Finite Group Databasebeta

← #41×#123 #7630331

Subgroups — #41×#123 #7630331

Order 512.

9251 conjugacy classes of subgroups.

The subgroup lattice has 1063 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×#41C211yesmaximal, characteristic
2C22×C4×#41C211yesmaximal, characteristic, complemented
3#36626C213yesmaximal, complemented
4#36578C211yesmaximal, characteristic, complemented
5Q8×#123C211yesmaximal, characteristic, complemented
6#36483C211yesmaximal, characteristic, complemented
7#36482C211yesmaximal, characteristic, complemented
8#36433C212yesmaximal, complemented
9#36432C212yesmaximal, complemented
10#36237C213yesmaximal, complemented
11#36236C213yesmaximal, complemented
12#36217C216yesmaximal, complemented
13#36216C216yesmaximal, complemented
14#36155C213yesmaximal, complemented
15D4×#123C213yesmaximal, complemented
16#34810C213yesmaximal, complemented
17#34809C213yesmaximal, complemented
18#34744C216yesmaximal, complemented
19#34742C216yesmaximal, complemented
20C4⋊C4×#41C212yesmaximal, complemented
21C22⋊C4×#41C212yesmaximal, complemented
22C22⋊C4×#41C211yesmaximal, characteristic, complemented
23C2×C4×#123C213yesmaximal, complemented
24C23×#41C2211yescharacteristic
25C23×#41C2211yescharacteristic
26D4×#41—216no—
27C2×#550C2211yescharacteristic
28C2×D4×Q8C2211yescharacteristic
29C2×#548C2211yescharacteristic
30C2×#548C2211yescharacteristic
31C2×#547C2213yes—
32C2×#546C2213yes—
33C2×#546C2213yes—
34C2×D42C2213yes—
35C2×#532C2213yes—
36C2×#525C2213yes—
37C2×#525C2213yes—
38C22×#123C2213yes—
39C2×C4×#41—216no—
40C2×C4×#41C2212yes—
41C2×C4×#41C2212yes—
42C2×C4×#41C2211yescharacteristic
43C2×C4×#41C2212yescomplemented
44C2×C4×#41C2216yescomplemented
45C2×C4×#41C2216yescomplemented
46C22×C4×Q8C2211yescharacteristic, complemented
47C22×C4×Q8C2211yescharacteristic, complemented
48C22×C4×D4C2213yes—
49C22×C4×D4C2213yescomplemented
50C22×C4×D4C2213yescomplemented
51C22×#117C2213yescomplemented
52C23×C42C2213yescomplemented
53#2855C2213yescomplemented
54#2855C2216yescomplemented
55#2855C2213yescomplemented
56#2854C2216yescomplemented
57#2854C2213yescomplemented
58#2854C2213yescomplemented
59#2853C22112yescomplemented
60#2849C2216yescomplemented
61#2849C2216yescomplemented
62#2504C2213yescomplemented
63#2503C2213yescomplemented
64#2502C2213yescomplemented
65#2501C2213yescomplemented
66#2500C2216yescomplemented
67#2499C2216yescomplemented
68#2498C22112yescomplemented
69#2487C2213yes—
70#2487C2213yescomplemented
71#2486C2213yes—
72#2486C2213yescomplemented
73#2485C2216yescomplemented
74#2485C2216yescomplemented
75#2484C2216yescomplemented
76#2483C2216yescomplemented
77#2482C2216yescomplemented
78#2448C2216yescomplemented
79#2448C2216yescomplemented
80#2447C2216yescomplemented
81#2447C2216yescomplemented
82#2446C2216yescomplemented
83#2446C2216yescomplemented
84#2445C2216yescomplemented
85#2445C2216yescomplemented
86#2444C22112yescomplemented
87#2444C22112yescomplemented
88#2443C22112yescomplemented
89#2443C22112yescomplemented
90#2423C2216yescomplemented
91#2423C2216yescomplemented
92#2422C2216yescomplemented
93#2422C2216yescomplemented
94#2421C2216yescomplemented
95#2421C2216yescomplemented
96#2420C2216yescomplemented
97#2420C2216yescomplemented
98#2419C22112yescomplemented
99#2419C22112yescomplemented
100#2418C22112yescomplemented
101#2418C22112yescomplemented
102#2412C2216yescomplemented
103#2412C2216yescomplemented
104#2405C2216yes—
105#2395C2216yescomplemented
106#2395C22112yescomplemented
107#2395C2216yescomplemented
108#2351C2212yescomplemented
109#2351C2212yescomplemented
110Q8×C4⋊C4C2212yescomplemented
111Q8×C4⋊C4C2212yescomplemented
112#2349C2216yescomplemented
113#2349C2216yescomplemented
114D4×C4⋊C4C2216yescomplemented
115D4×C4⋊C4C2216yescomplemented
116#2341C2212yescomplemented
117#2341C2212yescomplemented
118#2341C2212yescomplemented
119Q8×C22⋊C4C2212yescomplemented
120Q8×C22⋊C4C2212yescomplemented
121Q8×C22⋊C4C2211yescharacteristic, complemented
122Q8×C22⋊C4C2211yescharacteristic, complemented
123#2339C2216yescomplemented
124#2339C2216yescomplemented
125#2339C2216yescomplemented
126D4×C22⋊C4C2213yescomplemented
127D4×C22⋊C4C2216yescomplemented
128D4×C22⋊C4C2216yescomplemented
129D4×C22⋊C4C2213yescomplemented
130C4×#123C2213yes—
131C4×#123C2213yes—
132C4×#123C2211yescharacteristic
133C4×#123C2213yes—
134C4×#123C2213yescomplemented
135C4×#123C22112yescomplemented
136C4×#123C2216yescomplemented
137C4×#123C2213yescomplemented
138C4×#123C2216yescomplemented
139C4×#123C2216yescomplemented
140C4×#123C2213yescomplemented
141C4×#123C2216yescomplemented
142C4×#123C2216yescomplemented
143C4×#123C2213yescomplemented
144#2297C2216yescomplemented
145#2297C2216yescomplemented
146#2297C2216yescomplemented
147#2296C2216yescomplemented
148#2296C2216yescomplemented
149C2×#388C2216yescomplemented
150C2×#387C2216yescomplemented
151C2×#386C2213yes—
152C2×#385C2213yescomplemented
153#2285C2216yescomplemented
154#2280C2213yescomplemented
155#2280C2216yescomplemented
156C2×#381C2213yescomplemented
157C2×C4×C4⋊C4C2216yescomplemented
158C2×C4×C22⋊C4C2216yescomplemented
159C2×C4×C22⋊C4C2213yescomplemented
160C22×#41—216no—
161C22×#41—28no—
162C22×#41—216no—
163C22×#41D4116yes—
164C22×#41C2313yes—
165C22×#41C2311yescharacteristic
166C22×#41C2313yes—
167C22×#41C2313yes—
168C22×#41C2311yescharacteristic
169C22×#41C2313yes—
170C22×#41C2311yescharacteristic
171C23×Q8C2311yescharacteristic
172C23×Q8C2311yescharacteristic
173C23×D4C2313yes—
174C23×D4C2313yes—
175C23×D4C2313yes—
176C24×C4C2313yes—
177C24×C4C2313yes—
178C24×C4C2313yes—
179C24×C4C2313yes—
180#550—28no—
181D4×Q8—28no—
182#548—28no—
183#548—28no—
184#547—224no—
185#546—224no—
186#546—224no—
187D42—224no—
188#532—224no—
189C2×C4⋊Q8C2313yes—
190C2×#127C2313yes—
191C2×#124C2313yes—
192C2×#124C2313yes—
193#525—224no—
194#525—224no—
195C2×#123—224no—
196C2×#123C2313yes—
197C2×#123C2316yes—
198C2×#123C2313yes—
199C2×#123C2313yes—
200C2×#123C2316yes—
201C2×#123C2316yes—
202C2×#123C2316yes—
203C2×#123C2316yes—
204C2×#123C23112yes—
205C2×#123C2311yescharacteristic
206C2×C22⋊Q8C2313yes—
207C2×C22⋊Q8C2313yes—
208C2×C22⋊Q8C2313yes—
209C2×C22⋊Q8C2313yes—
210C2×#121C2313yes—
211C2×#121C2313yes—
212C2×#121C2313yes—
213C2×#121C2313yes—
214C2×#121C2316yes—
215C2×#121C2316yes—
216C2×#120C2316yes—
217C2×#120C2316yes—
218C4×#41—216no—
219C4×#41—248no—
220C4×#41—248no—
221C4×#41—216no—
222C4×#41—28no—
223C4×#41—216no—
224C2×C4×Q8—28no—
225C2×C4×Q8—28no—
226C2×C4×Q8C2312yes—
227C2×C4×Q8C2312yes—
228C2×C4×Q8C2312yes—
229C2×C4×Q8C2312yes—
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2316yes—
233C2×C4×Q8C2316yes—
234C2×C4×D4—224no—
235C2×C4×D4—224no—
236C2×C4×D4—224no—
237C2×C4×D4C2316yes—
238C2×C4×D4C2316yes—
239C2×C4×D4C2316yes—
240C2×C4×D4C2316yes—
241C2×C4×D4C2313yes—
242C2×C4×D4C2313yes—
243C2×C4×D4C2313yes—
244C2×C4×D4C2313yes—
245C2×C4×D4C2316yes—
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2313yes—
248C2×C4×D4C2313yes—
249C2×C4×D4C2313yes—
250C2×C4×D4C2313yes—
251C2×C4×D4C2313yes—
252C2×C4×D4C23112yes—
253C2×C4×D4C23112yes—
254C2×C4×D4C2316yes—
255C2×C4×D4C2316yes—
256C2×#117—224no—
257C2×#117C2316yes—
258C2×#117C2316yes—
259C2×#117C2316yes—
260C2×#117C2316yes—
261C2×#117C2313yes—
262C2×#117C2316yes—
263C22×C4⋊C4C2316yes—
264C22×C4⋊C4C2313yes—
265C22×C4⋊C4C2313yes—
266C22×C4⋊C4C2313yes—
267C22×C4⋊C4C2316yes—
268C22×C22⋊C4C2313yes—
269C22×C22⋊C4C2316yes—
270C22×C22⋊C4C2316yes—
271C22×C22⋊C4C2313yes—
272C22×C22⋊C4C2313yes—
273C22×C22⋊C4C2313yes—
274C22×C22⋊C4C2316yes—
275C22×C42—224no—
276C22×C42C2316yes—
277C22×C42C2313yes—
278C22×C42C2313yes—
279C22×C42C2316yes—
280C22×C42C2311yescharacteristic
281C22×C42C2313yes—
282C22×C42C2316yes—
283C22×C42C2316yes—
284C22×C42C2313yes—
285C22×C42C2316yes—
286#400C2316yes—
287#400C23112yes—
288#400C2316yes—
289#399C2316yes—
290#399C23112yes—
291#399C2316yes—
292#398C2316yes—
293#398C23112yes—
294#398C2316yes—
295#397C23112yes—
296#397C23112yes—
297#397C2316yes—
298#397C23112yes—
299#397C23112yes—
300#397C23112yes—
301#397C2316yes—
302#394C23112yes—
303#394C23112yes—
304#394C23112yes—
305#394C23112yes—
306#391C2316yes—
307#391C2316yes—
308#391C2316yes—
309#391C2316yes—
310#391C2316yes—
311#391C2316yes—
312#390C2316yes—
313#390C2316yes—
314#390C2316yes—
315#390C2316yes—
316#390C2316yes—
317#390C2316yes—
318#389C2316yes—
319#389C2316yes—
320#389C2316yes—
321#389C2316yes—
322#389C2316yes—
323#389C2316yes—
324#389C2316yes—
325#389C2316yes—
326#388C2316yes—
327#388C23112yes—
328#388C23112yes—
329#388C23112yes—
330#388C2316yes—
331#388C2316yes—
332#388C2316yes—
333#388C2316yes—
334#388C2316yes—
335#388C2316yes—
336#388C2312yes—
337#387C2316yes—
338#387C23112yes—
339#387C23112yes—
340#387C23112yes—
341#387C2316yes—
342#387C2316yes—
343#387C2316yes—
344#387C2316yes—
345#387C2316yes—
346#387C2316yes—
347#387C2312yes—
348#386C2313yes—
349#386C23112yes—
350#386C23112yes—
351#386C2316yes—
352#386C23112yes—
353#386C23112yes—
354#386C23112yes—
355#386C23112yes—
356#386C23112yes—
357#386C2313yes—
358#386C2313yes—
359#386C2316yes—
360#386C2316yes—
361#386C2311yescharacteristic
362#385C2313yes—
363#385C23112yes—
364#385C23112yes—
365#385C2316yes—
366#385C23112yes—
367#385C23112yes—
368#385C23112yes—
369#385C2313yes—
370#385C2316yes—
371#385C2316yes—
372#385C2313yes—
373#385C2311yescharacteristic
374#384C2316yes—
375#384C2316yes—
376#382C2316yes—
377#382C2316yes—
378#381C2313yes—
379#381C2316yes—
380#381C23112yes—
381#381C2316yes—
382#381C23112yes—
383#381C2313yes—
384#381C2316yes—
385#381C2316yes—
386#381C2313yes—
387#381C2311yescharacteristic
388#380C2313yes—
389#380C2313yes—
390#380C2316yes—
391#380C2316yes—
392#380C2316yes—
393#380C2316yes—
394#380C2316yes—
395#380C23112yes—
396#380C23112yes—
397#379C2316yes—
398#379C23112yes—
399C4×C4⋊C4C2316yes—
400C4×C4⋊C4C2316yes—
401C4×C4⋊C4C2316yes—
402C4×C4⋊C4C2316yes—
403C4×C4⋊C4C2316yes—
404C4×C4⋊C4C2316yes—
405C4×C4⋊C4C23112yes—
406C4×C4⋊C4C2312yes—
407C4×C4⋊C4C2316yes—
408C4×C22⋊C4C2316yes—
409C4×C22⋊C4C2316yes—
410C4×C22⋊C4C2313yes—
411C4×C22⋊C4C2313yes—
412C4×C22⋊C4C2316yes—
413C4×C22⋊C4C2316yes—
414C4×C22⋊C4C2316yes—
415C4×C22⋊C4C2316yes—
416C4×C22⋊C4C2316yes—
417C4×C22⋊C4C2316yes—
418C4×C22⋊C4C23112yes—
419C4×C22⋊C4C2316yes—
420C4×C22⋊C4C2312yes—
421C4×C22⋊C4C2311yescharacteristic
422C4×C22⋊C4C2313yes—
423C4×C22⋊C4C2316yes—
424C2×#95C2316yes—
425C2×#95C2316yes—
426C2×#95C2316yes—
427C2×#95C2316yes—
428C2×#95C2316yes—
429C25C2413yes—
430C25C2413yes—
431C2×#41—2128no—
432C2×#41—24no—
433C2×#41—28no—
434C2×#41—28no—
435C2×#41—212no—
436C2×#41—224no—
437C2×#41—224no—
438C2×#41—212no—
439C2×#41—224no—
440C2×#41—224no—
441C2×#41—464no—
442C2×#41C2×D4124yes—
443C2×#41C2×D4124yes—
444C2×#41C2×D418yes—
445C2×#41C2×D418yes—
446C2×#41#41116yes—
447C22×Q8—28no—
448C22×Q8—24no—
449C22×Q8—28no—
450C22×Q8C2×D418yes—
451C22×Q8C2413yes—
452C22×Q8C2413yes—
453C22×Q8C2411yescharacteristic
454C22×D4—224no—
455C22×D4—212no—
456C22×D4—212no—
457C22×D4—212no—
458C22×D4—224no—
459C22×D4—46no—
460C22×D4C2×D4124yes—
461C22×D4C2413yes—
462C22×D4C2416yes—
463C22×D4C2413yes—
464C22×D4C2413yes—
465C22×D4C2413yes—
466C22×D4C2416yes—
467C22×D4C2413yes—
468C22×D4C2411yescharacteristic
469C22×D4C2416yes—
470C22×D4C2413yes—
471C23×C4—224no—
472C23×C4—212no—
473C23×C4—212no—
474C23×C4—212no—
475C23×C4—224no—
476C23×C4—212no—
477C23×C4—412no—
478C23×C4—46no—
479C23×C4C2×D4124yes—
480C23×C4C2413yes—
481C23×C4C2413yes—
482C23×C4C2413yes—
483C23×C4C2413yes—
484C23×C4C2411yescharacteristic
485C23×C4C2411yescharacteristic
486C23×C4C2413yes—
487C23×C4C2416yes—
488C23×C4C2416yes—
489C23×C4C2416yes—
490C23×C4C2413yes—
491C23×C4C2416yes—
492C23×C4C2416yes—
493C23×C4C2413yes—
494C23×C4C2413yes—
495C23×C4C2413yes—
496C23×C4C2413yes—
497C23×C4C2411yescharacteristic
498C23×C4C2411yescharacteristic
499C23×C4C2413yes—
500C23×C4C2413yes—
501C23×C4C2416yes—
502C23×C4C2413yes—
503C4⋊Q8—212no—
504#127—212no—
505#124—212no—
506#124—212no—
507#123—224no—
508#123—212no—
509#123—224no—
510#123—212no—
511#123—224no—
512#123—224no—
513#123—212no—
514#123—424no—
515#123—412no—
516#123#4118yesdirect product factor
517C22⋊Q8—212no—
518C22⋊Q8—212no—
519C22⋊Q8—212no—
520C22⋊Q8—212no—
521#121—212no—
522#121—212no—
523#121—224no—
524#121—224no—
525#121—212no—
526#121—212no—
527#120—224no—
528#120—224no—
529C4×Q8—224no—
530C4×Q8—224no—
531C4×Q8—28no—
532C4×Q8—28no—
533C4×Q8—24no—
534C4×Q8—24no—
535C4×Q8—28no—
536C4×Q8—28no—
537C4×D4—248no—
538C4×D4—248no—
539C4×D4—224no—
540C4×D4—224no—
541C4×D4—224no—
542C4×D4—224no—
543C4×D4—212no—
544C4×D4—212no—
545C4×D4—224no—
546C4×D4—224no—
547C4×D4—24no—
548C4×D4—212no—
549C4×D4—212no—
550C4×D4—212no—
551C4×D4—212no—
552C4×D4—212no—
553C4×D4—212no—
554C4×D4—212no—
555C4×D4—224no—
556#117—224no—
557#117—224no—
558#117—224no—
559#117—224no—
560#117—212no—
561#117—224no—
562C2×C4⋊C4—212no—
563C2×C4⋊C4—212no—
564C2×C4⋊C4—212no—
565C2×C4⋊C4—224no—
566C2×C4⋊C4—412no—
567C2×C4⋊C4C2411yescharacteristic
568C2×C4⋊C4C2412yes—
569C2×C4⋊C4C2416yes—
570C2×C4⋊C4C2416yes—
571C2×C4⋊C4C2416yes—
572C2×C4⋊C4C2416yes—
573C2×C4⋊C4C2413yes—
574C2×C4⋊C4C2413yes—
575C2×C4⋊C4C2413yes—
576C2×C4⋊C4C2416yes—
577C2×C4⋊C4C2416yes—
578C2×C4⋊C4C2416yes—
579C2×C4⋊C4C2416yes—
580C2×C4⋊C4C2413yes—
581C2×C4⋊C4C2413yes—
582C2×C4⋊C4C2416yes—
583C2×C4⋊C4C2416yes—
584C2×C4⋊C4C2416yes—
585C2×C4⋊C4C2416yes—
586C2×C4⋊C4C2416yes—
587C2×C4⋊C4C24112yes—
588C2×C4⋊C4C24112yes—
589C2×C4⋊C4C2412yes—
590C2×C22⋊C4—224no—
591C2×C22⋊C4—212no—
592C2×C22⋊C4—212no—
593C2×C22⋊C4—212no—
594C2×C22⋊C4—224no—
595C2×C22⋊C4—412no—
596C2×C22⋊C4—46no—
597C2×C22⋊C4C2411yescharacteristic
598C2×C22⋊C4C2411yescharacteristic
599C2×C22⋊C4C2411yescharacteristic
600C2×C22⋊C4C2412yes—
601C2×C22⋊C4C24112yes—
602C2×C22⋊C4C24112yes—
603C2×C22⋊C4C2413yes—
604C2×C22⋊C4C2413yes—
605C2×C22⋊C4C2413yes—
606C2×C22⋊C4C2413yes—
607C2×C22⋊C4C2413yes—
608C2×C22⋊C4C2413yes—
609C2×C22⋊C4C2413yes—
610C2×C22⋊C4C2413yes—
611C2×C22⋊C4C2416yes—
612C2×C22⋊C4C2416yes—
613C2×C22⋊C4C2416yes—
614C2×C22⋊C4C2416yes—
615C2×C22⋊C4C2416yes—
616C2×C22⋊C4C2416yes—
617C2×C22⋊C4C24112yes—
618C2×C22⋊C4C2416yes—
619C2×C22⋊C4C2416yes—
620C2×C22⋊C4C2416yes—
621C2×C22⋊C4C2416yes—
622C2×C22⋊C4C2416yes—
623C2×C22⋊C4C24112yes—
624C2×C22⋊C4C24112yes—
625C2×C22⋊C4C24112yes—
626C2×C22⋊C4C2411yescharacteristic
627C2×C22⋊C4C2412yes—
628C2×C42—212no—
629C2×C42—212no—
630C2×C42—212no—
631C2×C42—212no—
632C2×C42—224no—
633C2×C42—224no—
634C2×C42—224no—
635C2×C42—224no—
636C2×C42—24no—
637C2×C42—224no—
638C2×C42C2416yes—
639C2×C42C2413yes—
640C2×C42C2413yes—
641C2×C42C2416yes—
642C2×C42C2416yes—
643C2×C42C2416yes—
644C2×C42C2416yes—
645C2×C42C2416yes—
646C2×C42C2416yes—
647C2×C42C2412yes—
648C2×C42C2416yes—
649C2×C42C2413yes—
650C2×C42C2416yes—
651C2×C42C2411yescharacteristic
652C2×C42C2412yes—
653C2×C42C2412yes—
654#95C2412yes—
655#95C2412yes—
656#95C2412yes—
657#95C2412yes—
658#95C2412yes—
659#95C2416yes—
660#95C2416yes—
661#95C2416yes—
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#95C24112yes—
675#95C24112yes—
676#95C2416yes—
677#95C2416yes—
678#95C24112yes—
679#95C24112yes—
680C24—26no—
681C24—212no—
682C24—26no—
683C24—26no—
684C24—26no—
685C24—212no—
686C24—46no—
687C24—46no—
688C24—43no—
689C24C22×D4112yes—
690C24C2513yes—
691C24C2513yes—
692C24C2511yescharacteristic
693C24C2513yes—
694C24C2511yescharacteristic
695#41—232no—
696#41—296no—
697#41—296no—
698#41—416no—
699#41—448no—
700#41—448no—
701#41#123164yesdirect product factor
702C2×Q8—232no—
703C2×Q8—26no—
704C2×Q8—212no—
705C2×Q8—212no—
706C2×Q8—416no—
707C2×Q8C22×D4112yes—
708C2×Q8C22×D414yes—
709C2×Q8C2×#4118yes—
710C2×D4—22no—
711C2×D4—224no—
712C2×D4—22no—
713C2×D4—296no—
714C2×D4—26no—
715C2×D4—26no—
716C2×D4—26no—
717C2×D4—212no—
718C2×D4—26no—
719C2×D4—26no—
720C2×D4—224no—
721C2×D4—26no—
722C2×D4—212no—
723C2×D4—26no—
724C2×D4—212no—
725C2×D4—26no—
726C2×D4—212no—
727C2×D4—43no—
728C2×D4—43no—
729C2×D4—412no—
730C2×D4—448no—
731C2×D4—448no—
732C2×D4C22×D4124yes—
733C2×D4C22×D4112yes—
734C2×D4C22×D4112yes—
735C2×D4C2×#4114yes—
736C2×D4C2×#41124yes—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—212no—
740C22×C4—22no—
741C22×C4—296no—
742C22×C4—24no—
743C22×C4—212no—
744C22×C4—212no—
745C22×C4—212no—
746C22×C4—24no—
747C22×C4—26no—
748C22×C4—26no—
749C22×C4—212no—
750C22×C4—212no—
751C22×C4—212no—
752C22×C4—212no—
753C22×C4—26no—
754C22×C4—26no—
755C22×C4—212no—
756C22×C4—26no—
757C22×C4—212no—
758C22×C4—26no—
759C22×C4—26no—
760C22×C4—212no—
761C22×C4—22no—
762C22×C4—26no—
763C22×C4—26no—
764C22×C4—26no—
765C22×C4—212no—
766C22×C4—212no—
767C22×C4—26no—
768C22×C4—212no—
769C22×C4—24no—
770C22×C4—212no—
771C22×C4—212no—
772C22×C4—212no—
773C22×C4—212no—
774C22×C4—212no—
775C22×C4—46no—
776C22×C4—46no—
777C22×C4—46no—
778C22×C4—46no—
779C22×C4—46no—
780C22×C4—46no—
781C22×C4—43no—
782C22×C4—46no—
783C22×C4—46no—
784C22×C4—46no—
785C22×C4—448no—
786C22×C4—448no—
787C22×C4—448no—
788C22×C4C22×D414yes—
789C22×C4C22×D4112yes—
790C22×C4C22×D4112yes—
791C22×C4C22×D4112yes—
792C22×C4C22×D4112yes—
793C22×C4C22×D4112yes—
794C22×C4C2×#41124yes—
795C22×C4C2×#4114yescomplemented
796C22×C4C2512yes—
797C22×C4C2511yescharacteristic
798C22×C4C2513yes—
799C22×C4C2516yes—
800C22×C4C2516yes—
801C22×C4C2511yescharacteristic
802C22×C4C2516yes—
803C22×C4C2516yes—
804C22×C4C2513yes—
805C22×C4C2513yes—
806C22×C4C2511yescharacteristic
807C22×C4C2513yes—
808C22×C4C2512yes—
809C22×C4C2512yes—
810C22×C4C2511yescharacteristic
811C22×C4C2512yes—
812C22×C4C2513yes—
813C22×C4C2511yescharacteristic
814C4⋊C4—22no—
815C4⋊C4—212no—
816C4⋊C4—212no—
817C4⋊C4—212no—
818C4⋊C4—212no—
819C4⋊C4—26no—
820C4⋊C4—26no—
821C4⋊C4—26no—
822C4⋊C4—26no—
823C4⋊C4—26no—
824C4⋊C4—212no—
825C4⋊C4—212no—
826C4⋊C4—212no—
827C4⋊C4—212no—
828C4⋊C4—212no—
829C4⋊C4—212no—
830C4⋊C4—24no—
831C4⋊C4—212no—
832C4⋊C4—46no—
833C4⋊C4—46no—
834C4⋊C4—412no—
835C4⋊C4—412no—
836C4⋊C4C2×#4118yescomplemented
837C22⋊C4—22no—
838C22⋊C4—224no—
839C22⋊C4—224no—
840C22⋊C4—26no—
841C22⋊C4—26no—
842C22⋊C4—26no—
843C22⋊C4—212no—
844C22⋊C4—212no—
845C22⋊C4—26no—
846C22⋊C4—212no—
847C22⋊C4—224no—
848C22⋊C4—22no—
849C22⋊C4—26no—
850C22⋊C4—22no—
851C22⋊C4—26no—
852C22⋊C4—26no—
853C22⋊C4—26no—
854C22⋊C4—212no—
855C22⋊C4—212no—
856C22⋊C4—212no—
857C22⋊C4—212no—
858C22⋊C4—24no—
859C22⋊C4—212no—
860C22⋊C4—46no—
861C22⋊C4—46no—
862C22⋊C4—46no—
863C22⋊C4—412no—
864C22⋊C4—412no—
865C22⋊C4—412no—
866C22⋊C4C2×#4114yescomplemented
867C22⋊C4C2×#4118yescomplemented
868C42—24no—
869C42—24no—
870C42—212no—
871C42—212no—
872C42—22no—
873C42—212no—
874C42—212no—
875C42—212no—
876C42—212no—
877C42—26no—
878C42—26no—
879C42—26no—
880C42—24no—
881C42—212no—
882C42—212no—
883C42—212no—
884C23—23no—
885C23—22no—
886C23—26no—
887C23—22no—
888C23—23no—
889C23—21no—
890C23—23no—
891C23—22no—
892C23—26no—
893C23—22no—
894C23—26no—
895C23—23no—
896C23—21no—
897C23—224no—
898C23—224no—
899C23—23no—
900C23—23no—
901C23—26no—
902C23—26no—
903C23—23no—
904C23—412no—
905C23—424no—
906C23—424no—
907C23—412no—
908C23—424no—
909C23—412no—
910C23—86no—
911C23—812no—
912C23C23×D416yes—
913C23C23×D416yes—
914C23C23×D412yes—
915C23C22×#4112yes—
916C23C22×#41112yes—
917C23C22×#4112yes—
918C23#58512yes—
919C23C2611yescharacteristic
920Q8—224no—
921Q8—412no—
922Q8C2×#123116yescomplemented
923D4—248no—
924D4—28no—
925D4—224no—
926D4—412no—
927D4—412no—
928D4—424no—
929D4—412no—
930D4—412no—
931D4—812no—
932D4C2×#123148yescomplemented
933C2×C4—28no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—21no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—26no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—21no—
944C2×C4—224no—
945C2×C4—28no—
946C2×C4—28no—
947C2×C4—224no—
948C2×C4—224no—
949C2×C4—224no—
950C2×C4—21no—
951C2×C4—26no—
952C2×C4—26no—
953C2×C4—23no—
954C2×C4—23no—
955C2×C4—21no—
956C2×C4—23no—
957C2×C4—22no—
958C2×C4—26no—
959C2×C4—26no—
960C2×C4—26no—
961C2×C4—26no—
962C2×C4—23no—
963C2×C4—22no—
964C2×C4—26no—
965C2×C4—26no—
966C2×C4—26no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—26no—
970C2×C4—26no—
971C2×C4—26no—
972C2×C4—26no—
973C2×C4—22no—
974C2×C4—26no—
975C2×C4—23no—
976C2×C4—424no—
977C2×C4—424no—
978C2×C4—424no—
979C2×C4—424no—
980C2×C4—424no—
981C2×C4—412no—
982C2×C4—412no—
983C2×C4—412no—
984C2×C4—412no—
985C2×C4—44no—
986C2×C4—412no—
987C2×C4—412no—
988C2×C4—412no—
989C2×C4—86no—
990C2×C4—812no—
991C2×C4C2×#123148yescomplemented
992C2×C4C23×D412yes—
993C2×C4C23×D416yes—
994C2×C4C23×D412yes—
995C2×C4C23×D416yes—
996C2×C4C22×#4114yes—
997C2×C4C22×#4114yes—
998C2×C4C22×#4112yes—
999C2×C4C22×#4114yes—
1000C2×C4C22×#41112yes—
1001C2×C4#58514yes—
1002C22—22no—
1003C22—26no—
1004C22—212no—
1005C22—24no—
1006C22—22no—
1007C22—26no—
1008C22—212no—
1009C22—24no—
1010C22—26no—
1011C22—26no—
1012C22—26no—
1013C22—22no—
1014C22—24no—
1015C22—448no—
1016C22—41no—
1017C22—46no—
1018C22—42no—
1019C22—41no—
1020C22—46no—
1021C22—43no—
1022C22—46no—
1023C22—43no—
1024C22—43no—
1025C22—46no—
1026C22—824no—
1027C22C22×#123112yes—
1028C22D4×#4114yes—
1029C22C24×D411yescharacteristic
1030C22C23×#4112yes—
1031C22C23×#4111yescharacteristic
1032C22C2×#58512yes—
1033C22C2×#58511yescharacteristic
1034C4—24no—
1035C4—22no—
1036C4—26no—
1037C4—24no—
1038C4—22no—
1039C4—24no—
1040C4—46no—
1041C4—41no—
1042C4—43no—
1043C4—46no—
1044C4—42no—
1045C4—41no—
1046C4—43no—
1047C4—46no—
1048C4—43no—
1049C4—46no—
1050C4C22×#12314yes—
1051C4C22×#123112yes—
1052C2—24no—
1053C2—212no—
1054C2—46no—
1055C2—42no—
1056C2—83no—
1057C2C23×#12311yescharacteristic
1058C2C2×D4×#4111yescharacteristic
1059C2#41212yes—
1060C2#6281111yescharacteristic
1061C2#6281612yes—
subgroupG/H
centerC22×C4C25
commutator, Frattini, socle, cosocleC23C26
prime radicalC2×D4×#41C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×C4×#41C2semidirect
3. #36626C2semidirect
4. #36578C2semidirect
5. Q8×#123C2semidirect
6. #36483C2semidirect
7. #36482C2semidirect
8. #36433C2semidirect
9. #36432C2semidirect
10. #36237C2semidirect
11. #36236C2semidirect
12. #36217C2semidirect
13. #36216C2semidirect
14. #36155C2semidirect
15. D4×#123C2semidirect
16. #34810C2semidirect
17. #34809C2semidirect
18. #34744C2semidirect
19. #34742C2semidirect
20. C4⋊C4×#41C2semidirect
21. C22⋊C4×#41C2semidirect
22. C22⋊C4×#41C2semidirect
23. C2×C4×#123C2semidirect
43. C2×C4×#41C22semidirect
44. C2×C4×#41C22semidirect
45. C2×C4×#41C22semidirect
46. C22×C4×Q8C22semidirect
47. C22×C4×Q8C22semidirect
49. C22×C4×D4C22semidirect
50. C22×C4×D4C22semidirect
51. C22×#117C22semidirect
52. C23×C42C22semidirect
53. #2855C22semidirect
54. #2855C22semidirect
55. #2855C22semidirect
56. #2854C22semidirect
57. #2854C22semidirect
58. #2854C22semidirect
59. #2853C22semidirect
60. #2849C22semidirect
61. #2849C22semidirect
62. #2504C22semidirect
63. #2503C22semidirect
64. #2502C22semidirect
65. #2501C22semidirect
66. #2500C22semidirect
67. #2499C22semidirect
68. #2498C22semidirect
70. #2487C22semidirect
72. #2486C22semidirect
73. #2485C22semidirect
74. #2485C22semidirect
75. #2484C22semidirect
76. #2483C22semidirect
77. #2482C22semidirect
78. #2448C22semidirect
79. #2448C22semidirect
80. #2447C22semidirect
81. #2447C22semidirect
82. #2446C22semidirect
83. #2446C22semidirect
84. #2445C22semidirect
85. #2445C22semidirect
86. #2444C22semidirect
87. #2444C22semidirect
88. #2443C22semidirect
89. #2443C22semidirect
90. #2423C22semidirect
91. #2423C22semidirect
92. #2422C22semidirect
93. #2422C22semidirect
94. #2421C22semidirect
95. #2421C22semidirect
96. #2420C22semidirect
97. #2420C22semidirect
98. #2419C22semidirect
99. #2419C22semidirect
100. #2418C22semidirect
101. #2418C22semidirect
102. #2412C22semidirect
103. #2412C22semidirect
105. #2395C22semidirect
106. #2395C22semidirect
107. #2395C22semidirect
108. #2351C22semidirect
109. #2351C22semidirect
110. Q8×C4⋊C4C22semidirect
111. Q8×C4⋊C4C22semidirect
112. #2349C22semidirect
113. #2349C22semidirect
114. D4×C4⋊C4C22semidirect
115. D4×C4⋊C4C22semidirect
116. #2341C22semidirect
117. #2341C22semidirect
118. #2341C22semidirect
119. Q8×C22⋊C4C22semidirect
120. Q8×C22⋊C4C22semidirect
121. Q8×C22⋊C4C22semidirect
122. Q8×C22⋊C4C22semidirect
123. #2339C22semidirect
124. #2339C22semidirect
125. #2339C22semidirect
126. D4×C22⋊C4C22semidirect
127. D4×C22⋊C4C22semidirect
128. D4×C22⋊C4C22semidirect
129. D4×C22⋊C4C22semidirect
134. C4×#123C22semidirect
135. C4×#123C22semidirect
136. C4×#123C22semidirect
137. C4×#123C22semidirect
138. C4×#123C22semidirect
139. C4×#123C22semidirect
140. C4×#123C22semidirect
141. C4×#123C22semidirect
142. C4×#123C22semidirect
143. C4×#123C22semidirect
144. #2297C22semidirect
145. #2297C22semidirect
146. #2297C22semidirect
147. #2296C22semidirect
148. #2296C22semidirect
149. C2×#388C22semidirect
150. C2×#387C22semidirect
152. C2×#385C22semidirect
153. #2285C22semidirect
154. #2280C22semidirect
155. #2280C22semidirect
156. C2×#381C22semidirect
157. C2×C4×C4⋊C4C22semidirect
158. C2×C4×C22⋊C4C22semidirect
159. C2×C4×C22⋊C4C22semidirect
516. #123#41direct (N × H)
701. #41#123direct (N × H)
795. C22×C4C2×#41semidirect
836. C4⋊C4C2×#41semidirect
866. C22⋊C4C2×#41semidirect
867. C22⋊C4C2×#41semidirect
922. Q8C2×#123semidirect
932. D4C2×#123semidirect
991. C2×C4C2×#123semidirect

Maximal subgroups

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

subgroupindex
C2×D4×#412
C22×C4×#412
#366262
#365782
Q8×#1232
#364832
#364822
#364332
#364322
#362372
#362362
#362172
#362162
#361552
D4×#1232
#348102
#348092
#347442
#347422
C4⋊C4×#412
C22⋊C4×#412
C2×C4×#1232