Finite Group Databasebeta

← #49097297

Subgroups — #49097297

Order 35968.

246 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 41 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#31824197C211yesmaximal, characteristic, complemented
2#31823653C211yesmaximal, characteristic, complemented
3#31823631C211yesmaximal, characteristic
4#31823255C211yesmaximal, characteristic, complemented
5#31823253C211yesmaximal, characteristic, complemented
6#31823252C211yesmaximal, characteristic, complemented
7#458×C281C211yesmaximal, characteristic, complemented
8#22582904—21no—
9#22582875C2211yescharacteristic
10#22582865—21no—
11#22582865—21no—
12#22582864—21no—
13#22582860—21no—
14#22582860C2211yescharacteristic
15#22582844—21no—
16C4×C22⋊D281—21no—
17#22582839—21no—
18#22582806—21no—
19#22582796C2211yescharacteristic
20#22582794—21no—
21#22582794C2211yescharacteristic
22H(5,𝔽2)×C281C2211yescharacteristic
23#123×C281—21no—
24#123×C281C2211yescharacteristic
25#99×C281—21no—
26#99×C281C2211yescharacteristic
27C2×Dic562—21no—
28C2×D1124D411yescharacteristic
29C2×C22⋊D281—21no—
30C2×C22⋊D281—21no—
31C22×Dic281D411yescharacteristic
32C2×C4×D281—21no—
33#17985125—41no—
34#17985123—41no—
35#17985122—21no—
36#17985117—21no—
37#17985117—21no—
38#17985117—41no—
39C22⋊Dic281—21no—
40C22⋊Dic281—21no—
41C22⋊Dic281—41no—
42C22⋊Dic281D411yescharacteristic
43#17985115—21no—
44#17985115—21no—
45#17985115—21no—
46C4×Dic281—21no—
47C4×Dic281—21no—
48C4×Dic281D411yescharacteristic
49#41×C281—21no—
50#41×C281—41no—
51C2×D4×C281—21no—
52C2×D4×C281—21no—
53C2×D4×C281—41no—
54C2×D4×C281C2311yescharacteristic
55C22×C4×C281D411yescharacteristic
56C4⋊C4×C281—21no—
57C4⋊C4×C281—41no—
58C22⋊C4×C281—21no—
59C22⋊C4×C281—21no—
60C22⋊C4×C281—41no—
61C22⋊C4×C281D411yescharacteristic
62C22×D281—21no—
63Dic562—42no—
64D1124—41no—
65C22⋊D281—42no—
66C22⋊D281—42no—
67C2×Dic281—21no—
68C2×Dic281—21no—
69C2×Dic281—21no—
70C2×Dic281—41no—
71C2×Dic281—41no—
72C4×D281—81no—
73#14555886—41no—
74C23×C281—21no—
75C23×C281—21no—
76C23×C281C2×D411yescharacteristic
77C23×C281C2×D411yescharacteristic
78Q8×C281—21no—
79D4×C281—21no—
80D4×C281—41no—
81D4×C281—41no—
82D4×C281—41no—
83D4×C281—41no—
84C2×C4×C281—21no—
85C2×C4×C281—21no—
86C2×C4×C281—21no—
87C2×C4×C281—21no—
88C2×C4×C281—41no—
89C2×C4×C281—41no—
90C2×C4×C281—41no—
91C2×C4×C281C2×D411yescharacteristic
92C22×C281—21no—
93C22×C281—21no—
94C22×C281—41no—
95C22×C281—41no—
96C22×C281—41no—
97C22×C281—81no—
98C22×C281—81no—
99C22×C281#12011yescharacteristic
100C2×D281—41no—
101C2×D281—41no—
102C2×D281—41no—
103C4×C281—21no—
104C4×C281—41no—
105C4×C281—41no—
106C4×C281—41no—
107C4×C281—81no—
108Dic281—22no—
109Dic281—41no—
110Dic281—41no—
111Dic281—81no—
112C2×C281—21no—
113C2×C281—41no—
114C2×C281—41no—
115C2×C281—81no—
116C2×C281B(4,𝔽2)11yescharacteristic
117D281—81no—
118C281#219811yescharacteristic, complemented, Sylow
119#2198—2811nomaximal, Sylow
120#559—2811no—
121#458—2811no—
122#458D28111yescharacteristic, complemented
123#453—2811no—
124#353—2811no—
125#352—2811no—
126#352—2811no—
127H(5,𝔽2)C2×D28111yescharacteristic
128AGL(1,ℤ/8)—5621no—
129#127—2811no—
130#124—5621no—
131#124—5621no—
132#123—21no—
133#123—2811no—
134#123—5621no—
135#123—5621no—
136#123C2×D28111yescharacteristic
137C4×Q8—5621no—
138C4×D4—5621no—
139C4×D4—5621no—
140#104—5621no—
141#100—2811no—
142#99—21no—
143#99—2811no—
144#99—5621no—
145#99C2×D28111yescharacteristic
146#41—21no—
147#41—41no—
148C2×Q8—5621no—
149C2×D4—21no—
150C2×D4—21no—
151C2×D4—41no—
152C2×D4—2811no—
153C2×D4—5621no—
154C2×D4—5621no—
155C2×D4C22×D28111yescharacteristic
156C22×C4—2811no—
157C22×C4—5621no—
158C22×C4C22⋊D28111yescharacteristic
159SD16—11241no—
160D8—11241no—
161M16—5621no—
162C4⋊C4—21no—
163C4⋊C4—41no—
164C4⋊C4—5621no—
165C4⋊C4—5621no—
166C4⋊C4—11241no—
167C22⋊C4—21no—
168C22⋊C4—21no—
169C22⋊C4—41no—
170C22⋊C4—2811no—
171C22⋊C4—5621no—
172C22⋊C4—5621no—
173C22⋊C4—5621no—
174C22⋊C4—5621no—
175C22⋊C4—5621no—
176C22⋊C4—11241no—
177C22⋊C4C22⋊D28111yescharacteristic
178C42—2811no—
179C42—5621no—
180C42—5621no—
181C23—21no—
182C23—21no—
183C23—5621no—
184C23D4×D28111yescharacteristic
185C23C2×C22⋊D28111yescharacteristic
186Q8—21no—
187Q8—11242no—
188D4—21no—
189D4—41no—
190D4—41no—
191D4—41no—
192D4—41no—
193D4—11241no—
194D4—11242no—
195D4—11242no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—5621no—
204C2×C4—5621no—
205C2×C4—5621no—
206C2×C4—11241no—
207C2×C4—11241no—
208C2×C4—22481no—
209C2×C4D4×D28111yescharacteristic
210C8—11241no—
211C22—21no—
212C22—21no—
213C22—41no—
214C22—41no—
215C22—41no—
216C22—81no—
217C22—81no—
218C22—11241no—
219C22—11241no—
220C22—11241no—
221C22#2258284711yescharacteristic
222C4—21no—
223C4—41no—
224C4—41no—
225C4—41no—
226C4—81no—
227C4—5622no—
228C4—11241no—
229C4—11241no—
230C4—22481no—
231C2—21no—
232C2—41no—
233C2—41no—
234C2—81no—
235C2—22481no—
236C2#3182364911yescharacteristic
subgroupG/H
centerC2#31823649
commutator, cosocleC2×D4×C281C23
FrattiniC2×D4C22×D281
Fitting#458×C281C2
socleC2×C281B(4,𝔽2)
prime radical#31823631C2
hypercenter#458D281
hypocenterC281#2198
LCSG ▷ C2×D4×C281 ▷ C22×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #458

Complements

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

NH ≅ G/Ntype
1. #31824197C2semidirect
2. #31823653C2semidirect
4. #31823255C2semidirect
5. #31823253C2semidirect
6. #31823252C2semidirect
7. #458×C281C2semidirect
118. C281#2198semidirect
122. #458D281semidirect

Maximal subgroups

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

subgroupindex
#318241972
#318236532
#318236312
#318232552
#318232532
#318232522
#458×C2812
#2198281