Finite Group Databasebeta

← #11790809

Subgroups — #11790809

Order 1152.

630 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 70 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#10596139C211yesmaximal, characteristic
2C2×#63785C212yesmaximal, complemented
3C2×#63783C212yesmaximal, complemented
4#10593733C211yesmaximal, characteristic, complemented
5#10593728C211yesmaximal, characteristic, complemented
6C2×#3832C2211yescharacteristic
7C2×#3830C2211yescharacteristic
8C2×C4×#157C2212yes—
9C2×#3788C2212yes—
10C32×#124C411yescharacteristic, complemented
11#64153C411yescharacteristic, complemented
12#64149C411yescharacteristic, complemented
13#64093—22no—
14#64090—22no—
15#64084C411yescharacteristic, complemented
16C42×C3⋊D3C2211yescharacteristic
17#63785—24no—
18#63783—24no—
19#63781—22no—
20C4⋊#622—22no—
21#5668—62no—
22C22×#157—22no—
23C2×C32×Q8C2×C411yescharacteristic
24C2×C32×D4C2×C411yescharacteristic
25C2×#638—21no—
26C2×#638—22no—
27C22×C3⋊Dic3—21no—
28#3832—22no—
29#3832—22no—
30#3830—22no—
31#3830—22no—
32C2×C4⋊(C3⋊D3)—21no—
33C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
34C2×C4×C3⋊D3—21no—
35C2×C4×C3⋊D3D412yes—
36C2×C4×C3⋊D3C2311yescharacteristic
37C2×#634C2×C411yescharacteristic
38C2×#622—22no—
39C4×#157—22no—
40C4×#157D414yescomplemented
41#3788—22no—
42#3788—22no—
43C32×C22⋊C4—22no—
44C32×C42C2×C411yescharacteristic
45#3752—22no—
46#3750—22no—
47C4×C3⋊Dic3C2×C411yescharacteristic
48C4×C3⋊Dic3D412yes—
49#1963—91nomaximal, Sylow
50C2×#239—62no—
51C2×#237—62no—
52C3×#124—22no—
53#944—62no—
54#940—62no—
55#884—68no—
56#67⋊C4—68no—
57#875—62no—
58C42×D3—62no—
59C23×C32—21no—
60C22×C3⋊D3—21no—
61C22×C3⋊D3C2×D411yescharacteristic
62C2×#157—24no—
63C2×#157—44no—
64C32×Q8—22no—
65C32×D4—22no—
66C2×C32×C4—21no—
67C2×C32×C4C22⋊C412yes—
68C2×C32×C4C22×C411yescharacteristic
69#638—44no—
70#638—42no—
71C2×C3⋊Dic3—21no—
72C2×C3⋊Dic3—41no—
73C2×C3⋊Dic3—41no—
74C2×C3⋊Dic3C22⋊C412yes—
75C2×C3⋊Dic3C2×D411yescharacteristic
76C4⋊(C3⋊D3)—22no—
77C4⋊(C3⋊D3)—42no—
78C4×C3⋊D3—42no—
79C4×C3⋊D3—41no—
80C4×C3⋊D3—41no—
81C4×C3⋊D3C2×D412yes—
82C4×C3⋊D3#4112yes—
83#634—22no—
84#622—42no—
85#532—91no—
86#423—91no—
87C2×#104—92no—
88C2×#104—92no—
89#376—91no—
90C2×C3×Q8—22no—
91C2×C3×D4—22no—
92C2×#67—68no—
93C2×#67—64no—
94C22×Dic3—64no—
95#239—124no—
96#239—124no—
97#237—124no—
98#237—124no—
99C2×D12—62no—
100C2×D12—64no—
101C2×C4×D3—62no—
102C2×C4×D3—64no—
103C2×C4×D3—64no—
104C2×Dic6—62no—
105C3×C22⋊C4—28no—
106C3×C42—22no—
107(C2×D3)⋊C4—68no—
108Dic3⋊C4—68no—
109C4×Dic3—64no—
110C4×Dic3—62no—
111C22×C32—41no—
112C22×C32—42no—
113C22×C32C2×C22⋊C411yescharacteristic
114C2×C3⋊D3—22no—
115C2×C3⋊D3—41no—
116C2×C3⋊D3—42no—
117C2×C3⋊D3#12112yes—
118#157—44no—
119C32×C4—22no—
120C32×C4—41no—
121C32×C4C4×D412yes—
122C3⋊Dic3—22no—
123C3⋊Dic3—41no—
124C3⋊Dic3#12411yescharacteristic
125C3⋊Dic3#12711yescharacteristic
126C2×#41—91no—
127C2×#41—91no—
128C2×M16—92no—
129C4⋊Q8—91no—
130#127—91no—
131#124—91no—
132#124#15711yescharacteristic, complemented
133#121—182no—
134C4×D4—182no—
135C2×C42—91no—
136C2×C42—92no—
137C4⋊C8—182no—
138#104—184no—
139#104—184no—
140#95—182no—
141C23×C3—24no—
142C22×D3—62no—
143C22×D3—64no—
144C3×Q8—44no—
145C3×D4—44no—
146C2×C3×C4—24no—
147C2×C3×C4—22no—
148C2×C3×C4—24no—
149#67—1216no—
150#67—128no—
151C2×Dic3—64no—
152C2×Dic3—62no—
153C2×Dic3—64no—
154C2×Dic3—124no—
155C2×Dic3—124no—
156D12—124no—
157D12—128no—
158C4×D3—64no—
159C4×D3—64no—
160C4×D3—128no—
161C4×D3—124no—
162C4×D3—124no—
163Dic6—124no—
164C2×C32—81no—
165C2×C32#39011yescharacteristic
166C2×C32#42112yes—
167C3⋊D3—22no—
168C3⋊D3—81no—
169#41—182no—
170#41—182no—
171#41—182no—
172#41—182no—
173C2×Q8—91no—
174C2×Q8C2×#15711yescharacteristic
175C2×D4—91no—
176C2×D4—181no—
177C2×D4—182no—
178C2×D4—181no—
179C2×D4C2×#15711yescharacteristic
180C22×C4—91no—
181C22×C4—92no—
182C22×C4—181no—
183C22×C4—181no—
184C22×C4—182no—
185M16—182no—
186M16—182no—
187C2×C8—182no—
188C4⋊C4—182no—
189C22⋊C4—22no—
190C22⋊C4—182no—
191C42—91no—
192C42—92no—
193C42—94no—
194C42—182no—
195C42C2×#15711yescharacteristic
196C22×C3—22no—
197C22×C3—44no—
198C22×C3—48no—
199C2×D3—64no—
200C2×D3—124no—
201C2×D3—124no—
202C2×D3—128no—
203C3×C4—24no—
204C3×C4—44no—
205C3×C4—44no—
206Dic3—62no—
207Dic3—62no—
208Dic3—68no—
209Dic3—124no—
210C32#196311yescharacteristic, complemented, Sylow
211C23—21no—
212C23—91no—
213C23—181no—
214Q8—22no—
215Q8—182no—
216D4—22no—
217D4—182no—
218D4—362no—
219D4—364no—
220D4—362no—
221C2×C4—21no—
222C2×C4—91no—
223C2×C4—92no—
224C2×C4—92no—
225C2×C4—92no—
226C2×C4—184no—
227C2×C4—181no—
228C2×C4—362no—
229C2×C4—361no—
230C2×C4—361no—
231C2×C4—361no—
232C2×C4—361no—
233C2×C4—364no—
234C2×C4C22⋊#15712yes—
235C2×C4C22×#15711yescharacteristic
236C8—362no—
237C2×C3—22no—
238C2×C3—24no—
239C2×C3—84no—
240D3—124no—
241D3—244no—
242C22—41no—
243C22—42no—
244C22—92no—
245C22—182no—
246C22—361no—
247C22—362no—
248C22C2×C22⋊#15711yescharacteristic
249C4—22no—
250C4—41no—
251C4—91no—
252C4—91no—
253C4—182no—
254C4—364no—
255C4—361no—
256C4D4×#15712yes—
257C3—22no—
258C2—81no—
259C2—182no—
260C2—721no—
261C2#1059382711yescharacteristic
262C2#1059384212yes—
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×#124C4
socleC22×C32C2×C22⋊C4
prime radical#10596139C2
cosocleC2×C4×C3⋊D3C23
hypercenter#124#157
hypocenterC32#1963
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. C2×#63785C2semidirect
3. C2×#63783C2semidirect
4. #10593733C2semidirect
5. #10593728C2semidirect
10. C32×#124C4semidirect
11. #64153C4semidirect
12. #64149C4semidirect
15. #64084C4semidirect
40. C4×#157D4semidirect
132. #124#157semidirect
210. C32#1963semidirect

Maximal subgroups

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

subgroupindex
#105961392
C2×#637852
C2×#637832
#105937332
#105937282
#19639