Finite Group Databasebeta

← #11785488

Subgroups — #11785488

Order 1152.

526 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 72 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
1C2×#64110C211yesmaximal, characteristic
2#10593792C212yesmaximal
3#10593768C212yesmaximal, complemented
4#10590184C212yesmaximal, complemented
5C2×#3828C2211yescharacteristic
6#64286C2214yes—
7C22×C32×C8C411yescharacteristic, complemented
8C2×#3748C411yescharacteristic, complemented
9#64110—22no—
10#64110—22no—
11C2×#3743C411yescharacteristic, complemented
12C2×#3743C2211yescharacteristic
13C2×C8×C3⋊D3C411yescharacteristic, complemented
14C2×C8×C3⋊D3C2211yescharacteristic
15#63786—22no—
16#63774—22no—
17#63769—22no—
18#63768—22no—
19C2×#901—62no—
20C22×C32×C4C2×C411yescharacteristic
21C2×#638D411yescharacteristic
22C2×#638Q811yescharacteristic
23#3828—22no—
24#3828—22no—
25C2×C4⋊(C3⋊D3)D411yescharacteristic
26C2×C4×C3⋊D3C2×C411yescharacteristic
27C2×C4×C3⋊D3C2311yescharacteristic
28C2×#634Q811yescharacteristic
29C22⋊#157—24no—
30C4⋊#157—24no—
31C4×#157—24no—
32C2×C32×C8—21no—
33C2×C32×C8—21no—
34C2×C32×C8C2×C411yescharacteristic
35C2×C32×C8C2×C411yescharacteristic
36#3748—22no—
37C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
38C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
39#3743—22no—
40#3743—22no—
41C8×C3⋊D3—21no—
42C8×C3⋊D3—21no—
43C8×C3⋊D3D412yes—
44C8×C3⋊D3D412yes—
45#1812—91nomaximal, Sylow
46C2×#235—62no—
47C22×C3×C8—22no—
48C2×#208—62no—
49#901—68no—
50#901—68no—
51C2×ΓL(1,𝔽25)—62no—
52C2×ΓL(1,𝔽25)—62no—
53C2×D3×C8—62no—
54C2×D3×C8—62no—
55C23×C32C4⋊C411yescharacteristic
56C22×C3⋊D3C4⋊C411yescharacteristic
57C22×C3⋊D3C2×D411yescharacteristic
58C2×#157—44no—
59C2×C32×C4—21no—
60C2×C32×C4—21no—
61C2×C32×C4C4⋊C411yescharacteristic
62C2×C32×C4C22×C411yescharacteristic
63#638—22no—
64#638—22no—
65C2×C3⋊Dic3C4⋊C411yescharacteristic
66C2×C3⋊Dic3C2×Q811yescharacteristic
67C4⋊(C3⋊D3)—22no—
68C4×C3⋊D3—21no—
69C4×C3⋊D3—21no—
70C4×C3⋊D3C2×D412yes—
71C4×C3⋊D3#4112yes—
72#634—22no—
73C32×C8—21no—
74C32×C8C22⋊C411yescharacteristic
75C32×C8C22⋊C411yescharacteristic
76C3⋊(C3⋊C8)—21no—
77C3⋊(C3⋊C8)C22⋊C412yes—
78C2×#131—91no—
79#427—92no—
80#410—92no—
81H(3,ℤ/4)—92no—
82C22×C3×C4—22no—
83C2×#67—62no—
84C2×#67—62no—
85#235—68no—
86#235—68no—
87C2×D12—62no—
88C2×C4×D3—62no—
89C2×C4×D3—62no—
90C2×Dic6—62no—
91C2×C3×C8—24no—
92C2×C3×C8—24no—
93C2×C3×C8—22no—
94C2×C3×C8—22no—
95#208—68no—
96C2×C3⋊C8—62no—
97C2×C3⋊C8—62no—
98ΓL(1,𝔽25)—68no—
99ΓL(1,𝔽25)—68no—
100D3×C8—64no—
101D3×C8—64no—
102D3×C8—64no—
103D3×C8—64no—
104C22×C32—21no—
105C22×C32—41no—
106C22×C32C2×C4⋊C411yescharacteristic
107C2×C3⋊D3—21no—
108C2×C3⋊D3—41no—
109C2×C3⋊D3—41no—
110C2×C3⋊D3#12112yes—
111#157—84no—
112C32×C4—21no—
113C32×C4C2×C22⋊C411yescharacteristic
114C32×C4#11711yescharacteristic
115C3⋊Dic3—21no—
116C3⋊Dic3C22⋊Q812yes—
117C2×#41—91no—
118#131—182no—
119#131—182no—
120C2×M16—91no—
121C2×M16—91no—
122C2×M16—91no—
123C22×C8—91no—
124C22×C8—91no—
125C22×C8#15711yescharacteristic, complemented
126#117—94no—
127#107—182no—
128#106—182no—
129#99—182no—
130#99—182no—
131C23×C3—22no—
132C22×D3—62no—
133C22×D3—62no—
134C2×C3×C4—24no—
135C2×C3×C4—24no—
136C2×C3×C4—22no—
137C2×C3×C4—22no—
138#67—68no—
139#67—68no—
140C2×Dic3—62no—
141C2×Dic3—62no—
142D12—68no—
143C4×D3—64no—
144C4×D3—64no—
145C4×D3—64no—
146C4×D3—64no—
147Dic6—68no—
148C3×C8—24no—
149C3×C8—22no—
150C3×C8—22no—
151C3⋊C8—64no—
152C3⋊C8—64no—
153C2×C32—21no—
154C2×C32—41no—
155C2×C32#38011yescharacteristic
156C3⋊D3—22no—
157C3⋊D3—41no—
158#41—182no—
159#41—182no—
160C2×Q8—91no—
161C2×D4—91no—
162C2×D4—91no—
163C2×D4—91no—
164C22×C4—91no—
165C22×C4—91no—
166C22×C4C2×#15711yescharacteristic
167M16—182no—
168M16—182no—
169M16—182no—
170C2×C8—21no—
171C2×C8—21no—
172C2×C8—91no—
173C2×C8—92no—
174C2×C8—92no—
175C2×C8—91no—
176C2×C8—181no—
177C2×C8—181no—
178C2×C8C2×#15711yescharacteristic
179C2×C8C2×#15711yescharacteristic
180C4⋊C4—184no—
181C22⋊C4—184no—
182C42—184no—
183C22×C3—24no—
184C22×C3—22no—
185C22×C3—44no—
186C2×D3—64no—
187C2×D3—64no—
188C2×D3—124no—
189C2×D3—124no—
190C3×C4—24no—
191C3×C4—22no—
192C3×C4—22no—
193Dic3—64no—
194Dic3—64no—
195C32#181211yescharacteristic, complemented, Sylow
196C23—91no—
197C23—91no—
198C23C4⋊#15711yescharacteristic
199Q8—182no—
200D4—182no—
201D4—182no—
202D4—182no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—91no—
206C2×C4—92no—
207C2×C4—92no—
208C2×C4—91no—
209C2×C4—181no—
210C2×C4—181no—
211C2×C4—364no—
212C2×C4C4⋊#15711yescharacteristic
213C2×C4C22×#15711yescharacteristic
214C8—21no—
215C8—92no—
216C8—181no—
217C8C22⋊#15711yescharacteristic
218C8C22⋊#15711yescharacteristic
219C2×C3—24no—
220C2×C3—22no—
221C2×C3—44no—
222D3—124no—
223D3—124no—
224C22—21no—
225C22—41no—
226C22—92no—
227C22—181no—
228C22—361no—
229C22—361no—
230C22C2×C4⋊#15711yescharacteristic
231C4—21no—
232C4—92no—
233C4—181no—
234C4—724no—
235C4#6428611yescharacteristic
236C4C2×C22⋊#15711yescharacteristic
237C3—22no—
238C2—21no—
239C2—41no—
240C2—182no—
241C2—361no—
242C2#1059381211yescharacteristic
subgroupG/H
centerC4#64286
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC22×C32×C8C4
socleC2×C32#380
prime radicalC2×#3828C22
cosocleC2×C4×C3⋊D3C23
hypercenterC22×C8#157
hypocenterC32#1812
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C8 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
3. #10593768C2semidirect
4. #10590184C2semidirect
7. C22×C32×C8C4semidirect
8. C2×#3748C4semidirect
11. C2×#3743C4semidirect
13. C2×C8×C3⋊D3C4semidirect
125. C22×C8#157semidirect
195. C32#1812semidirect

Maximal subgroups

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

subgroupindex
C2×#641102
#105937922
#105937682
#105901842
#18129