Finite Group Databasebeta

← #49133368

Subgroups — #49133368

Order 36224.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827170C211yesmaximal, characteristic, complemented
2#31827126C211yesmaximal, characteristic
3#31826826C211yesmaximal, characteristic, complemented
4#31826794C211yesmaximal, characteristic, complemented
5#31826783C211yesmaximal, characteristic, complemented
6#31826748C211yesmaximal, characteristic, complemented
7#31826722C211yesmaximal, characteristic, complemented
8#31826694C211yesmaximal, characteristic, complemented
9#31826690C211yesmaximal, characteristic, complemented
10#31826630C211yesmaximal, characteristic, complemented
11#31826621C211yesmaximal, characteristic, complemented
12#31826569C211yesmaximal, characteristic, complemented
13#31826536C211yesmaximal, characteristic, complemented
14#31826465C211yesmaximal, characteristic, complemented
15C2×#103×C283C211yesmaximal, characteristic, complemented
16C2×#17985393C2211yescharacteristic
17C2×#17985382C2211yescharacteristic
18C2×#17985382C2211yescharacteristic
19C2×#17985381C2211yescharacteristic
20C2×#17985375C2211yescharacteristic
21#22583609C2211yescharacteristic
22#22583600—21no—
23#22583599—21no—
24#22583599C2211yescharacteristic
25#22583590C2211yescharacteristic
26#22583589—21no—
27#22583589C2211yescharacteristic
28#22583588—21no—
29#22583586—21no—
30#22583586C2211yescharacteristic
31#22583584—21no—
32#22583584C2211yescharacteristic
33Q8×Dic283C2211yescharacteristic
34#22583575C2211yescharacteristic
35C4×C22⋊D283—21no—
36C4×C22⋊D283—21no—
37C4×C22⋊D283C2211yescharacteristic
38C4⋊C4×D283C2211yescharacteristic
39#22583542C2211yescharacteristic
40#22583541C2211yescharacteristic
41#22583541C2211yescharacteristic
42Dic283⋊C8C2211yescharacteristic
43#22583535C2211yescharacteristic
44#22583534C2211yescharacteristic
45#22583534C2211yescharacteristic
46#22583532C2211yescharacteristic
47#22583530C2211yescharacteristic
48#22583530C2211yescharacteristic
49C22⋊(C283⋊C8)C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51#22583520C2211yescharacteristic
52C22×Q8×C283C2211yescharacteristic
53C22×C8×C283C2211yescharacteristic
54C2×C4⋊C4×C283C2211yescharacteristic
55#103×C283C2211yescharacteristic
56#103×C283C2211yescharacteristic
57#103×C283C2211yescharacteristic
58#103×C283C2211yescharacteristic
59#17985393—22no—
60#17985393—41no—
61C2×Dic566—21no—
62C2×Dic566C2311yescharacteristic
63C2×D1132—21no—
64C2×D1132C2311yescharacteristic
65C2×C22⋊D283—21no—
66C2×C22⋊D283D411yescharacteristic
67C2×C4×D283—21no—
68C2×C4×D283—21no—
69C2×C4×D283C2311yescharacteristic
70#17985382—22no—
71#17985382—41no—
72#17985381—41no—
73#17985375—41no—
74C2×C283⋊C8C2311yescharacteristic
75C2×C283⋊C8C2311yescharacteristic
76C4⋊Dic283—21no—
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⋊Dic283D411yescharacteristic
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)⋊C4D411yescharacteristic
94C4×Dic283—21no—
95C4×Dic283—21no—
96C4×Dic283C2311yescharacteristic
97C2×Q8×C283—21no—
98C2×Q8×C283—22no—
99C2×Q8×C283—41no—
100C2×Q8×C283C2311yescharacteristic
101C2×Q8×C283C2311yescharacteristic
102C22×C4×C283—21no—
103C22×C4×C283—21no—
104C22×C4×C283C2311yescharacteristic
105C2×C8×C283—41no—
106C2×C8×C283C2311yescharacteristic
107C2×C8×C283C2311yescharacteristic
108C4⋊C4×C283—21no—
109C4⋊C4×C283C2311yescharacteristic
110C4⋊C4×C283C2311yescharacteristic
111C22×D283—21no—
112C22×D283C2×D411yescharacteristic
113Dic566—21no—
114Dic566—21no—
115Dic566—81no—
116D1132—21no—
117D1132—21no—
118D1132—42no—
119C22⋊D283—22no—
120C22⋊D283—42no—
121C2×Dic283—21no—
122C2×Dic283—21no—
123C2×Dic283—21no—
124C2×Dic283C2×D411yescharacteristic
125C2×Dic283C2×D411yescharacteristic
126C2×Dic283C2×D411yescharacteristic
127C4×D283—21no—
128C4×D283—21no—
129C4×D283—42no—
130C4×D283—81no—
131C283⋊C8—21no—
132C283⋊C8—21no—
133C23×C283C2×D411yescharacteristic
134Q8×C283—21no—
135Q8×C283—21no—
136Q8×C283—21no—
137Q8×C283—42no—
138Q8×C283#4112yes—
139C2×C4×C283—21no—
140C2×C4×C283—21no—
141C2×C4×C283—21no—
142C2×C4×C283—21no—
143C2×C4×C283—21no—
144C2×C4×C283—21no—
145C2×C4×C283—42no—
146C2×C4×C283—81no—
147C2×C4×C283C2×D411yescharacteristic
148C2×C4×C283C2411yescharacteristic
149C8×C283—21no—
150C8×C283—21no—
151C22×C283—21no—
152C22×C283—21no—
153C22×C283#13712yes—
154C22×C283C22×D411yescharacteristic
155C2×D283—21no—
156C2×D283—21no—
157C2×D283—21no—
158C2×D283—41no—
159C2×D283—41no—
160C2×D283—41no—
161C4×C283—21no—
162C4×C283—22no—
163C4×C283—41no—
164C4×C283—41no—
165C4×C283—41no—
166C4×C283C2×#4111yescharacteristic
167C4×C283H(5,𝔽2)11yescharacteristic
168Dic283—21no—
169Dic283—21no—
170Dic283—21no—
171Dic283—41no—
172Dic283—41no—
173Dic283—41no—
174C2×C283—22no—
175C2×C283#54611yescharacteristic
176C2×C283C2×#13711yescharacteristic
177C2×C283#57711yescharacteristic
178D283—41no—
179D283—81no—
180C283#331611yescharacteristic, complemented, Sylow
181#3316—2831nomaximal, Sylow
182#554—2831no—
183#548—2831no—
184#489—2831no—
185#483—2831no—
186#481—2831no—
187#475—2831no—
188#470—2831no—
189#465—2831no—
190#464—2831no—
191#452—2831no—
192#451—2831no—
193#441—2831no—
194#435—2831no—
195#417—2831no—
196C2×#103D28311yescharacteristic, complemented
197C2×#41—2831no—
198C22×Q8C2×D28311yescharacteristic
199C2×Q16—2831no—
200C2×Q16—2831no—
201C2×SD16—2831no—
202C2×M16—2831no—
203C22×C8C2×D28311yescharacteristic
204C4⋊Q8—2831no—
205#125—5661no—
206#124—2831no—
207#124—5661no—
208C22⋊Q8—2831no—
209C22⋊Q8—2831no—
210C22⋊Q8—2831no—
211C22⋊Q8—5661no—
212C22⋊Q8—5661no—
213C22⋊Q8—5661no—
214#121—2831no—
215#121—5661no—
216C4×Q8—2831no—
217C4×Q8—2831no—
218C4×D4—2831no—
219C4×D4—5661no—
220C4×D4—5661no—
221C2×C4⋊C4—2831no—
222C2×C4⋊C4C2×D28311yescharacteristic
223#106—2831no—
224#106—2831no—
225#106—2831no—
226C4⋊C8—2831no—
227#103—2831no—
228#103—2831no—
229#103—2831no—
230#103C2×D28311yescharacteristic
231#103C2×D28311yescharacteristic
232#103C2×D28311yescharacteristic
233#103C2×D28311yescharacteristic
234#102—2831no—
235#102—2831no—
236#102—2831no—
237C22⋊C8—2831no—
238C22⋊C8—2831no—
239#97—2831no—
240#41—5662no—
241#41—11321no—
242C2×Q8—21no—
243C2×Q8—22no—
244C2×Q8—41no—
245C2×Q8—2831no—
246C2×Q8—5661no—
247C2×Q8C22×D28311yescharacteristic
248C2×Q8C22×D28311yescharacteristic
249C2×D4—2831no—
250C2×D4—2831no—
251C2×D4—5661no—
252C2×D4—5661no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—2831no—
256C22×C4—5661no—
257C22×C4—5661no—
258C22×C4C22×D28311yescharacteristic
259Q16—5662no—
260Q16—11321no—
261SD16—11321no—
262M16—11321no—
263C2×C8—41no—
264C2×C8—2831no—
265C2×C8—2831no—
266C2×C8C22×D28311yescharacteristic
267C2×C8C22×D28311yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—2831no—
270C4⋊C4—2831no—
271C4⋊C4—2831no—
272C4⋊C4—5661no—
273C4⋊C4—5661no—
274C4⋊C4—5661no—
275C4⋊C4—5661no—
276C4⋊C4—5661no—
277C4⋊C4—5661no—
278C4⋊C4—5661no—
279C4⋊C4C22×D28311yescharacteristic
280C4⋊C4C22×D28311yescharacteristic
281C22⋊C4—2831no—
282C22⋊C4—2831no—
283C22⋊C4—5661no—
284C22⋊C4—5661no—
285C22⋊C4—5661no—
286C22⋊C4—5661no—
287C22⋊C4—5661no—
288C22⋊C4—5661no—
289C42—2831no—
290C42—5661no—
291C42—5661no—
292C23—2831no—
293C23—5661no—
294C23D4×D28311yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—42no—
299Q8—5661no—
300Q8—5661no—
301Q8—22641no—
302Q8#1798539212yes—
303D4—5662no—
304D4—5661no—
305D4—5661no—
306D4—11322no—
307D4—11322no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—42no—
315C2×C4—81no—
316C2×C4—2831no—
317C2×C4—2831no—
318C2×C4—2831no—
319C2×C4—5661no—
320C2×C4—5661no—
321C2×C4—5661no—
322C2×C4—5661no—
323C2×C4—5661no—
324C2×C4—11322no—
325C2×C4—22641no—
326C2×C4D4×D28311yescharacteristic
327C2×C4C23×D28311yescharacteristic
328C8—21no—
329C8—21no—
330C8—5661no—
331C8—5661no—
332C22—21no—
333C22—21no—
334C22—5661no—
335C22—5661no—
336C22—5661no—
337C22—11321no—
338C22—11321no—
339C22—11321no—
340C22#2258364212yes—
341C22C2×D4×D28311yescharacteristic
342C4—21no—
343C4—22no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—5661no—
348C4—5661no—
349C4—5661no—
350C4—11321no—
351C4—11321no—
352C4—11321no—
353C4C2×#1798539211yescharacteristic
354C4#2258365511yescharacteristic
355C2—22no—
356C2—11321no—
357C2—22641no—
358C2#3182710511yescharacteristic
359C2C2×#2258364211yescharacteristic
360C2#3182727111yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC2×#103×C283C2
socleC22×C283C22×D4
prime radical#31827126C2
hypercenterC2×#103D283
hypocenterC283#3316
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. #31827170C2semidirect
3. #31826826C2semidirect
4. #31826794C2semidirect
5. #31826783C2semidirect
6. #31826748C2semidirect
7. #31826722C2semidirect
8. #31826694C2semidirect
9. #31826690C2semidirect
10. #31826630C2semidirect
11. #31826621C2semidirect
12. #31826569C2semidirect
13. #31826536C2semidirect
14. #31826465C2semidirect
15. C2×#103×C283C2semidirect
180. C283#3316semidirect
196. C2×#103D283semidirect

Maximal subgroups

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

subgroupindex
#318271702
#318271262
#318268262
#318267942
#318267832
#318267482
#318267222
#318266942
#318266902
#318266302
#318266212
#318265692
#318265362
#318264652
C2×#103×C2832
#3316283