Finite Group Databasebeta

← C2×#31823252 #49096938

Subgroups — C2×#31823252 #49096938

Order 35968.

278 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 69 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×#22582860C211yesmaximal, characteristic
2C2×#22582796C211yesmaximal, characteristic
3#31823252C214yesmaximal, direct product factor
4C2×#99×C281C211yesmaximal, characteristic
5C23×Dic281C411yescharacteristic, complemented
6C2×#17985122—21no—
7#22582860—21no—
8#22582860—21no—
9#22582860C412yescomplemented
10#22582860C2212yes—
11C2×#17985117—21no—
12C2×C22⋊Dic281—21no—
13C2×C22⋊Dic281C411yescharacteristic, complemented
14#22582796—21no—
15#22582796C2212yes—
16C22×D4×C281C2211yescharacteristic
17C2×C22⋊C4×C281—21no—
18#99×C281—21no—
19#99×C281C2212yes—
20C22×Dic281—21no—
21C22×Dic281—21no—
22C22×Dic281—21no—
23C22×Dic281—41no—
24C22×Dic281—41no—
25C22×Dic281C2×C412yescomplemented
26#17985122—22no—
27#17985122—41no—
28C2×#14555886—41no—
29#17985117—22no—
30#17985117—22no—
31C22⋊Dic281—22no—
32C22⋊Dic281—21no—
33C22⋊Dic281—22no—
34C22⋊Dic281C2×C412yescomplemented
35C24×C281C2×C411yescharacteristic
36C24×C281D411yescharacteristic
37C2×D4×C281—41no—
38C2×D4×C281—41no—
39C2×D4×C281C2×C411yescharacteristic
40C2×D4×C281D411yescharacteristic
41C2×D4×C281D411yescharacteristic
42C2×D4×C281C2311yescharacteristic
43C22×C4×C281—41no—
44C22×C4×C281D411yescharacteristic
45C22⋊C4×C281—22no—
46C22⋊C4×C281—41no—
47C2×Dic281—22no—
48C2×Dic281—22no—
49C2×Dic281—42no—
50C2×Dic281—42no—
51C2×Dic281—41no—
52C2×Dic281—41no—
53C2×Dic281—42no—
54#14555886—42no—
55C23×C281—21no—
56C23×C281—21no—
57C23×C281—21no—
58C23×C281—21no—
59C23×C281—42no—
60C23×C281—42no—
61C23×C281C22⋊C411yescharacteristic
62C23×C281C22⋊C411yescharacteristic
63C23×C281C22⋊C411yescharacteristic
64C23×C281C22×C411yescharacteristic
65C23×C281C2×D411yescharacteristic
66D4×C281—41no—
67D4×C281—41no—
68D4×C281—41no—
69D4×C281—41no—
70C2×C4×C281—21no—
71C2×C4×C281—21no—
72C2×C4×C281—42no—
73C2×C4×C281—82no—
74C2×C4×C281C22⋊C411yescharacteristic
75C2×C4×C281C2×D411yescharacteristic
76C22×C281—22no—
77C22×C281—21no—
78C22×C281—21no—
79C22×C281—21no—
80C22×C281—21no—
81C22×C281—41no—
82C22×C281—41no—
83C22×C281—41no—
84C22×C281—41no—
85C22×C281—42no—
86C22×C281—42no—
87C22×C281—42no—
88C22×C281—81no—
89C22×C281#9911yescharacteristic
90C22×C281#9911yescharacteristic
91C22×C281C2×C22⋊C411yescharacteristic
92C4×C281—21no—
93C4×C281—21no—
94C4×C281—82no—
95Dic281—42no—
96Dic281—42no—
97C2×C281—21no—
98C2×C281—21no—
99C2×C281—41no—
100C2×C281—41no—
101C2×C281—41no—
102C2×C281—41no—
103C2×C281#35212yescomplemented
104C2×C281C2×#9911yescharacteristic
105C281C2×#35211yescharacteristic, complemented, Sylow
106C2×#352—2811nomaximal, Sylow
107C2×#123—2811no—
108C2×#100—2811no—
109C2×#99D28111yescharacteristic
110#352—2814no—
111C22×D4C2×D28111yescharacteristic
112C23×C4—2811no—
113C2×M16—5621no—
114#123—2812no—
115#123—2812no—
116#123—5621no—
117#123—5621no—
118C2×C4⋊C4—5621no—
119C2×C22⋊C4—21no—
120C2×C22⋊C4—2811no—
121C2×C22⋊C4—5621no—
122#100—2812no—
123#100—5621no—
124#99—21no—
125#99C2×D28112yes—
126C24C4×D28111yescharacteristic
127C24C22⋊D28111yescharacteristic
128C2×D4—41no—
129C2×D4—41no—
130C2×D4C4×D28111yescharacteristic
131C2×D4C22⋊D28111yescharacteristic
132C2×D4D112411yescharacteristic
133C2×D4C22×D28111yescharacteristic
134C22×C4—41no—
135C22×C4—2812no—
136C22×C4—5621no—
137C22×C4—5621no—
138C22×C4—5621no—
139C22×C4—11241no—
140C22×C4—11241no—
141C22×C4D112411yescharacteristic
142M16—5622no—
143M16—11241no—
144C2×C8—11241no—
145C4⋊C4—5622no—
146C4⋊C4—5622no—
147C22⋊C4—22no—
148C22⋊C4—41no—
149C22⋊C4—2812no—
150C22⋊C4—5621no—
151C22⋊C4—5622no—
152C22⋊C4—5622no—
153C23—21no—
154C23—21no—
155C23—21no—
156C23—21no—
157C23—42no—
158C23—42no—
159C23#1798511511yescharacteristic
160C23#1798511511yescharacteristic
161C23#1798511511yescharacteristic
162C23C2×C4×D28111yescharacteristic
163C23C2×C22⋊D28111yescharacteristic
164D4—41no—
165D4—41no—
166D4—41no—
167D4—41no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—42no—
171C2×C4—82no—
172C2×C4—5622no—
173C2×C4—5622no—
174C2×C4—11242no—
175C2×C4—11242no—
176C2×C4—11241no—
177C2×C4—11241no—
178C2×C4—11242no—
179C2×C4#1798511511yescharacteristic
180C2×C4C2×D112411yescharacteristic
181C8—11242no—
182C22—22no—
183C22—21no—
184C22—21no—
185C22—21no—
186C22—21no—
187C22—41no—
188C22—41no—
189C22—41no—
190C22—41no—
191C22—42no—
192C22—42no—
193C22—42no—
194C22—81no—
195C22#2258279311yescharacteristic
196C22#2258279311yescharacteristic
197C22C2×#1798511511yescharacteristic
198C4—21no—
199C4—21no—
200C4—82no—
201C4—11242no—
202C4—11242no—
203C2—21no—
204C2—21no—
205C2—41no—
206C2—41no—
207C2—41no—
208C2—41no—
209C2#3182325212yesdirect product factor
210C2C2×#2258279311yescharacteristic
subgroupG/H
centerC22#22582793
commutatorC23×C281C22×C4
FrattiniC2×D4C22×D281
FittingC2×#99×C281C2
socleC22×C281#99
prime radicalC22×D4×C281C22
cosocleC2×D4×C281C23
hypercenterC2×#99D281
hypocenterC281C2×#352
LCSG ▷ C23×C281 ▷ C22×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
3. #31823252C2direct (N × H)
5. C23×Dic281C4semidirect
9. #22582860C4semidirect
13. C2×C22⋊Dic281C4semidirect
25. C22×Dic281C2×C4semidirect
34. C22⋊Dic281C2×C4semidirect
103. C2×C281#352semidirect
105. C281C2×#352semidirect
209. C2#31823252direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#225828602
C2×#225827962
#318232522
C2×#99×C2812
C2×#352281