Finite Group Databasebeta

← #46822781

Subgroups — #46822781

Order 34432.

398 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771264C211yesmaximal, characteristic, complemented
2#31770962C211yesmaximal, characteristic, complemented
3#31770946C211yesmaximal, characteristic, complemented
4#31770923C211yesmaximal, characteristic, complemented
5#31770909C211yesmaximal, characteristic, complemented
6#31770839C211yesmaximal, characteristic, complemented
7#31770832C211yesmaximal, characteristic, complemented
8#31770820C211yesmaximal, characteristic, complemented
9#31770748C211yesmaximal, characteristic, complemented
10#31770743C211yesmaximal, characteristic, complemented
11C4×#16864390C211yesmaximal, characteristic, complemented
12D4×#14524130C211yesmaximal, characteristic, complemented
13#31770599C211yesmaximal, characteristic, complemented
14C2×#22575376C211yesmaximal, characteristic, complemented
15#553×C269C211yesmaximal, characteristic, complemented
16C2×#16864402C2211yescharacteristic
17C22×Dic538C2211yescharacteristic
18C2×#16864390C2211yescharacteristic
19C2×#16864390C2211yescharacteristic
20C2×#16864387C2211yescharacteristic
21C22×#14524130C2211yescharacteristic
22C22×#14524130C2211yescharacteristic
23#22575441C2211yescharacteristic
24#22575439—21no—
25#22575432C2211yescharacteristic
26#22575431—21no—
27#22575427C2211yescharacteristic
28#22575425—21no—
29C4×Dic538C2211yescharacteristic
30#22575413—21no—
31#22575386C2211yescharacteristic
32#22575384C2211yescharacteristic
33#22575384C2211yescharacteristic
34C4⋊#14524130C2211yescharacteristic
35#22575376C2211yescharacteristic
36#22575376C2211yescharacteristic
37#22575376C2211yescharacteristic
38#22575376C2211yescharacteristic
39#22575376C2211yescharacteristic
40#22575376C2211yescharacteristic
41#22575374C2211yescharacteristic
42#22575373C2211yescharacteristic
43#22575373C2211yescharacteristic
44#22575373C2211yescharacteristic
45C22⋊#14524130C2211yescharacteristic
46C22⋊#14524130C2211yescharacteristic
47C4×#14524130C2211yescharacteristic
48#126×C269—21no—
49#125×C269C2211yescharacteristic
50#123×C269—21no—
51#121×C269—21no—
52#121×C269C2211yescharacteristic
53#121×C269C2211yescharacteristic
54C4×D4×C269—21no—
55C4×D4×C269C2211yescharacteristic
56C4×D4×C269C2211yescharacteristic
57#117×C269C2211yescharacteristic
58C2×C4⋊C4×C269C2211yescharacteristic
59#16864402—22no—
60#16864402—41no—
61C2×Dic538—22no—
62C2×Dic538—21no—
63C2×Dic538—41no—
64C2×Dic538C2311yescharacteristic
65C2×Dic538C2311yescharacteristic
66C2×D1076C2311yescharacteristic
67C2×C22⋊D269—21no—
68C2×C22⋊D269—21no—
69C22×Dic269—21no—
70C2×C4×D269—21no—
71#16864390—22no—
72#16864390—41no—
73#16864387—41no—
74C2×#14524130—41no—
75C2×#14524130—41no—
76C2×#14524130C2311yescharacteristic
77C2×#14524130C2311yescharacteristic
78C2×#14524130C2311yescharacteristic
79C2×#14524130C2311yescharacteristic
80C4⋊Dic269C2311yescharacteristic
81#16864381—21no—
82#16864381—21no—
83C22⋊Dic269—21no—
84#16864379—21no—
85#16864379—21no—
86#16864379—21no—
87C4×Dic269—21no—
88C2×D4×C269—21no—
89C2×D4×C269—21no—
90C2×D4×C269D411yescharacteristic
91C2×D4×C269C2311yescharacteristic
92C22×C4×C269—21no—
93C22×C4×C269—21no—
94C22×C4×C269C2311yescharacteristic
95C22×C4×C269C2311yescharacteristic
96C4⋊C4×C269—21no—
97C4⋊C4×C269—21no—
98C4⋊C4×C269—21no—
99C4⋊C4×C269D411yescharacteristic
100C4⋊C4×C269C2311yescharacteristic
101C4⋊C4×C269C2311yescharacteristic
102C4⋊C4×C269C2311yescharacteristic
103C22⋊C4×C269—21no—
104C22⋊C4×C269—21no—
105C22⋊C4×C269—21no—
106C22⋊C4×C269—21no—
107C22⋊C4×C269D411yescharacteristic
108C22⋊C4×C269D411yescharacteristic
109C42×C269—21no—
110C42×C269C2311yescharacteristic
111C22×D269—21no—
112Dic538—21no—
113Dic538—21no—
114Dic538—21no—
115Dic538—42no—
116Dic538#4112yes—
117D1076—21no—
118D1076—21no—
119C22⋊D269—42no—
120C22⋊D269—42no—
121C2×Dic269—21no—
122C2×Dic269—21no—
123C2×Dic269—21no—
124C2×Dic269—42no—
125C4×D269—42no—
126#14524130—21no—
127#14524130—21no—
128#14524130—21no—
129#14524130—21no—
130C23×C269—21no—
131C23×C269C2×D411yescharacteristic
132C23×C269C2×D411yescharacteristic
133D4×C269—22no—
134D4×C269—21no—
135D4×C269—21no—
136D4×C269—42no—
137D4×C269—81no—
138C2×C4×C269—21no—
139C2×C4×C269—21no—
140C2×C4×C269—21no—
141C2×C4×C269—21no—
142C2×C4×C269—21no—
143C2×C4×C269—21no—
144C2×C4×C269—21no—
145C2×C4×C269—81no—
146C2×C4×C269—81no—
147C2×C4×C269C2×D411yescharacteristic
148C2×C4×C269C2×D411yescharacteristic
149C2×C4×C269C2×D411yescharacteristic
150C2×C4×C269C2×D411yescharacteristic
151C2×C4×C269C2411yescharacteristic
152C22×C269—21no—
153C22×C269—21no—
154C22×C269—21no—
155C22×C269—21no—
156C22×C269—21no—
157C22×C269—41no—
158C22×C269—41no—
159C22×C269—41no—
160C22×C269#13512yes—
161C22×C269C22×D411yescharacteristic
162C2×D269—41no—
163C2×D269—41no—
164C2×D269—41no—
165C4×C269—21no—
166C4×C269—21no—
167C4×C269—21no—
168C4×C269—21no—
169C4×C269—41no—
170C4×C269—41no—
171C4×C269—41no—
172C4×C269C2×#4111yescharacteristic
173C4×C269H(5,𝔽2)11yescharacteristic
174Dic269—22no—
175Dic269—41no—
176Dic269—41no—
177C2×C269—22no—
178C2×C269—41no—
179C2×C269—81no—
180C2×C269#54611yescharacteristic
181C2×C269C2×#13511yescharacteristic
182C2×C269#57711yescharacteristic
183D269—81no—
184C269#330111yescharacteristic, complemented, Sylow
185#3301—2691nomaximal, Sylow
186#553D26911yescharacteristic, complemented
187#548—2691no—
188#488—2691no—
189#485—2691no—
190#481—2691no—
191#479—2691no—
192#466—2691no—
193#465—2691no—
194#463—2691no—
195#449—2691no—
196#448—2691no—
197C4×SD16—2691no—
198C8×D4—2691no—
199#416—2691no—
200C2×#103—2691no—
201C2×#41—2691no—
202C22×Q8—2691no—
203C2×SD16—2691no—
204C2×SD16—2691no—
205C2×D8—2691no—
206C22×C8—2691no—
207C22×C8—2691no—
208#126—21no—
209#125C2×D26911yescharacteristic
210#124—2691no—
211#124—5381no—
212#123—21no—
213C22⋊Q8—2691no—
214C22⋊Q8—5381no—
215#121—21no—
216#121—2691no—
217#121—5381no—
218#121C2×D26911yescharacteristic
219#121C2×D26911yescharacteristic
220C4×Q8—2691no—
221C4×D4—21no—
222C4×D4—5381no—
223C4×D4C2×D26911yescharacteristic
224C4×D4C2×D26911yescharacteristic
225#117C2×D26911yescharacteristic
226C2×C4⋊C4C2×D26911yescharacteristic
227#107—2691no—
228#106—2691no—
229#106—2691no—
230C4⋊C8—2691no—
231#103—2691no—
232#103—2691no—
233#103—2691no—
234#103—2691no—
235#103—2691no—
236#103—2691no—
237#102—2691no—
238#102—2691no—
239#102—2691no—
240#102—2691no—
241C22⋊C8—2691no—
242C22⋊C8—2691no—
243C4×C8—2691no—
244#41—5382no—
245#41—10761no—
246C2×Q8—2691no—
247C2×Q8—2691no—
248C2×Q8—5382no—
249C2×Q8—5381no—
250C2×Q8—10761no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—2691no—
254C2×D4—5381no—
255C2×D4—5381no—
256C2×D4C22⋊D26911yescharacteristic
257C2×D4C22×D26911yescharacteristic
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—5381no—
261C22×C4—5381no—
262C22×C4C22×D26911yescharacteristic
263C22×C4C22×D26911yescharacteristic
264SD16—5382no—
265SD16—10761no—
266D8—10761no—
267C2×C8—2691no—
268C2×C8—2691no—
269C2×C8—2691no—
270C2×C8—2691no—
271C2×C8—10761no—
272C2×C8—10761no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—2691no—
277C4⋊C4—5381no—
278C4⋊C4—5381no—
279C4⋊C4C22⋊D26911yescharacteristic
280C4⋊C4C22×D26911yescharacteristic
281C4⋊C4C22×D26911yescharacteristic
282C4⋊C4C22×D26911yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—5381no—
288C22⋊C4—5381no—
289C22⋊C4—5381no—
290C22⋊C4—5381no—
291C22⋊C4C22⋊D26911yescharacteristic
292C22⋊C4C22⋊D26911yescharacteristic
293C42—21no—
294C42—5381no—
295C42C22×D26911yescharacteristic
296C23—21no—
297C23—5381no—
298C23C2×C22⋊D26911yescharacteristic
299C23C2×C22⋊D26911yescharacteristic
300Q8—2692no—
301Q8—5381no—
302Q8—5381no—
303Q8—5381no—
304Q8—10762no—
305D4—22no—
306D4—21no—
307D4—21no—
308D4—42no—
309D4—81no—
310D4—5381no—
311D4—5381no—
312D4—10762no—
313D4—10762no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—5381no—
324C2×C4—5381no—
325C2×C4—5381no—
326C2×C4—10762no—
327C2×C4—10762no—
328C2×C4C2×C22⋊D26911yescharacteristic
329C2×C4C2×C22⋊D26911yescharacteristic
330C2×C4C2×C22⋊D26911yescharacteristic
331C2×C4C2×C22⋊D26911yescharacteristic
332C2×C4C23×D26911yescharacteristic
333C8—5381no—
334C8—5381no—
335C8—5381no—
336C8—5381no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—10761no—
346C22—10761no—
347C22—10761no—
348C22#2257547312yes—
349C22C22×C22⋊D26911yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—5382no—
358C4—10761no—
359C4—10761no—
360C4#41×D26911yescharacteristic
361C4#2257549911yescharacteristic
362C2—22no—
363C2—41no—
364C2—81no—
365C2—21521no—
366C2#3177124311yescharacteristic
367C2C2×#2257547311yescharacteristic
368C2#3177141611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#553×C269C2
socleC22×C269C22×D4
hypercenter#553D269
hypocenterC269#3301
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #31771264C2semidirect
2. #31770962C2semidirect
3. #31770946C2semidirect
4. #31770923C2semidirect
5. #31770909C2semidirect
6. #31770839C2semidirect
7. #31770832C2semidirect
8. #31770820C2semidirect
9. #31770748C2semidirect
10. #31770743C2semidirect
11. C4×#16864390C2semidirect
12. D4×#14524130C2semidirect
13. #31770599C2semidirect
14. C2×#22575376C2semidirect
15. #553×C269C2semidirect
184. C269#3301semidirect
186. #553D269semidirect

Maximal subgroups

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

subgroupindex
#317712642
#317709622
#317709462
#317709232
#317709092
#317708392
#317708322
#317708202
#317707482
#317707432
C4×#168643902
D4×#145241302
#317705992
C2×#225753762
#553×C2692
#3301269