Finite Group Databasebeta

← #49094261

Subgroups — #49094261

Order 35968.

256 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 51 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#31824088C211yesmaximal, characteristic
2#31823621C211yesmaximal, characteristic, complemented
3#31823618C211yesmaximal, characteristic, complemented
4#31823376C211yesmaximal, characteristic
5#31823199C211yesmaximal, characteristic, complemented
6#31823186C211yesmaximal, characteristic
7#328×C281C211yesmaximal, characteristic, complemented
8C22×Dic562C2211yescharacteristic
9C2×Dic1124—21no—
10C2×#17985128—21no—
11#22582859—21no—
12#22582858C2211yescharacteristic
13#22582857—21no—
14#22582857—21no—
15#22582856—21no—
16#22582855—21no—
17C2×#17985115—21no—
18C2×#17985115C2211yescharacteristic
19C22⋊C4×D281—21no—
20#22582804—21no—
21#22582802—21no—
22C22⋊#14555886C2211yescharacteristic
23#22582786—21no—
24C22⋊Q8×C281C2211yescharacteristic
25C22⋊C8×C281C2211yescharacteristic
26#95×C281C2211yescharacteristic
27C23×D281D411yescharacteristic
28C2×Dic562—21no—
29C2×Dic562—21no—
30C2×Dic562—21no—
31C2×Dic562—42no—
32C2×Dic562D411yescharacteristic
33C22×Dic281—21no—
34C22×Dic281D411yescharacteristic
35C2×C4×D281—21no—
36C2×C4×D281—21no—
37Dic1124—42no—
38#17985128—42no—
39C2×#14555886—21no—
40C4⋊Dic281—21no—
41C4⋊Dic281D411yescharacteristic
42#17985117—21no—
43#17985117—21no—
44#17985117—21no—
45C22⋊Dic281—21no—
46#17985115—21no—
47#17985115—21no—
48#17985115—21no—
49#17985115—21no—
50#17985115—42no—
51C2×Q8×C281D411yescharacteristic
52C22×C4×C281—21no—
53C22×C4×C281C2311yescharacteristic
54C2×C8×C281—21no—
55C4⋊C4×C281—21no—
56C4⋊C4×C281D411yescharacteristic
57C22⋊C4×C281—21no—
58C22×D281—21no—
59C22×D281—21no—
60C22×D281—41no—
61C22×D281—41no—
62C22×D281Q1612yescomplemented
63Dic562—22no—
64Dic562—22no—
65Dic562—41no—
66Dic562—41no—
67Dic562—41no—
68Dic562—81no—
69C2×Dic281—22no—
70C2×Dic281—21no—
71C2×Dic281—21no—
72C2×Dic281—21no—
73C2×Dic281—41no—
74C2×Dic281—41no—
75C2×Dic281—41no—
76C4×D281—81no—
77C4×D281—81no—
78#14555886—41no—
79C23×C281C2×D411yescharacteristic
80Q8×C281—41no—
81C2×C4×C281—21no—
82C2×C4×C281—21no—
83C2×C4×C281—41no—
84C2×C4×C281—41no—
85C2×C4×C281—41no—
86C2×C4×C281—41no—
87C2×C4×C281C2×D411yescharacteristic
88C2×C4×C281C2×D411yescharacteristic
89C8×C281—41no—
90C22×C281—21no—
91C22×C281—21no—
92C22×C281#12011yescharacteristic
93C22×C281C2×Q1611yescharacteristic
94C22×C281#13711yescharacteristic
95C2×D281—22no—
96C2×D281—41no—
97C2×D281—41no—
98C2×D281—42no—
99C2×D281—81no—
100C4×C281—21no—
101C4×C281—21no—
102C4×C281—41no—
103C4×C281—41no—
104C4×C281—81no—
105Dic281—41no—
106Dic281—41no—
107Dic281—41no—
108Dic281—42no—
109C2×C281—21no—
110C2×C281—21no—
111C2×C281#45111yescharacteristic
112C2×C281#45511yescharacteristic
113C2×C281B(4,𝔽2)11yescharacteristic
114D281—42no—
115C281#160211yescharacteristic, complemented, Sylow
116#1602—2811nomaximal, Sylow
117#543—2811no—
118#451—2811no—
119#451—2811no—
120#393—2811no—
121#328—2811no—
122#328D28111yescharacteristic, complemented
123#323—2811no—
124C22×Q8—2811no—
125C2×Q16—5621no—
126C2×Q16—5621no—
127C22⋊Q8—2811no—
128C22⋊Q8—5621no—
129C22⋊Q8—5621no—
130C22⋊Q8—5621no—
131C22⋊Q8—5621no—
132C22⋊Q8—5621no—
133C22⋊Q8C2×D28111yescharacteristic
134C2×C22⋊C4—2811no—
135C2×C22⋊C4—5621no—
136C2×C22⋊C4—5621no—
137#103—5621no—
138#103—5621no—
139C22⋊C8—2811no—
140C22⋊C8C2×D28111yescharacteristic
141#95—5621no—
142#95C2×D28111yescharacteristic
143C24—2811no—
144C2×Q8—2811no—
145C2×Q8—5621no—
146C2×Q8—5621no—
147C2×Q8—5621no—
148C2×Q8—11242no—
149C2×Q8D112411yescharacteristic
150C22×C4—21no—
151C22×C4—2811no—
152C22×C4—5621no—
153C22×C4—5621no—
154C22×C4—5621no—
155C22×C4C22×D28111yescharacteristic
156Q16—11242no—
157Q16—11242no—
158C2×C8—21no—
159C2×C8—5621no—
160C4⋊C4—21no—
161C4⋊C4—2811no—
162C4⋊C4—5621no—
163C4⋊C4—5621no—
164C4⋊C4—5621no—
165C4⋊C4—5621no—
166C4⋊C4D112411yescharacteristic
167C22⋊C4—21no—
168C22⋊C4—5621no—
169C22⋊C4—5621no—
170C22⋊C4—5621no—
171C22⋊C4—5621no—
172C22⋊C4—5621no—
173C22⋊C4—11242no—
174C23—2812no—
175C23—5621no—
176C23—5621no—
177C23—11241no—
178C23—11241no—
179C23D4×D28111yescharacteristic
180Q8—41no—
181Q8—5622no—
182Q8—5622no—
183Q8—11241no—
184Q8—11241no—
185Q8—11241no—
186Q8—22481no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—5622no—
194C2×C4—5621no—
195C2×C4—5621no—
196C2×C4—5621no—
197C2×C4—11241no—
198C2×C4—11241no—
199C2×C4—11241no—
200C2×C4—22481no—
201C2×C4—22481no—
202C2×C4D4×D28111yescharacteristic
203C2×C4C2×D112411yescharacteristic
204C8—41no—
205C8—11241no—
206C22—21no—
207C22—21no—
208C22—5622no—
209C22—11242no—
210C22—11241no—
211C22—11241no—
212C22—22481no—
213C22#2258284911yescharacteristic
214C22Q16×D28111yescharacteristic
215C22#2258290811yescharacteristic
216C4—21no—
217C4—21no—
218C4—41no—
219C4—41no—
220C4—81no—
221C4—11241no—
222C4—11241no—
223C4—11242no—
224C4—11241no—
225C2—21no—
226C2—21no—
227C2—11242no—
228C2#3182362011yescharacteristic
229C2#3182364211yescharacteristic
230C2#3182365111yescharacteristic
subgroupG/H
centerC22#22582849
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#328×C281C2
socleC22×C281#120
prime radicalC23×D281D4
hypercenter#328D281
hypocenterC281#1602
LCSG ▷ C22×C4×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #31823621C2semidirect
3. #31823618C2semidirect
5. #31823199C2semidirect
7. #328×C281C2semidirect
62. C22×D281Q16semidirect
115. C281#1602semidirect
122. #328D281semidirect

Maximal subgroups

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

subgroupindex
#318240882
#318236212
#318236182
#318233762
#318231992
#318231862
#328×C2812
#1602281