Finite Group Databasebeta

← #6459843

Subgroups — #6459843

Order 512.

1832 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35532C211yesmaximal, characteristic
2#35519C211yesmaximal, characteristic
3#28788C212yesmaximal, complemented
4#28783C212yesmaximal, complemented
5#28782C212yesmaximal, complemented
6#28781C212yesmaximal, complemented
7#28780C212yesmaximal, complemented
8#28776C212yesmaximal, complemented
9#28774C212yesmaximal, complemented
10#28771C212yesmaximal, complemented
11#23662C211yesmaximal, characteristic, complemented
12C2×#2084C211yesmaximal, characteristic, complemented
13#23556C211yesmaximal, characteristic, complemented
14#23551C211yesmaximal, characteristic, complemented
15#21326C211yesmaximal, characteristic, complemented
16#21322C211yesmaximal, characteristic, complemented
17#21159C211yesmaximal, characteristic, complemented
18#21155C211yesmaximal, characteristic, complemented
19#20849C211yesmaximal, characteristic
20#20848C211yesmaximal, characteristic
21#20662C211yesmaximal, characteristic
22#20387C211yesmaximal, characteristic
23#20348C211yesmaximal, characteristic
24C22×#131C2211yescharacteristic
25C2×#544C2211yescharacteristic
26C2×#533C2211yescharacteristic
27C2×#520C2211yescharacteristic
28C2×#520C2211yescharacteristic
29C2×#428C2211yescharacteristic
30C2×#428C2211yescharacteristic
31C2×#427C2211yescharacteristic
32C2×#427C2211yescharacteristic
33C22×#106C2211yescharacteristic
34C22×#106C2211yescharacteristic
35C2×#408C2211yescharacteristic
36C2×#405C2211yescharacteristic
37C2×C4×M16C2211yescharacteristic
38#2582—21no—
39#2581—21no—
40#2580—21no—
41#2567—21no—
42#2566—21no—
43#2565—21no—
44#2542—21no—
45#2538—21no—
46#2450—22no—
47#2449—22no—
48#2449—22no—
49#2449—22no—
50#2442C2212yes—
51#2441C2212yes—
52#2441C2212yes—
53#2441C2212yes—
54#2440C2212yes—
55#2440C2212yes—
56#2440C2212yes—
57#2439C2212yes—
58#2317C2211yescharacteristic
59#2317C2211yescharacteristic
60#2317C2211yescharacteristic
61#2311C2211yescharacteristic
62#2311C2211yescharacteristic
63#2297C2211yescharacteristic
64#2296C2211yescharacteristic
65C2×#389C2211yescharacteristic
66C2×#384C2211yescharacteristic
67#2085C2212yes—
68#2085C2212yes—
69#2084C2212yes—
70#2084C2212yes—
71#2084C2212yes—
72#2084C2212yes—
73#2084C2212yes—
74#2083C2212yes—
75#2059C2212yes—
76#2059C2212yes—
77#2059C2211yescharacteristic
78#2059C2211yescharacteristic
79#2059C2211yescharacteristic
80#2059C2211yescharacteristic
81#2058C2212yes—
82#2058C2212yes—
83#2058C2211yescharacteristic
84#2058C2211yescharacteristic
85#2057C2211yescharacteristic
86#2057C2211yescharacteristic
87#1993C2212yes—
88#1992C2212yes—
89#1992C2212yes—
90#1992C2212yes—
91#1991C2212yes—
92#1990C2212yes—
93#1990C2212yes—
94#1990C2212yes—
95#1944C2212yes—
96#1943C2212yes—
97#1943C2212yes—
98#1943C2212yes—
99#1942C2212yes—
100#1941C2212yes—
101#1941C2212yes—
102#1941C2212yes—
103#1854C2212yes—
104#1854C2212yes—
105#1854C2212yes—
106#1854C2212yes—
107#1853C2212yes—
108#1853C2212yes—
109#1853C2212yes—
110#1852C2212yes—
111#1809C2212yes—
112#1809C2212yes—
113#1807C2212yes—
114#1807C2212yes—
115#1753C2212yes—
116#1753C2212yes—
117#1752C2212yes—
118C8×C22⋊C4C2212yes—
119#1736C2211yescharacteristic
120#1736C2211yescharacteristic
121#1736C2211yescharacteristic
122#1736C2211yescharacteristic
123#1736C2211yescharacteristic
124#1736C2212yes—
125#1736C2212yes—
126#1736C2211yescharacteristic
127#1735C2211yescharacteristic
128#1735C2211yescharacteristic
129#1735C2212yes—
130C2×#340C2211yescharacteristic
131C2×#340C2212yes—
132C2×#340C2211yescharacteristic
133#1729C2211yescharacteristic
134C2×#336C2211yescharacteristic
135C22×#41C2311yescharacteristic
136C2×#131—42no—
137C2×#131—42no—
138C2×#131Q818yescomplemented
139C22×M16C2311yescharacteristic
140C22×M16C2311yescharacteristic
141C22×M16C2312yes—
142C23×C8C2311yescharacteristic
143C23×C8C2311yescharacteristic
144C23×C8C2312yes—
145#544—24no—
146#544—42no—
147#533—24no—
148#533—42no—
149C2×C4⋊Q8—21no—
150C2×C4⋊Q8C2311yescharacteristic
151C2×C4⋊Q8C2311yescharacteristic
152C2×C4⋊Q8C2312yes—
153C2×#125—21no—
154C2×#125C2311yescharacteristic
155C2×#125C2311yescharacteristic
156C2×#125C2312yes—
157C2×C22⋊Q8—21no—
158C2×C22⋊Q8—21no—
159C2×C22⋊Q8—22no—
160C2×C22⋊Q8—22no—
161C2×C22⋊Q8—22no—
162C2×C22⋊Q8—22no—
163#520—24no—
164#520—24no—
165#520—42no—
166#520—42no—
167C2×C4×Q8—21no—
168C2×C4×Q8—21no—
169C2×C4×Q8—21no—
170C2×C4×Q8—21no—
171C2×C4×D4—21no—
172C2×C4×D4—21no—
173C2×C4×D4—22no—
174C2×C4×D4—22no—
175C2×#117C2311yescharacteristic
176C2×#117C2311yescharacteristic
177C2×#117C2312yes—
178C2×#117C2312yes—
179C2×#117C2311yescharacteristic
180C2×#117C2311yescharacteristic
181C2×#117C2311yescharacteristic
182C22×C4⋊C4—21no—
183C22×C4⋊C4—21no—
184C22×C4⋊C4—21no—
185C22×C4⋊C4C2311yescharacteristic
186C22×C4⋊C4C2311yescharacteristic
187C22×C4⋊C4C2311yescharacteristic
188C22×C4⋊C4C2311yescharacteristic
189C22×C4⋊C4C2312yes—
190C22×C4⋊C4C2312yes—
191C22×C42C2311yescharacteristic
192#428—24no—
193#428—42no—
194#427—24no—
195#427—42no—
196C2×#107C2311yescharacteristic
197C2×#107C2311yescharacteristic
198C2×#107C2312yes—
199C2×#107C2311yescharacteristic
200C2×#107C2311yescharacteristic
201C2×#107C2312yes—
202C2×#106—42no—
203C2×#106—42no—
204C2×#106C2312yes—
205C2×#106C2311yescharacteristic
206C2×#106C2311yescharacteristic
207C2×#106C2312yes—
208C2×#106C2311yescharacteristic
209C2×#106C2311yescharacteristic
210C2×#106C2312yes—
211C2×#106C2312yes—
212C2×#106C2312yes—
213C2×#106C2312yes—
214#408Q818yescomplemented
215C2×C22⋊C8C2312yes—
216C2×C22⋊C8C2312yes—
217#405—42no—
218C4×M16—42no—
219C2×#97C2312yes—
220C2×#97C2312yes—
221C2×C4×C8C2312yes—
222C2×C4×C8C2312yes—
223#400—22no—
224#399—22no—
225#399—22no—
226#399—22no—
227#398—22no—
228#398—22no—
229#398—22no—
230#398—22no—
231#396—22no—
232#396—22no—
233#396—22no—
234#396—22no—
235#395—22no—
236#395—22no—
237#395—22no—
238#393—22no—
239#391—21no—
240#391—21no—
241#391—22no—
242#391D411yescharacteristic
243#391D411yescharacteristic
244#390—21no—
245#390—21no—
246#390D411yescharacteristic
247#390D411yescharacteristic
248#389—21no—
249#389—21no—
250#389—21no—
251#389—21no—
252#389—22no—
253#389—22no—
254#389—22no—
255#389C2311yescharacteristic
256#389C2311yescharacteristic
257#389C2312yes—
258#389C2312yes—
259#389C2311yescharacteristic
260#389C2311yescharacteristic
261#389C2312yes—
262#389C2312yes—
263#389C2312yes—
264#389C2312yes—
265#387—22no—
266#387—22no—
267#387—22no—
268#387—22no—
269#386—22no—
270#386—22no—
271#386D412yes—
272#386D412yes—
273#385—21no—
274#385—21no—
275#385—22no—
276#385—22no—
277#385—22no—
278#385—22no—
279#385—22no—
280#385—22no—
281#385—22no—
282#384—21no—
283#384—21no—
284#384—21no—
285#384—21no—
286#384C2312yes—
287#384C2312yes—
288#384C2312yes—
289#382—21no—
290#382—21no—
291#382C2312yes—
292#380—22no—
293#380C2312yes—
294#380C2312yes—
295#380C2312yes—
296#380C2312yes—
297C4×C4⋊C4—21no—
298C4×C4⋊C4—21no—
299C4×C22⋊C4C2312yes—
300C4×C22⋊C4C2312yes—
301C2×#95—21no—
302#340C2311yescharacteristic
303#340C2311yescharacteristic
304#340C2311yescharacteristic
305#340C2311yescharacteristic
306#340C2311yescharacteristic
307#340C2311yescharacteristic
308#340C2312yes—
309#340C2311yescharacteristic
310#340C2312yes—
311#340C2311yescharacteristic
312#340C2312yes—
313#340C2312yes—
314#340C2312yes—
315#340C2312yes—
316#340C2312yes—
317#340C2312yes—
318#340C2312yes—
319#340C2312yes—
320#340C2312yes—
321#340C2312yes—
322#340C2312yes—
323#340C2312yes—
324#340C2312yes—
325#340C2312yes—
326#336C2311yescharacteristic
327#336C2311yescharacteristic
328#336C2312yes—
329#336C2312yes—
330#336C2311yescharacteristic
331#336C2311yescharacteristic
332C2×#41—22no—
333C2×#41—22no—
334C2×#41—22no—
335C2×#41—22no—
336C2×#41C2×Q814yes—
337C2×#41C2×Q814yes—
338C22×Q8—21no—
339C22×Q8—21no—
340C22×Q8—22no—
341C22×Q8C2×D411yescharacteristic
342C22×D4C2×D412yes—
343C22×D4C2×D411yescharacteristic
344C23×C4—21no—
345C23×C4—21no—
346C23×C4—21no—
347C23×C4—21no—
348C23×C4—22no—
349C23×C4—22no—
350C23×C4C2×D411yescharacteristic
351C23×C4C2×D411yescharacteristic
352C23×C4C2412yes—
353C23×C4C2411yescharacteristic
354#131—416no—
355C2×M16—22no—
356C2×M16—22no—
357C2×M16—22no—
358C2×M16—22no—
359C2×M16—42no—
360C2×M16—42no—
361C2×M16C2×Q814yes—
362C2×M16C2×Q814yes—
363C2×M16C2×Q818yes—
364C22×C8—22no—
365C22×C8—22no—
366C22×C8—22no—
367C22×C8—22no—
368C22×C8—42no—
369C22×C8—42no—
370C22×C8C2×Q814yes—
371C22×C8C2×Q814yes—
372C22×C8C2×Q818yes—
373C22×C8C2411yescharacteristic
374C22×C8C2411yescharacteristic
375C22×C8C2412yes—
376C22×C8C2411yescharacteristic
377C22×C8C2411yescharacteristic
378C22×C8C2412yes—
379C4⋊Q8—22no—
380C4⋊Q8—22no—
381C4⋊Q8—24no—
382C4⋊Q8—41no—
383C4⋊Q8—41no—
384C4⋊Q8—42no—
385C4⋊Q8—44no—
386#125—22no—
387#125—22no—
388#125—24no—
389#125—41no—
390#125—41no—
391#125—42no—
392#125—44no—
393C22⋊Q8—48no—
394C22⋊Q8—44no—
395C22⋊Q8—44no—
396C22⋊Q8—84no—
397C22⋊Q8—84no—
398C22⋊Q8—84no—
399C4×Q8—44no—
400C4×Q8—44no—
401C4×Q8—44no—
402C4×Q8—44no—
403C4×D4—44no—
404C4×D4—44no—
405C4×D4—48no—
406C4×D4—48no—
407#117—22no—
408#117—22no—
409#117—22no—
410#117—22no—
411#117—22no—
412#117—22no—
413#117—22no—
414#117—22no—
415#117—24no—
416#117—24no—
417#117—42no—
418#117—42no—
419#117#4114yes—
420#117#4114yes—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—24no—
430C2×C4⋊C4—24no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—42no—
463C2×C4⋊C4—42no—
464C2×C4⋊C4—82no—
465C2×C4⋊C4—82no—
466C2×C4⋊C4—82no—
467C2×C4⋊C4C2×D411yescharacteristic
468C2×C4⋊C4C2×D411yescharacteristic
469C2×C4⋊C4C2412yes—
470C2×C4⋊C4C2412yes—
471C2×C4⋊C4C2412yes—
472C2×C4⋊C4C2412yes—
473C2×C4⋊C4C2411yescharacteristic
474C2×C4⋊C4C2411yescharacteristic
475C2×C4⋊C4C2411yescharacteristic
476C2×C4⋊C4C2411yescharacteristic
477C2×C4⋊C4C2411yescharacteristic
478C2×C4⋊C4C2411yescharacteristic
479C2×C4⋊C4C2411yescharacteristic
480C2×C4⋊C4C2411yescharacteristic
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4C2×D412yes—
492C2×C22⋊C4C2×D412yes—
493C2×C22⋊C4C2×D412yes—
494C2×C22⋊C4C2×D412yes—
495C2×C22⋊C4C2×D412yes—
496C2×C42—21no—
497C2×C42—21no—
498C2×C42—22no—
499C2×C42—22no—
500C2×C42—22no—
501C2×C42—22no—
502C2×C42—21no—
503C2×C42—21no—
504C2×C42C2×D411yescharacteristic
505C2×C42C2×D411yescharacteristic
506C2×C42C2412yes—
507C2×C42C2411yescharacteristic
508C2×C42C2411yescharacteristic
509#107—22no—
510#107—22no—
511#107—24no—
512#107—41no—
513#107—41no—
514#107—42no—
515#106—22no—
516#106—22no—
517#106—24no—
518#106—42no—
519#106—42no—
520#106—42no—
521#106—42no—
522#106—41no—
523#106—41no—
524#106—42no—
525C22⋊C8C2×Q818yes—
526C22⋊C8C2×Q818yes—
527#97—42no—
528#97—42no—
529C4×C8—42no—
530C4×C8—42no—
531#95—22no—
532#95—22no—
533#95—21no—
534#95—21no—
535#95—21no—
536#95—21no—
537#95—22no—
538#95—22no—
539#95—22no—
540#95—22no—
541#95—22no—
542#95—22no—
543#95—22no—
544#95—22no—
545#95—22no—
546#95—22no—
547#95C2×D412yes—
548#95C2×D412yes—
549#95C2×D412yes—
550#95C2×D412yes—
551C24C22×D412yes—
552C24C22×D411yescharacteristic
553#41—28no—
554#41—28no—
555#41—28no—
556#41—28no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—42no—
560C2×Q8—42no—
561C2×Q8—44no—
562C2×Q8—42no—
563C2×Q8—42no—
564C2×Q8—81no—
565C2×Q8—81no—
566C2×Q8—82no—
567C2×Q8—82no—
568C2×Q8C4⋊Q814yes—
569C2×D4—24no—
570C2×D4—24no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4C4⋊Q818yes—
574C2×D4C4⋊Q814yes—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—21no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—41no—
596C22×C4—41no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—81no—
604C22×C4—81no—
605C22×C4—81no—
606C22×C4—81no—
607C22×C4—81no—
608C22×C4—81no—
609C22×C4—81no—
610C22×C4—82no—
611C22×C4—82no—
612C22×C4—82no—
613C22×C4—82no—
614C22×C4—81no—
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D412yes—
617C22×C4C22×D412yes—
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D412yes—
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D411yescharacteristic
623C22×C4C22×Q814yes—
624C22×C4C22×Q814yes—
625C22×C4C22×Q812yes—
626C22×C4C22×Q812yes—
627C22×C4C2×#4112yes—
628C22×C4C2×#4112yes—
629C22×C4H(5,𝔽2)12yes—
630C22×C4H(5,𝔽2)12yes—
631C22×C4C2511yescharacteristic
632M16—28no—
633M16—28no—
634M16—48no—
635C2×C8—28no—
636C2×C8—28no—
637C2×C8—21no—
638C2×C8—22no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—48no—
650C2×C8C22×Q812yes—
651C2×C8C22×Q812yes—
652C2×C8C22×Q814yes—
653C2×C8C22×Q812yes—
654C2×C8C22×Q812yes—
655C2×C8C22×Q814yes—
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—22no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—22no—
666C4⋊C4—22no—
667C4⋊C4—22no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—22no—
671C4⋊C4—21no—
672C4⋊C4—22no—
673C4⋊C4—22no—
674C4⋊C4—21no—
675C4⋊C4—22no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—44no—
679C4⋊C4—44no—
680C4⋊C4—42no—
681C4⋊C4—42no—
682C4⋊C4—42no—
683C4⋊C4—42no—
684C4⋊C4—42no—
685C4⋊C4—42no—
686C4⋊C4—44no—
687C4⋊C4—44no—
688C4⋊C4—44no—
689C4⋊C4—42no—
690C4⋊C4—44no—
691C4⋊C4—42no—
692C4⋊C4—42no—
693C4⋊C4—42no—
694C4⋊C4—42no—
695C4⋊C4—42no—
696C4⋊C4—42no—
697C4⋊C4—44no—
698C4⋊C4—44no—
699C4⋊C4—42no—
700C4⋊C4—82no—
701C4⋊C4—82no—
702C4⋊C4—82no—
703C4⋊C4—82no—
704C4⋊C4—82no—
705C4⋊C4—82no—
706C4⋊C4—82no—
707C4⋊C4—82no—
708C4⋊C4—82no—
709C4⋊C4C2×#4112yes—
710C4⋊C4C2×#4112yes—
711C4⋊C4C2×#4112yes—
712C4⋊C4C2×#4112yes—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—24no—
716C22⋊C4—24no—
717C22⋊C4—24no—
718C22⋊C4—42no—
719C22⋊C4—42no—
720C22⋊C4—44no—
721C22⋊C4—44no—
722C22⋊C4—42no—
723C22⋊C4—42no—
724C22⋊C4—82no—
725C22⋊C4—82no—
726C22⋊C4—82no—
727C22⋊C4—82no—
728C42—22no—
729C42—22no—
730C42—24no—
731C42—24no—
732C42—21no—
733C42—21no—
734C42—22no—
735C42—21no—
736C42—22no—
737C42—21no—
738C42—44no—
739C42—44no—
740C42—42no—
741C42—42no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23C2×C4⋊Q814yes—
753C23C2×C4⋊Q812yes—
754C23#54612yes—
755C23#54612yes—
756C23C23×D411yescharacteristic
757Q8—28no—
758Q8—84no—
759Q8—84no—
760Q8—164no—
761D4—216no—
762D4—28no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—21no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—41no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—84no—
824C2×C4—164no—
825C2×C4—164no—
826C2×C4—162no—
827C2×C4—162no—
828C2×C4—162no—
829C2×C4C2×C4⋊Q814yes—
830C2×C4C2×C4⋊Q812yes—
831C2×C4#53314yes—
832C2×C4#54314yes—
833C2×C4#54612yes—
834C2×C4#54612yes—
835C2×C4#55414yes—
836C2×C4#55414yes—
837C2×C4#57712yes—
838C2×C4#57712yes—
839C2×C4C23×Q811yescharacteristic
840C2×C4C23×Q811yescharacteristic
841C2×C4C22×#4111yescharacteristic
842C2×C4C22×#4111yescharacteristic
843C2×C4C2×H(5,𝔽2)11yescharacteristic
844C2×C4C2×H(5,𝔽2)11yescharacteristic
845C8—22no—
846C8—22no—
847C8—24no—
848C8—22no—
849C8—22no—
850C8—24no—
851C22—22no—
852C22—22no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—24no—
858C22—24no—
859C22—24no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22#254914yes—
865C22C22×C4⋊Q811yescharacteristic
866C22C2×#54611yescharacteristic
867C22C2×#54611yescharacteristic
868C22C2×#57711yescharacteristic
869C22C2×#57711yescharacteristic
870C22#358511yescharacteristic
871C22#358611yescharacteristic
872C4—24no—
873C4—22no—
874C4—22no—
875C4—41no—
876C4—42no—
877C4—41no—
878C4—42no—
879C4—42no—
880C4—42no—
881C4—42no—
882C4—42no—
883C4—81no—
884C4—82no—
885C4—81no—
886C4—81no—
887C4—81no—
888C4—82no—
889C4—82no—
890C4—82no—
891C4#254914yes—
892C4C2×#53311yescharacteristic
893C4C2×#54311yescharacteristic
894C4C2×#55411yescharacteristic
895C4C2×#55411yescharacteristic
896C2—24no—
897C2—44no—
898C2C2×#254911yescharacteristic
899C2#6066511yescharacteristic
900C2#6066811yescharacteristic
901C2#6119211yescharacteristic
902C2#6119311yescharacteristic
903C2#6120611yescharacteristic
904C2#6120911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#41C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2297 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #28788C2semidirect
4. #28783C2semidirect
5. #28782C2semidirect
6. #28781C2semidirect
7. #28780C2semidirect
8. #28776C2semidirect
9. #28774C2semidirect
10. #28771C2semidirect
11. #23662C2semidirect
12. C2×#2084C2semidirect
13. #23556C2semidirect
14. #23551C2semidirect
15. #21326C2semidirect
16. #21322C2semidirect
17. #21159C2semidirect
18. #21155C2semidirect
138. C2×#131Q8semidirect
214. #408Q8semidirect

Maximal subgroups

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

subgroupindex
#355322
#355192
#287882
#287832
#287822
#287812
#287802
#287762
#287742
#287712
#236622
C2×#20842
#235562
#235512
#213262
#213222
#211592
#211552
#208492
#208482
#206622
#203872
#203482