Finite Group Databasebeta

← #41×C22⋊Q8 #7630330

Subgroups — #41×C22⋊Q8 #7630330

Order 512.

8652 conjugacy classes of subgroups.

The subgroup lattice has 1072 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×#41C211yesmaximal, characteristic, complemented
2C22×C4×#41C211yesmaximal, characteristic
3#36625C213yesmaximal, complemented
4#36577C211yesmaximal, characteristic, complemented
5Q8×C22⋊Q8C211yesmaximal, characteristic, complemented
6#36456C211yesmaximal, characteristic, complemented
7#36445C211yesmaximal, characteristic, complemented
8#36435C212yesmaximal, complemented
9#36431C212yesmaximal, complemented
10#36275C213yesmaximal, complemented
11#36274C213yesmaximal, complemented
12#36219C216yesmaximal, complemented
13#36215C216yesmaximal, complemented
14#36154C213yesmaximal, complemented
15D4×C22⋊Q8C213yesmaximal, complemented
16#34952C213yesmaximal, complemented
17#34947C213yesmaximal, complemented
18#34745C216yesmaximal, complemented
19#34739C216yesmaximal, complemented
20C4⋊C4×#41C211yesmaximal, characteristic, complemented
21C4⋊C4×#41C212yesmaximal, complemented
22C22⋊C4×#41C212yesmaximal
23C2×C4×C22⋊Q8C213yesmaximal, complemented
24C23×#41C2211yescharacteristic
25Q8×#41—216no—
26C2×Q82C2211yescharacteristic, complemented
27C2×#557C2212yescomplemented
28C2×#557C2211yescharacteristic, complemented
29C2×#554C2213yescomplemented
30C2×#554C2216yescomplemented
31C2×D4×Q8C2213yescomplemented
32C2×#533C2213yescomplemented
33C2×#533C2216yescomplemented
34C22×C22⋊Q8C2213yes—
35C2×C4×#41—216no—
36C2×C4×#41C2212yes—
37C2×C4×#41C2212yes—
38C2×C4×#41C2211yescharacteristic
39C2×C4×#41C2211yescharacteristic
40C2×C4×#41C2211yescharacteristic
41C2×C4×#41C2213yes—
42C2×C4×#41C2213yes—
43C2×C4×#41C2213yes—
44C2×C4×#41C2213yes—
45C2×C4×#41C2211yescharacteristic
46C22×C4×Q8C2211yescharacteristic
47C22×C4×Q8C2211yescharacteristic
48C22×C4×Q8C2213yescomplemented
49C22×C4×D4C2213yes—
50C22×C4×D4C2213yes—
51C22×#117C2213yes—
52C23×C42C2213yes—
53#2857C2213yes—
54#2857C2213yes—
55#2857C2213yescomplemented
56#2857C2213yescomplemented
57#2855C2216yescomplemented
58#2855C2216yescomplemented
59#2851C2216yes—
60#2851C2216yescomplemented
61#2848C2216yes—
62#2848C2216yes—
63#2582C2213yescomplemented
64#2582C2213yescomplemented
65#2581C2216yescomplemented
66#2580C2216yescomplemented
67#2579C22112yescomplemented
68#2568C2213yescomplemented
69#2567C2213yescomplemented
70#2566C2216yescomplemented
71#2565C2216yescomplemented
72#2564C22112yescomplemented
73#2563C2213yescomplemented
74#2542C2213yescomplemented
75#2538C2213yescomplemented
76#2538C2213yescomplemented
77#2487C2216yescomplemented
78#2454C2216yescomplemented
79#2454C2216yescomplemented
80#2453C2216yescomplemented
81#2453C2216yescomplemented
82#2452C2216yescomplemented
83#2452C2216yescomplemented
84#2451C2216yescomplemented
85#2451C2216yescomplemented
86#2450C22112yescomplemented
87#2450C22112yescomplemented
88#2449C22112yescomplemented
89#2449C22112yescomplemented
90#2442C2216yes—
91#2442C2216yes—
92#2441C2216yescomplemented
93#2441C2216yescomplemented
94#2440C2216yes—
95#2440C2216yes—
96#2439C2216yescomplemented
97#2439C2216yescomplemented
98#2438C22112yescomplemented
99#2438C22112yescomplemented
100#2437C22112yes—
101#2437C22112yes—
102#2417C2216yescomplemented
103#2417C2216yescomplemented
104#2409C2216yescomplemented
105#2396C22112yescomplemented
106#2396C22112yescomplemented
107#2351C2212yescomplemented
108#2351C2212yescomplemented
109#2351C2212yescomplemented
110Q8×C4⋊C4C2212yescomplemented
111Q8×C4⋊C4C2212yescomplemented
112Q8×C4⋊C4C2211yescharacteristic, complemented
113Q8×C4⋊C4C2211yescharacteristic, complemented
114#2349C2216yescomplemented
115#2349C2216yescomplemented
116#2349C2216yescomplemented
117D4×C4⋊C4C2213yescomplemented
118D4×C4⋊C4C2216yescomplemented
119D4×C4⋊C4C2216yescomplemented
120D4×C4⋊C4C2213yescomplemented
121#2341C2212yes—
122#2341C2212yes—
123Q8×C22⋊C4C2212yes—
124Q8×C22⋊C4C2212yes—
125#2339C2216yes—
126#2339C2216yes—
127D4×C22⋊C4C2216yes—
128D4×C22⋊C4C2216yes—
129C4×C22⋊Q8C2213yes—
130C4×C22⋊Q8C2216yes—
131C4×C22⋊Q8C2213yes—
132C4×C22⋊Q8C2216yes—
133C4×C22⋊Q8C2216yes—
134C4×C22⋊Q8C2213yes—
135C4×C22⋊Q8C2211yescharacteristic
136C4×C22⋊Q8C2216yescomplemented
137C4×C22⋊Q8C2216yescomplemented
138C4×C22⋊Q8C2216yescomplemented
139C4×C22⋊Q8C2213yescomplemented
140C4×C22⋊Q8C2213yescomplemented
141C4×C22⋊Q8C2213yescomplemented
142C4×C22⋊Q8C2213yescomplemented
143C4×C22⋊Q8C2216yescomplemented
144#2297C2216yes—
145#2297C2216yes—
146#2296C2216yescomplemented
147#2296C2216yescomplemented
148#2296C2216yescomplemented
149C2×#391C2213yescomplemented
150C2×#389C2213yescomplemented
151C2×#387C2216yescomplemented
152C2×#385C2216yes—
153#2285C2213yescomplemented
154#2285C2216yescomplemented
155#2280C2216yes—
156C2×#380C2213yes—
157C2×C4×C4⋊C4C2213yescomplemented
158C2×C4×C4⋊C4C2216yescomplemented
159C2×C4×C22⋊C4C2216yes—
160C22×#41—28no—
161C22×#41—28no—
162C22×#41Q8116yescomplemented
163C22×#41C2313yes—
164C22×#41C2311yescharacteristic
165C22×#41C2313yes—
166C22×#41C2311yescharacteristic
167C23×Q8C2313yes—
168C23×Q8C2311yescharacteristic
169C23×D4C2313yes—
170C24×C4C2313yes—
171C24×C4C2313yes—
172C24×C4C2313yes—
173Q82—28no—
174#557—28no—
175#557—216no—
176#554—248no—
177#554—224no—
178D4×Q8—224no—
179#533—248no—
180#533—224no—
181C2×C4⋊Q8C2313yes—
182C2×C4⋊Q8C2313yes—
183C2×C4⋊Q8C2316yes—
184C2×C4⋊Q8C2316yes—
185C2×#125C2316yes—
186C2×#125C2316yes—
187C2×#125C2316yes—
188C2×C22⋊Q8—224no—
189C2×C22⋊Q8C2316yes—
190C2×C22⋊Q8C2313yes—
191C2×C22⋊Q8C2316yes—
192C2×C22⋊Q8C2313yes—
193C2×C22⋊Q8C2313yes—
194C2×C22⋊Q8C2316yes—
195C2×C22⋊Q8C2316yes—
196C2×C22⋊Q8C23112yes—
197C2×C22⋊Q8C23112yes—
198C2×C22⋊Q8C2316yes—
199C2×C22⋊Q8C2316yes—
200C2×C22⋊Q8C2316yes—
201C2×C22⋊Q8C2311yescharacteristic
202C4×#41—28no—
203C4×#41—216no—
204C4×#41—216no—
205C4×#41—28no—
206C4×#41—28no—
207C4×#41—224no—
208C4×#41—224no—
209C4×#41—224no—
210C4×#41—224no—
211C4×#41D4116yes—
212C2×C4×Q8—28no—
213C2×C4×Q8—28no—
214C2×C4×Q8—224no—
215C2×C4×Q8C2313yes—
216C2×C4×Q8C2313yes—
217C2×C4×Q8C2316yes—
218C2×C4×Q8C2313yes—
219C2×C4×Q8C2313yes—
220C2×C4×Q8C2312yes—
221C2×C4×Q8C2312yes—
222C2×C4×Q8C2312yes—
223C2×C4×Q8C2312yes—
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2316yes—
227C2×C4×Q8C2316yes—
228C2×C4×Q8C2313yes—
229C2×C4×Q8C2313yes—
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2313yes—
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×D4—224no—
235C2×C4×D4—224no—
236C2×C4×D4C2313yes—
237C2×C4×D4C2316yes—
238C2×C4×D4C2313yes—
239C2×C4×D4C2316yes—
240C2×C4×D4C2316yes—
241C2×C4×D4C2316yes—
242C2×C4×D4C2316yes—
243C2×C4×D4C2313yes—
244C2×C4×D4C2313yes—
245C2×C4×D4C2316yes—
246C2×C4×D4C2316yes—
247C2×C4×D4C2316yes—
248C2×C4×D4C2313yes—
249C2×C4×D4C2313yes—
250C2×C4×D4C2313yes—
251C2×C4×D4C2313yes—
252C2×#117—224no—
253C2×#117C2316yes—
254C2×#117C2316yes—
255C2×#117C2313yes—
256C2×#117C2313yes—
257C2×#117C2313yes—
258C2×#117C2316yes—
259C2×#117C2316yes—
260C2×#117C2313yes—
261C22×C4⋊C4C2316yes—
262C22×C4⋊C4C2313yes—
263C22×C4⋊C4C2316yes—
264C22×C4⋊C4C2313yes—
265C22×C4⋊C4C2313yes—
266C22×C4⋊C4C2313yes—
267C22×C4⋊C4C2313yes—
268C22×C4⋊C4C2316yes—
269C22×C22⋊C4C2316yes—
270C22×C22⋊C4C2316yes—
271C22×C22⋊C4C2316yes—
272C22×C42—224no—
273C22×C42C2313yes—
274C22×C42C2313yes—
275C22×C42C2313yes—
276C22×C42C2313yes—
277C22×C42C2313yes—
278C22×C42C2313yes—
279C22×C42C2311yescharacteristic
280C22×C42C2313yes—
281C22×C42C2313yes—
282C22×C42C2313yes—
283C22×C42C2313yes—
284C22×C42C2316yes—
285C22×C42C2316yes—
286C22×C42C2313yes—
287#400C23112yes—
288#400C23112yes—
289#399C23112yes—
290#399C23112yes—
291#398C23112yes—
292#398C23112yes—
293#398C23112yes—
294#398C23112yes—
295#396C23112yes—
296#396C23112yes—
297#396C23112yes—
298#396C23112yes—
299#395C23112yes—
300#395C23112yes—
301#393C23112yes—
302#393C23112yes—
303#391C2316yes—
304#391C2316yes—
305#391C2313yes—
306#391C2316yes—
307#391C2316yes—
308#391C2316yes—
309#391C2313yes—
310#391C2313yes—
311#391C2316yes—
312#391C2316yes—
313#391C2316yes—
314#391C2316yes—
315#391C2311yescharacteristic
316#390C2316yes—
317#390C2316yes—
318#390C2316yes—
319#390C2316yes—
320#389C2313yes—
321#389C2316yes—
322#389C2316yes—
323#389C2316yes—
324#389C2316yes—
325#389C2316yes—
326#389C2313yes—
327#389C2316yes—
328#389C2316yes—
329#389C2316yes—
330#389C2316yes—
331#389C2313yes—
332#389C2316yes—
333#389C2316yes—
334#389C2316yes—
335#389C2316yes—
336#389C2316yes—
337#389C2316yes—
338#389C2316yes—
339#389C2316yes—
340#389C2311yescharacteristic
341#387C2316yes—
342#387C23112yes—
343#387C2316yes—
344#387C23112yes—
345#387C2316yes—
346#387C23112yes—
347#387C2316yes—
348#387C2316yes—
349#387C2316yes—
350#387C2316yes—
351#387C2312yes—
352#386C23112yes—
353#386C23112yes—
354#386C23112yes—
355#386C23112yes—
356#385C2316yes—
357#385C23112yes—
358#385C2316yes—
359#385C23112yes—
360#385C23112yes—
361#385C2316yes—
362#385C23112yes—
363#385C23112yes—
364#385C23112yes—
365#385C23112yes—
366#385C23112yes—
367#385C23112yes—
368#385C2316yes—
369#385C2316yes—
370#385C2316yes—
371#385C2316yes—
372#385C2312yes—
373#384C2316yes—
374#384C2316yes—
375#384C2313yes—
376#384C2313yes—
377#382C2316yes—
378#382C2316yes—
379#382C2316yes—
380#381C23112yes—
381#380C2313yes—
382#380C2316yes—
383#380C23112yes—
384#380C23112yes—
385#380C2316yes—
386#380C2313yes—
387#380C2316yes—
388#380C2316yes—
389#380C2316yes—
390#380C2316yes—
391#380C2316yes—
392#380C2316yes—
393#380C2316yes—
394#380C2316yes—
395#380C2316yes—
396#380C2313yes—
397#380C2311yescharacteristic
398#379C23112yes—
399C4×C4⋊C4C2313yes—
400C4×C4⋊C4C2316yes—
401C4×C4⋊C4C2313yes—
402C4×C4⋊C4C2316yes—
403C4×C4⋊C4C2316yes—
404C4×C4⋊C4C2316yes—
405C4×C4⋊C4C2316yes—
406C4×C4⋊C4C2316yes—
407C4×C4⋊C4C2316yes—
408C4×C4⋊C4C2316yes—
409C4×C4⋊C4C23112yes—
410C4×C4⋊C4C2316yes—
411C4×C4⋊C4C2312yes—
412C4×C4⋊C4C2311yescharacteristic
413C4×C4⋊C4C2313yes—
414C4×C4⋊C4C2316yes—
415C4×C22⋊C4C2316yes—
416C4×C22⋊C4C2316yes—
417C4×C22⋊C4C2316yes—
418C4×C22⋊C4C2316yes—
419C4×C22⋊C4C2316yes—
420C4×C22⋊C4C2316yes—
421C4×C22⋊C4C23112yes—
422C4×C22⋊C4C2312yes—
423C4×C22⋊C4C2316yes—
424C2×#95C2316yes—
425C2×#95C2316yes—
426C2×#95C2316yes—
427C2×#95C2316yes—
428C2×#95C2316yes—
429C25C2413yes—
430C2×#41—2128no—
431C2×#41—24no—
432C2×#41—24no—
433C2×#41—212no—
434C2×#41—212no—
435C2×#41—212no—
436C2×#41—212no—
437C2×#41C2×D418yes—
438C2×#41C2×Q818yes—
439C2×#41C2×Q818yescomplemented
440C2×#41C2×Q8124yescomplemented
441C2×#41C2×Q8124yescomplemented
442C2×#41#4118yes—
443C22×Q8—24no—
444C22×Q8—24no—
445C22×Q8—212no—
446C22×Q8—212no—
447C22×Q8—46no—
448C22×Q8C2×Q818yescomplemented
449C22×Q8C2413yes—
450C22×Q8C2416yes—
451C22×Q8C2413yes—
452C22×Q8C2411yescharacteristic
453C22×Q8C2416yes—
454C22×Q8C2411yescharacteristic
455C22×D4—212no—
456C22×D4—212no—
457C22×D4C2×Q8124yescomplemented
458C22×D4C2416yes—
459C22×D4C2413yes—
460C22×D4C2413yes—
461C23×C4—212no—
462C23×C4—212no—
463C23×C4—212no—
464C23×C4—212no—
465C23×C4—212no—
466C23×C4—46no—
467C23×C4—46no—
468C23×C4—46no—
469C23×C4C2×Q8124yescomplemented
470C23×C4C2413yes—
471C23×C4C2411yescharacteristic
472C23×C4C2413yes—
473C23×C4C2413yes—
474C23×C4C2416yes—
475C23×C4C2416yes—
476C23×C4C2413yes—
477C23×C4C2413yes—
478C23×C4C2413yes—
479C23×C4C2413yes—
480C23×C4C2413yes—
481C23×C4C2413yes—
482C23×C4C2413yes—
483C23×C4C2413yes—
484C23×C4C2413yes—
485C23×C4C2411yescharacteristic
486C23×C4C2411yescharacteristic
487C23×C4C2416yes—
488C23×C4C2416yes—
489C23×C4C2413yes—
490C23×C4C2413yes—
491C23×C4C2413yes—
492C4⋊Q8—224no—
493C4⋊Q8—224no—
494C4⋊Q8—212no—
495C4⋊Q8—212no—
496#125—224no—
497#125—224no—
498#125—224no—
499C22⋊Q8—212no—
500C22⋊Q8—224no—
501C22⋊Q8—224no—
502C22⋊Q8—212no—
503C22⋊Q8—212no—
504C22⋊Q8—224no—
505C22⋊Q8—248no—
506C22⋊Q8—248no—
507C22⋊Q8—224no—
508C22⋊Q8—412no—
509C22⋊Q8—412no—
510C22⋊Q8—412no—
511C22⋊Q8#4118yesdirect product factor
512C4×Q8—24no—
513C4×Q8—24no—
514C4×Q8—28no—
515C4×Q8—28no—
516C4×Q8—28no—
517C4×Q8—28no—
518C4×Q8—212no—
519C4×Q8—212no—
520C4×Q8—24no—
521C4×Q8—212no—
522C4×Q8—212no—
523C4×Q8—224no—
524C4×Q8—212no—
525C4×Q8—212no—
526C4×Q8—212no—
527C4×Q8—224no—
528C4×Q8—224no—
529C4×Q8C2×D418yes—
530C4×Q8C2×D418yes—
531C4×D4—212no—
532C4×D4—212no—
533C4×D4—224no—
534C4×D4—224no—
535C4×D4—224no—
536C4×D4—224no—
537C4×D4—224no—
538C4×D4—224no—
539C4×D4—212no—
540C4×D4—212no—
541C4×D4—224no—
542C4×D4—224no—
543C4×D4—212no—
544C4×D4—212no—
545C4×D4C2×D4124yes—
546C4×D4C2×D4124yes—
547#117—212no—
548#117—224no—
549#117—224no—
550#117—212no—
551#117—212no—
552#117—224no—
553#117—224no—
554#117C2×D4124yes—
555C2×C4⋊C4—224no—
556C2×C4⋊C4—212no—
557C2×C4⋊C4—212no—
558C2×C4⋊C4—212no—
559C2×C4⋊C4—212no—
560C2×C4⋊C4—224no—
561C2×C4⋊C4—46no—
562C2×C4⋊C4—412no—
563C2×C4⋊C4C2411yescharacteristic
564C2×C4⋊C4C2412yes—
565C2×C4⋊C4C2411yescharacteristic
566C2×C4⋊C4C2412yes—
567C2×C4⋊C4C2413yes—
568C2×C4⋊C4C2413yes—
569C2×C4⋊C4C2416yes—
570C2×C4⋊C4C2416yes—
571C2×C4⋊C4C2416yes—
572C2×C4⋊C4C2416yes—
573C2×C4⋊C4C2416yes—
574C2×C4⋊C4C2413yes—
575C2×C4⋊C4C2416yes—
576C2×C4⋊C4C2413yes—
577C2×C4⋊C4C2413yes—
578C2×C4⋊C4C2416yes—
579C2×C4⋊C4C2416yes—
580C2×C4⋊C4C2416yes—
581C2×C4⋊C4C2416yes—
582C2×C4⋊C4C2416yes—
583C2×C4⋊C4C2416yes—
584C2×C4⋊C4C2416yes—
585C2×C4⋊C4C2416yes—
586C2×C4⋊C4C2416yes—
587C2×C4⋊C4C2416yes—
588C2×C4⋊C4C24112yes—
589C2×C4⋊C4C2416yes—
590C2×C4⋊C4C2416yes—
591C2×C4⋊C4C2416yes—
592C2×C4⋊C4C2416yes—
593C2×C4⋊C4C2416yes—
594C2×C4⋊C4C24112yes—
595C2×C4⋊C4C24112yes—
596C2×C4⋊C4C2413yes—
597C2×C4⋊C4C2413yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2411yescharacteristic
600C2×C22⋊C4—224no—
601C2×C22⋊C4—224no—
602C2×C22⋊C4—412no—
603C2×C22⋊C4C2412yes—
604C2×C22⋊C4C2416yes—
605C2×C22⋊C4C2416yes—
606C2×C22⋊C4C2416yes—
607C2×C22⋊C4C2416yes—
608C2×C22⋊C4C2416yes—
609C2×C22⋊C4C2416yes—
610C2×C22⋊C4C2416yes—
611C2×C22⋊C4C24112yes—
612C2×C22⋊C4C24112yes—
613C2×C22⋊C4C2416yes—
614C2×C22⋊C4C2416yes—
615C2×C22⋊C4C24112yes—
616C2×C22⋊C4C24112yes—
617C2×C22⋊C4C2416yes—
618C2×C22⋊C4C2412yes—
619C2×C42—224no—
620C2×C42—212no—
621C2×C42—212no—
622C2×C42—212no—
623C2×C42—224no—
624C2×C42—212no—
625C2×C42—212no—
626C2×C42—212no—
627C2×C42—212no—
628C2×C42—212no—
629C2×C42—212no—
630C2×C42—212no—
631C2×C42—24no—
632C2×C42C2×D4124yes—
633C2×C42C2413yes—
634C2×C42C2413yes—
635C2×C42C2413yes—
636C2×C42C2413yes—
637C2×C42C2413yes—
638C2×C42C2413yes—
639C2×C42C2413yes—
640C2×C42C2413yes—
641C2×C42C2416yes—
642C2×C42C2416yes—
643C2×C42C2416yes—
644C2×C42C2416yes—
645C2×C42C2411yescharacteristic
646C2×C42C2411yescharacteristic
647C2×C42C2413yes—
648C2×C42C2416yes—
649C2×C42C2416yes—
650C2×C42C2412yes—
651C2×C42C2412yes—
652C2×C42C2411yescharacteristic
653C2×C42C2413yes—
654C2×C42C2413yes—
655C2×C42C2413yes—
656C2×C42C2411yescharacteristic
657#95C2412yes—
658#95C2412yes—
659#95C2412yes—
660#95C2412yes—
661#95C2412yes—
662#95C2416yes—
663#95C2416yes—
664#95C2416yes—
665#95C2416yes—
666#95C2416yes—
667#95C2416yes—
668#95C2416yes—
669#95C2416yes—
670#95C2416yes—
671#95C2416yes—
672#95C2416yes—
673#95C2416yes—
674#95C2416yes—
675#95C2416yes—
676#95C2416yes—
677#95C24112yes—
678#95C24112yes—
679#95C24112yes—
680#95C24112yes—
681#95C24112yes—
682C24—26no—
683C24—26no—
684C24—26no—
685C24—26no—
686C24—43no—
687C24—43no—
688C24C22×Q8112yes—
689C24C2513yes—
690C24C2513yes—
691C24C2511yescharacteristic
692#41—232no—
693#41—296no—
694#41—296no—
695#41C22⋊Q8164yesdirect product factor
696C2×Q8—232no—
697C2×Q8—22no—
698C2×Q8—26no—
699C2×Q8—212no—
700C2×Q8—26no—
701C2×Q8—212no—
702C2×Q8—26no—
703C2×Q8—212no—
704C2×Q8—26no—
705C2×Q8—22no—
706C2×Q8—26no—
707C2×Q8—46no—
708C2×Q8—46no—
709C2×Q8—46no—
710C2×Q8—448no—
711C2×Q8C22×D414yes—
712C2×Q8C22×Q8112yes—
713C2×Q8C22×Q814yes—
714C2×Q8C2×#4114yes—
715C2×Q8C2×#4114yescomplemented
716C2×D4—212no—
717C2×D4—212no—
718C2×D4—296no—
719C2×D4—26no—
720C2×D4—26no—
721C2×D4C22×D4112yes—
722C2×D4C22×Q8124yes—
723C2×D4C22×Q8112yes—
724C2×D4C22×Q8112yes—
725C2×D4C2×#41112yes—
726C22×C4—26no—
727C22×C4—26no—
728C22×C4—22no—
729C22×C4—296no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—26no—
734C22×C4—26no—
735C22×C4—26no—
736C22×C4—26no—
737C22×C4—22no—
738C22×C4—26no—
739C22×C4—26no—
740C22×C4—26no—
741C22×C4—26no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—26no—
745C22×C4—26no—
746C22×C4—212no—
747C22×C4—212no—
748C22×C4—26no—
749C22×C4—26no—
750C22×C4—212no—
751C22×C4—212no—
752C22×C4—26no—
753C22×C4—26no—
754C22×C4—26no—
755C22×C4—26no—
756C22×C4—26no—
757C22×C4—26no—
758C22×C4—212no—
759C22×C4—212no—
760C22×C4—26no—
761C22×C4—26no—
762C22×C4—26no—
763C22×C4—26no—
764C22×C4—26no—
765C22×C4—26no—
766C22×C4—46no—
767C22×C4—43no—
768C22×C4—43no—
769C22×C4—43no—
770C22×C4—43no—
771C22×C4—43no—
772C22×C4—43no—
773C22×C4—43no—
774C22×C4—43no—
775C22×C4—43no—
776C22×C4—43no—
777C22×C4—46no—
778C22×C4—448no—
779C22×C4—46no—
780C22×C4—46no—
781C22×C4—46no—
782C22×C4—46no—
783C22×C4—448no—
784C22×C4C22×D4112yes—
785C22×C4C22×D4112yes—
786C22×C4C22×D4112yes—
787C22×C4C22×Q814yes—
788C22×C4C22×Q8112yes—
789C22×C4C22×Q8112yes—
790C22×C4C22×Q8112yes—
791C22×C4C22×Q8112yes—
792C22×C4C22×Q8112yes—
793C22×C4C2×#4114yes—
794C22×C4C2×#41112yes—
795C22×C4C2512yes—
796C22×C4C2516yes—
797C22×C4C2516yes—
798C22×C4C2513yes—
799C22×C4C2513yes—
800C22×C4C2512yes—
801C22×C4C2516yes—
802C22×C4C2516yes—
803C22×C4C2511yescharacteristic
804C22×C4C2513yes—
805C22×C4C2513yes—
806C22×C4C2511yescharacteristic
807C22×C4C2513yes—
808C22×C4C2511yescharacteristic
809C22×C4C2512yes—
810C22×C4C2512yes—
811C22×C4C2511yescharacteristic
812C22×C4C2513yes—
813C22×C4C2511yescharacteristic
814C22×C4C2511yescharacteristic
815C4⋊C4—24no—
816C4⋊C4—22no—
817C4⋊C4—212no—
818C4⋊C4—212no—
819C4⋊C4—26no—
820C4⋊C4—26no—
821C4⋊C4—212no—
822C4⋊C4—212no—
823C4⋊C4—212no—
824C4⋊C4—212no—
825C4⋊C4—26no—
826C4⋊C4—212no—
827C4⋊C4—212no—
828C4⋊C4—212no—
829C4⋊C4—224no—
830C4⋊C4—212no—
831C4⋊C4—26no—
832C4⋊C4—212no—
833C4⋊C4—212no—
834C4⋊C4—212no—
835C4⋊C4—212no—
836C4⋊C4—212no—
837C4⋊C4—24no—
838C4⋊C4—22no—
839C4⋊C4—26no—
840C4⋊C4—212no—
841C4⋊C4—46no—
842C4⋊C4—46no—
843C4⋊C4—46no—
844C4⋊C4—46no—
845C4⋊C4—46no—
846C4⋊C4—412no—
847C4⋊C4—412no—
848C4⋊C4C22×D4112yes—
849C4⋊C4C22×D4112yes—
850C4⋊C4C2×#4114yescomplemented
851C4⋊C4C2×#4118yescomplemented
852C22⋊C4—212no—
853C22⋊C4—224no—
854C22⋊C4—212no—
855C22⋊C4—224no—
856C22⋊C4—24no—
857C22⋊C4—212no—
858C22⋊C4—212no—
859C22⋊C4—212no—
860C22⋊C4—212no—
861C22⋊C4—212no—
862C22⋊C4—46no—
863C22⋊C4—46no—
864C22⋊C4—412no—
865C22⋊C4—412no—
866C22⋊C4C22×D4124yes—
867C22⋊C4C2×#4118yes—
868C42—22no—
869C42—22no—
870C42—22no—
871C42—26no—
872C42—26no—
873C42—26no—
874C42—26no—
875C42—26no—
876C42—26no—
877C42—26no—
878C42—26no—
879C42—26no—
880C42—24no—
881C42—212no—
882C42—212no—
883C42—212no—
884C42—24no—
885C42—212no—
886C42—212no—
887C42—212no—
888C42C22×D414yes—
889C42C22×D4112yes—
890C42C22×D4112yes—
891C42C22×D4112yes—
892C23—21no—
893C23—23no—
894C23—21no—
895C23—23no—
896C23—23no—
897C23—21no—
898C23—21no—
899C23—23no—
900C23—23no—
901C23—23no—
902C23—23no—
903C23—23no—
904C23—23no—
905C23—23no—
906C23—224no—
907C23—224no—
908C23—412no—
909C23—412no—
910C23—412no—
911C23—412no—
912C23—412no—
913C23C23×D416yes—
914C23C23×Q816yes—
915C23C23×Q816yes—
916C23C23×Q812yes—
917C23C22×#4116yes—
918C23C22×#4112yes—
919C23#58512yes—
920C23C2611yescharacteristic
921Q8—224no—
922Q8—28no—
923Q8—424no—
924Q8—412no—
925Q8—812no—
926Q8C2×C22⋊Q8116yescomplemented
927D4—248no—
928D4—224no—
929D4C2×C22⋊Q8148yescomplemented
930C2×C4—28no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—23no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—23no—
938C2×C4—21no—
939C2×C4—23no—
940C2×C4—22no—
941C2×C4—23no—
942C2×C4—23no—
943C2×C4—23no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—22no—
949C2×C4—224no—
950C2×C4—28no—
951C2×C4—224no—
952C2×C4—224no—
953C2×C4—224no—
954C2×C4—28no—
955C2×C4—224no—
956C2×C4—23no—
957C2×C4—23no—
958C2×C4—22no—
959C2×C4—26no—
960C2×C4—26no—
961C2×C4—22no—
962C2×C4—26no—
963C2×C4—26no—
964C2×C4—26no—
965C2×C4—26no—
966C2×C4—23no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—26no—
970C2×C4—26no—
971C2×C4—26no—
972C2×C4—26no—
973C2×C4—26no—
974C2×C4—26no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—23no—
978C2×C4—23no—
979C2×C4—23no—
980C2×C4—412no—
981C2×C4—412no—
982C2×C4—412no—
983C2×C4—424no—
984C2×C4—412no—
985C2×C4—412no—
986C2×C4—412no—
987C2×C4—412no—
988C2×C4—424no—
989C2×C4—412no—
990C2×C4—412no—
991C2×C4—812no—
992C2×C4—812no—
993C2×C4C2×C22⋊Q8148yescomplemented
994C2×C4C23×D412yes—
995C2×C4C23×D416yes—
996C2×C4C23×D416yes—
997C2×C4C23×D412yes—
998C2×C4C23×D416yes—
999C2×C4C23×D412yes—
1000C2×C4C23×Q812yes—
1001C2×C4C23×Q816yes—
1002C2×C4C23×Q812yes—
1003C2×C4C23×Q816yes—
1004C2×C4C22×#4114yes—
1005C2×C4C22×#4114yes—
1006C2×C4C22×#4112yes—
1007C2×C4C22×#4112yes—
1008C2×C4C22×#4116yes—
1009C2×C4C22×#4112yes—
1010C2×C4#58512yes—
1011C2×C4#58512yes—
1012C22—22no—
1013C22—26no—
1014C22—22no—
1015C22—26no—
1016C22—26no—
1017C22—22no—
1018C22—22no—
1019C22—22no—
1020C22—26no—
1021C22—26no—
1022C22—26no—
1023C22—22no—
1024C22—26no—
1025C22—26no—
1026C22—26no—
1027C22—448no—
1028C22—43no—
1029C22—43no—
1030C22—43no—
1031C22—43no—
1032C22C22×C22⋊Q8112yes—
1033C22Q8×#4114yescomplemented
1034C22C24×D411yescharacteristic
1035C22C24×Q811yescharacteristic
1036C22C23×#4111yescharacteristic
1037C22C23×#4111yescharacteristic
1038C22C2×#58511yescharacteristic
1039C22C2×#58511yescharacteristic
1040C22C2×#58511yescharacteristic
1041C4—22no—
1042C4—22no—
1043C4—26no—
1044C4—22no—
1045C4—26no—
1046C4—22no—
1047C4—26no—
1048C4—24no—
1049C4—24no—
1050C4—43no—
1051C4—42no—
1052C4—46no—
1053C4—46no—
1054C4—42no—
1055C4—43no—
1056C4—46no—
1057C4—46no—
1058C4C22×C22⋊Q814yes—
1059C4C22×C22⋊Q8112yes—
1060C4D4×#4114yes—
1061C2—24no—
1062C2—212no—
1063C2—46no—
1064C2C23×C22⋊Q811yescharacteristic
1065C2C2×D4×#4111yescharacteristic
1066C2C2×Q8×#4111yescharacteristic
1067C2#41211yescharacteristic
1068C2#6281111yescharacteristic
1069C2#6281311yescharacteristic
1070C2#6281611yescharacteristic
subgroupG/H
centerC22×C4C25
commutator, Frattini, socle, cosocleC23C26
prime radicalC23×#41C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×Q8×#41C2semidirect
3. #36625C2semidirect
4. #36577C2semidirect
5. Q8×C22⋊Q8C2semidirect
6. #36456C2semidirect
7. #36445C2semidirect
8. #36435C2semidirect
9. #36431C2semidirect
10. #36275C2semidirect
11. #36274C2semidirect
12. #36219C2semidirect
13. #36215C2semidirect
14. #36154C2semidirect
15. D4×C22⋊Q8C2semidirect
16. #34952C2semidirect
17. #34947C2semidirect
18. #34745C2semidirect
19. #34739C2semidirect
20. C4⋊C4×#41C2semidirect
21. C4⋊C4×#41C2semidirect
23. C2×C4×C22⋊Q8C2semidirect
26. C2×Q82C22semidirect
27. C2×#557C22semidirect
28. C2×#557C22semidirect
29. C2×#554C22semidirect
30. C2×#554C22semidirect
31. C2×D4×Q8C22semidirect
32. C2×#533C22semidirect
33. C2×#533C22semidirect
48. C22×C4×Q8C22semidirect
55. #2857C22semidirect
56. #2857C22semidirect
57. #2855C22semidirect
58. #2855C22semidirect
60. #2851C22semidirect
63. #2582C22semidirect
64. #2582C22semidirect
65. #2581C22semidirect
66. #2580C22semidirect
67. #2579C22semidirect
68. #2568C22semidirect
69. #2567C22semidirect
70. #2566C22semidirect
71. #2565C22semidirect
72. #2564C22semidirect
73. #2563C22semidirect
74. #2542C22semidirect
75. #2538C22semidirect
76. #2538C22semidirect
77. #2487C22semidirect
78. #2454C22semidirect
79. #2454C22semidirect
80. #2453C22semidirect
81. #2453C22semidirect
82. #2452C22semidirect
83. #2452C22semidirect
84. #2451C22semidirect
85. #2451C22semidirect
86. #2450C22semidirect
87. #2450C22semidirect
88. #2449C22semidirect
89. #2449C22semidirect
92. #2441C22semidirect
93. #2441C22semidirect
96. #2439C22semidirect
97. #2439C22semidirect
98. #2438C22semidirect
99. #2438C22semidirect
102. #2417C22semidirect
103. #2417C22semidirect
104. #2409C22semidirect
105. #2396C22semidirect
106. #2396C22semidirect
107. #2351C22semidirect
108. #2351C22semidirect
109. #2351C22semidirect
110. Q8×C4⋊C4C22semidirect
111. Q8×C4⋊C4C22semidirect
112. Q8×C4⋊C4C22semidirect
113. Q8×C4⋊C4C22semidirect
114. #2349C22semidirect
115. #2349C22semidirect
116. #2349C22semidirect
117. D4×C4⋊C4C22semidirect
118. D4×C4⋊C4C22semidirect
119. D4×C4⋊C4C22semidirect
120. D4×C4⋊C4C22semidirect
136. C4×C22⋊Q8C22semidirect
137. C4×C22⋊Q8C22semidirect
138. C4×C22⋊Q8C22semidirect
139. C4×C22⋊Q8C22semidirect
140. C4×C22⋊Q8C22semidirect
141. C4×C22⋊Q8C22semidirect
142. C4×C22⋊Q8C22semidirect
143. C4×C22⋊Q8C22semidirect
146. #2296C22semidirect
147. #2296C22semidirect
148. #2296C22semidirect
149. C2×#391C22semidirect
150. C2×#389C22semidirect
151. C2×#387C22semidirect
153. #2285C22semidirect
154. #2285C22semidirect
157. C2×C4×C4⋊C4C22semidirect
158. C2×C4×C4⋊C4C22semidirect
162. C22×#41Q8semidirect
439. C2×#41C2×Q8semidirect
440. C2×#41C2×Q8semidirect
441. C2×#41C2×Q8semidirect
448. C22×Q8C2×Q8semidirect
457. C22×D4C2×Q8semidirect
469. C23×C4C2×Q8semidirect
511. C22⋊Q8#41direct (N × H)
695. #41C22⋊Q8direct (N × H)
715. C2×Q8C2×#41semidirect
850. C4⋊C4C2×#41semidirect
851. C4⋊C4C2×#41semidirect
926. Q8C2×C22⋊Q8semidirect
929. D4C2×C22⋊Q8semidirect
993. C2×C4C2×C22⋊Q8semidirect
1033. C22Q8×#41semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×#412
C22×C4×#412
#366252
#365772
Q8×C22⋊Q82
#364562
#364452
#364352
#364312
#362752
#362742
#362192
#362152
#361542
D4×C22⋊Q82
#349522
#349472
#347452
#347392
C4⋊C4×#412
C22⋊C4×#412
C2×C4×C22⋊Q82