Finite Group Databasebeta

← #21424294

Subgroups — #21424294

Order 7552.

316 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 99 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
1C2×#14273685C211yesmaximal, characteristic
2C2×#14273660C211yesmaximal, characteristic, complemented
3C2×(C2×D59)⋊C8C211yesmaximal, characteristic
4#16837259C211yesmaximal, characteristic
5#16837165C211yesmaximal, characteristic, complemented
6#16837164C211yesmaximal, characteristic, complemented
7C2×#106×C59C211yesmaximal, characteristic, complemented
8C22×C4×D59C2211yescharacteristic
9C22×C59⋊C8C2211yescharacteristic
10#14273685—22no—
11#14273685—22no—
12C2×C4⋊Dic59C2211yescharacteristic
13C2×C4⋊Dic59C2211yescharacteristic
14C2×(C2×D59)⋊C4—21no—
15C2×(C2×D59)⋊C4—21no—
16C2×C4×Dic59—21no—
17#14273660—22no—
18(C2×D59)⋊C8C414yescomplemented
19C59⋊#95—21no—
20C22×C8×C59C2211yescharacteristic
21C2×C4⋊C4×C59C2211yescharacteristic
22C2×C4⋊C4×C59C2211yescharacteristic
23#106×C59—22no—
24C23×D59D411yescharacteristic
25C22×C4×C59—21no—
26C22×C4×C59—21no—
27C22×C4×C59C2311yescharacteristic
28C22×Dic59—21no—
29C22×Dic59—21no—
30C22×Dic59D411yescharacteristic
31C2×C4×D59—21no—
32C2×C4×D59—21no—
33C2×C4×D59—21no—
34C2×C4×D59—21no—
35C2×C4×D59C2×C412yes—
36C2×C4×D59Q812yes—
37C2×C8×C59—21no—
38C2×C8×C59—21no—
39C2×C8×C59C2×C412yes—
40C4⋊C4×C59—21no—
41C4⋊C4×C59—21no—
42C4⋊C4×C59—21no—
43C4⋊C4×C59D412yes—
44(C2×D59)⋊C4—24no—
45(C2×D59)⋊C4—42no—
46C4⋊Dic59—21no—
47C4⋊Dic59—21no—
48C4⋊Dic59—21no—
49C4⋊Dic59D412yes—
50C4×Dic59—24no—
51C2×C59⋊C8—21no—
52C2×C59⋊C8—21no—
53C2×C59⋊C8C2×C412yes—
54C23×C59C2×D411yescharacteristic
55C22×D59—21no—
56C22×D59—21no—
57C22×D59—21no—
58C22×D59—21no—
59C22×D59—21no—
60C22×D59—21no—
61C22×D59C4⋊C412yes—
62C2×C4×C59—22no—
63C2×C4×C59—41no—
64C2×C4×C59—41no—
65C2×C4×C59—41no—
66C2×C4×C59—41no—
67C2×C4×C59—41no—
68C2×C4×C59C22×C411yescharacteristic
69C2×C4×C59C2×D411yescharacteristic
70C2×C4×C59C2×D411yescharacteristic
71C2×C4×C59C2×Q811yescharacteristic
72C2×C4×C59#4111yescharacteristic
73C2×C4×C59#4111yescharacteristic
74C2×Dic59—21no—
75C2×Dic59—21no—
76C2×Dic59—22no—
77C2×Dic59—41no—
78C2×Dic59—41no—
79C2×Dic59—41no—
80C2×Dic59—41no—
81C2×Dic59—41no—
82C2×Dic59C4⋊C412yes—
83C4×D59—22no—
84C4×D59—22no—
85C4×D59—22no—
86C4×D59—22no—
87C8×C59—22no—
88C59⋊C8—22no—
89C22×C59C2×C4⋊C411yescharacteristic
90C22×C59#12011yescharacteristic
91C22×C59#12311yescharacteristic
92C22×C59#13511yescharacteristic
93C22×C59#13511yescharacteristic
94C22×C59AGL(1,ℤ/8)11yescharacteristic
95C22×C59#13711yescharacteristic
96C2×D59—22no—
97C2×D59—22no—
98C2×D59—22no—
99C2×D59—41no—
100C2×D59—41no—
101C2×D59—41no—
102C2×D59—41no—
103C4×C59—42no—
104C4×C59—81no—
105C4×C59C4×D411yescharacteristic
106C4×C59C4×D411yescharacteristic
107C4×C59C22⋊Q811yescharacteristic
108C4×C59C22⋊Q811yescharacteristic
109Dic59—22no—
110Dic59—42no—
111Dic59—81no—
112#1854—591nomaximal, Sylow
113C2×C59#38511yescharacteristic
114C2×C59#42711yescharacteristic
115C2×C59#42811yescharacteristic
116C2×C59#44911yescharacteristic
117C2×C59#45211yescharacteristic
118C2×C59#48211yescharacteristic
119C2×C59#48511yescharacteristic
120D59—42no—
121C2×#117—591no—
122C2×#107—591no—
123C2×#106D5911yescharacteristic, complemented
124C2×C22⋊C8—591no—
125#380—591no—
126#340—591no—
127#340—591no—
128C59#185411yescharacteristic, complemented, Sylow
129C23×C4—591no—
130C22×C8—591no—
131C22×C8C2×D5911yescharacteristic
132#117—1182no—
133#117—1182no—
134C2×C4⋊C4—591no—
135C2×C4⋊C4—591no—
136C2×C4⋊C4C2×D5911yescharacteristic
137C2×C4⋊C4C2×D5911yescharacteristic
138C2×C22⋊C4—1181no—
139C2×C22⋊C4—1181no—
140C2×C42—1181no—
141#107—1182no—
142#106—22no—
143C22⋊C8—594no—
144#95—1181no—
145C24—591no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—591no—
149C22×C4—592no—
150C22×C4—592no—
151C22×C4—1181no—
152C22×C4—1181no—
153C22×C4—1181no—
154C22×C4—1181no—
155C22×C4—1181no—
156C22×C4—1181no—
157C22×C4C22×D5911yescharacteristic
158C2×C8—21no—
159C2×C8—21no—
160C2×C8—592no—
161C2×C8—1181no—
162C2×C8—1181no—
163C2×C8C4×D5912yes—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—592no—
168C4⋊C4—1181no—
169C4⋊C4—1181no—
170C4⋊C4—1181no—
171C4⋊C4C22⋊D5912yes—
172C22⋊C4—1184no—
173C22⋊C4—2362no—
174C42—1184no—
175C23—592no—
176C23—1181no—
177C23—1181no—
178C23—1181no—
179C23—1181no—
180C23—1181no—
181C23—1181no—
182C23D4×D5911yescharacteristic
183C2×C4—22no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—592no—
190C2×C4—1181no—
191C2×C4—1181no—
192C2×C4—1182no—
193C2×C4—1182no—
194C2×C4—1182no—
195C2×C4—1182no—
196C2×C4—1182no—
197C2×C4—2361no—
198C2×C4—2361no—
199C2×C4—2361no—
200C2×C4—2361no—
201C2×C4—2361no—
202C2×C4C2×C4×D5911yescharacteristic
203C2×C4#1174568511yescharacteristic
204C2×C4D4×D5911yescharacteristic
205C2×C4Q8×D5911yescharacteristic
206C2×C4#1174568911yescharacteristic
207C2×C4C2×C22⋊D5911yescharacteristic
208C8—22no—
209C8—1182no—
210C22—1182no—
211C22—1182no—
212C22—1182no—
213C22—2361no—
214C22—2361no—
215C22—2361no—
216C22—2361no—
217C22C4⋊C4×D5911yescharacteristic
218C22#1427369511yescharacteristic
219C22#1427371211yescharacteristic
220C22#1427374811yescharacteristic
221C22#1427374811yescharacteristic
222C22#1427375411yescharacteristic
223C22#1427375611yescharacteristic
224C4—42no—
225C4—81no—
226C4—1182no—
227C4—4721no—
228C4—2362no—
229C4C4×C22⋊D5911yescharacteristic
230C4#1427368911yescharacteristic
231C4#1427370311yescharacteristic
232C4#1427370511yescharacteristic
233C2—2362no—
234C2#1683727311yescharacteristic
235C2#1683743711yescharacteristic
236C2#1683744111yescharacteristic
237C2#1683754611yescharacteristic
238C2#1683756111yescharacteristic
239C2#1683772811yescharacteristic
240C2#1683774611yescharacteristic
subgroupG/H
centerC23D4×D59
commutatorC2×C4×C59C22×C4
FrattiniC22×C4C22×D59
FittingC2×#106×C59C2
socleC23×C59C2×D4
hypercenterC2×#106D59
hypocenterC59#1854
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
2. C2×#14273660C2semidirect
5. #16837165C2semidirect
6. #16837164C2semidirect
7. C2×#106×C59C2semidirect
18. (C2×D59)⋊C8C4semidirect
123. C2×#106D59semidirect
128. C59#1854semidirect