Finite Group Databasebeta

← #21436975

Subgroups — #21436975

Order 7552.

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

normal subgroups only

This group has 338 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#16838127C211yesmaximal, characteristic, complemented
2#16838109C211yesmaximal, characteristic
3#16837803C212yesmaximal, complemented
4#16837798C211yesmaximal, characteristic, complemented
5#16837708C212yesmaximal, complemented
6#16837700C212yesmaximal
7#16837698C211yesmaximal, characteristic, complemented
8#16837526C211yesmaximal, characteristic, complemented
9#16837493C212yesmaximal
10C4×#11745670C211yesmaximal, characteristic
11C59×#474C211yesmaximal, characteristic
12C2×#11745670C2211yescharacteristic
13#14273727C2211yescharacteristic
14#14273725—21no—
15#14273718C2212yes—
16#14273718C2212yes—
17#14273717—22no—
18#14273706—21no—
19#14273704—22no—
20Q8×Dic59—21no—
21C4×Dic118C2211yescharacteristic
22C4×Dic118C2211yescharacteristic
23#14273692C2212yes—
24D4×Dic59C2212yes—
25C2×C4⋊Dic59—21no—
26#14273661C2212yes—
27#14273658C2212yes—
28#14273658C2211yescharacteristic
29#14273658C2212yes—
30Dic59⋊C8C2212yes—
31#14273652C2212yes—
32#14273650C2211yescharacteristic
33#14273648C2211yescharacteristic
34C4×C59⋊C8C2211yescharacteristic
35C8×Dic59C2212yes—
36C4⋊Q8×C59C2211yescharacteristic
37C4×D4×C59C2211yescharacteristic
38#107×C59C2212yes—
39C4⋊C8×C59C2211yescharacteristic
40#102×C59C2212yes—
41C2×Q8×C59—21no—
42C2×D4×C59C2311yescharacteristic
43C22×C4×C59—21no—
44C22×Dic59—22no—
45C2×Dic118—21no—
46C2×Dic118D411yescharacteristic
47C2×Dic118C2311yescharacteristic
48C2×C8×C59C2312yes—
49C4⋊C4×C59—21no—
50C4⋊C4×C59C2312yes—
51C4⋊C4×C59C2311yescharacteristic
52C22⋊C4×C59—21no—
53C42×C59C2311yescharacteristic
54C22⋊Dic59—22no—
55#11745670Q814yescomplemented
56C4⋊Dic59—21no—
57C4⋊Dic59—22no—
58C4⋊Dic59—22no—
59C4⋊Dic59D411yescharacteristic
60C4⋊Dic59C2311yescharacteristic
61C4⋊Dic59C2312yes—
62Dic59⋊C4—21no—
63Dic59⋊C4—22no—
64Dic59⋊C4—22no—
65Dic59⋊C4—22no—
66Dic59⋊C4D412yes—
67C4×Dic59—21no—
68C4×Dic59—22no—
69C4×Dic59C2312yes—
70C2×C59⋊C8C2311yescharacteristic
71C2×C59⋊C8C2311yescharacteristic
72C23×C59—21no—
73Q8×C59—42no—
74D4×C59—21no—
75D4×C59C2×Q812yes—
76C2×C4×C59—22no—
77C2×C4×C59—21no—
78C2×C4×C59—42no—
79C2×C4×C59C2×D411yescharacteristic
80C2×C4×C59C2×D411yescharacteristic
81C2×C4×C59C2411yescharacteristic
82C2×Dic59—21no—
83C2×Dic59—21no—
84C2×Dic59—22no—
85C2×Dic59—82no—
86C2×Dic59C2×D412yes—
87C2×Dic59C2×D412yes—
88Dic118—22no—
89Dic118—21no—
90Dic118—81no—
91Dic118C2×Q812yes—
92C8×C59—22no—
93C59⋊C8—21no—
94C59⋊C8C2×Q812yes—
95C22×C59—22no—
96C22×C59—41no—
97C22×C59—41no—
98C22×C59C22×D411yescharacteristic
99C4×C59—21no—
100C4×C59—41no—
101C4×C59—42no—
102C4×C59#13512yes—
103C4×C59C22×Q811yescharacteristic
104C4×C592−1+411yescharacteristic
105Dic59—22no—
106Dic59—22no—
107Dic59—22no—
108Dic59—42no—
109Dic59—41no—
110#3381—591nomaximal, Sylow
111C2×C59—42no—
112C2×C59D4×Q811yescharacteristic
113C2×C59C2×#13511yescharacteristic
114C2×C59#57711yescharacteristic
115#557—591no—
116#554—591no—
117#499—592no—
118#498—591no—
119#479—592no—
120#478—592no—
121#477—591no—
122#474D5911yescharacteristic
123C8×Q8—591no—
124C4×SD16—591no—
125C4×SD16—592no—
126C59#338111yescharacteristic, complemented, Sylow
127C2×SD16—591no—
128C4⋊Q8—591no—
129C4⋊Q8—1181no—
130C4⋊Q8C2×D5911yescharacteristic
131#125—592no—
132#125—592no—
133#125—1182no—
134C22⋊Q8—1182no—
135C22⋊Q8—1181no—
136C4×Q8—591no—
137C4×Q8—592no—
138C4×Q8—591no—
139C4×Q8—1181no—
140C4×D4—592no—
141C4×D4C2×D5911yescharacteristic
142C2×C4⋊C4—1181no—
143#107—592no—
144#107C2×D5912yes—
145#106—592no—
146#106—591no—
147#106—592no—
148C4⋊C8—592no—
149C4⋊C8C2×D5911yescharacteristic
150#103—592no—
151#103—591no—
152#102—591no—
153#102C2×D5912yes—
154C4×C8—592no—
155C4×C8—591no—
156C2×Q8—21no—
157C2×Q8—591no—
158C2×Q8—591no—
159C2×Q8—1181no—
160C2×D4C22×D5911yescharacteristic
161C22×C4—21no—
162C22×C4—1182no—
163SD16—594no—
164C2×C8—591no—
165C2×C8—591no—
166C2×C8C22×D5912yes—
167C4⋊C4—21no—
168C4⋊C4—591no—
169C4⋊C4—592no—
170C4⋊C4—591no—
171C4⋊C4—592no—
172C4⋊C4—1182no—
173C4⋊C4—1182no—
174C4⋊C4—1182no—
175C4⋊C4—1182no—
176C4⋊C4—1182no—
177C4⋊C4—1181no—
178C4⋊C4—1181no—
179C4⋊C4C22×D5912yes—
180C4⋊C4C22×D5911yescharacteristic
181C22⋊C4—21no—
182C22⋊C4—1182no—
183C42—592no—
184C42—1182no—
185C42—1181no—
186C42C22×D5911yescharacteristic
187C23—21no—
188Q8—42no—
189Q8—592no—
190Q8—1182no—
191Q8—1181no—
192Q8—4721no—
193D4—21no—
194D4Q8×D5912yes—
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—42no—
198C2×C4—592no—
199C2×C4—592no—
200C2×C4—1181no—
201C2×C4—1181no—
202C2×C4—1182no—
203C2×C4—4722no—
204C2×C4D4×D5911yescharacteristic
205C2×C4D4×D5911yescharacteristic
206C2×C4C23×D5911yescharacteristic
207C8—22no—
208C8—592no—
209C8—1181no—
210C22—22no—
211C22—41no—
212C22—41no—
213C22C2×D4×D5911yescharacteristic
214C4—21no—
215C4—41no—
216C4—42no—
217C4—1182no—
218C4—1182no—
219C4—1182no—
220C4—2362no—
221C4—2361no—
222C4#1427374612yes—
223C4C2×Q8×D5911yescharacteristic
224C4#1427377411yescharacteristic
225C2—42no—
226C2#1683806511yescharacteristic
227C2C2×#1427374611yescharacteristic
228C2#1683821111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#474C2
socleC22×C59C22×D4
hypercenter#474D59
hypocenterC59#3381
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #16838127C2semidirect
3. #16837803C2semidirect
4. #16837798C2semidirect
5. #16837708C2semidirect
7. #16837698C2semidirect
8. #16837526C2semidirect
55. #11745670Q8semidirect
126. C59#3381semidirect