Finite Group Databasebeta

← #46820558

Subgroups — #46820558

Order 34432.

504 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22575480C211yesmaximal, characteristic, complemented
2C2×#22575459C211yesmaximal, characteristic, complemented
3#31771185C211yesmaximal, characteristic, complemented
4#31771171C211yesmaximal, characteristic, complemented
5#31770859C211yesmaximal, characteristic, complemented
6#31770856C211yesmaximal, characteristic, complemented
7#31770853C211yesmaximal, characteristic, complemented
8#31770848C211yesmaximal, characteristic, complemented
9#31770841C211yesmaximal, characteristic, complemented
10#31770840C211yesmaximal, characteristic, complemented
11#31770837C211yesmaximal, characteristic, complemented
12#31770644C211yesmaximal, characteristic, complemented
13#31770600C211yesmaximal, characteristic, complemented
14#102×D269C211yesmaximal, characteristic, complemented
15#465×C269C211yesmaximal, characteristic, complemented
16C2×#16864403C2211yescharacteristic
17C2×#16864402C2211yescharacteristic
18C2×D4×D269C2211yescharacteristic
19#22575480—24no—
20C2×#16864389C2211yescharacteristic
21C2×D2152C2211yescharacteristic
22C2×#16864387C2211yescharacteristic
23#22575459—24no—
24C2×#16864386C2211yescharacteristic, complemented
25C2×#16864385C2211yescharacteristic
26C2×#16864385C2211yescharacteristic, complemented
27C2×C8×D269C2211yescharacteristic
28C2×C8×D269C2211yescharacteristic, complemented
29#22575449—21no—
30#22575439—21no—
31#22575431—21no—
32#22575429C2211yescharacteristic, complemented
33#22575428—21no—
34#22575428C2211yescharacteristic
35#22575428C2211yescharacteristic, complemented
36#22575427C2211yescharacteristic
37#22575427C2211yescharacteristic, complemented
38#22575426—21no—
39#22575426—21no—
40#22575424C2211yescharacteristic
41#22575423—21no—
42#22575421—21no—
43#22575411C2211yescharacteristic
44C4⋊C4×D269C2211yescharacteristic
45#22575387C2211yescharacteristic, complemented
46#22575386C2211yescharacteristic, complemented
47#22575384C2211yescharacteristic, complemented
48#22575377C2211yescharacteristic, complemented
49#22575375C2211yescharacteristic
50#22575375C2211yescharacteristic, complemented
51#22575374C2211yescharacteristic
52#22575373C2211yescharacteristic
53#22575373C2211yescharacteristic, complemented
54C2×SD16×C269C2211yescharacteristic
55C22×C8×C269C2211yescharacteristic, complemented
56C22⋊Q8×C269C2211yescharacteristic, complemented
57#121×C269C2211yescharacteristic
58#106×C269C2211yescharacteristic, complemented
59#103×C269C2211yescharacteristic, complemented
60#102×C269C2211yescharacteristic
61C23×D269—21no—
62#16864403—22no—
63#16864403—22no—
64#16864402—22no—
65#16864402—22no—
66C2×Dic538D411yescharacteristic
67C2×D1076—21no—
68C2×D1076—21no—
69C2×D1076—21no—
70C2×D1076D411yescharacteristic
71C2×D1076C2311yescharacteristic
72C2×D1076C2311yescharacteristic
73C2×C22⋊D269—21no—
74C2×C22⋊D269—21no—
75C2×C22⋊D269—21no—
76C2×C22⋊D269—21no—
77C2×C22⋊D269D411yescharacteristic
78C2×C22⋊D269D411yescharacteristic
79D4×D269—22no—
80D4×D269—22no—
81C2×C4×D269—21no—
82C2×C4×D269—21no—
83C2×C4×D269C2311yescharacteristic
84C2×C4×D269C2311yescharacteristic
85#16864389—22no—
86D2152—22no—
87#16864387—22no—
88#16864386—22no—
89#16864385—22no—
90#16864385D414yescomplemented
91C2×#14524130C2311yescharacteristic
92C2×#14524130C2311yescharacteristic
93C8×D269—22no—
94C8×D269—22no—
95C4⋊Dic269C2311yescharacteristic
96C4⋊Dic269C2311yescharacteristic
97#16864381—21no—
98#16864381—21no—
99C22⋊Dic269—21no—
100#16864379—21no—
101#16864379—21no—
102#16864379—21no—
103#16864379—21no—
104#16864379—21no—
105#16864379—21no—
106C4×Dic269—21no—
107C2×Q8×C269C2311yescharacteristic
108C2×D4×C269—21no—
109C2×D4×C269C2311yescharacteristic
110C22×C4×C269C2311yescharacteristic
111SD16×C269—22no—
112C2×C8×C269—22no—
113C2×C8×C269C2311yescharacteristic
114C2×C8×C269C2311yescharacteristic
115C4⋊C4×C269—21no—
116C4⋊C4×C269C2311yescharacteristic
117C4⋊C4×C269C2311yescharacteristic
118C22⋊C4×C269—21no—
119C22⋊C4×C269—21no—
120C22×D269—21no—
121C22×D269—21no—
122C22×D269—42no—
123C22×D269—81no—
124C22×D269—81no—
125C22×D269C2×D411yescharacteristic
126C22×D269C2×D411yescharacteristic
127Dic538—22no—
128D1076—22no—
129D1076—21no—
130D1076—21no—
131D1076—21no—
132D1076—21no—
133D1076—42no—
134D1076—81no—
135D1076—81no—
136C22⋊D269—22no—
137C22⋊D269—22no—
138C22⋊D269—42no—
139C22⋊D269—81no—
140C22⋊D269—81no—
141C22⋊D269—81no—
142C2×Dic269—21no—
143C2×Dic269—21no—
144C2×Dic269C2×D411yescharacteristic
145C2×Dic269C2×D411yescharacteristic
146C4×D269—21no—
147C4×D269—21no—
148C4×D269—42no—
149C4×D269—81no—
150C4×D269C2×D412yes—
151C4×D269#4112yes—
152#14524130—21no—
153#14524130C2×D412yes—
154C23×C269—21no—
155C23×C269C2×D411yescharacteristic
156Q8×C269—21no—
157Q8×C269—21no—
158D4×C269—21no—
159D4×C269—21no—
160D4×C269—81no—
161C2×C4×C269—21no—
162C2×C4×C269—21no—
163C2×C4×C269—21no—
164C2×C4×C269—21no—
165C2×C4×C269—21no—
166C2×C4×C269C2×D411yescharacteristic
167C2×C4×C269C2411yescharacteristic
168C8×C269—21no—
169C8×C269C2×D412yes—
170C22×C269—21no—
171C22×C269—21no—
172C22×C269—21no—
173C22×C269—41no—
174C22×C269—41no—
175C22×C269—41no—
176C22×C269C22×D411yescharacteristic
177C2×D269—21no—
178C2×D269—21no—
179C2×D269—21no—
180C2×D269—21no—
181C2×D269—21no—
182C2×D269—41no—
183C2×D269—41no—
184C2×D269—41no—
185C2×D269—41no—
186C2×D269—41no—
187C2×D269—41no—
188C2×D269—84no—
189C2×D269#12112yes—
190C4×C269—21no—
191C4×C269—41no—
192C4×C269—41no—
193C4×C269—41no—
194C4×C269C22×D411yescharacteristic
195C4×C269C2×#4111yescharacteristic
196Dic269—21no—
197Dic269—41no—
198Dic269—41no—
199Dic269#12112yes—
200C2×C269—41no—
201C2×C269—81no—
202C2×C269C2×#12111yescharacteristic
203C2×C269#57611yescharacteristic
204C2×C269#57711yescharacteristic
205D269—22no—
206D269—41no—
207D269—81no—
208D269—81no—
209C269#306211yescharacteristic, complemented, Sylow
210#3062—2691nomaximal, Sylow
211C2×AGL(1,ℤ/8)—2691no—
212C2×#131—2691no—
213#537—2691no—
214#535—2691no—
215#469—2691no—
216#469—2691no—
217#468—2691no—
218#468—2691no—
219#466—2691no—
220#466—2691no—
221#465—2691no—
222#465D26911yescharacteristic, complemented
223#428—2691no—
224#416—2691no—
225C2×#102—2691no—
226C2×#41—2691no—
227C2×#41—2691no—
228C22×D4—2691no—
229AGL(1,ℤ/8)—5384no—
230C2×SD16—2691no—
231C2×SD16C2×D26911yescharacteristic
232C2×D8—2691no—
233C2×D8—2691no—
234#131—5384no—
235C2×M16—2691no—
236C2×M16—2691no—
237C2×M16—2691no—
238C22×C8—2691no—
239C22×C8—2691no—
240C22×C8C2×D26911yescharacteristic, complemented
241#127—5381no—
242#124—5381no—
243C22⋊Q8—2691no—
244C22⋊Q8—5381no—
245C22⋊Q8C2×D26911yescharacteristic, complemented
246#121—2691no—
247#121—2691no—
248#121—2691no—
249#121—2691no—
250#121—2691no—
251#121—5381no—
252#121—5381no—
253#121—5381no—
254#121C2×D26911yescharacteristic
255#120—5381no—
256#120—5381no—
257#117—2691no—
258C2×C4⋊C4—2691no—
259#107—2691no—
260#107—2691no—
261#106—2691no—
262#106C2×D26911yescharacteristic, complemented
263#103—2691no—
264#103C2×D26911yescharacteristic, complemented
265#102—2691no—
266#102—2691no—
267#102—2691no—
268#102—2691no—
269#102—2691no—
270#102C2×D26911yescharacteristic
271C24—5381no—
272#41—5382no—
273#41—5382no—
274#41—5382no—
275#41—5382no—
276C2×Q8—2691no—
277C2×Q8C22×D26911yescharacteristic
278C2×D4—21no—
279C2×D4—2691no—
280C2×D4—2691no—
281C2×D4—2691no—
282C2×D4—2691no—
283C2×D4—2691no—
284C2×D4—5381no—
285C2×D4—5381no—
286C2×D4—5381no—
287C2×D4—5382no—
288C2×D4—5382no—
289C2×D4—5381no—
290C2×D4—5381no—
291C2×D4—5381no—
292C2×D4—5381no—
293C2×D4C22×D26911yescharacteristic
294C22×C4—2691no—
295C22×C4—2691no—
296C22×C4—5381no—
297C22×C4—5381no—
298C22×C4C22×D26911yescharacteristic
299SD16—22no—
300SD16—5382no—
301D8—5382no—
302D8—5382no—
303M16—2694no—
304M16—5382no—
305M16—5382no—
306C2×C8—22no—
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—2691no—
316C4⋊C4—5381no—
317C4⋊C4—5381no—
318C4⋊C4C22×D26911yescharacteristic
319C4⋊C4C22×D26911yescharacteristic
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—5381no—
323C22⋊C4—5381no—
324C22⋊C4—5381no—
325C22⋊C4—5381no—
326C22⋊C4—5381no—
327C22⋊C4—5381no—
328C22⋊C4—5381no—
329C42—5381no—
330C23—21no—
331C23—2691no—
332C23—2691no—
333C23—5381no—
334C23—5381no—
335C23—10762no—
336C23—21521no—
337C23—21521no—
338C23D4×D26911yescharacteristic
339Q8—21no—
340Q8—21no—
341Q8—5382no—
342D4—21no—
343D4—21no—
344D4—81no—
345D4—5382no—
346D4—5382no—
347D4—5382no—
348D4—5381no—
349D4—5381no—
350D4—5381no—
351D4—5381no—
352D4—10762no—
353D4—10762no—
354D4—21521no—
355D4—21521no—
356D4—21521no—
357D4—21521no—
358D4—21521no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—2691no—
365C2×C4—2692no—
366C2×C4—2692no—
367C2×C4—2691no—
368C2×C4—5381no—
369C2×C4—5381no—
370C2×C4—5381no—
371C2×C4—5381no—
372C2×C4—10762no—
373C2×C4—21521no—
374C2×C4D4×D26911yescharacteristic
375C2×C4C23×D26911yescharacteristic
376C8—21no—
377C8—2692no—
378C8—5381no—
379C8D4×D26912yes—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—2692no—
387C22—5381no—
388C22—5381no—
389C22—5381no—
390C22—5381no—
391C22—5381no—
392C22—10761no—
393C22—10761no—
394C22—10761no—
395C22—10761no—
396C22—10761no—
397C22—10761no—
398C22—21524no—
399C22C2×D4×D26911yescharacteristic
400C4—21no—
401C4—41no—
402C4—41no—
403C4—41no—
404C4—2692no—
405C4—5381no—
406C4—10761no—
407C4—10761no—
408C4C2×D4×D26911yescharacteristic
409C4#41×D26911yescharacteristic
410C2—41no—
411C2—81no—
412C2—5382no—
413C2—10761no—
414C2—21521no—
415C2—21521no—
416C2#121×D26911yescharacteristic
417C2#3177140711yescharacteristic
418C2#3177141111yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#465×C269C2
socleC22×C269C22×D4
hypercenter#465D269
hypocenterC269#3062
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. C2×#22575480C2semidirect
2. C2×#22575459C2semidirect
3. #31771185C2semidirect
4. #31771171C2semidirect
5. #31770859C2semidirect
6. #31770856C2semidirect
7. #31770853C2semidirect
8. #31770848C2semidirect
9. #31770841C2semidirect
10. #31770840C2semidirect
11. #31770837C2semidirect
12. #31770644C2semidirect
13. #31770600C2semidirect
14. #102×D269C2semidirect
15. #465×C269C2semidirect
24. C2×#16864386C22semidirect
26. C2×#16864385C22semidirect
28. C2×C8×D269C22semidirect
32. #22575429C22semidirect
35. #22575428C22semidirect
37. #22575427C22semidirect
45. #22575387C22semidirect
46. #22575386C22semidirect
47. #22575384C22semidirect
48. #22575377C22semidirect
50. #22575375C22semidirect
53. #22575373C22semidirect
55. C22×C8×C269C22semidirect
56. C22⋊Q8×C269C22semidirect
58. #106×C269C22semidirect
59. #103×C269C22semidirect
90. #16864385D4semidirect
209. C269#3062semidirect
222. #465D269semidirect
240. C22×C8C2×D269semidirect
245. C22⋊Q8C2×D269semidirect
262. #106C2×D269semidirect
264. #103C2×D269semidirect

Maximal subgroups

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

subgroupindex
C2×#225754802
C2×#225754592
#317711852
#317711712
#317708592
#317708562
#317708532
#317708482
#317708412
#317708402
#317708372
#317706442
#317706002
#102×D2692
#465×C2692
#3062269