Finite Group Databasebeta

← #7629682

Subgroups — #7629682

Order 512.

8114 conjugacy classes of subgroups.

The subgroup lattice has 998 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×#41C211yesmaximal, characteristic, complemented
2C2×#3428C211yesmaximal, characteristic
3#36040C211yesmaximal, characteristic, complemented
4#36031C213yesmaximal, complemented
5#35845C211yesmaximal, characteristic, complemented
6#35836C213yesmaximal, complemented
7#35816C212yesmaximal, complemented
8#35806C216yesmaximal, complemented
9#35786C212yesmaximal, complemented
10#35776C216yesmaximal, complemented
11#35748C211yesmaximal, characteristic, complemented
12#35739C213yesmaximal, complemented
13#35711C211yesmaximal, characteristic, complemented
14#35702C213yesmaximal, complemented
15#34952C213yesmaximal, complemented
16#34947C213yesmaximal, complemented
17#34745C216yesmaximal, complemented
18#34739C216yesmaximal, complemented
19#34634C213yesmaximal, complemented
20C2×#2396C213yesmaximal, complemented
21C4⋊C4×#41C212yesmaximal, complemented
22C4⋊C4×#41C211yesmaximal, characteristic, complemented
23C22⋊C4×#41C212yesmaximal
24C23×#41C2211yescharacteristic
25Q8×#41—216no—
26C2×Q82C2211yescharacteristic, complemented
27C2×#557C2211yescharacteristic, complemented
28C2×#557C2212yescomplemented
29C2×#554C2213yescomplemented
30C2×#554C2216yescomplemented
31C2×D4×Q8C2213yescomplemented
32C2×#533C2213yescomplemented
33C2×#533C2216yescomplemented
34#3428—216no—
35C2×#520C2213yes—
36C2×#520C2211yescharacteristic
37C2×#520C2213yes—
38C2×#520C2211yescharacteristic
39C2×#519C2211yescharacteristic
40C2×#519C2211yescharacteristic
41C2×#518C2213yes—
42C2×#518C2213yes—
43C2×C4×#41C2212yes—
44C2×C4×#41C2212yes—
45C2×C4×#41C2211yescharacteristic
46C2×C4×#41C2213yes—
47C2×C4×#41C2213yes—
48C2×C4×#41C2211yescharacteristic
49C22×C4×Q8C2213yescomplemented
50C22×#117C2213yes—
51C22×#117C2213yes—
52#2629C2216yes—
53#2629C2216yescomplemented
54#2628C2213yes—
55#2628C2213yes—
56#2628C2213yescomplemented
57#2628C2213yescomplemented
58#2627C2216yescomplemented
59#2627C2216yescomplemented
60#2626C2216yes—
61#2626C2216yes—
62#2582C2216yescomplemented
63#2581C2213yescomplemented
64#2581C2213yescomplemented
65#2580C2213yescomplemented
66#2580C2213yescomplemented
67#2579C22112yescomplemented
68#2568C2213yescomplemented
69#2567C2213yescomplemented
70#2566C2216yescomplemented
71#2565C2216yescomplemented
72#2564C2216yescomplemented
73#2564C2216yescomplemented
74#2563C2213yescomplemented
75#2542C2213yescomplemented
76#2538C2216yescomplemented
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#2442C2216yescomplemented
91#2442C2216yescomplemented
92#2441C2216yes—
93#2441C2216yes—
94#2440C2216yescomplemented
95#2440C2216yescomplemented
96#2439C2216yes—
97#2439C2216yes—
98#2438C22112yescomplemented
99#2438C22112yescomplemented
100#2437C22112yes—
101#2437C22112yes—
102#2417C22112yescomplemented
103#2409C2216yescomplemented
104#2396C2213yes—
105#2396C2213yes—
106#2396C2216yes—
107#2396C2213yes—
108#2396C2216yes—
109#2396C2216yes—
110#2396C2211yescharacteristic
111#2396C2216yescomplemented
112#2396C2216yescomplemented
113#2396C2213yescomplemented
114#2396C2213yescomplemented
115#2396C2213yescomplemented
116#2396C2216yescomplemented
117#2396C2213yescomplemented
118#2396C2216yescomplemented
119C2×#400C2213yescomplemented
120C2×#399C2213yes—
121C2×#398C2216yescomplemented
122C2×#396C2216yes—
123C2×#395C2213yescomplemented
124C2×#393C2213yes—
125#2351C2211yescharacteristic, complemented
126#2351C2211yescharacteristic, complemented
127#2351C2212yescomplemented
128#2351C2212yescomplemented
129Q8×C4⋊C4C2212yescomplemented
130Q8×C4⋊C4C2212yescomplemented
131Q8×C4⋊C4C2212yescomplemented
132#2349C2213yescomplemented
133#2349C2216yescomplemented
134#2349C2213yescomplemented
135#2349C2216yescomplemented
136D4×C4⋊C4C2216yescomplemented
137D4×C4⋊C4C2216yescomplemented
138D4×C4⋊C4C2216yescomplemented
139#2341C2212yes—
140#2341C2212yes—
141Q8×C22⋊C4C2212yes—
142Q8×C22⋊C4C2212yes—
143#2339C2216yes—
144#2339C2216yes—
145D4×C22⋊C4C2216yes—
146D4×C22⋊C4C2216yes—
147C4×C22⋊Q8C22112yescomplemented
148C4×C22⋊Q8C22112yescomplemented
149#2297C2216yes—
150#2297C2216yes—
151#2296C2216yescomplemented
152#2296C2216yescomplemented
153#2296C2216yescomplemented
154#2285C2213yescomplemented
155#2285C2216yescomplemented
156#2280C2216yes—
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×Q8C2311yescharacteristic
168C23×Q8C2313yes—
169C23×D4C2313yes—
170C24×C4C2313yes—
171Q82—28no—
172#557—28no—
173#557—216no—
174#554—248no—
175#554—224no—
176D4×Q8—224no—
177#533—248no—
178#533—224no—
179C2×C4⋊Q8C2313yes—
180C2×C4⋊Q8C2313yes—
181C2×C4⋊Q8C2316yes—
182C2×C4⋊Q8C2316yes—
183C2×#125C2316yes—
184C2×#125C2316yes—
185C2×#125C2316yes—
186C2×C22⋊Q8C2316yes—
187C2×C22⋊Q8C2316yes—
188C2×C22⋊Q8C23112yes—
189C2×C22⋊Q8C23112yes—
190C2×C22⋊Q8C23112yes—
191C2×C22⋊Q8C23112yes—
192#520—28no—
193#520—28no—
194#520—224no—
195#520—224no—
196#519—28no—
197#519—28no—
198#518—224no—
199#518—224no—
200C4×#41—28no—
201C4×#41—216no—
202C4×#41—216no—
203C4×#41—224no—
204C4×#41—224no—
205C4×#41D4116yes—
206C2×C4×Q8—224no—
207C2×C4×Q8C2313yes—
208C2×C4×Q8C2313yes—
209C2×C4×Q8C2313yes—
210C2×C4×Q8C2313yes—
211C2×C4×Q8C2316yes—
212C2×C4×Q8C2312yes—
213C2×C4×Q8C2312yes—
214C2×C4×Q8C2312yes—
215C2×C4×Q8C2312yes—
216C2×C4×Q8C2311yescharacteristic
217C2×C4×Q8C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2313yes—
220C2×C4×Q8C2316yes—
221C2×C4×Q8C2316yes—
222C2×C4×Q8C2313yes—
223C2×C4×Q8C2313yes—
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×D4C2313yes—
227C2×C4×D4C2316yes—
228C2×C4×D4C2313yes—
229C2×C4×D4C2316yes—
230C2×C4×D4C2316yes—
231C2×C4×D4C2316yes—
232C2×C4×D4C2316yes—
233C2×C4×D4C2316yes—
234C2×C4×D4C2313yes—
235C2×C4×D4C2313yes—
236C2×C4×D4C2316yes—
237C2×C4×D4C2316yes—
238C2×C4×D4C2313yes—
239C2×C4×D4C2313yes—
240C2×C4×D4C2313yes—
241C2×C4×D4C2313yes—
242C2×#117—224no—
243C2×#117—224no—
244C2×#117C2313yes—
245C2×#117C2313yes—
246C2×#117C2313yes—
247C2×#117C2313yes—
248C2×#117C2311yescharacteristic
249C2×#117C2313yes—
250C2×#117C2313yes—
251C2×#117C2313yes—
252C2×#117C2313yes—
253C2×#117C2313yes—
254C2×#117C2313yes—
255C2×#117C2316yes—
256C2×#117C2316yes—
257C2×#117C2316yes—
258C2×#117C2313yes—
259C22×C4⋊C4C2316yes—
260C22×C4⋊C4C2313yes—
261C22×C4⋊C4C2313yes—
262C22×C4⋊C4C2313yes—
263C22×C4⋊C4C2313yes—
264C22×C4⋊C4C2313yes—
265C22×C4⋊C4C2316yes—
266C22×C4⋊C4C2316yes—
267C22×C4⋊C4C2316yes—
268C22×C22⋊C4C2313yes—
269C22×C22⋊C4C2313yes—
270C22×C22⋊C4C2316yes—
271C22×C22⋊C4C2316yes—
272C22×C22⋊C4C2316yes—
273C22×C42C2313yes—
274C22×C42C2316yes—
275C22×C42C2316yes—
276C22×C42C2316yes—
277C22×C42C2313yes—
278#400C2313yes—
279#400C2316yes—
280#400C2313yes—
281#400C2313yes—
282#400C2316yes—
283#400C2316yes—
284#400C2311yescharacteristic
285#400C2316yes—
286#400C2316yes—
287#399C2313yes—
288#399C2316yes—
289#399C2313yes—
290#399C2313yes—
291#399C2316yes—
292#399C2316yes—
293#399C2311yescharacteristic
294#399C2316yes—
295#399C2316yes—
296#398C2316yes—
297#398C23112yes—
298#398C2316yes—
299#398C2316yes—
300#398C23112yes—
301#398C23112yes—
302#398C2312yes—
303#398C2316yes—
304#398C2316yes—
305#398C2316yes—
306#398C2316yes—
307#396C2316yes—
308#396C23112yes—
309#396C2316yes—
310#396C2316yes—
311#396C23112yes—
312#396C23112yes—
313#396C2312yes—
314#396C2316yes—
315#396C2316yes—
316#396C2316yes—
317#396C2316yes—
318#395C2313yes—
319#395C2316yes—
320#395C2313yes—
321#395C2313yes—
322#395C2316yes—
323#395C2316yes—
324#395C2311yescharacteristic
325#395C2316yes—
326#395C2316yes—
327#393C2313yes—
328#393C2316yes—
329#393C2313yes—
330#393C2313yes—
331#393C2316yes—
332#393C2316yes—
333#393C2311yescharacteristic
334#393C2316yes—
335#393C2316yes—
336#391C2316yes—
337#391C2316yes—
338#391C23112yes—
339#391C2316yes—
340#391C2316yes—
341#391C23112yes—
342#390C2316yes—
343#390C2316yes—
344#390C2316yes—
345#390C2316yes—
346#389C23112yes—
347#389C2316yes—
348#389C2316yes—
349#389C2316yes—
350#389C2316yes—
351#389C23112yes—
352#389C2316yes—
353#389C2316yes—
354#389C2316yes—
355#389C2316yes—
356#389C2316yes—
357#389C2316yes—
358#389C2316yes—
359#389C2316yes—
360#387C23112yes—
361#387C23112yes—
362#387C23112yes—
363#387C23112yes—
364#386C23112yes—
365#386C23112yes—
366#386C23112yes—
367#386C23112yes—
368#385C23112yes—
369#385C23112yes—
370#385C23112yes—
371#385C23112yes—
372#385C23112yes—
373#385C23112yes—
374#385C23112yes—
375#385C23112yes—
376#385C23112yes—
377#385C23112yes—
378#384C2316yes—
379#384C2316yes—
380#384C2316yes—
381#382C2316yes—
382#382C2316yes—
383#382C2313yes—
384#382C2313yes—
385#381C23112yes—
386#380C23112yes—
387#380C23112yes—
388#380C23112yes—
389#380C2316yes—
390#380C2316yes—
391#380C2316yes—
392#380C2316yes—
393#380C2316yes—
394#380C2316yes—
395#380C23112yes—
396#379C23112yes—
397C4×C4⋊C4C2313yes—
398C4×C4⋊C4C2316yes—
399C4×C4⋊C4C2313yes—
400C4×C4⋊C4C2316yes—
401C4×C4⋊C4C2316yes—
402C4×C4⋊C4C2316yes—
403C4×C4⋊C4C2316yes—
404C4×C4⋊C4C2312yes—
405C4×C4⋊C4C2311yescharacteristic
406C4×C4⋊C4C2313yes—
407C4×C4⋊C4C2316yes—
408C4×C4⋊C4C2316yes—
409C4×C4⋊C4C2316yes—
410C4×C4⋊C4C2316yes—
411C4×C4⋊C4C23112yes—
412C4×C4⋊C4C2316yes—
413C4×C22⋊C4C2316yes—
414C4×C22⋊C4C2316yes—
415C4×C22⋊C4C2316yes—
416C4×C22⋊C4C2316yes—
417C4×C22⋊C4C2312yes—
418C4×C22⋊C4C2316yes—
419C4×C22⋊C4C2316yes—
420C4×C22⋊C4C2316yes—
421C4×C22⋊C4C23112yes—
422C2×#95C2313yes—
423C2×#95C2313yes—
424C2×#95C2316yes—
425C2×#95C2316yes—
426C2×#95C2316yes—
427C2×#95C2316yes—
428C25C2413yes—
429C2×#41—2128no—
430C2×#41—24no—
431C2×#41—24no—
432C2×#41—212no—
433C2×#41—212no—
434C2×#41—212no—
435C2×#41—212no—
436C2×#41C2×D418yes—
437C2×#41C2×Q818yes—
438C2×#41C2×Q818yescomplemented
439C2×#41C2×Q8124yescomplemented
440C2×#41C2×Q8124yescomplemented
441C2×#41#4118yes—
442C22×Q8—24no—
443C22×Q8—24no—
444C22×Q8—212no—
445C22×Q8—412no—
446C22×Q8C2×Q818yescomplemented
447C22×Q8C2411yescharacteristic
448C22×Q8C2416yes—
449C22×Q8C2413yes—
450C22×Q8C2413yes—
451C22×Q8C2416yes—
452C22×Q8C2411yescharacteristic
453C22×D4—212no—
454C22×D4—212no—
455C22×D4C2×Q8124yescomplemented
456C22×D4C2416yes—
457C22×D4C2413yes—
458C22×D4C2413yes—
459C23×C4—212no—
460C23×C4—212no—
461C23×C4C2×Q8124yescomplemented
462C23×C4C2416yes—
463C23×C4C2416yes—
464C23×C4C2413yes—
465C23×C4C2413yes—
466C23×C4C2413yes—
467C23×C4C2411yescharacteristic
468C23×C4C2413yes—
469C23×C4C2413yes—
470C23×C4C2413yes—
471C23×C4C2416yes—
472C23×C4C2416yes—
473C23×C4C2416yes—
474C23×C4C2416yes—
475C23×C4C2413yes—
476C23×C4C2413yes—
477C23×C4C2413yes—
478C4⋊Q8—224no—
479C4⋊Q8—224no—
480C4⋊Q8—212no—
481C4⋊Q8—212no—
482#125—224no—
483#125—224no—
484#125—224no—
485C22⋊Q8—224no—
486C22⋊Q8—224no—
487C22⋊Q8—248no—
488C22⋊Q8—248no—
489C22⋊Q8—424no—
490C22⋊Q8—424no—
491C4×Q8—24no—
492C4×Q8—24no—
493C4×Q8—28no—
494C4×Q8—28no—
495C4×Q8—28no—
496C4×Q8—28no—
497C4×Q8—212no—
498C4×Q8—212no—
499C4×Q8—24no—
500C4×Q8—224no—
501C4×Q8—212no—
502C4×Q8—212no—
503C4×Q8—212no—
504C4×Q8—224no—
505C4×Q8—212no—
506C4×Q8—212no—
507C4×Q8—224no—
508C4×Q8C2×D418yes—
509C4×Q8C2×D418yes—
510C4×D4—212no—
511C4×D4—212no—
512C4×D4—224no—
513C4×D4—224no—
514C4×D4—224no—
515C4×D4—224no—
516C4×D4—224no—
517C4×D4—224no—
518C4×D4—212no—
519C4×D4—212no—
520C4×D4—224no—
521C4×D4—224no—
522C4×D4—212no—
523C4×D4—212no—
524C4×D4C2×D4124yes—
525C4×D4C2×D4124yes—
526#117—212no—
527#117—224no—
528#117—224no—
529#117—212no—
530#117—212no—
531#117—224no—
532#117—212no—
533#117—24no—
534#117—212no—
535#117—212no—
536#117—212no—
537#117—212no—
538#117—212no—
539#117—212no—
540#117C2×D4124yes—
541C2×C4⋊C4—212no—
542C2×C4⋊C4—212no—
543C2×C4⋊C4—224no—
544C2×C4⋊C4—212no—
545C2×C4⋊C4—212no—
546C2×C4⋊C4—212no—
547C2×C4⋊C4—412no—
548C2×C4⋊C4—412no—
549C2×C4⋊C4—412no—
550C2×C4⋊C4C2411yescharacteristic
551C2×C4⋊C4C2413yes—
552C2×C4⋊C4C2413yes—
553C2×C4⋊C4C2411yescharacteristic
554C2×C4⋊C4C2412yes—
555C2×C4⋊C4C2411yescharacteristic
556C2×C4⋊C4C2412yes—
557C2×C4⋊C4C2412yes—
558C2×C4⋊C4C2412yes—
559C2×C4⋊C4C2413yes—
560C2×C4⋊C4C2413yes—
561C2×C4⋊C4C2413yes—
562C2×C4⋊C4C2413yes—
563C2×C4⋊C4C2413yes—
564C2×C4⋊C4C2413yes—
565C2×C4⋊C4C2416yes—
566C2×C4⋊C4C2416yes—
567C2×C4⋊C4C2416yes—
568C2×C4⋊C4C2416yes—
569C2×C4⋊C4C2413yes—
570C2×C4⋊C4C2416yes—
571C2×C4⋊C4C2416yes—
572C2×C4⋊C4C2416yes—
573C2×C4⋊C4C2416yes—
574C2×C4⋊C4C2416yes—
575C2×C4⋊C4C2416yes—
576C2×C4⋊C4C2416yes—
577C2×C4⋊C4C2416yes—
578C2×C4⋊C4C24112yes—
579C2×C4⋊C4C2416yes—
580C2×C4⋊C4C2416yes—
581C2×C4⋊C4C2416yes—
582C2×C4⋊C4C2416yes—
583C2×C4⋊C4C2416yes—
584C2×C4⋊C4C2416yes—
585C2×C4⋊C4C24112yes—
586C2×C4⋊C4C24112yes—
587C2×C4⋊C4C24112yes—
588C2×C4⋊C4C2413yes—
589C2×C4⋊C4C2413yes—
590C2×C22⋊C4—212no—
591C2×C22⋊C4—212no—
592C2×C22⋊C4—224no—
593C2×C22⋊C4—412no—
594C2×C22⋊C4—412no—
595C2×C22⋊C4C2411yescharacteristic
596C2×C22⋊C4C2413yes—
597C2×C22⋊C4C2413yes—
598C2×C22⋊C4C2411yescharacteristic
599C2×C22⋊C4C2412yes—
600C2×C22⋊C4C2412yes—
601C2×C22⋊C4C2416yes—
602C2×C22⋊C4C2413yes—
603C2×C22⋊C4C2413yes—
604C2×C22⋊C4C2413yes—
605C2×C22⋊C4C2413yes—
606C2×C22⋊C4C2416yes—
607C2×C22⋊C4C2416yes—
608C2×C22⋊C4C24112yes—
609C2×C22⋊C4C24112yes—
610C2×C22⋊C4C2416yes—
611C2×C22⋊C4C2416yes—
612C2×C22⋊C4C2416yes—
613C2×C22⋊C4C2416yes—
614C2×C22⋊C4C24112yes—
615C2×C22⋊C4C24112yes—
616C2×C22⋊C4C2416yes—
617C2×C42—212no—
618C2×C42—224no—
619C2×C42—224no—
620C2×C42—224no—
621C2×C42C2×D4124yes—
622C2×C42C2413yes—
623C2×C42C2413yes—
624C2×C42C2416yes—
625C2×C42C2416yes—
626C2×C42C2416yes—
627C2×C42C2416yes—
628C2×C42C2416yes—
629C2×C42C2416yes—
630C2×C42C2411yescharacteristic
631C2×C42C2413yes—
632C2×C42C2416yes—
633C2×C42C2416yes—
634C2×C42C2412yes—
635C2×C42C2412yes—
636C2×C42C2413yes—
637C2×C42C2413yes—
638C2×C42C2413yes—
639C2×C42C2411yescharacteristic
640#95C2412yes—
641#95C2412yes—
642#95C2412yes—
643#95C2411yescharacteristic
644#95C2411yescharacteristic
645#95C2412yes—
646#95C2416yes—
647#95C2416yes—
648#95C2416yes—
649#95C2416yes—
650#95C2416yes—
651#95C2416yes—
652#95C2416yes—
653#95C2416yes—
654#95C2413yes—
655#95C2413yes—
656#95C2416yes—
657#95C2416yes—
658#95C2416yes—
659#95C2416yes—
660#95C2416yes—
661#95C2416yes—
662#95C24112yes—
663#95C24112yes—
664#95C24112yes—
665#95C24112yes—
666#95C2416yes—
667#95C2416yes—
668C24—26no—
669C24—26no—
670C24—46no—
671C24—46no—
672C24C22×Q8112yes—
673C24C2511yescharacteristic
674C24C2513yes—
675C24C2513yes—
676#41—232no—
677#41—296no—
678#41—296no—
679#41C22⋊Q8164yescomplemented
680C2×Q8—232no—
681C2×Q8—22no—
682C2×Q8—26no—
683C2×Q8—212no—
684C2×Q8—26no—
685C2×Q8—212no—
686C2×Q8—26no—
687C2×Q8—24no—
688C2×Q8—212no—
689C2×Q8—46no—
690C2×Q8—46no—
691C2×Q8—412no—
692C2×Q8—448no—
693C2×Q8C22×D414yes—
694C2×Q8C22×Q8112yes—
695C2×Q8C22×Q814yes—
696C2×Q8C2×#4114yes—
697C2×D4—212no—
698C2×D4—212no—
699C2×D4—296no—
700C2×D4—26no—
701C2×D4—26no—
702C2×D4C22×D4112yes—
703C2×D4C22×Q8124yes—
704C2×D4C22×Q8112yes—
705C2×D4C22×Q8112yes—
706C2×D4C2×#41112yes—
707C22×C4—26no—
708C22×C4—26no—
709C22×C4—296no—
710C22×C4—26no—
711C22×C4—26no—
712C22×C4—22no—
713C22×C4—26no—
714C22×C4—22no—
715C22×C4—26no—
716C22×C4—26no—
717C22×C4—26no—
718C22×C4—212no—
719C22×C4—212no—
720C22×C4—26no—
721C22×C4—26no—
722C22×C4—212no—
723C22×C4—212no—
724C22×C4—212no—
725C22×C4—212no—
726C22×C4—212no—
727C22×C4—212no—
728C22×C4—46no—
729C22×C4—46no—
730C22×C4—46no—
731C22×C4—46no—
732C22×C4—46no—
733C22×C4—46no—
734C22×C4—46no—
735C22×C4—46no—
736C22×C4—46no—
737C22×C4—46no—
738C22×C4—412no—
739C22×C4—412no—
740C22×C4C22×D4112yes—
741C22×C4C22×D4112yes—
742C22×C4C22×D4112yes—
743C22×C4C22×Q814yes—
744C22×C4C22×Q8112yes—
745C22×C4C22×Q8112yes—
746C22×C4C22×Q8112yes—
747C22×C4C22×Q8112yes—
748C22×C4C22×Q8112yes—
749C22×C4C2×#41112yes—
750C22×C4C2512yes—
751C22×C4C2516yes—
752C22×C4C2516yes—
753C22×C4C2511yescharacteristic
754C22×C4C2511yescharacteristic
755C22×C4C2513yes—
756C22×C4C2513yes—
757C22×C4C2512yes—
758C22×C4C2516yes—
759C22×C4C2516yes—
760C22×C4C2511yescharacteristic
761C22×C4C2513yes—
762C22×C4C2513yes—
763C22×C4C2511yescharacteristic
764C22×C4C2513yes—
765C22×C4C2511yescharacteristic
766C22×C4C2512yes—
767C22×C4C2512yes—
768C22×C4C2513yes—
769C22×C4C2511yescharacteristic
770C4⋊C4—26no—
771C4⋊C4—26no—
772C4⋊C4—22no—
773C4⋊C4—22no—
774C4⋊C4—24no—
775C4⋊C4—22no—
776C4⋊C4—26no—
777C4⋊C4—26no—
778C4⋊C4—26no—
779C4⋊C4—26no—
780C4⋊C4—26no—
781C4⋊C4—26no—
782C4⋊C4—212no—
783C4⋊C4—212no—
784C4⋊C4—212no—
785C4⋊C4—212no—
786C4⋊C4—26no—
787C4⋊C4—212no—
788C4⋊C4—212no—
789C4⋊C4—212no—
790C4⋊C4—224no—
791C4⋊C4—212no—
792C4⋊C4—212no—
793C4⋊C4—24no—
794C4⋊C4—24no—
795C4⋊C4—24no—
796C4⋊C4—212no—
797C4⋊C4—212no—
798C4⋊C4—212no—
799C4⋊C4—46no—
800C4⋊C4—46no—
801C4⋊C4—46no—
802C4⋊C4—46no—
803C4⋊C4—46no—
804C4⋊C4—46no—
805C4⋊C4—412no—
806C4⋊C4—412no—
807C4⋊C4—412no—
808C4⋊C4C22×D4112yes—
809C4⋊C4C22×D4112yes—
810C22⋊C4—212no—
811C22⋊C4—224no—
812C22⋊C4—224no—
813C22⋊C4—26no—
814C22⋊C4—26no—
815C22⋊C4—22no—
816C22⋊C4—22no—
817C22⋊C4—26no—
818C22⋊C4—26no—
819C22⋊C4—26no—
820C22⋊C4—26no—
821C22⋊C4—24no—
822C22⋊C4—24no—
823C22⋊C4—212no—
824C22⋊C4—212no—
825C22⋊C4—46no—
826C22⋊C4—46no—
827C22⋊C4—46no—
828C22⋊C4—46no—
829C22⋊C4—412no—
830C22⋊C4—412no—
831C22⋊C4C22×D4124yes—
832C42—22no—
833C42—26no—
834C42—24no—
835C42—212no—
836C42—212no—
837C42—26no—
838C42—26no—
839C42—212no—
840C42—212no—
841C42—212no—
842C42—24no—
843C42—212no—
844C42—212no—
845C42—212no—
846C42C22×D4112yes—
847C42C22×D414yes—
848C42C22×D4112yes—
849C42C22×D4112yes—
850C23—26no—
851C23—26no—
852C23—21no—
853C23—23no—
854C23—21no—
855C23—23no—
856C23—26no—
857C23—26no—
858C23—22no—
859C23—22no—
860C23—224no—
861C23—424no—
862C23—86no—
863C23—86no—
864C23—812no—
865C23C23×D416yes—
866C23C23×Q812yes—
867C23C23×Q816yes—
868C23C23×Q816yes—
869C23C22×#4116yes—
870C23C2611yescharacteristic
871Q8—28no—
872Q8—224no—
873Q8—424no—
874Q8—412no—
875Q8—812no—
876Q8C2×C22⋊Q8116yes—
877D4—248no—
878D4—224no—
879D4C2×C22⋊Q8148yes—
880C2×C4—23no—
881C2×C4—22no—
882C2×C4—21no—
883C2×C4—22no—
884C2×C4—21no—
885C2×C4—23no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—26no—
889C2×C4—26no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—224no—
893C2×C4—28no—
894C2×C4—224no—
895C2×C4—224no—
896C2×C4—224no—
897C2×C4—23no—
898C2×C4—21no—
899C2×C4—23no—
900C2×C4—21no—
901C2×C4—22no—
902C2×C4—26no—
903C2×C4—26no—
904C2×C4—22no—
905C2×C4—26no—
906C2×C4—26no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—26no—
910C2×C4—26no—
911C2×C4—26no—
912C2×C4—26no—
913C2×C4—26no—
914C2×C4—26no—
915C2×C4—26no—
916C2×C4—26no—
917C2×C4—22no—
918C2×C4—26no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—26no—
922C2×C4—22no—
923C2×C4—412no—
924C2×C4—412no—
925C2×C4—424no—
926C2×C4—424no—
927C2×C4—812no—
928C2×C4—812no—
929C2×C4—86no—
930C2×C4—86no—
931C2×C4—812no—
932C2×C4—812no—
933C2×C4C2×C22⋊Q8148yes—
934C2×C4C23×D416yes—
935C2×C4C23×D416yes—
936C2×C4C23×D412yes—
937C2×C4C23×D412yes—
938C2×C4C23×D412yes—
939C2×C4C23×D416yes—
940C2×C4C23×Q812yes—
941C2×C4C23×Q816yes—
942C2×C4C23×Q812yes—
943C2×C4C23×Q816yes—
944C2×C4C22×#4112yes—
945C2×C4C22×#4116yes—
946C2×C4#58514yes—
947C2×C4#58514yes—
948C22—26no—
949C22—26no—
950C22—212no—
951C22—212no—
952C22—24no—
953C22—212no—
954C22—22no—
955C22—26no—
956C22—43no—
957C22—41no—
958C22—43no—
959C22—41no—
960C22—46no—
961C22—42no—
962C22—824no—
963C22C22×C22⋊Q8112yes—
964C22C24×D411yescharacteristic
965C22C24×Q811yescharacteristic
966C22C23×#4111yescharacteristic
967C22C2×#58512yes—
968C22C2×#58512yes—
969C4—22no—
970C4—24no—
971C4—26no—
972C4—22no—
973C4—26no—
974C4—24no—
975C4—22no—
976C4—26no—
977C4—46no—
978C4—43no—
979C4—41no—
980C4—43no—
981C4—41no—
982C4—42no—
983C4—46no—
984C4—46no—
985C4—46no—
986C4—42no—
987C4C22×C22⋊Q814yes—
988C4C22×C22⋊Q8112yes—
989C2—212no—
990C2—46no—
991C2—42no—
992C2C23×C22⋊Q811yescharacteristic
993C2#6281111yescharacteristic
994C2#6281211yescharacteristic
995C2#6281312yes—
996C2#6281612yes—
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. #36040C2semidirect
4. #36031C2semidirect
5. #35845C2semidirect
6. #35836C2semidirect
7. #35816C2semidirect
8. #35806C2semidirect
9. #35786C2semidirect
10. #35776C2semidirect
11. #35748C2semidirect
12. #35739C2semidirect
13. #35711C2semidirect
14. #35702C2semidirect
15. #34952C2semidirect
16. #34947C2semidirect
17. #34745C2semidirect
18. #34739C2semidirect
19. #34634C2semidirect
20. C2×#2396C2semidirect
21. C4⋊C4×#41C2semidirect
22. C4⋊C4×#41C2semidirect
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
49. C22×C4×Q8C22semidirect
53. #2629C22semidirect
56. #2628C22semidirect
57. #2628C22semidirect
58. #2627C22semidirect
59. #2627C22semidirect
62. #2582C22semidirect
63. #2581C22semidirect
64. #2581C22semidirect
65. #2580C22semidirect
66. #2580C22semidirect
67. #2579C22semidirect
68. #2568C22semidirect
69. #2567C22semidirect
70. #2566C22semidirect
71. #2565C22semidirect
72. #2564C22semidirect
73. #2564C22semidirect
74. #2563C22semidirect
75. #2542C22semidirect
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
90. #2442C22semidirect
91. #2442C22semidirect
94. #2440C22semidirect
95. #2440C22semidirect
98. #2438C22semidirect
99. #2438C22semidirect
102. #2417C22semidirect
103. #2409C22semidirect
111. #2396C22semidirect
112. #2396C22semidirect
113. #2396C22semidirect
114. #2396C22semidirect
115. #2396C22semidirect
116. #2396C22semidirect
117. #2396C22semidirect
118. #2396C22semidirect
119. C2×#400C22semidirect
121. C2×#398C22semidirect
123. C2×#395C22semidirect
125. #2351C22semidirect
126. #2351C22semidirect
127. #2351C22semidirect
128. #2351C22semidirect
129. Q8×C4⋊C4C22semidirect
130. Q8×C4⋊C4C22semidirect
131. Q8×C4⋊C4C22semidirect
132. #2349C22semidirect
133. #2349C22semidirect
134. #2349C22semidirect
135. #2349C22semidirect
136. D4×C4⋊C4C22semidirect
137. D4×C4⋊C4C22semidirect
138. D4×C4⋊C4C22semidirect
147. C4×C22⋊Q8C22semidirect
148. C4×C22⋊Q8C22semidirect
151. #2296C22semidirect
152. #2296C22semidirect
153. #2296C22semidirect
154. #2285C22semidirect
155. #2285C22semidirect
157. C2×C4×C4⋊C4C22semidirect
158. C2×C4×C4⋊C4C22semidirect
162. C22×#41Q8semidirect
438. C2×#41C2×Q8semidirect
439. C2×#41C2×Q8semidirect
440. C2×#41C2×Q8semidirect
446. C22×Q8C2×Q8semidirect
455. C22×D4C2×Q8semidirect
461. C23×C4C2×Q8semidirect
679. #41C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×#412
C2×#34282
#360402
#360312
#358452
#358362
#358162
#358062
#357862
#357762
#357482
#357392
#357112
#357022
#349522
#349472
#347452
#347392
#346342
C2×#23962
C4⋊C4×#412
C22⋊C4×#412