Finite Group Databasebeta

← #21435173

Subgroups — #21435173

Order 7552.

364 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 117 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#16837978C211yesmaximal, characteristic
2#16837794C211yesmaximal, characteristic, complemented
3#16837781C211yesmaximal, characteristic, complemented
4#16837772C211yesmaximal, characteristic, complemented
5#16837759C211yesmaximal, characteristic, complemented
6#16837624C212yesmaximal, complemented
7#16837612C212yesmaximal, complemented
8#16837562C212yesmaximal
9#16837557C212yesmaximal, complemented
10#16837463C211yesmaximal, characteristic, complemented
11C59×#541C211yesmaximal, characteristic, complemented
12C2×#11745685C2211yescharacteristic
13C22×Dic118C2211yescharacteristic
14C2×#11745672C2212yes—
15C2×#11745672C2212yes—
16C2×#11745672C2212yes—
17C2×#11745671C2212yes—
18#14273727C2211yescharacteristic
19#14273727C2211yescharacteristic
20#14273715C2211yescharacteristic
21#14273715C2211yescharacteristic
22#14273711—22no—
23#14273707—22no—
24C4⋊(C59⋊C8)C2212yes—
25#14273650C2212yes—
26#14273650C2212yes—
27#14273650C2212yes—
28#14273647C2212yes—
29C22⋊(C59⋊C8)C2212yes—
30#14273638C2211yescharacteristic
31C4×C59⋊C8C2211yescharacteristic
32C4⋊Q8×C59C2211yescharacteristic
33#126×C59—22no—
34#125×C59—22no—
35#125×C59C2211yescharacteristic
36C22⋊Q8×C59C2212yes—
37C4×Q8×C59C2212yes—
38#117×C59C2211yescharacteristic
39C2×Q8×C59C2312yes—
40C22×C4×C59C2311yescharacteristic
41C2×C22⋊D59—21no—
42C22×Dic59—21no—
43#11745685—42no—
44C2×D236C2311yescharacteristic
45C2×C4×D59—21no—
46C2×Dic118—21no—
47C2×Dic118—42no—
48C2×Dic118C2311yescharacteristic
49C2×Dic118C2311yescharacteristic
50C2×Dic118C2311yescharacteristic
51C4⋊C4×C59—22no—
52C4⋊C4×C59—22no—
53C4⋊C4×C59—22no—
54C4⋊C4×C59—22no—
55C4⋊C4×C59D412yes—
56C4⋊C4×C59C2312yes—
57C22⋊C4×C59—22no—
58C22⋊C4×C59D412yes—
59C42×C59—22no—
60C42×C59C2311yescharacteristic
61C42×C59C2311yescharacteristic
62#11745672—42no—
63#11745672—42no—
64#11745672—42no—
65#11745671—42no—
66(C2×D59)⋊C4—22no—
67(C2×D59)⋊C4—22no—
68C4⋊Dic59—22no—
69C4⋊Dic59—22no—
70C2×C59⋊C8C2312yes—
71C2×C59⋊C8C2312yes—
72C23×C59C2×D411yescharacteristic
73C22×D59—21no—
74Q8×C59—22no—
75Q8×C59—22no—
76C2×C4×C59—22no—
77C2×C4×C59—22no—
78C2×C4×C59—22no—
79C2×C4×C59C2×D412yes—
80C2×C4×C59C2×D412yes—
81C2×C4×C59C2×D411yescharacteristic
82C2×C4×C59C2411yescharacteristic
83C22⋊D59—42no—
84C2×Dic59—21no—
85C2×Dic59—21no—
86C2×Dic59—21no—
87C2×Dic59—42no—
88D236—22no—
89C4×D59—42no—
90Dic118—22no—
91Dic118—22no—
92Dic118—22no—
93Dic118—42no—
94C59⋊C8—22no—
95C59⋊C8—22no—
96C22×C59—21no—
97C22×C59—22no—
98C22×C59C22×D411yescharacteristic
99C2×D59—41no—
100C2×D59—42no—
101C4×C59—21no—
102C4×C59—22no—
103C4×C59—22no—
104C4×C59—42no—
105C4×C59—42no—
106C4×C59H(5,𝔽2)12yes—
107Dic59—41no—
108Dic59—41no—
109Dic59—41no—
110#3223—591nomaximal, Sylow
111C2×C59—41no—
112C2×C59#53511yescharacteristic
113C2×C59#57812yes—
114D59—81no—
115#541D5911yescharacteristic, complemented
116#536—591no—
117#497—591no—
118#494—591no—
119#491—591no—
120#488—591no—
121#464—592no—
122#462—592no—
123#452—592no—
124#451—592no—
125#433—591no—
126C59#322311yescharacteristic, complemented, Sylow
127C2×#41—591no—
128C22×Q8—591no—
129C2×Q16—592no—
130C2×Q16—592no—
131C2×Q16—592no—
132C2×SD16—592no—
133C4⋊Q8—591no—
134C4⋊Q8—591no—
135C4⋊Q8C2×D5911yescharacteristic
136#126—22no—
137#125—22no—
138#125C2×D5911yescharacteristic
139#124—591no—
140#124—591no—
141#123—1182no—
142C22⋊Q8—1182no—
143C22⋊Q8C2×D5912yes—
144C4×Q8C2×D5912yes—
145#117C2×D5911yescharacteristic
146C4⋊C8—592no—
147#103—592no—
148#103—592no—
149#103—592no—
150#102—592no—
151C22⋊C8—592no—
152#97—591no—
153C4×C8—591no—
154#41—2362no—
155C2×Q8—591no—
156C2×Q8—591no—
157C2×Q8—591no—
158C2×Q8—1181no—
159C2×Q8—2362no—
160C2×Q8C22×D5912yes—
161C2×D4—591no—
162C2×D4—1181no—
163C22×C4—1181no—
164C22×C4—1181no—
165C22×C4C22×D5911yescharacteristic
166Q16—2362no—
167Q16—2362no—
168Q16—2362no—
169SD16—2362no—
170C2×C8—592no—
171C2×C8—592no—
172C4⋊C4—22no—
173C4⋊C4—22no—
174C4⋊C4—22no—
175C4⋊C4—22no—
176C4⋊C4—1182no—
177C4⋊C4—1182no—
178C4⋊C4C22⋊D5912yes—
179C4⋊C4C22×D5912yes—
180C22⋊C4—22no—
181C22⋊C4—1182no—
182C22⋊C4—1182no—
183C22⋊C4C22⋊D5912yes—
184C42—22no—
185C42C22×D5911yescharacteristic
186C42C22×D5911yescharacteristic
187C23—1181no—
188C23C2×C22⋊D5911yescharacteristic
189Q8—22no—
190Q8—22no—
191Q8—1182no—
192Q8—1182no—
193Q8—1182no—
194Q8—2362no—
195D4—1182no—
196D4—2362no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—1181no—
201C2×C4—1181no—
202C2×C4—1181no—
203C2×C4—2362no—
204C2×C4—2362no—
205C2×C4C2×C22⋊D5912yes—
206C2×C4C2×C22⋊D5912yes—
207C2×C4C2×C22⋊D5911yescharacteristic
208C2×C4C23×D5911yescharacteristic
209C8—1182no—
210C8—1182no—
211C22—22no—
212C22—21no—
213C22—2362no—
214C22—2361no—
215C22C22×C22⋊D5911yescharacteristic
216C4—22no—
217C4—22no—
218C4—21no—
219C4—42no—
220C4—42no—
221C4—2361no—
222C4—2361no—
223C4—2361no—
224C4#1427377312yes—
225C2—41no—
226C2—4721no—
227C2#1683796611yescharacteristic
228C2#1683821712yes—
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#541C2
socleC22×C59C22×D4
hypercenter#541D59
hypocenterC59#3223
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
2. #16837794C2semidirect
3. #16837781C2semidirect
4. #16837772C2semidirect
5. #16837759C2semidirect
6. #16837624C2semidirect
7. #16837612C2semidirect
9. #16837557C2semidirect
10. #16837463C2semidirect
11. C59×#541C2semidirect
115. #541D59semidirect
126. C59#3223semidirect