Finite Group Databasebeta

← #46822594

Subgroups — #46822594

Order 34432.

504 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22575474C211yesmaximal, characteristic, complemented
2C2×SD16×D269C211yesmaximal, characteristic, complemented
3#31771267C211yesmaximal, characteristic, complemented
4#31771250C211yesmaximal, characteristic, complemented
5#31770989C211yesmaximal, characteristic, complemented
6#31770835C211yesmaximal, characteristic, complemented
7#31770835C211yesmaximal, characteristic, complemented
8#31770827C211yesmaximal, characteristic, complemented
9#31770820C211yesmaximal, characteristic, complemented
10#31770768C211yesmaximal, characteristic, complemented
11#31770762C211yesmaximal, characteristic, complemented
12#31770753C211yesmaximal, characteristic, complemented
13#31770740C211yesmaximal, characteristic, complemented
14C8×D1076C211yesmaximal, characteristic, complemented
15C4×SD16×C269C211yesmaximal, characteristic, complemented
16C2×#16864403C2211yescharacteristic, complemented
17C2×#16864401C2211yescharacteristic
18C2×Q8×D269C2211yescharacteristic
19C2×D4×D269C2211yescharacteristic
20#22575474—24no—
21C2×Dic1076C2211yescharacteristic, complemented
22C2×#16864392C2211yescharacteristic, complemented
23C2×#16864391C2211yescharacteristic
24C2×#16864391C2211yescharacteristic, complemented
25C2×#16864390C2211yescharacteristic
26C2×#16864389C2211yescharacteristic
27SD16×D269—24no—
28C2×D2152C2211yescharacteristic
29C2×#16864387C2211yescharacteristic
30C2×C8×D269C2211yescharacteristic
31C2×C8×D269C2211yescharacteristic, complemented
32#22575441—21no—
33#22575441C2211yescharacteristic
34#22575441C2211yescharacteristic, complemented
35#22575437—21no—
36#22575433—21no—
37#22575433C2211yescharacteristic
38#22575433C2211yescharacteristic, complemented
39#22575428—21no—
40#22575428C2211yescharacteristic
41#22575428C2211yescharacteristic
42#22575427—21no—
43#22575423—21no—
44C4×D1076—21no—
45C4×D1076C2211yescharacteristic
46C2×#16864379—21no—
47C4⋊#14524130C2211yescharacteristic, complemented
48#22575376C2211yescharacteristic, complemented
49#22575376C2211yescharacteristic, complemented
50#22575373C2211yescharacteristic
51#22575373C2211yescharacteristic, complemented
52#22575365C2211yescharacteristic
53#22575365C2211yescharacteristic, complemented
54C2×SD16×C269C2211yescharacteristic
55C4×Q8×C269C2211yescharacteristic, complemented
56C4×D4×C269C2211yescharacteristic
57#106×C269C2211yescharacteristic, complemented
58#103×C269C2211yescharacteristic, complemented
59#102×C269C2211yescharacteristic
60C4×C8×C269C2211yescharacteristic, complemented
61C23×D269—21no—
62#16864403—22no—
63#16864403—41no—
64#16864401—22no—
65#16864401—41no—
66C2×Dic538—21no—
67C2×Dic538C2311yescharacteristic
68C2×Dic538C2311yescharacteristic
69Q8×D269—22no—
70Q8×D269—41no—
71C2×D1076—21no—
72C2×D1076—21no—
73C2×D1076—21no—
74C2×D1076D411yescharacteristic
75C2×D1076C2311yescharacteristic
76C2×D1076C2311yescharacteristic
77C2×C22⋊D269—21no—
78C2×C22⋊D269—21no—
79D4×D269—22no—
80D4×D269—41no—
81C22×Dic269—21no—
82C2×C4×D269—21no—
83C2×C4×D269—21no—
84C2×C4×D269C2311yescharacteristic
85C2×C4×D269C2311yescharacteristic
86Dic1076—41no—
87#16864392—22no—
88#16864391—22no—
89#16864391—22no—
90#16864390—22no—
91#16864389—22no—
92D2152—41no—
93#16864387—22no—
94C2×#14524130C2311yescharacteristic
95C2×#14524130C2311yescharacteristic
96C8×D269—22no—
97C8×D269—22no—
98C4⋊Dic269—21no—
99C4⋊Dic269—21no—
100C4⋊Dic269D411yescharacteristic
101#16864379—21no—
102#16864379—21no—
103#16864379—21no—
104#16864379—21no—
105#16864379—21no—
106#16864379—21no—
107#16864379—21no—
108#16864379—21no—
109#16864379D411yescharacteristic
110#16864379D411yescharacteristic
111C2×Q8×C269C2311yescharacteristic
112C2×D4×C269C2311yescharacteristic
113C22×C4×C269—21no—
114SD16×C269D414yescomplemented
115C2×C8×C269C2311yescharacteristic
116C2×C8×C269C2311yescharacteristic
117C4⋊C4×C269—21no—
118C4⋊C4×C269C2311yescharacteristic
119C4⋊C4×C269C2311yescharacteristic
120C22⋊C4×C269—21no—
121C42×C269—21no—
122C42×C269C2311yescharacteristic
123C22×D269—21no—
124C22×D269—21no—
125C22×D269—42no—
126C22×D269—42no—
127C22×D269—81no—
128C22×D269C2×D411yescharacteristic
129C22×D269C2×D411yescharacteristic
130Dic538—21no—
131Dic538—21no—
132Dic538—21no—
133Dic538—21no—
134Dic538—42no—
135D1076—22no—
136D1076—21no—
137D1076—21no—
138D1076—21no—
139D1076—21no—
140D1076—42no—
141D1076—42no—
142D1076—81no—
143C22⋊D269—42no—
144C22⋊D269—42no—
145C2×Dic269—21no—
146C2×Dic269—21no—
147C2×Dic269—42no—
148C2×Dic269C2×D411yescharacteristic
149C2×Dic269C2×D411yescharacteristic
150C4×D269—21no—
151C4×D269—21no—
152C4×D269—21no—
153C4×D269—21no—
154C4×D269—42no—
155C4×D269—42no—
156#14524130—21no—
157#14524130—21no—
158C23×C269—21no—
159Q8×C269—21no—
160Q8×C269C2×D412yes—
161D4×C269—21no—
162D4×C269C2×D412yes—
163C2×C4×C269—21no—
164C2×C4×C269—21no—
165C2×C4×C269—21no—
166C2×C4×C269—81no—
167C2×C4×C269C2×D411yescharacteristic
168C2×C4×C269C2×D411yescharacteristic
169C2×C4×C269C2411yescharacteristic
170C8×C269—21no—
171C8×C269C2×D412yes—
172C22×C269—22no—
173C22×C269—41no—
174C22×C269—41no—
175C22×C269C22×D411yescharacteristic
176C2×D269—21no—
177C2×D269—21no—
178C2×D269—21no—
179C2×D269—21no—
180C2×D269—21no—
181C2×D269—41no—
182C2×D269—41no—
183C2×D269—41no—
184C2×D269—41no—
185C2×D269—41no—
186C2×D269—41no—
187C2×D269—84no—
188C2×D269#13512yescomplemented
189C4×C269—22no—
190C4×C269—21no—
191C4×C269—21no—
192C4×C269—41no—
193C4×C269—41no—
194C4×C269C22×D411yescharacteristic
195C4×C269H(5,𝔽2)11yescharacteristic
196Dic269—21no—
197Dic269—21no—
198Dic269—41no—
199Dic269—41no—
200C2×C269—42no—
201C2×C269D4211yescharacteristic
202C2×C269C2×#13511yescharacteristic
203C2×C269#57711yescharacteristic
204D269—22no—
205D269—41no—
206D269—81no—
207D269—81no—
208C269#328211yescharacteristic, complemented, Sylow
209#3282—2691nomaximal, Sylow
210C2×#135—2691no—
211C22×SD16—2691no—
212#548—2691no—
213#546—2691no—
214#495—2691no—
215#465—2691no—
216#465—2691no—
217#464—2691no—
218#463—2691no—
219#452—2691no—
220#451—2691no—
221#449—2691no—
222#447—2691no—
223C4×SD16D26911yescharacteristic, complemented
224C8×D4—2691no—
225C2×#41—2691no—
226C2×#41—2691no—
227C22×Q8—2691no—
228C22×D4—2691no—
229#135—5384no—
230C2×Q16—2691no—
231C2×Q16—2691no—
232C2×SD16—2691no—
233C2×SD16—2691no—
234C2×SD16—2691no—
235C2×SD16—2691no—
236C2×SD16—5384no—
237C2×SD16C2×D26911yescharacteristic
238C2×D8—2691no—
239C2×D8—2691no—
240C22×C8—2691no—
241C22×C8—2691no—
242#124—2691no—
243#124—2691no—
244#124—5381no—
245#123—5381no—
246C22⋊Q8—2691no—
247C22⋊Q8—2691no—
248C22⋊Q8—5381no—
249#121—2691no—
250#121—2691no—
251#121—5381no—
252#121—5381no—
253#120—5381no—
254C4×Q8C2×D26911yescharacteristic, complemented
255C4×D4—2691no—
256C4×D4—5381no—
257C4×D4C2×D26911yescharacteristic
258C2×C22⋊C4—5381no—
259#106C2×D26911yescharacteristic, complemented
260C4⋊C8—2691no—
261#103—2691no—
262#103—2691no—
263#103C2×D26911yescharacteristic, complemented
264#102—2691no—
265#102—2691no—
266#102C2×D26911yescharacteristic
267C22⋊C8—2691no—
268C22⋊C8—2691no—
269C4×C8C2×D26911yescharacteristic, complemented
270C24—5381no—
271#41—5382no—
272#41—5382no—
273#41—10761no—
274#41—10761no—
275C2×Q8—2691no—
276C2×Q8—2691no—
277C2×Q8—5381no—
278C2×Q8—5382no—
279C2×Q8—10761no—
280C2×Q8C22×D26911yescharacteristic
281C2×D4—2691no—
282C2×D4—2691no—
283C2×D4—2691no—
284C2×D4—5381no—
285C2×D4—5381no—
286C2×D4—5381no—
287C2×D4—5381no—
288C2×D4—5382no—
289C2×D4—5381no—
290C2×D4—10761no—
291C2×D4C22×D26911yescharacteristic
292C22×C4—21no—
293C22×C4—2691no—
294C22×C4—2691no—
295C22×C4—5381no—
296C22×C4—5381no—
297C22×C4—5381no—
298Q16—5382no—
299Q16—10761no—
300SD16—5382no—
301SD16—5382no—
302SD16—5382no—
303SD16—5382no—
304SD16D107614yescomplemented
305D8—5382no—
306D8—10761no—
307C2×C8—2691no—
308C2×C8—2691no—
309C2×C8—5382no—
310C2×C8—5382no—
311C2×C8C22×D26911yescharacteristic
312C2×C8C22×D26911yescharacteristic
313C4⋊C4—21no—
314C4⋊C4—2691no—
315C4⋊C4—5381no—
316C4⋊C4—5381no—
317C4⋊C4C22×D26911yescharacteristic
318C4⋊C4C22×D26911yescharacteristic
319C22⋊C4—21no—
320C22⋊C4—2691no—
321C22⋊C4—2691no—
322C22⋊C4—5381no—
323C22⋊C4—5381no—
324C22⋊C4—5381no—
325C22⋊C4—5381no—
326C22⋊C4—5381no—
327C22⋊C4—5381no—
328C22⋊C4—5381no—
329C22⋊C4—5381no—
330C42—21no—
331C42C22×D26911yescharacteristic
332C23—21no—
333C23—2691no—
334C23—2691no—
335C23—5381no—
336C23—5381no—
337C23—10762no—
338C23—10762no—
339C23—21521no—
340Q8—21no—
341Q8—5381no—
342Q8—5381no—
343Q8—5381no—
344Q8—5381no—
345Q8—10762no—
346Q8C2×D107612yes—
347D4—21no—
348D4—5382no—
349D4—5381no—
350D4—5381no—
351D4—5381no—
352D4—5381no—
353D4—10762no—
354D4—10762no—
355D4—10762no—
356D4—10762no—
357D4—21521no—
358D4C2×D107612yes—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—81no—
363C2×C4—2691no—
364C2×C4—2691no—
365C2×C4—5381no—
366C2×C4—5381no—
367C2×C4—5381no—
368C2×C4—5381no—
369C2×C4—5381no—
370C2×C4—5381no—
371C2×C4—10762no—
372C2×C4—10762no—
373C2×C4—10762no—
374C2×C4D4×D26911yescharacteristic
375C2×C4D4×D26911yescharacteristic
376C2×C4C23×D26911yescharacteristic
377C8—21no—
378C8—5381no—
379C8—5381no—
380C8C2×D107612yes—
381C22—22no—
382C22—41no—
383C22—41no—
384C22—2692no—
385C22—5381no—
386C22—5381no—
387C22—5381no—
388C22—5381no—
389C22—5381no—
390C22—10761no—
391C22—10761no—
392C22—10761no—
393C22—10761no—
394C22—10761no—
395C22—10761no—
396C22—21524no—
397C22C2×D4×D26911yescharacteristic
398C4—21no—
399C4—22no—
400C4—21no—
401C4—41no—
402C4—41no—
403C4—5381no—
404C4—5381no—
405C4—10761no—
406C4—10761no—
407C4C22×D107611yescharacteristic
408C4#2257549911yescharacteristic
409C2—42no—
410C2—5382no—
411C2—10761no—
412C2—21521no—
413C2—21521no—
414C2D4×D107611yescharacteristic
415C2#135×D26911yescharacteristic
416C2#3177141111yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
FittingC4×SD16×C269C2
socleC22×C269C22×D4
hypercenterC4×SD16D269
hypocenterC269#3282
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#22575474C2semidirect
2. C2×SD16×D269C2semidirect
3. #31771267C2semidirect
4. #31771250C2semidirect
5. #31770989C2semidirect
6. #31770835C2semidirect
7. #31770835C2semidirect
8. #31770827C2semidirect
9. #31770820C2semidirect
10. #31770768C2semidirect
11. #31770762C2semidirect
12. #31770753C2semidirect
13. #31770740C2semidirect
14. C8×D1076C2semidirect
15. C4×SD16×C269C2semidirect
16. C2×#16864403C22semidirect
21. C2×Dic1076C22semidirect
22. C2×#16864392C22semidirect
24. C2×#16864391C22semidirect
31. C2×C8×D269C22semidirect
34. #22575441C22semidirect
38. #22575433C22semidirect
47. C4⋊#14524130C22semidirect
48. #22575376C22semidirect
49. #22575376C22semidirect
51. #22575373C22semidirect
53. #22575365C22semidirect
55. C4×Q8×C269C22semidirect
57. #106×C269C22semidirect
58. #103×C269C22semidirect
60. C4×C8×C269C22semidirect
114. SD16×C269D4semidirect
188. C2×D269#135semidirect
208. C269#3282semidirect
223. C4×SD16D269semidirect
254. C4×Q8C2×D269semidirect
259. #106C2×D269semidirect
263. #103C2×D269semidirect
269. C4×C8C2×D269semidirect
304. SD16D1076semidirect

Maximal subgroups

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

subgroupindex
C2×#225754742
C2×SD16×D2692
#317712672
#317712502
#317709892
#317708352
#317708272
#317708202
#317707682
#317707622
#317707532
#317707402
C8×D10762
C4×SD16×C2692
#3282269