Finite Group Databasebeta

← C2×#14543919 #17962675

Subgroups — C2×#14543919 #17962675

Order 4352.

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×#11763720C212yesmaximal, complemented
2#14543919C214yesmaximal, direct product factor
3C2×#11763181C211yesmaximal, characteristic
4C2×#10587545—22no—
5#11763720—22no—
6#11763720C2214yescomplemented
7C22×#63229—22no—
8C2×#10587555C2211yescharacteristic
9#11763181—22no—
10#11763181C412yes—
11#11763181C2212yes—
12C2×C4×#3622C411yescharacteristic
13C2×C17×#127C411yescharacteristic
14C22×D4×C17—21no—
15C22×D4×C17—41no—
16C22×Dic34D412yes—
17C2×#63247—42no—
18C17×#127—21no—
19C17×#127—41no—
20C17×#127C2×C412yes—
21C2×C42×C17C2×C411yescharacteristic
22C2×#63229—24no—
23C2×#63229—24no—
24C2×#63229—44no—
25C2×#63229—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—
36C24×C17—41no—
37C2×D4×C17—22no—
38C2×D4×C17—42no—
39C2×D4×C17—42no—
40C2×D4×C17—42no—
41C2×D4×C17—42no—
42C2×D4×C17—41no—
43C2×D4×C17—84no—
44C22×C4×C17—21no—
45C22×C4×C17C22⋊C411yescharacteristic
46C22×Dic17—22no—
47C2×Dic34—22no—
48C2×Dic34—42no—
49C2×Dic34—42no—
50C2×Dic34C22⋊C412yes—
51C2×Dic34C2×D412yes—
52#63247—44no—
53#63247—82no—
54C2×#3624—82no—
55C42×C17—21no—
56C42×C17C22⋊C411yescharacteristic
57C42×C17C22×C411yescharacteristic
58#63229—48no—
59#63229—48no—
60C4⋊Dic17—41no—
61C4⋊Dic17—42no—
62C4⋊Dic17—41no—
63C2×#3622—22no—
64C2×#3622—22no—
65C2×#3622—22no—
66C2×#1410—171nomaximal, Sylow
67C23×C17—42no—
68C23×C17—84no—
69C23×C17—81no—
70C23×C17—81no—
71C23×C17#9911yescharacteristic
72D4×C17—44no—
73D4×C17—82no—
74D4×C17—84no—
75D4×C17—84no—
76C2×C4×C17—24no—
77C2×C4×C17—21no—
78C2×C4×C17—21no—
79C2×C4×C17—21no—
80C2×C4×C17—21no—
81C2×C4×C17#9911yescharacteristic
82C2×C4×C17C2×C22⋊C411yescharacteristic
83C2×Dic17—22no—
84C2×Dic17—22no—
85C2×Dic17—42no—
86C2×Dic17—42no—
87Dic34—42no—
88Dic34—42no—
89Dic34—82no—
90#3624—84no—
91#3622—24no—
92C2×#492—171no—
93C2×#356—172no—
94#1410—174no—
95C22×C17—22no—
96C22×C17—84no—
97C22×C17—82no—
98C22×C17—162no—
99C22×C17—162no—
100C22×C17#35311yescharacteristic
101C22×C17#35311yescharacteristic
102C22×C17C2×#9911yescharacteristic
103C4×C17—22no—
104C4×C17—22no—
105C4×C17—21no—
106C4×C17—21no—
107Dic17—42no—
108Dic17—42no—
109C22×SD16—342no—
110C2×C4⋊Q8—171no—
111C2×#127#59511yescharacteristic
112#492—172no—
113#492—172no—
114#492—342no—
115C2×#101—342no—
116C2×C4×C8—171no—
117#356—174no—
118#356—342no—
119C2×C17—21no—
120C2×C17—21no—
121C2×C17—162no—
122C2×C17#141012yescomplemented
123C2×C17C2×#35311yescharacteristic
124C22×Q8—172no—
125C22×D4—21no—
126C22×D4—41no—
127C2×SD16—344no—
128C2×SD16—344no—
129C2×SD16—684no—
130C2×SD16—684no—
131C2×M16—682no—
132C22×C8—341no—
133C4⋊Q8—172no—
134C4⋊Q8—171no—
135C4⋊Q8—171no—
136C4⋊Q8—681no—
137#127—21no—
138#127—41no—
139#127C2×#59512yes—
140C2×C4⋊C4—681no—
141C2×C42C2×#59511yescharacteristic
142#101—344no—
143#101—682no—
144C4×C8—172no—
145C4×C8—341no—
146C17C2×#141011yescharacteristic, complemented, Sylow
147C24—41no—
148C2×Q8—172no—
149C2×Q8—172no—
150C2×Q8—342no—
151C2×Q8—682no—
152C2×Q8—682no—
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—342no—
162C22×C4C22⋊#59511yescharacteristic
163SD16—688no—
164SD16—688no—
165M16—684no—
166M16—1362no—
167C2×C8—342no—
168C2×C8—342no—
169C2×C8—342no—
170C2×C8—1362no—
171C4⋊C4—682no—
172C4⋊C4—681no—
173C4⋊C4—681no—
174C42—21no—
175C42C22⋊#59511yescharacteristic
176C42C22×#59511yescharacteristic
177C23—42no—
178C23—84no—
179C23—81no—
180C23—81no—
181C23#1058755111yescharacteristic
182Q8—682no—
183Q8—682no—
184Q8—1362no—
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—342no—
195C2×C4—342no—
196C2×C4—682no—
197C2×C4—682no—
198C2×C4#1058755111yescharacteristic
199C2×C4C2×C22⋊#59511yescharacteristic
200C8—344no—
201C8—1364no—
202C22—22no—
203C22—84no—
204C22—82no—
205C22—162no—
206C22—162no—
207C22#1176371311yescharacteristic
208C22#1176371311yescharacteristic
209C22C2×#1058755111yescharacteristic
210C4—22no—
211C4—22no—
212C4—21no—
213C4—21no—
214C4—682no—
215C4—682no—
216C2—21no—
217C2—21no—
218C2—162no—
219C2#1454391912yesdirect product factor
220C2C2×#1176371311yescharacteristic
subgroupG/H
centerC22#11763713
commutatorC42×C17C22×C4
FrattiniC42C22×#595
Fitting, prime radicalC2×C17×#127C4
socleC22×C17#353
cosocle#10587555C23
hypercenterC2×#127#595
hypocenterC17C2×#1410
LCSG ▷ C42×C17 ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
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×#11763720C2semidirect
2. #14543919C2direct (N × H)
6. #11763720C22semidirect
122. C2×C17#1410semidirect
146. C17C2×#1410semidirect
219. C2#14543919direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117637202
#145439192
C2×#117631812
C2×#141017