Finite Group Databasebeta

← #49131523

Subgroups — #49131523

Order 36224.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827086C211yesmaximal, characteristic, complemented
2#31826800C211yesmaximal, characteristic, complemented
3#31826778C211yesmaximal, characteristic, complemented
4#31826760C211yesmaximal, characteristic, complemented
5#31826745C211yesmaximal, characteristic, complemented
6#31826687C211yesmaximal, characteristic, complemented
7#31826680C211yesmaximal, characteristic, complemented
8#31826627C211yesmaximal, characteristic, complemented
9#31826610C211yesmaximal, characteristic
10#31826565C211yesmaximal, characteristic, complemented
11#31826563C211yesmaximal, characteristic, complemented
12C4×#17985382C211yesmaximal, characteristic, complemented
13C4×#17985377C211yesmaximal, characteristic, complemented
14#31826526C211yesmaximal, characteristic, complemented
15#520×C283C211yesmaximal, characteristic, complemented
16C2×#17985382C2211yescharacteristic
17C2×#17985380C2211yescharacteristic
18C2×#17985379C2211yescharacteristic
19C2×#17985377C2211yescharacteristic
20#22583610C2211yescharacteristic
21#22583605—21no—
22#22583598C2211yescharacteristic
23#22583596—21no—
24#22583592—21no—
25#22583589C2211yescharacteristic
26#22583588—21no—
27#22583584C2211yescharacteristic
28C4×Dic566C2211yescharacteristic
29C4×D1132C2211yescharacteristic
30#22583543C2211yescharacteristic
31#22583543C2211yescharacteristic
32#22583543C2211yescharacteristic
33#22583543C2211yescharacteristic
34C4⋊(C283⋊C8)C2211yescharacteristic
35C4⋊(C283⋊C8)C2211yescharacteristic
36#22583534C2211yescharacteristic
37#22583534C2211yescharacteristic
38#22583533C2211yescharacteristic
39#22583533C2211yescharacteristic
40#22583531C2211yescharacteristic
41#22583531C2211yescharacteristic
42#22583530C2211yescharacteristic
43#22583530C2211yescharacteristic
44C22⋊(C283⋊C8)C2211yescharacteristic
45C22⋊(C283⋊C8)C2211yescharacteristic
46#22583521C2211yescharacteristic
47C4×C283⋊C8C2211yescharacteristic
48C2×#41×C283C2211yescharacteristic
49C4×Q8×C283C2211yescharacteristic
50C4×Q8×C283C2211yescharacteristic
51C4×D4×C283—21no—
52C4×D4×C283—21no—
53C4×D4×C283C2211yescharacteristic
54C4×D4×C283C2211yescharacteristic
55#117×C283—21no—
56#117×C283C2211yescharacteristic
57C2×C4⋊C4×C283—21no—
58C2×C4⋊C4×C283C2211yescharacteristic
59C2×Dic566—21no—
60C2×Dic566C2311yescharacteristic
61C2×D1132C2311yescharacteristic
62C2×C22⋊D283—21no—
63C2×C4×D283—21no—
64#17985382—22no—
65#17985380—22no—
66#17985379—22no—
67#17985377—22no—
68C2×C283⋊C8C2311yescharacteristic
69C2×C283⋊C8C2311yescharacteristic
70C2×C283⋊C8C2311yescharacteristic
71C2×C283⋊C8C2311yescharacteristic
72C4⋊Dic283—21no—
73C4⋊Dic283C2311yescharacteristic
74C4⋊Dic283C2311yescharacteristic
75Dic283⋊C4—21no—
76Dic283⋊C4—21no—
77C22⋊Dic283—21no—
78(C2×D283)⋊C4—21no—
79(C2×D283)⋊C4—21no—
80(C2×D283)⋊C4—21no—
81(C2×D283)⋊C4—21no—
82C4×Dic283—21no—
83#41×C283—22no—
84#41×C283—22no—
85C2×Q8×C283C2311yescharacteristic
86C2×D4×C283—21no—
87C2×D4×C283C2311yescharacteristic
88C22×C4×C283—21no—
89C22×C4×C283—21no—
90C22×C4×C283—21no—
91C22×C4×C283—21no—
92C22×C4×C283C2311yescharacteristic
93C4⋊C4×C283—21no—
94C4⋊C4×C283—21no—
95C4⋊C4×C283—21no—
96C4⋊C4×C283D411yescharacteristic
97C4⋊C4×C283D411yescharacteristic
98C4⋊C4×C283C2311yescharacteristic
99C4⋊C4×C283C2311yescharacteristic
100C22⋊C4×C283—21no—
101C22⋊C4×C283—21no—
102C22⋊C4×C283D411yescharacteristic
103C22⋊C4×C283D411yescharacteristic
104C42×C283—21no—
105C42×C283—21no—
106C42×C283C2311yescharacteristic
107C42×C283C2311yescharacteristic
108C22×D283—21no—
109Dic566—21no—
110Dic566—21no—
111Dic566—81no—
112D1132—21no—
113D1132—21no—
114C22⋊D283—81no—
115C2×Dic283—21no—
116C2×Dic283—21no—
117C2×Dic283—21no—
118C4×D283—81no—
119C283⋊C8—21no—
120C283⋊C8—21no—
121C283⋊C8—21no—
122C283⋊C8—21no—
123C23×C283—21no—
124C23×C283C2×D411yescharacteristic
125Q8×C283—21no—
126Q8×C283#4112yes—
127D4×C283—24no—
128D4×C283—21no—
129D4×C283#4112yes—
130C2×C4×C283—24no—
131C2×C4×C283—21no—
132C2×C4×C283—21no—
133C2×C4×C283—21no—
134C2×C4×C283—21no—
135C2×C4×C283—21no—
136C2×C4×C283—81no—
137C2×C4×C283—81no—
138C2×C4×C283—81no—
139C2×C4×C283C2×D411yescharacteristic
140C2×C4×C283C2×D411yescharacteristic
141C2×C4×C283C2×D411yescharacteristic
142C2×C4×C283C2×D411yescharacteristic
143C2×C4×C283C2×D411yescharacteristic
144C2×C4×C283C2411yescharacteristic
145C22×C283—21no—
146C22×C283—22no—
147C22×C283—21no—
148C22×C283—21no—
149C22×C283—41no—
150C22×C283—41no—
151C22×C283C22×D411yescharacteristic
152C2×D283—41no—
153C2×D283—41no—
154C2×D283—41no—
155C4×C283—21no—
156C4×C283—22no—
157C4×C283—21no—
158C4×C283—21no—
159C4×C283—21no—
160C4×C283—21no—
161C4×C283—41no—
162C4×C283—41no—
163C4×C283C2×#4111yescharacteristic
164C4×C283C2×#4111yescharacteristic
165Dic283—41no—
166Dic283—41no—
167Dic283—41no—
168C2×C283—41no—
169C2×C283—42no—
170C2×C283#52511yescharacteristic
171C2×C283#57611yescharacteristic
172C2×C283#57811yescharacteristic
173D283—81no—
174C283#312411yescharacteristic, complemented, Sylow
175#3124—2831nomaximal, Sylow
176#542—2831no—
177#520D28311yescharacteristic, complemented
178#484—2831no—
179#480—2831no—
180#477—2831no—
181#474—2831no—
182#464—2831no—
183#463—2831no—
184#452—2831no—
185#449—2831no—
186#440—2831no—
187#440—2831no—
188C4×Q16—2831no—
189C4×D8—2831no—
190#433—2831no—
191C2×#41C2×D28311yescharacteristic
192C2×Q16—2831no—
193C2×SD16—2831no—
194C2×SD16—2831no—
195C2×D8—2831no—
196C4⋊Q8—2831no—
197#126—5661no—
198#124—2831no—
199#124—5661no—
200#123—5661no—
201C22⋊Q8—2831no—
202C22⋊Q8—5661no—
203#121—2831no—
204C4×Q8—2831no—
205C4×Q8C2×D28311yescharacteristic
206C4×Q8C2×D28311yescharacteristic
207C4×D4—21no—
208C4×D4—21no—
209C4×D4—2831no—
210C4×D4C2×D28311yescharacteristic
211C4×D4C2×D28311yescharacteristic
212#117—21no—
213#117C2×D28311yescharacteristic
214C2×C4⋊C4—21no—
215C2×C4⋊C4C2×D28311yescharacteristic
216#107—2831no—
217#107—2831no—
218#107—2831no—
219#107—2831no—
220C4⋊C8—2831no—
221C4⋊C8—2831no—
222#103—2831no—
223#103—2831no—
224#103—2831no—
225#103—2831no—
226#102—2831no—
227#102—2831no—
228#102—2831no—
229#102—2831no—
230C22⋊C8—2831no—
231C22⋊C8—2831no—
232#97—2831no—
233C4×C8—2831no—
234#41—22no—
235#41—22no—
236C2×Q8—2831no—
237C2×Q8—5661no—
238C2×Q8C22×D28311yescharacteristic
239C2×D4—21no—
240C2×D4—2831no—
241C2×D4—5661no—
242C2×D4C22×D28311yescharacteristic
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—5661no—
248C22×C4C22×D28311yescharacteristic
249Q16—5662no—
250SD16—5662no—
251SD16—5662no—
252D8—5662no—
253C2×C8—2831no—
254C2×C8—2831no—
255C2×C8—2831no—
256C2×C8—2831no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—2831no—
261C4⋊C4—2831no—
262C4⋊C4—5661no—
263C4⋊C4—5661no—
264C4⋊C4—5661no—
265C4⋊C4C22⋊D28311yescharacteristic
266C4⋊C4C22⋊D28311yescharacteristic
267C4⋊C4C22×D28311yescharacteristic
268C4⋊C4C22×D28311yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—5661no—
272C22⋊C4—5661no—
273C22⋊C4—5661no—
274C22⋊C4—5661no—
275C22⋊C4—5661no—
276C22⋊C4C22⋊D28311yescharacteristic
277C22⋊C4C22⋊D28311yescharacteristic
278C42—21no—
279C42—21no—
280C42—5661no—
281C42C22×D28311yescharacteristic
282C42C22×D28311yescharacteristic
283C23—21no—
284C23—5661no—
285C23C2×C22⋊D28311yescharacteristic
286Q8—21no—
287Q8—5661no—
288Q8—5661no—
289Q8—22641no—
290Q8#1798539212yes—
291D4—24no—
292D4—21no—
293D4—5661no—
294D4—5661no—
295D4—22641no—
296D4#1798539212yes—
297C2×C4—24no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—5661no—
307C2×C4—5661no—
308C2×C4—5661no—
309C2×C4—22641no—
310C2×C4C2×C22⋊D28311yescharacteristic
311C2×C4C2×C22⋊D28311yescharacteristic
312C2×C4C2×C22⋊D28311yescharacteristic
313C2×C4C2×C22⋊D28311yescharacteristic
314C2×C4C2×C22⋊D28311yescharacteristic
315C2×C4C23×D28311yescharacteristic
316C8—5661no—
317C8—5661no—
318C8—5661no—
319C8—5661no—
320C22—21no—
321C22—22no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—11321no—
327C22—11321no—
328C22—11321no—
329C22C22×C22⋊D28311yescharacteristic
330C4—21no—
331C4—22no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—41no—
337C4—41no—
338C4—11321no—
339C4—11321no—
340C4—11321no—
341C4C2×#1798539211yescharacteristic
342C4C2×#1798539211yescharacteristic
343C2—41no—
344C2—42no—
345C2—22641no—
346C2#3182697611yescharacteristic
347C2#3182726811yescharacteristic
348C2#3182728011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#520×C283C2
socleC22×C283C22×D4
prime radical#31826610C2
hypercenter#520D283
hypocenterC283#3124
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ #117 ◁ #520

Complements

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

NH ≅ G/Ntype
1. #31827086C2semidirect
2. #31826800C2semidirect
3. #31826778C2semidirect
4. #31826760C2semidirect
5. #31826745C2semidirect
6. #31826687C2semidirect
7. #31826680C2semidirect
8. #31826627C2semidirect
10. #31826565C2semidirect
11. #31826563C2semidirect
12. C4×#17985382C2semidirect
13. C4×#17985377C2semidirect
14. #31826526C2semidirect
15. #520×C283C2semidirect
174. C283#3124semidirect
177. #520D283semidirect

Maximal subgroups

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

subgroupindex
#318270862
#318268002
#318267782
#318267602
#318267452
#318266872
#318266802
#318266272
#318266102
#318265652
#318265632
C4×#179853822
C4×#179853772
#318265262
#520×C2832
#3124283