Finite Group Databasebeta

← #49133144

Subgroups — #49133144

Order 36224.

386 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827150C211yesmaximal, characteristic, complemented
2#31827126C211yesmaximal, characteristic
3#31826821C211yesmaximal, characteristic, complemented
4#31826804C211yesmaximal, characteristic, complemented
5#31826778C211yesmaximal, characteristic, complemented
6#31826770C211yesmaximal, characteristic, complemented
7#31826705C211yesmaximal, characteristic, complemented
8#31826694C211yesmaximal, characteristic, complemented
9#31826690C211yesmaximal, characteristic, complemented
10#31826630C211yesmaximal, characteristic, complemented
11#31826621C211yesmaximal, characteristic, complemented
12#31826557C211yesmaximal, characteristic, complemented
13C8×C22⋊D283C211yesmaximal, characteristic, complemented
14#31826460C211yesmaximal, characteristic, complemented
15C2×#103×C283C211yesmaximal, characteristic, complemented
16C2×#17985393C2211yescharacteristic
17C2×#17985382C2211yescharacteristic
18C2×#17985382C2211yescharacteristic
19C2×#17985381C2211yescharacteristic
20C2×C8×D283C2211yescharacteristic
21#22583605—21no—
22#22583601C2211yescharacteristic
23#22583600—21no—
24#22583599—21no—
25#22583599C2211yescharacteristic
26#22583593—21no—
27#22583590C2211yescharacteristic
28#22583589C2211yescharacteristic
29#22583586—21no—
30#22583586C2211yescharacteristic
31#22583584—21no—
32#22583584C2211yescharacteristic
33Q8×Dic283C2211yescharacteristic
34#22583575C2211yescharacteristic
35C4×C22⋊D283—21no—
36C4×C22⋊D283C2211yescharacteristic
37#22583569—21no—
38#22583568C2211yescharacteristic
39#22583543C2211yescharacteristic
40#22583543C2211yescharacteristic
41#22583542C2211yescharacteristic
42Dic283⋊C8C2211yescharacteristic
43#22583535C2211yescharacteristic
44#22583534C2211yescharacteristic
45#22583534C2211yescharacteristic
46#22583532C2211yescharacteristic
47#22583530C2211yescharacteristic
48#22583530C2211yescharacteristic
49C22⋊(C283⋊C8)C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51C8×Dic283C2211yescharacteristic
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×Dic566C2311yescharacteristic
62C2×D1132—21no—
63C2×D1132C2311yescharacteristic
64C2×C22⋊D283—21no—
65C2×C22⋊D283D411yescharacteristic
66C2×C4×D283—21no—
67C2×C4×D283C2311yescharacteristic
68#17985382—22no—
69#17985382—41no—
70#17985381—41no—
71C2×C283⋊C8C2311yescharacteristic
72C2×C283⋊C8C2311yescharacteristic
73C8×D283—41no—
74C4⋊Dic283—21no—
75C4⋊Dic283—21no—
76C4⋊Dic283—21no—
77C4⋊Dic283C2311yescharacteristic
78C4⋊Dic283C2311yescharacteristic
79Dic283⋊C4—21no—
80Dic283⋊C4—21no—
81Dic283⋊C4—21no—
82Dic283⋊C4—21no—
83Dic283⋊C4D411yescharacteristic
84C22⋊Dic283—21no—
85C22⋊Dic283D411yescharacteristic
86(C2×D283)⋊C4—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)⋊C4D411yescharacteristic
93C4×Dic283—21no—
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—
115D1132—21no—
116D1132—21no—
117D1132—42no—
118C22⋊D283—22no—
119C22⋊D283—42no—
120C2×Dic283—21no—
121C2×Dic283—21no—
122C2×Dic283—21no—
123C2×Dic283C2×D411yescharacteristic
124C2×Dic283C2×D411yescharacteristic
125C2×Dic283C2×D411yescharacteristic
126C4×D283—21no—
127C4×D283—21no—
128C4×D283—42no—
129C283⋊C8—21no—
130C283⋊C8—21no—
131C23×C283C2×D411yescharacteristic
132Q8×C283—21no—
133Q8×C283—21no—
134Q8×C283—21no—
135Q8×C283—42no—
136Q8×C283#4112yes—
137C2×C4×C283—21no—
138C2×C4×C283—21no—
139C2×C4×C283—21no—
140C2×C4×C283—21no—
141C2×C4×C283—21no—
142C2×C4×C283—21no—
143C2×C4×C283—42no—
144C2×C4×C283—42no—
145C2×C4×C283C2×D411yescharacteristic
146C2×C4×C283C2411yescharacteristic
147C8×C283—21no—
148C8×C283—21no—
149C22×C283—21no—
150C22×C283—21no—
151C22×C283#13512yes—
152C22×C283C22×D411yescharacteristic
153C2×D283—21no—
154C2×D283—21no—
155C2×D283—21no—
156C2×D283—41no—
157C2×D283—41no—
158C2×D283—41no—
159C4×C283—21no—
160C4×C283—22no—
161C4×C283—41no—
162C4×C283—41no—
163C4×C283—41no—
164C4×C283C2×#4111yescharacteristic
165C4×C283H(5,𝔽2)11yescharacteristic
166Dic283—21no—
167Dic283—21no—
168Dic283—21no—
169Dic283—41no—
170Dic283—41no—
171Dic283—41no—
172C2×C283—22no—
173C2×C283#54611yescharacteristic
174C2×C283C2×#13511yescharacteristic
175C2×C283#57811yescharacteristic
176D283—41no—
177D283—81no—
178C283#330011yescharacteristic, complemented, Sylow
179#3300—2831nomaximal, Sylow
180#552—2831no—
181#548—2831no—
182#488—2831no—
183#485—2831no—
184#480—2831no—
185#479—2831no—
186#467—2831no—
187#465—2831no—
188#464—2831no—
189#452—2831no—
190#451—2831no—
191C4×Q16—2831no—
192C8×D4—2831no—
193#416—2831no—
194C2×#103D28311yescharacteristic, complemented
195C2×#41—2831no—
196C22×Q8C2×D28311yescharacteristic
197C2×Q16—2831no—
198C2×Q16—2831no—
199C2×SD16—2831no—
200C22×C8—2831no—
201C22×C8C2×D28311yescharacteristic
202#126—5661no—
203#125—2831no—
204#125—5661no—
205#124—2831no—
206#124—5661no—
207#123—5661no—
208C22⋊Q8—2831no—
209C22⋊Q8—2831no—
210C22⋊Q8—2831no—
211C22⋊Q8—5661no—
212#121—2831no—
213#121—5661no—
214C4×Q8—2831no—
215C4×Q8—2831no—
216C4×D4—2831no—
217C4×D4—5661no—
218#117—2831no—
219#117—5661no—
220C2×C4⋊C4C2×D28311yescharacteristic
221#107—2831no—
222#107—2831no—
223#106—2831no—
224C4⋊C8—2831no—
225#103—2831no—
226#103—2831no—
227#103—2831no—
228#103C2×D28311yescharacteristic
229#103C2×D28311yescharacteristic
230#103C2×D28311yescharacteristic
231#103C2×D28311yescharacteristic
232#102—2831no—
233#102—2831no—
234#102—2831no—
235C22⋊C8—2831no—
236C22⋊C8—2831no—
237C4×C8—2831no—
238#41—5662no—
239#41—11321no—
240C2×Q8—21no—
241C2×Q8—22no—
242C2×Q8—41no—
243C2×Q8—2831no—
244C2×Q8C22×D28311yescharacteristic
245C2×Q8C22×D28311yescharacteristic
246C2×D4—2831no—
247C2×D4—2831no—
248C2×D4—5661no—
249C2×D4—5661no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—2831no—
253C22×C4—5661no—
254C22×C4C22×D28311yescharacteristic
255Q16—5662no—
256Q16—11321no—
257SD16—11321no—
258C2×C8—41no—
259C2×C8—2831no—
260C2×C8—2831no—
261C2×C8—11321no—
262C2×C8C22×D28311yescharacteristic
263C2×C8C22×D28311yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—2831no—
266C4⋊C4—2831no—
267C4⋊C4—2831no—
268C4⋊C4—5661no—
269C4⋊C4—5661no—
270C4⋊C4—5661no—
271C4⋊C4—5661no—
272C4⋊C4—5661no—
273C4⋊C4—5661no—
274C4⋊C4—5661no—
275C4⋊C4C22×D28311yescharacteristic
276C4⋊C4C22×D28311yescharacteristic
277C22⋊C4—2831no—
278C22⋊C4—2831no—
279C22⋊C4—5661no—
280C22⋊C4—5661no—
281C22⋊C4—5661no—
282C22⋊C4—5661no—
283C22⋊C4—5661no—
284C22⋊C4—5661no—
285C22⋊C4—5661no—
286C42—2831no—
287C42—5661no—
288C42—5661no—
289C42—5661no—
290C23—2831no—
291C23—5661no—
292C23D4×D28311yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—42no—
297Q8—5661no—
298Q8—5661no—
299Q8#1798539212yes—
300D4—5662no—
301D4—5661no—
302D4—5661no—
303D4—11322no—
304D4—11322no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—2831no—
314C2×C4—2831no—
315C2×C4—2831no—
316C2×C4—5661no—
317C2×C4—5661no—
318C2×C4—5661no—
319C2×C4—5661no—
320C2×C4—5661no—
321C2×C4—11322no—
322C2×C4D4×D28311yescharacteristic
323C2×C4C23×D28311yescharacteristic
324C8—21no—
325C8—21no—
326C8—5661no—
327C8—5661no—
328C22—21no—
329C22—21no—
330C22—5661no—
331C22—5661no—
332C22—5661no—
333C22—11321no—
334C22—11321no—
335C22—11321no—
336C22#2258363112yes—
337C22C2×D4×D28311yescharacteristic
338C4—21no—
339C4—22no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—5661no—
344C4—5661no—
345C4—5661no—
346C4—11321no—
347C4—11321no—
348C4—11321no—
349C4C2×#1798539211yescharacteristic
350C4#2258365511yescharacteristic
351C2—22no—
352C2—11321no—
353C2—22641no—
354C2#3182710511yescharacteristic
355C2C2×#2258363111yescharacteristic
356C2#3182727811yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC2×#103×C283C2
socleC22×C283C22×D4
prime radical#31827126C2
hypercenterC2×#103D283
hypocenterC283#3300
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. #31827150C2semidirect
3. #31826821C2semidirect
4. #31826804C2semidirect
5. #31826778C2semidirect
6. #31826770C2semidirect
7. #31826705C2semidirect
8. #31826694C2semidirect
9. #31826690C2semidirect
10. #31826630C2semidirect
11. #31826621C2semidirect
12. #31826557C2semidirect
13. C8×C22⋊D283C2semidirect
14. #31826460C2semidirect
15. C2×#103×C283C2semidirect
178. C283#3300semidirect
194. C2×#103D283semidirect

Maximal subgroups

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

subgroupindex
#318271502
#318271262
#318268212
#318268042
#318267782
#318267702
#318267052
#318266942
#318266902
#318266302
#318266212
#318265572
C8×C22⋊D2832
#318264602
C2×#103×C2832
#3300283