Finite Group Databasebeta

← #46822863

Subgroups — #46822863

Order 34432.

394 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#31771301C211yesmaximal, characteristic, complemented
2#31771260C211yesmaximal, characteristic, complemented
3#31770974C211yesmaximal, characteristic, complemented
4#31770947C211yesmaximal, characteristic, complemented
5#31770936C211yesmaximal, characteristic, complemented
6#31770906C211yesmaximal, characteristic, complemented
7#31770851C211yesmaximal, characteristic, complemented
8#31770834C211yesmaximal, characteristic, complemented
9#31770811C211yesmaximal, characteristic, complemented
10#31770752C211yesmaximal, characteristic, complemented
11#31770752C211yesmaximal, characteristic, complemented
12#31770718C211yesmaximal, characteristic, complemented
13#31770607C211yesmaximal, characteristic, complemented
14#31770602C211yesmaximal, characteristic, complemented
15#435×C269C211yesmaximal, characteristic, complemented
16C2×#16864402C2211yescharacteristic
17C2×#16864402C2211yescharacteristic
18C2×#16864391C2211yescharacteristic
19C2×#16864391C2211yescharacteristic
20C2×D2152C2211yescharacteristic
21#22575453C2211yescharacteristic
22#22575448—21no—
23#22575445C2211yescharacteristic
24#22575435—21no—
25#22575435—21no—
26#22575435—21no—
27#22575432C2211yescharacteristic
28#22575432C2211yescharacteristic
29#22575427C2211yescharacteristic
30#22575427C2211yescharacteristic
31#22575425—21no—
32#22575424—21no—
33C4×D1076C2211yescharacteristic
34C4×D1076C2211yescharacteristic
35#22575413—21no—
36#22575412C2211yescharacteristic
37C2×C4⋊Dic269C2211yescharacteristic
38C4⋊C4×D269—21no—
39#22575387C2211yescharacteristic
40#22575385C2211yescharacteristic
41#22575385C2211yescharacteristic
42#22575378C2211yescharacteristic
43#22575378C2211yescharacteristic
44#22575378C2211yescharacteristic
45#22575378C2211yescharacteristic
46#22575378C2211yescharacteristic
47#22575378C2211yescharacteristic
48#22575375C2211yescharacteristic
49#22575375C2211yescharacteristic
50#22575375C2211yescharacteristic
51#22575375C2211yescharacteristic
52C2×M16×C269C2211yescharacteristic
53C22×C8×C269C2211yescharacteristic
54C4×D4×C269C2211yescharacteristic
55C4⋊C8×C269C2211yescharacteristic
56C22⋊C8×C269C2211yescharacteristic
57C22⋊C8×C269C2211yescharacteristic
58#97×C269C2211yescharacteristic
59#16864402—22no—
60#16864402—22no—
61#16864402—41no—
62#16864402—41no—
63C2×Dic538C2311yescharacteristic
64C2×Dic538C2311yescharacteristic
65C2×D1076C2311yescharacteristic
66C2×D1076C2311yescharacteristic
67C2×C22⋊D269—21no—
68C2×C22⋊D269—21no—
69C2×C22⋊D269—21no—
70C2×C22⋊D269—21no—
71C22×Dic269—21no—
72C2×C4×D269—21no—
73C2×C4×D269—21no—
74C2×C4×D269—21no—
75C2×C4×D269—21no—
76#16864391—41no—
77#16864391—41no—
78D2152—22no—
79C4⋊Dic269—21no—
80C4⋊Dic269—21no—
81C4⋊Dic269—21no—
82C4⋊Dic269C2311yescharacteristic
83C4⋊Dic269C2311yescharacteristic
84C4⋊Dic269C2311yescharacteristic
85C4⋊Dic269C2311yescharacteristic
86#16864381—21no—
87#16864381—21no—
88#16864381—21no—
89#16864381—21no—
90C22⋊Dic269—21no—
91C22⋊Dic269—21no—
92C22⋊Dic269—21no—
93#16864379—21no—
94#16864379—21no—
95#16864379—21no—
96#16864379—21no—
97C4×Dic269—21no—
98C2×D4×C269D411yescharacteristic
99C22×C4×C269C2311yescharacteristic
100C22×C4×C269C2311yescharacteristic
101M16×C269—41no—
102C2×C8×C269—41no—
103C2×C8×C269C2311yescharacteristic
104C2×C8×C269C2311yescharacteristic
105C2×C8×C269C2311yescharacteristic
106C2×C8×C269C2311yescharacteristic
107C4⋊C4×C269D411yescharacteristic
108C22⋊C4×C269D411yescharacteristic
109C22⋊C4×C269D411yescharacteristic
110C42×C269C2311yescharacteristic
111C22×D269—21no—
112C22×D269—21no—
113Dic538—21no—
114Dic538—21no—
115Dic538—21no—
116Dic538—21no—
117D1076—21no—
118D1076—21no—
119D1076—21no—
120D1076#4112yes—
121C22⋊D269—42no—
122C22⋊D269—42no—
123C22⋊D269—42no—
124C22⋊D269—81no—
125C2×Dic269—21no—
126C2×Dic269—21no—
127C2×Dic269—21no—
128C2×Dic269—21no—
129C2×Dic269—21no—
130C2×Dic269—21no—
131C2×Dic269—81no—
132C4×D269—42no—
133C4×D269—42no—
134C4×D269—42no—
135C4×D269—81no—
136C23×C269C2×D411yescharacteristic
137C23×C269C2×D411yescharacteristic
138D4×C269—41no—
139C2×C4×C269—21no—
140C2×C4×C269—21no—
141C2×C4×C269—21no—
142C2×C4×C269—21no—
143C2×C4×C269C2×D411yescharacteristic
144C2×C4×C269C2×D411yescharacteristic
145C2×C4×C269C2×D411yescharacteristic
146C2×C4×C269C2×D411yescharacteristic
147C2×C4×C269C2411yescharacteristic
148C8×C269—21no—
149C8×C269—21no—
150C8×C269—21no—
151C8×C269—21no—
152C22×C269—21no—
153C22×C269—21no—
154C22×C269—21no—
155C22×C269—21no—
156C22×C269—21no—
157C22×C269—21no—
158C22×C269C22×D411yescharacteristic
159C2×D269—22no—
160C2×D269—41no—
161C2×D269—41no—
162C2×D269—41no—
163C2×D269—41no—
164C2×D269—41no—
165C4×C269—21no—
166C4×C269—21no—
167C4×C269—21no—
168C4×C269—21no—
169C4×C269C2×#4111yescharacteristic
170C4×C269H(5,𝔽2)11yescharacteristic
171Dic269—41no—
172Dic269—41no—
173Dic269—41no—
174Dic269—41no—
175Dic269—41no—
176Dic269—41no—
177C2×C269—41no—
178C2×C269—41no—
179C2×C269#54611yescharacteristic
180C2×C269#57511yescharacteristic
181C2×C269#57711yescharacteristic
182D269—42no—
183D269—81no—
184C269#330711yescharacteristic, complemented, Sylow
185#3307—2691nomaximal, Sylow
186#553—2691no—
187#547—2691no—
188#491—2691no—
189#485—2691no—
190#483—2691no—
191#478—2691no—
192#468—2691no—
193#465—2691no—
194#461—2691no—
195#449—2691no—
196#449—2691no—
197#442—2691no—
198#435D26911yescharacteristic, complemented
199#417—2691no—
200#416—2691no—
201C2×#41—2691no—
202C2×#41—2691no—
203C2×SD16—2691no—
204C2×SD16—2691no—
205C2×D8—2691no—
206C2×M16C2×D26911yescharacteristic
207C22×C8C2×D26911yescharacteristic
208C4⋊Q8—2691no—
209#126—5381no—
210#125—2691no—
211#123—5381no—
212#123—5381no—
213#123—5381no—
214C22⋊Q8—2691no—
215C22⋊Q8—2691no—
216#121—2691no—
217#121—2691no—
218#121—5381no—
219#121—5381no—
220C4×D4—2691no—
221C4×D4—2691no—
222C4×D4—5381no—
223C4×D4C2×D26911yescharacteristic
224#117—2691no—
225C2×C4⋊C4—2691no—
226C2×C4⋊C4—5381no—
227#107—2691no—
228#106—2691no—
229#106—2691no—
230C4⋊C8C2×D26911yescharacteristic
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⋊C8C2×D26911yescharacteristic
242C22⋊C8C2×D26911yescharacteristic
243#97C2×D26911yescharacteristic
244#41—5382no—
245#41—5382no—
246#41—10761no—
247#41—10761no—
248C2×Q8—2691no—
249C2×Q8—2691no—
250C2×D4—2691no—
251C2×D4—2691no—
252C2×D4—5381no—
253C2×D4—5381no—
254C2×D4—5381no—
255C2×D4—5381no—
256C2×D4D107611yescharacteristic
257C22×C4—5381no—
258C22×C4—5381no—
259C22×C4—5381no—
260C22×C4—5381no—
261C22×C4—5381no—
262C22×C4C22×D26911yescharacteristic
263C22×C4C22×D26911yescharacteristic
264SD16—10761no—
265SD16—10761no—
266D8—5382no—
267M16—41no—
268C2×C8—41no—
269C2×C8C22×D26911yescharacteristic
270C2×C8C22×D26911yescharacteristic
271C2×C8C22×D26911yescharacteristic
272C2×C8C22×D26911yescharacteristic
273C4⋊C4—2691no—
274C4⋊C4—2691no—
275C4⋊C4—2691no—
276C4⋊C4—2691no—
277C4⋊C4—5381no—
278C4⋊C4—5381no—
279C4⋊C4—5381no—
280C4⋊C4—5381no—
281C4⋊C4—5381no—
282C4⋊C4—5381no—
283C4⋊C4—5381no—
284C4⋊C4D107611yescharacteristic
285C22⋊C4—5381no—
286C22⋊C4—5381no—
287C22⋊C4—5381no—
288C22⋊C4—5381no—
289C22⋊C4—5381no—
290C22⋊C4—5381no—
291C22⋊C4—5381no—
292C22⋊C4D107611yescharacteristic
293C22⋊C4D107611yescharacteristic
294C42—5381no—
295C42C22×D26911yescharacteristic
296C23—5381no—
297C23—5381no—
298C23C2×D107611yescharacteristic
299C23C2×D107611yescharacteristic
300Q8—5381no—
301Q8—5381no—
302Q8—5381no—
303Q8—5381no—
304D4—41no—
305D4—2692no—
306D4—5381no—
307D4—5381no—
308D4—5381no—
309D4—10762no—
310D4—10762no—
311D4—10762no—
312D4—21521no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—5381no—
318C2×C4—5381no—
319C2×C4—5381no—
320C2×C4—5381no—
321C2×C4—5381no—
322C2×C4—5381no—
323C2×C4—10762no—
324C2×C4—10762no—
325C2×C4—10762no—
326C2×C4—21521no—
327C2×C4—21521no—
328C2×C4C2×D107611yescharacteristic
329C2×C4C2×D107611yescharacteristic
330C2×C4C2×D107611yescharacteristic
331C2×C4C2×D107611yescharacteristic
332C2×C4C23×D26911yescharacteristic
333C8—21no—
334C8—21no—
335C8—21no—
336C8—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—5382no—
344C22—10761no—
345C22—10761no—
346C22—10761no—
347C22—10761no—
348C22—10761no—
349C22C22×D107611yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—10761no—
355C4—10761no—
356C4—10761no—
357C4—10761no—
358C4—10761no—
359C4—10761no—
360C4#41×D26911yescharacteristic
361C4#2257549811yescharacteristic
362C2—41no—
363C2—41no—
364C2—10762no—
365C2—21521no—
366C2#3177125011yescharacteristic
367C2#3177140511yescharacteristic
368C2#3177141711yescharacteristic
subgroupG/H
centerC22C22×D1076
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#435×C269C2
socleC22×C269C22×D4
hypercenter#435D269
hypocenterC269#3307
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #31771301C2semidirect
2. #31771260C2semidirect
3. #31770974C2semidirect
4. #31770947C2semidirect
5. #31770936C2semidirect
6. #31770906C2semidirect
7. #31770851C2semidirect
8. #31770834C2semidirect
9. #31770811C2semidirect
10. #31770752C2semidirect
11. #31770752C2semidirect
12. #31770718C2semidirect
13. #31770607C2semidirect
14. #31770602C2semidirect
15. #435×C269C2semidirect
184. C269#3307semidirect
198. #435D269semidirect

Maximal subgroups

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

subgroupindex
#317713012
#317712602
#317709742
#317709472
#317709362
#317709062
#317708512
#317708342
#317708112
#317707522
#317707182
#317706072
#317706022
#435×C2692
#3307269