Finite Group Databasebeta

← #35292812

Subgroups — #35292812

Order 21248.

468 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24915772C211yesmaximal, characteristic
2#24907530C211yesmaximal, characteristic
3#24907220C211yesmaximal, characteristic
4#24905287C211yesmaximal, characteristic, complemented
5#24905286C211yesmaximal, characteristic, complemented
6#24905285C211yesmaximal, characteristic, complemented
7C83×#1271C211yesmaximal, characteristic, complemented
8C2×#14581783C411yescharacteristic
9C2×C42×D83C2211yescharacteristic
10C2×(C2×D83)⋊C8—21no—
11C2×(C2×D83)⋊C8—21no—
12C2×C8×Dic83—21no—
13#19127599C2211yescharacteristic
14#19127587—21no—
15#19127583—21no—
16#19127575—21no—
17#19127572—21no—
18#19127566C411yescharacteristic
19#19127558C411yescharacteristic
20#19127558C411yescharacteristic
21#19127456C2211yescharacteristic
22#19127456C2211yescharacteristic
23#19127455—21no—
24#389×C83C2211yescharacteristic
25#336×C83C2211yescharacteristic
26#336×C83C2211yescharacteristic
27C22×C4×D83C2×C411yescharacteristic
28C22×C4×D83D411yescharacteristic
29C22×C4×D83D411yescharacteristic
30C22×C83⋊C8—21no—
31C22×C83⋊C8—21no—
32#14581783—42no—
33C2×C4⋊Dic83—21no—
34C2×C4⋊Dic83C2×C411yescharacteristic
35C2×C4⋊Dic83C2×C411yescharacteristic
36C2×Dic83⋊C4—21no—
37C2×Dic83⋊C4—21no—
38C2×(C2×D83)⋊C4—21no—
39C2×(C2×D83)⋊C4—21no—
40C2×C4×Dic83C2×C411yescharacteristic
41C2×C4×Dic83D411yescharacteristic
42C2×C4×Dic83D411yescharacteristic
43C42×D83—42no—
44(C2×D83)⋊C8—24no—
45(C2×D83)⋊C8—42no—
46C8×Dic83—42no—
47C83⋊#95—21no—
48C83⋊#95—21no—
49C83⋊#95—21no—
50C83⋊#95—21no—
51C83⋊#95—21no—
52C22×C8×C83—21no—
53C22×C8×C83—21no—
54C2×C4⋊C4×C83—21no—
55C2×C4⋊C4×C83C2×C411yescharacteristic
56C2×C4⋊C4×C83C2×C411yescharacteristic
57C2×C42×C83C2311yescharacteristic
58#95×C83—21no—
59C23×D83C22⋊C411yescharacteristic
60C22×Dic83—21no—
61C22×Dic83—21no—
62C22×Dic83C22⋊C411yescharacteristic
63C22×Dic83C22⋊C411yescharacteristic
64C22×Dic83C22⋊C411yescharacteristic
65C2×C4×D83—22no—
66C2×C4×D83—21no—
67C2×C4×D83—21no—
68C2×C4×D83—21no—
69C2×C4×D83—21no—
70C2×C4×D83—21no—
71C2×C4×D83—21no—
72C2×C4×D83—22no—
73C2×C4×D83—22no—
74C2×C4×D83—41no—
75C2×C4×D83—41no—
76C2×C4×D83—41no—
77C2×C83⋊C8—22no—
78C2×C83⋊C8—41no—
79C2×C83⋊C8—41no—
80C2×C83⋊C8—41no—
81C2×C83⋊C8—41no—
82C2×C83⋊C8—41no—
83C4⋊Dic83—21no—
84C4⋊Dic83—21no—
85C4⋊Dic83—42no—
86C4⋊Dic83—41no—
87Dic83⋊C4—42no—
88Dic83⋊C4—41no—
89Dic83⋊C4—41no—
90(C2×D83)⋊C4—42no—
91(C2×D83)⋊C4—42no—
92C4×Dic83—22no—
93C4×Dic83—22no—
94C4×Dic83—41no—
95C22×C4×C83—21no—
96C22×C4×C83—21no—
97C22×C4×C83C22×C411yescharacteristic
98C22×C4×C83C2×D411yescharacteristic
99C22×C4×C83C2×D411yescharacteristic
100C2×C8×C83—22no—
101C2×C8×C83—41no—
102C2×C8×C83—41no—
103C2×C8×C83—41no—
104C2×C8×C83—41no—
105C2×C8×C83—41no—
106C4⋊C4×C83—21no—
107C4⋊C4×C83—21no—
108C4⋊C4×C83—41no—
109C4⋊C4×C83—41no—
110C4⋊C4×C83—41no—
111C42×C83—41no—
112C23×C83C2×C22⋊C411yescharacteristic
113C22×D83—21no—
114C22×D83—21no—
115C22×D83—21no—
116C22×D83—21no—
117C22×D83—21no—
118C22×D83—21no—
119C22×D83#10412yes—
120C2×C4×C83—21no—
121C2×C4×C83—21no—
122C2×C4×C83—21no—
123C2×C4×C83—21no—
124C2×C4×C83—21no—
125C2×C4×C83—21no—
126C2×C4×C83—41no—
127C2×C4×C83—41no—
128C2×C4×C83—41no—
129C2×C4×C83—41no—
130C2×C4×C83—41no—
131C2×C4×C83—41no—
132C2×C4×C83#13111yescharacteristic
133C2×C4×C83#13111yescharacteristic
134C2×C4×C83#13511yescharacteristic
135C2×C4×C83#13511yescharacteristic
136C2×C4×C83#13511yescharacteristic
137C2×C4×C83#13511yescharacteristic
138C2×Dic83—21no—
139C2×Dic83—21no—
140C2×Dic83—21no—
141C2×Dic83—21no—
142C2×Dic83—21no—
143C2×Dic83—21no—
144C2×Dic83—21no—
145C2×Dic83—41no—
146C2×Dic83—41no—
147C2×Dic83—41no—
148C2×Dic83—41no—
149C2×Dic83—41no—
150C2×Dic83—41no—
151C2×Dic83#9912yes—
152C2×Dic83#10112yes—
153C4×D83—42no—
154C4×D83—42no—
155C4×D83—42no—
156C4×D83—42no—
157C4×D83—42no—
158C4×D83—42no—
159C8×C83—42no—
160C8×C83—81no—
161C83⋊C8—42no—
162C83⋊C8—81no—
163C22×C83#40811yescharacteristic
164C22×C83C2×#9911yescharacteristic
165C22×C83C2×#10111yescharacteristic
166C22×C83#41611yescharacteristic
167C22×C83#41611yescharacteristic
168C22×C83C2×#10411yescharacteristic
169C22×C83#42111yescharacteristic
170C2×D83—22no—
171C2×D83—22no—
172C2×D83—22no—
173C2×D83—41no—
174C2×D83—41no—
175C2×D83—41no—
176C2×D83—41no—
177C4×C83—21no—
178C4×C83—21no—
179C4×C83—21no—
180C4×C83—21no—
181C4×C83—21no—
182C4×C83—21no—
183C4×C83—81no—
184C4×C83—81no—
185Dic83—22no—
186Dic83—22no—
187Dic83—41no—
188Dic83—81no—
189Dic83—81no—
190#7671—831nomaximal, Sylow
191C2×C83#147211yescharacteristic
192C2×C83#148211yescharacteristic
193C2×C83#149411yescharacteristic
194C2×C83#150111yescharacteristic
195C2×C83#151611yescharacteristic
196C2×C83#152811yescharacteristic
197C2×C83#154411yescharacteristic
198D83—42no—
199#2851—831no—
200#1817—831no—
201C4×C22⋊C8—831no—
202#1271—831no—
203#1271—831no—
204#1271—831no—
205#1271D8311yescharacteristic, complemented
206C83#767111yescharacteristic, complemented, Sylow
207C2×#125—831no—
208C22×C42—831no—
209C2×C22⋊C8—1661no—
210C2×C22⋊C8—1661no—
211C2×C4×C8—1661no—
212#389—831no—
213#389C2×D8311yescharacteristic
214#387—1661no—
215#387—1661no—
216#385—1661no—
217#385—1661no—
218#382—831no—
219#380—831no—
220#380—831no—
221#336—831no—
222#336—831no—
223#336—1661no—
224#336C2×D8311yescharacteristic
225#336C2×D8311yescharacteristic
226C23×C4—831no—
227C23×C4—831no—
228C23×C4—831no—
229C22×C8—21no—
230C22×C8—21no—
231C22×C8—1661no—
232C22×C8—1661no—
233#125—3322no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—831no—
236C2×C4⋊C4—831no—
237C2×C4⋊C4—1661no—
238C2×C4⋊C4—1661no—
239C2×C4⋊C4—1661no—
240C2×C4⋊C4C4×D8311yescharacteristic
241C2×C4⋊C4C4×D8311yescharacteristic
242C2×C22⋊C4—1661no—
243C2×C22⋊C4—1661no—
244C2×C42—3322no—
245C2×C42—831no—
246C2×C42—831no—
247C2×C42—831no—
248C2×C42C22×D8311yescharacteristic
249C22⋊C8—3322no—
250C22⋊C8—1664no—
251C4×C8—3322no—
252#95—21no—
253#95—1661no—
254#95—1661no—
255#95—1661no—
256#95—1661no—
257#95—1661no—
258C24—831no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—3321no—
262C22×C4—3321no—
263C22×C4—3321no—
264C22×C4—831no—
265C22×C4—831no—
266C22×C4—831no—
267C22×C4—1662no—
268C22×C4—1662no—
269C22×C4—1662no—
270C22×C4—1661no—
271C22×C4—1661no—
272C22×C4—1661no—
273C22×C4—1661no—
274C22×C4—1661no—
275C22×C4—1661no—
276C22×C4—1661no—
277C22×C4—1661no—
278C22×C4C2×C4×D8311yescharacteristic
279C22×C4D4×D8311yescharacteristic
280C22×C4D4×D8311yescharacteristic
281C2×C8—22no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—3321no—
288C2×C8—3321no—
289C2×C8—3321no—
290C2×C8—3321no—
291C2×C8—3321no—
292C2×C8—1662no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—3321no—
299C4⋊C4—3322no—
300C4⋊C4—3322no—
301C4⋊C4—3321no—
302C4⋊C4—3321no—
303C4⋊C4—1661no—
304C4⋊C4—1661no—
305C22⋊C4—3322no—
306C22⋊C4—3322no—
307C42—41no—
308C42—3321no—
309C42—1662no—
310C42—1662no—
311C23—832no—
312C23—1661no—
313C23—1661no—
314C23—1661no—
315C23—1661no—
316C23—1661no—
317C23—1661no—
318C23C22⋊C4×D8311yescharacteristic
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—3322no—
332C2×C4—3322no—
333C2×C4—3322no—
334C2×C4—3322no—
335C2×C4—3322no—
336C2×C4—3322no—
337C2×C4—3321no—
338C2×C4—3321no—
339C2×C4—3321no—
340C2×C4—3321no—
341C2×C4—3321no—
342C2×C4—3321no—
343C2×C4—832no—
344C2×C4—832no—
345C2×C4—1661no—
346C2×C4—1661no—
347C2×C4—1661no—
348C2×C4—1661no—
349C2×C4—1661no—
350C2×C4—1661no—
351C2×C4—1661no—
352C2×C4#1458179811yescharacteristic
353C2×C4#1458180011yescharacteristic
354C2×C4#1458181111yescharacteristic
355C2×C4#1458181311yescharacteristic
356C2×C4#1458181311yescharacteristic
357C2×C4#1458181511yescharacteristic
358C8—42no—
359C8—81no—
360C8—3322no—
361C8—6641no—
362C22—3321no—
363C22—3321no—
364C22—3321no—
365C22—3321no—
366C22—1662no—
367C22—1662no—
368C22—1662no—
369C22#1912766611yescharacteristic
370C22#99×D8311yescharacteristic
371C22#101×D8311yescharacteristic
372C22#1912769411yescharacteristic
373C22#1912769611yescharacteristic
374C22#104×D8311yescharacteristic
375C22#1912771611yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—81no—
383C4—81no—
384C4—3321no—
385C4—6641no—
386C4—6641no—
387C4—1662no—
388C4—1662no—
389C2—3322no—
390C2#2490582511yescharacteristic
391C2#2490586811yescharacteristic
392C2#2490592211yescharacteristic
393C2#2490595111yescharacteristic
394C2#2490601811yescharacteristic
395C2#2490606311yescharacteristic
396C2#2490612611yescharacteristic
subgroupG/H
centerC23C22⋊C4×D83
commutatorC22×C4×C83C22×C4
FrattiniC2×C42C22×D83
FittingC83×#1271C2
socleC23×C83C2×C22⋊C4
prime radicalC23×D83C22⋊C4
cosocleC2×C42×C83C23
hypercenter#1271D83
hypocenterC83#7671
LCSG ▷ C22×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
4. #24905287C2semidirect
5. #24905286C2semidirect
6. #24905285C2semidirect
7. C83×#1271C2semidirect
205. #1271D83semidirect
206. C83#7671semidirect

Maximal subgroups

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

subgroupindex
#249157722
#249075302
#249072202
#249052872
#249052862
#249052852
C83×#12712
#767183