Finite Group Databasebeta

← #7625757

Subgroups — #7625757

Order 512.

11372 conjugacy classes of subgroups.

The subgroup lattice has 1138 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3488C211yesmaximal, characteristic
2C2×C4×H(5,𝔽2)C211yesmaximal, characteristic, complemented
3C2×#3428C211yesmaximal, characteristic, complemented
4#34313C212yesmaximal, complemented
5#34312C212yesmaximal, complemented
6#34310C216yesmaximal, complemented
7#34309C216yesmaximal, complemented
8#34295C212yesmaximal, complemented
9#34293C212yesmaximal, complemented
10#34290C216yesmaximal, complemented
11#34288C216yesmaximal, complemented
12#34269C213yesmaximal, complemented
13#34267C213yesmaximal, complemented
14#34258C211yesmaximal, characteristic, complemented
15#34250C211yesmaximal, characteristic, complemented
16#34204C213yesmaximal, complemented
17#34202C213yesmaximal, complemented
18#34175C211yesmaximal, characteristic, complemented
19C4×#537C213yesmaximal, complemented
20C4×#535C213yesmaximal, complemented
21#34065C213yesmaximal, complemented
22C2×#2324C213yesmaximal, complemented
23C4×#520C211yesmaximal, characteristic, complemented
24C22×H(5,𝔽2)C2211yescharacteristic
25C23×#41C2211yescharacteristic
26#3488C4132yescomplemented
27C2×#550C2212yes—
28C2×#548C2212yes—
29C2×#546C2216yes—
30C2×D42C2216yes—
31C2×#537C2213yes—
32C2×#535C2213yes—
33C2×#525C2213yes—
34C22×#121C2213yes—
35C4×H(5,𝔽2)—216no—
36#3428—216no—
37C2×#520C2211yescharacteristic
38C2×#520C2211yescharacteristic
39C2×#520C2211yescharacteristic
40C2×#520C2213yescomplemented
41C2×#520C2212yescomplemented
42C2×#520C2211yescharacteristic, complemented
43C2×#520C2213yescomplemented
44C2×#520C2213yescomplemented
45C2×#520C2211yescharacteristic, complemented
46C2×#519C2211yescharacteristic, complemented
47C2×#519C2211yescharacteristic, complemented
48C2×#518C2216yescomplemented
49C2×#518C2213yescomplemented
50C2×#518C2213yescomplemented
51C2×#518C2213yescomplemented
52C2×C4×#41C2211yescharacteristic
53C2×C4×#41C2211yescharacteristic
54C2×C4×#41C2213yescomplemented
55C2×C4×#41C2213yescomplemented
56C2×C4×#41C2213yescomplemented
57C2×C4×#41C2212yescomplemented
58C22×C4×D4C2213yescomplemented
59C22×C4×D4C2216yescomplemented
60C22×#117C2213yescomplemented
61C22×#117C2213yescomplemented
62#2367C2216yescomplemented
63#2367C2216yescomplemented
64#2366C2216yescomplemented
65#2366C2216yescomplemented
66#2364C22112yescomplemented
67#2363C2216yescomplemented
68#2363C2216yescomplemented
69#2363C2216yescomplemented
70#2362C2216yescomplemented
71#2361C2216yescomplemented
72#2361C22112yescomplemented
73#2361C2216yescomplemented
74#2361C2216yescomplemented
75#2360C2216yescomplemented
76#2359C22112yescomplemented
77#2358C22112yescomplemented
78#2358C22112yescomplemented
79#2358C22112yescomplemented
80#2354C2216yescomplemented
81#2352C2216yescomplemented
82#2352C2216yescomplemented
83#2351C2212yescomplemented
84Q8×C4⋊C4C2212yescomplemented
85#2349C2216yescomplemented
86D4×C4⋊C4C2216yescomplemented
87D4×C4⋊C4C2216yescomplemented
88#2342C22112yescomplemented
89#2341C2212yescomplemented
90#2341C2212yescomplemented
91#2341C2212yescomplemented
92Q8×C22⋊C4C2212yescomplemented
93#2339C2216yescomplemented
94D4×C22⋊C4C2216yescomplemented
95D4×C22⋊C4C2216yescomplemented
96D4×C22⋊C4C22112yescomplemented
97D4×C22⋊C4C2216yescomplemented
98#2328C2216yescomplemented
99#2326C2216yescomplemented
100#2325C22112yescomplemented
101#2324C2216yescomplemented
102#2324C2216yescomplemented
103#2324C2216yescomplemented
104#2324C2213yescomplemented
105#2324C2216yescomplemented
106#2324C2216yescomplemented
107#2324C2216yescomplemented
108#2324C2216yescomplemented
109#2324C2216yescomplemented
110#2324C2213yescomplemented
111#2324C2213yescomplemented
112#2324C2213yescomplemented
113#2323C2216yescomplemented
114#2323C2211yescharacteristic, complemented
115#2323C2213yescomplemented
116#2323C2213yescomplemented
117#2323C2213yescomplemented
118#2322C2216yescomplemented
119#2322C2216yescomplemented
120#2321C22112yescomplemented
121#2321C2216yescomplemented
122#2321C2216yescomplemented
123#2317C2213yescomplemented
124#2316C2213yescomplemented
125#2311C2213yescomplemented
126#2311C2213yescomplemented
127#2311C2213yescomplemented
128#2309C2213yescomplemented
129C4×#127C2216yescomplemented
130C4×#124C2216yescomplemented
131C4×C22⋊Q8C2216yescomplemented
132C4×C22⋊Q8C2216yescomplemented
133C4×#121C22112yescomplemented
134C4×#121C2216yescomplemented
135C4×#121C2216yescomplemented
136C4×#121C2216yescomplemented
137C4×#121C2216yescomplemented
138C4×#120C22112yescomplemented
139#2297C2213yescomplemented
140#2296C2213yescomplemented
141#2293C2216yescomplemented
142#2293C2216yescomplemented
143C2×#390C2216yescomplemented
144C2×#390C2213yescomplemented
145C2×#389C2213yescomplemented
146#2290C2216yescomplemented
147#2290C2216yescomplemented
148C2×#388C2216yescomplemented
149C2×#386C2216yescomplemented
150C2×#385C2216yescomplemented
151#2280C2213yescomplemented
152C2×#380C2213yescomplemented
153#2276C2212yescomplemented
154#2275C2216yescomplemented
155#2274C2213yescomplemented
156#2274C2213yescomplemented
157C42×Q8C2212yescomplemented
158C42×D4C2216yescomplemented
159C4×#117C2213yescomplemented
160C2×C4×C4⋊C4C2213yescomplemented
161C2×H(5,𝔽2)—28no—
162C2×H(5,𝔽2)—28no—
163C2×H(5,𝔽2)C2×C4116yescomplemented
164C22×#41—28no—
165C22×#41—28no—
166C22×#41C2×C4116yescomplemented
167C22×#41C2313yes—
168C22×#41C2312yes—
169C22×#41C2313yes—
170C22×#41C2313yes—
171C22×#41C2311yescharacteristic
172C22×#41C2311yescharacteristic
173C23×Q8C2311yescharacteristic
174C23×D4C2313yes—
175C23×D4C2316yes—
176C23×D4C2313yes—
177C23×D4C2316yes—
178C24×C4C2313yes—
179C24×C4C2316yes—
180#550C2×C4132yescomplemented
181#548C2×C4132yescomplemented
182#546C2×C4196yescomplemented
183D42C2×C4196yescomplemented
184#537C2×C4148yescomplemented
185#535C2×C4148yescomplemented
186C2×#127C2316yes—
187C2×#124C2316yes—
188#525C2×C4148yescomplemented
189C2×#123C2316yes—
190C2×C22⋊Q8C2311yescharacteristic
191C2×C22⋊Q8C2313yes—
192C2×C22⋊Q8C2316yes—
193C2×#121C2×C4148yescomplemented
194C2×#121C2313yes—
195C2×#121C2316yes—
196C2×#121C2316yes—
197C2×#121C2316yes—
198C2×#121C2313yes—
199C2×#121C2316yes—
200C2×#121C23112yes—
201C2×#120C2316yes—
202C2×#120C23112yes—
203#520—28no—
204#520—28no—
205#520—28no—
206#520—28no—
207#520—216no—
208#520—224no—
209#520—224no—
210#520—224no—
211#520C2×C4116yescomplemented
212#519—28no—
213#519—28no—
214#518—224no—
215#518—224no—
216#518—248no—
217#518—224no—
218C4×#41—28no—
219C4×#41—216no—
220C4×#41—224no—
221C4×#41—224no—
222C4×#41—224no—
223C4×#41D4116yescomplemented
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2313yes—
226C2×C4×Q8C2313yes—
227C2×C4×Q8C2313yes—
228C2×C4×Q8C2312yes—
229C2×C4×Q8C2312yes—
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2313yes—
233C2×C4×Q8C2313yes—
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×D4—248no—
238C2×C4×D4—224no—
239C2×C4×D4C2313yes—
240C2×C4×D4C2316yes—
241C2×C4×D4C2316yes—
242C2×C4×D4C2316yes—
243C2×C4×D4C2316yes—
244C2×C4×D4C2313yes—
245C2×C4×D4C2316yes—
246C2×C4×D4C2316yes—
247C2×C4×D4C2313yes—
248C2×C4×D4C2316yes—
249C2×C4×D4C2313yes—
250C2×C4×D4C2316yes—
251C2×C4×D4C2313yes—
252C2×C4×D4C2313yes—
253C2×C4×D4C2316yes—
254C2×C4×D4C2316yes—
255C2×C4×D4C2316yes—
256C2×C4×D4C23112yes—
257C2×C4×D4C2313yes—
258C2×C4×D4C2316yes—
259C2×C4×D4C2316yes—
260C2×C4×D4C2313yes—
261C2×C4×D4C23112yes—
262C2×C4×D4C23112yes—
263C2×C4×D4C23112yes—
264C2×C4×D4C2316yes—
265C2×C4×D4C2316yes—
266C2×C4×D4C2316yes—
267C2×C4×D4C2313yes—
268C2×C4×D4C2313yes—
269C2×#117—224no—
270C2×#117—224no—
271C2×#117C2313yes—
272C2×#117C2313yes—
273C2×#117C2313yes—
274C2×#117C2311yescharacteristic
275C2×#117C2313yes—
276C2×#117C2313yes—
277C2×#117C2313yes—
278C2×#117C2316yes—
279C2×#117C2313yes—
280C2×#117C2313yes—
281C2×#117C2313yes—
282C2×#117C2313yes—
283C2×#117C2316yes—
284C2×#117C2313yes—
285C2×#117C2316yes—
286C2×#117C2313yes—
287C2×#117C2313yes—
288C2×#117C2313yes—
289C22×C4⋊C4C2313yes—
290C22×C4⋊C4C2313yes—
291C22×C4⋊C4C2313yes—
292C22×C4⋊C4C2313yes—
293C22×C4⋊C4C2313yes—
294C22×C4⋊C4C2316yes—
295C22×C4⋊C4C2313yes—
296C22×C4⋊C4C2316yes—
297C22×C4⋊C4C2313yes—
298C22×C22⋊C4C2313yes—
299C22×C22⋊C4C2313yes—
300C22×C22⋊C4C2316yes—
301C22×C22⋊C4C2316yes—
302C22×C22⋊C4C23112yes—
303C22×C22⋊C4C2316yes—
304C22×C22⋊C4C2316yes—
305C22×C22⋊C4C2316yes—
306C22×C22⋊C4C2316yes—
307C22×C42C2313yes—
308C22×C42C2316yes—
309C22×C42C2316yes—
310C22×C42C2316yes—
311C22×C42C2313yes—
312#391C2313yes—
313#391C2316yes—
314#391C2316yes—
315#391C2311yescharacteristic
316#390C2316yes—
317#390C2316yes—
318#390C2316yes—
319#390C23112yes—
320#390C2313yes—
321#390C2316yes—
322#390C2316yes—
323#390C2316yes—
324#390C2316yes—
325#390C2316yes—
326#390C2316yes—
327#390C2313yes—
328#390C2316yes—
329#390C2316yes—
330#390C23112yes—
331#390C23112yes—
332#389C2313yes—
333#389C2316yes—
334#389C2316yes—
335#389C2316yes—
336#389C2313yes—
337#389C2312yes—
338#389C2316yes—
339#389C2316yes—
340#389C2316yes—
341#389C2313yes—
342#389C2311yescharacteristic
343#389C2316yes—
344#389C2316yes—
345#388C2312yes—
346#388C2312yes—
347#388C2316yes—
348#388C23112yes—
349#388C2316yes—
350#388C2316yes—
351#388C2316yes—
352#388C2316yes—
353#388C2316yes—
354#388C2316yes—
355#388C23112yes—
356#388C23112yes—
357#388C2316yes—
358#388C2316yes—
359#388C2316yes—
360#388C23112yes—
361#388C23112yes—
362#388C23112yes—
363#387C2312yes—
364#387C2316yes—
365#387C2316yes—
366#387C2316yes—
367#387C23112yes—
368#386C23112yes—
369#386C23112yes—
370#386C23112yes—
371#386C2316yes—
372#386C2316yes—
373#386C2316yes—
374#386C2316yes—
375#386C2316yes—
376#386C2316yes—
377#386C23112yes—
378#386C23112yes—
379#386C23112yes—
380#386C23112yes—
381#386C23112yes—
382#386C23112yes—
383#385C23112yes—
384#385C2316yes—
385#385C2316yes—
386#385C2316yes—
387#385C2316yes—
388#385C2316yes—
389#385C2316yes—
390#385C23112yes—
391#385C23112yes—
392#385C23112yes—
393#385C23112yes—
394#384C2316yes—
395#382C2316yes—
396#381C2316yes—
397#380C2313yes—
398#380C2313yes—
399#380C2316yes—
400#380C2316yes—
401#380C2316yes—
402#380C23112yes—
403#380C2313yes—
404#380C2311yescharacteristic
405#380C2316yes—
406#380C2316yes—
407#379C23112yes—
408#379C2316yes—
409C4×C4⋊C4C2313yes—
410C4×C4⋊C4C2316yes—
411C4×C4⋊C4C2311yescharacteristic
412C4×C4⋊C4C2313yes—
413C4×C4⋊C4C2313yes—
414C4×C4⋊C4C2316yes—
415C4×C4⋊C4C2316yes—
416C4×C4⋊C4C2316yes—
417C4×C4⋊C4C2316yes—
418C4×C4⋊C4C2316yes—
419C4×C4⋊C4C2316yes—
420C4×C4⋊C4C23112yes—
421C4×C4⋊C4C2316yes—
422C4×C4⋊C4C2316yes—
423C4×C22⋊C4C2316yes—
424C4×C22⋊C4C2316yes—
425C4×C22⋊C4C2316yes—
426C4×C22⋊C4C2316yes—
427C4×C22⋊C4C2316yes—
428C4×C22⋊C4C23112yes—
429C4×C22⋊C4C2316yes—
430C4×C22⋊C4C23112yes—
431C4×C22⋊C4C23112yes—
432C4×C22⋊C4C23112yes—
433C4×C22⋊C4C23112yes—
434C4×C22⋊C4C23112yes—
435#376C2316yes—
436C2×#95C2316yes—
437C2×#95C2316yes—
438C2×#95C2316yes—
439C43C2316yes—
440C25C2413yes—
441C25C2416yes—
442H(5,𝔽2)—2128no—
443C2×#41—2128no—
444C2×#41—28no—
445C2×#41—24no—
446C2×#41—24no—
447C2×#41—28no—
448C2×#41—212no—
449C2×#41—212no—
450C2×#41—212no—
451C2×#41—212no—
452C2×#41—212no—
453C2×#41—212no—
454C2×#41C22×C4124yes—
455C2×#41C22×C4116yes—
456C2×#41C22×C418yes—
457C2×#41C22×C4124yescomplemented
458C2×#41C22×C4124yescomplemented
459C2×#41C22×C418yescomplemented
460C2×#41C2×D418yes—
461C2×#41#4118yes—
462C22×Q8—24no—
463C22×Q8—24no—
464C22×Q8C22×C418yescomplemented
465C22×Q8C2411yescharacteristic
466C22×Q8C2413yes—
467C22×Q8C2411yescharacteristic
468C22×D4—224no—
469C22×D4—212no—
470C22×D4—212no—
471C22×D4—224no—
472C22×D4—212no—
473C22×D4—212no—
474C22×D4—86no—
475C22×D4—86no—
476C22×D4C22×C4124yes—
477C22×D4C22×C4148yes—
478C22×D4C22×C4124yescomplemented
479C22×D4C22×C4148yescomplemented
480C22×D4C2416yes—
481C22×D4C2416yes—
482C22×D4C2413yes—
483C22×D4C2416yes—
484C22×D4C2413yes—
485C22×D4C2416yes—
486C22×D4C24112yes—
487C22×D4C2416yes—
488C22×D4C2413yes—
489C23×C4—212no—
490C23×C4—212no—
491C23×C4—224no—
492C23×C4—86no—
493C23×C4—86no—
494C23×C4C22×C4124yescomplemented
495C23×C4C2413yes—
496C23×C4C2413yes—
497C23×C4C2416yes—
498C23×C4C2413yes—
499C23×C4C2411yescharacteristic
500C23×C4C2413yes—
501C23×C4C2413yes—
502C23×C4C2413yes—
503C23×C4C2416yes—
504C23×C4C2416yes—
505C23×C4C2416yes—
506C23×C4C2416yes—
507C23×C4C24112yes—
508C23×C4C2416yes—
509C23×C4C2416yes—
510C23×C4C2416yes—
511C23×C4C2413yes—
512C23×C4C2413yes—
513C23×C4C2413yes—
514#127C22×C4148yescomplemented
515#124C22×C4148yescomplemented
516#123C22×C4148yescomplemented
517C22⋊Q8C22×C418yescomplemented
518C22⋊Q8C22×C4124yescomplemented
519C22⋊Q8C22×C4148yescomplemented
520#121C22×C4124yescomplemented
521#121C22×C4148yescomplemented
522#121C22×C4148yescomplemented
523#121C22×C4148yescomplemented
524#121C22×C4124yescomplemented
525#121C22×C4196yescomplemented
526#121C22×C4148yescomplemented
527#120C22×C4148yescomplemented
528#120C22×C4196yescomplemented
529C4×Q8—24no—
530C4×Q8—24no—
531C4×Q8—28no—
532C4×Q8—28no—
533C4×Q8—212no—
534C4×Q8—212no—
535C4×Q8—24no—
536C4×Q8—212no—
537C4×Q8—212no—
538C4×Q8—212no—
539C4×Q8C22×C4116yescomplemented
540C4×Q8C2×D418yescomplemented
541C4×Q8C2×D418yescomplemented
542C4×D4—224no—
543C4×D4—212no—
544C4×D4—212no—
545C4×D4—224no—
546C4×D4—224no—
547C4×D4—224no—
548C4×D4—224no—
549C4×D4—224no—
550C4×D4—224no—
551C4×D4—224no—
552C4×D4—212no—
553C4×D4—212no—
554C4×D4—248no—
555C4×D4—224no—
556C4×D4—224no—
557C4×D4—224no—
558C4×D4—212no—
559C4×D4—224no—
560C4×D4—224no—
561C4×D4—212no—
562C4×D4—212no—
563C4×D4—212no—
564C4×D4—812no—
565C4×D4—812no—
566C4×D4—812no—
567C4×D4C22×C4148yescomplemented
568C4×D4C22×C4148yescomplemented
569C4×D4C22×C4148yescomplemented
570C4×D4C2×D4124yescomplemented
571C4×D4C2×D4124yescomplemented
572#117—212no—
573#117—212no—
574#117—212no—
575#117—212no—
576#117—212no—
577#117—224no—
578#117—224no—
579#117—212no—
580#117—24no—
581#117—212no—
582#117—212no—
583#117—212no—
584#117—212no—
585#117—212no—
586#117—212no—
587#117—224no—
588#117C22×C4124yescomplemented
589#117C2×D4124yescomplemented
590C2×C4⋊C4—212no—
591C2×C4⋊C4—212no—
592C2×C4⋊C4—212no—
593C2×C4⋊C4—212no—
594C2×C4⋊C4—212no—
595C2×C4⋊C4—212no—
596C2×C4⋊C4—224no—
597C2×C4⋊C4—86no—
598C2×C4⋊C4C22×C4124yescomplemented
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2413yes—
601C2×C4⋊C4C2413yes—
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2413yes—
604C2×C4⋊C4C2416yes—
605C2×C4⋊C4C2416yes—
606C2×C4⋊C4C2413yes—
607C2×C4⋊C4C2413yes—
608C2×C4⋊C4C2413yes—
609C2×C4⋊C4C2413yes—
610C2×C4⋊C4C2413yes—
611C2×C4⋊C4C2413yes—
612C2×C4⋊C4C2413yes—
613C2×C4⋊C4C2416yes—
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2416yes—
618C2×C4⋊C4C24112yes—
619C2×C4⋊C4C2416yes—
620C2×C4⋊C4C2416yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2413yes—
623C2×C4⋊C4C2416yes—
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2416yes—
627C2×C4⋊C4C2413yes—
628C2×C4⋊C4C2413yes—
629C2×C22⋊C4—212no—
630C2×C22⋊C4—212no—
631C2×C22⋊C4—224no—
632C2×C22⋊C4—224no—
633C2×C22⋊C4—248no—
634C2×C22⋊C4—86no—
635C2×C22⋊C4—86no—
636C2×C22⋊C4—86no—
637C2×C22⋊C4C22×C4148yescomplemented
638C2×C22⋊C4C2411yescharacteristic
639C2×C22⋊C4C2413yes—
640C2×C22⋊C4C2413yes—
641C2×C22⋊C4C2411yescharacteristic
642C2×C22⋊C4C2416yes—
643C2×C22⋊C4C2416yes—
644C2×C22⋊C4C24112yes—
645C2×C22⋊C4C2416yes—
646C2×C22⋊C4C2416yes—
647C2×C22⋊C4C2413yes—
648C2×C22⋊C4C2413yes—
649C2×C22⋊C4C2413yes—
650C2×C22⋊C4C2413yes—
651C2×C22⋊C4C2416yes—
652C2×C22⋊C4C2416yes—
653C2×C22⋊C4C2416yes—
654C2×C22⋊C4C2416yes—
655C2×C22⋊C4C24112yes—
656C2×C22⋊C4C24112yes—
657C2×C22⋊C4C24112yes—
658C2×C22⋊C4C2416yes—
659C2×C22⋊C4C2416yes—
660C2×C22⋊C4C2416yes—
661C2×C22⋊C4C2412yes—
662C2×C22⋊C4C2416yes—
663C2×C22⋊C4C2416yes—
664C2×C22⋊C4C24112yes—
665C2×C22⋊C4C2416yes—
666C2×C22⋊C4C2412yes—
667C2×C22⋊C4C2416yes—
668C2×C22⋊C4C2416yes—
669C2×C22⋊C4C2416yes—
670C2×C42—212no—
671C2×C42—224no—
672C2×C42—224no—
673C2×C42—86no—
674C2×C42C2×D4124yescomplemented
675C2×C42C2413yes—
676C2×C42C2411yescharacteristic
677C2×C42C2416yes—
678C2×C42C2416yes—
679C2×C42C2416yes—
680C2×C42C2416yes—
681C2×C42C2413yes—
682C2×C42C2413yes—
683C2×C42C2416yes—
684C2×C42C2412yes—
685C2×C42C2416yes—
686C2×C42C2416yes—
687C2×C42C24112yes—
688C2×C42C2412yes—
689C2×C42C2416yes—
690C2×C42C2416yes—
691C2×C42C2413yes—
692C2×C42C2413yes—
693C2×C42C2411yescharacteristic
694C2×C42C2413yes—
695#95C2416yes—
696#95C2416yes—
697#95C2416yes—
698#95C24112yes—
699#95C24112yes—
700#95C24112yes—
701#95C2412yes—
702#95C2416yes—
703#95C2416yes—
704#95C2416yes—
705#95C2412yes—
706#95C2416yes—
707#95C2416yes—
708#95C2412yes—
709#95C2412yes—
710#95C2416yes—
711#95C2416yes—
712#95C2416yes—
713#95C2412yes—
714C24—26no—
715C24—212no—
716C24—26no—
717C24—212no—
718C24—43no—
719C24—46no—
720C24—46no—
721C24—46no—
722C24—43no—
723C24—43no—
724C24—43no—
725C24—46no—
726C24C23×C4124yes—
727C24C23×C4112yes—
728C24C2511yescharacteristic
729C24C2516yes—
730C24C2513yes—
731C24C2513yes—
732#41—232no—
733#41—264no—
734#41—296no—
735#41—296no—
736#41—296no—
737#41C4×D4164yescomplemented
738C2×Q8—232no—
739C2×Q8—26no—
740C2×Q8—22no—
741C2×Q8—26no—
742C2×Q8—22no—
743C2×Q8C23×C414yes—
744C2×Q8C23×C4112yes—
745C2×Q8C23×C414yes—
746C2×Q8C22×D414yes—
747C2×Q8C2×#4114yes—
748C2×D4—212no—
749C2×D4—212no—
750C2×D4—212no—
751C2×D4—212no—
752C2×D4—2192no—
753C2×D4—296no—
754C2×D4—296no—
755C2×D4—26no—
756C2×D4—212no—
757C2×D4—26no—
758C2×D4—212no—
759C2×D4—26no—
760C2×D4—26no—
761C2×D4—46no—
762C2×D4—412no—
763C2×D4—412no—
764C2×D4—46no—
765C2×D4—46no—
766C2×D4—46no—
767C2×D4—848no—
768C2×D4C23×C4124yes—
769C2×D4C23×C4124yes—
770C2×D4C23×C4112yes—
771C2×D4C23×C4124yes—
772C2×D4C23×C4112yes—
773C2×D4C23×C4124yes—
774C2×D4C23×C4124yes—
775C2×D4C23×C4148yes—
776C2×D4C23×C4112yes—
777C2×D4C22×D4112yes—
778C2×D4C2×#41112yes—
779C22×C4—26no—
780C22×C4—26no—
781C22×C4—296no—
782C22×C4—26no—
783C22×C4—212no—
784C22×C4—26no—
785C22×C4—22no—
786C22×C4—26no—
787C22×C4—22no—
788C22×C4—26no—
789C22×C4—26no—
790C22×C4—26no—
791C22×C4—212no—
792C22×C4—26no—
793C22×C4—26no—
794C22×C4—212no—
795C22×C4—212no—
796C22×C4—212no—
797C22×C4—212no—
798C22×C4—212no—
799C22×C4—212no—
800C22×C4—224no—
801C22×C4—43no—
802C22×C4—46no—
803C22×C4—46no—
804C22×C4—43no—
805C22×C4—43no—
806C22×C4—46no—
807C22×C4—46no—
808C22×C4—43no—
809C22×C4—46no—
810C22×C4—46no—
811C22×C4—43no—
812C22×C4—43no—
813C22×C4—46no—
814C22×C4—43no—
815C22×C4—46no—
816C22×C4—46no—
817C22×C4—46no—
818C22×C4—46no—
819C22×C4—46no—
820C22×C4—412no—
821C22×C4—412no—
822C22×C4—46no—
823C22×C4—46no—
824C22×C4—43no—
825C22×C4—848no—
826C22×C4C23×C4112yes—
827C22×C4C23×C4112yes—
828C22×C4C23×C4112yes—
829C22×C4C23×C4124yes—
830C22×C4C23×C414yes—
831C22×C4C23×C4112yes—
832C22×C4C23×C4124yes—
833C22×C4C23×C4112yes—
834C22×C4C22×D4112yes—
835C22×C4C22×D4112yes—
836C22×C4C22×D4112yes—
837C22×C4C2×#41112yes—
838C22×C4C2512yes—
839C22×C4C2516yes—
840C22×C4C2512yes—
841C22×C4C2511yescharacteristic
842C22×C4C2513yes—
843C22×C4C2516yes—
844C22×C4C2511yescharacteristic
845C22×C4C2513yes—
846C22×C4C2512yes—
847C22×C4C2516yes—
848C22×C4C2513yes—
849C22×C4C2512yes—
850C22×C4C2511yescharacteristic
851C22×C4C2511yescharacteristic
852C22×C4C2513yes—
853C22×C4C2513yes—
854C22×C4C2511yescharacteristic
855C22×C4C2513yes—
856C22×C4C2511yescharacteristic
857C4⋊C4—26no—
858C4⋊C4—22no—
859C4⋊C4—26no—
860C4⋊C4—22no—
861C4⋊C4—212no—
862C4⋊C4—26no—
863C4⋊C4—212no—
864C4⋊C4—26no—
865C4⋊C4—26no—
866C4⋊C4—26no—
867C4⋊C4—26no—
868C4⋊C4—26no—
869C4⋊C4—26no—
870C4⋊C4—24no—
871C4⋊C4—22no—
872C4⋊C4—26no—
873C4⋊C4—212no—
874C4⋊C4—22no—
875C4⋊C4—46no—
876C4⋊C4—412no—
877C4⋊C4—42no—
878C4⋊C4—46no—
879C4⋊C4—46no—
880C4⋊C4C23×C4112yes—
881C4⋊C4C23×C4124yes—
882C4⋊C4C23×C414yes—
883C4⋊C4C23×C418yes—
884C4⋊C4C23×C4124yes—
885C4⋊C4C22×D4112yes—
886C4⋊C4C22×D4112yes—
887C22⋊C4—212no—
888C22⋊C4—212no—
889C22⋊C4—212no—
890C22⋊C4—26no—
891C22⋊C4—22no—
892C22⋊C4—26no—
893C22⋊C4—22no—
894C22⋊C4—212no—
895C22⋊C4—224no—
896C22⋊C4—212no—
897C22⋊C4—26no—
898C22⋊C4—26no—
899C22⋊C4—26no—
900C22⋊C4—26no—
901C22⋊C4—46no—
902C22⋊C4—46no—
903C22⋊C4—46no—
904C22⋊C4—412no—
905C22⋊C4—412no—
906C22⋊C4—412no—
907C22⋊C4—46no—
908C22⋊C4—42no—
909C22⋊C4—46no—
910C22⋊C4—46no—
911C22⋊C4—46no—
912C22⋊C4C23×C4124yes—
913C22⋊C4C23×C4148yes—
914C22⋊C4C23×C4124yes—
915C22⋊C4C23×C418yes—
916C22⋊C4C23×C4124yes—
917C22⋊C4C23×C4124yes—
918C22⋊C4C22×D4124yes—
919C42—22no—
920C42—26no—
921C42—24no—
922C42—212no—
923C42—212no—
924C42—212no—
925C42—212no—
926C42—26no—
927C42—26no—
928C42—212no—
929C42—46no—
930C42—412no—
931C42—42no—
932C42—46no—
933C42—46no—
934C42C23×C4124yes—
935C42C22×D4112yes—
936C42C22×D4112yes—
937C42C22×D414yes—
938C42C22×D4112yes—
939C23—23no—
940C23—23no—
941C23—23no—
942C23—23no—
943C23—21no—
944C23—23no—
945C23—26no—
946C23—21no—
947C23—23no—
948C23—26no—
949C23—21no—
950C23—23no—
951C23—26no—
952C23—26no—
953C23—23no—
954C23—23no—
955C23—26no—
956C23—21no—
957C23—21no—
958C23—21no—
959C23—26no—
960C23—23no—
961C23—224no—
962C23—248no—
963C23—412no—
964C23—424no—
965C23—412no—
966C23—424no—
967C23—812no—
968C23—86no—
969C23—86no—
970C23—812no—
971C23—86no—
972C23—812no—
973C23—86no—
974C23—812no—
975C23C24×C4112yes—
976C23C24×C412yes—
977C23C24×C416yes—
978C23C24×C416yes—
979C23C23×D416yes—
980C23C22×#4116yes—
981C23C2611yescharacteristic
982Q8—224no—
983Q8—28no—
984Q8C2×C4×D4116yes—
985D4—248no—
986D4—248no—
987D4—224no—
988D4—248no—
989D4—224no—
990D4—424no—
991D4—448no—
992D4—424no—
993D4C2×C4×D4148yes—
994C2×C4—22no—
995C2×C4—23no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—22no—
999C2×C4—23no—
1000C2×C4—21no—
1001C2×C4—23no—
1002C2×C4—22no—
1003C2×C4—26no—
1004C2×C4—23no—
1005C2×C4—23no—
1006C2×C4—26no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—22no—
1011C2×C4—23no—
1012C2×C4—224no—
1013C2×C4—28no—
1014C2×C4—224no—
1015C2×C4—224no—
1016C2×C4—224no—
1017C2×C4—248no—
1018C2×C4—22no—
1019C2×C4—23no—
1020C2×C4—21no—
1021C2×C4—23no—
1022C2×C4—21no—
1023C2×C4—26no—
1024C2×C4—22no—
1025C2×C4—26no—
1026C2×C4—22no—
1027C2×C4—26no—
1028C2×C4—26no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—23no—
1032C2×C4—23no—
1033C2×C4—22no—
1034C2×C4—26no—
1035C2×C4—23no—
1036C2×C4—26no—
1037C2×C4—21no—
1038C2×C4—22no—
1039C2×C4—23no—
1040C2×C4—22no—
1041C2×C4—21no—
1042C2×C4—412no—
1043C2×C4—424no—
1044C2×C4—412no—
1045C2×C4—424no—
1046C2×C4—812no—
1047C2×C4—812no—
1048C2×C4—812no—
1049C2×C4—824no—
1050C2×C4—86no—
1051C2×C4—86no—
1052C2×C4—812no—
1053C2×C4—812no—
1054C2×C4C2×C4×D4148yes—
1055C2×C4C24×C414yes—
1056C2×C4C24×C4112yes—
1057C2×C4C24×C412yes—
1058C2×C4C24×C416yes—
1059C2×C4C24×C414yes—
1060C2×C4C24×C416yes—
1061C2×C4C24×C412yes—
1062C2×C4C23×D416yes—
1063C2×C4C23×D412yes—
1064C2×C4C23×D416yes—
1065C2×C4C23×D412yes—
1066C2×C4C23×D412yes—
1067C2×C4C23×D416yes—
1068C2×C4C22×#4116yes—
1069C2×C4C22×#4112yes—
1070C22—26no—
1071C22—26no—
1072C22—26no—
1073C22—26no—
1074C22—26no—
1075C22—26no—
1076C22—22no—
1077C22—26no—
1078C22—212no—
1079C22—22no—
1080C22—26no—
1081C22—212no—
1082C22—26no—
1083C22—212no—
1084C22—22no—
1085C22—46no—
1086C22—43no—
1087C22—41no—
1088C22—43no—
1089C22—46no—
1090C22—41no—
1091C22—43no—
1092C22—46no—
1093C22—41no—
1094C22—43no—
1095C22—46no—
1096C22—41no—
1097C22—824no—
1098C22—848no—
1099C22C22×C4×D4112yes—
1100C22C25×C411yescharacteristic
1101C22C24×D411yescharacteristic
1102C22C23×#4111yescharacteristic
1103C22H(7,𝔽2)11yescharacteristic
1104C22H(7,𝔽2)11yescharacteristic
1105C22H(7,𝔽2)11yescharacteristic
1106C222−1+611yescharacteristic
1107C4—22no—
1108C4—26no—
1109C4—22no—
1110C4—26no—
1111C4—22no—
1112C4—24no—
1113C4—26no—
1114C4—212no—
1115C4—24no—
1116C4—46no—
1117C4—41no—
1118C4—43no—
1119C4—42no—
1120C4—41no—
1121C4—43no—
1122C4—42no—
1123C4—46no—
1124C4C22×C4×D414yes—
1125C4C22×C4×D4112yes—
1126C2—212no—
1127C2—46no—
1128C2—412no—
1129C2—42no—
1130C2C23×C4×D411yescharacteristic
1131C2#6265211yescharacteristic
1132C2#6265411yescharacteristic
1133C2#6285211yescharacteristic
1134C2#6285311yescharacteristic
1135C2#6285711yescharacteristic
1136C2#6285811yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC23C26
commutatorC22C25×C4
prime radicalC2×#3488C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×C4×H(5,𝔽2)C2semidirect
3. C2×#3428C2semidirect
4. #34313C2semidirect
5. #34312C2semidirect
6. #34310C2semidirect
7. #34309C2semidirect
8. #34295C2semidirect
9. #34293C2semidirect
10. #34290C2semidirect
11. #34288C2semidirect
12. #34269C2semidirect
13. #34267C2semidirect
14. #34258C2semidirect
15. #34250C2semidirect
16. #34204C2semidirect
17. #34202C2semidirect
18. #34175C2semidirect
19. C4×#537C2semidirect
20. C4×#535C2semidirect
21. #34065C2semidirect
22. C2×#2324C2semidirect
23. C4×#520C2semidirect
26. #3488C4semidirect
40. C2×#520C22semidirect
41. C2×#520C22semidirect
42. C2×#520C22semidirect
43. C2×#520C22semidirect
44. C2×#520C22semidirect
45. C2×#520C22semidirect
46. C2×#519C22semidirect
47. C2×#519C22semidirect
48. C2×#518C22semidirect
49. C2×#518C22semidirect
50. C2×#518C22semidirect
51. C2×#518C22semidirect
54. C2×C4×#41C22semidirect
55. C2×C4×#41C22semidirect
56. C2×C4×#41C22semidirect
57. C2×C4×#41C22semidirect
58. C22×C4×D4C22semidirect
59. C22×C4×D4C22semidirect
60. C22×#117C22semidirect
61. C22×#117C22semidirect
62. #2367C22semidirect
63. #2367C22semidirect
64. #2366C22semidirect
65. #2366C22semidirect
66. #2364C22semidirect
67. #2363C22semidirect
68. #2363C22semidirect
69. #2363C22semidirect
70. #2362C22semidirect
71. #2361C22semidirect
72. #2361C22semidirect
73. #2361C22semidirect
74. #2361C22semidirect
75. #2360C22semidirect
76. #2359C22semidirect
77. #2358C22semidirect
78. #2358C22semidirect
79. #2358C22semidirect
80. #2354C22semidirect
81. #2352C22semidirect
82. #2352C22semidirect
83. #2351C22semidirect
84. Q8×C4⋊C4C22semidirect
85. #2349C22semidirect
86. D4×C4⋊C4C22semidirect
87. D4×C4⋊C4C22semidirect
88. #2342C22semidirect
89. #2341C22semidirect
90. #2341C22semidirect
91. #2341C22semidirect
92. Q8×C22⋊C4C22semidirect
93. #2339C22semidirect
94. D4×C22⋊C4C22semidirect
95. D4×C22⋊C4C22semidirect
96. D4×C22⋊C4C22semidirect
97. D4×C22⋊C4C22semidirect
98. #2328C22semidirect
99. #2326C22semidirect
100. #2325C22semidirect
101. #2324C22semidirect
102. #2324C22semidirect
103. #2324C22semidirect
104. #2324C22semidirect
105. #2324C22semidirect
106. #2324C22semidirect
107. #2324C22semidirect
108. #2324C22semidirect
109. #2324C22semidirect
110. #2324C22semidirect
111. #2324C22semidirect
112. #2324C22semidirect
113. #2323C22semidirect
114. #2323C22semidirect
115. #2323C22semidirect
116. #2323C22semidirect
117. #2323C22semidirect
118. #2322C22semidirect
119. #2322C22semidirect
120. #2321C22semidirect
121. #2321C22semidirect
122. #2321C22semidirect
123. #2317C22semidirect
124. #2316C22semidirect
125. #2311C22semidirect
126. #2311C22semidirect
127. #2311C22semidirect
128. #2309C22semidirect
129. C4×#127C22semidirect
130. C4×#124C22semidirect
131. C4×C22⋊Q8C22semidirect
132. C4×C22⋊Q8C22semidirect
133. C4×#121C22semidirect
134. C4×#121C22semidirect
135. C4×#121C22semidirect
136. C4×#121C22semidirect
137. C4×#121C22semidirect
138. C4×#120C22semidirect
139. #2297C22semidirect
140. #2296C22semidirect
141. #2293C22semidirect
142. #2293C22semidirect
143. C2×#390C22semidirect
144. C2×#390C22semidirect
145. C2×#389C22semidirect
146. #2290C22semidirect
147. #2290C22semidirect
148. C2×#388C22semidirect
149. C2×#386C22semidirect
150. C2×#385C22semidirect
151. #2280C22semidirect
152. C2×#380C22semidirect
153. #2276C22semidirect
154. #2275C22semidirect
155. #2274C22semidirect
156. #2274C22semidirect
157. C42×Q8C22semidirect
158. C42×D4C22semidirect
159. C4×#117C22semidirect
160. C2×C4×C4⋊C4C22semidirect
163. C2×H(5,𝔽2)C2×C4semidirect
166. C22×#41C2×C4semidirect
180. #550C2×C4semidirect
181. #548C2×C4semidirect
182. #546C2×C4semidirect
183. D42C2×C4semidirect
184. #537C2×C4semidirect
185. #535C2×C4semidirect
188. #525C2×C4semidirect
193. C2×#121C2×C4semidirect
211. #520C2×C4semidirect
223. C4×#41D4semidirect
457. C2×#41C22×C4semidirect
458. C2×#41C22×C4semidirect
459. C2×#41C22×C4semidirect
464. C22×Q8C22×C4semidirect
478. C22×D4C22×C4semidirect
479. C22×D4C22×C4semidirect
494. C23×C4C22×C4semidirect
514. #127C22×C4semidirect
515. #124C22×C4semidirect
516. #123C22×C4semidirect
517. C22⋊Q8C22×C4semidirect
518. C22⋊Q8C22×C4semidirect
519. C22⋊Q8C22×C4semidirect
520. #121C22×C4semidirect
521. #121C22×C4semidirect
522. #121C22×C4semidirect
523. #121C22×C4semidirect
524. #121C22×C4semidirect
525. #121C22×C4semidirect
526. #121C22×C4semidirect
527. #120C22×C4semidirect
528. #120C22×C4semidirect
539. C4×Q8C22×C4semidirect
540. C4×Q8C2×D4semidirect
541. C4×Q8C2×D4semidirect
567. C4×D4C22×C4semidirect
568. C4×D4C22×C4semidirect
569. C4×D4C22×C4semidirect
570. C4×D4C2×D4semidirect
571. C4×D4C2×D4semidirect
588. #117C22×C4semidirect
589. #117C2×D4semidirect
598. C2×C4⋊C4C22×C4semidirect
637. C2×C22⋊C4C22×C4semidirect
674. C2×C42C2×D4semidirect
737. #41C4×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#34882
C2×C4×H(5,𝔽2)2
C2×#34282
#343132
#343122
#343102
#343092
#342952
#342932
#342902
#342882
#342692
#342672
#342582
#342502
#342042
#342022
#341752
C4×#5372
C4×#5352
#340652
C2×#23242
C4×#5202