Finite Group Databasebeta

← #46822221

Subgroups — #46822221

Order 34432.

354 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771159C211yesmaximal, characteristic, complemented
2#31771140C211yesmaximal, characteristic
3#31770909C211yesmaximal, characteristic, complemented
4#31770889C211yesmaximal, characteristic, complemented
5#31770884C211yesmaximal, characteristic, complemented
6#31770847C211yesmaximal, characteristic, complemented
7#31770845C211yesmaximal, characteristic, complemented
8#31770837C211yesmaximal, characteristic
9#31770835C211yesmaximal, characteristic
10#31770828C211yesmaximal, characteristic, complemented
11#31770827C211yesmaximal, characteristic, complemented
12#31770814C211yesmaximal, characteristic, complemented
13#31770809C211yesmaximal, characteristic, complemented
14C4⋊C8×D269C211yesmaximal, characteristic, complemented
15#479×C269C211yesmaximal, characteristic, complemented
16C2×Dic1076C2211yescharacteristic
17C2×#16864392C2211yescharacteristic
18C2×#16864391C2211yescharacteristic
19C2×#16864389C2211yescharacteristic
20C2×C8×D269C2211yescharacteristic
21C2×C8×D269C2211yescharacteristic
22#22575452C2211yescharacteristic
23#22575451C2211yescharacteristic
24#22575448—21no—
25#22575443—21no—
26#22575441C2211yescharacteristic
27#22575438—21no—
28#22575433C2211yescharacteristic
29#22575433C2211yescharacteristic
30#22575431—21no—
31#22575429C2211yescharacteristic
32#22575428C2211yescharacteristic
33C4×Dic538—21no—
34C4×Dic538C2211yescharacteristic
35#22575418C2211yescharacteristic
36#22575415—21no—
37#22575415C2211yescharacteristic
38#22575411—21no—
39#22575410—21no—
40C42×D269C2211yescharacteristic
41#22575386C2211yescharacteristic
42#22575384C2211yescharacteristic
43C4⋊#14524130C2211yescharacteristic
44#22575382C2211yescharacteristic
45#22575382C2211yescharacteristic
46#22575378C2211yescharacteristic
47#22575376C2211yescharacteristic
48#22575376C2211yescharacteristic
49#22575376C2211yescharacteristic
50#22575375C2211yescharacteristic
51#22575373C2211yescharacteristic
52#125×C269C2211yescharacteristic
53C4×Q8×C269C2211yescharacteristic
54#107×C269C2211yescharacteristic
55#106×C269C2211yescharacteristic
56C4⋊C8×C269C2211yescharacteristic
57#103×C269C2211yescharacteristic
58#103×C269C2211yescharacteristic
59C2×Dic538—21no—
60C2×Dic538C2311yescharacteristic
61C2×Dic538C2311yescharacteristic
62C2×D1076—21no—
63C2×D1076C2311yescharacteristic
64C2×C4×D269—21no—
65C2×C4×D269D411yescharacteristic
66C2×C4×D269D411yescharacteristic
67C2×C4×D269C2311yescharacteristic
68Dic1076—41no—
69#16864392—41no—
70#16864391—41no—
71#16864389—41no—
72C2×#14524130C2311yescharacteristic
73C2×#14524130C2311yescharacteristic
74C8×D269—41no—
75C8×D269—41no—
76C4⋊Dic269—21no—
77C4⋊Dic269—21no—
78C4⋊Dic269C2311yescharacteristic
79#16864381—21no—
80#16864381—21no—
81#16864381—21no—
82#16864381—21no—
83#16864381—21no—
84#16864381—21no—
85#16864379—21no—
86#16864379—21no—
87#16864379—21no—
88#16864379—21no—
89#16864379—21no—
90#16864379—21no—
91#16864379—21no—
92C4×Dic269—21no—
93C4×Dic269—21no—
94C4×Dic269D411yescharacteristic
95C4×Dic269D411yescharacteristic
96C4×Dic269C2311yescharacteristic
97C2×Q8×C269C2311yescharacteristic
98C2×C8×C269C2311yescharacteristic
99C2×C8×C269C2311yescharacteristic
100C4⋊C4×C269—21no—
101C4⋊C4×C269—21no—
102C4⋊C4×C269—21no—
103C4⋊C4×C269C2311yescharacteristic
104C4⋊C4×C269C2311yescharacteristic
105C4⋊C4×C269C2311yescharacteristic
106C42×C269—21no—
107C42×C269C2311yescharacteristic
108C22×D269—21no—
109C22×D269C2×D411yescharacteristic
110Dic538—21no—
111Dic538—21no—
112Dic538—21no—
113Dic538—21no—
114Dic538—42no—
115D1076—21no—
116D1076—21no—
117D1076—42no—
118C2×Dic269—21no—
119C2×Dic269—21no—
120C2×Dic269—21no—
121C2×Dic269C2×D411yescharacteristic
122C2×Dic269C2×D411yescharacteristic
123C2×Dic269C2×D411yescharacteristic
124C4×D269—22no—
125C4×D269—21no—
126C4×D269—21no—
127C4×D269—22no—
128C4×D269—42no—
129#14524130—21no—
130#14524130—21no—
131Q8×C269—21no—
132Q8×C269—21no—
133C2×C4×C269—21no—
134C2×C4×C269—21no—
135C2×C4×C269—21no—
136C2×C4×C269—21no—
137C2×C4×C269C2×D411yescharacteristic
138C2×C4×C269C2×D411yescharacteristic
139C2×C4×C269C2411yescharacteristic
140C8×C269—21no—
141C8×C269—21no—
142C22×C269C22×D411yescharacteristic
143C2×D269—21no—
144C2×D269—21no—
145C2×D269—41no—
146C2×D269—41no—
147C2×D269—41no—
148C2×D269#13712yes—
149C4×C269—21no—
150C4×C269—21no—
151C4×C269—41no—
152C4×C269—41no—
153C4×C269—41no—
154C4×C269—41no—
155C4×C269H(5,𝔽2)11yescharacteristic
156C4×C2692−1+411yescharacteristic
157Dic269—21no—
158Dic269—21no—
159Dic269—41no—
160Dic269—41no—
161Dic269—41no—
162Dic269#13512yes—
163C2×C269#53711yescharacteristic
164C2×C269C2×#13511yescharacteristic
165C2×C269C2×#13711yescharacteristic
166D269—22no—
167D269—81no—
168C269#324811yescharacteristic, complemented, Sylow
169#3248—2691nomaximal, Sylow
170#533—2691no—
171#529—2691no—
172#479—2691no—
173#479D26911yescharacteristic, complemented
174#475—2691no—
175#474—2691no—
176#467—2691no—
177#467—2691no—
178#465—2691no—
179#465—2691no—
180#464—2691no—
181#464—2691no—
182#462—2691no—
183#461—2691no—
184C2×C4⋊C8—2691no—
185C2×Q16—2691no—
186C2×Q16—2691no—
187C2×SD16—2691no—
188C2×SD16—2691no—
189C22×C8—2691no—
190C22×C8—2691no—
191C4⋊Q8—2691no—
192C4⋊Q8—2691no—
193#126—5381no—
194#125—5381no—
195#125C2×D26911yescharacteristic
196#124—2691no—
197#123—5381no—
198C22⋊Q8—2691no—
199C22⋊Q8—2691no—
200C22⋊Q8—2691no—
201C22⋊Q8—5381no—
202#121—2691no—
203C4×Q8—2691no—
204C4×Q8—2691no—
205C4×Q8—5381no—
206C4×Q8C2×D26911yescharacteristic
207C4×D4—2691no—
208C4×D4—5381no—
209#117—5381no—
210#117—5381no—
211C2×C42—2691no—
212#107—2691no—
213#107C2×D26911yescharacteristic
214#106—2691no—
215#106C2×D26911yescharacteristic
216C4⋊C8—2691no—
217C4⋊C8—2691no—
218C4⋊C8—2691no—
219C4⋊C8C2×D26911yescharacteristic
220#103—2691no—
221#103—2691no—
222#103—2691no—
223#103—2691no—
224#103C2×D26911yescharacteristic
225#103C2×D26911yescharacteristic
226#102—2691no—
227#102—2691no—
228C2×Q8—2691no—
229C2×Q8—2691no—
230C2×Q8—5381no—
231C2×Q8C22×D26911yescharacteristic
232C2×D4—2691no—
233C2×D4—5381no—
234C22×C4—2691no—
235C22×C4—2691no—
236C22×C4—2691no—
237C22×C4—5381no—
238Q16—10761no—
239Q16—10761no—
240SD16—10761no—
241SD16—10761no—
242C2×C8—2691no—
243C2×C8—2691no—
244C2×C8—10761no—
245C2×C8—10761no—
246C2×C8C22×D26911yescharacteristic
247C2×C8C22×D26911yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—2691no—
252C4⋊C4—5381no—
253C4⋊C4—5381no—
254C4⋊C4—5381no—
255C4⋊C4—5381no—
256C4⋊C4—5381no—
257C4⋊C4—5381no—
258C4⋊C4—5381no—
259C4⋊C4—5381no—
260C4⋊C4C22×D26911yescharacteristic
261C4⋊C4C22×D26911yescharacteristic
262C4⋊C4C22×D26911yescharacteristic
263C22⋊C4—5381no—
264C22⋊C4—5381no—
265C22⋊C4—5381no—
266C22⋊C4—5381no—
267C22⋊C4—5381no—
268C22⋊C4—5381no—
269C22⋊C4—5381no—
270C42—21no—
271C42—2691no—
272C42—2691no—
273C42—2691no—
274C42—5381no—
275C42—5381no—
276C42C22×D26911yescharacteristic
277C23—2691no—
278C23—5381no—
279Q8—21no—
280Q8—21no—
281Q8—5381no—
282Q8—5381no—
283Q8—5381no—
284Q8—5381no—
285Q8—10762no—
286D4—5381no—
287D4—5381no—
288D4—10762no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—2691no—
294C2×C4—2691no—
295C2×C4—2691no—
296C2×C4—5382no—
297C2×C4—5382no—
298C2×C4—5381no—
299C2×C4—5381no—
300C2×C4—5381no—
301C2×C4—5381no—
302C2×C4—5381no—
303C2×C4—10762no—
304C2×C4D4×D26911yescharacteristic
305C2×C4D4×D26911yescharacteristic
306C2×C4C23×D26911yescharacteristic
307C8—21no—
308C8—21no—
309C8—5381no—
310C8—5381no—
311C22—2692no—
312C22—5381no—
313C22—5381no—
314C22—10761no—
315C22—10761no—
316C22—10761no—
317C22C2×D4×D26911yescharacteristic
318C4—21no—
319C4—21no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—2692no—
325C4—5381no—
326C4—5381no—
327C4—10761no—
328C4—10761no—
329C4—10761no—
330C4#2257549911yescharacteristic
331C4#2257550111yescharacteristic
332C2—5382no—
333C2—21521no—
334C2#3177118511yescharacteristic
335C2#135×D26911yescharacteristic
336C2#137×D26911yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#479×C269C2
socleC22×C269C22×D4
prime radical#22575428C22
hypercenter#479D269
hypocenterC269#3248
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. #31771159C2semidirect
3. #31770909C2semidirect
4. #31770889C2semidirect
5. #31770884C2semidirect
6. #31770847C2semidirect
7. #31770845C2semidirect
10. #31770828C2semidirect
11. #31770827C2semidirect
12. #31770814C2semidirect
13. #31770809C2semidirect
14. C4⋊C8×D269C2semidirect
15. #479×C269C2semidirect
168. C269#3248semidirect
173. #479D269semidirect

Maximal subgroups

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

subgroupindex
#317711592
#317711402
#317709092
#317708892
#317708842
#317708472
#317708452
#317708372
#317708352
#317708282
#317708272
#317708142
#317708092
C4⋊C8×D2692
#479×C2692
#3248269