Finite Group Databasebeta

← #11785496

Subgroups — #11785496

Order 1152.

653 conjugacy classes of subgroups; only the 148 normal subgroups are shown.

normal subgroups only

This group has 653 conjugacy classes of subgroups — too many to draw. Only its 148 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×#64157C211yesmaximal, characteristic
2C3×#5240C212yesmaximal
3#10591138C212yesmaximal, complemented
4#10589157C212yesmaximal, complemented
5#70041—32nomaximal
6C2×C32×#41C2211yescharacteristic
7#64157—22no—
8#64157—22no—
9C2×#3748C412yescomplemented
10C2×#3748C2211yescharacteristic
11C22×C3⋊(C3⋊C8)C412yescomplemented
12C22×C3⋊(C3⋊C8)C2211yescharacteristic
13C3×#926C2214yes—
14C3×#834—24no—
15#63576—22no—
16#63574—22no—
17C2×#948—32no—
18C2×#948—61no—
19C3×#410—32no—
20#5240D312yes—
21#4998—34no—
22#4531—34no—
23C32×#41—22no—
24C32×#41—22no—
25C2×C32×Q8Q811yescharacteristic
26C2×C32×D4D412yes—
27C2×C32×D4Q811yescharacteristic
28C22×C32×C4C2×C412yes—
29C22×C32×C4C2311yescharacteristic
30#3748—22no—
31#3748—24no—
32C2×C3⋊(C3⋊C8)—22no—
33C2×C3⋊(C3⋊C8)—22no—
34C2×C3⋊(C3⋊C8)C2×C412yes—
35C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
36C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
37C2×C3⋊(C3⋊C8)D412yes—
38C2×C3⋊(C3⋊C8)D412yes—
39C3×#217—24no—
40C3×C4⋊Dic3—24no—
41C3×C4×Dic3—24no—
42#1812—91noSylow
43C2×C3×#41—21no—
44C2×C3×#41C2×D312yes—
45C3×#117—34no—
46#948—64no—
47#948—64no—
48#948—64no—
49#948—64no—
50#926C2×D314yes—
51C2×#208—34no—
52C2×#208—32no—
53C2×#208—62no—
54C2×#208—61no—
55C22×C3⋊C8—32no—
56C22×C3⋊C8—34no—
57C22×C3⋊C8—62no—
58C22×C3⋊C8—61no—
59C3×#99—64no—
60#834—24no—
61#808—64no—
62#807—64no—
63C23×C32C4⋊C412yes—
64C23×C32C2×D411yescharacteristic
65C32×Q8—22no—
66C32×D4—24no—
67C32×D4—22no—
68C2×C32×C4—22no—
69C2×C32×C4—22no—
70C2×C32×C4C4⋊C412yes—
71C2×C32×C4C22×C411yescharacteristic
72C2×C32×C4C2×D412yes—
73C2×C32×C4C2×Q811yescharacteristic
74C2×C32×C4#4112yes—
75C2×C3×Dic3—44no—
76C3⋊(C3⋊C8)—22no—
77C3⋊(C3⋊C8)C22⋊C411yescharacteristic
78C3⋊(C3⋊C8)C22⋊C411yescharacteristic
79C3⋊(C3⋊C8)C22⋊C412yes—
80C2×#131—91no—
81#427—92no—
82#410—32no—
83H(3,ℤ/4)—92no—
84C3×#41—24no—
85C3×#41—24no—
86C3×#41—24no—
87C3×#41—24no—
88C2×C3×Q8—21no—
89C2×C3×Q8Dic612yes—
90C2×C3×D4—22no—
91C2×C3×D4—21no—
92C2×C3×D4Dic612yes—
93C2×C3×D4#6714yes—
94C22×C3×C4—22no—
95C22×C3×C4—21no—
96C22×C3×C4C4×D314yes—
97C22×C3×C4C22×D312yes—
98C3×C4⋊C4—64no—
99C3×C22⋊C4—64no—
100C3×C42—64no—
101#217—24no—
102C4⋊Dic3—24no—
103C4×Dic3—24no—
104#208—68no—
105#208—68no—
106#208—64no—
107#208—64no—
108C2×C3⋊C8—32no—
109C2×C3⋊C8—32no—
110C2×C3⋊C8—34no—
111C2×C3⋊C8—34no—
112C2×C3⋊C8—34no—
113C2×C3⋊C8—61no—
114C2×C3⋊C8—61no—
115C2×C3⋊C8—62no—
116C2×C3⋊C8—62no—
117C2×C3⋊C8—62no—
118C2×C3⋊C8—64no—
119C2×C3⋊C8—64no—
120C2×C3⋊C8—64no—
121C2×C3⋊C8—64no—
122C22×C32—22no—
123C22×C32—41no—
124C22×C32—42no—
125C22×C32C2×C4⋊C411yescharacteristic
126C22×C32#12112yes—
127C32×C4—22no—
128C32×C4C2×C22⋊C411yescharacteristic
129C32×C4#11711yescharacteristic
130C32×C4C22⋊Q812yes—
131C3×Dic3—84no—
132C2×#41D3211yescharacteristic
133#131—182no—
134#131—182no—
135C2×M16—92no—
136C2×M16—91no—
137C22×C8—91no—
138C22×C8—92no—
139#117—34no—
140#107—182no—
141#106—182no—
142#99—64no—
143C23×C3—22no—
144C23×C3—21no—
145C23×C3Dic3⋊C414yes—
146C23×C3C2×#6712yes—
147C3×Q8—24no—
148C3×Q8—24no—
149C3×D4—28no—
150C3×D4—24no—
151C3×D4—28no—
152C3×D4—24no—
153C2×C3×C4—24no—
154C2×C3×C4—24no—
155C2×C3×C4—24no—
156C2×C3×C4—24no—
157C2×C3×C4—22no—
158C2×C3×C4—22no—
159C2×C3×C4—21no—
160C2×C3×C4—21no—
161C2×C3×C4—22no—
162C2×C3×C4—124no—
163C2×C3×C4Dic3⋊C414yes—
164C2×C3×C4C2×Dic612yes—
165C2×C3×C4C2×C4×D312yes—
166C2×C3×C4D3×D414yes—
167C2×C3×C4#23714yes—
168C2×Dic3—44no—
169C3⋊C8—32no—
170C3⋊C8—32no—
171C3⋊C8—34no—
172C3⋊C8—61no—
173C3⋊C8—61no—
174C3⋊C8—62no—
175C3⋊C8—64no—
176C3⋊C8—64no—
177C2×C32—21no—
178C2×C32—22no—
179C2×C32—42no—
180C2×C32#38011yescharacteristic
181#41—22no—
182#41—22no—
183C2×Q8#62711yescharacteristic
184C2×D4#62512yes—
185C2×D4#62711yescharacteristic
186C22×C4#62412yes—
187C22×C4C2×D3211yescharacteristic
188M16—184no—
189M16—182no—
190C2×C8—91no—
191C2×C8—91no—
192C2×C8—92no—
193C2×C8—92no—
194C2×C8—92no—
195C2×C8—182no—
196C2×C8—182no—
197C4⋊C4—64no—
198C22⋊C4—64no—
199C42—64no—
200C22×C3—24no—
201C22×C3—24no—
202C22×C3—21no—
203C22×C3—22no—
204C22×C3—42no—
205C22×C3—44no—
206C22×C3—42no—
207C22×C3—44no—
208C22×C3C2×Dic3⋊C412yes—
209C22×C3#93914yes—
210C3×C4—24no—
211C3×C4—24no—
212C3×C4—21no—
213C3×C4—21no—
214C3×C4—22no—
215C3×C4—244no—
216C3×C4#87712yes—
217C3×C4#87814yes—
218C3×C4D3×C22⋊C412yes—
219Dic3—84no—
220C32#181211yescharacteristic, complemented, Sylow
221C23#372412yes—
222C23C2×#62511yescharacteristic
223Q8—22no—
224D4—24no—
225D4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—124no—
229C2×C4#372412yes—
230C2×C4#380512yes—
231C2×C4C2×#62411yescharacteristic
232C2×C4C2×#62711yescharacteristic
233C2×C4#381112yes—
234C8—91no—
235C8—91no—
236C8—92no—
237C8—182no—
238C2×C3—22no—
239C2×C3—24no—
240C2×C3—22no—
241C2×C3—21no—
242C2×C3—42no—
243C2×C3—44no—
244C2×C3—44no—
245C2×C3#494212yes—
246C22—22no—
247C22—41no—
248C22—42no—
249C22C2×#372411yescharacteristic
250C22#6398012yes—
251C4—22no—
252C4—244no—
253C4#6395711yescharacteristic
254C4#6397411yescharacteristic
255C4#6398212yes—
256C3—21no—
257C3#7004112yescomplemented
258C2—22no—
259C2—21no—
260C2—42no—
261C2#1059172011yescharacteristic
subgroupG/H
centerC4#63957
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
Fitting, prime radicalC2×C32×#41C22
socleC2×C32#380
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1812
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
3. #10591138C2semidirect
4. #10589157C2semidirect
9. C2×#3748C4semidirect
11. C22×C3⋊(C3⋊C8)C4semidirect
220. C32#1812semidirect
257. C3#70041semidirect

Maximal subgroups

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

subgroupindex
C2×#641572
C3×#52402
#105911382
#105891572
#700413