Finite Group Databasebeta

← #49133872

Subgroups — #49133872

Order 36224.

342 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827183C211yesmaximal, characteristic
2#31827170C211yesmaximal, characteristic
3#31826862C211yesmaximal, characteristic, complemented
4#31826808C211yesmaximal, characteristic, complemented
5#31826806C211yesmaximal, characteristic, complemented
6#31826797C211yesmaximal, characteristic, complemented
7#31826795C211yesmaximal, characteristic, complemented
8#31826759C211yesmaximal, characteristic, complemented
9#31826749C211yesmaximal, characteristic, complemented
10#31826724C211yesmaximal, characteristic, complemented
11#31826723C211yesmaximal, characteristic, complemented
12#31826559C211yesmaximal, characteristic, complemented
13#31826541C211yesmaximal, characteristic
14#31826506C211yesmaximal, characteristic, complemented
15#428×C283C211yesmaximal, characteristic, complemented
16C2×Dic1132C2211yescharacteristic
17C2×#17985375C2211yescharacteristic
18#22583609C2211yescharacteristic
19#22583609C2211yescharacteristic
20#22583604—21no—
21#22583603—21no—
22#22583600—21no—
23#22583596—21no—
24#22583590C2211yescharacteristic
25#22583590C2211yescharacteristic
26#22583589—21no—
27#22583589C2211yescharacteristic
28#22583589C2211yescharacteristic
29#22583588—21no—
30C4×Dic566—21no—
31#22583575C2211yescharacteristic
32#22583575C2211yescharacteristic
33C4×C22⋊D283—21no—
34C4×C22⋊D283C2211yescharacteristic
35#22583568C2211yescharacteristic
36C4⋊C4×D283C2211yescharacteristic
37#22583543C2211yescharacteristic
38#22583542C2211yescharacteristic
39#22583541C2211yescharacteristic
40#22583541C2211yescharacteristic
41#22583541C2211yescharacteristic
42Dic283⋊C8C2211yescharacteristic
43#22583535C2211yescharacteristic
44#22583535C2211yescharacteristic
45#22583533C2211yescharacteristic
46#22583533C2211yescharacteristic
47#22583533C2211yescharacteristic
48#22583533C2211yescharacteristic
49C22⋊(C283⋊C8)C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51C8×Dic283C2211yescharacteristic
52C2×M16×C283C2211yescharacteristic
53#117×C283C2211yescharacteristic
54C2×C4⋊C4×C283C2211yescharacteristic
55#107×C283C2211yescharacteristic
56#107×C283C2211yescharacteristic
57#106×C283C2211yescharacteristic
58#106×C283C2211yescharacteristic
59C2×Dic566—21no—
60C2×Dic566—21no—
61C2×Dic566C2311yescharacteristic
62C2×Dic566C2311yescharacteristic
63C2×C22⋊D283D411yescharacteristic
64C2×C4×D283—21no—
65C2×C4×D283C2311yescharacteristic
66Dic1132—22no—
67#17985375—22no—
68C2×C283⋊C8C2311yescharacteristic
69C2×C283⋊C8C2311yescharacteristic
70C4⋊Dic283—21no—
71C4⋊Dic283—21no—
72C4⋊Dic283C2311yescharacteristic
73C4⋊Dic283C2311yescharacteristic
74Dic283⋊C4—21no—
75Dic283⋊C4—21no—
76Dic283⋊C4—21no—
77Dic283⋊C4—21no—
78Dic283⋊C4—21no—
79Dic283⋊C4—21no—
80Dic283⋊C4—21no—
81Dic283⋊C4D411yescharacteristic
82C22⋊Dic283—21no—
83C22⋊Dic283—21no—
84C22⋊Dic283D411yescharacteristic
85(C2×D283)⋊C4—21no—
86(C2×D283)⋊C4—21no—
87(C2×D283)⋊C4—21no—
88(C2×D283)⋊C4D411yescharacteristic
89C4×Dic283—21no—
90C4×Dic283—21no—
91C4×Dic283—21no—
92C4×Dic283C2311yescharacteristic
93C22×C4×C283—21no—
94C22×C4×C283C2311yescharacteristic
95M16×C283—22no—
96C2×C8×C283C2311yescharacteristic
97C2×C8×C283C2311yescharacteristic
98C4⋊C4×C283—21no—
99C4⋊C4×C283C2311yescharacteristic
100C4⋊C4×C283C2311yescharacteristic
101C4⋊C4×C283C2311yescharacteristic
102C4⋊C4×C283C2311yescharacteristic
103C22⋊C4×C283—21no—
104C42×C283—21no—
105C22×D283C2×D411yescharacteristic
106Dic566—21no—
107Dic566—21no—
108Dic566—21no—
109Dic566—21no—
110Dic566—42no—
111Dic566—81no—
112C22⋊D283—22no—
113C2×Dic283—21no—
114C2×Dic283—21no—
115C2×Dic283—21no—
116C2×Dic283—21no—
117C2×Dic283C2×D411yescharacteristic
118C2×Dic283C2×D411yescharacteristic
119C2×Dic283C2×D411yescharacteristic
120C4×D283—21no—
121C4×D283—21no—
122C4×D283—81no—
123C283⋊C8—21no—
124C283⋊C8—21no—
125C23×C283C2×D411yescharacteristic
126C2×C4×C283—21no—
127C2×C4×C283—21no—
128C2×C4×C283—21no—
129C2×C4×C283—21no—
130C2×C4×C283—21no—
131C2×C4×C283—21no—
132C2×C4×C283—81no—
133C2×C4×C283C2×D411yescharacteristic
134C2×C4×C283C2411yescharacteristic
135C8×C283—21no—
136C8×C283#4112yes—
137C22×C283—21no—
138C22×C283—21no—
139C22×C283—21no—
140C22×C283C22×D411yescharacteristic
141C2×D283—21no—
142C2×D283—21no—
143C2×D283—21no—
144C4×C283—21no—
145C4×C283—41no—
146C4×C283—41no—
147C4×C283—41no—
148C4×C283—41no—
149C4×C283C2×#4111yescharacteristic
150C4×C2832−1+411yescharacteristic
151Dic283—21no—
152Dic283—21no—
153Dic283—41no—
154Dic283—41no—
155Dic283—41no—
156Dic283—41no—
157Dic283#13712yes—
158C2×C283—41no—
159C2×C283#54711yescharacteristic
160C2×C283C2×#13711yescharacteristic
161C2×C283#57711yescharacteristic
162D283—41no—
163C283#335611yescharacteristic, complemented, Sylow
164#3356—2831nomaximal, Sylow
165#556—2831no—
166#554—2831no—
167#498—2831no—
168#485—2831no—
169#485—2831no—
170#483—2831no—
171#483—2831no—
172#477—2831no—
173#475—2831no—
174#470—2831no—
175#470—2831no—
176C4×Q16—2831no—
177#436—2831no—
178#428—2831no—
179#428D28311yescharacteristic, complemented
180C2×Q16—2831no—
181C2×M16—2831no—
182C2×M16C2×D28311yescharacteristic
183C4⋊Q8—2831no—
184C4⋊Q8—2831no—
185#126—5661no—
186#126—5661no—
187#125—5661no—
188#124—5661no—
189C22⋊Q8—2831no—
190C22⋊Q8—2831no—
191C22⋊Q8—2831no—
192C22⋊Q8—2831no—
193C22⋊Q8—5661no—
194C22⋊Q8—5661no—
195C4×Q8—2831no—
196C4×Q8—2831no—
197C4×Q8—5661no—
198C4×D4—2831no—
199C4×D4—5661no—
200#117—2831no—
201#117C2×D28311yescharacteristic
202C2×C4⋊C4—2831no—
203C2×C4⋊C4C2×D28311yescharacteristic
204#107—2831no—
205#107C2×D28311yescharacteristic
206#107C2×D28311yescharacteristic
207#106—2831no—
208#106—2831no—
209#106—2831no—
210#106—2831no—
211#106C2×D28311yescharacteristic
212#106C2×D28311yescharacteristic
213C4⋊C8—2831no—
214#103—2831no—
215#103—2831no—
216#103—2831no—
217#103—2831no—
218#103—2831no—
219#103—2831no—
220C22⋊C8—2831no—
221C22⋊C8—2831no—
222C4×C8—2831no—
223C2×Q8—2831no—
224C2×Q8—2831no—
225C2×Q8—5661no—
226C2×Q8—5661no—
227C2×D4—2831no—
228C22×C4—21no—
229C22×C4—2831no—
230C22×C4—5661no—
231C22×C4C22×D28311yescharacteristic
232Q16—5662no—
233M16—22no—
234M16—5662no—
235C2×C8—2831no—
236C2×C8—2831no—
237C2×C8C22×D28311yescharacteristic
238C2×C8C22×D28311yescharacteristic
239C4⋊C4—21no—
240C4⋊C4—2831no—
241C4⋊C4—2831no—
242C4⋊C4—2831no—
243C4⋊C4—5661no—
244C4⋊C4—5661no—
245C4⋊C4—5661no—
246C4⋊C4—5661no—
247C4⋊C4—5661no—
248C4⋊C4—5661no—
249C4⋊C4—5661no—
250C4⋊C4—5661no—
251C4⋊C4—5661no—
252C4⋊C4C22×D28311yescharacteristic
253C4⋊C4C22×D28311yescharacteristic
254C4⋊C4C22×D28311yescharacteristic
255C4⋊C4C22×D28311yescharacteristic
256C22⋊C4—21no—
257C22⋊C4—2831no—
258C22⋊C4—2831no—
259C22⋊C4—5661no—
260C22⋊C4—5661no—
261C22⋊C4—5661no—
262C22⋊C4—5661no—
263C22⋊C4—5661no—
264C42—21no—
265C42—2831no—
266C42—5661no—
267C42—5661no—
268C42—5661no—
269C23—2831no—
270C23D4×D28311yescharacteristic
271Q8—5661no—
272Q8—5661no—
273Q8—5661no—
274Q8—5661no—
275Q8—11322no—
276Q8—22641no—
277D4—5662no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—81no—
285C2×C4—2831no—
286C2×C4—2831no—
287C2×C4—2831no—
288C2×C4—5661no—
289C2×C4—5661no—
290C2×C4—5661no—
291C2×C4—5661no—
292C2×C4—5661no—
293C2×C4—5661no—
294C2×C4—22641no—
295C2×C4D4×D28311yescharacteristic
296C2×C4C23×D28311yescharacteristic
297C8—21no—
298C8—5661no—
299C8—5661no—
300C8#1798539212yes—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—5661no—
305C22—5661no—
306C22—5661no—
307C22C2×D4×D28311yescharacteristic
308C4—21no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—2832no—
314C4—5661no—
315C4—5661no—
316C4—11321no—
317C4—11321no—
318C4—11321no—
319C4—11321no—
320C4C2×#1798539211yescharacteristic
321C4#2258365811yescharacteristic
322C2—41no—
323C2—11321no—
324C2#3182711611yescharacteristic
325C2#137×D28311yescharacteristic
326C2#3182727511yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#428×C283C2
socleC22×C283C22×D4
prime radicalC2×C22⋊D283D4
hypercenter#428D283
hypocenterC283#3356
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
3. #31826862C2semidirect
4. #31826808C2semidirect
5. #31826806C2semidirect
6. #31826797C2semidirect
7. #31826795C2semidirect
8. #31826759C2semidirect
9. #31826749C2semidirect
10. #31826724C2semidirect
11. #31826723C2semidirect
12. #31826559C2semidirect
14. #31826506C2semidirect
15. #428×C283C2semidirect
163. C283#3356semidirect
179. #428D283semidirect

Maximal subgroups

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

subgroupindex
#318271832
#318271702
#318268622
#318268082
#318268062
#318267972
#318267952
#318267592
#318267492
#318267242
#318267232
#318265592
#318265412
#318265062
#428×C2832
#3356283