Finite Group Databasebeta

← #21436897

Subgroups — #21436897

Order 7552.

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

normal subgroups only

This group has 326 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#16838131C211yesmaximal, characteristic
2#16838130C211yesmaximal, characteristic
3#16837769C212yesmaximal
4#16837753C211yesmaximal, characteristic
5#16837708C212yesmaximal
6#16837687C211yesmaximal, characteristic
7#16837612C211yesmaximal, characteristic
8#16837610C212yesmaximal
9#16837532C211yesmaximal, characteristic
10#16837506C212yesmaximal
11C4×Q16×C59C211yesmaximal, characteristic
12C2×#11745672C2212yes—
13#14273727—21no—
14#14273727C2211yescharacteristic
15#14273727C2211yescharacteristic
16#14273725C2212yes—
17#14273719—21no—
18#14273718—22no—
19#14273718C2212yes—
20#14273717—22no—
21Q8×Dic59C2212yes—
22C4×Dic118—21no—
23C4×Dic118—21no—
24C4×Dic118C2211yescharacteristic
25#14273692C2212yes—
26#14273658C2212yes—
27C4⋊(C59⋊C8)C2211yescharacteristic
28Dic59⋊C8C2212yes—
29#14273652C2212yes—
30#14273652C2212yes—
31#14273651C2212yes—
32#14273650C2212yes—
33#14273637C2212yes—
34C2×Q16×C59C2211yescharacteristic
35C4×Q8×C59C2211yescharacteristic
36C4×Q8×C59C2211yescharacteristic
37#107×C59C2211yescharacteristic
38#103×C59C2211yescharacteristic
39#103×C59C2211yescharacteristic
40C4×C8×C59C2211yescharacteristic
41C2×Q8×C59C2311yescharacteristic
42C2×Q8×C59C2311yescharacteristic
43C2×Dic118—21no—
44C2×Dic118D411yescharacteristic
45C2×Dic118C2312yes—
46Q16×C59—22no—
47C2×C8×C59C2311yescharacteristic
48C2×C8×C59C2311yescharacteristic
49C4⋊C4×C59—21no—
50C4⋊C4×C59—21no—
51C4⋊C4×C59C2311yescharacteristic
52C4⋊C4×C59C2311yescharacteristic
53C42×C59—21no—
54C42×C59—21no—
55C42×C59C2311yescharacteristic
56#11745672—24no—
57C4⋊Dic59—21no—
58C4⋊Dic59—21no—
59C4⋊Dic59—21no—
60C4⋊Dic59—22no—
61C4⋊Dic59—22no—
62C4⋊Dic59D411yescharacteristic
63C4⋊Dic59C2312yes—
64Dic59⋊C4—22no—
65Dic59⋊C4—22no—
66Dic59⋊C4—22no—
67Dic59⋊C4—22no—
68Dic59⋊C4D412yes—
69C4×Dic59—22no—
70C4×Dic59—22no—
71C4×Dic59C2312yes—
72C2×C59⋊C8C2312yes—
73Q8×C59—21no—
74Q8×C59—21no—
75Q8×C59—21no—
76Q8×C59#4112yes—
77C2×C4×C59—21no—
78C2×C4×C59—21no—
79C2×C4×C59—21no—
80C2×C4×C59—21no—
81C2×C4×C59C2×D411yescharacteristic
82C2×C4×C59C2×D411yescharacteristic
83C2×C4×C59C2411yescharacteristic
84C2×Dic59—22no—
85C2×Dic59—22no—
86C2×Dic59C2×D412yes—
87C2×Dic59C2×D412yes—
88Dic118—22no—
89Dic118—22no—
90Dic118—22no—
91Dic118—42no—
92C8×C59—21no—
93C8×C59—21no—
94C59⋊C8—22no—
95C22×C59C22×D411yescharacteristic
96C4×C59—22no—
97C4×C59—21no—
98C4×C59—41no—
99C4×C59—41no—
100C4×C59—41no—
101C4×C59#13712yes—
102C4×C59C2×#4111yescharacteristic
103C4×C592−1+411yescharacteristic
104Dic59—22no—
105Dic59—22no—
106Dic59—42no—
107Dic59—42no—
108#3374—591nomaximal, Sylow
109C2×C59#54811yescharacteristic
110C2×C59C2×#13711yescharacteristic
111C2×C59#57811yescharacteristic
112#557—591no—
113#557—591no—
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×Q16D5911yescharacteristic
123C59#337411yescharacteristic, complemented, Sylow
124C2×Q16—592no—
125C2×Q16C2×D5911yescharacteristic
126C4⋊Q8—592no—
127C4⋊Q8—591no—
128C4⋊Q8—591no—
129C4⋊Q8—1181no—
130#125—592no—
131#125—1181no—
132#125—1182no—
133#125—1182no—
134C4×Q8—591no—
135C4×Q8—592no—
136C4×Q8—592no—
137C4×Q8—1181no—
138C4×Q8—1181no—
139C4×Q8C2×D5911yescharacteristic
140C4×Q8C2×D5911yescharacteristic
141#107C2×D5911yescharacteristic
142#106—592no—
143C4⋊C8—592no—
144C4⋊C8—591no—
145#103—592no—
146#103—592no—
147#103—592no—
148#103—592no—
149#103C2×D5911yescharacteristic
150#103C2×D5911yescharacteristic
151#97—592no—
152C4×C8C2×D5911yescharacteristic
153C2×Q8—591no—
154C2×Q8—592no—
155C2×Q8—1181no—
156C2×Q8C22×D5911yescharacteristic
157C2×Q8C22×D5911yescharacteristic
158Q16—22no—
159Q16—1184no—
160C2×C8—592no—
161C2×C8C22×D5911yescharacteristic
162C2×C8C22×D5911yescharacteristic
163C4⋊C4—21no—
164C4⋊C4—21no—
165C4⋊C4—591no—
166C4⋊C4—592no—
167C4⋊C4—592no—
168C4⋊C4—1182no—
169C4⋊C4—1182no—
170C4⋊C4—1182no—
171C4⋊C4—1182no—
172C4⋊C4—1182no—
173C4⋊C4—1182no—
174C4⋊C4—1181no—
175C4⋊C4—1181no—
176C4⋊C4—1181no—
177C4⋊C4C22×D5911yescharacteristic
178C4⋊C4C22×D5911yescharacteristic
179C42—21no—
180C42—21no—
181C42—592no—
182C42—1182no—
183C42—1182no—
184C42C22×D5911yescharacteristic
185Q8—21no—
186Q8—21no—
187Q8—21no—
188Q8—1182no—
189Q8—1182no—
190Q8—1182no—
191Q8—2362no—
192Q8#1174568512yes—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—592no—
198C2×C4—592no—
199C2×C4—1182no—
200C2×C4—1182no—
201C2×C4D4×D5911yescharacteristic
202C2×C4D4×D5911yescharacteristic
203C2×C4C23×D5911yescharacteristic
204C8—21no—
205C8—21no—
206C8—1182no—
207C22C2×D4×D5911yescharacteristic
208C4—21no—
209C4—22no—
210C4—41no—
211C4—41no—
212C4—41no—
213C4—1182no—
214C4—1182no—
215C4—2362no—
216C4—2362no—
217C4#1427375912yes—
218C4C2×#1174568511yescharacteristic
219C4#1427377411yescharacteristic
220C2#1683806111yescharacteristic
221C2C2×#1427375911yescharacteristic
222C2#1683821611yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC4×Q16×C59C2
socleC22×C59C22×D4
hypercenterC4×Q16D59
hypocenterC59#3374
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
123. C59#3374semidirect