Finite Group Databasebeta

← #11775161

Subgroups — #11775161

Order 1152.

516 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 57 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#10593804C211yesmaximal, characteristic, complemented
3#10591252C211yesmaximal, characteristic, complemented
4#10590071C214yesmaximal, complemented
5C2×C3×#235—21no—
6C2×C4×C3⋊Dic3C2211yescharacteristic
7#63980—21no—
8#63980C2212yes—
9C2×Dic32—21no—
10#63914C411yescharacteristic, complemented
11C4×#625—21no—
12C4×#625C412yescomplemented
13#63873C411yescharacteristic, complemented
14#63863—21no—
15C22⋊#622C2212yes—
16#63779—21no—
17#63777—21no—
18C3×C3⋊#95—21no—
19#63579C2212yes—
20#5832—61no—
21#4648—61no—
22C22×C32×C4D411yescharacteristic
23C22×C3⋊Dic3D411yescharacteristic
24C22×C3⋊Dic3C2311yescharacteristic
25C2×C3×#67—22no—
26C22×C3×Dic3—22no—
27C3×#235—44no—
28C2×C3×D12—21no—
29C2×C3×C4×D3—22no—
30C2×C3×Dic6—21no—
31C2×#625—21no—
32C2×#625C2×C412yes—
33C2×#622—22no—
34C4×C3⋊Dic3C2×C411yescharacteristic
35C4×C3⋊Dic3C2×C411yescharacteristic
36C4×C3⋊Dic3D411yescharacteristic
37C4×C3⋊Dic3D411yescharacteristic
38#3724—21no—
39#3724C2×C412yes—
40(C2×D3)⋊Dic3—22no—
41(C2×D3)⋊Dic3—22no—
42Dic32—24no—
43#1505—91nomaximal, Sylow
44C2×C3×#41—61no—
45C2×#235—21no—
46#947—61no—
47#944—61no—
48#940—61no—
49#939—62no—
50#939—62no—
51#936—61no—
52C4×#67—62no—
53C4×#67—62no—
54C2×C4×Dic3—61no—
55C2×C4×Dic3—61no—
56C2×C4×Dic3—62no—
57C3×#95—61no—
58C3⋊#95—21no—
59C3⋊#95—62no—
60C23×C32C2×D411yescharacteristic
61C22×C3×D3—22no—
62C2×C32×C4—22no—
63C2×C32×C4C22⋊C411yescharacteristic
64C2×C32×C4C22⋊C411yescharacteristic
65C2×C3⋊Dic3—22no—
66C2×C3⋊Dic3—41no—
67C2×C3⋊Dic3C22⋊C411yescharacteristic
68C2×C3⋊Dic3C22⋊C411yescharacteristic
69C2×C3⋊Dic3C22×C411yescharacteristic
70C2×C3⋊Dic3C2×D411yescharacteristic
71C3×#67—44no—
72C2×C3×Dic3—24no—
73C2×C3×Dic3—22no—
74C2×C3×Dic3—42no—
75C2×C3×Dic3—42no—
76C3×D12—42no—
77C3×C4×D3—44no—
78C3×Dic6—42no—
79#625—42no—
80#625—42no—
81#622—42no—
82#532—91no—
83#432—91no—
84#376—91no—
85#327—94no—
86C3×#41—124no—
87C2×C3×Q8—61no—
88C2×C3×D4—61no—
89C2×C3×D4—62no—
90C22×C3×C4—21no—
91C22×C3×C4—21no—
92C22×C3×C4—62no—
93C22×C3×C4—62no—
94C2×#67—22no—
95C2×#67—62no—
96C2×#67—62no—
97C22×Dic3—22no—
98C22×Dic3—61no—
99C22×Dic3—61no—
100C22×Dic3—61no—
101C22×Dic3—61no—
102#235—44no—
103C2×D12—21no—
104C2×C4×D3—22no—
105C2×Dic6—21no—
106#217—62no—
107#217—62no—
108(C2×D3)⋊C4—62no—
109(C2×D3)⋊C4—62no—
110Dic3⋊C4—62no—
111Dic3⋊C4—62no—
112C4×Dic3—61no—
113C4×Dic3—61no—
114C4×Dic3—61no—
115C4×Dic3—61no—
116C4×Dic3—61no—
117C4×Dic3—61no—
118C4×Dic3—61no—
119C4×Dic3—61no—
120C4×Dic3—68no—
121C22×C32—21no—
122C22×C32—21no—
123C22×C32C2×C22⋊C411yescharacteristic
124C22×C32AGL(1,ℤ/8)12yes—
125C2×C3×D3—42no—
126C2×C3×D3—42no—
127C2×C3×D3—42no—
128C32×C4—21no—
129C32×C4—21no—
130C3⋊Dic3—21no—
131C3⋊Dic3—21no—
132C3⋊Dic3—21no—
133C3⋊Dic3#10412yes—
134C3×Dic3—44no—
135C3×Dic3—42no—
136C2×#41—61no—
137C4⋊Q8—91no—
138#127—91no—
139#124—181no—
140#121—92no—
141#121—181no—
142C4×D4—92no—
143C4×D4—181no—
144C2×C42—91no—
145C2×C42—181no—
146C4⋊C8—181no—
147C22⋊C8—92no—
148#97—181no—
149#95—61no—
150#95—92no—
151C23×C3—21no—
152C23×C3—21no—
153C23×C3—62no—
154C22×D3—22no—
155C3×Q8—122no—
156C3×D4—122no—
157C3×D4—124no—
158C2×C3×C4—24no—
159C2×C3×C4—21no—
160C2×C3×C4—21no—
161C2×C3×C4—21no—
162C2×C3×C4—21no—
163C2×C3×C4—42no—
164C2×C3×C4—64no—
165C2×C3×C4—62no—
166C2×C3×C4—124no—
167C2×C3×C4—122no—
168C2×C3×C4—122no—
169#67—44no—
170#67—124no—
171#67—124no—
172C2×Dic3—24no—
173C2×Dic3—22no—
174C2×Dic3—42no—
175C2×Dic3—42no—
176C2×Dic3—61no—
177C2×Dic3—61no—
178C2×Dic3—61no—
179C2×Dic3—61no—
180C2×Dic3—61no—
181C2×Dic3—61no—
182C2×Dic3—61no—
183C2×Dic3—61no—
184C2×Dic3—64no—
185C2×Dic3—122no—
186C2×Dic3—122no—
187C2×Dic3—121no—
188C2×Dic3—121no—
189D12—42no—
190C4×D3—44no—
191Dic6—42no—
192C2×C32—22no—
193C2×C32#41011yescharacteristic
194C2×C32#41811yescharacteristic
195C2×C32C2×#10411yescharacteristic
196C3×D3—82no—
197#41—124no—
198C2×Q8—61no—
199C2×D4—62no—
200C2×D4—61no—
201C2×D4—92no—
202C2×D4—181no—
203C22×C4—62no—
204C22×C4—62no—
205C22×C4—91no—
206C22×C4—91no—
207C22×C4GO+(4,𝔽2)11yescharacteristic
208C2×C8—182no—
209C4⋊C4—92no—
210C4⋊C4—181no—
211C22⋊C4—182no—
212C22⋊C4—182no—
213C42—91no—
214C42—91no—
215C42—91no—
216C42—91no—
217C42—184no—
218C22×C3—22no—
219C22×C3—21no—
220C22×C3—21no—
221C22×C3—21no—
222C22×C3—21no—
223C22×C3—22no—
224C22×C3—22no—
225C22×C3—41no—
226C22×C3—41no—
227C22×C3—122no—
228C22×C3—122no—
229C22×C3—122no—
230C2×D3—42no—
231C2×D3—42no—
232C2×D3—42no—
233C3×C4—22no—
234C3×C4—22no—
235C3×C4—41no—
236C3×C4—41no—
237C3×C4—122no—
238C3×C4—124no—
239Dic3—42no—
240Dic3—44no—
241Dic3—62no—
242Dic3—62no—
243Dic3—62no—
244Dic3—62no—
245Dic3—121no—
246Dic3—121no—
247Dic3—121no—
248Dic3—121no—
249C32#150511yescharacteristic, complemented, Sylow
250C23—62no—
251C23C2×GO+(4,𝔽2)11yescharacteristic
252Q8—122no—
253D4—122no—
254D4—124no—
255D4—362no—
256D4—362no—
257C2×C4—22no—
258C2×C4—64no—
259C2×C4—62no—
260C2×C4—91no—
261C2×C4—91no—
262C2×C4—91no—
263C2×C4—91no—
264C2×C4—124no—
265C2×C4—122no—
266C2×C4—122no—
267C2×C4—182no—
268C2×C4—361no—
269C2×C4D32⋊C411yescharacteristic
270C2×C4D32⋊C411yescharacteristic
271C8—362no—
272C2×C3—22no—
273C2×C3—22no—
274C2×C3—21no—
275C2×C3—21no—
276C2×C3—21no—
277C2×C3—21no—
278C2×C3—21no—
279C2×C3—21no—
280C2×C3—42no—
281C2×C3—242no—
282D3—82no—
283C22—21no—
284C22—21no—
285C22—122no—
286C22—122no—
287C22—122no—
288C22C2×D32⋊C411yescharacteristic
289C22#6423612yes—
290C4—21no—
291C4—21no—
292C4—92no—
293C4—124no—
294C4—122no—
295C4—181no—
296C4—181no—
297C4—181no—
298C3—21no—
299C3—21no—
300C2—22no—
301C2—242no—
302C2#1059334611yescharacteristic
303C2#1059338011yescharacteristic
304C2#1059349311yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC23C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radical#10595032C2
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1505
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #10593804C2semidirect
3. #10591252C2semidirect
4. #10590071C2semidirect
10. #63914C4semidirect
12. C4×#625C4semidirect
13. #63873C4semidirect
249. C32#1505semidirect

Maximal subgroups

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

subgroupindex
#105950322
#105938042
#105912522
#105900712
#15059