Finite Group Databasebeta

← #21435040

Subgroups — #21435040

Order 7552.

384 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 125 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#16837957C211yesmaximal, characteristic
2C4⋊Q8×D59C211yesmaximal, characteristic
3#16837781C211yesmaximal, characteristic, complemented
4#16837753C211yesmaximal, characteristic, complemented
5#16837752C211yesmaximal, characteristic, complemented
6#16837610C214yesmaximal, complemented
7#16837556C214yesmaximal
8#16837453C211yesmaximal, characteristic
9C59×#494C211yesmaximal, characteristic, complemented
10C2×Q8×D59C2212yes—
11C2×#11745672C2214yes—
12#14273727C2211yescharacteristic
13#14273727C2211yescharacteristic
14#14273726—21no—
15#14273726—21no—
16#14273725C2212yes—
17#14273718—21no—
18#14273707—21no—
19#14273703C2212yes—
20Q8×Dic59C2212yes—
21#14273692—21no—
22#14273685—21no—
23C4⋊C4×D59—21no—
24C4⋊C4×D59—21no—
25C42×D59C2211yescharacteristic
26Dic59⋊C8C2212yes—
27#14273652C2214yes—
28#14273651C2214yes—
29(C2×D59)⋊C8C2212yes—
30C4×C59⋊C8C2211yescharacteristic
31C2×Q16×C59C2214yes—
32C4⋊Q8×C59C2211yescharacteristic
33C4⋊Q8×C59C2211yescharacteristic
34C4×C8×C59C2211yescharacteristic
35C2×Q8×C59C2312yes—
36C2×Q8×C59C2312yes—
37Q8×D59—44no—
38C2×C4×D59—22no—
39C2×C4×D59D411yescharacteristic
40C2×C4×D59D411yescharacteristic
41C2×C4×D59C2311yescharacteristic
42C2×Dic118—21no—
43C2×Dic118—22no—
44C2×Dic118C2312yes—
45Q16×C59—44no—
46C2×C8×C59C2312yes—
47C4⋊C4×C59—21no—
48C4⋊C4×C59—21no—
49C4⋊C4×C59—21no—
50C4⋊C4×C59—21no—
51C42×C59C2311yescharacteristic
52#11745672—44no—
53(C2×D59)⋊C4—22no—
54C4⋊Dic59—21no—
55C4⋊Dic59—21no—
56C4⋊Dic59—21no—
57C4⋊Dic59—22no—
58C4⋊Dic59C2312yes—
59Dic59⋊C4—22no—
60Dic59⋊C4—22no—
61Dic59⋊C4—22no—
62C4×Dic59—22no—
63C4×Dic59D411yescharacteristic
64C4×Dic59D411yescharacteristic
65C4×Dic59C2311yescharacteristic
66C2×C59⋊C8C2312yes—
67C22×D59C2×D411yescharacteristic
68Q8×C59—24no—
69Q8×C59—24no—
70C2×C4×C59—22no—
71C2×C4×C59—22no—
72C2×C4×C59C2×D411yescharacteristic
73C2×C4×C59C2×D411yescharacteristic
74C2×C4×C59C2411yescharacteristic
75C2×Dic59—22no—
76C2×Dic59—22no—
77C2×Dic59C2×D411yescharacteristic
78C2×Dic59C2×D411yescharacteristic
79C2×Dic59C2×D411yescharacteristic
80C4×D59—22no—
81C4×D59—22no—
82C4×D59—44no—
83C4×D59Q1614yescomplemented
84Dic118—24no—
85Dic118—44no—
86Dic118—42no—
87C8×C59—22no—
88C59⋊C8—22no—
89C22×C59C22×D411yescharacteristic
90C2×D59—21no—
91C2×D59—21no—
92C2×D59C2×Q1612yes—
93C4×C59—42no—
94C4×C59—42no—
95C4×C59C2×Q1612yes—
96C4×C59#13712yes—
97C4×C59H(5,𝔽2)12yes—
98Dic59—21no—
99Dic59—21no—
100Dic59—42no—
101Dic59—42no—
102Dic59C2×Q1612yes—
103#3209—591nomaximal, Sylow
104C2×C59#53511yescharacteristic
105C2×C59C22×Q1611yescharacteristic
106C2×C59C2×#13711yescharacteristic
107D59—22no—
108#533—591no—
109C2×C4⋊Q8—591no—
110#494—591no—
111#494D5911yescharacteristic, complemented
112#487—591no—
113#487—591no—
114#462—594no—
115#451—594no—
116#431—591no—
117C59#320911yescharacteristic, complemented, Sylow
118C22×Q8—592no—
119C2×Q16—594no—
120C2×Q16C2×D5914yes—
121C4⋊Q8—592no—
122C4⋊Q8—591no—
123C4⋊Q8—591no—
124C4⋊Q8—1181no—
125C4⋊Q8—1181no—
126C4⋊Q8C2×D5911yescharacteristic
127C4⋊Q8C2×D5911yescharacteristic
128#125—1181no—
129C22⋊Q8—592no—
130C22⋊Q8—1181no—
131C4×Q8—592no—
132C4×Q8—1181no—
133#117—1181no—
134C2×C4⋊C4—1181no—
135C2×C4⋊C4—1181no—
136C2×C42—591no—
137C4⋊C8—592no—
138#103—594no—
139#103—594no—
140C22⋊C8—592no—
141C4×C8—591no—
142C4×C8C2×D5911yescharacteristic
143C2×Q8—592no—
144C2×Q8—1182no—
145C2×Q8—1181no—
146C2×Q8—2364no—
147C2×Q8C22×D5912yes—
148C2×Q8C22×D5912yes—
149C22×C4—591no—
150C22×C4—591no—
151C22×C4—591no—
152C22×C4—1182no—
153Q16—44no—
154Q16—2364no—
155C2×C8—592no—
156C2×C8C22×D5912yes—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—592no—
162C4⋊C4—1182no—
163C4⋊C4—1182no—
164C4⋊C4—1182no—
165C4⋊C4—1182no—
166C4⋊C4—1181no—
167C4⋊C4—1181no—
168C4⋊C4—1181no—
169C22⋊C4—1182no—
170C42—591no—
171C42—591no—
172C42—591no—
173C42—1182no—
174C42C22×D5911yescharacteristic
175C23—591no—
176Q8—24no—
177Q8—24no—
178Q8—1184no—
179Q8—2364no—
180Q8—2362no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—591no—
184C2×C4—594no—
185C2×C4—591no—
186C2×C4—591no—
187C2×C4—1182no—
188C2×C4—1182no—
189C2×C4—1182no—
190C2×C4—1182no—
191C2×C4—2364no—
192C2×C4D4×D5911yescharacteristic
193C2×C4D4×D5911yescharacteristic
194C2×C4C23×D5911yescharacteristic
195C8—22no—
196C8—1182no—
197C22—592no—
198C22—1181no—
199C22—1181no—
200C22C2×D4×D5911yescharacteristic
201C4—42no—
202C4—42no—
203C4—592no—
204C4—1181no—
205C4—1181no—
206C4—2362no—
207C4—2362no—
208C4Q16×D5912yes—
209C4#1427375912yes—
210C4#1427377212yes—
211C2—1182no—
212C2#1683796511yescharacteristic
213C2C2×Q16×D5911yescharacteristic
214C2C2×#1427375911yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#494C2
socleC22×C59C22×D4
hypercenter#494D59
hypocenterC59#3209
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
3. #16837781C2semidirect
4. #16837753C2semidirect
5. #16837752C2semidirect
6. #16837610C2semidirect
9. C59×#494C2semidirect
83. C4×D59Q16semidirect
111. #494D59semidirect
117. C59#3209semidirect