Finite Group Databasebeta

← #21436882

Subgroups — #21436882

Order 7552.

340 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 115 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#16838127C211yesmaximal, characteristic, complemented
2#16838113C211yesmaximal, characteristic
3#16837769C212yesmaximal, complemented
4#16837707C212yesmaximal, complemented
5#16837694C211yesmaximal, characteristic, complemented
6#16837606C212yesmaximal
7#16837604C211yesmaximal, characteristic
8#16837532C211yesmaximal, characteristic, complemented
9#16837505C212yesmaximal
10C4×#11745660C211yesmaximal, characteristic
11C59×#487C211yesmaximal, characteristic, complemented
12C2×#11745660C2211yescharacteristic
13C2×#11745671C2212yes—
14#14273725C2212yes—
15#14273718—21no—
16#14273718C2212yes—
17#14273717—22no—
18#14273707—21no—
19#14273703—22no—
20Q8×Dic59C2212yes—
21C4×Dic118C2211yescharacteristic
22C4×Dic118C2211yescharacteristic
23#14273692—21no—
24C4×D236C2211yescharacteristic
25#14273689C2212yes—
26C4⋊C4×D59—21no—
27#14273660C2212yes—
28#14273659C2211yescharacteristic
29C4⋊(C59⋊C8)C2211yescharacteristic
30Dic59⋊C8C2212yes—
31#14273652C2211yescharacteristic
32#14273651C2212yes—
33#14273650C2212yes—
34#14273649C2211yescharacteristic
35#14273637C2212yes—
36C4⋊Q8×C59C2211yescharacteristic
37C4⋊Q8×C59C2211yescharacteristic
38#103×C59C2212yes—
39#103×C59C2212yes—
40C4×C8×C59C2211yescharacteristic
41C2×Q8×C59—21no—
42C2×Q8×C59C2312yes—
43C2×D236C2311yescharacteristic
44C2×C4×D59—21no—
45C2×C4×D59—22no—
46C2×Dic118D411yescharacteristic
47C2×Dic118C2311yescharacteristic
48C2×C8×C59C2311yescharacteristic
49C2×C8×C59C2311yescharacteristic
50C4⋊C4×C59—21no—
51C4⋊C4×C59—21no—
52C4⋊C4×C59—21no—
53C4⋊C4×C59C2312yes—
54C42×C59C2311yescharacteristic
55#11745671—24no—
56(C2×D59)⋊C4—21no—
57(C2×D59)⋊C4—22no—
58C4⋊Dic59—22no—
59C4⋊Dic59—22no—
60C4⋊Dic59D411yescharacteristic
61C4⋊Dic59C2311yescharacteristic
62C4⋊Dic59C2311yescharacteristic
63Dic59⋊C4—21no—
64Dic59⋊C4—22no—
65Dic59⋊C4—22no—
66Dic59⋊C4—22no—
67Dic59⋊C4D412yes—
68C4×Dic59—21no—
69C4×Dic59—22no—
70C4×Dic59C2312yes—
71C2×C59⋊C8C2312yes—
72#11745660—22no—
73C22×D59—21no—
74Q8×C59—22no—
75Q8×C59—22no—
76Q8×C59—81no—
77C2×C4×C59—22no—
78C2×C4×C59—22no—
79C2×C4×C59C2×D411yescharacteristic
80C2×C4×C59C2×D411yescharacteristic
81C2×C4×C59C2411yescharacteristic
82C2×Dic59—21no—
83C2×Dic59—21no—
84C2×Dic59—21no—
85C2×Dic59C2×D412yes—
86C2×Dic59C2×D412yes—
87D236—21no—
88D236#4112yes—
89C4×D59—42no—
90C4×D59—82no—
91Dic118—22no—
92Dic118—21no—
93Dic118—21no—
94C8×C59—21no—
95C8×C59—21no—
96C59⋊C8—22no—
97C22×C59C22×D411yescharacteristic
98C2×D59—22no—
99C2×D59—41no—
100C2×D59—41no—
101C4×C59—21no—
102C4×C59—42no—
103C4×C59—42no—
104C4×C59#13712yes—
105C4×C59C2×#4111yescharacteristic
106C4×C592−1+411yescharacteristic
107Dic59—22no—
108Dic59—22no—
109Dic59—41no—
110Dic59—41no—
111Dic59—41no—
112#3372—591nomaximal, Sylow
113C2×C59#54811yescharacteristic
114C2×C59C2×#13711yescharacteristic
115C2×C59#57711yescharacteristic
116D59—42no—
117#557—591no—
118#554—591no—
119#491—592no—
120#487D5911yescharacteristic, complemented
121#479—592no—
122#477—591no—
123#461—591no—
124#461—592no—
125#446—591no—
126#440—592no—
127C4×SD16—591no—
128C59#337211yescharacteristic, complemented, Sylow
129C2×SD16—592no—
130C2×SD16—591no—
131C4⋊Q8—592no—
132C4⋊Q8C2×D5911yescharacteristic
133C4⋊Q8C2×D5911yescharacteristic
134#125—592no—
135#125—1182no—
136#125—1181no—
137C22⋊Q8—1181no—
138C22⋊Q8—1182no—
139C4×Q8—591no—
140C4×Q8—592no—
141C4×Q8—591no—
142C4×Q8—1181no—
143C4×D4—592no—
144C4×D4—591no—
145C2×C4⋊C4—1181no—
146#107—592no—
147#106—591no—
148C4⋊C8—592no—
149C4⋊C8—591no—
150#103—592no—
151#103—591no—
152#103—592no—
153#103C2×D5912yes—
154#103C2×D5912yes—
155#102—591no—
156#97—592no—
157C4×C8C2×D5911yescharacteristic
158C2×Q8—21no—
159C2×Q8—591no—
160C2×Q8—591no—
161C2×Q8C22×D5912yes—
162C2×D4—591no—
163C22×C4—1182no—
164C22×C4—1181no—
165SD16—1182no—
166SD16—1184no—
167C2×C8—592no—
168C2×C8C22×D5911yescharacteristic
169C2×C8C22×D5911yescharacteristic
170C4⋊C4—21no—
171C4⋊C4—21no—
172C4⋊C4—21no—
173C4⋊C4—591no—
174C4⋊C4—592no—
175C4⋊C4—591no—
176C4⋊C4—591no—
177C4⋊C4—1182no—
178C4⋊C4—1182no—
179C4⋊C4—1182no—
180C4⋊C4—1182no—
181C4⋊C4—1182no—
182C4⋊C4—1181no—
183C4⋊C4C22×D5912yes—
184C22⋊C4—1182no—
185C22⋊C4—1181no—
186C42—592no—
187C42—1182no—
188C42—1181no—
189C42C22×D5911yescharacteristic
190C23—1181no—
191Q8—22no—
192Q8—22no—
193Q8—81no—
194Q8—1182no—
195Q8—1181no—
196Q8—1181no—
197D4—592no—
198D4—1181no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—592no—
202C2×C4—592no—
203C2×C4—1181no—
204C2×C4—1181no—
205C2×C4—1181no—
206C2×C4—4722no—
207C2×C4—2362no—
208C2×C4D4×D5911yescharacteristic
209C2×C4D4×D5911yescharacteristic
210C2×C4C23×D5911yescharacteristic
211C8—21no—
212C8—21no—
213C8—1182no—
214C22—1182no—
215C22—2361no—
216C22—2361no—
217C22C2×D4×D5911yescharacteristic
218C4—21no—
219C4—42no—
220C4—42no—
221C4—1182no—
222C4—1182no—
223C4—2361no—
224C4—2361no—
225C4—2361no—
226C4#1427375912yes—
227C4#41×D5911yescharacteristic
228C4#1427377411yescharacteristic
229C2—2362no—
230C2#1683806011yescharacteristic
231C2C2×#1427375911yescharacteristic
232C2#1683820811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#487C2
socleC22×C59C22×D4
hypercenter#487D59
hypocenterC59#3372
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. #16838127C2semidirect
3. #16837769C2semidirect
4. #16837707C2semidirect
5. #16837694C2semidirect
8. #16837532C2semidirect
11. C59×#487C2semidirect
120. #487D59semidirect
128. C59#3372semidirect