Finite Group Databasebeta

← C2×#22625066 #34014335

Subgroups — C2×#22625066 #34014335

Order 18688.

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

normal subgroups only

This group has 450 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, complemented
2#22625066C214yesmaximal, direct product factor
3C2×#17988959C211yesmaximal, characteristic
4C2×#14556652—22no—
5#17989498—22no—
6#17989498C2214yescomplemented
7C22×#11924016—22no—
8C2×#14556591C2211yescharacteristic
9#17988959—22no—
10#17988959C412yes—
11#17988959C2212yes—
12C2×C4×#10596831C411yescharacteristic
13C2×#127×C73C411yescharacteristic
14C2×#11924037—42no—
15#14556652—24no—
16#14556652—42no—
17C22×Dic146D412yes—
18C2×#11924016—24no—
19C2×#11924016—24no—
20C2×#11924016—44no—
21C2×#11924016—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×D4×C73—21no—
31C22×D4×C73—41no—
32#127×C73—21no—
33#127×C73—41no—
34#127×C73C2×C412yes—
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#11924016—48no—
46#11924016—48no—
47C2×#10596831—22no—
48C2×#10596831—22no—
49C2×#10596831—22no—
50C4⋊Dic73—41no—
51C4⋊Dic73—42no—
52C4⋊Dic73—41no—
53C24×C73—41no—
54C2×D4×C73—22no—
55C2×D4×C73—42no—
56C2×D4×C73—42no—
57C2×D4×C73—42no—
58C2×D4×C73—42no—
59C2×D4×C73—41no—
60C2×D4×C73—84no—
61C22×C4×C73—21no—
62C22×C4×C73C22⋊C411yescharacteristic
63C42×C73—21no—
64C42×C73C22⋊C411yescharacteristic
65C42×C73C22×C411yescharacteristic
66C23×C73—42no—
67C23×C73—84no—
68C23×C73—81no—
69C23×C73—81no—
70C23×C73#9911yescharacteristic
71D4×C73—44no—
72D4×C73—82no—
73D4×C73—84no—
74D4×C73—84no—
75C2×C4×C73—24no—
76C2×C4×C73—21no—
77C2×C4×C73—21no—
78C2×C4×C73—21no—
79C2×C4×C73—21no—
80C2×C4×C73#9911yescharacteristic
81C2×C4×C73C2×C22⋊C411yescharacteristic
82C2×Dic73—22no—
83C2×Dic73—22no—
84C2×Dic73—42no—
85C2×Dic73—42no—
86Dic146—42no—
87Dic146—42no—
88Dic146—82no—
89#10596833—84no—
90#10596831—24no—
91C22×C73—22no—
92C22×C73—84no—
93C22×C73—82no—
94C22×C73—162no—
95C22×C73—162no—
96C22×C73#35311yescharacteristic
97C22×C73#35311yescharacteristic
98C22×C73C2×#9911yescharacteristic
99C4×C73—22no—
100C4×C73—22no—
101C4×C73—21no—
102C4×C73—21no—
103Dic73—42no—
104Dic73—42no—
105C2×#1410—731nomaximal, Sylow
106C2×C73—21no—
107C2×C73—21no—
108C2×C73—162no—
109C2×C73#141012yescomplemented
110C2×C73C2×#35311yescharacteristic
111C2×#492—731no—
112C2×#356—732no—
113#1410—734no—
114C73C2×#141011yescharacteristic, complemented, Sylow
115C22×SD16—1462no—
116C2×C4⋊Q8—731no—
117C2×#127#6440811yescharacteristic
118#492—732no—
119#492—732no—
120#492—1462no—
121C2×#101—1462no—
122C2×C4×C8—731no—
123#356—734no—
124#356—1462no—
125C22×Q8—732no—
126C22×D4—21no—
127C22×D4—41no—
128C2×SD16—2924no—
129C2×SD16—2924no—
130C2×SD16—1464no—
131C2×SD16—1464no—
132C2×M16—2922no—
133C22×C8—1461no—
134C4⋊Q8—2921no—
135C4⋊Q8—732no—
136C4⋊Q8—731no—
137C4⋊Q8—731no—
138#127—21no—
139#127—41no—
140#127C2×#6440812yes—
141C2×C4⋊C4—2921no—
142C2×C42C2×#6440811yescharacteristic
143#101—2922no—
144#101—1464no—
145C4×C8—732no—
146C4×C8—1461no—
147C24—41no—
148C2×Q8—2922no—
149C2×Q8—2922no—
150C2×Q8—732no—
151C2×Q8—732no—
152C2×Q8—1462no—
153C2×D4—22no—
154C2×D4—42no—
155C2×D4—42no—
156C2×D4—42no—
157C2×D4—42no—
158C2×D4—41no—
159C2×D4—84no—
160C22×C4—21no—
161C22×C4—1462no—
162C22×C4C22⋊#6440811yescharacteristic
163SD16—2928no—
164SD16—2928no—
165M16—2924no—
166M16—5842no—
167C2×C8—5842no—
168C2×C8—1462no—
169C2×C8—1462no—
170C2×C8—1462no—
171C4⋊C4—2922no—
172C4⋊C4—2921no—
173C4⋊C4—2921no—
174C42—21no—
175C42C22⋊#6440811yescharacteristic
176C42C22×#6440811yescharacteristic
177C23—42no—
178C23—84no—
179C23—81no—
180C23—81no—
181C23#1455664911yescharacteristic
182Q8—2922no—
183Q8—2922no—
184Q8—5842no—
185D4—44no—
186D4—82no—
187D4—84no—
188D4—84no—
189C2×C4—24no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—2922no—
195C2×C4—2922no—
196C2×C4—1462no—
197C2×C4—1462no—
198C2×C4#1455664911yescharacteristic
199C2×C4C2×C22⋊#6440811yescharacteristic
200C8—5844no—
201C8—1464no—
202C22—22no—
203C22—84no—
204C22—82no—
205C22—162no—
206C22—162no—
207C22#1798949111yescharacteristic
208C22#1798949111yescharacteristic
209C22C2×#1455664911yescharacteristic
210C4—22no—
211C4—22no—
212C4—21no—
213C4—21no—
214C4—2922no—
215C4—2922no—
216C2—21no—
217C2—21no—
218C2—162no—
219C2#2262506612yesdirect product factor
220C2C2×#1798949111yescharacteristic
subgroupG/H
centerC22#17989491
commutatorC42×C73C22×C4
FrattiniC42C22×#64408
Fitting, prime radicalC2×#127×C73C4
socleC22×C73#353
cosocle#14556591C23
hypercenterC2×#127#64408
hypocenterC73C2×#1410
LCSG ▷ C42×C73 ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C2×#17989498C2semidirect
2. #22625066C2direct (N × H)
6. #17989498C22semidirect
109. C2×C73#1410semidirect
114. C73C2×#1410semidirect
219. C2#22625066direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179894982
#226250662
C2×#179889592
C2×#141073