Finite Group Databasebeta

← #7556795

Subgroups — #7556795

Order 512.

1424 conjugacy classes of subgroups.

The subgroup lattice has 1131 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59333C211yesmaximal, characteristic
2#36133C211yesmaximal, characteristic
3#32497C211yesmaximal, characteristic, complemented
4#32483C211yesmaximal, characteristic, complemented
5#32335C211yesmaximal, characteristic, complemented
6#32313C211yesmaximal, characteristic, complemented
7#28801C211yesmaximal, characteristic, complemented
8#27969C211yesmaximal, characteristic
9#27713C211yesmaximal, characteristic
10#27697C211yesmaximal, characteristic
11#27142C211yesmaximal, characteristic, complemented
12#27127C211yesmaximal, characteristic, complemented
13#26521C211yesmaximal, characteristic, complemented
14#26521C211yesmaximal, characteristic, complemented
15#26513C211yesmaximal, characteristic, complemented
16#26294C211yesmaximal, characteristic, complemented
17#26038C211yesmaximal, characteristic, complemented
18#25994C211yesmaximal, characteristic
19#25988C211yesmaximal, characteristic
20#25483C211yesmaximal, characteristic, complemented
21#25004C211yesmaximal, characteristic, complemented
22#24837C211yesmaximal, characteristic
23#24580C211yesmaximal, characteristic
24#24577C211yesmaximal, characteristic
25#23073C211yesmaximal, characteristic, complemented
26#22954C211yesmaximal, characteristic
27#22743C211yesmaximal, characteristic, complemented
28#22615C211yesmaximal, characteristic
29#22611C211yesmaximal, characteristic
30#21579C211yesmaximal, characteristic
31C2×#1949C211yesmaximal, characteristic
32C2×#533—21no—
33C2×#483C2211yescharacteristic
34C2×#477C2211yescharacteristic
35C2×#446C2211yescharacteristic
36C22×#107C2211yescharacteristic
37C22×#106C2211yescharacteristic
38C22×C4⋊C8C2211yescharacteristic
39#2857C2211yescharacteristic
40#2855—21no—
41#2767—21no—
42#2762—21no—
43#2581C2211yescharacteristic
44#2571C2211yescharacteristic
45#2570C2211yescharacteristic
46#2570C2211yescharacteristic
47#2551C2211yescharacteristic
48#2546C2211yescharacteristic
49#2528—21no—
50#2524—21no—
51#2514C2211yescharacteristic
52#2514C2211yescharacteristic
53#2506C2211yescharacteristic
54#2506C2211yescharacteristic
55#2503C2211yescharacteristic
56#2502C2211yescharacteristic
57#2493—21no—
58#2493—21no—
59#2462—21no—
60#2462—21no—
61#2451—21no—
62#2446—21no—
63#2440C2211yescharacteristic
64#2440C2211yescharacteristic
65#2438—21no—
66#2438—21no—
67#2438—21no—
68#2365C2211yescharacteristic
69#2365C2211yescharacteristic
70#2365C2211yescharacteristic
71#2356C2211yescharacteristic
72#2355C2211yescharacteristic
73Q8×C4⋊C4C2211yescharacteristic
74#2345C2211yescharacteristic
75#2344C2211yescharacteristic
76#2344C2211yescharacteristic
77#2344C2211yescharacteristic
78#2343—21no—
79C4×C22⋊Q8C2211yescharacteristic
80C4×C22⋊Q8C2211yescharacteristic
81C2×#382C2211yescharacteristic
82C2×C4×C4⋊C4C2211yescharacteristic
83#2101C2211yescharacteristic
84#2101C2211yescharacteristic
85#2101C2211yescharacteristic
86#2101C2211yescharacteristic
87#2101C2211yescharacteristic
88#2101C2211yescharacteristic
89#2100C2211yescharacteristic
90#2100C2211yescharacteristic
91#2100C2211yescharacteristic
92#2099C2211yescharacteristic
93#2087C2211yescharacteristic
94#2087C2211yescharacteristic
95#2087C2211yescharacteristic
96#2087C2211yescharacteristic
97#2086C2211yescharacteristic
98#2086C2211yescharacteristic
99#2085C2211yescharacteristic
100#2085C2211yescharacteristic
101#2084C2211yescharacteristic
102#2084C2211yescharacteristic
103#2072C2211yescharacteristic
104#2072C2211yescharacteristic
105#2068C2211yescharacteristic
106#2068C2211yescharacteristic
107#2068C2211yescharacteristic
108#2068C2211yescharacteristic
109#2066C2211yescharacteristic
110#2066C2211yescharacteristic
111#2057C2211yescharacteristic
112#2057C2211yescharacteristic
113#2024C2211yescharacteristic
114#2024C2211yescharacteristic
115#1993C2211yescharacteristic
116#1993C2211yescharacteristic
117#1993C2211yescharacteristic
118#1990C2211yescharacteristic
119#1988C2211yescharacteristic
120#1987C2211yescharacteristic
121#1987C2211yescharacteristic
122#1985C2211yescharacteristic
123#1949C2211yescharacteristic
124#1949C2211yescharacteristic
125#1949C2211yescharacteristic
126#1949C2211yescharacteristic
127#1949C2211yescharacteristic
128#1949C2211yescharacteristic
129#1949C2211yescharacteristic
130#1949C2211yescharacteristic
131#1949C2211yescharacteristic
132#1949C2211yescharacteristic
133#1948C2211yescharacteristic
134#1948C2211yescharacteristic
135#1947C2211yescharacteristic
136#1947C2211yescharacteristic
137#1947C2211yescharacteristic
138#1944C2211yescharacteristic
139#1944C2211yescharacteristic
140#1942C2211yescharacteristic
141#1942C2211yescharacteristic
142#1940C2211yescharacteristic
143#1940C2211yescharacteristic
144#1939C2211yescharacteristic
145#1935C2211yescharacteristic
146#1935C2211yescharacteristic
147#1933C2211yescharacteristic
148#1933C2211yescharacteristic
149#1928C2211yescharacteristic
150#1928C2211yescharacteristic
151#1928C2211yescharacteristic
152#1928C2211yescharacteristic
153#1927C2211yescharacteristic
154#1927C2211yescharacteristic
155#1921C2211yescharacteristic
156#1921C2211yescharacteristic
157#1920C2211yescharacteristic
158#1920C2211yescharacteristic
159#1919C2211yescharacteristic
160#1919C2211yescharacteristic
161#1919C2211yescharacteristic
162#1919C2211yescharacteristic
163#1918C2211yescharacteristic
164#1918C2211yescharacteristic
165#1918C2211yescharacteristic
166#1918C2211yescharacteristic
167#1918C2211yescharacteristic
168#1918C2211yescharacteristic
169#1917C2211yescharacteristic
170#1916C2211yescharacteristic
171#1892C2211yescharacteristic
172#1892C2211yescharacteristic
173#1872C2211yescharacteristic
174#1852C2211yescharacteristic
175#1850C2211yescharacteristic
176#1850C2211yescharacteristic
177#1836C2211yescharacteristic
178#1836C2211yescharacteristic
179#1836C2211yescharacteristic
180#1834C2211yescharacteristic
181#1824C2211yescharacteristic
182#1824C2211yescharacteristic
183#1823C2211yescharacteristic
184#1823C2211yescharacteristic
185#1823C2211yescharacteristic
186#1808C2211yescharacteristic
187#1808C2211yescharacteristic
188#1803C2211yescharacteristic
189#1776C2211yescharacteristic
190#1776C2211yescharacteristic
191#1776C2211yescharacteristic
192#1776C2211yescharacteristic
193C4×#107C2211yescharacteristic
194C4×#107C2211yescharacteristic
195#1771C2211yescharacteristic
196#1763C2211yescharacteristic
197#1763C2211yescharacteristic
198#1752C2211yescharacteristic
199C8×C22⋊C4C2211yescharacteristic
200#1749C2211yescharacteristic
201C2×#340C2211yescharacteristic
202C2×#340C2211yescharacteristic
203C23×C8C2311yescharacteristic
204C23×C8C2311yescharacteristic
205#533—48no—
206C2×C4⋊Q8—21no—
207C2×C4⋊Q8—21no—
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×#125—21no—
212C2×#125—21no—
213C2×C22⋊Q8—21no—
214C2×C22⋊Q8—21no—
215C2×C22⋊Q8—21no—
216C2×C22⋊Q8D411yescharacteristic
217C2×C22⋊Q8C2311yescharacteristic
218C2×C4×Q8—21no—
219C2×C4×Q8—21no—
220C2×C4×Q8—21no—
221C2×C4×Q8—21no—
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2311yescharacteristic
224C2×#117—21no—
225C2×#117—21no—
226C2×#117—21no—
227C22×C4⋊C4C2311yescharacteristic
228C22×C4⋊C4C2311yescharacteristic
229C22×C4⋊C4C2311yescharacteristic
230C22×C4⋊C4C2311yescharacteristic
231C22×C42—21no—
232C22×C42C2311yescharacteristic
233#483—24no—
234#477—24no—
235#446—24no—
236C2×#107—24no—
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#106—24no—
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×C4⋊C8—24no—
255C2×C4⋊C8C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×C22⋊C8C2311yescharacteristic
272C2×C22⋊C8C2311yescharacteristic
273C2×#97C2311yescharacteristic
274C2×#97C2311yescharacteristic
275C2×#97C2311yescharacteristic
276C2×#97C2311yescharacteristic
277C2×C4×C8C2311yescharacteristic
278C2×C4×C8C2311yescharacteristic
279#401—21no—
280#401—21no—
281#400—21no—
282#400—21no—
283#400—21no—
284#400—21no—
285#400—21no—
286#400—21no—
287#400—21no—
288#400—21no—
289#400—21no—
290#400—21no—
291#400—21no—
292#398—21no—
293#398—21no—
294#398—21no—
295#398—21no—
296#398—21no—
297#398—21no—
298#398—21no—
299#398—21no—
300#398—21no—
301#398—21no—
302#395—21no—
303#395—21no—
304#395—21no—
305#395—21no—
306#395—21no—
307#391—21no—
308#391—21no—
309#391—21no—
310#391—21no—
311#391—21no—
312#391—21no—
313#391D411yescharacteristic
314#391C2311yescharacteristic
315#391C2311yescharacteristic
316#391C2311yescharacteristic
317#391C2311yescharacteristic
318#391C2311yescharacteristic
319#389—21no—
320#389—21no—
321#389—21no—
322#389—21no—
323#389—21no—
324#389—21no—
325#389D411yescharacteristic
326#389C2311yescharacteristic
327#389C2311yescharacteristic
328#389C2311yescharacteristic
329#389C2311yescharacteristic
330#389C2311yescharacteristic
331#389C2311yescharacteristic
332#389C2311yescharacteristic
333#389C2311yescharacteristic
334#389C2311yescharacteristic
335#389C2311yescharacteristic
336#389C2311yescharacteristic
337#389C2311yescharacteristic
338#389C2311yescharacteristic
339#389C2311yescharacteristic
340#389C2311yescharacteristic
341#387—21no—
342#387—21no—
343#387—21no—
344#387—21no—
345#387—21no—
346#387—21no—
347#387—21no—
348#387—21no—
349#387—21no—
350#387—21no—
351#387—21no—
352#387—21no—
353#387—21no—
354#387—21no—
355#387—21no—
356#387—21no—
357#387—21no—
358#387—21no—
359#387—21no—
360#387—21no—
361#387—21no—
362#387—21no—
363#387—21no—
364#387—21no—
365#387—21no—
366#387—21no—
367#387—21no—
368#387—21no—
369#387—21no—
370#387D411yescharacteristic
371#387D411yescharacteristic
372#385—21no—
373#385—21no—
374#385—21no—
375#385—21no—
376#385—21no—
377#385D411yescharacteristic
378#385D411yescharacteristic
379#384C2311yescharacteristic
380#384C2311yescharacteristic
381#384C2311yescharacteristic
382#384C2311yescharacteristic
383#384C2311yescharacteristic
384#383—21no—
385#383—21no—
386#383—21no—
387#382—21no—
388#382—21no—
389#382—21no—
390#382C2311yescharacteristic
391#382C2311yescharacteristic
392#382C2311yescharacteristic
393#382C2311yescharacteristic
394#382C2311yescharacteristic
395#382C2311yescharacteristic
396#381—21no—
397#381—21no—
398#381—21no—
399#381—21no—
400#381—21no—
401#380—21no—
402#380—21no—
403#380D411yescharacteristic
404#380C2311yescharacteristic
405#380C2311yescharacteristic
406#380C2311yescharacteristic
407C4×C4⋊C4—21no—
408C4×C4⋊C4—21no—
409C4×C4⋊C4—21no—
410C4×C4⋊C4—21no—
411C4×C4⋊C4C2311yescharacteristic
412C4×C4⋊C4C2311yescharacteristic
413C4×C4⋊C4C2311yescharacteristic
414C4×C4⋊C4C2311yescharacteristic
415C4×C4⋊C4C2311yescharacteristic
416C4×C4⋊C4C2311yescharacteristic
417C4×C4⋊C4C2311yescharacteristic
418C4×C4⋊C4C2311yescharacteristic
419C4×C4⋊C4C2311yescharacteristic
420C4×C4⋊C4C2311yescharacteristic
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C22⋊C4—21no—
428C4×C22⋊C4—21no—
429C4×C22⋊C4C2311yescharacteristic
430C4×C22⋊C4C2311yescharacteristic
431#376—21no—
432C2×#95—21no—
433C2×#95—21no—
434C2×#95—21no—
435#340C2311yescharacteristic
436#340C2311yescharacteristic
437#340C2311yescharacteristic
438#340C2311yescharacteristic
439#340C2311yescharacteristic
440#340C2311yescharacteristic
441#340C2311yescharacteristic
442#340C2311yescharacteristic
443#340C2311yescharacteristic
444#340C2311yescharacteristic
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
485C22×Q8—21no—
486C22×Q8—21no—
487C22×Q8—21no—
488C22×Q8C2×D411yescharacteristic
489C22×Q8C2411yescharacteristic
490C23×C4—21no—
491C23×C4—21no—
492C23×C4—21no—
493C23×C4—21no—
494C23×C4C2×D411yescharacteristic
495C23×C4C2×D411yescharacteristic
496C23×C4C2411yescharacteristic
497C22×C8—22no—
498C22×C8—22no—
499C22×C8—22no—
500C22×C8—22no—
501C22×C8—41no—
502C22×C8—41no—
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C22×C8C2411yescharacteristic
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C4⋊Q8—22no—
512C4⋊Q8—22no—
513C4⋊Q8—22no—
514C4⋊Q8—22no—
515C4⋊Q8—41no—
516C4⋊Q8—41no—
517C4⋊Q8—44no—
518C4⋊Q8—44no—
519#125—44no—
520#125—44no—
521C22⋊Q8—24no—
522C22⋊Q8—22no—
523C22⋊Q8—22no—
524C22⋊Q8—44no—
525C22⋊Q8—44no—
526C22⋊Q8—44no—
527C4×Q8—22no—
528C4×Q8—22no—
529C4×Q8—22no—
530C4×Q8—22no—
531C4×Q8—44no—
532C4×Q8—44no—
533C4×Q8—44no—
534C4×Q8—44no—
535#117—44no—
536#117—44no—
537#117—44no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—22no—
540C2×C4⋊C4—22no—
541C2×C4⋊C4—22no—
542C2×C4⋊C4—22no—
543C2×C4⋊C4—22no—
544C2×C4⋊C4—22no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—41no—
579C2×C4⋊C4C2×D411yescharacteristic
580C2×C4⋊C4C2×D411yescharacteristic
581C2×C4⋊C4C2×D411yescharacteristic
582C2×C4⋊C4C2×D411yescharacteristic
583C2×C4⋊C4C2×D411yescharacteristic
584C2×C4⋊C4C2×D411yescharacteristic
585C2×C4⋊C4C2×D411yescharacteristic
586C2×C4⋊C4C2×D411yescharacteristic
587C2×C4⋊C4C2×D411yescharacteristic
588C2×C4⋊C4#4114yes—
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4C2×D411yescharacteristic
609C2×C22⋊C4C2×D411yescharacteristic
610C2×C22⋊C4C2×D411yescharacteristic
611C2×C22⋊C4C2×D411yescharacteristic
612C2×C42—22no—
613C2×C42—22no—
614C2×C42—21no—
615C2×C42—21no—
616C2×C42—21no—
617C2×C42—21no—
618C2×C42—21no—
619C2×C42—21no—
620C2×C42—21no—
621C2×C42—21no—
622C2×C42—21no—
623C2×C42—21no—
624C2×C42—21no—
625C2×C42—21no—
626C2×C42—21no—
627C2×C42—21no—
628C2×C42—44no—
629C2×C42C2×D411yescharacteristic
630C2×C42C2×D411yescharacteristic
631C2×C42C2411yescharacteristic
632C2×C42C2411yescharacteristic
633C2×C42C2411yescharacteristic
634C2×C42C2411yescharacteristic
635C2×C42C2411yescharacteristic
636C2×C42C2411yescharacteristic
637#107—22no—
638#107—22no—
639#107—22no—
640#107—22no—
641#107—22no—
642#107—22no—
643#107—22no—
644#107—41no—
645#107—41no—
646#107—41no—
647#106—22no—
648#106—22no—
649#106—22no—
650#106—22no—
651#106—22no—
652#106—22no—
653C4⋊C8—22no—
654C4⋊C8—22no—
655C4⋊C8—22no—
656C4⋊C8—22no—
657C4⋊C8—22no—
658C4⋊C8—41no—
659C4⋊C8—41no—
660C4⋊C8#4114yes—
661#103—22no—
662#103—22no—
663#103—22no—
664#103—22no—
665#103—22no—
666#103—41no—
667#103—41no—
668#103—41no—
669C22⋊C8—22no—
670C22⋊C8—22no—
671#97—22no—
672#97—22no—
673#97—22no—
674#97—41no—
675C4×C8—22no—
676C4×C8—41no—
677#95—21no—
678#95—21no—
679#95—21no—
680#95—21no—
681#95—21no—
682#95—21no—
683#95—21no—
684#95—21no—
685#95—21no—
686#95—21no—
687#95—21no—
688#95—21no—
689#95—21no—
690#95—21no—
691#95—21no—
692#95—21no—
693#95—21no—
694#95—21no—
695#95—21no—
696#95—21no—
697#95—21no—
698#95—21no—
699#95—21no—
700#95—21no—
701#95—21no—
702#95—21no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95—21no—
709#95—21no—
710#95—21no—
711#95—21no—
712#95—21no—
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#95C2×D411yescharacteristic
731#95C2×D411yescharacteristic
732#95C2×D411yescharacteristic
733#95C2×D411yescharacteristic
734#95C2×D411yescharacteristic
735#95C2×D411yescharacteristic
736#95C2×D411yescharacteristic
737#95C2×D411yescharacteristic
738#95C2×D411yescharacteristic
739#95C2×D411yescharacteristic
740C24C22×D411yescharacteristic
741C2×Q8—22no—
742C2×Q8—22no—
743C2×Q8—21no—
744C2×Q8—21no—
745C2×Q8—21no—
746C2×Q8—21no—
747C2×Q8—21no—
748C2×Q8—21no—
749C2×Q8—41no—
750C2×Q8—42no—
751C2×Q8—42no—
752C2×Q8—42no—
753C2×Q8—42no—
754C2×Q8—42no—
755C2×Q8—42no—
756C2×Q8—42no—
757C2×Q8—81no—
758C2×Q8—81no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—24no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—41no—
785C22×C4—41no—
786C22×C4—42no—
787C22×C4—42no—
788C22×C4—42no—
789C22×C4—42no—
790C22×C4—42no—
791C22×C4—42no—
792C22×C4—42no—
793C22×C4—42no—
794C22×C4—81no—
795C22×C4—81no—
796C22×C4—81no—
797C22×C4C22×D411yescharacteristic
798C22×C4C22×D411yescharacteristic
799C22×C4C22×D411yescharacteristic
800C22×C4C22×D411yescharacteristic
801C22×C4C22×D411yescharacteristic
802C22×C4C22×D411yescharacteristic
803C22×C4C22×D411yescharacteristic
804C22×C4C22×D411yescharacteristic
805C22×C4C22×D411yescharacteristic
806C22×C4C22×D411yescharacteristic
807C22×C4C22×D411yescharacteristic
808C22×C4C22×D411yescharacteristic
809C22×C4C22×D411yescharacteristic
810C22×C4C2×#4112yes—
811C22×C42−1+412yes—
812C22×C4C2511yescharacteristic
813C2×C8—21no—
814C2×C8—21no—
815C2×C8—21no—
816C2×C8—21no—
817C2×C8—21no—
818C2×C8—21no—
819C2×C8—21no—
820C2×C8—21no—
821C2×C8—21no—
822C2×C8—21no—
823C2×C8—21no—
824C2×C8—21no—
825C2×C8—21no—
826C2×C8—21no—
827C2×C8—21no—
828C2×C8—21no—
829C2×C8—21no—
830C2×C8—21no—
831C2×C8—21no—
832C2×C8—21no—
833C2×C8—21no—
834C2×C8—21no—
835C2×C8—44no—
836C2×C8—44no—
837C2×C8C2×#4112yes—
838C2×C8C2×#4112yes—
839C4⋊C4—22no—
840C4⋊C4—22no—
841C4⋊C4—22no—
842C4⋊C4—24no—
843C4⋊C4—22no—
844C4⋊C4—22no—
845C4⋊C4—22no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—21no—
855C4⋊C4—21no—
856C4⋊C4—21no—
857C4⋊C4—21no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—21no—
873C4⋊C4—41no—
874C4⋊C4—41no—
875C4⋊C4—41no—
876C4⋊C4—42no—
877C4⋊C4—42no—
878C4⋊C4—42no—
879C4⋊C4—42no—
880C4⋊C4—42no—
881C4⋊C4—42no—
882C4⋊C4—42no—
883C4⋊C4—42no—
884C4⋊C4—42no—
885C4⋊C4—42no—
886C4⋊C4—42no—
887C4⋊C4—42no—
888C4⋊C4—42no—
889C4⋊C4—42no—
890C4⋊C4—42no—
891C4⋊C4—42no—
892C4⋊C4—42no—
893C4⋊C4—42no—
894C4⋊C4—42no—
895C4⋊C4—42no—
896C4⋊C4—42no—
897C4⋊C4—42no—
898C4⋊C4—42no—
899C4⋊C4—81no—
900C4⋊C4—81no—
901C4⋊C4—81no—
902C4⋊C4—81no—
903C4⋊C4—81no—
904C4⋊C4—81no—
905C4⋊C4—81no—
906C4⋊C4—81no—
907C4⋊C4—81no—
908C4⋊C4—81no—
909C4⋊C4C2×#4112yes—
910C4⋊C4C2×#4112yes—
911C4⋊C42−1+412yes—
912C22⋊C4—22no—
913C22⋊C4—22no—
914C22⋊C4—22no—
915C22⋊C4—42no—
916C22⋊C4—42no—
917C22⋊C4—42no—
918C22⋊C4—42no—
919C22⋊C4AGL(1,ℤ/8)14yes—
920C42—22no—
921C42—22no—
922C42—21no—
923C42—21no—
924C42—21no—
925C42—21no—
926C42—21no—
927C42—21no—
928C42—21no—
929C42—21no—
930C42—21no—
931C42—21no—
932C42—42no—
933C42—42no—
934C42—42no—
935C42—42no—
936C42—42no—
937C42—42no—
938C42—42no—
939C42—42no—
940C42—42no—
941C42—42no—
942C42—42no—
943C42—81no—
944C42—81no—
945C42—81no—
946C42C2×#4112yes—
947C422−1+412yes—
948C23—21no—
949C23—21no—
950C23—21no—
951C23—21no—
952C23#54812yes—
953C23C2×AGL(1,ℤ/8)12yes—
954C23#57812yes—
955C23C23×D411yescharacteristic
956Q8—44no—
957Q8—41no—
958Q8—41no—
959Q8—41no—
960Q8—41no—
961Q8—84no—
962Q8—84no—
963Q8—84no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—22no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—44no—
1006C2×C4—44no—
1007C2×C4—41no—
1008C2×C4—48no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—84no—
1054C2×C4—84no—
1055C2×C4—162no—
1056C2×C4#54712yes—
1057C2×C4#54712yes—
1058C2×C4#54812yes—
1059C2×C4C2×AGL(1,ℤ/8)12yes—
1060C2×C4C2×AGL(1,ℤ/8)12yes—
1061C2×C4C22×#4111yescharacteristic
1062C2×C4C22×#4111yescharacteristic
1063C2×C4C2×2−1+411yescharacteristic
1064C2×C4C2×2−1+411yescharacteristic
1065C2×C4C2×2−1+411yescharacteristic
1066C2×C4#58511yescharacteristic
1067C8—22no—
1068C8—22no—
1069C8—41no—
1070C8—41no—
1071C8—41no—
1072C8—41no—
1073C8—41no—
1074C8—41no—
1075C22—22no—
1076C22—22no—
1077C22—22no—
1078C22—22no—
1079C22—22no—
1080C22—22no—
1081C22#336714yes—
1082C22C2×#54711yescharacteristic
1083C22C2×#54811yescharacteristic
1084C22#348911yescharacteristic
1085C22C22×AGL(1,ℤ/8)11yescharacteristic
1086C22C2×#57811yescharacteristic
1087C22#358411yescharacteristic
1088C22#358611yescharacteristic
1089C4—22no—
1090C4—22no—
1091C4—22no—
1092C4—22no—
1093C4—22no—
1094C4—41no—
1095C4—41no—
1096C4—41no—
1097C4—41no—
1098C4—41no—
1099C4—42no—
1100C4—42no—
1101C4—41no—
1102C4—42no—
1103C4—41no—
1104C4—41no—
1105C4—81no—
1106C4—81no—
1107C4—81no—
1108C4—81no—
1109C4—81no—
1110C4—81no—
1111C4—81no—
1112C4—81no—
1113C4—81no—
1114C4—81no—
1115C4—81no—
1116C4—81no—
1117C4—81no—
1118C4#347511yescharacteristic
1119C4#350911yescharacteristic
1120C4#352311yescharacteristic
1121C4#356311yescharacteristic
1122C2—24no—
1123C2#5911111yescharacteristic
1124C2#6125211yescharacteristic
1125C2#6126411yescharacteristic
1126C2C2×#336711yescharacteristic
1127C2#6134411yescharacteristic
1128C2#6213711yescharacteristic
1129C2#6216811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #32497C2semidirect
4. #32483C2semidirect
5. #32335C2semidirect
6. #32313C2semidirect
7. #28801C2semidirect
11. #27142C2semidirect
12. #27127C2semidirect
13. #26521C2semidirect
14. #26521C2semidirect
15. #26513C2semidirect
16. #26294C2semidirect
17. #26038C2semidirect
20. #25483C2semidirect
21. #25004C2semidirect
25. #23073C2semidirect
27. #22743C2semidirect

Maximal subgroups

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

subgroupindex
#593332
#361332
#324972
#324832
#323352
#323132
#288012
#279692
#277132
#276972
#271422
#271272
#265212
#265132
#262942
#260382
#259942
#259882
#254832
#250042
#248372
#245802
#245772
#230732
#229542
#227432
#226152
#226112
#215792
C2×#19492