Finite Group Databasebeta

← #7632706

Subgroups — #7632706

Order 512.

8530 conjugacy classes of subgroups.

The subgroup lattice has 1011 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3503C211yesmaximal, characteristic, complemented
2C2×C4×H(5,𝔽2)C211yesmaximal, characteristic
3#36456C212yesmaximal, complemented
4#36431C212yesmaximal, complemented
5#36215C216yesmaximal, complemented
6D4×C22⋊Q8C216yesmaximal, complemented
7#35816C212yesmaximal, complemented
8#35776C216yesmaximal, complemented
9#35748C212yesmaximal, complemented
10#35702C216yesmaximal, complemented
11#35575C213yesmaximal, complemented
12#35574C213yesmaximal, complemented
13#35529C213yesmaximal, complemented
14#35515C213yesmaximal, complemented
15#35257C213yesmaximal, complemented
16#35174C213yesmaximal, complemented
17#34745C213yesmaximal, complemented
18C2×#2452C213yesmaximal, complemented
19#34258C211yesmaximal, characteristic
20#34258C211yesmaximal, characteristic
21#34250C211yesmaximal, characteristic, complemented
22#34250C211yesmaximal, characteristic, complemented
23C4⋊C4×#41C211yesmaximal, characteristic, complemented
24C22×H(5,𝔽2)C2211yescharacteristic
25#3503—216no—
26C2×Q82C2212yescomplemented
27C2×#557C2212yescomplemented
28C2×#554C2216yescomplemented
29C2×D4×Q8C2216yescomplemented
30C2×#544C2213yescomplemented
31C2×#544C2213yescomplemented
32C2×#533C2213yescomplemented
33C22×C4⋊Q8C2213yescomplemented
34C22×C22⋊Q8C2216yescomplemented
35C4×H(5,𝔽2)—216no—
36C2×#520C2211yescharacteristic
37C2×#520C2212yes—
38C2×#520C2213yes—
39C2×#520C2211yescharacteristic
40C2×#520C2211yescharacteristic
41C2×#518C2216yes—
42C2×#518C2213yes—
43C2×C4×#41C2211yescharacteristic
44C2×C4×#41C2211yescharacteristic
45C2×C4×#41C2211yescharacteristic
46C2×C4×#41C2212yes—
47C2×C4×#41C2213yes—
48C22×C4×D4C2213yes—
49C22×C4×D4C2216yes—
50#2857C2216yescomplemented
51#2851C2216yescomplemented
52#2848C22112yescomplemented
53#2629C2216yescomplemented
54#2628C2216yescomplemented
55#2626C22112yescomplemented
56#2580C2216yescomplemented
57#2580C2216yescomplemented
58#2579C22112yescomplemented
59#2566C2216yescomplemented
60#2566C2216yescomplemented
61#2564C22112yescomplemented
62#2563C2216yescomplemented
63#2542C2216yescomplemented
64#2538C2216yescomplemented
65#2538C2216yescomplemented
66#2454C2216yescomplemented
67#2454C2213yescomplemented
68#2454C2216yescomplemented
69#2454C2216yescomplemented
70#2454C2213yescomplemented
71#2454C2216yescomplemented
72#2453C2213yescomplemented
73#2453C2213yescomplemented
74#2452C2216yescomplemented
75#2452C2216yescomplemented
76#2452C2216yescomplemented
77#2452C2216yescomplemented
78#2452C2216yescomplemented
79#2452C2216yescomplemented
80#2452C2216yescomplemented
81#2452C2213yescomplemented
82#2452C2216yescomplemented
83#2452C2216yescomplemented
84#2452C2216yescomplemented
85#2452C2213yescomplemented
86#2451C2211yescharacteristic, complemented
87#2451C2213yescomplemented
88#2451C2216yescomplemented
89#2450C2216yescomplemented
90#2450C22112yescomplemented
91#2450C2216yescomplemented
92#2449C22112yescomplemented
93#2449C2216yescomplemented
94#2449C2216yescomplemented
95#2442C2216yescomplemented
96#2441C2216yescomplemented
97#2440C2216yescomplemented
98#2440C2216yescomplemented
99#2440C2216yescomplemented
100#2439C2216yescomplemented
101#2439C2216yescomplemented
102#2439C2216yescomplemented
103#2437C22112yescomplemented
104#2437C22112yescomplemented
105#2437C22112yescomplemented
106#2437C22112yescomplemented
107#2417C22112yescomplemented
108#2409C22112yescomplemented
109#2396C2216yescomplemented
110#2396C2216yescomplemented
111C2×#396C2216yescomplemented
112C2×#393C2216yescomplemented
113#2351C2211yescharacteristic, complemented
114#2351C2211yescharacteristic, complemented
115#2351C2212yescomplemented
116#2351C2212yescomplemented
117Q8×C4⋊C4C2211yescharacteristic, complemented
118Q8×C4⋊C4C2211yescharacteristic, complemented
119Q8×C4⋊C4C2212yescomplemented
120Q8×C4⋊C4C2212yescomplemented
121#2349C2213yescomplemented
122#2349C2213yescomplemented
123#2349C2216yescomplemented
124#2349C2216yescomplemented
125D4×C4⋊C4C2213yescomplemented
126D4×C4⋊C4C2213yescomplemented
127D4×C4⋊C4C2216yescomplemented
128D4×C4⋊C4C2216yescomplemented
129#2341C2212yes—
130#2341C2212yes—
131#2341C2212yes—
132#2341C2212yes—
133D4×C22⋊C4C2216yes—
134D4×C22⋊C4C2216yes—
135D4×C22⋊C4C2216yes—
136D4×C22⋊C4C2216yes—
137#2317C2213yescomplemented
138#2317C2213yescomplemented
139#2316C2213yescomplemented
140#2316C2213yescomplemented
141#2311C2213yes—
142#2311C2213yes—
143#2309C2213yes—
144#2309C2213yes—
145C4×C22⋊Q8C2216yescomplemented
146C4×C22⋊Q8C2216yescomplemented
147#2297C2213yes—
148#2297C2213yes—
149#2296C2213yescomplemented
150#2296C2213yescomplemented
151#2296C2213yescomplemented
152#2296C2213yescomplemented
153C2×#390C2213yes—
154C2×#390C2213yes—
155C2×#389C2213yescomplemented
156C2×#389C2213yescomplemented
157C2×#385C2216yescomplemented
158#2285C2213yescomplemented
159C2×C4×C4⋊C4C2213yescomplemented
160C2×H(5,𝔽2)—28no—
161C2×H(5,𝔽2)—28no—
162C2×H(5,𝔽2)Q8116yescomplemented
163C22×#41C2313yes—
164C22×#41C2312yes—
165C22×#41C2311yescharacteristic
166C23×Q8C2316yes—
167C23×D4C2313yes—
168C23×D4C2316yes—
169C24×C4C2316yes—
170Q82—216no—
171#557—216no—
172#554—248no—
173D4×Q8—248no—
174#544—224no—
175#544—224no—
176#533—224no—
177C2×C4⋊Q8—224no—
178C2×C4⋊Q8C2316yes—
179C2×C4⋊Q8C2313yes—
180C2×C4⋊Q8C2316yes—
181C2×C4⋊Q8C2316yes—
182C2×C4⋊Q8C2316yes—
183C2×C4⋊Q8C2311yescharacteristic
184C2×C4⋊Q8C2316yes—
185C2×#125C2316yes—
186C2×#125C2313yes—
187C2×#125C2313yes—
188C2×#125C2316yes—
189C2×C22⋊Q8—424no—
190C2×C22⋊Q8C23112yes—
191C2×C22⋊Q8C2316yes—
192C2×C22⋊Q8C2316yes—
193C2×C22⋊Q8C2316yes—
194C2×C22⋊Q8C23112yes—
195C2×C22⋊Q8C23112yes—
196C2×C22⋊Q8C23112yes—
197C2×C22⋊Q8C23112yes—
198C2×C22⋊Q8C2316yes—
199C2×C22⋊Q8C23112yes—
200#520—28no—
201#520—28no—
202#520—216no—
203#520—224no—
204#520D4116yes—
205#518—248no—
206#518—224no—
207C4×#41—28no—
208C4×#41—28no—
209C4×#41—28no—
210C4×#41—216no—
211C4×#41—224no—
212C2×C4×Q8C2316yes—
213C2×C4×Q8C2316yes—
214C2×C4×Q8C2311yescharacteristic
215C2×C4×Q8C2311yescharacteristic
216C2×C4×Q8C2312yes—
217C2×C4×Q8C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2312yes—
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2313yes—
224C2×C4×Q8C2312yes—
225C2×C4×D4—248no—
226C2×C4×D4—224no—
227C2×C4×D4C2316yes—
228C2×C4×D4C23112yes—
229C2×C4×D4C2316yes—
230C2×C4×D4C2313yes—
231C2×C4×D4C2316yes—
232C2×C4×D4C2313yes—
233C2×C4×D4C2313yes—
234C2×C4×D4C2316yes—
235C2×C4×D4C2313yes—
236C2×C4×D4C2313yes—
237C2×C4×D4C2313yes—
238C2×C4×D4C2316yes—
239C2×C4×D4C2313yes—
240C2×C4×D4C2316yes—
241C2×C4×D4C2316yes—
242C2×C4×D4C2316yes—
243C2×C4×D4C2316yes—
244C2×C4×D4C2313yes—
245C2×C4×D4C2316yes—
246C2×#117C2313yes—
247C2×#117C2313yes—
248C2×#117C2313yes—
249C2×#117C2313yes—
250C2×#117C2313yes—
251C2×#117C2316yes—
252C2×#117C2316yes—
253C2×#117C2313yes—
254C22×C4⋊C4C2313yes—
255C22×C4⋊C4C2313yes—
256C22×C4⋊C4C2316yes—
257C22×C4⋊C4C2313yes—
258C22×C4⋊C4C2316yes—
259C22×C4⋊C4C2313yes—
260C22×C4⋊C4C2316yes—
261C22×C4⋊C4C2316yes—
262C22×C4⋊C4C2313yes—
263C22×C22⋊C4C2316yes—
264C22×C22⋊C4C23112yes—
265C22×C22⋊C4C2316yes—
266C22×C22⋊C4C2316yes—
267C22×C22⋊C4C2316yes—
268C22×C22⋊C4C2316yes—
269C22×C42C2316yes—
270C22×C42C2313yes—
271C22×C42C2313yes—
272C22×C42C2313yes—
273#400C2316yes—
274#400C2316yes—
275#399C23112yes—
276#399C23112yes—
277#399C2316yes—
278#399C2316yes—
279#398C2316yes—
280#398C23112yes—
281#398C2316yes—
282#398C2312yes—
283#398C2316yes—
284#396C2316yes—
285#396C23112yes—
286#396C23112yes—
287#396C23112yes—
288#396C23112yes—
289#396C2316yes—
290#396C23112yes—
291#396C23112yes—
292#396C2316yes—
293#396C2316yes—
294#395C23112yes—
295#395C2312yes—
296#395C2316yes—
297#393C23112yes—
298#393C23112yes—
299#393C2316yes—
300#393C23112yes—
301#393C23112yes—
302#393C2316yes—
303#391C2313yes—
304#391C2313yes—
305#391C23112yes—
306#391C2316yes—
307#391C2312yes—
308#391C2311yescharacteristic
309#391C2311yescharacteristic
310#390C2316yes—
311#390C2316yes—
312#390C2313yes—
313#390C2313yes—
314#390C2316yes—
315#390C2316yes—
316#390C2316yes—
317#390C2316yes—
318#390C2316yes—
319#390C2316yes—
320#390C2316yes—
321#390C2316yes—
322#390C2313yes—
323#390C2313yes—
324#389C2313yes—
325#389C2313yes—
326#389C2316yes—
327#389C2316yes—
328#389C2316yes—
329#389C2316yes—
330#389C2316yes—
331#389C2316yes—
332#389C2313yes—
333#389C2313yes—
334#389C2313yes—
335#389C2313yes—
336#389C2313yes—
337#389C2316yes—
338#389C2313yes—
339#389C2316yes—
340#389C2313yes—
341#389C2313yes—
342#389C2313yes—
343#389C2316yes—
344#389C2313yes—
345#389C2316yes—
346#389C2316yes—
347#389C2316yes—
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2313yes—
351#389C2313yes—
352#387C2316yes—
353#387C23112yes—
354#387C2316yes—
355#387C2316yes—
356#387C2312yes—
357#386C2316yes—
358#386C23112yes—
359#386C23112yes—
360#386C2316yes—
361#386C2316yes—
362#386C2316yes—
363#385C23112yes—
364#385C23112yes—
365#385C2316yes—
366#385C23112yes—
367#385C23112yes—
368#385C23112yes—
369#385C23112yes—
370#385C2316yes—
371#385C23112yes—
372#385C2316yes—
373#385C2316yes—
374#385C2316yes—
375#385C2316yes—
376#385C23112yes—
377#385C2316yes—
378#385C2316yes—
379#385C2316yes—
380#385C2316yes—
381#385C2316yes—
382#385C2316yes—
383#384C2313yes—
384#384C2316yes—
385#384C2316yes—
386#384C2313yes—
387#382C2313yes—
388#382C2316yes—
389#382C2313yes—
390#382C2316yes—
391#380C2316yes—
392#380C23112yes—
393#380C2316yes—
394#380C23112yes—
395#380C2316yes—
396#380C2316yes—
397#380C2316yes—
398#380C2316yes—
399#380C23112yes—
400#380C2316yes—
401#380C23112yes—
402#380C2316yes—
403#379C23112yes—
404#379C23112yes—
405C4×C4⋊C4C2316yes—
406C4×C4⋊C4C2316yes—
407C4×C4⋊C4C2313yes—
408C4×C4⋊C4C2313yes—
409C4×C4⋊C4C2316yes—
410C4×C4⋊C4C2316yes—
411C4×C4⋊C4C2313yes—
412C4×C4⋊C4C2313yes—
413C4×C4⋊C4C2311yescharacteristic
414C4×C4⋊C4C2313yes—
415C4×C4⋊C4C2316yes—
416C4×C4⋊C4C2313yes—
417C4×C4⋊C4C2313yes—
418C4×C22⋊C4C2316yes—
419C4×C22⋊C4C2316yes—
420C4×C22⋊C4C2316yes—
421C4×C22⋊C4C2316yes—
422C2×#95C2316yes—
423C2×#95C2313yes—
424C2×#95C2316yes—
425C2×#95C2313yes—
426C25C2416yes—
427H(5,𝔽2)—2128no—
428C2×#41—28no—
429C2×#41—28no—
430C2×#41—212no—
431C2×#41—212no—
432C2×#41C2×D418yes—
433C2×#41C2×Q818yes—
434C2×#41C2×Q8116yescomplemented
435C2×#41C2×Q8124yescomplemented
436C2×#41#4118yes—
437C22×Q8—224no—
438C22×Q8—412no—
439C22×Q8—86no—
440C22×Q8C2412yes—
441C22×Q8C2416yes—
442C22×Q8C2411yescharacteristic
443C22×Q8C24112yes—
444C22×Q8C2411yescharacteristic
445C22×D4—224no—
446C22×D4—224no—
447C22×D4—212no—
448C22×D4—212no—
449C22×D4C2×Q8148yescomplemented
450C22×D4C2×Q8124yescomplemented
451C22×D4C2416yes—
452C22×D4C2416yes—
453C22×D4C2413yes—
454C22×D4C2413yes—
455C23×C4—224no—
456C23×C4—412no—
457C23×C4—86no—
458C23×C4C2413yes—
459C23×C4C2413yes—
460C23×C4C2413yes—
461C23×C4C2413yes—
462C23×C4C2416yes—
463C23×C4C2416yes—
464C23×C4C2416yes—
465C23×C4C2416yes—
466C23×C4C2413yes—
467C23×C4C2416yes—
468C23×C4C2413yes—
469C23×C4C24112yes—
470C23×C4C2416yes—
471C23×C4C2413yes—
472C4⋊Q8—212no—
473C4⋊Q8—224no—
474C4⋊Q8—224no—
475C4⋊Q8—224no—
476C4⋊Q8—24no—
477C4⋊Q8—224no—
478C4⋊Q8—224no—
479#125—212no—
480#125—212no—
481#125—224no—
482#125—224no—
483C22⋊Q8—248no—
484C22⋊Q8—224no—
485C22⋊Q8—224no—
486C22⋊Q8—224no—
487C22⋊Q8—248no—
488C22⋊Q8—424no—
489C22⋊Q8—424no—
490C22⋊Q8—412no—
491C22⋊Q8—424no—
492C22⋊Q8—812no—
493C4×Q8—24no—
494C4×Q8—24no—
495C4×Q8—24no—
496C4×Q8—24no—
497C4×Q8—28no—
498C4×Q8—24no—
499C4×Q8—24no—
500C4×Q8—28no—
501C4×Q8—24no—
502C4×Q8—212no—
503C4×Q8—224no—
504C4×Q8—224no—
505C4×Q8C2×D4116yes—
506C4×D4—212no—
507C4×D4—212no—
508C4×D4—212no—
509C4×D4—212no—
510C4×D4—224no—
511C4×D4—212no—
512C4×D4—212no—
513C4×D4—224no—
514C4×D4—248no—
515C4×D4—224no—
516C4×D4—212no—
517C4×D4—224no—
518C4×D4—224no—
519C4×D4—212no—
520C4×D4—224no—
521C4×D4—224no—
522C4×D4—224no—
523C4×D4—224no—
524C4×D4C2×D4148yes—
525#117—212no—
526#117—212no—
527#117—212no—
528#117—212no—
529#117—212no—
530#117—224no—
531#117—224no—
532#117C2×D4124yes—
533C2×C4⋊C4—212no—
534C2×C4⋊C4—224no—
535C2×C4⋊C4—212no—
536C2×C4⋊C4—224no—
537C2×C4⋊C4—212no—
538C2×C4⋊C4—46no—
539C2×C4⋊C4—412no—
540C2×C4⋊C4—412no—
541C2×C4⋊C4C2×D4124yes—
542C2×C4⋊C4C2411yescharacteristic
543C2×C4⋊C4C2413yes—
544C2×C4⋊C4C2416yes—
545C2×C4⋊C4C2413yes—
546C2×C4⋊C4C2413yes—
547C2×C4⋊C4C2416yes—
548C2×C4⋊C4C2416yes—
549C2×C4⋊C4C2416yes—
550C2×C4⋊C4C2416yes—
551C2×C4⋊C4C2416yes—
552C2×C4⋊C4C2413yes—
553C2×C4⋊C4C2413yes—
554C2×C4⋊C4C2413yes—
555C2×C4⋊C4C24112yes—
556C2×C4⋊C4C2413yes—
557C2×C4⋊C4C2413yes—
558C2×C4⋊C4C2412yes—
559C2×C4⋊C4C2411yescharacteristic
560C2×C4⋊C4C2411yescharacteristic
561C2×C4⋊C4C2413yes—
562C2×C4⋊C4C2413yes—
563C2×C4⋊C4C2413yes—
564C2×C4⋊C4C2413yes—
565C2×C4⋊C4C2412yes—
566C2×C4⋊C4C2416yes—
567C2×C4⋊C4C2416yes—
568C2×C4⋊C4C2416yes—
569C2×C4⋊C4C2416yes—
570C2×C4⋊C4C24112yes—
571C2×C4⋊C4C24112yes—
572C2×C4⋊C4C2413yes—
573C2×C4⋊C4C2413yes—
574C2×C4⋊C4C2416yes—
575C2×C4⋊C4C2416yes—
576C2×C4⋊C4C2416yes—
577C2×C4⋊C4C2416yes—
578C2×C4⋊C4C2416yes—
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2416yes—
582C2×C4⋊C4C2416yes—
583C2×C4⋊C4C2413yes—
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C22⋊C4—224no—
587C2×C22⋊C4—248no—
588C2×C22⋊C4—412no—
589C2×C22⋊C4—412no—
590C2×C22⋊C4—412no—
591C2×C22⋊C4—86no—
592C2×C22⋊C4C2416yes—
593C2×C22⋊C4C2416yes—
594C2×C22⋊C4C24112yes—
595C2×C22⋊C4C2416yes—
596C2×C22⋊C4C2416yes—
597C2×C22⋊C4C2416yes—
598C2×C22⋊C4C2416yes—
599C2×C22⋊C4C2416yes—
600C2×C22⋊C4C2416yes—
601C2×C22⋊C4C2416yes—
602C2×C22⋊C4C2416yes—
603C2×C22⋊C4C2416yes—
604C2×C22⋊C4C24112yes—
605C2×C22⋊C4C24112yes—
606C2×C22⋊C4C24112yes—
607C2×C22⋊C4C24112yes—
608C2×C22⋊C4C2416yes—
609C2×C22⋊C4C2416yes—
610C2×C22⋊C4C2416yes—
611C2×C22⋊C4C2416yes—
612C2×C22⋊C4C2416yes—
613C2×C42—212no—
614C2×C42—212no—
615C2×C42—212no—
616C2×C42—224no—
617C2×C42C2413yes—
618C2×C42C2413yes—
619C2×C42C2416yes—
620C2×C42C2413yes—
621C2×C42C2413yes—
622C2×C42C2416yes—
623C2×C42C2416yes—
624C2×C42C2413yes—
625C2×C42C2411yescharacteristic
626C2×C42C2412yes—
627C2×C42C2413yes—
628C2×C42C2413yes—
629C2×C42C2413yes—
630C2×C42C2413yes—
631C2×C42C2411yescharacteristic
632C2×C42C2411yescharacteristic
633C2×C42C2416yes—
634#95C2411yescharacteristic
635#95C2411yescharacteristic
636#95C2416yes—
637#95C2416yes—
638#95C2413yes—
639#95C2413yes—
640#95C2413yes—
641#95C2413yes—
642#95C2413yes—
643#95C2413yes—
644#95C24112yes—
645#95C24112yes—
646#95C2412yes—
647#95C2412yes—
648#95C2412yes—
649#95C2412yes—
650#95C2416yes—
651#95C2416yes—
652#95C2416yes—
653#95C2416yes—
654#95C2412yes—
655#95C2412yes—
656#95C2416yes—
657#95C2416yes—
658#95C2416yes—
659#95C2416yes—
660#95C2416yes—
661#95C2416yes—
662C24—212no—
663C24—212no—
664C24—46no—
665C24—46no—
666C24—46no—
667C24—46no—
668C24C22×Q8124yes—
669C24C2516yes—
670C24C2513yes—
671#41—264no—
672#41—296no—
673#41C22⋊Q8164yescomplemented
674C2×Q8—22no—
675C2×Q8—24no—
676C2×Q8—212no—
677C2×Q8—224no—
678C2×Q8—22no—
679C2×Q8—212no—
680C2×Q8—24no—
681C2×Q8—46no—
682C2×Q8—42no—
683C2×Q8—412no—
684C2×Q8—412no—
685C2×Q8—848no—
686C2×Q8C22×D414yes—
687C2×Q8C22×Q814yes—
688C2×Q8C22×Q814yes—
689C2×Q8C2×#4114yes—
690C2×D4—212no—
691C2×D4—212no—
692C2×D4—2192no—
693C2×D4—296no—
694C2×D4—26no—
695C2×D4—212no—
696C2×D4—212no—
697C2×D4—26no—
698C2×D4C22×D4112yes—
699C2×D4C22×Q8124yes—
700C2×D4C22×Q8124yes—
701C2×D4C22×Q8112yes—
702C2×D4C22×Q8112yes—
703C2×D4C2×#41112yes—
704C22×C4—212no—
705C22×C4—212no—
706C22×C4—26no—
707C22×C4—26no—
708C22×C4—26no—
709C22×C4—26no—
710C22×C4—26no—
711C22×C4—212no—
712C22×C4—26no—
713C22×C4—212no—
714C22×C4—212no—
715C22×C4—26no—
716C22×C4—26no—
717C22×C4—26no—
718C22×C4—212no—
719C22×C4—26no—
720C22×C4—212no—
721C22×C4—224no—
722C22×C4—46no—
723C22×C4—43no—
724C22×C4—46no—
725C22×C4—43no—
726C22×C4—46no—
727C22×C4—43no—
728C22×C4—43no—
729C22×C4—46no—
730C22×C4—46no—
731C22×C4—46no—
732C22×C4—43no—
733C22×C4—46no—
734C22×C4—43no—
735C22×C4—412no—
736C22×C4—46no—
737C22×C4—412no—
738C22×C4—46no—
739C22×C4—43no—
740C22×C4—43no—
741C22×C4—848no—
742C22×C4C22×D4124yes—
743C22×C4C22×D4112yes—
744C22×C4C22×Q8124yes—
745C22×C4C22×Q8112yes—
746C22×C4C2×#41112yes—
747C22×C4C2511yescharacteristic
748C22×C4C2513yes—
749C22×C4C2511yescharacteristic
750C22×C4C2513yes—
751C22×C4C2512yes—
752C22×C4C2516yes—
753C22×C4C2513yes—
754C22×C4C2512yes—
755C22×C4C2513yes—
756C22×C4C2513yes—
757C22×C4C2513yes—
758C22×C4C2516yes—
759C22×C4C2512yes—
760C22×C4C2516yes—
761C22×C4C2512yes—
762C22×C4C2511yescharacteristic
763C22×C4C2511yescharacteristic
764C22×C4C2511yescharacteristic
765C22×C4C2511yescharacteristic
766C22×C4C2511yescharacteristic
767C22×C4C2513yes—
768C4⋊C4—212no—
769C4⋊C4—26no—
770C4⋊C4—26no—
771C4⋊C4—212no—
772C4⋊C4—212no—
773C4⋊C4—224no—
774C4⋊C4—24no—
775C4⋊C4—26no—
776C4⋊C4—22no—
777C4⋊C4—26no—
778C4⋊C4—26no—
779C4⋊C4—24no—
780C4⋊C4—212no—
781C4⋊C4—212no—
782C4⋊C4—212no—
783C4⋊C4—212no—
784C4⋊C4—26no—
785C4⋊C4—212no—
786C4⋊C4—22no—
787C4⋊C4—26no—
788C4⋊C4—26no—
789C4⋊C4—26no—
790C4⋊C4—26no—
791C4⋊C4—26no—
792C4⋊C4—212no—
793C4⋊C4—212no—
794C4⋊C4—22no—
795C4⋊C4—26no—
796C4⋊C4—43no—
797C4⋊C4—43no—
798C4⋊C4—412no—
799C4⋊C4—412no—
800C4⋊C4—42no—
801C4⋊C4—42no—
802C4⋊C4—46no—
803C4⋊C4—46no—
804C4⋊C4—46no—
805C4⋊C4—46no—
806C4⋊C4—46no—
807C4⋊C4—46no—
808C4⋊C4C22×D4124yes—
809C4⋊C4C22×D4112yes—
810C4⋊C4C22×D414yes—
811C4⋊C4H(5,𝔽2)14yescomplemented
812C22⋊C4—212no—
813C22⋊C4—212no—
814C22⋊C4—212no—
815C22⋊C4—212no—
816C22⋊C4—212no—
817C22⋊C4—212no—
818C22⋊C4—224no—
819C22⋊C4—212no—
820C22⋊C4—212no—
821C22⋊C4—212no—
822C22⋊C4—212no—
823C22⋊C4—412no—
824C22⋊C4—412no—
825C22⋊C4—412no—
826C22⋊C4—46no—
827C22⋊C4—412no—
828C22⋊C4—46no—
829C22⋊C4—46no—
830C22⋊C4—46no—
831C22⋊C4—46no—
832C22⋊C4C22×D4124yes—
833C42—24no—
834C42—22no—
835C42—26no—
836C42—22no—
837C42—212no—
838C42—26no—
839C42—26no—
840C42—26no—
841C42—26no—
842C42—26no—
843C42—212no—
844C42—22no—
845C42—26no—
846C42—26no—
847C42—26no—
848C42—212no—
849C42C22×D4124yes—
850C23—23no—
851C23—23no—
852C23—23no—
853C23—23no—
854C23—26no—
855C23—26no—
856C23—26no—
857C23—26no—
858C23—26no—
859C23—26no—
860C23—248no—
861C23—424no—
862C23—424no—
863C23—812no—
864C23—812no—
865C23—812no—
866C23—812no—
867C23C23×D416yes—
868C23C23×Q8112yes—
869C23C23×Q816yes—
870C23C22×#4116yes—
871C23C2611yescharacteristic
872Q8—28no—
873Q8—48no—
874Q8—424no—
875Q8—824no—
876Q8C2×C22⋊Q8116yescomplemented
877D4—248no—
878D4—248no—
879D4—224no—
880D4C2×C22⋊Q8148yescomplemented
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—22no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—22no—
887C2×C4—26no—
888C2×C4—21no—
889C2×C4—22no—
890C2×C4—26no—
891C2×C4—21no—
892C2×C4—21no—
893C2×C4—22no—
894C2×C4—21no—
895C2×C4—248no—
896C2×C4—23no—
897C2×C4—21no—
898C2×C4—22no—
899C2×C4—23no—
900C2×C4—23no—
901C2×C4—23no—
902C2×C4—26no—
903C2×C4—21no—
904C2×C4—22no—
905C2×C4—23no—
906C2×C4—23no—
907C2×C4—26no—
908C2×C4—26no—
909C2×C4—26no—
910C2×C4—23no—
911C2×C4—23no—
912C2×C4—23no—
913C2×C4—26no—
914C2×C4—23no—
915C2×C4—22no—
916C2×C4—23no—
917C2×C4—21no—
918C2×C4—23no—
919C2×C4—21no—
920C2×C4—23no—
921C2×C4—22no—
922C2×C4—26no—
923C2×C4—23no—
924C2×C4—23no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—23no—
928C2×C4—23no—
929C2×C4—23no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—424no—
933C2×C4—424no—
934C2×C4—412no—
935C2×C4—412no—
936C2×C4—412no—
937C2×C4—412no—
938C2×C4—812no—
939C2×C4—824no—
940C2×C4—86no—
941C2×C4—812no—
942C2×C4—86no—
943C2×C4—812no—
944C2×C4C2×C22⋊Q8148yescomplemented
945C2×C4C23×D414yes—
946C2×C4C23×D4112yes—
947C2×C4C23×D412yes—
948C2×C4C23×D416yes—
949C2×C4C23×Q814yes—
950C2×C4C23×Q816yes—
951C2×C4C23×Q812yes—
952C2×C4C22×#4116yes—
953C2×C4C22×#4112yes—
954C2×C4C2×H(5,𝔽2)12yes—
955C2×C4C2×H(5,𝔽2)12yes—
956C2×C4C2×H(5,𝔽2)12yes—
957C2×C4#58512yes—
958C22—26no—
959C22—26no—
960C22—26no—
961C22—26no—
962C22—26no—
963C22—26no—
964C22—212no—
965C22—212no—
966C22—212no—
967C22—46no—
968C22—46no—
969C22—46no—
970C22—46no—
971C22—848no—
972C22C22×C22⋊Q8112yes—
973C22C24×D411yescharacteristic
974C22C24×Q811yescharacteristic
975C22C23×#4111yescharacteristic
976C22C22×H(5,𝔽2)11yescharacteristic
977C22C2×#58511yescharacteristic
978C22H(7,𝔽2)11yescharacteristic
979C222−1+611yescharacteristic
980C4—22no—
981C4—212no—
982C4—22no—
983C4—22no—
984C4—24no—
985C4—22no—
986C4—24no—
987C4—43no—
988C4—43no—
989C4—46no—
990C4—43no—
991C4—43no—
992C4—41no—
993C4—42no—
994C4—43no—
995C4—46no—
996C4—42no—
997C4—43no—
998C4—41no—
999C4C22×C22⋊Q8112yes—
1000C4C22×C22⋊Q814yes—
1001C2—212no—
1002C2—412no—
1003C2C23×C22⋊Q811yescharacteristic
1004C2#6280011yescharacteristic
1005C2#6285711yescharacteristic
1006C2D4×H(5,𝔽2)11yescharacteristic
1007C2Q8×H(5,𝔽2)11yescharacteristic
1008C2#6298911yescharacteristic
1009C2#6300211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×H(5,𝔽2)C22
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. #36456C2semidirect
4. #36431C2semidirect
5. #36215C2semidirect
6. D4×C22⋊Q8C2semidirect
7. #35816C2semidirect
8. #35776C2semidirect
9. #35748C2semidirect
10. #35702C2semidirect
11. #35575C2semidirect
12. #35574C2semidirect
13. #35529C2semidirect
14. #35515C2semidirect
15. #35257C2semidirect
16. #35174C2semidirect
17. #34745C2semidirect
18. C2×#2452C2semidirect
21. #34250C2semidirect
22. #34250C2semidirect
23. C4⋊C4×#41C2semidirect
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
34. C22×C22⋊Q8C22semidirect
50. #2857C22semidirect
51. #2851C22semidirect
52. #2848C22semidirect
53. #2629C22semidirect
54. #2628C22semidirect
55. #2626C22semidirect
56. #2580C22semidirect
57. #2580C22semidirect
58. #2579C22semidirect
59. #2566C22semidirect
60. #2566C22semidirect
61. #2564C22semidirect
62. #2563C22semidirect
63. #2542C22semidirect
64. #2538C22semidirect
65. #2538C22semidirect
66. #2454C22semidirect
67. #2454C22semidirect
68. #2454C22semidirect
69. #2454C22semidirect
70. #2454C22semidirect
71. #2454C22semidirect
72. #2453C22semidirect
73. #2453C22semidirect
74. #2452C22semidirect
75. #2452C22semidirect
76. #2452C22semidirect
77. #2452C22semidirect
78. #2452C22semidirect
79. #2452C22semidirect
80. #2452C22semidirect
81. #2452C22semidirect
82. #2452C22semidirect
83. #2452C22semidirect
84. #2452C22semidirect
85. #2452C22semidirect
86. #2451C22semidirect
87. #2451C22semidirect
88. #2451C22semidirect
89. #2450C22semidirect
90. #2450C22semidirect
91. #2450C22semidirect
92. #2449C22semidirect
93. #2449C22semidirect
94. #2449C22semidirect
95. #2442C22semidirect
96. #2441C22semidirect
97. #2440C22semidirect
98. #2440C22semidirect
99. #2440C22semidirect
100. #2439C22semidirect
101. #2439C22semidirect
102. #2439C22semidirect
103. #2437C22semidirect
104. #2437C22semidirect
105. #2437C22semidirect
106. #2437C22semidirect
107. #2417C22semidirect
108. #2409C22semidirect
109. #2396C22semidirect
110. #2396C22semidirect
111. C2×#396C22semidirect
112. C2×#393C22semidirect
113. #2351C22semidirect
114. #2351C22semidirect
115. #2351C22semidirect
116. #2351C22semidirect
117. Q8×C4⋊C4C22semidirect
118. Q8×C4⋊C4C22semidirect
119. Q8×C4⋊C4C22semidirect
120. Q8×C4⋊C4C22semidirect
121. #2349C22semidirect
122. #2349C22semidirect
123. #2349C22semidirect
124. #2349C22semidirect
125. D4×C4⋊C4C22semidirect
126. D4×C4⋊C4C22semidirect
127. D4×C4⋊C4C22semidirect
128. D4×C4⋊C4C22semidirect
137. #2317C22semidirect
138. #2317C22semidirect
139. #2316C22semidirect
140. #2316C22semidirect
145. C4×C22⋊Q8C22semidirect
146. C4×C22⋊Q8C22semidirect
149. #2296C22semidirect
150. #2296C22semidirect
151. #2296C22semidirect
152. #2296C22semidirect
155. C2×#389C22semidirect
156. C2×#389C22semidirect
157. C2×#385C22semidirect
158. #2285C22semidirect
159. C2×C4×C4⋊C4C22semidirect
162. C2×H(5,𝔽2)Q8semidirect
434. C2×#41C2×Q8semidirect
435. C2×#41C2×Q8semidirect
449. C22×D4C2×Q8semidirect
450. C22×D4C2×Q8semidirect
673. #41C22⋊Q8semidirect
811. C4⋊C4H(5,𝔽2)semidirect
876. Q8C2×C22⋊Q8semidirect
880. D4C2×C22⋊Q8semidirect
944. C2×C4C2×C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#35032
C2×C4×H(5,𝔽2)2
#364562
#364312
#362152
D4×C22⋊Q82
#358162
#357762
#357482
#357022
#355752
#355742
#355292
#355152
#352572
#351742
#347452
C2×#24522
#342582
#342502
C4⋊C4×#412