Finite Group Databasebeta

← #7557594

Subgroups — #7557594

Order 512.

1383 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59323C211yesmaximal, characteristic
2#36478C211yesmaximal, characteristic, complemented
3#32510C211yesmaximal, characteristic, complemented
4#32505C211yesmaximal, characteristic, complemented
5#32354C211yesmaximal, characteristic, complemented
6#32342C211yesmaximal, characteristic, complemented
7#28810C211yesmaximal, characteristic, complemented
8#27951C211yesmaximal, characteristic, complemented
9#26865C211yesmaximal, characteristic, complemented
10#26862C211yesmaximal, characteristic, complemented
11#26448C211yesmaximal, characteristic, complemented
12#26347C211yesmaximal, characteristic
13#26343C211yesmaximal, characteristic
14#26286C211yesmaximal, characteristic, complemented
15#26066C211yesmaximal, characteristic, complemented
16#26061C211yesmaximal, characteristic, complemented
17#26051C211yesmaximal, characteristic, complemented
18#25999C211yesmaximal, characteristic, complemented
19#25989C211yesmaximal, characteristic, complemented
20#25473C211yesmaximal, characteristic, complemented
21#25457C211yesmaximal, characteristic, complemented
22#25451C211yesmaximal, characteristic, complemented
23#25064C211yesmaximal, characteristic, complemented
24#24839C211yesmaximal, characteristic
25#22966C211yesmaximal, characteristic, complemented
26#22952C211yesmaximal, characteristic, complemented
27#22923C211yesmaximal, characteristic
28#22923C211yesmaximal, characteristic
29#22727C211yesmaximal, characteristic, complemented
30C4×#482C211yesmaximal, characteristic
31#21169C211yesmaximal, characteristic, complemented
32C2×#499C2211yescharacteristic
33C2×#498C2211yescharacteristic
34C2×#482C2211yescharacteristic
35C2×#478C2211yescharacteristic
36C2×#478C2211yescharacteristic
37C2×#476C2211yescharacteristic
38C2×C8×Q8C2211yescharacteristic
39C2×#427C2211yescharacteristic
40C2×#427C2211yescharacteristic
41C22×C4⋊C8C2211yescharacteristic
42#2863—21no—
43#2851C2211yescharacteristic
44#2748—21no—
45#2692—21no—
46#2606—21no—
47#2605—21no—
48#2589—21no—
49#2589—21no—
50#2587—21no—
51#2584C2211yescharacteristic
52#2580C2211yescharacteristic
53#2574—21no—
54#2566C2211yescharacteristic
55#2556—21no—
56#2556—21no—
57#2550C2211yescharacteristic
58#2550C2211yescharacteristic
59#2542C2211yescharacteristic
60#2522—21no—
61#2508C2211yescharacteristic
62#2507C2211yescharacteristic
63#2506C2211yescharacteristic
64#2506C2211yescharacteristic
65#2454—21no—
66#2450—21no—
67#2441C2211yescharacteristic
68#2441C2211yescharacteristic
69#2439C2211yescharacteristic
70#2439C2211yescharacteristic
71#2370C2211yescharacteristic
72#2370C2211yescharacteristic
73#2369C2211yescharacteristic
74#2368—21no—
75#2363C2211yescharacteristic
76#2363C2211yescharacteristic
77#2355C2211yescharacteristic
78#2355C2211yescharacteristic
79#2349C2211yescharacteristic
80#2347C2211yescharacteristic
81#2347C2211yescharacteristic
82C4×#125—21no—
83C4×C22⋊Q8C2211yescharacteristic
84C4×#121C2211yescharacteristic
85#2285C2211yescharacteristic
86C4×#117C2211yescharacteristic
87#2101C2211yescharacteristic
88#2099C2211yescharacteristic
89#2093C2211yescharacteristic
90#2092C2211yescharacteristic
91#2088C2211yescharacteristic
92#2088C2211yescharacteristic
93#2088C2211yescharacteristic
94#2088C2211yescharacteristic
95#2088C2211yescharacteristic
96#2087C2211yescharacteristic
97#2087C2211yescharacteristic
98#2086C2211yescharacteristic
99#2085C2211yescharacteristic
100#2085C2211yescharacteristic
101#2084C2211yescharacteristic
102#2084C2211yescharacteristic
103#2084C2211yescharacteristic
104#2084C2211yescharacteristic
105#2083C2211yescharacteristic
106#2083C2211yescharacteristic
107#2067C2211yescharacteristic
108#2067C2211yescharacteristic
109#2065C2211yescharacteristic
110#2065C2211yescharacteristic
111#2059C2211yescharacteristic
112#2059C2211yescharacteristic
113#2059C2211yescharacteristic
114#2059C2211yescharacteristic
115#2057C2211yescharacteristic
116#2057C2211yescharacteristic
117#2057C2211yescharacteristic
118#2057C2211yescharacteristic
119#1991C2211yescharacteristic
120#1991C2211yescharacteristic
121#1989C2211yescharacteristic
122#1989C2211yescharacteristic
123#1988C2211yescharacteristic
124#1984C2211yescharacteristic
125#1949C2211yescharacteristic
126#1949C2211yescharacteristic
127#1949C2211yescharacteristic
128#1949C2211yescharacteristic
129#1949C2211yescharacteristic
130#1949C2211yescharacteristic
131#1949C2211yescharacteristic
132#1948C2211yescharacteristic
133#1948C2211yescharacteristic
134#1948C2211yescharacteristic
135#1948C2211yescharacteristic
136#1947C2211yescharacteristic
137#1947C2211yescharacteristic
138#1942C2211yescharacteristic
139#1942C2211yescharacteristic
140#1941C2211yescharacteristic
141#1941C2211yescharacteristic
142#1941C2211yescharacteristic
143#1941C2211yescharacteristic
144#1939C2211yescharacteristic
145#1939C2211yescharacteristic
146#1939C2211yescharacteristic
147#1934C2211yescharacteristic
148#1934C2211yescharacteristic
149#1926C2211yescharacteristic
150#1926C2211yescharacteristic
151#1926C2211yescharacteristic
152#1925C2211yescharacteristic
153#1921C2211yescharacteristic
154#1921C2211yescharacteristic
155#1921C2211yescharacteristic
156#1921C2211yescharacteristic
157#1921C2211yescharacteristic
158#1921C2211yescharacteristic
159#1920C2211yescharacteristic
160#1920C2211yescharacteristic
161#1920C2211yescharacteristic
162#1919C2211yescharacteristic
163#1919C2211yescharacteristic
164#1918C2211yescharacteristic
165#1916C2211yescharacteristic
166#1916C2211yescharacteristic
167#1893C2211yescharacteristic
168#1893C2211yescharacteristic
169#1875C2211yescharacteristic
170#1864C2211yescharacteristic
171#1862C2211yescharacteristic
172#1862C2211yescharacteristic
173#1862C2211yescharacteristic
174#1854C2211yescharacteristic
175#1854C2211yescharacteristic
176#1854C2211yescharacteristic
177#1854C2211yescharacteristic
178#1854C2211yescharacteristic
179#1850C2211yescharacteristic
180#1850C2211yescharacteristic
181#1846C2211yescharacteristic
182#1846C2211yescharacteristic
183#1846C2211yescharacteristic
184#1845C2211yescharacteristic
185#1825C2211yescharacteristic
186#1808C2211yescharacteristic
187#1807C2211yescharacteristic
188#1804C2211yescharacteristic
189C4×#107C2211yescharacteristic
190C4×#107C2211yescharacteristic
191C4×#107C2211yescharacteristic
192C4×#106C2211yescharacteristic
193C8×C4⋊C4C2211yescharacteristic
194C4×#102C2211yescharacteristic
195C4×#102C2211yescharacteristic
196C4×#102C2211yescharacteristic
197C4×#102C2211yescharacteristic
198C8×C22⋊C4C2211yescharacteristic
199C8×C22⋊C4C2211yescharacteristic
200C4×C22⋊C8C2211yescharacteristic
201#1735C2211yescharacteristic
202#1735C2211yescharacteristic
203C23×C8C2311yescharacteristic
204C23×C8C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×#125—21no—
208C2×#125—21no—
209C2×#125C2311yescharacteristic
210C2×#125C2311yescharacteristic
211C2×#125C2311yescharacteristic
212C2×C22⋊Q8—21no—
213C2×C22⋊Q8—21no—
214C2×C22⋊Q8D411yescharacteristic
215C2×#121C2311yescharacteristic
216C2×C4×Q8C2311yescharacteristic
217C2×C4×D4—21no—
218C2×C4×D4C2311yescharacteristic
219C2×C4×D4C2311yescharacteristic
220C2×C4×D4C2311yescharacteristic
221C2×#117C2311yescharacteristic
222C2×#117C2311yescharacteristic
223C2×#117C2311yescharacteristic
224C2×#117C2311yescharacteristic
225C22×C42C2311yescharacteristic
226#499—42no—
227#498—42no—
228#482Q818yescomplemented
229#478—24no—
230#478—42no—
231#476—42no—
232C8×Q8—24no—
233#427—42no—
234#427—42no—
235C2×#107C2311yescharacteristic
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×C4⋊C8—24no—
260C2×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×C22⋊C8C2311yescharacteristic
277C2×C22⋊C8C2311yescharacteristic
278C2×C4×C8C2311yescharacteristic
279C2×C4×C8C2311yescharacteristic
280C2×C4×C8C2311yescharacteristic
281C2×C4×C8C2311yescharacteristic
282C2×C4×C8C2311yescharacteristic
283C2×C4×C8C2311yescharacteristic
284#400—21no—
285#400—21no—
286#400—21no—
287#399—21no—
288#399—21no—
289#399—21no—
290#399—21no—
291#399—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#396—21no—
301#396—21no—
302#396—21no—
303#396—21no—
304#396—21no—
305#396—21no—
306#395—21no—
307#395—21no—
308#395—21no—
309#393—21no—
310#393—21no—
311#393—21no—
312#391—21no—
313#391—21no—
314#391—21no—
315#391—21no—
316#391—21no—
317#391—21no—
318#391—21no—
319#391—21no—
320#391D411yescharacteristic
321#390—21no—
322#390—21no—
323#390C2311yescharacteristic
324#390C2311yescharacteristic
325#390C2311yescharacteristic
326#389—21no—
327#389—21no—
328#389—21no—
329#389—21no—
330#389—21no—
331#389—21no—
332#389—21no—
333#389—21no—
334#389—21no—
335#389—21no—
336#389D411yescharacteristic
337#389C2311yescharacteristic
338#389C2311yescharacteristic
339#389C2311yescharacteristic
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#388—21no—
355#388—21no—
356#388—21no—
357#388—21no—
358#388—21no—
359#388—21no—
360#388—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#387D411yescharacteristic
380#387D411yescharacteristic
381#386—21no—
382#386—21no—
383#386—21no—
384#385—21no—
385#385—21no—
386#385—21no—
387#385—21no—
388#385—21no—
389#385—21no—
390#385—21no—
391#385—21no—
392#385D411yescharacteristic
393#385D411yescharacteristic
394#384C2311yescharacteristic
395#384C2311yescharacteristic
396#384C2311yescharacteristic
397#384C2311yescharacteristic
398#383—21no—
399#383—21no—
400#382—21no—
401#382C2311yescharacteristic
402#382C2311yescharacteristic
403#382C2311yescharacteristic
404#382C2311yescharacteristic
405#382C2311yescharacteristic
406#380—21no—
407#380—21no—
408#380—21no—
409#380D411yescharacteristic
410#380C2311yescharacteristic
411#380C2311yescharacteristic
412#380C2311yescharacteristic
413C4×C4⋊C4—21no—
414C4×C4⋊C4—21no—
415C4×C4⋊C4—21no—
416C4×C4⋊C4—21no—
417C4×C4⋊C4—21no—
418C4×C4⋊C4—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4—21no—
421C4×C4⋊C4—21no—
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
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C22⋊C4—21no—
437C4×C22⋊C4—21no—
438C4×C22⋊C4—21no—
439C4×C22⋊C4—21no—
440C4×C22⋊C4—21no—
441C4×C22⋊C4C2311yescharacteristic
442C4×C22⋊C4C2311yescharacteristic
443#376—21no—
444C2×#95—21no—
445C43—21no—
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#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488C22×Q8—21no—
489C22×Q8—21no—
490C22×Q8C2×D411yescharacteristic
491C22×D4—21no—
492C22×D4C2411yescharacteristic
493C23×C4—21no—
494C23×C4—21no—
495C23×C4—21no—
496C23×C4C2×D411yescharacteristic
497C23×C4C2×D411yescharacteristic
498C23×C4C2411yescharacteristic
499C22×C8—22no—
500C22×C8—22no—
501C22×C8—22no—
502C22×C8—22no—
503C22×C8—41no—
504C22×C8—41no—
505C22×C8C2411yescharacteristic
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C4⋊Q8—22no—
514C4⋊Q8—41no—
515C4⋊Q8—41no—
516C4⋊Q8—41no—
517#125—22no—
518#125—22no—
519#125—22no—
520#125—41no—
521#125—41no—
522#125—41no—
523#125—44no—
524#125—82no—
525C22⋊Q8—24no—
526C22⋊Q8—44no—
527C22⋊Q8—82no—
528#121—22no—
529#121C2×Q814yes—
530C4×Q8—22no—
531C4×Q8—22no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—41no—
535C4×D4—41no—
536C4×D4—41no—
537C4×D4—41no—
538C4×D4—82no—
539#117—22no—
540#117—22no—
541#117—41no—
542#117—41no—
543#117—41no—
544#117—41no—
545#117—41no—
546#117C2×Q814yes—
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—21no—
579C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
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⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4C2×D411yescharacteristic
622C2×C22⋊C4C2×D411yescharacteristic
623C2×C22⋊C4C2×D411yescharacteristic
624C2×C22⋊C4C2×D411yescharacteristic
625C2×C42—21no—
626C2×C42—22no—
627C2×C42—22no—
628C2×C42—21no—
629C2×C42—21no—
630C2×C42—21no—
631C2×C42—21no—
632C2×C42—21no—
633C2×C42—21no—
634C2×C42—21no—
635C2×C42—21no—
636C2×C42—21no—
637C2×C42—21no—
638C2×C42—21no—
639C2×C42—21no—
640C2×C42—21no—
641C2×C42—21no—
642C2×C42C2×D411yescharacteristic
643C2×C42C2×D411yescharacteristic
644C2×C42C2411yescharacteristic
645C2×C42C2411yescharacteristic
646C2×C42C2411yescharacteristic
647C2×C42C2411yescharacteristic
648C2×C42C2411yescharacteristic
649C2×C42C2411yescharacteristic
650#107—22no—
651#107—22no—
652#107—22no—
653#107—41no—
654#107—41no—
655#107—41no—
656#107—41no—
657#107—41no—
658#107—41no—
659#107—41no—
660#107—41no—
661#107C2×Q814yes—
662#106—22no—
663#106—22no—
664#106—22no—
665#106—22no—
666#106—41no—
667#106—41no—
668#106—41no—
669#106—41no—
670#106—41no—
671#106—41no—
672#106—41no—
673#106C2×Q814yes—
674C4⋊C8—22no—
675C4⋊C8—22no—
676C4⋊C8—22no—
677C4⋊C8—22no—
678C4⋊C8—22no—
679C4⋊C8—41no—
680C4⋊C8—41no—
681C4⋊C8#4114yes—
682#102—22no—
683#102—22no—
684#102—22no—
685#102—41no—
686#102—41no—
687#102—41no—
688#102C2×Q814yes—
689#102C2×Q814yes—
690C22⋊C8—22no—
691C22⋊C8C2×Q814yes—
692C4×C8—22no—
693C4×C8—22no—
694C4×C8—22no—
695C4×C8—22no—
696C4×C8—41no—
697C4×C8—41no—
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#95—21no—
738#95—21no—
739#95C2×D411yescharacteristic
740#95C2×D411yescharacteristic
741#95C2×D411yescharacteristic
742#95C2×D411yescharacteristic
743#95C2×D411yescharacteristic
744#95C2×D411yescharacteristic
745#95C2×D411yescharacteristic
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749C24—21no—
750C24C22×D411yescharacteristic
751C2×Q8—22no—
752C2×Q8—22no—
753C2×Q8—41no—
754C2×Q8—42no—
755C2×Q8—42no—
756C2×Q8—81no—
757C2×Q8—81no—
758C2×Q8—81no—
759C2×Q8—81no—
760C2×D4—24no—
761C2×D4—21no—
762C2×D4—21no—
763C2×D4—21no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—81no—
767C2×D4—81no—
768C2×D4C22×Q812yes—
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—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—41no—
792C22×C4—41no—
793C22×C4—41no—
794C22×C4—42no—
795C22×C4—42no—
796C22×C4—81no—
797C22×C4—81no—
798C22×C4—81no—
799C22×C4—81no—
800C22×C4—81no—
801C22×C4—81no—
802C22×C4—81no—
803C22×C4C22×D411yescharacteristic
804C22×C4C22×D411yescharacteristic
805C22×C4C22×D411yescharacteristic
806C22×C4C22×D411yescharacteristic
807C22×C4C22×D411yescharacteristic
808C22×C4C22×D411yescharacteristic
809C22×C4C22×D411yescharacteristic
810C22×C4C22×D411yescharacteristic
811C22×C4C22×D411yescharacteristic
812C22×C4C22×D411yescharacteristic
813C22×C4C22×D411yescharacteristic
814C22×C4C22×D411yescharacteristic
815C22×C4C22×D411yescharacteristic
816C22×C4C22×Q812yes—
817C22×C42−1+412yes—
818C22×C4C2511yescharacteristic
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—21no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—44no—
840C2×C8—44no—
841C2×C8C22×Q812yes—
842C2×C8C22×Q812yes—
843C2×C8C2×#4112yes—
844C2×C8C2×#4112yes—
845C4⋊C4—22no—
846C4⋊C4—22no—
847C4⋊C4—22no—
848C4⋊C4—22no—
849C4⋊C4—22no—
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—21no—
874C4⋊C4—21no—
875C4⋊C4—21no—
876C4⋊C4—41no—
877C4⋊C4—41no—
878C4⋊C4—41no—
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—81no—
894C4⋊C4—81no—
895C4⋊C4—81no—
896C4⋊C4—81no—
897C4⋊C4—81no—
898C4⋊C4—81no—
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⋊C4—81no—
910C4⋊C4—81no—
911C4⋊C4—81no—
912C4⋊C4#13514yes—
913C4⋊C4C22×Q812yes—
914C4⋊C4C22×Q812yes—
915C4⋊C4C22×Q812yes—
916C4⋊C4H(5,𝔽2)12yes—
917C22⋊C4—24no—
918C22⋊C4—24no—
919C22⋊C4—22no—
920C22⋊C4—22no—
921C22⋊C4—41no—
922C22⋊C4—41no—
923C22⋊C4—42no—
924C22⋊C4—42no—
925C22⋊C4—42no—
926C22⋊C4—42no—
927C22⋊C4—42no—
928C22⋊C4—81no—
929C22⋊C4—81no—
930C22⋊C4—81no—
931C22⋊C4—81no—
932C22⋊C4—81no—
933C22⋊C4—81no—
934C22⋊C4—81no—
935C22⋊C4—81no—
936C22⋊C4—81no—
937C22⋊C4—81no—
938C42—22no—
939C42—22no—
940C42—24no—
941C42—21no—
942C42—21no—
943C42—21no—
944C42—21no—
945C42—21no—
946C42—21no—
947C42—21no—
948C42—21no—
949C42—21no—
950C42—21no—
951C42—42no—
952C42—42no—
953C42—81no—
954C42—81no—
955C42—81no—
956C42—81no—
957C42—81no—
958C42—81no—
959C42—81no—
960C42—81no—
961C42—81no—
962C42—81no—
963C42—81no—
964C42—81no—
965C42C2×#4112yes—
966C422−1+412yes—
967C23—21no—
968C23—21no—
969C23—21no—
970C23—21no—
971C23—21no—
972C23—21no—
973C23—22no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23D4×Q812yes—
981C23C23×D411yescharacteristic
982Q8—44no—
983Q8—162no—
984Q8—162no—
985D4—22no—
986D4—22no—
987D4—41no—
988D4—41no—
989D4—84no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—22no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—44no—
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—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
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—82no—
1074C2×C4—162no—
1075C2×C4—162no—
1076C2×C4—162no—
1077C2×C4#54712yes—
1078C2×C4#54712yes—
1079C2×C4D4×Q812yes—
1080C2×C4C2×#13512yes—
1081C2×C4C2×#13512yes—
1082C2×C4C2×#13512yes—
1083C2×C4C23×Q811yescharacteristic
1084C2×C4C22×#4111yescharacteristic
1085C2×C4C2×H(5,𝔽2)11yescharacteristic
1086C2×C4C2×2−1+411yescharacteristic
1087C2×C4C2×2−1+411yescharacteristic
1088C2×C4#58511yescharacteristic
1089C8—22no—
1090C8—22no—
1091C8—22no—
1092C8—22no—
1093C8—41no—
1094C8—41no—
1095C8—41no—
1096C8—41no—
1097C22—22no—
1098C22—22no—
1099C22—22no—
1100C22—41no—
1101C22—41no—
1102C22—41no—
1103C22—41no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22—81no—
1111C22C2×#54711yescharacteristic
1112C22C2×D4×Q811yescharacteristic
1113C22#348811yescharacteristic
1114C22C22×#13511yescharacteristic
1115C22#358411yescharacteristic
1116C22#358411yescharacteristic
1117C22#358511yescharacteristic
1118C4—22no—
1119C4—22no—
1120C4—22no—
1121C4—22no—
1122C4—22no—
1123C4—22no—
1124C4—41no—
1125C4—41no—
1126C4—41no—
1127C4—41no—
1128C4—41no—
1129C4—41no—
1130C4—41no—
1131C4—42no—
1132C4—42no—
1133C4—42no—
1134C4—42no—
1135C4—81no—
1136C4—81no—
1137C4—81no—
1138C4—81no—
1139C4—81no—
1140C4—81no—
1141C4—81no—
1142C4—81no—
1143C4—81no—
1144C4—81no—
1145C4—81no—
1146C4Q8×#4111yescharacteristic
1147C4#350311yescharacteristic
1148C4#352011yescharacteristic
1149C4#356311yescharacteristic
1150C2—42no—
1151C2—82no—
1152C2#5911311yescharacteristic
1153C2#6123411yescharacteristic
1154C2#6127611yescharacteristic
1155C2Q8×#13511yescharacteristic
1156C2#6138511yescharacteristic
1157C2#6195311yescharacteristic
1158C2#6205911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
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
2. #36478C2semidirect
3. #32510C2semidirect
4. #32505C2semidirect
5. #32354C2semidirect
6. #32342C2semidirect
7. #28810C2semidirect
8. #27951C2semidirect
9. #26865C2semidirect
10. #26862C2semidirect
11. #26448C2semidirect
14. #26286C2semidirect
15. #26066C2semidirect
16. #26061C2semidirect
17. #26051C2semidirect
18. #25999C2semidirect
19. #25989C2semidirect
20. #25473C2semidirect
21. #25457C2semidirect
22. #25451C2semidirect
23. #25064C2semidirect
25. #22966C2semidirect
26. #22952C2semidirect
29. #22727C2semidirect
31. #21169C2semidirect
228. #482Q8semidirect

Maximal subgroups

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

subgroupindex
#593232
#364782
#325102
#325052
#323542
#323422
#288102
#279512
#268652
#268622
#264482
#263472
#263432
#262862
#260662
#260612
#260512
#259992
#259892
#254732
#254572
#254512
#250642
#248392
#229662
#229522
#229232
#227272
C4×#4822
#211692