Finite Group Databasebeta

← #21425246

Subgroups — #21425246

Order 7552.

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×#14273718C211yesmaximal, characteristic
2C2×#14273652C211yesmaximal, characteristic
3C2×#14273650C211yesmaximal, characteristic
4#16837307C211yesmaximal, characteristic
5#16837164C211yesmaximal, characteristic
6#16837156C211yesmaximal, characteristic
7C59×#340C211yesmaximal, characteristic
8C22×Dic118C2211yescharacteristic
9C22×C59⋊C8C2211yescharacteristic
10#14273718—22no—
11#14273718—22no—
12C2×C4⋊Dic59—21no—
13C2×C4⋊Dic59C2211yescharacteristic
14C2×Dic59⋊C4—21no—
15C2×C4×Dic59C2211yescharacteristic
16#14273652—22no—
17#14273650—22no—
18C59⋊#95—21no—
19C59⋊#95—21no—
20C22×C8×C59C2211yescharacteristic
21C2×C4⋊C4×C59C2211yescharacteristic
22C2×C4⋊C4×C59C2211yescharacteristic
23C22×C4×C59—21no—
24C22×C4×C59—21no—
25C22×C4×C59C2311yescharacteristic
26C22×Dic59—21no—
27C22×Dic59—21no—
28C22×Dic59D411yescharacteristic
29C22×Dic59D411yescharacteristic
30C2×Dic118—21no—
31C2×Dic118—21no—
32C2×Dic118—21no—
33C2×Dic118—21no—
34C2×Dic118—21no—
35C2×Dic118Q812yes—
36C2×C8×C59—21no—
37C2×C8×C59—21no—
38C2×C8×C59—21no—
39C4⋊C4×C59—21no—
40C4⋊C4×C59—21no—
41C4⋊C4×C59—21no—
42C4⋊C4×C59D412yes—
43C4⋊Dic59—24no—
44C4⋊Dic59—21no—
45C4⋊Dic59D412yes—
46Dic59⋊C4—24no—
47C4×Dic59—21no—
48C4×Dic59—21no—
49C2×C59⋊C8—21no—
50C2×C59⋊C8—21no—
51C2×C59⋊C8—21no—
52C23×C59C2×D411yescharacteristic
53C2×C4×C59—22no—
54C2×C4×C59—41no—
55C2×C4×C59—41no—
56C2×C4×C59—41no—
57C2×C4×C59—41no—
58C2×C4×C59—41no—
59C2×C4×C59C2×D411yescharacteristic
60C2×C4×C59C2×D411yescharacteristic
61C2×C4×C59C2×Q811yescharacteristic
62C2×C4×C59#4111yescharacteristic
63C2×C4×C59#4111yescharacteristic
64C2×C4×C59#4111yescharacteristic
65C2×Dic59—21no—
66C2×Dic59—21no—
67C2×Dic59—22no—
68C2×Dic59—22no—
69C2×Dic59—21no—
70C2×Dic59—21no—
71C2×Dic59—21no—
72C2×Dic59—21no—
73C2×Dic59—41no—
74C2×Dic59—41no—
75C2×Dic59—41no—
76C2×Dic59—41no—
77Dic118—22no—
78Dic118—22no—
79Dic118—41no—
80Dic118—41no—
81C8×C59—41no—
82C59⋊C8—41no—
83C22×C59#12011yescharacteristic
84C22×C59C22⋊Q811yescharacteristic
85C22×C59#12411yescharacteristic
86C22×C59#13511yescharacteristic
87C22×C59#13511yescharacteristic
88C22×C59#13711yescharacteristic
89C22×C59#13711yescharacteristic
90C4×C59—42no—
91C4×C59—81no—
92C4×C59C22⋊Q811yescharacteristic
93C4×C59C22⋊Q811yescharacteristic
94C4×C59#12411yescharacteristic
95C4×C59#12411yescharacteristic
96Dic59—42no—
97Dic59—41no—
98Dic59—41no—
99Dic59—42no—
100#2026—591nomaximal, Sylow
101C2×C59#39311yescharacteristic
102C2×C59#45211yescharacteristic
103C2×C59#45211yescharacteristic
104C2×C59#47911yescharacteristic
105C2×C59#47911yescharacteristic
106C2×C59#48811yescharacteristic
107C2×C59#49111yescharacteristic
108C2×#125—591no—
109C2×#103—591no—
110C2×#103—591no—
111#391—591no—
112#340—591no—
113#340D5911yescharacteristic
114#336—591no—
115C59#202611yescharacteristic, complemented, Sylow
116C22×Q8—591no—
117C22×C8—591no—
118C22×C8C2×D5911yescharacteristic
119#125—1182no—
120#125—1182no—
121C2×C4⋊C4—591no—
122C2×C4⋊C4—1181no—
123C2×C4⋊C4—1181no—
124C2×C4⋊C4C2×D5911yescharacteristic
125C2×C4⋊C4C2×D5911yescharacteristic
126C2×C42—591no—
127#103—1182no—
128#103—1182no—
129#95—1181no—
130#95—1181no—
131C2×Q8—592no—
132C2×Q8—1181no—
133C2×Q8—1181no—
134C2×Q8—1181no—
135C2×Q8—1181no—
136C2×Q8—1181no—
137C22×C4—21no—
138C22×C4—21no—
139C22×C4—591no—
140C22×C4—591no—
141C22×C4—1181no—
142C22×C4—1181no—
143C22×C4C22×D5911yescharacteristic
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—21no—
147C2×C8—1181no—
148C2×C8—1181no—
149C2×C8—1181no—
150C4⋊C4—21no—
151C4⋊C4—21no—
152C4⋊C4—21no—
153C4⋊C4—592no—
154C4⋊C4—1184no—
155C4⋊C4—1184no—
156C4⋊C4—1181no—
157C4⋊C4D23612yes—
158C42—1181no—
159C42—1181no—
160C23D4×D5911yescharacteristic
161Q8—1182no—
162Q8—1182no—
163Q8—2361no—
164Q8—2361no—
165C2×C4—22no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—1181no—
172C2×C4—1181no—
173C2×C4—1182no—
174C2×C4—1182no—
175C2×C4—1181no—
176C2×C4—1181no—
177C2×C4—1181no—
178C2×C4—1181no—
179C2×C4—2361no—
180C2×C4—2361no—
181C2×C4—2361no—
182C2×C4—2361no—
183C2×C4C2×D23611yescharacteristic
184C2×C4#1174568511yescharacteristic
185C2×C4#1174568511yescharacteristic
186C2×C4D4×D5911yescharacteristic
187C2×C4#1174568711yescharacteristic
188C2×C4Q8×D5911yescharacteristic
189C8—41no—
190C8—2361no—
191C22#1427369711yescharacteristic
192C22#1427370511yescharacteristic
193C22#1427371311yescharacteristic
194C22#1427374611yescharacteristic
195C22#1427374811yescharacteristic
196C22#1427375611yescharacteristic
197C22#1427375911yescharacteristic
198C4—42no—
199C4—81no—
200C4—2361no—
201C4—2361no—
202C4—2362no—
203C4—2362no—
204C4#1427370511yescharacteristic
205C4#1427370711yescharacteristic
206C4#1427371311yescharacteristic
207C4#1427371511yescharacteristic
208C2#1683731511yescharacteristic
209C2#1683756511yescharacteristic
210C2#1683756711yescharacteristic
211C2#1683770811yescharacteristic
212C2#1683771211yescharacteristic
213C2#1683775511yescharacteristic
214C2#1683776911yescharacteristic
subgroupG/H
centerC23D4×D59
commutatorC22×C4×C59C23
FrattiniC22×C4C22×D59
FittingC59×#340C2
socleC23×C59C2×D4
hypercenter#340D59
hypocenterC59#2026
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
115. C59#2026semidirect