Finite Group Databasebeta

← #49094244

Subgroups — #49094244

Order 35968.

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

normal subgroups only

This group has 266 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#31824092C211yesmaximal, characteristic, complemented
2#31823616C211yesmaximal, characteristic
3#31823613C211yesmaximal, characteristic
4#31823381C211yesmaximal, characteristic
5#31823199C211yesmaximal, characteristic, complemented
6#31823188C211yesmaximal, characteristic, complemented
7#328×C281C211yesmaximal, characteristic, complemented
8C22×D1124C2211yescharacteristic
9C2×#17985127—21no—
10C2×#17985125—21no—
11#22582878—21no—
12#22582877—21no—
13#22582869—21no—
14#22582869—21no—
15#22582858C2211yescharacteristic
16#22582856—21no—
17#22582835—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×Dic562—21no—
29C2×Dic562D411yescharacteristic
30C2×D1124—21no—
31C2×D1124—21no—
32C2×D1124—42no—
33C22×Dic281D411yescharacteristic
34C22×Dic281D411yescharacteristic
35#17985127—42no—
36#17985125—42no—
37C2×#14555886—21no—
38C4⋊Dic281—21no—
39C4⋊Dic281D411yescharacteristic
40#17985117—21no—
41#17985117—21no—
42#17985117—21no—
43#17985117—21no—
44#17985117—21no—
45#17985117—21no—
46#17985117—21no—
47C22⋊Dic281—21no—
48#17985115—42no—
49#17985115—42no—
50C4×Dic281—21no—
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—41no—
61C22×D281—41no—
62C22×D281—41no—
63C22×D281—41no—
64C22×D281—41no—
65C22×D281—41no—
66Dic562—41no—
67Dic562—81no—
68D1124—22no—
69D1124—22no—
70D1124—41no—
71D1124—41no—
72C2×Dic281—21no—
73C2×Dic281—21no—
74C2×Dic281—21no—
75C2×Dic281—21no—
76C2×Dic281—21no—
77C2×Dic281—41no—
78C2×Dic281SD1612yescomplemented
79#14555886—41no—
80C23×C281C2×D411yescharacteristic
81Q8×C281—41no—
82C2×C4×C281—21no—
83C2×C4×C281—21no—
84C2×C4×C281—41no—
85C2×C4×C281—41no—
86C2×C4×C281—41no—
87C2×C4×C281—41no—
88C2×C4×C281C2×D411yescharacteristic
89C2×C4×C281C2×D411yescharacteristic
90C8×C281—41no—
91C22×C281—21no—
92C22×C281—21no—
93C22×C281#12011yescharacteristic
94C22×C281C2×SD1611yescharacteristic
95C22×C281#13711yescharacteristic
96C2×D281—42no—
97C2×D281—42no—
98C2×D281—42no—
99C2×D281—81no—
100C2×D281—81no—
101C2×D281—81no—
102C2×D281—81no—
103C4×C281—21no—
104C4×C281—21no—
105C4×C281—41no—
106C4×C281—41no—
107C4×C281—81no—
108Dic281—22no—
109Dic281—41no—
110Dic281—41no—
111Dic281—41no—
112C2×C281—21no—
113C2×C281—21no—
114C2×C281#44811yescharacteristic
115C2×C281#45411yescharacteristic
116C2×C281B(4,𝔽2)11yescharacteristic
117D281—82no—
118C281#159911yescharacteristic, complemented, Sylow
119#1599—2811nomaximal, Sylow
120#544—2811no—
121#450—2811no—
122#450—2811no—
123#394—2811no—
124#328—2811no—
125#328D28111yescharacteristic, complemented
126#324—2811no—
127C22×D4—2811no—
128C2×SD16—5621no—
129C2×SD16—5621no—
130C4⋊Q8—5621no—
131C4⋊Q8—5621no—
132#125—5621no—
133#125—5621no—
134C22⋊Q8—2811no—
135C22⋊Q8—5621no—
136C22⋊Q8C2×D28111yescharacteristic
137#117—5621no—
138C2×C4⋊C4—2811no—
139C2×C22⋊C4—5621no—
140C2×C22⋊C4—5621no—
141#102—5621no—
142#102—5621no—
143C22⋊C8—2811no—
144C22⋊C8C2×D28111yescharacteristic
145#95C2×D28111yescharacteristic
146C24—5621no—
147C2×Q8—2811no—
148C2×Q8—5621no—
149C2×Q8D112411yescharacteristic
150C2×D4—5621no—
151C2×D4—5621no—
152C2×D4—11242no—
153C22×C4—21no—
154C22×C4—2811no—
155C22×C4—2811no—
156C22×C4C22×D28111yescharacteristic
157SD16—11242no—
158SD16—11242no—
159C2×C8—21no—
160C2×C8—5621no—
161C4⋊C4—21no—
162C4⋊C4—2811no—
163C4⋊C4—5621no—
164C4⋊C4—5621no—
165C4⋊C4—5621no—
166C4⋊C4—5621no—
167C4⋊C4—5621no—
168C4⋊C4—5621no—
169C4⋊C4—5621no—
170C4⋊C4—5621no—
171C4⋊C4D112411yescharacteristic
172C22⋊C4—21no—
173C22⋊C4—5621no—
174C22⋊C4—11242no—
175C22⋊C4—11242no—
176C42—5621no—
177C42—5621no—
178C23—5622no—
179C23—11241no—
180C23—11241no—
181C23—11241no—
182C23—11241no—
183C23—11241no—
184C23—11241no—
185C23D4×D28111yescharacteristic
186Q8—41no—
187Q8—11241no—
188Q8—22481no—
189D4—5622no—
190D4—5622no—
191D4—11241no—
192D4—11241no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—2812no—
200C2×C4—5621no—
201C2×C4—5621no—
202C2×C4—5621no—
203C2×C4—5621no—
204C2×C4—5621no—
205C2×C4—11241no—
206C2×C4D4×D28111yescharacteristic
207C2×C4C2×D112411yescharacteristic
208C8—41no—
209C8—11241no—
210C22—21no—
211C22—21no—
212C22—11242no—
213C22—11242no—
214C22—11242no—
215C22—22481no—
216C22—22481no—
217C22—22481no—
218C22—22481no—
219C22#2258284911yescharacteristic
220C22SD16×D28111yescharacteristic
221C22#2258291111yescharacteristic
222C4—21no—
223C4—21no—
224C4—41no—
225C4—41no—
226C4—81no—
227C4—5622no—
228C4—11241no—
229C4—11241no—
230C4—11241no—
231C2—21no—
232C2—21no—
233C2—22482no—
234C2#3182360311yescharacteristic
235C2#3182363711yescharacteristic
236C2#3182365111yescharacteristic
subgroupG/H
centerC22#22582849
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#328×C281C2
socleC22×C281#120
prime radicalC22×D1124C22
hypercenter#328D281
hypocenterC281#1599
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. #31824092C2semidirect
5. #31823199C2semidirect
6. #31823188C2semidirect
7. #328×C281C2semidirect
78. C2×Dic281SD16semidirect
118. C281#1599semidirect
125. #328D281semidirect

Maximal subgroups

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

subgroupindex
#318240922
#318236162
#318236132
#318233812
#318231992
#318231882
#328×C2812
#1599281