Finite Group Databasebeta

← #11796518

Subgroups — #11796518

Order 1152.

690 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 690 conjugacy classes of subgroups — too many to draw. Only its 157 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#10596287C211yesmaximal, characteristic
2C2×C32×#101C211yesmaximal, characteristic, complemented
3C2×#63663C211yesmaximal, characteristic, complemented
4#10589344C212yesmaximal, complemented
5#10589343C212yesmaximal, complemented
6#70128—34nomaximal
7C22×C32×Q8C2211yescharacteristic
8C2×#3828C411yescharacteristic
9C2×C32×M16—21no—
10#64156C411yescharacteristic
11#64156C2211yescharacteristic
12#64155—21no—
13#64155—21no—
14#64153C411yescharacteristic
15#64153C2211yescharacteristic
16#64138—21no—
17#64138—21no—
18#64135C411yescharacteristic
19C2×#3748—21no—
20C32×#101—21no—
21C32×#101C2212yes—
22#63663—21no—
23#63663C2212yes—
24#5816—34no—
25C2×C3×#101D314yescomplemented
26C2×#836—34no—
27#4478—38no—
28#4477—38no—
29C2×C32×Q8—41no—
30C2×C32×Q8—41no—
31C2×C32×Q8C2×C411yescharacteristic
32C2×C32×Q8D411yescharacteristic
33C2×C32×Q8D411yescharacteristic
34C2×C32×Q8C2311yescharacteristic
35C22×C32×C4C2×C411yescharacteristic
36C22×C32×C4D411yescharacteristic
37C22×C32×C4D411yescharacteristic
38C2×#638—21no—
39#3828—41no—
40#3828—41no—
41C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
42C2×C4×C3⋊D3—21no—
43C2×#634C2×C411yescharacteristic
44C32×M16—22no—
45C32×M16—41no—
46C2×C32×C8—41no—
47#3757—21no—
48#3752—21no—
49#3752—21no—
50#3752—21no—
51#3752—21no—
52C4⋊(C3⋊Dic3)—21no—
53#3750—21no—
54#3750—21no—
55#3750—21no—
56#3750—21no—
57C4×C3⋊Dic3C2×C411yescharacteristic
58C4×C3⋊Dic3C2×C411yescharacteristic
59#3748—22no—
60#3748—41no—
61C2×C3⋊(C3⋊C8)—41no—
62#2133—91noSylow
63C22×C3×Q8C2×D314yes—
64C2×#235—34no—
65C2×C3×M16—24no—
66#947—34no—
67#947—34no—
68#946—64no—
69#946—64no—
70#944—34no—
71#944—34no—
72#929—64no—
73#929—64no—
74#926—34no—
75C2×#208—64no—
76C3×#101—24no—
77C3×#101C2×D318yes—
78#836—38no—
79#836—64no—
80C23×C32C22⋊C411yescharacteristic
81C22×C3⋊D3—21no—
82C32×Q8—41no—
83C32×Q8—41no—
84C32×Q8—41no—
85C32×Q8—41no—
86C2×C32×C4—21no—
87C2×C32×C4—21no—
88C2×C32×C4—21no—
89C2×C32×C4—21no—
90C2×C32×C4—21no—
91C2×C32×C4—21no—
92C2×C32×C4C22⋊C411yescharacteristic
93C2×C32×C4C22⋊C411yescharacteristic
94C2×C32×C4C22⋊C411yescharacteristic
95C2×C32×C4C22×C411yescharacteristic
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98#638—41no—
99#638—41no—
100C2×C3⋊Dic3—21no—
101C2×C3⋊Dic3—21no—
102C2×C3⋊Dic3—21no—
103C4⋊(C3⋊D3)—41no—
104C4×C3⋊D3—42no—
105#634—41no—
106C32×C8—42no—
107C3⋊(C3⋊C8)—42no—
108#536—91no—
109C2×#101—91no—
110C2×#101C3⋊D311yescharacteristic, complemented
111#356—92no—
112#355—92no—
113C2×C3×Q8—44no—
114C2×C3×Q8—44no—
115C2×C3×Q8C4×D314yes—
116C2×C3×Q8D1214yes—
117C2×C3×Q8#6714yes—
118C2×C3×Q8C22×D314yes—
119C22×C3×C4C4×D314yes—
120C22×C3×C4D1214yes—
121C22×C3×C4#6714yes—
122C2×#67—64no—
123#235—124no—
124#235—124no—
125C2×D12—34no—
126C2×C4×D3—64no—
127C2×Dic6—34no—
128C3×M16—28no—
129C3×M16—44no—
130C2×C3×C8—44no—
131#217—64no—
132(C2×D3)⋊C4—64no—
133(C2×D3)⋊C4—64no—
134(C2×D3)⋊C4—64no—
135(C2×D3)⋊C4—64no—
136C4⋊Dic3—64no—
137Dic3⋊C4—64no—
138Dic3⋊C4—64no—
139Dic3⋊C4—64no—
140Dic3⋊C4—64no—
141C4×Dic3—34no—
142C4×Dic3—34no—
143#208—68no—
144#208—124no—
145C2×C3⋊C8—124no—
146C22×C32—41no—
147C22×C32#9911yescharacteristic
148C22×C32#9911yescharacteristic
149C22×C32C2×C22⋊C411yescharacteristic
150C2×C3⋊D3—42no—
151C2×C3⋊D3—41no—
152C32×C4—21no—
153C32×C4—21no—
154C32×C4—21no—
155C32×C4—21no—
156C32×C4—21no—
157C32×C4—21no—
158C3⋊Dic3—41no—
159C3⋊Dic3—41no—
160C3⋊Dic3—41no—
161C2×#41—91no—
162C22×Q8C2×C3⋊D311yescharacteristic
163C2×M16—21no—
164C2×M16—181no—
165C4⋊Q8—91no—
166C4⋊Q8—91no—
167#124—91no—
168#124—91no—
169#123—181no—
170#123—181no—
171C22⋊Q8—181no—
172C22⋊Q8—181no—
173#117—91no—
174#101—21no—
175#101—92no—
176#101—181no—
177#101C2×C3⋊D312yes—
178C23×C3(C2×D3)⋊C414yes—
179C22×D3—64no—
180C3×Q8—44no—
181C3×Q8—44no—
182C3×Q8—44no—
183C3×Q8—44no—
184C2×C3×C4—24no—
185C2×C3×C4—24no—
186C2×C3×C4—24no—
187C2×C3×C4—24no—
188C2×C3×C4—24no—
189C2×C3×C4—24no—
190C2×C3×C4(C2×D3)⋊C414yes—
191C2×C3×C4(C2×D3)⋊C414yes—
192C2×C3×C4(C2×D3)⋊C414yes—
193C2×C3×C4C2×C4×D314yes—
194C2×C3×C4C2×D1214yes—
195C2×C3×C4C2×#6714yes—
196#67—124no—
197#67—124no—
198C2×Dic3—64no—
199C2×Dic3—64no—
200C2×Dic3—64no—
201D12—124no—
202C4×D3—128no—
203Dic6—124no—
204C3×C8—48no—
205C3⋊C8—128no—
206C2×C32—21no—
207C2×C32—21no—
208C2×C32—21no—
209C2×C32C2×#9911yescharacteristic
210C3⋊D3—81no—
211#41—361no—
212#41—361no—
213C2×Q8—41no—
214C2×Q8—41no—
215C2×Q8—91no—
216C2×Q8C4×C3⋊D311yescharacteristic
217C2×Q8C4⋊(C3⋊D3)11yescharacteristic
218C2×Q8#63811yescharacteristic
219C2×Q8C22×C3⋊D311yescharacteristic
220C2×D4—91no—
221C2×D4—181no—
222C22×C4—181no—
223C22×C4C4×C3⋊D311yescharacteristic
224C22×C4C4⋊(C3⋊D3)11yescharacteristic
225C22×C4#63811yescharacteristic
226M16—22no—
227M16—41no—
228M16—182no—
229M16—361no—
230C2×C8—41no—
231C2×C8—361no—
232C4⋊C4—181no—
233C4⋊C4—181no—
234C4⋊C4—181no—
235C4⋊C4—181no—
236C4⋊C4—181no—
237C22⋊C4—181no—
238C22⋊C4—181no—
239C22⋊C4—181no—
240C22⋊C4—181no—
241C22⋊C4—181no—
242C42—91no—
243C42—91no—
244C22×C3—44no—
245C22×C3#80614yes—
246C22×C3#80614yes—
247C22×C3C2×(C2×D3)⋊C414yes—
248C2×D3—128no—
249C2×D3—124no—
250C3×C4—24no—
251C3×C4—24no—
252C3×C4—24no—
253C3×C4—24no—
254C3×C4—24no—
255C3×C4—24no—
256Dic3—124no—
257Dic3—124no—
258Dic3—124no—
259C32#213311yescharacteristic, complemented, Sylow
260C23—181no—
261C23#375211yescharacteristic
262Q8—41no—
263Q8—41no—
264Q8—41no—
265Q8—41no—
266Q8—361no—
267D4—361no—
268D4—361no—
269D4—361no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—181no—
277C2×C4—181no—
278C2×C4—181no—
279C2×C4—362no—
280C2×C4#375211yescharacteristic
281C2×C4#375211yescharacteristic
282C2×C4#375211yescharacteristic
283C2×C4C2×C4×C3⋊D311yescharacteristic
284C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
285C2×C4C2×#63811yescharacteristic
286C8—42no—
287C8—362no—
288C2×C3—24no—
289C2×C3—24no—
290C2×C3—24no—
291C2×C3C2×#80614yes—
292D3—244no—
293C22—41no—
294C22—362no—
295C22—361no—
296C22#6363311yescharacteristic
297C22#6363311yescharacteristic
298C22C2×#375211yescharacteristic
299C4—21no—
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—21no—
305C4—361no—
306C4—361no—
307C4—361no—
308C3#7012814yescomplemented
309C2—21no—
310C2—21no—
311C2—21no—
312C2—721no—
313C2C2×#6363311yescharacteristic
subgroupG/H
centerC2C2×#63633
commutatorC2×C32×C4C22×C4
FrattiniC2×Q8C22×C3⋊D3
FittingC2×C32×#101C2
socleC2×C32C2×#99
prime radicalC2×#3828C4
cosocleC2×C32×Q8C23
hypercenterC2×#101C3⋊D3
hypocenterC32#2133
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C23 ◁ C22×Q8 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. C2×C32×#101C2semidirect
3. C2×#63663C2semidirect
4. #10589344C2semidirect
5. #10589343C2semidirect
25. C2×C3×#101D3semidirect
110. C2×#101C3⋊D3semidirect
259. C32#2133semidirect
308. C3#70128semidirect

Maximal subgroups

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

subgroupindex
#105962872
C2×C32×#1012
C2×#636632
#105893442
#105893432
#701283