Finite Group Databasebeta

← #46822878

Subgroups — #46822878

Order 34432.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771264C211yesmaximal, characteristic, complemented
2#31771259C211yesmaximal, characteristic, complemented
3#31770965C211yesmaximal, characteristic, complemented
4#31770941C211yesmaximal, characteristic, complemented
5#31770919C211yesmaximal, characteristic, complemented
6#31770901C211yesmaximal, characteristic, complemented
7#31770851C211yesmaximal, characteristic, complemented
8#31770841C211yesmaximal, characteristic, complemented
9#31770821C211yesmaximal, characteristic, complemented
10#31770752C211yesmaximal, characteristic, complemented
11#31770746C211yesmaximal, characteristic, complemented
12#31770707C211yesmaximal, characteristic, complemented
13#31770607C211yesmaximal, characteristic, complemented
14C2×#22575378C211yesmaximal, characteristic, complemented
15#435×C269C211yesmaximal, characteristic, complemented
16C2×#16864402C2211yescharacteristic
17C2×#16864401—21no—
18C22×Dic538C2211yescharacteristic
19C2×#16864391C2211yescharacteristic
20C2×#16864391C2211yescharacteristic
21C2×D2152C2211yescharacteristic
22#22575453C2211yescharacteristic
23#22575441C2211yescharacteristic
24#22575439—21no—
25#22575437—21no—
26#22575437—21no—
27#22575433—21no—
28#22575432C2211yescharacteristic
29#22575431—21no—
30#22575427C2211yescharacteristic
31#22575427C2211yescharacteristic
32#22575427C2211yescharacteristic
33#22575425—21no—
34C4×Dic538C2211yescharacteristic
35C4×D1076C2211yescharacteristic
36#22575413—21no—
37C2×C4⋊Dic269C2211yescharacteristic
38C2×C4⋊Dic269C2211yescharacteristic
39#22575387C2211yescharacteristic
40#22575387C2211yescharacteristic
41#22575387C2211yescharacteristic
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—41no—
61#16864401—44no—
62C2×Dic538—22no—
63C2×Dic538—21no—
64C2×Dic538—21no—
65C2×Dic538—41no—
66C2×Dic538C2311yescharacteristic
67C2×Dic538C2311yescharacteristic
68C2×D1076C2311yescharacteristic
69C2×D1076C2311yescharacteristic
70C2×C22⋊D269—21no—
71C2×C22⋊D269—21no—
72C2×C22⋊D269—21no—
73C2×C22⋊D269—21no—
74C22×Dic269—21no—
75C22×Dic269—21no—
76C22×Dic269—21no—
77C2×C4×D269—21no—
78C2×C4×D269—21no—
79#16864391—22no—
80#16864391—41no—
81D2152—41no—
82C4⋊Dic269—21no—
83C4⋊Dic269—21no—
84C4⋊Dic269—21no—
85C4⋊Dic269C2311yescharacteristic
86C4⋊Dic269C2311yescharacteristic
87C4⋊Dic269C2311yescharacteristic
88C4⋊Dic269C2311yescharacteristic
89#16864381—21no—
90#16864381—21no—
91C22⋊Dic269—21no—
92#16864379—21no—
93#16864379—21no—
94#16864379—21no—
95#16864379—21no—
96#16864379—21no—
97#16864379—21no—
98C4×Dic269—21no—
99C2×D4×C269D411yescharacteristic
100C22×C4×C269C2311yescharacteristic
101C22×C4×C269C2311yescharacteristic
102M16×C269—41no—
103C2×C8×C269—41no—
104C2×C8×C269C2311yescharacteristic
105C2×C8×C269C2311yescharacteristic
106C2×C8×C269C2311yescharacteristic
107C2×C8×C269C2311yescharacteristic
108C4⋊C4×C269D411yescharacteristic
109C22⋊C4×C269D411yescharacteristic
110C22⋊C4×C269D411yescharacteristic
111C42×C269C2311yescharacteristic
112C22×D269—21no—
113C22×D269—21no—
114Dic538—21no—
115Dic538—21no—
116Dic538—21no—
117Dic538—42no—
118Dic538—42no—
119Dic538#4112yescomplemented
120D1076—21no—
121D1076—21no—
122D1076—21no—
123D1076—21no—
124C22⋊D269—42no—
125C22⋊D269—42no—
126C22⋊D269—42no—
127C22⋊D269—42no—
128C2×Dic269—21no—
129C2×Dic269—21no—
130C2×Dic269—21no—
131C2×Dic269—21no—
132C2×Dic269—21no—
133C2×Dic269—21no—
134C2×Dic269—42no—
135C2×Dic269—42no—
136C2×Dic269—42no—
137C4×D269—42no—
138C4×D269—42no—
139C23×C269C2×D411yescharacteristic
140C23×C269C2×D411yescharacteristic
141D4×C269—22no—
142C2×C4×C269—21no—
143C2×C4×C269—21no—
144C2×C4×C269—21no—
145C2×C4×C269—21no—
146C2×C4×C269C2×D411yescharacteristic
147C2×C4×C269C2×D411yescharacteristic
148C2×C4×C269C2×D411yescharacteristic
149C2×C4×C269C2×D411yescharacteristic
150C2×C4×C269C2411yescharacteristic
151C8×C269—21no—
152C8×C269—21no—
153C8×C269—21no—
154C8×C269—21no—
155C22×C269—21no—
156C22×C269—21no—
157C22×C269—21no—
158C22×C269—21no—
159C22×C269—21no—
160C22×C269AGL(1,ℤ/8)12yes—
161C22×C269C22×D411yescharacteristic
162C2×D269—41no—
163C2×D269—41no—
164C2×D269—41no—
165C2×D269—41no—
166C2×D269—41no—
167C2×D269—41no—
168C4×C269—21no—
169C4×C269—21no—
170C4×C269—21no—
171C4×C269—21no—
172C4×C269C2×#4111yescharacteristic
173C4×C269H(5,𝔽2)11yescharacteristic
174Dic269—22no—
175Dic269—41no—
176Dic269—41no—
177Dic269—41no—
178Dic269—41no—
179Dic269—41no—
180C2×C269—22no—
181C2×C269—41no—
182C2×C269#54611yescharacteristic
183C2×C269C2×AGL(1,ℤ/8)11yescharacteristic
184C2×C269#57811yescharacteristic
185D269—81no—
186D269—81no—
187C269#330811yescharacteristic, complemented, Sylow
188#3308—2691nomaximal, Sylow
189#548—2691no—
190#547—2691no—
191#489—2691no—
192#484—2691no—
193#480—2691no—
194#477—2691no—
195#468—2691no—
196#466—2691no—
197#463—2691no—
198#449—2691no—
199#448—2691no—
200#440—2691no—
201#435D26911yescharacteristic, complemented
202#417—2691no—
203C2×#103—2691no—
204C2×#41—2691no—
205C2×#41—5381no—
206C22×Q8—2691no—
207C2×SD16—2691no—
208C2×SD16—2691no—
209C2×D8—2691no—
210C2×M16C2×D26911yescharacteristic
211C22×C8C2×D26911yescharacteristic
212C4⋊Q8—2691no—
213#124—2691no—
214#124—5381no—
215#123—5381no—
216#123—5381no—
217C22⋊Q8—2691no—
218C22⋊Q8—5381no—
219C22⋊Q8—5381no—
220#121—2691no—
221#121—2691no—
222#121—2691no—
223#121—5381no—
224C4×Q8—2691no—
225C4×D4—2691no—
226C4×D4—5381no—
227C4×D4C2×D26911yescharacteristic
228C2×C4⋊C4—2691no—
229C2×C4⋊C4—2691no—
230#107—2691no—
231#107—2691no—
232#107—2691no—
233C4⋊C8C2×D26911yescharacteristic
234#103—2691no—
235#103—2691no—
236#103—2691no—
237#103—2691no—
238#103—2691no—
239#103—2691no—
240#102—2691no—
241#102—2691no—
242#102—2691no—
243#102—2691no—
244C22⋊C8C2×D26911yescharacteristic
245C22⋊C8C2×D26911yescharacteristic
246#97C2×D26911yescharacteristic
247#41—5382no—
248#41—10761no—
249#41—10764no—
250C2×Q8—2691no—
251C2×Q8—2691no—
252C2×Q8—5382no—
253C2×Q8—5381no—
254C2×Q8—5381no—
255C2×Q8—10761no—
256C2×D4—2691no—
257C2×D4—2691no—
258C2×D4—5381no—
259C2×D4—5381no—
260C2×D4—5381no—
261C2×D4—5381no—
262C2×D4D107611yescharacteristic
263C22×C4—5381no—
264C22×C4—5381no—
265C22×C4—5381no—
266C22×C4—5381no—
267C22×C4—5381no—
268C22×C4C22×D26911yescharacteristic
269C22×C4C22×D26911yescharacteristic
270SD16—5382no—
271SD16—10761no—
272D8—10761no—
273M16—41no—
274C2×C8—41no—
275C2×C8C22×D26911yescharacteristic
276C2×C8C22×D26911yescharacteristic
277C2×C8C22×D26911yescharacteristic
278C2×C8C22×D26911yescharacteristic
279C4⋊C4—2691no—
280C4⋊C4—2691no—
281C4⋊C4—2691no—
282C4⋊C4—2691no—
283C4⋊C4—5381no—
284C4⋊C4—5381no—
285C4⋊C4—5381no—
286C4⋊C4—5381no—
287C4⋊C4—5381no—
288C4⋊C4D107611yescharacteristic
289C22⋊C4—5381no—
290C22⋊C4—5381no—
291C22⋊C4—5381no—
292C22⋊C4—5381no—
293C22⋊C4—5381no—
294C22⋊C4—5381no—
295C22⋊C4—5381no—
296C22⋊C4D107611yescharacteristic
297C22⋊C4D107611yescharacteristic
298C42—5381no—
299C42C22×D26911yescharacteristic
300C23—5381no—
301C23—5381no—
302C23C2×D107611yescharacteristic
303C23C2×D107611yescharacteristic
304Q8—2692no—
305Q8—5381no—
306Q8—5381no—
307Q8—5381no—
308Q8—10762no—
309Q8—10762no—
310D4—22no—
311D4—5381no—
312D4—5381no—
313D4—5381no—
314D4—5381no—
315D4—10762no—
316D4—10762no—
317D4—10762no—
318D4—10762no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—5381no—
324C2×C4—5381no—
325C2×C4—5381no—
326C2×C4—5381no—
327C2×C4—5381no—
328C2×C4—5381no—
329C2×C4—10762no—
330C2×C4—10762no—
331C2×C4—10762no—
332C2×C4—10762no—
333C2×C4—10762no—
334C2×C4C2×D107611yescharacteristic
335C2×C4C2×D107611yescharacteristic
336C2×C4C2×D107611yescharacteristic
337C2×C4C2×D107611yescharacteristic
338C2×C4C23×D26911yescharacteristic
339C8—21no—
340C8—21no—
341C8—21no—
342C8—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—10761no—
349C22—10761no—
350C22—10761no—
351C22—10761no—
352C22—10761no—
353C22—10761no—
354C22#2257548112yes—
355C22C22×D107611yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—5382no—
361C4—10761no—
362C4—10761no—
363C4—10761no—
364C4—10761no—
365C4—10761no—
366C4#41×D26911yescharacteristic
367C4#2257549811yescharacteristic
368C2—22no—
369C2—41no—
370C2—21521no—
371C2—21521no—
372C2#3177125011yescharacteristic
373C2C2×#2257548111yescharacteristic
374C2#3177142211yescharacteristic
subgroupG/H
centerC22C22×D1076
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#435×C269C2
socleC22×C269C22×D4
hypercenter#435D269
hypocenterC269#3308
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. #31771264C2semidirect
2. #31771259C2semidirect
3. #31770965C2semidirect
4. #31770941C2semidirect
5. #31770919C2semidirect
6. #31770901C2semidirect
7. #31770851C2semidirect
8. #31770841C2semidirect
9. #31770821C2semidirect
10. #31770752C2semidirect
11. #31770746C2semidirect
12. #31770707C2semidirect
13. #31770607C2semidirect
14. C2×#22575378C2semidirect
15. #435×C269C2semidirect
119. Dic538#41semidirect
187. C269#3308semidirect
201. #435D269semidirect

Maximal subgroups

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

subgroupindex
#317712642
#317712592
#317709652
#317709412
#317709192
#317709012
#317708512
#317708412
#317708212
#317707522
#317707462
#317707072
#317706072
C2×#225753782
#435×C2692
#3308269