Finite Group Databasebeta

← #6491868

Subgroups — #6491868

Order 512.

1504 conjugacy classes of subgroups.

The subgroup lattice has 1166 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35132C211yesmaximal, characteristic
2#34128C211yesmaximal, characteristic
3#33202C211yesmaximal, characteristic, complemented
4#33200C211yesmaximal, characteristic, complemented
5#33071C211yesmaximal, characteristic, complemented
6#33071C211yesmaximal, characteristic, complemented
7#30001C211yesmaximal, characteristic, complemented
8#30001C211yesmaximal, characteristic, complemented
9#29989C211yesmaximal, characteristic, complemented
10#29985C211yesmaximal, characteristic, complemented
11#26116C211yesmaximal, characteristic, complemented
12#26114C211yesmaximal, characteristic, complemented
13#26097C211yesmaximal, characteristic, complemented
14#26095C211yesmaximal, characteristic, complemented
15#26050C211yesmaximal, characteristic, complemented
16#26048C211yesmaximal, characteristic, complemented
17#26031C211yesmaximal, characteristic, complemented
18#26029C211yesmaximal, characteristic, complemented
19#25998C211yesmaximal, characteristic
20#25996C211yesmaximal, characteristic
21#25990C211yesmaximal, characteristic
22#25988C211yesmaximal, characteristic
23#25965C211yesmaximal, characteristic
24#25963C211yesmaximal, characteristic
25#25957C211yesmaximal, characteristic
26#25955C211yesmaximal, characteristic
27#21983C211yesmaximal, characteristic
28#21972C211yesmaximal, characteristic
29#21960C211yesmaximal, characteristic
30#20735C211yesmaximal, characteristic
31C2×#1805C211yesmaximal, characteristic
32C22×C4×Q8C2211yescharacteristic
33C2×#479C2211yescharacteristic
34C2×#479C2211yescharacteristic
35C2×#477C2211yescharacteristic
36C2×#475C2211yescharacteristic
37C2×#431C2211yescharacteristic
38C22×C4⋊C8C2211yescharacteristic
39C22×#103C2211yescharacteristic
40C22×#103C2211yescharacteristic
41#2864C2211yescharacteristic
42#2864C2211yescharacteristic
43#2862C2211yescharacteristic
44#2859C2211yescharacteristic
45#2666—21no—
46#2666—21no—
47#2612—21no—
48#2612—21no—
49#2570C2211yescharacteristic
50#2570C2211yescharacteristic
51#2550C2211yescharacteristic
52#2550C2211yescharacteristic
53#2442C2211yescharacteristic
54#2442C2211yescharacteristic
55#2440C2211yescharacteristic
56#2440C2211yescharacteristic
57#2438—21no—
58#2438—21no—
59#2356—21no—
60#2356—21no—
61#2356C2211yescharacteristic
62#2356C2211yescharacteristic
63#2351C2211yescharacteristic
64#2351C2211yescharacteristic
65#2344—21no—
66#2344—21no—
67#2344C2211yescharacteristic
68#2344C2211yescharacteristic
69Q8×C22⋊C4C2211yescharacteristic
70Q8×C22⋊C4C2211yescharacteristic
71#2329—21no—
72#2329—21no—
73#2295—21no—
74#2295—21no—
75#2295C2211yescharacteristic
76#2295C2211yescharacteristic
77#2283—21no—
78#2283C2211yescharacteristic
79#2283C2211yescharacteristic
80C2×#382C2211yescharacteristic
81C42×Q8C2211yescharacteristic
82C42×Q8C2211yescharacteristic
83C4×#117—21no—
84C4×#117C2211yescharacteristic
85#2101C2211yescharacteristic
86#2101C2211yescharacteristic
87#2100C2211yescharacteristic
88#2099C2211yescharacteristic
89#2097C2211yescharacteristic
90#2097C2211yescharacteristic
91#2096C2211yescharacteristic
92#2095C2211yescharacteristic
93#2088C2211yescharacteristic
94#2088C2211yescharacteristic
95#2088C2211yescharacteristic
96#2088C2211yescharacteristic
97#2087C2211yescharacteristic
98#2087C2211yescharacteristic
99#2086C2211yescharacteristic
100#2086C2211yescharacteristic
101#2068C2211yescharacteristic
102#2068C2211yescharacteristic
103#2068C2211yescharacteristic
104#2068C2211yescharacteristic
105#2066C2211yescharacteristic
106#2066C2211yescharacteristic
107#2066C2211yescharacteristic
108#2066C2211yescharacteristic
109#2059C2211yescharacteristic
110#2059C2211yescharacteristic
111#2058C2211yescharacteristic
112#2057C2211yescharacteristic
113#2026C2211yescharacteristic
114#2026C2211yescharacteristic
115#2024C2211yescharacteristic
116#2024C2211yescharacteristic
117#1989C2211yescharacteristic
118#1989C2211yescharacteristic
119#1988C2211yescharacteristic
120#1987C2211yescharacteristic
121#1949C2211yescharacteristic
122#1949C2211yescharacteristic
123#1949C2211yescharacteristic
124#1949C2211yescharacteristic
125#1949C2211yescharacteristic
126#1949C2211yescharacteristic
127#1949C2211yescharacteristic
128#1949C2211yescharacteristic
129#1949C2211yescharacteristic
130#1949C2211yescharacteristic
131#1949C2211yescharacteristic
132#1949C2211yescharacteristic
133#1949C2211yescharacteristic
134#1949C2211yescharacteristic
135#1948C2211yescharacteristic
136#1947C2211yescharacteristic
137#1939C2211yescharacteristic
138#1939C2211yescharacteristic
139#1939C2211yescharacteristic
140#1939C2211yescharacteristic
141#1921C2211yescharacteristic
142#1921C2211yescharacteristic
143#1920C2211yescharacteristic
144#1920C2211yescharacteristic
145#1919C2211yescharacteristic
146#1919C2211yescharacteristic
147#1918C2211yescharacteristic
148#1918C2211yescharacteristic
149#1865C2211yescharacteristic
150#1865C2211yescharacteristic
151#1865C2211yescharacteristic
152#1865C2211yescharacteristic
153#1863C2211yescharacteristic
154#1863C2211yescharacteristic
155#1863C2211yescharacteristic
156#1863C2211yescharacteristic
157#1853C2211yescharacteristic
158#1853C2211yescharacteristic
159#1852C2211yescharacteristic
160#1852C2211yescharacteristic
161#1850C2211yescharacteristic
162#1850C2211yescharacteristic
163#1850C2211yescharacteristic
164#1850C2211yescharacteristic
165#1846C2211yescharacteristic
166#1846C2211yescharacteristic
167#1842C2211yescharacteristic
168#1842C2211yescharacteristic
169#1835C2211yescharacteristic
170#1835C2211yescharacteristic
171#1831C2211yescharacteristic
172#1831C2211yescharacteristic
173#1823C2211yescharacteristic
174#1823C2211yescharacteristic
175#1808C2211yescharacteristic
176#1808C2211yescharacteristic
177#1807C2211yescharacteristic
178#1807C2211yescharacteristic
179#1805C2211yescharacteristic
180#1805C2211yescharacteristic
181#1805C2211yescharacteristic
182#1805C2211yescharacteristic
183#1805C2211yescharacteristic
184#1805C2211yescharacteristic
185#1805C2211yescharacteristic
186#1805C2211yescharacteristic
187#1805C2211yescharacteristic
188#1805C2211yescharacteristic
189#1805C2211yescharacteristic
190#1805C2211yescharacteristic
191#1805C2211yescharacteristic
192#1805C2211yescharacteristic
193#1803C2211yescharacteristic
194#1803C2211yescharacteristic
195#1787C2211yescharacteristic
196#1787C2211yescharacteristic
197C4×#103C2211yescharacteristic
198C4×#103C2211yescharacteristic
199C4×#103C2211yescharacteristic
200C4×#103C2211yescharacteristic
201C2×#340C2211yescharacteristic
202C2×#340C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204C23×C8C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×#125C2311yescharacteristic
209C2×#125C2311yescharacteristic
210C2×C22⋊Q8—21no—
211C2×C22⋊Q8—21no—
212C2×C4×Q8—21no—
213C2×C4×Q8—21no—
214C2×C4×Q8—24no—
215C2×C4×Q8Q818yescomplemented
216C2×C4×Q8C2311yescharacteristic
217C2×C4×Q8C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2311yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2311yescharacteristic
224C2×#117—21no—
225C2×#117—21no—
226C2×#117D411yescharacteristic
227C2×#117D411yescharacteristic
228C22×C4⋊C4—21no—
229C22×C4⋊C4C2311yescharacteristic
230C22×C4⋊C4C2311yescharacteristic
231C22×C4⋊C4C2311yescharacteristic
232C22×C42—21no—
233C22×C42C2311yescharacteristic
234#479—42no—
235#479—42no—
236#477—42no—
237#475—42no—
238#431—24no—
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×C4⋊C8—24no—
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
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×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×#103—42no—
271C2×#103—42no—
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×C22⋊C8C2311yescharacteristic
289C2×C22⋊C8C2311yescharacteristic
290C2×C4×C8C2311yescharacteristic
291C2×C4×C8C2311yescharacteristic
292#400—21no—
293#400—21no—
294#400—21no—
295#400—21no—
296#398—21no—
297#398—21no—
298#398—21no—
299#398—21no—
300#398—21no—
301#398—21no—
302#398—21no—
303#398—21no—
304#395—21no—
305#395—21no—
306#395—21no—
307#395—21no—
308#391—21no—
309#391—21no—
310#391—21no—
311#391—21no—
312#391—21no—
313#391—21no—
314#391—21no—
315#391—21no—
316#391—21no—
317#391—21no—
318#391C2311yescharacteristic
319#391C2311yescharacteristic
320#391C2311yescharacteristic
321#391C2311yescharacteristic
322#389—21no—
323#389—21no—
324#389—21no—
325#389—21no—
326#389—21no—
327#389—21no—
328#389—21no—
329#389—21no—
330#389—21no—
331#389—21no—
332#389C2311yescharacteristic
333#389C2311yescharacteristic
334#389C2311yescharacteristic
335#389C2311yescharacteristic
336#389C2311yescharacteristic
337#389C2311yescharacteristic
338#389C2311yescharacteristic
339#389C2311yescharacteristic
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#389C2311yescharacteristic
343#389C2311yescharacteristic
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#385—21no—
369#385—21no—
370#385—21no—
371#385—21no—
372#384C2311yescharacteristic
373#384C2311yescharacteristic
374#383—21no—
375#383—21no—
376#383—21no—
377#383—21no—
378#382—21no—
379#382—21no—
380#382—21no—
381#382—21no—
382#382C2311yescharacteristic
383#382C2311yescharacteristic
384#382C2311yescharacteristic
385#382C2311yescharacteristic
386#382C2311yescharacteristic
387#382C2311yescharacteristic
388#382C2311yescharacteristic
389#382C2311yescharacteristic
390#382C2311yescharacteristic
391#382C2311yescharacteristic
392#381—21no—
393#381—21no—
394#381—21no—
395#381—21no—
396#380—21no—
397#380—21no—
398#380—21no—
399#380—21no—
400#380C2311yescharacteristic
401#380C2311yescharacteristic
402#380C2311yescharacteristic
403#380C2311yescharacteristic
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⋊C4—21no—
412C4×C4⋊C4—21no—
413C4×C4⋊C4—21no—
414C4×C4⋊C4D411yescharacteristic
415C4×C4⋊C4D411yescharacteristic
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×C22⋊C4—21no—
427C4×C22⋊C4—21no—
428C4×C22⋊C4—21no—
429C4×C22⋊C4—21no—
430C4×C22⋊C4D411yescharacteristic
431C4×C22⋊C4D411yescharacteristic
432C4×C22⋊C4C2311yescharacteristic
433C4×C22⋊C4C2311yescharacteristic
434#376—21no—
435#376—21no—
436#376—21no—
437#376—21no—
438#376—21no—
439#376—21no—
440#376D411yescharacteristic
441#376D411yescharacteristic
442C2×#95—21no—
443C2×#95—21no—
444C43—21no—
445C43—21no—
446C43C2311yescharacteristic
447C43C2311yescharacteristic
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#340C2311yescharacteristic
479#340C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488C22×Q8—21no—
489C22×Q8—21no—
490C22×Q8—21no—
491C22×Q8—22no—
492C22×Q8—22no—
493C22×Q8—22no—
494C22×Q8—41no—
495C22×Q8—41no—
496C22×Q8C2×Q814yes—
497C22×Q8C2411yescharacteristic
498C22×Q8C2411yescharacteristic
499C23×C4—21no—
500C23×C4—21no—
501C23×C4—21no—
502C23×C4—21no—
503C23×C4C2×D411yescharacteristic
504C23×C4C2×D411yescharacteristic
505C23×C4C2411yescharacteristic
506C22×C8—22no—
507C22×C8—22no—
508C22×C8—41no—
509C22×C8—41no—
510C22×C8—41no—
511C22×C8—41no—
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C4⋊Q8—41no—
521C4⋊Q8—41no—
522C4⋊Q8—41no—
523C4⋊Q8—41no—
524#125—41no—
525#125—41no—
526#125—41no—
527#125—41no—
528C22⋊Q8—44no—
529C22⋊Q8—44no—
530C4×Q8—28no—
531C4×Q8—28no—
532C4×Q8—22no—
533C4×Q8—22no—
534C4×Q8—22no—
535C4×Q8—22no—
536C4×Q8—22no—
537C4×Q8—22no—
538C4×Q8—22no—
539C4×Q8—22no—
540C4×Q8—41no—
541C4×Q8—41no—
542C4×Q8—41no—
543C4×Q8—41no—
544C4×Q8C2×Q814yes—
545C4×Q8C2×Q814yes—
546C4×Q8C2×Q814yes—
547C4×Q8C2×Q814yes—
548#117—24no—
549#117—42no—
550#117—44no—
551#117—44no—
552C2×C4⋊C4—28no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—22no—
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⋊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—41no—
588C2×C4⋊C4—41no—
589C2×C4⋊C4—41no—
590C2×C4⋊C4—41no—
591C2×C4⋊C4C2×D411yescharacteristic
592C2×C4⋊C4C2×D411yescharacteristic
593C2×C4⋊C4C2×D411yescharacteristic
594C2×C4⋊C4C2×D411yescharacteristic
595C2×C4⋊C4C2×Q814yes—
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×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4C2×D411yescharacteristic
615C2×C22⋊C4C2×D411yescharacteristic
616C2×C22⋊C4C2×D411yescharacteristic
617C2×C22⋊C4C2×D411yescharacteristic
618C2×C42—28no—
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—21no—
629C2×C42—21no—
630C2×C42—21no—
631C2×C42—21no—
632C2×C42—21no—
633C2×C42—21no—
634C2×C42—21no—
635C2×C42C2×D411yescharacteristic
636C2×C42C2×D411yescharacteristic
637C2×C42C2×D411yescharacteristic
638C2×C42C2×D411yescharacteristic
639C2×C42C2×D411yescharacteristic
640C2×C42C2×D411yescharacteristic
641C2×C42C2×D411yescharacteristic
642C2×C42C2×D411yescharacteristic
643C2×C42C2×D411yescharacteristic
644C2×C42C2×D411yescharacteristic
645C2×C42C2×Q814yes—
646C2×C42#4114yes—
647C2×C42C2411yescharacteristic
648C2×C42C2411yescharacteristic
649C2×C42C2411yescharacteristic
650C2×C42C2411yescharacteristic
651C2×C42C2411yescharacteristic
652C2×C42C2411yescharacteristic
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#106—41no—
662#106—41no—
663#106—41no—
664#106—41no—
665#106—41no—
666#106—41no—
667#106—41no—
668#106—41no—
669C4⋊C8—22no—
670C4⋊C8—22no—
671C4⋊C8—22no—
672C4⋊C8—22no—
673C4⋊C8—22no—
674C4⋊C8—22no—
675C4⋊C8—41no—
676C4⋊C8—41no—
677C4⋊C8—41no—
678C4⋊C8—41no—
679C4⋊C8—41no—
680C4⋊C8—41no—
681C4⋊C8—41no—
682C4⋊C8—41no—
683#103—22no—
684#103—22no—
685#103—22no—
686#103—22no—
687#103—22no—
688#103—22no—
689#103—22no—
690#103—22no—
691#103—41no—
692#103—41no—
693#103—41no—
694#103—41no—
695#103—41no—
696#103—41no—
697#103—41no—
698#103—41no—
699C22⋊C8—22no—
700C22⋊C8—22no—
701C4×C8—22no—
702C4×C8—22no—
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#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
763C24C22×D411yescharacteristic
764C2×Q8—24no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—28no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—42no—
775C2×Q8—42no—
776C2×Q8—44no—
777C2×Q8—44no—
778C2×Q8—44no—
779C2×Q8—42no—
780C2×Q8—42no—
781C2×Q8—81no—
782C2×Q8—81no—
783C2×Q8—81no—
784C2×Q8—81no—
785C2×Q8C22×Q812yes—
786C2×Q8C22×Q812yes—
787C2×Q8H(5,𝔽2)12yes—
788C2×Q82−1+412yes—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—24no—
797C22×C4—24no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—41no—
814C22×C4—41no—
815C22×C4—42no—
816C22×C4—42no—
817C22×C4—42no—
818C22×C4—42no—
819C22×C4—42no—
820C22×C4—42no—
821C22×C4—81no—
822C22×C4—81no—
823C22×C4—81no—
824C22×C4—81no—
825C22×C4C22⋊Q814yes—
826C22×C4C22⋊Q814yes—
827C22×C4C22×D411yescharacteristic
828C22×C4C22×D411yescharacteristic
829C22×C4C22×D411yescharacteristic
830C22×C4C22×D411yescharacteristic
831C22×C4C22×D411yescharacteristic
832C22×C4C22×D411yescharacteristic
833C22×C4C22×D411yescharacteristic
834C22×C4C22×D411yescharacteristic
835C22×C4C22×D411yescharacteristic
836C22×C4C22×D411yescharacteristic
837C22×C4C22×D411yescharacteristic
838C22×C4C22×D411yescharacteristic
839C22×C4C22×D411yescharacteristic
840C22×C4C22×Q812yes—
841C22×C4C2×#4112yes—
842C22×C4C2511yescharacteristic
843C2×C8—21no—
844C2×C8—21no—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—21no—
849C2×C8—21no—
850C2×C8—21no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
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—82no—
868C2×C8—82no—
869C4⋊C4—24no—
870C4⋊C4—24no—
871C4⋊C4—24no—
872C4⋊C4—24no—
873C4⋊C4—24no—
874C4⋊C4—22no—
875C4⋊C4—22no—
876C4⋊C4—21no—
877C4⋊C4—21no—
878C4⋊C4—21no—
879C4⋊C4—21no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—21no—
886C4⋊C4—21no—
887C4⋊C4—21no—
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—41no—
903C4⋊C4—41no—
904C4⋊C4—42no—
905C4⋊C4—42no—
906C4⋊C4—42no—
907C4⋊C4—42no—
908C4⋊C4—42no—
909C4⋊C4—42no—
910C4⋊C4—42no—
911C4⋊C4—42no—
912C4⋊C4—42no—
913C4⋊C4—42no—
914C4⋊C4—42no—
915C4⋊C4—42no—
916C4⋊C4—42no—
917C4⋊C4—42no—
918C4⋊C4—81no—
919C4⋊C4—81no—
920C4⋊C4—81no—
921C4⋊C4—81no—
922C4⋊C4—81no—
923C4⋊C4—81no—
924C4⋊C4—81no—
925C4⋊C4—81no—
926C4⋊C4—81no—
927C4⋊C4—81no—
928C4⋊C4—81no—
929C4⋊C4—81no—
930C4⋊C4—81no—
931C4⋊C4—81no—
932C4⋊C4C22×Q812yes—
933C4⋊C4C22×Q812yes—
934C22⋊C4—22no—
935C22⋊C4—22no—
936C22⋊C4—22no—
937C22⋊C4—42no—
938C22⋊C4—42no—
939C22⋊C4—42no—
940C22⋊C4—42no—
941C22⋊C4#13514yes—
942C42—24no—
943C42—24no—
944C42—24no—
945C42—24no—
946C42—22no—
947C42—22no—
948C42—21no—
949C42—21no—
950C42—21no—
951C42—21no—
952C42—21no—
953C42—21no—
954C42—21no—
955C42—21no—
956C42—41no—
957C42—41no—
958C42—41no—
959C42—41no—
960C42—41no—
961C42—41no—
962C42—42no—
963C42—42no—
964C42—42no—
965C42—42no—
966C42—42no—
967C42—42no—
968C42—42no—
969C42—42no—
970C42—42no—
971C42—42no—
972C42—81no—
973C42—81no—
974C42C22⋊Q814yes—
975C42C22⋊Q814yes—
976C42C22×Q812yes—
977C42C22×Q812yes—
978C42C2×#4112yes—
979C42C2×#4112yes—
980C23—21no—
981C23—21no—
982C23—21no—
983C23—21no—
984C23C2×C22⋊Q812yes—
985C23C2×#13512yes—
986C23#57512yes—
987C23C23×D411yescharacteristic
988Q8—22no—
989Q8—22no—
990Q8—22no—
991Q8—22no—
992Q8—22no—
993Q8—48no—
994Q8—41no—
995Q8—41no—
996Q8—162no—
997Q8—162no—
998Q8#54414yes—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—28no—
1006C2×C4—22no—
1007C2×C4—21no—
1008C2×C4—22no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—22no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—44no—
1043C2×C4—48no—
1044C2×C4—48no—
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—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—162no—
1088C2×C4—162no—
1089C2×C4C2×C22⋊Q812yes—
1090C2×C4C2×C22⋊Q812yes—
1091C2×C4C2×C22⋊Q812yes—
1092C2×C4C2×C22⋊Q812yes—
1093C2×C4C2×C22⋊Q812yes—
1094C2×C4C2×#13512yes—
1095C2×C4C2×#13512yes—
1096C2×C4C23×Q811yescharacteristic
1097C2×C4C22×#4111yescharacteristic
1098C2×C4C2×H(5,𝔽2)11yescharacteristic
1099C2×C4C2×2−1+411yescharacteristic
1100C2×C4#58511yescharacteristic
1101C2×C4#58511yescharacteristic
1102C8—41no—
1103C8—41no—
1104C8—41no—
1105C8—41no—
1106C8—41no—
1107C8—41no—
1108C8—41no—
1109C8—41no—
1110C22—22no—
1111C22—22no—
1112C22—22no—
1113C22—22no—
1114C22—22no—
1115C22—22no—
1116C22#307614yes—
1117C22C22×C22⋊Q811yescharacteristic
1118C22#348811yescharacteristic
1119C22#348911yescharacteristic
1120C22C22×#13511yescharacteristic
1121C22C2×#57511yescharacteristic
1122C22#358611yescharacteristic
1123C22#358611yescharacteristic
1124C4—22no—
1125C4—22no—
1126C4—22no—
1127C4—22no—
1128C4—22no—
1129C4—22no—
1130C4—22no—
1131C4—24no—
1132C4—41no—
1133C4—41no—
1134C4—41no—
1135C4—42no—
1136C4—42no—
1137C4—41no—
1138C4—41no—
1139C4—41no—
1140C4—42no—
1141C4—81no—
1142C4—81no—
1143C4—81no—
1144C4—81no—
1145C4—81no—
1146C4—81no—
1147C4—81no—
1148C4—81no—
1149C4—81no—
1150C4—81no—
1151C4—81no—
1152C4—81no—
1153C4C2×#54411yescharacteristic
1154C4#345811yescharacteristic
1155C4#349411yescharacteristic
1156C4#349511yescharacteristic
1157C2—24no—
1158C2#3525311yescharacteristic
1159C2C2×#307611yescharacteristic
1160C2#6049111yescharacteristic
1161C2#6195611yescharacteristic
1162C2#6197211yescharacteristic
1163C2#6210411yescharacteristic
1164C2#6212011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #33202C2semidirect
4. #33200C2semidirect
5. #33071C2semidirect
6. #33071C2semidirect
7. #30001C2semidirect
8. #30001C2semidirect
9. #29989C2semidirect
10. #29985C2semidirect
11. #26116C2semidirect
12. #26114C2semidirect
13. #26097C2semidirect
14. #26095C2semidirect
15. #26050C2semidirect
16. #26048C2semidirect
17. #26031C2semidirect
18. #26029C2semidirect
215. C2×C4×Q8Q8semidirect

Maximal subgroups

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

subgroupindex
#351322
#341282
#332022
#332002
#330712
#300012
#299892
#299852
#261162
#261142
#260972
#260952
#260502
#260482
#260312
#260292
#259982
#259962
#259902
#259882
#259652
#259632
#259572
#259552
#219832
#219722
#219602
#207352
C2×#18052