Finite Group Databasebeta

← #49131381

Subgroups — #49131381

Order 36224.

424 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827012C211yesmaximal, characteristic
2C4×Q8×D283C211yesmaximal, characteristic, complemented
3#31826780C211yesmaximal, characteristic, complemented
4#31826777C211yesmaximal, characteristic, complemented
5#31826759C211yesmaximal, characteristic, complemented
6#31826758C211yesmaximal, characteristic, complemented
7#31826664C211yesmaximal, characteristic, complemented
8#31826663C211yesmaximal, characteristic, complemented
9#31826605C211yesmaximal, characteristic, complemented
10#31826602C211yesmaximal, characteristic, complemented
11#31826567C211yesmaximal, characteristic, complemented
12#31826565C211yesmaximal, characteristic, complemented
13#31826563C211yesmaximal, characteristic, complemented
14#31826520C211yesmaximal, characteristic, complemented
15#440×C283C211yesmaximal, characteristic, complemented
16C2×#17985392—21no—
17C2×Q8×D283C2211yescharacteristic
18C2×#17985381C2211yescharacteristic
19C2×#17985380C2211yescharacteristic
20C2×#17985379C2211yescharacteristic
21#22583609C2211yescharacteristic
22#22583606C2211yescharacteristic
23#22583596—21no—
24#22583585C2211yescharacteristic
25#22583583—21no—
26#22583581C2211yescharacteristic
27Q8×Dic283C2211yescharacteristic
28C4×Dic566—21no—
29C4×Dic566C2211yescharacteristic
30#22583575—21no—
31#22583575C2211yescharacteristic
32C4×D1132C2211yescharacteristic
33C4×C22⋊D283—21no—
34C4⋊C4×D283—21no—
35C4⋊C4×D283C2211yescharacteristic
36C42×D283—21no—
37C42×D283C2211yescharacteristic
38#22583544C2211yescharacteristic
39#22583543C2211yescharacteristic
40#22583543C2211yescharacteristic
41Dic283⋊C8C2211yescharacteristic
42Dic283⋊C8C2211yescharacteristic
43#22583535C2211yescharacteristic
44#22583534C2211yescharacteristic
45#22583533C2211yescharacteristic
46#22583532C2211yescharacteristic
47#22583531C2211yescharacteristic
48#22583530C2211yescharacteristic
49(C2×D283)⋊C8C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51#22583521C2211yescharacteristic
52C2×SD16×C283C2211yescharacteristic
53C4×Q8×C283C2211yescharacteristic
54C4×D4×C283C2211yescharacteristic
55#107×C283C2211yescharacteristic
56#103×C283C2211yescharacteristic
57#102×C283C2211yescharacteristic
58#97×C283C2211yescharacteristic
59#17985392—44no—
60C2×Dic566—21no—
61C2×Dic566—21no—
62C2×Dic566C2311yescharacteristic
63Q8×D283—22no—
64Q8×D283—22no—
65C2×D1132—21no—
66C2×D1132C2311yescharacteristic
67C2×C22⋊D283—21no—
68C2×C22⋊D283—21no—
69C2×C22⋊D283—21no—
70C2×C4×D283—21no—
71C2×C4×D283—21no—
72C2×C4×D283—21no—
73C2×C4×D283D411yescharacteristic
74C2×C4×D283D411yescharacteristic
75C2×C4×D283C2311yescharacteristic
76#17985381—22no—
77#17985380—22no—
78#17985379—22no—
79C2×C283⋊C8C2311yescharacteristic
80C2×C283⋊C8C2311yescharacteristic
81C4⋊Dic283—21no—
82C4⋊Dic283C2311yescharacteristic
83C4⋊Dic283C2311yescharacteristic
84Dic283⋊C4—21no—
85Dic283⋊C4—21no—
86Dic283⋊C4—21no—
87Dic283⋊C4—21no—
88C22⋊Dic283—21no—
89(C2×D283)⋊C4—21no—
90(C2×D283)⋊C4—21no—
91C4×Dic283—21no—
92C4×Dic283—21no—
93C4×Dic283—21no—
94C4×Dic283D411yescharacteristic
95C4×Dic283D411yescharacteristic
96C4×Dic283C2311yescharacteristic
97C2×Q8×C283C2311yescharacteristic
98C2×D4×C283C2311yescharacteristic
99C22×C4×C283—21no—
100SD16×C283—22no—
101C2×C8×C283C2311yescharacteristic
102C2×C8×C283C2311yescharacteristic
103C4⋊C4×C283—21no—
104C4⋊C4×C283C2311yescharacteristic
105C4⋊C4×C283C2311yescharacteristic
106C22⋊C4×C283—21no—
107C42×C283—21no—
108C42×C283C2311yescharacteristic
109C22×D283—21no—
110C22×D283C2×D411yescharacteristic
111Dic566—24no—
112Dic566—21no—
113Dic566—42no—
114Dic566#4112yescomplemented
115D1132—21no—
116D1132—21no—
117D1132—42no—
118C22⋊D283—42no—
119C22⋊D283—42no—
120C22⋊D283—42no—
121C2×Dic283—21no—
122C2×Dic283—21no—
123C2×Dic283—21no—
124C2×Dic283C2×D411yescharacteristic
125C2×Dic283C2×D411yescharacteristic
126C2×Dic283C2×D411yescharacteristic
127C4×D283—24no—
128C4×D283—22no—
129C4×D283—21no—
130C4×D283—21no—
131C4×D283—22no—
132C4×D283—42no—
133C4×D283—42no—
134C283⋊C8—21no—
135C283⋊C8—21no—
136C23×C283—21no—
137Q8×C283—21no—
138Q8×C283#4112yescomplemented
139D4×C283—21no—
140D4×C283—21no—
141C2×C4×C283—21no—
142C2×C4×C283—21no—
143C2×C4×C283—21no—
144C2×C4×C283—42no—
145C2×C4×C283C2×D411yescharacteristic
146C2×C4×C283C2×D411yescharacteristic
147C2×C4×C283C2411yescharacteristic
148C8×C283—21no—
149C8×C283—21no—
150C22×C283—41no—
151C22×C283—41no—
152C22×C283—41no—
153C22×C283C22×D411yescharacteristic
154C2×D283—21no—
155C2×D283—21no—
156C2×D283—41no—
157C2×D283—41no—
158C2×D283—41no—
159C2×D283AGL(1,ℤ/8)12yes—
160C4×C283—22no—
161C4×C283—21no—
162C4×C283—21no—
163C4×C283—41no—
164C4×C283—41no—
165C4×C283C2×#4111yescharacteristic
166C4×C283C2×#4111yescharacteristic
167Dic283—22no—
168Dic283—21no—
169Dic283—21no—
170Dic283—41no—
171Dic283—41no—
172Dic283#13712yes—
173C2×C283—81no—
174C2×C283#52511yescharacteristic
175C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
176C2×C283C2×#13711yescharacteristic
177D283—22no—
178D283—81no—
179C283#311211yescharacteristic, complemented, Sylow
180#3112—2831nomaximal, Sylow
181#532—2831no—
182C2×C4×Q8—2831no—
183#480—2831no—
184#480—2831no—
185#477—2831no—
186#477—2831no—
187#460—2831no—
188#460—2831no—
189#448—2831no—
190#448—2831no—
191#440—2831no—
192#440—2831no—
193#440—2831no—
194#440D28311yescharacteristic, complemented
195#432—2831no—
196C2×#41—5661no—
197C22×Q8—2831no—
198C2×SD16—2831no—
199C2×SD16—2831no—
200C2×SD16—2831no—
201C2×SD16C2×D28311yescharacteristic
202C4⋊Q8—2831no—
203#127—2831no—
204#124—5661no—
205#121—2831no—
206#121—2831no—
207#121—5661no—
208C4×Q8—2831no—
209C4×Q8—2831no—
210C4×Q8—2831no—
211C4×Q8—5661no—
212C4×Q8—5661no—
213C4×Q8C2×D28311yescharacteristic
214C4×D4—2831no—
215C4×D4—5661no—
216C4×D4C2×D28311yescharacteristic
217C2×C4⋊C4—2831no—
218C2×C4⋊C4—5661no—
219C2×C42—2831no—
220C2×C42—5661no—
221#107—2831no—
222#107—2831no—
223#107—2831no—
224#107C2×D28311yescharacteristic
225C4⋊C8—2831no—
226C4⋊C8—2831no—
227#103—2831no—
228#103—2831no—
229#103—2831no—
230#103C2×D28311yescharacteristic
231#102—2831no—
232#102—2831no—
233#102—2831no—
234#102C2×D28311yescharacteristic
235C22⋊C8—2831no—
236C22⋊C8—2831no—
237#97—2831no—
238#97C2×D28311yescharacteristic
239#41—11324no—
240C2×Q8—2831no—
241C2×Q8—5661no—
242C2×Q8—5661no—
243C2×Q8—5662no—
244C2×Q8—5662no—
245C2×Q8C22×D28311yescharacteristic
246C2×D4—2831no—
247C2×D4—5661no—
248C2×D4—5661no—
249C2×D4—5661no—
250C2×D4—5661no—
251C2×D4C22×D28311yescharacteristic
252C22×C4—21no—
253C22×C4—2831no—
254C22×C4—2831no—
255C22×C4—2831no—
256C22×C4—5661no—
257C22×C4—5661no—
258C22×C4—5661no—
259SD16—22no—
260SD16—5662no—
261SD16—5662no—
262SD16—5662no—
263C2×C8—2831no—
264C2×C8—2831no—
265C2×C8C22×D28311yescharacteristic
266C2×C8C22×D28311yescharacteristic
267C4⋊C4—21no—
268C4⋊C4—2831no—
269C4⋊C4—2831no—
270C4⋊C4—5661no—
271C4⋊C4—5661no—
272C4⋊C4—5661no—
273C4⋊C4—5661no—
274C4⋊C4—5661no—
275C4⋊C4C22×D28311yescharacteristic
276C4⋊C4C22×D28311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—5661no—
279C22⋊C4—5661no—
280C22⋊C4—5661no—
281C42—21no—
282C42—2831no—
283C42—2831no—
284C42—2831no—
285C42—5661no—
286C42—5661no—
287C42—5661no—
288C42C22×D28311yescharacteristic
289C23—21no—
290C23—2831no—
291C23—5661no—
292Q8—21no—
293Q8—2832no—
294Q8—5664no—
295Q8—5661no—
296Q8—11322no—
297Q8#1798539212yescomplemented
298D4—21no—
299D4—21no—
300D4—5661no—
301D4—5661no—
302D4—11322no—
303D4—11322no—
304D4—11322no—
305D4—11322no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—2831no—
311C2×C4—2831no—
312C2×C4—2831no—
313C2×C4—5662no—
314C2×C4—5662no—
315C2×C4—5664no—
316C2×C4—5661no—
317C2×C4—5661no—
318C2×C4—5661no—
319C2×C4—5661no—
320C2×C4—5661no—
321C2×C4—11322no—
322C2×C4—11322no—
323C2×C4D4×D28311yescharacteristic
324C2×C4D4×D28311yescharacteristic
325C2×C4C23×D28311yescharacteristic
326C8—21no—
327C8—21no—
328C8—5661no—
329C8—5661no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—2832no—
334C22—5661no—
335C22—5661no—
336C22—11321no—
337C22—11321no—
338C22—11321no—
339C22C2×D4×D28311yescharacteristic
340C4—22no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—2832no—
346C4—5661no—
347C4—5662no—
348C4—5661no—
349C4—11321no—
350C4—11321no—
351C4#41×D28311yescharacteristic
352C4C2×#1798539211yescharacteristic
353C2—81no—
354C2—5662no—
355C2—22641no—
356C2#3182697411yescharacteristic
357C2AGL(1,ℤ/8)×D28311yescharacteristic
358C2#137×D28311yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#440×C283C2
socleC22×C283C22×D4
prime radical#31827012C2
hypercenter#440D283
hypocenterC283#3112
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D283C2semidirect
3. #31826780C2semidirect
4. #31826777C2semidirect
5. #31826759C2semidirect
6. #31826758C2semidirect
7. #31826664C2semidirect
8. #31826663C2semidirect
9. #31826605C2semidirect
10. #31826602C2semidirect
11. #31826567C2semidirect
12. #31826565C2semidirect
13. #31826563C2semidirect
14. #31826520C2semidirect
15. #440×C283C2semidirect
114. Dic566#41semidirect
138. Q8×C283#41semidirect
179. C283#3112semidirect
194. #440D283semidirect
297. Q8#17985392semidirect

Maximal subgroups

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

subgroupindex
#318270122
C4×Q8×D2832
#318267802
#318267772
#318267592
#318267582
#318266642
#318266632
#318266052
#318266022
#318265672
#318265652
#318265632
#318265202
#440×C2832
#3112283