Finite Group Databasebeta

← #49093827

Subgroups — #49093827

Order 35968.

242 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 63 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#31823999C211yesmaximal, characteristic
2#31823517C211yesmaximal, characteristic, complemented
3#31823314C211yesmaximal, characteristic, complemented
4#31823200C211yesmaximal, characteristic, complemented
5#31823198C211yesmaximal, characteristic
6#31823196C211yesmaximal, characteristic
7#328×C281C211yesmaximal, characteristic, complemented
8#22582874—21no—
9#22582870C411yescharacteristic, complemented
10#22582868C411yescharacteristic, complemented
11#22582863—21no—
12#22582853C2211yescharacteristic
13Q8×Dic281C411yescharacteristic, complemented
14#22582841C411yescharacteristic, complemented
15#22582839—21no—
16#22582837—21no—
17C2×#17985117—21no—
18C2×C4×Dic281—21no—
19C2×C4×Dic281C2211yescharacteristic
20#22582808—21no—
21C22⋊#14555886C2211yescharacteristic
22#22582789—21no—
23#22582786C2211yescharacteristic
24C22⋊Q8×C281C2211yescharacteristic
25C22⋊C8×C281C2211yescharacteristic
26#95×C281C2211yescharacteristic
27C2×D1124C2×C411yescharacteristic
28C2×C22⋊D281—21no—
29C22×Dic281—21no—
30C22×Dic281D411yescharacteristic
31C22×Dic281D411yescharacteristic
32C2×C4×D281—21no—
33C2×#14555886—21no—
34C4⋊Dic281—21no—
35C4⋊Dic281—21no—
36C4⋊Dic281C2×C411yescharacteristic
37#17985117—24no—
38#17985117—21no—
39#17985115—21no—
40#17985115—21no—
41#17985115—21no—
42#17985115—21no—
43C4×Dic281—21no—
44C4×Dic281—42no—
45C4×Dic281C2×C411yescharacteristic
46C4×Dic281C2×C411yescharacteristic
47C4×Dic281D411yescharacteristic
48C4×Dic281D411yescharacteristic
49C2×Q8×C281C2×C411yescharacteristic
50C22×C4×C281—21no—
51C22×C4×C281C2311yescharacteristic
52C2×C8×C281—21no—
53C4⋊C4×C281—21no—
54C4⋊C4×C281C2×C411yescharacteristic
55C22⋊C4×C281—21no—
56C22×D281—21no—
57D1124—41no—
58C22⋊D281—41no—
59C22⋊D281—41no—
60C2×Dic281—21no—
61C2×Dic281—21no—
62C2×Dic281—22no—
63C2×Dic281—22no—
64C2×Dic281—21no—
65C2×Dic281—41no—
66C2×Dic281—41no—
67C2×Dic281C22⋊C411yescharacteristic
68C2×Dic281C22⋊C411yescharacteristic
69C2×Dic281C22⋊C411yescharacteristic
70C2×Dic281C22⋊C411yescharacteristic
71C4×D281—42no—
72#14555886—41no—
73C23×C281C2×D411yescharacteristic
74Q8×C281—41no—
75C2×C4×C281—22no—
76C2×C4×C281—21no—
77C2×C4×C281—21no—
78C2×C4×C281—41no—
79C2×C4×C281—41no—
80C2×C4×C281—41no—
81C2×C4×C281C22×C411yescharacteristic
82C2×C4×C281C2×D411yescharacteristic
83C8×C281—41no—
84C22×C281—21no—
85C22×C281—21no—
86C22×C281C2×C22⋊C411yescharacteristic
87C22×C281AGL(1,ℤ/8)11yescharacteristic
88C22×C281#13711yescharacteristic
89C2×D281—41no—
90C2×D281—41no—
91C2×D281—41no—
92C4×C281—21no—
93C4×C281—21no—
94C4×C281—42no—
95C4×C281—41no—
96C4×C281—41no—
97Dic281—21no—
98Dic281—21no—
99Dic281—21no—
100Dic281—42no—
101Dic281—41no—
102Dic281#10412yes—
103C2×C281—21no—
104C2×C281—21no—
105C2×C281#41011yescharacteristic
106C2×C281#41711yescharacteristic
107C2×C281C2×#10411yescharacteristic
108D281—81no—
109C281#150911yescharacteristic, complemented, Sylow
110#1509—2811nomaximal, Sylow
111#529—2811no—
112#432—2811no—
113C4×C4⋊C4—2811no—
114#328—2811no—
115#328D28111yescharacteristic, complemented
116#327—2811no—
117#327—2811no—
118#126—5621no—
119#125—2811no—
120#124—2811no—
121#123—5621no—
122C22⋊Q8C2×D28111yescharacteristic
123#121—2811no—
124C4×Q8—2811no—
125C4×D4—2811no—
126C4×D4—5621no—
127#117—5621no—
128C2×C4⋊C4—5621no—
129C2×C42—2811no—
130C2×C42—5621no—
131C4⋊C8—5621no—
132C22⋊C8—2811no—
133C22⋊C8C2×D28111yescharacteristic
134#97—5621no—
135#95—2811no—
136#95C2×D28111yescharacteristic
137C2×Q8C4×D28111yescharacteristic
138C2×D4—2811no—
139C2×D4—5621no—
140C22×C4—21no—
141C22×C4—2811no—
142C22×C4—2811no—
143C22×C4—5621no—
144C22×C4—5621no—
145C22×C4C22×D28111yescharacteristic
146C2×C8—21no—
147C2×C8—5621no—
148C4⋊C4—21no—
149C4⋊C4—2811no—
150C4⋊C4—5621no—
151C4⋊C4—5621no—
152C4⋊C4—5621no—
153C4⋊C4—5624no—
154C4⋊C4C4×D28111yescharacteristic
155C22⋊C4—21no—
156C22⋊C4—5621no—
157C22⋊C4—5621no—
158C22⋊C4—5621no—
159C22⋊C4—5621no—
160C42—2811no—
161C42—2811no—
162C42—2811no—
163C42—2811no—
164C42—5621no—
165C42—11242no—
166C23—5621no—
167C23D4×D28111yescharacteristic
168Q8—41no—
169D4—11241no—
170D4—11241no—
171D4—11241no—
172C2×C4—22no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—2811no—
179C2×C4—2811no—
180C2×C4—2811no—
181C2×C4—2811no—
182C2×C4—5622no—
183C2×C4—5621no—
184C2×C4—5621no—
185C2×C4—5622no—
186C2×C4—5621no—
187C2×C4—11242no—
188C2×C4—11241no—
189C2×C4—11241no—
190C2×C4C2×C4×D28111yescharacteristic
191C2×C4D4×D28111yescharacteristic
192C8—41no—
193C8—11241no—
194C22—21no—
195C22—21no—
196C22—11241no—
197C22—11241no—
198C22—11241no—
199C22C22⋊C4×D28111yescharacteristic
200C22#2258290611yescharacteristic
201C22#2258291111yescharacteristic
202C4—21no—
203C4—21no—
204C4—42no—
205C4—41no—
206C4—41no—
207C4—2812no—
208C4—5621no—
209C4—5621no—
210C4—5621no—
211C4—11242no—
212C4—11241no—
213C2—21no—
214C2—21no—
215C2—22481no—
216C2#3182343511yescharacteristic
217C2#3182346311yescharacteristic
218C2#104×D28111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D281
commutatorC2×C4×C281C22×C4
FrattiniC22×C4C22×D281
Fitting#328×C281C2
socleC22×C281C2×C22⋊C4
prime radical#22582853C22
cosocleC22×C4×C281C23
hypercenter#328D281
hypocenterC281#1509
LCSG ▷ C2×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. #31823517C2semidirect
3. #31823314C2semidirect
4. #31823200C2semidirect
7. #328×C281C2semidirect
9. #22582870C4semidirect
10. #22582868C4semidirect
13. Q8×Dic281C4semidirect
14. #22582841C4semidirect
109. C281#1509semidirect
115. #328D281semidirect

Maximal subgroups

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

subgroupindex
#318239992
#318235172
#318233142
#318232002
#318231982
#318231962
#328×C2812
#1509281