Finite Group Databasebeta

← C2×#89267 #11727770

Subgroups — C2×#89267 #11727770

Order 896.

278 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 69 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×#6498C211yesmaximal, characteristic
2C2×C7×#99C211yesmaximal, characteristic
3C2×#6407C211yesmaximal, characteristic
4#89267C214yesmaximal, direct product factor
5C22×C7×D4C2211yescharacteristic
6C23×Dic7C411yescharacteristic, complemented
7C2×C7×C22⋊C4—21no—
8C2×C22⋊Dic7—21no—
9C2×C22⋊Dic7C411yescharacteristic, complemented
10#6498—21no—
11#6498—21no—
12#6498C412yescomplemented
13#6498C2212yes—
14C2×Dic7⋊C4—21no—
15C2×#1136—21no—
16C7×#99—21no—
17C7×#99C2212yes—
18#6407—21no—
19#6407C2212yes—
20C2×#352—71nomaximal, Sylow
21C24×C7C2×C411yescharacteristic
22C24×C7D411yescharacteristic
23C2×C7×D4—41no—
24C2×C7×D4—41no—
25C2×C7×D4C2×C411yescharacteristic
26C2×C7×D4D411yescharacteristic
27C2×C7×D4D411yescharacteristic
28C2×C7×D4C2311yescharacteristic
29C22×C4×C7—41no—
30C22×C4×C7D411yescharacteristic
31C22×Dic7—21no—
32C22×Dic7—21no—
33C22×Dic7—21no—
34C22×Dic7—41no—
35C22×Dic7—41no—
36C22×Dic7C2×C412yescomplemented
37C7×C22⋊C4—22no—
38C7×C22⋊C4—41no—
39C22⋊Dic7—21no—
40C22⋊Dic7—22no—
41C22⋊Dic7—22no—
42C22⋊Dic7C2×C412yescomplemented
43Dic7⋊C4—22no—
44Dic7⋊C4—22no—
45#1136—22no—
46#1136—41no—
47C2×C7⋊C8—41no—
48C2×#123—71no—
49C2×#100—71no—
50C2×#99D711yescharacteristic
51#352—74no—
52C23×C7—21no—
53C23×C7—21no—
54C23×C7—21no—
55C23×C7—21no—
56C23×C7—42no—
57C23×C7—42no—
58C23×C7C22⋊C411yescharacteristic
59C23×C7C22⋊C411yescharacteristic
60C23×C7C22⋊C411yescharacteristic
61C23×C7C22×C411yescharacteristic
62C23×C7C2×D411yescharacteristic
63C7×D4—41no—
64C7×D4—41no—
65C7×D4—41no—
66C7×D4—41no—
67C2×C4×C7—21no—
68C2×C4×C7—21no—
69C2×C4×C7—42no—
70C2×C4×C7—82no—
71C2×C4×C7C22⋊C411yescharacteristic
72C2×C4×C7C2×D411yescharacteristic
73C2×Dic7—22no—
74C2×Dic7—22no—
75C2×Dic7—42no—
76C2×Dic7—42no—
77C2×Dic7—41no—
78C2×Dic7—41no—
79C2×Dic7—42no—
80C7⋊C8—42no—
81C22×D4C2×D711yescharacteristic
82C23×C4—71no—
83C2×M16—141no—
84#123—72no—
85#123—72no—
86#123—141no—
87#123—141no—
88C2×C4⋊C4—141no—
89C2×C22⋊C4—21no—
90C2×C22⋊C4—71no—
91C2×C22⋊C4—141no—
92#100—72no—
93#100—141no—
94#99—21no—
95#99C2×D712yes—
96C22×C7—22no—
97C22×C7—21no—
98C22×C7—21no—
99C22×C7—21no—
100C22×C7—21no—
101C22×C7—41no—
102C22×C7—41no—
103C22×C7—41no—
104C22×C7—41no—
105C22×C7—42no—
106C22×C7—42no—
107C22×C7—42no—
108C22×C7—81no—
109C22×C7#9911yescharacteristic
110C22×C7#9911yescharacteristic
111C22×C7C2×C22⋊C411yescharacteristic
112C4×C7—21no—
113C4×C7—21no—
114C4×C7—82no—
115Dic7—42no—
116Dic7—42no—
117C24C4×D711yescharacteristic
118C24C22⋊D711yescharacteristic
119C2×D4—41no—
120C2×D4—41no—
121C2×D4C4×D711yescharacteristic
122C2×D4D2811yescharacteristic
123C2×D4C22⋊D711yescharacteristic
124C2×D4C22×D711yescharacteristic
125C22×C4—41no—
126C22×C4—72no—
127C22×C4—141no—
128C22×C4—141no—
129C22×C4—141no—
130C22×C4—281no—
131C22×C4—281no—
132C22×C4D2811yescharacteristic
133M16—142no—
134M16—281no—
135C2×C8—281no—
136C4⋊C4—142no—
137C4⋊C4—142no—
138C22⋊C4—22no—
139C22⋊C4—41no—
140C22⋊C4—72no—
141C22⋊C4—141no—
142C22⋊C4—142no—
143C22⋊C4—142no—
144C2×C7—21no—
145C2×C7—21no—
146C2×C7—41no—
147C2×C7—41no—
148C2×C7—41no—
149C2×C7—41no—
150C2×C7#35212yescomplemented
151C2×C7C2×#9911yescharacteristic
152C23—21no—
153C23—21no—
154C23—21no—
155C23—21no—
156C23—42no—
157C23—42no—
158C23(C2×D7)⋊C411yescharacteristic
159C23(C2×D7)⋊C411yescharacteristic
160C23(C2×D7)⋊C411yescharacteristic
161C23C2×C4×D711yescharacteristic
162C23C2×C22⋊D711yescharacteristic
163D4—41no—
164D4—41no—
165D4—41no—
166D4—41no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—42no—
170C2×C4—82no—
171C2×C4—142no—
172C2×C4—142no—
173C2×C4—282no—
174C2×C4—282no—
175C2×C4—281no—
176C2×C4—281no—
177C2×C4—282no—
178C2×C4(C2×D7)⋊C411yescharacteristic
179C2×C4C2×D2811yescharacteristic
180C8—282no—
181C7C2×#35211yescharacteristic, complemented, Sylow
182C22—22no—
183C22—21no—
184C22—21no—
185C22—21no—
186C22—21no—
187C22—41no—
188C22—41no—
189C22—41no—
190C22—41no—
191C22—42no—
192C22—42no—
193C22—42no—
194C22—81no—
195C22#638011yescharacteristic
196C22#638011yescharacteristic
197C22C2×(C2×D7)⋊C411yescharacteristic
198C4—21no—
199C4—21no—
200C4—82no—
201C4—282no—
202C4—282no—
203C2—21no—
204C2—21no—
205C2—41no—
206C2—41no—
207C2—41no—
208C2—41no—
209C2#8926712yesdirect product factor
210C2C2×#638011yescharacteristic
subgroupG/H
centerC22#6380
commutatorC23×C7C22×C4
FrattiniC2×D4C22×D7
FittingC2×C7×#99C2
socleC22×C7#99
prime radicalC22×C7×D4C22
cosocleC2×C7×D4C23
hypercenterC2×#99D7
hypocenterC7C2×#352
LCSG ▷ C23×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
4. #89267C2direct (N × H)
6. C23×Dic7C4semidirect
9. C2×C22⋊Dic7C4semidirect
12. #6498C4semidirect
36. C22×Dic7C2×C4semidirect
42. C22⋊Dic7C2×C4semidirect
150. C2×C7#352semidirect
181. C7C2×#352semidirect
209. C2#89267direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#64982
C2×C7×#992
C2×#64072
#892672
C2×#3527