Finite Group Databasebeta

← #21436899

Subgroups — #21436899

Order 7552.

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

normal subgroups only

This group has 326 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#16838131C211yesmaximal, characteristic
2#16837772C212yesmaximal
3#16837754C211yesmaximal, characteristic
4#16837706C212yesmaximal
5#16837684C211yesmaximal, characteristic
6#16837612C211yesmaximal, characteristic
7#16837612C212yesmaximal
8#16837533C211yesmaximal, characteristic
9#16837507C212yesmaximal
10C4×#11745672C211yesmaximal, characteristic
11C59×#557C211yesmaximal, characteristic
12C2×#11745672C2211yescharacteristic
13C2×#11745672C2212yes—
14#14273727C2211yescharacteristic
15#14273727C2212yes—
16#14273718—21no—
17#14273718—22no—
18Q8×Dic59—21no—
19C4×Dic118C2211yescharacteristic
20C4×Dic118C2212yes—
21#14273660C2211yescharacteristic
22#14273658C2212yes—
23C4⋊(C59⋊C8)C2211yescharacteristic
24C4⋊(C59⋊C8)C2212yes—
25#14273651C2211yescharacteristic
26#14273650C2212yes—
27#14273650C2212yes—
28#14273650C2212yes—
29#14273650C2211yescharacteristic
30#14273650C2212yes—
31#14273638C2212yes—
32C4×C59⋊C8C2211yescharacteristic
33C4⋊Q8×C59—21no—
34C4⋊Q8×C59C2211yescharacteristic
35#125×C59—22no—
36#125×C59C2212yes—
37C4×Q8×C59—21no—
38C4×Q8×C59C2211yescharacteristic
39C4×Q8×C59C2212yes—
40C4×Q8×C59C2211yescharacteristic
41C2×Q8×C59—21no—
42C2×Q8×C59D411yescharacteristic
43C2×Q8×C59C2311yescharacteristic
44C2×Dic118C2311yescharacteristic
45C2×Dic118C2312yes—
46C4⋊C4×C59—22no—
47C4⋊C4×C59—21no—
48C4⋊C4×C59—22no—
49C4⋊C4×C59—21no—
50C4⋊C4×C59—22no—
51C4⋊C4×C59D411yescharacteristic
52C4⋊C4×C59D412yes—
53C4⋊C4×C59C2311yescharacteristic
54C4⋊C4×C59C2312yes—
55C42×C59—22no—
56C42×C59—21no—
57C42×C59C2312yes—
58C42×C59C2311yescharacteristic
59#11745672—22no—
60#11745672—24no—
61C4⋊Dic59—22no—
62C4⋊Dic59—21no—
63C4⋊Dic59—22no—
64C4⋊Dic59—21no—
65C4⋊Dic59C2311yescharacteristic
66Dic59⋊C4—22no—
67Dic59⋊C4—21no—
68C4×Dic59—22no—
69C4×Dic59—21no—
70C2×C59⋊C8C2311yescharacteristic
71C2×C59⋊C8C2311yescharacteristic
72C2×C59⋊C8C2312yes—
73Q8×C59—22no—
74Q8×C59—21no—
75Q8×C59—42no—
76Q8×C59#4112yes—
77C2×C4×C59—21no—
78C2×C4×C59—21no—
79C2×C4×C59—22no—
80C2×C4×C59C2×D412yes—
81C2×C4×C59C2×D412yes—
82C2×C4×C59C2×D411yescharacteristic
83C2×C4×C59C2×D411yescharacteristic
84C2×C4×C59C2411yescharacteristic
85C2×Dic59—21no—
86C2×Dic59—22no—
87C2×Dic59—21no—
88Dic118—21no—
89Dic118—22no—
90Dic118—21no—
91Dic118—22no—
92C59⋊C8—21no—
93C59⋊C8—22no—
94C59⋊C8—21no—
95C22×C59C22×D411yescharacteristic
96C4×C59—22no—
97C4×C59—22no—
98C4×C59—22no—
99C4×C59—21no—
100C4×C59—42no—
101C4×C59—41no—
102C4×C59#13712yes—
103C4×C59C2×#4111yescharacteristic
104C4×C592−1+411yescharacteristic
105Dic59—41no—
106Dic59—42no—
107Dic59—41no—
108#3374—591nomaximal, Sylow
109C2×C59#54811yescharacteristic
110C2×C59C2×#13711yescharacteristic
111C2×C59#57811yescharacteristic
112#557—591no—
113#557D5911yescharacteristic
114#491—592no—
115#487—591no—
116#479—592no—
117#475—591no—
118#462—592no—
119#462—591no—
120#446—591no—
121#441—592no—
122C4×Q16—591no—
123C59#337411yescharacteristic, complemented, Sylow
124C2×Q16—591no—
125C2×Q16—592no—
126C4⋊Q8—21no—
127C4⋊Q8—591no—
128C4⋊Q8—592no—
129C4⋊Q8C2×D5911yescharacteristic
130#125—22no—
131#125—1181no—
132#125—1182no—
133#125C2×D5912yes—
134C4×Q8—21no—
135C4×Q8—591no—
136C4×Q8—592no—
137C4×Q8—1181no—
138C4×Q8C2×D5911yescharacteristic
139C4×Q8C2×D5912yes—
140C4×Q8C2×D5911yescharacteristic
141#107—591no—
142#106—592no—
143C4⋊C8—591no—
144C4⋊C8—592no—
145#103—591no—
146#103—591no—
147#103—592no—
148#103—592no—
149#103—592no—
150#103—592no—
151#97—592no—
152C4×C8—591no—
153C2×Q8—21no—
154C2×Q8—591no—
155C2×Q8—592no—
156C2×Q8C22⋊D5911yescharacteristic
157C2×Q8C22×D5911yescharacteristic
158Q16—1182no—
159Q16—1184no—
160C2×C8—591no—
161C2×C8—591no—
162C2×C8—592no—
163C4⋊C4—22no—
164C4⋊C4—21no—
165C4⋊C4—22no—
166C4⋊C4—21no—
167C4⋊C4—22no—
168C4⋊C4—591no—
169C4⋊C4—1182no—
170C4⋊C4—1181no—
171C4⋊C4—1182no—
172C4⋊C4—1181no—
173C4⋊C4—1182no—
174C4⋊C4—1181no—
175C4⋊C4C22⋊D5911yescharacteristic
176C4⋊C4C22⋊D5912yes—
177C4⋊C4C22×D5912yes—
178C4⋊C4C22×D5911yescharacteristic
179C42—22no—
180C42—21no—
181C42—1182no—
182C42—1181no—
183C42C22×D5911yescharacteristic
184C42C22×D5912yes—
185Q8—22no—
186Q8—21no—
187Q8—42no—
188Q8—1181no—
189Q8—1182no—
190Q8—1181no—
191Q8—1182no—
192Q8#1174568912yes—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—1181no—
197C2×C4—1182no—
198C2×C4—1181no—
199C2×C4C2×C22⋊D5912yes—
200C2×C4C2×C22⋊D5912yes—
201C2×C4C2×C22⋊D5911yescharacteristic
202C2×C4C2×C22⋊D5911yescharacteristic
203C2×C4C23×D5911yescharacteristic
204C8—1181no—
205C8—1182no—
206C8—1181no—
207C22C22×C22⋊D5911yescharacteristic
208C4—22no—
209C4—22no—
210C4—21no—
211C4—22no—
212C4—42no—
213C4—41no—
214C4—2361no—
215C4—2362no—
216C4—2361no—
217C4#1427375712yes—
218C4C2×#1174568911yescharacteristic
219C4#1427377511yescharacteristic
220C2#1683806311yescharacteristic
221C2C2×#1427375711yescharacteristic
222C2#1683821711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#557C2
socleC22×C59C22×D4
hypercenter#557D59
hypocenterC59#3374
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #557

Complements

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

NH ≅ G/Ntype
123. C59#3374semidirect