Finite Group Databasebeta

← #7712670

Subgroups — #7712670

Order 512.

6854 conjugacy classes of subgroups.

The subgroup lattice has 1031 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3538C211yesmaximal, characteristic, complemented
2C2×#3444C211yesmaximal, characteristic
3#59010C218yesmaximal, complemented
4#45771C218yesmaximal, complemented
5#38043C214yesmaximal, complemented
6#38027C214yesmaximal, complemented
7#37763C214yesmaximal, complemented
8#37755C214yesmaximal, complemented
9#37698C214yesmaximal, complemented
10#37689C214yesmaximal, complemented
11#37442C212yesmaximal, complemented
12#37377C212yesmaximal, complemented
13#37376C212yesmaximal, complemented
14C2×#2855C212yesmaximal, complemented
15#36375C214yesmaximal, complemented
16#36274C214yesmaximal, complemented
17#35309C212yesmaximal, complemented
18#35307C212yesmaximal, complemented
19#34360C211yesmaximal, characteristic, complemented
20#3538—216no—
21C2×#563C2214yes—
22C2×#552C2214yes—
23C2×#551C2214yes—
24C2×D4×Q8C2214yes—
25C2×#544C2214yes—
26C2×#541C2212yes—
27C2×#539C2214yes—
28C2×#536C2212yes—
29#3444—216no—
30C2×#533C2211yescharacteristic
31C2×#533C2212yes—
32C2×#532C2211yescharacteristic
33C2×#532C2212yes—
34C2×#529C2212yes—
35C2×#529C2212yes—
36C2×#529C2214yes—
37C2×#529C2214yes—
38C2×#525C2211yescharacteristic
39C2×#525C2214yes—
40C2×#525C2211yescharacteristic
41C22×C22⋊Q8C2212yes—
42C2×C4×#41C2214yes—
43C2×C4×#41C2211yescharacteristic
44C2×C4×#41C2211yescharacteristic
45C23×C42C2211yescharacteristic
46#2857C2212yescomplemented
47#2855C2214yes—
48#2855C2214yes—
49#2855C2214yes—
50#2855C2214yes—
51#2855C2214yes—
52#2855C2214yes—
53#2855C2214yes—
54#2855C2214yes—
55#2855C2214yescomplemented
56#2851C2212yescomplemented
57#2814C2218yes—
58#2734C2214yescomplemented
59#2731C2214yescomplemented
60#2726C2218yescomplemented
61#2725C2218yescomplemented
62#2722C2218yescomplemented
63#2719C2218yescomplemented
64#2717C2214yescomplemented
65#2716C2218yescomplemented
66#2715C2218yescomplemented
67#2713C2218yescomplemented
68#2713C2218yescomplemented
69#2709C2214yescomplemented
70#2701C2218yes—
71#2700C2218yescomplemented
72#2698C2218yes—
73#2698C2218yescomplemented
74#2689C2218yes—
75#2686C2218yes—
76#2659C2214yes—
77#2639C2214yes—
78#2629C2212yescomplemented
79#2627C2214yes—
80#2625C2214yes—
81#2625C2214yescomplemented
82#2621C2212yescomplemented
83#2618C2214yes—
84#2616C2214yes—
85#2584C2214yescomplemented
86#2582C2214yescomplemented
87#2581C2214yescomplemented
88#2568C2214yescomplemented
89#2549C2218yes—
90#2488C2218yes—
91#2486C2214yes—
92#2486C2218yes—
93#2485C2214yescomplemented
94#2478C2218yescomplemented
95#2475C2218yescomplemented
96#2468C2218yes—
97#2466C2218yes—
98#2466C2218yescomplemented
99#2462C2218yescomplemented
100#2462C2218yescomplemented
101#2460C2218yescomplemented
102#2451C2218yescomplemented
103#2450C2218yes—
104#2450C2218yescomplemented
105#2447C2218yes—
106#2446C2218yescomplemented
107#2444C2218yes—
108#2439C2218yescomplemented
109#2438C2218yes—
110#2438C2218yes—
111#2438C2218yescomplemented
112#2425C2218yes—
113#2419C2218yes—
114#2419C2218yes—
115#2419C2218yes—
116#2419C2218yescomplemented
117#2417C2214yes—
118#2417C2214yes—
119#2417C2214yescomplemented
120#2415C2214yescomplemented
121#2413C2218yes—
122#2412C2218yes—
123#2409C2214yes—
124#2409C2214yescomplemented
125#2406C2218yes—
126#2376C2214yes—
127#2359C2218yes—
128#2358C2214yes—
129#2352C2214yes—
130#2349C2218yes—
131D4×C4⋊C4C2214yes—
132#2344C2218yes—
133#2339C2218yes—
134#2329C2214yes—
135#2325C2214yes—
136#2323C2214yescomplemented
137#2316C2212yescomplemented
138#2314C2212yes—
139#2311C2212yes—
140#2310C2212yescomplemented
141C4×C22⋊Q8C2214yescomplemented
142#2296C2212yescomplemented
143C2×#391C2212yes—
144C2×#391C2212yes—
145C2×#391C2212yescomplemented
146C2×#389C2212yes—
147C2×#389C2212yes—
148C2×#387C2214yes—
149C2×#387C2214yes—
150C2×#385C2214yes—
151C2×#381C2214yes—
152C2×#380C2212yes—
153C22×#41C2314yes—
154C22×#41C2311yescharacteristic
155C22×#41C2311yescharacteristic
156C23×Q8C2312yes—
157C23×Q8C2312yes—
158C24×C4C2312yes—
159C24×C4C2311yescharacteristic
160#563—232no—
161#552—232no—
162#551—232no—
163D4×Q8—232no—
164#544—232no—
165#541—216no—
166#539—232no—
167#536—216no—
168#533—216no—
169#533—28no—
170#532—28no—
171#532—216no—
172C2×C4⋊Q8C2312yes—
173C2×C4⋊Q8C2312yes—
174C2×C4⋊Q8C2311yescharacteristic
175C2×C4⋊Q8C2314yes—
176C2×C4⋊Q8C2318yes—
177C2×#127C2311yescharacteristic
178#529—232no—
179#529—216no—
180#529—216no—
181#529—232no—
182C2×#126C2314yes—
183C2×#126C2314yes—
184C2×#126C2318yes—
185C2×#126C2318yes—
186C2×#125C2312yes—
187C2×#125C2314yes—
188C2×#125C2312yes—
189C2×#125C2318yes—
190C2×#125C2318yes—
191C2×#124C2314yes—
192C2×#124C2311yescharacteristic
193C2×#124C2311yescharacteristic
194C2×#124C2314yes—
195#525—28no—
196#525—232no—
197#525D4116yes—
198C2×#123C2318yes—
199C2×#123C2314yes—
200C2×#123C2314yes—
201C2×#123C2312yes—
202C2×#123C2314yes—
203C2×#123C2314yes—
204C2×#123C2318yes—
205C2×#123C2312yes—
206C2×C22⋊Q8—216no—
207C2×C22⋊Q8C2314yes—
208C2×C22⋊Q8C2314yes—
209C2×C22⋊Q8C2314yes—
210C2×C22⋊Q8C2314yes—
211C2×C22⋊Q8C2314yes—
212C2×C22⋊Q8C2312yes—
213C2×C22⋊Q8C2314yes—
214C2×C22⋊Q8C2314yes—
215C2×C22⋊Q8C2318yes—
216C2×C22⋊Q8C2318yes—
217C2×C22⋊Q8C2314yes—
218C2×C22⋊Q8C2314yes—
219C2×C22⋊Q8C2312yes—
220C2×#121C2312yes—
221C2×#121C2314yes—
222C2×#121C2314yes—
223C2×#121C2312yes—
224C2×#120C2312yes—
225C2×#120C2312yes—
226C4×#41—28no—
227C4×#41—232no—
228C4×#41—28no—
229C2×C4×Q8C2314yes—
230C2×C4×Q8C2314yes—
231C2×C4×Q8C2312yes—
232C2×C4×Q8C2314yes—
233C2×C4×Q8C2312yes—
234C2×C4×D4C2318yes—
235C2×C4×D4C2314yes—
236C2×C4×D4C2314yes—
237C2×C4×D4C2314yes—
238C2×C4×D4C2314yes—
239C2×C4×D4C2314yes—
240C2×C4×D4C2314yes—
241C2×C4×D4C2312yes—
242C2×C4×D4C2314yes—
243C2×C4×D4C2312yes—
244C2×C4×D4C2318yes—
245C2×C4×D4C2314yes—
246C2×#117C2312yes—
247C2×#117C2312yes—
248C2×#117C2312yes—
249C2×#117C2314yes—
250C2×#117C2318yes—
251C2×#117C2311yescharacteristic
252C2×#117C2314yes—
253C2×#117C2314yes—
254C2×#117C2312yes—
255C2×#117C2311yescharacteristic
256C22×C4⋊C4C2314yes—
257C22×C4⋊C4C2314yes—
258C22×C4⋊C4C2312yes—
259C22×C4⋊C4C2312yes—
260C22×C4⋊C4C2312yes—
261C22×C4⋊C4C2312yes—
262C22×C4⋊C4C2314yes—
263C22×C22⋊C4C2314yes—
264C22×C22⋊C4C2314yes—
265C22×C42—28no—
266C22×C42C2312yes—
267C22×C42C2311yescharacteristic
268C22×C42C2312yes—
269C22×C42C2311yescharacteristic
270C22×C42C2312yes—
271C22×C42C2312yes—
272C22×C42C2312yes—
273C22×C42C2312yes—
274C22×C42C2312yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#400C2318yes—
280#398C2318yes—
281#398C2318yes—
282#398C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#397C2318yes—
292#397C2318yes—
293#397C2318yes—
294#397C2318yes—
295#397C2318yes—
296#397C2318yes—
297#397C2318yes—
298#397C2318yes—
299#396C2318yes—
300#396C2318yes—
301#396C2318yes—
302#396C2318yes—
303#395C2318yes—
304#395C2318yes—
305#395C2318yes—
306#395C2318yes—
307#395C2318yes—
308#394C2318yes—
309#394C2318yes—
310#394C2318yes—
311#394C2318yes—
312#394C2318yes—
313#393C2318yes—
314#393C2318yes—
315#391C2314yes—
316#391C2314yes—
317#391C2318yes—
318#391C2314yes—
319#391C2314yes—
320#391C2314yes—
321#391C2314yes—
322#391C2318yes—
323#391C2318yes—
324#391C2314yes—
325#391C2314yes—
326#391C2314yes—
327#391C2314yes—
328#391C2314yes—
329#391C2318yes—
330#390C2314yes—
331#389C2314yes—
332#389C2314yes—
333#389C2318yes—
334#389C2318yes—
335#389C2314yes—
336#389C2314yes—
337#389C2314yes—
338#389C2318yes—
339#389C2318yes—
340#389C2318yes—
341#389C2318yes—
342#389C2314yes—
343#389C2314yes—
344#389C2314yes—
345#389C2314yes—
346#389C2314yes—
347#389C2318yes—
348#389C2318yes—
349#388C2318yes—
350#388C2318yes—
351#388C2318yes—
352#388C2318yes—
353#388C2318yes—
354#388C2318yes—
355#387C2318yes—
356#387C2318yes—
357#387C2318yes—
358#387C2318yes—
359#387C2318yes—
360#387C2318yes—
361#387C2318yes—
362#387C2318yes—
363#387C2318yes—
364#387C2318yes—
365#387C2318yes—
366#387C2318yes—
367#387C2318yes—
368#387C2318yes—
369#387C2318yes—
370#387C2318yes—
371#387C2318yes—
372#387C2318yes—
373#386C2314yes—
374#386C2314yes—
375#386C2318yes—
376#386C2318yes—
377#386C2318yes—
378#386C2318yes—
379#386C2318yes—
380#386C2318yes—
381#385C2318yes—
382#385C2318yes—
383#385C2318yes—
384#385C2318yes—
385#385C2318yes—
386#385C2318yes—
387#385C2318yes—
388#385C2318yes—
389#385C2318yes—
390#385C2318yes—
391#385C2318yes—
392#385C2318yes—
393#384C2312yes—
394#382C2318yes—
395#382C2312yes—
396#381C2318yes—
397#381C2318yes—
398#381C2318yes—
399#381C2318yes—
400#381C2318yes—
401#381C2318yes—
402#381C2318yes—
403#380C2314yes—
404#380C2314yes—
405#380C2318yes—
406#380C2314yes—
407#380C2314yes—
408#380C2318yes—
409#380C2314yes—
410#380C2314yes—
411#380C2318yes—
412#380C2318yes—
413#380C2318yes—
414#380C2314yes—
415C4×C4⋊C4C2314yes—
416C4×C4⋊C4C2318yes—
417C4×C4⋊C4C2318yes—
418C4×C22⋊C4C2318yes—
419C4×C22⋊C4C2318yes—
420C2×#95C2314yes—
421C2×#95C2314yes—
422C2×#95C2318yes—
423C2×#95C2314yes—
424C2×#95C2314yes—
425C2×#95C2314yes—
426C2×#95C2314yes—
427C2×#95C2314yes—
428C25C2411yescharacteristic
429C2×#41—216no—
430C2×#41—24no—
431C2×#41—216no—
432C2×#41—42no—
433C2×#41—42no—
434C2×#41—42no—
435C2×#41—42no—
436C2×#41—48no—
437C2×#41C2×D418yes—
438C22×Q8—28no—
439C22×Q8—28no—
440C22×Q8—44no—
441C22×Q8—44no—
442C22×Q8—44no—
443C22×Q8—44no—
444C22×Q8C2414yes—
445C22×Q8C2414yes—
446C22×Q8C2411yescharacteristic
447C22×Q8C2414yes—
448C22×Q8C2414yes—
449C22×Q8C2411yescharacteristic
450C22×D4C2414yes—
451C22×D4C2414yes—
452C22×D4C2414yes—
453C22×D4C2412yes—
454C22×D4C2411yescharacteristic
455C22×D4C2412yes—
456C22×D4C2411yescharacteristic
457C23×C4—28no—
458C23×C4—28no—
459C23×C4—42no—
460C23×C4—42no—
461C23×C4—44no—
462C23×C4C2×D418yes—
463C23×C4C2414yes—
464C23×C4C2412yes—
465C23×C4C2412yes—
466C23×C4C2414yes—
467C23×C4C2414yes—
468C23×C4C2412yes—
469C23×C4C2412yes—
470C23×C4C2412yes—
471C23×C4C2412yes—
472C23×C4C2412yes—
473C23×C4C2412yes—
474C23×C4C2411yescharacteristic
475C23×C4C2412yes—
476C23×C4C2414yes—
477C23×C4C2414yes—
478C23×C4C2414yes—
479C23×C4C2414yes—
480C23×C4C2414yes—
481C23×C4C2412yes—
482C23×C4C2411yescharacteristic
483C4⋊Q8—24no—
484C4⋊Q8—216no—
485C4⋊Q8—28no—
486C4⋊Q8—232no—
487C4⋊Q8—28no—
488#127—24no—
489#126—216no—
490#126—216no—
491#126—232no—
492#126—232no—
493#125—216no—
494#125—28no—
495#125—232no—
496#125—232no—
497#125—28no—
498#124—24no—
499#124—24no—
500#124—216no—
501#124—216no—
502#123—216no—
503#123—216no—
504#123—216no—
505#123—232no—
506#123—28no—
507#123—216no—
508#123—416no—
509#123C2×D4116yes—
510C22⋊Q8—216no—
511C22⋊Q8—216no—
512C22⋊Q8—216no—
513C22⋊Q8—216no—
514C22⋊Q8—28no—
515C22⋊Q8—216no—
516C22⋊Q8—216no—
517C22⋊Q8—216no—
518C22⋊Q8—232no—
519C22⋊Q8—232no—
520C22⋊Q8—48no—
521C22⋊Q8—48no—
522C22⋊Q8C2×D4116yes—
523#121—216no—
524#121—216no—
525#121—28no—
526#121C2×D4116yes—
527#120—28no—
528#120C2×D4116yes—
529C4×Q8—28no—
530C4×Q8—216no—
531C4×Q8—28no—
532C4×Q8—216no—
533C4×Q8—216no—
534C4×D4—216no—
535C4×D4—216no—
536C4×D4—28no—
537C4×D4—232no—
538C4×D4—216no—
539C4×D4—216no—
540C4×D4—28no—
541C4×D4—216no—
542C4×D4—216no—
543C4×D4—216no—
544C4×D4—416no—
545C4×D4C2×D4132yes—
546#117—24no—
547#117—28no—
548#117—28no—
549#117—216no—
550#117—216no—
551#117—216no—
552#117—232no—
553#117—28no—
554#117—44no—
555#117C2×D418yes—
556C2×C4⋊C4—216no—
557C2×C4⋊C4—28no—
558C2×C4⋊C4—216no—
559C2×C4⋊C4—44no—
560C2×C4⋊C4—44no—
561C2×C4⋊C4—44no—
562C2×C4⋊C4—48no—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2414yes—
565C2×C4⋊C4C2414yes—
566C2×C4⋊C4C2418yes—
567C2×C4⋊C4C2418yes—
568C2×C4⋊C4C2414yes—
569C2×C4⋊C4C2418yes—
570C2×C4⋊C4C2418yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2412yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2414yes—
576C2×C4⋊C4C2414yes—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2418yes—
580C2×C4⋊C4C2418yes—
581C2×C4⋊C4C2418yes—
582C2×C4⋊C4C2418yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2418yes—
586C2×C4⋊C4C2418yes—
587C2×C4⋊C4C2414yes—
588C2×C4⋊C4C2418yes—
589C2×C4⋊C4C2418yes—
590C2×C4⋊C4C2418yes—
591C2×C4⋊C4C2418yes—
592C2×C4⋊C4C2418yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2414yes—
595C2×C22⋊C4—216no—
596C2×C22⋊C4—48no—
597C2×C22⋊C4C2418yes—
598C2×C22⋊C4C2418yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C2414yes—
601C2×C22⋊C4C2412yes—
602C2×C22⋊C4C2414yes—
603C2×C22⋊C4C2414yes—
604C2×C22⋊C4C2414yes—
605C2×C22⋊C4C2414yes—
606C2×C22⋊C4C2414yes—
607C2×C22⋊C4C2414yes—
608C2×C22⋊C4C2418yes—
609C2×C22⋊C4C2418yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C2418yes—
612C2×C22⋊C4C2418yes—
613C2×C22⋊C4C2418yes—
614C2×C22⋊C4C2418yes—
615C2×C22⋊C4C2418yes—
616C2×C22⋊C4C2414yes—
617C2×C22⋊C4C2412yes—
618C2×C22⋊C4C2414yes—
619C2×C42—28no—
620C2×C42—28no—
621C2×C42—24no—
622C2×C42—28no—
623C2×C42—28no—
624C2×C42—28no—
625C2×C42—28no—
626C2×C42—24no—
627C2×C42—28no—
628C2×C42C2412yes—
629C2×C42C2411yescharacteristic
630C2×C42C2414yes—
631C2×C42C2414yes—
632C2×C42C2414yes—
633C2×C42C2412yes—
634C2×C42C2418yes—
635C2×C42C2412yes—
636C2×C42C2412yes—
637C2×C42C2412yes—
638C2×C42C2411yescharacteristic
639C2×C42C2412yes—
640C2×C42C2412yes—
641C2×C42C2411yescharacteristic
642C2×C42C2411yescharacteristic
643C2×C42C2414yes—
644C2×C42C2418yes—
645C2×C42C2412yes—
646#95C2418yes—
647#95C2418yes—
648#95C2418yes—
649#95C2418yes—
650#95C2418yes—
651#95C2418yes—
652#95C2418yes—
653#95C2418yes—
654#95C2418yes—
655#95C2418yes—
656#95C2418yes—
657#95C2418yes—
658#95C2418yes—
659#95C2418yes—
660#95C2418yes—
661#95C2418yes—
662#95C2418yes—
663#95C2418yes—
664#95C2418yes—
665#95C2418yes—
666#95C2418yes—
667#95C2418yes—
668#95C2418yes—
669#95C2418yes—
670#95C2418yes—
671C24—24no—
672C24—24no—
673C24—41no—
674C24—41no—
675C24C22×D414yes—
676C24C2512yes—
677C24C2511yescharacteristic
678C24C2512yes—
679C24C2512yes—
680#41—416no—
681#41—464no—
682#41—416no—
683C2×Q8—28no—
684C2×Q8—22no—
685C2×Q8—28no—
686C2×Q8—28no—
687C2×Q8—28no—
688C2×Q8—28no—
689C2×Q8—28no—
690C2×Q8—28no—
691C2×Q8—44no—
692C2×Q8—41no—
693C2×Q8—41no—
694C2×Q8—41no—
695C2×Q8—41no—
696C2×Q8—44no—
697C2×Q8—44no—
698C2×Q8—44no—
699C2×Q8—44no—
700C2×Q8—816no—
701C2×Q8—816no—
702C2×Q8C22×D414yes—
703C2×D4—28no—
704C2×D4—28no—
705C2×D4—24no—
706C2×D4—28no—
707C2×D4—28no—
708C2×D4—28no—
709C2×D4—28no—
710C2×D4—22no—
711C2×D4—28no—
712C2×D4—42no—
713C2×D4—42no—
714C2×D4—41no—
715C2×D4—41no—
716C2×D4—44no—
717C2×D4—41no—
718C2×D4—41no—
719C2×D4—42no—
720C2×D4—42no—
721C2×D4C22×D4116yes—
722C2×D4C22×D418yes—
723C2×D4C22×D414yes—
724C22×C4—24no—
725C22×C4—24no—
726C22×C4—24no—
727C22×C4—24no—
728C22×C4—24no—
729C22×C4—24no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—24no—
733C22×C4—24no—
734C22×C4—24no—
735C22×C4—24no—
736C22×C4—24no—
737C22×C4—28no—
738C22×C4—28no—
739C22×C4—28no—
740C22×C4—24no—
741C22×C4—24no—
742C22×C4—28no—
743C22×C4—28no—
744C22×C4—28no—
745C22×C4—28no—
746C22×C4—28no—
747C22×C4—28no—
748C22×C4—24no—
749C22×C4—24no—
750C22×C4—24no—
751C22×C4—24no—
752C22×C4—24no—
753C22×C4—28no—
754C22×C4—28no—
755C22×C4—24no—
756C22×C4—24no—
757C22×C4—416no—
758C22×C4—41no—
759C22×C4—41no—
760C22×C4—42no—
761C22×C4—42no—
762C22×C4—42no—
763C22×C4—42no—
764C22×C4—42no—
765C22×C4—42no—
766C22×C4—44no—
767C22×C4—44no—
768C22×C4—44no—
769C22×C4—44no—
770C22×C4—44no—
771C22×C4—44no—
772C22×C4—44no—
773C22×C4—44no—
774C22×C4—44no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4—48no—
778C22×C4—432no—
779C22×C4C22×D418yes—
780C22×C4C22×D414yes—
781C22×C4C22×D418yes—
782C22×C4C22×D418yes—
783C22×C4C22×D414yes—
784C22×C42−1+418yes—
785C22×C4C2518yes—
786C22×C4C2518yes—
787C22×C4C2512yes—
788C22×C4C2512yes—
789C22×C4C2514yes—
790C22×C4C2518yes—
791C22×C4C2518yes—
792C22×C4C2512yes—
793C22×C4C2511yescharacteristic
794C22×C4C2514yes—
795C22×C4C2512yes—
796C22×C4C2512yes—
797C22×C4C2512yes—
798C22×C4C2512yes—
799C22×C4C2511yescharacteristic
800C4⋊C4—28no—
801C4⋊C4—216no—
802C4⋊C4—216no—
803C4⋊C4—28no—
804C4⋊C4—28no—
805C4⋊C4—28no—
806C4⋊C4—24no—
807C4⋊C4—28no—
808C4⋊C4—28no—
809C4⋊C4—28no—
810C4⋊C4—28no—
811C4⋊C4—28no—
812C4⋊C4—216no—
813C4⋊C4—216no—
814C4⋊C4—216no—
815C4⋊C4—216no—
816C4⋊C4—216no—
817C4⋊C4—216no—
818C4⋊C4—28no—
819C4⋊C4—28no—
820C4⋊C4—44no—
821C4⋊C4—44no—
822C4⋊C4—44no—
823C4⋊C4—48no—
824C4⋊C4—48no—
825C4⋊C4—48no—
826C4⋊C4—48no—
827C4⋊C4—48no—
828C4⋊C4—48no—
829C4⋊C4—48no—
830C4⋊C4C22×D4116yes—
831C4⋊C4C22×D418yes—
832C22⋊C4—216no—
833C22⋊C4—216no—
834C22⋊C4—24no—
835C22⋊C4—28no—
836C22⋊C4—28no—
837C22⋊C4—28no—
838C22⋊C4—28no—
839C22⋊C4—216no—
840C22⋊C4—216no—
841C22⋊C4—28no—
842C22⋊C4—28no—
843C22⋊C4—28no—
844C22⋊C4—48no—
845C22⋊C4—44no—
846C22⋊C4—48no—
847C22⋊C4—48no—
848C22⋊C4—48no—
849C22⋊C4—48no—
850C22⋊C4—48no—
851C22⋊C4C22×D4116yes—
852C22⋊C4C22×D4116yes—
853C22⋊C4C22×D418yes—
854C42—22no—
855C42—24no—
856C42—22no—
857C42—24no—
858C42—24no—
859C42—24no—
860C42—24no—
861C42—22no—
862C42—24no—
863C42—22no—
864C42—28no—
865C42—28no—
866C42—24no—
867C42—28no—
868C42—216no—
869C42—44no—
870C42—48no—
871C42C22×D418yes—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—24no—
878C23—22no—
879C23—22no—
880C23—24no—
881C23—22no—
882C23—21no—
883C23—21no—
884C23—216no—
885C23—22no—
886C23—24no—
887C23—22no—
888C23—22no—
889C23—24no—
890C23—44no—
891C23—48no—
892C23—44no—
893C23—44no—
894C23C23×D412yes—
895C23C23×D414yes—
896C23C23×D414yes—
897C23C2×2−1+414yes—
898C23#58514yes—
899C23C2611yescharacteristic
900Q8—44no—
901Q8—416no—
902Q8—44no—
903Q8—416no—
904Q8—88no—
905Q8—88no—
906D4—232no—
907D4—44no—
908D4—48no—
909D4—416no—
910D4—44no—
911D4—48no—
912D4—416no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—24no—
916C2×C4—24no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—22no—
925C2×C4—216no—
926C2×C4—216no—
927C2×C4—28no—
928C2×C4—216no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—28no—
932C2×C4—22no—
933C2×C4—24no—
934C2×C4—28no—
935C2×C4—28no—
936C2×C4—28no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—24no—
940C2×C4—28no—
941C2×C4—28no—
942C2×C4—28no—
943C2×C4—28no—
944C2×C4—28no—
945C2×C4—28no—
946C2×C4—28no—
947C2×C4—28no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—24no—
953C2×C4—48no—
954C2×C4—44no—
955C2×C4—416no—
956C2×C4—48no—
957C2×C4—48no—
958C2×C4—48no—
959C2×C4—48no—
960C2×C4—416no—
961C2×C4—416no—
962C2×C4—48no—
963C2×C4—48no—
964C2×C4—88no—
965C2×C4—88no—
966C2×C4—88no—
967C2×C4—88no—
968C2×C4—164no—
969C2×C4C23×D414yes—
970C2×C4C23×D414yes—
971C2×C4C23×D412yes—
972C2×C4C23×D418yes—
973C2×C4C23×D412yes—
974C2×C4C2×2−1+414yes—
975C2×C4C2×2−1+414yes—
976C2×C4#58512yes—
977C2×C4#58512yes—
978C22—24no—
979C22—24no—
980C22—24no—
981C22—24no—
982C22—24no—
983C22—24no—
984C22—22no—
985C22—24no—
986C22—24no—
987C22—28no—
988C22—416no—
989C22—44no—
990C22—42no—
991C22—42no—
992C22—41no—
993C22—42no—
994C22—41no—
995C22—44no—
996C22—42no—
997C22—44no—
998C22—42no—
999C22—42no—
1000C22#348918yes—
1001C22C24×D411yescharacteristic
1002C22C22×2−1+412yes—
1003C22C2×#58511yescharacteristic
1004C22C2×#58512yes—
1005C22C2×#58511yescharacteristic
1006C4—22no—
1007C4—24no—
1008C4—24no—
1009C4—24no—
1010C4—24no—
1011C4—28no—
1012C4—48no—
1013C4—42no—
1014C4—48no—
1015C4—48no—
1016C4—42no—
1017C4—42no—
1018C4—44no—
1019C4—48no—
1020C4#348514yes—
1021C2—28no—
1022C2—44no—
1023C2—42no—
1024C2—82no—
1025C2#6275212yes—
1026C2C2×#348511yescharacteristic
1027C2C2×#348912yes—
1028C2#6282911yescharacteristic
1029C2#6283711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#3444C2
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×#3538C2semidirect
3. #59010C2semidirect
4. #45771C2semidirect
5. #38043C2semidirect
6. #38027C2semidirect
7. #37763C2semidirect
8. #37755C2semidirect
9. #37698C2semidirect
10. #37689C2semidirect
11. #37442C2semidirect
12. #37377C2semidirect
13. #37376C2semidirect
14. C2×#2855C2semidirect
15. #36375C2semidirect
16. #36274C2semidirect
17. #35309C2semidirect
18. #35307C2semidirect
19. #34360C2semidirect
46. #2857C22semidirect
55. #2855C22semidirect
56. #2851C22semidirect
58. #2734C22semidirect
59. #2731C22semidirect
60. #2726C22semidirect
61. #2725C22semidirect
62. #2722C22semidirect
63. #2719C22semidirect
64. #2717C22semidirect
65. #2716C22semidirect
66. #2715C22semidirect
67. #2713C22semidirect
68. #2713C22semidirect
69. #2709C22semidirect
71. #2700C22semidirect
73. #2698C22semidirect
78. #2629C22semidirect
81. #2625C22semidirect
82. #2621C22semidirect
85. #2584C22semidirect
86. #2582C22semidirect
87. #2581C22semidirect
88. #2568C22semidirect
93. #2485C22semidirect
94. #2478C22semidirect
95. #2475C22semidirect
98. #2466C22semidirect
99. #2462C22semidirect
100. #2462C22semidirect
101. #2460C22semidirect
102. #2451C22semidirect
104. #2450C22semidirect
106. #2446C22semidirect
108. #2439C22semidirect
111. #2438C22semidirect
116. #2419C22semidirect
119. #2417C22semidirect
120. #2415C22semidirect
124. #2409C22semidirect
136. #2323C22semidirect
137. #2316C22semidirect
140. #2310C22semidirect
141. C4×C22⋊Q8C22semidirect
142. #2296C22semidirect
145. C2×#391C22semidirect

Maximal subgroups

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

subgroupindex
C2×#35382
C2×#34442
#590102
#457712
#380432
#380272
#377632
#377552
#376982
#376892
#374422
#373772
#373762
C2×#28552
#363752
#362742
#353092
#353072
#343602