42C2412yes—
835C2×C42C2414yes—
836C2×C42C2414yes—
837C2×C42C2411yescharacteristic
838C2×C42C2412yes—
839C2×C42C2412yes—
840C2×C42C2411yescharacteristic
841C2×C42C2411yescharacteristic
842C2×C42C2418yes—
843C2×C42C2412yes—
844C2×C42C2412yes—
845C2×C42C2411yescharacteristic
846C4⋊C8C2414yes—
847C4⋊C8C2414yes—
848C4⋊C8C2414yes—
849C4⋊C8C2418yes—
850C4⋊C8C2418yes—
851C4⋊C8C2414yes—
852C4⋊C8C2418yes—
853C4⋊C8C2418yes—
854C4⋊C8C2418yes—
855C4⋊C8C2418yes—
856C4⋊C8C2414yes—
857C4⋊C8C2414yes—
858C4⋊C8C2414yes—
859C4⋊C8C2414yes—
860C4⋊C8C2414yes—
861C4⋊C8C2414yes—
862C4⋊C8C2418yes—
863C4⋊C8C2418yes—
864C4⋊C8C2418yes—
865C4⋊C8C2418yes—
866C22⋊C8C2414yes—
867C22⋊C8C2414yes—
868C22⋊C8C2418yes—
869C22⋊C8C2418yes—
870C22⋊C8C2414yes—
871C22⋊C8C2418yes—
872C22⋊C8C2414yes—
873C22⋊C8C2414yes—
874C22⋊C8C2418yes—
875C22⋊C8C2418yes—
876C22⋊C8C2418yes—
877C22⋊C8C2418yes—
878C22⋊C8C2418yes—
879C22⋊C8C2418yes—
880C22⋊C8C2414yes—
881C22⋊C8C2414yes—
882C22⋊C8C2414yes—
883C22⋊C8C2414yes—
884C22⋊C8C2414yes—
885C22⋊C8C2418yes—
886#97C2414yes—
887#97C2414yes—
888#97C2418yes—
889#97C2418yes—
890#97C2414yes—
891#97C2414yes—
892#97C2414yes—
893#97C2414yes—
894#97C2418yes—
895#97C2418yes—
896#97C2418yes—
897#97C2418yes—
898C4×C8C2411yescharacteristic
899C4×C8C2411yescharacteristic
900C4×C8C2412yes—
901C4×C8C2412yes—
902C4×C8C2412yes—
903C4×C8C2412yes—
904C4×C8C2411yescharacteristic
905C4×C8C2411yescharacteristic
906C4×C8C2412yes—
907C4×C8C2412yes—
908C4×C8C2412yes—
909C4×C8C2412yes—
910C4×C8C2418yes—
911C4×C8C2412yes—
912C4×C8C2412yes—
913C4×C8C2418yes—
914C4×C8C2414yes—
915C4×C8C2418yes—
916C4×C8C2414yes—
917C4×C8C2418yes—
918C24C23×C414yes—
919C24C23×C411yescharacteristic
920C24C23×C411yescharacteristic
921C24C23×C414yes—
922C24C23×C411yescharacteristic
923#41—48no—
924#41—48no—
925#41—48no—
926#41—48no—
927#41—416no—
928#41—48no—
929C2×Q8—42no—
930C2×Q8—44no—
931C2×Q8—44no—
932C2×Q8C23×C414yes—
933C2×Q8C23×C414yes—
934C2×Q8C23×C414yes—
935C2×Q8C23×C414yes—
936C2×Q8C23×C414yes—
937C2×Q8C23×C414yes—
938C2×D4—24no—
939C2×D4—24no—
940C2×D4—216no—
941C2×D4—44no—
942C2×D4—44no—
943C2×D4—42no—
944C2×D4—416no—
945C2×D4—48no—
946C2×D4C23×C414yes—
947C2×D4C23×C414yes—
948C2×D4C23×C418yes—
949C2×D4C23×C418yes—
950C2×D4C23×C414yes—
951C2×D4C23×C414yes—
952C2×D4C23×C418yes—
953C2×D4C23×C414yes—
954C2×D4C23×C414yes—
955C2×D4C23×C418yes—
956C2×D4C23×C418yes—
957C2×D4C23×C414yes—
958C2×D4C23×C414yes—
959C22×C4—24no—
960C22×C4—42no—
961C22×C4—44no—
962C22×C4—42no—
963C22×C4—44no—
964C22×C4—42no—
965C22×C4—48no—
966C22×C4—42no—
967C22×C4—42no—
968C22×C4—42no—
969C22×C4—42no—
970C22×C4—42no—
971C22×C4C23×C411yescharacteristic
972C22×C4C23×C411yescharacteristic
973C22×C4C23×C412yes—
974C22×C4C23×C412yes—
975C22×C4C23×C411yescharacteristic
976C22×C4C23×C412yes—
977C22×C4C23×C412yes—
978C22×C4C23×C411yescharacteristic
979C22×C4C23×C411yescharacteristic
980C22×C4C23×C412yes—
981C22×C4C23×C414yes—
982C22×C4C23×C412yes—
983C22×C4C23×C411yescharacteristic
984C22×C4C23×C411yescharacteristic
985C22×C4C23×C412yes—
986C22×C4C23×C411yescharacteristic
987C22×C4C23×C412yes—
988C22×C4C23×C412yes—
989C22×C4C23×C412yes—
990C22×C4C23×C411yescharacteristic
991C22×C4C23×C412yes—
992C22×C4C23×C412yes—
993C22×C4C23×C411yescharacteristic
994C22×C4C23×C411yescharacteristic
995C22×C4C23×C412yes—
996C22×C4C23×C412yes—
997C22×C4C23×C412yes—
998C22×C4C23×C414yes—
999C22×C4C23×C414yes—
1000C22×C4C23×C418yes—
1001C22×C4C23×C414yes—
1002C22×C4C23×C418yes—
1003C22×C4C23×C414yes—
1004C22×C4C23×C414yes—
1005C22×C4C23×C418yes—
1006C22×C4C23×C418yes—
1007C22×C4C2512yes—
1008C22×C4C2511yescharacteristic
1009C22×C4C2512yes—
1010C22×C4C2512yes—
1011C22×C4C2518yes—
1012M16—28no—
1013M16—216no—
1014M16—28no—
1015M16—48no—
1016M16—48no—
1017M16—44no—
1018M16—48no—
1019M16—44no—
1020M16—48no—
1021C2×C8—24no—
1022C2×C8—24no—
1023C2×C8—24no—
1024C2×C8—216no—
1025C2×C8—48no—
1026C2×C8—42no—
1027C2×C8—42no—
1028C2×C8—44no—
1029C2×C8—42no—
1030C2×C8—42no—
1031C2×C8—44no—
1032C2×C8—42no—
1033C2×C8—48no—
1034C2×C8—48no—
1035C2×C8—48no—
1036C2×C8C2512yes—
1037C2×C8C2512yes—
1038C2×C8C2512yes—
1039C2×C8C2514yes—
1040C2×C8C2514yes—
1041C2×C8C2518yes—
1042C2×C8C2518yes—
1043C2×C8C2512yes—
1044C4⋊C4C23×C414yes—
1045C4⋊C4C23×C418yes—
1046C4⋊C4C23×C418yes—
1047C4⋊C4C23×C414yes—
1048C4⋊C4C23×C414yes—
1049C4⋊C4C23×C418yes—
1050C4⋊C4C23×C418yes—
1051C4⋊C4C23×C418yes—
1052C4⋊C4C23×C414yes—
1053C4⋊C4C23×C418yes—
1054C4⋊C4C23×C414yes—
1055C4⋊C4C23×C414yes—
1056C4⋊C4C23×C414yes—
1057C4⋊C4C23×C414yes—
1058C4⋊C4C23×C414yes—
1059C4⋊C4C23×C418yes—
1060C4⋊C4C23×C418yes—
1061C4⋊C4C23×C418yes—
1062C4⋊C4C23×C418yes—
1063C4⋊C4C23×C414yes—
1064C4⋊C4C23×C414yes—
1065C4⋊C4C23×C414yes—
1066C4⋊C4C23×C414yes—
1067C4⋊C4C23×C418yes—
1068C4⋊C4C23×C418yes—
1069C4⋊C4C23×C414yes—
1070C4⋊C4C23×C418yes—
1071C4⋊C4C23×C418yes—
1072C4⋊C4C23×C414yes—
1073C4⋊C4C23×C414yes—
1074C22⋊C4C23×C414yes—
1075C22⋊C4C23×C414yes—
1076C22⋊C4C23×C418yes—
1077C22⋊C4C23×C418yes—
1078C22⋊C4C23×C418yes—
1079C22⋊C4C23×C418yes—
1080C22⋊C4C23×C418yes—
1081C22⋊C4C23×C418yes—
1082C22⋊C4C23×C418yes—
1083C22⋊C4C23×C418yes—
1084C22⋊C4C23×C418yes—
1085C22⋊C4C23×C418yes—
1086C22⋊C4C23×C414yes—
1087C22⋊C4C23×C414yes—
1088C22⋊C4C23×C414yes—
1089C22⋊C4C23×C414yes—
1090C22⋊C4C23×C418yes—
1091C22⋊C4C23×C418yes—
1092C22⋊C4C23×C418yes—
1093C22⋊C4C23×C418yes—
1094C22⋊C4C23×C418yes—
1095C22⋊C4C23×C418yes—
1096C22⋊C4C23×C418yes—
1097C22⋊C4C23×C418yes—
1098C22⋊C4C23×C418yes—
1099C42C23×C411yescharacteristic
1100C42C23×C411yescharacteristic
1101C42C23×C412yes—
1102C42C23×C412yes—
1103C42C23×C412yes—
1104C42C23×C412yes—
1105C42C23×C412yes—
1106C42C23×C412yes—
1107C42C23×C412yes—
1108C42C23×C412yes—
1109C42C23×C412yes—
1110C42C23×C412yes—
1111C42C23×C412yes—
1112C42C23×C412yes—
1113C42C23×C412yes—
1114C42C23×C412yes—
1115C42C23×C412yes—
1116C42C23×C418yes—
1117C42C23×C418yes—
1118C42C23×C418yes—
1119C42C23×C418yes—
1120C42C2511yescharacteristic
1121C42C2511yescharacteristic
1122C42C2518yes—
1123C42C2512yes—
1124C42C2512yes—
1125C42C2512yes—
1126C23—22no—
1127C23—22no—
1128C23—28no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—44no—
1135C23—41no—
1136C23—44no—
1137C23—44no—
1138C23—44no—
1139C23—44no—
1140C23#56814yes—
1141C23C24×C418yes—
1142C23C24×C412yes—
1143C23C24×C412yes—
1144C23C24×C412yes—
1145C23C24×C411yescharacteristic
1146Q8—28no—
1147Q8—44no—
1148Q8—44no—
1149Q8—44no—
1150Q8—44no—
1151Q8—44no—
1152D4—28no—
1153D4—216no—
1154D4—216no—
1155D4—28no—
1156D4—28no—
1157D4—44no—
1158D4—48no—
1159D4—44no—
1160D4—44no—
1161D4—44no—
1162D4—48no—
1163D4—48no—
1164D4—44no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—24no—
1168C2×C4—24no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—28no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—28no—
1176C2×C4—24no—
1177C2×C4—28no—
1178C2×C4—24no—
1179C2×C4—22no—
1180C2×C4—24no—
1181C2×C4—24no—
1182C2×C4—24no—
1183C2×C4—41no—
1184C2×C4—42no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—42no—
1191C2×C4—41no—
1192C2×C4—42no—
1193C2×C4—48no—
1194C2×C4—48no—
1195C2×C4—42no—
1196C2×C4—44no—
1197C2×C4—44no—
1198C2×C4—41no—
1199C2×C4—42no—
1200C2×C4—42no—
1201C2×C4—42no—
1202C2×C4—42no—
1203C2×C4—48no—
1204C2×C4—44no—
1205C2×C4—44no—
1206C2×C4—44no—
1207C2×C4—48no—
1208C2×C4C24×C411yescharacteristic
1209C2×C4C24×C412yes—
1210C2×C4C24×C412yes—
1211C2×C4C24×C411yescharacteristic
1212C2×C4C24×C411yescharacteristic
1213C2×C4C24×C411yescharacteristic
1214C2×C4C24×C412yes—
1215C2×C4C24×C412yes—
1216C2×C4C24×C412yes—
1217C2×C4C24×C418yes—
1218C2×C4C24×C412yes—
1219C2×C4C24×C412yes—
1220C2×C4C24×C412yes—
1221C2×C4C24×C412yes—
1222C2×C4C24×C418yes—
1223C2×C4C24×C418yes—
1224C2×C4C24×C411yescharacteristic
1225C2×C4C2611yescharacteristic
1226C8—22no—
1227C8—28no—
1228C8—22no—
1229C8—22no—
1230C8—24no—
1231C8—28no—
1232C8—24no—
1233C8#58514yes—
1234C22—21no—
1235C22—22no—
1236C22—22no—
1237C22—21no—
1238C22—22no—
1239C22—22no—
1240C22—28no—
1241C22—22no—
1242C22—22no—
1243C22—28no—
1244C22—22no—
1245C22—28no—
1246C22—22no—
1247C22—44no—
1248C22—82no—
1249C22—88no—
1250C22—82no—
1251C22—164no—
1252C22C2×#56812yes—
1253C22C2×#56814yes—
1254C22C25×C411yescharacteristic
1255C4—21no—
1256C4—21no—
1257C4—22no—
1258C4—22no—
1259C4—28no—
1260C4—22no—
1261C4—21no—
1262C4—22no—
1263C4—22no—
1264C4—22no—
1265C4—28no—
1266C4—22no—
1267C4—21no—
1268C4—22no—
1269C4—28no—
1270C4—22no—
1271C4#357312yes—
1272C4C2×#58512yes—
1273C2—22no—
1274C2—24no—
1275C2—42no—
1276C2—48no—
1277C2—42no—
1278C2C4×#58511yescharacteristic
1279C2C22×#56811yescharacteristic
1280C2C2×#357311yescharacteristic
subgroupG/H
center, Frattini, cosocleC2×C4C26
commutator, socleC22C25×C4
prime radical#62781C2
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. #60342C2semidirect
3. #60340C2semidirect
4. #60335C2semidirect
5. #60324C2semidirect
6. #60322C2semidirect
7. #60311C2semidirect
8. #60310C2semidirect
9. #60309C2semidirect
10. #60299C2semidirect
11. #60294C2semidirect
12. #60290C2semidirect
13. #60288C2semidirect
14. #60282C2semidirect
15. #60216C2semidirect
16. #60214C2semidirect
17. #60211C2semidirect
18. C2×#2966C2semidirect
19. C2×#2965C2semidirect
43. #2995C22semidirect
44. #2995C22semidirect
45. #2994C22semidirect
46. #2994C22semidirect
47. #2994C22semidirect
48. #2994C22semidirect
49. #2993C22semidirect
50. #2993C22semidirect
51. #2993C22semidirect
52. #2992C22semidirect
53. #2992C22semidirect
54. #2992C22semidirect
55. #2992C22semidirect
56. #2990C22semidirect
57. #2990C22semidirect
58. #2990C22semidirect
59. #2990C22semidirect
60. #2989C22semidirect
61. #2989C22semidirect
62. #2988C22semidirect
63. #2987C22semidirect
64. #2985C22semidirect
65. #2985C22semidirect
66. #2985C22semidirect
67. #2984C22semidirect
68. #2983C22semidirect
69. #2983C22semidirect
70. #2982C22semidirect
71. #2981C22semidirect
72. #2981C22semidirect
73. #2978C22semidirect
74. #2977C22semidirect
75. #2977C22semidirect
76. #2976C22semidirect
77. #2976C22semidirect
78. #2975C22semidirect
79. #2974C22semidirect
80. #2974C22semidirect
81. #2974C22semidirect
83. #2973C22semidirect
84. #2973C22semidirect
85. #2973C22semidirect
86. #2972C22semidirect
87. #2972C22semidirect
88. #2972C22semidirect
89. #2971C22semidirect
90. #2970C22semidirect
91. #2970C22semidirect
92. #2970C22semidirect
93. #2970C22semidirect
94. #2969C22semidirect
95. #2969C22semidirect
96. #2969C22semidirect
97. #2969C22semidirect
98. #2968C22semidirect
99. #2968C22semidirect
100. #2968C22semidirect
101. #2968C22semidirect
102. #2968C22semidirect
103. #2967C22semidirect
104. #2967C22semidirect
105. #2967C22semidirect
106. #2967C22semidirect
107. #2967C22semidirect
108. #2967C22semidirect
109. #2966C22semidirect
110. #2966C22semidirect
111. #2966C22semidirect
112. #2966C22semidirect
113. #2966C22semidirect
114. #2966C22semidirect
115. #2966C22semidirect
116. #2966C22semidirect
117. #2966C22semidirect
118. #2966C22semidirect
119. #2966C22semidirect
120. #2965C22semidirect
121. #2965C22semidirect
122. #2965C22semidirect
123. #2965C22semidirect
124. #2965C22semidirect
125. Q8×M16C22semidirect
126. #2962C22semidirect
127. #2962C22semidirect
128. #2961C22semidirect
129. C2×#446C22semidirect
130. C2×#446C22semidirect
131. C2×C8×Q8C22semidirect
132. #2935C22semidirect
133. D4×M16C22semidirect
134. D4×M16C22semidirect
135. D4×M16C22semidirect
136. #2933C22semidirect
137. #2933C22semidirect
138. #2933C22semidirect
139. #2930C22semidirect
140. #2929C22semidirect
141. C2×#436C22semidirect
142. C2×#436C22semidirect
144. C2×#435C22semidirect
145. C2×#435C22semidirect
146. C2×#435C22semidirect
147. C2×C8×D4C22semidirect
148. C2×C8×D4C22semidirect
149. #2925C22semidirect
150. #2924C22semidirect
151. #2924C22semidirect
152. #2923C22semidirect
153. #2921C22semidirect
154. #2920C22semidirect
155. C2×#433C22semidirect
156. C2×#432C22semidirect
157. C2×#432C22semidirect
158. C2×#431C22semidirect
159. C2×#431C22semidirect
160. C2×#431C22semidirect
161. #2875C22semidirect
162. #2873C22semidirect
163. C2×#405C22semidirect
164. C2×C4×M16C22semidirect
165. C2×C4×M16C22semidirect
166. C22×C4×C8C22semidirect

Maximal subgroups

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

subgroupindex
#627812
#603422
#603402
#603352
#603242
#603222
#603112
#603102
#603092
#602992
#602942
#602902
#602882
#602822
#602162
#602142
#602112
C2×#29662
C2×#29652