Finite Group Databasebeta

← #21424405

Subgroups — #21424405

Order 7552.

360 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 99 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
1C2×#14273703C211yesmaximal, characteristic
2C2×#14273685C211yesmaximal, characteristic
3C2×#14273651C211yesmaximal, characteristic, complemented
4C2×(C2×D59)⋊C8C211yesmaximal, characteristic
5#16837165C211yesmaximal, characteristic, complemented
6#16837164C211yesmaximal, characteristic, complemented
7C2×#103×C59C211yesmaximal, characteristic, complemented
8C22×C4×D59C2211yescharacteristic
9C22×C59⋊C8C2211yescharacteristic
10#14273703—22no—
11#14273703C414yescomplemented
12#14273685—22no—
13#14273685—22no—
14C2×C4⋊Dic59C2211yescharacteristic
15C2×C4⋊Dic59C2211yescharacteristic
16C2×Dic59⋊C4—21no—
17C2×(C2×D59)⋊C4—21no—
18C2×(C2×D59)⋊C4—21no—
19C2×C4×Dic59—21no—
20#14273651—22no—
21(C2×D59)⋊C8—22no—
22C22×Q8×C59C2211yescharacteristic
23C22×C8×C59C2211yescharacteristic
24C2×C4⋊C4×C59C2211yescharacteristic
25#103×C59—22no—
26C23×D59D411yescharacteristic
27C2×Q8×C59—21no—
28C2×Q8×C59—21no—
29C2×Q8×C59—21no—
30C2×Q8×C59—21no—
31C2×Q8×C59—21no—
32C2×Q8×C59C2×C412yes—
33C22×C4×C59—21no—
34C22×C4×C59—21no—
35C22×C4×C59C2311yescharacteristic
36C22×Dic59—21no—
37C22×Dic59—21no—
38C22×Dic59D411yescharacteristic
39C2×C4×D59—21no—
40C2×C4×D59—21no—
41C2×C4×D59—21no—
42C2×C4×D59—21no—
43C2×C4×D59C2×C412yes—
44C2×C4×D59D412yes—
45C2×C8×C59—21no—
46C2×C8×C59—21no—
47C2×C8×C59—21no—
48C4⋊C4×C59—21no—
49C4⋊C4×C59D412yes—
50(C2×D59)⋊C4—24no—
51(C2×D59)⋊C4—24no—
52C4⋊Dic59—21no—
53C4⋊Dic59—21no—
54C4⋊Dic59C2×C412yes—
55C4⋊Dic59D412yes—
56Dic59⋊C4—24no—
57C4×Dic59—24no—
58C2×C59⋊C8—21no—
59C2×C59⋊C8—21no—
60C2×C59⋊C8—21no—
61C23×C59C2×D411yescharacteristic
62C22×D59—21no—
63C22×D59—21no—
64C22×D59—21no—
65C22×D59—21no—
66C22×D59—21no—
67C22×D59—21no—
68C22×D59C22⋊C412yes—
69Q8×C59—22no—
70Q8×C59—22no—
71Q8×C59—41no—
72Q8×C59—41no—
73C2×C4×C59—22no—
74C2×C4×C59—22no—
75C2×C4×C59—41no—
76C2×C4×C59—41no—
77C2×C4×C59—41no—
78C2×C4×C59—41no—
79C2×C4×C59C22×C411yescharacteristic
80C2×C4×C59C2×D411yescharacteristic
81C2×C4×C59C2×D411yescharacteristic
82C2×C4×C59C2×D411yescharacteristic
83C2×C4×C59#4111yescharacteristic
84C2×C4×C59#4111yescharacteristic
85C2×Dic59—21no—
86C2×Dic59—21no—
87C2×Dic59—22no—
88C2×Dic59—22no—
89C2×Dic59—41no—
90C2×Dic59—41no—
91C2×Dic59—41no—
92C2×Dic59—41no—
93C2×Dic59C22⋊C412yes—
94C4×D59—22no—
95C4×D59—22no—
96C4×D59—22no—
97C4×D59—22no—
98C8×C59—41no—
99C59⋊C8—41no—
100C22×C59C2×C22⋊C411yescharacteristic
101C22×C59#12011yescharacteristic
102C22×C59#12311yescharacteristic
103C22×C59#13511yescharacteristic
104C22×C59#13511yescharacteristic
105C22×C59#13711yescharacteristic
106C22×C59#13711yescharacteristic
107C2×D59—22no—
108C2×D59—22no—
109C2×D59—22no—
110C2×D59—41no—
111C2×D59—41no—
112C2×D59—41no—
113C2×D59—41no—
114C4×C59—42no—
115C4×C59—42no—
116C4×C59C4×D411yescharacteristic
117C4×C59C4×D411yescharacteristic
118C4×C59#12111yescharacteristic
119C4×C59#12111yescharacteristic
120Dic59—22no—
121Dic59—42no—
122Dic59—42no—
123#1873—591nomaximal, Sylow
124C2×C59#38611yescharacteristic
125C2×C59#41611yescharacteristic
126C2×C59#41911yescharacteristic
127C2×C59#45211yescharacteristic
128C2×C59#45211yescharacteristic
129C2×C59#48511yescharacteristic
130C2×C59#48511yescharacteristic
131D59—42no—
132C2×C22⋊Q8—591no—
133C2×#117—591no—
134C2×#103—591no—
135C2×#103D5911yescharacteristic, complemented
136C2×C22⋊C8—591no—
137#340—591no—
138#340—591no—
139C59#187311yescharacteristic, complemented, Sylow
140C22×Q8C2×D5911yescharacteristic
141C23×C4—591no—
142C22×C8—591no—
143C22×C8C2×D5911yescharacteristic
144C22⋊Q8—594no—
145C22⋊Q8—1182no—
146#117—1182no—
147#117—1182no—
148C2×C4⋊C4—591no—
149C2×C4⋊C4—591no—
150C2×C4⋊C4—1181no—
151C2×C4⋊C4C2×D5911yescharacteristic
152C2×C22⋊C4—1181no—
153C2×C22⋊C4—1181no—
154C2×C42—1181no—
155#103—22no—
156#103—1182no—
157C22⋊C8—1182no—
158C24—591no—
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8—21no—
162C2×Q8—21no—
163C2×Q8—21no—
164C2×Q8C4×D5912yes—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—591no—
168C22×C4—592no—
169C22×C4—592no—
170C22×C4—1181no—
171C22×C4—1181no—
172C22×C4—1181no—
173C22×C4—1181no—
174C22×C4—1181no—
175C22×C4—1181no—
176C22×C4C22×D5911yescharacteristic
177C2×C8—21no—
178C2×C8—21no—
179C2×C8—21no—
180C2×C8—1181no—
181C2×C8—1181no—
182C2×C8—1181no—
183C4⋊C4—21no—
184C4⋊C4—592no—
185C4⋊C4—592no—
186C4⋊C4—1184no—
187C4⋊C4—1181no—
188C4⋊C4—1181no—
189C4⋊C4C22⋊D5912yes—
190C22⋊C4—1184no—
191C22⋊C4—1184no—
192C42—1184no—
193C23—592no—
194C23—1181no—
195C23—1181no—
196C23—1181no—
197C23—1181no—
198C23—1181no—
199C23—1181no—
200C23D4×D5911yescharacteristic
201Q8—22no—
202Q8—22no—
203Q8—41no—
204Q8—41no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—592no—
212C2×C4—1181no—
213C2×C4—1181no—
214C2×C4—1182no—
215C2×C4—1182no—
216C2×C4—1182no—
217C2×C4—1182no—
218C2×C4—1182no—
219C2×C4—1182no—
220C2×C4—2361no—
221C2×C4—2361no—
222C2×C4—2361no—
223C2×C4—2361no—
224C2×C4C2×C4×D5911yescharacteristic
225C2×C4#1174568511yescharacteristic
226C2×C4D4×D5911yescharacteristic
227C2×C4D4×D5911yescharacteristic
228C2×C4#1174568711yescharacteristic
229C2×C4C2×C22⋊D5911yescharacteristic
230C8—41no—
231C8—2361no—
232C22—1182no—
233C22—1182no—
234C22—1182no—
235C22—2361no—
236C22—2361no—
237C22—2361no—
238C22—2361no—
239C22C22⋊C4×D5911yescharacteristic
240C22#1427369511yescharacteristic
241C22#1427370911yescharacteristic
242C22#1427374811yescharacteristic
243C22#1427375011yescharacteristic
244C22#1427375611yescharacteristic
245C22#1427375911yescharacteristic
246C4—42no—
247C4—42no—
248C4—1182no—
249C4—2362no—
250C4—2362no—
251C4(C22⋊D59)⋊C411yescharacteristic
252C4C4×C22⋊D5911yescharacteristic
253C4#1427369811yescharacteristic
254C4#1427370011yescharacteristic
255C2—2362no—
256C2#1683727811yescharacteristic
257C2#1683739711yescharacteristic
258C2#1683740911yescharacteristic
259C2#1683756111yescharacteristic
260C2#1683756311yescharacteristic
261C2#1683774111yescharacteristic
262C2#1683774211yescharacteristic
subgroupG/H
centerC23D4×D59
commutatorC2×C4×C59C22×C4
FrattiniC22×C4C22×D59
FittingC2×#103×C59C2
socleC23×C59C2×D4
hypercenterC2×#103D59
hypocenterC59#1873
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
3. C2×#14273651C2semidirect
5. #16837165C2semidirect
6. #16837164C2semidirect
7. C2×#103×C59C2semidirect
11. #14273703C4semidirect
135. C2×#103D59semidirect
139. C59#1873semidirect