Finite Group Databasebeta

← #21434473

Subgroups — #21434473

Order 7552.

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

normal subgroups only

This group has 380 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#16837769C214yesmaximal, complemented
4#16837754C211yesmaximal, characteristic, complemented
5#16837753C211yesmaximal, characteristic, complemented
6#16837752C211yesmaximal, characteristic, complemented
7#16837409C214yesmaximal
8C4×#11745659C211yesmaximal, characteristic
9C59×#487C211yesmaximal, characteristic, complemented
10C2×Q8×D59C2212yes—
11C2×#11745659C2212yes—
12#14273727C2211yescharacteristic
13#14273727C2211yescharacteristic
14#14273726—21no—
15#14273726—21no—
16#14273725C2212yes—
17#14273718C2212yes—
18#14273707—21no—
19#14273703—21no—
20Q8×Dic59—21no—
21#14273692—21no—
22#14273685C2212yes—
23C4⋊C4×D59—21no—
24C4⋊C4×D59—21no—
25C42×D59C2211yescharacteristic
26#14273652C2214yes—
27#14273651C2214yes—
28#14273650C2214yes—
29#14273637C2212yes—
30C4×C59⋊C8C2211yescharacteristic
31C4⋊Q8×C59C2211yescharacteristic
32C4⋊Q8×C59C2211yescharacteristic
33#103×C59C2214yes—
34C4×C8×C59C2211yescharacteristic
35C2×Q8×C59—21no—
36C2×Q8×C59C2312yes—
37Q8×D59—28no—
38C2×C4×D59—22no—
39C2×C4×D59D411yescharacteristic
40C2×C4×D59D411yescharacteristic
41C2×C4×D59C2311yescharacteristic
42C2×Dic118—21no—
43C2×Dic118—22no—
44C2×Dic118C2312yes—
45C2×C8×C59C2312yes—
46C4⋊C4×C59—21no—
47C4⋊C4×C59—21no—
48C4⋊C4×C59—21no—
49C4⋊C4×C59C2312yes—
50C42×C59C2311yescharacteristic
51(C2×D59)⋊C4—22no—
52C4⋊Dic59—21no—
53C4⋊Dic59—21no—
54C4⋊Dic59—21no—
55C4⋊Dic59—22no—
56C4⋊Dic59C2312yes—
57Dic59⋊C4—22no—
58Dic59⋊C4—22no—
59Dic59⋊C4—22no—
60C4×Dic59—22no—
61C4×Dic59D411yescharacteristic
62C4×Dic59D411yescharacteristic
63C4×Dic59C2311yescharacteristic
64C2×C59⋊C8C2312yes—
65#11745659—24no—
66C22×D59C2×D411yescharacteristic
67Q8×C59—24no—
68Q8×C59—42no—
69C2×C4×C59—22no—
70C2×C4×C59—22no—
71C2×C4×C59C2×D411yescharacteristic
72C2×C4×C59C2×D411yescharacteristic
73C2×C4×C59C2411yescharacteristic
74C2×Dic59—22no—
75C2×Dic59—22no—
76C2×Dic59C2×D411yescharacteristic
77C2×Dic59C2×D411yescharacteristic
78C2×Dic59C2×D411yescharacteristic
79C4×D59—22no—
80C4×D59—22no—
81C4×D59—44no—
82C4×D59#4114yes—
83Dic118—24no—
84Dic118—42no—
85Dic118—44no—
86C8×C59—22no—
87C59⋊C8—22no—
88C22×C59C22×D411yescharacteristic
89C2×D59—21no—
90C2×D59—21no—
91C2×D59#12412yes—
92C4×C59—42no—
93C4×C59—42no—
94C4×C59#13712yes—
95C4×C59#13712yes—
96C4×C59C2×#4112yes—
97Dic59—21no—
98Dic59—21no—
99Dic59—42no—
100Dic59—42no—
101Dic59#12412yes—
102#3139—591nomaximal, Sylow
103C2×C59C2×#12411yescharacteristic
104C2×C59C2×#13711yescharacteristic
105C2×C59C2×#13711yescharacteristic
106D59—22no—
107#533—591no—
108C2×C4⋊Q8—591no—
109#491—594no—
110#487—591no—
111#487—591no—
112#487—591no—
113#487D5911yescharacteristic, complemented
114#419—594no—
115C4×M16—591no—
116C59#313911yescharacteristic, complemented, Sylow
117C22×Q8—592no—
118C2×M16—592no—
119C4⋊Q8—592no—
120C4⋊Q8—591no—
121C4⋊Q8—591no—
122C4⋊Q8—1181no—
123C4⋊Q8—1181no—
124C4⋊Q8C2×D5911yescharacteristic
125C4⋊Q8C2×D5911yescharacteristic
126#125—592no—
127C22⋊Q8—1181no—
128C22⋊Q8—1181no—
129C4×Q8—1181no—
130C4×Q8—1181no—
131#117—592no—
132C2×C4⋊C4—1181no—
133C2×C4⋊C4—1181no—
134C2×C42—591no—
135#103—594no—
136#103—594no—
137#103—594no—
138#103C2×D5914yes—
139#97—592no—
140C4×C8—591no—
141C4×C8C2×D5911yescharacteristic
142C2×Q8—21no—
143C2×Q8—592no—
144C2×Q8—1182no—
145C2×Q8—1188no—
146C2×Q8—1181no—
147C2×Q8C22×D5912yes—
148C22×C4—591no—
149C22×C4—591no—
150C22×C4—591no—
151C22×C4—1182no—
152M16—1184no—
153C2×C8—592no—
154C2×C8C22×D5912yes—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—592no—
159C4⋊C4—1182no—
160C4⋊C4—1182no—
161C4⋊C4—1182no—
162C4⋊C4—1182no—
163C4⋊C4—1181no—
164C4⋊C4—1181no—
165C4⋊C4—1181no—
166C4⋊C4C22×D5912yes—
167C22⋊C4—1182no—
168C42—591no—
169C42—591no—
170C42—591no—
171C42—1182no—
172C42C22×D5911yescharacteristic
173C23—591no—
174Q8—24no—
175Q8—42no—
176Q8—1184no—
177Q8—2364no—
178Q8—2362no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—591no—
182C2×C4—594no—
183C2×C4—591no—
184C2×C4—591no—
185C2×C4—1182no—
186C2×C4—1182no—
187C2×C4—1182no—
188C2×C4—1182no—
189C2×C4—2364no—
190C2×C4D4×D5911yescharacteristic
191C2×C4D4×D5911yescharacteristic
192C2×C4C23×D5911yescharacteristic
193C8—22no—
194C8—1182no—
195C22—592no—
196C22—1181no—
197C22—1181no—
198C22C2×D4×D5911yescharacteristic
199C4—42no—
200C4—42no—
201C4—592no—
202C4—1181no—
203C4—1181no—
204C4—2362no—
205C4—2362no—
206C4#1427375612yes—
207C4#1427375912yes—
208C4#41×D5912yes—
209C2—1182no—
210C2#124×D5911yescharacteristic
211C2C2×#1427375611yescharacteristic
212C2C2×#1427375911yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#487C2
socleC22×C59C22×D4
hypercenter#487D59
hypocenterC59#3139
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
3. #16837769C2semidirect
4. #16837754C2semidirect
5. #16837753C2semidirect
6. #16837752C2semidirect
9. C59×#487C2semidirect
113. #487D59semidirect
116. C59#3139semidirect