Finite Group Databasebeta

← #46822357

Subgroups — #46822357

Order 34432.

346 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771229C211yesmaximal, characteristic, complemented
2#31771220C211yesmaximal, characteristic, complemented
3#31770894C211yesmaximal, characteristic, complemented
4#31770889C211yesmaximal, characteristic, complemented
5#31770887C211yesmaximal, characteristic, complemented
6#31770864C211yesmaximal, characteristic, complemented
7#31770857C211yesmaximal, characteristic
8#31770835C211yesmaximal, characteristic, complemented
9#31770833C211yesmaximal, characteristic, complemented
10#31770828C211yesmaximal, characteristic, complemented
11#31770826C211yesmaximal, characteristic, complemented
12#31770820C211yesmaximal, characteristic, complemented
13#31770819C211yesmaximal, characteristic, complemented
14#31770630C211yesmaximal, characteristic, complemented
15#476×C269C211yesmaximal, characteristic, complemented
16C2×Dic1076C2211yescharacteristic
17C2×#16864391C2211yescharacteristic
18C2×#16864390C2211yescharacteristic
19C2×#16864387C2211yescharacteristic
20C2×#16864385C2211yescharacteristic
21C2×C8×D269C2211yescharacteristic
22#22575452C2211yescharacteristic
23#22575448—21no—
24#22575446—21no—
25#22575442—21no—
26#22575441C2211yescharacteristic
27#22575440C2211yescharacteristic
28#22575439—21no—
29#22575438—21no—
30#22575436—21no—
31#22575433C2211yescharacteristic
32#22575433C2211yescharacteristic
33#22575432—21no—
34#22575429—21no—
35#22575428C2211yescharacteristic
36#22575424C2211yescharacteristic
37C4×Dic538C2211yescharacteristic
38#22575418C2211yescharacteristic
39#22575415C2211yescharacteristic
40#22575410C2211yescharacteristic
41#22575384C2211yescharacteristic
42#22575384C2211yescharacteristic
43C4⋊#14524130C2211yescharacteristic
44#22575382C2211yescharacteristic
45#22575382C2211yescharacteristic
46#22575378C2211yescharacteristic
47#22575376C2211yescharacteristic
48#22575376C2211yescharacteristic
49#22575376C2211yescharacteristic
50#22575375C2211yescharacteristic
51#22575373C2211yescharacteristic
52C4⋊Q8×C269C2211yescharacteristic
53C4×D4×C269C2211yescharacteristic
54#106×C269C2211yescharacteristic
55#106×C269C2211yescharacteristic
56C4⋊C8×C269C2211yescharacteristic
57#102×C269C2211yescharacteristic
58#102×C269C2211yescharacteristic
59C2×Dic538—21no—
60C2×Dic538C2311yescharacteristic
61C2×Dic538C2311yescharacteristic
62C2×D1076—21no—
63C2×D1076C2311yescharacteristic
64C2×C22⋊D269—21no—
65C2×C4×D269—21no—
66C2×C4×D269C2311yescharacteristic
67Dic1076—41no—
68#16864391—41no—
69#16864390—41no—
70#16864387—41no—
71#16864385—41no—
72C2×#14524130C2311yescharacteristic
73C2×#14524130C2311yescharacteristic
74C8×D269—41no—
75C4⋊Dic269—21no—
76C4⋊Dic269—21no—
77C4⋊Dic269C2311yescharacteristic
78#16864381—21no—
79#16864381—21no—
80#16864381—21no—
81#16864381D411yescharacteristic
82#16864381D411yescharacteristic
83C22⋊Dic269—21no—
84C22⋊Dic269—21no—
85C22⋊Dic269—21no—
86#16864379—21no—
87#16864379—21no—
88#16864379—21no—
89#16864379—21no—
90#16864379—21no—
91#16864379—21no—
92#16864379D411yescharacteristic
93#16864379D411yescharacteristic
94C4×Dic269—21no—
95C4×Dic269—21no—
96C4×Dic269C2311yescharacteristic
97C2×Q8×C269—21no—
98C2×D4×C269C2311yescharacteristic
99C22×C4×C269—21no—
100C2×C8×C269C2311yescharacteristic
101C2×C8×C269C2311yescharacteristic
102C4⋊C4×C269—21no—
103C4⋊C4×C269C2311yescharacteristic
104C4⋊C4×C269C2311yescharacteristic
105C4⋊C4×C269C2311yescharacteristic
106C22⋊C4×C269—21no—
107C42×C269C2311yescharacteristic
108C22×D269—21no—
109C22×D269C2×D411yescharacteristic
110Dic538—21no—
111Dic538—21no—
112Dic538—21no—
113Dic538—21no—
114Dic538—81no—
115D1076—21no—
116D1076—21no—
117D1076—81no—
118C22⋊D269—81no—
119C2×Dic269—21no—
120C2×Dic269—21no—
121C2×Dic269—21no—
122C2×Dic269C2×D411yescharacteristic
123C2×Dic269C2×D411yescharacteristic
124C2×Dic269C2×D411yescharacteristic
125C4×D269—21no—
126C4×D269—21no—
127C4×D269—81no—
128#14524130—21no—
129#14524130—21no—
130C23×C269—21no—
131Q8×C269—81no—
132D4×C269—21no—
133D4×C269—21no—
134C2×C4×C269—21no—
135C2×C4×C269—21no—
136C2×C4×C269—21no—
137C2×C4×C269—81no—
138C2×C4×C269C2×D411yescharacteristic
139C2×C4×C269C2×D411yescharacteristic
140C2×C4×C269C2411yescharacteristic
141C8×C269—21no—
142C8×C269—21no—
143C22×C269—41no—
144C22×C269—41no—
145C22×C269—41no—
146C22×C269C22×D411yescharacteristic
147C2×D269—21no—
148C2×D269—21no—
149C2×D269—21no—
150C2×D269—41no—
151C2×D269—41no—
152C2×D269—41no—
153C4×C269—21no—
154C4×C269—21no—
155C4×C269—41no—
156C4×C269—41no—
157C4×C269—41no—
158C4×C269H(5,𝔽2)11yescharacteristic
159C4×C2692−1+411yescharacteristic
160Dic269—21no—
161Dic269—21no—
162Dic269—21no—
163Dic269—41no—
164Dic269—41no—
165Dic269—41no—
166C2×C269—81no—
167C2×C269#53711yescharacteristic
168C2×C269#57711yescharacteristic
169C2×C269#57711yescharacteristic
170D269—41no—
171D269—81no—
172C269#326311yescharacteristic, complemented, Sylow
173#3263—2691nomaximal, Sylow
174#542—2691no—
175#542—2691no—
176#476—2691no—
177#476D26911yescharacteristic, complemented
178#475—2691no—
179#475—2691no—
180#470—2691no—
181#469—2691no—
182#465—2691no—
183#465—2691no—
184#464—2691no—
185#464—2691no—
186#463—2691no—
187#463—2691no—
188#424—2691no—
189C2×Q16—2691no—
190C2×SD16—2691no—
191C2×SD16—2691no—
192C2×D8—2691no—
193C2×M16—2691no—
194C22×C8—2691no—
195C4⋊Q8—2691no—
196C4⋊Q8C2×D26911yescharacteristic
197#126—5381no—
198#126—5381no—
199#124—2691no—
200#124—2691no—
201#124—5381no—
202#124—5381no—
203#123—5381no—
204#123—5381no—
205C22⋊Q8—2691no—
206C22⋊Q8—2691no—
207C22⋊Q8—5381no—
208C22⋊Q8—5381no—
209#121—2691no—
210#121—2691no—
211C4×Q8—2691no—
212C4×Q8—2691no—
213C4×D4—2691no—
214C4×D4C2×D26911yescharacteristic
215#117—2691no—
216#106—2691no—
217#106—2691no—
218#106C2×D26911yescharacteristic
219#106C2×D26911yescharacteristic
220C4⋊C8—2691no—
221C4⋊C8—2691no—
222C4⋊C8—2691no—
223C4⋊C8C2×D26911yescharacteristic
224#103—2691no—
225#103—2691no—
226#103—2691no—
227#103—2691no—
228#102—2691no—
229#102—2691no—
230#102C2×D26911yescharacteristic
231#102C2×D26911yescharacteristic
232C2×Q8—21no—
233C2×Q8—2691no—
234C2×Q8—2691no—
235C2×Q8—5381no—
236C2×D4—2691no—
237C2×D4—5381no—
238C2×D4—5381no—
239C2×D4C22×D26911yescharacteristic
240C22×C4—21no—
241C22×C4—2691no—
242C22×C4—5381no—
243Q16—10761no—
244SD16—10761no—
245SD16—10761no—
246D8—10761no—
247M16—10761no—
248C2×C8—2691no—
249C2×C8—2691no—
250C2×C8—10761no—
251C2×C8C22×D26911yescharacteristic
252C2×C8C22×D26911yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—2691no—
255C4⋊C4—2691no—
256C4⋊C4—2691no—
257C4⋊C4—5381no—
258C4⋊C4—5381no—
259C4⋊C4—5381no—
260C4⋊C4—5381no—
261C4⋊C4—5381no—
262C4⋊C4C22×D26911yescharacteristic
263C4⋊C4C22×D26911yescharacteristic
264C4⋊C4C22×D26911yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—2691no—
267C22⋊C4—2691no—
268C22⋊C4—5381no—
269C22⋊C4—5381no—
270C22⋊C4—5381no—
271C22⋊C4—5381no—
272C22⋊C4—5381no—
273C22⋊C4—5381no—
274C22⋊C4—5381no—
275C22⋊C4—5381no—
276C22⋊C4—5381no—
277C42—2691no—
278C42—5381no—
279C42—5381no—
280C42C22×D26911yescharacteristic
281C23—21no—
282C23—2691no—
283C23—5381no—
284Q8—81no—
285Q8—5381no—
286Q8—5381no—
287Q8—5381no—
288Q8—5381no—
289Q8—21521no—
290D4—21no—
291D4—21no—
292D4—5381no—
293D4—5381no—
294D4—21521no—
295D4—21521no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—81no—
300C2×C4—2691no—
301C2×C4—2691no—
302C2×C4—2691no—
303C2×C4—5381no—
304C2×C4—5381no—
305C2×C4—5381no—
306C2×C4—5381no—
307C2×C4—5381no—
308C2×C4—21521no—
309C2×C4D4×D26911yescharacteristic
310C2×C4D4×D26911yescharacteristic
311C2×C4C23×D26911yescharacteristic
312C8—21no—
313C8—21no—
314C8—5381no—
315C8—5381no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—5381no—
320C22—5381no—
321C22—5381no—
322C22—10761no—
323C22—10761no—
324C22—10761no—
325C22C2×D4×D26911yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—5381no—
332C4—5381no—
333C4—5381no—
334C4—10761no—
335C4—10761no—
336C4—10761no—
337C4#2257549911yescharacteristic
338C4#2257550111yescharacteristic
339C2—81no—
340C2—10761no—
341C2—21521no—
342C2#3177118511yescharacteristic
343C2#3177141111yescharacteristic
344C2#3177141511yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#476×C269C2
socleC22×C269C22×D4
prime radical#31770857C2
hypercenter#476D269
hypocenterC269#3263
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #31771229C2semidirect
2. #31771220C2semidirect
3. #31770894C2semidirect
4. #31770889C2semidirect
5. #31770887C2semidirect
6. #31770864C2semidirect
8. #31770835C2semidirect
9. #31770833C2semidirect
10. #31770828C2semidirect
11. #31770826C2semidirect
12. #31770820C2semidirect
13. #31770819C2semidirect
14. #31770630C2semidirect
15. #476×C269C2semidirect
172. C269#3263semidirect
177. #476D269semidirect

Maximal subgroups

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

subgroupindex
#317712292
#317712202
#317708942
#317708892
#317708872
#317708642
#317708572
#317708352
#317708332
#317708282
#317708262
#317708202
#317708192
#317706302
#476×C2692
#3263269