Finite Group Databasebeta

← #21422633

Subgroups — #21422633

Order 7552.

222 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 61 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#16837938C211yesmaximal, characteristic
2#16837456C211yesmaximal, characteristic, complemented
3#16837266C211yesmaximal, characteristic, complemented
4#16837139C211yesmaximal, characteristic, complemented
5#16837137C211yesmaximal, characteristic
6#16837135C211yesmaximal, characteristic
7C59×#328C211yesmaximal, characteristic, complemented
8#14273722—21no—
9#14273718C411yescharacteristic, complemented
10#14273716C411yescharacteristic, complemented
11#14273711—21no—
12#14273701C2211yescharacteristic
13Q8×Dic59C411yescharacteristic, complemented
14#14273689C411yescharacteristic, complemented
15(C22⋊D59)⋊C4—21no—
16#14273685—21no—
17C2×Dic59⋊C4—21no—
18C2×C4×Dic59C2211yescharacteristic
19Dic59⋊C8—21no—
20C22⋊(C59⋊C8)C2211yescharacteristic
21#14273637—21no—
22C59⋊#95—21no—
23C59⋊#95C2211yescharacteristic
24C22⋊Q8×C59C2211yescharacteristic
25C22⋊C8×C59C2211yescharacteristic
26#95×C59C2211yescharacteristic
27C2×Q8×C59C2×C411yescharacteristic
28C22×C4×C59—21no—
29C22×C4×C59C2311yescharacteristic
30C2×C22⋊D59—21no—
31C22×Dic59—21no—
32C22×Dic59D411yescharacteristic
33C22×Dic59D411yescharacteristic
34C2×D236C2×C411yescharacteristic
35C2×C4×D59—21no—
36C2×C8×C59—21no—
37C4⋊C4×C59—21no—
38C4⋊C4×C59C2×C411yescharacteristic
39C22⋊C4×C59—21no—
40(C2×D59)⋊C4—21no—
41(C2×D59)⋊C4—21no—
42(C2×D59)⋊C4—21no—
43(C2×D59)⋊C4—21no—
44C4⋊Dic59—21no—
45C4⋊Dic59—21no—
46C4⋊Dic59C2×C411yescharacteristic
47Dic59⋊C4—21no—
48Dic59⋊C4—42no—
49C4×Dic59—21no—
50C4×Dic59C2×C411yescharacteristic
51C4×Dic59C2×C411yescharacteristic
52C4×Dic59D411yescharacteristic
53C4×Dic59D411yescharacteristic
54C2×C59⋊C8—21no—
55C23×C59C2×D411yescharacteristic
56C22×D59—21no—
57Q8×C59—41no—
58C2×C4×C59—21no—
59C2×C4×C59—21no—
60C2×C4×C59—41no—
61C2×C4×C59—41no—
62C2×C4×C59—41no—
63C2×C4×C59—41no—
64C2×C4×C59C22×C411yescharacteristic
65C2×C4×C59C2×D411yescharacteristic
66C22⋊D59—41no—
67C22⋊D59—41no—
68C2×Dic59—21no—
69C2×Dic59—21no—
70C2×Dic59—21no—
71C2×Dic59—41no—
72C2×Dic59—41no—
73C2×Dic59—41no—
74C2×Dic59—41no—
75C2×Dic59C22⋊C411yescharacteristic
76C2×Dic59C22⋊C411yescharacteristic
77C2×Dic59C22⋊C411yescharacteristic
78C2×Dic59C22⋊C411yescharacteristic
79D236—41no—
80C4×D59—42no—
81C8×C59—41no—
82C59⋊C8—41no—
83C22×C59—21no—
84C22×C59—21no—
85C22×C59C2×C22⋊C411yescharacteristic
86C22×C59AGL(1,ℤ/8)11yescharacteristic
87C22×C59#13711yescharacteristic
88C2×D59—41no—
89C2×D59—41no—
90C2×D59—41no—
91C4×C59—21no—
92C4×C59—21no—
93C4×C59—41no—
94C4×C59—41no—
95C4×C59—81no—
96Dic59—21no—
97Dic59—21no—
98Dic59—21no—
99Dic59—21no—
100Dic59—41no—
101Dic59—81no—
102#1512—591nomaximal, Sylow
103C2×C59—21no—
104C2×C59—21no—
105C2×C59#41011yescharacteristic
106C2×C59#41711yescharacteristic
107C2×C59#42111yescharacteristic
108D59—81no—
109#529—591no—
110#432—591no—
111#382—591no—
112#328—591no—
113#328D5911yescharacteristic, complemented
114#327—591no—
115#327—591no—
116C59#151211yescharacteristic, complemented, Sylow
117#126—1181no—
118#125—591no—
119#124—591no—
120#123—1181no—
121C22⋊Q8C2×D5911yescharacteristic
122#121—591no—
123C4×Q8—591no—
124C4×D4—591no—
125C4×D4—1181no—
126#117—1181no—
127C2×C4⋊C4—1181no—
128C2×C42—591no—
129C4⋊C8—1181no—
130C22⋊C8—591no—
131C22⋊C8C2×D5911yescharacteristic
132#97—1181no—
133#95—591no—
134#95—1181no—
135#95C2×D5911yescharacteristic
136C2×Q8C4×D5911yescharacteristic
137C2×D4—591no—
138C2×D4—1181no—
139C22×C4—21no—
140C22×C4—591no—
141C22×C4—591no—
142C22×C4—1181no—
143C22×C4—1181no—
144C22×C4C22×D5911yescharacteristic
145C2×C8—21no—
146C2×C8—1181no—
147C4⋊C4—21no—
148C4⋊C4—591no—
149C4⋊C4—1181no—
150C4⋊C4—1181no—
151C4⋊C4—1181no—
152C4⋊C4—2362no—
153C4⋊C4C4×D5911yescharacteristic
154C22⋊C4—21no—
155C22⋊C4—1181no—
156C22⋊C4—1181no—
157C22⋊C4—1181no—
158C22⋊C4—1181no—
159C42—591no—
160C42—591no—
161C42—591no—
162C42—591no—
163C42—1181no—
164C23—1181no—
165C23D4×D5911yescharacteristic
166Q8—41no—
167D4—2361no—
168D4—2361no—
169D4—2361no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—591no—
177C2×C4—591no—
178C2×C4—591no—
179C2×C4—591no—
180C2×C4—1181no—
181C2×C4—1181no—
182C2×C4—1181no—
183C2×C4—2362no—
184C2×C4—2361no—
185C2×C4—2361no—
186C2×C4—2361no—
187C2×C4—2361no—
188C2×C4C2×C4×D5911yescharacteristic
189C2×C4D4×D5911yescharacteristic
190C8—41no—
191C8—2361no—
192C22—21no—
193C22—21no—
194C22—2361no—
195C22—2361no—
196C22—2361no—
197C22C22⋊C4×D5911yescharacteristic
198C22#1427375411yescharacteristic
199C22#1427375911yescharacteristic
200C4—21no—
201C4—21no—
202C4—41no—
203C4—41no—
204C4—81no—
205C4—1181no—
206C4—1181no—
207C4—1181no—
208C4—1181no—
209C4—4721no—
210C4—2361no—
211C2—21no—
212C2—21no—
213C2—4721no—
214C2#1683737411yescharacteristic
215C2#1683740211yescharacteristic
216C2#1683741711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D59
commutatorC2×C4×C59C22×C4
FrattiniC22×C4C22×D59
FittingC59×#328C2
socleC22×C59C2×C22⋊C4
hypercenter#328D59
hypocenterC59#1512
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #16837456C2semidirect
3. #16837266C2semidirect
4. #16837139C2semidirect
7. C59×#328C2semidirect
9. #14273718C4semidirect
10. #14273716C4semidirect
13. Q8×Dic59C4semidirect
14. #14273689C4semidirect
113. #328D59semidirect
116. C59#1512semidirect