Finite Group Databasebeta

← #49133980

Subgroups — #49133980

Order 36224.

372 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827187C211yesmaximal, characteristic, complemented
2D4×Dic566C211yesmaximal, characteristic, complemented
3#31826826C211yesmaximal, characteristic, complemented
4#31826825C211yesmaximal, characteristic, complemented
5#31826814C211yesmaximal, characteristic, complemented
6#31826760C211yesmaximal, characteristic, complemented
7#31826759C211yesmaximal, characteristic, complemented
8#31826744C211yesmaximal, characteristic, complemented
9#31826682C211yesmaximal, characteristic
10#31826680C211yesmaximal, characteristic
11#31826668C211yesmaximal, characteristic, complemented
12#31826593C211yesmaximal, characteristic, complemented
13#31826562C211yesmaximal, characteristic, complemented
14#31826545C211yesmaximal, characteristic
15#440×C283C211yesmaximal, characteristic, complemented
16C22×Dic566—21no—
17C2×#17985380C2211yescharacteristic
18C2×#17985377C2211yescharacteristic
19#22583610C2211yescharacteristic
20#22583609C2211yescharacteristic
21#22583609C2211yescharacteristic
22#22583608C2211yescharacteristic
23#22583605—21no—
24#22583604—21no—
25#22583599C2211yescharacteristic
26#22583598C2211yescharacteristic
27#22583589—21no—
28#22583588—21no—
29#22583587—21no—
30#22583587—21no—
31C4×Dic566C2211yescharacteristic
32#22583575C2211yescharacteristic
33D4×Dic283C2211yescharacteristic
34D4×Dic283C2211yescharacteristic
35#22583572C2211yescharacteristic
36#22583567—21no—
37#22583543C2211yescharacteristic
38#22583543C2211yescharacteristic
39C4⋊(C283⋊C8)C2211yescharacteristic
40Dic283⋊C8C2211yescharacteristic
41Dic283⋊C8C2211yescharacteristic
42#22583535C2211yescharacteristic
43#22583535C2211yescharacteristic
44#22583534C2211yescharacteristic
45#22583534C2211yescharacteristic
46#22583533C2211yescharacteristic
47#22583532C2211yescharacteristic
48#22583532C2211yescharacteristic
49#22583530C2211yescharacteristic
50#22583520C2211yescharacteristic
51C8×Dic283C2211yescharacteristic
52C2×SD16×C283C2211yescharacteristic
53C4×Q8×C283C2211yescharacteristic
54C4×D4×C283C2211yescharacteristic
55#107×C283C2211yescharacteristic
56#103×C283C2211yescharacteristic
57#102×C283C2211yescharacteristic
58#97×C283C2211yescharacteristic
59C2×Dic566—21no—
60C2×Dic566—21no—
61C2×Dic566—21no—
62C2×Dic566—44no—
63C2×Dic566D411yescharacteristic
64C2×Dic566C2311yescharacteristic
65C2×D1132C2311yescharacteristic
66C22×Dic283—21no—
67C22×Dic283—21no—
68C2×C4×D283—21no—
69#17985380—22no—
70#17985377—22no—
71C2×C283⋊C8C2311yescharacteristic
72C2×C283⋊C8C2311yescharacteristic
73C4⋊Dic283—21no—
74C4⋊Dic283D411yescharacteristic
75C4⋊Dic283C2311yescharacteristic
76C4⋊Dic283C2311yescharacteristic
77Dic283⋊C4—21no—
78Dic283⋊C4—21no—
79Dic283⋊C4—21no—
80Dic283⋊C4—21no—
81Dic283⋊C4—21no—
82Dic283⋊C4D411yescharacteristic
83Dic283⋊C4D411yescharacteristic
84C22⋊Dic283—21no—
85C22⋊Dic283—21no—
86(C2×D283)⋊C4—21no—
87(C2×D283)⋊C4—21no—
88(C2×D283)⋊C4—21no—
89(C2×D283)⋊C4—21no—
90(C2×D283)⋊C4—21no—
91C4×Dic283—21no—
92C4×Dic283C2311yescharacteristic
93C4×Dic283C2311yescharacteristic
94C2×Q8×C283C2311yescharacteristic
95C2×D4×C283C2311yescharacteristic
96C22×C4×C283—21no—
97SD16×C283—22no—
98C2×C8×C283C2311yescharacteristic
99C2×C8×C283C2311yescharacteristic
100C4⋊C4×C283—21no—
101C4⋊C4×C283C2311yescharacteristic
102C4⋊C4×C283C2311yescharacteristic
103C22⋊C4×C283—21no—
104C42×C283—21no—
105C42×C283C2311yescharacteristic
106C22×D283—21no—
107Dic566—22no—
108Dic566—21no—
109Dic566—21no—
110Dic566—42no—
111Dic566—42no—
112Dic566—42no—
113D1132—21no—
114D1132—21no—
115C2×Dic283—21no—
116C2×Dic283—21no—
117C2×Dic283—21no—
118C2×Dic283—42no—
119C2×Dic283—42no—
120C2×Dic283C2×D411yescharacteristic
121C2×Dic283C2×D411yescharacteristic
122C2×Dic283C2×D411yescharacteristic
123C2×Dic283C2×D411yescharacteristic
124C4×D283—42no—
125C283⋊C8—21no—
126C283⋊C8—21no—
127C23×C283—21no—
128Q8×C283—21no—
129Q8×C283—21no—
130D4×C283—21no—
131D4×C283#4112yes—
132C2×C4×C283—21no—
133C2×C4×C283—21no—
134C2×C4×C283—21no—
135C2×C4×C283—42no—
136C2×C4×C283C2×D411yescharacteristic
137C2×C4×C283C2×D411yescharacteristic
138C2×C4×C283C2411yescharacteristic
139C8×C283—21no—
140C8×C283—21no—
141C22×C283—22no—
142C22×C283—41no—
143C22×C283—41no—
144C22×C283C22×D411yescharacteristic
145C2×D283—41no—
146C2×D283—41no—
147C2×D283—41no—
148C4×C283—21no—
149C4×C283—21no—
150C4×C283—41no—
151C4×C283—41no—
152C4×C283—41no—
153C4×C283C2×#4111yescharacteristic
154C4×C2832−1+411yescharacteristic
155Dic283—21no—
156Dic283—21no—
157Dic283—21no—
158Dic283—41no—
159Dic283—41no—
160Dic283—41no—
161Dic283AGL(1,ℤ/8)12yes—
162C2×C283—42no—
163C2×C283#54811yescharacteristic
164C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
165C2×C283#57811yescharacteristic
166D283—81no—
167C283#336711yescharacteristic, complemented, Sylow
168#3367—2831nomaximal, Sylow
169#556—2831no—
170D4×Q8—2831no—
171#489—2831no—
172#489—2831no—
173#487—2831no—
174#477—2831no—
175#477—2831no—
176#474—2831no—
177#463—2831no—
178#463—2831no—
179#461—2831no—
180#446—2831no—
181#440—2831no—
182#440D28311yescharacteristic, complemented
183C4×D8—2831no—
184C22×Q8—5661no—
185C2×SD16—2831no—
186C2×SD16C2×D28311yescharacteristic
187C2×D8—2831no—
188C4⋊Q8—2831no—
189C4⋊Q8—2831no—
190C4⋊Q8—2831no—
191C4⋊Q8—2831no—
192#126—5661no—
193#126—5661no—
194#124—2831no—
195#124—2831no—
196C22⋊Q8—5661no—
197C22⋊Q8—5661no—
198C22⋊Q8—5661no—
199C22⋊Q8—5661no—
200C4×Q8—2831no—
201C4×Q8—2831no—
202C4×Q8C2×D28311yescharacteristic
203C4×D4—2831no—
204C4×D4—2831no—
205C4×D4—2831no—
206C4×D4C2×D28311yescharacteristic
207#117—5661no—
208#107—2831no—
209#107—2831no—
210#107C2×D28311yescharacteristic
211C4⋊C8—2831no—
212C4⋊C8—2831no—
213C4⋊C8—2831no—
214#103—2831no—
215#103—2831no—
216#103—2831no—
217#103—2831no—
218#103—2831no—
219#103C2×D28311yescharacteristic
220#102—2831no—
221#102—2831no—
222#102—2831no—
223#102C2×D28311yescharacteristic
224#97—2831no—
225#97C2×D28311yescharacteristic
226C4×C8—2831no—
227C2×Q8—2831no—
228C2×Q8—2831no—
229C2×Q8—5661no—
230C2×Q8—5661no—
231C2×Q8—5661no—
232C2×Q8—11324no—
233C2×Q8C22×D28311yescharacteristic
234C2×D4—2831no—
235C2×D4C22×D28311yescharacteristic
236C22×C4—21no—
237C22×C4—5661no—
238C22×C4—5661no—
239C22×C4—5661no—
240SD16—22no—
241SD16—5662no—
242D8—5662no—
243C2×C8—2831no—
244C2×C8—2831no—
245C2×C8C22×D28311yescharacteristic
246C2×C8C22×D28311yescharacteristic
247C4⋊C4—21no—
248C4⋊C4—2831no—
249C4⋊C4—2831no—
250C4⋊C4—2831no—
251C4⋊C4—2831no—
252C4⋊C4—2831no—
253C4⋊C4—5661no—
254C4⋊C4—5661no—
255C4⋊C4—5661no—
256C4⋊C4—5661no—
257C4⋊C4—5661no—
258C4⋊C4—5661no—
259C4⋊C4C22×D28311yescharacteristic
260C4⋊C4C22×D28311yescharacteristic
261C22⋊C4—21no—
262C22⋊C4—5661no—
263C22⋊C4—5661no—
264C22⋊C4—5661no—
265C22⋊C4—5661no—
266C22⋊C4—5661no—
267C22⋊C4—5661no—
268C22⋊C4—5661no—
269C42—21no—
270C42—2831no—
271C42—2831no—
272C42—5661no—
273C42C22×D28311yescharacteristic
274C23—21no—
275C23—5661no—
276Q8—21no—
277Q8—21no—
278Q8—5662no—
279Q8—5661no—
280Q8—5661no—
281Q8—11322no—
282Q8—11322no—
283Q8—11322no—
284D4—21no—
285D4—5661no—
286D4—5661no—
287D4#1798539212yes—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—42no—
292C2×C4—2831no—
293C2×C4—2831no—
294C2×C4—2831no—
295C2×C4—2831no—
296C2×C4—5661no—
297C2×C4—5661no—
298C2×C4—5661no—
299C2×C4—11322no—
300C2×C4—11322no—
301C2×C4—11322no—
302C2×C4D4×D28311yescharacteristic
303C2×C4D4×D28311yescharacteristic
304C2×C4C23×D28311yescharacteristic
305C8—21no—
306C8—21no—
307C8—5661no—
308C8—5661no—
309C22—22no—
310C22—41no—
311C22—41no—
312C22—11321no—
313C22—11321no—
314C22—11321no—
315C22C2×D4×D28311yescharacteristic
316C4—21no—
317C4—21no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—2832no—
322C4—5661no—
323C4—5661no—
324C4—5661no—
325C4—11321no—
326C4—11321no—
327C4—11321no—
328C4C2×#1798539211yescharacteristic
329C4#2258365711yescharacteristic
330C2—42no—
331C2—22641no—
332C2#3182712411yescharacteristic
333C2AGL(1,ℤ/8)×D28311yescharacteristic
334C2#3182728111yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#440×C283C2
socleC22×C283C22×D4
prime radicalC2×#17985377C22
hypercenter#440D283
hypocenterC283#3367
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #31827187C2semidirect
2. D4×Dic566C2semidirect
3. #31826826C2semidirect
4. #31826825C2semidirect
5. #31826814C2semidirect
6. #31826760C2semidirect
7. #31826759C2semidirect
8. #31826744C2semidirect
11. #31826668C2semidirect
12. #31826593C2semidirect
13. #31826562C2semidirect
15. #440×C283C2semidirect
167. C283#3367semidirect
182. #440D283semidirect

Maximal subgroups

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

subgroupindex
#318271872
D4×Dic5662
#318268262
#318268252
#318268142
#318267602
#318267592
#318267442
#318266822
#318266802
#318266682
#318265932
#318265622
#318265452
#440×C2832
#3367283