Finite Group Databasebeta

← #7508716

Subgroups — #7508716

Order 512.

1760 conjugacy classes of subgroups.

The subgroup lattice has 927 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35517C211yesmaximal, characteristic
2#35289C211yesmaximal, characteristic
3#32277C212yesmaximal, complemented
4#32276C212yesmaximal, complemented
5#32271C212yesmaximal, complemented
6#32268C212yesmaximal, complemented
7#32267C212yesmaximal, complemented
8#32266C212yesmaximal, complemented
9#32261C212yesmaximal, complemented
10#32258C212yesmaximal, complemented
11#23643C211yesmaximal, characteristic, complemented
12#23643C211yesmaximal, characteristic, complemented
13#23641C211yesmaximal, characteristic, complemented
14#23639C211yesmaximal, characteristic, complemented
15#23552C211yesmaximal, characteristic, complemented
16C2×#2057C211yesmaximal, characteristic, complemented
17#21034C211yesmaximal, characteristic, complemented
18#21032C211yesmaximal, characteristic, complemented
19#20900C211yesmaximal, characteristic
20#20847C211yesmaximal, characteristic, complemented
21#20847C211yesmaximal, characteristic, complemented
22#20664C211yesmaximal, characteristic, complemented
23#20663C211yesmaximal, characteristic, complemented
24C22×#131C2211yescharacteristic
25C2×#532C2211yescharacteristic
26C22×C4⋊Q8C2211yescharacteristic
27C2×#520C2211yescharacteristic
28C2×#428C2211yescharacteristic
29C2×#428C2211yescharacteristic
30C2×#428C2211yescharacteristic
31C2×#427C2211yescharacteristic
32C22×#107C2211yescharacteristic
33C22×#107C2211yescharacteristic
34C2×#408C2211yescharacteristic
35C2×#408C2211yescharacteristic
36C2×#408C2211yescharacteristic
37#2862—21no—
38#2858—21no—
39#2640—21no—
40#2640—21no—
41#2563C2212yes—
42#2563C2212yes—
43#2547C2212yes—
44#2547C2212yes—
45#2504—22no—
46#2487C2212yes—
47#2486C2212yes—
48#2485C2212yes—
49#2485C2212yes—
50#2448—21no—
51#2447—21no—
52#2446—21no—
53#2445—21no—
54#2444—22no—
55#2443—22no—
56#2436—22no—
57#2311C2211yescharacteristic
58#2311C2211yescharacteristic
59#2311C2211yescharacteristic
60#2311C2211yescharacteristic
61#2311C2211yescharacteristic
62#2311C2211yescharacteristic
63#2311C2211yescharacteristic
64#2296C2211yescharacteristic
65C2×#389C2211yescharacteristic
66C4×#117C2211yescharacteristic
67#2077C2212yes—
68#2077C2212yes—
69#2077C2212yes—
70#2077C2212yes—
71#2077C2212yes—
72#2077C2212yes—
73#2076C2212yes—
74#2076C2212yes—
75#2076C2212yes—
76#2076C2212yes—
77#2076C2212yes—
78#2075C2212yes—
79#2075C2212yes—
80#2075C2212yes—
81#2075C2212yes—
82#2075C2212yes—
83#2058C2212yes—
84#2058C2212yes—
85#2057C2212yes—
86#2057C2212yes—
87#2057C2212yes—
88#2057C2212yes—
89#2057C2212yes—
90#2057C2212yes—
91#1921C2211yescharacteristic
92#1921C2212yes—
93#1921C2211yescharacteristic
94#1920C2212yes—
95#1920C2211yescharacteristic
96#1920C2211yescharacteristic
97#1919C2212yes—
98#1919C2211yescharacteristic
99#1919C2211yescharacteristic
100#1918C2211yescharacteristic
101#1918C2212yes—
102#1918C2211yescharacteristic
103#1870C2212yes—
104#1870C2212yes—
105#1869C2212yes—
106#1869C2212yes—
107#1854C2212yes—
108#1854C2212yes—
109#1854C2212yes—
110#1854C2212yes—
111#1852C2212yes—
112#1852C2212yes—
113#1852C2212yes—
114#1852C2212yes—
115#1809C2212yes—
116#1809C2212yes—
117#1809C2212yes—
118#1809C2212yes—
119#1808C2212yes—
120#1808C2212yes—
121#1808C2212yes—
122#1807C2212yes—
123#1736C2211yescharacteristic
124#1736C2211yescharacteristic
125#1736C2211yescharacteristic
126#1736C2211yescharacteristic
127#1736C2211yescharacteristic
128#1735C2211yescharacteristic
129#1735C2211yescharacteristic
130#1735C2211yescharacteristic
131C2×#340C2211yescharacteristic
132C2×#340C2211yescharacteristic
133#1728C2211yescharacteristic
134C2×#336C2211yescharacteristic
135C22×#41C2311yescharacteristic
136C22×#41C2311yescharacteristic
137C23×Q8—21no—
138C2×#131—24no—
139C2×#131—24no—
140C2×#131—42no—
141C22×M16C2311yescharacteristic
142C22×M16C2312yes—
143C22×M16C2311yescharacteristic
144C23×C8C2311yescharacteristic
145C23×C8C2312yes—
146C23×C8C2311yescharacteristic
147#532—42no—
148#532—42no—
149C2×C4⋊Q8—21no—
150C2×C4⋊Q8—21no—
151C2×C4⋊Q8—42no—
152C2×C4⋊Q8—42no—
153C2×C4⋊Q8D411yescharacteristic
154C2×C4⋊Q8C2312yes—
155C2×C4⋊Q8C2312yes—
156C2×#127D411yescharacteristic
157C2×#124—22no—
158C2×#124—22no—
159C2×#124D411yescharacteristic
160C2×#124D411yescharacteristic
161C2×#123—22no—
162C2×#121D412yes—
163C2×#121D412yes—
164#520—42no—
165#520—42no—
166C2×C4×Q8—21no—
167C2×C4×D4—22no—
168C2×C4×D4—21no—
169C2×C4×D4C2312yes—
170C2×C4×D4C2312yes—
171C2×#117C2311yescharacteristic
172C2×#117C2311yescharacteristic
173C2×#117C2311yescharacteristic
174C2×#117C2311yescharacteristic
175C2×#117C2312yes—
176C22×C4⋊C4—21no—
177C22×C4⋊C4—21no—
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2311yescharacteristic
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2311yescharacteristic
182C22×C4⋊C4C2312yes—
183C22×C42C2311yescharacteristic
184#428—24no—
185#428—42no—
186#428—42no—
187#427—24no—
188C2×#107—42no—
189C2×#107—42no—
190C2×#107C2311yescharacteristic
191C2×#107C2311yescharacteristic
192C2×#107C2312yes—
193C2×#107C2312yes—
194C2×#107C2312yes—
195C2×#107C2312yes—
196C2×#107C2312yes—
197C2×#107C2312yes—
198C2×#107C2312yes—
199C2×#106C2312yes—
200C2×#106C2311yescharacteristic
201C2×#106C2311yescharacteristic
202C2×#106C2312yes—
203C2×#106C2312yes—
204#408—24no—
205#408—24no—
206#408—42no—
207C2×C22⋊C8C2312yes—
208C2×C22⋊C8C2312yes—
209C2×C22⋊C8C2312yes—
210C2×C22⋊C8C2312yes—
211C2×C22⋊C8C2312yes—
212C2×C22⋊C8C2312yes—
213#400—22no—
214#399—22no—
215#398—22no—
216#397—22no—
217#397—22no—
218#397—22no—
219#397—22no—
220#397—22no—
221#397—22no—
222#397—22no—
223#394—22no—
224#394—22no—
225#393—22no—
226#393—22no—
227#393—22no—
228#393—22no—
229#391—21no—
230#391—21no—
231#391—21no—
232#391—21no—
233#391—21no—
234#391—21no—
235#391—21no—
236#391—22no—
237#391—22no—
238#390—22no—
239#390—22no—
240#390—21no—
241#390—21no—
242#390—21no—
243#390—21no—
244#390—21no—
245#390—21no—
246#390—21no—
247#389—21no—
248#389—21no—
249#389C2312yes—
250#389C2311yescharacteristic
251#389C2312yes—
252#389C2311yescharacteristic
253#389C2311yescharacteristic
254#389C2311yescharacteristic
255#388—22no—
256#388—22no—
257#387—22no—
258#387—22no—
259#386—22no—
260#386—22no—
261#386—22no—
262#386—22no—
263#386—22no—
264#386—22no—
265#386—22no—
266#386—22no—
267#385—21no—
268#385—21no—
269#385—22no—
270#382—22no—
271#382—22no—
272#381—22no—
273#380C2312yes—
274#380C2312yes—
275#380C2312yes—
276#380C2312yes—
277#380C2312yes—
278#380C2312yes—
279#380C2312yes—
280#380C2312yes—
281#380C2312yes—
282#380C2312yes—
283#380C2312yes—
284#380C2312yes—
285#380C2312yes—
286#380C2312yes—
287C4×C4⋊C4—21no—
288C4×C4⋊C4—21no—
289C4×C4⋊C4C2311yescharacteristic
290C4×C4⋊C4C2311yescharacteristic
291C4×C4⋊C4C2311yescharacteristic
292C4×C4⋊C4C2311yescharacteristic
293C4×C22⋊C4—21no—
294C4×C22⋊C4—21no—
295#376—21no—
296C2×#95—21no—
297C43—21no—
298#340C2312yes—
299#340C2312yes—
300#340C2312yes—
301#340C2312yes—
302#340C2312yes—
303#340C2312yes—
304#340C2312yes—
305#340C2312yes—
306#340C2311yescharacteristic
307#340C2311yescharacteristic
308#340C2312yes—
309#340C2312yes—
310#340C2311yescharacteristic
311#340C2311yescharacteristic
312#340C2311yescharacteristic
313#340C2312yes—
314#340C2311yescharacteristic
315#340C2311yescharacteristic
316#340C2312yes—
317#340C2312yes—
318#340C2311yescharacteristic
319#340C2311yescharacteristic
320#340C2312yes—
321#340C2311yescharacteristic
322#340C2311yescharacteristic
323#340C2311yescharacteristic
324#336C2311yescharacteristic
325#336C2311yescharacteristic
326#336C2311yescharacteristic
327#336C2311yescharacteristic
328#336C2312yes—
329#336C2312yes—
330C2×#41—22no—
331C2×#41—22no—
332C2×#41—22no—
333C2×#41—22no—
334C2×#41—22no—
335C2×#41—22no—
336C2×#41—22no—
337C2×#41—22no—
338C2×#41—22no—
339C2×#41—22no—
340C2×#41—22no—
341C2×#41—22no—
342C22×Q8—22no—
343C22×Q8—22no—
344C22×Q8—44no—
345C22×Q8—82no—
346C22×Q8—82no—
347C22×Q8C2×D411yescharacteristic
348C22×Q8C2×D411yescharacteristic
349C22×D4C2×D412yes—
350C22×D4C2×D411yescharacteristic
351C22×D4C2×D412yes—
352C22×D4C2×D411yescharacteristic
353C22×D4C2×D412yes—
354C22×D4C2×D412yes—
355C23×C4—21no—
356C23×C4—21no—
357C23×C4—21no—
358C23×C4—21no—
359C23×C4—22no—
360C23×C4C2×D411yescharacteristic
361C23×C4C2×D411yescharacteristic
362C23×C4C2412yes—
363C23×C4C2412yes—
364C23×C4C2411yescharacteristic
365#131—416no—
366C2×M16—22no—
367C2×M16—22no—
368C2×M16—22no—
369C2×M16—22no—
370C2×M16—22no—
371C2×M16—24no—
372C2×M16—24no—
373C2×M16—42no—
374C2×M16#4114yes—
375C22×C8—22no—
376C22×C8—22no—
377C22×C8—22no—
378C22×C8—22no—
379C22×C8—22no—
380C22×C8—24no—
381C22×C8—24no—
382C22×C8—42no—
383C22×C8#4114yes—
384C22×C8C2411yescharacteristic
385C22×C8C2411yescharacteristic
386C22×C8C2412yes—
387C22×C8C2411yescharacteristic
388C22×C8C2412yes—
389C22×C8C2411yescharacteristic
390C4⋊Q8—42no—
391C4⋊Q8—42no—
392C4⋊Q8—42no—
393C4⋊Q8—42no—
394C4⋊Q8—42no—
395C4⋊Q8—44no—
396C4⋊Q8—44no—
397#127—42no—
398#124—42no—
399#124—42no—
400#124—84no—
401#124—84no—
402#123—84no—
403#121—44no—
404#121—44no—
405C4×Q8—44no—
406C4×D4—42no—
407C4×D4—42no—
408C4×D4—42no—
409C4×D4—42no—
410C4×D4—48no—
411C4×D4—44no—
412#117—22no—
413#117—22no—
414#117—22no—
415#117—22no—
416#117—22no—
417#117—22no—
418#117—22no—
419#117—22no—
420#117—42no—
421#117—42no—
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—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—42no—
444C2×C4⋊C4—42no—
445C2×C4⋊C4—44no—
446C2×C4⋊C4—82no—
447C2×C4⋊C4C2×D412yes—
448C2×C4⋊C4C2×D412yes—
449C2×C4⋊C4C2412yes—
450C2×C4⋊C4C2411yescharacteristic
451C2×C4⋊C4C2412yes—
452C2×C4⋊C4C2412yes—
453C2×C4⋊C4C2412yes—
454C2×C4⋊C4C2411yescharacteristic
455C2×C4⋊C4C2411yescharacteristic
456C2×C4⋊C4C2411yescharacteristic
457C2×C4⋊C4C2411yescharacteristic
458C2×C4⋊C4C2411yescharacteristic
459C2×C4⋊C4C2411yescharacteristic
460C2×C4⋊C4C2411yescharacteristic
461C2×C22⋊C4—21no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4C2×D412yes—
481C2×C22⋊C4C2×D412yes—
482C2×C22⋊C4C2×D412yes—
483C2×C22⋊C4C2×D412yes—
484C2×C42—22no—
485C2×C42—22no—
486C2×C42—21no—
487C2×C42—22no—
488C2×C42—21no—
489C2×C42—21no—
490C2×C42—21no—
491C2×C42—21no—
492C2×C42—21no—
493C2×C42—21no—
494C2×C42—21no—
495C2×C42C2×D411yescharacteristic
496C2×C42C2×D411yescharacteristic
497C2×C42C2411yescharacteristic
498C2×C42C2411yescharacteristic
499#107—22no—
500#107—22no—
501#107—24no—
502#107—42no—
503#107—42no—
504#107—42no—
505#107—42no—
506#107—42no—
507#107—42no—
508#106—22no—
509#106—22no—
510#106—24no—
511#106—42no—
512#106—42no—
513C22⋊C8—24no—
514C22⋊C8—24no—
515C22⋊C8—24no—
516C22⋊C8—24no—
517C22⋊C8—42no—
518C22⋊C8—42no—
519#95—22no—
520#95—22no—
521#95—21no—
522#95—21no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95—21no—
527#95—21no—
528#95—21no—
529#95—22no—
530#95—22no—
531#95—22no—
532#95—22no—
533#95—22no—
534#95—22no—
535#95—22no—
536#95—22no—
537#95—22no—
538#95—22no—
539#95—22no—
540#95—22no—
541#95—22no—
542#95—22no—
543C24C22×D412yes—
544C24C22×D412yes—
545C24C22×D411yescharacteristic
546#41—44no—
547#41—44no—
548#41—44no—
549#41—44no—
550#41—44no—
551#41—44no—
552#41—44no—
553#41—44no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—44no—
561C2×Q8—44no—
562C2×Q8—44no—
563C2×Q8—44no—
564C2×Q8—82no—
565C2×Q8—82no—
566C2×Q8—816no—
567C2×D4—24no—
568C2×D4—24no—
569C2×D4—24no—
570C2×D4—24no—
571C2×D4—24no—
572C2×D4—24no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—24no—
580C2×D4—24no—
581C2×D4—42no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—42no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—22no—
608C22×C4—21no—
609C22×C4—22no—
610C22×C4—21no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—44no—
619C22×C4—42no—
620C22×C4—81no—
621C22×C4—81no—
622C22×C4—81no—
623C22×C4—81no—
624C22×C4—81no—
625C22×C4—81no—
626C22×C4—81no—
627C22×C4—82no—
628C22×C4—81no—
629C22×C4—82no—
630C22×C4C22×D412yes—
631C22×C4C22×D412yes—
632C22×C4C22×D411yescharacteristic
633C22×C4C22×D411yescharacteristic
634C22×C4C22×D411yescharacteristic
635C22×C4C22×D411yescharacteristic
636C22×C4C22×D411yescharacteristic
637C22×C4C2×#4112yes—
638C22×C4C2×#4112yes—
639C22×C4H(5,𝔽2)12yes—
640C22×C4H(5,𝔽2)12yes—
641C22×C42−1+412yes—
642C22×C42−1+412yes—
643C22×C4C2511yescharacteristic
644M16—28no—
645M16—48no—
646M16—44no—
647C2×C8—28no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—22no—
657C2×C8—22no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—22no—
663C2×C8—48no—
664C2×C8—44no—
665C2×C8C2×#4112yes—
666C2×C8C2×#4114yes—
667C2×C8C2×#4112yes—
668C4⋊C4—21no—
669C4⋊C4—22no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—22no—
678C4⋊C4—22no—
679C4⋊C4—22no—
680C4⋊C4—22no—
681C4⋊C4—22no—
682C4⋊C4—22no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—22no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—42no—
693C4⋊C4—42no—
694C4⋊C4—44no—
695C4⋊C4—44no—
696C4⋊C4—44no—
697C4⋊C4—42no—
698C4⋊C4—42no—
699C4⋊C4—42no—
700C4⋊C4—42no—
701C4⋊C4—44no—
702C4⋊C4—42no—
703C4⋊C4—42no—
704C4⋊C4—81no—
705C4⋊C4—81no—
706C4⋊C4—82no—
707C22⋊C4—42no—
708C22⋊C4—42no—
709C22⋊C4—42no—
710C22⋊C4—42no—
711C22⋊C4—44no—
712C22⋊C4—42no—
713C22⋊C4—42no—
714C22⋊C4—42no—
715C22⋊C4—42no—
716C22⋊C4—82no—
717C22⋊C4—82no—
718C22⋊C4—82no—
719C22⋊C4—82no—
720C22⋊C4—82no—
721C22⋊C4—82no—
722C22⋊C4—82no—
723C22⋊C4—82no—
724C22⋊C4—82no—
725C22⋊C4—82no—
726C22⋊C4—82no—
727C22⋊C4—82no—
728C22⋊C4—82no—
729C22⋊C4—82no—
730C42—22no—
731C42—22no—
732C42—21no—
733C42—21no—
734C42—21no—
735C42—21no—
736C42—42no—
737C42—44no—
738C42—42no—
739C42—42no—
740C42—42no—
741C42—42no—
742C42—42no—
743C42—42no—
744C42—42no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—21no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23#53412yes—
764C23#54712yes—
765C23#54712yes—
766C23C23×D411yescharacteristic
767Q8—44no—
768Q8—44no—
769Q8—88no—
770Q8—88no—
771D4—48no—
772D4—48no—
773D4—44no—
774D4—44no—
775D4—84no—
776D4—84no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—41no—
810C2×C4—41no—
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—42no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—42no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—42no—
831C2×C4—41no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—84no—
840C2×C4—84no—
841C2×C4—84no—
842C2×C4—162no—
843C2×C4—164no—
844C2×C4#53412yes—
845C2×C4#54214yes—
846C2×C4#54214yes—
847C2×C4#54712yes—
848C2×C4#54712yes—
849C2×C4#55114yes—
850C2×C4#56314yes—
851C2×C4#57612yes—
852C2×C4#57812yes—
853C2×C4C22×#4111yescharacteristic
854C2×C4C22×#4111yescharacteristic
855C2×C4C2×H(5,𝔽2)11yescharacteristic
856C2×C4C2×H(5,𝔽2)11yescharacteristic
857C2×C4C2×2−1+411yescharacteristic
858C2×C4C2×2−1+411yescharacteristic
859C8—22no—
860C8—22no—
861C8—24no—
862C8—41no—
863C8—41no—
864C8—42no—
865C22—22no—
866C22—22no—
867C22—22no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—42no—
881C22—42no—
882C22—42no—
883C22—42no—
884C22—42no—
885C22#271714yes—
886C22C2×#53411yescharacteristic
887C22C2×#54711yescharacteristic
888C22C2×#54711yescharacteristic
889C22C2×#57611yescharacteristic
890C22C2×#57811yescharacteristic
891C22#358511yescharacteristic
892C22#358611yescharacteristic
893C4—22no—
894C4—22no—
895C4—41no—
896C4—41no—
897C4—42no—
898C4—42no—
899C4—82no—
900C4—82no—
901C4—82no—
902C4—81no—
903C4—81no—
904C4—81no—
905C4—82no—
906C4—81no—
907C4—81no—
908C4—81no—
909C4—81no—
910C4—81no—
911C4#271714yes—
912C4C2×#54211yescharacteristic
913C4C2×#54211yescharacteristic
914C4C2×#55111yescharacteristic
915C4C2×#56311yescharacteristic
916C2—24no—
917C2—82no—
918C2—82no—
919C2C2×#271711yescharacteristic
920C2#6075611yescharacteristic
921C2#6075911yescharacteristic
922C2#6127811yescharacteristic
923C2#6128211yescharacteristic
924C2#6128711yescharacteristic
925C2#6129411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#532C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#532 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #32277C2semidirect
4. #32276C2semidirect
5. #32271C2semidirect
6. #32268C2semidirect
7. #32267C2semidirect
8. #32266C2semidirect
9. #32261C2semidirect
10. #32258C2semidirect
11. #23643C2semidirect
12. #23643C2semidirect
13. #23641C2semidirect
14. #23639C2semidirect
15. #23552C2semidirect
16. C2×#2057C2semidirect
17. #21034C2semidirect
18. #21032C2semidirect
20. #20847C2semidirect
21. #20847C2semidirect
22. #20664C2semidirect
23. #20663C2semidirect

Maximal subgroups

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

subgroupindex
#355172
#352892
#322772
#322762
#322712
#322682
#322672
#322662
#322612
#322582
#236432
#236412
#236392
#235522
C2×#20572
#210342
#210322
#209002
#208472
#206642
#206632