Finite Group Databasebeta

← #46823600

Subgroups — #46823600

Order 34432.

372 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771324C211yesmaximal, characteristic, complemented
2#31771270C211yesmaximal, characteristic, complemented
3#31770963C211yesmaximal, characteristic, complemented
4#31770954C211yesmaximal, characteristic, complemented
5#31770898C211yesmaximal, characteristic, complemented
6#31770897C211yesmaximal, characteristic, complemented
7#31770883C211yesmaximal, characteristic, complemented
8#31770819C211yesmaximal, characteristic
9#31770817C211yesmaximal, characteristic
10#31770809C211yesmaximal, characteristic, complemented
11#31770733C211yesmaximal, characteristic, complemented
12#31770708C211yesmaximal, characteristic, complemented
13#31770707C211yesmaximal, characteristic, complemented
14#31770685C211yesmaximal, characteristic
15#489×C269C211yesmaximal, characteristic, complemented
16C2×Q8×D269—21no—
17C2×#16864391C2211yescharacteristic
18C2×#16864389C2211yescharacteristic
19C2×#16864387C2211yescharacteristic
20#22575452C2211yescharacteristic
21#22575452C2211yescharacteristic
22#22575451C2211yescharacteristic
23#22575446—21no—
24#22575446—21no—
25#22575440C2211yescharacteristic
26#22575431—21no—
27#22575431—21no—
28#22575430—21no—
29#22575429—21no—
30Q8×Dic269C2211yescharacteristic
31C4×Dic538C2211yescharacteristic
32C4×Dic538C2211yescharacteristic
33C4×D1076C2211yescharacteristic
34D4×Dic269C2211yescharacteristic
35#22575415C2211yescharacteristic
36#22575415C2211yescharacteristic
37#22575409—21no—
38#22575387C2211yescharacteristic
39#22575386C2211yescharacteristic
40#22575386C2211yescharacteristic
41C4⋊#14524130C2211yescharacteristic
42#22575382C2211yescharacteristic
43#22575382C2211yescharacteristic
44#22575378C2211yescharacteristic
45#22575377C2211yescharacteristic
46#22575376C2211yescharacteristic
47#22575376C2211yescharacteristic
48#22575375C2211yescharacteristic
49#22575374C2211yescharacteristic
50#22575363C2211yescharacteristic
51C8×Dic269C2211yescharacteristic
52C4⋊Q8×C269C2211yescharacteristic
53#124×C269C2211yescharacteristic
54#103×C269C2211yescharacteristic
55#103×C269C2211yescharacteristic
56#102×C269C2211yescharacteristic
57#102×C269C2211yescharacteristic
58#97×C269C2211yescharacteristic
59C2×Dic538—21no—
60C2×Dic538—21no—
61C2×Dic538D411yescharacteristic
62C2×Dic538C2311yescharacteristic
63Q8×D269—44no—
64C2×D1076C2311yescharacteristic
65C22×Dic269—21no—
66C2×C4×D269—21no—
67C2×C4×D269—21no—
68C2×C4×D269—21no—
69#16864391—22no—
70#16864389—22no—
71#16864387—22no—
72C2×#14524130C2311yescharacteristic
73C2×#14524130C2311yescharacteristic
74C4⋊Dic269—21no—
75C4⋊Dic269D411yescharacteristic
76C4⋊Dic269C2311yescharacteristic
77C4⋊Dic269C2311yescharacteristic
78#16864381—21no—
79#16864381—21no—
80#16864381—21no—
81#16864381—21no—
82#16864381—21no—
83#16864381D411yescharacteristic
84#16864381D411yescharacteristic
85C22⋊Dic269—21no—
86C22⋊Dic269—21no—
87C22⋊Dic269—21no—
88#16864379—21no—
89#16864379—21no—
90#16864379—21no—
91C4×Dic269—21no—
92C4×Dic269—21no—
93C4×Dic269C2311yescharacteristic
94C4×Dic269C2311yescharacteristic
95C2×Q8×C269—21no—
96C2×Q8×C269C2311yescharacteristic
97C2×D4×C269C2311yescharacteristic
98C2×C8×C269C2311yescharacteristic
99C2×C8×C269C2311yescharacteristic
100C4⋊C4×C269—21no—
101C4⋊C4×C269C2311yescharacteristic
102C4⋊C4×C269C2311yescharacteristic
103C22⋊C4×C269—21no—
104C22⋊C4×C269—21no—
105C42×C269C2311yescharacteristic
106C22×D269—21no—
107Dic538—22no—
108Dic538—21no—
109Dic538—21no—
110Dic538—42no—
111Dic538—42no—
112D1076—21no—
113D1076#4112yes—
114C2×Dic269—21no—
115C2×Dic269—21no—
116C2×Dic269—21no—
117C2×Dic269—42no—
118C2×Dic269C2×D411yescharacteristic
119C2×Dic269C2×D411yescharacteristic
120C2×Dic269C2×D411yescharacteristic
121C2×Dic269C2×D411yescharacteristic
122C4×D269—42no—
123C4×D269—42no—
124C4×D269—42no—
125#14524130—21no—
126#14524130—21no—
127C23×C269—21no—
128Q8×C269—21no—
129Q8×C269—21no—
130Q8×C269—42no—
131D4×C269—21no—
132D4×C269—21no—
133C2×C4×C269—21no—
134C2×C4×C269—21no—
135C2×C4×C269—21no—
136C2×C4×C269C2×D411yescharacteristic
137C2×C4×C269C2×D411yescharacteristic
138C2×C4×C269C2411yescharacteristic
139C8×C269—21no—
140C8×C269—21no—
141C22×C269—41no—
142C22×C269—41no—
143C22×C269—41no—
144C22×C269C22×D411yescharacteristic
145C2×D269—22no—
146C2×D269—41no—
147C2×D269—41no—
148C4×C269—21no—
149C4×C269—21no—
150C4×C269—41no—
151C4×C269—41no—
152C4×C269—41no—
153C4×C269C2×#4111yescharacteristic
154C4×C2692−1+411yescharacteristic
155Dic269—21no—
156Dic269—21no—
157Dic269—21no—
158Dic269—41no—
159Dic269—41no—
160Dic269—41no—
161Dic269AGL(1,ℤ/8)12yes—
162C2×C269—81no—
163C2×C269#54811yescharacteristic
164C2×C269C2×AGL(1,ℤ/8)11yescharacteristic
165C2×C269#57811yescharacteristic
166D269—42no—
167C269#336711yescharacteristic, complemented, Sylow
168#3367—2691nomaximal, Sylow
169#556—2691no—
170D4×Q8—2691no—
171#489—2691no—
172#489D26911yescharacteristic, complemented
173#487—2691no—
174#477—2691no—
175#477—2691no—
176#474—2691no—
177#463—2691no—
178#463—2691no—
179#461—2691no—
180#446—2691no—
181#440—2691no—
182#440—2691no—
183C4×D8—2691no—
184C22×Q8—5381no—
185C2×SD16—2691no—
186C2×SD16—2691no—
187C2×D8—2691no—
188C4⋊Q8—2691no—
189C4⋊Q8—2691no—
190C4⋊Q8—2691no—
191C4⋊Q8C2×D26911yescharacteristic
192#126—5381no—
193#126—5381no—
194#124—2691no—
195#124C2×D26911yescharacteristic
196C22⋊Q8—5381no—
197C22⋊Q8—5381no—
198C22⋊Q8—5381no—
199C22⋊Q8—5381no—
200C4×Q8—2691no—
201C4×Q8—2691no—
202C4×Q8—2691no—
203C4×D4—2691no—
204C4×D4—2691no—
205C4×D4—2691no—
206C4×D4—2691no—
207#117—5381no—
208#107—2691no—
209#107—2691no—
210#107—2691no—
211C4⋊C8—2691no—
212C4⋊C8—2691no—
213C4⋊C8—2691no—
214#103—2691no—
215#103—2691no—
216#103—2691no—
217#103—2691no—
218#103C2×D26911yescharacteristic
219#103C2×D26911yescharacteristic
220#102—2691no—
221#102—2691no—
222#102C2×D26911yescharacteristic
223#102C2×D26911yescharacteristic
224#97—2691no—
225#97C2×D26911yescharacteristic
226C4×C8—2691no—
227C2×Q8—21no—
228C2×Q8—2691no—
229C2×Q8—2691no—
230C2×Q8—5381no—
231C2×Q8—5381no—
232C2×Q8—10764no—
233C2×Q8C22×D26911yescharacteristic
234C2×D4—2691no—
235C2×D4C22×D26911yescharacteristic
236C22×C4—5381no—
237C22×C4—5381no—
238C22×C4—5381no—
239C22×C4—5381no—
240SD16—5382no—
241SD16—5382no—
242D8—5382no—
243C2×C8—2691no—
244C2×C8—2691no—
245C2×C8C22×D26911yescharacteristic
246C2×C8C22×D26911yescharacteristic
247C4⋊C4—21no—
248C4⋊C4—2691no—
249C4⋊C4—2691no—
250C4⋊C4—2691no—
251C4⋊C4—2691no—
252C4⋊C4—2691no—
253C4⋊C4—5381no—
254C4⋊C4—5381no—
255C4⋊C4—5381no—
256C4⋊C4—5381no—
257C4⋊C4—5381no—
258C4⋊C4—5381no—
259C4⋊C4C22×D26911yescharacteristic
260C4⋊C4C22×D26911yescharacteristic
261C22⋊C4—21no—
262C22⋊C4—21no—
263C22⋊C4—5381no—
264C22⋊C4—5381no—
265C22⋊C4—5381no—
266C22⋊C4—5381no—
267C22⋊C4—5381no—
268C22⋊C4—5381no—
269C42—2691no—
270C42—2691no—
271C42—5381no—
272C42—5381no—
273C42C22×D26911yescharacteristic
274C23—21no—
275C23—5381no—
276Q8—21no—
277Q8—21no—
278Q8—42no—
279Q8—5382no—
280Q8—5381no—
281Q8—5381no—
282Q8—10762no—
283Q8—10762no—
284D4—21no—
285D4—21no—
286D4—2692no—
287D4—5381no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—2691no—
292C2×C4—2691no—
293C2×C4—2691no—
294C2×C4—2691no—
295C2×C4—5381no—
296C2×C4—5381no—
297C2×C4—5381no—
298C2×C4—10762no—
299C2×C4—10762no—
300C2×C4—10762no—
301C2×C4—10762no—
302C2×C4D4×D26911yescharacteristic
303C2×C4D4×D26911yescharacteristic
304C2×C4C23×D26911yescharacteristic
305C8—21no—
306C8—21no—
307C8—5381no—
308C8—5381no—
309C22—41no—
310C22—41no—
311C22—41no—
312C22—5382no—
313C22—10761no—
314C22—10761no—
315C22C2×D4×D26911yescharacteristic
316C4—21no—
317C4—21no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—2692no—
322C4—5381no—
323C4—5381no—
324C4—5381no—
325C4—10761no—
326C4—10761no—
327C4—10761no—
328C4#41×D26911yescharacteristic
329C4#2257550011yescharacteristic
330C2—81no—
331C2—10762no—
332C2#3177126311yescharacteristic
333C2AGL(1,ℤ/8)×D26911yescharacteristic
334C2#3177142111yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#489×C269C2
socleC22×C269C22×D4
prime radicalC2×#16864387C22
hypercenter#489D269
hypocenterC269#3367
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #31771324C2semidirect
2. #31771270C2semidirect
3. #31770963C2semidirect
4. #31770954C2semidirect
5. #31770898C2semidirect
6. #31770897C2semidirect
7. #31770883C2semidirect
10. #31770809C2semidirect
11. #31770733C2semidirect
12. #31770708C2semidirect
13. #31770707C2semidirect
15. #489×C269C2semidirect
167. C269#3367semidirect
172. #489D269semidirect

Maximal subgroups

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

subgroupindex
#317713242
#317712702
#317709632
#317709542
#317708982
#317708972
#317708832
#317708192
#317708172
#317708092
#317707332
#317707082
#317707072
#317706852
#489×C2692
#3367269