Finite Group Databasebeta

← #6554752

Subgroups — #6554752

Order 512.

1364 conjugacy classes of subgroups.

The subgroup lattice has 1105 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36383C211yesmaximal, characteristic
2#34328C211yesmaximal, characteristic
3#30155C211yesmaximal, characteristic
4#30148C211yesmaximal, characteristic
5#30001C211yesmaximal, characteristic
6#29541C211yesmaximal, characteristic
7#29541C211yesmaximal, characteristic
8#29431C211yesmaximal, characteristic
9#29430C211yesmaximal, characteristic
10#29180C211yesmaximal, characteristic
11#28287C211yesmaximal, characteristic
12#27371C211yesmaximal, characteristic
13#27362C211yesmaximal, characteristic
14#27205C211yesmaximal, characteristic
15#27196C211yesmaximal, characteristic
16#26865C211yesmaximal, characteristic
17#26856C211yesmaximal, characteristic
18#26699C211yesmaximal, characteristic
19#26690C211yesmaximal, characteristic
20#25067C211yesmaximal, characteristic
21#25001C211yesmaximal, characteristic
22#24336C211yesmaximal, characteristic
23#24336C211yesmaximal, characteristic
24#23779C211yesmaximal, characteristic
25#23777C211yesmaximal, characteristic
26#23679C211yesmaximal, characteristic
27#23064C211yesmaximal, characteristic
28#22967C211yesmaximal, characteristic
29#22821C211yesmaximal, characteristic
30#22809C211yesmaximal, characteristic
31#22769C211yesmaximal, characteristic
32C2×#557C2211yescharacteristic
33C2×#479C2211yescharacteristic
34C2×#479C2211yescharacteristic
35C2×C4×Q16C2211yescharacteristic
36C2×C4×Q16C2211yescharacteristic
37#2864C2211yescharacteristic
38#2863C2211yescharacteristic
39#2863C2211yescharacteristic
40#2581C2211yescharacteristic
41#2581C2211yescharacteristic
42#2533—21no—
43#2533—21no—
44#2524—21no—
45#2524—21no—
46#2506C2211yescharacteristic
47#2506C2211yescharacteristic
48#2462—21no—
49#2462—21no—
50#2446C2211yescharacteristic
51#2446C2211yescharacteristic
52#2371—21no—
53#2371—21no—
54#2371—21no—
55#2371—21no—
56#2370C2211yescharacteristic
57#2370C2211yescharacteristic
58#2365—21no—
59#2365C2211yescharacteristic
60#2356—21no—
61#2356C2211yescharacteristic
62#2356C2211yescharacteristic
63#2356C2211yescharacteristic
64#2355C2211yescharacteristic
65#2355C2211yescharacteristic
66#2351C2211yescharacteristic
67#2336—21no—
68#2336—21no—
69#2327—21no—
70C4×C4⋊Q8C2211yescharacteristic
71C4×C4⋊Q8C2211yescharacteristic
72C4×#125C2211yescharacteristic
73C4×#125C2211yescharacteristic
74#2295C2211yescharacteristic
75#2295C2211yescharacteristic
76#2295C2211yescharacteristic
77#2295C2211yescharacteristic
78#2295C2211yescharacteristic
79#2276—21no—
80C42×Q8C2211yescharacteristic
81#2101C2211yescharacteristic
82#2100C2211yescharacteristic
83#2097C2211yescharacteristic
84#2095C2211yescharacteristic
85#2088C2211yescharacteristic
86#2088C2211yescharacteristic
87#2088C2211yescharacteristic
88#2088C2211yescharacteristic
89#2087C2211yescharacteristic
90#2087C2211yescharacteristic
91#2086C2211yescharacteristic
92#2086C2211yescharacteristic
93#2085C2211yescharacteristic
94#2084C2211yescharacteristic
95#2083C2211yescharacteristic
96#2074C2211yescharacteristic
97#2072C2211yescharacteristic
98#2072C2211yescharacteristic
99#2068C2211yescharacteristic
100#2068C2211yescharacteristic
101#2068C2211yescharacteristic
102#2068C2211yescharacteristic
103#2068C2211yescharacteristic
104#2068C2211yescharacteristic
105#2066C2211yescharacteristic
106#2066C2211yescharacteristic
107#2066C2211yescharacteristic
108#2066C2211yescharacteristic
109#2059C2211yescharacteristic
110#2059C2211yescharacteristic
111#2057C2211yescharacteristic
112#2057C2211yescharacteristic
113#2056C2211yescharacteristic
114#2056C2211yescharacteristic
115#2043C2211yescharacteristic
116#2026C2211yescharacteristic
117#2026C2211yescharacteristic
118#2024C2211yescharacteristic
119#2024C2211yescharacteristic
120#2016C2211yescharacteristic
121#1991C2211yescharacteristic
122#1991C2211yescharacteristic
123#1984C2211yescharacteristic
124#1984C2211yescharacteristic
125#1981C2211yescharacteristic
126#1981C2211yescharacteristic
127#1969C2211yescharacteristic
128#1969C2211yescharacteristic
129#1949C2211yescharacteristic
130#1949C2211yescharacteristic
131#1948C2211yescharacteristic
132#1947C2211yescharacteristic
133#1942C2211yescharacteristic
134#1941C2211yescharacteristic
135#1933C2211yescharacteristic
136#1933C2211yescharacteristic
137#1933C2211yescharacteristic
138#1933C2211yescharacteristic
139#1928C2211yescharacteristic
140#1928C2211yescharacteristic
141#1927C2211yescharacteristic
142#1927C2211yescharacteristic
143#1927C2211yescharacteristic
144#1927C2211yescharacteristic
145#1927C2211yescharacteristic
146#1927C2211yescharacteristic
147#1927C2211yescharacteristic
148#1927C2211yescharacteristic
149#1921C2211yescharacteristic
150#1921C2211yescharacteristic
151#1920C2211yescharacteristic
152#1920C2211yescharacteristic
153#1920C2211yescharacteristic
154#1919C2211yescharacteristic
155#1919C2211yescharacteristic
156#1918C2211yescharacteristic
157#1918C2211yescharacteristic
158#1918C2211yescharacteristic
159#1918C2211yescharacteristic
160#1918C2211yescharacteristic
161#1918C2211yescharacteristic
162#1918C2211yescharacteristic
163#1916C2211yescharacteristic
164#1916C2211yescharacteristic
165#1916C2211yescharacteristic
166#1916C2211yescharacteristic
167#1878C2211yescharacteristic
168#1878C2211yescharacteristic
169#1878C2211yescharacteristic
170#1878C2211yescharacteristic
171#1878C2211yescharacteristic
172#1878C2211yescharacteristic
173#1865C2211yescharacteristic
174#1865C2211yescharacteristic
175#1865C2211yescharacteristic
176#1863C2211yescharacteristic
177#1863C2211yescharacteristic
178#1863C2211yescharacteristic
179#1846C2211yescharacteristic
180#1842C2211yescharacteristic
181#1835C2211yescharacteristic
182#1831C2211yescharacteristic
183#1831C2211yescharacteristic
184#1805C2211yescharacteristic
185#1805C2211yescharacteristic
186#1805C2211yescharacteristic
187#1805C2211yescharacteristic
188C4×#107C2211yescharacteristic
189C4×#107C2211yescharacteristic
190C4×#107C2211yescharacteristic
191C4×#106C2211yescharacteristic
192C8×C4⋊C4C2211yescharacteristic
193C8×C4⋊C4C2211yescharacteristic
194C4×C4⋊C8C2211yescharacteristic
195C4×C4⋊C8C2211yescharacteristic
196C4×C4⋊C8C2211yescharacteristic
197C4×#103C2211yescharacteristic
198C4×#103C2211yescharacteristic
199C4×#103C2211yescharacteristic
200C4×#103C2211yescharacteristic
201C4×#103C2211yescharacteristic
202C4×#103C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205#557—24no—
206#557—24no—
207C2×C4⋊Q8—21no—
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×#125—21no—
211C2×#125—21no—
212C2×#125—21no—
213C2×#125—21no—
214C2×#125C2311yescharacteristic
215C2×#125C2311yescharacteristic
216C2×C4×Q8—21no—
217C2×C4×Q8—21no—
218C2×C4×Q8—21no—
219C2×C4×Q8D411yescharacteristic
220C2×C4×Q8D411yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2311yescharacteristic
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2311yescharacteristic
229#479—24no—
230#479—24no—
231C4×Q16—24no—
232C4×Q16—24no—
233C2×#107C2311yescharacteristic
234C2×#107C2311yescharacteristic
235C2×#107C2311yescharacteristic
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×C4⋊C8C2311yescharacteristic
248C2×C4⋊C8C2311yescharacteristic
249C2×C4⋊C8C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252C2×C4⋊C8C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
254C2×C4⋊C8C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×#103C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×C4×C8C2311yescharacteristic
276C2×C4×C8C2311yescharacteristic
277C2×C4×C8C2311yescharacteristic
278C2×C4×C8C2311yescharacteristic
279C2×C4×C8C2311yescharacteristic
280C2×C4×C8C2311yescharacteristic
281#400—21no—
282#400—21no—
283#400—21no—
284#400—21no—
285#400—21no—
286#400—21no—
287#398—21no—
288#398—21no—
289#398—21no—
290#398—21no—
291#395—21no—
292#395—21no—
293#391—21no—
294#391—21no—
295#391—21no—
296#391C2311yescharacteristic
297#391C2311yescharacteristic
298#391C2311yescharacteristic
299#391C2311yescharacteristic
300#391C2311yescharacteristic
301#391C2311yescharacteristic
302#391C2311yescharacteristic
303#391C2311yescharacteristic
304#391C2311yescharacteristic
305#391C2311yescharacteristic
306#391C2311yescharacteristic
307#391C2311yescharacteristic
308#389—21no—
309#389—21no—
310#389—21no—
311#389—21no—
312#389—21no—
313#389—21no—
314#389—21no—
315#389C2311yescharacteristic
316#389C2311yescharacteristic
317#389C2311yescharacteristic
318#389C2311yescharacteristic
319#389C2311yescharacteristic
320#389C2311yescharacteristic
321#389C2311yescharacteristic
322#389C2311yescharacteristic
323#389C2311yescharacteristic
324#389C2311yescharacteristic
325#389C2311yescharacteristic
326#389C2311yescharacteristic
327#389C2311yescharacteristic
328#389C2311yescharacteristic
329#389C2311yescharacteristic
330#389C2311yescharacteristic
331#387—21no—
332#387—21no—
333#387—21no—
334#387—21no—
335#387—21no—
336#387—21no—
337#387—21no—
338#387—21no—
339#387—21no—
340#387—21no—
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#387—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#384C2311yescharacteristic
382#384C2311yescharacteristic
383#383—21no—
384#383—21no—
385#383—21no—
386#383—21no—
387#383—21no—
388#382—21no—
389#382—21no—
390#382C2311yescharacteristic
391#382C2311yescharacteristic
392#382C2311yescharacteristic
393#382C2311yescharacteristic
394C4×C4⋊C4—21no—
395C4×C4⋊C4—21no—
396C4×C4⋊C4—21no—
397C4×C4⋊C4—21no—
398C4×C4⋊C4—21no—
399C4×C4⋊C4—21no—
400C4×C4⋊C4—21no—
401C4×C4⋊C4—21no—
402C4×C4⋊C4—21no—
403C4×C4⋊C4—21no—
404C4×C4⋊C4—21no—
405C4×C4⋊C4—21no—
406C4×C4⋊C4—21no—
407C4×C4⋊C4—21no—
408C4×C4⋊C4—21no—
409C4×C4⋊C4—21no—
410C4×C4⋊C4—21no—
411C4×C4⋊C4D411yescharacteristic
412C4×C4⋊C4D411yescharacteristic
413C4×C4⋊C4D411yescharacteristic
414C4×C4⋊C4D411yescharacteristic
415C4×C4⋊C4D411yescharacteristic
416C4×C4⋊C4D411yescharacteristic
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×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431#376—21no—
432#376—21no—
433#376—21no—
434#376—21no—
435#376—21no—
436#376—21no—
437#376—21no—
438#376—21no—
439C43C2311yescharacteristic
440C43C2311yescharacteristic
441C43C2311yescharacteristic
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#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484C22×Q8—21no—
485C22×Q8C2×D411yescharacteristic
486C22×Q8C2411yescharacteristic
487C22×Q8C2411yescharacteristic
488C22×Q8C2411yescharacteristic
489C2×Q16—22no—
490C2×Q16—22no—
491C2×Q16—22no—
492C2×Q16—22no—
493C2×Q16—41no—
494C2×Q16—41no—
495C22×C8C2411yescharacteristic
496C22×C8C2411yescharacteristic
497C22×C8C2411yescharacteristic
498C22×C8C2411yescharacteristic
499C22×C8C2411yescharacteristic
500C22×C8C2411yescharacteristic
501C22×C8C2411yescharacteristic
502C22×C8C2411yescharacteristic
503C4⋊Q8—28no—
504C4⋊Q8—22no—
505C4⋊Q8—22no—
506C4⋊Q8—22no—
507C4⋊Q8—41no—
508#125—28no—
509#125—28no—
510#125—22no—
511#125—22no—
512#125—22no—
513#125—44no—
514#125—44no—
515#125#4114yes—
516C4×Q8—28no—
517C4×Q8—22no—
518C4×Q8—22no—
519C4×Q8—24no—
520C4×Q8—22no—
521C4×Q8—22no—
522C4×Q8—22no—
523C4×Q8—22no—
524C4×Q8—22no—
525C4×Q8—22no—
526C4×Q8—22no—
527C4×Q8—22no—
528C4×Q8—22no—
529C4×Q8—22no—
530C4×Q8—22no—
531C4×Q8—42no—
532C4×Q8—41no—
533C4×Q8—41no—
534C4×Q8—44no—
535C4×Q8—44no—
536C4×Q8#4114yes—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
572C2×C4⋊C4C2×D411yescharacteristic
573C2×C4⋊C4C2×D411yescharacteristic
574C2×C4⋊C4C2×D411yescharacteristic
575C2×C4⋊C4C2×D411yescharacteristic
576C2×C4⋊C4C2×D411yescharacteristic
577C2×C4⋊C4C2×D411yescharacteristic
578C2×C4⋊C4C2×D411yescharacteristic
579C2×C4⋊C4C2×D411yescharacteristic
580C2×C4⋊C4C2411yescharacteristic
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C42—21no—
594C2×C42—21no—
595C2×C42—21no—
596C2×C42—21no—
597C2×C42—21no—
598C2×C42—21no—
599C2×C42—21no—
600C2×C42—21no—
601C2×C42—21no—
602C2×C42—21no—
603C2×C42—21no—
604C2×C42—21no—
605C2×C42—21no—
606C2×C42—21no—
607C2×C42—21no—
608C2×C42—21no—
609C2×C42—21no—
610C2×C42—21no—
611C2×C42C2×D411yescharacteristic
612C2×C42C2×D411yescharacteristic
613C2×C42C2×D411yescharacteristic
614C2×C42C2×D411yescharacteristic
615C2×C42C2×D411yescharacteristic
616C2×C42C2×D411yescharacteristic
617C2×C42C2×D411yescharacteristic
618C2×C42C2×D411yescharacteristic
619C2×C42C2×D411yescharacteristic
620C2×C42C2×D411yescharacteristic
621C2×C42C2×D411yescharacteristic
622C2×C42C2×D411yescharacteristic
623C2×C42C2411yescharacteristic
624C2×C42C2411yescharacteristic
625C2×C42C2411yescharacteristic
626C2×C42C2411yescharacteristic
627C2×C42C2411yescharacteristic
628C2×C42C2411yescharacteristic
629C2×C42C2411yescharacteristic
630#107—22no—
631#107—22no—
632#107—22no—
633#107—22no—
634#107—22no—
635#107—22no—
636#107—41no—
637#107—41no—
638#106—22no—
639#106—22no—
640#106—41no—
641#106—41no—
642#106—41no—
643#106—41no—
644C4⋊C8—22no—
645C4⋊C8—22no—
646C4⋊C8—22no—
647C4⋊C8—41no—
648C4⋊C8—41no—
649C4⋊C8—41no—
650C4⋊C8—41no—
651C4⋊C8—41no—
652#103—22no—
653#103—22no—
654#103—22no—
655#103—22no—
656#103—22no—
657#103—22no—
658#103—22no—
659#103—22no—
660#103—22no—
661#103—22no—
662#103—41no—
663#103—41no—
664#103—41no—
665#103—41no—
666#103—41no—
667#103—41no—
668#103—41no—
669#103—41no—
670#103—41no—
671#103—41no—
672C4×C8—22no—
673C4×C8—22no—
674C4×C8—41no—
675C4×C8—41no—
676C4×C8—41no—
677C4×C8—41no—
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#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95C2×D411yescharacteristic
738#95C2×D411yescharacteristic
739#95C2×D411yescharacteristic
740#95C2×D411yescharacteristic
741#95C2×D411yescharacteristic
742#95C2×D411yescharacteristic
743C2×Q8—24no—
744C2×Q8—22no—
745C2×Q8—22no—
746C2×Q8—21no—
747C2×Q8—21no—
748C2×Q8—21no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8—21no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—41no—
763C2×Q8—42no—
764C2×Q8—42no—
765C2×Q8C2×#4112yes—
766C2×Q82−1+412yes—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
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×C4C22×D411yescharacteristic
784C22×C4C22×D411yescharacteristic
785C22×C4C22×D411yescharacteristic
786C22×C4C22×D411yescharacteristic
787C22×C4C22×D411yescharacteristic
788C22×C4C22×D411yescharacteristic
789C22×C4C22×D411yescharacteristic
790C22×C4C22×D411yescharacteristic
791C22×C4C22×D411yescharacteristic
792C22×C4C22×D411yescharacteristic
793C22×C4C22×D411yescharacteristic
794C22×C4C22×D411yescharacteristic
795C22×C4C22×D411yescharacteristic
796C22×C4C22×D411yescharacteristic
797C22×C4C2511yescharacteristic
798Q16—44no—
799Q16—44no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—21no—
809C2×C8—21no—
810C2×C8—21no—
811C2×C8—21no—
812C2×C8—21no—
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×C82−1+412yes—
824C4⋊C4—24no—
825C4⋊C4—24no—
826C4⋊C4—24no—
827C4⋊C4—24no—
828C4⋊C4—24no—
829C4⋊C4—24no—
830C4⋊C4—24no—
831C4⋊C4—24no—
832C4⋊C4—22no—
833C4⋊C4—22no—
834C4⋊C4—22no—
835C4⋊C4—22no—
836C4⋊C4—22no—
837C4⋊C4—22no—
838C4⋊C4—22no—
839C4⋊C4—21no—
840C4⋊C4—21no—
841C4⋊C4—21no—
842C4⋊C4—21no—
843C4⋊C4—21no—
844C4⋊C4—21no—
845C4⋊C4—21no—
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—41no—
863C4⋊C4—42no—
864C4⋊C4—42no—
865C4⋊C4—42no—
866C4⋊C4—42no—
867C4⋊C4—42no—
868C4⋊C4—42no—
869C4⋊C4—42no—
870C4⋊C4—42no—
871C4⋊C4—42no—
872C4⋊C4—42no—
873C4⋊C4—42no—
874C4⋊C4—42no—
875C4⋊C4—42no—
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—81no—
888C4⋊C4—81no—
889C4⋊C4#13514yes—
890C4⋊C4C2×#4112yes—
891C4⋊C4C2×#4112yes—
892C4⋊C4C2×#4112yes—
893C42—24no—
894C42—24no—
895C42—24no—
896C42—22no—
897C42—22no—
898C42—22no—
899C42—22no—
900C42—22no—
901C42—22no—
902C42—22no—
903C42—21no—
904C42—21no—
905C42—21no—
906C42—21no—
907C42—21no—
908C42—21no—
909C42—21no—
910C42—21no—
911C42—21no—
912C42—21no—
913C42—21no—
914C42—21no—
915C42—41no—
916C42—41no—
917C42—41no—
918C42—41no—
919C42—41no—
920C42—42no—
921C42—42no—
922C42—42no—
923C42—42no—
924C42—42no—
925C42—42no—
926C42—42no—
927C42—42no—
928C42—42no—
929C42—42no—
930C42—42no—
931C42—81no—
932C42—81no—
933C42—81no—
934C42—81no—
935C42C2×#4112yes—
936C42C2×#4112yes—
937C23C23×D411yescharacteristic
938Q8—22no—
939Q8—22no—
940Q8—22no—
941Q8—22no—
942Q8—44no—
943Q8—48no—
944Q8—41no—
945Q8—41no—
946Q8—41no—
947Q8—41no—
948Q8—41no—
949Q8—41no—
950Q8—41no—
951Q8—41no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—22no—
972C2×C4—21no—
973C2×C4—22no—
974C2×C4—21no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—22no—
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—21no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
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#52512yes—
1036C2×C4#52512yes—
1037C2×C4C2×#13512yes—
1038C2×C4C2×#13512yes—
1039C2×C4C2×#13512yes—
1040C2×C4#57512yes—
1041C2×C4#57812yes—
1042C2×C4C22×#4111yescharacteristic
1043C2×C4C22×#4111yescharacteristic
1044C2×C4C2×2−1+411yescharacteristic
1045C2×C4C2×2−1+411yescharacteristic
1046C2×C4#58511yescharacteristic
1047C2×C4#58511yescharacteristic
1048C8—22no—
1049C8—41no—
1050C8—41no—
1051C8—41no—
1052C8—41no—
1053C8—41no—
1054C8—41no—
1055C8—41no—
1056C22C2×#52511yescharacteristic
1057C22#348911yescharacteristic
1058C22#349711yescharacteristic
1059C22C22×#13511yescharacteristic
1060C22C2×#57511yescharacteristic
1061C22C2×#57811yescharacteristic
1062C22#358611yescharacteristic
1063C4—22no—
1064C4—22no—
1065C4—22no—
1066C4—22no—
1067C4—22no—
1068C4—22no—
1069C4—22no—
1070C4—41no—
1071C4—42no—
1072C4—42no—
1073C4—41no—
1074C4—41no—
1075C4—41no—
1076C4—42no—
1077C4—41no—
1078C4—41no—
1079C4—41no—
1080C4—42no—
1081C4—42no—
1082C4—81no—
1083C4—81no—
1084C4—81no—
1085C4—81no—
1086C4—81no—
1087C4—81no—
1088C4—81no—
1089C4—81no—
1090C4—81no—
1091C4—81no—
1092C4—81no—
1093C4#349511yescharacteristic
1094C4#349511yescharacteristic
1095C4#352311yescharacteristic
1096C4#352411yescharacteristic
1097C2#3583211yescharacteristic
1098C2#6053611yescharacteristic
1099C2#6059411yescharacteristic
1100C2#6210411yescharacteristic
1101C2#6213011yescharacteristic
1102C2#6236411yescharacteristic
1103C2#6239911yescharacteristic
subgroupG/H
center, socle, prime radicalC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#363832
#343282
#301552
#301482
#300012
#295412
#294312
#294302
#291802
#282872
#273712
#273622
#272052
#271962
#268652
#268562
#266992
#266902
#250672
#250012
#243362
#237792
#237772
#236792
#230642
#229672
#228212
#228092
#227692