Finite Group Databasebeta

← #21433939

Subgroups — #21433939

Order 7552.

362 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 141 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#16838030C211yesmaximal, characteristic
2#16837879C211yesmaximal, characteristic
3#16837710C212yesmaximal, complemented
4#16837710C212yesmaximal, complemented
5#16837698C212yesmaximal, complemented
6#16837688C212yesmaximal, complemented
7#16837444C211yesmaximal, characteristic
8#16837440C211yesmaximal, characteristic
9#16837412C211yesmaximal, characteristic
10C2×#14273652C211yesmaximal, characteristic
11C59×#424C211yesmaximal, characteristic
12C22×Dic118C2211yescharacteristic
13#14273727C2212yes—
14#14273726—21no—
15#14273719C2212yes—
16#14273718—21no—
17#14273704—22no—
18C4×Dic118C2212yes—
19C4×Dic118C2212yes—
20#14273692—21no—
21#14273692—21no—
22#14273686C2211yescharacteristic
23#14273686C2211yescharacteristic
24#14273683—22no—
25C2×C4⋊Dic59C2211yescharacteristic
26#14273661C2211yescharacteristic
27#14273661C2211yescharacteristic
28#14273661C2212yes—
29#14273659C2211yescharacteristic
30#14273659C2212yes—
31#14273659C2211yescharacteristic
32#14273652C2212yes—
33#14273652C2212yes—
34#14273652C2212yes—
35#14273652C2212yes—
36C2×M16×C59C2211yescharacteristic
37C22×C8×C59C2211yescharacteristic
38#117×C59C2211yescharacteristic
39C4⋊C8×C59C2212yes—
40C4⋊C8×C59C2212yes—
41C22×C4×C59C2311yescharacteristic
42C22×Dic59—21no—
43C22×Dic59—21no—
44C2×Dic118—21no—
45C2×Dic118—22no—
46C2×Dic118—22no—
47C2×Dic118Q814yescomplemented
48C2×Dic118C2312yes—
49M16×C59—22no—
50C2×C8×C59—22no—
51C2×C8×C59C2311yescharacteristic
52C2×C8×C59C2311yescharacteristic
53C2×C8×C59C2312yes—
54C4⋊C4×C59D411yescharacteristic
55C4⋊C4×C59D411yescharacteristic
56C22⋊C4×C59D412yes—
57C42×C59C2312yes—
58C22⋊Dic59—21no—
59C22⋊Dic59—21no—
60C4⋊Dic59—21no—
61C4⋊Dic59—22no—
62C4⋊Dic59C2312yes—
63C4⋊Dic59C2311yescharacteristic
64C4⋊Dic59C2311yescharacteristic
65C4⋊Dic59C2311yescharacteristic
66C4⋊Dic59C2311yescharacteristic
67Dic59⋊C4—22no—
68Dic59⋊C4—22no—
69Dic59⋊C4—22no—
70Dic59⋊C4—22no—
71C4×Dic59—22no—
72C4×Dic59—22no—
73C4×Dic59—21no—
74C4×Dic59—21no—
75C23×C59C2×D411yescharacteristic
76C2×C4×C59C2×D412yes—
77C2×C4×C59C2×D412yes—
78C2×C4×C59C2×D411yescharacteristic
79C2×C4×C59C2×Q812yes—
80C2×C4×C59#4112yes—
81C2×C4×C59C2411yescharacteristic
82C2×Dic59—24no—
83C2×Dic59—22no—
84C2×Dic59—21no—
85C2×Dic59—21no—
86C2×Dic59—21no—
87C2×Dic59—21no—
88C2×Dic59—22no—
89C2×Dic59—81no—
90Dic118—24no—
91Dic118—22no—
92Dic118—82no—
93Dic118C2×Q814yes—
94C8×C59—21no—
95C8×C59—21no—
96C8×C59—22no—
97C22×C59—21no—
98C22×C59—21no—
99C22×C59C22⋊Q812yes—
100C22×C59C22×D411yescharacteristic
101C4×C59—22no—
102C4×C59—22no—
103C4×C59C22⋊Q812yes—
104C4×C59C22×Q811yescharacteristic
105C4×C59C2×#4111yescharacteristic
106Dic59—24no—
107Dic59—41no—
108Dic59—42no—
109Dic59—41no—
110Dic59—41no—
111Dic59—41no—
112#3082—591nomaximal, Sylow
113C2×C59—22no—
114C2×C59C2×C22⋊Q811yescharacteristic
115C2×C59#57711yescharacteristic
116C2×C59#57811yescharacteristic
117#544—591no—
118#519—591no—
119#479—592no—
120#479—592no—
121#477—592no—
122#475—592no—
123#428—591no—
124#427—591no—
125#424D5911yescharacteristic
126#419—591no—
127C2×#103—591no—
128C59#308211yescharacteristic, complemented, Sylow
129C22×Q8—591no—
130C2×M16C2×D5911yescharacteristic
131C22×C8C2×D5911yescharacteristic
132C4⋊Q8—592no—
133C4⋊Q8—1181no—
134#125—592no—
135#125—1181no—
136C22⋊Q8—1182no—
137C4×Q8—592no—
138C4×Q8—592no—
139C4×Q8—1181no—
140C4×Q8—1181no—
141#117—591no—
142#117—591no—
143#117—1182no—
144#117C2×D5911yescharacteristic
145C2×C4⋊C4—591no—
146#107—591no—
147#107—591no—
148#107—592no—
149#106—591no—
150#106—591no—
151#106—592no—
152C4⋊C8C2×D5912yes—
153C4⋊C8C2×D5912yes—
154#103—592no—
155#103—592no—
156#103—592no—
157#103—592no—
158C2×Q8—594no—
159C2×Q8—592no—
160C2×Q8—1181no—
161C2×Q8—1182no—
162C2×Q8—1182no—
163C22×C4—1181no—
164C22×C4—1181no—
165C22×C4C22×D5911yescharacteristic
166M16—22no—
167C2×C8—22no—
168C2×C8C22×D5911yescharacteristic
169C2×C8C22×D5912yes—
170C2×C8C22×D5911yescharacteristic
171C4⋊C4—592no—
172C4⋊C4—591no—
173C4⋊C4—591no—
174C4⋊C4—591no—
175C4⋊C4—591no—
176C4⋊C4—1181no—
177C4⋊C4—1182no—
178C4⋊C4—1182no—
179C4⋊C4—1182no—
180C4⋊C4—1182no—
181C4⋊C4—1182no—
182C4⋊C4D23611yescharacteristic
183C4⋊C4D23611yescharacteristic
184C22⋊C4—1181no—
185C22⋊C4—1181no—
186C22⋊C4D23612yes—
187C42—1181no—
188C42—1181no—
189C42—1182no—
190C42—1182no—
191C42C22×D5912yes—
192C23C2×D23611yescharacteristic
193Q8—594no—
194Q8—1184no—
195Q8—1182no—
196Q8—4722no—
197C2×C4—1184no—
198C2×C4—1182no—
199C2×C4—1181no—
200C2×C4—1181no—
201C2×C4—1181no—
202C2×C4—1181no—
203C2×C4—1182no—
204C2×C4—4721no—
205C2×C4C2×D23612yes—
206C2×C4C2×D23612yes—
207C2×C4C2×D23611yescharacteristic
208C2×C4#1174568712yes—
209C2×C4Q8×D5912yes—
210C2×C4C23×D5911yescharacteristic
211C8—21no—
212C8—21no—
213C8—22no—
214C22—21no—
215C22—21no—
216C22#1427370712yes—
217C22C22×D23611yescharacteristic
218C4—22no—
219C4—22no—
220C4—1184no—
221C4—2362no—
222C4—2361no—
223C4—2361no—
224C4—2361no—
225C4—2361no—
226C4#1427370712yes—
227C4C2×Q8×D5911yescharacteristic
228C4C2×#1174568711yescharacteristic
229C2—22no—
230C2C2×#1427370711yescharacteristic
231C2#1683821411yescharacteristic
232C2#1683821911yescharacteristic
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#424C2
socleC22×C59C22×D4
hypercenter#424D59
hypocenterC59#3082
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
3. #16837710C2semidirect
4. #16837710C2semidirect
5. #16837698C2semidirect
6. #16837688C2semidirect
47. C2×Dic118Q8semidirect
128. C59#3082semidirect