Finite Group Databasebeta

← #16847735

Subgroups — #16847735

Order 3968.

236 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 41 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#14521761C211yesmaximal, characteristic, complemented
2#14521232C211yesmaximal, characteristic, complemented
3#14521222C211yesmaximal, characteristic, complemented
4#14520847C211yesmaximal, characteristic, complemented
5#14520846C211yesmaximal, characteristic, complemented
6#14520845C211yesmaximal, characteristic, complemented
7C31×#454C211yesmaximal, characteristic, complemented
8C31×2−1+4C2211yescharacteristic
9C31×AGL(1,ℤ/8)—21no—
10C31×#124C2211yescharacteristic
11#11758528—21no—
12#11758526—21no—
13#11758524C2211yescharacteristic
14#11758521C2211yescharacteristic
15#11758516—21no—
16#11758462—21no—
17#11758461—21no—
18(C22⋊D31)⋊C4—21no—
19#11758454—21no—
20#11758449—21no—
21C31×#104—21no—
22C31×#101C2211yescharacteristic
23#11758425—21no—
24#11758425—21no—
25#11758424C2211yescharacteristic
26#11758424C2211yescharacteristic
27#41×C31—21no—
28#41×C31—21no—
29#41×C31—21no—
30#41×C31—41no—
31C2×Q8×C31—41no—
32C2×Q8×C31C2311yescharacteristic
33C2×D4×C31D411yescharacteristic
34C2×C22⋊D31—21no—
35C2×C22⋊D31—21no—
36C22×Dic31—21no—
37C2×D124D411yescharacteristic
38C2×C4×D31—21no—
39C2×Dic62D411yescharacteristic
40SD16×C31—41no—
41D8×C31—41no—
42M16×C31—21no—
43C22⋊C4×C31—21no—
44C22⋊C4×C31—21no—
45C42×C31D411yescharacteristic
46C22⋊Dic31—21no—
47#92482—41no—
48#92481—41no—
49#92480—41no—
50#92479—41no—
51(C2×D31)⋊C4—21no—
52(C2×D31)⋊C4—21no—
53(C2×D31)⋊C4—21no—
54Dic31⋊C4—21no—
55Dic31⋊C4—21no—
56Dic31⋊C4—21no—
57C4×Dic31—21no—
58C4×Dic31D411yescharacteristic
59C4×Dic31D411yescharacteristic
60#92474—21no—
61#92474—21no—
62C23×C31—21no—
63C22×D31—21no—
64Q8×C31—21no—
65Q8×C31—21no—
66Q8×C31—21no—
67Q8×C31—41no—
68D4×C31—21no—
69D4×C31—21no—
70D4×C31—21no—
71D4×C31—41no—
72D4×C31—41no—
73C2×C4×C31—21no—
74C2×C4×C31—41no—
75C2×C4×C31—41no—
76C2×C4×C31—41no—
77C2×C4×C31C2×D411yescharacteristic
78C2×C4×C31C2×D411yescharacteristic
79C2×C4×C31C2×D411yescharacteristic
80C22⋊D31—42no—
81C22⋊D31—81no—
82C2×Dic31—21no—
83C2×Dic31—21no—
84C2×Dic31—21no—
85C2×Dic31—42no—
86D124—41no—
87C4×D31—42no—
88Dic62—41no—
89C8×C31—41no—
90C31⋊C8—41no—
91C31⋊C8—41no—
92#2204—311nomaximal, Sylow
93C22×C31—41no—
94C22×C31—41no—
95C22×C31—41no—
96C22×C31—41no—
97C22×C31#12011yescharacteristic
98C2×D31—41no—
99C2×D31—41no—
100C2×D31—41no—
101C4×C31—21no—
102C4×C31—21no—
103C4×C31—21no—
104C4×C31—41no—
105C4×C31—41no—
106Dic31—22no—
107Dic31—41no—
108Dic31—41no—
109#555—311no—
110#456—311no—
111#454—311no—
112#454D3111yescharacteristic, complemented
113#356—311no—
114#355—311no—
115#355—311no—
116C2×C31—21no—
117C2×C31—81no—
118C2×C31—81no—
119C2×C31B(4,𝔽2)11yescharacteristic
120D31—81no—
1212−1+4C2×D3111yescharacteristic
122#137—621no—
123AGL(1,ℤ/8)—21no—
124AGL(1,ℤ/8)—621no—
125C4⋊Q8—311no—
126#124—311no—
127#124—621no—
128#124C2×D3111yescharacteristic
129#121—621no—
130#121—621no—
131C4×D4—621no—
132#117—621no—
133#117—621no—
134#104—21no—
135#104—621no—
136#104—621no—
137#101—311no—
138#101—311no—
139#101C2×D3111yescharacteristic
140C31#220411yescharacteristic, complemented, Sylow
141#41—21no—
142#41—21no—
143#41—21no—
144#41—41no—
145C2×Q8—41no—
146C2×Q8—311no—
147C2×Q8C22×D3111yescharacteristic
148C2×D4—311no—
149C2×D4—621no—
150C2×D4—621no—
151C2×D4C22⋊D3111yescharacteristic
152C22×C4—621no—
153C22×C4—621no—
154Q16—1241no—
155SD16—41no—
156SD16—1241no—
157SD16—1241no—
158D8—41no—
159D8—1241no—
160M16—21no—
161M16—621no—
162M16—621no—
163C4⋊C4—621no—
164C4⋊C4—621no—
165C4⋊C4—621no—
166C22⋊C4—21no—
167C22⋊C4—21no—
168C22⋊C4—621no—
169C22⋊C4—621no—
170C22⋊C4—621no—
171C22⋊C4—621no—
172C42—311no—
173C42—311no—
174C42—621no—
175C42C22⋊D3111yescharacteristic
176C23—21no—
177C23—621no—
178Q8—21no—
179Q8—21no—
180Q8—21no—
181Q8—41no—
182Q8—1241no—
183D4—21no—
184D4—21no—
185D4—21no—
186D4—41no—
187D4—41no—
188D4—1241no—
189D4—1242no—
190D4—2481no—
191C2×C4—21no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—621no—
196C2×C4—621no—
197C2×C4—621no—
198C2×C4—1242no—
199C2×C4—1242no—
200C2×C4D4×D3111yescharacteristic
201C2×C4D4×D3111yescharacteristic
202C2×C4C2×C22⋊D3111yescharacteristic
203C8—41no—
204C8—1241no—
205C8—1241no—
206C22—41no—
207C22—41no—
208C22—41no—
209C22—41no—
210C22—1241no—
211C22—1241no—
212C22—1241no—
213C22#1175851411yescharacteristic
214C4—21no—
215C4—21no—
216C4—21no—
217C4—41no—
218C4—41no—
219C4—622no—
220C4—1241no—
221C4—1241no—
222C2—21no—
223C2—81no—
224C2—81no—
225C2—2481no—
226C2#1452123511yescharacteristic
subgroupG/H
centerC2#14521235
commutator, cosocleC2×Q8×C31C23
FrattiniC2×Q8C22×D31
FittingC31×#454C2
socleC2×C31B(4,𝔽2)
hypercenter#454D31
hypocenterC31#2204
LCSG ▷ C2×Q8×C31 ▷ C22×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #454

Complements

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

NH ≅ G/Ntype
1. #14521761C2semidirect
2. #14521232C2semidirect
3. #14521222C2semidirect
4. #14520847C2semidirect
5. #14520846C2semidirect
6. #14520845C2semidirect
7. C31×#454C2semidirect
112. #454D31semidirect
140. C31#2204semidirect

Maximal subgroups

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

subgroupindex
#145217612
#145212322
#145212222
#145208472
#145208462
#145208452
C31×#4542
#220431