Finite Group Databasebeta

← #46823548

Subgroups — #46823548

Order 34432.

362 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771338C211yesmaximal, characteristic, complemented
2#31771311C211yesmaximal, characteristic, complemented
3#31770962C211yesmaximal, characteristic, complemented
4#31770958C211yesmaximal, characteristic, complemented
5#31770950C211yesmaximal, characteristic, complemented
6#31770904C211yesmaximal, characteristic, complemented
7#31770899C211yesmaximal, characteristic, complemented
8#31770821C211yesmaximal, characteristic, complemented
9#31770819C211yesmaximal, characteristic, complemented
10#31770799C211yesmaximal, characteristic
11#31770729C211yesmaximal, characteristic, complemented
12#31770692C211yesmaximal, characteristic, complemented
13#31770687C211yesmaximal, characteristic, complemented
14C4×#16864387C211yesmaximal, characteristic, complemented
15#478×C269C211yesmaximal, characteristic, complemented
16C2×#16864391C2211yescharacteristic
17C2×D2152C2211yescharacteristic
18C2×#16864387C2211yescharacteristic
19#22575452C2211yescharacteristic
20#22575449C2211yescharacteristic
21#22575444C2211yescharacteristic
22#22575441C2211yescharacteristic
23#22575440C2211yescharacteristic
24#22575439—21no—
25#22575436—21no—
26#22575435—21no—
27#22575433—21no—
28#22575431—21no—
29#22575431—21no—
30C4×Dic538C2211yescharacteristic
31#22575418C2211yescharacteristic
32C4×D1076C2211yescharacteristic
33#22575415C2211yescharacteristic
34#22575415C2211yescharacteristic
35#22575415C2211yescharacteristic
36C4×C22⋊D269—21no—
37C4⋊C4×D269—21no—
38#22575386C2211yescharacteristic
39#22575382C2211yescharacteristic
40#22575382C2211yescharacteristic
41#22575378C2211yescharacteristic
42#22575376C2211yescharacteristic
43#22575376C2211yescharacteristic
44#22575375C2211yescharacteristic
45#22575374C2211yescharacteristic
46#22575373C2211yescharacteristic
47#22575373C2211yescharacteristic
48#22575373C2211yescharacteristic
49C4×#14524130C2211yescharacteristic
50C8×Dic269C2211yescharacteristic
51C8×Dic269C2211yescharacteristic
52#125×C269C2211yescharacteristic
53C4×D4×C269C2211yescharacteristic
54#107×C269C2211yescharacteristic
55#106×C269C2211yescharacteristic
56C4⋊C8×C269C2211yescharacteristic
57#102×C269C2211yescharacteristic
58#102×C269C2211yescharacteristic
59C2×Dic538—21no—
60C2×Dic538D411yescharacteristic
61C2×Dic538C2311yescharacteristic
62C2×D1076C2311yescharacteristic
63C2×D1076C2311yescharacteristic
64C2×C22⋊D269—21no—
65C2×C22⋊D269—21no—
66C2×C4×D269—21no—
67C2×C4×D269—21no—
68C2×C4×D269—21no—
69C2×C4×D269—21no—
70#16864391—22no—
71D2152—22no—
72#16864387—22no—
73C2×#14524130C2311yescharacteristic
74C2×#14524130C2311yescharacteristic
75C4⋊Dic269—21no—
76C4⋊Dic269D411yescharacteristic
77C4⋊Dic269C2311yescharacteristic
78#16864381—21no—
79#16864381—21no—
80#16864381—21no—
81#16864381D411yescharacteristic
82#16864381D411yescharacteristic
83C22⋊Dic269—21no—
84C22⋊Dic269—21no—
85#16864379—21no—
86#16864379—21no—
87#16864379—21no—
88#16864379—21no—
89#16864379—21no—
90#16864379—21no—
91C4×Dic269—21no—
92C4×Dic269C2311yescharacteristic
93C4×Dic269C2311yescharacteristic
94C2×D4×C269C2311yescharacteristic
95C22×C4×C269—21no—
96C2×C8×C269C2311yescharacteristic
97C2×C8×C269C2311yescharacteristic
98C4⋊C4×C269—21no—
99C4⋊C4×C269—21no—
100C4⋊C4×C269C2311yescharacteristic
101C4⋊C4×C269C2311yescharacteristic
102C4⋊C4×C269C2311yescharacteristic
103C22⋊C4×C269—21no—
104C42×C269C2311yescharacteristic
105C22×D269—21no—
106C22×D269—21no—
107Dic538—22no—
108Dic538—21no—
109Dic538—21no—
110Dic538—81no—
111D1076—21no—
112D1076—21no—
113D1076—21no—
114D1076#4112yes—
115C22⋊D269—42no—
116C22⋊D269—81no—
117C2×Dic269—21no—
118C2×Dic269—21no—
119C2×Dic269C2×D411yescharacteristic
120C2×Dic269C2×D411yescharacteristic
121C2×Dic269C2×D411yescharacteristic
122C2×Dic269C2×D411yescharacteristic
123C4×D269—42no—
124C4×D269—81no—
125C4×D269—81no—
126C4×D269—81no—
127#14524130—21no—
128#14524130—21no—
129C23×C269—21no—
130D4×C269—21no—
131D4×C269—21no—
132C2×C4×C269—21no—
133C2×C4×C269—21no—
134C2×C4×C269—21no—
135C2×C4×C269—81no—
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—
148C2×D269—41no—
149C2×D269—41no—
150C2×D269—41no—
151C4×C269—21no—
152C4×C269—21no—
153C4×C269—41no—
154C4×C269—41no—
155C4×C269—41no—
156C4×C269C2×#4111yescharacteristic
157C4×C2692−1+411yescharacteristic
158Dic269—21no—
159Dic269—21no—
160Dic269—21no—
161Dic269—41no—
162Dic269—41no—
163Dic269#13512yes—
164C2×C269—81no—
165C2×C269#54811yescharacteristic
166C2×C269C2×#13511yescharacteristic
167C2×C269#57611yescharacteristic
168D269—42no—
169D269—81no—
170C269#336111yescharacteristic, complemented, Sylow
171#3361—2691nomaximal, Sylow
172#559—2691no—
173#554—2691no—
174#488—2691no—
175#488—2691no—
176#486—2691no—
177#478—2691no—
178#478D26911yescharacteristic, complemented
179#477—2691no—
180#463—2691no—
181#463—2691no—
182#459—2691no—
183C8×Q8—2691no—
184C4×SD16—2691no—
185C4×D8—2691no—
186C4×D8—2691no—
187C2×SD16—2691no—
188C2×D8—2691no—
189C2×D8—2691no—
190C4⋊Q8—2691no—
191#127—2691no—
192#125—2691no—
193#125C2×D26911yescharacteristic
194#124—2691no—
195#124—2691no—
196#124—5381no—
197#123—5381no—
198#123—5381no—
199C22⋊Q8—5381no—
200C22⋊Q8—5381no—
201C22⋊Q8—5381no—
202C4×Q8—2691no—
203C4×Q8—2691no—
204C4×D4—2691no—
205C4×D4—2691no—
206C4×D4—2691no—
207C4×D4—2691no—
208C4×D4—5381no—
209C4×D4C2×D26911yescharacteristic
210C2×C4⋊C4—5381no—
211#107—2691no—
212#107C2×D26911yescharacteristic
213#106C2×D26911yescharacteristic
214C4⋊C8—2691no—
215C4⋊C8—2691no—
216C4⋊C8C2×D26911yescharacteristic
217#103—2691no—
218#103—2691no—
219#103—2691no—
220#102—2691no—
221#102—2691no—
222#102—2691no—
223#102—2691no—
224#102—2691no—
225#102C2×D26911yescharacteristic
226#102C2×D26911yescharacteristic
227C4×C8—2691no—
228C4×C8—2691no—
229C4×C8—2691no—
230C2×Q8—2691no—
231C2×Q8—2691no—
232C2×Q8—5381no—
233C2×D4—2691no—
234C2×D4—2691no—
235C2×D4—5381no—
236C2×D4—5381no—
237C2×D4C22×D26911yescharacteristic
238C22×C4—21no—
239C22×C4—5381no—
240C22×C4—5381no—
241C22×C4—5381no—
242C22×C4—5381no—
243SD16—5382no—
244D8—5382no—
245D8—5382no—
246C2×C8—2691no—
247C2×C8—2691no—
248C2×C8C22×D26911yescharacteristic
249C2×C8C22×D26911yescharacteristic
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—2691no—
253C4⋊C4—2691no—
254C4⋊C4—2691no—
255C4⋊C4—2691no—
256C4⋊C4—5381no—
257C4⋊C4—5381no—
258C4⋊C4—5381no—
259C4⋊C4—5381no—
260C4⋊C4C22×D26911yescharacteristic
261C4⋊C4C22×D26911yescharacteristic
262C4⋊C4C22×D26911yescharacteristic
263C22⋊C4—21no—
264C22⋊C4—5381no—
265C22⋊C4—5381no—
266C22⋊C4—5381no—
267C22⋊C4—5381no—
268C22⋊C4—5381no—
269C22⋊C4—5381no—
270C22⋊C4—5381no—
271C22⋊C4—5381no—
272C42—2691no—
273C42—2691no—
274C42—5381no—
275C42C22×D26911yescharacteristic
276C23—21no—
277C23—5381no—
278C23—5381no—
279Q8—5382no—
280Q8—5381no—
281Q8—5381no—
282Q8—21521no—
283D4—21no—
284D4—21no—
285D4—2692no—
286D4—5381no—
287D4—5381no—
288D4—5381no—
289D4—10762no—
290D4—21521no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—81no—
295C2×C4—2691no—
296C2×C4—2691no—
297C2×C4—2691no—
298C2×C4—2691no—
299C2×C4—5381no—
300C2×C4—5381no—
301C2×C4—10762no—
302C2×C4—21521no—
303C2×C4—21521no—
304C2×C4—21521no—
305C2×C4D4×D26911yescharacteristic
306C2×C4D4×D26911yescharacteristic
307C2×C4C23×D26911yescharacteristic
308C8—21no—
309C8—21no—
310C8—5381no—
311C8—5381no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—5382no—
316C22—10761no—
317C22—10761no—
318C22—10761no—
319C22—10761no—
320C22—10761no—
321C22C2×D4×D26911yescharacteristic
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—2692no—
328C4—5381no—
329C4—5381no—
330C4—5381no—
331C4—10761no—
332C4—10761no—
333C4#41×D26911yescharacteristic
334C4#2257550111yescharacteristic
335C2—81no—
336C2—10762no—
337C2—21521no—
338C2#3177126511yescharacteristic
339C2#135×D26911yescharacteristic
340C2#3177140911yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#478×C269C2
socleC22×C269C22×D4
prime radical#31770799C2
hypercenter#478D269
hypocenterC269#3361
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #31771338C2semidirect
2. #31771311C2semidirect
3. #31770962C2semidirect
4. #31770958C2semidirect
5. #31770950C2semidirect
6. #31770904C2semidirect
7. #31770899C2semidirect
8. #31770821C2semidirect
9. #31770819C2semidirect
11. #31770729C2semidirect
12. #31770692C2semidirect
13. #31770687C2semidirect
14. C4×#16864387C2semidirect
15. #478×C269C2semidirect
170. C269#3361semidirect
178. #478D269semidirect

Maximal subgroups

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

subgroupindex
#317713382
#317713112
#317709622
#317709582
#317709502
#317709042
#317708992
#317708212
#317708192
#317707992
#317707292
#317706922
#317706872
C4×#168643872
#478×C2692
#3361269