Finite Group Databasebeta

← #49094268

Subgroups — #49094268

Order 35968.

244 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 49 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
1#31824060C211yesmaximal, characteristic
2#31823621C211yesmaximal, characteristic, complemented
3#31823604C211yesmaximal, characteristic
4#31823383C211yesmaximal, characteristic, complemented
5#31823201C211yesmaximal, characteristic, complemented
6#31823198C211yesmaximal, characteristic
7#324×C281C211yesmaximal, characteristic, complemented
8C22×Dic562C2211yescharacteristic
9C2×Dic1124—21no—
10C2×#17985127—21no—
11#22582874—21no—
12#22582869—21no—
13#22582864—21no—
14#22582862—21no—
15#22582858C2211yescharacteristic
16#22582857—21no—
17#22582853C2211yescharacteristic
18C4×C22⋊D281—21no—
19C2×#17985117—21no—
20#22582804—21no—
21#22582804—21no—
22#22582786—21no—
23#22582786C2211yescharacteristic
24C2×C4⋊C4×C281C2211yescharacteristic
25C22⋊C8×C281C2211yescharacteristic
26C22⋊C8×C281C2211yescharacteristic
27C2×Dic562—21no—
28C2×Dic562—21no—
29C2×Dic562—42no—
30C2×Dic562D411yescharacteristic
31C2×D1124D411yescharacteristic
32C2×C22⋊D281—21no—
33C22×Dic281—21no—
34C22×Dic281—21no—
35C2×C4×D281—21no—
36Dic1124—42no—
37#17985127—42no—
38C4⋊Dic281D411yescharacteristic
39C4⋊Dic281D411yescharacteristic
40#17985117—21no—
41#17985117—21no—
42#17985117—21no—
43#17985117—21no—
44#17985117—42no—
45C22⋊Dic281—21no—
46#17985115—21no—
47#17985115—21no—
48#17985115—21no—
49#17985115—21no—
50C4×Dic281—21no—
51C22×C4×C281D411yescharacteristic
52C22×C4×C281D411yescharacteristic
53C22×C4×C281C2311yescharacteristic
54C2×C8×C281—21no—
55C2×C8×C281—21no—
56C4⋊C4×C281—21no—
57C4⋊C4×C281—21no—
58C22×D281—21no—
59Dic562—22no—
60Dic562—22no—
61Dic562—41no—
62Dic562—41no—
63Dic562—41no—
64D1124—41no—
65C22⋊D281—41no—
66C22⋊D281—41no—
67C2×Dic281—22no—
68C2×Dic281—22no—
69C2×Dic281—21no—
70C2×Dic281—21no—
71C2×Dic281—21no—
72C2×Dic281—41no—
73C2×Dic281—41no—
74C2×Dic281—41no—
75C2×Dic281—41no—
76C4×D281—81no—
77C23×C281C2×D411yescharacteristic
78C2×C4×C281—21no—
79C2×C4×C281—21no—
80C2×C4×C281—21no—
81C2×C4×C281—21no—
82C2×C4×C281—41no—
83C2×C4×C281—41no—
84C2×C4×C281C2×D411yescharacteristic
85C2×C4×C281C2×D411yescharacteristic
86C8×C281—41no—
87C8×C281—41no—
88C22×C281—21no—
89C22×C281—21no—
90C22×C281#12011yescharacteristic
91C22×C281#13511yescharacteristic
92C22×C281#13711yescharacteristic
93C2×D281—41no—
94C2×D281—41no—
95C2×D281—41no—
96C4×C281—21no—
97C4×C281—21no—
98C4×C281—41no—
99C4×C281—41no—
100Dic281—42no—
101Dic281—41no—
102Dic281—41no—
103Dic281—41no—
104Dic281—42no—
105C2×C281—21no—
106C2×C281—21no—
107C2×C281#45211yescharacteristic
108C2×C281#45611yescharacteristic
109C2×C281B(4,𝔽2)11yescharacteristic
110D281—81no—
111C281#160311yescharacteristic, complemented, Sylow
112#1603—2811nomaximal, Sylow
113#539—2811no—
114#451—2811no—
115#448—2811no—
116#395—2811no—
117#328—2811no—
118#327—2811no—
119#324D28111yescharacteristic, complemented
120C22×Q8—2811no—
121C2×Q16—5621no—
122C2×SD16—5621no—
123#126—5621no—
124#125—5621no—
125#123—5621no—
126#123—5621no—
127C22⋊Q8—2811no—
128C22⋊Q8—5621no—
129#121—2811no—
130C4×D4—5621no—
131C2×C4⋊C4—5621no—
132C2×C4⋊C4C2×D28111yescharacteristic
133#103—5621no—
134#103—5621no—
135C22⋊C8C2×D28111yescharacteristic
136C22⋊C8C2×D28111yescharacteristic
137#95—2811no—
138#95—5621no—
139C2×Q8—2811no—
140C2×Q8—5621no—
141C2×Q8—5621no—
142C2×Q8—11242no—
143C2×D4—2811no—
144C2×D4—5621no—
145C22×C4—5621no—
146C22×C4—5621no—
147C22×C4—5621no—
148C22×C4D112411yescharacteristic
149C22×C4D112411yescharacteristic
150C22×C4C22×D28111yescharacteristic
151Q16—11242no—
152SD16—11242no—
153C2×C8—21no—
154C2×C8—21no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—2811no—
158C4⋊C4—2811no—
159C4⋊C4—5621no—
160C4⋊C4—5621no—
161C4⋊C4—5621no—
162C4⋊C4—5621no—
163C4⋊C4—11242no—
164C22⋊C4—5621no—
165C22⋊C4—5621no—
166C22⋊C4—5621no—
167C22⋊C4—5621no—
168C22⋊C4—5621no—
169C42—5621no—
170C23—5621no—
171C23C2×D112411yescharacteristic
172Q8—5622no—
173Q8—5622no—
174Q8—11241no—
175Q8—11241no—
176Q8—11241no—
177D4—11241no—
178D4—11241no—
179D4—11241no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—5622no—
187C2×C4—5622no—
188C2×C4—5621no—
189C2×C4—5621no—
190C2×C4—5621no—
191C2×C4—11241no—
192C2×C4—11241no—
193C2×C4—11241no—
194C2×C4—11241no—
195C2×C4—22481no—
196C2×C4D4×D28111yescharacteristic
197C2×C4D4×D28111yescharacteristic
198C8—41no—
199C8—41no—
200C22—21no—
201C22—21no—
202C22—11241no—
203C22—11241no—
204C22—11241no—
205C22#2258284911yescharacteristic
206C22#2258290111yescharacteristic
207C22#2258291211yescharacteristic
208C4—21no—
209C4—21no—
210C4—41no—
211C4—41no—
212C4—11242no—
213C4—11241no—
214C4—11241no—
215C4—11242no—
216C4—11241no—
217C2—21no—
218C2—21no—
219C2—22481no—
220C2#3182362711yescharacteristic
221C2#3182364811yescharacteristic
222C2#3182365111yescharacteristic
subgroupG/H
centerC22#22582849
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#324×C281C2
socleC22×C281#120
prime radical#22582853C22
hypercenter#324D281
hypocenterC281#1603
LCSG ▷ C22×C4×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #31823621C2semidirect
4. #31823383C2semidirect
5. #31823201C2semidirect
7. #324×C281C2semidirect
111. C281#1603semidirect
119. #324D281semidirect

Maximal subgroups

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

subgroupindex
#318240602
#318236212
#318236042
#318233832
#318232012
#318231982
#324×C2812
#1603281