Finite Group Databasebeta

← #49094273

Subgroups — #49094273

Order 35968.

282 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 51 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#31824040C211yesmaximal, characteristic
2#31823604C211yesmaximal, characteristic, complemented
3#31823601C211yesmaximal, characteristic, complemented
4#31823384C211yesmaximal, characteristic, complemented
5#31823196C211yesmaximal, characteristic, complemented
6#31823188C211yesmaximal, characteristic, complemented
7#327×C281C211yesmaximal, characteristic, complemented
8C2×#17985137—21no—
9C22×Dic562C2211yescharacteristic
10C2×#17985127—21no—
11C2×#17985126—21no—
12#22582857—21no—
13#22582856—21no—
14#22582853C2211yescharacteristic
15#22582852—21no—
16#22582851—21no—
17#22582851—21no—
18C2×C4⋊Dic281—21no—
19C2×#17985117C2211yescharacteristic
20#22582804—21no—
21#22582802—21no—
22C22⋊#14555886C2211yescharacteristic
23#22582786—21no—
24#121×C281C2211yescharacteristic
25C22⋊C8×C281C2211yescharacteristic
26#95×C281C2211yescharacteristic
27#17985137—42no—
28#17985137—42no—
29C2×Dic562—21no—
30C2×Dic562—21no—
31C2×Dic562—21no—
32C2×Dic562—42no—
33C2×D1124D411yescharacteristic
34C2×C22⋊D281—21no—
35C2×C22⋊D281—21no—
36C2×C22⋊D281—21no—
37C22×Dic281—21no—
38C22×Dic281—21no—
39C22×Dic281D411yescharacteristic
40C22×Dic281D411yescharacteristic
41C2×C4×D281—21no—
42#17985127—42no—
43#17985126—42no—
44C2×#14555886—21no—
45C4⋊Dic281—42no—
46C4⋊Dic281D411yescharacteristic
47#17985117—21no—
48#17985117—21no—
49#17985117—21no—
50C22⋊Dic281—21no—
51#17985115—21no—
52#17985115—21no—
53C2×D4×C281—21no—
54C2×D4×C281D411yescharacteristic
55C22×C4×C281—21no—
56C22×C4×C281C2311yescharacteristic
57C2×C8×C281—21no—
58C4⋊C4×C281D411yescharacteristic
59C22⋊C4×C281—21no—
60C22×D281—21no—
61Dic562—22no—
62Dic562—22no—
63Dic562—42no—
64Dic562—41no—
65Dic562—41no—
66D1124—41no—
67C22⋊D281—42no—
68C22⋊D281—41no—
69C22⋊D281—41no—
70C22⋊D281—81no—
71C2×Dic281—21no—
72C2×Dic281—21no—
73C2×Dic281—22no—
74C2×Dic281—21no—
75C2×Dic281—21no—
76C2×Dic281—42no—
77C2×Dic281—41no—
78C2×Dic281—41no—
79C2×Dic281—41no—
80C2×Dic281SD1612yescomplemented
81C4×D281—42no—
82#14555886—41no—
83C23×C281—21no—
84C23×C281C2×D411yescharacteristic
85D4×C281—41no—
86D4×C281—41no—
87D4×C281—41no—
88C2×C4×C281—22no—
89C2×C4×C281—21no—
90C2×C4×C281—41no—
91C2×C4×C281—41no—
92C2×C4×C281—41no—
93C2×C4×C281C2×D411yescharacteristic
94C2×C4×C281C2×D411yescharacteristic
95C8×C281—41no—
96C22×C281—21no—
97C22×C281—21no—
98C22×C281—41no—
99C22×C281—41no—
100C22×C281—41no—
101C22×C281#12011yescharacteristic
102C22×C281C2×SD1611yescharacteristic
103C22×C281AGL(1,ℤ/8)11yescharacteristic
104C2×D281—41no—
105C2×D281—41no—
106C2×D281—41no—
107C4×C281—21no—
108C4×C281—21no—
109C4×C281—42no—
110C4×C281—41no—
111Dic281—22no—
112Dic281—41no—
113Dic281—42no—
114Dic281—41no—
115C2×C281—21no—
116C2×C281—21no—
117C2×C281—81no—
118C2×C281#45011yescharacteristic
119C2×C281#45611yescharacteristic
120C2×C281B(4,𝔽2)11yescharacteristic
121D281—81no—
122C281#160411yescharacteristic, complemented, Sylow
123#1604—2811nomaximal, Sylow
124#537—2811no—
125#448—2811no—
126#448—2811no—
127#395—2811no—
128#327—2811no—
129#327D28111yescharacteristic, complemented
130#324—2811no—
131C2×#41—5621no—
132C22×Q8—2811no—
133C2×SD16—5621no—
134C2×SD16—5621no—
135C22⋊Q8—5621no—
136C22⋊Q8—5621no—
137#121—2811no—
138#121—5621no—
139#121—5621no—
140#121—5621no—
141#121C2×D28111yescharacteristic
142C2×C4⋊C4—2811no—
143C2×C4⋊C4—5621no—
144#103—5621no—
145#103—5621no—
146C22⋊C8—2811no—
147C22⋊C8C2×D28111yescharacteristic
148#95—5621no—
149#95C2×D28111yescharacteristic
150#41—11242no—
151#41—11242no—
152C2×Q8—5621no—
153C2×Q8—5621no—
154C2×Q8—5621no—
155C2×Q8—11242no—
156C2×D4—21no—
157C2×D4—2811no—
158C2×D4—5621no—
159C2×D4—5621no—
160C2×D4—5621no—
161C2×D4D112411yescharacteristic
162C22×C4—21no—
163C22×C4—2811no—
164C22×C4—2811no—
165C22×C4—5621no—
166C22×C4—5621no—
167C22×C4—5621no—
168C22×C4C22×D28111yescharacteristic
169SD16—11242no—
170SD16—11242no—
171C2×C8—21no—
172C2×C8—5621no—
173C4⋊C4—2811no—
174C4⋊C4—5621no—
175C4⋊C4—5621no—
176C4⋊C4—5621no—
177C4⋊C4—11242no—
178C4⋊C4D112411yescharacteristic
179C22⋊C4—21no—
180C22⋊C4—5621no—
181C22⋊C4—5621no—
182C22⋊C4—5621no—
183C23—21no—
184C23—5621no—
185C23D4×D28111yescharacteristic
186Q8—5622no—
187Q8—5622no—
188Q8—11241no—
189Q8—11241no—
190Q8—11242no—
191D4—41no—
192D4—41no—
193D4—41no—
194D4—11241no—
195D4—11242no—
196D4—11241no—
197D4—11241no—
198D4—22481no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—2812no—
205C2×C4—5621no—
206C2×C4—5621no—
207C2×C4—5622no—
208C2×C4—5621no—
209C2×C4—5621no—
210C2×C4—11242no—
211C2×C4—11242no—
212C2×C4—11241no—
213C2×C4—11241no—
214C2×C4—11241no—
215C2×C4D4×D28111yescharacteristic
216C2×C4C2×D112411yescharacteristic
217C8—41no—
218C8—11241no—
219C22—21no—
220C22—21no—
221C22—41no—
222C22—41no—
223C22—41no—
224C22—11241no—
225C22—11241no—
226C22—11241no—
227C22#2258284911yescharacteristic
228C22SD16×D28111yescharacteristic
229C22#2258290311yescharacteristic
230C4—21no—
231C4—21no—
232C4—42no—
233C4—41no—
234C4—5622no—
235C4—11242no—
236C4—11241no—
237C4—11241no—
238C2—21no—
239C2—21no—
240C2—81no—
241C2—22481no—
242C2#3182361511yescharacteristic
243C2#3182364711yescharacteristic
244C2#3182365111yescharacteristic
subgroupG/H
centerC22#22582849
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#327×C281C2
socleC22×C281#120
prime radical#31824040C2
hypercenter#327D281
hypocenterC281#1604
LCSG ▷ C22×C4×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #31823604C2semidirect
3. #31823601C2semidirect
4. #31823384C2semidirect
5. #31823196C2semidirect
6. #31823188C2semidirect
7. #327×C281C2semidirect
80. C2×Dic281SD16semidirect
122. C281#1604semidirect
129. #327D281semidirect

Maximal subgroups

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

subgroupindex
#318240402
#318236042
#318236012
#318233842
#318231962
#318231882
#327×C2812
#1604281