Finite Group Databasebeta

← #46820724

Subgroups — #46820724

Order 34432.

362 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771235C211yesmaximal, characteristic
2#31771081C211yesmaximal, characteristic
3#31770915C211yesmaximal, characteristic, complemented
4#31770910C211yesmaximal, characteristic, complemented
5#31770909C211yesmaximal, characteristic, complemented
6#31770900C211yesmaximal, characteristic, complemented
7#31770899C211yesmaximal, characteristic, complemented
8#31770891C211yesmaximal, characteristic, complemented
9#31770888C211yesmaximal, characteristic, complemented
10#31770646C211yesmaximal, characteristic
11#31770640C211yesmaximal, characteristic
12#31770630C211yesmaximal, characteristic
13#31770612C211yesmaximal, characteristic
14#103×D269C211yesmaximal, characteristic
15#479×C269C211yesmaximal, characteristic, complemented
16C2×Q8×D269C2211yescharacteristic
17C2×#16864385C2211yescharacteristic
18C2×C8×D269C2211yescharacteristic
19#22575453C2211yescharacteristic
20#22575452—21no—
21#22575452C2211yescharacteristic
22#22575444C2211yescharacteristic
23#22575443—21no—
24#22575433—21no—
25#22575431—21no—
26Q8×Dic269C2211yescharacteristic
27C4×Dic538—21no—
28C4×Dic538C2211yescharacteristic
29#22575418—21no—
30#22575418C2211yescharacteristic
31#22575411—21no—
32#22575411C2211yescharacteristic
33#22575411C2211yescharacteristic
34#22575410—21no—
35#22575410C2211yescharacteristic
36C4⋊C4×D269C2211yescharacteristic
37#22575386C2211yescharacteristic
38#22575386C2211yescharacteristic
39#22575386C2211yescharacteristic
40#22575385C2211yescharacteristic
41#22575385C2211yescharacteristic
42#22575384C2211yescharacteristic
43C4⋊#14524130C2211yescharacteristic
44#22575382C2211yescharacteristic
45#22575382C2211yescharacteristic
46#22575378C2211yescharacteristic
47#22575378C2211yescharacteristic
48#22575377C2211yescharacteristic
49#22575377C2211yescharacteristic
50#22575376C2211yescharacteristic
51#22575376C2211yescharacteristic
52#125×C269C2211yescharacteristic
53C4×Q8×C269C2211yescharacteristic
54#107×C269C2211yescharacteristic
55#106×C269C2211yescharacteristic
56C4⋊C8×C269C2211yescharacteristic
57#103×C269C2211yescharacteristic
58#103×C269C2211yescharacteristic
59C2×Dic538—21no—
60C2×Dic538—21no—
61C2×Dic538—21no—
62C2×Dic538C2311yescharacteristic
63Q8×D269—22no—
64Q8×D269Q814yescomplemented
65C2×C4×D269—21no—
66C2×C4×D269—21no—
67C2×C4×D269C2311yescharacteristic
68#16864385—22no—
69C2×#14524130C2311yescharacteristic
70C2×#14524130C2311yescharacteristic
71C8×D269—22no—
72C4⋊Dic269—21no—
73C4⋊Dic269—21no—
74C4⋊Dic269—21no—
75C4⋊Dic269C2311yescharacteristic
76C4⋊Dic269C2311yescharacteristic
77C4⋊Dic269C2311yescharacteristic
78#16864381—21no—
79#16864381—21no—
80#16864381—21no—
81#16864381—21no—
82#16864381—21no—
83#16864381D411yescharacteristic
84#16864381D411yescharacteristic
85#16864379—21no—
86#16864379—21no—
87#16864379D411yescharacteristic
88#16864379D411yescharacteristic
89C4×Dic269—21no—
90C4×Dic269—21no—
91C4×Dic269—21no—
92C4×Dic269—21no—
93C4×Dic269—21no—
94C4×Dic269C2311yescharacteristic
95C2×Q8×C269C2311yescharacteristic
96C2×C8×C269C2311yescharacteristic
97C2×C8×C269C2311yescharacteristic
98C4⋊C4×C269—21no—
99C4⋊C4×C269—21no—
100C4⋊C4×C269—21no—
101C4⋊C4×C269C2311yescharacteristic
102C4⋊C4×C269C2311yescharacteristic
103C4⋊C4×C269C2311yescharacteristic
104C42×C269—21no—
105C42×C269C2311yescharacteristic
106C22×D269C2×D411yescharacteristic
107Dic538—21no—
108Dic538—24no—
109Dic538—81no—
110Dic538—81no—
111Dic538C2×Q812yes—
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—81no—
121C4×D269C2×Q812yes—
122C4×D269#4112yes—
123#14524130—21no—
124#14524130—21no—
125Q8×C269—21no—
126Q8×C269C2×Q812yes—
127C2×C4×C269—21no—
128C2×C4×C269—21no—
129C2×C4×C269—21no—
130C2×C4×C269—21no—
131C2×C4×C269C2×D411yescharacteristic
132C2×C4×C269C2×D411yescharacteristic
133C2×C4×C269C2411yescharacteristic
134C8×C269—21no—
135C8×C269—21no—
136C22×C269C22×D411yescharacteristic
137C2×D269—21no—
138C2×D269—21no—
139C2×D269C22⋊Q812yes—
140C4×C269—22no—
141C4×C269—21no—
142C4×C269—21no—
143C4×C269—41no—
144C4×C269—41no—
145C4×C269—41no—
146C4×C269C22×Q811yescharacteristic
147C4×C269C2×#4111yescharacteristic
148Dic269—22no—
149Dic269—21no—
150Dic269—21no—
151Dic269—41no—
152Dic269—41no—
153Dic269—41no—
154Dic269C22⋊Q812yes—
155C2×C269C2×C22⋊Q811yescharacteristic
156C2×C269#57711yescharacteristic
157C2×C269#57811yescharacteristic
158D269—22no—
159C269#308211yescharacteristic, complemented, Sylow
160#3082—2691nomaximal, Sylow
161#544—2691no—
162#519—2691no—
163#479—2691no—
164#479—2691no—
165#479—2691no—
166#479D26911yescharacteristic, complemented
167#477—2691no—
168#477—2691no—
169#475—2691no—
170#475—2691no—
171#428—2691no—
172#427—2691no—
173#424—2691no—
174#419—2691no—
175C2×#103—2691no—
176C22×Q8—2691no—
177C2×M16—2691no—
178C22×C8—2691no—
179C4⋊Q8—2691no—
180C4⋊Q8—2691no—
181C4⋊Q8—5381no—
182#125—2691no—
183#125—5381no—
184#125C2×D26911yescharacteristic
185C22⋊Q8—5381no—
186C22⋊Q8—5381no—
187C4×Q8—2691no—
188C4×Q8—2691no—
189C4×Q8—2691no—
190C4×Q8—5381no—
191C4×Q8—5381no—
192C4×Q8C2×D26911yescharacteristic
193#117—2691no—
194#117—2691no—
195#117—2691no—
196#117—5381no—
197#117—5381no—
198C2×C4⋊C4—2691no—
199#107—2691no—
200#107—2691no—
201#107—2691no—
202#107C2×D26911yescharacteristic
203#106—2691no—
204#106—2691no—
205#106—2691no—
206#106C2×D26911yescharacteristic
207C4⋊C8—2691no—
208C4⋊C8—2691no—
209C4⋊C8—2691no—
210C4⋊C8C2×D26911yescharacteristic
211#103—2691no—
212#103—2691no—
213#103—2691no—
214#103—2691no—
215#103—2691no—
216#103—2691no—
217#103C2×D26911yescharacteristic
218#103C2×D26911yescharacteristic
219C2×Q8—2694no—
220C2×Q8—2691no—
221C2×Q8—5381no—
222C2×Q8—5381no—
223C2×Q8—5382no—
224C2×Q8—5381no—
225C2×Q8C22×D26911yescharacteristic
226C22×C4—2691no—
227C22×C4—5381no—
228C22×C4—5381no—
229M16—5382no—
230C2×C8—2691no—
231C2×C8—2691no—
232C2×C8—5382no—
233C2×C8C22×D26911yescharacteristic
234C2×C8C22×D26911yescharacteristic
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—2691no—
239C4⋊C4—2691no—
240C4⋊C4—2691no—
241C4⋊C4—2691no—
242C4⋊C4—2691no—
243C4⋊C4—5381no—
244C4⋊C4—5381no—
245C4⋊C4—5381no—
246C4⋊C4—5381no—
247C4⋊C4—5381no—
248C4⋊C4—5381no—
249C4⋊C4—5381no—
250C4⋊C4—5381no—
251C4⋊C4C22×D26911yescharacteristic
252C4⋊C4C22×D26911yescharacteristic
253C4⋊C4C22×D26911yescharacteristic
254C22⋊C4—2691no—
255C22⋊C4—2691no—
256C22⋊C4—5381no—
257C22⋊C4—5381no—
258C42—21no—
259C42—2691no—
260C42—5381no—
261C42—5381no—
262C42—5381no—
263C42—5381no—
264C42—5381no—
265C42C22×D26911yescharacteristic
266C23—2691no—
267Q8—21no—
268Q8—2692no—
269Q8—5384no—
270Q8—5381no—
271Q8—21521no—
272Q8—21521no—
273Q8Q8×D26912yes—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—2691no—
279C2×C4—2692no—
280C2×C4—2692no—
281C2×C4—2691no—
282C2×C4—2691no—
283C2×C4—5384no—
284C2×C4—5381no—
285C2×C4—5381no—
286C2×C4—5381no—
287C2×C4—5381no—
288C2×C4—21521no—
289C2×C4D4×D26911yescharacteristic
290C2×C4D4×D26911yescharacteristic
291C2×C4C23×D26911yescharacteristic
292C8—21no—
293C8—21no—
294C8—5381no—
295C8—5381no—
296C22—2692no—
297C22—5381no—
298C22—5381no—
299C22C2×D4×D26911yescharacteristic
300C4—21no—
301C4—21no—
302C4—22no—
303C4—41no—
304C4—41no—
305C4—41no—
306C4—2692no—
307C4—5381no—
308C4—5381no—
309C4—5382no—
310C4—10761no—
311C4—10761no—
312C4—10761no—
313C4C2×Q8×D26911yescharacteristic
314C4#41×D26911yescharacteristic
315C2—5382no—
316C2C22⋊Q8×D26911yescharacteristic
317C2#3177141211yescharacteristic
318C2#3177142111yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#479×C269C2
socleC22×C269C22×D4
prime radicalC22×D269C2×D4
hypercenter#479D269
hypocenterC269#3082
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
3. #31770915C2semidirect
4. #31770910C2semidirect
5. #31770909C2semidirect
6. #31770900C2semidirect
7. #31770899C2semidirect
8. #31770891C2semidirect
9. #31770888C2semidirect
15. #479×C269C2semidirect
64. Q8×D269Q8semidirect
159. C269#3082semidirect
166. #479D269semidirect

Maximal subgroups

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

subgroupindex
#317712352
#317710812
#317709152
#317709102
#317709092
#317709002
#317708992
#317708912
#317708882
#317706462
#317706402
#317706302
#317706122
#103×D2692
#479×C2692
#3082269