Finite Group Databasebeta

← #7508692

Subgroups — #7508692

Order 512.

1849 conjugacy classes of subgroups.

The subgroup lattice has 885 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34946C211yesmaximal, characteristic
2#34809C211yesmaximal, characteristic
3#32267C212yesmaximal, complemented
4#32266C212yesmaximal, complemented
5#32265C212yesmaximal, complemented
6#32264C212yesmaximal, complemented
7#32263C212yesmaximal, complemented
8#32262C212yesmaximal, complemented
9#32261C211yesmaximal, characteristic, complemented
10#32260C211yesmaximal, characteristic, complemented
11#32259C211yesmaximal, characteristic, complemented
12#32258C211yesmaximal, characteristic, complemented
13#23638C212yesmaximal, complemented
14#23638C212yesmaximal, complemented
15#23551C212yesmaximal, complemented
16#21032C212yesmaximal, complemented
17C2×#1869C211yesmaximal, characteristic
18#20843C212yesmaximal, complemented
19#20658C212yesmaximal, complemented
20C24×C8C2211yescharacteristic
21C2×#533C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic
23C22×#117C2211yescharacteristic
24C2×#427C2212yes—
25C2×#427C2212yes—
26C2×#427C2212yes—
27C22×C22⋊C8C2212yes—
28C22×C22⋊C8C2211yescharacteristic
29#2563C2211yescharacteristic
30#2563C2211yescharacteristic
31#2562C2212yes—
32#2562C2212yes—
33#2561—21no—
34#2561—21no—
35#2547C2211yescharacteristic
36#2547C2211yescharacteristic
37#2503—21no—
38#2487C2211yescharacteristic
39#2487C2211yescharacteristic
40#2486C2211yescharacteristic
41#2486C2211yescharacteristic
42#2485C2212yes—
43#2485C2212yes—
44#2484—21no—
45#2483—21no—
46#2482—21no—
47#2435—21no—
48#2405—21no—
49#2398—21no—
50#2398—21no—
51#2395—21no—
52#2395—21no—
53C4×#124—21no—
54C4×#124—21no—
55C4×#123—21no—
56C4×#123—21no—
57#2296C2212yes—
58#2280C2211yescharacteristic
59#2280C2212yes—
60#2280C2212yes—
61#2280C2212yes—
62C4×#117C2211yescharacteristic
63#2077C2212yescomplemented
64#2077C2212yescomplemented
65#2077C2212yescomplemented
66#2077C2212yescomplemented
67#2077C2212yescomplemented
68#2077C2212yescomplemented
69#2077C2212yescomplemented
70#2077C2212yescomplemented
71#2076C2212yescomplemented
72#2076C2212yescomplemented
73#2076C2212yescomplemented
74#2076C2212yescomplemented
75#2075C2212yescomplemented
76#2075C2212yescomplemented
77#2075C2212yescomplemented
78#2075C2212yescomplemented
79#2059C2212yescomplemented
80#2059C2212yescomplemented
81#2059C2212yescomplemented
82#2059C2212yescomplemented
83#2058C2212yescomplemented
84#2058C2212yescomplemented
85#2057C2212yescomplemented
86#2057C2212yescomplemented
87#1921C2212yescomplemented
88#1921C2212yescomplemented
89#1920C2212yescomplemented
90#1920C2212yescomplemented
91#1919C2212yescomplemented
92#1919C2212yescomplemented
93#1918C2212yescomplemented
94#1918C2212yescomplemented
95#1869C2211yescharacteristic
96#1869C2211yescharacteristic
97#1869C2211yescharacteristic
98#1869C2211yescharacteristic
99#1869C2212yes—
100#1869C2212yes—
101#1854C2212yescomplemented
102#1854C2212yescomplemented
103#1854C2212yescomplemented
104#1854C2212yescomplemented
105#1853C2212yescomplemented
106#1853C2212yescomplemented
107#1852C2212yescomplemented
108#1852C2212yescomplemented
109#1808C2212yescomplemented
110#1808C2212yescomplemented
111#1808C2212yescomplemented
112#1808C2212yescomplemented
113#1807C2212yescomplemented
114#1807C2212yescomplemented
115#1807C2212yescomplemented
116#1807C2212yescomplemented
117#1735C2212yes—
118#1735C2212yes—
119#1735C2212yes—
120#1735C2212yes—
121#1735C2212yes—
122C2×#336C2212yes—
123C23×D4D411yescharacteristic
124C24×C4C2311yescharacteristic
125C24×C4C2311yescharacteristic
126C23×C8—28no—
127C23×C8—42no—
128C23×C8C2312yes—
129C23×C8C2311yescharacteristic
130C23×C8C2312yes—
131C23×C8C2311yescharacteristic
132C23×C8C2312yes—
133#533—42no—
134#533—42no—
135C2×C4⋊Q8C2311yescharacteristic
136C2×C4⋊Q8C2311yescharacteristic
137C2×#125C2312yes—
138C2×#124—21no—
139C2×#124—21no—
140C2×#123—21no—
141C2×#123—21no—
142C2×C22⋊Q8—21no—
143C2×C22⋊Q8—21no—
144C2×C4×Q8—21no—
145C2×C4×Q8—21no—
146C2×C4×D4—42no—
147C2×C4×D4—42no—
148C2×C4×D4D411yescharacteristic
149C2×C4×D4D411yescharacteristic
150C2×C4×D4D411yescharacteristic
151C2×C4×D4D411yescharacteristic
152C2×C4×D4C2311yescharacteristic
153C2×C4×D4C2311yescharacteristic
154C2×C4×D4C2311yescharacteristic
155C2×C4×D4C2311yescharacteristic
156C2×#117—21no—
157C2×#117—21no—
158C2×#117—42no—
159C2×#117—42no—
160C2×#117C2312yes—
161C2×#117C2312yes—
162C2×#117C2312yes—
163C2×#117C2312yes—
164C2×#117C2312yes—
165C22×C4⋊C4D411yescharacteristic
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2311yescharacteristic
168C22×C22⋊C4—21no—
169C22×C22⋊C4D411yescharacteristic
170C22×C22⋊C4D411yescharacteristic
171C22×C42—21no—
172C22×C42C2311yescharacteristic
173#427—28no—
174#427—44no—
175#427—44no—
176C2×#107C2312yes—
177C2×#107C2312yes—
178C2×#107C2312yes—
179C2×#107C2312yes—
180C2×#107C2312yes—
181C2×#107C2312yes—
182C2×#106C2312yes—
183C2×#106C2312yes—
184C2×#106C2312yes—
185C2×#106C2312yes—
186C2×#106C2312yes—
187C2×#106C2312yes—
188C2×C22⋊C8—28no—
189C2×C22⋊C8—42no—
190C2×C22⋊C8C2312yes—
191C2×C22⋊C8C2312yes—
192C2×C22⋊C8C2312yes—
193C2×C22⋊C8C2312yes—
194C2×C22⋊C8C2311yescharacteristic
195C2×C22⋊C8C2312yes—
196C2×C22⋊C8C2311yescharacteristic
197#400—22no—
198#400—22no—
199#400—21no—
200#400—21no—
201#399—21no—
202#399—21no—
203#398—21no—
204#398—21no—
205#397—21no—
206#397—21no—
207#397—21no—
208#397—21no—
209#397—21no—
210#397—21no—
211#397—22no—
212#397—22no—
213#394—22no—
214#394—22no—
215#394—22no—
216#394—22no—
217#393—21no—
218#393—21no—
219#393—21no—
220#393—21no—
221#391—21no—
222#391—21no—
223#390—21no—
224#390—21no—
225#389C2312yes—
226#389C2312yes—
227#389C2312yes—
228#389C2312yes—
229#388—22no—
230#388—22no—
231#388—22no—
232#388—22no—
233#388—22no—
234#388—22no—
235#387—22no—
236#387—22no—
237#386—21no—
238#386—21no—
239#385—22no—
240#385—22no—
241#385—21no—
242#385—21no—
243#382—21no—
244#382—21no—
245#381—22no—
246#381—22no—
247#381—21no—
248#381—22no—
249#381—21no—
250#381—21no—
251#380C2312yes—
252#380C2312yes—
253#380C2312yes—
254#380C2312yes—
255#380C2312yes—
256#380C2312yes—
257#380C2312yes—
258#380C2312yes—
259#380C2312yes—
260#380C2312yes—
261#380C2312yes—
262#380C2312yes—
263#380C2311yescharacteristic
264#380C2312yes—
265#380C2311yescharacteristic
266#379—22no—
267#379—22no—
268#379—22no—
269#379—21no—
270C4×C4⋊C4—22no—
271C4×C4⋊C4—22no—
272C4×C4⋊C4C2312yes—
273C4×C4⋊C4C2311yescharacteristic
274C4×C4⋊C4C2311yescharacteristic
275C4×C22⋊C4—21no—
276C4×C22⋊C4—21no—
277C4×C22⋊C4—22no—
278C4×C22⋊C4—22no—
279C4×C22⋊C4—22no—
280C4×C22⋊C4—22no—
281C4×C22⋊C4—22no—
282C4×C22⋊C4—22no—
283C4×C22⋊C4—21no—
284C4×C22⋊C4—21no—
285#376—21no—
286C43—21no—
287#340C2312yes—
288#340C2312yes—
289#340C2312yes—
290#340C2312yes—
291#340C2312yes—
292#340C2312yes—
293#340C2312yes—
294#340C2312yes—
295#340C2312yes—
296#340C2312yes—
297#340C2312yes—
298#340C2312yes—
299#340C2312yes—
300#340C2312yes—
301#340C2312yes—
302#340C2312yes—
303#340C2312yes—
304#340C2312yes—
305#340C2312yes—
306#340C2312yes—
307#336C2312yes—
308#336C2312yes—
309#336C2312yes—
310#336C2312yes—
311C25C2×D411yescharacteristic
312C25C2×D411yescharacteristic
313C22×Q8—21no—
314C22×Q8—21no—
315C22×D4—24no—
316C22×D4—42no—
317C22×D4—42no—
318C22×D4C2×D411yescharacteristic
319C22×D4C2×D411yescharacteristic
320C22×D4C2×D411yescharacteristic
321C22×D4C2×D411yescharacteristic
322C23×C4—24no—
323C23×C4—24no—
324C23×C4—22no—
325C23×C4—22no—
326C23×C4—22no—
327C23×C4—22no—
328C23×C4—24no—
329C23×C4—24no—
330C23×C4—21no—
331C23×C4—21no—
332C23×C4C2×D411yescharacteristic
333C23×C4C2×D411yescharacteristic
334C23×C4C2×D411yescharacteristic
335C23×C4C2×D411yescharacteristic
336C23×C4C2×D411yescharacteristic
337C23×C4C2×D411yescharacteristic
338C23×C4C2×D411yescharacteristic
339C23×C4C2×D411yescharacteristic
340C23×C4C2411yescharacteristic
341C23×C4C2411yescharacteristic
342C23×C4C2411yescharacteristic
343C23×C4C2411yescharacteristic
344C23×C4C2411yescharacteristic
345C22×C8—24no—
346C22×C8—24no—
347C22×C8—24no—
348C22×C8—24no—
349C22×C8—24no—
350C22×C8—24no—
351C22×C8—24no—
352C22×C8—24no—
353C22×C8—24no—
354C22×C8—41no—
355C22×C8—42no—
356C22×C8—41no—
357C22×C8—416no—
358C22×C8#4118yes—
359C22×C8C2412yes—
360C22×C8C2412yes—
361C22×C8C2412yes—
362C22×C8C2412yes—
363C4⋊Q8—41no—
364C4⋊Q8—41no—
365C4⋊Q8—41no—
366C4⋊Q8—41no—
367#125—42no—
368#125—42no—
369#124—44no—
370#124—44no—
371#123—44no—
372#123—44no—
373C22⋊Q8—44no—
374C22⋊Q8—44no—
375C4×Q8—44no—
376C4×Q8—44no—
377C4×D4—42no—
378C4×D4—42no—
379C4×D4—42no—
380C4×D4—42no—
381C4×D4—41no—
382C4×D4—41no—
383C4×D4—41no—
384C4×D4—41no—
385C4×D4—41no—
386C4×D4—41no—
387C4×D4—41no—
388C4×D4—41no—
389#117—24no—
390#117—24no—
391#117—24no—
392#117—24no—
393#117—24no—
394#117—24no—
395#117—24no—
396#117—24no—
397#117—42no—
398#117—42no—
399#117—44no—
400#117—44no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—41no—
412C2×C4⋊C4—41no—
413C2×C4⋊C4—41no—
414C2×C4⋊C4—41no—
415C2×C4⋊C4—42no—
416C2×C4⋊C4C2×D411yescharacteristic
417C2×C4⋊C4C2×D411yescharacteristic
418C2×C4⋊C4C2×D411yescharacteristic
419C2×C4⋊C4C2×D411yescharacteristic
420C2×C4⋊C4C2412yes—
421C2×C4⋊C4C2412yes—
422C2×C4⋊C4C2412yes—
423C2×C4⋊C4C2412yes—
424C2×C4⋊C4C2412yes—
425C2×C4⋊C4C2412yes—
426C2×C4⋊C4C2412yes—
427C2×C4⋊C4C2412yes—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—42no—
449C2×C22⋊C4—42no—
450C2×C22⋊C4—44no—
451C2×C22⋊C4C2×D411yescharacteristic
452C2×C22⋊C4C2×D411yescharacteristic
453C2×C22⋊C4C2×D411yescharacteristic
454C2×C22⋊C4C2×D411yescharacteristic
455C2×C22⋊C4C2×D411yescharacteristic
456C2×C22⋊C4C2×D411yescharacteristic
457C2×C22⋊C4C2×D411yescharacteristic
458C2×C22⋊C4C2×D411yescharacteristic
459C2×C42—22no—
460C2×C42—22no—
461C2×C42—22no—
462C2×C42—21no—
463C2×C42—21no—
464C2×C42—22no—
465C2×C42—22no—
466C2×C42—22no—
467C2×C42—22no—
468C2×C42—22no—
469C2×C42—44no—
470C2×C42C2×D411yescharacteristic
471C2×C42C2×D411yescharacteristic
472C2×C42C2411yescharacteristic
473C2×C42C2411yescharacteristic
474#107—24no—
475#107—24no—
476#107—42no—
477#107—42no—
478#107—42no—
479#107—42no—
480#106—24no—
481#106—24no—
482#106—42no—
483#106—42no—
484#106—42no—
485#106—42no—
486C22⋊C8—24no—
487C22⋊C8—24no—
488C22⋊C8—24no—
489C22⋊C8—24no—
490C22⋊C8—41no—
491C22⋊C8—42no—
492C22⋊C8—41no—
493#95—21no—
494#95—21no—
495#95—22no—
496#95—22no—
497#95—22no—
498#95—22no—
499#95—22no—
500#95—22no—
501#95—22no—
502#95—22no—
503#95—22no—
504#95—22no—
505#95—22no—
506#95—22no—
507#95—22no—
508#95—22no—
509#95—21no—
510#95—21no—
511#95—22no—
512#95—22no—
513#95—22no—
514#95—22no—
515C24—22no—
516C24—22no—
517C24—22no—
518C24—24no—
519C24—22no—
520C24—22no—
521C24—24no—
522C24—42no—
523C24—41no—
524C24—42no—
525C24C22×D411yescharacteristic
526C24C22×D411yescharacteristic
527C24C22×D411yescharacteristic
528C24C22×D411yescharacteristic
529C24C22×D411yescharacteristic
530C2×Q8—42no—
531C2×Q8—42no—
532C2×Q8—42no—
533C2×Q8—42no—
534C2×Q8—82no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—41no—
541C2×D4—41no—
542C2×D4—41no—
543C2×D4—41no—
544C2×D4—41no—
545C2×D4—41no—
546C2×D4—416no—
547C2×D4#13514yes—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—41no—
588C22×C4—42no—
589C22×C4—48no—
590C22×C4—48no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—82no—
600C22×C4C22×D411yescharacteristic
601C22×C4C22×D411yescharacteristic
602C22×C4C22×D411yescharacteristic
603C22×C4C22×D411yescharacteristic
604C22×C4C22×D411yescharacteristic
605C22×C4C22×D411yescharacteristic
606C22×C4C22×D411yescharacteristic
607C22×C4C22×D411yescharacteristic
608C22×C4C22×D411yescharacteristic
609C22×C4C2×#4114yes—
610C22×C4H(5,𝔽2)12yes—
611C22×C4H(5,𝔽2)12yes—
612C22×C42−1+414yes—
613C22×C4C2511yescharacteristic
614C2×C8—216no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—22no—
621C2×C8—22no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—44no—
626C2×C8—48no—
627C2×C8—44no—
628C2×C8—48no—
629C2×C8C2×#4114yes—
630C2×C8C2×#4114yes—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—41no—
648C4⋊C4—41no—
649C4⋊C4—41no—
650C4⋊C4—41no—
651C4⋊C4—42no—
652C4⋊C4—42no—
653C4⋊C4—44no—
654C4⋊C4—44no—
655C4⋊C4—42no—
656C4⋊C4—42no—
657C4⋊C4—44no—
658C4⋊C4—44no—
659C4⋊C4—82no—
660C4⋊C4—82no—
661C22⋊C4—41no—
662C22⋊C4—41no—
663C22⋊C4—41no—
664C22⋊C4—41no—
665C22⋊C4—41no—
666C22⋊C4—41no—
667C22⋊C4—41no—
668C22⋊C4—41no—
669C22⋊C4—44no—
670C22⋊C4—42no—
671C22⋊C4—44no—
672C22⋊C4—44no—
673C22⋊C4—44no—
674C22⋊C4—44no—
675C22⋊C4—44no—
676C22⋊C4—42no—
677C22⋊C4—44no—
678C22⋊C4—44no—
679C22⋊C4—44no—
680C22⋊C4—44no—
681C22⋊C4—44no—
682C22⋊C4—82no—
683C22⋊C4—82no—
684C22⋊C4—82no—
685C22⋊C4—82no—
686C22⋊C4—82no—
687C22⋊C4—82no—
688C22⋊C4—82no—
689C42—22no—
690C42—22no—
691C42—21no—
692C42—21no—
693C42—21no—
694C42—21no—
695C42—44no—
696C42—42no—
697C42—44no—
698C42—44no—
699C42—44no—
700C42—44no—
701C42—42no—
702C42—82no—
703C23—22no—
704C23—21no—
705C23—21no—
706C23—28no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—22no—
720C23—21no—
721C23—22no—
722C23—21no—
723C23—21no—
724C23—48no—
725C23—48no—
726C23—44no—
727C23—48no—
728C23—44no—
729C23—44no—
730C23—44no—
731C23—84no—
732C23—82no—
733C23#53412yes—
734C23#54714yes—
735C23C2×#13512yes—
736C23C2×#13512yes—
737C23#57512yes—
738C23C23×D411yescharacteristic
739Q8—84no—
740Q8—84no—
741D4—44no—
742D4—44no—
743D4—44no—
744D4—44no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
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—42no—
804C2×C4—42no—
805C2×C4—82no—
806C2×C4—84no—
807C2×C4—84no—
808C2×C4#53412yes—
809C2×C4#54218yes—
810C2×C4#54714yes—
811C2×C4#55114yes—
812C2×C4#56314yes—
813C2×C4C2×#13512yes—
814C2×C4C22×#4112yes—
815C2×C4C2×H(5,𝔽2)11yescharacteristic
816C2×C4C2×H(5,𝔽2)11yescharacteristic
817C2×C4C2×2−1+412yes—
818C8—24no—
819C8—24no—
820C8—42no—
821C8—42no—
822C22—24no—
823C22—24no—
824C22—22no—
825C22—22no—
826C22—24no—
827C22—24no—
828C22—24no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—416no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—42no—
843C22—42no—
844C22—41no—
845C22—41no—
846C22—41no—
847C22—88no—
848C22#271714yes—
849C22C2×#53411yescharacteristic
850C22C2×#54712yes—
851C22C22×#13511yescharacteristic
852C22C2×#57511yescharacteristic
853C22#358412yes—
854C4—22no—
855C4—41no—
856C4—41no—
857C4—41no—
858C4—41no—
859C4—41no—
860C4—41no—
861C4—41no—
862C4—82no—
863C4—82no—
864C4—82no—
865C4—82no—
866C4—82no—
867C4—82no—
868C4—82no—
869C4—82no—
870C4#271714yes—
871C4C2×#54212yes—
872C4C2×#55111yescharacteristic
873C4C2×#56311yescharacteristic
874C2—24no—
875C2—42no—
876C2—42no—
877C2—42no—
878C2—81no—
879C2C2×#271711yescharacteristic
880C2#6073411yescharacteristic
881C2#6074911yescharacteristic
882C2#6123412yes—
883C2#6124312yes—
subgroupG/H
centerC22×C4C22×D4
commutator, Frattini, cosocleC22×C4C25
socleC23C23×D4
prime radicalC23×D4D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #32267C2semidirect
4. #32266C2semidirect
5. #32265C2semidirect
6. #32264C2semidirect
7. #32263C2semidirect
8. #32262C2semidirect
9. #32261C2semidirect
10. #32260C2semidirect
11. #32259C2semidirect
12. #32258C2semidirect
13. #23638C2semidirect
14. #23638C2semidirect
15. #23551C2semidirect
16. #21032C2semidirect
18. #20843C2semidirect
19. #20658C2semidirect
63. #2077C22semidirect
64. #2077C22semidirect
65. #2077C22semidirect
66. #2077C22semidirect
67. #2077C22semidirect
68. #2077C22semidirect
69. #2077C22semidirect
70. #2077C22semidirect
71. #2076C22semidirect
72. #2076C22semidirect
73. #2076C22semidirect
74. #2076C22semidirect
75. #2075C22semidirect
76. #2075C22semidirect
77. #2075C22semidirect
78. #2075C22semidirect
79. #2059C22semidirect
80. #2059C22semidirect
81. #2059C22semidirect
82. #2059C22semidirect
83. #2058C22semidirect
84. #2058C22semidirect
85. #2057C22semidirect
86. #2057C22semidirect
87. #1921C22semidirect
88. #1921C22semidirect
89. #1920C22semidirect
90. #1920C22semidirect
91. #1919C22semidirect
92. #1919C22semidirect
93. #1918C22semidirect
94. #1918C22semidirect
101. #1854C22semidirect
102. #1854C22semidirect
103. #1854C22semidirect
104. #1854C22semidirect
105. #1853C22semidirect
106. #1853C22semidirect
107. #1852C22semidirect
108. #1852C22semidirect
109. #1808C22semidirect
110. #1808C22semidirect
111. #1808C22semidirect
112. #1808C22semidirect
113. #1807C22semidirect
114. #1807C22semidirect
115. #1807C22semidirect
116. #1807C22semidirect

Maximal subgroups

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

subgroupindex
#349462
#348092
#322672
#322662
#322652
#322642
#322632
#322622
#322612
#322602
#322592
#322582
#236382
#235512
#210322
C2×#18692
#208432
#206582