Finite Group Databasebeta

← #49094280

Subgroups — #49094280

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#31824050C211yesmaximal, characteristic
2#31823619C211yesmaximal, characteristic, complemented
3#31823374C211yesmaximal, characteristic, complemented
4#31823201C211yesmaximal, characteristic, complemented
5#31823197C211yesmaximal, characteristic, complemented
6#31823186C211yesmaximal, characteristic, complemented
7#448×C281C211yesmaximal, characteristic, complemented
8C2×#17985128—21no—
9#22582874—21no—
10#22582865—21no—
11#22582863—21no—
12#22582858C2211yescharacteristic
13#22582851—21no—
14#22582847—21no—
15D4×Dic281—21no—
16C2×#17985115—21no—
17C2×#17985115C2211yescharacteristic
18#22582803—21no—
19C22⋊#14555886C2211yescharacteristic
20#22582786—21no—
21#22582786C2211yescharacteristic
22C22×Q8×C281C2211yescharacteristic
23C2×SD16×C281—21no—
24#121×C281C2211yescharacteristic
25#103×C281—21no—
26C22⋊C8×C281C2211yescharacteristic
27C23×D281D411yescharacteristic
28C2×Dic562D411yescharacteristic
29C2×C22⋊D281—21no—
30C2×C22⋊D281—21no—
31C22×Dic281—21no—
32C22×Dic281—21no—
33C22×Dic281D411yescharacteristic
34#17985128—42no—
35C2×#14555886—21no—
36C4⋊Dic281—21no—
37C4⋊Dic281D411yescharacteristic
38#17985117—21no—
39C22⋊Dic281—21no—
40C22⋊Dic281—21no—
41#17985115—21no—
42#17985115—21no—
43#17985115—21no—
44#17985115—21no—
45#17985115—42no—
46C4×Dic281—21no—
47C2×Q8×C281—21no—
48C2×Q8×C281—21no—
49C2×Q8×C281—42no—
50C2×D4×C281—21no—
51C2×D4×C281D411yescharacteristic
52C22×C4×C281—21no—
53C22×C4×C281C2311yescharacteristic
54SD16×C281—42no—
55C2×C8×C281—21no—
56C4⋊C4×C281D411yescharacteristic
57C22⋊C4×C281—21no—
58C22×D281—21no—
59C22×D281—21no—
60C22×D281—21no—
61C22×D281—41no—
62C22×D281—41no—
63Dic562—41no—
64C22⋊D281—81no—
65C22⋊D281—81no—
66C2×Dic281—21no—
67C2×Dic281—21no—
68C2×Dic281—21no—
69C2×Dic281—41no—
70C2×Dic281—41no—
71C2×Dic281—41no—
72C2×Dic281—41no—
73C2×Dic281—81no—
74#14555886—41no—
75C23×C281—21no—
76C23×C281C2×D411yescharacteristic
77Q8×C281—22no—
78Q8×C281—22no—
79Q8×C281—41no—
80Q8×C281—41no—
81D4×C281—41no—
82D4×C281—41no—
83D4×C281—41no—
84C2×C4×C281—22no—
85C2×C4×C281—21no—
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—41no—
95C22×C281—41no—
96C22×C281—41no—
97C22×C281#12011yescharacteristic
98C22×C281#13511yescharacteristic
99C22×C281#13711yescharacteristic
100C2×D281—42no—
101C2×D281—41no—
102C2×D281—41no—
103C2×D281—41no—
104C2×D281—81no—
105C4×C281—21no—
106C4×C281—21no—
107C4×C281—41no—
108C4×C281—42no—
109Dic281—41no—
110Dic281—41no—
111Dic281—41no—
112Dic281—81no—
113C2×C281—21no—
114C2×C281—21no—
115C2×C281—81no—
116C2×C281#45211yescharacteristic
117C2×C281#45511yescharacteristic
118C2×C281B(4,𝔽2)11yescharacteristic
119D281—81no—
120C281#160611yescharacteristic, complemented, Sylow
121#1606—2811nomaximal, Sylow
122#538—2811no—
123#451—2811no—
124#448D28111yescharacteristic, complemented
125#393—2811no—
126#328—2811no—
127#327—2811no—
128#323—2811no—
129C22×Q8C2×D28111yescharacteristic
130C2×Q16—5621no—
131C2×SD16—21no—
132#126—5621no—
133#124—5621no—
134#123—5621no—
135C22⋊Q8—2811no—
136#121—5621no—
137#121C2×D28111yescharacteristic
138#120—5621no—
139C4×D4—5621no—
140C2×C22⋊C4—2811no—
141C2×C22⋊C4—5621no—
142#103—21no—
143#103—5621no—
144C22⋊C8—2811no—
145C22⋊C8C2×D28111yescharacteristic
146#95—2811no—
147#95—5621no—
148C24—2811no—
149C2×Q8—21no—
150C2×Q8—21no—
151C2×Q8—42no—
152C2×Q8—2811no—
153C2×D4—21no—
154C2×D4—5621no—
155C2×D4—5621no—
156C2×D4C22⋊D28111yescharacteristic
157C22×C4—21no—
158C22×C4—2811no—
159C22×C4—5621no—
160C22×C4—5621no—
161C22×C4C22×D28111yescharacteristic
162Q16—11242no—
163SD16—42no—
164C2×C8—21no—
165C2×C8—5621no—
166C4⋊C4—2811no—
167C4⋊C4—5621no—
168C4⋊C4—5621no—
169C4⋊C4C22⋊D28111yescharacteristic
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—21no—
180C23—5621no—
181C23—5621no—
182C23—5621no—
183C23—11241no—
184C23—11241no—
185C23D4×D28111yescharacteristic
186Q8—22no—
187Q8—22no—
188Q8—41no—
189Q8—41no—
190Q8—11241no—
191D4—41no—
192D4—41no—
193D4—41no—
194D4—22481no—
195D4—22481no—
196C2×C4—22no—
197C2×C4—21no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—5621no—
202C2×C4—5621no—
203C2×C4—5621no—
204C2×C4—11241no—
205C2×C4—11241no—
206C2×C4—11241no—
207C2×C4—11241no—
208C2×C4—22481no—
209C2×C4D4×D28111yescharacteristic
210C2×C4C2×C22⋊D28111yescharacteristic
211C8—41no—
212C8—11241no—
213C22—21no—
214C22—21no—
215C22—41no—
216C22—41no—
217C22—41no—
218C22—11242no—
219C22—11241no—
220C22—11241no—
221C22—11241no—
222C22—22481no—
223C22#2258284711yescharacteristic
224C22#2258290011yescharacteristic
225C22#2258290811yescharacteristic
226C4—21no—
227C4—21no—
228C4—41no—
229C4—42no—
230C4—11241no—
231C4—11241no—
232C4—11241no—
233C4—22481no—
234C2—21no—
235C2—21no—
236C2—81no—
237C2—22481no—
238C2#3182362211yescharacteristic
239C2#3182363911yescharacteristic
240C2#3182364911yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#448×C281C2
socleC22×C281#120
prime radical#31824050C2
hypercenter#448D281
hypocenterC281#1606
LCSG ▷ C22×C4×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
2. #31823619C2semidirect
3. #31823374C2semidirect
4. #31823201C2semidirect
5. #31823197C2semidirect
6. #31823186C2semidirect
7. #448×C281C2semidirect
120. C281#1606semidirect
124. #448D281semidirect

Maximal subgroups

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

subgroupindex
#318240502
#318236192
#318233742
#318232012
#318231972
#318231862
#448×C2812
#1606281