Finite Group Databasebeta

← #46822768

Subgroups — #46822768

Order 34432.

386 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771290C211yesmaximal, characteristic, complemented
2#31771266C211yesmaximal, characteristic
3#31770961C211yesmaximal, characteristic, complemented
4#31770944C211yesmaximal, characteristic, complemented
5#31770918C211yesmaximal, characteristic, complemented
6#31770910C211yesmaximal, characteristic, complemented
7#31770845C211yesmaximal, characteristic, complemented
8#31770834C211yesmaximal, characteristic, complemented
9#31770830C211yesmaximal, characteristic, complemented
10#31770770C211yesmaximal, characteristic, complemented
11#31770761C211yesmaximal, characteristic, complemented
12#31770697C211yesmaximal, characteristic, complemented
13C8×C22⋊D269C211yesmaximal, characteristic, complemented
14#31770600C211yesmaximal, characteristic, complemented
15C2×#103×C269C211yesmaximal, characteristic, complemented
16C2×#16864403C2211yescharacteristic
17C2×#16864392C2211yescharacteristic
18C2×#16864392C2211yescharacteristic
19C2×#16864391C2211yescharacteristic
20C2×C8×D269C2211yescharacteristic
21#22575448—21no—
22#22575444C2211yescharacteristic
23#22575443—21no—
24#22575442—21no—
25#22575442C2211yescharacteristic
26#22575436—21no—
27#22575433C2211yescharacteristic
28#22575432C2211yescharacteristic
29#22575429—21no—
30#22575429C2211yescharacteristic
31#22575427—21no—
32#22575427C2211yescharacteristic
33Q8×Dic269C2211yescharacteristic
34#22575418C2211yescharacteristic
35C4×C22⋊D269—21no—
36C4×C22⋊D269C2211yescharacteristic
37#22575412—21no—
38#22575411C2211yescharacteristic
39#22575386C2211yescharacteristic
40#22575386C2211yescharacteristic
41#22575385C2211yescharacteristic
42#22575382C2211yescharacteristic
43#22575378C2211yescharacteristic
44#22575377C2211yescharacteristic
45#22575377C2211yescharacteristic
46#22575375C2211yescharacteristic
47#22575373C2211yescharacteristic
48#22575373C2211yescharacteristic
49C22⋊#14524130C2211yescharacteristic
50#22575365C2211yescharacteristic
51C8×Dic269C2211yescharacteristic
52C22×Q8×C269C2211yescharacteristic
53C22×C8×C269C2211yescharacteristic
54C2×C4⋊C4×C269C2211yescharacteristic
55#103×C269C2211yescharacteristic
56#103×C269C2211yescharacteristic
57#103×C269C2211yescharacteristic
58#103×C269C2211yescharacteristic
59#16864403—22no—
60#16864403—41no—
61C2×Dic538C2311yescharacteristic
62C2×D1076—21no—
63C2×D1076C2311yescharacteristic
64C2×C22⋊D269—21no—
65C2×C22⋊D269D411yescharacteristic
66C2×C4×D269—21no—
67C2×C4×D269C2311yescharacteristic
68#16864392—22no—
69#16864392—41no—
70#16864391—41no—
71C2×#14524130C2311yescharacteristic
72C2×#14524130C2311yescharacteristic
73C8×D269—41no—
74C4⋊Dic269—21no—
75C4⋊Dic269—21no—
76C4⋊Dic269—21no—
77C4⋊Dic269C2311yescharacteristic
78C4⋊Dic269C2311yescharacteristic
79#16864381—21no—
80#16864381—21no—
81#16864381—21no—
82#16864381—21no—
83#16864381D411yescharacteristic
84C22⋊Dic269—21no—
85C22⋊Dic269D411yescharacteristic
86#16864379—21no—
87#16864379—21no—
88#16864379—21no—
89#16864379—21no—
90#16864379—21no—
91#16864379—21no—
92#16864379D411yescharacteristic
93C4×Dic269—21no—
94C4×Dic269—21no—
95C4×Dic269—21no—
96C4×Dic269C2311yescharacteristic
97C2×Q8×C269—21no—
98C2×Q8×C269—22no—
99C2×Q8×C269—41no—
100C2×Q8×C269C2311yescharacteristic
101C2×Q8×C269C2311yescharacteristic
102C22×C4×C269—21no—
103C22×C4×C269—21no—
104C22×C4×C269C2311yescharacteristic
105C2×C8×C269—41no—
106C2×C8×C269C2311yescharacteristic
107C2×C8×C269C2311yescharacteristic
108C4⋊C4×C269—21no—
109C4⋊C4×C269C2311yescharacteristic
110C4⋊C4×C269C2311yescharacteristic
111C22×D269—21no—
112C22×D269C2×D411yescharacteristic
113Dic538—21no—
114Dic538—21no—
115D1076—21no—
116D1076—21no—
117D1076—42no—
118C22⋊D269—22no—
119C22⋊D269—42no—
120C2×Dic269—21no—
121C2×Dic269—21no—
122C2×Dic269—21no—
123C2×Dic269C2×D411yescharacteristic
124C2×Dic269C2×D411yescharacteristic
125C2×Dic269C2×D411yescharacteristic
126C4×D269—21no—
127C4×D269—21no—
128C4×D269—42no—
129#14524130—21no—
130#14524130—21no—
131C23×C269C2×D411yescharacteristic
132Q8×C269—21no—
133Q8×C269—21no—
134Q8×C269—21no—
135Q8×C269—42no—
136Q8×C269#4112yes—
137C2×C4×C269—21no—
138C2×C4×C269—21no—
139C2×C4×C269—21no—
140C2×C4×C269—21no—
141C2×C4×C269—21no—
142C2×C4×C269—21no—
143C2×C4×C269—42no—
144C2×C4×C269—42no—
145C2×C4×C269C2×D411yescharacteristic
146C2×C4×C269C2411yescharacteristic
147C8×C269—21no—
148C8×C269—21no—
149C22×C269—21no—
150C22×C269—21no—
151C22×C269#13512yes—
152C22×C269C22×D411yescharacteristic
153C2×D269—21no—
154C2×D269—21no—
155C2×D269—21no—
156C2×D269—41no—
157C2×D269—41no—
158C2×D269—41no—
159C4×C269—21no—
160C4×C269—22no—
161C4×C269—41no—
162C4×C269—41no—
163C4×C269—41no—
164C4×C269C2×#4111yescharacteristic
165C4×C269H(5,𝔽2)11yescharacteristic
166Dic269—21no—
167Dic269—21no—
168Dic269—21no—
169Dic269—41no—
170Dic269—41no—
171Dic269—41no—
172C2×C269—22no—
173C2×C269#54611yescharacteristic
174C2×C269C2×#13511yescharacteristic
175C2×C269#57811yescharacteristic
176D269—41no—
177D269—81no—
178C269#330011yescharacteristic, complemented, Sylow
179#3300—2691nomaximal, Sylow
180#552—2691no—
181#548—2691no—
182#488—2691no—
183#485—2691no—
184#480—2691no—
185#479—2691no—
186#467—2691no—
187#465—2691no—
188#464—2691no—
189#452—2691no—
190#451—2691no—
191C4×Q16—2691no—
192C8×D4—2691no—
193#416—2691no—
194C2×#103D26911yescharacteristic, complemented
195C2×#41—2691no—
196C22×Q8C2×D26911yescharacteristic
197C2×Q16—2691no—
198C2×Q16—2691no—
199C2×SD16—2691no—
200C22×C8—2691no—
201C22×C8C2×D26911yescharacteristic
202#126—5381no—
203#125—2691no—
204#125—5381no—
205#124—2691no—
206#124—5381no—
207#123—5381no—
208C22⋊Q8—2691no—
209C22⋊Q8—2691no—
210C22⋊Q8—2691no—
211C22⋊Q8—5381no—
212#121—2691no—
213#121—5381no—
214C4×Q8—2691no—
215C4×Q8—2691no—
216C4×D4—2691no—
217C4×D4—5381no—
218#117—2691no—
219#117—5381no—
220C2×C4⋊C4C2×D26911yescharacteristic
221#107—2691no—
222#107—2691no—
223#106—2691no—
224C4⋊C8—2691no—
225#103—2691no—
226#103—2691no—
227#103—2691no—
228#103C2×D26911yescharacteristic
229#103C2×D26911yescharacteristic
230#103C2×D26911yescharacteristic
231#103C2×D26911yescharacteristic
232#102—2691no—
233#102—2691no—
234#102—2691no—
235C22⋊C8—2691no—
236C22⋊C8—2691no—
237C4×C8—2691no—
238#41—5382no—
239#41—10761no—
240C2×Q8—21no—
241C2×Q8—22no—
242C2×Q8—41no—
243C2×Q8—2691no—
244C2×Q8C22×D26911yescharacteristic
245C2×Q8C22×D26911yescharacteristic
246C2×D4—2691no—
247C2×D4—2691no—
248C2×D4—5381no—
249C2×D4—5381no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—2691no—
253C22×C4—5381no—
254C22×C4C22×D26911yescharacteristic
255Q16—5382no—
256Q16—10761no—
257SD16—10761no—
258C2×C8—41no—
259C2×C8—2691no—
260C2×C8—2691no—
261C2×C8—10761no—
262C2×C8C22×D26911yescharacteristic
263C2×C8C22×D26911yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—2691no—
266C4⋊C4—2691no—
267C4⋊C4—2691no—
268C4⋊C4—5381no—
269C4⋊C4—5381no—
270C4⋊C4—5381no—
271C4⋊C4—5381no—
272C4⋊C4—5381no—
273C4⋊C4—5381no—
274C4⋊C4—5381no—
275C4⋊C4C22×D26911yescharacteristic
276C4⋊C4C22×D26911yescharacteristic
277C22⋊C4—2691no—
278C22⋊C4—2691no—
279C22⋊C4—5381no—
280C22⋊C4—5381no—
281C22⋊C4—5381no—
282C22⋊C4—5381no—
283C22⋊C4—5381no—
284C22⋊C4—5381no—
285C22⋊C4—5381no—
286C42—2691no—
287C42—5381no—
288C42—5381no—
289C42—5381no—
290C23—2691no—
291C23—5381no—
292C23D4×D26911yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—42no—
297Q8—5381no—
298Q8—5381no—
299Q8#1686440212yes—
300D4—5382no—
301D4—5381no—
302D4—5381no—
303D4—10762no—
304D4—10762no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—2691no—
314C2×C4—2691no—
315C2×C4—2691no—
316C2×C4—5381no—
317C2×C4—5381no—
318C2×C4—5381no—
319C2×C4—5381no—
320C2×C4—5381no—
321C2×C4—10762no—
322C2×C4D4×D26911yescharacteristic
323C2×C4C23×D26911yescharacteristic
324C8—21no—
325C8—21no—
326C8—5381no—
327C8—5381no—
328C22—21no—
329C22—21no—
330C22—5381no—
331C22—5381no—
332C22—5381no—
333C22—10761no—
334C22—10761no—
335C22—10761no—
336C22#2257547412yes—
337C22C2×D4×D26911yescharacteristic
338C4—21no—
339C4—22no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—5381no—
344C4—5381no—
345C4—5381no—
346C4—10761no—
347C4—10761no—
348C4—10761no—
349C4C2×#1686440211yescharacteristic
350C4#2257549811yescharacteristic
351C2—22no—
352C2—10761no—
353C2—21521no—
354C2#3177124511yescharacteristic
355C2C2×#2257547411yescharacteristic
356C2#3177141811yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
FittingC2×#103×C269C2
socleC22×C269C22×D4
prime radical#31771266C2
hypercenterC2×#103D269
hypocenterC269#3300
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. #31771290C2semidirect
3. #31770961C2semidirect
4. #31770944C2semidirect
5. #31770918C2semidirect
6. #31770910C2semidirect
7. #31770845C2semidirect
8. #31770834C2semidirect
9. #31770830C2semidirect
10. #31770770C2semidirect
11. #31770761C2semidirect
12. #31770697C2semidirect
13. C8×C22⋊D269C2semidirect
14. #31770600C2semidirect
15. C2×#103×C269C2semidirect
178. C269#3300semidirect
194. C2×#103D269semidirect

Maximal subgroups

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

subgroupindex
#317712902
#317712662
#317709612
#317709442
#317709182
#317709102
#317708452
#317708342
#317708302
#317707702
#317707612
#317706972
C8×C22⋊D2692
#317706002
C2×#103×C2692
#3300269