Finite Group Databasebeta

← #21422545

Subgroups — #21422545

Order 7552.

276 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 75 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#16837949C211yesmaximal, characteristic
2#16837424C211yesmaximal, characteristic, complemented
3C4×C8×D59C211yesmaximal, characteristic, complemented
4#16837131C211yesmaximal, characteristic, complemented
5D4⋊(C59⋊C8)C211yesmaximal, characteristic, complemented
6#16837129C211yesmaximal, characteristic, complemented
7C59×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#11745685—21no—
9C2×#11745659—21no—
10C2×C8×D59—21no—
11#14273726C411yescharacteristic
12#14273723C411yescharacteristic
13#14273713—21no—
14#14273702C411yescharacteristic
15#14273700—21no—
16#14273698C411yescharacteristic
17C4×D236C2211yescharacteristic
18C4×C22⋊D59—21no—
19C42×D59C2211yescharacteristic
20C4⋊(C59⋊C8)C2211yescharacteristic
21Dic59⋊C8—21no—
22C4×C59⋊C8C2211yescharacteristic
23C8×Dic59—21no—
24C4×D4×C59C2211yescharacteristic
25C4⋊C8×C59C2211yescharacteristic
26C4×C8×C59C2211yescharacteristic
27C2×D4×C59C2×C411yescharacteristic
28C22×C4×C59—21no—
29C2×C22⋊D59—21no—
30C2×C22⋊D59—21no—
31C2×C22⋊D59—21no—
32#11745685—42no—
33#11745685—42no—
34C2×D236—21no—
35C2×D236C2×C411yescharacteristic
36C2×C4×D59—21no—
37C2×C4×D59C2×C411yescharacteristic
38C2×C4×D59D411yescharacteristic
39C2×C4×D59D411yescharacteristic
40C2×Dic118—21no—
41C2×C8×C59—21no—
42C2×C8×C59—21no—
43C4⋊C4×C59C2×C411yescharacteristic
44C22⋊C4×C59—21no—
45C42×C59C2311yescharacteristic
46C22⋊Dic59—21no—
47(C2×D59)⋊C4—21no—
48(C2×D59)⋊C4—21no—
49C4⋊Dic59C2×C411yescharacteristic
50Dic59⋊C4—21no—
51C4×Dic59C2×C411yescharacteristic
52C4×Dic59D411yescharacteristic
53C4×Dic59D411yescharacteristic
54C2×C59⋊C8—21no—
55C2×C59⋊C8—21no—
56#11745659—42no—
57C8×D59—24no—
58C23×C59—21no—
59C22×D59—21no—
60C22×D59C22⋊C411yescharacteristic
61D4×C59—21no—
62D4×C59—21no—
63C2×C4×C59—21no—
64C2×C4×C59—41no—
65C2×C4×C59—41no—
66C2×C4×C59C22×C411yescharacteristic
67C2×C4×C59C2×D411yescharacteristic
68C2×C4×C59C2×D411yescharacteristic
69C22⋊D59—42no—
70C22⋊D59—42no—
71C22⋊D59—42no—
72C2×Dic59—21no—
73C2×Dic59C22⋊C411yescharacteristic
74C2×Dic59C22⋊C411yescharacteristic
75C2×Dic59C22⋊C411yescharacteristic
76D236—21no—
77D236—21no—
78D236—42no—
79C4×D59—21no—
80C4×D59—21no—
81C4×D59—22no—
82C4×D59—41no—
83C4×D59—41no—
84C4×D59D812yes—
85C4×D59SD1612yes—
86Dic118—42no—
87C8×C59—22no—
88C8×C59—41no—
89C59⋊C8—22no—
90C59⋊C8—41no—
91C22×C59—41no—
92C22×C59—41no—
93C22×C59—41no—
94C22×C59C2×C22⋊C411yescharacteristic
95C2×D59—21no—
96C2×D59—21no—
97C2×D59—41no—
98C2×D59—41no—
99C2×D59—41no—
100C2×D59#10212yes—
101C4×C59—21no—
102C4×C59—41no—
103C4×C59#13111yescharacteristic
104C4×C59#13111yescharacteristic
105C4×C59C2×D811yescharacteristic
106C4×C59C2×SD1611yescharacteristic
107Dic59—21no—
108Dic59—41no—
109Dic59#10212yes—
110Dic59#10412yes—
111#1492—591nomaximal, Sylow
112C2×C59—81no—
113C2×C59#40811yescharacteristic
114C2×C59C2×#10211yescharacteristic
115C2×C59C2×#10411yescharacteristic
116D59—22no—
117D59—81no—
118#532—591no—
119#423—591no—
120C2×C4×C8—591no—
121D4⋊C8—591no—
122D4⋊C8—591no—
123D4⋊C8—591no—
124D4⋊C8D5911yescharacteristic, complemented
125C59#149211yescharacteristic, complemented, Sylow
126C2×#41—1181no—
127C2×M16—1181no—
128C22×C8—1181no—
129C4⋊Q8—591no—
130#127—591no—
131#124—1181no—
132#121—591no—
133#121—591no—
134#121—1181no—
135C4×D4—591no—
136C4×D4—1181no—
137C4×D4C2×D5911yescharacteristic
138C2×C42—591no—
139C4⋊C8—591no—
140C4⋊C8—1181no—
141C4⋊C8C2×D5911yescharacteristic
142C4×C8—591no—
143C4×C8—1181no—
144C4×C8C2×D5911yescharacteristic
145#41—2362no—
146#41—2362no—
147C2×Q8—1181no—
148C2×D4—591no—
149C2×D4—1181no—
150C2×D4—1181no—
151C2×D4—1181no—
152C2×D4—1181no—
153C2×D4C4×D5911yescharacteristic
154C22×C4—21no—
155C22×C4—591no—
156C22×C4—591no—
157C22×C4—591no—
158C22×C4—1181no—
159M16—2362no—
160C2×C8—21no—
161C2×C8—21no—
162C2×C8—1184no—
163C2×C8—1181no—
164C2×C8—1181no—
165C4⋊C4—591no—
166C4⋊C4—1181no—
167C4⋊C4C4×D5911yescharacteristic
168C22⋊C4—21no—
169C22⋊C4—1181no—
170C22⋊C4—1181no—
171C22⋊C4—1181no—
172C42—591no—
173C42—591no—
174C42—591no—
175C42C22×D5911yescharacteristic
176C23—21no—
177C23—591no—
178C23—1181no—
179Q8—2362no—
180D4—21no—
181D4—21no—
182D4—1181no—
183D4—1181no—
184D4—2362no—
185D4—2362no—
186D4—2362no—
187D4—2362no—
188C2×C4—21no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—591no—
192C2×C4—591no—
193C2×C4—592no—
194C2×C4—592no—
195C2×C4—591no—
196C2×C4—1182no—
197C2×C4—1181no—
198C2×C4—1181no—
199C2×C4—1181no—
200C2×C4—2361no—
201C2×C4—2361no—
202C2×C4C2×C4×D5911yescharacteristic
203C2×C4D4×D5911yescharacteristic
204C2×C4D4×D5911yescharacteristic
205C8—22no—
206C8—41no—
207C8—1182no—
208C8—2361no—
209C22—41no—
210C22—41no—
211C22—41no—
212C22—592no—
213C22—1181no—
214C22—1181no—
215C22—2361no—
216C22—2361no—
217C22—2361no—
218C22C22⋊C4×D5911yescharacteristic
219C4—21no—
220C4—41no—
221C4—592no—
222C4—592no—
223C4—1181no—
224C4—2361no—
225C4#1427373311yescharacteristic
226C4#1427373511yescharacteristic
227C4D8×D5911yescharacteristic
228C4SD16×D5911yescharacteristic
229C2—81no—
230C2—1182no—
231C2—4721no—
232C2#1683736711yescharacteristic
233C2#102×D5911yescharacteristic
234C2#104×D5911yescharacteristic
subgroupG/H
centerC2×C4D4×D59
commutatorC2×C4×C59C22×C4
FrattiniC42C22×D59
FittingC59×D4⋊C8C2
socleC22×C59C2×C22⋊C4
hypercenterD4⋊C8D59
hypocenterC59#1492
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #16837424C2semidirect
3. C4×C8×D59C2semidirect
4. #16837131C2semidirect
5. D4⋊(C59⋊C8)C2semidirect
6. #16837129C2semidirect
7. C59×D4⋊C8C2semidirect
124. D4⋊C8D59semidirect
125. C59#1492semidirect