Finite Group Databasebeta

← #11861206

Subgroups — #11861206

Order 1152.

718 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 718 conjugacy classes of subgroups — too many to draw. Only its 158 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#10596640C212yesmaximal, complemented
2C2×#64121C211yesmaximal, characteristic
3#10593816C212yesmaximal, complemented
4#10593780C214yesmaximal, complemented
5#10593779C214yesmaximal, complemented
6#10593771C211yesmaximal, characteristic, complemented
7#10593765C211yesmaximal, characteristic, complemented
8C2×#3830C2212yes—
9C2×#3792—24no—
10#64287—24no—
11#64287C2218yescomplemented
12#64286C2211yescharacteristic
13#64283C2212yes—
14#64283C2211yescharacteristic
15C2×C32×D8C411yescharacteristic, complemented
16C2×#3754C412yescomplemented
17#64121C412yescomplemented
18#64121C412yescomplemented
19#64121C2212yes—
20#64121C2212yes—
21C2×#3746C411yescharacteristic, complemented
22C2×C8×C3⋊D3C2211yescharacteristic
23#63783C2218yescomplemented
24#63771C2212yescomplemented
25#63770C2212yescomplemented
26#63767C2212yescomplemented
27C8×#157C2212yescomplemented
28C2×#912—62no—
29C2×C32×D4C2×C412yes—
30C2×#638—22no—
31C22×C3⋊Dic3—22no—
32#3830—22no—
33#3830—22no—
34#3830C2×C414yes—
35#3830C2314yes—
36C2×C4×C3⋊D3C2311yescharacteristic
37C2×#634C2×C412yes—
38C22⋊#157—21no—
39#3792—22no—
40#3792—28no—
41#3792D412yes—
42C2×#622—28no—
43C4⋊#157—21no—
44C4×#157C2312yes—
45#3788D412yes—
46#3788C2314yes—
47#3787—22no—
48#3787C2312yes—
49C32×D8C2×C412yes—
50C32×D8C2×C412yes—
51C2×C32×C8C2×C411yescharacteristic
52#3754C2×C414yes—
53#3754C2×C414yes—
54C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
55#3746C2×C412yes—
56#3746C2×C412yes—
57C8×C3⋊D3C2×C411yescharacteristic
58C8×C3⋊D3C2×C411yescharacteristic
59C8×C3⋊D3C2311yescharacteristic
60C8×C3⋊D3C2311yescharacteristic
61#2957—91nomaximal, Sylow
62C2×#237—64no—
63C2×C3×D8—22no—
64C2×#214—64no—
65#912—64no—
66#912—64no—
67#912—64no—
68#912—64no—
69C2×Dic12—62no—
70C2×D3×C8—62no—
71C23×C32—22no—
72C22×C3⋊D3#4111yescharacteristic
73C2×#157—22no—
74C32×D4—22no—
75C32×D4C22×C414yes—
76C2×C32×C4C22×C411yescharacteristic
77#638—24no—
78#638—24no—
79C2×C3⋊Dic3—22no—
80C2×C3⋊Dic3—24no—
81C2×C3⋊Dic3—24no—
82C2×C3⋊Dic3C2×D411yescharacteristic
83C4×C3⋊D3C22×C411yescharacteristic
84C4×C3⋊D3C2×D411yescharacteristic
85C4×C3⋊D3#4111yescharacteristic
86C4×C3⋊D3C2411yescharacteristic
87#634—22no—
88#634C22×C414yes—
89#622—24no—
90#622C2×D414yes—
91C32×C8C22×C411yescharacteristic
92C32×C8C22×C411yescharacteristic
93C3⋊(C3⋊C8)C22×C411yescharacteristic
94C3⋊(C3⋊C8)C22×C411yescharacteristic
95C2×#135—91no—
96#568—92no—
97#444—94no—
98#443—94no—
99C2×#108—91no—
100#421—92no—
101#405—91no—
102C2×C3×D4—24no—
103C2×#67—124no—
104C22×Dic3—124no—
105#237—68no—
106#237—68no—
107#237—124no—
108#237—124no—
109C2×C4×D3—62no—
110C2×Dic6—64no—
111C3×D8—24no—
112C3×D8—24no—
113C2×C3×C8—22no—
114#214—68no—
115#214—68no—
116C2×C3⋊C8—62no—
117Dic12—64no—
118Dic12—64no—
119D3×C8—62no—
120D3×C8—62no—
121D3×C8—62no—
122D3×C8—62no—
123C22×C32—24no—
124C22×C32—82no—
125C22×C32C4×D411yescharacteristic
126C2×C3⋊D3—41no—
127C2×C3⋊D3C4×D411yescharacteristic
128C2×C3⋊D3C2×#4111yescharacteristic
129#157—42no—
130C32×C4C4×D411yescharacteristic
131C32×C4C23×C411yescharacteristic
132C3⋊Dic3—24no—
133C3⋊Dic3C4×D411yescharacteristic
134C3⋊Dic3C22×D411yescharacteristic
135C2×#41—92no—
136#135—92no—
137#135—92no—
138#135—92no—
139#135—92no—
140C2×Q16—91no—
141C2×SD16—92no—
142C2×D8#15711yescharacteristic, complemented
143#131—98no—
144#131—184no—
145C2×M16—91no—
146C2×M16—92no—
147C2×M16—184no—
148C22×C8—91no—
149#117—91no—
150#108—92no—
151#108—92no—
152#104—98no—
153#97—92no—
154C4×C8—92no—
155C23×C3—44no—
156C22×D3—62no—
157C3×D4—28no—
158C3×D4—44no—
159C2×C3×C4—22no—
160#67—128no—
161#67—128no—
162C2×Dic3—62no—
163C2×Dic3—128no—
164C2×Dic3—128no—
165C2×Dic3—124no—
166C4×D3—62no—
167C4×D3—62no—
168C4×D3—62no—
169C4×D3—62no—
170Dic6—68no—
171Dic6—124no—
172C3×C8—22no—
173C3×C8—22no—
174C3⋊C8—62no—
175C3⋊C8—62no—
176C2×C32—21no—
177C2×C32—44no—
178C2×C32C2×C4×D411yescharacteristic
179C3⋊D3—21no—
180C3⋊D3—21no—
181#41—94no—
182#41—94no—
183#41—182no—
184#41—182no—
185C2×Q8—92no—
186C2×D4—182no—
187C2×D4C2×#15712yes—
188C22×C4—91no—
189C22×C4—182no—
190Q16—92no—
191Q16—92no—
192SD16—94no—
193SD16—94no—
194D8C2×#15712yes—
195D8C2×#15712yes—
196M16—92no—
197M16—92no—
198M16—94no—
199M16—188no—
200M16—182no—
201C2×C8—92no—
202C2×C8—91no—
203C2×C8—91no—
204C2×C8—91no—
205C2×C8—91no—
206C2×C8—91no—
207C2×C8—188no—
208C2×C8—182no—
209C2×C8C2×#15711yescharacteristic
210C4⋊C4—181no—
211C22⋊C4—181no—
212C42—92no—
213C22×C3—22no—
214C22×C3—48no—
215C22×C3—88no—
216C2×D3—62no—
217C2×D3—62no—
218C2×D3—124no—
219C3×C4—22no—
220C3×C4—22no—
221Dic3—62no—
222Dic3—62no—
223Dic3—128no—
224C32#295711yescharacteristic, complemented, Sylow
225C23—22no—
226C23—91no—
227Q8—94no—
228Q8—182no—
229D4—22no—
230D4—184no—
231D4—184no—
232D4C22×#15714yes—
233C2×C4—91no—
234C2×C4—91no—
235C2×C4—91no—
236C2×C4—91no—
237C2×C4—91no—
238C2×C4—184no—
239C2×C4—184no—
240C2×C4—182no—
241C2×C4—182no—
242C2×C4C22×#15711yescharacteristic
243C8—94no—
244C8—91no—
245C8—91no—
246C8—184no—
247C8C22×#15711yescharacteristic
248C8C22×#15711yescharacteristic
249C2×C3—24no—
250C2×C3—22no—
251C2×C3—88no—
252D3—122no—
253D3—122no—
254C22—24no—
255C22—82no—
256C22—91no—
257C22—91no—
258C22—361no—
259C22D4×#15711yescharacteristic
260C4—91no—
261C4—91no—
262C4—184no—
263C4—362no—
264C4D4×#15711yescharacteristic
265C4C23×#15711yescharacteristic
266C3—22no—
267C2—21no—
268C2—44no—
269C2—181no—
270C2—181no—
271C2C2×D4×#15711yescharacteristic
subgroupG/H
centerC2C2×D4×#157
commutatorC32×C4C23×C4
FrattiniC4C23×#157
FittingC2×C32×D8C4
socleC2×C32C2×C4×D4
prime radicalC2×#64121C2
cosocleC4×C3⋊D3C24
hypercenterC2×D8#157
hypocenterC32#2957
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. #10596640C2semidirect
3. #10593816C2semidirect
4. #10593780C2semidirect
5. #10593779C2semidirect
6. #10593771C2semidirect
7. #10593765C2semidirect
11. #64287C22semidirect
15. C2×C32×D8C4semidirect
16. C2×#3754C4semidirect
17. #64121C4semidirect
18. #64121C4semidirect
21. C2×#3746C4semidirect
23. #63783C22semidirect
24. #63771C22semidirect
25. #63770C22semidirect
26. #63767C22semidirect
27. C8×#157C22semidirect
142. C2×D8#157semidirect
224. C32#2957semidirect

Maximal subgroups

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

subgroupindex
#105966402
C2×#641212
#105938162
#105937802
#105937792
#105937712
#105937652
#29579