Finite Group Databasebeta

← #49094295

Subgroups — #49094295

Order 35968.

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

normal subgroups only

This group has 228 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#31824088C211yesmaximal, characteristic
2#31823794C211yesmaximal, characteristic, complemented
3#31823791C211yesmaximal, characteristic, complemented
4#31823390C211yesmaximal, characteristic
5#31823199C211yesmaximal, characteristic, complemented
6#31823186C211yesmaximal, characteristic
7#328×C281C211yesmaximal, characteristic, complemented
8#22582859—21no—
9#22582858C2211yescharacteristic
10#22582857—21no—
11#22582857—21no—
12#22582856—21no—
13#22582855—21no—
14C2×C4⋊Dic281C2211yescharacteristic
15C2×#17985115—21no—
16C2×#17985115C2211yescharacteristic
17C22⋊C4×D281—21no—
18#22582811—21no—
19#22582810—21no—
20#22582804—21no—
21#22582803—21no—
22C22⋊#14555886C2211yescharacteristic
23#22582786—21no—
24C22⋊Q8×C281C2211yescharacteristic
25C22⋊C8×C281C2211yescharacteristic
26#95×C281C2211yescharacteristic
27C23×D281D411yescharacteristic
28C2×Dic562—21no—
29C2×Dic562D411yescharacteristic
30C22×Dic281—21no—
31C22×Dic281D411yescharacteristic
32C2×C4×D281—21no—
33C2×C4×D281—21no—
34C2×#14555886—21no—
35C4⋊Dic281—21no—
36C4⋊Dic281—21no—
37C4⋊Dic281—21no—
38C4⋊Dic281D411yescharacteristic
39#17985117—21no—
40#17985117—21no—
41#17985117—21no—
42C22⋊Dic281—21no—
43#17985115—21no—
44#17985115—21no—
45#17985115—21no—
46#17985115—21no—
47#17985115—42no—
48C2×Q8×C281D411yescharacteristic
49C22×C4×C281—21no—
50C22×C4×C281C2311yescharacteristic
51C2×C8×C281—21no—
52C4⋊C4×C281—21no—
53C4⋊C4×C281D411yescharacteristic
54C22⋊C4×C281—21no—
55C22×D281—21no—
56C22×D281—21no—
57C22×D281—41no—
58C22×D281—41no—
59C22×D281SD1612yes—
60Dic562—41no—
61Dic562—81no—
62C2×Dic281—21no—
63C2×Dic281—21no—
64C2×Dic281—21no—
65C2×Dic281—41no—
66C2×Dic281—41no—
67C2×Dic281—41no—
68C2×Dic281—41no—
69C4×D281—81no—
70C4×D281—81no—
71#14555886—41no—
72C23×C281C2×D411yescharacteristic
73Q8×C281—41no—
74C2×C4×C281—21no—
75C2×C4×C281—21no—
76C2×C4×C281—41no—
77C2×C4×C281—41no—
78C2×C4×C281—41no—
79C2×C4×C281—41no—
80C2×C4×C281C2×D411yescharacteristic
81C2×C4×C281C2×D411yescharacteristic
82C8×C281—41no—
83C22×C281—21no—
84C22×C281—21no—
85C22×C281#12011yescharacteristic
86C22×C281C2×SD1611yescharacteristic
87C22×C281#13711yescharacteristic
88C2×D281—22no—
89C2×D281—41no—
90C2×D281—41no—
91C2×D281—42no—
92C2×D281—81no—
93C4×C281—21no—
94C4×C281—21no—
95C4×C281—41no—
96C4×C281—41no—
97C4×C281—81no—
98Dic281—41no—
99Dic281—41no—
100Dic281—41no—
101Dic281—81no—
102C2×C281—21no—
103C2×C281—21no—
104C2×C281#44811yescharacteristic
105C2×C281#45511yescharacteristic
106C2×C281#45811yescharacteristic
107D281—42no—
108C281#160811yescharacteristic, complemented, Sylow
109#1608—2811nomaximal, Sylow
110#543—2811no—
111#483—2811no—
112#483—2811no—
113#397—2811no—
114#328—2811no—
115#328D28111yescharacteristic, complemented
116#323—2811no—
117C22⋊Q8—2811no—
118C22⋊Q8—5621no—
119C22⋊Q8—5621no—
120C22⋊Q8—5621no—
121C22⋊Q8—5621no—
122C22⋊Q8—5621no—
123C22⋊Q8C2×D28111yescharacteristic
124C2×C4⋊C4—2811no—
125C2×C22⋊C4—2811no—
126C2×C22⋊C4—5621no—
127C2×C22⋊C4—5621no—
128#106—5621no—
129#106—5621no—
130#103—5621no—
131#103—5621no—
132C22⋊C8—2811no—
133C22⋊C8C2×D28111yescharacteristic
134#95—5621no—
135#95C2×D28111yescharacteristic
136C24—2811no—
137C2×Q8—2811no—
138C2×Q8—5621no—
139C2×Q8D112411yescharacteristic
140C22×C4—21no—
141C22×C4—2811no—
142C22×C4—5621no—
143C22×C4—5621no—
144C22×C4—5621no—
145C22×C4C22×D28111yescharacteristic
146C2×C8—21no—
147C2×C8—5621no—
148C4⋊C4—21no—
149C4⋊C4—2811no—
150C4⋊C4—5621no—
151C4⋊C4—5621no—
152C4⋊C4—5621no—
153C4⋊C4—5621no—
154C4⋊C4—5621no—
155C4⋊C4—5621no—
156C4⋊C4D112411yescharacteristic
157C22⋊C4—21no—
158C22⋊C4—5621no—
159C22⋊C4—5621no—
160C22⋊C4—5621no—
161C22⋊C4—5621no—
162C22⋊C4—5621no—
163C22⋊C4—11242no—
164C23—2812no—
165C23—5621no—
166C23—5621no—
167C23—11241no—
168C23—11241no—
169C23D4×D28111yescharacteristic
170Q8—41no—
171Q8—11241no—
172Q8—22481no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—5621no—
180C2×C4—5621no—
181C2×C4—5621no—
182C2×C4—11241no—
183C2×C4—11241no—
184C2×C4—11241no—
185C2×C4—11241no—
186C2×C4—22481no—
187C2×C4—22481no—
188C2×C4D4×D28111yescharacteristic
189C2×C4C2×D112411yescharacteristic
190C8—41no—
191C8—11241no—
192C22—21no—
193C22—21no—
194C22—5622no—
195C22—11242no—
196C22—11241no—
197C22—11241no—
198C22—22481no—
199C22#2258284911yescharacteristic
200C22SD16×D28111yescharacteristic
201C22#2258291111yescharacteristic
202C4—21no—
203C4—21no—
204C4—41no—
205C4—41no—
206C4—81no—
207C4—11241no—
208C4—11241no—
209C4—11241no—
210C4—22481no—
211C2—21no—
212C2—21no—
213C2—11242no—
214C2#3182360311yescharacteristic
215C2#3182364211yescharacteristic
216C2#3182365411yescharacteristic
subgroupG/H
centerC22#22582849
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#328×C281C2
socleC22×C281#120
prime radicalC23×D281D4
hypercenter#328D281
hypocenterC281#1608
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. #31823794C2semidirect
3. #31823791C2semidirect
5. #31823199C2semidirect
7. #328×C281C2semidirect
108. C281#1608semidirect
115. #328D281semidirect

Maximal subgroups

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

subgroupindex
#318240882
#318237942
#318237912
#318233902
#318231992
#318231862
#328×C2812
#1608281