Finite Group Databasebeta

← #46820383

Subgroups — #46820383

Order 34432.

526 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22575477C211yesmaximal, characteristic, complemented
2C2×D8×D269C211yesmaximal, characteristic, complemented
3#31771168C211yesmaximal, characteristic, complemented
4#31771077C211yesmaximal, characteristic, complemented
5#31770821C211yesmaximal, characteristic, complemented
6#31770820C211yesmaximal, characteristic, complemented
7#31770819C211yesmaximal, characteristic, complemented
8#31770818C211yesmaximal, characteristic, complemented
9#31770799C211yesmaximal, characteristic, complemented
10#31770798C211yesmaximal, characteristic, complemented
11#31770797C211yesmaximal, characteristic, complemented
12#31770630C211yesmaximal, characteristic, complemented
13#31770608C211yesmaximal, characteristic, complemented
14#31770598C211yesmaximal, characteristic, complemented
15#459×C269C211yesmaximal, characteristic, complemented
16C2×#16864401C2211yescharacteristic
17C2×D4×D269C2211yescharacteristic
18C2×D4×D269C2211yescharacteristic
19#22575477—24no—
20C2×#16864391C2211yescharacteristic, complemented
21C2×#16864390C2211yescharacteristic, complemented
22C2×D2152C2211yescharacteristic
23C2×#16864387C2211yescharacteristic
24C2×#16864387C2211yescharacteristic
25C2×#16864387C2211yescharacteristic, complemented
26D8×D269—24no—
27C2×#16864385C2211yescharacteristic
28C2×C8×D269C2211yescharacteristic
29#22575449C2211yescharacteristic, complemented
30#22575441C2211yescharacteristic, complemented
31#22575440C2211yescharacteristic, complemented
32#22575425—21no—
33#22575425—21no—
34#22575421—21no—
35#22575421—21no—
36C4×D1076C2211yescharacteristic, complemented
37D4×Dic269C2211yescharacteristic, complemented
38#22575415C2211yescharacteristic, complemented
39C4×C22⋊D269—21no—
40#22575413—21no—
41#22575411C2211yescharacteristic
42#22575410C2211yescharacteristic
43C2×#16864379—21no—
44C22⋊C4×D269—21no—
45C4⋊#14524130C2211yescharacteristic, complemented
46#22575382C2211yescharacteristic, complemented
47#22575382C2211yescharacteristic, complemented
48#22575378C2211yescharacteristic, complemented
49#22575376C2211yescharacteristic, complemented
50#22575375C2211yescharacteristic, complemented
51#22575374C2211yescharacteristic, complemented
52#22575374C2211yescharacteristic, complemented
53#22575373C2211yescharacteristic, complemented
54C2×D8×C269C2211yescharacteristic
55C2×D8×C269C2211yescharacteristic, complemented
56#127×C269C2211yescharacteristic, complemented
57C4×D4×C269C2211yescharacteristic, complemented
58C4⋊C8×C269C2211yescharacteristic, complemented
59#102×C269C2211yescharacteristic, complemented
60#102×C269C2211yescharacteristic, complemented
61C23×D269—21no—
62C23×D269—21no—
63#16864401—22no—
64#16864401—22no—
65C2×Dic538C2311yescharacteristic
66C2×D1076C2311yescharacteristic
67C2×D1076C2311yescharacteristic
68C2×C22⋊D269—21no—
69C2×C22⋊D269—21no—
70C2×C22⋊D269—21no—
71C2×C22⋊D269—21no—
72C2×C22⋊D269—21no—
73D4×D269—22no—
74D4×D269—22no—
75D4×D269—22no—
76D4×D269D414yescomplemented
77C22×Dic269—21no—
78C22×Dic269—21no—
79C2×C4×D269—21no—
80C2×C4×D269—21no—
81C2×C4×D269C2311yescharacteristic
82#16864391—22no—
83#16864390—22no—
84D2152—22no—
85#16864387—22no—
86#16864387—22no—
87#16864387—22no—
88#16864385—22no—
89C2×#14524130C2311yescharacteristic
90C2×#14524130C2311yescharacteristic
91C8×D269—22no—
92C4⋊Dic269C2311yescharacteristic
93#16864381D411yescharacteristic
94#16864381D411yescharacteristic
95C22⋊Dic269—21no—
96C22⋊Dic269—21no—
97C22⋊Dic269—21no—
98#16864379—21no—
99#16864379—21no—
100#16864379—21no—
101#16864379—21no—
102#16864379—21no—
103#16864379D411yescharacteristic
104#16864379D411yescharacteristic
105C4×Dic269—21no—
106C4×Dic269C2311yescharacteristic
107C2×D4×C269—21no—
108C2×D4×C269—21no—
109C2×D4×C269C2311yescharacteristic
110C2×D4×C269C2311yescharacteristic
111C2×D4×C269C2311yescharacteristic
112C22×C4×C269—21no—
113D8×C269—22no—
114D8×C269—22no—
115C2×C8×C269C2311yescharacteristic
116C2×C8×C269C2311yescharacteristic
117C4⋊C4×C269C2311yescharacteristic
118C22⋊C4×C269—21no—
119C42×C269C2311yescharacteristic
120C22×D269—21no—
121C22×D269—24no—
122C22×D269—21no—
123C22×D269—42no—
124C22×D269—81no—
125C22×D269—81no—
126C22×D269—81no—
127C22×D269—81no—
128C22×D269C2×D411yescharacteristic
129Dic538—21no—
130Dic538—21no—
131D1076—21no—
132D1076—21no—
133D1076—21no—
134D1076C2×D412yes—
135C22⋊D269—24no—
136C22⋊D269—42no—
137C22⋊D269—42no—
138C22⋊D269—81no—
139C22⋊D269—81no—
140C2×Dic269—21no—
141C2×Dic269—21no—
142C2×Dic269—42no—
143C2×Dic269—81no—
144C2×Dic269C2×D411yescharacteristic
145C2×Dic269C2×D411yescharacteristic
146C2×Dic269C2×D411yescharacteristic
147C4×D269—81no—
148C4×D269—81no—
149C4×D269C2×D412yes—
150C4×D269#4112yes—
151#14524130—21no—
152#14524130—21no—
153C23×C269—21no—
154C23×C269—21no—
155C23×C269—21no—
156D4×C269—21no—
157D4×C269—21no—
158D4×C269—21no—
159D4×C269—21no—
160D4×C269—21no—
161D4×C269—81no—
162D4×C269—81no—
163D4×C269C2×D412yes—
164C2×C4×C269—21no—
165C2×C4×C269—81no—
166C2×C4×C269C2×D411yescharacteristic
167C2×C4×C269C2×D411yescharacteristic
168C2×C4×C269C2411yescharacteristic
169C8×C269—21no—
170C8×C269—21no—
171C22×C269—22no—
172C22×C269—41no—
173C22×C269—41no—
174C22×C269—41no—
175C22×C269—41no—
176C22×C269—41no—
177C22×C269—41no—
178C22×C269—41no—
179C22×C269—41no—
180C22×C269C22×D411yescharacteristic
181C2×D269—21no—
182C2×D269—21no—
183C2×D269—22no—
184C2×D269—41no—
185C2×D269—41no—
186C2×D269—41no—
187C2×D269—41no—
188C2×D269—41no—
189C2×D269—84no—
190C2×D269—84no—
191C2×D269#12112yes—
192C4×C269—21no—
193C4×C269—21no—
194C4×C269—41no—
195C4×C269C22×D411yescharacteristic
196C4×C269C2×#4111yescharacteristic
197Dic269—21no—
198Dic269—21no—
199Dic269—41no—
200Dic269—41no—
201Dic269#12112yes—
202C2×C269—42no—
203C2×C269—81no—
204C2×C269—81no—
205C2×C269C2×#12111yescharacteristic
206C2×C269#57611yescharacteristic
207C2×C269#57611yescharacteristic
208D269—22no—
209D269—42no—
210D269—81no—
211C269#304111yescharacteristic, complemented, Sylow
212#3041—2691nomaximal, Sylow
213C2×AGL(1,ℤ/8)—2691no—
214C22×D8—2691no—
215#535—2691no—
216#518—2691no—
217#463—2691no—
218#463—2691no—
219#463—2691no—
220#463—2691no—
221#459—2691no—
222#459—2691no—
223#459—2691no—
224#459D26911yescharacteristic, complemented
225#424—2691no—
226#418—2691no—
227#416—2691no—
228C2×#41—2691no—
229C22×D4—2691no—
230C22×D4—2691no—
231AGL(1,ℤ/8)—5384no—
232C2×SD16—2691no—
233C2×SD16—2691no—
234C2×D8—2691no—
235C2×D8—2691no—
236C2×D8—2691no—
237C2×D8—2691no—
238C2×D8—5384no—
239C2×D8C2×D26911yescharacteristic
240C2×D8C2×D26911yescharacteristic, complemented
241C2×M16—2691no—
242C22×C8—2691no—
243#127—2691no—
244#127C2×D26911yescharacteristic, complemented
245#124—2691no—
246#124—2691no—
247#121—5381no—
248#121—5381no—
249#120—5381no—
250#120—5381no—
251C4×D4—2691no—
252C4×D4—2691no—
253C4×D4—2691no—
254C4×D4—5381no—
255C4×D4—5381no—
256C4×D4C2×D26911yescharacteristic, complemented
257#117—2691no—
258#117—2691no—
259C2×C22⋊C4—5381no—
260C2×C22⋊C4—5381no—
261C4⋊C8—2691no—
262C4⋊C8—2691no—
263C4⋊C8—2691no—
264C4⋊C8C2×D26911yescharacteristic, complemented
265#103—2691no—
266#103—2691no—
267#102—2691no—
268#102—2691no—
269#102—2691no—
270#102—2691no—
271#102C2×D26911yescharacteristic, complemented
272#102C2×D26911yescharacteristic, complemented
273C24—5381no—
274C24—5381no—
275#41—5382no—
276#41—5382no—
277C2×Q8—2691no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4—2694no—
281C2×D4—2691no—
282C2×D4—2691no—
283C2×D4—5382no—
284C2×D4—5382no—
285C2×D4—5382no—
286C2×D4—5381no—
287C2×D4—5381no—
288C2×D4—5381no—
289C2×D4—5381no—
290C2×D4—5381no—
291C2×D4C22×D26911yescharacteristic
292C2×D4C22×D26911yescharacteristic
293C2×D4C22×D26911yescharacteristic
294C22×C4—21no—
295C22×C4—2691no—
296C22×C4—5381no—
297C22×C4—5381no—
298C22×C4—5381no—
299C22×C4—5381no—
300SD16—5382no—
301SD16—5382no—
302D8—22no—
303D8—22no—
304D8—5382no—
305D8—5382no—
306D8—5382no—
307D8—5382no—
308M16—5382no—
309C2×C8—2691no—
310C2×C8—2691no—
311C2×C8—5382no—
312C2×C8C22×D26911yescharacteristic
313C2×C8C22×D26911yescharacteristic
314C4⋊C4—2691no—
315C4⋊C4—2691no—
316C4⋊C4—2691no—
317C4⋊C4C22×D26911yescharacteristic
318C22⋊C4—21no—
319C22⋊C4—2691no—
320C22⋊C4—2691no—
321C22⋊C4—5381no—
322C22⋊C4—5381no—
323C22⋊C4—5381no—
324C22⋊C4—5381no—
325C22⋊C4—5381no—
326C22⋊C4—5381no—
327C22⋊C4—5381no—
328C22⋊C4—5381no—
329C42—2691no—
330C42—5381no—
331C42C22×D26911yescharacteristic
332C23—21no—
333C23—21no—
334C23—21no—
335C23—2691no—
336C23—5384no—
337C23—5381no—
338C23—5381no—
339C23—10762no—
340C23—21521no—
341C23—21521no—
342C23—21521no—
343C23—21521no—
344Q8—5381no—
345Q8—5381no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—21no—
351D4—81no—
352D4—81no—
353D4—2692no—
354D4—5384no—
355D4—5381no—
356D4—5381no—
357D4—5381no—
358D4—10762no—
359D4—10762no—
360D4—21521no—
361D4—21521no—
362D4D4×D26912yes—
363C2×C4—21no—
364C2×C4—81no—
365C2×C4—2691no—
366C2×C4—2692no—
367C2×C4—2692no—
368C2×C4—2691no—
369C2×C4—2691no—
370C2×C4—5381no—
371C2×C4—5381no—
372C2×C4—10762no—
373C2×C4—21521no—
374C2×C4—21521no—
375C2×C4—21521no—
376C2×C4D4×D26911yescharacteristic
377C2×C4D4×D26911yescharacteristic
378C2×C4C23×D26911yescharacteristic
379C8—21no—
380C8—21no—
381C8—5381no—
382C8—5381no—
383C22—22no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—2692no—
393C22—5381no—
394C22—5381no—
395C22—5382no—
396C22—10761no—
397C22—10761no—
398C22—10761no—
399C22—10761no—
400C22—10761no—
401C22—21524no—
402C22—21524no—
403C22C2×D4×D26911yescharacteristic
404C4—21no—
405C4—21no—
406C4—41no—
407C4—2692no—
408C4—5381no—
409C4—5381no—
410C4—10761no—
411C4—10761no—
412C4C2×D4×D26911yescharacteristic
413C4#41×D26911yescharacteristic
414C2—42no—
415C2—81no—
416C2—81no—
417C2—5382no—
418C2—10762no—
419C2—21521no—
420C2#121×D26911yescharacteristic
421C2#3177140611yescharacteristic
422C2#3177140911yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#459×C269C2
socleC22×C269C22×D4
hypercenter#459D269
hypocenterC269#3041
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×#22575477C2semidirect
2. C2×D8×D269C2semidirect
3. #31771168C2semidirect
4. #31771077C2semidirect
5. #31770821C2semidirect
6. #31770820C2semidirect
7. #31770819C2semidirect
8. #31770818C2semidirect
9. #31770799C2semidirect
10. #31770798C2semidirect
11. #31770797C2semidirect
12. #31770630C2semidirect
13. #31770608C2semidirect
14. #31770598C2semidirect
15. #459×C269C2semidirect
20. C2×#16864391C22semidirect
21. C2×#16864390C22semidirect
25. C2×#16864387C22semidirect
29. #22575449C22semidirect
30. #22575441C22semidirect
31. #22575440C22semidirect
36. C4×D1076C22semidirect
37. D4×Dic269C22semidirect
38. #22575415C22semidirect
45. C4⋊#14524130C22semidirect
46. #22575382C22semidirect
47. #22575382C22semidirect
48. #22575378C22semidirect
49. #22575376C22semidirect
50. #22575375C22semidirect
51. #22575374C22semidirect
52. #22575374C22semidirect
53. #22575373C22semidirect
55. C2×D8×C269C22semidirect
56. #127×C269C22semidirect
57. C4×D4×C269C22semidirect
58. C4⋊C8×C269C22semidirect
59. #102×C269C22semidirect
60. #102×C269C22semidirect
76. D4×D269D4semidirect
211. C269#3041semidirect
224. #459D269semidirect
240. C2×D8C2×D269semidirect
244. #127C2×D269semidirect
256. C4×D4C2×D269semidirect
264. C4⋊C8C2×D269semidirect
271. #102C2×D269semidirect
272. #102C2×D269semidirect

Maximal subgroups

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

subgroupindex
C2×#225754772
C2×D8×D2692
#317711682
#317710772
#317708212
#317708202
#317708192
#317708182
#317707992
#317707982
#317707972
#317706302
#317706082
#317705982
#459×C2692
#3041269