Finite Group Databasebeta

← #46821034

Subgroups — #46821034

Order 34432.

430 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771152C211yesmaximal, characteristic, complemented
2C4×#16864403C211yesmaximal, characteristic, complemented
3#31770932C211yesmaximal, characteristic, complemented
4#31770928C211yesmaximal, characteristic, complemented
5#31770888C211yesmaximal, characteristic, complemented
6#31770884C211yesmaximal, characteristic, complemented
7#31770803C211yesmaximal, characteristic, complemented
8#31770799C211yesmaximal, characteristic, complemented
9#31770753C211yesmaximal, characteristic, complemented
10#31770749C211yesmaximal, characteristic, complemented
11#31770718C211yesmaximal, characteristic, complemented
12#31770715C211yesmaximal, characteristic, complemented
13#31770703C211yesmaximal, characteristic, complemented
14#31770660C211yesmaximal, characteristic, complemented
15#440×C269C211yesmaximal, characteristic, complemented
16C2×#16864403C2211yescharacteristic
17C2×#16864402—21no—
18C2×#16864389C2211yescharacteristic
19C2×D2152C2211yescharacteristic
20C2×#16864387C2211yescharacteristic
21#22575452C2211yescharacteristic
22#22575449C2211yescharacteristic
23#22575439—21no—
24#22575428C2211yescharacteristic
25#22575426—21no—
26#22575424C2211yescharacteristic
27Q8×Dic269C2211yescharacteristic
28C4×D1076—21no—
29C4×D1076C2211yescharacteristic
30C4×D1076C2211yescharacteristic
31#22575415—21no—
32#22575415C2211yescharacteristic
33C4×C22⋊D269—21no—
34#22575411—21no—
35#22575411C2211yescharacteristic
36C42×D269—21no—
37C42×D269C2211yescharacteristic
38#22575386C2211yescharacteristic
39#22575385C2211yescharacteristic
40#22575384C2211yescharacteristic
41#22575382C2211yescharacteristic
42#22575382C2211yescharacteristic
43#22575377C2211yescharacteristic
44#22575375C2211yescharacteristic
45#22575375C2211yescharacteristic
46#22575374C2211yescharacteristic
47#22575373C2211yescharacteristic
48#22575373C2211yescharacteristic
49#22575365C2211yescharacteristic
50#22575365C2211yescharacteristic
51#22575364C2211yescharacteristic
52C2×SD16×C269C2211yescharacteristic
53C4×Q8×C269C2211yescharacteristic
54C4×D4×C269C2211yescharacteristic
55#107×C269C2211yescharacteristic
56#103×C269C2211yescharacteristic
57#102×C269C2211yescharacteristic
58#97×C269C2211yescharacteristic
59#16864403—22no—
60#16864403—22no—
61#16864402—44no—
62C2×Dic538—21no—
63C2×D1076—21no—
64C2×D1076—21no—
65C2×D1076C2311yescharacteristic
66C2×D1076C2311yescharacteristic
67C2×C22⋊D269—21no—
68C2×C22⋊D269—21no—
69C2×C22⋊D269—21no—
70C2×C4×D269—21no—
71C2×C4×D269—21no—
72C2×C4×D269—21no—
73C2×C4×D269—21no—
74C2×C4×D269D411yescharacteristic
75C2×C4×D269D411yescharacteristic
76C2×C4×D269C2311yescharacteristic
77#16864389—22no—
78D2152—22no—
79#16864387—22no—
80C2×#14524130C2311yescharacteristic
81C2×#14524130C2311yescharacteristic
82C4⋊Dic269—21no—
83C4⋊Dic269C2311yescharacteristic
84C4⋊Dic269C2311yescharacteristic
85#16864381—21no—
86C22⋊Dic269—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×D4×C269C2311yescharacteristic
99C22×C4×C269—21no—
100SD16×C269—22no—
101C2×C8×C269C2311yescharacteristic
102C2×C8×C269C2311yescharacteristic
103C4⋊C4×C269—21no—
104C4⋊C4×C269C2311yescharacteristic
105C4⋊C4×C269C2311yescharacteristic
106C22⋊C4×C269—21no—
107C42×C269—21no—
108C42×C269C2311yescharacteristic
109C22×D269—21no—
110C22×D269—21no—
111C22×D269C2×D411yescharacteristic
112Dic538—42no—
113D1076—24no—
114D1076—21no—
115D1076—21no—
116D1076—21no—
117D1076—42no—
118D1076#4112yescomplemented
119C22⋊D269—42no—
120C22⋊D269—42no—
121C22⋊D269—42no—
122C2×Dic269—21no—
123C2×Dic269—21no—
124C2×Dic269C2×D411yescharacteristic
125C2×Dic269C2×D411yescharacteristic
126C2×Dic269C2×D411yescharacteristic
127C4×D269—24no—
128C4×D269—21no—
129C4×D269—21no—
130C4×D269—22no—
131C4×D269—41no—
132C4×D269—42no—
133C4×D269—42no—
134C4×D269—42no—
135#14524130—21no—
136#14524130—21no—
137C23×C269—21no—
138Q8×C269—21no—
139Q8×C269#4112yescomplemented
140D4×C269—21no—
141D4×C269—21no—
142C2×C4×C269—21no—
143C2×C4×C269—21no—
144C2×C4×C269—21no—
145C2×C4×C269—42no—
146C2×C4×C269C2×D411yescharacteristic
147C2×C4×C269C2×D411yescharacteristic
148C2×C4×C269C2411yescharacteristic
149C8×C269—21no—
150C8×C269—21no—
151C22×C269—41no—
152C22×C269—41no—
153C22×C269—41no—
154C22×C269C22×D411yescharacteristic
155C2×D269—21no—
156C2×D269—22no—
157C2×D269—21no—
158C2×D269—21no—
159C2×D269—41no—
160C2×D269—41no—
161C2×D269—41no—
162C2×D269—41no—
163C2×D269—41no—
164C4×C269—22no—
165C4×C269—21no—
166C4×C269—21no—
167C4×C269—41no—
168C4×C269—41no—
169C4×C269C2×#4111yescharacteristic
170C4×C269C2×#4111yescharacteristic
171Dic269—21no—
172Dic269—21no—
173Dic269—41no—
174Dic269—41no—
175Dic269AGL(1,ℤ/8)12yes—
176C2×C269—81no—
177C2×C269#52511yescharacteristic
178C2×C269C2×AGL(1,ℤ/8)11yescharacteristic
179C2×C269#57511yescharacteristic
180D269—41no—
181D269—42no—
182D269—81no—
183C269#311511yescharacteristic, complemented, Sylow
184#3115—2691nomaximal, Sylow
185#532—2691no—
186C4×#41—2691no—
187#482—2691no—
188#482—2691no—
189#475—2691no—
190#474—2691no—
191#460—2691no—
192#459—2691no—
193#449—2691no—
194#449—2691no—
195#442—2691no—
196#442—2691no—
197#440—2691no—
198#440D26911yescharacteristic, complemented
199#432—2691no—
200C2×#41—2691no—
201C2×#41—5381no—
202C2×SD16—2691no—
203C2×SD16C2×D26911yescharacteristic
204C2×D8—2691no—
205C2×D8—2691no—
206C4⋊Q8—2691no—
207#127—2691no—
208#124—5381no—
209#121—2691no—
210#121—2691no—
211#121—5381no—
212C4×Q8—2691no—
213C4×Q8C2×D26911yescharacteristic
214C4×D4—2691no—
215C4×D4—2691no—
216C4×D4—2691no—
217C4×D4—5381no—
218C4×D4—5381no—
219C4×D4—5381no—
220C4×D4C2×D26911yescharacteristic
221#117—2691no—
222#117—5381no—
223C2×C42—2691no—
224C2×C42—5381no—
225#107—2691no—
226#107C2×D26911yescharacteristic
227#106—2691no—
228#106—2691no—
229C4⋊C8—2691no—
230C4⋊C8—2691no—
231#103—2691no—
232#103C2×D26911yescharacteristic
233#102—2691no—
234#102—2691no—
235#102—2691no—
236#102—2691no—
237#102—2691no—
238#102C2×D26911yescharacteristic
239C22⋊C8—2691no—
240C22⋊C8—2691no—
241#97—2691no—
242#97C2×D26911yescharacteristic
243#41—5382no—
244#41—5382no—
245#41—10764no—
246C2×Q8—5381no—
247C2×Q8C22×D26911yescharacteristic
248C2×D4—2691no—
249C2×D4—2691no—
250C2×D4—5381no—
251C2×D4—5381no—
252C2×D4—5381no—
253C2×D4—5381no—
254C2×D4—5381no—
255C2×D4C22×D26911yescharacteristic
256C22×C4—21no—
257C22×C4—2691no—
258C22×C4—2691no—
259C22×C4—2691no—
260C22×C4—5381no—
261C22×C4—5381no—
262C22×C4—5381no—
263C22×C4—5381no—
264SD16—22no—
265SD16—5382no—
266D8—5382no—
267D8—5382no—
268C2×C8—2691no—
269C2×C8—2691no—
270C2×C8C22×D26911yescharacteristic
271C2×C8C22×D26911yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—2691no—
274C4⋊C4—2691no—
275C4⋊C4—5381no—
276C4⋊C4—5381no—
277C4⋊C4C22×D26911yescharacteristic
278C4⋊C4C22×D26911yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—5381no—
281C22⋊C4—5381no—
282C22⋊C4—5381no—
283C22⋊C4—5381no—
284C22⋊C4—5381no—
285C22⋊C4—5381no—
286C42—21no—
287C42—2691no—
288C42—2691no—
289C42—2691no—
290C42—5381no—
291C42—5381no—
292C42C22×D26911yescharacteristic
293C23—21no—
294C23—2691no—
295C23—5381no—
296C23—5381no—
297Q8—21no—
298Q8—10762no—
299Q8#1686440212yescomplemented
300D4—21no—
301D4—21no—
302D4—2692no—
303D4—5384no—
304D4—5381no—
305D4—5381no—
306D4—5381no—
307D4—10762no—
308D4—10762no—
309D4—10762no—
310D4—10762no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—42no—
315C2×C4—2691no—
316C2×C4—2691no—
317C2×C4—2691no—
318C2×C4—5382no—
319C2×C4—5384no—
320C2×C4—5381no—
321C2×C4—5381no—
322C2×C4—5381no—
323C2×C4—5381no—
324C2×C4—10761no—
325C2×C4—10762no—
326C2×C4—10762no—
327C2×C4—10762no—
328C2×C4D4×D26911yescharacteristic
329C2×C4D4×D26911yescharacteristic
330C2×C4C23×D26911yescharacteristic
331C8—21no—
332C8—21no—
333C8—5381no—
334C8—5381no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—5381no—
339C22—5382no—
340C22—5381no—
341C22—5381no—
342C22—10761no—
343C22—10761no—
344C22—10761no—
345C22—10761no—
346C22—10761no—
347C22C2×D4×D26911yescharacteristic
348C4—21no—
349C4—22no—
350C4—21no—
351C4—41no—
352C4—41no—
353C4—2692no—
354C4—5381no—
355C4—5381no—
356C4—10761no—
357C4—10761no—
358C4#41×D26911yescharacteristic
359C4C2×#1686440211yescharacteristic
360C2—81no—
361C2—10761no—
362C2—10762no—
363C2—21521no—
364C2#3177111411yescharacteristic
365C2AGL(1,ℤ/8)×D26911yescharacteristic
366C2#3177140411yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#440×C269C2
socleC22×C269C22×D4
hypercenter#440D269
hypocenterC269#3115
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #31771152C2semidirect
2. C4×#16864403C2semidirect
3. #31770932C2semidirect
4. #31770928C2semidirect
5. #31770888C2semidirect
6. #31770884C2semidirect
7. #31770803C2semidirect
8. #31770799C2semidirect
9. #31770753C2semidirect
10. #31770749C2semidirect
11. #31770718C2semidirect
12. #31770715C2semidirect
13. #31770703C2semidirect
14. #31770660C2semidirect
15. #440×C269C2semidirect
118. D1076#41semidirect
139. Q8×C269#41semidirect
183. C269#3115semidirect
198. #440D269semidirect
299. Q8#16864402semidirect

Maximal subgroups

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

subgroupindex
#317711522
C4×#168644032
#317709322
#317709282
#317708882
#317708842
#317708032
#317707992
#317707532
#317707492
#317707182
#317707152
#317707032
#317706602
#440×C2692
#3115269