Finite Group Databasebeta

← #49131485

Subgroups — #49131485

Order 36224.

370 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827082C211yesmaximal, characteristic
2#31826942C211yesmaximal, characteristic, complemented
3#31826806C211yesmaximal, characteristic, complemented
4#31826759C211yesmaximal, characteristic, complemented
5#31826749C211yesmaximal, characteristic, complemented
6#31826686C211yesmaximal, characteristic, complemented
7#31826686C211yesmaximal, characteristic, complemented
8#31826623C211yesmaximal, characteristic, complemented
9#31826603C211yesmaximal, characteristic
10#31826571C211yesmaximal, characteristic, complemented
11#31826562C211yesmaximal, characteristic, complemented
12#31826559C211yesmaximal, characteristic, complemented
13#31826556C211yesmaximal, characteristic, complemented
14#31826523C211yesmaximal, characteristic, complemented
15#482×C283C211yesmaximal, characteristic
16C22×Dic566C2211yescharacteristic
17C2×Dic1132C2211yescharacteristic
18C2×Dic1132C2211yescharacteristic
19C2×#17985380C2211yescharacteristic
20C2×#17985380C2211yescharacteristic
21#22583609C2211yescharacteristic
22#22583603—21no—
23#22583597—21no—
24#22583597C2211yescharacteristic
25#22583591—21no—
26#22583589C2211yescharacteristic
27#22583587—21no—
28C4×Dic566—21no—
29C4×Dic566—21no—
30#22583575C2211yescharacteristic
31#22583575C2211yescharacteristic
32#22583575C2211yescharacteristic
33#22583575C2211yescharacteristic
34#22583575C2211yescharacteristic
35D4×Dic283C2211yescharacteristic
36#22583569C2211yescharacteristic
37#22583566—21no—
38#22583566—21no—
39#22583543C2211yescharacteristic
40#22583541C2211yescharacteristic
41Dic283⋊C8C2211yescharacteristic
42Dic283⋊C8C2211yescharacteristic
43#22583535C2211yescharacteristic
44#22583535C2211yescharacteristic
45#22583533C2211yescharacteristic
46#22583533C2211yescharacteristic
47#22583533C2211yescharacteristic
48#22583533C2211yescharacteristic
49C22⋊(C283⋊C8)C2211yescharacteristic
50#22583520C2211yescharacteristic
51C8×Dic283C2211yescharacteristic
52#121×C283C2211yescharacteristic
53#117×C283C2211yescharacteristic
54#107×C283C2211yescharacteristic
55#106×C283C2211yescharacteristic
56#102×C283C2211yescharacteristic
57#102×C283C2211yescharacteristic
58C22⋊C8×C283C2211yescharacteristic
59C2×Dic566—22no—
60C2×Dic566—22no—
61C2×Dic566—21no—
62C2×Dic566—21no—
63C2×Dic566C2311yescharacteristic
64C2×Dic566C2311yescharacteristic
65C2×Dic566C2311yescharacteristic
66C22×Dic283—21no—
67C22×Dic283—21no—
68Dic1132—22no—
69Dic1132—22no—
70#17985380—22no—
71#17985380—22no—
72C2×C283⋊C8C2311yescharacteristic
73C2×C283⋊C8C2311yescharacteristic
74C4⋊Dic283D411yescharacteristic
75C4⋊Dic283D411yescharacteristic
76C4⋊Dic283C2311yescharacteristic
77Dic283⋊C4—21no—
78Dic283⋊C4—21no—
79Dic283⋊C4—21no—
80Dic283⋊C4—21no—
81Dic283⋊C4—21no—
82Dic283⋊C4—21no—
83Dic283⋊C4—21no—
84C22⋊Dic283—21no—
85C22⋊Dic283—21no—
86C22⋊Dic283—21no—
87C22⋊Dic283—21no—
88C22⋊Dic283D411yescharacteristic
89C22⋊Dic283D411yescharacteristic
90C4×Dic283—21no—
91C4×Dic283—21no—
92C4×Dic283—21no—
93C4×Dic283—21no—
94C4×Dic283—21no—
95C4×Dic283C2311yescharacteristic
96C4×Dic283C2311yescharacteristic
97C2×D4×C283—21no—
98C2×D4×C283C2311yescharacteristic
99C22×C4×C283C2311yescharacteristic
100C2×C8×C283C2311yescharacteristic
101C2×C8×C283C2311yescharacteristic
102C4⋊C4×C283C2311yescharacteristic
103C4⋊C4×C283C2311yescharacteristic
104C4⋊C4×C283C2311yescharacteristic
105C22⋊C4×C283—21no—
106C22⋊C4×C283—21no—
107C42×C283—21no—
108Dic566—24no—
109Dic566—21no—
110Dic566—21no—
111Dic566—21no—
112Dic566—21no—
113Dic566—81no—
114Dic566#4112yes—
115Dic566#4112yes—
116C2×Dic283—24no—
117C2×Dic283—21no—
118C2×Dic283—21no—
119C2×Dic283—21no—
120C2×Dic283—21no—
121C2×Dic283—81no—
122C2×Dic283C2×D411yescharacteristic
123C2×Dic283C2×D411yescharacteristic
124C2×Dic283C2×D411yescharacteristic
125C2×Dic283C2×D411yescharacteristic
126C283⋊C8—21no—
127C283⋊C8—21no—
128C23×C283—21no—
129C23×C283C2×D411yescharacteristic
130D4×C283—21no—
131D4×C283—21no—
132D4×C283—81no—
133C2×C4×C283—21no—
134C2×C4×C283—21no—
135C2×C4×C283—21no—
136C2×C4×C283—21no—
137C2×C4×C283—21no—
138C2×C4×C283C2×D411yescharacteristic
139C2×C4×C283C2411yescharacteristic
140C8×C283—21no—
141C8×C283—21no—
142C22×C283—21no—
143C22×C283—21no—
144C22×C283—21no—
145C22×C283—41no—
146C22×C283—41no—
147C22×C283—41no—
148C22×C283C22×D411yescharacteristic
149C4×C283—21no—
150C4×C283—41no—
151C4×C283—41no—
152C4×C283—41no—
153C4×C283C2×#4111yescharacteristic
154C4×C283C2×#4111yescharacteristic
155Dic283—22no—
156Dic283—22no—
157Dic283—21no—
158Dic283—21no—
159Dic283—21no—
160Dic283—21no—
161Dic283—41no—
162Dic283—41no—
163C2×C283—41no—
164C2×C283—81no—
165C2×C283#52511yescharacteristic
166C2×C283#57711yescharacteristic
167C2×C283#57811yescharacteristic
168C283#312111yescharacteristic, complemented, Sylow
169#3121—2831nomaximal, Sylow
170#542—2831no—
171#519—2831no—
172#485—2831no—
173#482D28311yescharacteristic
174#477—2831no—
175#475—2831no—
176#464—2831no—
177#464—2831no—
178#451—2831no—
179#448—2831no—
180#441—2831no—
181#440—2831no—
182C4×Q16—2831no—
183C4×SD16—2831no—
184#433—2831no—
185C22×Q8—2831no—
186C2×Q16—2831no—
187C2×Q16—2831no—
188C2×SD16—2831no—
189C2×SD16—2831no—
190C4⋊Q8—2831no—
191#126—5661no—
192#124—2831no—
193#124—5661no—
194#123—5661no—
195C22⋊Q8—2831no—
196C22⋊Q8—5661no—
197#121C2×D28311yescharacteristic
198C4×Q8—2831no—
199C4×Q8—2831no—
200C4×Q8—2831no—
201C4×Q8—2831no—
202C4×Q8—2831no—
203C4×Q8—5661no—
204C4×Q8—5661no—
205C4×D4—2831no—
206#117—2831no—
207#117—5661no—
208#117—5661no—
209#117C2×D28311yescharacteristic
210#107—2831no—
211#107C2×D28311yescharacteristic
212#106—2831no—
213#106C2×D28311yescharacteristic
214C4⋊C8—2831no—
215C4⋊C8—2831no—
216#103—2831no—
217#103—2831no—
218#103—2831no—
219#103—2831no—
220#103—2831no—
221#103—2831no—
222#102C2×D28311yescharacteristic
223#102C2×D28311yescharacteristic
224C22⋊C8—2831no—
225C22⋊C8C2×D28311yescharacteristic
226#97—2831no—
227C4×C8—2831no—
228C2×Q8—2831no—
229C2×Q8—2831no—
230C2×Q8—2831no—
231C2×Q8—5661no—
232C2×Q8—5662no—
233C2×Q8—5662no—
234C2×Q8—5661no—
235C2×D4—21no—
236C2×D4C22×D28311yescharacteristic
237C22×C4—5661no—
238C22×C4—5661no—
239C22×C4C22×D28311yescharacteristic
240Q16—5662no—
241Q16—5662no—
242SD16—5662no—
243SD16—5662no—
244C2×C8—2831no—
245C2×C8—2831no—
246C2×C8C22×D28311yescharacteristic
247C2×C8C22×D28311yescharacteristic
248C4⋊C4—2831no—
249C4⋊C4—2831no—
250C4⋊C4—2831no—
251C4⋊C4—5661no—
252C4⋊C4—5661no—
253C4⋊C4—5661no—
254C4⋊C4—5661no—
255C4⋊C4—5661no—
256C4⋊C4—5661no—
257C4⋊C4—5661no—
258C4⋊C4C22×D28311yescharacteristic
259C4⋊C4C22×D28311yescharacteristic
260C4⋊C4C22×D28311yescharacteristic
261C22⋊C4—21no—
262C22⋊C4—21no—
263C22⋊C4—2831no—
264C22⋊C4—2831no—
265C22⋊C4—5661no—
266C22⋊C4—5661no—
267C22⋊C4—5661no—
268C22⋊C4—5661no—
269C42—21no—
270C42—2831no—
271C42—2831no—
272C42—5661no—
273C42—5661no—
274C42—5661no—
275C42—5661no—
276C42—5661no—
277C23—21no—
278C23D4×D28311yescharacteristic
279Q8—2832no—
280Q8—2832no—
281Q8—5664no—
282Q8—5661no—
283Q8—5661no—
284Q8—5661no—
285Q8—5661no—
286Q8—22641no—
287D4—21no—
288D4—21no—
289D4—81no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—2831no—
296C2×C4—2831no—
297C2×C4—2831no—
298C2×C4—2831no—
299C2×C4—5664no—
300C2×C4—5661no—
301C2×C4—5661no—
302C2×C4—5661no—
303C2×C4—5661no—
304C2×C4—22641no—
305C2×C4D4×D28311yescharacteristic
306C2×C4C23×D28311yescharacteristic
307C8—21no—
308C8—21no—
309C8—5661no—
310C8—5661no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22C2×D4×D28311yescharacteristic
318C4—21no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—5662no—
323C4—5662no—
324C4—5661no—
325C4—5661no—
326C4—5661no—
327C4—5661no—
328C4—11321no—
329C4—11321no—
330C4#41×D28311yescharacteristic
331C4#41×D28311yescharacteristic
332C2—41no—
333C2—81no—
334C2#3182697311yescharacteristic
335C2#3182727511yescharacteristic
336C2#3182727911yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#482×C283C2
socleC22×C283C22×D4
prime radical#121×C283C22
hypercenter#482D283
hypocenterC283#3121
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. #31826942C2semidirect
3. #31826806C2semidirect
4. #31826759C2semidirect
5. #31826749C2semidirect
6. #31826686C2semidirect
7. #31826686C2semidirect
8. #31826623C2semidirect
10. #31826571C2semidirect
11. #31826562C2semidirect
12. #31826559C2semidirect
13. #31826556C2semidirect
14. #31826523C2semidirect
168. C283#3121semidirect

Maximal subgroups

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

subgroupindex
#318270822
#318269422
#318268062
#318267592
#318267492
#318266862
#318266232
#318266032
#318265712
#318265622
#318265592
#318265562
#318265232
#482×C2832
#3121283