Finite Group Databasebeta

← #21424372

Subgroups — #21424372

Order 7552.

270 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C2×#14273735C211yesmaximal, characteristic
2C2×#14273662C211yesmaximal, characteristic, complemented
3#16837429C211yesmaximal, characteristic, complemented
4C2×#14273655C211yesmaximal, characteristic
5#16837396C211yesmaximal, characteristic
6#16837157C211yesmaximal, characteristic, complemented
7C59×#339C211yesmaximal, characteristic, complemented
8C2×#11745685C2211yescharacteristic
9#14273735—22no—
10#14273735—22no—
11C2×#11745664C2211yescharacteristic
12C2×#11745659—21no—
13C22×C59⋊C8C2211yescharacteristic
14C22×C59⋊C8C2211yescharacteristic
15C2×C8×D59—21no—
16#14273662—22no—
17C4⋊(C59⋊C8)—21no—
18C4⋊(C59⋊C8)—21no—
19#14273655—22no—
20#14273650C411yescharacteristic, complemented
21#14273650C411yescharacteristic, complemented
22#14273647C411yescharacteristic, complemented
23#14273647C411yescharacteristic, complemented
24C2×M16×C59C2211yescharacteristic
25#117×C59C2211yescharacteristic
26C2×C42×C59C2211yescharacteristic
27C22×C4×C59—21no—
28C22×C4×C59C2311yescharacteristic
29C2×C22⋊D59—21no—
30#11745685—21no—
31#11745685—21no—
32#11745685D412yes—
33#11745685Q812yes—
34C2×D236C2×C411yescharacteristic
35C2×C4×D59—21no—
36C2×Dic118C2×C411yescharacteristic
37M16×C59—21no—
38M16×C59D412yes—
39C2×C8×C59—21no—
40C4⋊C4×C59C2×C411yescharacteristic
41C4⋊C4×C59C2×C411yescharacteristic
42C22⋊C4×C59—21no—
43C42×C59—21no—
44C42×C59—21no—
45C42×C59—21no—
46#11745664—21no—
47#11745664—21no—
48C2×C59⋊C8—21no—
49C2×C59⋊C8—21no—
50C2×C59⋊C8—21no—
51C2×C59⋊C8—21no—
52C2×C59⋊C8—21no—
53C2×C59⋊C8C2×C411yescharacteristic
54C2×C59⋊C8C2×C411yescharacteristic
55C2×C59⋊C8D411yescharacteristic
56C2×C59⋊C8D411yescharacteristic
57#11745659—24no—
58C8×D59—24no—
59C23×C59#4111yescharacteristic
60C22×D59—21no—
61C2×C4×C59—22no—
62C2×C4×C59—21no—
63C2×C4×C59—21no—
64C2×C4×C59—41no—
65C2×C4×C59—41no—
66C2×C4×C59C22×C411yescharacteristic
67C2×C4×C59C2×D411yescharacteristic
68C2×C4×C59C2×D411yescharacteristic
69C2×C4×C59C2×D411yescharacteristic
70C2×C4×C59C2×Q811yescharacteristic
71C2×C4×C59#4111yescharacteristic
72C22⋊D59—22no—
73C22⋊D59—22no—
74C2×Dic59—21no—
75D236—21no—
76D236C4⋊C412yes—
77C4×D59—22no—
78C4×D59—22no—
79Dic118—21no—
80Dic118C4⋊C412yes—
81C8×C59—22no—
82C59⋊C8—21no—
83C59⋊C8—21no—
84C59⋊C8—21no—
85C59⋊C8—21no—
86C59⋊C8—41no—
87C22×C59—21no—
88C22×C59—21no—
89C22×C59C4×D411yescharacteristic
90C22×C59C22⋊Q811yescharacteristic
91C22×C59#12311yescharacteristic
92C2×D59—22no—
93C2×D59—41no—
94C2×D59—41no—
95C4×C59—42no—
96C4×C59—41no—
97C4×C59—41no—
98C4×C59C2×C4⋊C411yescharacteristic
99C4×C59C4×D411yescharacteristic
100C4×C59#12011yescharacteristic
101C4×C59C22⋊Q811yescharacteristic
102Dic59—22no—
103#1866—591nomaximal, Sylow
104C2×C59—21no—
105C2×C59—21no—
106C2×C59#38511yescharacteristic
107C2×C59#44311yescharacteristic
108C2×C59#44411yescharacteristic
109D59—42no—
110C2×#131—591no—
111C2×#108—591no—
112#424—591no—
113C2×#104—591no—
114#416—591no—
115#339D5911yescharacteristic, complemented
116#336—591no—
117C59#186611yescharacteristic, complemented, Sylow
118C2×#41—591no—
119#131—1182no—
120#131—1182no—
121C2×M16—591no—
122C2×M16—1181no—
123C2×M16C2×D5911yescharacteristic
124C22×C8—591no—
125C22×C8—591no—
126C22×C8—1181no—
127#117C2×D5911yescharacteristic
128C2×C42C2×D5911yescharacteristic
129#108—1182no—
130C4⋊C8—1181no—
131C4⋊C8—1181no—
132#104—1182no—
133#103—591no—
134#103—591no—
135#102—591no—
136#102—591no—
137#41—592no—
138#41—592no—
139#41—1181no—
140#41—1181no—
141C2×Q8—591no—
142C2×D4—591no—
143C2×D4—1181no—
144C22×C4—21no—
145C22×C4—1181no—
146C22×C4C22×D5911yescharacteristic
147M16—21no—
148M16—1184no—
149M16—1181no—
150M16—1181no—
151M16D23612yes—
152C2×C8—21no—
153C2×C8—591no—
154C2×C8—591no—
155C2×C8—591no—
156C2×C8—591no—
157C2×C8—1184no—
158C2×C8—1181no—
159C2×C8—1181no—
160C2×C8—1181no—
161C2×C8—1181no—
162C2×C8—1181no—
163C4⋊C4C4×D5911yescharacteristic
164C4⋊C4C4×D5911yescharacteristic
165C22⋊C4—21no—
166C42—21no—
167C42—21no—
168C42—21no—
169C23—1181no—
170C23#1174568711yescharacteristic
171Q8—592no—
172Q8—1181no—
173D4—592no—
174D4—1182no—
175D4—1182no—
176D4—1181no—
177C2×C4—22no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—1181no—
183C2×C4—1182no—
184C2×C4—1182no—
185C2×C4C2×C4×D5911yescharacteristic
186C2×C4C2×D23611yescharacteristic
187C2×C4#1174568511yescharacteristic
188C2×C4D4×D5911yescharacteristic
189C2×C4D4×D5911yescharacteristic
190C2×C4Q8×D5911yescharacteristic
191C8—22no—
192C8—1181no—
193C8—1181no—
194C8—1181no—
195C8—1181no—
196C8—2361no—
197C22—21no—
198C22—21no—
199C22—1182no—
200C22—2361no—
201C22—2361no—
202C22(C22⋊D59)⋊C411yescharacteristic
203C22#1427370711yescharacteristic
204C22#1427370911yescharacteristic
205C4—42no—
206C4—41no—
207C4—41no—
208C4—1182no—
209C4C4⋊C4×D5911yescharacteristic
210C4C4×D23611yescharacteristic
211C4#1427369711yescharacteristic
212C4#1427370511yescharacteristic
213C2—21no—
214C2—21no—
215C2—2362no—
216C2#1683727611yescharacteristic
217C2#1683751611yescharacteristic
218C2#1683752111yescharacteristic
subgroupG/H
centerC2×C4D4×D59
commutatorC2×C4×C59C22×C4
FrattiniC22×C4C22×D59
FittingC59×#339C2
socleC22×C59C4×D4
hypercenter#339D59
hypocenterC59#1866
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. C2×#14273662C2semidirect
3. #16837429C2semidirect
6. #16837157C2semidirect
7. C59×#339C2semidirect
20. #14273650C4semidirect
21. #14273650C4semidirect
22. #14273647C4semidirect
23. #14273647C4semidirect
115. #339D59semidirect
117. C59#1866semidirect