Finite Group Databasebeta

← #49133965

Subgroups — #49133965

Order 36224.

396 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#31827171C211yesmaximal, characteristic, complemented
2#31827135C211yesmaximal, characteristic, complemented
3#31826828C211yesmaximal, characteristic, complemented
4#31826810C211yesmaximal, characteristic, complemented
5#31826767C211yesmaximal, characteristic, complemented
6#31826762C211yesmaximal, characteristic, complemented
7#31826753C211yesmaximal, characteristic, complemented
8#31826659C211yesmaximal, characteristic, complemented
9#31826659C211yesmaximal, characteristic, complemented
10#31826657C211yesmaximal, characteristic, complemented
11#31826593C211yesmaximal, characteristic, complemented
12#31826578C211yesmaximal, characteristic, complemented
13#31826574C211yesmaximal, characteristic, complemented
14#31826545C211yesmaximal, characteristic, complemented
15#490×C283C211yesmaximal, characteristic, complemented
16C2×#17985391—21no—
17C2×D2264C2211yescharacteristic
18C2×#17985377C2211yescharacteristic
19C2×#17985377C2211yescharacteristic
20#22583609C2211yescharacteristic
21#22583606C2211yescharacteristic
22#22583606C2211yescharacteristic
23#22583601C2211yescharacteristic
24#22583590—21no—
25#22583588—21no—
26#22583588—21no—
27#22583582—21no—
28#22583582—21no—
29#22583581—21no—
30C4×Dic566C2211yescharacteristic
31C4×D1132C2211yescharacteristic
32C4×D1132C2211yescharacteristic
33D4×Dic283C2211yescharacteristic
34D4×Dic283C2211yescharacteristic
35#22583572C2211yescharacteristic
36#22583572C2211yescharacteristic
37C4⋊C4×D283—21no—
38#22583543C2211yescharacteristic
39#22583542C2211yescharacteristic
40#22583541C2211yescharacteristic
41C4⋊(C283⋊C8)C2211yescharacteristic
42Dic283⋊C8C2211yescharacteristic
43Dic283⋊C8C2211yescharacteristic
44#22583532C2211yescharacteristic
45#22583532C2211yescharacteristic
46#22583531C2211yescharacteristic
47#22583531C2211yescharacteristic
48#22583530C2211yescharacteristic
49#22583530C2211yescharacteristic
50#22583520C2211yescharacteristic
51C8×Dic283C2211yescharacteristic
52#127×C283C2211yescharacteristic
53#125×C283C2211yescharacteristic
54#102×C283C2211yescharacteristic
55#102×C283C2211yescharacteristic
56#102×C283C2211yescharacteristic
57#102×C283C2211yescharacteristic
58#97×C283C2211yescharacteristic
59#17985391—44no—
60C2×Dic566—21no—
61C2×Dic566D411yescharacteristic
62C2×D1132C2311yescharacteristic
63C2×D1132C2311yescharacteristic
64C2×C22⋊D283—21no—
65C2×C22⋊D283—21no—
66C2×C22⋊D283—21no—
67C2×C22⋊D283—21no—
68C22×Dic283—21no—
69C22×Dic283—21no—
70C2×C4×D283—21no—
71C2×C4×D283—21no—
72C2×C4×D283—21no—
73C2×C4×D283—21no—
74D2264—22no—
75#17985377—22no—
76#17985377—22no—
77C2×C283⋊C8C2311yescharacteristic
78C2×C283⋊C8C2311yescharacteristic
79C4⋊Dic283—21no—
80C4⋊Dic283D411yescharacteristic
81C4⋊Dic283C2311yescharacteristic
82C4⋊Dic283C2311yescharacteristic
83Dic283⋊C4—21no—
84Dic283⋊C4—21no—
85Dic283⋊C4D411yescharacteristic
86Dic283⋊C4D411yescharacteristic
87C22⋊Dic283—21no—
88C22⋊Dic283—21no—
89(C2×D283)⋊C4—21no—
90(C2×D283)⋊C4—21no—
91(C2×D283)⋊C4—21no—
92(C2×D283)⋊C4—21no—
93C4×Dic283C2311yescharacteristic
94C4×Dic283C2311yescharacteristic
95C2×D4×C283—21no—
96C2×D4×C283—21no—
97C2×D4×C283C2311yescharacteristic
98C2×D4×C283C2311yescharacteristic
99C2×C8×C283C2311yescharacteristic
100C2×C8×C283C2311yescharacteristic
101C4⋊C4×C283—21no—
102C4⋊C4×C283—21no—
103C4⋊C4×C283C2311yescharacteristic
104C4⋊C4×C283C2311yescharacteristic
105C42×C283C2311yescharacteristic
106C22×D283—21no—
107C22×D283—21no—
108Dic566—22no—
109Dic566—81no—
110D1132—21no—
111D1132—21no—
112D1132—21no—
113D1132#4112yescomplemented
114C22⋊D283—42no—
115C22⋊D283—42no—
116C22⋊D283—81no—
117C22⋊D283—81no—
118C2×Dic283—21no—
119C2×Dic283—21no—
120C2×Dic283—42no—
121C2×Dic283—42no—
122C2×Dic283C2×D411yescharacteristic
123C2×Dic283C2×D411yescharacteristic
124C2×Dic283C2×D411yescharacteristic
125C2×Dic283C2×D411yescharacteristic
126C4×D283—42no—
127C4×D283—42no—
128C4×D283—81no—
129C4×D283—81no—
130C283⋊C8—21no—
131C283⋊C8—21no—
132C23×C283—21no—
133C23×C283—21no—
134D4×C283—21no—
135D4×C283—21no—
136D4×C283—21no—
137D4×C283—21no—
138D4×C283—42no—
139D4×C283—81no—
140C2×C4×C283—21no—
141C2×C4×C283—21no—
142C2×C4×C283C2×D411yescharacteristic
143C2×C4×C283C2×D411yescharacteristic
144C2×C4×C283C2411yescharacteristic
145C8×C283—21no—
146C8×C283—21no—
147C22×C283—41no—
148C22×C283—41no—
149C22×C283—41no—
150C22×C283—41no—
151C22×C283—41no—
152C22×C283—41no—
153C22×C283C22×D411yescharacteristic
154C2×D283—22no—
155C2×D283—41no—
156C2×D283—41no—
157C2×D283—41no—
158C2×D283—41no—
159C2×D283—41no—
160C4×C283—21no—
161C4×C283—21no—
162C4×C283—41no—
163C4×C283—41no—
164C4×C283C2×#4111yescharacteristic
165C4×C2832−1+411yescharacteristic
166Dic283—21no—
167Dic283—21no—
168Dic283—21no—
169Dic283—41no—
170Dic283—41no—
171Dic283AGL(1,ℤ/8)12yes—
172C2×C283—81no—
173C2×C283—81no—
174C2×C283#54811yescharacteristic
175C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
176C2×C283#57611yescharacteristic
177D283—42no—
178D283—81no—
179C283#336611yescharacteristic, complemented, Sylow
180#3366—2831nomaximal, Sylow
181#554—2831no—
182#550—2831no—
183#490—2831no—
184#490D28311yescharacteristic, complemented
185#486—2831no—
186#478—2831no—
187#478—2831no—
188#476—2831no—
189#459—2831no—
190#459—2831no—
191#459—2831no—
192#446—2831no—
193#442—2831no—
194#442—2831no—
195C4×D8—2831no—
196C2×#41—5661no—
197C2×D8—2831no—
198C2×D8—2831no—
199C2×D8—2831no—
200C4⋊Q8—2831no—
201#127—2831no—
202#127—2831no—
203#127C2×D28311yescharacteristic
204#125—2831no—
205#125C2×D28311yescharacteristic
206C22⋊Q8—5661no—
207C22⋊Q8—5661no—
208C22⋊Q8—5661no—
209#121—5661no—
210#121—5661no—
211#121—5661no—
212C4×Q8—2831no—
213C4×D4—2831no—
214C4×D4—2831no—
215C4×D4—2831no—
216C4×D4—2831no—
217C4×D4—2831no—
218C4×D4—2831no—
219C2×C4⋊C4—5661no—
220#107—2831no—
221#106—2831no—
222#106—2831no—
223C4⋊C8—2831no—
224C4⋊C8—2831no—
225C4⋊C8—2831no—
226#102—2831no—
227#102—2831no—
228#102—2831no—
229#102—2831no—
230#102—2831no—
231#102—2831no—
232#102C2×D28311yescharacteristic
233#102C2×D28311yescharacteristic
234#102C2×D28311yescharacteristic
235#102C2×D28311yescharacteristic
236#97—2831no—
237#97C2×D28311yescharacteristic
238C4×C8—2831no—
239#41—11324no—
240C2×Q8—2831no—
241C2×Q8—5661no—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—2831no—
245C2×D4—2831no—
246C2×D4—5661no—
247C2×D4—5661no—
248C2×D4—5661no—
249C2×D4—5661no—
250C2×D4C22×D28311yescharacteristic
251C2×D4C22×D28311yescharacteristic
252C22×C4—5661no—
253C22×C4—5661no—
254C22×C4—5661no—
255C22×C4—5661no—
256C22×C4—5661no—
257C22×C4—5661no—
258D8—5662no—
259D8—5662no—
260D8—5662no—
261C2×C8—2831no—
262C2×C8—2831no—
263C2×C8C22×D28311yescharacteristic
264C2×C8C22×D28311yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—2831no—
268C4⋊C4—2831no—
269C4⋊C4—2831no—
270C4⋊C4—2831no—
271C4⋊C4—2831no—
272C4⋊C4—5661no—
273C4⋊C4—5661no—
274C4⋊C4—5661no—
275C4⋊C4C22×D28311yescharacteristic
276C4⋊C4C22×D28311yescharacteristic
277C22⋊C4—5661no—
278C22⋊C4—5661no—
279C22⋊C4—5661no—
280C22⋊C4—5661no—
281C22⋊C4—5661no—
282C22⋊C4—5661no—
283C42—2831no—
284C42—2831no—
285C42C22×D28311yescharacteristic
286C23—21no—
287C23—21no—
288C23—5661no—
289C23—5661no—
290Q8—5662no—
291Q8—22641no—
292D4—21no—
293D4—21no—
294D4—21no—
295D4—21no—
296D4—42no—
297D4—81no—
298D4—2832no—
299D4—5661no—
300D4—5661no—
301D4—5661no—
302D4—11322no—
303D4—11322no—
304D4—22641no—
305D4—22641no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—2831no—
309C2×C4—2831no—
310C2×C4—2831no—
311C2×C4—2831no—
312C2×C4—5661no—
313C2×C4—5661no—
314C2×C4—11322no—
315C2×C4—11322no—
316C2×C4—11322no—
317C2×C4—11322no—
318C2×C4—22641no—
319C2×C4—22641no—
320C2×C4D4×D28311yescharacteristic
321C2×C4D4×D28311yescharacteristic
322C2×C4C23×D28311yescharacteristic
323C8—21no—
324C8—21no—
325C8—5661no—
326C8—5661no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—5662no—
334C22—11321no—
335C22—11321no—
336C22—11321no—
337C22—11321no—
338C22—11321no—
339C22C2×D4×D28311yescharacteristic
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—2832no—
345C4—5661no—
346C4—5661no—
347C4—5661no—
348C4—11321no—
349C4—11321no—
350C4#41×D28311yescharacteristic
351C4#2258365711yescharacteristic
352C2—81no—
353C2—81no—
354C2—11322no—
355C2—22641no—
356C2#3182712311yescharacteristic
357C2AGL(1,ℤ/8)×D28311yescharacteristic
358C2#3182726911yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#490×C283C2
socleC22×C283C22×D4
hypercenter#490D283
hypocenterC283#3366
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #31827171C2semidirect
2. #31827135C2semidirect
3. #31826828C2semidirect
4. #31826810C2semidirect
5. #31826767C2semidirect
6. #31826762C2semidirect
7. #31826753C2semidirect
8. #31826659C2semidirect
9. #31826659C2semidirect
10. #31826657C2semidirect
11. #31826593C2semidirect
12. #31826578C2semidirect
13. #31826574C2semidirect
14. #31826545C2semidirect
15. #490×C283C2semidirect
113. D1132#41semidirect
179. C283#3366semidirect
184. #490D283semidirect

Maximal subgroups

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

subgroupindex
#318271712
#318271352
#318268282
#318268102
#318267672
#318267622
#318267532
#318266592
#318266572
#318265932
#318265782
#318265742
#318265452
#490×C2832
#3366283