Finite Group Databasebeta

← #46821116

Subgroups — #46821116

Order 34432.

370 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771226C211yesmaximal, characteristic
2#31771082C211yesmaximal, characteristic, complemented
3#31770947C211yesmaximal, characteristic, complemented
4#31770930C211yesmaximal, characteristic
5#31770901C211yesmaximal, characteristic, complemented
6#31770891C211yesmaximal, characteristic, complemented
7#31770828C211yesmaximal, characteristic, complemented
8#31770828C211yesmaximal, characteristic, complemented
9#31770763C211yesmaximal, characteristic, complemented
10#31770746C211yesmaximal, characteristic
11#31770713C211yesmaximal, characteristic, complemented
12#31770707C211yesmaximal, characteristic, complemented
13C4×Dic1076C211yesmaximal, characteristic, complemented
14C4×#16864391C211yesmaximal, characteristic, complemented
15#433×C269C211yesmaximal, characteristic, complemented
16C22×Dic538C2211yescharacteristic
17C2×Dic1076C2211yescharacteristic
18C2×Dic1076C2211yescharacteristic
19C2×#16864391C2211yescharacteristic
20C2×#16864391C2211yescharacteristic
21#22575453C2211yescharacteristic
22#22575448—21no—
23#22575441C2211yescharacteristic
24#22575439—21no—
25#22575435—21no—
26#22575432C2211yescharacteristic
27#22575431—21no—
28#22575427C2211yescharacteristic
29C4×Dic538C2211yescharacteristic
30C4×Dic538C2211yescharacteristic
31C4×Dic538C2211yescharacteristic
32C4×Dic538C2211yescharacteristic
33C4×Dic538C2211yescharacteristic
34#22575418—21no—
35#22575418—21no—
36C4×D1076C2211yescharacteristic
37#22575412C2211yescharacteristic
38#22575409—21no—
39#22575409—21no—
40#22575387C2211yescharacteristic
41#22575387C2211yescharacteristic
42#22575385C2211yescharacteristic
43#22575385C2211yescharacteristic
44#22575378C2211yescharacteristic
45#22575378C2211yescharacteristic
46#22575378C2211yescharacteristic
47#22575378C2211yescharacteristic
48#22575378C2211yescharacteristic
49#22575378C2211yescharacteristic
50#22575375C2211yescharacteristic
51#22575375C2211yescharacteristic
52#117×C269C2211yescharacteristic
53C4⋊C8×C269C2211yescharacteristic
54C4⋊C8×C269C2211yescharacteristic
55C22⋊C8×C269C2211yescharacteristic
56C22⋊C8×C269C2211yescharacteristic
57#97×C269C2211yescharacteristic
58C4×C8×C269C2211yescharacteristic
59C2×Dic538—22no—
60C2×Dic538—22no—
61C2×Dic538—21no—
62C2×Dic538—21no—
63C2×Dic538C2311yescharacteristic
64C2×Dic538C2311yescharacteristic
65C2×Dic538C2311yescharacteristic
66C2×D1076C2311yescharacteristic
67C2×C22⋊D269—21no—
68C22×Dic269—21no—
69C2×C4×D269—21no—
70Dic1076—22no—
71Dic1076—22no—
72#16864391—22no—
73#16864391—22no—
74C4⋊Dic269—21no—
75C4⋊Dic269C2311yescharacteristic
76C4⋊Dic269C2311yescharacteristic
77C4⋊Dic269C2311yescharacteristic
78C4⋊Dic269C2311yescharacteristic
79#16864381—21no—
80#16864381—21no—
81#16864381—21no—
82#16864381—21no—
83#16864381—21no—
84#16864381—21no—
85C22⋊Dic269—21no—
86C22⋊Dic269—21no—
87#16864379—21no—
88#16864379—21no—
89#16864379—21no—
90#16864379—21no—
91C4×Dic269—21no—
92C4×Dic269—21no—
93C4×Dic269—21no—
94C4×Dic269—21no—
95C4×Dic269—21no—
96C4×Dic269—21no—
97C22×C4×C269C2311yescharacteristic
98C2×C8×C269C2311yescharacteristic
99C2×C8×C269C2311yescharacteristic
100C2×C8×C269C2311yescharacteristic
101C2×C8×C269C2311yescharacteristic
102C4⋊C4×C269D411yescharacteristic
103C4⋊C4×C269D411yescharacteristic
104C22⋊C4×C269D411yescharacteristic
105C22⋊C4×C269D411yescharacteristic
106C42×C269C2311yescharacteristic
107C42×C269C2311yescharacteristic
108C22×D269—21no—
109Dic538—24no—
110Dic538—21no—
111Dic538—21no—
112Dic538—21no—
113Dic538—21no—
114Dic538—81no—
115Dic538#4112yes—
116Dic538#4112yes—
117D1076—21no—
118D1076—21no—
119C22⋊D269—81no—
120C2×Dic269—24no—
121C2×Dic269—21no—
122C2×Dic269—21no—
123C2×Dic269—21no—
124C2×Dic269—21no—
125C2×Dic269—21no—
126C2×Dic269—21no—
127C2×Dic269—21no—
128C4×D269—81no—
129C23×C269C2×D411yescharacteristic
130C2×C4×C269—21no—
131C2×C4×C269—21no—
132C2×C4×C269C2×D411yescharacteristic
133C2×C4×C269C2×D411yescharacteristic
134C2×C4×C269C2×D411yescharacteristic
135C2×C4×C269C2×D411yescharacteristic
136C2×C4×C269C2×D411yescharacteristic
137C2×C4×C269C2411yescharacteristic
138C8×C269—21no—
139C8×C269—21no—
140C8×C269—21no—
141C8×C269—21no—
142C22×C269—21no—
143C22×C269—21no—
144C22×C269—21no—
145C22×C269C22×D411yescharacteristic
146C2×D269—41no—
147C2×D269—41no—
148C2×D269—41no—
149C4×C269—21no—
150C4×C269—21no—
151C4×C269—21no—
152C4×C269—21no—
153C4×C269—21no—
154C4×C269C2×#4111yescharacteristic
155C4×C269C2×#4111yescharacteristic
156Dic269—22no—
157Dic269—22no—
158Dic269—41no—
159Dic269—41no—
160Dic269—41no—
161Dic269—41no—
162Dic269—41no—
163C2×C269—41no—
164C2×C269#52511yescharacteristic
165C2×C269#57711yescharacteristic
166C2×C269#57811yescharacteristic
167D269—81no—
168C269#312111yescharacteristic, complemented, Sylow
169#3121—2691nomaximal, Sylow
170#542—2691no—
171#519—2691no—
172#485—2691no—
173#482—2691no—
174#477—2691no—
175#475—2691no—
176#464—2691no—
177#464—2691no—
178#451—2691no—
179#448—2691no—
180#441—2691no—
181#440—2691no—
182C4×Q16—2691no—
183C4×SD16—2691no—
184#433D26911yescharacteristic, complemented
185C22×Q8—2691no—
186C2×Q16—2691no—
187C2×Q16—2691no—
188C2×SD16—2691no—
189C2×SD16—2691no—
190C4⋊Q8—2691no—
191#126—5381no—
192#124—2691no—
193#124—5381no—
194#123—5381no—
195C22⋊Q8—2691no—
196C22⋊Q8—5381no—
197#121—2691no—
198C4×Q8—2691no—
199C4×Q8—2691no—
200C4×Q8—2691no—
201C4×Q8—2691no—
202C4×Q8—2691no—
203C4×Q8—5381no—
204C4×Q8—5381no—
205C4×D4—2691no—
206#117—2691no—
207#117—5381no—
208#117—5381no—
209#117C2×D26911yescharacteristic
210#107—2691no—
211#107—2691no—
212#106—2691no—
213#106—2691no—
214C4⋊C8C2×D26911yescharacteristic
215C4⋊C8C2×D26911yescharacteristic
216#103—2691no—
217#103—2691no—
218#103—2691no—
219#103—2691no—
220#103—2691no—
221#103—2691no—
222#102—2691no—
223#102—2691no—
224C22⋊C8C2×D26911yescharacteristic
225C22⋊C8C2×D26911yescharacteristic
226#97C2×D26911yescharacteristic
227C4×C8C2×D26911yescharacteristic
228C2×Q8—2691no—
229C2×Q8—2691no—
230C2×Q8—2691no—
231C2×Q8—5382no—
232C2×Q8—5382no—
233C2×Q8—5381no—
234C2×Q8—5381no—
235C2×D4—2691no—
236C2×D4—5381no—
237C22×C4—5381no—
238C22×C4—5381no—
239C22×C4C22×D26911yescharacteristic
240Q16—5382no—
241Q16—5382no—
242SD16—5382no—
243SD16—5382no—
244C2×C8C22×D26911yescharacteristic
245C2×C8C22×D26911yescharacteristic
246C2×C8C22×D26911yescharacteristic
247C2×C8C22×D26911yescharacteristic
248C4⋊C4—2691no—
249C4⋊C4—2691no—
250C4⋊C4—2691no—
251C4⋊C4—2691no—
252C4⋊C4—5381no—
253C4⋊C4—5381no—
254C4⋊C4—5381no—
255C4⋊C4—5381no—
256C4⋊C4—5381no—
257C4⋊C4—5381no—
258C4⋊C4—5381no—
259C4⋊C4D107611yescharacteristic
260C4⋊C4D107611yescharacteristic
261C22⋊C4—5381no—
262C22⋊C4—5381no—
263C22⋊C4—5381no—
264C22⋊C4—5381no—
265C22⋊C4—5381no—
266C22⋊C4—5381no—
267C22⋊C4D107611yescharacteristic
268C22⋊C4D107611yescharacteristic
269C42—5381no—
270C42—5381no—
271C42—5381no—
272C42—5381no—
273C42—5381no—
274C42—5381no—
275C42C22×D26911yescharacteristic
276C42C22×D26911yescharacteristic
277C23—5381no—
278C23C2×D107611yescharacteristic
279Q8—2692no—
280Q8—2692no—
281Q8—5384no—
282Q8—5381no—
283Q8—5381no—
284Q8—5381no—
285Q8—5381no—
286Q8—21521no—
287D4—5381no—
288D4—5381no—
289D4—21521no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—5384no—
293C2×C4—5381no—
294C2×C4—5381no—
295C2×C4—5381no—
296C2×C4—5381no—
297C2×C4—5381no—
298C2×C4—5381no—
299C2×C4—5381no—
300C2×C4—21521no—
301C2×C4C2×D107611yescharacteristic
302C2×C4C2×D107611yescharacteristic
303C2×C4C2×D107611yescharacteristic
304C2×C4C2×D107611yescharacteristic
305C2×C4C2×D107611yescharacteristic
306C2×C4C23×D26911yescharacteristic
307C8—21no—
308C8—21no—
309C8—21no—
310C8—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—10761no—
315C22—10761no—
316C22—10761no—
317C22C22×D107611yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—5382no—
324C4—5382no—
325C4—10761no—
326C4—10761no—
327C4—10761no—
328C4—10761no—
329C4—10761no—
330C4#41×D26911yescharacteristic
331C4#41×D26911yescharacteristic
332C2—41no—
333C2—21521no—
334C2#3177111711yescharacteristic
335C2#3177141711yescharacteristic
336C2#3177142211yescharacteristic
subgroupG/H
centerC22C22×D1076
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#433×C269C2
socleC22×C269C22×D4
prime radical#22575427C22
hypercenter#433D269
hypocenterC269#3121
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
2. #31771082C2semidirect
3. #31770947C2semidirect
5. #31770901C2semidirect
6. #31770891C2semidirect
7. #31770828C2semidirect
8. #31770828C2semidirect
9. #31770763C2semidirect
11. #31770713C2semidirect
12. #31770707C2semidirect
13. C4×Dic1076C2semidirect
14. C4×#16864391C2semidirect
15. #433×C269C2semidirect
168. C269#3121semidirect
184. #433D269semidirect

Maximal subgroups

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

subgroupindex
#317712262
#317710822
#317709472
#317709302
#317709012
#317708912
#317708282
#317707632
#317707462
#317707132
#317707072
C4×Dic10762
C4×#168643912
#433×C2692
#3121269