Finite Group Databasebeta

← C2×#14543921 #17962678

Subgroups — C2×#14543921 #17962678

Order 4352.

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×#11763720C212yesmaximal
2#14543921C214yesmaximal, direct product factor
3C2×#11763188C211yesmaximal, characteristic
4C2×#10587545—22no—
5#11763720—22no—
6#11763720C2214yes—
7C22×#63231—22no—
8C2×#10587555C2211yescharacteristic
9#11763188—22no—
10#11763188C412yes—
11#11763188C2212yes—
12C2×C4×#3622C411yescharacteristic
13C2×C17×C4⋊Q8C411yescharacteristic
14C22×Q8×C17—21no—
15C22×Dic34D412yes—
16C2×#63247—42no—
17C17×C4⋊Q8—21no—
18C17×C4⋊Q8—41no—
19C17×C4⋊Q8C2×C412yes—
20C2×C4⋊C4×C17—41no—
21C2×C42×C17C2×C411yescharacteristic
22C2×#63231—24no—
23C2×#63231—24no—
24C2×#63231—44no—
25C2×#63231—44no—
26C2×C4⋊Dic17—41no—
27C22×#3622—21no—
28#10587555—41no—
29#10587555C2×C411yescharacteristic
30#10587555D412yes—
31#10587555C2311yescharacteristic
32#10587545—24no—
33#10587545—42no—
34C4×#3622—21no—
35C4×#3622C2×C412yes—
36C2×Q8×C17—22no—
37C2×Q8×C17—42no—
38C2×Q8×C17—42no—
39C2×Q8×C17—41no—
40C22×C4×C17—21no—
41C22×C4×C17—41no—
42C22×C4×C17C22⋊C411yescharacteristic
43C22×Dic17—22no—
44C2×Dic34—22no—
45C2×Dic34—42no—
46C2×Dic34—42no—
47C2×Dic34C22⋊C412yes—
48C2×Dic34C2×D412yes—
49#63247—44no—
50#63247—82no—
51C2×#3624—82no—
52C4⋊C4×C17—42no—
53C4⋊C4×C17—42no—
54C42×C17—21no—
55C42×C17C22⋊C411yescharacteristic
56C42×C17C22×C411yescharacteristic
57#63231—48no—
58#63231—48no—
59C4⋊Dic17—41no—
60C4⋊Dic17—42no—
61C4⋊Dic17—41no—
62C2×#3622—22no—
63C2×#3622—22no—
64C2×#3622—22no—
65C2×#1411—171nomaximal, Sylow
66C23×C17#9911yescharacteristic
67Q8×C17—44no—
68Q8×C17—82no—
69C2×C4×C17—24no—
70C2×C4×C17—21no—
71C2×C4×C17—21no—
72C2×C4×C17—21no—
73C2×C4×C17—21no—
74C2×C4×C17—42no—
75C2×C4×C17—81no—
76C2×C4×C17—81no—
77C2×C4×C17#9911yescharacteristic
78C2×C4×C17C2×C22⋊C411yescharacteristic
79C2×Dic17—22no—
80C2×Dic17—22no—
81C2×Dic17—42no—
82C2×Dic17—42no—
83Dic34—42no—
84Dic34—42no—
85Dic34—82no—
86#3624—84no—
87#3622—24no—
88C2×#494—171no—
89C2×#356—172no—
90#1411—174no—
91C22×C17—22no—
92C22×C17#35311yescharacteristic
93C22×C17#35311yescharacteristic
94C22×C17C2×#9911yescharacteristic
95C4×C17—22no—
96C4×C17—22no—
97C4×C17—21no—
98C4×C17—21no—
99C4×C17—82no—
100Dic17—42no—
101Dic17—42no—
102C22×Q16—342no—
103C2×C4⋊Q8—171no—
104C2×C4⋊Q8#59511yescharacteristic
105#494—172no—
106#494—172no—
107#494—342no—
108C2×#101—342no—
109C2×C4×C8—171no—
110#356—174no—
111#356—342no—
112C2×C17—21no—
113C2×C17—21no—
114C2×C17#141112yescomplemented
115C2×C17C2×#35311yescharacteristic
116C22×Q8—21no—
117C22×Q8—172no—
118C2×Q16—344no—
119C2×Q16—344no—
120C2×Q16—684no—
121C2×Q16—684no—
122C2×M16—682no—
123C22×C8—341no—
124C4⋊Q8—21no—
125C4⋊Q8—41no—
126C4⋊Q8—172no—
127C4⋊Q8—171no—
128C4⋊Q8—171no—
129C4⋊Q8—681no—
130C4⋊Q8C2×#59512yes—
131C2×C4⋊C4—41no—
132C2×C4⋊C4—681no—
133C2×C42C2×#59511yescharacteristic
134#101—344no—
135#101—682no—
136C4×C8—172no—
137C4×C8—341no—
138C17C2×#141111yescharacteristic, complemented, Sylow
139C2×Q8—22no—
140C2×Q8—42no—
141C2×Q8—42no—
142C2×Q8—41no—
143C2×Q8—172no—
144C2×Q8—172no—
145C2×Q8—342no—
146C2×Q8—682no—
147C2×Q8—682no—
148C22×C4—21no—
149C22×C4—41no—
150C22×C4—342no—
151C22×C4C22⋊#59511yescharacteristic
152Q16—688no—
153Q16—688no—
154M16—684no—
155M16—1362no—
156C2×C8—342no—
157C2×C8—342no—
158C2×C8—342no—
159C2×C8—1362no—
160C4⋊C4—42no—
161C4⋊C4—42no—
162C4⋊C4—682no—
163C4⋊C4—681no—
164C4⋊C4—681no—
165C42—21no—
166C42C22⋊#59511yescharacteristic
167C42C22×#59511yescharacteristic
168C23#1058755111yescharacteristic
169Q8—44no—
170Q8—82no—
171Q8—682no—
172Q8—682no—
173Q8—1362no—
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—342no—
183C2×C4—342no—
184C2×C4—682no—
185C2×C4—682no—
186C2×C4#1058755111yescharacteristic
187C2×C4C2×C22⋊#59511yescharacteristic
188C8—344no—
189C8—1364no—
190C22—22no—
191C22#1176371311yescharacteristic
192C22#1176371311yescharacteristic
193C22C2×#1058755111yescharacteristic
194C4—22no—
195C4—22no—
196C4—21no—
197C4—21no—
198C4—82no—
199C4—682no—
200C4—682no—
201C2—21no—
202C2—21no—
203C2#1454392112yesdirect product factor
204C2C2×#1176371311yescharacteristic
subgroupG/H
centerC22#11763713
commutatorC42×C17C22×C4
FrattiniC42C22×#595
FittingC2×C17×C4⋊Q8C4
socleC22×C17#353
prime radicalC23×C17#99
cosocle#10587555C23
hypercenterC2×C4⋊Q8#595
hypocenterC17C2×#1411
LCSG ▷ C42×C17 ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
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. #14543921C2direct (N × H)
114. C2×C17#1411semidirect
138. C17C2×#1411semidirect
203. C2#14543921direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117637202
#145439212
C2×#117631882
C2×#141117