Finite Group Databasebeta

← #49131447

Subgroups — #49131447

Order 36224.

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#31827086C211yesmaximal, characteristic, complemented
2#31826939C211yesmaximal, characteristic, complemented
3#31826807C211yesmaximal, characteristic, complemented
4#31826790C211yesmaximal, characteristic, complemented
5#31826756C211yesmaximal, characteristic, complemented
6#31826746C211yesmaximal, characteristic, complemented
7#31826681C211yesmaximal, characteristic, complemented
8#31826681C211yesmaximal, characteristic, complemented
9#31826618C211yesmaximal, characteristic, complemented
10#31826601C211yesmaximal, characteristic
11#31826578C211yesmaximal, characteristic, complemented
12#31826567C211yesmaximal, characteristic, complemented
13C4×#17985381C211yesmaximal, characteristic, complemented
14C4×D2264C211yesmaximal, characteristic, complemented
15#433×C283C211yesmaximal, characteristic, complemented
16C22×D1132C2211yescharacteristic
17C2×#17985381C2211yescharacteristic
18C2×#17985381C2211yescharacteristic
19C2×D2264C2211yescharacteristic
20C2×D2264C2211yescharacteristic
21#22583610C2211yescharacteristic, complemented
22#22583605—21no—
23#22583598C2211yescharacteristic, complemented
24#22583596—21no—
25#22583592—21no—
26#22583589C2211yescharacteristic
27#22583588—21no—
28#22583584C2211yescharacteristic
29C4×Dic566C2211yescharacteristic, complemented
30C4×D1132C2211yescharacteristic
31C4×D1132C2211yescharacteristic
32C4×D1132C2211yescharacteristic
33C4×D1132C2211yescharacteristic
34C4×D1132C2211yescharacteristic, complemented
35#22583572—21no—
36#22583572—21no—
37#22583569C2211yescharacteristic
38C22⋊C4×D283—21no—
39C22⋊C4×D283—21no—
40#22583544C2211yescharacteristic, complemented
41#22583544C2211yescharacteristic, complemented
42#22583542C2211yescharacteristic, complemented
43#22583542C2211yescharacteristic, complemented
44#22583535C2211yescharacteristic, complemented
45#22583535C2211yescharacteristic, complemented
46#22583532C2211yescharacteristic
47#22583532C2211yescharacteristic
48#22583532C2211yescharacteristic
49#22583532C2211yescharacteristic
50#22583532C2211yescharacteristic, complemented
51#22583532C2211yescharacteristic, complemented
52#117×C283C2211yescharacteristic
53C4⋊C8×C283C2211yescharacteristic, complemented
54C4⋊C8×C283C2211yescharacteristic, complemented
55C22⋊C8×C283C2211yescharacteristic
56C22⋊C8×C283C2211yescharacteristic
57#97×C283C2211yescharacteristic, complemented
58C4×C8×C283C2211yescharacteristic, complemented
59C23×D283—21no—
60C2×Dic566—21no—
61C2×Dic566C2311yescharacteristic
62C2×D1132—22no—
63C2×D1132—22no—
64C2×D1132—21no—
65C2×D1132C2311yescharacteristic
66C2×D1132C2311yescharacteristic
67C2×D1132C2311yescharacteristic
68C2×C22⋊D283—21no—
69C2×C4×D283—21no—
70C2×C4×D283—21no—
71C2×C4×D283—21no—
72C2×C4×D283—21no—
73C2×C4×D283—21no—
74#17985381—22no—
75#17985381—22no—
76D2264—22no—
77D2264—22no—
78C4⋊Dic283—21no—
79C4⋊Dic283C2311yescharacteristic
80C4⋊Dic283C2311yescharacteristic
81C4⋊Dic283C2311yescharacteristic
82C4⋊Dic283C2311yescharacteristic
83Dic283⋊C4—21no—
84Dic283⋊C4—21no—
85C22⋊Dic283—21no—
86C22⋊Dic283—21no—
87(C2×D283)⋊C4—21no—
88(C2×D283)⋊C4—21no—
89(C2×D283)⋊C4—21no—
90(C2×D283)⋊C4—21no—
91(C2×D283)⋊C4—21no—
92(C2×D283)⋊C4—21no—
93(C2×D283)⋊C4—21no—
94(C2×D283)⋊C4—21no—
95C4×Dic283—21no—
96C4×Dic283—21no—
97C22×C4×C283C2311yescharacteristic
98C2×C8×C283C2311yescharacteristic
99C2×C8×C283C2311yescharacteristic
100C2×C8×C283C2311yescharacteristic
101C2×C8×C283C2311yescharacteristic
102C4⋊C4×C283D411yescharacteristic
103C4⋊C4×C283D411yescharacteristic
104C22⋊C4×C283D411yescharacteristic
105C22⋊C4×C283D411yescharacteristic
106C42×C283C2311yescharacteristic
107C42×C283C2311yescharacteristic
108C22×D283—21no—
109C22×D283—21no—
110C22×D283—24no—
111C22×D283—21no—
112C22×D283—81no—
113C22×D283—81no—
114Dic566—21no—
115Dic566—21no—
116Dic566—81no—
117D1132—24no—
118D1132—21no—
119D1132—21no—
120D1132—21no—
121D1132—21no—
122D1132#4112yes—
123D1132#4112yes—
124C22⋊D283—81no—
125C2×Dic283—21no—
126C2×Dic283—21no—
127C2×Dic283—21no—
128C2×Dic283—21no—
129C2×Dic283—21no—
130C4×D283—81no—
131C4×D283—81no—
132C4×D283—81no—
133C4×D283—81no—
134C4×D283—81no—
135C23×C283C2×D411yescharacteristic
136C2×C4×C283—21no—
137C2×C4×C283—21no—
138C2×C4×C283C2×D411yescharacteristic
139C2×C4×C283C2×D411yescharacteristic
140C2×C4×C283C2×D411yescharacteristic
141C2×C4×C283C2×D411yescharacteristic
142C2×C4×C283C2×D411yescharacteristic
143C2×C4×C283C2411yescharacteristic
144C8×C283—21no—
145C8×C283—21no—
146C8×C283—21no—
147C8×C283—21no—
148C22×C283—21no—
149C22×C283—21no—
150C22×C283—21no—
151C22×C283C22×D411yescharacteristic
152C2×D283—22no—
153C2×D283—22no—
154C2×D283—41no—
155C2×D283—41no—
156C2×D283—41no—
157C2×D283—41no—
158C2×D283—41no—
159C2×D283—41no—
160C2×D283—41no—
161C2×D283—84no—
162C4×C283—21no—
163C4×C283—21no—
164C4×C283—21no—
165C4×C283—21no—
166C4×C283—21no—
167C4×C283C2×#4111yescharacteristic
168C4×C283C2×#4111yescharacteristic
169Dic283—41no—
170Dic283—41no—
171Dic283—41no—
172Dic283—41no—
173Dic283—41no—
174C2×C283—41no—
175C2×C283#52511yescharacteristic
176C2×C283#57611yescharacteristic
177C2×C283#57711yescharacteristic
178D283—42no—
179D283—42no—
180D283—81no—
181C283#311811yescharacteristic, complemented, Sylow
182#3118—2831nomaximal, Sylow
183#542—2831no—
184#518—2831no—
185#485—2831no—
186#482—2831no—
187#476—2831no—
188#474—2831no—
189#463—2831no—
190#463—2831no—
191#450—2831no—
192#447—2831no—
193#442—2831no—
194#440—2831no—
195C4×SD16—2831no—
196C4×D8—2831no—
197#433D28311yescharacteristic, complemented
198C22×D4—2831no—
199C2×SD16—2831no—
200C2×SD16—2831no—
201C2×D8—2831no—
202C2×D8—2831no—
203C4⋊Q8—2831no—
204#126—5661no—
205#124—2831no—
206#124—5661no—
207#123—5661no—
208C22⋊Q8—2831no—
209C22⋊Q8—5661no—
210#121—2831no—
211C4×Q8—2831no—
212C4×D4—2831no—
213C4×D4—2831no—
214C4×D4—2831no—
215C4×D4—2831no—
216C4×D4—2831no—
217C4×D4—5661no—
218C4×D4—5661no—
219#117—2831no—
220#117C2×D28311yescharacteristic
221C2×C22⋊C4—5661no—
222C2×C22⋊C4—5661no—
223#107—2831no—
224#107—2831no—
225#106—2831no—
226#106—2831no—
227C4⋊C8C2×D28311yescharacteristic, complemented
228C4⋊C8C2×D28311yescharacteristic, complemented
229#103—2831no—
230#103—2831no—
231#102—2831no—
232#102—2831no—
233#102—2831no—
234#102—2831no—
235#102—2831no—
236#102—2831no—
237C22⋊C8C2×D28311yescharacteristic
238C22⋊C8C2×D28311yescharacteristic
239#97C2×D28311yescharacteristic, complemented
240C4×C8C2×D28311yescharacteristic, complemented
241C24—5661no—
242C2×Q8—2831no—
243C2×Q8—5661no—
244C2×D4—2831no—
245C2×D4—2831no—
246C2×D4—2831no—
247C2×D4—5662no—
248C2×D4—5662no—
249C2×D4—5661no—
250C2×D4—5661no—
251C22×C4—5661no—
252C22×C4—5661no—
253C22×C4—5661no—
254C22×C4—5661no—
255C22×C4—5661no—
256C22×C4C22×D28311yescharacteristic
257SD16—5662no—
258SD16—5662no—
259D8—5662no—
260D8—5662no—
261C2×C8C22×D28311yescharacteristic
262C2×C8C22×D28311yescharacteristic
263C2×C8C22×D28311yescharacteristic
264C2×C8C22×D28311yescharacteristic
265C4⋊C4—2831no—
266C4⋊C4—2831no—
267C4⋊C4—2831no—
268C4⋊C4—2831no—
269C4⋊C4—5661no—
270C4⋊C4—5661no—
271C4⋊C4—5661no—
272C4⋊C4D113211yescharacteristic
273C4⋊C4D113211yescharacteristic
274C22⋊C4—5661no—
275C22⋊C4—5661no—
276C22⋊C4—5661no—
277C22⋊C4—5661no—
278C22⋊C4—5661no—
279C22⋊C4—5661no—
280C22⋊C4—5661no—
281C22⋊C4—5661no—
282C22⋊C4—5661no—
283C22⋊C4—5661no—
284C22⋊C4D113211yescharacteristic
285C22⋊C4D113211yescharacteristic
286C42—5661no—
287C42—5661no—
288C42C22×D28311yescharacteristic
289C42C22×D28311yescharacteristic
290C23—5664no—
291C23—5661no—
292C23—5661no—
293C23—5661no—
294C23—22641no—
295C23—22641no—
296C23C2×D113211yescharacteristic
297Q8—5661no—
298Q8—5661no—
299Q8—22641no—
300D4—2832no—
301D4—2832no—
302D4—5664no—
303D4—5661no—
304D4—5661no—
305D4—5661no—
306D4—5661no—
307D4—22641no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—5661no—
311C2×C4—5661no—
312C2×C4—5661no—
313C2×C4—5661no—
314C2×C4—5661no—
315C2×C4—22641no—
316C2×C4—22641no—
317C2×C4—22641no—
318C2×C4—22641no—
319C2×C4—22641no—
320C2×C4C2×D113211yescharacteristic
321C2×C4C2×D113211yescharacteristic
322C2×C4C2×D113211yescharacteristic
323C2×C4C2×D113211yescharacteristic
324C2×C4C2×D113211yescharacteristic
325C2×C4C23×D28311yescharacteristic
326C8—21no—
327C8—21no—
328C8—21no—
329C8—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—5662no—
334C22—5662no—
335C22—11321no—
336C22—11321no—
337C22—11321no—
338C22—11321no—
339C22—11321no—
340C22—11321no—
341C22—11321no—
342C22—22644no—
343C22C22×D113211yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—11321no—
350C4—11321no—
351C4—11321no—
352C4—11321no—
353C4—11321no—
354C4#41×D28311yescharacteristic
355C4#41×D28311yescharacteristic
356C2—41no—
357C2—11322no—
358C2—11322no—
359C2—22641no—
360C2#3182697711yescharacteristic
361C2#3182727011yescharacteristic
362C2#3182727711yescharacteristic
subgroupG/H
centerC22C22×D1132
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#433×C283C2
socleC22×C283C22×D4
prime radical#31826601C2
hypercenter#433D283
hypocenterC283#3118
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #31827086C2semidirect
2. #31826939C2semidirect
3. #31826807C2semidirect
4. #31826790C2semidirect
5. #31826756C2semidirect
6. #31826746C2semidirect
7. #31826681C2semidirect
8. #31826681C2semidirect
9. #31826618C2semidirect
11. #31826578C2semidirect
12. #31826567C2semidirect
13. C4×#17985381C2semidirect
14. C4×D2264C2semidirect
15. #433×C283C2semidirect
21. #22583610C22semidirect
23. #22583598C22semidirect
29. C4×Dic566C22semidirect
34. C4×D1132C22semidirect
40. #22583544C22semidirect
41. #22583544C22semidirect
42. #22583542C22semidirect
43. #22583542C22semidirect
44. #22583535C22semidirect
45. #22583535C22semidirect
50. #22583532C22semidirect
51. #22583532C22semidirect
53. C4⋊C8×C283C22semidirect
54. C4⋊C8×C283C22semidirect
57. #97×C283C22semidirect
58. C4×C8×C283C22semidirect
181. C283#3118semidirect
197. #433D283semidirect
227. C4⋊C8C2×D283semidirect
228. C4⋊C8C2×D283semidirect
239. #97C2×D283semidirect
240. C4×C8C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318270862
#318269392
#318268072
#318267902
#318267562
#318267462
#318266812
#318266182
#318266012
#318265782
#318265672
C4×#179853812
C4×D22642
#433×C2832
#3118283