Finite Group Databasebeta

← C2×#22625069 #34014340

Subgroups — C2×#22625069 #34014340

Order 18688.

398 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 64 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×#17989498C212yesmaximal
2#22625069C214yesmaximal, direct product factor
3C2×#17988967C211yesmaximal, characteristic
4C2×#14556652—22no—
5#17989498—22no—
6#17989498C2214yes—
7C22×Dic292—22no—
8C2×#14556591C411yescharacteristic
9C2×#14556591C2211yescharacteristic
10#17988967—22no—
11#17988967C412yes—
12#17988967C2212yes—
13C2×C4×C8×C73C411yescharacteristic
14C2×#11924037—42no—
15#14556652—24no—
16#14556652—42no—
17C22×Dic146—21no—
18C22×Dic146D412yes—
19C2×Dic292—24no—
20C2×Dic292—24no—
21C2×Dic292—44no—
22C2×Dic292—44no—
23#14556591—21no—
24#14556591—41no—
25#14556591—41no—
26#14556591C2×C412yes—
27#14556591C2×C411yescharacteristic
28#14556591D412yes—
29#14556591C2311yescharacteristic
30C2×C4⋊Dic73—41no—
31C2×C4⋊Dic73—41no—
32C22×C8×C73—21no—
33C2×C42×C73C2×C411yescharacteristic
34C4×C8×C73—21no—
35C4×C8×C73C2×C412yes—
36#11924037—44no—
37#11924037—82no—
38C2×#10596833—82no—
39C2×Dic146—22no—
40C2×Dic146—22no—
41C2×Dic146—42no—
42C2×Dic146—42no—
43C2×Dic146—42no—
44C2×Dic146—42no—
45C2×Dic146—41no—
46C2×Dic146C22⋊C412yes—
47C2×Dic146C2×D412yes—
48C22×Dic73—22no—
49C22×Dic73—41no—
50Dic292—48no—
51Dic292—48no—
52C4⋊Dic73—41no—
53C4⋊Dic73—42no—
54C4⋊Dic73—41no—
55C4⋊Dic73—42no—
56C4⋊Dic73—42no—
57C22×C4×C73—21no—
58C22×C4×C73C22⋊C411yescharacteristic
59C2×C8×C73—22no—
60C2×C8×C73—22no—
61C2×C8×C73—22no—
62C42×C73—21no—
63C42×C73C22⋊C411yescharacteristic
64C42×C73C22×C411yescharacteristic
65C23×C73#9911yescharacteristic
66C2×C4×C73—24no—
67C2×C4×C73—21no—
68C2×C4×C73—21no—
69C2×C4×C73—21no—
70C2×C4×C73—21no—
71C2×C4×C73#9911yescharacteristic
72C2×C4×C73C2×C22⋊C411yescharacteristic
73C2×Dic73—22no—
74C2×Dic73—22no—
75C2×Dic73—42no—
76C2×Dic73—42no—
77C2×Dic73—42no—
78C2×Dic73—81no—
79C2×Dic73—81no—
80Dic146—42no—
81Dic146—42no—
82Dic146—44no—
83Dic146—82no—
84Dic146—82no—
85#10596833—84no—
86C8×C73—24no—
87C22×C73—22no—
88C22×C73#35311yescharacteristic
89C22×C73#35311yescharacteristic
90C22×C73C2×#9911yescharacteristic
91C4×C73—22no—
92C4×C73—22no—
93C4×C73—21no—
94C4×C73—21no—
95Dic73—42no—
96Dic73—42no—
97Dic73—82no—
98C2×#1411—731nomaximal, Sylow
99C2×C73—21no—
100C2×C73—21no—
101C2×C73#141112yescomplemented
102C2×C73C2×#35311yescharacteristic
103C2×#494—731no—
104C2×#356—732no—
105#1411—734no—
106C73C2×#141111yescharacteristic, complemented, Sylow
107C22×Q16—1462no—
108C2×C4⋊Q8—731no—
109C2×C4⋊Q8—731no—
110#494—732no—
111#494—732no—
112#494—1462no—
113C2×#101—1462no—
114C2×C4×C8#6440811yescharacteristic
115#356—734no—
116#356—1462no—
117C22×Q8—732no—
118C22×Q8—1461no—
119C2×Q16—2924no—
120C2×Q16—2924no—
121C2×Q16—1464no—
122C2×Q16—1464no—
123C2×M16—2922no—
124C22×C8—21no—
125C4⋊Q8—2921no—
126C4⋊Q8—2921no—
127C4⋊Q8—732no—
128C4⋊Q8—731no—
129C4⋊Q8—731no—
130C4⋊Q8—732no—
131C4⋊Q8—1461no—
132C2×C4⋊C4—2921no—
133C2×C4⋊C4—2921no—
134C2×C42C2×#6440811yescharacteristic
135#101—2922no—
136#101—1464no—
137C4×C8—21no—
138C4×C8C2×#6440812yes—
139C2×Q8—2922no—
140C2×Q8—2922no—
141C2×Q8—2922no—
142C2×Q8—2922no—
143C2×Q8—2921no—
144C2×Q8—732no—
145C2×Q8—732no—
146C2×Q8—1462no—
147C2×Q8—1462no—
148C22×C4—21no—
149C22×C4—2921no—
150C22×C4—1462no—
151C22×C4C22⋊#6440811yescharacteristic
152Q16—2928no—
153Q16—2928no—
154M16—2924no—
155M16—5842no—
156C2×C8—22no—
157C2×C8—22no—
158C2×C8—22no—
159C2×C8—5842no—
160C4⋊C4—2922no—
161C4⋊C4—2922no—
162C4⋊C4—2922no—
163C4⋊C4—2921no—
164C4⋊C4—2921no—
165C42—21no—
166C42C22⋊#6440811yescharacteristic
167C42C22×#6440811yescharacteristic
168C23#1455665011yescharacteristic
169Q8—2922no—
170Q8—2922no—
171Q8—2924no—
172Q8—5842no—
173Q8—5842no—
174C2×C4—24no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—2922no—
180C2×C4—2922no—
181C2×C4—2922no—
182C2×C4—5841no—
183C2×C4—5841no—
184C2×C4—1462no—
185C2×C4—1462no—
186C2×C4#1455665011yescharacteristic
187C2×C4C2×C22⋊#6440811yescharacteristic
188C8—24no—
189C8—5844no—
190C22—22no—
191C22#1798949211yescharacteristic
192C22#1798949211yescharacteristic
193C22C2×#1455665011yescharacteristic
194C4—22no—
195C4—22no—
196C4—21no—
197C4—21no—
198C4—2922no—
199C4—2922no—
200C4—5842no—
201C2—21no—
202C2—21no—
203C2#2262506912yesdirect product factor
204C2C2×#1798949211yescharacteristic
subgroupG/H
centerC22#17989492
commutatorC42×C73C22×C4
FrattiniC42C22×#64408
FittingC2×C4×C8×C73C4
socleC22×C73#353
prime radicalC23×C73#99
cosocle#14556591C23
hypercenterC2×C4×C8#64408
hypocenterC73C2×#1411
LCSG ▷ C42×C73 ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×C8

Complements

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

NH ≅ G/Ntype
2. #22625069C2direct (N × H)
101. C2×C73#1411semidirect
106. C73C2×#1411semidirect
203. C2#22625069direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179894982
#226250692
C2×#179889672
C2×#141173