Finite Group Databasebeta

← #21422705

Subgroups — #21422705

Order 7552.

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

normal subgroups only

This group has 256 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#16837951C211yesmaximal, characteristic
2#16837457C211yesmaximal, characteristic, complemented
3#97×D59C211yesmaximal, characteristic, complemented
4#16837142C211yesmaximal, characteristic, complemented
5#16837141C211yesmaximal, characteristic, complemented
6#16837141C211yesmaximal, characteristic, complemented
7C59×#329C211yesmaximal, characteristic, complemented
8C2×#11745689C411yescharacteristic
9C2×#11745687C411yescharacteristic
10C2×C8×D59—21no—
11#14273725C411yescharacteristic
12#14273723C411yescharacteristic
13#14273715C2211yescharacteristic
14#14273700—21no—
15#14273700—21no—
16(C22⋊D59)⋊C4—21no—
17(C22⋊D59)⋊C4—21no—
18C42×D59C2211yescharacteristic
19Dic59⋊C8—21no—
20(C2×D59)⋊C8—21no—
21#14273638C2211yescharacteristic
22#14273638C2211yescharacteristic
23#14273637—21no—
24#124×C59C2211yescharacteristic
25#97×C59C2211yescharacteristic
26#97×C59C2211yescharacteristic
27C2×Q8×C59C2×C411yescharacteristic
28C2×D4×C59C2×C411yescharacteristic
29C2×C22⋊D59—21no—
30C2×C22⋊D59—21no—
31C2×C22⋊D59—21no—
32C22×Dic59—21no—
33#11745689—42no—
34#11745687—42no—
35C2×D236—21no—
36C2×D236C2×C411yescharacteristic
37C2×C4×D59—21no—
38C2×C4×D59C2×C411yescharacteristic
39C2×C4×D59D411yescharacteristic
40C2×C4×D59D411yescharacteristic
41C2×Dic118C2×C411yescharacteristic
42C2×C8×C59—21no—
43C2×C8×C59—21no—
44C22⋊C4×C59—21no—
45C22⋊C4×C59—21no—
46C42×C59C2311yescharacteristic
47(C2×D59)⋊C4—21no—
48(C2×D59)⋊C4—21no—
49Dic59⋊C4—21no—
50Dic59⋊C4—21no—
51C4×Dic59C2×C411yescharacteristic
52C4×Dic59D411yescharacteristic
53C4×Dic59D411yescharacteristic
54C2×C59⋊C8—21no—
55C2×C59⋊C8—21no—
56C8×D59—24no—
57C23×C59—21no—
58C22×D59—21no—
59C22×D59C22⋊C411yescharacteristic
60Q8×C59—41no—
61D4×C59—41no—
62C2×C4×C59—21no—
63C2×C4×C59C22×C411yescharacteristic
64C2×C4×C59C2×D411yescharacteristic
65C2×C4×C59C2×D411yescharacteristic
66C22⋊D59—42no—
67C22⋊D59—42no—
68C22⋊D59—42no—
69C2×Dic59—21no—
70C2×Dic59—42no—
71C2×Dic59C22⋊C411yescharacteristic
72C2×Dic59C22⋊C411yescharacteristic
73C2×Dic59C22⋊C411yescharacteristic
74D236—41no—
75D236—42no—
76C4×D59—22no—
77C4×D59—22no—
78C4×D59—41no—
79C4×D59—42no—
80Dic118—41no—
81C8×C59—22no—
82C8×C59—41no—
83C59⋊C8—22no—
84C59⋊C8—41no—
85C22×C59—41no—
86C22×C59—41no—
87C22×C59—41no—
88C22×C59C2×C22⋊C411yescharacteristic
89C2×D59—21no—
90C2×D59—21no—
91C2×D59—41no—
92C2×D59—41no—
93C2×D59—41no—
94C2×D59#10012yes—
95C4×C59—21no—
96C4×C59—21no—
97C4×C59—21no—
98C4×C59—41no—
99Dic59—21no—
100Dic59—21no—
101Dic59—41no—
102Dic59#10412yes—
103#1530—591nomaximal, Sylow
104C2×C59—81no—
105C2×C59C2×#10011yescharacteristic
106C2×C59C2×#10411yescharacteristic
107C2×C59#42111yescharacteristic
108D59—22no—
109D59—81no—
110#532—591no—
111#432—591no—
112C2×#97—591no—
113#329—591no—
114#329—591no—
115#329—591no—
116#329D5911yescharacteristic, complemented
117C59#153011yescharacteristic, complemented, Sylow
118C2×#41—591no—
119C2×#41—591no—
120C22×C8—1181no—
121C4⋊Q8—591no—
122#127—591no—
123#124—591no—
124#124C2×D5911yescharacteristic
125#121—1181no—
126#121—1181no—
127C4×D4—1181no—
128C4×D4—1181no—
129C2×C42—591no—
130C4⋊C8—1181no—
131C22⋊C8—1181no—
132#97—591no—
133#97—591no—
134#97—1181no—
135#97C2×D5911yescharacteristic
136#97C2×D5911yescharacteristic
137#41—2362no—
138#41—2362no—
139C2×Q8—591no—
140C2×Q8C4×D5911yescharacteristic
141C2×D4—591no—
142C2×D4—1181no—
143C2×D4—1181no—
144C2×D4—1181no—
145C2×D4—1181no—
146C2×D4C4×D5911yescharacteristic
147C22×C4—591no—
148C22×C4—591no—
149C22×C4—591no—
150C22×C4—1181no—
151C22×C4—1181no—
152C2×C8—21no—
153C2×C8—21no—
154C2×C8—1184no—
155C2×C8—1181no—
156C2×C8—1181no—
157C4⋊C4—1181no—
158C4⋊C4—1181no—
159C22⋊C4—21no—
160C22⋊C4—21no—
161C22⋊C4—1181no—
162C22⋊C4—1181no—
163C42—591no—
164C42—591no—
165C42—591no—
166C42C22×D5911yescharacteristic
167C23—21no—
168C23—591no—
169C23—1181no—
170Q8—41no—
171Q8—2361no—
172D4—41no—
173D4—2361no—
174D4—2362no—
175D4—2362no—
176D4—2362no—
177D4—2362no—
178C2×C4—21no—
179C2×C4—591no—
180C2×C4—591no—
181C2×C4—591no—
182C2×C4—1182no—
183C2×C4—1182no—
184C2×C4—1181no—
185C2×C4—2361no—
186C2×C4—2362no—
187C2×C4—2362no—
188C2×C4C2×C4×D5911yescharacteristic
189C2×C4D4×D5911yescharacteristic
190C2×C4D4×D5911yescharacteristic
191C8—22no—
192C8—41no—
193C8—1182no—
194C8—2361no—
195C22—41no—
196C22—41no—
197C22—41no—
198C22—592no—
199C22—1181no—
200C22—1181no—
201C22—2361no—
202C22—2361no—
203C22—2361no—
204C22C22⋊C4×D5911yescharacteristic
205C4—21no—
206C4—21no—
207C4—21no—
208C4—41no—
209C4—592no—
210C4—1181no—
211C4—1181no—
212C4—2361no—
213C2—81no—
214C2—1182no—
215C2—4721no—
216C2#100×D5911yescharacteristic
217C2#104×D5911yescharacteristic
218C2#1683741711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D59
commutatorC2×C4×C59C22×C4
FrattiniC42C22×D59
FittingC59×#329C2
socleC22×C59C2×C22⋊C4
hypercenter#329D59
hypocenterC59#1530
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #16837457C2semidirect
3. #97×D59C2semidirect
4. #16837142C2semidirect
5. #16837141C2semidirect
6. #16837141C2semidirect
7. C59×#329C2semidirect
116. #329D59semidirect
117. C59#1530semidirect