Finite Group Databasebeta

← #6688560

Subgroups — #6688560

Order 512.

1467 conjugacy classes of subgroups.

The subgroup lattice has 1182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42820C211yesmaximal, characteristic, complemented
2#35928C211yesmaximal, characteristic
3#33076C211yesmaximal, characteristic
4#32687C211yesmaximal, characteristic, complemented
5#32683C211yesmaximal, characteristic, complemented
6#32578C211yesmaximal, characteristic, complemented
7#32575C211yesmaximal, characteristic, complemented
8#32138C211yesmaximal, characteristic, complemented
9#32134C211yesmaximal, characteristic, complemented
10#30956C211yesmaximal, characteristic, complemented
11#30949C211yesmaximal, characteristic, complemented
12#30314C211yesmaximal, characteristic, complemented
13#29993C211yesmaximal, characteristic, complemented
14#28809C211yesmaximal, characteristic, complemented
15#28794C211yesmaximal, characteristic, complemented
16#27307C211yesmaximal, characteristic
17#27299C211yesmaximal, characteristic
18#26376C211yesmaximal, characteristic
19#26372C211yesmaximal, characteristic
20#26118C211yesmaximal, characteristic
21#26058C211yesmaximal, characteristic
22#26054C211yesmaximal, characteristic, complemented
23#26038C211yesmaximal, characteristic, complemented
24#25835C211yesmaximal, characteristic
25#25834C211yesmaximal, characteristic
26#24337C211yesmaximal, characteristic
27#24330C211yesmaximal, characteristic
28#22768C211yesmaximal, characteristic
29C4⋊C4×SD16C211yesmaximal, characteristic
30#22308C211yesmaximal, characteristic, complemented
31#21133C211yesmaximal, characteristic
32C2×#554C2211yescharacteristic
33C2×D4×Q8C2211yescharacteristic
34C2×#498C2211yescharacteristic
35C2×#498C2211yescharacteristic
36C2×#479C2211yescharacteristic
37C2×#475C2211yescharacteristic
38C2×#476C2211yescharacteristic
39C2×#474C2211yescharacteristic
40C2×C4×SD16C2211yescharacteristic
41C2×C4×SD16C2211yescharacteristic
42C2×C4×SD16C2211yescharacteristic
43#2843—21no—
44#2791—21no—
45#2755—21no—
46#2734—21no—
47#2713—21no—
48#2666—21no—
49#2660—21no—
50#2660C2211yescharacteristic
51#2659—21no—
52#2647C2211yescharacteristic
53#2605—21no—
54#2584C2211yescharacteristic
55#2583—21no—
56#2582C2211yescharacteristic
57#2581C2211yescharacteristic
58#2570C2211yescharacteristic
59#2567C2211yescharacteristic
60#2567C2211yescharacteristic
61#2551C2211yescharacteristic
62#2551C2211yescharacteristic
63#2551C2211yescharacteristic
64#2550C2211yescharacteristic
65#2550C2211yescharacteristic
66#2549—21no—
67#2549—21no—
68#2546C2211yescharacteristic
69#2508C2211yescharacteristic
70#2506C2211yescharacteristic
71#2451C2211yescharacteristic
72#2451C2211yescharacteristic
73#2440—21no—
74#2440—21no—
75#2434—21no—
76#2399C2211yescharacteristic
77C2×#395—21no—
78#2356C2211yescharacteristic
79Q8×C4⋊C4C2211yescharacteristic
80#2349C2211yescharacteristic
81#2349C2211yescharacteristic
82D4×C4⋊C4C2211yescharacteristic
83D4×C4⋊C4C2211yescharacteristic
84#2320C2211yescharacteristic
85#2275C2211yescharacteristic
86#2101C2211yescharacteristic
87#2101C2211yescharacteristic
88#2100C2211yescharacteristic
89#2099C2211yescharacteristic
90#2097C2211yescharacteristic
91#2096C2211yescharacteristic
92#2088C2211yescharacteristic
93#2088C2211yescharacteristic
94#2088C2211yescharacteristic
95#2088C2211yescharacteristic
96#2087C2211yescharacteristic
97#2087C2211yescharacteristic
98#2085C2211yescharacteristic
99#2085C2211yescharacteristic
100#2085C2211yescharacteristic
101#2084C2211yescharacteristic
102#2084C2211yescharacteristic
103#2084C2211yescharacteristic
104#2068C2211yescharacteristic
105#2066C2211yescharacteristic
106#2059C2211yescharacteristic
107#2059C2211yescharacteristic
108#2059C2211yescharacteristic
109#2059C2211yescharacteristic
110#2059C2211yescharacteristic
111#2058C2211yescharacteristic
112#2058C2211yescharacteristic
113#2058C2211yescharacteristic
114#2058C2211yescharacteristic
115#2058C2211yescharacteristic
116#2058C2211yescharacteristic
117#2058C2211yescharacteristic
118#2058C2211yescharacteristic
119#2058C2211yescharacteristic
120#2058C2211yescharacteristic
121#2057C2211yescharacteristic
122#2026C2211yescharacteristic
123#2024C2211yescharacteristic
124#2024C2211yescharacteristic
125#2024C2211yescharacteristic
126#1991C2211yescharacteristic
127#1990C2211yescharacteristic
128#1988C2211yescharacteristic
129#1987C2211yescharacteristic
130#1984C2211yescharacteristic
131#1984C2211yescharacteristic
132#1984C2211yescharacteristic
133#1984C2211yescharacteristic
134#1949C2211yescharacteristic
135#1949C2211yescharacteristic
136#1948C2211yescharacteristic
137#1948C2211yescharacteristic
138#1942C2211yescharacteristic
139#1941C2211yescharacteristic
140#1941C2211yescharacteristic
141#1941C2211yescharacteristic
142#1941C2211yescharacteristic
143#1941C2211yescharacteristic
144#1940C2211yescharacteristic
145#1940C2211yescharacteristic
146#1933C2211yescharacteristic
147#1933C2211yescharacteristic
148#1927C2211yescharacteristic
149#1927C2211yescharacteristic
150#1920C2211yescharacteristic
151#1920C2211yescharacteristic
152#1920C2211yescharacteristic
153#1920C2211yescharacteristic
154#1919C2211yescharacteristic
155#1919C2211yescharacteristic
156#1919C2211yescharacteristic
157#1919C2211yescharacteristic
158#1918C2211yescharacteristic
159#1918C2211yescharacteristic
160#1916C2211yescharacteristic
161#1916C2211yescharacteristic
162#1916C2211yescharacteristic
163#1916C2211yescharacteristic
164#1877C2211yescharacteristic
165#1877C2211yescharacteristic
166#1877C2211yescharacteristic
167#1877C2211yescharacteristic
168#1865C2211yescharacteristic
169#1865C2211yescharacteristic
170#1865C2211yescharacteristic
171#1864C2211yescharacteristic
172#1864C2211yescharacteristic
173#1864C2211yescharacteristic
174#1864C2211yescharacteristic
175#1864C2211yescharacteristic
176#1864C2211yescharacteristic
177#1864C2211yescharacteristic
178#1864C2211yescharacteristic
179#1864C2211yescharacteristic
180#1864C2211yescharacteristic
181#1863C2211yescharacteristic
182#1862C2211yescharacteristic
183#1862C2211yescharacteristic
184#1847C2211yescharacteristic
185#1844C2211yescharacteristic
186#1836C2211yescharacteristic
187#1835C2211yescharacteristic
188#1832C2211yescharacteristic
189#1805C2211yescharacteristic
190#1804C2211yescharacteristic
191#1804C2211yescharacteristic
192#1803C2211yescharacteristic
193#1802C2211yescharacteristic
194#1802C2211yescharacteristic
195C4×#106C2211yescharacteristic
196C8×C4⋊C4C2211yescharacteristic
197C8×C4⋊C4C2211yescharacteristic
198#1763C2211yescharacteristic
199#1762C2211yescharacteristic
200C4×#102C2211yescharacteristic
201C4×#102C2211yescharacteristic
202#1746C2211yescharacteristic
203C23×Q8—21no—
204C22×SD16C2311yescharacteristic
205#554—42no—
206#554—42no—
207D4×Q8—42no—
208D4×Q8—42no—
209C2×C4⋊Q8—21no—
210C2×C4⋊Q8—21no—
211C2×C4⋊Q8—21no—
212C2×C4⋊Q8—21no—
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×#125—21no—
220C2×#125C2311yescharacteristic
221C2×#125C2311yescharacteristic
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C22×C4⋊C4—21no—
241C22×C4⋊C4—21no—
242C22×C4⋊C4—21no—
243#498—42no—
244#498—42no—
245#479—42no—
246#476—42no—
247#475—42no—
248#474—42no—
249C4×SD16—42no—
250C4×SD16—42no—
251C4×SD16Q818yescomplemented
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#97C2311yescharacteristic
292C2×C4×C8C2311yescharacteristic
293C2×C4×C8C2311yescharacteristic
294C2×C4×C8C2311yescharacteristic
295C2×C4×C8C2311yescharacteristic
296C2×C4×C8C2311yescharacteristic
297#400—21no—
298#400—21no—
299#400—21no—
300#400—21no—
301#400—21no—
302#400—21no—
303#398—21no—
304#398—21no—
305#398—21no—
306#398—21no—
307#398—21no—
308#398—21no—
309#398—21no—
310#398—21no—
311#398—21no—
312#398—21no—
313#398—21no—
314#398—21no—
315#398—21no—
316#398—21no—
317#398—21no—
318#398—21no—
319#398D411yescharacteristic
320#398D411yescharacteristic
321#398D411yescharacteristic
322#398D411yescharacteristic
323#395—21no—
324#395—21no—
325#395—21no—
326#395—21no—
327#395—21no—
328#395—21no—
329#395—21no—
330#395—21no—
331#395—21no—
332#395—21no—
333#395—21no—
334#395—21no—
335#395—21no—
336#395—21no—
337#395—21no—
338#395—21no—
339#395—21no—
340#395—21no—
341#395D411yescharacteristic
342#395D411yescharacteristic
343#395D411yescharacteristic
344#395D411yescharacteristic
345#391—21no—
346#391—21no—
347#391—21no—
348#391—21no—
349#391—21no—
350#391—21no—
351#391—21no—
352#391—21no—
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#391C2311yescharacteristic
357#389—21no—
358#389—21no—
359#389—21no—
360#389—21no—
361#389—21no—
362#389—21no—
363#389—21no—
364#389—21no—
365#389—21no—
366#389—21no—
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#385—21no—
400#385—21no—
401#385—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#384—21no—
408#384—21no—
409#384—21no—
410#384C2311yescharacteristic
411#384C2311yescharacteristic
412#384C2311yescharacteristic
413#384C2311yescharacteristic
414#383—21no—
415#383—21no—
416#382—21no—
417#382—21no—
418#382C2311yescharacteristic
419#382C2311yescharacteristic
420#382C2311yescharacteristic
421#382C2311yescharacteristic
422#380—21no—
423#380—21no—
424#380—21no—
425#380—21no—
426C4×C4⋊C4—21no—
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C22⋊C4—21no—
438C4×C22⋊C4—21no—
439C4×C22⋊C4—21no—
440#376—21no—
441#376C2311yescharacteristic
442C2×#95—21no—
443C2×#95—21no—
444C2×#95—21no—
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491C22×Q8—21no—
492C22×Q8—21no—
493C22×Q8—21no—
494C22×Q8—21no—
495C22×Q8—21no—
496C22×Q8—21no—
497C22×Q8—44no—
498C22×Q8—82no—
499C22×Q8—82no—
500C22×Q8C2×D411yescharacteristic
501C22×Q8C2×D411yescharacteristic
502C22×Q8C2411yescharacteristic
503C22×D4C2411yescharacteristic
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C2×SD16—22no—
512C2×SD16—22no—
513C2×SD16C2×Q814yes—
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C4⋊Q8—22no—
523C4⋊Q8—22no—
524C4⋊Q8—22no—
525C4⋊Q8—41no—
526C4⋊Q8—41no—
527C4⋊Q8—41no—
528C4⋊Q8—41no—
529C4⋊Q8—41no—
530C4⋊Q8—41no—
531C4⋊Q8—41no—
532C4⋊Q8—41no—
533C4⋊Q8—41no—
534C4⋊Q8—82no—
535C4⋊Q8—82no—
536C4⋊Q8—82no—
537C4⋊Q8—82no—
538#125—22no—
539#125—41no—
540#125—41no—
541#125—41no—
542#125—82no—
543C22⋊Q8—44no—
544C22⋊Q8—44no—
545C22⋊Q8—44no—
546C22⋊Q8—44no—
547C22⋊Q8—44no—
548C22⋊Q8—44no—
549C4×Q8—22no—
550C4×Q8—41no—
551C4×Q8—41no—
552C4×Q8—41no—
553C4×Q8—41no—
554C4×Q8—41no—
555C4×Q8—41no—
556C4×Q8—41no—
557C4×Q8—41no—
558C4×Q8C2×Q814yescomplemented
559C4×D4—22no—
560C4×D4—22no—
561C4×D4—22no—
562C4×D4—22no—
563C4×D4—22no—
564C4×D4—22no—
565C4×D4—22no—
566C4×D4—22no—
567C4×D4—22no—
568C4×D4—41no—
569C4×D4—41no—
570C4×D4—41no—
571C4×D4—41no—
572C4×D4C2×Q814yes—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—44no—
615C2×C4⋊C4—82no—
616C2×C4⋊C4—82no—
617C2×C4⋊C4C2×D411yescharacteristic
618C2×C4⋊C4C2×D411yescharacteristic
619C2×C4⋊C4C2×D411yescharacteristic
620C2×C4⋊C4C2×D411yescharacteristic
621C2×C4⋊C4C2×D411yescharacteristic
622C2×C4⋊C4C2×D411yescharacteristic
623C2×C4⋊C4C2×D411yescharacteristic
624C2×C4⋊C4C2×D411yescharacteristic
625C2×C4⋊C4C2×D411yescharacteristic
626C2×C4⋊C4C2×D411yescharacteristic
627C2×C4⋊C4C2×D411yescharacteristic
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2×D411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C42—21no—
653C2×C42—21no—
654C2×C42—21no—
655C2×C42—21no—
656C2×C42—21no—
657C2×C42—21no—
658C2×C42—21no—
659C2×C42—21no—
660C2×C42—21no—
661C2×C42C2411yescharacteristic
662C2×C42C2411yescharacteristic
663C2×C42C2411yescharacteristic
664C2×C42C2411yescharacteristic
665C2×C42C2411yescharacteristic
666C2×C42C2411yescharacteristic
667C2×C42C2411yescharacteristic
668#107—22no—
669#107—41no—
670#107—41no—
671#107—41no—
672#106—22no—
673#106—22no—
674#106—22no—
675#106—22no—
676#106—22no—
677#106—41no—
678#106—41no—
679#106—41no—
680#106—41no—
681#106—41no—
682#106—41no—
683#106—41no—
684#106—41no—
685#106—41no—
686#106C2×Q814yescomplemented
687C4⋊C8—22no—
688C4⋊C8—22no—
689C4⋊C8—41no—
690C4⋊C8—41no—
691C4⋊C8—41no—
692C4⋊C8—41no—
693#103—22no—
694#103—22no—
695#103—41no—
696#103—41no—
697#103—41no—
698#103—41no—
699#103C2×Q814yescomplemented
700#102—22no—
701#102—22no—
702#102—22no—
703#102—22no—
704#102—22no—
705#102—22no—
706#102C2×Q814yes—
707#97—22no—
708C4×C8—41no—
709C4×C8—41no—
710C4×C8—41no—
711C4×C8—41no—
712C4×C8C2×Q814yescomplemented
713#95—21no—
714#95—21no—
715#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95C2×D411yescharacteristic
756#95C2×D411yescharacteristic
757#95C2×D411yescharacteristic
758#95C2×D411yescharacteristic
759#95C2×D411yescharacteristic
760#95C2×D411yescharacteristic
761#95C2×D411yescharacteristic
762#95C2×D411yescharacteristic
763#95C2×D411yescharacteristic
764#95C2×D411yescharacteristic
765#95C2×D411yescharacteristic
766#95C2×D411yescharacteristic
767C24—21no—
768C2×Q8—22no—
769C2×Q8—22no—
770C2×Q8—22no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—21no—
775C2×Q8—21no—
776C2×Q8—41no—
777C2×Q8—41no—
778C2×Q8—41no—
779C2×Q8—42no—
780C2×Q8—42no—
781C2×Q8—42no—
782C2×Q8—42no—
783C2×Q8—42no—
784C2×Q8—42no—
785C2×Q8—42no—
786C2×Q8—81no—
787C2×Q8—81no—
788C2×Q8—81no—
789C2×Q8—81no—
790C2×Q8—81no—
791C2×Q8—81no—
792C2×Q8—81no—
793C2×Q8—81no—
794C2×Q8—81no—
795C2×Q8—81no—
796C2×Q8—81no—
797C2×Q8—816no—
798C2×Q8C22×Q812yes—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4C22×Q812yes—
803C2×D4H(5,𝔽2)12yes—
804C2×D42−1+412yes—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—24no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—42no—
824C22×C4—42no—
825C22×C4—42no—
826C22×C4—42no—
827C22×C4—42no—
828C22×C4—42no—
829C22×C4—42no—
830C22×C4—81no—
831C22×C4—81no—
832C22×C4—81no—
833C22×C4—81no—
834C22×C4—81no—
835C22×C4—81no—
836C22×C4—81no—
837C22×C4—81no—
838C22×C4—81no—
839C22×C4—81no—
840C22×C4—81no—
841C22×C4C22×D411yescharacteristic
842C22×C4C22×D411yescharacteristic
843C22×C4C22×D411yescharacteristic
844C22×C4C22×D411yescharacteristic
845C22×C4C22×D411yescharacteristic
846C22×C4C22×D411yescharacteristic
847C22×C4C22×D411yescharacteristic
848C22×C4C22×D411yescharacteristic
849C22×C4C22×D411yescharacteristic
850C22×C4C22×D411yescharacteristic
851C22×C4C22×D411yescharacteristic
852C22×C4C22×D411yescharacteristic
853C22×C4C22×D411yescharacteristic
854C22×C4C22×D411yescharacteristic
855C22×C4C2511yescharacteristic
856SD16—28no—
857C2×C8—21no—
858C2×C8—21no—
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8—21no—
867C2×C8—21no—
868C2×C8—21no—
869C2×C8—21no—
870C2×C8—21no—
871C2×C8—21no—
872C2×C8—21no—
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—21no—
878C2×C8—21no—
879C2×C8C22×Q812yes—
880C2×C8C22×Q812yes—
881C4⋊C4—24no—
882C4⋊C4—22no—
883C4⋊C4—22no—
884C4⋊C4—22no—
885C4⋊C4—22no—
886C4⋊C4—22no—
887C4⋊C4—22no—
888C4⋊C4—21no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—21no—
896C4⋊C4—21no—
897C4⋊C4—21no—
898C4⋊C4—21no—
899C4⋊C4—21no—
900C4⋊C4—21no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—21no—
907C4⋊C4—21no—
908C4⋊C4—21no—
909C4⋊C4—21no—
910C4⋊C4—21no—
911C4⋊C4—21no—
912C4⋊C4—41no—
913C4⋊C4—41no—
914C4⋊C4—41no—
915C4⋊C4—41no—
916C4⋊C4—41no—
917C4⋊C4—41no—
918C4⋊C4—41no—
919C4⋊C4—41no—
920C4⋊C4—42no—
921C4⋊C4—42no—
922C4⋊C4—42no—
923C4⋊C4—42no—
924C4⋊C4—42no—
925C4⋊C4—42no—
926C4⋊C4—42no—
927C4⋊C4—42no—
928C4⋊C4—42no—
929C4⋊C4—42no—
930C4⋊C4—42no—
931C4⋊C4—42no—
932C4⋊C4—81no—
933C4⋊C4—81no—
934C4⋊C4—81no—
935C4⋊C4—81no—
936C4⋊C4—81no—
937C4⋊C4—81no—
938C4⋊C4—81no—
939C4⋊C4—81no—
940C4⋊C4—81no—
941C4⋊C4—81no—
942C4⋊C4—81no—
943C4⋊C4—81no—
944C4⋊C4—81no—
945C4⋊C4—81no—
946C4⋊C4—81no—
947C4⋊C4—81no—
948C4⋊C4—81no—
949C4⋊C4—81no—
950C4⋊C4—81no—
951C4⋊C4—81no—
952C4⋊C4—81no—
953C4⋊C4—81no—
954C4⋊C4—81no—
955C4⋊C4—81no—
956C4⋊C4—81no—
957C4⋊C4—81no—
958C4⋊C4—81no—
959C4⋊C4—81no—
960C4⋊C4C22×Q812yes—
961C4⋊C4C22×Q812yes—
962C4⋊C4H(5,𝔽2)12yes—
963C4⋊C42−1+412yes—
964C22⋊C4—24no—
965C22⋊C4—24no—
966C22⋊C4—24no—
967C22⋊C4—42no—
968C22⋊C4—42no—
969C22⋊C4—42no—
970C22⋊C4—42no—
971C42—24no—
972C42—21no—
973C42—21no—
974C42—21no—
975C42—21no—
976C42—21no—
977C42—21no—
978C42—21no—
979C42—21no—
980C42—21no—
981C42—21no—
982C42—21no—
983C42—21no—
984C42—42no—
985C42—42no—
986C42—81no—
987C42—81no—
988C42—81no—
989C42—81no—
990C42—81no—
991C42—81no—
992C42C22×Q812yes—
993C422−1+412yes—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23C23×D411yescharacteristic
1002Q8—22no—
1003Q8—22no—
1004Q8—44no—
1005Q8—41no—
1006Q8—41no—
1007Q8—82no—
1008Q8—84no—
1009Q8—84no—
1010Q8—84no—
1011Q8—162no—
1012Q8—162no—
1013Q8—162no—
1014D4—22no—
1015D4—22no—
1016D4—22no—
1017D4#54414yes—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—22no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—22no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—84no—
1101C2×C4—84no—
1102C2×C4—84no—
1103C2×C4—84no—
1104C2×C4—84no—
1105C2×C4—84no—
1106C2×C4—162no—
1107C2×C4D4×Q812yes—
1108C2×C4D4×Q812yes—
1109C2×C4#57712yes—
1110C2×C4#57712yes—
1111C2×C4#57712yes—
1112C2×C4C23×Q811yescharacteristic
1113C2×C4C2×H(5,𝔽2)11yescharacteristic
1114C2×C4C2×H(5,𝔽2)11yescharacteristic
1115C2×C4C2×2−1+411yescharacteristic
1116C2×C4C2×2−1+411yescharacteristic
1117C2×C4C2×2−1+411yescharacteristic
1118C8—22no—
1119C8—22no—
1120C8—41no—
1121C8—41no—
1122C8—41no—
1123C8—41no—
1124C8—41no—
1125C8—41no—
1126C22—24no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22C2×D4×Q811yescharacteristic
1134C22#348411yescharacteristic
1135C22#348611yescharacteristic
1136C22C2×#57711yescharacteristic
1137C22C2×#57711yescharacteristic
1138C22C2×#57711yescharacteristic
1139C22#358411yescharacteristic
1140C4—22no—
1141C4—22no—
1142C4—22no—
1143C4—22no—
1144C4—22no—
1145C4—42no—
1146C4—41no—
1147C4—42no—
1148C4—41no—
1149C4—42no—
1150C4—42no—
1151C4—41no—
1152C4—41no—
1153C4—41no—
1154C4—42no—
1155C4—41no—
1156C4—41no—
1157C4—41no—
1158C4—41no—
1159C4—81no—
1160C4—81no—
1161C4—81no—
1162C4—81no—
1163C4—81no—
1164C4—81no—
1165C4—81no—
1166C4—81no—
1167C4—81no—
1168C4—81no—
1169C4C2×#54411yescharacteristic
1170C4#350311yescharacteristic
1171C4#354411yescharacteristic
1172C4#355211yescharacteristic
1173C2—44no—
1174C2#3768611yescharacteristic
1175C2#6137111yescharacteristic
1176C2#6137411yescharacteristic
1177C2#6163111yescharacteristic
1178C2#6164111yescharacteristic
1179C2#6186411yescharacteristic
1180C2#6187111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2399 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42820C2semidirect
4. #32687C2semidirect
5. #32683C2semidirect
6. #32578C2semidirect
7. #32575C2semidirect
8. #32138C2semidirect
9. #32134C2semidirect
10. #30956C2semidirect
11. #30949C2semidirect
12. #30314C2semidirect
13. #29993C2semidirect
14. #28809C2semidirect
15. #28794C2semidirect
22. #26054C2semidirect
23. #26038C2semidirect
30. #22308C2semidirect
251. C4×SD16Q8semidirect
558. C4×Q8C2×Q8semidirect
686. #106C2×Q8semidirect
699. #103C2×Q8semidirect
712. C4×C8C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#428202
#359282
#330762
#326872
#326832
#325782
#325752
#321382
#321342
#309562
#309492
#303142
#299932
#288092
#287942
#273072
#272992
#263762
#263722
#261182
#260582
#260542
#260382
#258352
#258342
#243372
#243302
#227682
C4⋊C4×SD162
#223082
#211332