Finite Group Databasebeta

← #21436838

Subgroups — #21436838

Order 7552.

338 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 123 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
1Q8×Dic118C211yesmaximal, characteristic, complemented
2#16838125C211yesmaximal, characteristic
3#16837762C212yesmaximal
4#16837753C211yesmaximal, characteristic, complemented
5#16837693C211yesmaximal, characteristic
6#16837688C212yesmaximal, complemented
7#16837625C212yesmaximal
8#16837613C211yesmaximal, characteristic, complemented
9#16837510C212yesmaximal, complemented
10C4×#11745660C211yesmaximal, characteristic
11C59×#446C211yesmaximal, characteristic, complemented
12C2×Dic236C2212yes—
13C2×#11745660C2211yescharacteristic
14#14273727C2211yescharacteristic
15#14273727C2212yes—
16#14273727C2211yescharacteristic
17#14273726—21no—
18#14273726—22no—
19#14273722—22no—
20#14273715C2212yes—
21#14273703—21no—
22Q8×Dic59—21no—
23C4×Dic118C2212yes—
24C4×Dic118C2211yescharacteristic
25C4×Dic118C2212yes—
26C4×D236C2211yescharacteristic
27#14273685—21no—
28#14273659C2211yescharacteristic
29#14273659C2212yes—
30#14273652C2212yes—
31#14273652C2212yes—
32#14273652C2211yescharacteristic
33#14273652C2212yes—
34#14273649C2212yes—
35#14273649C2211yescharacteristic
36C4×Q8×C59C2211yescharacteristic
37C4⋊C8×C59C2212yes—
38C4⋊C8×C59C2211yescharacteristic
39#97×C59C2212yes—
40C4×C8×C59C2211yescharacteristic
41C2×Q8×C59D411yescharacteristic
42C2×D236C2311yescharacteristic
43C2×C4×D59—21no—
44C2×Dic118—22no—
45C2×Dic118—21no—
46C2×Dic118C2312yes—
47C2×Dic118C2311yescharacteristic
48C2×C8×C59C2311yescharacteristic
49C2×C8×C59C2311yescharacteristic
50C2×C8×C59C2312yes—
51C4⋊C4×C59D411yescharacteristic
52C4⋊C4×C59D412yes—
53C42×C59C2311yescharacteristic
54C42×C59C2312yes—
55(C2×D59)⋊C4—22no—
56(C2×D59)⋊C4—21no—
57(C2×D59)⋊C4—22no—
58C4⋊Dic59—21no—
59C4⋊Dic59—22no—
60C4⋊Dic59—21no—
61C4⋊Dic59—21no—
62C4⋊Dic59C2312yes—
63C4⋊Dic59C2311yescharacteristic
64C4⋊Dic59C2311yescharacteristic
65Dic59⋊C4—22no—
66Dic59⋊C4—22no—
67Dic59⋊C4—21no—
68C4×Dic59—22no—
69C4×Dic59—22no—
70C4×Dic59—21no—
71Dic236—24no—
72#11745660—22no—
73C22×D59—21no—
74Q8×C59—22no—
75C2×C4×C59C2×D412yes—
76C2×C4×C59C2×D412yes—
77C2×C4×C59C2×D411yescharacteristic
78C2×C4×C59C2×D411yescharacteristic
79C2×C4×C59C2411yescharacteristic
80C2×Dic59—21no—
81C2×Dic59—21no—
82C2×Dic59—22no—
83C2×Dic59—21no—
84C2×Dic59—22no—
85D236—21no—
86D236—21no—
87C4×D59—42no—
88Dic118—21no—
89Dic118—22no—
90Dic118—22no—
91Dic118—82no—
92Dic118—81no—
93Dic118#4112yes—
94C8×C59—21no—
95C8×C59—22no—
96C8×C59—21no—
97C22×C59C22×D411yescharacteristic
98C2×D59—41no—
99C2×D59—41no—
100C2×D59—41no—
101C4×C59—22no—
102C4×C59—22no—
103C4×C59—21no—
104C4×C59#13712yes—
105C4×C59C2×#4111yescharacteristic
106C4×C592−1+411yescharacteristic
107Dic59—22no—
108Dic59—42no—
109Dic59—41no—
110Dic59—41no—
111Dic59—42no—
112#3369—591nomaximal, Sylow
113C2×C59#54811yescharacteristic
114C2×C59C2×#13711yescharacteristic
115C2×C59#57711yescharacteristic
116D59—81no—
117Q82—591no—
118#556—591no—
119#489—592no—
120#487—591no—
121#476—591no—
122#475—592no—
123#464—592no—
124#462—591no—
125#446D5911yescharacteristic, complemented
126#441—592no—
127C4×SD16—591no—
128C59#336911yescharacteristic, complemented, Sylow
129C2×Q16—592no—
130C2×SD16—591no—
131C4⋊Q8—592no—
132C4⋊Q8—591no—
133C4⋊Q8—591no—
134C4⋊Q8—1181no—
135C4⋊Q8—1182no—
136#126—1182no—
137#124—592no—
138C22⋊Q8—1181no—
139C4×Q8—592no—
140C4×Q8—591no—
141C4×Q8—592no—
142C4×Q8—1181no—
143C4×Q8C2×D5911yescharacteristic
144C4×D4—591no—
145#117—1181no—
146#106—591no—
147#106—592no—
148C4⋊C8C2×D5911yescharacteristic
149C4⋊C8C2×D5912yes—
150#103—591no—
151#103—592no—
152#103—592no—
153#103—592no—
154#102—591no—
155#102—592no—
156#97C2×D5912yes—
157C4×C8C2×D5911yescharacteristic
158C2×Q8—591no—
159C2×Q8—592no—
160C2×Q8—1182no—
161C2×Q8—1181no—
162C2×Q8D23611yescharacteristic
163C2×D4—591no—
164C22×C4—1181no—
165Q16—1184no—
166SD16—1182no—
167C2×C8C22×D5911yescharacteristic
168C2×C8C22×D5911yescharacteristic
169C2×C8C22×D5912yes—
170C4⋊C4—591no—
171C4⋊C4—592no—
172C4⋊C4—591no—
173C4⋊C4—1181no—
174C4⋊C4—1182no—
175C4⋊C4—1182no—
176C4⋊C4—1181no—
177C4⋊C4—1182no—
178C4⋊C4—1181no—
179C4⋊C4—1181no—
180C4⋊C4D23611yescharacteristic
181C4⋊C4D23612yes—
182C22⋊C4—1182no—
183C22⋊C4—1181no—
184C22⋊C4—1182no—
185C42—1182no—
186C42—1182no—
187C42—1181no—
188C42C22×D5911yescharacteristic
189C42C22×D5912yes—
190C23—1181no—
191Q8—22no—
192Q8—592no—
193Q8—1181no—
194Q8—1182no—
195Q8—1182no—
196Q8—4722no—
197Q8—4721no—
198D4—1181no—
199D4—1181no—
200C2×C4—1181no—
201C2×C4—1181no—
202C2×C4—1182no—
203C2×C4—1182no—
204C2×C4—1181no—
205C2×C4—2362no—
206C2×C4C2×D23612yes—
207C2×C4C2×D23612yes—
208C2×C4C2×D23611yescharacteristic
209C2×C4C2×D23611yescharacteristic
210C2×C4C23×D5911yescharacteristic
211C8—21no—
212C8—22no—
213C8—21no—
214C22—2361no—
215C22—2361no—
216C22—2361no—
217C22C22×D23611yescharacteristic
218C4—22no—
219C4—22no—
220C4—21no—
221C4—1182no—
222C4—2361no—
223C4—2362no—
224C4—2361no—
225C4—2362no—
226C4#1427376012yes—
227C4#41×D5911yescharacteristic
228C4#1427377511yescharacteristic
229C2—4721no—
230C2#1683806411yescharacteristic
231C2C2×#1427376011yescharacteristic
232C2#1683821411yescharacteristic
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#446C2
socleC22×C59C22×D4
hypercenter#446D59
hypocenterC59#3369
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
1. Q8×Dic118C2semidirect
4. #16837753C2semidirect
6. #16837688C2semidirect
8. #16837613C2semidirect
9. #16837510C2semidirect
11. C59×#446C2semidirect
125. #446D59semidirect
128. C59#3369semidirect