Finite Group Databasebeta

← #46821032

Subgroups — #46821032

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×#16864401C211yesmaximal, characteristic, complemented
3#31770931C211yesmaximal, characteristic, complemented
4#31770927C211yesmaximal, characteristic, complemented
5#31770889C211yesmaximal, characteristic, complemented
6#31770883C211yesmaximal, characteristic, complemented
7#31770804C211yesmaximal, characteristic, complemented
8#31770798C211yesmaximal, characteristic, complemented
9#31770751C211yesmaximal, characteristic, complemented
10#31770747C211yesmaximal, characteristic, complemented
11#31770715C211yesmaximal, characteristic, complemented
12#31770707C211yesmaximal, characteristic, complemented
13#31770705C211yesmaximal, characteristic, complemented
14#31770660C211yesmaximal, characteristic, complemented
15#442×C269C211yesmaximal, characteristic, complemented
16C2×#16864402—21no—
17C2×#16864401C2211yescharacteristic
18C2×#16864391C2211yescharacteristic
19C2×#16864390C2211yescharacteristic
20C2×#16864387C2211yescharacteristic
21#22575452C2211yescharacteristic
22#22575449C2211yescharacteristic
23#22575439—21no—
24#22575428C2211yescharacteristic
25#22575426—21no—
26#22575424C2211yescharacteristic
27C4×Dic538C2211yescharacteristic
28#22575418C2211yescharacteristic
29C4×D1076C2211yescharacteristic
30D4×Dic269C2211yescharacteristic
31C4×C22⋊D269—21no—
32C4×C22⋊D269—21no—
33#22575413—21no—
34#22575411C2211yescharacteristic
35#22575409—21no—
36C2×C4×Dic269—21no—
37C42×D269C2211yescharacteristic
38#22575387C2211yescharacteristic
39#22575386C2211yescharacteristic
40#22575384C2211yescharacteristic
41#22575382C2211yescharacteristic
42#22575382C2211yescharacteristic
43#22575378C2211yescharacteristic
44#22575376C2211yescharacteristic
45#22575375C2211yescharacteristic
46#22575374C2211yescharacteristic
47#22575374C2211yescharacteristic
48#22575373C2211yescharacteristic
49#22575365C2211yescharacteristic
50#22575365C2211yescharacteristic
51#22575364C2211yescharacteristic
52C2×D8×C269C2211yescharacteristic
53C4×D4×C269C2211yescharacteristic
54C4×D4×C269C2211yescharacteristic
55#106×C269C2211yescharacteristic
56#102×C269C2211yescharacteristic
57#102×C269C2211yescharacteristic
58#97×C269C2211yescharacteristic
59#16864402—44no—
60#16864401—22no—
61#16864401—22no—
62C2×Dic538—21no—
63C2×Dic538C2311yescharacteristic
64C2×D1076—21no—
65C2×D1076C2311yescharacteristic
66C2×C22⋊D269—21no—
67C2×C22⋊D269—21no—
68C2×C22⋊D269—21no—
69C2×C22⋊D269—21no—
70C22×Dic269—21no—
71C22×Dic269—21no—
72C2×C4×D269—21no—
73C2×C4×D269D411yescharacteristic
74C2×C4×D269D411yescharacteristic
75C2×C4×D269C2311yescharacteristic
76#16864391—22no—
77#16864390—22no—
78#16864387—22no—
79C2×#14524130C2311yescharacteristic
80C2×#14524130C2311yescharacteristic
81C4⋊Dic269C2311yescharacteristic
82C4⋊Dic269C2311yescharacteristic
83#16864381—21no—
84#16864381—21no—
85#16864381—21no—
86C22⋊Dic269—21no—
87C22⋊Dic269—21no—
88#16864379—21no—
89#16864379—21no—
90#16864379—21no—
91C4×Dic269—21no—
92C4×Dic269—21no—
93C4×Dic269—21no—
94C4×Dic269D411yescharacteristic
95C4×Dic269D411yescharacteristic
96C4×Dic269C2311yescharacteristic
97C2×D4×C269C2311yescharacteristic
98C2×D4×C269C2311yescharacteristic
99C22×C4×C269—21no—
100C22×C4×C269—21no—
101D8×C269—22no—
102C2×C8×C269C2311yescharacteristic
103C2×C8×C269C2311yescharacteristic
104C4⋊C4×C269C2311yescharacteristic
105C4⋊C4×C269C2311yescharacteristic
106C22⋊C4×C269—21no—
107C22⋊C4×C269—21no—
108C42×C269C2311yescharacteristic
109C22×D269—21no—
110C22×D269C2×D411yescharacteristic
111Dic538—21no—
112Dic538—42no—
113Dic538#4112yescomplemented
114D1076—21no—
115D1076—21no—
116D1076—42no—
117C22⋊D269—24no—
118C22⋊D269—42no—
119C22⋊D269—42no—
120C22⋊D269—42no—
121C2×Dic269—24no—
122C2×Dic269—21no—
123C2×Dic269—21no—
124C2×Dic269—21no—
125C2×Dic269—42no—
126C2×Dic269C2×D411yescharacteristic
127C2×Dic269C2×D411yescharacteristic
128C2×Dic269C2×D411yescharacteristic
129C4×D269—21no—
130C4×D269—21no—
131C4×D269—22no—
132C4×D269—41no—
133C4×D269—42no—
134#14524130—21no—
135#14524130—21no—
136C23×C269—21no—
137C23×C269—21no—
138D4×C269—21no—
139D4×C269—21no—
140D4×C269—21no—
141D4×C269#4112yescomplemented
142C2×C4×C269—21no—
143C2×C4×C269—21no—
144C2×C4×C269—42no—
145C2×C4×C269—42no—
146C2×C4×C269C2×D411yescharacteristic
147C2×C4×C269C2×D411yescharacteristic
148C2×C4×C269C2411yescharacteristic
149C8×C269—21no—
150C8×C269—21no—
151C22×C269—22no—
152C22×C269—41no—
153C22×C269—41no—
154C22×C269—41no—
155C22×C269—41no—
156C22×C269—41no—
157C22×C269C22×D411yescharacteristic
158C2×D269—21no—
159C2×D269—21no—
160C2×D269—21no—
161C2×D269—41no—
162C2×D269—41no—
163C2×D269—41no—
164C4×C269—21no—
165C4×C269—21no—
166C4×C269—41no—
167C4×C269—41no—
168C4×C269C2×#4111yescharacteristic
169C4×C269C2×#4111yescharacteristic
170Dic269—21no—
171Dic269—22no—
172Dic269—21no—
173Dic269—41no—
174Dic269—41no—
175Dic269AGL(1,ℤ/8)12yes—
176C2×C269—42no—
177C2×C269—81no—
178C2×C269#52511yescharacteristic
179C2×C269C2×AGL(1,ℤ/8)11yescharacteristic
180C2×C269#57511yescharacteristic
181D269—41no—
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#442D26911yescharacteristic, complemented
197#440—2691no—
198#440—2691no—
199#432—2691no—
200C2×#41—2691no—
201C2×#41—5381no—
202C2×SD16—2691no—
203C2×SD16—2691no—
204C2×D8—2691no—
205C2×D8C2×D26911yescharacteristic
206C4⋊Q8—2691no—
207#127—2691no—
208#124—5381no—
209#121—2691no—
210#121—2691no—
211#121—5381no—
212C4×Q8—2691no—
213C4×Q8—2691no—
214C4×D4—2691no—
215C4×D4—2691no—
216C4×D4—5381no—
217C4×D4—5381no—
218C4×D4—5381no—
219C4×D4C2×D26911yescharacteristic
220C4×D4C2×D26911yescharacteristic
221#117—2691no—
222#117—5381no—
223C2×C42—2691no—
224C2×C42—5381no—
225#107—2691no—
226#107—2691no—
227#106—2691no—
228#106C2×D26911yescharacteristic
229C4⋊C8—2691no—
230C4⋊C8—2691no—
231#103—2691no—
232#103—2691no—
233#102—2691no—
234#102—2691no—
235#102—2691no—
236#102—2691no—
237#102C2×D26911yescharacteristic
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—2691no—
247C2×Q8—5381no—
248C2×D4—2691no—
249C2×D4—5381no—
250C2×D4—5381no—
251C2×D4—5381no—
252C2×D4—5381no—
253C2×D4—5381no—
254C2×D4C22×D26911yescharacteristic
255C2×D4C22×D26911yescharacteristic
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—2691no—
259C22×C4—2691no—
260C22×C4—2691no—
261C22×C4—5381no—
262C22×C4—5381no—
263C22×C4—5381no—
264SD16—5382no—
265SD16—5382no—
266D8—22no—
267D8—5382no—
268C2×C8—2691no—
269C2×C8—2691no—
270C2×C8C22×D26911yescharacteristic
271C2×C8C22×D26911yescharacteristic
272C4⋊C4—2691no—
273C4⋊C4—2691no—
274C4⋊C4—5381no—
275C4⋊C4—5381no—
276C4⋊C4—5381no—
277C4⋊C4C22×D26911yescharacteristic
278C4⋊C4C22×D26911yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—5381no—
282C22⋊C4—5381no—
283C22⋊C4—5381no—
284C22⋊C4—5381no—
285C22⋊C4—5381no—
286C42—2691no—
287C42—2691no—
288C42—2691no—
289C42—5381no—
290C42—5381no—
291C42—5381no—
292C42C22×D26911yescharacteristic
293C23—21no—
294C23—21no—
295C23—2691no—
296C23—5381no—
297Q8—2692no—
298Q8—5381no—
299Q8—10762no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—5384no—
304D4—5381no—
305D4—5381no—
306D4—10762no—
307D4—10762no—
308D4—10762no—
309D4—10762no—
310D4#1686440212yescomplemented
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
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—5381no—
325C2×C4—10761no—
326C2×C4—10762no—
327C2×C4—10762no—
328C2×C4D4×D26911yescharacteristic
329C2×C4D4×D26911yescharacteristic
330C2×C4C23×D26911yescharacteristic
331C8—21no—
332C8—21no—
333C8—5381no—
334C8—5381no—
335C22—22no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—5381no—
342C22—5381no—
343C22—5381no—
344C22—10761no—
345C22—10761no—
346C22—10761no—
347C22C2×D4×D26911yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—2692no—
353C4—5381no—
354C4—5381no—
355C4—5382no—
356C4—10761no—
357C4—10761no—
358C4#41×D26911yescharacteristic
359C4C2×#1686440211yescharacteristic
360C2—42no—
361C2—81no—
362C2—10761no—
363C2—21521no—
364C2#3177111411yescharacteristic
365C2AGL(1,ℤ/8)×D26911yescharacteristic
366C2#3177140111yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#442×C269C2
socleC22×C269C22×D4
hypercenter#442D269
hypocenterC269#3115
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #31771152C2semidirect
2. C4×#16864401C2semidirect
3. #31770931C2semidirect
4. #31770927C2semidirect
5. #31770889C2semidirect
6. #31770883C2semidirect
7. #31770804C2semidirect
8. #31770798C2semidirect
9. #31770751C2semidirect
10. #31770747C2semidirect
11. #31770715C2semidirect
12. #31770707C2semidirect
13. #31770705C2semidirect
14. #31770660C2semidirect
15. #442×C269C2semidirect
113. Dic538#41semidirect
141. D4×C269#41semidirect
183. C269#3115semidirect
196. #442D269semidirect
310. D4#16864402semidirect

Maximal subgroups

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

subgroupindex
#317711522
C4×#168644012
#317709312
#317709272
#317708892
#317708832
#317708042
#317707982
#317707512
#317707472
#317707152
#317707072
#317707052
#317706602
#442×C2692
#3115269