Finite Group Databasebeta

← #16846620

Subgroups — #16846620

Order 3968.

316 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C22×#92479C211yesmaximal, characteristic
2C2×#11758410C211yesmaximal, characteristic, complemented
3#14521053C211yesmaximal, characteristic, complemented
4C2×#11758421C211yesmaximal, characteristic, complemented
5C2×#11758411C211yesmaximal, characteristic, complemented
6#14521005C211yesmaximal, characteristic, complemented
7C31×#418C211yesmaximal, characteristic, complemented
8C22×D4×C31C2211yescharacteristic
9C22×D124C2211yescharacteristic
10C2×M16×C31C2211yescharacteristic
11C31×#117C2211yescharacteristic
12C2×#92479—21no—
13C2×#92479—21no—
14C2×#92479—22no—
15C2×#92479C414yescomplemented
16C2×#92474C2211yescharacteristic
17C2×#92474C2211yescharacteristic
18C22×C31⋊C8C2211yescharacteristic
19C31×#102—22no—
20#11758421—22no—
21#11758411—22no—
22#11758410—22no—
23#11758397—22no—
24#11758391—21no—
25C4×C31⋊C8—21no—
26C24×C31—21no—
27C23×D31—21no—
28C2×D4×C31—21no—
29C2×D4×C31—21no—
30C2×D4×C31—21no—
31C2×D4×C31—21no—
32C2×D4×C31—21no—
33C2×D4×C31C2×C412yes—
34C22×C4×C31C2311yescharacteristic
35C2×D124—21no—
36C2×D124—21no—
37C2×D124—21no—
38C2×D124—21no—
39C2×D124—21no—
40C2×D124C2×C412yes—
41M16×C31—21no—
42M16×C31—21no—
43C2×C8×C31—21no—
44C4⋊C4×C31D412yes—
45C22⋊C4×C31—21no—
46C42×C31—21no—
47#92479—24no—
48#92479—24no—
49#92474—21no—
50#92474—21no—
51#92474—21no—
52#92474D412yes—
53C2×C31⋊C8—21no—
54C2×C31⋊C8—21no—
55C2×C31⋊C8C2×C412yes—
56C2×C31⋊C8D411yescharacteristic
57C2×C31⋊C8D411yescharacteristic
58C2×C31⋊C8D412yes—
59C23×C31—22no—
60C23×C31—41no—
61C23×C31—41no—
62C23×C31—82no—
63C23×C31#4111yescharacteristic
64C22×D31—22no—
65C22×D31—41no—
66C22×D31—41no—
67C22×D31—82no—
68D4×C31—22no—
69D4×C31—22no—
70D4×C31—41no—
71D4×C31—41no—
72C2×C4×C31—22no—
73C2×C4×C31C22×C411yescharacteristic
74C2×C4×C31C2×D411yescharacteristic
75C2×C4×C31C2×D411yescharacteristic
76C2×C4×C31C2×D411yescharacteristic
77C2×C4×C31C2×D411yescharacteristic
78C2×C4×C31#4111yescharacteristic
79D124—22no—
80D124—22no—
81D124—41no—
82D124—41no—
83C8×C31—41no—
84C31⋊C8—22no—
85C31⋊C8—41no—
86C31⋊C8C22⋊C412yes—
87C31⋊C8C22⋊C412yes—
88#1978—311nomaximal, Sylow
89C22×C31—22no—
90C22×C31—42no—
91C22×C31—82no—
92C22×C31—82no—
93C22×C31—82no—
94C22×C31C4×D411yescharacteristic
95C22×C31#12111yescharacteristic
96C22×C31#12411yescharacteristic
97C2×D31—42no—
98C2×D31—82no—
99C2×D31—82no—
100C2×D31—82no—
101C4×C31—42no—
102C4×C31C2×C22⋊C411yescharacteristic
103C4×C31C4×D411yescharacteristic
104C4×C31#12111yescharacteristic
105C4×C31#12711yescharacteristic
106C22×D8—311no—
107C2×#108—311no—
108#418—311no—
109#418D3111yescharacteristic, complemented
110C2×#100—311no—
111C2×#100—311no—
112#405—311no—
113C2×C31—21no—
114C2×C31—21no—
115C2×C31—82no—
116C2×C31#39011yescharacteristic
117C2×C31#47212yes—
118D31—82no—
119C22×D4—311no—
120C22×D4C2×D3111yescharacteristic
121C2×D8—314no—
122C2×D8—621no—
123C2×D8—621no—
124C2×D8—622no—
125C2×M16—311no—
126C2×M16—311no—
127C2×M16C2×D3111yescharacteristic
128C22×C8—311no—
129#117C2×D3111yescharacteristic
130#108—622no—
131#102—22no—
132#102—622no—
133#100—622no—
134#100—622no—
135#97—621no—
136C4×C8—621no—
137C31#197811yescharacteristic, complemented, Sylow
138C24—21no—
139C24—621no—
140C2×D4—21no—
141C2×D4—21no—
142C2×D4—21no—
143C2×D4—21no—
144C2×D4—21no—
145C2×D4—312no—
146C2×D4—621no—
147C2×D4—621no—
148C2×D4—621no—
149C2×D4—621no—
150C2×D4—621no—
151C2×D4C4×D3112yes—
152C22×C4C22×D3111yescharacteristic
153D8—624no—
154D8—624no—
155M16—21no—
156M16—21no—
157M16—312no—
158M16—621no—
159M16—621no—
160M16—621no—
161C2×C8—21no—
162C2×C8—312no—
163C2×C8—311no—
164C2×C8—311no—
165C2×C8—312no—
166C2×C8—621no—
167C2×C8—621no—
168C4⋊C4C22⋊D3112yes—
169C22⋊C4—21no—
170C42—21no—
171C23—22no—
172C23—41no—
173C23—41no—
174C23—82no—
175C23—622no—
176C23—1241no—
177C23—1241no—
178C23—2482no—
179C23#9249711yescharacteristic
180D4—22no—
181D4—22no—
182D4—41no—
183D4—41no—
184D4—622no—
185D4—622no—
186D4—1241no—
187D4—1241no—
188C2×C4—22no—
189C2×C4C2×C4×D3111yescharacteristic
190C2×C4#9249511yescharacteristic
191C2×C4D4×D3111yescharacteristic
192C2×C4D4×D3111yescharacteristic
193C2×C4D4×D3111yescharacteristic
194C2×C4C2×C22⋊D3111yescharacteristic
195C8—41no—
196C8—312no—
197C8—312no—
198C8—622no—
199C8—1241no—
200C22—22no—
201C22—42no—
202C22—82no—
203C22—82no—
204C22—82no—
205C22—1242no—
206C22—2482no—
207C22—2482no—
208C22—2482no—
209C22(C22⋊D31)⋊C411yescharacteristic
210C22#1175846211yescharacteristic
211C22#1175851611yescharacteristic
212C4—42no—
213C4C22⋊C4×D3111yescharacteristic
214C4#1175846111yescharacteristic
215C4C4×C22⋊D3111yescharacteristic
216C4#1175851711yescharacteristic
217C2—21no—
218C2—21no—
219C2—82no—
220C2—2482no—
221C2#1452094911yescharacteristic
222C2#1452131712yes—
subgroupG/H
centerC22#11758516
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#418C2
socleC22×C31#121
prime radicalC22×#92479C2
cosocleC22×C4×C31C23
hypercenter#418D31
hypocenterC31#1978
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
2. C2×#11758410C2semidirect
3. #14521053C2semidirect
4. C2×#11758421C2semidirect
5. C2×#11758411C2semidirect
6. #14521005C2semidirect
7. C31×#418C2semidirect
15. C2×#92479C4semidirect
109. #418D31semidirect
137. C31#1978semidirect

Maximal subgroups

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

subgroupindex
C22×#924792
C2×#117584102
#145210532
C2×#117584212
C2×#117584112
#145210052
C31×#4182
#197831