Finite Group Databasebeta

← #6446201

Subgroups — #6446201

Order 512.

1885 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3084C211yesmaximal, characteristic
2C2×#2962C211yesmaximal, characteristic, complemented
3#35566C211yesmaximal, characteristic, complemented
4#35519C211yesmaximal, characteristic
5#25487C212yesmaximal, complemented
6#25486C212yesmaximal, complemented
7#25485C212yesmaximal, complemented
8#25484C212yesmaximal, complemented
9#25477C212yesmaximal, complemented
10#25476C212yesmaximal, complemented
11#25473C212yesmaximal, complemented
12#25472C212yesmaximal, complemented
13#23671C211yesmaximal, characteristic, complemented
14C2×#2088C211yesmaximal, characteristic, complemented
15#23616C211yesmaximal, characteristic
16#23609C211yesmaximal, characteristic
17#21326C211yesmaximal, characteristic, complemented
18#21175C211yesmaximal, characteristic, complemented
19#21159C211yesmaximal, characteristic, complemented
20#21155C211yesmaximal, characteristic, complemented
21#21093C211yesmaximal, characteristic
22#21092C211yesmaximal, characteristic
23#20415C211yesmaximal, characteristic
24C2×#544C2211yescharacteristic
25C2×#533C2211yescharacteristic
26C2×#520C2211yescharacteristic
27#3084—28no—
28C2×#479C2212yes—
29C2×#475C2212yes—
30C2×#478C2212yes—
31C2×#476C2212yes—
32#2962—28no—
33C2×#446C2212yes—
34C2×#446C2212yes—
35C2×#446C2212yes—
36C2×C8×Q8C2212yes—
37C2×#428C2211yescharacteristic
38C2×#428C2211yescharacteristic
39C2×#427C2211yescharacteristic
40C22×#106C2211yescharacteristic
41C2×#424C2211yescharacteristic
42C2×#424C2211yescharacteristic
43C22×C4⋊C8C2211yescharacteristic
44C2×#417C2211yescharacteristic
45C2×#417C2211yescharacteristic
46C2×#416C2211yescharacteristic
47C2×#416C2211yescharacteristic
48C2×#405C2211yescharacteristic
49C2×#405C2211yescharacteristic
50C2×C4×M16C2211yescharacteristic
51#2584C2212yes—
52#2584C2212yes—
53#2582C2212yes—
54#2581C2212yes—
55#2580C2212yes—
56#2567C2212yes—
57#2552—21no—
58#2551—21no—
59#2550—21no—
60#2550—21no—
61#2549—22no—
62#2546C2212yes—
63#2538C2212yes—
64#2450—22no—
65#2449—22no—
66#2442—21no—
67#2441—21no—
68#2440—21no—
69#2440—22no—
70#2439—21no—
71#2317C2211yescharacteristic
72#2317C2211yescharacteristic
73#2317C2211yescharacteristic
74#2316C2211yescharacteristic
75#2311C2211yescharacteristic
76#2297C2211yescharacteristic
77#2296C2211yescharacteristic
78C2×#389C2211yescharacteristic
79C2×#389C2211yescharacteristic
80#2274C2211yescharacteristic
81#2088C2212yes—
82#2088C2212yes—
83#2088C2212yes—
84#2088C2212yes—
85#2088C2212yes—
86#2088C2212yes—
87#2087C2212yes—
88#2086C2212yes—
89#2068C2211yescharacteristic
90#2068C2211yescharacteristic
91#2068C2212yes—
92#2067C2211yescharacteristic
93#2067C2211yescharacteristic
94#2067C2212yes—
95#2066C2211yescharacteristic
96#2066C2211yescharacteristic
97#2066C2212yes—
98#2065C2211yescharacteristic
99#2065C2211yescharacteristic
100#2065C2212yes—
101#1993C2212yes—
102#1992C2212yes—
103#1991C2212yes—
104#1990C2212yes—
105#1949C2212yes—
106#1949C2212yes—
107#1948C2212yes—
108#1947C2212yes—
109#1944C2212yes—
110#1943C2212yes—
111#1943C2212yes—
112#1943C2212yes—
113#1942C2212yes—
114#1941C2212yes—
115#1941C2212yes—
116#1941C2212yes—
117#1936C2212yes—
118#1936C2212yes—
119#1935C2212yes—
120#1935C2212yes—
121#1934C2212yes—
122#1934C2212yes—
123#1933C2212yes—
124#1933C2212yes—
125#1763C2212yes—
126#1762C2212yes—
127C4×#103C2212yes—
128C4×#102C2212yes—
129#1736C2211yescharacteristic
130#1736C2211yescharacteristic
131#1736C2211yescharacteristic
132#1736C2211yescharacteristic
133#1735C2211yescharacteristic
134C2×#340C2211yescharacteristic
135C2×#340C2211yescharacteristic
136C2×#340C2211yescharacteristic
137C22×#41C2311yescharacteristic
138C22×M16C2311yescharacteristic
139C22×M16C2311yescharacteristic
140C23×C8C2311yescharacteristic
141C23×C8C2311yescharacteristic
142#544—24no—
143#544—24no—
144#533—24no—
145#533—24no—
146C2×C4⋊Q8—22no—
147C2×C4⋊Q8—21no—
148C2×C4⋊Q8D411yescharacteristic
149C2×C4⋊Q8D411yescharacteristic
150C2×C4⋊Q8C2312yes—
151C2×#125—21no—
152C2×#125D411yescharacteristic
153C2×#125D411yescharacteristic
154C2×#125C2312yes—
155C2×C22⋊Q8—22no—
156C2×C22⋊Q8—22no—
157C2×C22⋊Q8D412yes—
158C2×C22⋊Q8D412yes—
159#520—24no—
160#520—24no—
161C2×C4×Q8C2312yes—
162C2×C4×Q8C2312yes—
163C2×C4×Q8C2312yes—
164C2×C4×D4—22no—
165C2×C4×D4C2312yes—
166C2×#117—21no—
167C2×#117C2311yescharacteristic
168C2×#117C2311yescharacteristic
169C2×#117C2311yescharacteristic
170C2×#117C2311yescharacteristic
171C2×#117C2311yescharacteristic
172C22×C4⋊C4—21no—
173C22×C4⋊C4—21no—
174C22×C4⋊C4—21no—
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2311yescharacteristic
179C22×C42C2311yescharacteristic
180#479—28no—
181#478—28no—
182#476—28no—
183#475—28no—
184#446—28no—
185#446—28no—
186#446—28no—
187C8×Q8—28no—
188#428—24no—
189#428—24no—
190#427—24no—
191C2×#107C2312yes—
192C2×#107C2311yescharacteristic
193C2×#107C2311yescharacteristic
194C2×#107C2312yes—
195C2×#106—24no—
196C2×#106C2312yes—
197C2×#106C2312yes—
198C2×#106C2312yes—
199C2×#106C2311yescharacteristic
200C2×#106C2311yescharacteristic
201C2×#106C2312yes—
202#424—24no—
203#424D418yes—
204C2×C4⋊C8—24no—
205C2×C4⋊C8C2311yescharacteristic
206C2×C4⋊C8C2311yescharacteristic
207C2×C4⋊C8C2312yes—
208C2×C4⋊C8C2312yes—
209C2×C4⋊C8C2311yescharacteristic
210C2×C4⋊C8C2311yescharacteristic
211C2×C4⋊C8C2312yes—
212C2×C4⋊C8C2312yes—
213#417—24no—
214#417Q818yescomplemented
215#416—24no—
216#416—24no—
217C2×#103C2311yescharacteristic
218C2×#103C2312yes—
219C2×#103C2311yescharacteristic
220C2×#103C2311yescharacteristic
221C2×#103C2311yescharacteristic
222C2×#103C2312yes—
223C2×#102C2311yescharacteristic
224C2×#102C2312yes—
225C2×#102C2311yescharacteristic
226C2×#102C2311yescharacteristic
227C2×#102C2311yescharacteristic
228C2×#102C2312yes—
229#405—24no—
230#405—24no—
231C4×M16—24no—
232C2×#97C2312yes—
233C2×#97C2312yes—
234C2×#97C2312yes—
235C2×C4×C8C2312yes—
236C2×C4×C8C2312yes—
237C2×C4×C8C2312yes—
238#400—22no—
239#399—22no—
240#398—22no—
241#398—22no—
242#398—22no—
243#398—22no—
244#398—22no—
245#398—22no—
246#396—22no—
247#396—22no—
248#395—22no—
249#395—22no—
250#395—22no—
251#395—22no—
252#395—22no—
253#393—22no—
254#391—22no—
255#391—22no—
256#391—22no—
257#391C2312yes—
258#391C2311yescharacteristic
259#391C2311yescharacteristic
260#390C2312yes—
261#390C2311yescharacteristic
262#390C2311yescharacteristic
263#389—21no—
264#389—21no—
265#389—21no—
266#389—21no—
267#389—22no—
268#389—22no—
269#389—22no—
270#389—22no—
271#389—22no—
272#389—21no—
273#389—21no—
274#389—21no—
275#389—21no—
276#389C2311yescharacteristic
277#389C2312yes—
278#389C2312yes—
279#389C2312yes—
280#389C2312yes—
281#389C2312yes—
282#389C2312yes—
283#389C2312yes—
284#389C2311yescharacteristic
285#389C2311yescharacteristic
286#389C2311yescharacteristic
287#389C2312yes—
288#389C2312yes—
289#389C2312yes—
290#387—22no—
291#387—22no—
292#386—21no—
293#386—21no—
294#386—22no—
295#385—21no—
296#385—21no—
297#385—22no—
298#385—22no—
299#385—22no—
300#385—22no—
301#385—22no—
302#384—22no—
303#384—21no—
304#384—21no—
305#384C2312yes—
306#382—21no—
307#382—21no—
308#382C2312yes—
309#380—21no—
310#380—21no—
311#380—22no—
312#380—22no—
313C4×C4⋊C4—21no—
314C4×C4⋊C4—21no—
315C4×C4⋊C4—21no—
316C4×C4⋊C4—21no—
317C4×C4⋊C4C2312yes—
318C4×C4⋊C4C2312yes—
319C4×C22⋊C4—22no—
320C4×C22⋊C4—21no—
321C4×C22⋊C4—21no—
322C2×#95—21no—
323C2×#95—21no—
324#340C2311yescharacteristic
325#340C2311yescharacteristic
326#340C2312yes—
327#340C2312yes—
328#340C2311yescharacteristic
329#340C2311yescharacteristic
330#340C2312yes—
331#340C2312yes—
332#340C2312yes—
333#340C2312yes—
334#340C2312yes—
335#340C2312yes—
336#340C2312yes—
337#340C2312yes—
338#340C2312yes—
339#340C2312yes—
340#340C2312yes—
341#340C2312yes—
342C2×#41—22no—
343C2×#41—22no—
344C2×#41—22no—
345C2×#41—22no—
346C2×#41—22no—
347C2×#41C2×Q814yes—
348C22×Q8—22no—
349C22×Q8C2×D412yes—
350C22×Q8C2×D412yes—
351C22×Q8C2411yescharacteristic
352C22×D4—21no—
353C22×D4C2411yescharacteristic
354C23×C4—21no—
355C23×C4—21no—
356C23×C4—21no—
357C23×C4—21no—
358C23×C4—21no—
359C23×C4—22no—
360C23×C4C2×D411yescharacteristic
361C23×C4C2×D411yescharacteristic
362C23×C4C2411yescharacteristic
363C2×M16—22no—
364C2×M16—22no—
365C2×M16—22no—
366C2×M16—22no—
367C2×M16C2×D414yes—
368C2×M16C2×Q814yes—
369C22×C8—22no—
370C22×C8—22no—
371C22×C8—22no—
372C22×C8—22no—
373C22×C8—22no—
374C22×C8C2×D414yes—
375C22×C8C2411yescharacteristic
376C22×C8C2411yescharacteristic
377C22×C8C2411yescharacteristic
378C22×C8C2411yescharacteristic
379C22×C8C2412yes—
380C22×C8C2412yes—
381C4⋊Q8—24no—
382C4⋊Q8—24no—
383C4⋊Q8—24no—
384C4⋊Q8—24no—
385C4⋊Q8—44no—
386C4⋊Q8—84no—
387#125—24no—
388#125—24no—
389#125—24no—
390#125—24no—
391#125—44no—
392C22⋊Q8—28no—
393C22⋊Q8—28no—
394C22⋊Q8—48no—
395C22⋊Q8—84no—
396C4×Q8—24no—
397C4×Q8—24no—
398C4×Q8—24no—
399C4×Q8—24no—
400C4×Q8—24no—
401C4×Q8—24no—
402C4×D4—24no—
403C4×D4—24no—
404C4×D4—48no—
405#117—22no—
406#117—22no—
407#117—22no—
408#117—22no—
409#117—22no—
410#117—22no—
411#117—22no—
412#117—44no—
413#117C2×D414yes—
414#117#4114yes—
415#117#4114yes—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—44no—
448C2×C4⋊C4—82no—
449C2×C4⋊C4—82no—
450C2×C4⋊C4C2×D411yescharacteristic
451C2×C4⋊C4C2×D411yescharacteristic
452C2×C4⋊C4C2×D412yes—
453C2×C4⋊C4C2×D412yes—
454C2×C4⋊C4C2×D412yes—
455C2×C4⋊C4C2×D412yes—
456C2×C4⋊C4C2×D412yes—
457C2×C4⋊C4C2×D412yes—
458C2×C4⋊C4C2×D411yescharacteristic
459C2×C4⋊C4C2×D411yescharacteristic
460C2×C4⋊C4C2×Q814yes—
461C2×C4⋊C4C2412yes—
462C2×C4⋊C4C2412yes—
463C2×C4⋊C4C2412yes—
464C2×C4⋊C4C2411yescharacteristic
465C2×C4⋊C4C2411yescharacteristic
466C2×C4⋊C4C2411yescharacteristic
467C2×C4⋊C4C2411yescharacteristic
468C2×C4⋊C4C2412yes—
469C2×C4⋊C4C2411yescharacteristic
470C2×C4⋊C4C2411yescharacteristic
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4C2×D412yes—
482C2×C22⋊C4C2×D412yes—
483C2×C42—21no—
484C2×C42—22no—
485C2×C42—22no—
486C2×C42—22no—
487C2×C42—21no—
488C2×C42—21no—
489C2×C42—22no—
490C2×C42—22no—
491C2×C42C2×D411yescharacteristic
492C2×C42C2×D411yescharacteristic
493C2×C42C2412yes—
494C2×C42C2411yescharacteristic
495C2×C42C2411yescharacteristic
496C2×C42C2412yes—
497#107—24no—
498#107—22no—
499#107—22no—
500#107—24no—
501#106—24no—
502#106—24no—
503#106—24no—
504#106—22no—
505#106—22no—
506#106—24no—
507C4⋊C8—22no—
508C4⋊C8—22no—
509C4⋊C8—22no—
510C4⋊C8—22no—
511C4⋊C8—24no—
512C4⋊C8—24no—
513C4⋊C8C2×D418yes—
514C4⋊C8C2×D418yes—
515#103—22no—
516#103—22no—
517#103—24no—
518#103—22no—
519#103—22no—
520#103C2×Q818yes—
521#102—22no—
522#102—22no—
523#102—24no—
524#102—22no—
525#102—22no—
526#102C2×Q818yes—
527#97—24no—
528#97—24no—
529#97—24no—
530C4×C8—24no—
531C4×C8—24no—
532C4×C8—24no—
533#95—22no—
534#95—22no—
535#95—22no—
536#95—22no—
537#95—22no—
538#95—22no—
539#95—21no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95—21no—
544#95—21no—
545#95—21no—
546#95—21no—
547#95—22no—
548#95—22no—
549#95—22no—
550#95—22no—
551#95—22no—
552#95—22no—
553#95—22no—
554#95—22no—
555#95—22no—
556#95—22no—
557C24—21no—
558C24C22×D411yescharacteristic
559#41—28no—
560#41—28no—
561#41—44no—
562#41—44no—
563C2×Q8—24no—
564C2×Q8—24no—
565C2×Q8—24no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—42no—
572C2×Q8—42no—
573C2×Q8—42no—
574C2×Q8—44no—
575C2×Q8—82no—
576C2×Q8—82no—
577C2×Q8C22×Q812yes—
578C2×D4—24no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4C22×Q812yes—
587C22×C4—22no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—24no—
594C22×C4—24no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—22no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—22no—
601C22×C4—21no—
602C22×C4—22no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—44no—
612C22×C4—82no—
613C22×C4—82no—
614C22×C4—81no—
615C22×C4—81no—
616C22×C4—81no—
617C22×C4—81no—
618C22×C4—81no—
619C22×C4—81no—
620C22×C4—81no—
621C22×C4—81no—
622C22×C4C22×D411yescharacteristic
623C22×C4C22×D411yescharacteristic
624C22×C4C22×D411yescharacteristic
625C22×C4C22×D412yes—
626C22×C4C22×D412yes—
627C22×C4C22×D412yes—
628C22×C4C22×D412yes—
629C22×C4C22×D411yescharacteristic
630C22×C4C22×D411yescharacteristic
631C22×C4C22×D412yes—
632C22×C4C22×Q812yes—
633C22×C4C2×#4112yes—
634C22×C4C2×#4112yes—
635C22×C42−1+412yes—
636C22×C42−1+412yes—
637C22×C4C2511yescharacteristic
638M16—28no—
639M16—28no—
640C2×C8—28no—
641C2×C8—22no—
642C2×C8—21no—
643C2×C8—22no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—22no—
648C2×C8—22no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—44no—
656C2×C8C22×D412yes—
657C2×C8C22×D414yes—
658C2×C8C22×D412yes—
659C2×C8C22×Q814yes—
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—24no—
663C4⋊C4—24no—
664C4⋊C4—24no—
665C4⋊C4—24no—
666C4⋊C4—24no—
667C4⋊C4—24no—
668C4⋊C4—24no—
669C4⋊C4—22no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—22no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—22no—
676C4⋊C4—22no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—22no—
680C4⋊C4—22no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—22no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—42no—
687C4⋊C4—44no—
688C4⋊C4—42no—
689C4⋊C4—42no—
690C4⋊C4—44no—
691C4⋊C4—44no—
692C4⋊C4—44no—
693C4⋊C4—44no—
694C4⋊C4—42no—
695C4⋊C4—44no—
696C4⋊C4—42no—
697C4⋊C4—82no—
698C4⋊C4—81no—
699C4⋊C4—82no—
700C4⋊C4—82no—
701C4⋊C4—81no—
702C4⋊C4—82no—
703C4⋊C4—82no—
704C4⋊C4—82no—
705C4⋊C4—82no—
706C4⋊C4—82no—
707C4⋊C4—82no—
708C4⋊C4—82no—
709C4⋊C4#12114yes—
710C4⋊C4#12114yes—
711C4⋊C4C22×Q814yes—
712C4⋊C4C2×#4112yes—
713C4⋊C4C2×#4112yes—
714C22⋊C4—24no—
715C22⋊C4—24no—
716C22⋊C4—42no—
717C22⋊C4—42no—
718C22⋊C4—42no—
719C22⋊C4—44no—
720C22⋊C4—42no—
721C22⋊C4—81no—
722C22⋊C4—82no—
723C22⋊C4—81no—
724C22⋊C4—82no—
725C22⋊C4#12118yes—
726C42—22no—
727C42—22no—
728C42—24no—
729C42—21no—
730C42—22no—
731C42—21no—
732C42—21no—
733C42—21no—
734C42—22no—
735C42—42no—
736C42—44no—
737C42—42no—
738C42—82no—
739C42—82no—
740C42C22×D414yes—
741C42C2×#4114yes—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—22no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23C2×#12112yes—
754C23#54812yes—
755C23D4×Q812yes—
756C23C23×D411yescharacteristic
757Q8—22no—
758Q8—22no—
759Q8—48no—
760Q8—41no—
761Q8—41no—
762Q8—84no—
763Q8—164no—
764D4—22no—
765D4—22no—
766D4—48no—
767D4—41no—
768D4—41no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—22no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—24no—
791C2×C4—22no—
792C2×C4—21no—
793C2×C4—22no—
794C2×C4—44no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—48no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—42no—
815C2×C4—41no—
816C2×C4—42no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—42no—
822C2×C4—41no—
823C2×C4—42no—
824C2×C4—41no—
825C2×C4—82no—
826C2×C4—84no—
827C2×C4—84no—
828C2×C4—164no—
829C2×C4—162no—
830C2×C4—162no—
831C2×C4C2×#12114yes—
832C2×C4C2×#12114yes—
833C2×C4C2×#12112yes—
834C2×C4#53314yes—
835C2×C4#54114yes—
836C2×C4#54714yes—
837C2×C4#54812yes—
838C2×C4D4×Q812yes—
839C2×C4D4×Q814yes—
840C2×C4#57712yes—
841C2×C4C23×D411yescharacteristic
842C2×C4C23×Q811yescharacteristic
843C2×C4C22×#4111yescharacteristic
844C2×C4C22×#4111yescharacteristic
845C2×C4C2×2−1+411yescharacteristic
846C2×C4C2×2−1+411yescharacteristic
847C8—22no—
848C8—22no—
849C8—24no—
850C8—24no—
851C8—41no—
852C8—41no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—22no—
858C22—22no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22#242914yes—
867C22C22×#12111yescharacteristic
868C22C2×#54811yescharacteristic
869C22C2×D4×Q811yescharacteristic
870C22C2×#57711yescharacteristic
871C22#358411yescharacteristic
872C22#358511yescharacteristic
873C22#358611yescharacteristic
874C4—22no—
875C4—24no—
876C4—24no—
877C4—41no—
878C4—42no—
879C4—41no—
880C4—41no—
881C4—42no—
882C4—42no—
883C4—42no—
884C4—42no—
885C4—44no—
886C4—82no—
887C4—81no—
888C4—81no—
889C4—82no—
890C4—81no—
891C4—81no—
892C4—82no—
893C4#242914yes—
894C4C2×#53311yescharacteristic
895C4C2×#54111yescharacteristic
896C4C2×#54711yescharacteristic
897C4C2×D4×Q811yescharacteristic
898C2—24no—
899C2—82no—
900C2C2×#242911yescharacteristic
901C2#6045711yescharacteristic
902C2#6046011yescharacteristic
903C2#6134611yescharacteristic
904C2#6134911yescharacteristic
905C2#6138211yescharacteristic
906C2#6138611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#41C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#533 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2962C2semidirect
3. #35566C2semidirect
5. #25487C2semidirect
6. #25486C2semidirect
7. #25485C2semidirect
8. #25484C2semidirect
9. #25477C2semidirect
10. #25476C2semidirect
11. #25473C2semidirect
12. #25472C2semidirect
13. #23671C2semidirect
14. C2×#2088C2semidirect
17. #21326C2semidirect
18. #21175C2semidirect
19. #21159C2semidirect
20. #21155C2semidirect
214. #417Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#30842
C2×#29622
#355662
#355192
#254872
#254862
#254852
#254842
#254772
#254762
#254732
#254722
#236712
C2×#20882
#236162
#236092
#213262
#211752
#211592
#211552
#210932
#210922
#204152