Finite Group Databasebeta

← #21436487

Subgroups — #21436487

Order 7552.

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

normal subgroups only

This group has 356 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
1#16838113C211yesmaximal, characteristic
2#16838112C211yesmaximal, characteristic
3#16837805C211yesmaximal, characteristic, complemented
4#16837739C212yesmaximal, complemented
5#16837736C212yesmaximal, complemented
6#16837698C211yesmaximal, characteristic, complemented
7#16837642C212yesmaximal, complemented
8C4×#11745672C211yesmaximal, characteristic, complemented
9#16837467C211yesmaximal, characteristic
10#107×D59C212yesmaximal, complemented
11C59×#477C211yesmaximal, characteristic, complemented
12C2×#11745672C2211yescharacteristic
13C2×C8×D59C2212yes—
14#14273727C2211yescharacteristic
15#14273719—21no—
16#14273718—21no—
17#14273707C2212yes—
18#14273705—22no—
19#14273703—22no—
20#14273703C2212yes—
21C4×Dic118C2211yescharacteristic
22C4×D236—21no—
23C4×D236C2211yescharacteristic
24#14273689—21no—
25C4⋊C4×D59C2212yes—
26C4⋊C4×D59C2212yes—
27#14273661C2212yes—
28#14273660C2212yes—
29#14273660C2211yescharacteristic
30#14273660C2212yes—
31#14273652C2212yes—
32#14273651C2211yescharacteristic
33#14273650C2211yescharacteristic
34(C2×D59)⋊C8C2212yes—
35C4×C59⋊C8C2211yescharacteristic
36C4⋊Q8×C59C2211yescharacteristic
37C4×Q8×C59C2211yescharacteristic
38#107×C59C2212yes—
39C4⋊C8×C59C2211yescharacteristic
40#103×C59C2212yes—
41C2×Q8×C59—21no—
42C2×Q8×C59C2311yescharacteristic
43C2×D236D411yescharacteristic
44C2×C4×D59—22no—
45C2×C4×D59—22no—
46C2×C4×D59C2312yes—
47C2×Dic118—21no—
48C2×Dic118C2311yescharacteristic
49C2×C8×C59C2312yes—
50C4⋊C4×C59—21no—
51C4⋊C4×C59—21no—
52C4⋊C4×C59C2312yes—
53C4⋊C4×C59C2311yescharacteristic
54C42×C59—21no—
55C42×C59C2311yescharacteristic
56#11745672—22no—
57(C2×D59)⋊C4—22no—
58(C2×D59)⋊C4—22no—
59(C2×D59)⋊C4D412yes—
60C4⋊Dic59—21no—
61C4⋊Dic59—22no—
62C4⋊Dic59D411yescharacteristic
63C4⋊Dic59C2311yescharacteristic
64C4⋊Dic59C2312yes—
65Dic59⋊C4—21no—
66Dic59⋊C4—22no—
67Dic59⋊C4—22no—
68Dic59⋊C4—22no—
69C4×Dic59—21no—
70C2×C59⋊C8C2311yescharacteristic
71C2×C59⋊C8C2311yescharacteristic
72C8×D59—24no—
73C22×D59C2×D412yes—
74Q8×C59—21no—
75Q8×C59—21no—
76Q8×C59—81no—
77C2×C4×C59—21no—
78C2×C4×C59—21no—
79C2×C4×C59—22no—
80C2×C4×C59C2×D411yescharacteristic
81C2×C4×C59C2×D411yescharacteristic
82C2×C4×C59C2411yescharacteristic
83C2×Dic59—21no—
84C2×Dic59—21no—
85C2×Dic59—22no—
86C2×Dic59C2×D412yes—
87D236Q1614yescomplemented
88C4×D59—22no—
89C4×D59—22no—
90C4×D59—82no—
91C4×D59—82no—
92Dic118—21no—
93Dic118—21no—
94Dic118—81no—
95C8×C59—22no—
96C59⋊C8—21no—
97C59⋊C8#4112yes—
98C22×C59C22×D411yescharacteristic
99C2×D59—22no—
100C2×D59—22no—
101C2×D59C2×Q1614yes—
102C4×C59—21no—
103C4×C59—41no—
104C4×C59—41no—
105C4×C59—42no—
106C4×C59C2×Q1612yes—
107C4×C59C2×#4111yescharacteristic
108C4×C592−1+411yescharacteristic
109Dic59—22no—
110Dic59—41no—
111Dic59—42no—
112Dic59—41no—
113#3338—591nomaximal, Sylow
114C2×C59#54711yescharacteristic
115C2×C59C22×Q1611yescharacteristic
116C2×C59#57611yescharacteristic
117D59—24no—
118#554—591no—
119#554—591no—
120#500—591no—
121#484—592no—
122#484—592no—
123#477—591no—
124#477D5911yescharacteristic, complemented
125#467—592no—
126C4×Q16—591no—
127C8×D4—591no—
128C2×#107—592no—
129C59#333811yescharacteristic, complemented, Sylow
130C2×Q16—591no—
131C22×C8—592no—
132C4⋊Q8—591no—
133C4⋊Q8C2×D5911yescharacteristic
134#125—1181no—
135#125—1181no—
136C22⋊Q8—592no—
137C22⋊Q8—592no—
138C22⋊Q8—1182no—
139C22⋊Q8—1182no—
140C4×Q8—591no—
141C4×Q8C2×D5911yescharacteristic
142C4×D4—591no—
143C4×D4—1181no—
144C4×D4—1181no—
145C2×C4⋊C4—592no—
146C2×C4⋊C4—592no—
147#107—592no—
148#107—591no—
149#107—592no—
150#107—592no—
151#107C2×D5912yes—
152C4⋊C8C2×D5911yescharacteristic
153#103—591no—
154#103—592no—
155#103—591no—
156#103C2×D5912yes—
157C22⋊C8—592no—
158C4×C8—591no—
159C2×Q8—21no—
160C2×Q8—591no—
161C2×Q8—1181no—
162C2×Q8C22×D5911yescharacteristic
163C2×D4—591no—
164C22×C4—592no—
165C22×C4—1182no—
166C22×C4—1182no—
167Q16—1182no—
168C2×C8—591no—
169C2×C8—591no—
170C2×C8—1184no—
171C2×C8C22×D5912yes—
172C4⋊C4—21no—
173C4⋊C4—21no—
174C4⋊C4—591no—
175C4⋊C4—591no—
176C4⋊C4—592no—
177C4⋊C4—1182no—
178C4⋊C4—1182no—
179C4⋊C4—1182no—
180C4⋊C4—1182no—
181C4⋊C4—1181no—
182C4⋊C4—1181no—
183C4⋊C4C22×D5911yescharacteristic
184C4⋊C4C22×D5912yes—
185C22⋊C4—592no—
186C22⋊C4—1182no—
187C22⋊C4—1182no—
188C42—21no—
189C42—1181no—
190C42C22×D5911yescharacteristic
191C23—592no—
192Q8—21no—
193Q8—21no—
194Q8—81no—
195Q8—1181no—
196Q8—1181no—
197Q8—4721no—
198D4—594no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—592no—
203C2×C4—1182no—
204C2×C4—1182no—
205C2×C4—1181no—
206C2×C4—1181no—
207C2×C4—1182no—
208C2×C4—4722no—
209C2×C4—4722no—
210C2×C4D4×D5911yescharacteristic
211C2×C4D4×D5911yescharacteristic
212C2×C4C23×D5911yescharacteristic
213C8—22no—
214C8—592no—
215C8—1181no—
216C22—594no—
217C22—1182no—
218C22—1182no—
219C22C2×D4×D5911yescharacteristic
220C4—21no—
221C4—41no—
222C4—42no—
223C4—41no—
224C4—1182no—
225C4—2361no—
226C4—2362no—
227C4—2361no—
228C4Q16×D5912yes—
229C4#41×D5911yescharacteristic
230C4#1427377511yescharacteristic
231C2—1184no—
232C2#1683805411yescharacteristic
233C2C2×Q16×D5911yescharacteristic
234C2#1683820611yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#477C2
socleC22×C59C22×D4
hypercenter#477D59
hypocenterC59#3338
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
3. #16837805C2semidirect
4. #16837739C2semidirect
5. #16837736C2semidirect
6. #16837698C2semidirect
7. #16837642C2semidirect
8. C4×#11745672C2semidirect
10. #107×D59C2semidirect
11. C59×#477C2semidirect
87. D236Q16semidirect
124. #477D59semidirect
129. C59#3338semidirect