Finite Group Databasebeta

← #49133343

Subgroups — #49133343

Order 36224.

410 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827170C211yesmaximal, characteristic, complemented
2#31827103C211yesmaximal, characteristic
3#31826826C211yesmaximal, characteristic, complemented
4#31826799C211yesmaximal, characteristic, complemented
5#31826778C211yesmaximal, characteristic, complemented
6#31826743C211yesmaximal, characteristic, complemented
7#31826711C211yesmaximal, characteristic, complemented
8#31826705C211yesmaximal, characteristic, complemented
9#31826690C211yesmaximal, characteristic, complemented
10#31826627C211yesmaximal, characteristic, complemented
11#31826617C211yesmaximal, characteristic, complemented
12#31826562C211yesmaximal, characteristic, complemented
13#31826534C211yesmaximal, characteristic, complemented
14#102×D283C211yesmaximal, characteristic, complemented
15#417×C283C211yesmaximal, characteristic, complemented
16C2×D4×D283C2211yescharacteristic
17C2×#17985382C2211yescharacteristic, complemented
18C2×#17985381C2211yescharacteristic
19C2×#17985380C2211yescharacteristic
20C2×C8×D283C2211yescharacteristic
21#22583609C2211yescharacteristic, complemented
22#22583600—21no—
23#22583599C2211yescharacteristic
24#22583593—21no—
25#22583590C2211yescharacteristic
26#22583589—21no—
27#22583589C2211yescharacteristic, complemented
28#22583588—21no—
29#22583586C2211yescharacteristic
30#22583584C2211yescharacteristic
31#22583582—21no—
32#22583578—21no—
33#22583575C2211yescharacteristic, complemented
34D4×Dic283C2211yescharacteristic
35C4×C22⋊D283—21no—
36C4×C22⋊D283C2211yescharacteristic
37C4⋊C4×D283C2211yescharacteristic
38C2×(C2×D283)⋊C4—21no—
39#22583544C2211yescharacteristic, complemented
40#22583543C2211yescharacteristic, complemented
41#22583543C2211yescharacteristic, complemented
42Dic283⋊C8C2211yescharacteristic, complemented
43#22583535C2211yescharacteristic, complemented
44#22583534C2211yescharacteristic, complemented
45#22583532C2211yescharacteristic
46#22583531C2211yescharacteristic
47#22583530C2211yescharacteristic
48#22583530C2211yescharacteristic
49C22⋊(C283⋊C8)C2211yescharacteristic, complemented
50(C2×D283)⋊C8C2211yescharacteristic
51#22583520C2211yescharacteristic, complemented
52C2×#41×C283C2211yescharacteristic
53C2×M16×C283C2211yescharacteristic, complemented
54C2×C4⋊C4×C283C2211yescharacteristic, complemented
55#103×C283C2211yescharacteristic, complemented
56#103×C283C2211yescharacteristic, complemented
57#102×C283C2211yescharacteristic
58#102×C283C2211yescharacteristic
59C23×D283—21no—
60C2×Dic566—21no—
61C2×Dic566C2311yescharacteristic
62C2×D1132C2311yescharacteristic
63C2×C22⋊D283—21no—
64C2×C22⋊D283—21no—
65C2×C22⋊D283D411yescharacteristic
66D4×D283—22no—
67D4×D283—41no—
68C22×Dic283—21no—
69C2×C4×D283—21no—
70C2×C4×D283C2311yescharacteristic
71#17985382—41no—
72#17985381—41no—
73#17985380—22no—
74C2×C283⋊C8C2311yescharacteristic
75C2×C283⋊C8C2311yescharacteristic
76C8×D283—41no—
77C4⋊Dic283—21no—
78C4⋊Dic283C2311yescharacteristic
79C4⋊Dic283C2311yescharacteristic
80Dic283⋊C4—21no—
81Dic283⋊C4—21no—
82Dic283⋊C4—21no—
83Dic283⋊C4—21no—
84Dic283⋊C4—21no—
85Dic283⋊C4D411yescharacteristic
86C22⋊Dic283—21no—
87C22⋊Dic283—21no—
88C22⋊Dic283D411yescharacteristic
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)⋊C4D411yescharacteristic
95C4×Dic283—21no—
96C4×Dic283C2311yescharacteristic
97#41×C283—22no—
98#41×C283—41no—
99C2×Q8×C283C2311yescharacteristic
100C2×D4×C283—21no—
101C2×D4×C283C2311yescharacteristic
102C22×C4×C283—21no—
103C22×C4×C283—21no—
104C22×C4×C283C2311yescharacteristic
105M16×C283—41no—
106C2×C8×C283C2311yescharacteristic
107C2×C8×C283C2311yescharacteristic
108C4⋊C4×C283—21no—
109C4⋊C4×C283C2311yescharacteristic
110C4⋊C4×C283C2311yescharacteristic
111C22×D283—21no—
112C22×D283—42no—
113C22×D283—42no—
114C22×D283—81no—
115C22×D283C2×D411yescharacteristic
116Dic566—21no—
117Dic566—21no—
118Dic566—81no—
119D1132—21no—
120D1132—21no—
121C22⋊D283—22no—
122C22⋊D283—42no—
123C22⋊D283—81no—
124C2×Dic283—21no—
125C2×Dic283—21no—
126C2×Dic283—21no—
127C2×Dic283—81no—
128C2×Dic283C2×D411yescharacteristic
129C2×Dic283C2×D411yescharacteristic
130C2×Dic283C2×D411yescharacteristic
131C4×D283—21no—
132C4×D283—21no—
133C4×D283—81no—
134C283⋊C8—21no—
135C283⋊C8—21no—
136C23×C283—21no—
137C23×C283C2×D411yescharacteristic
138Q8×C283—21no—
139Q8×C283—21no—
140D4×C283—21no—
141D4×C283—42no—
142D4×C283#4112yes—
143C2×C4×C283—21no—
144C2×C4×C283—21no—
145C2×C4×C283—21no—
146C2×C4×C283—21no—
147C2×C4×C283—21no—
148C2×C4×C283—42no—
149C2×C4×C283—81no—
150C2×C4×C283C2×D411yescharacteristic
151C2×C4×C283C2411yescharacteristic
152C8×C283—21no—
153C8×C283—21no—
154C22×C283—21no—
155C22×C283—22no—
156C22×C283—21no—
157C22×C283—21no—
158C22×C283—41no—
159C22×C283—41no—
160C22×C283C22×D411yescharacteristic
161C2×D283—21no—
162C2×D283—21no—
163C2×D283—41no—
164C2×D283—41no—
165C2×D283—41no—
166C2×D283—84no—
167C2×D283#13712yes—
168C4×C283—21no—
169C4×C283—41no—
170C4×C283—41no—
171C4×C283—41no—
172C4×C283C2×#4111yescharacteristic
173C4×C283H(5,𝔽2)11yescharacteristic
174Dic283—21no—
175Dic283—21no—
176Dic283—21no—
177Dic283—41no—
178Dic283—41no—
179Dic283—41no—
180C2×C283—42no—
181C2×C283—41no—
182C2×C283#54611yescharacteristic
183C2×C283C2×#13711yescharacteristic
184C2×C283#57611yescharacteristic
185D283—22no—
186D283—81no—
187C283#331411yescharacteristic, complemented, Sylow
188#3314—2831nomaximal, Sylow
189#554—2831no—
190#546—2831no—
191#489—2831no—
192#484—2831no—
193#480—2831no—
194#474—2831no—
195#468—2831no—
196#467—2831no—
197#464—2831no—
198#452—2831no—
199#450—2831no—
200#440—2831no—
201#435—2831no—
202#417D28311yescharacteristic, complemented
203C2×#102—2831no—
204C2×#41C2×D28311yescharacteristic
205C22×D4—2831no—
206C2×Q16—2831no—
207C2×SD16—2831no—
208C2×SD16—2831no—
209C2×M16C2×D28311yescharacteristic, complemented
210C22×C8—2831no—
211C4⋊Q8—2831no—
212#125—5661no—
213#124—2831no—
214#123—5661no—
215C22⋊Q8—2831no—
216C22⋊Q8—2831no—
217C22⋊Q8—2831no—
218C22⋊Q8—5661no—
219C22⋊Q8—5661no—
220#121—2831no—
221#121—5661no—
222#120—5661no—
223C4×Q8—2831no—
224C4×D4—2831no—
225C4×D4—2831no—
226C4×D4—5661no—
227C2×C4⋊C4—2831no—
228C2×C4⋊C4C2×D28311yescharacteristic, complemented
229C2×C22⋊C4—5661no—
230#107—2831no—
231#107—2831no—
232#107—2831no—
233C4⋊C8—2831no—
234#103—2831no—
235#103—2831no—
236#103C2×D28311yescharacteristic, complemented
237#103C2×D28311yescharacteristic, complemented
238#102—2831no—
239#102—2831no—
240#102—2831no—
241#102—2831no—
242#102C2×D28311yescharacteristic
243#102C2×D28311yescharacteristic
244C22⋊C8—2831no—
245C22⋊C8—2831no—
246#97—2831no—
247C24—5661no—
248#41—22no—
249#41—41no—
250C2×Q8—2831no—
251C2×Q8—5661no—
252C2×Q8C22×D28311yescharacteristic
253C2×D4—21no—
254C2×D4—2831no—
255C2×D4—2831no—
256C2×D4—5661no—
257C2×D4—5662no—
258C2×D4—5661no—
259C2×D4—11321no—
260C2×D4C22×D28311yescharacteristic
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—2831no—
264C22×C4—5661no—
265C22×C4—5661no—
266C22×C4C22×D28311yescharacteristic
267Q16—11321no—
268SD16—5662no—
269SD16—11321no—
270M16—41no—
271C2×C8—2831no—
272C2×C8—2831no—
273C2×C8—11321no—
274C2×C8C22×D28311yescharacteristic
275C2×C8C22×D28311yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—2831no—
278C4⋊C4—2831no—
279C4⋊C4—2831no—
280C4⋊C4—5661no—
281C4⋊C4—5661no—
282C4⋊C4—5661no—
283C4⋊C4—5661no—
284C4⋊C4—5661no—
285C4⋊C4—5661no—
286C4⋊C4C22×D28311yescharacteristic
287C4⋊C4C22×D28311yescharacteristic
288C22⋊C4—2831no—
289C22⋊C4—2831no—
290C22⋊C4—5661no—
291C22⋊C4—5661no—
292C22⋊C4—5661no—
293C22⋊C4—5661no—
294C22⋊C4—5661no—
295C22⋊C4—5661no—
296C22⋊C4—5661no—
297C42—2831no—
298C42—5661no—
299C23—21no—
300C23—2831no—
301C23—5661no—
302C23—11322no—
303C23—11322no—
304C23—22641no—
305C23D4×D28311yescharacteristic
306Q8—21no—
307Q8—21no—
308Q8—5661no—
309Q8—5661no—
310Q8—22641no—
311D4—21no—
312D4—42no—
313D4—5662no—
314D4—5661no—
315D4—5661no—
316D4—11322no—
317D4—22641no—
318D4#1798539212yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—42no—
325C2×C4—81no—
326C2×C4—2831no—
327C2×C4—2831no—
328C2×C4—2831no—
329C2×C4—5661no—
330C2×C4—5661no—
331C2×C4—5661no—
332C2×C4—5661no—
333C2×C4—5661no—
334C2×C4—22641no—
335C2×C4—22641no—
336C2×C4D4×D28311yescharacteristic
337C2×C4C23×D28311yescharacteristic
338C8—21no—
339C8—21no—
340C8—5661no—
341C8—5661no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—22no—
346C22—41no—
347C22—41no—
348C22—2832no—
349C22—5661no—
350C22—5661no—
351C22—11321no—
352C22—11321no—
353C22—11321no—
354C22—22644no—
355C22C2×D4×D28311yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—5661no—
361C4—5661no—
362C4—5661no—
363C4—11321no—
364C4—11321no—
365C4—11321no—
366C4C2×#1798539211yescharacteristic
367C4#2258365511yescharacteristic
368C2—41no—
369C2—42no—
370C2—5662no—
371C2—22641no—
372C2#3182710511yescharacteristic
373C2#137×D28311yescharacteristic
374C2#3182726911yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#417×C283C2
socleC22×C283C22×D4
prime radical#31827103C2
hypercenter#417D283
hypocenterC283#3314
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #31827170C2semidirect
3. #31826826C2semidirect
4. #31826799C2semidirect
5. #31826778C2semidirect
6. #31826743C2semidirect
7. #31826711C2semidirect
8. #31826705C2semidirect
9. #31826690C2semidirect
10. #31826627C2semidirect
11. #31826617C2semidirect
12. #31826562C2semidirect
13. #31826534C2semidirect
14. #102×D283C2semidirect
15. #417×C283C2semidirect
17. C2×#17985382C22semidirect
21. #22583609C22semidirect
27. #22583589C22semidirect
33. #22583575C22semidirect
39. #22583544C22semidirect
40. #22583543C22semidirect
41. #22583543C22semidirect
42. Dic283⋊C8C22semidirect
43. #22583535C22semidirect
44. #22583534C22semidirect
49. C22⋊(C283⋊C8)C22semidirect
51. #22583520C22semidirect
53. C2×M16×C283C22semidirect
54. C2×C4⋊C4×C283C22semidirect
55. #103×C283C22semidirect
56. #103×C283C22semidirect
187. C283#3314semidirect
202. #417D283semidirect
209. C2×M16C2×D283semidirect
228. C2×C4⋊C4C2×D283semidirect
236. #103C2×D283semidirect
237. #103C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318271702
#318271032
#318268262
#318267992
#318267782
#318267432
#318267112
#318267052
#318266902
#318266272
#318266172
#318265622
#318265342
#102×D2832
#417×C2832
#3314283