Finite Group Databasebeta

← C2×#16837745 #21433990

Subgroups — C2×#16837745 #21433990

Order 7552.

416 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14273707C211yesmaximal, characteristic
2C2×#14273685C211yesmaximal, characteristic
3#16837745C218yesmaximal, direct product factor
4C2×#14273658C211yesmaximal, characteristic, complemented
5C2×#14273652C211yesmaximal, characteristic, complemented
6C2×#14273650C211yesmaximal, characteristic, complemented
7C2×(C2×D59)⋊C8C211yesmaximal, characteristic
8C2×#107×C59C211yesmaximal, characteristic, complemented
9C22×Dic118C2211yescharacteristic
10C22×C4×D59C2211yescharacteristic
11C22×C59⋊C8C2211yescharacteristic
12#14273707—22no—
13#14273707C2214yes—
14#14273685—22no—
15#14273685C2214yes—
16C2×C4⋊Dic59—21no—
17C2×C4⋊Dic59C2211yescharacteristic
18C2×(C2×D59)⋊C4—21no—
19C2×(C2×D59)⋊C4—21no—
20C2×C4×Dic59—21no—
21#14273658C2214yescomplemented
22#14273652C2214yescomplemented
23#14273650C2214yescomplemented
24(C2×D59)⋊C8C2214yes—
25C22×C8×C59C2211yescharacteristic
26C2×C4⋊C4×C59C2211yescharacteristic
27C2×C4⋊C4×C59C2211yescharacteristic
28#107×C59C2214yescomplemented
29C23×D59D411yescharacteristic
30C22×C4×C59—21no—
31C22×C4×C59—21no—
32C22×C4×C59C2311yescharacteristic
33C22×Dic59—21no—
34C22×Dic59—21no—
35C22×Dic59D411yescharacteristic
36C2×C4×D59—22no—
37C2×C4×D59—22no—
38C2×C4×D59D412yes—
39C2×C4×D59C2312yes—
40C2×Dic118—22no—
41C2×Dic118—22no—
42C2×Dic118—21no—
43C2×Dic118C2312yes—
44C2×C8×C59—22no—
45C2×C8×C59C2312yes—
46C4⋊C4×C59—21no—
47C4⋊C4×C59—21no—
48C4⋊C4×C59C2312yes—
49C4⋊C4×C59C2312yes—
50(C2×D59)⋊C4—24no—
51(C2×D59)⋊C4—24no—
52C4⋊Dic59—21no—
53C4⋊Dic59—24no—
54C4⋊Dic59C2312yes—
55C4×Dic59—24no—
56C2×C59⋊C8—22no—
57C2×C59⋊C8C2312yes—
58C23×C59C2×D411yescharacteristic
59C22×D59—22no—
60C22×D59—22no—
61C22×D59—22no—
62C22×D59C2×D412yes—
63C2×C4×C59—22no—
64C2×C4×C59—22no—
65C2×C4×C59—42no—
66C2×C4×C59—42no—
67C2×C4×C59C2×D411yescharacteristic
68C2×C4×C59#4112yes—
69C2×C4×C59#4112yes—
70C2×C4×C59C2411yescharacteristic
71C2×Dic59—22no—
72C2×Dic59—22no—
73C2×Dic59—22no—
74C2×Dic59—42no—
75C2×Dic59—42no—
76C2×Dic59C2×D412yes—
77C4×D59—24no—
78C4×D59—22no—
79C4×D59—22no—
80Dic118—22no—
81Dic118—22no—
82Dic118—42no—
83C8×C59—22no—
84C59⋊C8—22no—
85C22×C59#12312yes—
86C22×C59#13512yes—
87C22×C59#13712yes—
88C22×C59C22×D411yescharacteristic
89C2×D59—22no—
90C2×D59—22no—
91C2×D59—22no—
92C2×D59—44no—
93C4×C59—42no—
94C4×C59—42no—
95C4×C59#12312yes—
96C4×C59C2×#4111yescharacteristic
97C4×C59C2×#4111yescharacteristic
98Dic59—22no—
99Dic59—42no—
100Dic59—42no—
101C2×#485—591nomaximal, Sylow
102C2×C59#48514yescomplemented
103C2×C59C2×#12311yescharacteristic
104C2×C59C2×#13511yescharacteristic
105C2×C59C2×#13711yescharacteristic
106D59—42no—
107C2×C22⋊Q8—591no—
108C2×#117—591no—
109#485—598no—
110C2×#107D5911yescharacteristic, complemented
111C2×#106—591no—
112C2×#103—591no—
113C2×#103—591no—
114C2×C22⋊C8—591no—
115C59C2×#48511yescharacteristic, complemented, Sylow
116C22×Q8—591no—
117C23×C4—591no—
118C22×C8—591no—
119C22×C8C2×D5911yescharacteristic
120C22⋊Q8—594no—
121C22⋊Q8—1182no—
122#117—594no—
123#117—1182no—
124C2×C4⋊C4—591no—
125C2×C4⋊C4—1181no—
126C2×C4⋊C4C2×D5911yescharacteristic
127C2×C4⋊C4C2×D5911yescharacteristic
128C2×C22⋊C4—1181no—
129C2×C22⋊C4—1181no—
130C2×C42—1181no—
131#107C2×D5914yescomplemented
132#106—594no—
133#103—594no—
134#103—594no—
135C22⋊C8—594no—
136C24—591no—
137C2×Q8—592no—
138C2×Q8—1181no—
139C2×Q8—1182no—
140C2×Q8—1182no—
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—591no—
144C22×C4—592no—
145C22×C4—592no—
146C22×C4—1182no—
147C22×C4—1182no—
148C22×C4—1181no—
149C22×C4—1181no—
150C22×C4C22×D5911yescharacteristic
151C2×C8—22no—
152C2×C8—592no—
153C2×C8—1182no—
154C2×C8C22×D5912yes—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—592no—
158C4⋊C4—1184no—
159C4⋊C4—1181no—
160C4⋊C4C22×D5912yes—
161C4⋊C4C22×D5912yes—
162C22⋊C4—1184no—
163C22⋊C4—1184no—
164C42—1184no—
165C23—592no—
166C23—1182no—
167C23—1182no—
168C23—1182no—
169C23D4×D5911yescharacteristic
170Q8—1182no—
171Q8—1182no—
172Q8—2362no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—592no—
178C2×C4—1182no—
179C2×C4—1184no—
180C2×C4—1182no—
181C2×C4—1182no—
182C2×C4—1182no—
183C2×C4—1182no—
184C2×C4—2362no—
185C2×C4—2362no—
186C2×C4#1174568512yes—
187C2×C4D4×D5911yescharacteristic
188C2×C4#1174568912yes—
189C2×C4C23×D5911yescharacteristic
190C8—22no—
191C8—1182no—
192C22—1182no—
193C22—1182no—
194C22—1182no—
195C22—2364no—
196C22#1427371212yes—
197C22#1427374612yes—
198C22#1427375912yes—
199C22C2×D4×D5911yescharacteristic
200C4—42no—
201C4—42no—
202C4—1182no—
203C4—2362no—
204C4—2362no—
205C4#1427371212yes—
206C4C2×#1174568511yescharacteristic
207C4C2×#1174568911yescharacteristic
208C2—2362no—
209C2#1683774514yesdirect product factor
210C2C2×#1427371211yescharacteristic
211C2C2×#1427374611yescharacteristic
212C2C2×#1427375911yescharacteristic
subgroupG/H
centerC23D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC2×#107×C59C2
socleC23×C59C2×D4
hypercenterC2×#107D59
hypocenterC59C2×#485
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
3. #16837745C2direct (N × H)
4. C2×#14273658C2semidirect
5. C2×#14273652C2semidirect
6. C2×#14273650C2semidirect
8. C2×#107×C59C2semidirect
21. #14273658C22semidirect
22. #14273652C22semidirect
23. #14273650C22semidirect
28. #107×C59C22semidirect
102. C2×C59#485semidirect
110. C2×#107D59semidirect
115. C59C2×#485semidirect
131. #107C2×D59semidirect
209. C2#16837745direct (N × H)