Finite Group Databasebeta

← #46822565

Subgroups — #46822565

Order 34432.

526 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22575474C211yesmaximal, characteristic, complemented
2C2×D8×D269C211yesmaximal, characteristic, complemented
3#31771250C211yesmaximal, characteristic, complemented
4#31771248C211yesmaximal, characteristic, complemented
5#31770987C211yesmaximal, characteristic, complemented
6#31770845C211yesmaximal, characteristic, complemented
7#31770840C211yesmaximal, characteristic, complemented
8#31770821C211yesmaximal, characteristic, complemented
9#31770757C211yesmaximal, characteristic, complemented
10#31770754C211yesmaximal, characteristic, complemented
11#31770753C211yesmaximal, characteristic, complemented
12#31770747C211yesmaximal, characteristic, complemented
13C4×#16864387C211yesmaximal, characteristic, complemented
14#31770670C211yesmaximal, characteristic, complemented
15#463×C269C211yesmaximal, characteristic, complemented
16C2×#16864403C2211yescharacteristic, complemented
17C2×#16864401C2211yescharacteristic, complemented
18C2×D4×D269C2211yescharacteristic
19C2×D4×D269C2211yescharacteristic
20#22575474—24no—
21C2×#16864392C2211yescharacteristic, complemented
22C2×#16864391C2211yescharacteristic, complemented
23C2×#16864390C2211yescharacteristic, complemented
24C2×#16864389C2211yescharacteristic, complemented
25C2×D2152C2211yescharacteristic
26C2×#16864387C2211yescharacteristic
27C2×#16864387C2211yescharacteristic
28D8×D269—24no—
29C2×C8×D269C2211yescharacteristic
30C2×C8×D269C2211yescharacteristic, complemented
31#22575441C2211yescharacteristic, complemented
32#22575437—21no—
33#22575435—21no—
34#22575433C2211yescharacteristic
35#22575429C2211yescharacteristic
36#22575428C2211yescharacteristic, complemented
37#22575427—21no—
38#22575426—21no—
39#22575424C2211yescharacteristic, complemented
40#22575423—21no—
41#22575423—21no—
42C4×D1076C2211yescharacteristic
43C4×D1076C2211yescharacteristic, complemented
44C2×#16864379—21no—
45C22⋊C4×D269—21no—
46#22575386C2211yescharacteristic, complemented
47#22575378C2211yescharacteristic, complemented
48#22575375C2211yescharacteristic, complemented
49#22575374C2211yescharacteristic, complemented
50#22575373C2211yescharacteristic, complemented
51#22575365C2211yescharacteristic
52#22575365C2211yescharacteristic, complemented
53C4×#14524130C2211yescharacteristic, complemented
54C2×SD16×C269C2211yescharacteristic, complemented
55C2×D8×C269C2211yescharacteristic
56#124×C269C2211yescharacteristic, complemented
57C4×D4×C269C2211yescharacteristic, complemented
58C4⋊C8×C269C2211yescharacteristic, complemented
59#103×C269C2211yescharacteristic, complemented
60#102×C269C2211yescharacteristic, complemented
61C23×D269—21no—
62C23×D269—21no—
63#16864403—22no—
64#16864403—41no—
65#16864401—22no—
66#16864401—41no—
67C2×Dic538C2311yescharacteristic
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—
77D4×D269—22no—
78D4×D269—22no—
79D4×D269—41no—
80D4×D269—41no—
81C22×Dic269—21no—
82C2×C4×D269—21no—
83C2×C4×D269—21no—
84C2×C4×D269C2311yescharacteristic
85C2×C4×D269C2311yescharacteristic
86#16864392—22no—
87#16864391—22no—
88#16864390—41no—
89#16864389—41no—
90D2152—22no—
91#16864387—22no—
92#16864387D414yescomplemented
93C2×#14524130C2311yescharacteristic
94C2×#14524130C2311yescharacteristic
95C8×D269—22no—
96C8×D269—22no—
97C4⋊Dic269—21no—
98C4⋊Dic269D411yescharacteristic
99C4⋊Dic269C2311yescharacteristic
100#16864381—21no—
101C22⋊Dic269—21no—
102#16864379—21no—
103#16864379—21no—
104#16864379—21no—
105#16864379—21no—
106#16864379—21no—
107#16864379—21no—
108#16864379D411yescharacteristic
109#16864379D411yescharacteristic
110C2×Q8×C269C2311yescharacteristic
111C2×D4×C269C2311yescharacteristic
112C2×D4×C269C2311yescharacteristic
113C22×C4×C269—21no—
114SD16×C269—22no—
115D8×C269—22no—
116C2×C8×C269C2311yescharacteristic
117C2×C8×C269C2311yescharacteristic
118C4⋊C4×C269C2311yescharacteristic
119C22⋊C4×C269—21no—
120C22⋊C4×C269—21no—
121C22⋊C4×C269—21no—
122C42×C269C2311yescharacteristic
123C22×D269—21no—
124C22×D269—21no—
125C22×D269—42no—
126C22×D269—42no—
127C22×D269—42no—
128C22×D269—42no—
129C22×D269—81no—
130C22×D269—81no—
131C22×D269C2×D411yescharacteristic
132C22×D269C2×D411yescharacteristic
133Dic538—21no—
134Dic538—21no—
135D1076—22no—
136D1076—21no—
137D1076—21no—
138D1076—21no—
139D1076—42no—
140D1076—81no—
141D1076C2×D412yes—
142C22⋊D269—42no—
143C22⋊D269—42no—
144C22⋊D269—42no—
145C22⋊D269—81no—
146C2×Dic269—21no—
147C2×Dic269—21no—
148C2×Dic269—42no—
149C2×Dic269C2×D411yescharacteristic
150C2×Dic269C2×D411yescharacteristic
151C4×D269—21no—
152C4×D269—21no—
153C4×D269—21no—
154C4×D269—21no—
155C4×D269—42no—
156C4×D269—81no—
157#14524130—21no—
158#14524130C2×D412yes—
159C23×C269—21no—
160C23×C269—21no—
161Q8×C269—21no—
162Q8×C269—21no—
163D4×C269—21no—
164D4×C269—21no—
165D4×C269—21no—
166D4×C269C2×D412yes—
167C2×C4×C269—21no—
168C2×C4×C269—21no—
169C2×C4×C269—81no—
170C2×C4×C269C2×D411yescharacteristic
171C2×C4×C269C2×D411yescharacteristic
172C2×C4×C269C2411yescharacteristic
173C8×C269—21no—
174C8×C269—21no—
175C22×C269—22no—
176C22×C269—41no—
177C22×C269—41no—
178C22×C269—41no—
179C22×C269—41no—
180C22×C269—41no—
181C22×C269C22×D411yescharacteristic
182C2×D269—21no—
183C2×D269—21no—
184C2×D269—21no—
185C2×D269—22no—
186C2×D269—21no—
187C2×D269—21no—
188C2×D269—41no—
189C2×D269—41no—
190C2×D269—41no—
191C2×D269—41no—
192C2×D269—41no—
193C2×D269—84no—
194C2×D269—84no—
195C2×D269#13512yescomplemented
196C4×C269—21no—
197C4×C269—21no—
198C4×C269—41no—
199C4×C269—41no—
200C4×C269C22×D411yescharacteristic
201C4×C269H(5,𝔽2)11yescharacteristic
202Dic269—21no—
203Dic269—21no—
204Dic269—41no—
205Dic269—41no—
206C2×C269—42no—
207C2×C269—81no—
208C2×C269D4211yescharacteristic
209C2×C269C2×#13511yescharacteristic
210C2×C269#57611yescharacteristic
211D269—22no—
212D269—41no—
213D269—42no—
214D269—81no—
215C269#328011yescharacteristic, complemented, Sylow
216#3280—2691nomaximal, Sylow
217C2×#135—2691no—
218C22×D8—2691no—
219#546—2691no—
220#546—2691no—
221#495—2691no—
222#467—2691no—
223#466—2691no—
224#463—2691no—
225#463D26911yescharacteristic, complemented
226#450—2691no—
227#450—2691no—
228#449—2691no—
229#449—2691no—
230C4×D8—2691no—
231C8×D4—2691no—
232C2×#41—2691no—
233C2×#41—2691no—
234C22×D4—2691no—
235C22×D4—2691no—
236#135—5384no—
237C2×Q16—2691no—
238C2×SD16—2691no—
239C2×SD16—2691no—
240C2×SD16—2691no—
241C2×SD16C2×D26911yescharacteristic, complemented
242C2×D8—2691no—
243C2×D8—2691no—
244C2×D8—2691no—
245C2×D8—5384no—
246C2×D8C2×D26911yescharacteristic
247C22×C8—2691no—
248C22×C8—2691no—
249#124—2691no—
250#124C2×D26911yescharacteristic, complemented
251#123—5381no—
252#123—5381no—
253C22⋊Q8—2691no—
254C22⋊Q8—2691no—
255#121—2691no—
256#121—2691no—
257#121—5381no—
258#121—5381no—
259#120—5381no—
260#120—5381no—
261C4×D4—2691no—
262C4×D4—2691no—
263C4×D4C2×D26911yescharacteristic, complemented
264C2×C22⋊C4—5381no—
265C2×C22⋊C4—5381no—
266#107—2691no—
267C4⋊C8C2×D26911yescharacteristic, complemented
268#103—2691no—
269#103C2×D26911yescharacteristic, complemented
270#102—2691no—
271#102—2691no—
272#102—2691no—
273#102C2×D26911yescharacteristic, complemented
274C22⋊C8—2691no—
275C22⋊C8—2691no—
276C4×C8—2691no—
277C24—5381no—
278C24—5381no—
279#41—5382no—
280#41—5382no—
281#41—10761no—
282#41—10761no—
283C2×Q8—2691no—
284C2×Q8C22×D26911yescharacteristic
285C2×D4—2691no—
286C2×D4—2691no—
287C2×D4—2691no—
288C2×D4—5381no—
289C2×D4—5381no—
290C2×D4—5381no—
291C2×D4—5381no—
292C2×D4—5382no—
293C2×D4—5382no—
294C2×D4—5381no—
295C2×D4—5381no—
296C2×D4—10761no—
297C2×D4—10761no—
298C2×D4C22×D26911yescharacteristic
299C2×D4C22×D26911yescharacteristic
300C22×C4—21no—
301C22×C4—2691no—
302C22×C4—2691no—
303C22×C4—5381no—
304C22×C4—5381no—
305C22×C4—5381no—
306Q16—5382no—
307SD16—22no—
308SD16—5382no—
309SD16—10761no—
310SD16—10761no—
311D8—22no—
312D8—2694no—
313D8—5382no—
314D8—5382no—
315C2×C8—2691no—
316C2×C8—2691no—
317C2×C8—5382no—
318C2×C8—5382no—
319C2×C8C22×D26911yescharacteristic
320C2×C8C22×D26911yescharacteristic
321C4⋊C4—2691no—
322C4⋊C4—2691no—
323C4⋊C4—5381no—
324C4⋊C4—5381no—
325C4⋊C4C22×D26911yescharacteristic
326C22⋊C4—21no—
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—2691no—
330C22⋊C4—2691no—
331C22⋊C4—5381no—
332C22⋊C4—5381no—
333C22⋊C4—5381no—
334C22⋊C4—5381no—
335C22⋊C4—5381no—
336C22⋊C4—5381no—
337C22⋊C4—5381no—
338C42C22×D26911yescharacteristic
339C23—21no—
340C23—21no—
341C23—2691no—
342C23—2691no—
343C23—5381no—
344C23—5381no—
345C23—10762no—
346C23—10762no—
347C23—10762no—
348C23—10762no—
349C23—21521no—
350C23—21521no—
351Q8—21no—
352Q8—21no—
353Q8—5381no—
354Q8—5381no—
355D4—21no—
356D4—21no—
357D4—21no—
358D4—2692no—
359D4—5382no—
360D4—5381no—
361D4—5381no—
362D4—5381no—
363D4—10762no—
364D4—10762no—
365D4—10762no—
366D4—10762no—
367D4—21521no—
368D4—21521no—
369D4D4×D26912yes—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—81no—
373C2×C4—2691no—
374C2×C4—2691no—
375C2×C4—5381no—
376C2×C4—5381no—
377C2×C4—5381no—
378C2×C4—5381no—
379C2×C4—5381no—
380C2×C4—5381no—
381C2×C4—10762no—
382C2×C4—10762no—
383C2×C4—21521no—
384C2×C4D4×D26911yescharacteristic
385C2×C4D4×D26911yescharacteristic
386C2×C4C23×D26911yescharacteristic
387C8—21no—
388C8—21no—
389C8—2692no—
390C8—5381no—
391C22—22no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—2692no—
398C22—5381no—
399C22—5381no—
400C22—5381no—
401C22—5381no—
402C22—5382no—
403C22—5381no—
404C22—10761no—
405C22—10761no—
406C22—10761no—
407C22—10761no—
408C22—10761no—
409C22—21524no—
410C22—21524no—
411C22C2×D4×D26911yescharacteristic
412C4—21no—
413C4—21no—
414C4—41no—
415C4—41no—
416C4—5381no—
417C4—5381no—
418C4—10761no—
419C4—10761no—
420C4C2×D4×D26911yescharacteristic
421C4#2257549911yescharacteristic
422C2—42no—
423C2—81no—
424C2—5382no—
425C2—10761no—
426C2—10762no—
427C2—21521no—
428C2#3177123911yescharacteristic
429C2#135×D26911yescharacteristic
430C2#3177140911yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#463×C269C2
socleC22×C269C22×D4
hypercenter#463D269
hypocenterC269#3280
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#22575474C2semidirect
2. C2×D8×D269C2semidirect
3. #31771250C2semidirect
4. #31771248C2semidirect
5. #31770987C2semidirect
6. #31770845C2semidirect
7. #31770840C2semidirect
8. #31770821C2semidirect
9. #31770757C2semidirect
10. #31770754C2semidirect
11. #31770753C2semidirect
12. #31770747C2semidirect
13. C4×#16864387C2semidirect
14. #31770670C2semidirect
15. #463×C269C2semidirect
16. C2×#16864403C22semidirect
17. C2×#16864401C22semidirect
21. C2×#16864392C22semidirect
22. C2×#16864391C22semidirect
23. C2×#16864390C22semidirect
24. C2×#16864389C22semidirect
30. C2×C8×D269C22semidirect
31. #22575441C22semidirect
36. #22575428C22semidirect
39. #22575424C22semidirect
43. C4×D1076C22semidirect
46. #22575386C22semidirect
47. #22575378C22semidirect
48. #22575375C22semidirect
49. #22575374C22semidirect
50. #22575373C22semidirect
52. #22575365C22semidirect
53. C4×#14524130C22semidirect
54. C2×SD16×C269C22semidirect
56. #124×C269C22semidirect
57. C4×D4×C269C22semidirect
58. C4⋊C8×C269C22semidirect
59. #103×C269C22semidirect
60. #102×C269C22semidirect
92. #16864387D4semidirect
195. C2×D269#135semidirect
215. C269#3280semidirect
225. #463D269semidirect
241. C2×SD16C2×D269semidirect
250. #124C2×D269semidirect
263. C4×D4C2×D269semidirect
267. C4⋊C8C2×D269semidirect
269. #103C2×D269semidirect
273. #102C2×D269semidirect

Maximal subgroups

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

subgroupindex
C2×#225754742
C2×D8×D2692
#317712502
#317712482
#317709872
#317708452
#317708402
#317708212
#317707572
#317707542
#317707532
#317707472
C4×#168643872
#317706702
#463×C2692
#3280269