Finite Group Databasebeta

← #49095531

Subgroups — #49095531

Order 35968.

302 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 97 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#31823946C211yesmaximal, characteristic
2#31823505C211yesmaximal, characteristic, complemented
3#31823464C211yesmaximal, characteristic
4#31823333C211yesmaximal, characteristic, complemented
5#31823231C211yesmaximal, characteristic, complemented
6#31823223C211yesmaximal, characteristic, complemented
7C2×#104×C281C211yesmaximal, characteristic
8C2×#17985122C2211yescharacteristic
9Q8×Dic281—21no—
10D4×Dic281—22no—
11D4×Dic281—21no—
12#22582838—21no—
13#22582838C2211yescharacteristic
14C2×C4⋊Dic281—21no—
15C2×C4⋊Dic281—22no—
16C2×C4⋊Dic281C2211yescharacteristic
17C2×C4⋊Dic281C2211yescharacteristic
18#22582813—21no—
19#22582811—21no—
20#22582803—21no—
21#22582800—21no—
22C2×#41×C281C2211yescharacteristic
23C2×M16×C281C2211yescharacteristic
24C2×C42×C281C2211yescharacteristic
25#104×C281C414yescomplemented
26C22×Dic281—22no—
27C22×Dic281—21no—
28C22×Dic281D412yes—
29#17985122—21no—
30#17985122—21no—
31C2×#14555886—21no—
32C4⋊Dic281—22no—
33C4⋊Dic281—21no—
34C4⋊Dic281—21no—
35C4⋊Dic281—21no—
36C4⋊Dic281—21no—
37C4⋊Dic281—44no—
38C4⋊Dic281D411yescharacteristic
39C4⋊Dic281D411yescharacteristic
40C22⋊Dic281—22no—
41C22⋊Dic281—21no—
42C4×Dic281—22no—
43C4×Dic281—21no—
44#41×C281—21no—
45#41×C281—21no—
46#41×C281C2×C412yes—
47#41×C281Q812yes—
48C2×Q8×C281D411yescharacteristic
49C2×D4×C281—21no—
50C2×D4×C281D411yescharacteristic
51C22×C4×C281—21no—
52C22×C4×C281—21no—
53C22×C4×C281C2311yescharacteristic
54M16×C281—21no—
55M16×C281C2×C412yescomplemented
56C2×C8×C281—21no—
57C42×C281—21no—
58C42×C281C2×C412yescomplemented
59C2×Dic281—21no—
60C2×Dic281—22no—
61C2×Dic281—21no—
62C2×Dic281—42no—
63C2×Dic281—42no—
64C2×Dic281—41no—
65C2×Dic281—82no—
66#14555886—41no—
67C23×C281—21no—
68C23×C281C2×D411yescharacteristic
69Q8×C281—21no—
70Q8×C281C4⋊C412yescomplemented
71D4×C281—22no—
72D4×C281—22no—
73D4×C281—21no—
74D4×C281C4⋊C412yescomplemented
75C2×C4×C281—22no—
76C2×C4×C281—22no—
77C2×C4×C281—22no—
78C2×C4×C281—21no—
79C2×C4×C281—22no—
80C2×C4×C281—22no—
81C2×C4×C281C22×C411yescharacteristic
82C2×C4×C281C2×D411yescharacteristic
83C2×C4×C281C2×D411yescharacteristic
84C2×C4×C281C2×Q811yescharacteristic
85C2×C4×C281#4111yescharacteristic
86C2×C4×C281#4111yescharacteristic
87C8×C281—22no—
88C22×C281—21no—
89C22×C281—21no—
90C22×C281—22no—
91C22×C281—41no—
92C22×C281—41no—
93C22×C281C4×D411yescharacteristic
94C22×C281#12011yescharacteristic
95C22×C281C22⋊Q811yescharacteristic
96C4×C281—24no—
97C4×C281—22no—
98C4×C281C2×C4⋊C411yescharacteristic
99C4×C281C4×D411yescharacteristic
100C4×C281C22⋊Q811yescharacteristic
101C4×C281#12311yescharacteristic
102Dic281—42no—
103Dic281—41no—
104Dic281—41no—
105Dic281—81no—
106C2×C281—21no—
107C2×C281—21no—
108C2×C281—42no—
109C2×C281#38511yescharacteristic
110C2×C281#45311yescharacteristic
111C2×C281#45611yescharacteristic
112C281#185911yescharacteristic, complemented, Sylow
113#1859—2811nomaximal, Sylow
114#520—2811no—
115#428—2811no—
116C2×#104D28111yescharacteristic
117#417—2811no—
118#384—2811no—
119#343—2811no—
120#339—2811no—
121C2×#41C2×D28111yescharacteristic
122C2×M16—2811no—
123C2×M16C2×D28111yescharacteristic
124C4×Q8—5621no—
125C4×D4—5622no—
126C4×D4—5621no—
127#117—2811no—
128#117—5621no—
129C2×C4⋊C4—2811no—
130C2×C4⋊C4—2811no—
131C2×C4⋊C4—5621no—
132C2×C4⋊C4—5622no—
133C2×C42C2×D28111yescharacteristic
134#107—5621no—
135#106—5621no—
136#104Dic28114yescomplemented
137#103—5621no—
138#102—5621no—
139#41—21no—
140#41—21no—
141#41C2×Dic28112yes—
142#41Dic56212yes—
143C2×Q8D112411yescharacteristic
144C2×D4—21no—
145C2×D4D112411yescharacteristic
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—2812no—
149C22×C4—5622no—
150C22×C4—5621no—
151C22×C4C22×D28111yescharacteristic
152M16—21no—
153M16—5621no—
154M16—5621no—
155M16C2×Dic28112yescomplemented
156C2×C8—21no—
157C2×C8—5621no—
158C4⋊C4—2811no—
159C4⋊C4—2811no—
160C4⋊C4—5622no—
161C4⋊C4—5621no—
162C4⋊C4—5621no—
163C4⋊C4—5621no—
164C4⋊C4—5621no—
165C4⋊C4—11244no—
166C22⋊C4—5622no—
167C22⋊C4—5621no—
168C42—21no—
169C42—5622no—
170C42—5621no—
171C42C2×Dic28112yescomplemented
172C23—21no—
173C23D4×D28111yescharacteristic
174Q8—21no—
175Q8C4⋊Dic28112yescomplemented
176D4—22no—
177D4—22no—
178D4—21no—
179D4C4⋊Dic28112yescomplemented
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—5621no—
187C2×C4—5621no—
188C2×C4—5622no—
189C2×C4—11242no—
190C2×C4—11242no—
191C2×C4—11241no—
192C2×C4—22482no—
193C2×C4C22×Dic28111yescharacteristic
194C2×C4D4×D28111yescharacteristic
195C2×C4C2×D112411yescharacteristic
196C2×C4C2×Dic56211yescharacteristic
197C2×C4#1798513711yescharacteristic
198C2×C4#1798513711yescharacteristic
199C8—22no—
200C8—11241no—
201C22—21no—
202C22—21no—
203C22—22no—
204C22—41no—
205C22—41no—
206C22D4×Dic28111yescharacteristic
207C22#2258284911yescharacteristic
208C22#2258285611yescharacteristic
209C4—24no—
210C4—22no—
211C4—11242no—
212C4—11241no—
213C4—11241no—
214C4—22481no—
215C4C2×C4⋊Dic28111yescharacteristic
216C4D4×Dic28111yescharacteristic
217C4#2258285611yescharacteristic
218C4#2258286311yescharacteristic
219C2—21no—
220C2—21no—
221C2—42no—
222C2#3182333811yescharacteristic
223C2#3182363211yescharacteristic
224C2#3182364711yescharacteristic
subgroupG/H
centerC22#22582849
commutatorC2×C4×C281C22×C4
FrattiniC22×C4C22×D281
FittingC2×#104×C281C2
socleC22×C281#120
prime radicalC2×#41×C281C22
cosocleC22×C4×C281C23
hypercenterC2×#104D281
hypocenterC281#1859
LCSG ▷ C2×C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. #31823505C2semidirect
4. #31823333C2semidirect
5. #31823231C2semidirect
6. #31823223C2semidirect
25. #104×C281C4semidirect
55. M16×C281C2×C4semidirect
58. C42×C281C2×C4semidirect
70. Q8×C281C4⋊C4semidirect
74. D4×C281C4⋊C4semidirect
112. C281#1859semidirect
136. #104Dic281semidirect
155. M16C2×Dic281semidirect
171. C42C2×Dic281semidirect
175. Q8C4⋊Dic281semidirect
179. D4C4⋊Dic281semidirect

Maximal subgroups

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

subgroupindex
#318239462
#318235052
#318234642
#318233332
#318232312
#318232232
C2×#104×C2812
#1859281