Finite Group Databasebeta

← #49094329

Subgroups — #49094329

Order 35968.

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

normal subgroups only

This group has 236 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#31823799C211yesmaximal, characteristic, complemented
3#31823796C211yesmaximal, characteristic, complemented
4#31823400C211yesmaximal, 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⋊Dic281—21no—
15C2×C4⋊Dic281C2211yescharacteristic
16C2×#17985115—21no—
17C2×#17985115C2211yescharacteristic
18C22⋊C4×D281—21no—
19#22582813—21no—
20#22582812—21no—
21#22582804—21no—
22#22582803—21no—
23C22⋊#14555886C2211yescharacteristic
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⋊Dic281—42no—
39C4⋊Dic281D411yescharacteristic
40#17985117—21no—
41#17985117—21no—
42#17985117—21no—
43C22⋊Dic281—21no—
44#17985115—21no—
45#17985115—21no—
46#17985115—21no—
47#17985115—21no—
48#17985115—42no—
49C2×Q8×C281D411yescharacteristic
50C22×C4×C281—21no—
51C22×C4×C281C2311yescharacteristic
52C2×C8×C281—21no—
53C4⋊C4×C281—21no—
54C4⋊C4×C281D411yescharacteristic
55C22⋊C4×C281—21no—
56C22×D281—21no—
57C22×D281—21no—
58C22×D281—41no—
59C22×D281—41no—
60C22×D281Q1612yes—
61Dic562—41no—
62Dic562—81no—
63C2×Dic281—21no—
64C2×Dic281—21no—
65C2×Dic281—21no—
66C2×Dic281—41no—
67C2×Dic281—41no—
68C2×Dic281—41no—
69C2×Dic281—41no—
70C4×D281—81no—
71C4×D281—81no—
72#14555886—41no—
73C23×C281C2×D411yescharacteristic
74Q8×C281—41no—
75C2×C4×C281—22no—
76C2×C4×C281—21no—
77C2×C4×C281—21no—
78C2×C4×C281—41no—
79C2×C4×C281—41no—
80C2×C4×C281—41no—
81C2×C4×C281C2×D411yescharacteristic
82C2×C4×C281C2×D411yescharacteristic
83C8×C281—41no—
84C22×C281—21no—
85C22×C281—21no—
86C22×C281#12011yescharacteristic
87C22×C281C2×Q1611yescharacteristic
88C22×C281#13711yescharacteristic
89C2×D281—22no—
90C2×D281—41no—
91C2×D281—41no—
92C2×D281—42no—
93C2×D281—81no—
94C4×C281—21no—
95C4×C281—21no—
96C4×C281—42no—
97C4×C281—41no—
98C4×C281—41no—
99Dic281—41no—
100Dic281—41no—
101Dic281—41no—
102Dic281—81no—
103C2×C281—21no—
104C2×C281—21no—
105C2×C281#45111yescharacteristic
106C2×C281#45311yescharacteristic
107C2×C281#45811yescharacteristic
108D281—42no—
109C281#161411yescharacteristic, complemented, Sylow
110#1614—2811nomaximal, Sylow
111#543—2811no—
112#484—2811no—
113#484—2811no—
114#399—2811no—
115#328—2811no—
116#328D28111yescharacteristic, complemented
117#323—2811no—
118C22⋊Q8—2811no—
119C22⋊Q8—5621no—
120C22⋊Q8—5621no—
121C22⋊Q8—5621no—
122C22⋊Q8—5621no—
123C22⋊Q8—5621no—
124C22⋊Q8C2×D28111yescharacteristic
125C2×C4⋊C4—2811no—
126C2×C4⋊C4—5621no—
127C2×C22⋊C4—2811no—
128C2×C22⋊C4—5621no—
129C2×C22⋊C4—5621no—
130#107—5621no—
131#107—5621no—
132#103—5621no—
133#103—5621no—
134C22⋊C8—2811no—
135C22⋊C8C2×D28111yescharacteristic
136#95C2×D28111yescharacteristic
137C24—2811no—
138C2×Q8—2811no—
139C2×Q8—5621no—
140C2×Q8D112411yescharacteristic
141C22×C4—21no—
142C22×C4—2811no—
143C22×C4—5621no—
144C22×C4—5621no—
145C22×C4—5621no—
146C22×C4C22×D28111yescharacteristic
147C2×C8—21no—
148C2×C8—5621no—
149C4⋊C4—21no—
150C4⋊C4—2811no—
151C4⋊C4—5621no—
152C4⋊C4—5621no—
153C4⋊C4—5621no—
154C4⋊C4—5621no—
155C4⋊C4—5621no—
156C4⋊C4—5621no—
157C4⋊C4—11242no—
158C4⋊C4D112411yescharacteristic
159C22⋊C4—21no—
160C22⋊C4—5621no—
161C22⋊C4—5621no—
162C22⋊C4—5621no—
163C22⋊C4—5621no—
164C22⋊C4—5621no—
165C22⋊C4—11242no—
166C23—2812no—
167C23—5621no—
168C23—5621no—
169C23—11241no—
170C23—11241no—
171C23D4×D28111yescharacteristic
172Q8—41no—
173Q8—11241no—
174Q8—22481no—
175C2×C4—22no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—5621no—
182C2×C4—5621no—
183C2×C4—5621no—
184C2×C4—11241no—
185C2×C4—11241no—
186C2×C4—11241no—
187C2×C4—11241no—
188C2×C4—22481no—
189C2×C4—22481no—
190C2×C4D4×D28111yescharacteristic
191C2×C4C2×D112411yescharacteristic
192C8—41no—
193C8—11241no—
194C22—21no—
195C22—21no—
196C22—5622no—
197C22—11242no—
198C22—11241no—
199C22—11241no—
200C22—22481no—
201C22#2258284911yescharacteristic
202C22Q16×D28111yescharacteristic
203C22#2258290811yescharacteristic
204C4—21no—
205C4—21no—
206C4—42no—
207C4—41no—
208C4—41no—
209C4—11241no—
210C4—11241no—
211C4—11241no—
212C4—22481no—
213C2—21no—
214C2—21no—
215C2—11242no—
216C2#3182362011yescharacteristic
217C2#3182363211yescharacteristic
218C2#3182365411yescharacteristic
subgroupG/H
centerC22#22582849
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#328×C281C2
socleC22×C281#120
prime radicalC23×D281D4
hypercenter#328D281
hypocenterC281#1614
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. #31823799C2semidirect
3. #31823796C2semidirect
5. #31823199C2semidirect
7. #328×C281C2semidirect
109. C281#1614semidirect
116. #328D281semidirect

Maximal subgroups

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

subgroupindex
#318240882
#318237992
#318237962
#318234002
#318231992
#318231862
#328×C2812
#1614281