Finite Group Databasebeta

← #49133882

Subgroups — #49133882

Order 36224.

354 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827179C211yesmaximal, characteristic
2#31827173C211yesmaximal, characteristic, complemented
3#31826869C211yesmaximal, characteristic, complemented
4#31826804C211yesmaximal, characteristic, complemented
5#31826803C211yesmaximal, characteristic, complemented
6#31826777C211yesmaximal, characteristic, complemented
7#31826776C211yesmaximal, characteristic, complemented
8#31826758C211yesmaximal, characteristic, complemented
9#31826753C211yesmaximal, characteristic, complemented
10#31826708C211yesmaximal, characteristic, complemented
11SD16×Dic283C211yesmaximal, characteristic, complemented
12#31826541C211yesmaximal, characteristic, complemented
13#31826507C211yesmaximal, characteristic, complemented
14#31826506C211yesmaximal, characteristic, complemented
15#468×C283C211yesmaximal, characteristic, complemented
16C2×#17985375C2211yescharacteristic
17#22583609C2211yescharacteristic
18#22583609C2211yescharacteristic
19#22583600—21no—
20#22583597—21no—
21#22583596—21no—
22#22583590—21no—
23#22583587—21no—
24#22583586C2211yescharacteristic
25#22583582—21no—
26#22583581C2211yescharacteristic
27Q8×Dic283C2211yescharacteristic
28D4×Dic283C2211yescharacteristic
29C4×C22⋊D283C2211yescharacteristic
30(C22⋊D283)⋊C4—21no—
31#22583569C2211yescharacteristic
32#22583568C2211yescharacteristic
33#22583566—21no—
34C2×C4⋊Dic283C2211yescharacteristic
35C4⋊C4×D283C2211yescharacteristic
36#22583544C2211yescharacteristic
37#22583544C2211yescharacteristic
38#22583543C2211yescharacteristic
39#22583543C2211yescharacteristic
40#22583543C2211yescharacteristic
41#22583542C2211yescharacteristic
42#22583542C2211yescharacteristic
43#22583541C2211yescharacteristic
44Dic283⋊C8C2211yescharacteristic
45#22583534C2211yescharacteristic
46#22583534C2211yescharacteristic
47#22583531C2211yescharacteristic
48#22583531C2211yescharacteristic
49C22⋊(C283⋊C8)C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51C8×Dic283C2211yescharacteristic
52C2×SD16×C283C2211yescharacteristic
53C2×M16×C283C2211yescharacteristic
54C22⋊Q8×C283C2211yescharacteristic
55#121×C283C2211yescharacteristic
56#107×C283C2211yescharacteristic
57#103×C283C2211yescharacteristic
58#102×C283C2211yescharacteristic
59C2×Dic566—21no—
60C2×Dic566—21no—
61C2×C22⋊D283—21no—
62C2×C22⋊D283D411yescharacteristic
63C22×Dic283—21no—
64C22×Dic283—21no—
65C2×C4×D283—21no—
66C2×C4×D283C2311yescharacteristic
67#17985375—22no—
68C2×C283⋊C8C2311yescharacteristic
69C2×C283⋊C8C2311yescharacteristic
70C4⋊Dic283—21no—
71C4⋊Dic283—21no—
72C4⋊Dic283C2311yescharacteristic
73C4⋊Dic283C2311yescharacteristic
74C4⋊Dic283C2311yescharacteristic
75C4⋊Dic283C2311yescharacteristic
76Dic283⋊C4—21no—
77Dic283⋊C4—21no—
78Dic283⋊C4—21no—
79Dic283⋊C4—21no—
80Dic283⋊C4D411yescharacteristic
81C22⋊Dic283—21no—
82C22⋊Dic283—21no—
83C22⋊Dic283—21no—
84C22⋊Dic283D411yescharacteristic
85(C2×D283)⋊C4—21no—
86(C2×D283)⋊C4—21no—
87(C2×D283)⋊C4D411yescharacteristic
88C4×Dic283—21no—
89C4×Dic283—21no—
90C4×Dic283—21no—
91C4×Dic283C2311yescharacteristic
92C2×Q8×C283C2311yescharacteristic
93C2×D4×C283—21no—
94C2×D4×C283C2311yescharacteristic
95C22×C4×C283C2311yescharacteristic
96SD16×C283—22no—
97M16×C283—22no—
98C2×C8×C283C2311yescharacteristic
99C2×C8×C283C2311yescharacteristic
100C4⋊C4×C283—21no—
101C4⋊C4×C283C2311yescharacteristic
102C4⋊C4×C283C2311yescharacteristic
103C22⋊C4×C283—21no—
104C22⋊C4×C283—21no—
105C22×D283C2×D411yescharacteristic
106Dic566—81no—
107Dic566—81no—
108C22⋊D283—22no—
109C22⋊D283—81no—
110C2×Dic283—21no—
111C2×Dic283—21no—
112C2×Dic283—21no—
113C2×Dic283—21no—
114C2×Dic283—42no—
115C2×Dic283—81no—
116C2×Dic283C2×D411yescharacteristic
117C2×Dic283C2×D411yescharacteristic
118C2×Dic283C2×D411yescharacteristic
119C4×D283—21no—
120C4×D283—21no—
121C4×D283—81no—
122C283⋊C8—21no—
123C283⋊C8—21no—
124C23×C283—21no—
125C23×C283C2×D411yescharacteristic
126Q8×C283—21no—
127Q8×C283—21no—
128D4×C283—21no—
129D4×C283—21no—
130D4×C283—81no—
131C2×C4×C283—21no—
132C2×C4×C283—21no—
133C2×C4×C283—21no—
134C2×C4×C283—21no—
135C2×C4×C283—21no—
136C2×C4×C283C2×D411yescharacteristic
137C2×C4×C283C2411yescharacteristic
138C8×C283—21no—
139C8×C283#4112yes—
140C22×C283—21no—
141C22×C283—21no—
142C22×C283—21no—
143C22×C283—41no—
144C22×C283—41no—
145C22×C283—41no—
146C22×C283C22×D411yescharacteristic
147C2×D283—21no—
148C2×D283—21no—
149C2×D283—21no—
150C4×C283—21no—
151C4×C283—41no—
152C4×C283—41no—
153C4×C283—41no—
154C4×C283C2×#4111yescharacteristic
155C4×C2832−1+411yescharacteristic
156Dic283—21no—
157Dic283—21no—
158Dic283—41no—
159Dic283—41no—
160Dic283—41no—
161Dic283—41no—
162Dic283#13712yes—
163C2×C283—41no—
164C2×C283—81no—
165C2×C283#54711yescharacteristic
166C2×C283C2×#13711yescharacteristic
167C2×C283#57611yescharacteristic
168D283—41no—
169C283#335711yescharacteristic, complemented, Sylow
170#3357—2831nomaximal, Sylow
171#555—2831no—
172#554—2831no—
173#500—2831no—
174#485—2831no—
175#485—2831no—
176#480—2831no—
177#480—2831no—
178#477—2831no—
179#476—2831no—
180#468—2831no—
181#468D28311yescharacteristic, complemented
182C4×SD16—2831no—
183#436—2831no—
184#428—2831no—
185#428—2831no—
186C2×SD16C2×D28311yescharacteristic
187C2×M16—2831no—
188C2×M16C2×D28311yescharacteristic
189C4⋊Q8—2831no—
190C4⋊Q8—2831no—
191#125—5661no—
192#124—5661no—
193#124—5661no—
194C22⋊Q8—2831no—
195C22⋊Q8—5661no—
196C22⋊Q8—5661no—
197C22⋊Q8C2×D28311yescharacteristic
198#121—2831no—
199#121—5661no—
200#121C2×D28311yescharacteristic
201C4×Q8—2831no—
202C4×D4—2831no—
203C4×D4—2831no—
204C4×D4—5661no—
205#117—2831no—
206#117—2831no—
207#117—5661no—
208C2×C4⋊C4—2831no—
209C2×C4⋊C4—2831no—
210#107—2831no—
211#107—2831no—
212#107—2831no—
213#107—2831no—
214#107—2831no—
215#107C2×D28311yescharacteristic
216#106—2831no—
217#106—2831no—
218#106—2831no—
219C4⋊C8—2831no—
220#103—2831no—
221#103—2831no—
222#103C2×D28311yescharacteristic
223#102—2831no—
224#102—2831no—
225#102C2×D28311yescharacteristic
226C22⋊C8—2831no—
227C22⋊C8—2831no—
228C4×C8—2831no—
229C2×Q8—5661no—
230C2×Q8—5661no—
231C2×Q8C22×D28311yescharacteristic
232C2×D4—21no—
233C2×D4—2831no—
234C2×D4—5661no—
235C2×D4C22×D28311yescharacteristic
236C22×C4—2831no—
237C22×C4—5661no—
238C22×C4—5661no—
239C22×C4—5661no—
240C22×C4C22×D28311yescharacteristic
241SD16—22no—
242M16—22no—
243M16—5662no—
244C2×C8—2831no—
245C2×C8—2831no—
246C2×C8C22×D28311yescharacteristic
247C2×C8C22×D28311yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—2831no—
250C4⋊C4—2831no—
251C4⋊C4—2831no—
252C4⋊C4—2831no—
253C4⋊C4—2831no—
254C4⋊C4—5661no—
255C4⋊C4—5661no—
256C4⋊C4—5661no—
257C4⋊C4—5661no—
258C4⋊C4—5661no—
259C4⋊C4—5661no—
260C4⋊C4C22×D28311yescharacteristic
261C4⋊C4C22×D28311yescharacteristic
262C22⋊C4—21no—
263C22⋊C4—21no—
264C22⋊C4—2831no—
265C22⋊C4—2831no—
266C22⋊C4—5661no—
267C22⋊C4—5661no—
268C22⋊C4—5661no—
269C22⋊C4—5661no—
270C22⋊C4—5661no—
271C42—2831no—
272C42—5661no—
273C42—5661no—
274C42—5661no—
275C23—21no—
276C23—2831no—
277C23D4×D28311yescharacteristic
278Q8—21no—
279Q8—21no—
280Q8—22641no—
281Q8—22641no—
282D4—21no—
283D4—21no—
284D4—81no—
285D4—5662no—
286D4—22641no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—2831no—
293C2×C4—2831no—
294C2×C4—2831no—
295C2×C4—5661no—
296C2×C4—5661no—
297C2×C4—5661no—
298C2×C4—5661no—
299C2×C4—5661no—
300C2×C4—5661no—
301C2×C4—11322no—
302C2×C4—22641no—
303C2×C4—22641no—
304C2×C4D4×D28311yescharacteristic
305C2×C4C23×D28311yescharacteristic
306C8—21no—
307C8—5661no—
308C8—5661no—
309C8#1798539112yes—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—5661no—
317C22—5661no—
318C22—5661no—
319C22C2×D4×D28311yescharacteristic
320C4—21no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—2832no—
325C4—5661no—
326C4—5661no—
327C4—11321no—
328C4—11321no—
329C4—11321no—
330C4—11321no—
331C4C2×#1798539111yescharacteristic
332C4#2258365711yescharacteristic
333C2—41no—
334C2—81no—
335C2—11321no—
336C2#3182711511yescharacteristic
337C2#137×D28311yescharacteristic
338C2#3182726911yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#468×C283C2
socleC22×C283C22×D4
prime radical#31827179C2
hypercenter#468D283
hypocenterC283#3357
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
2. #31827173C2semidirect
3. #31826869C2semidirect
4. #31826804C2semidirect
5. #31826803C2semidirect
6. #31826777C2semidirect
7. #31826776C2semidirect
8. #31826758C2semidirect
9. #31826753C2semidirect
10. #31826708C2semidirect
11. SD16×Dic283C2semidirect
12. #31826541C2semidirect
13. #31826507C2semidirect
14. #31826506C2semidirect
15. #468×C283C2semidirect
169. C283#3357semidirect
181. #468D283semidirect

Maximal subgroups

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

subgroupindex
#318271792
#318271732
#318268692
#318268042
#318268032
#318267772
#318267762
#318267582
#318267532
#318267082
SD16×Dic2832
#318265412
#318265072
#318265062
#468×C2832
#3357283