Finite Group Databasebeta

← #49133372

Subgroups — #49133372

Order 36224.

388 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#31827172C211yesmaximal, characteristic, complemented
2#31826824C211yesmaximal, characteristic, complemented
3#31826793C211yesmaximal, characteristic, complemented
4#31826781C211yesmaximal, characteristic, complemented
5#31826750C211yesmaximal, characteristic, complemented
6#31826721C211yesmaximal, characteristic, complemented
7#31826692C211yesmaximal, characteristic, complemented
8#31826684C211yesmaximal, characteristic, complemented
9#31826627C211yesmaximal, characteristic, complemented
10#31826621C211yesmaximal, characteristic, complemented
11#31826570C211yesmaximal, characteristic, complemented
12#31826537C211yesmaximal, characteristic, complemented
13#31826466C211yesmaximal, characteristic, complemented
14C2×#22583534C211yesmaximal, characteristic, complemented
15#548×C283C211yesmaximal, characteristic
16C2×#17985382C2211yescharacteristic
17C2×#17985382C2211yescharacteristic
18C2×#17985380C2211yescharacteristic
19C2×#17985376C2211yescharacteristic
20C22×C283⋊C8C2211yescharacteristic
21#22583610C2211yescharacteristic
22#22583601—21no—
23#22583589C2211yescharacteristic
24#22583589C2211yescharacteristic
25#22583587—21no—
26#22583587—21no—
27C4×Dic566C2211yescharacteristic
28D4×Dic283—21no—
29C2×C4⋊Dic283C2211yescharacteristic
30C2×C4⋊Dic283C2211yescharacteristic
31#22583541C2211yescharacteristic
32#22583541C2211yescharacteristic
33#22583541C2211yescharacteristic
34C4⋊(C283⋊C8)C2211yescharacteristic
35#22583534C2211yescharacteristic
36#22583534C2211yescharacteristic
37#22583534C2211yescharacteristic
38#22583534C2211yescharacteristic
39#22583534C2211yescharacteristic
40#22583534C2211yescharacteristic
41#22583533C2211yescharacteristic
42#22583531C2211yescharacteristic
43#22583531C2211yescharacteristic
44#22583531C2211yescharacteristic
45C22⋊(C283⋊C8)C2211yescharacteristic
46C22⋊(C283⋊C8)C2211yescharacteristic
47#22583521C2211yescharacteristic
48C2×#41×C283C2211yescharacteristic
49C22×Q8×C283C2211yescharacteristic
50#124×C283—21no—
51#124×C283C2211yescharacteristic
52C22⋊Q8×C283—21no—
53C22⋊Q8×C283C2211yescharacteristic
54#121×C283—21no—
55#121×C283C2211yescharacteristic
56C4×Q8×C283C2211yescharacteristic
57C4×D4×C283—21no—
58C4×D4×C283C2211yescharacteristic
59C2×Dic566—21no—
60C2×Dic566C2311yescharacteristic
61C22×Dic283—21no—
62C22×Dic283—21no—
63#17985382—22no—
64#17985382—41no—
65#17985380—41no—
66#17985376—41no—
67C2×C283⋊C8—41no—
68C2×C283⋊C8C2311yescharacteristic
69C2×C283⋊C8C2311yescharacteristic
70C2×C283⋊C8C2311yescharacteristic
71C2×C283⋊C8C2311yescharacteristic
72C4⋊Dic283—21no—
73C4⋊Dic283—21no—
74C4⋊Dic283—21no—
75C4⋊Dic283C2311yescharacteristic
76C4⋊Dic283C2311yescharacteristic
77C4⋊Dic283C2311yescharacteristic
78Dic283⋊C4—21no—
79Dic283⋊C4—21no—
80Dic283⋊C4—21no—
81C22⋊Dic283—21no—
82C22⋊Dic283—21no—
83C4×Dic283—21no—
84#41×C283—22no—
85#41×C283—41no—
86C2×Q8×C283—21no—
87C2×Q8×C283—22no—
88C2×Q8×C283—41no—
89C2×Q8×C283C2311yescharacteristic
90C2×Q8×C283C2311yescharacteristic
91C2×D4×C283—21no—
92C2×D4×C283—21no—
93C2×D4×C283D411yescharacteristic
94C2×D4×C283C2311yescharacteristic
95C22×C4×C283—21no—
96C22×C4×C283—21no—
97C22×C4×C283C2311yescharacteristic
98C22×C4×C283C2311yescharacteristic
99C4⋊C4×C283—21no—
100C4⋊C4×C283—21no—
101C4⋊C4×C283D411yescharacteristic
102C4⋊C4×C283C2311yescharacteristic
103C22⋊C4×C283—21no—
104C22⋊C4×C283—21no—
105C22⋊C4×C283—21no—
106C22⋊C4×C283—21no—
107C22⋊C4×C283D411yescharacteristic
108C22⋊C4×C283D411yescharacteristic
109C42×C283—21no—
110C42×C283C2311yescharacteristic
111Dic566—21no—
112Dic566—21no—
113Dic566—81no—
114C2×Dic283—21no—
115C2×Dic283—21no—
116C2×Dic283—21no—
117C2×Dic283—21no—
118C2×Dic283—81no—
119C2×Dic283—81no—
120C283⋊C8—21no—
121C283⋊C8—21no—
122C283⋊C8—21no—
123C283⋊C8—21no—
124C23×C283—21no—
125C23×C283C2×D411yescharacteristic
126C23×C283C2×D411yescharacteristic
127Q8×C283—21no—
128Q8×C283—21no—
129Q8×C283—21no—
130Q8×C283—42no—
131Q8×C283#4112yes—
132D4×C283—22no—
133D4×C283—21no—
134D4×C283—21no—
135D4×C283—42no—
136D4×C283—42no—
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—21no—
144C2×C4×C283—42no—
145C2×C4×C283—42no—
146C2×C4×C283C2×D411yescharacteristic
147C2×C4×C283C2×D411yescharacteristic
148C2×C4×C283C2×D411yescharacteristic
149C2×C4×C283C2×D411yescharacteristic
150C2×C4×C283C2411yescharacteristic
151C22×C283—21no—
152C22×C283—21no—
153C22×C283—21no—
154C22×C283—21no—
155C22×C283—21no—
156C22×C283—41no—
157C22×C283—41no—
158C22×C283—41no—
159C22×C283#13712yes—
160C22×C283C22×D411yescharacteristic
161C4×C283—21no—
162C4×C283—21no—
163C4×C283—22no—
164C4×C283—21no—
165C4×C283—21no—
166C4×C283—41no—
167C4×C283—41no—
168C4×C283C2×#4111yescharacteristic
169C4×C283H(5,𝔽2)11yescharacteristic
170Dic283—41no—
171Dic283—41no—
172Dic283—41no—
173Dic283—41no—
174C2×C283—22no—
175C2×C283—41no—
176C2×C283—81no—
177C2×C283#54611yescharacteristic
178C2×C283C2×#13711yescharacteristic
179C2×C283#57711yescharacteristic
180C283#331611yescharacteristic, complemented, Sylow
181#3316—2831nomaximal, Sylow
182#554—2831no—
183#548D28311yescharacteristic
184#489—2831no—
185#483—2831no—
186#481—2831no—
187#475—2831no—
188#470—2831no—
189#465—2831no—
190#464—2831no—
191#452—2831no—
192#451—2831no—
193#441—2831no—
194#435—2831no—
195#417—2831no—
196C2×#103—2831no—
197C2×#41C2×D28311yescharacteristic
198C22×Q8C2×D28311yescharacteristic
199C2×Q16—2831no—
200C2×Q16—2831no—
201C2×SD16—2831no—
202C2×M16—2831no—
203C22×C8—2831no—
204C4⋊Q8—2831no—
205#125—5661no—
206#124—21no—
207#124C2×D28311yescharacteristic
208C22⋊Q8—21no—
209C22⋊Q8—2831no—
210C22⋊Q8—2831no—
211C22⋊Q8—5661no—
212C22⋊Q8—5661no—
213C22⋊Q8C2×D28311yescharacteristic
214#121—21no—
215#121C2×D28311yescharacteristic
216C4×Q8—2831no—
217C4×Q8C2×D28311yescharacteristic
218C4×D4—21no—
219C4×D4—5661no—
220C4×D4C2×D28311yescharacteristic
221C2×C4⋊C4—2831no—
222C2×C4⋊C4—2831no—
223#106—2831no—
224#106—2831no—
225#106—2831no—
226C4⋊C8—2831no—
227#103—2831no—
228#103—2831no—
229#103—2831no—
230#103—2831no—
231#103—2831no—
232#103—2831no—
233#103—2831no—
234#102—2831no—
235#102—2831no—
236#102—2831no—
237C22⋊C8—2831no—
238C22⋊C8—2831no—
239#97—2831no—
240#41—22no—
241#41—41no—
242C2×Q8—21no—
243C2×Q8—22no—
244C2×Q8—41no—
245C2×Q8—2831no—
246C2×Q8—5661no—
247C2×Q8C22×D28311yescharacteristic
248C2×Q8C22×D28311yescharacteristic
249C2×D4—21no—
250C2×D4—21no—
251C2×D4C22⋊D28311yescharacteristic
252C2×D4C22×D28311yescharacteristic
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—5661no—
256C22×C4—5661no—
257C22×C4C22×D28311yescharacteristic
258C22×C4C22×D28311yescharacteristic
259Q16—5662no—
260Q16—11321no—
261SD16—11321no—
262M16—11321no—
263C2×C8—2831no—
264C2×C8—2831no—
265C2×C8—2831no—
266C2×C8—2831no—
267C2×C8—11321no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—2831no—
271C4⋊C4—2831no—
272C4⋊C4—2831no—
273C4⋊C4—5661no—
274C4⋊C4—5661no—
275C4⋊C4—5661no—
276C4⋊C4—5661no—
277C4⋊C4—5661no—
278C4⋊C4—5661no—
279C4⋊C4C22⋊D28311yescharacteristic
280C4⋊C4C22×D28311yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—5661no—
286C22⋊C4—5661no—
287C22⋊C4C22⋊D28311yescharacteristic
288C22⋊C4C22⋊D28311yescharacteristic
289C42—21no—
290C42—5661no—
291C42C22×D28311yescharacteristic
292C23—21no—
293C23C2×C22⋊D28311yescharacteristic
294C23C2×C22⋊D28311yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—42no—
299Q8—5661no—
300Q8—5661no—
301Q8—22641no—
302Q8#1798539112yes—
303D4—22no—
304D4—21no—
305D4—21no—
306D4—42no—
307D4—42no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—5661no—
318C2×C4—5661no—
319C2×C4—5661no—
320C2×C4—5661no—
321C2×C4—22641no—
322C2×C4—22641no—
323C2×C4C2×C22⋊D28311yescharacteristic
324C2×C4C2×C22⋊D28311yescharacteristic
325C2×C4C2×C22⋊D28311yescharacteristic
326C2×C4C2×C22⋊D28311yescharacteristic
327C2×C4C23×D28311yescharacteristic
328C8—5661no—
329C8—5661no—
330C8—5661no—
331C8—5661no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22#2258364012yes—
341C22C22×C22⋊D28311yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—22no—
347C4—41no—
348C4—41no—
349C4—11321no—
350C4—11321no—
351C4—11321no—
352C4—11321no—
353C4C2×#1798539111yescharacteristic
354C4#2258365511yescharacteristic
355C2—22no—
356C2—41no—
357C2—81no—
358C2#3182710911yescharacteristic
359C2C2×#2258364011yescharacteristic
360C2#3182727311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting, prime radical#548×C283C2
socleC22×C283C22×D4
hypercenter#548D283
hypocenterC283#3316
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #31827172C2semidirect
2. #31826824C2semidirect
3. #31826793C2semidirect
4. #31826781C2semidirect
5. #31826750C2semidirect
6. #31826721C2semidirect
7. #31826692C2semidirect
8. #31826684C2semidirect
9. #31826627C2semidirect
10. #31826621C2semidirect
11. #31826570C2semidirect
12. #31826537C2semidirect
13. #31826466C2semidirect
14. C2×#22583534C2semidirect
180. C283#3316semidirect

Maximal subgroups

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

subgroupindex
#318271722
#318268242
#318267932
#318267812
#318267502
#318267212
#318266922
#318266842
#318266272
#318266212
#318265702
#318265372
#318264662
C2×#225835342
#548×C2832
#3316283