Finite Group Databasebeta

← #46821149

Subgroups — #46821149

Order 34432.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771226C211yesmaximal, characteristic, complemented
2#31771085C211yesmaximal, characteristic, complemented
3#31770941C211yesmaximal, characteristic, complemented
4#31770919C211yesmaximal, characteristic, complemented
5#31770901C211yesmaximal, characteristic, complemented
6#31770886C211yesmaximal, characteristic, complemented
7#31770828C211yesmaximal, characteristic, complemented
8#31770821C211yesmaximal, characteristic, complemented
9#31770769C211yesmaximal, characteristic, complemented
10#31770752C211yesmaximal, characteristic
11#31770707C211yesmaximal, characteristic, complemented
12#31770707C211yesmaximal, characteristic, complemented
13C4×Dic1076C211yesmaximal, characteristic, complemented
14C4×D2152C211yesmaximal, characteristic, complemented
15#433×C269C211yesmaximal, characteristic, complemented
16C2×#16864402C2211yescharacteristic
17C2×Dic1076C2211yescharacteristic
18C2×#16864391C2211yescharacteristic
19C2×#16864391C2211yescharacteristic
20C2×D2152C2211yescharacteristic
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×D1076C2211yescharacteristic
33C4×D1076C2211yescharacteristic
34C4×D1076C2211yescharacteristic
35#22575413—21no—
36#22575413—21no—
37#22575411—21no—
38C2×C4⋊Dic269C2211yescharacteristic
39C4⋊C4×D269—21no—
40#22575387C2211yescharacteristic
41#22575387C2211yescharacteristic
42#22575387C2211yescharacteristic
43#22575387C2211yescharacteristic
44#22575378C2211yescharacteristic
45#22575378C2211yescharacteristic
46#22575378C2211yescharacteristic
47#22575378C2211yescharacteristic
48#22575375C2211yescharacteristic
49#22575375C2211yescharacteristic
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
59#16864402—22no—
60#16864402—22no—
61C2×Dic538—21no—
62C2×Dic538C2311yescharacteristic
63C2×Dic538C2311yescharacteristic
64C2×D1076C2311yescharacteristic
65C2×D1076C2311yescharacteristic
66C2×C22⋊D269—21no—
67C2×C22⋊D269—21no—
68C22×Dic269—21no—
69C2×C4×D269—21no—
70C2×C4×D269—21no—
71C2×C4×D269—21no—
72C2×C4×D269—21no—
73Dic1076—22no—
74#16864391—22no—
75#16864391—22no—
76D2152—22no—
77C4⋊Dic269—21no—
78C4⋊Dic269—21no—
79C4⋊Dic269C2311yescharacteristic
80C4⋊Dic269C2311yescharacteristic
81C4⋊Dic269C2311yescharacteristic
82C4⋊Dic269C2311yescharacteristic
83#16864381—21no—
84#16864381—21no—
85#16864381—21no—
86#16864381—21no—
87C22⋊Dic269—21no—
88#16864379—21no—
89#16864379—21no—
90#16864379—21no—
91#16864379—21no—
92#16864379—21no—
93#16864379—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—
109C22×D269—21no—
110Dic538—21no—
111Dic538—21no—
112Dic538—21no—
113Dic538—81no—
114Dic538#4112yes—
115D1076—21no—
116D1076—21no—
117D1076—21no—
118D1076#4112yes—
119C22⋊D269—24no—
120C22⋊D269—81no—
121C2×Dic269—21no—
122C2×Dic269—21no—
123C2×Dic269—21no—
124C2×Dic269—21no—
125C2×Dic269—21no—
126C2×Dic269—21no—
127C2×Dic269—81no—
128C4×D269—24no—
129C4×D269—81no—
130C4×D269—81no—
131C4×D269—81no—
132C23×C269C2×D411yescharacteristic
133C2×C4×C269—21no—
134C2×C4×C269—21no—
135C2×C4×C269C2×D411yescharacteristic
136C2×C4×C269C2×D411yescharacteristic
137C2×C4×C269C2×D411yescharacteristic
138C2×C4×C269C2×D411yescharacteristic
139C2×C4×C269C2×D411yescharacteristic
140C2×C4×C269C2411yescharacteristic
141C8×C269—21no—
142C8×C269—21no—
143C8×C269—21no—
144C8×C269—21no—
145C22×C269—21no—
146C22×C269—21no—
147C22×C269—21no—
148C22×C269C22×D411yescharacteristic
149C2×D269—22no—
150C2×D269—41no—
151C2×D269—41no—
152C2×D269—41no—
153C2×D269—41no—
154C2×D269—41no—
155C4×C269—21no—
156C4×C269—21no—
157C4×C269—21no—
158C4×C269—21no—
159C4×C269—21no—
160C4×C269C2×#4111yescharacteristic
161C4×C269C2×#4111yescharacteristic
162Dic269—22no—
163Dic269—41no—
164Dic269—41no—
165Dic269—41no—
166Dic269—41no—
167Dic269—41no—
168C2×C269—41no—
169C2×C269#52511yescharacteristic
170C2×C269#57611yescharacteristic
171C2×C269#57811yescharacteristic
172D269—42no—
173D269—81no—
174C269#312411yescharacteristic, complemented, Sylow
175#3124—2691nomaximal, Sylow
176#542—2691no—
177#520—2691no—
178#484—2691no—
179#480—2691no—
180#477—2691no—
181#474—2691no—
182#464—2691no—
183#463—2691no—
184#452—2691no—
185#449—2691no—
186#440—2691no—
187#440—2691no—
188C4×Q16—2691no—
189C4×D8—2691no—
190#433D26911yescharacteristic, complemented
191C2×#41—2691no—
192C2×Q16—2691no—
193C2×SD16—2691no—
194C2×SD16—2691no—
195C2×D8—2691no—
196C4⋊Q8—2691no—
197#126—5381no—
198#124—2691no—
199#124—5381no—
200#123—5381no—
201C22⋊Q8—2691no—
202C22⋊Q8—5381no—
203#121—2691no—
204C4×Q8—2691no—
205C4×Q8—2691no—
206C4×Q8—2691no—
207C4×D4—2691no—
208C4×D4—2691no—
209C4×D4—2691no—
210C4×D4—5381no—
211C4×D4—5381no—
212#117—5381no—
213#117C2×D26911yescharacteristic
214C2×C4⋊C4—2691no—
215C2×C4⋊C4—5381no—
216#107—2691no—
217#107—2691no—
218#107—2691no—
219#107—2691no—
220C4⋊C8C2×D26911yescharacteristic
221C4⋊C8C2×D26911yescharacteristic
222#103—2691no—
223#103—2691no—
224#103—2691no—
225#103—2691no—
226#102—2691no—
227#102—2691no—
228#102—2691no—
229#102—2691no—
230C22⋊C8C2×D26911yescharacteristic
231C22⋊C8C2×D26911yescharacteristic
232#97C2×D26911yescharacteristic
233C4×C8C2×D26911yescharacteristic
234#41—5382no—
235#41—5382no—
236C2×Q8—2691no—
237C2×Q8—2691no—
238C2×Q8—5381no—
239C2×D4—2691no—
240C2×D4—2691no—
241C2×D4—5381no—
242C2×D4—5381no—
243C22×C4—5381no—
244C22×C4—5381no—
245C22×C4—5381no—
246C22×C4—5381no—
247C22×C4—5381no—
248C22×C4C22×D26911yescharacteristic
249Q16—5382no—
250SD16—5382no—
251SD16—5382no—
252D8—5382no—
253C2×C8C22×D26911yescharacteristic
254C2×C8C22×D26911yescharacteristic
255C2×C8C22×D26911yescharacteristic
256C2×C8C22×D26911yescharacteristic
257C4⋊C4—2691no—
258C4⋊C4—2691no—
259C4⋊C4—2691no—
260C4⋊C4—2691no—
261C4⋊C4—5381no—
262C4⋊C4—5381no—
263C4⋊C4—5381no—
264C4⋊C4—5381no—
265C4⋊C4—5381no—
266C4⋊C4—5381no—
267C4⋊C4D107611yescharacteristic
268C4⋊C4D107611yescharacteristic
269C22⋊C4—5381no—
270C22⋊C4—5381no—
271C22⋊C4—5381no—
272C22⋊C4—5381no—
273C22⋊C4—5381no—
274C22⋊C4—5381no—
275C22⋊C4—5381no—
276C22⋊C4D107611yescharacteristic
277C22⋊C4D107611yescharacteristic
278C42—5381no—
279C42—5381no—
280C42—5381no—
281C42C22×D26911yescharacteristic
282C42C22×D26911yescharacteristic
283C23—5381no—
284C23—5381no—
285C23C2×D107611yescharacteristic
286Q8—2692no—
287Q8—5381no—
288Q8—5381no—
289Q8—5381no—
290Q8—21521no—
291D4—2692no—
292D4—5384no—
293D4—5381no—
294D4—5381no—
295D4—5381no—
296D4—21521no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—5384no—
300C2×C4—5381no—
301C2×C4—5381no—
302C2×C4—5381no—
303C2×C4—5381no—
304C2×C4—5381no—
305C2×C4—5381no—
306C2×C4—21521no—
307C2×C4—21521no—
308C2×C4—21521no—
309C2×C4—21521no—
310C2×C4C2×D107611yescharacteristic
311C2×C4C2×D107611yescharacteristic
312C2×C4C2×D107611yescharacteristic
313C2×C4C2×D107611yescharacteristic
314C2×C4C2×D107611yescharacteristic
315C2×C4C23×D26911yescharacteristic
316C8—21no—
317C8—21no—
318C8—21no—
319C8—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—5382no—
324C22—10761no—
325C22—10761no—
326C22—10761no—
327C22—10761no—
328C22—10761no—
329C22C22×D107611yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—5382no—
336C4—10761no—
337C4—10761no—
338C4—10761no—
339C4—10761no—
340C4—10761no—
341C4#41×D26911yescharacteristic
342C4#41×D26911yescharacteristic
343C2—41no—
344C2—10762no—
345C2—21521no—
346C2#3177111711yescharacteristic
347C2#3177141011yescharacteristic
348C2#3177142211yescharacteristic
subgroupG/H
centerC22C22×D1076
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#433×C269C2
socleC22×C269C22×D4
prime radical#31770752C2
hypercenter#433D269
hypocenterC269#3124
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
1. #31771226C2semidirect
2. #31771085C2semidirect
3. #31770941C2semidirect
4. #31770919C2semidirect
5. #31770901C2semidirect
6. #31770886C2semidirect
7. #31770828C2semidirect
8. #31770821C2semidirect
9. #31770769C2semidirect
11. #31770707C2semidirect
12. #31770707C2semidirect
13. C4×Dic1076C2semidirect
14. C4×D2152C2semidirect
15. #433×C269C2semidirect
174. C269#3124semidirect
190. #433D269semidirect

Maximal subgroups

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

subgroupindex
#317712262
#317710852
#317709412
#317709192
#317709012
#317708862
#317708282
#317708212
#317707692
#317707522
#317707072
C4×Dic10762
C4×D21522
#433×C2692
#3124269