Finite Group Databasebeta

← #21422579

Subgroups — #21422579

Order 7552.

238 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 63 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#16837933C211yesmaximal, characteristic
2#16837452C211yesmaximal, characteristic, complemented
3#16837247C211yesmaximal, characteristic, complemented
4#16837140C211yesmaximal, characteristic, complemented
5#16837138C211yesmaximal, characteristic, complemented
6#16837136C211yesmaximal, characteristic
7C59×#327C211yesmaximal, characteristic
8#14273720—21no—
9#14273718C411yescharacteristic, complemented
10#14273714C411yescharacteristic, complemented
11#14273708—21no—
12#14273706C2211yescharacteristic
13#14273692C411yescharacteristic, complemented
14D4×Dic59—21no—
15D4×Dic59C411yescharacteristic, complemented
16#14273683—21no—
17C2×C4×Dic59—21no—
18C2×C4×Dic59C2211yescharacteristic
19Dic59⋊C8—21no—
20C22⋊(C59⋊C8)C2211yescharacteristic
21C8×Dic59—21no—
22C59⋊#95—21no—
23C59⋊#95C2211yescharacteristic
24#121×C59C2211yescharacteristic
25C22⋊C8×C59C2211yescharacteristic
26#95×C59C2211yescharacteristic
27C2×D4×C59—21no—
28C2×D4×C59C2×C411yescharacteristic
29C22×C4×C59—21no—
30C22×C4×C59C2311yescharacteristic
31C22×Dic59—21no—
32C22×Dic59—21no—
33C22×Dic59D411yescharacteristic
34C22×Dic59D411yescharacteristic
35C2×Dic118C2×C411yescharacteristic
36C2×C8×C59—21no—
37C4⋊C4×C59C2×C411yescharacteristic
38C22⋊C4×C59—21no—
39C22⋊Dic59—21no—
40C22⋊Dic59—21no—
41C22⋊Dic59—21no—
42C22⋊Dic59—21no—
43C4⋊Dic59—21no—
44C4⋊Dic59C2×C411yescharacteristic
45Dic59⋊C4—21no—
46Dic59⋊C4—21no—
47Dic59⋊C4—21no—
48C4×Dic59—24no—
49C4×Dic59—21no—
50C4×Dic59C2×C411yescharacteristic
51C4×Dic59C2×C411yescharacteristic
52C4×Dic59D411yescharacteristic
53C4×Dic59D411yescharacteristic
54C2×C59⋊C8—21no—
55C23×C59—21no—
56C23×C59C2×D411yescharacteristic
57D4×C59—41no—
58D4×C59—41no—
59D4×C59—41no—
60C2×C4×C59—22no—
61C2×C4×C59—21no—
62C2×C4×C59—41no—
63C2×C4×C59—41no—
64C2×C4×C59—41no—
65C2×C4×C59C22×C411yescharacteristic
66C2×C4×C59C2×D411yescharacteristic
67C2×Dic59—21no—
68C2×Dic59—21no—
69C2×Dic59—22no—
70C2×Dic59—22no—
71C2×Dic59—21no—
72C2×Dic59—21no—
73C2×Dic59—41no—
74C2×Dic59—41no—
75C2×Dic59—42no—
76C2×Dic59C22⋊C411yescharacteristic
77C2×Dic59C22⋊C411yescharacteristic
78C2×Dic59C22⋊C411yescharacteristic
79C2×Dic59C22⋊C411yescharacteristic
80Dic118—41no—
81C8×C59—41no—
82C59⋊C8—41no—
83C22×C59—21no—
84C22×C59—21no—
85C22×C59—41no—
86C22×C59—41no—
87C22×C59—41no—
88C22×C59C2×C22⋊C411yescharacteristic
89C22×C59#13511yescharacteristic
90C22×C59#13511yescharacteristic
91C4×C59—21no—
92C4×C59—21no—
93C4×C59—42no—
94C4×C59—41no—
95Dic59—21no—
96Dic59—21no—
97Dic59—21no—
98Dic59—42no—
99Dic59—41no—
100Dic59—41no—
101Dic59#10412yes—
102#1500—591nomaximal, Sylow
103C2×C59—21no—
104C2×C59—21no—
105C2×C59—81no—
106C2×C59#41011yescharacteristic
107C2×C59#41611yescharacteristic
108C2×C59C2×#10411yescharacteristic
109#529—591no—
110#431—591no—
111#376—591no—
112#328—591no—
113#328—591no—
114#327—591no—
115#327D5911yescharacteristic
116C59#150011yescharacteristic, complemented, Sylow
117#126—1181no—
118#125—591no—
119#124—591no—
120#123—1181no—
121C22⋊Q8—591no—
122#121C2×D5911yescharacteristic
123C4×Q8—591no—
124C4×D4—591no—
125C4×D4—1181no—
126#117—1181no—
127C2×C42—591no—
128C2×C42—1181no—
129C4⋊C8—1181no—
130C22⋊C8—591no—
131C22⋊C8C2×D5911yescharacteristic
132C4×C8—1181no—
133#95—591no—
134#95—1181no—
135#95C2×D5911yescharacteristic
136C2×Q8—591no—
137C2×D4—21no—
138C2×D4C4×D5911yescharacteristic
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—591no—
148C4⋊C4—1181no—
149C4⋊C4—1181no—
150C4⋊C4—1181no—
151C4⋊C4—1181no—
152C4⋊C4C4×D5911yescharacteristic
153C22⋊C4—21no—
154C22⋊C4—1181no—
155C22⋊C4—1181no—
156C22⋊C4—1181no—
157C22⋊C4—1181no—
158C42—591no—
159C42—591no—
160C42—591no—
161C42—591no—
162C42—1181no—
163C42—1184no—
164C23—21no—
165C23D4×D5911yescharacteristic
166Q8—2361no—
167D4—41no—
168D4—41no—
169D4—41no—
170C2×C4—22no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—591no—
176C2×C4—591no—
177C2×C4—591no—
178C2×C4—591no—
179C2×C4—1182no—
180C2×C4—1181no—
181C2×C4—1181no—
182C2×C4—1182no—
183C2×C4—1181no—
184C2×C4—1181no—
185C2×C4—2362no—
186C2×C4—2361no—
187C2×C4—2361no—
188C2×C4C2×C4×D5911yescharacteristic
189C2×C4D4×D5911yescharacteristic
190C8—41no—
191C8—2361no—
192C22—21no—
193C22—21no—
194C22—41no—
195C22—41no—
196C22—41no—
197C22C22⋊C4×D5911yescharacteristic
198C22#1427374611yescharacteristic
199C22#1427374811yescharacteristic
200C4—21no—
201C4—21no—
202C4—42no—
203C4—41no—
204C4—592no—
205C4—1181no—
206C4—1181no—
207C4—1181no—
208C4—2362no—
209C4—2361no—
210C4—2361no—
211C2—21no—
212C2—21no—
213C2—81no—
214C2#1683737411yescharacteristic
215C2#1683739511yescharacteristic
216C2#104×D5911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D59
commutatorC2×C4×C59C22×C4
FrattiniC22×C4C22×D59
FittingC59×#327C2
socleC22×C59C2×C22⋊C4
hypercenter#327D59
hypocenterC59#1500
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #16837452C2semidirect
3. #16837247C2semidirect
4. #16837140C2semidirect
5. #16837138C2semidirect
9. #14273718C4semidirect
10. #14273714C4semidirect
13. #14273692C4semidirect
15. D4×Dic59C4semidirect
116. C59#1500semidirect