Finite Group Databasebeta

← #46823509

Subgroups — #46823509

Order 34432.

354 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771318C211yesmaximal, characteristic
2#31771313C211yesmaximal, characteristic, complemented
3#31771009C211yesmaximal, characteristic, complemented
4#31770945C211yesmaximal, characteristic, complemented
5#31770920C211yesmaximal, characteristic, complemented
6#31770919C211yesmaximal, characteristic, complemented
7#31770898C211yesmaximal, characteristic, complemented
8#31770894C211yesmaximal, characteristic, complemented
9#31770854C211yesmaximal, characteristic, complemented
10#31770853C211yesmaximal, characteristic, complemented
11#31770690C211yesmaximal, characteristic, complemented
12#31770680C211yesmaximal, characteristic, complemented
13#31770648C211yesmaximal, characteristic, complemented
14#31770644C211yesmaximal, characteristic, complemented
15#485×C269C211yesmaximal, characteristic, complemented
16C2×#16864389C2211yescharacteristic
17C2×#16864386C2211yescharacteristic
18C2×#16864385C2211yescharacteristic
19#22575452C2211yescharacteristic
20#22575452C2211yescharacteristic
21#22575443—21no—
22#22575441—21no—
23#22575439—21no—
24#22575433—21no—
25#22575430—21no—
26#22575429C2211yescharacteristic
27#22575428C2211yescharacteristic
28#22575427C2211yescharacteristic
29#22575426—21no—
30Q8×Dic269C2211yescharacteristic
31#22575415C2211yescharacteristic
32C4×C22⋊D269C2211yescharacteristic
33#22575413—21no—
34#22575411C2211yescharacteristic
35#22575410—21no—
36C2×C4⋊Dic269C2211yescharacteristic
37C4⋊C4×D269C2211yescharacteristic
38#22575387C2211yescharacteristic
39#22575387C2211yescharacteristic
40#22575386C2211yescharacteristic
41#22575386C2211yescharacteristic
42#22575386C2211yescharacteristic
43#22575384C2211yescharacteristic
44#22575384C2211yescharacteristic
45#22575382C2211yescharacteristic
46#22575377C2211yescharacteristic
47#22575375C2211yescharacteristic
48#22575375C2211yescharacteristic
49#22575373C2211yescharacteristic
50#22575365C2211yescharacteristic
51C8×Dic269C2211yescharacteristic
52C22⋊Q8×C269C2211yescharacteristic
53#117×C269C2211yescharacteristic
54#107×C269C2211yescharacteristic
55#106×C269C2211yescharacteristic
56#103×C269C2211yescharacteristic
57#103×C269C2211yescharacteristic
58C22⋊C8×C269C2211yescharacteristic
59C2×Dic538—21no—
60C2×Dic538—21no—
61C2×D1076—21no—
62C2×D1076C2311yescharacteristic
63C2×C22⋊D269—21no—
64C2×C22⋊D269D411yescharacteristic
65C22×Dic269—21no—
66C2×C4×D269—21no—
67C2×C4×D269—21no—
68C2×C4×D269C2311yescharacteristic
69#16864389—22no—
70#16864386—22no—
71#16864385—22no—
72C2×#14524130C2311yescharacteristic
73C2×#14524130C2311yescharacteristic
74C4⋊Dic269—21no—
75C4⋊Dic269—21no—
76C4⋊Dic269C2311yescharacteristic
77C4⋊Dic269C2311yescharacteristic
78C4⋊Dic269C2311yescharacteristic
79#16864381—21no—
80#16864381—21no—
81#16864381—21no—
82#16864381—21no—
83#16864381D411yescharacteristic
84C22⋊Dic269D411yescharacteristic
85#16864379—21no—
86#16864379—21no—
87#16864379—21no—
88#16864379—21no—
89#16864379—21no—
90#16864379D411yescharacteristic
91C4×Dic269—21no—
92C4×Dic269—21no—
93C4×Dic269C2311yescharacteristic
94C2×Q8×C269C2311yescharacteristic
95C22×C4×C269C2311yescharacteristic
96C2×C8×C269C2311yescharacteristic
97C2×C8×C269C2311yescharacteristic
98C4⋊C4×C269—21no—
99C4⋊C4×C269C2311yescharacteristic
100C4⋊C4×C269C2311yescharacteristic
101C4⋊C4×C269C2311yescharacteristic
102C22⋊C4×C269—21no—
103C22⋊C4×C269—21no—
104C42×C269—21no—
105C22×D269—21no—
106C22×D269C2×D411yescharacteristic
107Dic538—81no—
108Dic538—81no—
109D1076—21no—
110D1076—21no—
111D1076—81no—
112C22⋊D269—22no—
113C22⋊D269—81no—
114C2×Dic269—21no—
115C2×Dic269—21no—
116C2×Dic269—21no—
117C2×Dic269—81no—
118C2×Dic269C2×D411yescharacteristic
119C2×Dic269C2×D411yescharacteristic
120C2×Dic269C2×D411yescharacteristic
121C4×D269—21no—
122C4×D269—21no—
123C4×D269—42no—
124C4×D269—81no—
125#14524130—21no—
126#14524130#4112yes—
127C23×C269C2×D411yescharacteristic
128Q8×C269—21no—
129Q8×C269—21no—
130C2×C4×C269—21no—
131C2×C4×C269—21no—
132C2×C4×C269—21no—
133C2×C4×C269—21no—
134C2×C4×C269—21no—
135C2×C4×C269—21no—
136C2×C4×C269C2×D411yescharacteristic
137C2×C4×C269C2411yescharacteristic
138C8×C269—21no—
139C8×C269—21no—
140C22×C269—21no—
141C22×C269—21no—
142C22×C269—21no—
143C22×C269C22×D411yescharacteristic
144C2×D269—21no—
145C2×D269—21no—
146C2×D269—21no—
147C2×D269—41no—
148C2×D269—41no—
149C2×D269—41no—
150C4×C269—21no—
151C4×C269—41no—
152C4×C269—41no—
153C4×C269—41no—
154C4×C269—41no—
155C4×C269C2×#4111yescharacteristic
156C4×C2692−1+411yescharacteristic
157Dic269—21no—
158Dic269—21no—
159Dic269—41no—
160Dic269—41no—
161Dic269—41no—
162Dic269#13712yes—
163C2×C269—41no—
164C2×C269#54711yescharacteristic
165C2×C269C2×#13711yescharacteristic
166C2×C269#57611yescharacteristic
167D269—41no—
168D269—81no—
169C269#335711yescharacteristic, complemented, Sylow
170#3357—2691nomaximal, Sylow
171#555—2691no—
172#554—2691no—
173#500—2691no—
174#485—2691no—
175#485D26911yescharacteristic, complemented
176#480—2691no—
177#480—2691no—
178#477—2691no—
179#476—2691no—
180#468—2691no—
181#468—2691no—
182C4×SD16—2691no—
183#436—2691no—
184#428—2691no—
185#428—2691no—
186C2×SD16—2691no—
187C2×M16—2691no—
188C2×M16—2691no—
189C4⋊Q8—2691no—
190C4⋊Q8—2691no—
191#125—5381no—
192#124—5381no—
193#124—5381no—
194C22⋊Q8—2691no—
195C22⋊Q8—5381no—
196C22⋊Q8—5381no—
197C22⋊Q8C2×D26911yescharacteristic
198#121—2691no—
199#121—2691no—
200#121—5381no—
201C4×Q8—2691no—
202C4×D4—2691no—
203C4×D4—2691no—
204C4×D4—5381no—
205#117—2691no—
206#117—5381no—
207#117C2×D26911yescharacteristic
208C2×C4⋊C4—2691no—
209C2×C4⋊C4—2691no—
210#107—2691no—
211#107—2691no—
212#107—2691no—
213#107—2691no—
214#107—2691no—
215#107C2×D26911yescharacteristic
216#106—2691no—
217#106—2691no—
218#106C2×D26911yescharacteristic
219C4⋊C8—2691no—
220#103—2691no—
221#103C2×D26911yescharacteristic
222#103C2×D26911yescharacteristic
223#102—2691no—
224#102—2691no—
225#102—2691no—
226C22⋊C8—2691no—
227C22⋊C8C2×D26911yescharacteristic
228C4×C8—2691no—
229C2×Q8—5381no—
230C2×Q8—5381no—
231C2×Q8C22×D26911yescharacteristic
232C2×D4—2691no—
233C2×D4—2691no—
234C2×D4—5381no—
235C2×D4—5381no—
236C22×C4—2691no—
237C22×C4—5381no—
238C22×C4—5381no—
239C22×C4—5381no—
240C22×C4C22×D26911yescharacteristic
241SD16—5382no—
242M16—5382no—
243M16—5382no—
244C2×C8—2691no—
245C2×C8—2691no—
246C2×C8C22×D26911yescharacteristic
247C2×C8C22×D26911yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—2691no—
250C4⋊C4—2691no—
251C4⋊C4—2691no—
252C4⋊C4—2691no—
253C4⋊C4—5381no—
254C4⋊C4—5381no—
255C4⋊C4—5381no—
256C4⋊C4—5381no—
257C4⋊C4—5381no—
258C4⋊C4—5381no—
259C4⋊C4C22×D26911yescharacteristic
260C4⋊C4C22×D26911yescharacteristic
261C4⋊C4C22×D26911yescharacteristic
262C22⋊C4—21no—
263C22⋊C4—21no—
264C22⋊C4—2691no—
265C22⋊C4—2691no—
266C22⋊C4—5381no—
267C22⋊C4—5381no—
268C22⋊C4—5381no—
269C22⋊C4—5381no—
270C22⋊C4—5381no—
271C42—21no—
272C42—2691no—
273C42—5381no—
274C42—5381no—
275C23—2691no—
276C23—5381no—
277C23D4×D26911yescharacteristic
278Q8—21no—
279Q8—21no—
280Q8—21521no—
281Q8—21521no—
282D4—5382no—
283D4—5381no—
284D4—5381no—
285D4—21521no—
286D4—21521no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—2691no—
294C2×C4—2691no—
295C2×C4—2691no—
296C2×C4—5381no—
297C2×C4—5381no—
298C2×C4—5381no—
299C2×C4—5381no—
300C2×C4—5381no—
301C2×C4—10762no—
302C2×C4—21521no—
303C2×C4—21521no—
304C2×C4D4×D26911yescharacteristic
305C2×C4C23×D26911yescharacteristic
306C8—21no—
307C8—21no—
308C8—2692no—
309C8—5381no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—5381no—
314C22—5381no—
315C22—5381no—
316C22—10761no—
317C22—10761no—
318C22—10761no—
319C22C2×D4×D26911yescharacteristic
320C4—21no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—41no—
325C4—2692no—
326C4—5381no—
327C4—5381no—
328C4—10761no—
329C4—10761no—
330C4—10761no—
331C4#41×D26911yescharacteristic
332C4#2257550011yescharacteristic
333C2—41no—
334C2—10761no—
335C2—21521no—
336C2#3177125311yescharacteristic
337C2#137×D26911yescharacteristic
338C2#3177140711yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#485×C269C2
socleC22×C269C22×D4
prime radical#31771318C2
hypercenter#485D269
hypocenterC269#3357
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
2. #31771313C2semidirect
3. #31771009C2semidirect
4. #31770945C2semidirect
5. #31770920C2semidirect
6. #31770919C2semidirect
7. #31770898C2semidirect
8. #31770894C2semidirect
9. #31770854C2semidirect
10. #31770853C2semidirect
11. #31770690C2semidirect
12. #31770680C2semidirect
13. #31770648C2semidirect
14. #31770644C2semidirect
15. #485×C269C2semidirect
169. C269#3357semidirect
175. #485D269semidirect

Maximal subgroups

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

subgroupindex
#317713182
#317713132
#317710092
#317709452
#317709202
#317709192
#317708982
#317708942
#317708542
#317708532
#317706902
#317706802
#317706482
#317706442
#485×C2692
#3357269