Finite Group Databasebeta

← #46821072

Subgroups — #46821072

Order 34432.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771228C211yesmaximal, characteristic, complemented
2#31771079C211yesmaximal, characteristic, complemented
3#31770929C211yesmaximal, characteristic, complemented
4#31770894C211yesmaximal, characteristic, complemented
5#31770884C211yesmaximal, characteristic, complemented
6#31770823C211yesmaximal, characteristic, complemented
7#31770823C211yesmaximal, characteristic, complemented
8#31770755C211yesmaximal, characteristic, complemented
9#31770741C211yesmaximal, characteristic
10#31770716C211yesmaximal, characteristic, complemented
11#31770708C211yesmaximal, characteristic, complemented
12#31770690C211yesmaximal, characteristic, complemented
13#31770687C211yesmaximal, characteristic, complemented
14#31770663C211yesmaximal, characteristic, complemented
15#485×C269C211yesmaximal, characteristic, complemented
16C22×D1076C2211yescharacteristic
17C2×#16864389C2211yescharacteristic
18C2×#16864389C2211yescharacteristic
19C2×D2152C2211yescharacteristic
20C2×D2152C2211yescharacteristic
21#22575452C2211yescharacteristic, complemented
22#22575448—21no—
23#22575442C2211yescharacteristic, complemented
24#22575439—21no—
25#22575435—21no—
26#22575433—21no—
27#22575427C2211yescharacteristic
28Q8×Dic269C2211yescharacteristic, complemented
29C4×D1076—21no—
30C4×D1076—21no—
31#22575415C2211yescharacteristic
32#22575415C2211yescharacteristic
33#22575415C2211yescharacteristic
34#22575415C2211yescharacteristic
35#22575415C2211yescharacteristic, complemented
36#22575412C2211yescharacteristic
37C22⋊C4×D269—21no—
38C22⋊C4×D269—21no—
39#22575386C2211yescharacteristic, complemented
40#22575384C2211yescharacteristic, complemented
41#22575382C2211yescharacteristic, complemented
42#22575382C2211yescharacteristic, complemented
43#22575375C2211yescharacteristic
44#22575375C2211yescharacteristic
45#22575373C2211yescharacteristic
46#22575373C2211yescharacteristic
47#22575373C2211yescharacteristic, complemented
48#22575373C2211yescharacteristic, complemented
49C22⋊#14524130C2211yescharacteristic
50#22575363C2211yescharacteristic, complemented
51C8×Dic269C2211yescharacteristic, complemented
52C22⋊Q8×C269C2211yescharacteristic
53#117×C269C2211yescharacteristic
54#107×C269C2211yescharacteristic, complemented
55#106×C269C2211yescharacteristic, complemented
56#103×C269C2211yescharacteristic, complemented
57#103×C269C2211yescharacteristic, complemented
58C22⋊C8×C269C2211yescharacteristic
59C23×D269—21no—
60C2×Dic538—21no—
61C2×D1076—22no—
62C2×D1076—22no—
63C2×D1076—21no—
64C2×D1076C2311yescharacteristic
65C2×D1076C2311yescharacteristic
66C2×D1076C2311yescharacteristic
67C2×C22⋊D269—21no—
68C2×C4×D269—21no—
69C2×C4×D269—21no—
70C2×C4×D269—21no—
71C2×C4×D269—21no—
72C2×C4×D269—21no—
73#16864389—22no—
74#16864389—22no—
75D2152—22no—
76D2152—22no—
77C2×#14524130C2311yescharacteristic
78C2×#14524130C2311yescharacteristic
79C4⋊Dic269—21no—
80C4⋊Dic269D411yescharacteristic
81C4⋊Dic269D411yescharacteristic
82C4⋊Dic269C2311yescharacteristic
83#16864381—21no—
84C22⋊Dic269D411yescharacteristic
85C22⋊Dic269D411yescharacteristic
86#16864379—21no—
87#16864379—21no—
88#16864379—21no—
89#16864379—21no—
90#16864379—21no—
91#16864379—21no—
92#16864379—21no—
93#16864379—21no—
94C4×Dic269—21no—
95C4×Dic269C2311yescharacteristic
96C4×Dic269C2311yescharacteristic
97C2×Q8×C269C2311yescharacteristic
98C22×C4×C269C2311yescharacteristic
99C2×C8×C269C2311yescharacteristic
100C2×C8×C269C2311yescharacteristic
101C4⋊C4×C269—21no—
102C4⋊C4×C269C2311yescharacteristic
103C4⋊C4×C269C2311yescharacteristic
104C4⋊C4×C269C2311yescharacteristic
105C22⋊C4×C269—21no—
106C22⋊C4×C269—21no—
107C42×C269—21no—
108C22×D269—21no—
109C22×D269—21no—
110C22×D269—24no—
111C22×D269—21no—
112C22×D269—81no—
113C22×D269—81no—
114Dic538—81no—
115D1076—24no—
116D1076—21no—
117D1076—21no—
118D1076—21no—
119D1076—21no—
120D1076#4112yes—
121D1076#4112yes—
122C22⋊D269—81no—
123C2×Dic269—21no—
124C2×Dic269C2×D411yescharacteristic
125C2×Dic269C2×D411yescharacteristic
126C2×Dic269C2×D411yescharacteristic
127C2×Dic269C2×D411yescharacteristic
128C4×D269—81no—
129C4×D269—81no—
130C4×D269—81no—
131C4×D269—81no—
132C4×D269—81no—
133#14524130—21no—
134#14524130—21no—
135C23×C269C2×D411yescharacteristic
136Q8×C269—21no—
137Q8×C269—21no—
138C2×C4×C269—21no—
139C2×C4×C269—21no—
140C2×C4×C269—21no—
141C2×C4×C269—21no—
142C2×C4×C269—21no—
143C2×C4×C269—21no—
144C2×C4×C269C2×D411yescharacteristic
145C2×C4×C269C2411yescharacteristic
146C8×C269—21no—
147C8×C269—21no—
148C22×C269—21no—
149C22×C269—21no—
150C22×C269—21no—
151C22×C269C22×D411yescharacteristic
152C2×D269—22no—
153C2×D269—22no—
154C2×D269—41no—
155C2×D269—41no—
156C2×D269—41no—
157C2×D269—41no—
158C2×D269—41no—
159C2×D269—41no—
160C2×D269—41no—
161C2×D269—84no—
162C4×C269—21no—
163C4×C269—41no—
164C4×C269—41no—
165C4×C269—41no—
166C4×C269—41no—
167C4×C269C2×#4111yescharacteristic
168C4×C269C2×#4111yescharacteristic
169Dic269—21no—
170Dic269—21no—
171Dic269—21no—
172Dic269—21no—
173Dic269—41no—
174C2×C269—41no—
175C2×C269#52511yescharacteristic
176C2×C269#57611yescharacteristic
177C2×C269#57711yescharacteristic
178D269—42no—
179D269—42no—
180D269—81no—
181C269#311811yescharacteristic, complemented, Sylow
182#3118—2691nomaximal, Sylow
183#542—2691no—
184#518—2691no—
185#485D26911yescharacteristic, complemented
186#482—2691no—
187#476—2691no—
188#474—2691no—
189#463—2691no—
190#463—2691no—
191#450—2691no—
192#447—2691no—
193#442—2691no—
194#440—2691no—
195C4×SD16—2691no—
196C4×D8—2691no—
197#433—2691no—
198C22×D4—2691no—
199C2×SD16—2691no—
200C2×SD16—2691no—
201C2×D8—2691no—
202C2×D8—2691no—
203C4⋊Q8—2691no—
204#126—5381no—
205#124—2691no—
206#124—5381no—
207#123—5381no—
208C22⋊Q8—5381no—
209C22⋊Q8C2×D26911yescharacteristic
210#121—2691no—
211C4×Q8—2691no—
212C4×D4—2691no—
213C4×D4—2691no—
214C4×D4—2691no—
215C4×D4—2691no—
216C4×D4—2691no—
217C4×D4—5381no—
218C4×D4—5381no—
219#117—2691no—
220#117C2×D26911yescharacteristic
221C2×C22⋊C4—5381no—
222C2×C22⋊C4—5381no—
223#107—2691no—
224#107C2×D26911yescharacteristic, complemented
225#106—2691no—
226#106C2×D26911yescharacteristic, complemented
227C4⋊C8—2691no—
228C4⋊C8—2691no—
229#103C2×D26911yescharacteristic, complemented
230#103C2×D26911yescharacteristic, complemented
231#102—2691no—
232#102—2691no—
233#102—2691no—
234#102—2691no—
235#102—2691no—
236#102—2691no—
237C22⋊C8—2691no—
238C22⋊C8C2×D26911yescharacteristic
239#97—2691no—
240C4×C8—2691no—
241C24—5381no—
242C2×Q8—5381no—
243C2×Q8C22×D26911yescharacteristic
244C2×D4—2691no—
245C2×D4—2691no—
246C2×D4—2691no—
247C2×D4—5382no—
248C2×D4—5382no—
249C2×D4—5381no—
250C2×D4—5381no—
251C22×C4—5381no—
252C22×C4—5381no—
253C22×C4—5381no—
254C22×C4—5381no—
255C22×C4—5381no—
256C22×C4C22×D26911yescharacteristic
257SD16—5382no—
258SD16—5382no—
259D8—5382no—
260D8—5382no—
261C2×C8—2691no—
262C2×C8—2691no—
263C2×C8C22×D26911yescharacteristic
264C2×C8C22×D26911yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—2691no—
267C4⋊C4—2691no—
268C4⋊C4—2691no—
269C4⋊C4—5381no—
270C4⋊C4—5381no—
271C4⋊C4C22×D26911yescharacteristic
272C4⋊C4C22×D26911yescharacteristic
273C4⋊C4C22×D26911yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—2691no—
277C22⋊C4—2691no—
278C22⋊C4—5381no—
279C22⋊C4—5381no—
280C22⋊C4—5381no—
281C22⋊C4—5381no—
282C22⋊C4—5381no—
283C22⋊C4—5381no—
284C22⋊C4—5381no—
285C22⋊C4—5381no—
286C42—21no—
287C42—2691no—
288C42—2691no—
289C42—5381no—
290C23—5384no—
291C23—5381no—
292C23—5381no—
293C23—5381no—
294C23—21521no—
295C23—21521no—
296C23D4×D26911yescharacteristic
297Q8—21no—
298Q8—21no—
299Q8—21521no—
300D4—2692no—
301D4—2692no—
302D4—5384no—
303D4—5381no—
304D4—5381no—
305D4—5381no—
306D4—5381no—
307D4—21521no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—2691no—
315C2×C4—2691no—
316C2×C4—2691no—
317C2×C4—2691no—
318C2×C4—5381no—
319C2×C4—21521no—
320C2×C4—21521no—
321C2×C4—21521no—
322C2×C4—21521no—
323C2×C4—21521no—
324C2×C4D4×D26911yescharacteristic
325C2×C4C23×D26911yescharacteristic
326C8—21no—
327C8—21no—
328C8—5381no—
329C8—5381no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—5382no—
334C22—5382no—
335C22—10761no—
336C22—10761no—
337C22—10761no—
338C22—10761no—
339C22—10761no—
340C22—10761no—
341C22—10761no—
342C22—21524no—
343C22C2×D4×D26911yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—5381no—
350C4—5381no—
351C4—5381no—
352C4—5381no—
353C4—10761no—
354C4#41×D26911yescharacteristic
355C4#41×D26911yescharacteristic
356C2—41no—
357C2—10762no—
358C2—10762no—
359C2—21521no—
360C2#3177111311yescharacteristic
361C2#3177140711yescharacteristic
362C2#3177141411yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#485×C269C2
socleC22×C269C22×D4
prime radical#31770741C2
hypercenter#485D269
hypocenterC269#3118
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #31771228C2semidirect
2. #31771079C2semidirect
3. #31770929C2semidirect
4. #31770894C2semidirect
5. #31770884C2semidirect
6. #31770823C2semidirect
7. #31770823C2semidirect
8. #31770755C2semidirect
10. #31770716C2semidirect
11. #31770708C2semidirect
12. #31770690C2semidirect
13. #31770687C2semidirect
14. #31770663C2semidirect
15. #485×C269C2semidirect
21. #22575452C22semidirect
23. #22575442C22semidirect
28. Q8×Dic269C22semidirect
35. #22575415C22semidirect
39. #22575386C22semidirect
40. #22575384C22semidirect
41. #22575382C22semidirect
42. #22575382C22semidirect
47. #22575373C22semidirect
48. #22575373C22semidirect
50. #22575363C22semidirect
51. C8×Dic269C22semidirect
54. #107×C269C22semidirect
55. #106×C269C22semidirect
56. #103×C269C22semidirect
57. #103×C269C22semidirect
181. C269#3118semidirect
185. #485D269semidirect
224. #107C2×D269semidirect
226. #106C2×D269semidirect
229. #103C2×D269semidirect
230. #103C2×D269semidirect

Maximal subgroups

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

subgroupindex
#317712282
#317710792
#317709292
#317708942
#317708842
#317708232
#317707552
#317707412
#317707162
#317707082
#317706902
#317706872
#317706632
#485×C2692
#3118269