Finite Group Databasebeta

← #6457458

Subgroups — #6457458

Order 512.

1708 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35644C211yesmaximal, characteristic
2#35544C211yesmaximal, characteristic
3#28084C212yesmaximal, complemented
4#28083C212yesmaximal, complemented
5#28081C212yesmaximal, complemented
6#28078C212yesmaximal, complemented
7#28069C212yesmaximal, complemented
8#28066C212yesmaximal, complemented
9#28064C212yesmaximal, complemented
10#28063C212yesmaximal, complemented
11#23736C211yesmaximal, characteristic, complemented
12#23642C211yesmaximal, characteristic
13#23557C211yesmaximal, characteristic, complemented
14#23481C211yesmaximal, characteristic
15#21326C211yesmaximal, characteristic, complemented
16#21090C211yesmaximal, characteristic, complemented
17#21088C211yesmaximal, characteristic, complemented
18#21066C211yesmaximal, characteristic, complemented
19#21039C211yesmaximal, characteristic, complemented
20C2×#1892C211yesmaximal, characteristic
21#20658C211yesmaximal, characteristic
22#20453C211yesmaximal, characteristic, complemented
23#20385C211yesmaximal, characteristic
24C24×C8C2211yescharacteristic
25C2×#544C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic
27C2×#428C2211yescharacteristic
28C2×#428C2211yescharacteristic
29C2×#427C2211yescharacteristic
30C2×#427C2211yescharacteristic
31C2×#419C2211yescharacteristic
32C2×#419C2211yescharacteristic
33C22×#103C2211yescharacteristic
34C22×#103C2211yescharacteristic
35C2×#407C2211yescharacteristic
36C2×#405C2211yescharacteristic
37C2×#405C2211yescharacteristic
38#2561—22no—
39#2503—22no—
40#2497—21no—
41#2497C2212yes—
42#2496—21no—
43#2496C2212yes—
44#2495—21no—
45#2495C2212yes—
46#2494—21no—
47#2494C2212yes—
48#2493—22no—
49#2492—21no—
50#2492—21no—
51#2492C2212yes—
52#2492C2212yes—
53#2489—21no—
54#2489—21no—
55#2489C2212yes—
56#2489C2212yes—
57#2480—22no—
58#2317C2211yescharacteristic
59#2317C2211yescharacteristic
60#2316C2211yescharacteristic
61#2310C2211yescharacteristic
62#2310C2211yescharacteristic
63#2280C2211yescharacteristic
64#2280C2211yescharacteristic
65#2280C2211yescharacteristic
66C2×#380C2211yescharacteristic
67#2274C2211yescharacteristic
68#2274C2211yescharacteristic
69#2097C2212yescomplemented
70#2097C2212yescomplemented
71#2096C2212yescomplemented
72#2095C2212yescomplemented
73#2077C2212yes—
74#2077C2212yes—
75#2076C2212yes—
76#2075C2212yes—
77#2059C2212yescomplemented
78#2059C2212yescomplemented
79#2058C2212yescomplemented
80#2057C2212yescomplemented
81#2036C2212yes—
82#2036C2212yes—
83#2035C2212yes—
84#2035C2212yes—
85#1993C2212yescomplemented
86#1992C2212yescomplemented
87#1991C2212yescomplemented
88#1990C2212yescomplemented
89#1935C2212yescomplemented
90#1935C2212yescomplemented
91#1935C2212yescomplemented
92#1935C2212yescomplemented
93#1933C2212yescomplemented
94#1933C2212yescomplemented
95#1933C2212yescomplemented
96#1933C2212yescomplemented
97#1928C2212yescomplemented
98#1928C2212yescomplemented
99#1927C2212yescomplemented
100#1927C2212yescomplemented
101#1921C2212yescomplemented
102#1920C2212yescomplemented
103#1919C2212yescomplemented
104#1918C2212yescomplemented
105#1892C2212yes—
106#1892C2212yes—
107#1892C2212yes—
108#1892C2212yes—
109#1808C2211yescharacteristic
110#1808C2211yescharacteristic
111#1808C2211yescharacteristic
112#1808C2211yescharacteristic
113#1807C2211yescharacteristic
114#1807C2211yescharacteristic
115#1807C2211yescharacteristic
116#1807C2211yescharacteristic
117#1776C2212yescomplemented
118#1776C2212yescomplemented
119C4×#107C2212yescomplemented
120C4×#106C2212yescomplemented
121#1752C2212yes—
122#1752C2212yes—
123C8×C22⋊C4C2212yes—
124C8×C22⋊C4C2212yes—
125#1736C2211yescharacteristic
126#1736C2211yescharacteristic
127#1736C2211yescharacteristic
128#1736C2211yescharacteristic
129#1735C2211yescharacteristic
130#1735C2211yescharacteristic
131C2×#340C2211yescharacteristic
132C2×#340C2211yescharacteristic
133#1729C2211yescharacteristic
134#1729C2211yescharacteristic
135C23×Q8C2311yescharacteristic
136C24×C4C2311yescharacteristic
137C22×M16C2311yescharacteristic
138C22×M16C2311yescharacteristic
139C23×C8—24no—
140C23×C8—24no—
141C23×C8—42no—
142C23×C8C2311yescharacteristic
143C23×C8C2311yescharacteristic
144C23×C8C2311yescharacteristic
145C23×C8C2311yescharacteristic
146C23×C8C2311yescharacteristic
147C23×C8C2311yescharacteristic
148#544—24no—
149#544—42no—
150C2×C4⋊Q8—21no—
151C2×C4⋊Q8C2312yes—
152C2×#126—22no—
153C2×#125—21no—
154C2×#125C2312yes—
155C2×C22⋊Q8—21no—
156C2×C22⋊Q8—21no—
157C2×C22⋊Q8—22no—
158C2×C22⋊Q8—24no—
159C2×C22⋊Q8—42no—
160C2×C22⋊Q8C2312yes—
161C2×C22⋊Q8C2312yes—
162C2×#117C2311yescharacteristic
163C2×#117C2311yescharacteristic
164C2×#117C2311yescharacteristic
165C2×#117C2311yescharacteristic
166C2×#117C2311yescharacteristic
167C2×#117C2311yescharacteristic
168C22×C4⋊C4—21no—
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2311yescharacteristic
172C22×C22⋊C4—21no—
173C22×C22⋊C4—21no—
174#428—24no—
175#428—24no—
176#427—24no—
177#427—42no—
178C2×#107C2312yes—
179C2×#107C2311yescharacteristic
180C2×#107C2311yescharacteristic
181C2×#107C2312yes—
182C2×#107C2311yescharacteristic
183C2×#107C2311yescharacteristic
184C2×#106C2312yes—
185C2×#106C2311yescharacteristic
186C2×#106C2311yescharacteristic
187C2×#106C2312yes—
188C2×#106C2311yescharacteristic
189C2×#106C2311yescharacteristic
190#419—24no—
191#419—42no—
192C2×#103—24no—
193C2×#103—24no—
194C2×#103C2312yes—
195C2×#103C2312yes—
196C2×#103C2312yes—
197C2×#103C2312yes—
198C2×#103C2312yes—
199C2×#103C2312yes—
200C2×#103C2312yes—
201C2×#103C2312yes—
202#407—24no—
203C2×C22⋊C8C2312yes—
204C2×C22⋊C8C2312yes—
205#405—24no—
206#405—42no—
207C2×#97C2312yes—
208C2×#97C2312yes—
209C2×C4×C8C2312yes—
210C2×C4×C8C2312yes—
211#401—22no—
212#400—22no—
213#400—22no—
214#400—22no—
215#400—22no—
216#400—22no—
217#400—22no—
218#400—22no—
219#397—22no—
220#397—22no—
221#397—22no—
222#397—22no—
223#397—22no—
224#396—22no—
225#393—22no—
226#393—22no—
227#391—21no—
228#391—21no—
229#391—21no—
230#391—21no—
231#391—22no—
232#391—22no—
233#391C2312yes—
234#391C2312yes—
235#391C2312yes—
236#391C2312yes—
237#389—21no—
238#389—21no—
239#389—21no—
240#389—21no—
241#389C2312yes—
242#389C2312yes—
243#389C2312yes—
244#389C2312yes—
245#388—22no—
246#388—22no—
247#388—22no—
248#388—22no—
249#388—22no—
250#388—22no—
251#388—22no—
252#387—22no—
253#387—22no—
254#387—22no—
255#385—22no—
256#385—22no—
257#384—21no—
258#384C2312yes—
259#383—22no—
260#382—21no—
261#382—22no—
262#382—22no—
263#382C2312yes—
264#381—21no—
265#381—21no—
266#381—22no—
267#381—22no—
268#381D412yes—
269#380—21no—
270#380—21no—
271#380—22no—
272#380D411yescharacteristic
273#380D411yescharacteristic
274#380D411yescharacteristic
275#380D411yescharacteristic
276#380C2311yescharacteristic
277#380C2311yescharacteristic
278#380C2311yescharacteristic
279#380C2311yescharacteristic
280#380C2311yescharacteristic
281#380C2311yescharacteristic
282#380C2311yescharacteristic
283#380C2311yescharacteristic
284#380C2312yes—
285#380C2312yes—
286#379—21no—
287#379—21no—
288#379D412yes—
289C4×C4⋊C4—21no—
290C4×C4⋊C4—21no—
291C4×C4⋊C4—21no—
292C4×C4⋊C4—21no—
293C4×C4⋊C4C2312yes—
294C4×C4⋊C4C2312yes—
295C4×C4⋊C4C2312yes—
296C4×C4⋊C4C2312yes—
297C4×C22⋊C4—21no—
298C4×C22⋊C4—21no—
299C4×C22⋊C4—21no—
300C4×C22⋊C4—21no—
301C4×C22⋊C4—22no—
302C4×C22⋊C4—22no—
303C4×C22⋊C4C2312yes—
304C4×C22⋊C4C2312yes—
305C2×#95—21no—
306#340C2312yes—
307#340C2312yes—
308#340C2312yes—
309#340C2312yes—
310#340C2311yescharacteristic
311#340C2311yescharacteristic
312#340C2311yescharacteristic
313#340C2311yescharacteristic
314#340C2311yescharacteristic
315#340C2311yescharacteristic
316#340C2311yescharacteristic
317#340C2311yescharacteristic
318#340C2312yes—
319#340C2312yes—
320#340C2312yes—
321#340C2312yes—
322#340C2312yes—
323#340C2312yes—
324#340C2312yes—
325#340C2312yes—
326#336C2312yes—
327#336C2312yes—
328#336C2312yes—
329#336C2312yes—
330C25C2×D411yescharacteristic
331C22×Q8—21no—
332C22×Q8—22no—
333C22×Q8—22no—
334C22×Q8—22no—
335C22×Q8—22no—
336C22×Q8—22no—
337C22×Q8—22no—
338C22×Q8—22no—
339C22×Q8C2412yes—
340C23×C4—21no—
341C23×C4—22no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4—22no—
345C23×C4—22no—
346C23×C4—22no—
347C23×C4—21no—
348C23×C4—21no—
349C23×C4—21no—
350C23×C4C2×D411yescharacteristic
351C23×C4C2×D411yescharacteristic
352C23×C4C2×D411yescharacteristic
353C23×C4C2411yescharacteristic
354C23×C4C2411yescharacteristic
355C23×C4C2411yescharacteristic
356C2×M16—22no—
357C2×M16—22no—
358C2×M16—22no—
359C2×M16—22no—
360C2×M16—22no—
361C2×M16#4114yes—
362C22×C8—22no—
363C22×C8—22no—
364C22×C8—22no—
365C22×C8—22no—
366C22×C8—22no—
367C22×C8—22no—
368C22×C8—22no—
369C22×C8—22no—
370C22×C8—22no—
371C22×C8—22no—
372C22×C8—22no—
373C22×C8—22no—
374C22×C8—41no—
375C22×C8—41no—
376C22×C8—41no—
377C22×C8—41no—
378C22×C8—416no—
379C22×C8#4114yes—
380C22×C8#4114yes—
381C22×C8C2412yes—
382C22×C8C2411yescharacteristic
383C22×C8C2411yescharacteristic
384C22×C8C2411yescharacteristic
385C22×C8C2411yescharacteristic
386C22×C8C2412yes—
387C4⋊Q8—24no—
388C4⋊Q8—42no—
389C4⋊Q8—44no—
390#126—84no—
391#125—24no—
392#125—42no—
393#125—44no—
394C22⋊Q8—24no—
395C22⋊Q8—24no—
396C22⋊Q8—48no—
397C22⋊Q8—42no—
398C22⋊Q8—42no—
399C22⋊Q8—44no—
400C22⋊Q8—44no—
401#117—22no—
402#117—22no—
403#117—22no—
404#117—22no—
405#117—22no—
406#117—22no—
407#117—22no—
408#117—22no—
409#117—22no—
410#117—22no—
411#117—22no—
412#117—22no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
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—44no—
433C2×C4⋊C4C2×D411yescharacteristic
434C2×C4⋊C4C2×D411yescharacteristic
435C2×C4⋊C4C2×D411yescharacteristic
436C2×C4⋊C4C2×D411yescharacteristic
437C2×C4⋊C4#4114yes—
438C2×C4⋊C4C2412yes—
439C2×C4⋊C4C2412yes—
440C2×C4⋊C4C2411yescharacteristic
441C2×C4⋊C4C2411yescharacteristic
442C2×C4⋊C4C2411yescharacteristic
443C2×C4⋊C4C2411yescharacteristic
444C2×C4⋊C4C2411yescharacteristic
445C2×C4⋊C4C2411yescharacteristic
446C2×C4⋊C4C2411yescharacteristic
447C2×C4⋊C4C2411yescharacteristic
448C2×C4⋊C4C2412yes—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—44no—
466C2×C22⋊C4—82no—
467C2×C22⋊C4C2×D412yes—
468C2×C22⋊C4C2×D412yes—
469C2×C22⋊C4C2×D412yes—
470C2×C22⋊C4C2×D412yes—
471C2×C22⋊C4C2×D412yes—
472C2×C22⋊C4C2×D412yes—
473C2×C42—21no—
474C2×C42—21no—
475C2×C42—21no—
476C2×C42—21no—
477C2×C42—22no—
478C2×C42—22no—
479C2×C42—22no—
480C2×C42—22no—
481C2×C42C2412yes—
482C2×C42C2412yes—
483#107—22no—
484#107—22no—
485#107—24no—
486#107—24no—
487#107—41no—
488#107—41no—
489#106—22no—
490#106—22no—
491#106—24no—
492#106—24no—
493#106—41no—
494#106—41no—
495#103—24no—
496#103—24no—
497#103—24no—
498#103—24no—
499#103—24no—
500#103—24no—
501#103—42no—
502#103—42no—
503C22⋊C8—24no—
504C22⋊C8—24no—
505#97—24no—
506#97—42no—
507C4×C8—24no—
508C4×C8—42no—
509#95—22no—
510#95—22no—
511#95—22no—
512#95—22no—
513#95—22no—
514#95—22no—
515#95—21no—
516#95—21no—
517#95—21no—
518#95—21no—
519#95—21no—
520#95—21no—
521#95—21no—
522#95—21no—
523#95—22no—
524#95—22no—
525#95—22no—
526#95—22no—
527#95—22no—
528#95—22no—
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#95C2×D412yes—
538#95C2×D412yes—
539#95C2×D412yes—
540#95C2×D412yes—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—41no—
547C24—41no—
548C24C22×D411yescharacteristic
549C24C22×D411yescharacteristic
550C24C22×D411yescharacteristic
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—44no—
558C2×Q8—42no—
559C2×Q8—42no—
560C2×Q8—42no—
561C2×Q8—44no—
562C2×Q8—44no—
563C2×Q8—44no—
564C2×Q8—44no—
565C2×Q8—82no—
566C2×Q8—82no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—24no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—22no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—22no—
600C22×C4—21no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—81no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4—81no—
615C22×C4—81no—
616C22×C4C22×D411yescharacteristic
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D412yes—
619C22×C4C22×D412yes—
620C22×C4C22×D412yes—
621C22×C4C22×D412yes—
622C22×C4C22×D411yescharacteristic
623C22×C4C2×#4112yes—
624C22×C4C2×#4112yes—
625C22×C4C2×#4112yes—
626C22×C4C2×#4112yes—
627C22×C4H(5,𝔽2)12yes—
628C22×C42−1+412yes—
629C22×C4C2511yescharacteristic
630M16—28no—
631M16—44no—
632C2×C8—28no—
633C2×C8—28no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—22no—
647C2×C8—44no—
648C2×C8—44no—
649C2×C8—44no—
650C2×C8—44no—
651C2×C8C2×#4112yes—
652C2×C8C2×#4112yes—
653C2×C8C2×#4114yes—
654C2×C8C2×#4112yes—
655C2×C8C2×#4112yes—
656C4⋊C4—24no—
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—22no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—22no—
682C4⋊C4—44no—
683C4⋊C4—44no—
684C4⋊C4—44no—
685C4⋊C4—44no—
686C4⋊C4—44no—
687C4⋊C4—42no—
688C4⋊C4—42no—
689C4⋊C4—82no—
690C4⋊C4—82no—
691C4⋊C4—82no—
692C4⋊C4—82no—
693C4⋊C4—82no—
694C4⋊C4—82no—
695C4⋊C4C2×#4114yes—
696C22⋊C4—24no—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—24no—
700C22⋊C4—42no—
701C22⋊C4—42no—
702C22⋊C4—44no—
703C22⋊C4—44no—
704C22⋊C4—42no—
705C22⋊C4—42no—
706C22⋊C4—42no—
707C22⋊C4—42no—
708C22⋊C4—42no—
709C22⋊C4—44no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C22⋊C4—42no—
713C22⋊C4—81no—
714C22⋊C4—81no—
715C22⋊C4—81no—
716C22⋊C4—81no—
717C22⋊C4—82no—
718C42—22no—
719C42—22no—
720C42—22no—
721C42—22no—
722C42—42no—
723C42—42no—
724C42—42no—
725C42—42no—
726C42—82no—
727C42—82no—
728C42—82no—
729C42—82no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—28no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—44no—
748C23—44no—
749C23—44no—
750C23—44no—
751C23—44no—
752C23—44no—
753C23#53212yes—
754C23#54612yes—
755C23#54712yes—
756C23#57712yes—
757C23#57812yes—
758C23C23×D411yescharacteristic
759Q8—42no—
760Q8—42no—
761Q8—42no—
762Q8—42no—
763Q8—84no—
764Q8—164no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—24no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—44no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—41no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—84no—
831C2×C4—84no—
832C2×C4—162no—
833C2×C4—162no—
834C2×C4#52914yes—
835C2×C4#53212yes—
836C2×C4#54214yes—
837C2×C4#54612yes—
838C2×C4#54712yes—
839C2×C4#55114yes—
840C2×C4#55614yes—
841C2×C4C22×#4111yescharacteristic
842C2×C4C22×#4111yescharacteristic
843C2×C4C22×#4111yescharacteristic
844C2×C4C22×#4111yescharacteristic
845C2×C4C2×H(5,𝔽2)11yescharacteristic
846C2×C4C2×2−1+411yescharacteristic
847C8—24no—
848C8—22no—
849C8—22no—
850C8—22no—
851C8—22no—
852C8—42no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—22no—
858C22—22no—
859C22—22no—
860C22—22no—
861C22—22no—
862C22—22no—
863C22—22no—
864C22—22no—
865C22—416no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—41no—
873C22—41no—
874C22#252114yes—
875C22C2×#53211yescharacteristic
876C22C2×#54611yescharacteristic
877C22C2×#54711yescharacteristic
878C22C2×#57711yescharacteristic
879C22C2×#57811yescharacteristic
880C22#358411yescharacteristic
881C22#358411yescharacteristic
882C4—42no—
883C4—42no—
884C4—41no—
885C4—41no—
886C4—42no—
887C4—42no—
888C4—44no—
889C4—81no—
890C4—81no—
891C4—82no—
892C4—81no—
893C4—81no—
894C4—82no—
895C4—82no—
896C4—81no—
897C4—81no—
898C4—81no—
899C4—81no—
900C4#252114yes—
901C4C2×#52911yescharacteristic
902C4C2×#54211yescharacteristic
903C4C2×#55111yescharacteristic
904C4C2×#55611yescharacteristic
905C2—24no—
906C2—42no—
907C2—42no—
908C2C2×#252111yescharacteristic
909C2#6070611yescharacteristic
910C2#6070811yescharacteristic
911C2#6116811yescharacteristic
912C2#6116911yescharacteristic
913C2#6126311yescharacteristic
914C2#6126411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2280 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #28084C2semidirect
4. #28083C2semidirect
5. #28081C2semidirect
6. #28078C2semidirect
7. #28069C2semidirect
8. #28066C2semidirect
9. #28064C2semidirect
10. #28063C2semidirect
11. #23736C2semidirect
13. #23557C2semidirect
15. #21326C2semidirect
16. #21090C2semidirect
17. #21088C2semidirect
18. #21066C2semidirect
19. #21039C2semidirect
22. #20453C2semidirect
69. #2097C22semidirect
70. #2097C22semidirect
71. #2096C22semidirect
72. #2095C22semidirect
77. #2059C22semidirect
78. #2059C22semidirect
79. #2058C22semidirect
80. #2057C22semidirect
85. #1993C22semidirect
86. #1992C22semidirect
87. #1991C22semidirect
88. #1990C22semidirect
89. #1935C22semidirect
90. #1935C22semidirect
91. #1935C22semidirect
92. #1935C22semidirect
93. #1933C22semidirect
94. #1933C22semidirect
95. #1933C22semidirect
96. #1933C22semidirect
97. #1928C22semidirect
98. #1928C22semidirect
99. #1927C22semidirect
100. #1927C22semidirect
101. #1921C22semidirect
102. #1920C22semidirect
103. #1919C22semidirect
104. #1918C22semidirect
117. #1776C22semidirect
118. #1776C22semidirect
119. C4×#107C22semidirect
120. C4×#106C22semidirect

Maximal subgroups

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

subgroupindex
#356442
#355442
#280842
#280832
#280812
#280782
#280692
#280662
#280642
#280632
#237362
#236422
#235572
#234812
#213262
#210902
#210882
#210662
#210392
C2×#18922
#206582
#204532
#203852