Finite Group Databasebeta

← #49094352

Subgroups — #49094352

Order 35968.

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

normal subgroups only

This group has 240 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#31824050C211yesmaximal, characteristic
2#31823799C211yesmaximal, characteristic, complemented
3#31823779C211yesmaximal, characteristic, complemented
4#31823400C211yesmaximal, characteristic, complemented
5#31823199C211yesmaximal, characteristic, complemented
6#31823186C211yesmaximal, characteristic, complemented
7#327×C281C211yesmaximal, characteristic, complemented
8#22582874—21no—
9#22582865—21no—
10#22582863—21no—
11#22582858C2211yescharacteristic
12#22582851—21no—
13#22582847—21no—
14D4×Dic281—21no—
15C2×C4⋊Dic281—21no—
16C2×C4⋊Dic281C2211yescharacteristic
17C2×#17985115—21no—
18C2×#17985115C2211yescharacteristic
19#22582813—21no—
20#22582810—21no—
21#22582804—21no—
22#22582800—21no—
23C22⋊#14555886C2211yescharacteristic
24#121×C281C2211yescharacteristic
25C22⋊C8×C281C2211yescharacteristic
26#95×C281C2211yescharacteristic
27C23×D281D411yescharacteristic
28C2×Dic562D411yescharacteristic
29C2×C22⋊D281—21no—
30C2×C22⋊D281—21no—
31C22×Dic281—21no—
32C22×Dic281—21no—
33C22×Dic281D411yescharacteristic
34C2×#14555886—21no—
35C4⋊Dic281—21no—
36C4⋊Dic281—21no—
37C4⋊Dic281—21no—
38C4⋊Dic281—42no—
39C4⋊Dic281D411yescharacteristic
40#17985117—21no—
41C22⋊Dic281—21no—
42C22⋊Dic281—21no—
43#17985115—21no—
44#17985115—21no—
45#17985115—21no—
46#17985115—21no—
47#17985115—42no—
48C4×Dic281—21no—
49C2×D4×C281—21no—
50C2×D4×C281D411yescharacteristic
51C22×C4×C281—21no—
52C22×C4×C281C2311yescharacteristic
53C2×C8×C281—21no—
54C4⋊C4×C281D411yescharacteristic
55C22⋊C4×C281—21no—
56C22×D281—21no—
57C22×D281—21no—
58C22×D281—21no—
59C22×D281—41no—
60C22×D281—41no—
61Dic562—41no—
62C22⋊D281—81no—
63C22⋊D281—81no—
64C2×Dic281—21no—
65C2×Dic281—21no—
66C2×Dic281—21no—
67C2×Dic281—41no—
68C2×Dic281—41no—
69C2×Dic281—41no—
70C2×Dic281—41no—
71C2×Dic281—81no—
72#14555886—41no—
73C23×C281—21no—
74C23×C281C2×D411yescharacteristic
75D4×C281—41no—
76D4×C281—41no—
77D4×C281—41no—
78C2×C4×C281—22no—
79C2×C4×C281—21no—
80C2×C4×C281—41no—
81C2×C4×C281—41no—
82C2×C4×C281—41no—
83C2×C4×C281C2×D411yescharacteristic
84C2×C4×C281C2×D411yescharacteristic
85C8×C281—41no—
86C22×C281—21no—
87C22×C281—21no—
88C22×C281—41no—
89C22×C281—41no—
90C22×C281—41no—
91C22×C281#12011yescharacteristic
92C22×C281#13511yescharacteristic
93C22×C281#13711yescharacteristic
94C2×D281—42no—
95C2×D281—41no—
96C2×D281—41no—
97C2×D281—41no—
98C2×D281—81no—
99C4×C281—21no—
100C4×C281—21no—
101C4×C281—42no—
102C4×C281—41no—
103Dic281—41no—
104Dic281—41no—
105Dic281—41no—
106Dic281—81no—
107C2×C281—21no—
108C2×C281—21no—
109C2×C281—81no—
110C2×C281#45211yescharacteristic
111C2×C281#45311yescharacteristic
112C2×C281#45811yescharacteristic
113D281—81no—
114C281#161811yescharacteristic, complemented, Sylow
115#1618—2811nomaximal, Sylow
116#538—2811no—
117#484—2811no—
118#481—2811no—
119#399—2811no—
120#328—2811no—
121#327D28111yescharacteristic, complemented
122#323—2811no—
123#126—5621no—
124#124—5621no—
125#123—5621no—
126C22⋊Q8—2811no—
127#121—5621no—
128#121C2×D28111yescharacteristic
129#120—5621no—
130C4×D4—5621no—
131C2×C4⋊C4—2811no—
132C2×C4⋊C4—5621no—
133C2×C22⋊C4—2811no—
134C2×C22⋊C4—5621no—
135#107—5621no—
136#106—5621no—
137#103—5621no—
138#102—5621no—
139C22⋊C8—2811no—
140C22⋊C8C2×D28111yescharacteristic
141#95C2×D28111yescharacteristic
142C24—2811no—
143C2×Q8—2811no—
144C2×D4—21no—
145C2×D4—5621no—
146C2×D4—5621no—
147C2×D4D112411yescharacteristic
148C22×C4—21no—
149C22×C4—2811no—
150C22×C4—5621no—
151C22×C4—5621no—
152C22×C4C22×D28111yescharacteristic
153C2×C8—21no—
154C2×C8—5621no—
155C4⋊C4—2811no—
156C4⋊C4—5621no—
157C4⋊C4—5621no—
158C4⋊C4—5621no—
159C4⋊C4—5621no—
160C4⋊C4—11242no—
161C4⋊C4D112411yescharacteristic
162C22⋊C4—21no—
163C22⋊C4—5621no—
164C22⋊C4—5621no—
165C22⋊C4—5621no—
166C22⋊C4—5621no—
167C22⋊C4—5621no—
168C22⋊C4—5621no—
169C22⋊C4—11242no—
170C42—5621no—
171C23—21no—
172C23—5621no—
173C23—5621no—
174C23—5621no—
175C23—11241no—
176C23—11241no—
177C23D4×D28111yescharacteristic
178Q8—11241no—
179D4—41no—
180D4—41no—
181D4—41no—
182D4—22481no—
183D4—22481no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—5621no—
190C2×C4—5621no—
191C2×C4—5621no—
192C2×C4—11241no—
193C2×C4—11241no—
194C2×C4—11241no—
195C2×C4—11241no—
196C2×C4—22481no—
197C2×C4D4×D28111yescharacteristic
198C2×C4C2×D112411yescharacteristic
199C8—41no—
200C8—11241no—
201C22—21no—
202C22—21no—
203C22—41no—
204C22—41no—
205C22—41no—
206C22—11242no—
207C22—11241no—
208C22—11241no—
209C22—11241no—
210C22—22481no—
211C22#2258284911yescharacteristic
212C22#2258289811yescharacteristic
213C22#2258290811yescharacteristic
214C4—21no—
215C4—21no—
216C4—42no—
217C4—41no—
218C4—11241no—
219C4—11241no—
220C4—11241no—
221C4—22481no—
222C2—21no—
223C2—21no—
224C2—81no—
225C2—22481no—
226C2#3182362611yescharacteristic
227C2#3182363211yescharacteristic
228C2#3182365411yescharacteristic
subgroupG/H
centerC22#22582849
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#327×C281C2
socleC22×C281#120
prime radical#31824050C2
hypercenter#327D281
hypocenterC281#1618
LCSG ▷ C22×C4×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #31823799C2semidirect
3. #31823779C2semidirect
4. #31823400C2semidirect
5. #31823199C2semidirect
6. #31823186C2semidirect
7. #327×C281C2semidirect
114. C281#1618semidirect
121. #327D281semidirect

Maximal subgroups

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

subgroupindex
#318240502
#318237992
#318237792
#318234002
#318231992
#318231862
#327×C2812
#1618281