Finite Group Databasebeta

← #35304992

Subgroups — #35304992

Order 21248.

632 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 121 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
1C2×#19128034C212yesmaximal
2C2×#19127438C212yesmaximal
3#24905732C211yesmaximal, characteristic
4#24905306C211yesmaximal, characteristic
5C83×#2659C211yesmaximal, characteristic
6C22×C4⋊Dic83C2211yescharacteristic
7#19128034—24no—
8#19128034—24no—
9C2×#14581725—22no—
10C2×#14581716—22no—
11C2×C22⋊(C83⋊C8)C2212yes—
12C2×C83⋊#95—22no—
13C2×C83⋊#95C2211yescharacteristic
14#19127438—24no—
15C2×C22⋊Q8×C83C2212yes—
16#398×C83—22no—
17#395×C83—22no—
18#380×C83—22no—
19C2×#95×C83C2211yescharacteristic
20C23×Dic83—21no—
21C23×Dic83—21no—
22C22×C83⋊C8—22no—
23C2×C4⋊Dic83—22no—
24C2×C4⋊Dic83—22no—
25C2×C4⋊Dic83—21no—
26C2×C4⋊Dic83D412yes—
27#14581725—28no—
28#14581716—28no—
29C22⋊(C83⋊C8)—22no—
30C22⋊(C83⋊C8)D414yes—
31C83⋊#95—22no—
32C83⋊#95—44no—
33C22×Q8×C83D412yes—
34C23×C4×C83D412yes—
35C23×C4×C83C2311yescharacteristic
36C22⋊Q8×C83—22no—
37C22⋊Q8×C83—22no—
38C22⋊Q8×C83—22no—
39C22⋊Q8×C83—22no—
40C2×C4⋊C4×C83—22no—
41C2×C4⋊C4×C83—22no—
42C2×C4⋊C4×C83—22no—
43C2×C4⋊C4×C83D412yes—
44C2×C22⋊C4×C83—22no—
45#95×C83—24no—
46#95×C83—22no—
47C22×Dic83—22no—
48C22×Dic83—22no—
49C22×Dic83—41no—
50C22×Dic83—42no—
51C22×Dic83—42no—
52C22×Dic83—42no—
53C22×Dic83—41no—
54C22×Dic83—41no—
55C22×Dic83—41no—
56C22×Dic83—42no—
57C2×C83⋊C8—24no—
58C2×C83⋊C8—44no—
59C4⋊Dic83—24no—
60C4⋊Dic83—42no—
61C24×C83C2×D411yescharacteristic
62C2×Q8×C83—22no—
63C2×Q8×C83—22no—
64C2×Q8×C83—44no—
65C22×C4×C83—22no—
66C22×C4×C83—22no—
67C22×C4×C83—22no—
68C22×C4×C83—22no—
69C22×C4×C83—42no—
70C22×C4×C83—42no—
71C22×C4×C83—42no—
72C22×C4×C83Q1614yes—
73C22×C4×C83C2×D411yescharacteristic
74C22×C4×C83C2×D412yes—
75C22×C4×C83C2×D412yes—
76C22×C4×C83#4111yescharacteristic
77C4⋊C4×C83—22no—
78C4⋊C4×C83—22no—
79C4⋊C4×C83—42no—
80C4⋊C4×C83—42no—
81C4⋊C4×C83—82no—
82C4⋊C4×C83—82no—
83C22⋊C4×C83—42no—
84C22⋊C4×C83—42no—
85C23×C83—21no—
86C23×C83—21no—
87C23×C83—22no—
88C23×C83#12011yescharacteristic
89C23×C83#12111yescharacteristic
90C23×C83#12711yescharacteristic
91C23×C83C2×Q1612yes—
92C23×C83#13712yes—
93Q8×C83—44no—
94Q8×C83—82no—
95C2×C4×C83—24no—
96C2×C4×C83—24no—
97C2×C4×C83—41no—
98C2×C4×C83—42no—
99C2×C4×C83—41no—
100C2×C4×C83—42no—
101C2×C4×C83—42no—
102C2×C4×C83—44no—
103C2×C4×C83—42no—
104C2×C4×C83—42no—
105C2×C4×C83—42no—
106C2×C4×C83—42no—
107C2×C4×C83—44no—
108C2×C4×C83—82no—
109C2×C4×C83#12012yes—
110C2×C4×C83#12112yes—
111C2×Dic83—44no—
112C2×Dic83—42no—
113C2×Dic83—44no—
114C2×Dic83—42no—
115C2×Dic83—82no—
116C2×Dic83—81no—
117C2×Dic83—82no—
118C2×Dic83—81no—
119C2×Dic83—81no—
120C2×Dic83—81no—
121C83⋊C8—44no—
122C22×C83—22no—
123C22×C83—22no—
124C22×C83—22no—
125C22×C83—22no—
126C22×C83—21no—
127C22×C83—21no—
128C22×C83—21no—
129C22×C83—21no—
130C22×C83#39211yescharacteristic
131C22×C83#45112yes—
132C22×C83#45311yescharacteristic
133C22×C83#45411yescharacteristic
134C22×C83#45812yes—
135C22×C83#46212yes—
136C22×C83#49411yescharacteristic
137C22×C83#49711yescharacteristic
138C4×C83—22no—
139C4×C83—22no—
140C4×C83—44no—
141C4×C83—82no—
142C4×C83—82no—
143Dic83—82no—
144Dic83—82no—
145#9972—831nomaximal, Sylow
146C2×C83—21no—
147C2×C83—22no—
148C2×C83—21no—
149C2×C83#161412yes—
150C2×C83#161712yes—
151C2×C83#200611yescharacteristic
152C2×C83#201611yescharacteristic
153C2×C83#202211yescharacteristic
154C2×#484—832no—
155#2659D8311yescharacteristic
156C2×#328—832no—
157#1445—831no—
158#1280—831no—
159C83#997211yescharacteristic, complemented, Sylow
160C2×C22⋊Q8C2×D8312yes—
161C22×C4⋊C4—831no—
162#484—1664no—
163#484—1664no—
164C2×#107—1662no—
165C2×#103—1662no—
166C2×C22⋊C8—832no—
167#398—22no—
168#395—22no—
169#380—22no—
170C2×#95—831no—
171C2×#95—1662no—
172C2×#95C2×D8311yescharacteristic
173#328—1664no—
174C22×Q8C22⋊D8312yes—
175C23×C4—1661no—
176C23×C4—1661no—
177C23×C4C22⋊D8312yes—
178C23×C4C22×D8311yescharacteristic
179C22×C8—1662no—
180C22⋊Q8—22no—
181C22⋊Q8—22no—
182C22⋊Q8—22no—
183C22⋊Q8—22no—
184C2×C4⋊C4—22no—
185C2×C4⋊C4—22no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—832no—
188C2×C4⋊C4—1661no—
189C2×C4⋊C4—1662no—
190C2×C4⋊C4—1662no—
191C2×C4⋊C4C22⋊D8312yes—
192C2×C22⋊C4—22no—
193#107—1668no—
194#103—1668no—
195C22⋊C8—834no—
196C22⋊C8—1662no—
197#95—24no—
198#95—22no—
199#95—3324no—
200#95—1662no—
201C24C2×C22⋊D8311yescharacteristic
202C2×Q8—22no—
203C2×Q8—22no—
204C2×Q8—44no—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—42no—
210C22×C4—42no—
211C22×C4—42no—
212C22×C4—3322no—
213C22×C4—3321no—
214C22×C4—3322no—
215C22×C4—3322no—
216C22×C4—3321no—
217C22×C4—3321no—
218C22×C4—3321no—
219C22×C4—3322no—
220C22×C4—1662no—
221C22×C4—1662no—
222C22×C4#1305058014yes—
223C22×C4D4×D8311yescharacteristic
224C22×C4D4×D8312yes—
225C22×C4C2×C22⋊D8312yes—
226C22×C4#1305058911yescharacteristic
227C2×C8—3324no—
228C2×C8—1664no—
229C4⋊C4—22no—
230C4⋊C4—22no—
231C4⋊C4—42no—
232C4⋊C4—42no—
233C4⋊C4—82no—
234C4⋊C4—82no—
235C4⋊C4—3322no—
236C4⋊C4—1664no—
237C22⋊C4—42no—
238C22⋊C4—42no—
239C23—21no—
240C23—21no—
241C23—22no—
242C23#1458176111yescharacteristic
243C23#1458176311yescharacteristic
244C23#1458178811yescharacteristic
245C23C2×#1305058012yes—
246C23#1458182312yes—
247Q8—44no—
248Q8—82no—
249C2×C4—24no—
250C2×C4—24no—
251C2×C4—41no—
252C2×C4—42no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—44no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—44no—
262C2×C4—82no—
263C2×C4—3322no—
264C2×C4—3324no—
265C2×C4—3324no—
266C2×C4—3322no—
267C2×C4—6642no—
268C2×C4—6641no—
269C2×C4—6642no—
270C2×C4—6641no—
271C2×C4—6641no—
272C2×C4—6641no—
273C2×C4#1458176012yes—
274C2×C4#1458176412yes—
275C8—3324no—
276C22—22no—
277C22—22no—
278C22—21no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22—22no—
283C22—22no—
284C22#1912760911yescharacteristic
285C22#1912785712yes—
286C22#1912786911yescharacteristic
287C22#1912787411yescharacteristic
288C22#1912789112yes—
289C22#1912790812yes—
290C22#1912808011yescharacteristic
291C22#1912809311yescharacteristic
292C4—22no—
293C4—22no—
294C4—44no—
295C4—82no—
296C4—82no—
297C4—6642no—
298C4—6642no—
299C2—21no—
300C2—21no—
301C2—22no—
302C2#2490648812yes—
303C2#2490650512yes—
304C2#2490850511yescharacteristic
305C2#2490856311yescharacteristic
306C2#2490859211yescharacteristic
subgroupG/H
centerC23#14581761
commutator, cosocleC23×C4×C83C23
FrattiniC23×C4C22×D83
FittingC83×#2659C2
socleC23×C83#120
prime radicalC24×C83C2×D4
hypercenter#2659D83
hypocenterC83#9972
LCSG ▷ C23×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2659

Complements

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

NH ≅ G/Ntype
159. C83#9972semidirect

Maximal subgroups

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

subgroupindex
C2×#191280342
C2×#191274382
#249057322
#249053062
C83×#26592
#997283