Finite Group Databasebeta

← #36275141

Subgroups — #36275141

Order 21248.

2686 conjugacy classes of subgroups.

The subgroup lattice has 1060 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581766C211yesmaximal, characteristic, complemented
2#24918273C214yesmaximal, complemented
3#24918265C212yesmaximal, complemented
4#24918260C212yesmaximal, complemented
5#24918224C214yesmaximal, complemented
6#24918216C212yesmaximal, complemented
7#24918211C212yesmaximal, complemented
8#24917403C212yesmaximal, complemented
9#24917383C212yesmaximal, complemented
10#24917084C214yesmaximal, complemented
11#24916715C212yesmaximal, complemented
12#24916689C212yesmaximal, complemented
13C2×#19127665C211yesmaximal, characteristic, complemented
14C2×#525×C83C211yesmaximal, characteristic, complemented
15C23×D332C2211yescharacteristic, complemented
16C23×C22⋊D83—21no—
17C2×#14581817C2214yescomplemented
18C22×#13050574C2212yescomplemented
19C2×#14581766—21no—
20C2×#14581766—21no—
21C2×#14581766—21no—
22C2×#14581766—21no—
23C2×#14581766—21no—
24C2×#14581766—21no—
25C2×#14581766C2212yes—
26C2×#14581766C2212yes—
27C2×#14581766C2212yes—
28C2×#14581766C2212yescomplemented
29C2×#14581766C2212yescomplemented
30C2×#14581766C2212yescomplemented
31C22×C4⋊Dic83C2211yescharacteristic, complemented
32C22×(C2×D83)⋊C4—21no—
33#19128034C2214yescomplemented
34#19128029C2214yescomplemented
35#19128025C2218yescomplemented
36#19128019C2214yescomplemented
37#19128017C2214yescomplemented
38#19128014C2214yescomplemented
39#19128012C2214yescomplemented
40#19127952C2218yescomplemented
41#19127949C2218yescomplemented
42#19127935C2218yescomplemented
43#19127932C2218yescomplemented
44#19127851C2214yescomplemented
45#19127851C2214yescomplemented
46#19127846C2218yescomplemented
47#19127840C2214yescomplemented
48#19127835C2214yescomplemented
49#19127834C2214yescomplemented
50#19127834C2214yescomplemented
51#19127744C2214yescomplemented
52#19127705C2214yescomplemented
53#19127702C2214yescomplemented
54#19127665C2212yescomplemented
55#19127665C2212yescomplemented
56#19127665C2212yescomplemented
57#19127665C2212yescomplemented
58C2×C22⋊(C83⋊C8)C2212yescomplemented
59C2×C22⋊(C83⋊C8)C2212yescomplemented
60C22×#41×C83C2211yescharacteristic, complemented
61C24×C4×C83C2211yescharacteristic
62#525×C83—21no—
63#525×C83—21no—
64#525×C83—21no—
65#525×C83—21no—
66#525×C83C2212yes—
67#525×C83C2212yescomplemented
68#525×C83C2212yescomplemented
69#525×C83C2212yescomplemented
70C2×#123×C83—21no—
71C2×C22⋊Q8×C83C2211yescharacteristic, complemented
72C2×C22⋊Q8×C83C2211yescharacteristic, complemented
73C2×#121×C83C2211yescharacteristic, complemented
74C2×#121×C83C2211yescharacteristic, complemented
75C2×#120×C83—21no—
76C2×C4×D4×C83—21no—
77C2×C4×D4×C83—21no—
78C2×#117×C83C2211yescharacteristic, complemented
79C24×D83—21no—
80C22×D332—21no—
81C22×D332—21no—
82C22×D332—21no—
83C22×D332—44no—
84C22×D332C2312yes—
85C22×D332C2312yes—
86C22×D332C2312yes—
87C22×C22⋊D83—22no—
88C22×C22⋊D83—22no—
89C22×C22⋊D83—22no—
90C22×C22⋊D83—22no—
91C22×C22⋊D83—22no—
92C22×C22⋊D83—22no—
93C22×C22⋊D83—48no—
94C23×Dic83—21no—
95#14581817—48no—
96C2×#13050577C2318yescomplemented
97C2×#13050575C2318yescomplemented
98C2×#13050574—44no—
99C2×#13050574C2314yes—
100C2×#13050574C2314yescomplemented
101C22×C83⋊C8C2314yescomplemented
102#14581766—22no—
103#14581766—22no—
104#14581766—22no—
105#14581766—22no—
106#14581766—22no—
107#14581766—22no—
108#14581766—22no—
109#14581766—22no—
110#14581766—22no—
111#14581766—22no—
112#14581766—22no—
113#14581766—22no—
114#14581766C2314yes—
115#14581766C2314yes—
116#14581766C2314yes—
117#14581766C2314yes—
118C2×C4⋊Dic83—21no—
119C2×C4⋊Dic83—21no—
120C2×C4⋊Dic83—21no—
121C2×C4⋊Dic83C2312yes—
122C2×C4⋊Dic83C2312yes—
123C2×C4⋊Dic83C2312yes—
124C2×(C2×D83)⋊C4—22no—
125C2×(C2×D83)⋊C4—22no—
126C2×(C2×D83)⋊C4—22no—
127C2×(C2×D83)⋊C4—22no—
128C2×(C2×D83)⋊C4—22no—
129C2×(C2×D83)⋊C4—22no—
130#14581725C2318yescomplemented
131#14581723C2318yescomplemented
132#14581716C2318yescomplemented
133#14581713C2318yescomplemented
134#14581712C2318yescomplemented
135#14581712C2318yescomplemented
136C22⋊(C83⋊C8)C2314yes—
137C22⋊(C83⋊C8)C2314yes—
138C22⋊(C83⋊C8)C2314yescomplemented
139C22⋊(C83⋊C8)C2314yescomplemented
140C25×C83D411yescharacteristic
141C2×#41×C83—21no—
142C2×#41×C83—21no—
143C2×#41×C83—44no—
144C2×#41×C83C2312yes—
145C2×#41×C83C2312yescomplemented
146C22×Q8×C83C2311yescharacteristic, complemented
147C22×D4×C83—21no—
148C22×D4×C83—21no—
149C22×D4×C83—21no—
150C22×D4×C83C2311yescharacteristic, complemented
151C23×C4×C83—21no—
152C23×C4×C83—44no—
153C23×C4×C83D411yescharacteristic
154C23×C4×C83D411yescharacteristic
155C23×C4×C83D411yescharacteristic
156C23×C4×C83D411yescharacteristic
157C23×C4×C83D411yescharacteristic
158C23×C4×C83D411yescharacteristic
159C23×C4×C83D411yescharacteristic
160C23×C4×C83C2311yescharacteristic
161C23×C4×C83C2311yescharacteristic
162C23×C4×C83C2311yescharacteristic
163C23×C4×C83C2311yescharacteristic
164C23×C4×C83C2311yescharacteristic
165C23×C4×C83C2311yescharacteristic
166C23×C4×C83C2311yescharacteristic
167#123×C83—22no—
168#123×C83—22no—
169#123×C83—22no—
170#123×C83—22no—
171C22⋊Q8×C83—21no—
172C22⋊Q8×C83—21no—
173C22⋊Q8×C83—21no—
174C22⋊Q8×C83—21no—
175C22⋊Q8×C83C2312yes—
176C22⋊Q8×C83C2312yes—
177C22⋊Q8×C83C2312yescomplemented
178C22⋊Q8×C83C2312yescomplemented
179#121×C83—21no—
180#121×C83—21no—
181#121×C83—21no—
182#121×C83—21no—
183#121×C83C2312yes—
184#121×C83C2312yes—
185#121×C83C2312yescomplemented
186#121×C83C2312yescomplemented
187#120×C83—22no—
188#120×C83—22no—
189#120×C83—22no—
190#120×C83—22no—
191C4×D4×C83—22no—
192C4×D4×C83—22no—
193C4×D4×C83—22no—
194C4×D4×C83—22no—
195C4×D4×C83—22no—
196C4×D4×C83—22no—
197C4×D4×C83—22no—
198C4×D4×C83—22no—
199#117×C83—21no—
200#117×C83—21no—
201#117×C83C2312yes—
202#117×C83C2312yescomplemented
203C2×C4⋊C4×C83—21no—
204C2×C4⋊C4×C83—21no—
205C2×C4⋊C4×C83C2311yescharacteristic, complemented
206C2×C4⋊C4×C83C2311yescharacteristic, complemented
207C2×C22⋊C4×C83—21no—
208C2×C22⋊C4×C83—21no—
209C2×C22⋊C4×C83—21no—
210C2×C22⋊C4×C83—21no—
211C2×C22⋊C4×C83—21no—
212C2×C42×C83—21no—
213C23×D83—22no—
214C23×D83—22no—
215C23×D83—22no—
216C23×D83—44no—
217C23×D83—44no—
218C23×D83—44no—
219C2×D332—28no—
220C2×D332—22no—
221C2×D332—22no—
222C2×D332—22no—
223C2×D332—44no—
224C2×D332—44no—
225C2×D332—44no—
226C2×D332—44no—
227C2×D332—44no—
228C2×D332C2414yes—
229C2×C22⋊D83—24no—
230C2×C22⋊D83—24no—
231C2×C22⋊D83—24no—
232C2×C22⋊D83—24no—
233C2×C22⋊D83—48no—
234C2×C22⋊D83—48no—
235C2×C22⋊D83—48no—
236C2×C22⋊D83—48no—
237C2×C22⋊D83—48no—
238C2×C22⋊D83—48no—
239C22×Dic83—22no—
240C22×Dic83—22no—
241C22×Dic83—22no—
242C22×Dic83—44no—
243#13050577—48no—
244#13050575—48no—
245#13050574—28no—
246#13050574—44no—
247C2×C83⋊C8—44no—
248C2×C83⋊C8C2418yes—
249C4⋊Dic83—22no—
250C4⋊Dic83—22no—
251C4⋊Dic83—22no—
252C4⋊Dic83C2414yes—
253(C2×D83)⋊C4—24no—
254(C2×D83)⋊C4—24no—
255(C2×D83)⋊C4—24no—
256(C2×D83)⋊C4—24no—
257C24×C83—24no—
258C24×C83—21no—
259C24×C83—42no—
260C24×C83—42no—
261C24×C83C2×D411yescharacteristic
262C24×C83C2×D411yescharacteristic
263C24×C83C2×D411yescharacteristic
264C24×C83C2×D411yescharacteristic
265C24×C83C2×D411yescharacteristic
266C24×C83C2×D411yescharacteristic
267C24×C83C2×D411yescharacteristic
268#41×C83—28no—
269#41×C83—44no—
270#41×C83—44no—
271#41×C83—44no—
272C2×Q8×C83—21no—
273C2×Q8×C83—42no—
274C2×Q8×C83C2412yes—
275C2×D4×C83—22no—
276C2×D4×C83—22no—
277C2×D4×C83—22no—
278C2×D4×C83—22no—
279C2×D4×C83—22no—
280C2×D4×C83—22no—
281C2×D4×C83—21no—
282C2×D4×C83—42no—
283C2×D4×C83—44no—
284C2×D4×C83—44no—
285C2×D4×C83—44no—
286C2×D4×C83C2412yes—
287C22×C4×C83—24no—
288C22×C4×C83—24no—
289C22×C4×C83—24no—
290C22×C4×C83—21no—
291C22×C4×C83—21no—
292C22×C4×C83—21no—
293C22×C4×C83—22no—
294C22×C4×C83—22no—
295C22×C4×C83—42no—
296C22×C4×C83—42no—
297C22×C4×C83—42no—
298C22×C4×C83—42no—
299C22×C4×C83—42no—
300C22×C4×C83—42no—
301C22×C4×C83—42no—
302C22×C4×C83—42no—
303C22×C4×C83—42no—
304C22×C4×C83—42no—
305C22×C4×C83—42no—
306C22×C4×C83—44no—
307C22×C4×C83C2×D411yescharacteristic
308C22×C4×C83C2×D411yescharacteristic
309C22×C4×C83C2×D411yescharacteristic
310C22×C4×C83C2×D411yescharacteristic
311C22×C4×C83C2×D411yescharacteristic
312C22×C4×C83C2×D411yescharacteristic
313C22×C4×C83C2×D411yescharacteristic
314C22×C4×C83C2×D411yescharacteristic
315C22×C4×C83C2×D411yescharacteristic
316C22×C4×C83C2×D411yescharacteristic
317C22×C4×C83C2×D411yescharacteristic
318C22×C4×C83C2×D411yescharacteristic
319C22×C4×C83C2×D411yescharacteristic
320C22×C4×C83C2×D411yescharacteristic
321C22×C4×C83C2×D411yescharacteristic
322C22×C4×C83C2×D411yescharacteristic
323C22×C4×C83C2×D411yescharacteristic
324C22×C4×C83C2×D411yescharacteristic
325C22×C4×C83C2×D411yescharacteristic
326C22×C4×C83C2×D411yescharacteristic
327C22×C4×C83C2×D411yescharacteristic
328C22×C4×C83C2411yescharacteristic
329C22×C4×C83C2411yescharacteristic
330C22×C4×C83C2411yescharacteristic
331C22×C4×C83C2411yescharacteristic
332C22×C4×C83C2411yescharacteristic
333C22×C4×C83C2411yescharacteristic
334C22×C4×C83C2411yescharacteristic
335C4⋊C4×C83—22no—
336C4⋊C4×C83—22no—
337C4⋊C4×C83—22no—
338C4⋊C4×C83—22no—
339C4⋊C4×C83—21no—
340C4⋊C4×C83—21no—
341C4⋊C4×C83C2412yes—
342C4⋊C4×C83C2412yes—
343C22⋊C4×C83—22no—
344C22⋊C4×C83—22no—
345C22⋊C4×C83—22no—
346C22⋊C4×C83—22no—
347C22⋊C4×C83—22no—
348C22⋊C4×C83—22no—
349C22⋊C4×C83—22no—
350C22⋊C4×C83—22no—
351C22⋊C4×C83—22no—
352C22⋊C4×C83—22no—
353C42×C83—22no—
354C42×C83—22no—
355C23×C83—22no—
356C23×C83—22no—
357C23×C83—22no—
358C23×C83—22no—
359C23×C83—22no—
360C23×C83—22no—
361C23×C83—22no—
362C23×C83—22no—
363C23×C83—22no—
364C23×C83—22no—
365C23×C83—22no—
366C23×C83—22no—
367C23×C83—22no—
368C23×C83—41no—
369C23×C83—41no—
370C23×C83—41no—
371C23×C83—41no—
372C23×C83—41no—
373C23×C83—41no—
374C23×C83—41no—
375C23×C83—41no—
376C23×C83—416no—
377C23×C83—42no—
378C23×C83—42no—
379C23×C83—42no—
380C23×C83AGL(1,ℤ/8)14yescomplemented
381C23×C83C22×D411yescharacteristic
382C23×C83C22×D411yescharacteristic
383C23×C83C22×D411yescharacteristic
384C23×C83C22×D411yescharacteristic
385C23×C83C22×D411yescharacteristic
386C23×C83C22×D411yescharacteristic
387C23×C83C22×D411yescharacteristic
388C22×D83—24no—
389C22×D83—44no—
390C22×D83—44no—
391C22×D83—44no—
392C22×D83—44no—
393C22×D83—44no—
394C22×D83—44no—
395C22×D83—44no—
396C22×D83—44no—
397C22×D83—44no—
398C22×D83—816no—
399Q8×C83—24no—
400Q8×C83—42no—
401D4×C83—24no—
402D4×C83—42no—
403D4×C83—44no—
404D4×C83—44no—
405D4×C83—44no—
406D4×C83—44no—
407D4×C83—44no—
408D4×C83—44no—
409C2×C4×C83—22no—
410C2×C4×C83—22no—
411C2×C4×C83—22no—
412C2×C4×C83—22no—
413C2×C4×C83—22no—
414C2×C4×C83—22no—
415C2×C4×C83—22no—
416C2×C4×C83—22no—
417C2×C4×C83—22no—
418C2×C4×C83—22no—
419C2×C4×C83—22no—
420C2×C4×C83—22no—
421C2×C4×C83—22no—
422C2×C4×C83—22no—
423C2×C4×C83—22no—
424C2×C4×C83—22no—
425C2×C4×C83—22no—
426C2×C4×C83—22no—
427C2×C4×C83—41no—
428C2×C4×C83—41no—
429C2×C4×C83—41no—
430C2×C4×C83—41no—
431C2×C4×C83—41no—
432C2×C4×C83—41no—
433C2×C4×C83—41no—
434C2×C4×C83—41no—
435C2×C4×C83—41no—
436C2×C4×C83—41no—
437C2×C4×C83—41no—
438C2×C4×C83—41no—
439C2×C4×C83—44no—
440C2×C4×C83—42no—
441C2×C4×C83—42no—
442C2×C4×C83—42no—
443C2×C4×C83—44no—
444C2×C4×C83C22×D411yescharacteristic
445C2×C4×C83C22×D411yescharacteristic
446C2×C4×C83C22×D411yescharacteristic
447C2×C4×C83C22×D411yescharacteristic
448C2×C4×C83C22×D411yescharacteristic
449C2×C4×C83C22×D411yescharacteristic
450C2×C4×C83C22×D411yescharacteristic
451C2×C4×C83H(5,𝔽2)14yes—
452C2×C4×C83C2511yescharacteristic
453C22⋊D83—48no—
454C22⋊D83—48no—
455C22⋊D83—48no—
456C22⋊D83—48no—
457C2×Dic83—24no—
458C2×Dic83—44no—
459C2×Dic83—44no—
460C2×Dic83—44no—
461D332—28no—
462D332—44no—
463D332—44no—
464D332—44no—
465C83⋊C8—28no—
466C22×C83—28no—
467C22×C83—21no—
468C22×C83—21no—
469C22×C83—21no—
470C22×C83—21no—
471C22×C83—21no—
472C22×C83—21no—
473C22×C83—21no—
474C22×C83—21no—
475C22×C83—21no—
476C22×C83—21no—
477C22×C83—21no—
478C22×C83—21no—
479C22×C83—21no—
480C22×C83—21no—
481C22×C83—21no—
482C22×C83—21no—
483C22×C83—44no—
484C22×C83—44no—
485C22×C83—44no—
486C22×C83—44no—
487C22×C83—44no—
488C22×C83—44no—
489C22×C83—42no—
490C22×C83—42no—
491C22×C83—42no—
492C22×C83—84no—
493C22×C83#53412yes—
494C22×C83C2×AGL(1,ℤ/8)12yes—
495C22×C83C2×AGL(1,ℤ/8)12yes—
496C22×C83C2×AGL(1,ℤ/8)12yes—
497C22×C83#57512yes—
498C22×C83C23×D411yescharacteristic
499C2×D83—44no—
500C2×D83—44no—
501C2×D83—44no—
502C2×D83—88no—
503C2×D83—88no—
504C2×D83—88no—
505C4×C83—21no—
506C4×C83—21no—
507C4×C83—21no—
508C4×C83—21no—
509C4×C83—21no—
510C4×C83—21no—
511C4×C83—42no—
512C4×C83—42no—
513C4×C83—42no—
514C4×C83#53412yes—
515C4×C83C2×H(5,𝔽2)12yes—
516Dic83—44no—
517#60750—831nomaximal, Sylow
518C2×C83—22no—
519C2×C83—22no—
520C2×C83—22no—
521C2×C83—22no—
522C2×C83—22no—
523C2×C83—41no—
524C2×C83—41no—
525C2×C83—82no—
526C2×C83C2×#53411yescharacteristic
527C2×C83C22×AGL(1,ℤ/8)11yescharacteristic
528C2×C83C2×#57511yescharacteristic
529D83—84no—
530C2×#525D8311yescharacteristic, complemented
531C22×#121—831no—
532#3194—834no—
533#3193—832no—
534#3192—832no—
535#3188—834no—
536#3187—832no—
537#3186—832no—
538#3094—832no—
539#3092—832no—
540#3055—834no—
541#3006—832no—
542#3003—832no—
543C2×#407—831no—
544C83#6075011yescharacteristic, complemented, Sylow
545C22×#41C2×D8311yescharacteristic, complemented
546C23×D4—831no—
547C23×D4—1661no—
548C24×C4C2×D8311yescharacteristic
549C2×AGL(1,ℤ/8)—834no—
550C22×M16—832no—
551#525—21no—
552#525—21no—
553#525—21no—
554#525—21no—
555#525C2×D8312yes—
556#525C2×D8312yescomplemented
557#525C2×D8312yescomplemented
558#525C2×D8312yescomplemented
559C2×#123—21no—
560C2×C22⋊Q8C2×D8311yescharacteristic, complemented
561C2×C22⋊Q8C2×D8311yescharacteristic, complemented
562C2×#121—832no—
563C2×#121—832no—
564C2×#121—832no—
565C2×#121—832no—
566C2×#121—832no—
567C2×#121—832no—
568C2×#121—1661no—
569C2×#121—1661no—
570C2×#121—1661no—
571C2×#121—1661no—
572C2×#121—1661no—
573C2×#121—1661no—
574C2×#121C2×D8311yescharacteristic, complemented
575C2×#121C2×D8311yescharacteristic, complemented
576C2×#120—21no—
577C2×C4×D4—21no—
578C2×C4×D4—21no—
579C2×#117C2×D8311yescharacteristic, complemented
580C22×C4⋊C4—831no—
581C22×C22⋊C4—1661no—
582#484—834no—
583#483—834no—
584#482—838no—
585#481—834no—
586#481—834no—
587#480—834no—
588#480—834no—
589#469—838no—
590#468—838no—
591#466—838no—
592#465—838no—
593#450—834no—
594#450—834no—
595#449—838no—
596#448—834no—
597#447—834no—
598#447—834no—
599#447—834no—
600#428—834no—
601#418—834no—
602#417—834no—
603#407—832no—
604#407—832no—
605#407—832no—
606#407—832no—
607C2×C22⋊C8—832no—
608C2×C22⋊C8—832no—
609C25—1661no—
610C25C22⋊D8311yescharacteristic
611C2×#41—21no—
612C2×#41—21no—
613C2×#41—44no—
614C2×#41C22×D8312yes—
615C2×#41C22×D8312yescomplemented
616C22×Q8C22×D8311yescharacteristic, complemented
617C22×D4—21no—
618C22×D4—21no—
619C22×D4—21no—
620C22×D4—3324no—
621C22×D4—3328no—
622C22×D4—832no—
623C22×D4—832no—
624C22×D4—832no—
625C22×D4—1662no—
626C22×D4—1662no—
627C22×D4—1662no—
628C22×D4—1662no—
629C22×D4—1662no—
630C22×D4—1662no—
631C22×D4—1661no—
632C22×D4—1661no—
633C22×D4—1661no—
634C22×D4C22×D8311yescharacteristic, complemented
635C23×C4—21no—
636C23×C4—44no—
637C23×C4—1661no—
638C23×C4C22⋊D8311yescharacteristic
639C23×C4C22⋊D8311yescharacteristic
640C23×C4C22⋊D8311yescharacteristic
641C23×C4C22⋊D8311yescharacteristic
642C23×C4C22⋊D8311yescharacteristic
643C23×C4C22⋊D8311yescharacteristic
644C23×C4C22⋊D8311yescharacteristic
645C23×C4C22×D8311yescharacteristic
646C23×C4C22×D8311yescharacteristic
647C23×C4C22×D8311yescharacteristic
648C23×C4C22×D8311yescharacteristic
649C23×C4C22×D8311yescharacteristic
650C23×C4C22×D8311yescharacteristic
651C23×C4C22×D8311yescharacteristic
652AGL(1,ℤ/8)—3328no—
653C2×SD16—838no—
654C2×D8—838no—
655C2×M16—3324no—
656C2×M16—834no—
657C2×M16—834no—
658C22×C8—834no—
659#123—22no—
660#123—22no—
661#123—22no—
662#123—22no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8C22×D8312yes—
668C22⋊Q8C22×D8312yes—
669C22⋊Q8C22×D8312yescomplemented
670C22⋊Q8C22×D8312yescomplemented
671#121—21no—
672#121—21no—
673#121—21no—
674#121—21no—
675#121—834no—
676#121—834no—
677#121—834no—
678#121—834no—
679#121—1662no—
680#121—1662no—
681#121—1662no—
682#121—1662no—
683#121—1662no—
684#121—1662no—
685#121—1662no—
686#121—1662no—
687#121—1662no—
688#121—1662no—
689#121—1662no—
690#121—1662no—
691#121C22×D8312yes—
692#121C22×D8312yes—
693#121C22×D8312yescomplemented
694#121C22×D8312yescomplemented
695#120—22no—
696#120—22no—
697#120—22no—
698#120—22no—
699C4×D4—22no—
700C4×D4—22no—
701C4×D4—22no—
702C4×D4—22no—
703C4×D4—22no—
704C4×D4—22no—
705C4×D4—22no—
706C4×D4—22no—
707#117—21no—
708#117—21no—
709#117C22×D8312yes—
710#117C22×D8312yescomplemented
711C2×C4⋊C4—21no—
712C2×C4⋊C4—21no—
713C2×C4⋊C4—832no—
714C2×C4⋊C4—832no—
715C2×C4⋊C4—832no—
716C2×C4⋊C4—1661no—
717C2×C4⋊C4—1661no—
718C2×C4⋊C4—1661no—
719C2×C4⋊C4C22×D8311yescharacteristic, complemented
720C2×C4⋊C4C22×D8311yescharacteristic, complemented
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4—1662no—
727C2×C22⋊C4—1662no—
728C2×C22⋊C4—1662no—
729C2×C22⋊C4—1662no—
730C2×C22⋊C4—1662no—
731C2×C22⋊C4—1662no—
732C2×C42—21no—
733#107—838no—
734#106—838no—
735#103—838no—
736#102—838no—
737#102—838no—
738#102—838no—
739C22⋊C8—834no—
740C22⋊C8—834no—
741C22⋊C8—834no—
742C22⋊C8—834no—
743C24—24no—
744C24—21no—
745C24—42no—
746C24—42no—
747C24—3324no—
748C24—3324no—
749C24—3324no—
750C24—1662no—
751C24—1662no—
752C24—1662no—
753C24C2×C22⋊D8311yescharacteristic
754C24C2×C22⋊D8311yescharacteristic
755C24C2×C22⋊D8311yescharacteristic
756C24C2×C22⋊D8311yescharacteristic
757C24C2×C22⋊D8311yescharacteristic
758C24C2×C22⋊D8311yescharacteristic
759C24C2×C22⋊D8311yescharacteristic
760#41—28no—
761#41—44no—
762#41—44no—
763#41—44no—
764C2×Q8—21no—
765C2×Q8—42no—
766C2×Q8C23×D8312yes—
767C2×D4—22no—
768C2×D4—22no—
769C2×D4—22no—
770C2×D4—22no—
771C2×D4—22no—
772C2×D4—22no—
773C2×D4—21no—
774C2×D4—42no—
775C2×D4—44no—
776C2×D4—44no—
777C2×D4—44no—
778C2×D4—3324no—
779C2×D4—3324no—
780C2×D4—3324no—
781C2×D4—3324no—
782C2×D4—3324no—
783C2×D4—3328no—
784C2×D4—3328no—
785C2×D4—3328no—
786C2×D4—3328no—
787C2×D4—3328no—
788C2×D4—3328no—
789C2×D4—834no—
790C2×D4—1664no—
791C2×D4—1664no—
792C2×D4—1664no—
793C2×D4—1664no—
794C2×D4—1662no—
795C2×D4—1662no—
796C2×D4—1662no—
797C2×D4—1668no—
798C2×D4C23×D8312yes—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—42no—
808C22×C4—42no—
809C22×C4—42no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4—42no—
815C22×C4—42no—
816C22×C4—42no—
817C22×C4—42no—
818C22×C4—44no—
819C22×C4—3324no—
820C22×C4—1662no—
821C22×C4—1662no—
822C22×C4—1662no—
823C22×C4C2×C22⋊D8311yescharacteristic
824C22×C4C2×C22⋊D8311yescharacteristic
825C22×C4C2×C22⋊D8311yescharacteristic
826C22×C4C2×C22⋊D8311yescharacteristic
827C22×C4C2×C22⋊D8311yescharacteristic
828C22×C4C2×C22⋊D8311yescharacteristic
829C22×C4C2×C22⋊D8311yescharacteristic
830C22×C4C2×C22⋊D8311yescharacteristic
831C22×C4C2×C22⋊D8311yescharacteristic
832C22×C4C2×C22⋊D8311yescharacteristic
833C22×C4C2×C22⋊D8311yescharacteristic
834C22×C4C2×C22⋊D8311yescharacteristic
835C22×C4C2×C22⋊D8311yescharacteristic
836C22×C4C2×C22⋊D8311yescharacteristic
837C22×C4C2×C22⋊D8311yescharacteristic
838C22×C4C2×C22⋊D8311yescharacteristic
839C22×C4C2×C22⋊D8311yescharacteristic
840C22×C4C2×C22⋊D8311yescharacteristic
841C22×C4C2×C22⋊D8311yescharacteristic
842C22×C4C2×C22⋊D8311yescharacteristic
843C22×C4C2×C22⋊D8311yescharacteristic
844C22×C4C23×D8311yescharacteristic
845C22×C4C23×D8311yescharacteristic
846C22×C4C23×D8311yescharacteristic
847C22×C4C23×D8311yescharacteristic
848C22×C4C23×D8311yescharacteristic
849C22×C4C23×D8311yescharacteristic
850C22×C4C23×D8311yescharacteristic
851SD16—3328no—
852D8—3328no—
853M16—3324no—
854M16—1668no—
855C2×C8—3324no—
856C2×C8—838no—
857C4⋊C4—22no—
858C4⋊C4—22no—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—834no—
864C4⋊C4—1662no—
865C4⋊C4—1662no—
866C4⋊C4—1662no—
867C4⋊C4C23×D8312yes—
868C4⋊C4C23×D8312yes—
869C22⋊C4—22no—
870C22⋊C4—22no—
871C22⋊C4—22no—
872C22⋊C4—22no—
873C22⋊C4—22no—
874C22⋊C4—22no—
875C22⋊C4—22no—
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—22no—
879C22⋊C4—1664no—
880C22⋊C4—1664no—
881C22⋊C4—1664no—
882C22⋊C4—1664no—
883C42—22no—
884C42—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—416no—
907C23—42no—
908C23—42no—
909C23—42no—
910C23—3324no—
911C23—3324no—
912C23—3324no—
913C23—3324no—
914C23—3324no—
915C23—3324no—
916C23—3324no—
917C23—3324no—
918C23—3324no—
919C23—66416no—
920C23—1664no—
921C23#1458181714yescomplemented
922C23C22×C22⋊D8311yescharacteristic
923C23C22×C22⋊D8311yescharacteristic
924C23C22×C22⋊D8311yescharacteristic
925C23C22×C22⋊D8311yescharacteristic
926C23C22×C22⋊D8311yescharacteristic
927C23C22×C22⋊D8311yescharacteristic
928C23C22×C22⋊D8311yescharacteristic
929Q8—24no—
930Q8—42no—
931D4—24no—
932D4—42no—
933D4—44no—
934D4—44no—
935D4—44no—
936D4—44no—
937D4—44no—
938D4—44no—
939D4—3324no—
940D4—3324no—
941D4—3328no—
942D4—3328no—
943D4—3328no—
944D4—3328no—
945D4—3324no—
946D4—1668no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—44no—
978C2×C4—42no—
979C2×C4—42no—
980C2×C4—42no—
981C2×C4—44no—
982C2×C4—3324no—
983C2×C4—3324no—
984C2×C4—3324no—
985C2×C4—1664no—
986C2×C4C22×C22⋊D8311yescharacteristic
987C2×C4C22×C22⋊D8311yescharacteristic
988C2×C4C22×C22⋊D8311yescharacteristic
989C2×C4C22×C22⋊D8311yescharacteristic
990C2×C4C22×C22⋊D8311yescharacteristic
991C2×C4C22×C22⋊D8311yescharacteristic
992C2×C4C22×C22⋊D8311yescharacteristic
993C2×C4#1458183714yes—
994C2×C4C24×D8311yescharacteristic
995C8—1668no—
996C22—28no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—21no—
1013C22—44no—
1014C22—44no—
1015C22—44no—
1016C22—44no—
1017C22—44no—
1018C22—44no—
1019C22—42no—
1020C22—42no—
1021C22—42no—
1022C22—84no—
1023C22—3324no—
1024C22—3324no—
1025C22—3324no—
1026C22—6648no—
1027C22—6648no—
1028C22—6648no—
1029C22#1912826012yes—
1030C22C2×#1458181712yes—
1031C22C2×#1458181712yes—
1032C22C2×#1458181712yes—
1033C22#1912849912yes—
1034C22C23×C22⋊D8311yescharacteristic
1035C4—21no—
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—21no—
1041C4—42no—
1042C4—42no—
1043C4—42no—
1044C4—3324no—
1045C4#1912826012yes—
1046C4C2×#1458183712yes—
1047C2—22no—
1048C2—22no—
1049C2—22no—
1050C2—22no—
1051C2—22no—
1052C2—41no—
1053C2—41no—
1054C2—82no—
1055C2—6644no—
1056C2C2×#1912826011yescharacteristic
1057C2C22×#1458181711yescharacteristic
1058C2C2×#1912849911yescharacteristic
subgroupG/H
centerC22C23×C22⋊D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#525×C83C2
socleC22×C83C23×D4
hypercenterC2×#525D83
hypocenterC83#60750
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C22×#14581766C2semidirect
2. #24918273C2semidirect
3. #24918265C2semidirect
4. #24918260C2semidirect
5. #24918224C2semidirect
6. #24918216C2semidirect
7. #24918211C2semidirect
8. #24917403C2semidirect
9. #24917383C2semidirect
10. #24917084C2semidirect
11. #24916715C2semidirect
12. #24916689C2semidirect
13. C2×#19127665C2semidirect
14. C2×#525×C83C2semidirect
15. C23×D332C22semidirect
17. C2×#14581817C22semidirect
18. C22×#13050574C22semidirect
28. C2×#14581766C22semidirect
29. C2×#14581766C22semidirect
30. C2×#14581766C22semidirect
31. C22×C4⋊Dic83C22semidirect
33. #19128034C22semidirect
34. #19128029C22semidirect
35. #19128025C22semidirect
36. #19128019C22semidirect
37. #19128017C22semidirect
38. #19128014C22semidirect
39. #19128012C22semidirect
40. #19127952C22semidirect
41. #19127949C22semidirect
42. #19127935C22semidirect
43. #19127932C22semidirect
44. #19127851C22semidirect
45. #19127851C22semidirect
46. #19127846C22semidirect
47. #19127840C22semidirect
48. #19127835C22semidirect
49. #19127834C22semidirect
50. #19127834C22semidirect
51. #19127744C22semidirect
52. #19127705C22semidirect
53. #19127702C22semidirect
54. #19127665C22semidirect
55. #19127665C22semidirect
56. #19127665C22semidirect
57. #19127665C22semidirect
58. C2×C22⋊(C83⋊C8)C22semidirect
59. C2×C22⋊(C83⋊C8)C22semidirect
60. C22×#41×C83C22semidirect
67. #525×C83C22semidirect
68. #525×C83C22semidirect
69. #525×C83C22semidirect
71. C2×C22⋊Q8×C83C22semidirect
72. C2×C22⋊Q8×C83C22semidirect
73. C2×#121×C83C22semidirect
74. C2×#121×C83C22semidirect
78. C2×#117×C83C22semidirect
96. C2×#13050577C23semidirect
97. C2×#13050575C23semidirect
100. C2×#13050574C23semidirect
101. C22×C83⋊C8C23semidirect
130. #14581725C23semidirect
131. #14581723C23semidirect
132. #14581716C23semidirect
133. #14581713C23semidirect
134. #14581712C23semidirect
135. #14581712C23semidirect
138. C22⋊(C83⋊C8)C23semidirect
139. C22⋊(C83⋊C8)C23semidirect
145. C2×#41×C83C23semidirect
146. C22×Q8×C83C23semidirect
150. C22×D4×C83C23semidirect
177. C22⋊Q8×C83C23semidirect
178. C22⋊Q8×C83C23semidirect
185. #121×C83C23semidirect
186. #121×C83C23semidirect
202. #117×C83C23semidirect
205. C2×C4⋊C4×C83C23semidirect
206. C2×C4⋊C4×C83C23semidirect
380. C23×C83AGL(1,ℤ/8)semidirect
530. C2×#525D83semidirect
544. C83#60750semidirect
545. C22×#41C2×D83semidirect
556. #525C2×D83semidirect
557. #525C2×D83semidirect
558. #525C2×D83semidirect
560. C2×C22⋊Q8C2×D83semidirect
561. C2×C22⋊Q8C2×D83semidirect
574. C2×#121C2×D83semidirect
575. C2×#121C2×D83semidirect
579. C2×#117C2×D83semidirect
615. C2×#41C22×D83semidirect
616. C22×Q8C22×D83semidirect
634. C22×D4C22×D83semidirect
669. C22⋊Q8C22×D83semidirect
670. C22⋊Q8C22×D83semidirect
693. #121C22×D83semidirect
694. #121C22×D83semidirect
710. #117C22×D83semidirect
719. C2×C4⋊C4C22×D83semidirect
720. C2×C4⋊C4C22×D83semidirect
921. C23#14581817semidirect

Maximal subgroups

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

subgroupindex
C22×#145817662
#249182732
#249182652
#249182602
#249182242
#249182162
#249182112
#249174032
#249173832
#249170842
#249167152
#249166892
C2×#191276652
C2×#525×C832
#6075083