Finite Group Databasebeta

← #35292750

Subgroups — #35292750

Order 21248.

370 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 95 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#24915849C211yesmaximal, characteristic
2#24907605C211yesmaximal, characteristic
3#24907207C211yesmaximal, characteristic
4#24905287C211yesmaximal, characteristic
5#24905286C211yesmaximal, characteristic
6#24905285C211yesmaximal, characteristic
7C83×#1271C211yesmaximal, characteristic
8C2×C8×Dic83—21no—
9#19127600C411yescharacteristic
10#19127599C2211yescharacteristic
11#19127597C411yescharacteristic
12#19127587—21no—
13#19127586—21no—
14#19127583—21no—
15#19127582—21no—
16#19127566C411yescharacteristic
17#19127566C411yescharacteristic
18C42×Dic83C2211yescharacteristic
19#19127456C2211yescharacteristic
20#19127456C2211yescharacteristic
21#19127455—21no—
22#19127455—21no—
23#19127455—21no—
24#389×C83C2211yescharacteristic
25#336×C83C2211yescharacteristic
26#336×C83C2211yescharacteristic
27C22×C83⋊C8—21no—
28C22×C83⋊C8—21no—
29C2×C4⋊Dic83—21no—
30C2×C4⋊Dic83C2×C411yescharacteristic
31C2×C4⋊Dic83C2×C411yescharacteristic
32C2×Dic83⋊C4—21no—
33C2×Dic83⋊C4—21no—
34C2×C4×Dic83C2×C411yescharacteristic
35C2×C4×Dic83C2×C411yescharacteristic
36C2×C4×Dic83D411yescharacteristic
37C2×C4×Dic83D411yescharacteristic
38C2×C4×Dic83D411yescharacteristic
39C2×C4×Dic83D411yescharacteristic
40C8×Dic83—24no—
41C83⋊#95—21no—
42C83⋊#95—21no—
43C83⋊#95—21no—
44C83⋊#95—21no—
45C83⋊#95—21no—
46C83⋊#95—21no—
47C83⋊#95—21no—
48C22×C8×C83—21no—
49C22×C8×C83—21no—
50C2×C4⋊C4×C83—21no—
51C2×C4⋊C4×C83C2×C411yescharacteristic
52C2×C4⋊C4×C83C2×C411yescharacteristic
53C2×C42×C83C2311yescharacteristic
54#95×C83—21no—
55C22×Dic83—21no—
56C22×Dic83—21no—
57C22×Dic83C22⋊C411yescharacteristic
58C22×Dic83C22⋊C411yescharacteristic
59C22×Dic83C22⋊C411yescharacteristic
60C22×Dic83C22⋊C411yescharacteristic
61C2×C83⋊C8—22no—
62C2×C83⋊C8—41no—
63C2×C83⋊C8—41no—
64C2×C83⋊C8—41no—
65C2×C83⋊C8—41no—
66C2×C83⋊C8—41no—
67C4⋊Dic83—21no—
68C4⋊Dic83—21no—
69C4⋊Dic83—42no—
70C4⋊Dic83—41no—
71Dic83⋊C4—42no—
72Dic83⋊C4—41no—
73Dic83⋊C4—41no—
74C4×Dic83—21no—
75C4×Dic83—21no—
76C4×Dic83—21no—
77C4×Dic83—21no—
78C4×Dic83—21no—
79C4×Dic83—21no—
80C4×Dic83—22no—
81C4×Dic83—22no—
82C4×Dic83—41no—
83C22×C4×C83—21no—
84C22×C4×C83—21no—
85C22×C4×C83C22×C411yescharacteristic
86C22×C4×C83C2×D411yescharacteristic
87C22×C4×C83C2×D411yescharacteristic
88C2×C8×C83—22no—
89C2×C8×C83—41no—
90C2×C8×C83—41no—
91C2×C8×C83—41no—
92C2×C8×C83—41no—
93C2×C8×C83—41no—
94C4⋊C4×C83—21no—
95C4⋊C4×C83—21no—
96C4⋊C4×C83—41no—
97C4⋊C4×C83—41no—
98C4⋊C4×C83—41no—
99C42×C83—41no—
100C23×C83C2×C22⋊C411yescharacteristic
101C2×C4×C83—21no—
102C2×C4×C83—21no—
103C2×C4×C83—21no—
104C2×C4×C83—21no—
105C2×C4×C83—21no—
106C2×C4×C83—21no—
107C2×C4×C83—41no—
108C2×C4×C83—41no—
109C2×C4×C83—41no—
110C2×C4×C83—41no—
111C2×C4×C83—41no—
112C2×C4×C83—41no—
113C2×C4×C83#13111yescharacteristic
114C2×C4×C83#13111yescharacteristic
115C2×C4×C83#13511yescharacteristic
116C2×C4×C83#13511yescharacteristic
117C2×C4×C83#13511yescharacteristic
118C2×C4×C83#13511yescharacteristic
119C2×Dic83—21no—
120C2×Dic83—21no—
121C2×Dic83—21no—
122C2×Dic83—21no—
123C2×Dic83—21no—
124C2×Dic83—21no—
125C2×Dic83—21no—
126C2×Dic83—21no—
127C2×Dic83—21no—
128C2×Dic83—21no—
129C2×Dic83—41no—
130C2×Dic83—41no—
131C2×Dic83—41no—
132C2×Dic83—41no—
133C2×Dic83—41no—
134C2×Dic83—41no—
135C2×Dic83#10112yes—
136C2×Dic83#10412yes—
137C8×C83—42no—
138C8×C83—81no—
139C83⋊C8—42no—
140C83⋊C8—81no—
141C22×C83#40811yescharacteristic
142C22×C83#41011yescharacteristic
143C22×C83C2×#10111yescharacteristic
144C22×C83#41611yescharacteristic
145C22×C83#41611yescharacteristic
146C22×C83C2×#10411yescharacteristic
147C22×C83#42111yescharacteristic
148C4×C83—21no—
149C4×C83—21no—
150C4×C83—21no—
151C4×C83—21no—
152C4×C83—21no—
153C4×C83—21no—
154C4×C83—81no—
155C4×C83—81no—
156Dic83—22no—
157Dic83—22no—
158Dic83—41no—
159Dic83—41no—
160Dic83—81no—
161Dic83—81no—
162#7657—831nomaximal, Sylow
163C2×C83#147011yescharacteristic
164C2×C83#148211yescharacteristic
165C2×C83#149411yescharacteristic
166C2×C83#150011yescharacteristic
167C2×C83#152111yescharacteristic
168C2×C83#153111yescharacteristic
169C2×C83#154411yescharacteristic
170#2864—831no—
171#1839—831no—
172#1744—831no—
173#1271—831no—
174#1271—831no—
175#1271—831no—
176#1271D8311yescharacteristic
177C83#765711yescharacteristic, complemented, Sylow
178C2×C4×C8—1661no—
179#389—831no—
180#389—831no—
181#389—831no—
182#389C2×D8311yescharacteristic
183#387—1661no—
184#387—1661no—
185#387—1661no—
186#387—1661no—
187#382—831no—
188#382—831no—
189C43—831no—
190#336—831no—
191#336—831no—
192#336—1661no—
193#336—1661no—
194#336—1661no—
195#336C2×D8311yescharacteristic
196#336C2×D8311yescharacteristic
197C22×C8—21no—
198C22×C8—21no—
199C22×C8—1661no—
200C22×C8—1661no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—831no—
203C2×C4⋊C4—831no—
204C2×C4⋊C4—1661no—
205C2×C4⋊C4—1661no—
206C2×C4⋊C4—1661no—
207C2×C4⋊C4C4×D8311yescharacteristic
208C2×C4⋊C4C4×D8311yescharacteristic
209C2×C42—831no—
210C2×C42—831no—
211C2×C42—831no—
212C2×C42—831no—
213C2×C42—831no—
214C2×C42—831no—
215C2×C42C22×D8311yescharacteristic
216C4×C8—1664no—
217#95—21no—
218#95—1661no—
219#95—1661no—
220#95—1661no—
221#95—1661no—
222#95—1661no—
223#95—1661no—
224#95—1661no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—831no—
228C22×C4—831no—
229C22×C4—831no—
230C22×C4—831no—
231C22×C4—1661no—
232C22×C4—1661no—
233C22×C4C2×C4×D8311yescharacteristic
234C22×C4D4×D8311yescharacteristic
235C22×C4D4×D8311yescharacteristic
236C2×C8—22no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—3321no—
243C2×C8—3321no—
244C2×C8—3321no—
245C2×C8—3321no—
246C2×C8—3321no—
247C2×C8—1662no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—3321no—
254C4⋊C4—3322no—
255C4⋊C4—3322no—
256C4⋊C4—3321no—
257C4⋊C4—3321no—
258C4⋊C4—1661no—
259C4⋊C4—1661no—
260C42—41no—
261C42—3321no—
262C42—1662no—
263C42—1662no—
264C42—1661no—
265C42—1661no—
266C42—1661no—
267C42—1661no—
268C42—1661no—
269C42—1661no—
270C23C22⋊C4×D8311yescharacteristic
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—3321no—
284C2×C4—3321no—
285C2×C4—3321no—
286C2×C4—3321no—
287C2×C4—3321no—
288C2×C4—3321no—
289C2×C4—832no—
290C2×C4—832no—
291C2×C4—1661no—
292C2×C4—1661no—
293C2×C4—1661no—
294C2×C4—1661no—
295C2×C4—1661no—
296C2×C4—1661no—
297C2×C4—1661no—
298C2×C4—1661no—
299C2×C4—1661no—
300C2×C4—1661no—
301C2×C4#1458179811yescharacteristic
302C2×C4#1458180011yescharacteristic
303C2×C4#1458181111yescharacteristic
304C2×C4#1458181311yescharacteristic
305C2×C4#1458181311yescharacteristic
306C2×C4#1458181511yescharacteristic
307C8—42no—
308C8—81no—
309C8—3322no—
310C8—6641no—
311C22#1912766611yescharacteristic
312C22#1912767311yescharacteristic
313C22#101×D8311yescharacteristic
314C22#1912769411yescharacteristic
315C22#1912769611yescharacteristic
316C22#104×D8311yescharacteristic
317C22#1912771611yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—81no—
325C4—81no—
326C4—3321no—
327C4—3321no—
328C4—6641no—
329C4—6641no—
330C4—1662no—
331C4—1662no—
332C2#2490581711yescharacteristic
333C2#2490586811yescharacteristic
334C2#2490592211yescharacteristic
335C2#2490594611yescharacteristic
336C2#2490603911yescharacteristic
337C2#2490607611yescharacteristic
338C2#2490612611yescharacteristic
subgroupG/H
centerC23C22⋊C4×D83
commutatorC22×C4×C83C22×C4
FrattiniC2×C42C22×D83
FittingC83×#1271C2
socle, prime radicalC23×C83C2×C22⋊C4
cosocleC2×C42×C83C23
hypercenter#1271D83
hypocenterC83#7657
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
177. C83#7657semidirect

Maximal subgroups

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

subgroupindex
#249158492
#249076052
#249072072
#249052872
#249052862
#249052852
C83×#12712
#765783