Finite Group Databasebeta

← #7633041

Subgroups — #7633041

Order 512.

8460 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3503C211yesmaximal, characteristic, complemented
2C22×#520C211yesmaximal, characteristic
3Q8×C22⋊Q8C212yesmaximal, complemented
4#36435C212yesmaximal, complemented
5#36215C216yesmaximal, complemented
6D4×C22⋊Q8C216yesmaximal, complemented
7#35816C212yesmaximal, complemented
8#35806C216yesmaximal, complemented
9#35748C212yesmaximal, complemented
10#35739C216yesmaximal, complemented
11#35575C213yesmaximal, complemented
12#35574C213yesmaximal, complemented
13#35532C213yesmaximal, complemented
14#35519C213yesmaximal, complemented
15#35253C213yesmaximal, complemented
16#35224C213yesmaximal, complemented
17#34739C213yesmaximal, complemented
18C2×#2440C213yesmaximal, complemented
19#34250C211yesmaximal, characteristic, complemented
20#34250C211yesmaximal, characteristic, complemented
21#34183C211yesmaximal, characteristic, complemented
22#34175C211yesmaximal, characteristic
23C22⋊C4×#41C211yesmaximal, characteristic
24C23×#41C2211yescharacteristic
25#3503—216no—
26C2×Q82C2212yescomplemented
27C2×#557C2212yescomplemented
28C2×#554C2216yescomplemented
29C2×D4×Q8C2216yescomplemented
30C2×#544C2213yescomplemented
31C2×#544C2213yescomplemented
32C2×#533C2213yescomplemented
33C22×C4⋊Q8C2213yescomplemented
34C22×C22⋊Q8C2216yes—
35C2×#520—216no—
36C2×#520C2211yescharacteristic
37C2×#520C2211yescharacteristic
38C2×#520C2211yescharacteristic
39C2×#520C2216yes—
40C2×#520C2212yes—
41C2×#520C2213yes—
42C2×#520C2213yes—
43C2×#520C2211yescharacteristic
44C2×C4×#41C2211yescharacteristic
45C2×C4×#41C2211yescharacteristic
46C22×C4×Q8C2212yes—
47C22×C4×D4C2216yes—
48C22×#117C2213yes—
49C23×C4⋊C4C2213yes—
50#2857C2216yes—
51#2851C2216yes—
52#2848C22112yes—
53#2629C2216yescomplemented
54#2628C2216yescomplemented
55#2627C22112yescomplemented
56#2582C2216yescomplemented
57#2581C2216yescomplemented
58#2580C2216yescomplemented
59#2579C22112yescomplemented
60#2567C2216yescomplemented
61#2566C2216yescomplemented
62#2565C2216yescomplemented
63#2564C22112yescomplemented
64#2542C2216yescomplemented
65#2538C2216yescomplemented
66#2454C2216yescomplemented
67#2453C2216yescomplemented
68#2452C2216yescomplemented
69#2452C2216yescomplemented
70#2452C2216yescomplemented
71#2451C2216yescomplemented
72#2451C2216yescomplemented
73#2451C2216yescomplemented
74#2450C22112yescomplemented
75#2449C22112yescomplemented
76#2449C22112yescomplemented
77#2449C22112yescomplemented
78#2442C2216yes—
79#2442C2213yes—
80#2442C2213yes—
81#2442C2216yescomplemented
82#2442C2216yescomplemented
83#2441C2213yescomplemented
84#2441C2213yescomplemented
85#2441C2216yescomplemented
86#2440C2216yes—
87#2440C2213yes—
88#2440C2216yes—
89#2440C2216yes—
90#2440C2216yes—
91#2440C2211yescharacteristic
92#2440C2216yescomplemented
93#2440C2216yescomplemented
94#2440C2216yescomplemented
95#2440C2216yescomplemented
96#2440C2216yescomplemented
97#2440C2216yescomplemented
98#2439C2213yescomplemented
99#2439C2213yescomplemented
100#2439C2216yescomplemented
101#2438C2216yescomplemented
102#2438C22112yescomplemented
103#2438C2216yescomplemented
104#2437C2216yes—
105#2437C22112yes—
106#2437C2216yes—
107#2417C22112yescomplemented
108#2409C22112yescomplemented
109#2396C2216yescomplemented
110#2396C2216yescomplemented
111C2×#398C2216yescomplemented
112C2×#395C2216yescomplemented
113#2351C2212yescomplemented
114#2351C2212yescomplemented
115Q8×C4⋊C4C2212yescomplemented
116Q8×C4⋊C4C2212yescomplemented
117Q8×C4⋊C4C2212yescomplemented
118Q8×C4⋊C4C2212yescomplemented
119#2349C2216yescomplemented
120#2349C2216yescomplemented
121D4×C4⋊C4C2216yescomplemented
122D4×C4⋊C4C2216yescomplemented
123D4×C4⋊C4C2216yescomplemented
124D4×C4⋊C4C2216yescomplemented
125#2341C2211yescharacteristic
126#2341C2211yescharacteristic
127#2341C2212yes—
128Q8×C22⋊C4C2211yescharacteristic
129Q8×C22⋊C4C2211yescharacteristic
130Q8×C22⋊C4C2212yes—
131#2339C2213yes—
132#2339C2213yes—
133#2339C2216yes—
134D4×C22⋊C4C2213yes—
135D4×C22⋊C4C2213yes—
136D4×C22⋊C4C2216yes—
137#2317C2213yescomplemented
138#2317C2213yescomplemented
139#2317C2213yescomplemented
140#2317C2213yescomplemented
141#2316C2213yescomplemented
142#2316C2213yescomplemented
143#2311C2213yes—
144#2311C2213yes—
145C4×C22⋊Q8C2216yes—
146C4×C22⋊Q8C2216yes—
147#2297C2213yes—
148#2297C2213yes—
149#2296C2213yescomplemented
150#2296C2213yescomplemented
151C2×#389C2213yescomplemented
152C2×#389C2213yescomplemented
153C2×#385C2216yes—
154#2285C2213yescomplemented
155C2×#384C2213yescomplemented
156#2280C2213yes—
157#2280C2213yes—
158C2×#380C2213yes—
159C2×C4×C22⋊C4C2213yes—
160C22×#41—28no—
161C22×#41—28no—
162C22×#41Q8116yescomplemented
163C22×#41C2313yes—
164C22×#41C2313yes—
165C22×#41C2311yescharacteristic
166C22×#41C2311yescharacteristic
167C23×Q8C2311yescharacteristic
168C23×Q8C2316yes—
169C23×D4C2313yes—
170C24×C4C2313yes—
171C24×C4C2316yes—
172Q82—216no—
173#557—216no—
174#554—248no—
175D4×Q8—248no—
176#544—224no—
177#544—224no—
178#533—224no—
179C2×C4⋊Q8—224no—
180C2×C4⋊Q8C2316yes—
181C2×C4⋊Q8C2313yes—
182C2×C4⋊Q8C2316yes—
183C2×C4⋊Q8C2316yes—
184C2×C4⋊Q8C2316yes—
185C2×C4⋊Q8C2311yescharacteristic
186C2×C4⋊Q8C2316yes—
187C2×#125C2316yes—
188C2×#125C2313yes—
189C2×#125C2313yes—
190C2×#125C2316yes—
191C2×C22⋊Q8—424no—
192C2×C22⋊Q8C23112yes—
193C2×C22⋊Q8C2316yes—
194C2×C22⋊Q8C2316yes—
195C2×C22⋊Q8C2316yes—
196C2×C22⋊Q8C23112yes—
197C2×C22⋊Q8C2312yes—
198C2×C22⋊Q8C23112yes—
199C2×C22⋊Q8C23112yes—
200C2×C22⋊Q8C23112yes—
201C2×C22⋊Q8C23112yes—
202#520—28no—
203#520—28no—
204#520—28no—
205#520—216no—
206#520—248no—
207#520—224no—
208#520—224no—
209#520D4116yes—
210C4×#41—28no—
211C4×#41—28no—
212C2×C4×Q8—216no—
213C2×C4×Q8C2316yes—
214C2×C4×Q8C2316yes—
215C2×C4×Q8C2316yes—
216C2×C4×Q8C2311yescharacteristic
217C2×C4×Q8C2311yescharacteristic
218C2×C4×Q8C2312yes—
219C2×C4×Q8C2311yescharacteristic
220C2×C4×Q8C2312yes—
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2312yes—
223C2×C4×Q8C2316yes—
224C2×C4×Q8C2312yes—
225C2×C4×D4—248no—
226C2×C4×D4C23112yes—
227C2×C4×D4C2316yes—
228C2×C4×D4C2313yes—
229C2×C4×D4C2313yes—
230C2×C4×D4C2316yes—
231C2×C4×D4C2313yes—
232C2×C4×D4C2316yes—
233C2×C4×D4C2313yes—
234C2×C4×D4C2316yes—
235C2×C4×D4C23112yes—
236C2×C4×D4C2316yes—
237C2×C4×D4C2316yes—
238C2×#117—224no—
239C2×#117C2313yes—
240C2×#117C2313yes—
241C2×#117C2313yes—
242C2×#117C2313yes—
243C2×#117C2313yes—
244C2×#117C2316yes—
245C2×#117C2316yes—
246C2×#117C2313yes—
247C2×#117C2313yes—
248C2×#117C2313yes—
249C22×C4⋊C4—224no—
250C22×C4⋊C4C2313yes—
251C22×C4⋊C4C2313yes—
252C22×C4⋊C4C2313yes—
253C22×C4⋊C4C2316yes—
254C22×C4⋊C4C2316yes—
255C22×C4⋊C4C2313yes—
256C22×C4⋊C4C2316yes—
257C22×C4⋊C4C2316yes—
258C22×C4⋊C4C2316yes—
259C22×C4⋊C4C2311yescharacteristic
260C22×C4⋊C4C2316yes—
261C22×C4⋊C4C2316yes—
262C22×C4⋊C4C2316yes—
263C22×C4⋊C4C2316yes—
264C22×C4⋊C4C2313yes—
265C22×C22⋊C4C2313yes—
266C22×C22⋊C4C2313yes—
267C22×C22⋊C4C2316yes—
268C22×C22⋊C4C2316yes—
269C22×C42C2316yes—
270C22×C42C2313yes—
271C22×C42C2313yes—
272#400C23112yes—
273#400C2316yes—
274#400C2316yes—
275#399C2316yes—
276#399C23112yes—
277#399C2316yes—
278#398C23112yes—
279#398C23112yes—
280#398C23112yes—
281#398C23112yes—
282#398C2316yes—
283#398C23112yes—
284#398C2316yes—
285#398C2316yes—
286#398C2312yes—
287#396C2316yes—
288#396C23112yes—
289#396C2316yes—
290#396C23112yes—
291#396C2316yes—
292#396C2316yes—
293#395C23112yes—
294#395C23112yes—
295#395C23112yes—
296#395C23112yes—
297#395C2316yes—
298#395C2312yes—
299#393C23112yes—
300#393C2316yes—
301#393C2316yes—
302#391C2313yes—
303#391C2316yes—
304#391C2316yes—
305#391C2313yes—
306#391C2313yes—
307#391C2313yes—
308#391C2316yes—
309#391C23112yes—
310#391C2316yes—
311#390C2313yes—
312#390C2316yes—
313#390C2316yes—
314#390C2313yes—
315#390C2313yes—
316#390C2313yes—
317#389C2316yes—
318#389C23112yes—
319#389C2313yes—
320#389C2313yes—
321#389C2316yes—
322#389C2316yes—
323#389C2316yes—
324#389C2316yes—
325#389C2316yes—
326#389C2316yes—
327#389C2313yes—
328#389C2313yes—
329#389C2316yes—
330#389C2316yes—
331#389C2316yes—
332#389C2316yes—
333#389C2316yes—
334#389C2316yes—
335#389C2316yes—
336#389C2316yes—
337#389C2316yes—
338#389C2311yescharacteristic
339#389C2313yes—
340#389C2313yes—
341#389C2311yescharacteristic
342#387C2316yes—
343#387C23112yes—
344#387C2316yes—
345#387C23112yes—
346#387C2316yes—
347#387C2316yes—
348#386C2316yes—
349#386C23112yes—
350#386C23112yes—
351#386C2316yes—
352#386C2316yes—
353#386C2316yes—
354#385C23112yes—
355#385C23112yes—
356#385C23112yes—
357#385C23112yes—
358#385C23112yes—
359#385C23112yes—
360#385C23112yes—
361#385C2316yes—
362#385C23112yes—
363#385C2316yes—
364#385C23112yes—
365#385C2316yes—
366#385C2316yes—
367#385C2316yes—
368#385C2316yes—
369#385C2312yes—
370#385C2316yes—
371#384C2316yes—
372#384C2316yes—
373#384C2316yes—
374#384C2316yes—
375#384C2316yes—
376#384C2313yes—
377#384C2311yescharacteristic
378#382C2316yes—
379#382C2313yes—
380#382C2313yes—
381#382C2316yes—
382#381C2316yes—
383#381C2316yes—
384#380C2316yes—
385#380C23112yes—
386#380C2316yes—
387#380C2313yes—
388#380C2313yes—
389#380C23112yes—
390#380C2316yes—
391#380C23112yes—
392#380C2313yes—
393#380C2316yes—
394#380C2313yes—
395#380C2313yes—
396#380C2316yes—
397#380C2313yes—
398#380C2316yes—
399#380C2316yes—
400#380C2313yes—
401#380C2311yescharacteristic
402#379C2316yes—
403#379C2316yes—
404C4×C4⋊C4C2316yes—
405C4×C4⋊C4C2316yes—
406C4×C4⋊C4C2316yes—
407C4×C4⋊C4C2316yes—
408C4×C4⋊C4C2316yes—
409C4×C4⋊C4C2316yes—
410C4×C22⋊C4C2313yes—
411C4×C22⋊C4C2313yes—
412C4×C22⋊C4C2316yes—
413C4×C22⋊C4C2313yes—
414C4×C22⋊C4C2313yes—
415C4×C22⋊C4C2316yes—
416C4×C22⋊C4C2313yes—
417C4×C22⋊C4C2316yes—
418C4×C22⋊C4C2311yescharacteristic
419C4×C22⋊C4C2313yes—
420C4×C22⋊C4C2313yes—
421C2×#95C2316yes—
422C2×#95C2313yes—
423C2×#95C2316yes—
424C2×#95C2313yes—
425C2×#95C2316yes—
426C25C2413yes—
427C2×#41—2128no—
428C2×#41—24no—
429C2×#41—24no—
430C2×#41—212no—
431C2×#41—212no—
432C2×#41—212no—
433C2×#41—212no—
434C2×#41C2×D418yes—
435C2×#41C2×Q818yes—
436C2×#41C2×Q818yescomplemented
437C2×#41C2×Q8124yescomplemented
438C2×#41C2×Q8124yescomplemented
439C2×#41#4118yes—
440C22×Q8—24no—
441C22×Q8—24no—
442C22×Q8—224no—
443C22×Q8—412no—
444C22×Q8—86no—
445C22×Q8C2×Q818yescomplemented
446C22×Q8C2412yes—
447C22×Q8C2416yes—
448C22×Q8C2413yes—
449C22×Q8C24112yes—
450C22×Q8C2411yescharacteristic
451C22×D4—212no—
452C22×D4—212no—
453C22×D4C2×Q8124yescomplemented
454C22×D4C2416yes—
455C22×D4C2413yes—
456C22×D4C2413yes—
457C23×C4—212no—
458C23×C4—212no—
459C23×C4—224no—
460C23×C4—412no—
461C23×C4—86no—
462C23×C4C2×Q8124yescomplemented
463C23×C4C2412yes—
464C23×C4C2413yes—
465C23×C4C2416yes—
466C23×C4C2413yes—
467C23×C4C2413yes—
468C23×C4C2413yes—
469C23×C4C2411yescharacteristic
470C23×C4C2413yes—
471C23×C4C2413yes—
472C23×C4C2413yes—
473C23×C4C2413yes—
474C23×C4C2416yes—
475C23×C4C2416yes—
476C23×C4C2416yes—
477C23×C4C24112yes—
478C23×C4C2416yes—
479C23×C4C2413yes—
480C4⋊Q8—212no—
481C4⋊Q8—224no—
482C4⋊Q8—224no—
483C4⋊Q8—224no—
484C4⋊Q8—24no—
485C4⋊Q8—224no—
486C4⋊Q8—224no—
487#125—212no—
488#125—212no—
489#125—224no—
490#125—224no—
491C22⋊Q8—248no—
492C22⋊Q8—224no—
493C22⋊Q8—224no—
494C22⋊Q8—248no—
495C22⋊Q8—224no—
496C22⋊Q8—28no—
497C22⋊Q8—424no—
498C22⋊Q8—424no—
499C22⋊Q8—424no—
500C22⋊Q8—812no—
501C4×Q8—28no—
502C4×Q8—24no—
503C4×Q8—24no—
504C4×Q8—28no—
505C4×Q8—24no—
506C4×Q8—24no—
507C4×Q8—28no—
508C4×Q8—224no—
509C4×Q8—224no—
510C4×Q8—224no—
511C4×Q8—224no—
512C4×Q8C2×D4116yes—
513C4×D4—224no—
514C4×D4—212no—
515C4×D4—212no—
516C4×D4—224no—
517C4×D4—212no—
518C4×D4—212no—
519C4×D4—224no—
520C4×D4—248no—
521C4×D4—224no—
522C4×D4—248no—
523C4×D4—224no—
524C4×D4C2×D4148yes—
525#117—212no—
526#117—212no—
527#117—212no—
528#117—212no—
529#117—212no—
530#117—212no—
531#117—212no—
532#117—224no—
533#117—224no—
534#117C2×D4124yes—
535C2×C4⋊C4—224no—
536C2×C4⋊C4—212no—
537C2×C4⋊C4—212no—
538C2×C4⋊C4—224no—
539C2×C4⋊C4—212no—
540C2×C4⋊C4—212no—
541C2×C4⋊C4—224no—
542C2×C4⋊C4—224no—
543C2×C4⋊C4—224no—
544C2×C4⋊C4—24no—
545C2×C4⋊C4—412no—
546C2×C4⋊C4—412no—
547C2×C4⋊C4—412no—
548C2×C4⋊C4—86no—
549C2×C4⋊C4C2×D4124yes—
550C2×C4⋊C4C2413yes—
551C2×C4⋊C4C2416yes—
552C2×C4⋊C4C2416yes—
553C2×C4⋊C4C24112yes—
554C2×C4⋊C4C2413yes—
555C2×C4⋊C4C2413yes—
556C2×C4⋊C4C2416yes—
557C2×C4⋊C4C2416yes—
558C2×C4⋊C4C2416yes—
559C2×C4⋊C4C2416yes—
560C2×C4⋊C4C2411yescharacteristic
561C2×C4⋊C4C2412yes—
562C2×C4⋊C4C2416yes—
563C2×C4⋊C4C2416yes—
564C2×C4⋊C4C24112yes—
565C2×C4⋊C4C2411yescharacteristic
566C2×C4⋊C4C2411yescharacteristic
567C2×C4⋊C4C2413yes—
568C2×C4⋊C4C2413yes—
569C2×C4⋊C4C2413yes—
570C2×C4⋊C4C2413yes—
571C2×C4⋊C4C2412yes—
572C2×C4⋊C4C2416yes—
573C2×C4⋊C4C2416yes—
574C2×C4⋊C4C2416yes—
575C2×C4⋊C4C2416yes—
576C2×C4⋊C4C2412yes—
577C2×C4⋊C4C2412yes—
578C2×C4⋊C4C2412yes—
579C2×C4⋊C4C2416yes—
580C2×C4⋊C4C24112yes—
581C2×C4⋊C4C24112yes—
582C2×C4⋊C4C24112yes—
583C2×C4⋊C4C24112yes—
584C2×C4⋊C4C2416yes—
585C2×C4⋊C4C2416yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2416yes—
588C2×C4⋊C4C2416yes—
589C2×C4⋊C4C2413yes—
590C2×C4⋊C4C2416yes—
591C2×C4⋊C4C2411yescharacteristic
592C2×C22⋊C4—224no—
593C2×C22⋊C4—212no—
594C2×C22⋊C4—212no—
595C2×C22⋊C4—412no—
596C2×C22⋊C4C2416yes—
597C2×C22⋊C4C2416yes—
598C2×C22⋊C4C2416yes—
599C2×C22⋊C4C2416yes—
600C2×C22⋊C4C2413yes—
601C2×C22⋊C4C2413yes—
602C2×C22⋊C4C2413yes—
603C2×C22⋊C4C2413yes—
604C2×C22⋊C4C2413yes—
605C2×C22⋊C4C2413yes—
606C2×C22⋊C4C2416yes—
607C2×C22⋊C4C2416yes—
608C2×C22⋊C4C2416yes—
609C2×C22⋊C4C2416yes—
610C2×C22⋊C4C2412yes—
611C2×C22⋊C4C24112yes—
612C2×C22⋊C4C2416yes—
613C2×C22⋊C4C2416yes—
614C2×C22⋊C4C2416yes—
615C2×C22⋊C4C2416yes—
616C2×C22⋊C4C2416yes—
617C2×C22⋊C4C2411yescharacteristic
618C2×C22⋊C4C2411yescharacteristic
619C2×C42—212no—
620C2×C42—212no—
621C2×C42—224no—
622C2×C42C2416yes—
623C2×C42C2416yes—
624C2×C42C2416yes—
625C2×C42C2413yes—
626C2×C42C2413yes—
627C2×C42C2416yes—
628C2×C42C2416yes—
629C2×C42C2413yes—
630C2×C42C2413yes—
631C2×C42C2413yes—
632C2×C42C2413yes—
633C2×C42C2411yescharacteristic
634C2×C42C2411yescharacteristic
635C2×C42C2416yes—
636#95C2411yescharacteristic
637#95C2411yescharacteristic
638#95C2416yes—
639#95C2416yes—
640#95C2416yes—
641#95C2413yes—
642#95C2413yes—
643#95C2413yes—
644#95C2413yes—
645#95C2413yes—
646#95C2413yes—
647#95C24112yes—
648#95C24112yes—
649#95C24112yes—
650#95C2412yes—
651#95C2416yes—
652#95C2416yes—
653#95C2416yes—
654#95C2416yes—
655#95C2412yes—
656#95C2412yes—
657#95C2416yes—
658#95C2416yes—
659#95C2416yes—
660#95C2416yes—
661#95C2416yes—
662#95C2416yes—
663#95C2416yes—
664#95C2416yes—
665C24—26no—
666C24—26no—
667C24—26no—
668C24—26no—
669C24—43no—
670C24—43no—
671C24C22×Q8112yes—
672C24C2513yes—
673C24C2513yes—
674C24C2511yescharacteristic
675#41—232no—
676#41—296no—
677#41—296no—
678#41C22⋊Q8164yescomplemented
679C2×Q8—232no—
680C2×Q8—26no—
681C2×Q8—24no—
682C2×Q8—212no—
683C2×Q8—224no—
684C2×Q8—26no—
685C2×Q8—212no—
686C2×Q8—24no—
687C2×Q8—46no—
688C2×Q8—42no—
689C2×Q8—412no—
690C2×Q8—412no—
691C2×Q8—848no—
692C2×Q8C22×D414yes—
693C2×Q8C22×Q8112yes—
694C2×Q8C22×Q814yes—
695C2×Q8C2×#4114yes—
696C2×D4—212no—
697C2×D4—212no—
698C2×D4—296no—
699C2×D4—26no—
700C2×D4—26no—
701C2×D4C22×D4112yes—
702C2×D4C22×Q8124yes—
703C2×D4C22×Q8112yes—
704C2×D4C22×Q8112yes—
705C2×D4C2×#41112yes—
706C22×C4—26no—
707C22×C4—26no—
708C22×C4—296no—
709C22×C4—26no—
710C22×C4—22no—
711C22×C4—26no—
712C22×C4—26no—
713C22×C4—22no—
714C22×C4—26no—
715C22×C4—26no—
716C22×C4—26no—
717C22×C4—26no—
718C22×C4—26no—
719C22×C4—26no—
720C22×C4—26no—
721C22×C4—212no—
722C22×C4—24no—
723C22×C4—212no—
724C22×C4—212no—
725C22×C4—212no—
726C22×C4—24no—
727C22×C4—212no—
728C22×C4—26no—
729C22×C4—26no—
730C22×C4—26no—
731C22×C4—26no—
732C22×C4—224no—
733C22×C4—46no—
734C22×C4—43no—
735C22×C4—46no—
736C22×C4—46no—
737C22×C4—42no—
738C22×C4—43no—
739C22×C4—43no—
740C22×C4—43no—
741C22×C4—46no—
742C22×C4—46no—
743C22×C4—46no—
744C22×C4—46no—
745C22×C4—46no—
746C22×C4—412no—
747C22×C4—412no—
748C22×C4—46no—
749C22×C4—848no—
750C22×C4C22×D4124yes—
751C22×C4C22×D4112yes—
752C22×C4C22×Q814yes—
753C22×C4C22×Q8112yes—
754C22×C4C22×Q8112yes—
755C22×C4C22×Q8112yes—
756C22×C4C22×Q8112yes—
757C22×C4C22×Q8112yes—
758C22×C4C2×#41112yes—
759C22×C4C2513yes—
760C22×C4C2512yes—
761C22×C4C2516yes—
762C22×C4C2512yes—
763C22×C4C2512yes—
764C22×C4C2513yes—
765C22×C4C2513yes—
766C22×C4C2513yes—
767C22×C4C2516yes—
768C22×C4C2516yes—
769C22×C4C2512yes—
770C22×C4C2516yes—
771C22×C4C2513yes—
772C22×C4C2511yescharacteristic
773C22×C4C2511yescharacteristic
774C22×C4C2511yescharacteristic
775C22×C4C2511yescharacteristic
776C22×C4C2511yescharacteristic
777C22×C4C2513yes—
778C22×C4C2511yescharacteristic
779C4⋊C4—212no—
780C4⋊C4—26no—
781C4⋊C4—224no—
782C4⋊C4—212no—
783C4⋊C4—26no—
784C4⋊C4—212no—
785C4⋊C4—24no—
786C4⋊C4—22no—
787C4⋊C4—212no—
788C4⋊C4—224no—
789C4⋊C4—22no—
790C4⋊C4—26no—
791C4⋊C4—26no—
792C4⋊C4—24no—
793C4⋊C4—212no—
794C4⋊C4—212no—
795C4⋊C4—212no—
796C4⋊C4—212no—
797C4⋊C4—26no—
798C4⋊C4—212no—
799C4⋊C4—22no—
800C4⋊C4—26no—
801C4⋊C4—26no—
802C4⋊C4—212no—
803C4⋊C4—212no—
804C4⋊C4—212no—
805C4⋊C4—24no—
806C4⋊C4—24no—
807C4⋊C4—24no—
808C4⋊C4—412no—
809C4⋊C4—412no—
810C4⋊C4—412no—
811C4⋊C4—46no—
812C4⋊C4—412no—
813C4⋊C4—46no—
814C4⋊C4—42no—
815C4⋊C4—46no—
816C4⋊C4—46no—
817C4⋊C4—46no—
818C4⋊C4C22×D4112yes—
819C4⋊C4C22×D4124yes—
820C4⋊C4C22×D414yes—
821C22⋊C4—212no—
822C22⋊C4—212no—
823C22⋊C4—212no—
824C22⋊C4—212no—
825C22⋊C4—212no—
826C22⋊C4—26no—
827C22⋊C4—212no—
828C22⋊C4—26no—
829C22⋊C4—24no—
830C22⋊C4—212no—
831C22⋊C4—212no—
832C22⋊C4—26no—
833C22⋊C4—26no—
834C22⋊C4—26no—
835C22⋊C4—26no—
836C22⋊C4—412no—
837C22⋊C4—46no—
838C22⋊C4—46no—
839C22⋊C4—46no—
840C22⋊C4—46no—
841C22⋊C4C22×D4124yes—
842C22⋊C4H(5,𝔽2)14yes—
843C22⋊C42−1+414yes—
844C42—22no—
845C42—212no—
846C42—212no—
847C42—212no—
848C42—26no—
849C42—26no—
850C42—26no—
851C42—212no—
852C42—22no—
853C42—26no—
854C42—26no—
855C42—26no—
856C42—212no—
857C42C22×D4124yes—
858C23—21no—
859C23—21no—
860C23—23no—
861C23—23no—
862C23—23no—
863C23—21no—
864C23—23no—
865C23—21no—
866C23—23no—
867C23—23no—
868C23—23no—
869C23—23no—
870C23—23no—
871C23—23no—
872C23—224no—
873C23—224no—
874C23—412no—
875C23—412no—
876C23—412no—
877C23—412no—
878C23—412no—
879C23C23×D416yes—
880C23C23×Q816yes—
881C23C23×Q816yes—
882C23C23×Q812yes—
883C23C22×#4116yes—
884C23C2×H(5,𝔽2)12yes—
885C23C2×2−1+412yes—
886C23C2611yescharacteristic
887Q8—224no—
888Q8—48no—
889Q8—424no—
890Q8—824no—
891Q8C2×C22⋊Q8116yescomplemented
892D4—248no—
893D4—224no—
894D4C2×C22⋊Q8148yescomplemented
895C2×C4—21no—
896C2×C4—23no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—23no—
903C2×C4—26no—
904C2×C4—22no—
905C2×C4—21no—
906C2×C4—26no—
907C2×C4—21no—
908C2×C4—22no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—224no—
912C2×C4—28no—
913C2×C4—224no—
914C2×C4—224no—
915C2×C4—224no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—23no—
919C2×C4—26no—
920C2×C4—23no—
921C2×C4—26no—
922C2×C4—22no—
923C2×C4—23no—
924C2×C4—23no—
925C2×C4—26no—
926C2×C4—23no—
927C2×C4—23no—
928C2×C4—26no—
929C2×C4—26no—
930C2×C4—26no—
931C2×C4—23no—
932C2×C4—23no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—23no—
938C2×C4—23no—
939C2×C4—26no—
940C2×C4—26no—
941C2×C4—22no—
942C2×C4—23no—
943C2×C4—23no—
944C2×C4—26no—
945C2×C4—22no—
946C2×C4—424no—
947C2×C4—412no—
948C2×C4—412no—
949C2×C4—48no—
950C2×C4—412no—
951C2×C4—424no—
952C2×C4—412no—
953C2×C4—824no—
954C2×C4—812no—
955C2×C4—812no—
956C2×C4—812no—
957C2×C4C2×C22⋊Q8148yescomplemented
958C2×C4C23×D414yes—
959C2×C4C23×D4112yes—
960C2×C4C23×D416yes—
961C2×C4C23×D412yes—
962C2×C4C23×Q812yes—
963C2×C4C23×Q816yes—
964C2×C4C23×Q812yes—
965C2×C4C23×Q816yes—
966C2×C4C22×#4112yes—
967C2×C4C22×#4116yes—
968C2×C4C2×H(5,𝔽2)12yes—
969C2×C4C2×H(5,𝔽2)12yes—
970C2×C4C2×2−1+412yes—
971C2×C4C2×2−1+412yes—
972C22—22no—
973C22—26no—
974C22—26no—
975C22—22no—
976C22—22no—
977C22—26no—
978C22—26no—
979C22—22no—
980C22—26no—
981C22—22no—
982C22—26no—
983C22—22no—
984C22—26no—
985C22—26no—
986C22—26no—
987C22—448no—
988C22—43no—
989C22—43no—
990C22—43no—
991C22—43no—
992C22C22×C22⋊Q8112yes—
993C22#350314yescomplemented
994C22C24×D411yescharacteristic
995C22C24×Q811yescharacteristic
996C22C23×#4111yescharacteristic
997C22C22×H(5,𝔽2)11yescharacteristic
998C22C22×2−1+411yescharacteristic
999C22H(7,𝔽2)11yescharacteristic
1000C222−1+611yescharacteristic
1001C4—212no—
1002C4—22no—
1003C4—22no—
1004C4—22no—
1005C4—24no—
1006C4—22no—
1007C4—22no—
1008C4—26no—
1009C4—46no—
1010C4—43no—
1011C4—46no—
1012C4—43no—
1013C4—46no—
1014C4—42no—
1015C4—43no—
1016C4—42no—
1017C4—42no—
1018C4—43no—
1019C4C22×C22⋊Q814yes—
1020C4C22×C22⋊Q8112yes—
1021C2—24no—
1022C2—212no—
1023C2—46no—
1024C2C23×C22⋊Q811yescharacteristic
1025C2C2×#350311yescharacteristic
1026C2#6285411yescharacteristic
1027C2D4×H(5,𝔽2)11yescharacteristic
1028C2#6298511yescharacteristic
1029C2D4×2−1+411yescharacteristic
1030C2#6300011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC23×#41C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3503C2semidirect
3. Q8×C22⋊Q8C2semidirect
4. #36435C2semidirect
5. #36215C2semidirect
6. D4×C22⋊Q8C2semidirect
7. #35816C2semidirect
8. #35806C2semidirect
9. #35748C2semidirect
10. #35739C2semidirect
11. #35575C2semidirect
12. #35574C2semidirect
13. #35532C2semidirect
14. #35519C2semidirect
15. #35253C2semidirect
16. #35224C2semidirect
17. #34739C2semidirect
18. C2×#2440C2semidirect
19. #34250C2semidirect
20. #34250C2semidirect
21. #34183C2semidirect
26. C2×Q82C22semidirect
27. C2×#557C22semidirect
28. C2×#554C22semidirect
29. C2×D4×Q8C22semidirect
30. C2×#544C22semidirect
31. C2×#544C22semidirect
32. C2×#533C22semidirect
33. C22×C4⋊Q8C22semidirect
53. #2629C22semidirect
54. #2628C22semidirect
55. #2627C22semidirect
56. #2582C22semidirect
57. #2581C22semidirect
58. #2580C22semidirect
59. #2579C22semidirect
60. #2567C22semidirect
61. #2566C22semidirect
62. #2565C22semidirect
63. #2564C22semidirect
64. #2542C22semidirect
65. #2538C22semidirect
66. #2454C22semidirect
67. #2453C22semidirect
68. #2452C22semidirect
69. #2452C22semidirect
70. #2452C22semidirect
71. #2451C22semidirect
72. #2451C22semidirect
73. #2451C22semidirect
74. #2450C22semidirect
75. #2449C22semidirect
76. #2449C22semidirect
77. #2449C22semidirect
81. #2442C22semidirect
82. #2442C22semidirect
83. #2441C22semidirect
84. #2441C22semidirect
85. #2441C22semidirect
92. #2440C22semidirect
93. #2440C22semidirect
94. #2440C22semidirect
95. #2440C22semidirect
96. #2440C22semidirect
97. #2440C22semidirect
98. #2439C22semidirect
99. #2439C22semidirect
100. #2439C22semidirect
101. #2438C22semidirect
102. #2438C22semidirect
103. #2438C22semidirect
107. #2417C22semidirect
108. #2409C22semidirect
109. #2396C22semidirect
110. #2396C22semidirect
111. C2×#398C22semidirect
112. C2×#395C22semidirect
113. #2351C22semidirect
114. #2351C22semidirect
115. Q8×C4⋊C4C22semidirect
116. Q8×C4⋊C4C22semidirect
117. Q8×C4⋊C4C22semidirect
118. Q8×C4⋊C4C22semidirect
119. #2349C22semidirect
120. #2349C22semidirect
121. D4×C4⋊C4C22semidirect
122. D4×C4⋊C4C22semidirect
123. D4×C4⋊C4C22semidirect
124. D4×C4⋊C4C22semidirect
137. #2317C22semidirect
138. #2317C22semidirect
139. #2317C22semidirect
140. #2317C22semidirect
141. #2316C22semidirect
142. #2316C22semidirect
149. #2296C22semidirect
150. #2296C22semidirect
151. C2×#389C22semidirect
152. C2×#389C22semidirect
154. #2285C22semidirect
155. C2×#384C22semidirect
162. C22×#41Q8semidirect
436. C2×#41C2×Q8semidirect
437. C2×#41C2×Q8semidirect
438. C2×#41C2×Q8semidirect
445. C22×Q8C2×Q8semidirect
453. C22×D4C2×Q8semidirect
462. C23×C4C2×Q8semidirect
678. #41C22⋊Q8semidirect
891. Q8C2×C22⋊Q8semidirect
894. D4C2×C22⋊Q8semidirect
957. C2×C4C2×C22⋊Q8semidirect
993. C22#3503semidirect

Maximal subgroups

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

subgroupindex
C2×#35032
C22×#5202
Q8×C22⋊Q82
#364352
#362152
D4×C22⋊Q82
#358162
#358062
#357482
#357392
#355752
#355742
#355322
#355192
#352532
#352242
#347392
C2×#24402
#342502
#341832
#341752
C22⋊C4×#412