Finite Group Databasebeta

← #49094301

Subgroups — #49094301

Order 35968.

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

normal subgroups only

This group has 216 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#31824058C211yesmaximal, characteristic
2#31823794C211yesmaximal, characteristic, complemented
3#31823774C211yesmaximal, characteristic
4#31823395C211yesmaximal, characteristic, complemented
5#31823199C211yesmaximal, characteristic, complemented
6#31823188C211yesmaximal, characteristic, complemented
7#327×C281C211yesmaximal, characteristic
8#22582872—21no—
9#22582869—21no—
10#22582860—21no—
11#22582860—21no—
12#22582858C2211yescharacteristic
13#22582856—21no—
14D4×Dic281—21no—
15C2×C4⋊Dic281—21no—
16C2×C4⋊Dic281C2211yescharacteristic
17C2×#17985117C2211yescharacteristic
18#22582812—21no—
19#22582811—21no—
20#22582804—21no—
21#22582800—21no—
22C22⋊#14555886C2211yescharacteristic
23#22582786—21no—
24#121×C281C2211yescharacteristic
25C22⋊C8×C281C2211yescharacteristic
26#95×C281C2211yescharacteristic
27C2×Dic562D411yescharacteristic
28C22×Dic281—21no—
29C22×Dic281—21no—
30C22×Dic281D411yescharacteristic
31C22×Dic281D411yescharacteristic
32C2×#14555886—21no—
33C4⋊Dic281—21no—
34C4⋊Dic281—21no—
35C4⋊Dic281—21no—
36C4⋊Dic281—42no—
37C4⋊Dic281D411yescharacteristic
38#17985117—21no—
39#17985117—21no—
40#17985117—21no—
41#17985117—21no—
42#17985117—21no—
43C22⋊Dic281—21no—
44C22⋊Dic281—21no—
45C22⋊Dic281—21no—
46C22⋊Dic281—21no—
47C4×Dic281—21no—
48C2×D4×C281—21no—
49C2×D4×C281D411yescharacteristic
50C22×C4×C281—21no—
51C22×C4×C281C2311yescharacteristic
52C2×C8×C281—21no—
53C4⋊C4×C281D411yescharacteristic
54C22⋊C4×C281—21no—
55Dic562—41no—
56C2×Dic281—21no—
57C2×Dic281—21no—
58C2×Dic281—21no—
59C2×Dic281—21no—
60C2×Dic281—21no—
61C2×Dic281—21no—
62C2×Dic281—41no—
63C2×Dic281—41no—
64C2×Dic281—41no—
65C2×Dic281—41no—
66C2×Dic281—81no—
67#14555886—41no—
68C23×C281—21no—
69C23×C281C2×D411yescharacteristic
70D4×C281—41no—
71D4×C281—41no—
72D4×C281—41no—
73C2×C4×C281—22no—
74C2×C4×C281—21no—
75C2×C4×C281—41no—
76C2×C4×C281—41no—
77C2×C4×C281—41no—
78C2×C4×C281C2×D411yescharacteristic
79C2×C4×C281C2×D411yescharacteristic
80C8×C281—41no—
81C22×C281—21no—
82C22×C281—21no—
83C22×C281—41no—
84C22×C281—41no—
85C22×C281—41no—
86C22×C281#12011yescharacteristic
87C22×C281#13511yescharacteristic
88C22×C281AGL(1,ℤ/8)11yescharacteristic
89C4×C281—21no—
90C4×C281—21no—
91C4×C281—42no—
92C4×C281—41no—
93Dic281—41no—
94Dic281—41no—
95Dic281—41no—
96Dic281—41no—
97Dic281—81no—
98C2×C281—21no—
99C2×C281—21no—
100C2×C281—81no—
101C2×C281#44911yescharacteristic
102C2×C281#45611yescharacteristic
103C2×C281#45811yescharacteristic
104C281#160911yescharacteristic, complemented, Sylow
105#1609—2811nomaximal, Sylow
106#539—2811no—
107#483—2811no—
108#480—2811no—
109#398—2811no—
110#328—2811no—
111#327D28111yescharacteristic
112#324—2811no—
113#126—5621no—
114#125—5621no—
115#123—5621no—
116#123—5621no—
117C22⋊Q8—2811no—
118C22⋊Q8—5621no—
119#121C2×D28111yescharacteristic
120C4×D4—5621no—
121C2×C4⋊C4—2811no—
122C2×C4⋊C4—2811no—
123C2×C4⋊C4—5621no—
124#107—5621no—
125#106—5621no—
126#103—5621no—
127#102—5621no—
128C22⋊C8—2811no—
129C22⋊C8C2×D28111yescharacteristic
130#95—5621no—
131#95C2×D28111yescharacteristic
132C2×Q8—2811no—
133C2×D4—21no—
134C2×D4D112411yescharacteristic
135C22×C4—21no—
136C22×C4—2811no—
137C22×C4—2811no—
138C22×C4—5621no—
139C22×C4—5621no—
140C22×C4C22×D28111yescharacteristic
141C2×C8—21no—
142C2×C8—5621no—
143C4⋊C4—2811no—
144C4⋊C4—5621no—
145C4⋊C4—5621no—
146C4⋊C4—5621no—
147C4⋊C4—5621no—
148C4⋊C4—5621no—
149C4⋊C4—5621no—
150C4⋊C4—5621no—
151C4⋊C4—5621no—
152C4⋊C4—11242no—
153C4⋊C4D112411yescharacteristic
154C22⋊C4—21no—
155C22⋊C4—5621no—
156C22⋊C4—5621no—
157C22⋊C4—5621no—
158C22⋊C4—5621no—
159C42—5621no—
160C23—21no—
161C23D4×D28111yescharacteristic
162Q8—11241no—
163D4—41no—
164D4—41no—
165D4—41no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—5621no—
172C2×C4—5621no—
173C2×C4—5621no—
174C2×C4—5621no—
175C2×C4—5621no—
176C2×C4—5621no—
177C2×C4—11241no—
178C2×C4—11241no—
179C2×C4—11241no—
180C2×C4—11241no—
181C2×C4—22481no—
182C2×C4D4×D28111yescharacteristic
183C2×C4C2×D112411yescharacteristic
184C8—41no—
185C8—11241no—
186C22—21no—
187C22—21no—
188C22—41no—
189C22—41no—
190C22—41no—
191C22#2258284911yescharacteristic
192C22#2258290011yescharacteristic
193C22#2258290311yescharacteristic
194C4—21no—
195C4—21no—
196C4—42no—
197C4—41no—
198C4—11241no—
199C4—11241no—
200C4—11241no—
201C4—11241no—
202C4—22481no—
203C2—21no—
204C2—21no—
205C2—81no—
206C2#3182360911yescharacteristic
207C2#3182364711yescharacteristic
208C2#3182365411yescharacteristic
subgroupG/H
centerC22#22582849
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#327×C281C2
socleC22×C281#120
prime radical#121×C281C22
hypercenter#327D281
hypocenterC281#1609
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. #31823794C2semidirect
4. #31823395C2semidirect
5. #31823199C2semidirect
6. #31823188C2semidirect
104. C281#1609semidirect

Maximal subgroups

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

subgroupindex
#318240582
#318237942
#318237742
#318233952
#318231992
#318231882
#327×C2812
#1609281