Finite Group Databasebeta

← #49131460

Subgroups — #49131460

Order 36224.

396 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#31827070C211yesmaximal, characteristic, complemented
2#31826783C211yesmaximal, characteristic, complemented
3#31826778C211yesmaximal, characteristic, complemented
4#31826772C211yesmaximal, characteristic, complemented
5#31826765C211yesmaximal, characteristic, complemented
6#31826665C211yesmaximal, characteristic, complemented
7#31826660C211yesmaximal, characteristic, complemented
8#31826610C211yesmaximal, characteristic, complemented
9#31826610C211yesmaximal, characteristic, complemented
10#31826575C211yesmaximal, characteristic, complemented
11#31826563C211yesmaximal, characteristic, complemented
12C4×#17985379C211yesmaximal, characteristic, complemented
13C4×#17985377C211yesmaximal, characteristic, complemented
14#31826526C211yesmaximal, characteristic, complemented
15#520×C283C211yesmaximal, characteristic, complemented
16C2×#17985379C2211yescharacteristic
17C2×#17985379C2211yescharacteristic
18C2×#17985377C2211yescharacteristic
19C2×#17985377C2211yescharacteristic
20#22583607C2211yescharacteristic
21#22583602C2211yescharacteristic
22#22583595—21no—
23#22583595—21no—
24#22583584C2211yescharacteristic
25#22583584C2211yescharacteristic
26#22583583—21no—
27#22583583—21no—
28C4×D1132C2211yescharacteristic
29C4×D1132C2211yescharacteristic
30#22583543C2211yescharacteristic
31#22583543C2211yescharacteristic
32#22583541C2211yescharacteristic
33#22583541C2211yescharacteristic
34C4⋊(C283⋊C8)C2211yescharacteristic
35C4⋊(C283⋊C8)C2211yescharacteristic
36#22583534C2211yescharacteristic
37#22583534C2211yescharacteristic
38#22583531C2211yescharacteristic
39#22583531C2211yescharacteristic
40#22583530C2211yescharacteristic
41#22583530C2211yescharacteristic
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×D1132—21no—
60C2×D1132—21no—
61C2×D1132C2311yescharacteristic
62C2×D1132C2311yescharacteristic
63C2×C22⋊D283—21no—
64C2×C22⋊D283—21no—
65C2×C4×D283—21no—
66C2×C4×D283—21no—
67#17985379—22no—
68#17985379—22no—
69#17985377—22no—
70#17985377—22no—
71C2×C283⋊C8C2311yescharacteristic
72C2×C283⋊C8C2311yescharacteristic
73C2×C283⋊C8C2311yescharacteristic
74C2×C283⋊C8C2311yescharacteristic
75C4⋊Dic283C2311yescharacteristic
76C4⋊Dic283C2311yescharacteristic
77Dic283⋊C4—21no—
78Dic283⋊C4—21no—
79(C2×D283)⋊C4—21no—
80(C2×D283)⋊C4—21no—
81(C2×D283)⋊C4—21no—
82(C2×D283)⋊C4—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—
109C22×D283—21no—
110D1132—21no—
111D1132—21no—
112D1132—21no—
113D1132—21no—
114D1132—81no—
115D1132—81no—
116C22⋊D283—81no—
117C22⋊D283—81no—
118C2×Dic283—21no—
119C2×Dic283—21no—
120C4×D283—81no—
121C4×D283—81no—
122C283⋊C8—21no—
123C283⋊C8—21no—
124C283⋊C8—21no—
125C283⋊C8—21no—
126C23×C283—21no—
127C23×C283C2×D411yescharacteristic
128Q8×C283—21no—
129Q8×C283#4112yes—
130D4×C283—24no—
131D4×C283—21no—
132D4×C283#4112yes—
133C2×C4×C283—24no—
134C2×C4×C283—21no—
135C2×C4×C283—21no—
136C2×C4×C283—21no—
137C2×C4×C283—21no—
138C2×C4×C283—21no—
139C2×C4×C283—81no—
140C2×C4×C283—81no—
141C2×C4×C283—81no—
142C2×C4×C283C2×D411yescharacteristic
143C2×C4×C283C2×D411yescharacteristic
144C2×C4×C283C2×D411yescharacteristic
145C2×C4×C283C2×D411yescharacteristic
146C2×C4×C283C2×D411yescharacteristic
147C2×C4×C283C2411yescharacteristic
148C22×C283—21no—
149C22×C283—22no—
150C22×C283—21no—
151C22×C283—21no—
152C22×C283—41no—
153C22×C283—41no—
154C22×C283C22×D411yescharacteristic
155C2×D283—41no—
156C2×D283—41no—
157C2×D283—41no—
158C2×D283—41no—
159C2×D283—41no—
160C2×D283—41no—
161C4×C283—21no—
162C4×C283—22no—
163C4×C283—21no—
164C4×C283—21no—
165C4×C283—21no—
166C4×C283—21no—
167C4×C283—41no—
168C4×C283—41no—
169C4×C283C2×#4111yescharacteristic
170C4×C283C2×#4111yescharacteristic
171Dic283—41no—
172Dic283—41no—
173C2×C283—41no—
174C2×C283—42no—
175C2×C283#52511yescharacteristic
176C2×C283#57611yescharacteristic
177C2×C283#57711yescharacteristic
178D283—81no—
179D283—81no—
180C283#311911yescharacteristic, complemented, Sylow
181#3119—2831nomaximal, Sylow
182#540—2831no—
183#520D28311yescharacteristic, complemented
184#481—2831no—
185#480—2831no—
186#479—2831no—
187#478—2831no—
188#460—2831no—
189#459—2831no—
190#449—2831no—
191#449—2831no—
192#442—2831no—
193#440—2831no—
194C4×SD16—2831no—
195C4×D8—2831no—
196#433—2831no—
197C2×#41C2×D28311yescharacteristic
198C2×SD16—2831no—
199C2×SD16—2831no—
200C2×D8—2831no—
201C2×D8—2831no—
202#127—2831no—
203#125—2831no—
204#123—5661no—
205#123—5661no—
206#121—2831no—
207#121—2831no—
208#121—5661no—
209#121—5661no—
210C4×Q8C2×D28311yescharacteristic
211C4×Q8C2×D28311yescharacteristic
212C4×D4—21no—
213C4×D4—21no—
214C4×D4—2831no—
215C4×D4—2831no—
216C4×D4C2×D28311yescharacteristic
217C4×D4C2×D28311yescharacteristic
218#117—21no—
219#117C2×D28311yescharacteristic
220C2×C4⋊C4—21no—
221C2×C4⋊C4C2×D28311yescharacteristic
222#107—2831no—
223#107—2831no—
224#106—2831no—
225#106—2831no—
226C4⋊C8—2831no—
227C4⋊C8—2831no—
228#103—2831no—
229#103—2831no—
230#102—2831no—
231#102—2831no—
232#102—2831no—
233#102—2831no—
234#102—2831no—
235#102—2831no—
236C22⋊C8—2831no—
237C22⋊C8—2831no—
238#97—2831no—
239C4×C8—2831no—
240#41—22no—
241#41—22no—
242C2×Q8C22×D28311yescharacteristic
243C2×D4—21no—
244C2×D4—2831no—
245C2×D4—2831no—
246C2×D4—5661no—
247C2×D4—5661no—
248C2×D4—5661no—
249C2×D4—5661no—
250C2×D4C22×D28311yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—5661no—
256C22×C4—5661no—
257C22×C4C22×D28311yescharacteristic
258SD16—5662no—
259SD16—5662no—
260D8—5662no—
261D8—5662no—
262C2×C8—2831no—
263C2×C8—2831no—
264C2×C8—2831no—
265C2×C8—2831no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—2831no—
270C4⋊C4—2831no—
271C4⋊C4—5661no—
272C4⋊C4—5661no—
273C4⋊C4C22⋊D28311yescharacteristic
274C4⋊C4C22⋊D28311yescharacteristic
275C4⋊C4C22×D28311yescharacteristic
276C4⋊C4C22×D28311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—5661no—
280C22⋊C4—5661no—
281C22⋊C4—5661no—
282C22⋊C4—5661no—
283C22⋊C4C22⋊D28311yescharacteristic
284C22⋊C4C22⋊D28311yescharacteristic
285C42—21no—
286C42—21no—
287C42C22×D28311yescharacteristic
288C42C22×D28311yescharacteristic
289C23—21no—
290C23—5661no—
291C23—5661no—
292C23C2×C22⋊D28311yescharacteristic
293Q8—21no—
294Q8#1798539212yes—
295D4—24no—
296D4—21no—
297D4—5661no—
298D4—5661no—
299D4—5661no—
300D4—5661no—
301D4—22641no—
302D4—22641no—
303D4—22641no—
304D4—22641no—
305D4#1798539212yes—
306C2×C4—24no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—5661no—
316C2×C4—5661no—
317C2×C4—22641no—
318C2×C4—22641no—
319C2×C4C2×C22⋊D28311yescharacteristic
320C2×C4C2×C22⋊D28311yescharacteristic
321C2×C4C2×C22⋊D28311yescharacteristic
322C2×C4C2×C22⋊D28311yescharacteristic
323C2×C4C2×C22⋊D28311yescharacteristic
324C2×C4C23×D28311yescharacteristic
325C8—5661no—
326C8—5661no—
327C8—5661no—
328C8—5661no—
329C22—21no—
330C22—22no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—11321no—
336C22—11321no—
337C22—11321no—
338C22—11321no—
339C22—11321no—
340C22—11321no—
341C22C22×C22⋊D28311yescharacteristic
342C4—21no—
343C4—22no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—41no—
349C4—41no—
350C4—11321no—
351C4—11321no—
352C4C2×#1798539211yescharacteristic
353C4C2×#1798539211yescharacteristic
354C2—41no—
355C2—42no—
356C2—22641no—
357C2—22641no—
358C2#3182697611yescharacteristic
359C2#3182726811yescharacteristic
360C2#3182727311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#520×C283C2
socleC22×C283C22×D4
hypercenter#520D283
hypocenterC283#3119
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. #31827070C2semidirect
2. #31826783C2semidirect
3. #31826778C2semidirect
4. #31826772C2semidirect
5. #31826765C2semidirect
6. #31826665C2semidirect
7. #31826660C2semidirect
8. #31826610C2semidirect
9. #31826610C2semidirect
10. #31826575C2semidirect
11. #31826563C2semidirect
12. C4×#17985379C2semidirect
13. C4×#17985377C2semidirect
14. #31826526C2semidirect
15. #520×C283C2semidirect
180. C283#3119semidirect
183. #520D283semidirect

Maximal subgroups

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

subgroupindex
#318270702
#318267832
#318267782
#318267722
#318267652
#318266652
#318266602
#318266102
#318265752
#318265632
C4×#179853792
C4×#179853772
#318265262
#520×C2832
#3119283