Finite Group Databasebeta

← #46821162

Subgroups — #46821162

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#31770935C211yesmaximal, characteristic, complemented
3#31770923C211yesmaximal, characteristic, complemented
4#31770895C211yesmaximal, characteristic, complemented
5#31770890C211yesmaximal, characteristic, complemented
6#31770827C211yesmaximal, characteristic, complemented
7#31770820C211yesmaximal, characteristic, complemented
8#31770767C211yesmaximal, characteristic, complemented
9#31770750C211yesmaximal, characteristic
10#31770715C211yesmaximal, characteristic, complemented
11#31770710C211yesmaximal, characteristic, complemented
12C4×#16864389C211yesmaximal, characteristic, complemented
13C4×#16864390C211yesmaximal, characteristic, complemented
14#31770666C211yesmaximal, characteristic, complemented
15#520×C269C211yesmaximal, characteristic, complemented
16C2×#16864392C2211yescharacteristic
17C2×#16864390C2211yescharacteristic
18C2×#16864389C2211yescharacteristic
19C2×#16864387C2211yescharacteristic
20#22575453C2211yescharacteristic
21#22575448—21no—
22#22575441C2211yescharacteristic
23#22575439—21no—
24#22575435—21no—
25#22575432C2211yescharacteristic
26#22575431—21no—
27#22575427C2211yescharacteristic
28C4×Dic538C2211yescharacteristic
29C4×D1076C2211yescharacteristic
30#22575384C2211yescharacteristic
31#22575384C2211yescharacteristic
32#22575384C2211yescharacteristic
33#22575384C2211yescharacteristic
34C4⋊#14524130C2211yescharacteristic
35C4⋊#14524130C2211yescharacteristic
36#22575377C2211yescharacteristic
37#22575377C2211yescharacteristic
38#22575376C2211yescharacteristic
39#22575376C2211yescharacteristic
40#22575374C2211yescharacteristic
41#22575374C2211yescharacteristic
42#22575373C2211yescharacteristic
43#22575373C2211yescharacteristic
44C22⋊#14524130C2211yescharacteristic
45C22⋊#14524130C2211yescharacteristic
46#22575364C2211yescharacteristic
47C4×#14524130C2211yescharacteristic
48C2×#41×C269C2211yescharacteristic
49C4×Q8×C269C2211yescharacteristic
50C4×Q8×C269C2211yescharacteristic
51C4×D4×C269—21no—
52C4×D4×C269—21no—
53C4×D4×C269C2211yescharacteristic
54C4×D4×C269C2211yescharacteristic
55#117×C269—21no—
56#117×C269C2211yescharacteristic
57C2×C4⋊C4×C269—21no—
58C2×C4⋊C4×C269C2211yescharacteristic
59C2×Dic538—21no—
60C2×Dic538C2311yescharacteristic
61C2×D1076C2311yescharacteristic
62C2×C22⋊D269—21no—
63C2×C4×D269—21no—
64#16864392—22no—
65#16864390—22no—
66#16864389—22no—
67#16864387—22no—
68C2×#14524130C2311yescharacteristic
69C2×#14524130C2311yescharacteristic
70C2×#14524130C2311yescharacteristic
71C2×#14524130C2311yescharacteristic
72C4⋊Dic269—21no—
73C4⋊Dic269C2311yescharacteristic
74C4⋊Dic269C2311yescharacteristic
75#16864381—21no—
76#16864381—21no—
77C22⋊Dic269—21no—
78#16864379—21no—
79#16864379—21no—
80#16864379—21no—
81#16864379—21no—
82C4×Dic269—21no—
83#41×C269—22no—
84#41×C269—22no—
85C2×Q8×C269C2311yescharacteristic
86C2×D4×C269—21no—
87C2×D4×C269C2311yescharacteristic
88C22×C4×C269—21no—
89C22×C4×C269—21no—
90C22×C4×C269—21no—
91C22×C4×C269—21no—
92C22×C4×C269C2311yescharacteristic
93C4⋊C4×C269—21no—
94C4⋊C4×C269—21no—
95C4⋊C4×C269—21no—
96C4⋊C4×C269D411yescharacteristic
97C4⋊C4×C269D411yescharacteristic
98C4⋊C4×C269C2311yescharacteristic
99C4⋊C4×C269C2311yescharacteristic
100C22⋊C4×C269—21no—
101C22⋊C4×C269—21no—
102C22⋊C4×C269D411yescharacteristic
103C22⋊C4×C269D411yescharacteristic
104C42×C269—21no—
105C42×C269—21no—
106C42×C269C2311yescharacteristic
107C42×C269C2311yescharacteristic
108C22×D269—21no—
109Dic538—21no—
110Dic538—21no—
111Dic538—81no—
112D1076—21no—
113D1076—21no—
114C22⋊D269—81no—
115C2×Dic269—21no—
116C2×Dic269—21no—
117C2×Dic269—21no—
118C4×D269—81no—
119#14524130—21no—
120#14524130—21no—
121#14524130—21no—
122#14524130—21no—
123C23×C269—21no—
124C23×C269C2×D411yescharacteristic
125Q8×C269—21no—
126Q8×C269#4112yes—
127D4×C269—24no—
128D4×C269—21no—
129D4×C269#4112yes—
130C2×C4×C269—24no—
131C2×C4×C269—21no—
132C2×C4×C269—21no—
133C2×C4×C269—21no—
134C2×C4×C269—21no—
135C2×C4×C269—21no—
136C2×C4×C269—81no—
137C2×C4×C269—81no—
138C2×C4×C269—81no—
139C2×C4×C269C2×D411yescharacteristic
140C2×C4×C269C2×D411yescharacteristic
141C2×C4×C269C2×D411yescharacteristic
142C2×C4×C269C2×D411yescharacteristic
143C2×C4×C269C2×D411yescharacteristic
144C2×C4×C269C2411yescharacteristic
145C22×C269—21no—
146C22×C269—22no—
147C22×C269—21no—
148C22×C269—21no—
149C22×C269—41no—
150C22×C269—41no—
151C22×C269C22×D411yescharacteristic
152C2×D269—41no—
153C2×D269—41no—
154C2×D269—41no—
155C4×C269—21no—
156C4×C269—22no—
157C4×C269—21no—
158C4×C269—21no—
159C4×C269—21no—
160C4×C269—21no—
161C4×C269—41no—
162C4×C269—41no—
163C4×C269C2×#4111yescharacteristic
164C4×C269C2×#4111yescharacteristic
165Dic269—41no—
166Dic269—41no—
167Dic269—41no—
168C2×C269—41no—
169C2×C269—42no—
170C2×C269#52511yescharacteristic
171C2×C269#57711yescharacteristic
172C2×C269#57711yescharacteristic
173D269—81no—
174C269#312511yescharacteristic, complemented, Sylow
175#3125—2691nomaximal, Sylow
176#542—2691no—
177#520D26911yescharacteristic, complemented
178#483—2691no—
179#481—2691no—
180#476—2691no—
181#475—2691no—
182#464—2691no—
183#463—2691no—
184#452—2691no—
185#449—2691no—
186#442—2691no—
187#441—2691no—
188C4×SD16—2691no—
189C4×SD16—2691no—
190#433—2691no—
191C2×#41C2×D26911yescharacteristic
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×Q8C2×D26911yescharacteristic
206C4×Q8C2×D26911yescharacteristic
207C4×D4—21no—
208C4×D4—21no—
209C4×D4—2691no—
210C4×D4C2×D26911yescharacteristic
211C4×D4C2×D26911yescharacteristic
212#117—21no—
213#117C2×D26911yescharacteristic
214C2×C4⋊C4—21no—
215C2×C4⋊C4C2×D26911yescharacteristic
216#106—2691no—
217#106—2691no—
218#106—2691no—
219#106—2691no—
220C4⋊C8—2691no—
221C4⋊C8—2691no—
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⋊C8—2691no—
231C22⋊C8—2691no—
232#97—2691no—
233C4×C8—2691no—
234#41—22no—
235#41—22no—
236C2×Q8—2691no—
237C2×Q8—5381no—
238C2×Q8C22×D26911yescharacteristic
239C2×D4—21no—
240C2×D4—2691no—
241C2×D4—5381no—
242C2×D4C22×D26911yescharacteristic
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—5381no—
248C22×C4C22×D26911yescharacteristic
249Q16—5382no—
250SD16—5382no—
251SD16—5382no—
252D8—5382no—
253C2×C8—2691no—
254C2×C8—2691no—
255C2×C8—2691no—
256C2×C8—2691no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—2691no—
261C4⋊C4—2691no—
262C4⋊C4—5381no—
263C4⋊C4—5381no—
264C4⋊C4—5381no—
265C4⋊C4C22⋊D26911yescharacteristic
266C4⋊C4C22⋊D26911yescharacteristic
267C4⋊C4C22×D26911yescharacteristic
268C4⋊C4C22×D26911yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—5381no—
272C22⋊C4—5381no—
273C22⋊C4—5381no—
274C22⋊C4—5381no—
275C22⋊C4—5381no—
276C22⋊C4C22⋊D26911yescharacteristic
277C22⋊C4C22⋊D26911yescharacteristic
278C42—21no—
279C42—21no—
280C42—5381no—
281C42C22×D26911yescharacteristic
282C42C22×D26911yescharacteristic
283C23—21no—
284C23—5381no—
285C23C2×C22⋊D26911yescharacteristic
286Q8—21no—
287Q8—5381no—
288Q8—5381no—
289Q8—21521no—
290Q8#1686440212yes—
291D4—24no—
292D4—21no—
293D4—5381no—
294D4—5381no—
295D4—21521no—
296D4#1686440212yes—
297C2×C4—24no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—5381no—
307C2×C4—5381no—
308C2×C4—5381no—
309C2×C4—21521no—
310C2×C4C2×C22⋊D26911yescharacteristic
311C2×C4C2×C22⋊D26911yescharacteristic
312C2×C4C2×C22⋊D26911yescharacteristic
313C2×C4C2×C22⋊D26911yescharacteristic
314C2×C4C2×C22⋊D26911yescharacteristic
315C2×C4C23×D26911yescharacteristic
316C8—5381no—
317C8—5381no—
318C8—5381no—
319C8—5381no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—22no—
324C22—41no—
325C22—41no—
326C22—10761no—
327C22—10761no—
328C22—10761no—
329C22C22×C22⋊D26911yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—22no—
336C4—41no—
337C4—41no—
338C4—10761no—
339C4—10761no—
340C4—10761no—
341C4C2×#1686440211yescharacteristic
342C4C2×#1686440211yescharacteristic
343C2—41no—
344C2—42no—
345C2—21521no—
346C2#3177111611yescharacteristic
347C2#3177141311yescharacteristic
348C2#3177141611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#520×C269C2
socleC22×C269C22×D4
prime radical#31770750C2
hypercenter#520D269
hypocenterC269#3125
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ #117 ◁ #520

Complements

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

NH ≅ G/Ntype
1. #31771226C2semidirect
2. #31770935C2semidirect
3. #31770923C2semidirect
4. #31770895C2semidirect
5. #31770890C2semidirect
6. #31770827C2semidirect
7. #31770820C2semidirect
8. #31770767C2semidirect
10. #31770715C2semidirect
11. #31770710C2semidirect
12. C4×#16864389C2semidirect
13. C4×#16864390C2semidirect
14. #31770666C2semidirect
15. #520×C269C2semidirect
174. C269#3125semidirect
177. #520D269semidirect

Maximal subgroups

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

subgroupindex
#317712262
#317709352
#317709232
#317708952
#317708902
#317708272
#317708202
#317707672
#317707502
#317707152
#317707102
C4×#168643892
C4×#168643902
#317706662
#520×C2692
#3125269