Finite Group Databasebeta

← #49094235

Subgroups — #49094235

Order 35968.

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

normal subgroups only

This group has 272 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#31824062C211yesmaximal, characteristic, complemented
2#31823613C211yesmaximal, characteristic, complemented
3#31823599C211yesmaximal, characteristic
4#31823381C211yesmaximal, characteristic, complemented
5#31823196C211yesmaximal, characteristic, complemented
6#31823188C211yesmaximal, characteristic, complemented
7#328×C281C211yesmaximal, characteristic, complemented
8C22×D1124C2211yescharacteristic
9C2×#17985125—21no—
10C2×D2248—21no—
11#22582874—21no—
12#22582870—21no—
13#22582864—21no—
14#22582863—21no—
15#22582855—21no—
16#22582853C2211yescharacteristic
17#22582839—21no—
18C2×#17985117C2211yescharacteristic
19C2×#17985115—21no—
20C2×#17985115—21no—
21#22582801—21no—
22#22582799—21no—
23C22⋊#14555886C2211yescharacteristic
24C22⋊Q8×C281C2211yescharacteristic
25C22⋊C8×C281C2211yescharacteristic
26#95×C281C2211yescharacteristic
27C23×D281—21no—
28C2×D1124—21no—
29C2×D1124—21no—
30C2×D1124—42no—
31C2×D1124D411yescharacteristic
32C2×C22⋊D281—21no—
33C22×Dic281D411yescharacteristic
34C22×Dic281D411yescharacteristic
35C2×C4×D281—21no—
36#17985125—42no—
37D2248—42no—
38C2×#14555886—21no—
39C4⋊Dic281—21no—
40C4⋊Dic281—21no—
41C4⋊Dic281D411yescharacteristic
42#17985117—21no—
43#17985117—21no—
44#17985117—21no—
45#17985115—21no—
46#17985115—21no—
47#17985115—21no—
48#17985115—21no—
49#17985115—42no—
50#17985115—42no—
51C4×Dic281—21no—
52C2×Q8×C281D411yescharacteristic
53C22×C4×C281—21no—
54C22×C4×C281C2311yescharacteristic
55C2×C8×C281—21no—
56C4⋊C4×C281—21no—
57C4⋊C4×C281D411yescharacteristic
58C22⋊C4×C281—21no—
59C22×D281—22no—
60C22×D281—21no—
61C22×D281—41no—
62C22×D281—41no—
63C22×D281—41no—
64C22×D281—41no—
65C22×D281—41no—
66C22×D281—41no—
67D1124—22no—
68D1124—22no—
69D1124—41no—
70D1124—41no—
71D1124—41no—
72C22⋊D281—41no—
73C22⋊D281—41no—
74C2×Dic281—21no—
75C2×Dic281—21no—
76C2×Dic281—21no—
77C2×Dic281—21no—
78C2×Dic281—21no—
79C2×Dic281—41no—
80C4×D281—81no—
81#14555886—41no—
82C23×C281C2×D411yescharacteristic
83Q8×C281—41no—
84C2×C4×C281—21no—
85C2×C4×C281—21no—
86C2×C4×C281—41no—
87C2×C4×C281—41no—
88C2×C4×C281—41no—
89C2×C4×C281—41no—
90C2×C4×C281C2×D411yescharacteristic
91C2×C4×C281C2×D411yescharacteristic
92C8×C281—41no—
93C22×C281—21no—
94C22×C281—21no—
95C22×C281#12011yescharacteristic
96C22×C281#13511yescharacteristic
97C22×C281AGL(1,ℤ/8)11yescharacteristic
98C2×D281—42no—
99C2×D281—42no—
100C2×D281—41no—
101C2×D281—41no—
102C2×D281—41no—
103C2×D281—42no—
104C2×D281—81no—
105C2×D281—81no—
106C2×D281—81no—
107C2×D281—81no—
108C4×C281—21no—
109C4×C281—21no—
110C4×C281—41no—
111C4×C281—41no—
112C4×C281—81no—
113Dic281—41no—
114Dic281—41no—
115Dic281—41no—
116C2×C281—21no—
117C2×C281—21no—
118C2×C281#44911yescharacteristic
119C2×C281#45411yescharacteristic
120C2×C281B(4,𝔽2)11yescharacteristic
121D281—81no—
122D281—82no—
123C281#159711yescharacteristic, complemented, Sylow
124#1597—2811nomaximal, Sylow
125#539—2811no—
126#450—2811no—
127#447—2811no—
128#394—2811no—
129#328D28111yescharacteristic, complemented
130#327—2811no—
131#324—2811no—
132C22×D4—2811no—
133C2×SD16—5621no—
134C2×D8—5621no—
135#126—5621no—
136#125—5621no—
137#123—5621no—
138#123—5621no—
139C22⋊Q8—5621no—
140C22⋊Q8C2×D28111yescharacteristic
141#121—2811no—
142C4×D4—5621no—
143C2×C4⋊C4—2811no—
144C2×C22⋊C4—5621no—
145C2×C22⋊C4—5621no—
146#102—5621no—
147#102—5621no—
148C22⋊C8—2811no—
149C22⋊C8C2×D28111yescharacteristic
150#95C2×D28111yescharacteristic
151C24—5621no—
152C2×Q8D112411yescharacteristic
153C2×D4—2811no—
154C2×D4—5621no—
155C2×D4—5621no—
156C2×D4—5621no—
157C2×D4—11242no—
158C22×C4—21no—
159C22×C4—2811no—
160C22×C4—2811no—
161C22×C4—5621no—
162C22×C4C22×D28111yescharacteristic
163SD16—11242no—
164D8—11242no—
165C2×C8—21no—
166C2×C8—5621no—
167C4⋊C4—21no—
168C4⋊C4—2811no—
169C4⋊C4—5621no—
170C4⋊C4—5621no—
171C4⋊C4—5621no—
172C4⋊C4—5621no—
173C4⋊C4—5621no—
174C4⋊C4D112411yescharacteristic
175C22⋊C4—21no—
176C22⋊C4—5621no—
177C22⋊C4—5621no—
178C22⋊C4—5621no—
179C22⋊C4—5621no—
180C22⋊C4—11242no—
181C22⋊C4—11242no—
182C42—5621no—
183C23—5622no—
184C23—5621no—
185C23—11241no—
186C23—11241no—
187C23—11241no—
188C23—11241no—
189C23—11241no—
190C23—11241no—
191C23D4×D28111yescharacteristic
192Q8—41no—
193D4—5622no—
194D4—5622no—
195D4—11241no—
196D4—11241no—
197D4—11241no—
198D4—11241no—
199D4—11241no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—5621no—
207C2×C4—5621no—
208C2×C4—5621no—
209C2×C4—5621no—
210C2×C4—5621no—
211C2×C4—11241no—
212C2×C4—22481no—
213C2×C4D4×D28111yescharacteristic
214C2×C4C2×D112411yescharacteristic
215C8—41no—
216C8—11241no—
217C22—21no—
218C22—21no—
219C22—11242no—
220C22—11242no—
221C22—11241no—
222C22—11241no—
223C22—11242no—
224C22—11241no—
225C22—22481no—
226C22—22481no—
227C22—22481no—
228C22—22481no—
229C22#2258284911yescharacteristic
230C22#2258290211yescharacteristic
231C22#2258290611yescharacteristic
232C4—21no—
233C4—21no—
234C4—41no—
235C4—41no—
236C4—81no—
237C4—11241no—
238C4—11241no—
239C4—11241no—
240C2—21no—
241C2—21no—
242C2—22482no—
243C2—22481no—
244C2#3182361111yescharacteristic
245C2#3182363711yescharacteristic
246C2#3182365111yescharacteristic
subgroupG/H
centerC22#22582849
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#328×C281C2
socleC22×C281#120
prime radical#31823599C2
hypercenter#328D281
hypocenterC281#1597
LCSG ▷ C22×C4×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
1. #31824062C2semidirect
2. #31823613C2semidirect
4. #31823381C2semidirect
5. #31823196C2semidirect
6. #31823188C2semidirect
7. #328×C281C2semidirect
123. C281#1597semidirect
129. #328D281semidirect

Maximal subgroups

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

subgroupindex
#318240622
#318236132
#318235992
#318233812
#318231962
#318231882
#328×C2812
#1597281