Finite Group Databasebeta

← C2×#22625068 #34014338

Subgroups — C2×#22625068 #34014338

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#22625068C214yesmaximal, direct product factor
3C2×#17988966C211yesmaximal, characteristic
4C2×#14556652—22no—
5#17989498—22no—
6#17989498C2214yes—
7C22×#11924018—22no—
8C2×#14556591C2211yescharacteristic
9#17988966—22no—
10#17988966C412yes—
11#17988966C2212yes—
12C2×C4×#10596831C411yescharacteristic
13C2×C4⋊Q8×C73C411yescharacteristic
14C2×#11924037—42no—
15#14556652—24no—
16#14556652—42no—
17C22×Dic146D412yes—
18C2×#11924018—24no—
19C2×#11924018—24no—
20C2×#11924018—44no—
21C2×#11924018—44no—
22C22×#10596831—21no—
23#14556591—41no—
24#14556591C2×C411yescharacteristic
25#14556591D412yes—
26#14556591C2311yescharacteristic
27C2×C4⋊Dic73—41no—
28C4×#10596831—21no—
29C4×#10596831C2×C412yes—
30C22×Q8×C73—21no—
31C4⋊Q8×C73—21no—
32C4⋊Q8×C73—41no—
33C4⋊Q8×C73C2×C412yes—
34C2×C4⋊C4×C73—41no—
35C2×C42×C73C2×C411yescharacteristic
36#11924037—44no—
37#11924037—82no—
38C2×#10596833—82no—
39C2×Dic146—22no—
40C2×Dic146—42no—
41C2×Dic146—42no—
42C2×Dic146C22⋊C412yes—
43C2×Dic146C2×D412yes—
44C22×Dic73—22no—
45#11924018—48no—
46#11924018—48no—
47C2×#10596831—22no—
48C2×#10596831—22no—
49C2×#10596831—22no—
50C4⋊Dic73—41no—
51C4⋊Dic73—42no—
52C4⋊Dic73—41no—
53C2×Q8×C73—22no—
54C2×Q8×C73—42no—
55C2×Q8×C73—42no—
56C2×Q8×C73—41no—
57C22×C4×C73—21no—
58C22×C4×C73—41no—
59C22×C4×C73C22⋊C411yescharacteristic
60C4⋊C4×C73—42no—
61C4⋊C4×C73—42no—
62C42×C73—21no—
63C42×C73C22⋊C411yescharacteristic
64C42×C73C22×C411yescharacteristic
65C23×C73#9911yescharacteristic
66Q8×C73—44no—
67Q8×C73—82no—
68C2×C4×C73—24no—
69C2×C4×C73—21no—
70C2×C4×C73—21no—
71C2×C4×C73—21no—
72C2×C4×C73—21no—
73C2×C4×C73—42no—
74C2×C4×C73—81no—
75C2×C4×C73—81no—
76C2×C4×C73#9911yescharacteristic
77C2×C4×C73C2×C22⋊C411yescharacteristic
78C2×Dic73—22no—
79C2×Dic73—22no—
80C2×Dic73—42no—
81C2×Dic73—42no—
82Dic146—42no—
83Dic146—42no—
84Dic146—82no—
85#10596833—84no—
86#10596831—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—
95C4×C73—82no—
96Dic73—42no—
97Dic73—42no—
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#6440811yescharacteristic
110#494—732no—
111#494—732no—
112#494—1462no—
113C2×#101—1462no—
114C2×C4×C8—731no—
115#356—734no—
116#356—1462no—
117C22×Q8—21no—
118C22×Q8—732no—
119C2×Q16—2924no—
120C2×Q16—2924no—
121C2×Q16—1464no—
122C2×Q16—1464no—
123C2×M16—2922no—
124C22×C8—1461no—
125C4⋊Q8—21no—
126C4⋊Q8—41no—
127C4⋊Q8—2921no—
128C4⋊Q8—732no—
129C4⋊Q8—731no—
130C4⋊Q8—731no—
131C4⋊Q8C2×#6440812yes—
132C2×C4⋊C4—41no—
133C2×C4⋊C4—2921no—
134C2×C42C2×#6440811yescharacteristic
135#101—2922no—
136#101—1464no—
137C4×C8—732no—
138C4×C8—1461no—
139C2×Q8—22no—
140C2×Q8—42no—
141C2×Q8—42no—
142C2×Q8—41no—
143C2×Q8—2922no—
144C2×Q8—2922no—
145C2×Q8—732no—
146C2×Q8—732no—
147C2×Q8—1462no—
148C22×C4—21no—
149C22×C4—41no—
150C22×C4—1462no—
151C22×C4C22⋊#6440811yescharacteristic
152Q16—2928no—
153Q16—2928no—
154M16—2924no—
155M16—5842no—
156C2×C8—5842no—
157C2×C8—1462no—
158C2×C8—1462no—
159C2×C8—1462no—
160C4⋊C4—42no—
161C4⋊C4—42no—
162C4⋊C4—2922no—
163C4⋊C4—2921no—
164C4⋊C4—2921no—
165C42—21no—
166C42C22⋊#6440811yescharacteristic
167C42C22×#6440811yescharacteristic
168C23#1455664911yescharacteristic
169Q8—44no—
170Q8—82no—
171Q8—2922no—
172Q8—2922no—
173Q8—5842no—
174C2×C4—24no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—42no—
180C2×C4—81no—
181C2×C4—81no—
182C2×C4—2922no—
183C2×C4—2922no—
184C2×C4—1462no—
185C2×C4—1462no—
186C2×C4#1455664911yescharacteristic
187C2×C4C2×C22⋊#6440811yescharacteristic
188C8—5844no—
189C8—1464no—
190C22—22no—
191C22#1798949111yescharacteristic
192C22#1798949111yescharacteristic
193C22C2×#1455664911yescharacteristic
194C4—22no—
195C4—22no—
196C4—21no—
197C4—21no—
198C4—82no—
199C4—2922no—
200C4—2922no—
201C2—21no—
202C2—21no—
203C2#2262506812yesdirect product factor
204C2C2×#1798949111yescharacteristic
subgroupG/H
centerC22#17989491
commutatorC42×C73C22×C4
FrattiniC42C22×#64408
FittingC2×C4⋊Q8×C73C4
socleC22×C73#353
prime radicalC23×C73#99
cosocle#14556591C23
hypercenterC2×C4⋊Q8#64408
hypocenterC73C2×#1411
LCSG ▷ C42×C73 ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #22625068C2direct (N × H)
101. C2×C73#1411semidirect
106. C73C2×#1411semidirect
203. C2#22625068direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179894982
#226250682
C2×#179889662
C2×#141173