Finite Group Databasebeta

← #46822783

Subgroups — #46822783

Order 34432.

398 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771303C211yesmaximal, characteristic, complemented
2#31771266C211yesmaximal, characteristic, complemented
3#31770961C211yesmaximal, characteristic, complemented
4#31770945C211yesmaximal, characteristic, complemented
5#31770923C211yesmaximal, characteristic, complemented
6#31770914C211yesmaximal, characteristic, complemented
7#31770841C211yesmaximal, characteristic, complemented
8#31770837C211yesmaximal, characteristic, complemented
9#31770823C211yesmaximal, characteristic, complemented
10#31770753C211yesmaximal, characteristic, complemented
11#31770744C211yesmaximal, characteristic, complemented
12#31770690C211yesmaximal, characteristic, complemented
13C8×C22⋊D269C211yesmaximal, characteristic, complemented
14#31770600C211yesmaximal, characteristic, complemented
15C2×#103×C269C211yesmaximal, characteristic, complemented
16C2×#16864403C2211yescharacteristic
17C2×#16864389C2211yescharacteristic
18C2×#16864389C2211yescharacteristic
19C2×D2152C2211yescharacteristic
20C2×C8×D269C2211yescharacteristic
21#22575448—21no—
22#22575444C2211yescharacteristic
23#22575442—21no—
24#22575442C2211yescharacteristic
25#22575438—21no—
26#22575429—21no—
27#22575429C2211yescharacteristic
28#22575428C2211yescharacteristic
29#22575427—21no—
30#22575427—21no—
31#22575427C2211yescharacteristic
32#22575427C2211yescharacteristic
33Q8×Dic269C2211yescharacteristic
34#22575415C2211yescharacteristic
35C4×C22⋊D269—21no—
36C4×C22⋊D269—21no—
37C4×C22⋊D269C2211yescharacteristic
38#22575411C2211yescharacteristic
39#22575387C2211yescharacteristic
40#22575384C2211yescharacteristic
41#22575384C2211yescharacteristic
42#22575382C2211yescharacteristic
43#22575377C2211yescharacteristic
44#22575377C2211yescharacteristic
45#22575375C2211yescharacteristic
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×D1076—21no—
62C2×D1076—21no—
63C2×D1076C2311yescharacteristic
64C2×D1076C2311yescharacteristic
65C2×C22⋊D269—21no—
66C2×C22⋊D269—21no—
67C2×C22⋊D269D411yescharacteristic
68C2×C4×D269—21no—
69C2×C4×D269—21no—
70C2×C4×D269C2311yescharacteristic
71#16864389—22no—
72#16864389—41no—
73D2152—41no—
74C2×#14524130C2311yescharacteristic
75C2×#14524130C2311yescharacteristic
76C8×D269—41no—
77C4⋊Dic269—21no—
78C4⋊Dic269—21no—
79C4⋊Dic269C2311yescharacteristic
80C4⋊Dic269C2311yescharacteristic
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#16864379—21no—
91#16864379—21no—
92#16864379—21no—
93#16864379D411yescharacteristic
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×D269—21no—
113C22×D269C2×D411yescharacteristic
114D1076—21no—
115D1076—21no—
116D1076—21no—
117D1076—21no—
118D1076—42no—
119D1076—81no—
120C22⋊D269—22no—
121C22⋊D269—42no—
122C22⋊D269—42no—
123C2×Dic269—21no—
124C2×Dic269—21no—
125C2×Dic269C2×D411yescharacteristic
126C2×Dic269C2×D411yescharacteristic
127C2×Dic269C2×D411yescharacteristic
128C4×D269—21no—
129C4×D269—21no—
130C4×D269—42no—
131C4×D269—81no—
132#14524130—21no—
133#14524130—21no—
134C23×C269C2×D411yescharacteristic
135Q8×C269—21no—
136Q8×C269—21no—
137Q8×C269—21no—
138Q8×C269—42no—
139Q8×C269#4112yes—
140C2×C4×C269—21no—
141C2×C4×C269—21no—
142C2×C4×C269—21no—
143C2×C4×C269—21no—
144C2×C4×C269—21no—
145C2×C4×C269—21no—
146C2×C4×C269—42no—
147C2×C4×C269—81no—
148C2×C4×C269C2×D411yescharacteristic
149C2×C4×C269C2411yescharacteristic
150C8×C269—21no—
151C8×C269—21no—
152C22×C269—21no—
153C22×C269—21no—
154C22×C269#13512yes—
155C22×C269C22×D411yescharacteristic
156C2×D269—21no—
157C2×D269—21no—
158C2×D269—21no—
159C2×D269—41no—
160C2×D269—41no—
161C2×D269—41no—
162C2×D269—41no—
163C2×D269—41no—
164C2×D269—41no—
165C4×C269—21no—
166C4×C269—22no—
167C4×C269—41no—
168C4×C269—41no—
169C4×C269—41no—
170C4×C269C2×#4111yescharacteristic
171C4×C269H(5,𝔽2)11yescharacteristic
172Dic269—21no—
173Dic269—21no—
174Dic269—21no—
175Dic269—41no—
176Dic269—41no—
177C2×C269—22no—
178C2×C269#54611yescharacteristic
179C2×C269C2×#13511yescharacteristic
180C2×C269#57711yescharacteristic
181D269—41no—
182D269—81no—
183D269—81no—
184C269#330111yescharacteristic, complemented, Sylow
185#3301—2691nomaximal, Sylow
186#553—2691no—
187#548—2691no—
188#488—2691no—
189#485—2691no—
190#481—2691no—
191#479—2691no—
192#466—2691no—
193#465—2691no—
194#463—2691no—
195#449—2691no—
196#448—2691no—
197C4×SD16—2691no—
198C8×D4—2691no—
199#416—2691no—
200C2×#103D26911yescharacteristic, complemented
201C2×#41—2691no—
202C22×Q8C2×D26911yescharacteristic
203C2×SD16—2691no—
204C2×SD16—2691no—
205C2×D8—2691no—
206C22×C8—2691no—
207C22×C8C2×D26911yescharacteristic
208#126—5381no—
209#125—2691no—
210#124—2691no—
211#124—5381no—
212#123—5381no—
213C22⋊Q8—2691no—
214C22⋊Q8—5381no—
215#121—2691no—
216#121—2691no—
217#121—2691no—
218#121—5381no—
219#121—5381no—
220C4×Q8—2691no—
221C4×D4—2691no—
222C4×D4—2691no—
223C4×D4—5381no—
224C4×D4—5381no—
225#117—2691no—
226C2×C4⋊C4C2×D26911yescharacteristic
227#107—2691no—
228#106—2691no—
229#106—2691no—
230C4⋊C8—2691no—
231#103—2691no—
232#103—2691no—
233#103C2×D26911yescharacteristic
234#103C2×D26911yescharacteristic
235#103C2×D26911yescharacteristic
236#103C2×D26911yescharacteristic
237#102—2691no—
238#102—2691no—
239#102—2691no—
240#102—2691no—
241C22⋊C8—2691no—
242C22⋊C8—2691no—
243C4×C8—2691no—
244#41—5382no—
245#41—10761no—
246C2×Q8—21no—
247C2×Q8—22no—
248C2×Q8—41no—
249C2×Q8C22×D26911yescharacteristic
250C2×Q8C22×D26911yescharacteristic
251C2×D4—2691no—
252C2×D4—2691no—
253C2×D4—2691no—
254C2×D4—5381no—
255C2×D4—5381no—
256C2×D4—5381no—
257C2×D4—5381no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—2691no—
261C22×C4—5381no—
262C22×C4—5381no—
263C22×C4C22×D26911yescharacteristic
264SD16—5382no—
265SD16—10761no—
266D8—10761no—
267C2×C8—41no—
268C2×C8—2691no—
269C2×C8—2691no—
270C2×C8—10761no—
271C2×C8C22×D26911yescharacteristic
272C2×C8C22×D26911yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—2691no—
275C4⋊C4—2691no—
276C4⋊C4—2691no—
277C4⋊C4—5381no—
278C4⋊C4—5381no—
279C4⋊C4—5381no—
280C4⋊C4—5381no—
281C4⋊C4C22×D26911yescharacteristic
282C4⋊C4C22×D26911yescharacteristic
283C22⋊C4—2691no—
284C22⋊C4—2691no—
285C22⋊C4—5381no—
286C22⋊C4—5381no—
287C22⋊C4—5381no—
288C22⋊C4—5381no—
289C22⋊C4—5381no—
290C22⋊C4—5381no—
291C22⋊C4—5381no—
292C22⋊C4—5381no—
293C42—2691no—
294C42—5381no—
295C42—5381no—
296C23—2691no—
297C23—5381no—
298C23—5381no—
299C23D4×D26911yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8—42no—
304Q8#1686440212yes—
305D4—5382no—
306D4—5381no—
307D4—5381no—
308D4—5381no—
309D4—5381no—
310D4—10762no—
311D4—10762no—
312D4—10762no—
313D4—21521no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—42no—
321C2×C4—81no—
322C2×C4—2691no—
323C2×C4—2691no—
324C2×C4—2691no—
325C2×C4—5381no—
326C2×C4—5381no—
327C2×C4—5381no—
328C2×C4—5381no—
329C2×C4—10762no—
330C2×C4—21521no—
331C2×C4D4×D26911yescharacteristic
332C2×C4C23×D26911yescharacteristic
333C8—21no—
334C8—21no—
335C8—5381no—
336C8—5381no—
337C22—21no—
338C22—21no—
339C22—5381no—
340C22—5381no—
341C22—5381no—
342C22—10761no—
343C22—10761no—
344C22—10761no—
345C22—10761no—
346C22—10761no—
347C22—10761no—
348C22#2257547612yes—
349C22C2×D4×D26911yescharacteristic
350C4—21no—
351C4—22no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—5381no—
356C4—5381no—
357C4—5381no—
358C4—10761no—
359C4—10761no—
360C4C2×#1686440211yescharacteristic
361C4#2257549811yescharacteristic
362C2—22no—
363C2—10761no—
364C2—21521no—
365C2—21521no—
366C2#3177124511yescharacteristic
367C2C2×#2257547611yescharacteristic
368C2#3177141111yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
FittingC2×#103×C269C2
socleC22×C269C22×D4
hypercenterC2×#103D269
hypocenterC269#3301
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. #31771303C2semidirect
2. #31771266C2semidirect
3. #31770961C2semidirect
4. #31770945C2semidirect
5. #31770923C2semidirect
6. #31770914C2semidirect
7. #31770841C2semidirect
8. #31770837C2semidirect
9. #31770823C2semidirect
10. #31770753C2semidirect
11. #31770744C2semidirect
12. #31770690C2semidirect
13. C8×C22⋊D269C2semidirect
14. #31770600C2semidirect
15. C2×#103×C269C2semidirect
184. C269#3301semidirect
200. C2×#103D269semidirect

Maximal subgroups

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

subgroupindex
#317713032
#317712662
#317709612
#317709452
#317709232
#317709142
#317708412
#317708372
#317708232
#317707532
#317707442
#317706902
C8×C22⋊D2692
#317706002
C2×#103×C2692
#3301269