Finite Group Databasebeta

← #21425316

Subgroups — #21425316

Order 7552.

278 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 67 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#16837978C211yesmaximal, characteristic
2#16837445C211yesmaximal, characteristic, complemented
3C2×#14273655C211yesmaximal, characteristic
4#16837404C211yesmaximal, characteristic
5C2×#14273645C211yesmaximal, characteristic, complemented
6#16837308C211yesmaximal, characteristic, complemented
7C59×#339C211yesmaximal, characteristic, complemented
8C2×#11745685C2211yescharacteristic
9C22×Dic118C2211yescharacteristic
10C2×#11745664C2211yescharacteristic
11#14273727—21no—
12#14273715—21no—
13#14273711—22no—
14#14273707—21no—
15#14273707—21no—
16C2×C4⋊Dic59C2211yescharacteristic
17#14273660—21no—
18#14273658—21no—
19#14273655—22no—
20#14273652—21no—
21#14273649—21no—
22#14273645—22no—
23C59⋊#95—22no—
24C2×M16×C59C2211yescharacteristic
25#117×C59C2211yescharacteristic
26C2×C42×C59C2211yescharacteristic
27C22×C4×C59—21no—
28C22×C4×C59C2311yescharacteristic
29C2×C22⋊D59—21no—
30C22×Dic59—21no—
31C22×Dic59D412yes—
32#11745685—21no—
33#11745685—21no—
34#11745685—21no—
35#11745685—21no—
36C2×D236D411yescharacteristic
37C2×C4×D59—21no—
38C2×Dic118—21no—
39C2×Dic118—21no—
40C2×Dic118—21no—
41C2×Dic118—21no—
42C2×Dic118—21no—
43C2×Dic118—21no—
44C2×Dic118D411yescharacteristic
45M16×C59—21no—
46M16×C59—21no—
47C2×C8×C59—21no—
48C4⋊C4×C59D411yescharacteristic
49C4⋊C4×C59D411yescharacteristic
50C22⋊C4×C59—21no—
51C42×C59—21no—
52C42×C59—21no—
53C42×C59—21no—
54(C2×D59)⋊C4—22no—
55(C2×D59)⋊C4—22no—
56C4⋊Dic59—22no—
57C4⋊Dic59—22no—
58C4⋊Dic59—21no—
59C4⋊Dic59—21no—
60#11745664—21no—
61#11745664D412yes—
62C2×C59⋊C8—21no—
63C23×C59C2×D411yescharacteristic
64C22×D59—21no—
65C2×C4×C59—22no—
66C2×C4×C59—21no—
67C2×C4×C59—21no—
68C2×C4×C59—41no—
69C2×C4×C59—41no—
70C2×C4×C59C2×D411yescharacteristic
71C2×C4×C59C2×D411yescharacteristic
72C2×C4×C59C2×D411yescharacteristic
73C2×C4×C59#4111yescharacteristic
74C2×C4×C59#4111yescharacteristic
75C2×C4×C59#4111yescharacteristic
76C22⋊D59—41no—
77C22⋊D59—41no—
78C2×Dic59—21no—
79C2×Dic59—22no—
80C2×Dic59—22no—
81C2×Dic59—22no—
82C2×Dic59—42no—
83C2×Dic59—41no—
84D236—21no—
85D236—21no—
86C4×D59—41no—
87C4×D59—41no—
88Dic118—21no—
89Dic118—21no—
90Dic118—41no—
91Dic118—41no—
92Dic118—41no—
93Dic118—41no—
94C8×C59—41no—
95C59⋊C8—22no—
96C22×C59—21no—
97C22×C59—21no—
98C22×C59#12011yescharacteristic
99C22×C59#12111yescharacteristic
100C22×C59#12311yescharacteristic
101C2×D59—41no—
102C2×D59—41no—
103C2×D59—41no—
104C4×C59—42no—
105C4×C59—41no—
106C4×C59—41no—
107C4×C59#12111yescharacteristic
108C4×C59#12111yescharacteristic
109C4×C59#12311yescharacteristic
110C4×C59#12411yescharacteristic
111Dic59—41no—
112Dic59—42no—
113Dic59—81no—
114#2038—591nomaximal, Sylow
115C2×C59—21no—
116C2×C59—21no—
117C2×C59#39411yescharacteristic
118C2×C59#45411yescharacteristic
119C2×C59#45611yescharacteristic
120D59—81no—
121#536—591no—
122#428—591no—
123C2×#104—591no—
124#417—591no—
125C2×#101—591no—
126#391—591no—
127#339D5911yescharacteristic, complemented
128C59#203811yescharacteristic, complemented, Sylow
129C2×#41—591no—
130C22×Q8—591no—
131C2×M16—591no—
132C2×M16C2×D5911yescharacteristic
133C4⋊Q8—1181no—
134#124—1181no—
135#123—1182no—
136C22⋊Q8—1181no—
137C22⋊Q8—1181no—
138#117C2×D5911yescharacteristic
139C2×C4⋊C4—591no—
140C2×C42C2×D5911yescharacteristic
141#107—1181no—
142#106—1181no—
143#104—1182no—
144#103—1181no—
145#102—1181no—
146#101—1182no—
147#95—1182no—
148#41—1181no—
149#41—1181no—
150#41—1181no—
151#41—1181no—
152C2×Q8—591no—
153C2×Q8—1181no—
154C2×Q8—1181no—
155C2×Q8—1181no—
156C2×Q8—1181no—
157C2×Q8—1181no—
158C2×Q8—1181no—
159C2×D4—591no—
160C2×D4—1181no—
161C22×C4—21no—
162C22×C4—592no—
163C22×C4—1181no—
164C22×C4—1181no—
165C22×C4C22×D5911yescharacteristic
166M16—21no—
167M16—21no—
168M16—592no—
169M16—1181no—
170C2×C8—21no—
171C2×C8—1181no—
172C4⋊C4—1182no—
173C4⋊C4—1182no—
174C4⋊C4—1181no—
175C4⋊C4—1181no—
176C4⋊C4D23611yescharacteristic
177C4⋊C4D23611yescharacteristic
178C22⋊C4—21no—
179C22⋊C4—1182no—
180C22⋊C4—1182no—
181C42—21no—
182C42—21no—
183C42—21no—
184C23—1181no—
185C23D4×D5911yescharacteristic
186Q8—1181no—
187Q8—1181no—
188Q8—2361no—
189Q8—2361no—
190Q8—2361no—
191Q8—2361no—
192D4—1181no—
193D4—1181no—
194D4—2361no—
195D4—2361no—
196C2×C4—22no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—1182no—
202C2×C4—1181no—
203C2×C4—1182no—
204C2×C4—1182no—
205C2×C4—2362no—
206C2×C4—2361no—
207C2×C4—2361no—
208C2×C4—2361no—
209C2×C4C2×D23611yescharacteristic
210C2×C4#1174568511yescharacteristic
211C2×C4#1174568511yescharacteristic
212C2×C4D4×D5911yescharacteristic
213C2×C4D4×D5911yescharacteristic
214C2×C4#1174568911yescharacteristic
215C8—41no—
216C8—1182no—
217C22—21no—
218C22—21no—
219C22—2361no—
220C22—2361no—
221C22—2361no—
222C22#1427369711yescharacteristic
223C22#1427370011yescharacteristic
224C22#1427371211yescharacteristic
225C4—42no—
226C4—41no—
227C4—41no—
228C4—4721no—
229C4—2362no—
230C4—2361no—
231C4#1427370011yescharacteristic
232C4#1427370211yescharacteristic
233C4#1427371211yescharacteristic
234C4#1427371511yescharacteristic
235C2—21no—
236C2—21no—
237C2—4721no—
238C2#1683732011yescharacteristic
239C2#1683757611yescharacteristic
240C2#1683758611yescharacteristic
subgroupG/H
centerC22#14273697
commutatorC22×C4×C59C23
FrattiniC22×C4C22×D59
FittingC59×#339C2
socleC22×C59#120
hypercenter#339D59
hypocenterC59#2038
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. #16837445C2semidirect
5. C2×#14273645C2semidirect
6. #16837308C2semidirect
7. C59×#339C2semidirect
127. #339D59semidirect
128. C59#2038semidirect