Finite Group Databasebeta

← C83×#62862 #35290686

Subgroups — C83×#62862 #35290686

Order 21248.

7498 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#3545C214yesmaximal, complemented
2C83×#3543C214yesmaximal, complemented
3C83×#3542C2116yesmaximal, complemented
4C83×#3534C218yesmaximal, complemented
5C83×#3533C218yesmaximal, complemented
6C83×#3532C218yesmaximal, complemented
7C83×#3491C212yesmaximal, complemented
8C83×#3490C214yesmaximal, complemented
9C83×#3485C212yesmaximal, complemented
10C83×#3484C214yesmaximal, complemented
11C2×#535×C83C211yesmaximal, characteristic, complemented
12C2×#534×C83C212yesmaximal, complemented
13C2×H(5,𝔽2)×C83C2212yescomplemented
14C22×#41×C83C2211yescharacteristic, complemented
15C23×D4×C83C2211yescharacteristic, complemented
16C23×D4×C83C2212yescomplemented
17#563×C83C2214yescomplemented
18#562×C83C22116yescomplemented
19#562×C83C2218yescomplemented
20H(3,𝔽4)×C83C2214yescomplemented
21#560×C83C2218yescomplemented
22#560×C83C22116yescomplemented
23#560×C83C2218yescomplemented
24#559×C83C2214yescomplemented
25#555×C83C2218yescomplemented
26#553×C83C22116yescomplemented
27#552×C83C22116yescomplemented
28#551×C83C22116yescomplemented
29#551×C83C22116yescomplemented
30#551×C83C2218yescomplemented
31#551×C83C22116yescomplemented
32#550×C83C2218yescomplemented
33#547×C83C22116yescomplemented
34#546×C83C22116yescomplemented
35#546×C83C22116yescomplemented
36#546×C83C22116yescomplemented
37#546×C83C22116yescomplemented
38#546×C83C22116yescomplemented
39#546×C83C22116yescomplemented
40D42×C83C22116yescomplemented
41D42×C83C2214yescomplemented
42D42×C83C22116yescomplemented
43#543×C83C2212yescomplemented
44#542×C83C22116yescomplemented
45#540×C83C22116yescomplemented
46#540×C83C22116yescomplemented
47#539×C83C2218yescomplemented
48#539×C83C2218yescomplemented
49#538×C83C22116yescomplemented
50#538×C83C22116yescomplemented
51#538×C83C22116yescomplemented
52#538×C83C2218yescomplemented
53#537×C83C2218yescomplemented
54#536×C83C2214yescomplemented
55#535×C83C2218yescomplemented
56#535×C83C2218yescomplemented
57#535×C83C2218yescomplemented
58#535×C83C22116yescomplemented
59#534×C83C2212yes—
60#534×C83C2218yescomplemented
61#534×C83C2218yescomplemented
62#534×C83C2214yescomplemented
63#534×C83C2218yescomplemented
64#534×C83C2218yescomplemented
65#534×C83C2218yescomplemented
66#534×C83C2218yescomplemented
67#534×C83C2214yescomplemented
68C2×#127×C83C2212yescomplemented
69#529×C83C2218yescomplemented
70C2×#124×C83C2212yescomplemented
71#525×C83C22116yescomplemented
72#525×C83C2218yescomplemented
73#525×C83C2214yescomplemented
74C2×#123×C83C2214yescomplemented
75C2×#123×C83C2214yescomplemented
76C2×#123×C83C2214yescomplemented
77C2×#121×C83C2218yescomplemented
78C2×#121×C83C2214yescomplemented
79C2×#120×C83C2214yescomplemented
80C2×#120×C83C2214yescomplemented
81C2×#120×C83C2214yescomplemented
82C2×#120×C83C2218yescomplemented
83#518×C83C2214yescomplemented
84#518×C83C2212yescomplemented
85C2×#117×C83C2211yescharacteristic, complemented
86C22×C22⋊C4×C83C2212yescomplemented
87C25×C83C2312yes—
88C25×C83C2312yescomplemented
89H(5,𝔽2)×C83—48no—
90C2×#41×C83—44no—
91C2×#41×C83C2318yes—
92C2×#41×C83C2314yes—
93C2×#41×C83C2318yescomplemented
94C2×#41×C83C23116yescomplemented
95C22×Q8×C83C2311yescharacteristic, complemented
96C22×D4×C83—44no—
97C22×D4×C83—48no—
98C22×D4×C83C2312yes—
99C22×D4×C83C2314yes—
100C22×D4×C83C2314yes—
101C22×D4×C83C2318yes—
102C22×D4×C83C2312yes—
103C22×D4×C83C2314yes—
104C22×D4×C83C2314yes—
105C22×D4×C83C2312yes—
106C22×D4×C83C2318yes—
107C22×D4×C83C2318yes—
108C22×D4×C83C2314yescomplemented
109C22×D4×C83C2311yescharacteristic, complemented
110C22×D4×C83C2318yescomplemented
111C22×D4×C83C2318yescomplemented
112C22×D4×C83C23116yescomplemented
113C23×C4×C83C2311yescharacteristic
114C23×C4×C83C2312yescomplemented
115C23×C4×C83C2312yescomplemented
116C23×C4×C83C2314yescomplemented
117C4⋊Q8×C83C2318yescomplemented
118#127×C83C2314yes—
119#127×C83C2318yescomplemented
120#127×C83C2314yescomplemented
121#127×C83C23116yescomplemented
122#126×C83C23116yescomplemented
123#126×C83C23116yescomplemented
124#126×C83C23116yescomplemented
125#126×C83C23116yescomplemented
126#125×C83C2318yescomplemented
127#125×C83C23116yescomplemented
128#124×C83C2314yes—
129#124×C83C2318yescomplemented
130#124×C83C2314yescomplemented
131#124×C83C2318yescomplemented
132#124×C83C23116yescomplemented
133#124×C83C23116yescomplemented
134#124×C83C2318yescomplemented
135#124×C83C23116yescomplemented
136#123×C83C2318yes—
137#123×C83C23116yes—
138#123×C83C2318yes—
139#123×C83C2318yes—
140#123×C83C2318yescomplemented
141#123×C83C2318yescomplemented
142#123×C83C2318yescomplemented
143#123×C83C2318yescomplemented
144#123×C83C2318yescomplemented
145#123×C83C23116yescomplemented
146#123×C83C2318yescomplemented
147#123×C83C23116yescomplemented
148#123×C83C23116yescomplemented
149#123×C83C23116yescomplemented
150#123×C83C23116yescomplemented
151#123×C83C2318yescomplemented
152#123×C83C23116yescomplemented
153#123×C83C23116yescomplemented
154C22⋊Q8×C83C23116yescomplemented
155C22⋊Q8×C83C2318yescomplemented
156C22⋊Q8×C83C23116yescomplemented
157C22⋊Q8×C83C23116yescomplemented
158C22⋊Q8×C83C2318yescomplemented
159C22⋊Q8×C83C23116yescomplemented
160C22⋊Q8×C83C23116yescomplemented
161#121×C83C23116yes—
162#121×C83C23116yes—
163#121×C83C2318yes—
164#121×C83C23116yes—
165#121×C83C2318yes—
166#121×C83C23116yescomplemented
167#121×C83C23116yescomplemented
168#121×C83C2318yescomplemented
169#121×C83C23116yescomplemented
170#121×C83C2318yescomplemented
171#121×C83C23116yescomplemented
172#121×C83C23116yescomplemented
173#121×C83C23116yescomplemented
174#121×C83C23116yescomplemented
175#121×C83C23116yescomplemented
176#121×C83C23116yescomplemented
177#121×C83C23116yescomplemented
178#121×C83C23116yescomplemented
179#121×C83C23116yescomplemented
180#120×C83C2318yes—
181#120×C83C2318yes—
182#120×C83C2318yes—
183#120×C83C2318yes—
184#120×C83C23116yes—
185#120×C83C2318yes—
186#120×C83C23116yes—
187#120×C83C2318yescomplemented
188#120×C83C2318yescomplemented
189#120×C83C2318yescomplemented
190#120×C83C2318yescomplemented
191#120×C83C2318yescomplemented
192#120×C83C23116yescomplemented
193#120×C83C23116yescomplemented
194#120×C83C2318yescomplemented
195#120×C83C2318yescomplemented
196#120×C83C23116yescomplemented
197C4×Q8×C83C2318yescomplemented
198C4×D4×C83C23116yes—
199C4×D4×C83C23116yescomplemented
200C4×D4×C83C23116yescomplemented
201C4×D4×C83C23116yescomplemented
202C4×D4×C83C23116yescomplemented
203C4×D4×C83C23116yescomplemented
204C4×D4×C83C23116yescomplemented
205C4×D4×C83C23116yescomplemented
206C4×D4×C83C2318yescomplemented
207#117×C83C2318yescomplemented
208#117×C83C2318yescomplemented
209#117×C83C2314yescomplemented
210#117×C83C23116yescomplemented
211#117×C83C23116yescomplemented
212C2×C4⋊C4×C83C2312yescomplemented
213C2×C4⋊C4×C83C2318yescomplemented
214C2×C4⋊C4×C83C2318yescomplemented
215C2×C22⋊C4×C83C2314yes—
216C2×C22⋊C4×C83C2318yes—
217C2×C22⋊C4×C83C2312yes—
218C2×C22⋊C4×C83C2318yes—
219C2×C22⋊C4×C83C2314yescomplemented
220C2×C22⋊C4×C83C2318yescomplemented
221C2×C22⋊C4×C83C2318yescomplemented
222C2×C22⋊C4×C83C2314yescomplemented
223C2×C22⋊C4×C83C2318yescomplemented
224C2×C22⋊C4×C83C2318yescomplemented
225C2×C22⋊C4×C83C23116yescomplemented
226C2×C22⋊C4×C83C2318yescomplemented
227C2×C42×C83C2312yescomplemented
228C24×C83—28no—
229C24×C83—44no—
230C24×C83—84no—
231C24×C83—84no—
232C24×C83C2414yes—
233C24×C83C2414yes—
234C24×C83C2414yes—
235C24×C83C2412yes—
236C24×C83C2412yes—
237C24×C83C2412yes—
238C24×C83C2418yes—
239C24×C83C2414yes—
240C24×C83C2411yescharacteristic
241#41×C83—416no—
242#41×C83—416no—
243#41×C83—48no—
244#41×C83—816no—
245C2×Q8×C83—42no—
246C2×Q8×C83C2418yes—
247C2×Q8×C83C2414yes—
248C2×Q8×C83C2414yes—
249C2×D4×C83—216no—
250C2×D4×C83—28no—
251C2×D4×C83—44no—
252C2×D4×C83—44no—
253C2×D4×C83—48no—
254C2×D4×C83—48no—
255C2×D4×C83—48no—
256C2×D4×C83—42no—
257C2×D4×C83—416no—
258C2×D4×C83—416no—
259C2×D4×C83—48no—
260C2×D4×C83—416no—
261C2×D4×C83—88no—
262C2×D4×C83—88no—
263C2×D4×C83—816no—
264C2×D4×C83C2418yes—
265C2×D4×C83C2418yes—
266C2×D4×C83C2418yes—
267C2×D4×C83C24116yes—
268C2×D4×C83C24116yes—
269C2×D4×C83C2418yes—
270C2×D4×C83C24116yes—
271C2×D4×C83C24116yes—
272C2×D4×C83C24116yes—
273C2×D4×C83C2412yes—
274C2×D4×C83C2412yes—
275C2×D4×C83C2414yes—
276C2×D4×C83C2414yes—
277C2×D4×C83C2414yes—
278C2×D4×C83C2418yes—
279C2×D4×C83C2414yes—
280C2×D4×C83C24116yes—
281C2×D4×C83C2412yes—
282C2×D4×C83C2412yes—
283C22×C4×C83—24no—
284C22×C4×C83—44no—
285C22×C4×C83—44no—
286C22×C4×C83—84no—
287C22×C4×C83C2411yescharacteristic
288C22×C4×C83C2414yes—
289C22×C4×C83C2412yes—
290C22×C4×C83C2414yes—
291C22×C4×C83C2411yescharacteristic
292C22×C4×C83C2414yes—
293C22×C4×C83C2418yes—
294C22×C4×C83C24116yes—
295C22×C4×C83C2418yes—
296C22×C4×C83C24116yes—
297C22×C4×C83C2418yes—
298C22×C4×C83C2418yes—
299C22×C4×C83C2414yes—
300C22×C4×C83C2418yes—
301C4⋊C4×C83C24116yes—
302C4⋊C4×C83C2418yes—
303C4⋊C4×C83C24116yes—
304C4⋊C4×C83C24116yes—
305C4⋊C4×C83C24116yes—
306C4⋊C4×C83C24116yes—
307C4⋊C4×C83C2418yes—
308C4⋊C4×C83C2418yes—
309C4⋊C4×C83C2418yes—
310C22⋊C4×C83C2418yes—
311C22⋊C4×C83C2418yes—
312C22⋊C4×C83C2418yes—
313C22⋊C4×C83C2418yes—
314C22⋊C4×C83C2418yes—
315C22⋊C4×C83C24116yes—
316C22⋊C4×C83C24116yes—
317C22⋊C4×C83C24116yes—
318C22⋊C4×C83C24116yes—
319C22⋊C4×C83C24116yes—
320C22⋊C4×C83C24116yes—
321C22⋊C4×C83C24116yes—
322C22⋊C4×C83C24116yes—
323C22⋊C4×C83C24116yes—
324C22⋊C4×C83C2418yes—
325C22⋊C4×C83C24116yes—
326C42×C83C2414yes—
327C42×C83C2414yes—
328C42×C83C24116yes—
329C42×C83C2418yes—
330C23×C83—24no—
331C23×C83—24no—
332C23×C83—24no—
333C23×C83—28no—
334C23×C83—28no—
335C23×C83—28no—
336C23×C83—44no—
337C23×C83—42no—
338C23×C83—44no—
339C23×C83—48no—
340C23×C83—44no—
341C23×C83—48no—
342C23×C83—48no—
343C23×C83—48no—
344C23×C83—416no—
345C23×C83—44no—
346C23×C83—48no—
347C23×C83—816no—
348C23×C83—816no—
349C23×C83H(5,𝔽2)14yes—
350C23×C83C2514yes—
351C23×C83C2518yes—
352C23×C83C2514yes—
353C23×C83C2514yes—
354C23×C83C2512yes—
355C23×C83C2511yescharacteristic
356Q8×C83—44no—
357Q8×C83—44no—
358Q8×C83—48no—
359D4×C83—216no—
360D4×C83—216no—
361D4×C83—216no—
362D4×C83—42no—
363D4×C83—44no—
364D4×C83—42no—
365D4×C83—42no—
366D4×C83—44no—
367D4×C83—42no—
368D4×C83—416no—
369D4×C83—48no—
370D4×C83—44no—
371D4×C83—44no—
372D4×C83—416no—
373D4×C83—416no—
374D4×C83—48no—
375D4×C83—416no—
376D4×C83—416no—
377D4×C83—416no—
378C2×C4×C83—22no—
379C2×C4×C83—22no—
380C2×C4×C83—28no—
381C2×C4×C83—28no—
382C2×C4×C83—24no—
383C2×C4×C83—48no—
384C2×C4×C83—48no—
385C2×C4×C83—48no—
386C2×C4×C83—416no—
387C2×C4×C83—44no—
388C2×C4×C83—48no—
389C2×C4×C83—44no—
390C2×C4×C83—416no—
391C2×C4×C83—48no—
392C2×C4×C83C2518yes—
393C2×C4×C83C2512yes—
394C2×C4×C83C25116yes—
395C2×C4×C83C2514yes—
396C2×C4×C83C2518yes—
397C2×C4×C83C2512yes—
398C22×C83—24no—
399C22×C83—22no—
400C22×C83—24no—
401C22×C83—24no—
402C22×C83—28no—
403C22×C83—24no—
404C22×C83—28no—
405C22×C83—28no—
406C22×C83—216no—
407C22×C83—28no—
408C22×C83—44no—
409C22×C83—48no—
410C22×C83—48no—
411C22×C83—84no—
412C22×C83—88no—
413C22×C83—88no—
414C22×C83—88no—
415C22×C83—816no—
416C22×C83—164no—
417C22×C83C2×H(5,𝔽2)14yes—
418C22×C83C2×H(5,𝔽2)12yes—
419C22×C83C2611yescharacteristic
420C4×C83—22no—
421C4×C83—22no—
422C4×C83—28no—
423C4×C83—24no—
424C4×C83—216no—
425C4×C83—28no—
426#62862C8311yesmaximal, characteristic, direct product factor, Sylow
427C2×C83—24no—
428C2×C83—22no—
429C2×C83—44no—
430C2×C83—44no—
431C2×C83—48no—
432C2×C83—44no—
433C2×C83C22×H(5,𝔽2)11yescharacteristic
434C2×C83H(7,𝔽2)12yes—
435#3545C2×C8314yescomplemented
436#3543C2×C8314yescomplemented
437#3542C2×C83116yescomplemented
438#3534C2×C8318yescomplemented
439#3533C2×C8318yescomplemented
440#3532C2×C8318yescomplemented
441#3491C2×C8312yescomplemented
442#3490C2×C8314yescomplemented
443#3485C2×C8312yescomplemented
444#3484C2×C8314yescomplemented
445C2×#535C2×C8311yescharacteristic, complemented
446C2×#534C2×C8312yescomplemented
447C83#6286211yescharacteristic, direct product factor, Sylow
448C2×H(5,𝔽2)C22×C8312yescomplemented
449C22×#41C22×C8311yescharacteristic, complemented
450C23×D4C22×C8311yescharacteristic, complemented
451C23×D4C22×C8312yescomplemented
452#563C22×C8314yescomplemented
453#562C22×C83116yescomplemented
454#562C22×C8318yescomplemented
455H(3,𝔽4)C22×C8314yescomplemented
456#560C22×C8318yescomplemented
457#560C22×C83116yescomplemented
458#560C22×C8318yescomplemented
459#559C22×C8314yescomplemented
460#555C22×C8318yescomplemented
461#553C22×C83116yescomplemented
462#552C22×C83116yescomplemented
463#551C22×C83116yescomplemented
464#551C22×C83116yescomplemented
465#551C22×C8318yescomplemented
466#551C22×C83116yescomplemented
467#550C22×C8318yescomplemented
468#547C22×C83116yescomplemented
469#546C22×C83116yescomplemented
470#546C22×C83116yescomplemented
471#546C22×C83116yescomplemented
472#546C22×C83116yescomplemented
473#546C22×C83116yescomplemented
474#546C22×C83116yescomplemented
475D42C22×C83116yescomplemented
476D42C22×C8314yescomplemented
477D42C22×C83116yescomplemented
478#543C22×C8312yescomplemented
479#542C22×C83116yescomplemented
480#540C22×C83116yescomplemented
481#540C22×C83116yescomplemented
482#539C22×C8318yescomplemented
483#539C22×C8318yescomplemented
484#538C22×C83116yescomplemented
485#538C22×C83116yescomplemented
486#538C22×C83116yescomplemented
487#538C22×C8318yescomplemented
488#537C22×C8318yescomplemented
489#536C22×C8314yescomplemented
490#535C22×C8318yescomplemented
491#535C22×C8318yescomplemented
492#535C22×C8318yescomplemented
493#535C22×C83116yescomplemented
494#534C22×C8312yes—
495#534C22×C8318yescomplemented
496#534C22×C8318yescomplemented
497#534C22×C8314yescomplemented
498#534C22×C8318yescomplemented
499#534C22×C8318yescomplemented
500#534C22×C8318yescomplemented
501#534C22×C8318yescomplemented
502#534C22×C8314yescomplemented
503C2×#127C22×C8312yescomplemented
504#529C22×C8318yescomplemented
505C2×#124C22×C8312yescomplemented
506#525C22×C83116yescomplemented
507#525C22×C8318yescomplemented
508#525C22×C8314yescomplemented
509C2×#123C22×C8314yescomplemented
510C2×#123C22×C8314yescomplemented
511C2×#123C22×C8314yescomplemented
512C2×#121C22×C8318yescomplemented
513C2×#121C22×C8314yescomplemented
514C2×#120C22×C8314yescomplemented
515C2×#120C22×C8314yescomplemented
516C2×#120C22×C8314yescomplemented
517C2×#120C22×C8318yescomplemented
518#518C22×C8314yescomplemented
519#518C22×C8312yescomplemented
520C2×#117C22×C8311yescharacteristic, complemented
521C22×C22⋊C4C22×C8312yescomplemented
522C25C23×C8312yes—
523C25C23×C8312yescomplemented
524H(5,𝔽2)—48no—
525C2×#41—44no—
526C2×#41C23×C8318yes—
527C2×#41C23×C8314yes—
528C2×#41C23×C8318yescomplemented
529C2×#41C23×C83116yescomplemented
530C22×Q8C23×C8311yescharacteristic, complemented
531C22×D4—44no—
532C22×D4—48no—
533C22×D4C23×C8312yes—
534C22×D4C23×C8314yes—
535C22×D4C23×C8314yes—
536C22×D4C23×C8318yes—
537C22×D4C23×C8312yes—
538C22×D4C23×C8314yes—
539C22×D4C23×C8314yes—
540C22×D4C23×C8312yes—
541C22×D4C23×C8318yes—
542C22×D4C23×C8318yes—
543C22×D4C23×C8314yescomplemented
544C22×D4C23×C8311yescharacteristic, complemented
545C22×D4C23×C8318yescomplemented
546C22×D4C23×C8318yescomplemented
547C22×D4C23×C83116yescomplemented
548C23×C4C23×C8311yescharacteristic
549C23×C4C23×C8312yescomplemented
550C23×C4C23×C8312yescomplemented
551C23×C4C23×C8314yescomplemented
552C4⋊Q8C23×C8318yescomplemented
553#127C23×C8314yes—
554#127C23×C8318yescomplemented
555#127C23×C8314yescomplemented
556#127C23×C83116yescomplemented
557#126C23×C83116yescomplemented
558#126C23×C83116yescomplemented
559#126C23×C83116yescomplemented
560#126C23×C83116yescomplemented
561#125C23×C8318yescomplemented
562#125C23×C83116yescomplemented
563#124C23×C8314yes—
564#124C23×C8318yescomplemented
565#124C23×C8314yescomplemented
566#124C23×C8318yescomplemented
567#124C23×C83116yescomplemented
568#124C23×C83116yescomplemented
569#124C23×C8318yescomplemented
570#124C23×C83116yescomplemented
571#123C23×C8318yes—
572#123C23×C83116yes—
573#123C23×C8318yes—
574#123C23×C8318yes—
575#123C23×C8318yescomplemented
576#123C23×C8318yescomplemented
577#123C23×C8318yescomplemented
578#123C23×C8318yescomplemented
579#123C23×C8318yescomplemented
580#123C23×C83116yescomplemented
581#123C23×C8318yescomplemented
582#123C23×C83116yescomplemented
583#123C23×C83116yescomplemented
584#123C23×C83116yescomplemented
585#123C23×C83116yescomplemented
586#123C23×C8318yescomplemented
587#123C23×C83116yescomplemented
588#123C23×C83116yescomplemented
589C22⋊Q8C23×C83116yescomplemented
590C22⋊Q8C23×C8318yescomplemented
591C22⋊Q8C23×C83116yescomplemented
592C22⋊Q8C23×C83116yescomplemented
593C22⋊Q8C23×C8318yescomplemented
594C22⋊Q8C23×C83116yescomplemented
595C22⋊Q8C23×C83116yescomplemented
596#121C23×C83116yes—
597#121C23×C83116yes—
598#121C23×C8318yes—
599#121C23×C83116yes—
600#121C23×C8318yes—
601#121C23×C83116yescomplemented
602#121C23×C83116yescomplemented
603#121C23×C8318yescomplemented
604#121C23×C83116yescomplemented
605#121C23×C8318yescomplemented
606#121C23×C83116yescomplemented
607#121C23×C83116yescomplemented
608#121C23×C83116yescomplemented
609#121C23×C83116yescomplemented
610#121C23×C83116yescomplemented
611#121C23×C83116yescomplemented
612#121C23×C83116yescomplemented
613#121C23×C83116yescomplemented
614#121C23×C83116yescomplemented
615#120C23×C8318yes—
616#120C23×C8318yes—
617#120C23×C8318yes—
618#120C23×C8318yes—
619#120C23×C83116yes—
620#120C23×C8318yes—
621#120C23×C83116yes—
622#120C23×C8318yescomplemented
623#120C23×C8318yescomplemented
624#120C23×C8318yescomplemented
625#120C23×C8318yescomplemented
626#120C23×C8318yescomplemented
627#120C23×C83116yescomplemented
628#120C23×C83116yescomplemented
629#120C23×C8318yescomplemented
630#120C23×C8318yescomplemented
631#120C23×C83116yescomplemented
632C4×Q8C23×C8318yescomplemented
633C4×D4C23×C83116yes—
634C4×D4C23×C83116yescomplemented
635C4×D4C23×C83116yescomplemented
636C4×D4C23×C83116yescomplemented
637C4×D4C23×C83116yescomplemented
638C4×D4C23×C83116yescomplemented
639C4×D4C23×C83116yescomplemented
640C4×D4C23×C83116yescomplemented
641C4×D4C23×C8318yescomplemented
642#117C23×C8318yescomplemented
643#117C23×C8318yescomplemented
644#117C23×C8314yescomplemented
645#117C23×C83116yescomplemented
646#117C23×C83116yescomplemented
647C2×C4⋊C4C23×C8312yescomplemented
648C2×C4⋊C4C23×C8318yescomplemented
649C2×C4⋊C4C23×C8318yescomplemented
650C2×C22⋊C4C23×C8314yes—
651C2×C22⋊C4C23×C8318yes—
652C2×C22⋊C4C23×C8312yes—
653C2×C22⋊C4C23×C8318yes—
654C2×C22⋊C4C23×C8314yescomplemented
655C2×C22⋊C4C23×C8318yescomplemented
656C2×C22⋊C4C23×C8318yescomplemented
657C2×C22⋊C4C23×C8314yescomplemented
658C2×C22⋊C4C23×C8318yescomplemented
659C2×C22⋊C4C23×C8318yescomplemented
660C2×C22⋊C4C23×C83116yescomplemented
661C2×C22⋊C4C23×C8318yescomplemented
662C2×C42C23×C8312yescomplemented
663C24—28no—
664C24—44no—
665C24—84no—
666C24—84no—
667C24C24×C8314yes—
668C24C24×C8314yes—
669C24C24×C8314yes—
670C24C24×C8312yes—
671C24C24×C8312yes—
672C24C24×C8312yes—
673C24C24×C8318yes—
674C24C24×C8314yes—
675C24C24×C8311yescharacteristic
676#41—416no—
677#41—416no—
678#41—48no—
679#41—816no—
680C2×Q8—42no—
681C2×Q8C24×C8318yes—
682C2×Q8C24×C8314yes—
683C2×Q8C24×C8314yes—
684C2×D4—216no—
685C2×D4—28no—
686C2×D4—44no—
687C2×D4—44no—
688C2×D4—48no—
689C2×D4—48no—
690C2×D4—48no—
691C2×D4—42no—
692C2×D4—416no—
693C2×D4—416no—
694C2×D4—48no—
695C2×D4—416no—
696C2×D4—88no—
697C2×D4—88no—
698C2×D4—816no—
699C2×D4C24×C8318yes—
700C2×D4C24×C8318yes—
701C2×D4C24×C8318yes—
702C2×D4C24×C83116yes—
703C2×D4C24×C83116yes—
704C2×D4C24×C8318yes—
705C2×D4C24×C83116yes—
706C2×D4C24×C83116yes—
707C2×D4C24×C83116yes—
708C2×D4C24×C8312yes—
709C2×D4C24×C8312yes—
710C2×D4C24×C8314yes—
711C2×D4C24×C8314yes—
712C2×D4C24×C8314yes—
713C2×D4C24×C8318yes—
714C2×D4C24×C8314yes—
715C2×D4C24×C83116yes—
716C2×D4C24×C8312yes—
717C2×D4C24×C8312yes—
718C22×C4—24no—
719C22×C4—44no—
720C22×C4—44no—
721C22×C4—84no—
722C22×C4C24×C8311yescharacteristic
723C22×C4C24×C8314yes—
724C22×C4C24×C8312yes—
725C22×C4C24×C8314yes—
726C22×C4C24×C8311yescharacteristic
727C22×C4C24×C8314yes—
728C22×C4C24×C8318yes—
729C22×C4C24×C83116yes—
730C22×C4C24×C8318yes—
731C22×C4C24×C83116yes—
732C22×C4C24×C8318yes—
733C22×C4C24×C8318yes—
734C22×C4C24×C8314yes—
735C22×C4C24×C8318yes—
736C4⋊C4C24×C83116yes—
737C4⋊C4C24×C8318yes—
738C4⋊C4C24×C83116yes—
739C4⋊C4C24×C83116yes—
740C4⋊C4C24×C83116yes—
741C4⋊C4C24×C83116yes—
742C4⋊C4C24×C8318yes—
743C4⋊C4C24×C8318yes—
744C4⋊C4C24×C8318yes—
745C22⋊C4C24×C8318yes—
746C22⋊C4C24×C8318yes—
747C22⋊C4C24×C8318yes—
748C22⋊C4C24×C8318yes—
749C22⋊C4C24×C8318yes—
750C22⋊C4C24×C83116yes—
751C22⋊C4C24×C83116yes—
752C22⋊C4C24×C83116yes—
753C22⋊C4C24×C83116yes—
754C22⋊C4C24×C83116yes—
755C22⋊C4C24×C83116yes—
756C22⋊C4C24×C83116yes—
757C22⋊C4C24×C83116yes—
758C22⋊C4C24×C83116yes—
759C22⋊C4C24×C8318yes—
760C22⋊C4C24×C83116yes—
761C42C24×C8314yes—
762C42C24×C8314yes—
763C42C24×C83116yes—
764C42C24×C8318yes—
765C23—24no—
766C23—24no—
767C23—24no—
768C23—28no—
769C23—28no—
770C23—28no—
771C23—44no—
772C23—42no—
773C23—44no—
774C23—48no—
775C23—44no—
776C23—48no—
777C23—48no—
778C23—48no—
779C23—416no—
780C23—44no—
781C23—48no—
782C23—816no—
783C23—816no—
784C23H(5,𝔽2)×C8314yes—
785C23C25×C8314yes—
786C23C25×C8318yes—
787C23C25×C8314yes—
788C23C25×C8314yes—
789C23C25×C8312yes—
790C23C25×C8311yescharacteristic
791Q8—44no—
792Q8—44no—
793Q8—48no—
794D4—216no—
795D4—216no—
796D4—216no—
797D4—42no—
798D4—44no—
799D4—42no—
800D4—42no—
801D4—44no—
802D4—42no—
803D4—416no—
804D4—48no—
805D4—44no—
806D4—44no—
807D4—416no—
808D4—416no—
809D4—48no—
810D4—416no—
811D4—416no—
812D4—416no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—28no—
816C2×C4—28no—
817C2×C4—24no—
818C2×C4—48no—
819C2×C4—48no—
820C2×C4—48no—
821C2×C4—416no—
822C2×C4—44no—
823C2×C4—48no—
824C2×C4—44no—
825C2×C4—416no—
826C2×C4—48no—
827C2×C4C25×C8318yes—
828C2×C4C25×C8312yes—
829C2×C4C25×C83116yes—
830C2×C4C25×C8314yes—
831C2×C4C25×C8318yes—
832C2×C4C25×C8312yes—
833C22—24no—
834C22—22no—
835C22—24no—
836C22—24no—
837C22—28no—
838C22—24no—
839C22—28no—
840C22—28no—
841C22—216no—
842C22—28no—
843C22—44no—
844C22—48no—
845C22—48no—
846C22—88no—
847C22—88no—
848C22—88no—
849C22—84no—
850C22—816no—
851C22—164no—
852C22C2×H(5,𝔽2)×C8314yes—
853C22C2×H(5,𝔽2)×C8312yes—
854C22C26×C8311yescharacteristic
855C4—22no—
856C4—22no—
857C4—28no—
858C4—24no—
859C4—216no—
860C4—28no—
861C2—24no—
862C2—22no—
863C2—44no—
864C2—44no—
865C2—48no—
866C2—44no—
867C2C22×H(5,𝔽2)×C8311yescharacteristic
868C2C83×H(7,𝔽2)12yes—
subgroupG/H
center, socleC22×C83C26
commutator, Frattini, cosocleC22C26×C83
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C83 ◁ G

Complements

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

NH ≅ G/Ntype
1. C83×#3545C2semidirect
2. C83×#3543C2semidirect
3. C83×#3542C2semidirect
4. C83×#3534C2semidirect
5. C83×#3533C2semidirect
6. C83×#3532C2semidirect
7. C83×#3491C2semidirect
8. C83×#3490C2semidirect
9. C83×#3485C2semidirect
10. C83×#3484C2semidirect
11. C2×#535×C83C2semidirect
12. C2×#534×C83C2semidirect
13. C2×H(5,𝔽2)×C83C22semidirect
14. C22×#41×C83C22semidirect
15. C23×D4×C83C22semidirect
16. C23×D4×C83C22semidirect
17. #563×C83C22semidirect
18. #562×C83C22semidirect
19. #562×C83C22semidirect
20. H(3,𝔽4)×C83C22semidirect
21. #560×C83C22semidirect
22. #560×C83C22semidirect
23. #560×C83C22semidirect
24. #559×C83C22semidirect
25. #555×C83C22semidirect
26. #553×C83C22semidirect
27. #552×C83C22semidirect
28. #551×C83C22semidirect
29. #551×C83C22semidirect
30. #551×C83C22semidirect
31. #551×C83C22semidirect
32. #550×C83C22semidirect
33. #547×C83C22semidirect
34. #546×C83C22semidirect
35. #546×C83C22semidirect
36. #546×C83C22semidirect
37. #546×C83C22semidirect
38. #546×C83C22semidirect
39. #546×C83C22semidirect
40. D42×C83C22semidirect
41. D42×C83C22semidirect
42. D42×C83C22semidirect
43. #543×C83C22semidirect
44. #542×C83C22semidirect
45. #540×C83C22semidirect
46. #540×C83C22semidirect
47. #539×C83C22semidirect
48. #539×C83C22semidirect
49. #538×C83C22semidirect
50. #538×C83C22semidirect
51. #538×C83C22semidirect
52. #538×C83C22semidirect
53. #537×C83C22semidirect
54. #536×C83C22semidirect
55. #535×C83C22semidirect
56. #535×C83C22semidirect
57. #535×C83C22semidirect
58. #535×C83C22semidirect
60. #534×C83C22semidirect
61. #534×C83C22semidirect
62. #534×C83C22semidirect
63. #534×C83C22semidirect
64. #534×C83C22semidirect
65. #534×C83C22semidirect
66. #534×C83C22semidirect
67. #534×C83C22semidirect
68. C2×#127×C83C22semidirect
69. #529×C83C22semidirect
70. C2×#124×C83C22semidirect
71. #525×C83C22semidirect
72. #525×C83C22semidirect
73. #525×C83C22semidirect
74. C2×#123×C83C22semidirect
75. C2×#123×C83C22semidirect
76. C2×#123×C83C22semidirect
77. C2×#121×C83C22semidirect
78. C2×#121×C83C22semidirect
79. C2×#120×C83C22semidirect
80. C2×#120×C83C22semidirect
81. C2×#120×C83C22semidirect
82. C2×#120×C83C22semidirect
83. #518×C83C22semidirect
84. #518×C83C22semidirect
85. C2×#117×C83C22semidirect
86. C22×C22⋊C4×C83C22semidirect
88. C25×C83C23semidirect
93. C2×#41×C83C23semidirect
94. C2×#41×C83C23semidirect
95. C22×Q8×C83C23semidirect
108. C22×D4×C83C23semidirect
109. C22×D4×C83C23semidirect
110. C22×D4×C83C23semidirect
111. C22×D4×C83C23semidirect
112. C22×D4×C83C23semidirect
114. C23×C4×C83C23semidirect
115. C23×C4×C83C23semidirect
116. C23×C4×C83C23semidirect
117. C4⋊Q8×C83C23semidirect
119. #127×C83C23semidirect
120. #127×C83C23semidirect
121. #127×C83C23semidirect
122. #126×C83C23semidirect
123. #126×C83C23semidirect
124. #126×C83C23semidirect
125. #126×C83C23semidirect
126. #125×C83C23semidirect
127. #125×C83C23semidirect
129. #124×C83C23semidirect
130. #124×C83C23semidirect
131. #124×C83C23semidirect
132. #124×C83C23semidirect
133. #124×C83C23semidirect
134. #124×C83C23semidirect
135. #124×C83C23semidirect
140. #123×C83C23semidirect
141. #123×C83C23semidirect
142. #123×C83C23semidirect
143. #123×C83C23semidirect
144. #123×C83C23semidirect
145. #123×C83C23semidirect
146. #123×C83C23semidirect
147. #123×C83C23semidirect
148. #123×C83C23semidirect
149. #123×C83C23semidirect
150. #123×C83C23semidirect
151. #123×C83C23semidirect
152. #123×C83C23semidirect
153. #123×C83C23semidirect
154. C22⋊Q8×C83C23semidirect
155. C22⋊Q8×C83C23semidirect
156. C22⋊Q8×C83C23semidirect
157. C22⋊Q8×C83C23semidirect
158. C22⋊Q8×C83C23semidirect
159. C22⋊Q8×C83C23semidirect
160. C22⋊Q8×C83C23semidirect
166. #121×C83C23semidirect
167. #121×C83C23semidirect
168. #121×C83C23semidirect
169. #121×C83C23semidirect
170. #121×C83C23semidirect
171. #121×C83C23semidirect
172. #121×C83C23semidirect
173. #121×C83C23semidirect
174. #121×C83C23semidirect
175. #121×C83C23semidirect
176. #121×C83C23semidirect
177. #121×C83C23semidirect
178. #121×C83C23semidirect
179. #121×C83C23semidirect
187. #120×C83C23semidirect
188. #120×C83C23semidirect
189. #120×C83C23semidirect
190. #120×C83C23semidirect
191. #120×C83C23semidirect
192. #120×C83C23semidirect
193. #120×C83C23semidirect
194. #120×C83C23semidirect
195. #120×C83C23semidirect
196. #120×C83C23semidirect
197. C4×Q8×C83C23semidirect
199. C4×D4×C83C23semidirect
200. C4×D4×C83C23semidirect
201. C4×D4×C83C23semidirect
202. C4×D4×C83C23semidirect
203. C4×D4×C83C23semidirect
204. C4×D4×C83C23semidirect
205. C4×D4×C83C23semidirect
206. C4×D4×C83C23semidirect
207. #117×C83C23semidirect
208. #117×C83C23semidirect
209. #117×C83C23semidirect
210. #117×C83C23semidirect
211. #117×C83C23semidirect
212. C2×C4⋊C4×C83C23semidirect
213. C2×C4⋊C4×C83C23semidirect
214. C2×C4⋊C4×C83C23semidirect
219. C2×C22⋊C4×C83C23semidirect
220. C2×C22⋊C4×C83C23semidirect
221. C2×C22⋊C4×C83C23semidirect
222. C2×C22⋊C4×C83C23semidirect
223. C2×C22⋊C4×C83C23semidirect
224. C2×C22⋊C4×C83C23semidirect
225. C2×C22⋊C4×C83C23semidirect
226. C2×C22⋊C4×C83C23semidirect
227. C2×C42×C83C23semidirect
426. #62862C83direct (N × H)
435. #3545C2×C83semidirect
436. #3543C2×C83semidirect
437. #3542C2×C83semidirect
438. #3534C2×C83semidirect
439. #3533C2×C83semidirect
440. #3532C2×C83semidirect
441. #3491C2×C83semidirect
442. #3490C2×C83semidirect
443. #3485C2×C83semidirect
444. #3484C2×C83semidirect
445. C2×#535C2×C83semidirect
446. C2×#534C2×C83semidirect
447. C83#62862direct (N × H)
448. C2×H(5,𝔽2)C22×C83semidirect
449. C22×#41C22×C83semidirect
450. C23×D4C22×C83semidirect
451. C23×D4C22×C83semidirect
452. #563C22×C83semidirect
453. #562C22×C83semidirect
454. #562C22×C83semidirect
455. H(3,𝔽4)C22×C83semidirect
456. #560C22×C83semidirect
457. #560C22×C83semidirect
458. #560C22×C83semidirect
459. #559C22×C83semidirect
460. #555C22×C83semidirect
461. #553C22×C83semidirect
462. #552C22×C83semidirect
463. #551C22×C83semidirect
464. #551C22×C83semidirect
465. #551C22×C83semidirect
466. #551C22×C83semidirect
467. #550C22×C83semidirect
468. #547C22×C83semidirect
469. #546C22×C83semidirect
470. #546C22×C83semidirect
471. #546C22×C83semidirect
472. #546C22×C83semidirect
473. #546C22×C83semidirect
474. #546C22×C83semidirect
475. D42C22×C83semidirect
476. D42C22×C83semidirect
477. D42C22×C83semidirect
478. #543C22×C83semidirect
479. #542C22×C83semidirect
480. #540C22×C83semidirect
481. #540C22×C83semidirect
482. #539C22×C83semidirect
483. #539C22×C83semidirect
484. #538C22×C83semidirect
485. #538C22×C83semidirect
486. #538C22×C83semidirect
487. #538C22×C83semidirect
488. #537C22×C83semidirect
489. #536C22×C83semidirect
490. #535C22×C83semidirect
491. #535C22×C83semidirect
492. #535C22×C83semidirect
493. #535C22×C83semidirect
495. #534C22×C83semidirect
496. #534C22×C83semidirect
497. #534C22×C83semidirect
498. #534C22×C83semidirect
499. #534C22×C83semidirect
500. #534C22×C83semidirect
501. #534C22×C83semidirect
502. #534C22×C83semidirect
503. C2×#127C22×C83semidirect
504. #529C22×C83semidirect
505. C2×#124C22×C83semidirect
506. #525C22×C83semidirect
507. #525C22×C83semidirect
508. #525C22×C83semidirect
509. C2×#123C22×C83semidirect
510. C2×#123C22×C83semidirect
511. C2×#123C22×C83semidirect
512. C2×#121C22×C83semidirect
513. C2×#121C22×C83semidirect
514. C2×#120C22×C83semidirect
515. C2×#120C22×C83semidirect
516. C2×#120C22×C83semidirect
517. C2×#120C22×C83semidirect
518. #518C22×C83semidirect
519. #518C22×C83semidirect
520. C2×#117C22×C83semidirect
521. C22×C22⋊C4C22×C83semidirect
523. C25C23×C83semidirect
528. C2×#41C23×C83semidirect
529. C2×#41C23×C83semidirect
530. C22×Q8C23×C83semidirect
543. C22×D4C23×C83semidirect
544. C22×D4C23×C83semidirect
545. C22×D4C23×C83semidirect
546. C22×D4C23×C83semidirect
547. C22×D4C23×C83semidirect
549. C23×C4C23×C83semidirect
550. C23×C4C23×C83semidirect
551. C23×C4C23×C83semidirect
552. C4⋊Q8C23×C83semidirect
554. #127C23×C83semidirect
555. #127C23×C83semidirect
556. #127C23×C83semidirect
557. #126C23×C83semidirect
558. #126C23×C83semidirect
559. #126C23×C83semidirect
560. #126C23×C83semidirect
561. #125C23×C83semidirect
562. #125C23×C83semidirect
564. #124C23×C83semidirect
565. #124C23×C83semidirect
566. #124C23×C83semidirect
567. #124C23×C83semidirect
568. #124C23×C83semidirect
569. #124C23×C83semidirect
570. #124C23×C83semidirect
575. #123C23×C83semidirect
576. #123C23×C83semidirect
577. #123C23×C83semidirect
578. #123C23×C83semidirect
579. #123C23×C83semidirect
580. #123C23×C83semidirect
581. #123C23×C83semidirect
582. #123C23×C83semidirect
583. #123C23×C83semidirect
584. #123C23×C83semidirect
585. #123C23×C83semidirect
586. #123C23×C83semidirect
587. #123C23×C83semidirect
588. #123C23×C83semidirect
589. C22⋊Q8C23×C83semidirect
590. C22⋊Q8C23×C83semidirect
591. C22⋊Q8C23×C83semidirect
592. C22⋊Q8C23×C83semidirect
593. C22⋊Q8C23×C83semidirect
594. C22⋊Q8C23×C83semidirect
595. C22⋊Q8C23×C83semidirect
601. #121C23×C83semidirect
602. #121C23×C83semidirect
603. #121C23×C83semidirect
604. #121C23×C83semidirect
605. #121C23×C83semidirect
606. #121C23×C83semidirect
607. #121C23×C83semidirect
608. #121C23×C83semidirect
609. #121C23×C83semidirect
610. #121C23×C83semidirect
611. #121C23×C83semidirect
612. #121C23×C83semidirect
613. #121C23×C83semidirect
614. #121C23×C83semidirect
622. #120C23×C83semidirect
623. #120C23×C83semidirect
624. #120C23×C83semidirect
625. #120C23×C83semidirect
626. #120C23×C83semidirect
627. #120C23×C83semidirect
628. #120C23×C83semidirect
629. #120C23×C83semidirect
630. #120C23×C83semidirect
631. #120C23×C83semidirect
632. C4×Q8C23×C83semidirect
634. C4×D4C23×C83semidirect
635. C4×D4C23×C83semidirect
636. C4×D4C23×C83semidirect
637. C4×D4C23×C83semidirect
638. C4×D4C23×C83semidirect
639. C4×D4C23×C83semidirect
640. C4×D4C23×C83semidirect
641. C4×D4C23×C83semidirect
642. #117C23×C83semidirect
643. #117C23×C83semidirect
644. #117C23×C83semidirect
645. #117C23×C83semidirect
646. #117C23×C83semidirect
647. C2×C4⋊C4C23×C83semidirect
648. C2×C4⋊C4C23×C83semidirect
649. C2×C4⋊C4C23×C83semidirect
654. C2×C22⋊C4C23×C83semidirect
655. C2×C22⋊C4C23×C83semidirect
656. C2×C22⋊C4C23×C83semidirect
657. C2×C22⋊C4C23×C83semidirect
658. C2×C22⋊C4C23×C83semidirect
659. C2×C22⋊C4C23×C83semidirect
660. C2×C22⋊C4C23×C83semidirect
661. C2×C22⋊C4C23×C83semidirect
662. C2×C42C23×C83semidirect

Maximal subgroups

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

subgroupindex
C83×#35452
C83×#35432
C83×#35422
C83×#35342
C83×#35332
C83×#35322
C83×#34912
C83×#34902
C83×#34852
C83×#34842
C2×#535×C832
C2×#534×C832
#6286283