Finite Group Databasebeta

← #11790813

Subgroups — #11790813

Order 1152.

703 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 703 conjugacy classes of subgroups — too many to draw. Only its 130 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#10595032C211yesmaximal, characteristic
2#10592817C211yesmaximal, characteristic, complemented
3C2×C3×#825C212yesmaximal, complemented
4#10591222C211yesmaximal, characteristic, complemented
5C2×#63569C212yesmaximal, complemented
6#70357—32nomaximal
7C2×C3×#235C2212yes—
8C2×C32×M16C2211yescharacteristic
9C2×C4×C3⋊Dic3C2211yescharacteristic
10C2×#3748C2211yescharacteristic
11C2×C3×C4×Dic3C2212yes—
12#63980—22no—
13#63914C411yescharacteristic, complemented
14C4×#625—22no—
15#63873C411yescharacteristic, complemented
16#63863C412yescomplemented
17#63641—22no—
18C3×#825—24no—
19#63579—22no—
20#63569—24no—
21#5832—32no—
22C2×C3×#104—32no—
23C2×#837—32no—
24C2×#825D312yescomplemented
25#5118—32no—
26#5118—61no—
27#4932—32no—
28C2×#805—32no—
29C22×C32×C4C2311yescharacteristic
30C22×C3⋊Dic3D412yes—
31C2×C3×#67—22no—
32C22×C3×Dic3—22no—
33C3×#235—22no—
34C3×#235—22no—
35C3×#235—22no—
36C3×#235—22no—
37C2×C3×D12C2×C412yes—
38C2×C3×C4×D3—22no—
39C2×C3×Dic6C2×C412yes—
40C2×#625—22no—
41C32×M16—22no—
42C2×C32×C8—21no—
43C4×C3⋊Dic3C2×C411yescharacteristic
44C4×C3⋊Dic3C2×C411yescharacteristic
45C4×C3⋊Dic3D412yes—
46#3748—22no—
47C2×C3⋊(C3⋊C8)—21no—
48C3×C4×Dic3—22no—
49C3×C4×Dic3D414yescomplemented
50#3724—22no—
51(C2×D3)⋊Dic3—24no—
52#1963—91noSylow
53C2×C3×#41—32no—
54C2×#235C2×D312yes—
55C2×C3×M16—21no—
56C2×C3×M16C2×D312yes—
57C2×C3×C42—32no—
58#947—32no—
59#944—32no—
60#940—32no—
61#939—64no—
62#936—32no—
63C4×#67—64no—
64C2×C4×Dic3—32no—
65C2×C4×Dic3—61no—
66C2×C4×Dic3C2×D312yes—
67C2×#208—32no—
68C2×#208—61no—
69C3×#104—64no—
70#837—64no—
71C3⋊#95—64no—
72#825—24no—
73Dic3⋊C8—64no—
74Dic3⋊C8—64no—
75#805—64no—
76C23×C32C2×D411yescharacteristic
77C22×C3×D3—22no—
78C2×C32×C4C22×C411yescharacteristic
79C2×C32×C4C2×D411yescharacteristic
80C2×C32×C4C2×D412yes—
81C2×C32×C4#4112yes—
82C2×C3⋊Dic3—42no—
83C2×C3⋊Dic3C22⋊C412yes—
84C2×C3⋊Dic3C22⋊C412yes—
85C3×#67—42no—
86C3×#67—42no—
87C2×C3×Dic3—22no—
88C2×C3×Dic3—24no—
89C2×C3×Dic3—44no—
90C3×D12—22no—
91C3×D12—22no—
92C3×C4×D3—42no—
93C3×C4×D3—42no—
94C3×Dic6—22no—
95C3×Dic6—22no—
96#625—44no—
97C32×C8—41no—
98C3⋊(C3⋊C8)—41no—
99#532—91no—
100#423—91no—
101C2×#104—32no—
102C2×#104—92no—
103#376—91no—
104C3×#41—62no—
105C3×#41—62no—
106C3×#41—62no—
107C3×#41—62no—
108C2×C3×Q8—32no—
109C2×C3×D4—32no—
110C2×C3×D4—62no—
111C22×C3×C4—21no—
112C22×C3×C4—62no—
113C22×C3×C4—62no—
114C22×C3×C4C22×D312yes—
115C2×#67—22no—
116C2×#67—64no—
117C22×Dic3—22no—
118C22×Dic3—34no—
119C22×Dic3—62no—
120#235—22no—
121#235—22no—
122#235—22no—
123#235—22no—
124C2×D12C4×D312yes—
125C2×C4×D3—22no—
126C2×Dic6C4×D312yes—
127C3×M16—22no—
128C3×M16—22no—
129C3×M16—42no—
130C2×C3×C8—22no—
131C2×C3×C8—22no—
132C3×C42—34no—
133C3×C42—62no—
134#217—64no—
135(C2×D3)⋊C4—64no—
136Dic3⋊C4—64no—
137C4×Dic3—22no—
138C4×Dic3—32no—
139C4×Dic3—32no—
140C4×Dic3—34no—
141C4×Dic3—62no—
142C4×Dic3—61no—
143C4×Dic3—61no—
144C4×Dic3#6714yescomplemented
145#208—62no—
146#208—62no—
147#208—122no—
148C2×C3⋊C8—62no—
149C2×C3⋊C8—62no—
150C22×C32—22no—
151C22×C32C2×C22⋊C411yescharacteristic
152C22×C32#12112yes—
153C2×C3×D3—42no—
154C2×C3×D3—44no—
155C32×C4C4×D412yes—
156C32×C4#12411yescharacteristic
157C32×C4#12711yescharacteristic
158C3⋊Dic3—22no—
159C3⋊Dic3—22no—
160C3×Dic3—44no—
161C3×Dic3—42no—
162C2×#41—32no—
163C2×M16—91no—
164C2×M16D3211yescharacteristic
165C4⋊Q8—91no—
166#127—91no—
167#124—92no—
168#121—182no—
169C4×D4—182no—
170C2×C42—32no—
171C2×C42—91no—
172C4⋊C8—182no—
173#104—64no—
174#104—184no—
175#95—182no—
176C23×C3—21no—
177C23×C3—62no—
178C23×C3D3×D412yes—
179C22×D3—22no—
180C3×Q8—62no—
181C3×Q8—62no—
182C3×D4—62no—
183C3×D4—62no—
184C3×D4—122no—
185C3×D4—122no—
186C2×C3×C4—22no—
187C2×C3×C4—21no—
188C2×C3×C4—22no—
189C2×C3×C4—21no—
190C2×C3×C4—62no—
191C2×C3×C4—64no—
192C2×C3×C4—124no—
193C2×C3×C4—122no—
194C2×C3×C4—122no—
195C2×C3×C4C2×C4×D312yes—
196C2×C3×C4#23512yes—
197C2×C3×C4D3×D412yes—
198C2×C3×C4D3×D412yes—
199C2×C3×C4#23712yes—
200C2×C3×C4C2×#6712yes—
201#67—42no—
202#67—42no—
203#67—128no—
204C2×Dic3—22no—
205C2×Dic3—24no—
206C2×Dic3—34no—
207C2×Dic3—34no—
208C2×Dic3—44no—
209C2×Dic3—62no—
210C2×Dic3—62no—
211C2×Dic3—124no—
212C2×Dic3—124no—
213D12—22no—
214D12—22no—
215C4×D3—42no—
216C4×D3—42no—
217Dic6—22no—
218Dic6—22no—
219C3×C8—42no—
220C3×C8—42no—
221C3⋊C8—122no—
222C3⋊C8—122no—
223C2×C32—22no—
224C2×C32#39011yescharacteristic
225C2×C32#42112yes—
226C3×D3—82no—
227#41—62no—
228#41—62no—
229#41—62no—
230#41—62no—
231C2×Q8—32no—
232C2×D4—32no—
233C2×D4—62no—
234C2×D4—182no—
235C22×C4—62no—
236C22×C4—62no—
237C22×C4—92no—
238C22×C4C2×D3211yescharacteristic
239M16—22no—
240M16—182no—
241C2×C8—21no—
242C2×C8—181no—
243C4⋊C4—182no—
244C22⋊C4—184no—
245C42—34no—
246C42—62no—
247C42—91no—
248C42—91no—
249C42—92no—
250C22×C3—24no—
251C22×C3—22no—
252C22×C3—21no—
253C22×C3—42no—
254C22×C3—122no—
255C22×C3—124no—
256C22×C3D3×C22⋊C412yes—
257C22×C3#88412yes—
258C22×C3#93912yes—
259C2×D3—42no—
260C2×D3—44no—
261C3×C4—22no—
262C3×C4—21no—
263C3×C4—21no—
264C3×C4—124no—
265C3×C4—122no—
266C3×C4#67⋊C412yes—
267C3×C4#88512yes—
268C3×C4C4×#6712yes—
269C3×C4#94012yes—
270Dic3—44no—
271Dic3—42no—
272Dic3—64no—
273Dic3—64no—
274Dic3—64no—
275Dic3—122no—
276C32#196311yescharacteristic, complemented, Sylow
277C23—62no—
278C23#380211yescharacteristic
279Q8—62no—
280Q8—62no—
281D4—62no—
282D4—62no—
283D4—122no—
284D4—122no—
285D4—364no—
286C2×C4—64no—
287C2×C4—62no—
288C2×C4—92no—
289C2×C4—92no—
290C2×C4—124no—
291C2×C4—122no—
292C2×C4—122no—
293C2×C4—362no—
294C2×C4#379512yes—
295C2×C4C4×D3211yescharacteristic
296C2×C4D3×#6712yes—
297C2×C4#381111yescharacteristic
298C8—41no—
299C8—361no—
300C2×C3—22no—
301C2×C3—22no—
302C2×C3—22no—
303C2×C3—21no—
304C2×C3—42no—
305C2×C3—242no—
306C2×C3#482114yes—
307C2×C3#495712yes—
308D3—82no—
309C22—22no—
310C22—124no—
311C22—122no—
312C22#6388512yes—
313C22#6392111yescharacteristic
314C4—124no—
315C4—122no—
316C4—182no—
317C4—182no—
318C4#6387912yes—
319C4#6391311yescharacteristic
320C4#6397911yescharacteristic
321C3—21no—
322C3#7035712yescomplemented
323C2—22no—
324C2—242no—
325C2#1059100912yes—
326C2#1059138611yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C2×C22⋊C4
prime radical#10595032C2
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1963
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #10592817C2semidirect
3. C2×C3×#825C2semidirect
4. #10591222C2semidirect
5. C2×#63569C2semidirect
13. #63914C4semidirect
15. #63873C4semidirect
16. #63863C4semidirect
24. C2×#825D3semidirect
49. C3×C4×Dic3D4semidirect
144. C4×Dic3#67semidirect
276. C32#1963semidirect
322. C3#70357semidirect

Maximal subgroups

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

subgroupindex
#105950322
#105928172
C2×C3×#8252
#105912222
C2×#635692
#703573