Finite Group Databasebeta

← #21436378

Subgroups — #21436378

Order 7552.

374 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 115 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#16838126C211yesmaximal, characteristic
2#16838067C211yesmaximal, characteristic
3#16837742C212yesmaximal, complemented
4#16837684C211yesmaximal, characteristic, complemented
5#16837659C212yesmaximal, complemented
6#16837609C211yesmaximal, characteristic, complemented
7#16837559C212yesmaximal, complemented
8C4×Dic236C211yesmaximal, characteristic, complemented
9#16837481C211yesmaximal, characteristic
10#16837409C212yesmaximal, complemented
11C59×#487C211yesmaximal, characteristic, complemented
12C2×Q8×D59C2212yes—
13C2×Dic236C2211yescharacteristic
14C2×#11745672C2212yes—
15C2×#11745659C2212yes—
16#14273726—21no—
17#14273722—22no—
18#14273716—21no—
19#14273707C2212yes—
20#14273705—22no—
21#14273703C2212yes—
22Q8×Dic59—21no—
23C4×Dic118C2211yescharacteristic
24C4×Dic118C2211yescharacteristic
25C4×D236C2211yescharacteristic
26#14273689—21no—
27#14273685C2212yes—
28#14273661C2211yescharacteristic
29#14273658C2212yes—
30C4⋊(C59⋊C8)C2211yescharacteristic
31#14273652C2211yescharacteristic
32#14273652C2211yescharacteristic
33#14273651C2212yes—
34#14273650C2212yes—
35(C2×D59)⋊C8C2212yes—
36C4⋊Q8×C59C2211yescharacteristic
37C4⋊Q8×C59C2211yescharacteristic
38#103×C59C2212yes—
39#103×C59C2212yes—
40C4×C8×C59C2211yescharacteristic
41C2×Q8×C59—21no—
42C2×Q8×C59C2312yes—
43Q8×D59—24no—
44Q8×D59—42no—
45C2×D236D411yescharacteristic
46C2×C4×D59—22no—
47C2×C4×D59C2312yes—
48C2×Dic118—22no—
49C2×Dic118C2311yescharacteristic
50C2×Dic118C2311yescharacteristic
51C2×C8×C59C2311yescharacteristic
52C2×C8×C59C2311yescharacteristic
53C4⋊C4×C59—21no—
54C4⋊C4×C59—21no—
55C4⋊C4×C59—21no—
56C4⋊C4×C59C2312yes—
57C42×C59C2311yescharacteristic
58#11745672—42no—
59(C2×D59)⋊C4—22no—
60(C2×D59)⋊C4—22no—
61(C2×D59)⋊C4—22no—
62(C2×D59)⋊C4D412yes—
63C4⋊Dic59—22no—
64C4⋊Dic59D411yescharacteristic
65C4⋊Dic59C2311yescharacteristic
66C4⋊Dic59C2311yescharacteristic
67Dic59⋊C4—21no—
68Dic59⋊C4—21no—
69Dic59⋊C4—22no—
70C4×Dic59—21no—
71C4×Dic59—21no—
72C4×Dic59—22no—
73C2×C59⋊C8C2312yes—
74Dic236—22no—
75#11745659—42no—
76C22×D59C2×D412yes—
77Q8×C59—22no—
78Q8×C59—22no—
79Q8×C59—42no—
80C2×C4×C59—22no—
81C2×C4×C59—22no—
82C2×C4×C59C2×D411yescharacteristic
83C2×C4×C59C2×D411yescharacteristic
84C2×C4×C59C2411yescharacteristic
85C2×Dic59—21no—
86C2×Dic59—21no—
87C2×Dic59—21no—
88C2×Dic59—21no—
89C2×Dic59C2×D412yes—
90D236—22no—
91C4×D59—22no—
92C4×D59—22no—
93C4×D59—44no—
94Dic118—21no—
95Dic118—21no—
96Dic118—21no—
97Dic118—44no—
98Dic118#4112yes—
99C8×C59—21no—
100C8×C59—21no—
101C59⋊C8—22no—
102C22×C59C22×D411yescharacteristic
103C2×D59—22no—
104C2×D59—22no—
105C2×D59—22no—
106C4×C59—21no—
107C4×C59—42no—
108C4×C59—42no—
109C4×C59#13712yes—
110C4×C59C2×#4111yescharacteristic
111C4×C59H(5,𝔽2)11yescharacteristic
112Dic59—22no—
113Dic59—22no—
114Dic59—41no—
115Dic59—41no—
116Dic59—41no—
117#3328—591nomaximal, Sylow
118C2×C59#54611yescharacteristic
119C2×C59C2×#13711yescharacteristic
120C2×C59#57811yescharacteristic
121D59—42no—
122#556—591no—
123D4×Q8—591no—
124#487D5911yescharacteristic, complemented
125#485—592no—
126#475—591no—
127#470—592no—
128#462—591no—
129#451—592no—
130C4×Q16—591no—
131#436—591no—
132#419—592no—
133C59#332811yescharacteristic, complemented, Sylow
134C22×Q8—592no—
135C2×Q16—592no—
136C2×Q16—591no—
137C2×M16—592no—
138C4⋊Q8—1181no—
139C4⋊Q8C2×D5911yescharacteristic
140C4⋊Q8C2×D5911yescharacteristic
141#126—1182no—
142#124—1181no—
143C22⋊Q8—592no—
144C22⋊Q8—592no—
145C22⋊Q8—1182no—
146C4×Q8—591no—
147C4×Q8—591no—
148C4×Q8—1181no—
149C4×D4—591no—
150C4×D4—1181no—
151#117—592no—
152#107—591no—
153#106—592no—
154C4⋊C8—591no—
155#103—592no—
156#103—591no—
157#103—591no—
158#103—592no—
159#103C2×D5912yes—
160#103C2×D5912yes—
161C22⋊C8—592no—
162C4×C8C2×D5911yescharacteristic
163C2×Q8—21no—
164C2×Q8—591no—
165C2×Q8—591no—
166C2×Q8—1182no—
167C2×Q8—1184no—
168C2×Q8—2362no—
169C2×Q8C22×D5912yes—
170C2×D4—591no—
171C22×C4—592no—
172C22×C4—1182no—
173Q16—1182no—
174Q16—2362no—
175M16—2362no—
176C2×C8—592no—
177C2×C8C22×D5911yescharacteristic
178C2×C8C22×D5911yescharacteristic
179C4⋊C4—21no—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—591no—
183C4⋊C4—591no—
184C4⋊C4—591no—
185C4⋊C4—1182no—
186C4⋊C4—1182no—
187C4⋊C4—1181no—
188C4⋊C4—1181no—
189C4⋊C4C22×D5912yes—
190C22⋊C4—592no—
191C22⋊C4—1182no—
192C22⋊C4—1182no—
193C22⋊C4—1182no—
194C42—1182no—
195C42—1181no—
196C42—1181no—
197C42C22×D5911yescharacteristic
198C23—592no—
199Q8—22no—
200Q8—22no—
201Q8—42no—
202Q8—592no—
203Q8—1181no—
204Q8—1181no—
205Q8—1181no—
206Q8—2364no—
207D4—1182no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—592no—
211C2×C4—1181no—
212C2×C4—1182no—
213C2×C4—1182no—
214C2×C4—1181no—
215C2×C4—1181no—
216C2×C4—1181no—
217C2×C4—2364no—
218C2×C4D4×D5911yescharacteristic
219C2×C4D4×D5911yescharacteristic
220C2×C4C23×D5911yescharacteristic
221C8—21no—
222C8—21no—
223C8—1182no—
224C22—1182no—
225C22—1182no—
226C22—1182no—
227C22C2×D4×D5911yescharacteristic
228C4—21no—
229C4—42no—
230C4—42no—
231C4—1182no—
232C4—1182no—
233C4—2361no—
234C4—2361no—
235C4—2361no—
236C4#1427375612yes—
237C4#41×D5911yescharacteristic
238C4#1427377311yescharacteristic
239C2—2362no—
240C2#1683804511yescharacteristic
241C2C2×#1427375611yescharacteristic
242C2#1683821511yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#487C2
socleC22×C59C22×D4
hypercenter#487D59
hypocenterC59#3328
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. #16837742C2semidirect
4. #16837684C2semidirect
5. #16837659C2semidirect
6. #16837609C2semidirect
7. #16837559C2semidirect
8. C4×Dic236C2semidirect
10. #16837409C2semidirect
11. C59×#487C2semidirect
124. #487D59semidirect
133. C59#3328semidirect