Finite Group Databasebeta

← #46821183

Subgroups — #46821183

Order 34432.

358 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771216C211yesmaximal, characteristic
2#31771081C211yesmaximal, characteristic
3#31770945C211yesmaximal, characteristic
4#31770944C211yesmaximal, characteristic
5#31770913C211yesmaximal, characteristic, complemented
6#31770912C211yesmaximal, characteristic, complemented
7#31770812C211yesmaximal, characteristic, complemented
8#31770759C211yesmaximal, characteristic
9#31770759C211yesmaximal, characteristic
10#31770712C211yesmaximal, characteristic, complemented
11#31770709C211yesmaximal, characteristic, complemented
12Q16×Dic269C211yesmaximal, characteristic, complemented
13#31770697C211yesmaximal, characteristic, complemented
14#31770665C211yesmaximal, characteristic
15#462×C269C211yesmaximal, characteristic, complemented
16C2×Q8×D269C2211yescharacteristic
17C2×#16864392C2211yescharacteristic
18C2×#16864392C2211yescharacteristic
19#22575448—21no—
20#22575448—21no—
21#22575445C2211yescharacteristic
22#22575443—21no—
23#22575443—21no—
24#22575429C2211yescharacteristic
25#22575429C2211yescharacteristic
26Q8×Dic269C2211yescharacteristic
27Q8×Dic269C2211yescharacteristic
28Q8×Dic269C2211yescharacteristic
29C4×Dic538—21no—
30C4×Dic538C2211yescharacteristic
31#22575418—21no—
32#22575418C2211yescharacteristic
33#22575411—21no—
34#22575411C2211yescharacteristic
35#22575410—21no—
36#22575410C2211yescharacteristic
37#22575387C2211yescharacteristic
38#22575386C2211yescharacteristic
39#22575385C2211yescharacteristic
40#22575384C2211yescharacteristic
41C4⋊#14524130C2211yescharacteristic
42#22575378C2211yescharacteristic
43#22575378C2211yescharacteristic
44#22575377C2211yescharacteristic
45#22575377C2211yescharacteristic
46#22575377C2211yescharacteristic
47#22575377C2211yescharacteristic
48#22575365C2211yescharacteristic
49#22575365C2211yescharacteristic
50#22575363C2211yescharacteristic
51C8×Dic269C2211yescharacteristic
52C2×Q16×C269C2211yescharacteristic
53C2×Q16×C269C2211yescharacteristic
54C4⋊Q8×C269C2211yescharacteristic
55C4×Q8×C269C2211yescharacteristic
56C4⋊C8×C269C2211yescharacteristic
57#103×C269C2211yescharacteristic
58#103×C269C2211yescharacteristic
59C2×Dic538—21no—
60C2×Dic538C2311yescharacteristic
61Q8×D269—22no—
62Q8×D269—22no—
63C2×C4×D269—21no—
64C2×C4×D269C2311yescharacteristic
65#16864392—22no—
66#16864392—22no—
67C2×#14524130C2311yescharacteristic
68C2×#14524130C2311yescharacteristic
69C4⋊Dic269—21no—
70C4⋊Dic269—21no—
71C4⋊Dic269—21no—
72C4⋊Dic269C2311yescharacteristic
73C4⋊Dic269C2311yescharacteristic
74C4⋊Dic269C2311yescharacteristic
75#16864381—21no—
76#16864381—21no—
77#16864381—21no—
78#16864381—21no—
79#16864381—21no—
80#16864381—21no—
81#16864381D411yescharacteristic
82#16864381D411yescharacteristic
83#16864379—21no—
84#16864379—21no—
85#16864379—21no—
86#16864379D411yescharacteristic
87#16864379D411yescharacteristic
88C4×Dic269—21no—
89C4×Dic269—21no—
90C4×Dic269—21no—
91C4×Dic269—21no—
92C4×Dic269—21no—
93C4×Dic269—21no—
94C4×Dic269C2311yescharacteristic
95C2×Q8×C269C2311yescharacteristic
96C2×Q8×C269C2311yescharacteristic
97C2×Q8×C269C2311yescharacteristic
98Q16×C269—22no—
99Q16×C269—22no—
100C2×C8×C269C2311yescharacteristic
101C2×C8×C269C2311yescharacteristic
102C4⋊C4×C269—21no—
103C4⋊C4×C269—21no—
104C4⋊C4×C269—21no—
105C4⋊C4×C269C2311yescharacteristic
106C42×C269—21no—
107C42×C269C2311yescharacteristic
108C22×D269C2×D411yescharacteristic
109Dic538—24no—
110Dic538—21no—
111Dic538#4112yes—
112C2×Dic269—21no—
113C2×Dic269—21no—
114C2×Dic269—21no—
115C2×Dic269—21no—
116C2×Dic269C2×D411yescharacteristic
117C2×Dic269C2×D411yescharacteristic
118C2×Dic269C2×D411yescharacteristic
119C4×D269—24no—
120C4×D269—21no—
121C4×D269—21no—
122#14524130—21no—
123#14524130—21no—
124Q8×C269—21no—
125Q8×C269—21no—
126Q8×C269—21no—
127Q8×C269—21no—
128Q8×C269—21no—
129Q8×C269#4112yes—
130C2×C4×C269—21no—
131C2×C4×C269—21no—
132C2×C4×C269—21no—
133C2×C4×C269—21no—
134C2×C4×C269C2×D411yescharacteristic
135C2×C4×C269C2×D411yescharacteristic
136C2×C4×C269C2411yescharacteristic
137C8×C269—21no—
138C8×C269—21no—
139C22×C269C22×D411yescharacteristic
140C2×D269—21no—
141C2×D269—21no—
142C2×D269—21no—
143C4×C269—22no—
144C4×C269—21no—
145C4×C269—21no—
146C4×C269—41no—
147C4×C269—41no—
148C4×C269—41no—
149C4×C269C2×#4111yescharacteristic
150C4×C269C2×#4111yescharacteristic
151Dic269—22no—
152Dic269—21no—
153Dic269—21no—
154Dic269—21no—
155Dic269—41no—
156Dic269—41no—
157Dic269—41no—
158C2×C269#52511yescharacteristic
159C2×C269#57811yescharacteristic
160C2×C269#57811yescharacteristic
161D269—41no—
162C269#312711yescharacteristic, complemented, Sylow
163#3127—2691nomaximal, Sylow
164#541—2691no—
165#519—2691no—
166#485—2691no—
167#485—2691no—
168#479—2691no—
169#479—2691no—
170#462—2691no—
171#462D26911yescharacteristic, complemented
172#451—2691no—
173#451—2691no—
174#441—2691no—
175#441—2691no—
176C4×Q16—2691no—
177C4×Q16—2691no—
178#433—2691no—
179C22×Q8—2691no—
180C2×Q16—2691no—
181C2×Q16—2691no—
182C2×Q16C2×D26911yescharacteristic
183C2×Q16C2×D26911yescharacteristic
184C4⋊Q8C2×D26911yescharacteristic
185#126—5381no—
186#126—5381no—
187#125—2691no—
188#125—5381no—
189#125—5381no—
190C22⋊Q8—2691no—
191C22⋊Q8—2691no—
192C4×Q8—2691no—
193C4×Q8—2691no—
194C4×Q8—2691no—
195C4×Q8—2691no—
196C4×Q8—2691no—
197C4×Q8—5381no—
198C4×Q8—5381no—
199C4×Q8C2×D26911yescharacteristic
200#117—2691no—
201#117—2691no—
202#117—5381no—
203#117—5381no—
204#107—2691no—
205#107—2691no—
206#106—2691no—
207#106—2691no—
208C4⋊C8—2691no—
209C4⋊C8C2×D26911yescharacteristic
210#103—2691no—
211#103—2691no—
212#103—2691no—
213#103—2691no—
214#103—2691no—
215#103—2691no—
216#103C2×D26911yescharacteristic
217#103C2×D26911yescharacteristic
218C22⋊C8—2691no—
219C22⋊C8—2691no—
220#97—2691no—
221C4×C8—2691no—
222C2×Q8—2691no—
223C2×Q8—5381no—
224C2×Q8—5382no—
225C2×Q8—5382no—
226C2×Q8C22×D26911yescharacteristic
227C2×Q8C22×D26911yescharacteristic
228C2×Q8C22×D26911yescharacteristic
229C22×C4—2691no—
230C22×C4—5381no—
231Q16—22no—
232Q16—22no—
233Q16—5382no—
234Q16—5382no—
235C2×C8—2691no—
236C2×C8—2691no—
237C2×C8C22×D26911yescharacteristic
238C2×C8C22×D26911yescharacteristic
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—2691no—
243C4⋊C4—2691no—
244C4⋊C4—2691no—
245C4⋊C4—2691no—
246C4⋊C4—2691no—
247C4⋊C4—5381no—
248C4⋊C4—5381no—
249C4⋊C4—5381no—
250C4⋊C4—5381no—
251C4⋊C4—5381no—
252C4⋊C4—5381no—
253C4⋊C4—5381no—
254C4⋊C4—5381no—
255C4⋊C4—5381no—
256C4⋊C4C22×D26911yescharacteristic
257C22⋊C4—2691no—
258C22⋊C4—2691no—
259C22⋊C4—5381no—
260C22⋊C4—5381no—
261C22⋊C4—5381no—
262C42—21no—
263C42—2691no—
264C42—5381no—
265C42—5381no—
266C42—5381no—
267C42—5381no—
268C42—5381no—
269C42—5381no—
270C42C22×D26911yescharacteristic
271C23—2691no—
272Q8—21no—
273Q8—21no—
274Q8—21no—
275Q8—21no—
276Q8—21no—
277Q8—2692no—
278Q8—5384no—
279Q8—5381no—
280Q8#1686440112yes—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—2691no—
286C2×C4—2691no—
287C2×C4—2691no—
288C2×C4—5384no—
289C2×C4—5381no—
290C2×C4—5381no—
291C2×C4—5381no—
292C2×C4—5381no—
293C2×C4—5381no—
294C2×C4—5381no—
295C2×C4D4×D26911yescharacteristic
296C2×C4D4×D26911yescharacteristic
297C2×C4C23×D26911yescharacteristic
298C8—21no—
299C8—21no—
300C8—5381no—
301C8—5381no—
302C22—5381no—
303C22—5381no—
304C22—5381no—
305C22C2×D4×D26911yescharacteristic
306C4—21no—
307C4—21no—
308C4—22no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—5381no—
313C4—5381no—
314C4—5381no—
315C4—5382no—
316C4—10761no—
317C4—10761no—
318C4—10761no—
319C4#41×D26911yescharacteristic
320C4C2×#1686440111yescharacteristic
321C2—10761no—
322C2#3177111511yescharacteristic
323C2#3177141811yescharacteristic
324C2#3177142111yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#462×C269C2
socleC22×C269C22×D4
prime radicalC22×D269C2×D4
hypercenter#462D269
hypocenterC269#3127
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
5. #31770913C2semidirect
6. #31770912C2semidirect
7. #31770812C2semidirect
10. #31770712C2semidirect
11. #31770709C2semidirect
12. Q16×Dic269C2semidirect
13. #31770697C2semidirect
15. #462×C269C2semidirect
162. C269#3127semidirect
171. #462D269semidirect

Maximal subgroups

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

subgroupindex
#317712162
#317710812
#317709452
#317709442
#317709132
#317709122
#317708122
#317707592
#317707122
#317707092
Q16×Dic2692
#317706972
#317706652
#462×C2692
#3127269