Finite Group Databasebeta

← #24908613

Subgroups — #24908613

Order 10624.

258 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 83 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×#14581783C211yesmaximal, characteristic
2C2×#14581717C211yesmaximal, characteristic
3C2×#14581715C211yesmaximal, characteristic
4#19127606C211yesmaximal, characteristic
5#19127463C211yesmaximal, characteristic
6#19127455C211yesmaximal, characteristic
7#340×C83C211yesmaximal, characteristic
8C22×Dic166C2211yescharacteristic
9C22×C83⋊C8C2211yescharacteristic
10#14581783—22no—
11#14581783—22no—
12C2×C4⋊Dic83—21no—
13C2×C4⋊Dic83C2211yescharacteristic
14C2×Dic83⋊C4—21no—
15C2×C4×Dic83C2211yescharacteristic
16#14581717—22no—
17#14581715—22no—
18C83⋊#95—21no—
19C83⋊#95—21no—
20C22×C8×C83C2211yescharacteristic
21C2×C4⋊C4×C83C2211yescharacteristic
22C2×C4⋊C4×C83C2211yescharacteristic
23C2×Dic166—21no—
24C2×Dic166—21no—
25C2×Dic166—21no—
26C2×Dic166—21no—
27C2×Dic166—21no—
28C2×Dic166Q812yes—
29C22×Dic83—21no—
30C22×Dic83—21no—
31C22×Dic83D411yescharacteristic
32C22×Dic83D411yescharacteristic
33C2×C83⋊C8—21no—
34C2×C83⋊C8—21no—
35C2×C83⋊C8—21no—
36C4⋊Dic83—24no—
37C4⋊Dic83—21no—
38C4⋊Dic83D412yes—
39Dic83⋊C4—24no—
40C4×Dic83—21no—
41C4×Dic83—21no—
42C22×C4×C83—21no—
43C22×C4×C83—21no—
44C22×C4×C83C2311yescharacteristic
45C2×C8×C83—21no—
46C2×C8×C83—21no—
47C2×C8×C83—21no—
48C4⋊C4×C83—21no—
49C4⋊C4×C83—21no—
50C4⋊C4×C83—21no—
51C4⋊C4×C83D412yes—
52C23×C83C2×D411yescharacteristic
53C2×C4×C83—22no—
54C2×C4×C83—41no—
55C2×C4×C83—41no—
56C2×C4×C83—41no—
57C2×C4×C83—41no—
58C2×C4×C83—41no—
59C2×C4×C83C2×D411yescharacteristic
60C2×C4×C83C2×D411yescharacteristic
61C2×C4×C83C2×Q811yescharacteristic
62C2×C4×C83#4111yescharacteristic
63C2×C4×C83#4111yescharacteristic
64C2×C4×C83#4111yescharacteristic
65C2×Dic83—21no—
66C2×Dic83—21no—
67C2×Dic83—22no—
68C2×Dic83—22no—
69C2×Dic83—21no—
70C2×Dic83—21no—
71C2×Dic83—21no—
72C2×Dic83—21no—
73C2×Dic83—41no—
74C2×Dic83—41no—
75C2×Dic83—41no—
76C2×Dic83—41no—
77Dic166—22no—
78Dic166—22no—
79Dic166—41no—
80Dic166—41no—
81C8×C83—41no—
82C83⋊C8—41no—
83C22×C83#12011yescharacteristic
84C22×C83C22⋊Q811yescharacteristic
85C22×C83#12411yescharacteristic
86C22×C83#13511yescharacteristic
87C22×C83#13511yescharacteristic
88C22×C83#13711yescharacteristic
89C22×C83#13711yescharacteristic
90C4×C83—42no—
91C4×C83—81no—
92C4×C83C22⋊Q811yescharacteristic
93C4×C83C22⋊Q811yescharacteristic
94C4×C83#12411yescharacteristic
95C4×C83#12411yescharacteristic
96Dic83—42no—
97Dic83—41no—
98Dic83—41no—
99Dic83—42no—
100C2×C83#39311yescharacteristic
101C2×C83#45211yescharacteristic
102C2×C83#45211yescharacteristic
103C2×C83#47911yescharacteristic
104C2×C83#47911yescharacteristic
105C2×C83#48811yescharacteristic
106C2×C83#49111yescharacteristic
107#2026—831nomaximal, Sylow
108C83#202611yescharacteristic, complemented, Sylow
109C2×#125—831no—
110C2×#103—831no—
111C2×#103—831no—
112#391—831no—
113#340—831no—
114#340D8311yescharacteristic
115#336—831no—
116C22×Q8—831no—
117C22×C8—831no—
118C22×C8C2×D8311yescharacteristic
119#125—1662no—
120#125—1662no—
121C2×C4⋊C4—831no—
122C2×C4⋊C4—1661no—
123C2×C4⋊C4—1661no—
124C2×C4⋊C4C2×D8311yescharacteristic
125C2×C4⋊C4C2×D8311yescharacteristic
126C2×C42—831no—
127#103—1662no—
128#103—1662no—
129#95—1661no—
130#95—1661no—
131C2×Q8—832no—
132C2×Q8—1661no—
133C2×Q8—1661no—
134C2×Q8—1661no—
135C2×Q8—1661no—
136C2×Q8—1661no—
137C22×C4—21no—
138C22×C4—21no—
139C22×C4—831no—
140C22×C4—831no—
141C22×C4—1661no—
142C22×C4—1661no—
143C22×C4C22×D8311yescharacteristic
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—21no—
147C2×C8—1661no—
148C2×C8—1661no—
149C2×C8—1661no—
150C4⋊C4—21no—
151C4⋊C4—21no—
152C4⋊C4—21no—
153C4⋊C4—832no—
154C4⋊C4—1664no—
155C4⋊C4—1664no—
156C4⋊C4—1661no—
157C4⋊C4D33212yes—
158C42—1661no—
159C42—1661no—
160C23D4×D8311yescharacteristic
161Q8—3321no—
162Q8—3321no—
163Q8—1662no—
164Q8—1662no—
165C2×C4—22no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—3321no—
172C2×C4—3321no—
173C2×C4—3321no—
174C2×C4—3321no—
175C2×C4—1661no—
176C2×C4—1661no—
177C2×C4—1662no—
178C2×C4—1662no—
179C2×C4—1661no—
180C2×C4—1661no—
181C2×C4—1661no—
182C2×C4—1661no—
183C2×C4D4×D8311yescharacteristic
184C2×C4C2×D33211yescharacteristic
185C2×C4Q8×D8311yescharacteristic
186C2×C4#1305058911yescharacteristic
187C2×C4#1305059011yescharacteristic
188C2×C4#1305059011yescharacteristic
189C8—41no—
190C8—3321no—
191C22#1458176211yescharacteristic
192C22#1458177011yescharacteristic
193C22#1458177811yescharacteristic
194C22#1458181111yescharacteristic
195C22#1458181311yescharacteristic
196C22#1458182111yescharacteristic
197C22#1458182411yescharacteristic
198C4—42no—
199C4—81no—
200C4—3321no—
201C4—3322no—
202C4—3321no—
203C4—3322no—
204C4#1458177011yescharacteristic
205C4#1458177211yescharacteristic
206C4#1458177811yescharacteristic
207C4#1458178011yescharacteristic
208C2#1912761411yescharacteristic
209C2#1912786411yescharacteristic
210C2#1912786611yescharacteristic
211C2#1912800711yescharacteristic
212C2#1912801111yescharacteristic
213C2#1912805411yescharacteristic
214C2#1912806811yescharacteristic
subgroupG/H
centerC23D4×D83
commutator, cosocleC22×C4×C83C23
FrattiniC22×C4C22×D83
Fitting#340×C83C2
socle, prime radicalC23×C83C2×D4
hypercenter#340D83
hypocenterC83#2026
LCSG ▷ C22×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
108. C83#2026semidirect

Maximal subgroups

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

subgroupindex
C2×#145817832
C2×#145817172
C2×#145817152
#191276062
#191274632
#191274552
#340×C832
#202683