Finite Group Databasebeta

← #49094286

Subgroups — #49094286

Order 35968.

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

normal subgroups only

This group has 260 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#31824053C211yesmaximal, characteristic
2#31823618C211yesmaximal, characteristic, complemented
3#31823604C211yesmaximal, characteristic, complemented
4#31823376C211yesmaximal, characteristic, complemented
5#31823196C211yesmaximal, characteristic, complemented
6#31823186C211yesmaximal, characteristic, complemented
7#328×C281C211yesmaximal, characteristic, complemented
8C22×Dic562C2211yescharacteristic
9C2×#17985128—21no—
10C2×#17985127—21no—
11#22582874—21no—
12#22582868—21no—
13#22582864—21no—
14#22582854—21no—
15#22582853C2211yescharacteristic
16#22582849—21no—
17#22582839—21no—
18C2×#17985115—21no—
19C2×#17985115C2211yescharacteristic
20#22582804—21no—
21#22582802—21no—
22C22⋊#14555886C2211yescharacteristic
23#22582786—21no—
24C22⋊Q8×C281C2211yescharacteristic
25C22⋊C8×C281C2211yescharacteristic
26#95×C281C2211yescharacteristic
27C23×D281D411yescharacteristic
28C2×Dic562—21no—
29C2×Dic562—21no—
30C2×Dic562—42no—
31C2×D1124—21no—
32C2×D1124—21no—
33C2×D1124D411yescharacteristic
34C2×C22⋊D281—21no—
35C22×Dic281—21no—
36C22×Dic281D411yescharacteristic
37C2×C4×D281—21no—
38#17985128—42no—
39#17985127—42no—
40C2×#14555886—21no—
41C4⋊Dic281D411yescharacteristic
42#17985117—21no—
43#17985115—21no—
44#17985115—21no—
45#17985115—21no—
46#17985115—21no—
47#17985115—21no—
48#17985115—21no—
49#17985115—42no—
50C4×Dic281—21no—
51C2×Q8×C281D411yescharacteristic
52C22×C4×C281—21no—
53C22×C4×C281C2311yescharacteristic
54C2×C8×C281—21no—
55C4⋊C4×C281—21no—
56C4⋊C4×C281D411yescharacteristic
57C22⋊C4×C281—21no—
58C22×D281—21no—
59C22×D281—21no—
60C22×D281—21no—
61C22×D281—21no—
62C22×D281—41no—
63C22×D281—41no—
64Dic562—22no—
65Dic562—22no—
66Dic562—41no—
67Dic562—41no—
68D1124—41no—
69D1124—81no—
70D1124—81no—
71C22⋊D281—41no—
72C22⋊D281—41no—
73C2×Dic281—22no—
74C2×Dic281—21no—
75C2×Dic281—21no—
76C2×Dic281—41no—
77C2×Dic281—41no—
78C2×Dic281—41no—
79C4×D281—81no—
80#14555886—41no—
81C23×C281C2×D411yescharacteristic
82Q8×C281—41no—
83C2×C4×C281—21no—
84C2×C4×C281—21no—
85C2×C4×C281—41no—
86C2×C4×C281—41no—
87C2×C4×C281—41no—
88C2×C4×C281—41no—
89C2×C4×C281C2×D411yescharacteristic
90C2×C4×C281C2×D411yescharacteristic
91C8×C281—41no—
92C22×C281—21no—
93C22×C281—21no—
94C22×C281#12011yescharacteristic
95C22×C281#13511yescharacteristic
96C22×C281#13711yescharacteristic
97C2×D281—42no—
98C2×D281—41no—
99C2×D281—41no—
100C2×D281—41no—
101C2×D281—41no—
102C2×D281—41no—
103C2×D281—41no—
104C2×D281—81no—
105C4×C281—21no—
106C4×C281—21no—
107C4×C281—41no—
108C4×C281—41no—
109C4×C281—81no—
110Dic281—41no—
111Dic281—41no—
112Dic281—42no—
113C2×C281—21no—
114C2×C281—21no—
115C2×C281#45211yescharacteristic
116C2×C281#45511yescharacteristic
117C2×C281B(4,𝔽2)11yescharacteristic
118D281—81no—
119D281—81no—
120C281#160611yescharacteristic, complemented, Sylow
121#1606—2811nomaximal, Sylow
122#538—2811no—
123#451—2811no—
124#448—2811no—
125#393—2811no—
126#328D28111yescharacteristic, complemented
127#327—2811no—
128#323—2811no—
129C22×Q8—2811no—
130C2×Q16—5621no—
131C2×SD16—5621no—
132#126—5621no—
133#124—5621no—
134#123—5621no—
135C22⋊Q8C2×D28111yescharacteristic
136#121—2811no—
137#121—5621no—
138#120—5621no—
139C4×D4—5621no—
140C2×C22⋊C4—2811no—
141C2×C22⋊C4—5621no—
142#103—5621no—
143#103—5621no—
144C22⋊C8—2811no—
145C22⋊C8C2×D28111yescharacteristic
146#95—5621no—
147#95C2×D28111yescharacteristic
148C24—2811no—
149C2×Q8—5621no—
150C2×Q8—5621no—
151C2×Q8—11242no—
152C2×Q8D112411yescharacteristic
153C2×D4—2811no—
154C2×D4—5621no—
155C2×D4—5621no—
156C2×D4—5621no—
157C22×C4—21no—
158C22×C4—2811no—
159C22×C4—5621no—
160C22×C4—5621no—
161C22×C4C22×D28111yescharacteristic
162Q16—11242no—
163SD16—11242no—
164C2×C8—21no—
165C2×C8—5621no—
166C4⋊C4—21no—
167C4⋊C4—2811no—
168C4⋊C4—5621no—
169C4⋊C4D112411yescharacteristic
170C22⋊C4—21no—
171C22⋊C4—5621no—
172C22⋊C4—5621no—
173C22⋊C4—5621no—
174C22⋊C4—5621no—
175C22⋊C4—5621no—
176C22⋊C4—5621no—
177C22⋊C4—11242no—
178C42—5621no—
179C23—5621no—
180C23—5621no—
181C23—5621no—
182C23—5621no—
183C23—11241no—
184C23—11241no—
185C23D4×D28111yescharacteristic
186Q8—41no—
187Q8—5622no—
188Q8—5622no—
189Q8—11241no—
190Q8—11241no—
191D4—11241no—
192D4—11241no—
193D4—11241no—
194D4—22481no—
195D4—22481no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—5622no—
203C2×C4—5621no—
204C2×C4—5621no—
205C2×C4—11241no—
206C2×C4—11241no—
207C2×C4—11241no—
208C2×C4—22481no—
209C2×C4D4×D28111yescharacteristic
210C2×C4C2×D112411yescharacteristic
211C8—41no—
212C8—11241no—
213C22—21no—
214C22—21no—
215C22—11242no—
216C22—11241no—
217C22—11241no—
218C22—11241no—
219C22—11241no—
220C22—11241no—
221C22—11241no—
222C22—22481no—
223C22#2258284911yescharacteristic
224C22#2258290011yescharacteristic
225C22#2258291111yescharacteristic
226C4—21no—
227C4—21no—
228C4—41no—
229C4—41no—
230C4—81no—
231C4—11241no—
232C4—11241no—
233C4—11242no—
234C2—21no—
235C2—21no—
236C2—22481no—
237C2—22481no—
238C2#3182362811yescharacteristic
239C2#3182364211yescharacteristic
240C2#3182365111yescharacteristic
subgroupG/H
centerC22#22582849
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#328×C281C2
socleC22×C281#120
prime radical#31824053C2
hypercenter#328D281
hypocenterC281#1606
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
2. #31823618C2semidirect
3. #31823604C2semidirect
4. #31823376C2semidirect
5. #31823196C2semidirect
6. #31823186C2semidirect
7. #328×C281C2semidirect
120. C281#1606semidirect
126. #328D281semidirect

Maximal subgroups

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

subgroupindex
#318240532
#318236182
#318236042
#318233762
#318231962
#318231862
#328×C2812
#1606281