Finite Group Databasebeta

← #49133883

Subgroups — #49133883

Order 36224.

354 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827178C211yesmaximal, characteristic
2#31827170C211yesmaximal, characteristic, complemented
3#31826869C211yesmaximal, characteristic, complemented
4#31826809C211yesmaximal, characteristic, complemented
5#31826806C211yesmaximal, characteristic, complemented
6#31826780C211yesmaximal, characteristic, complemented
7#31826778C211yesmaximal, characteristic, complemented
8#31826759C211yesmaximal, characteristic, complemented
9#31826754C211yesmaximal, characteristic, complemented
10#31826712C211yesmaximal, characteristic, complemented
11#31826711C211yesmaximal, characteristic, complemented
12#31826552C211yesmaximal, characteristic, complemented
13#31826541C211yesmaximal, characteristic, complemented
14#31826504C211yesmaximal, characteristic, complemented
15#428×C283C211yesmaximal, characteristic, complemented
16C2×#17985381C2211yescharacteristic
17C2×#17985375C2211yescharacteristic
18#22583609C2211yescharacteristic
19#22583609C2211yescharacteristic
20#22583600—21no—
21#22583598—21no—
22#22583596—21no—
23#22583590C2211yescharacteristic
24#22583589—21no—
25#22583589C2211yescharacteristic
26#22583588—21no—
27#22583585C2211yescharacteristic
28#22583584C2211yescharacteristic
29#22583583—21no—
30#22583575C2211yescharacteristic
31#22583572C2211yescharacteristic
32C4×C22⋊D283—21no—
33C4×C22⋊D283C2211yescharacteristic
34#22583568C2211yescharacteristic
35#22583567—21no—
36C4⋊C4×D283C2211yescharacteristic
37#22583544C2211yescharacteristic
38#22583543C2211yescharacteristic
39#22583543C2211yescharacteristic
40#22583543C2211yescharacteristic
41#22583541C2211yescharacteristic
42Dic283⋊C8C2211yescharacteristic
43#22583535C2211yescharacteristic
44#22583533C2211yescharacteristic
45#22583533C2211yescharacteristic
46#22583532C2211yescharacteristic
47#22583530C2211yescharacteristic
48#22583530C2211yescharacteristic
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×D1132—21no—
63C2×D1132C2311yescharacteristic
64C2×C22⋊D283—21no—
65C2×C22⋊D283D411yescharacteristic
66C2×C4×D283—21no—
67C2×C4×D283—21no—
68C2×C4×D283C2311yescharacteristic
69#17985381—22no—
70#17985375—22no—
71C2×C283⋊C8C2311yescharacteristic
72C2×C283⋊C8C2311yescharacteristic
73C4⋊Dic283—21no—
74C4⋊Dic283C2311yescharacteristic
75C4⋊Dic283C2311yescharacteristic
76Dic283⋊C4—21no—
77Dic283⋊C4—21no—
78Dic283⋊C4—21no—
79Dic283⋊C4—21no—
80Dic283⋊C4—21no—
81Dic283⋊C4D411yescharacteristic
82C22⋊Dic283—21no—
83C22⋊Dic283D411yescharacteristic
84(C2×D283)⋊C4—21no—
85(C2×D283)⋊C4—21no—
86(C2×D283)⋊C4—21no—
87(C2×D283)⋊C4—21no—
88(C2×D283)⋊C4—21no—
89(C2×D283)⋊C4D411yescharacteristic
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×D283—21no—
106C22×D283C2×D411yescharacteristic
107Dic566—21no—
108Dic566—21no—
109Dic566—81no—
110Dic566—81no—
111D1132—21no—
112D1132—21no—
113D1132—81no—
114C22⋊D283—22no—
115C22⋊D283—81no—
116C2×Dic283—21no—
117C2×Dic283—21no—
118C2×Dic283—21no—
119C2×Dic283C2×D411yescharacteristic
120C2×Dic283C2×D411yescharacteristic
121C2×Dic283C2×D411yescharacteristic
122C4×D283—21no—
123C4×D283—21no—
124C4×D283—42no—
125C4×D283—81no—
126C283⋊C8—21no—
127C283⋊C8—21no—
128C23×C283C2×D411yescharacteristic
129C2×C4×C283—21no—
130C2×C4×C283—21no—
131C2×C4×C283—21no—
132C2×C4×C283—21no—
133C2×C4×C283—21no—
134C2×C4×C283—21no—
135C2×C4×C283—81no—
136C2×C4×C283C2×D411yescharacteristic
137C2×C4×C283C2411yescharacteristic
138C8×C283—21no—
139C8×C283#4112yes—
140C22×C283—21no—
141C22×C283—21no—
142C22×C283—21no—
143C22×C283C22×D411yescharacteristic
144C2×D283—21no—
145C2×D283—21no—
146C2×D283—21no—
147C2×D283—41no—
148C2×D283—41no—
149C2×D283—41no—
150C4×C283—21no—
151C4×C283—41no—
152C4×C283—41no—
153C4×C283—41no—
154C4×C283—41no—
155C4×C283C2×#4111yescharacteristic
156C4×C2832−1+411yescharacteristic
157Dic283—21no—
158Dic283—21no—
159Dic283—41no—
160Dic283—41no—
161Dic283—41no—
162Dic283#13712yes—
163C2×C283—41no—
164C2×C283#54711yescharacteristic
165C2×C283C2×#13711yescharacteristic
166C2×C283#57611yescharacteristic
167D283—41no—
168D283—81no—
169C283#335711yescharacteristic, complemented, Sylow
170#3357—2831nomaximal, Sylow
171#555—2831no—
172#554—2831no—
173#500—2831no—
174#485—2831no—
175#485—2831no—
176#480—2831no—
177#480—2831no—
178#477—2831no—
179#476—2831no—
180#468—2831no—
181#468—2831no—
182C4×SD16—2831no—
183#436—2831no—
184#428—2831no—
185#428D28311yescharacteristic, complemented
186C2×SD16—2831no—
187C2×M16—2831no—
188C2×M16C2×D28311yescharacteristic
189C4⋊Q8—2831no—
190C4⋊Q8—2831no—
191#125—5661no—
192#124—5661no—
193#124—5661no—
194C22⋊Q8—2831no—
195C22⋊Q8—2831no—
196C22⋊Q8—5661no—
197C22⋊Q8—5661no—
198#121—2831no—
199#121—2831no—
200#121—5661no—
201C4×Q8—2831no—
202C4×D4—2831no—
203C4×D4—2831no—
204C4×D4—5661no—
205#117—2831no—
206#117—5661no—
207#117C2×D28311yescharacteristic
208C2×C4⋊C4—2831no—
209C2×C4⋊C4C2×D28311yescharacteristic
210#107—2831no—
211#107—2831no—
212#107—2831no—
213#107—2831no—
214#107C2×D28311yescharacteristic
215#107C2×D28311yescharacteristic
216#106—2831no—
217#106C2×D28311yescharacteristic
218#106C2×D28311yescharacteristic
219C4⋊C8—2831no—
220#103—2831no—
221#103—2831no—
222#103—2831no—
223#102—2831no—
224#102—2831no—
225#102—2831no—
226C22⋊C8—2831no—
227C22⋊C8—2831no—
228C4×C8—2831no—
229C2×Q8—2831no—
230C2×Q8—5661no—
231C2×Q8—5661no—
232C2×D4—2831no—
233C2×D4—2831no—
234C2×D4—5661no—
235C2×D4—5661no—
236C22×C4—21no—
237C22×C4—2831no—
238C22×C4—5661no—
239C22×C4—5661no—
240C22×C4C22×D28311yescharacteristic
241SD16—5662no—
242M16—22no—
243M16—5662no—
244C2×C8—2831no—
245C2×C8—2831no—
246C2×C8C22×D28311yescharacteristic
247C2×C8C22×D28311yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—2831no—
250C4⋊C4—2831no—
251C4⋊C4—2831no—
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
261C4⋊C4C22×D28311yescharacteristic
262C22⋊C4—21no—
263C22⋊C4—2831no—
264C22⋊C4—2831no—
265C22⋊C4—5661no—
266C22⋊C4—5661no—
267C22⋊C4—5661no—
268C22⋊C4—5661no—
269C22⋊C4—5661no—
270C22⋊C4—5661no—
271C42—21no—
272C42—2831no—
273C42—5661no—
274C42—5661no—
275C23—2831no—
276C23—5661no—
277C23D4×D28311yescharacteristic
278Q8—5661no—
279Q8—5661no—
280Q8—22641no—
281Q8—22641no—
282D4—5662no—
283D4—5661no—
284D4—5661no—
285D4—22641no—
286D4—22641no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—81no—
294C2×C4—2831no—
295C2×C4—2831no—
296C2×C4—2831no—
297C2×C4—5661no—
298C2×C4—5661no—
299C2×C4—5661no—
300C2×C4—5661no—
301C2×C4—5661no—
302C2×C4—11322no—
303C2×C4—22641no—
304C2×C4D4×D28311yescharacteristic
305C2×C4C23×D28311yescharacteristic
306C8—21no—
307C8—5661no—
308C8—5661no—
309C8#1798539212yes—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—5661no—
314C22—5661no—
315C22—5661no—
316C22—11321no—
317C22—11321no—
318C22—11321no—
319C22C2×D4×D28311yescharacteristic
320C4—21no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—41no—
325C4—2832no—
326C4—5661no—
327C4—5661no—
328C4—11321no—
329C4—11321no—
330C4—11321no—
331C4C2×#1798539211yescharacteristic
332C4#2258365811yescharacteristic
333C2—41no—
334C2—11321no—
335C2—22641no—
336C2#3182711611yescharacteristic
337C2#137×D28311yescharacteristic
338C2#3182726911yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#428×C283C2
socleC22×C283C22×D4
prime radical#31827178C2
hypercenter#428D283
hypocenterC283#3357
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
2. #31827170C2semidirect
3. #31826869C2semidirect
4. #31826809C2semidirect
5. #31826806C2semidirect
6. #31826780C2semidirect
7. #31826778C2semidirect
8. #31826759C2semidirect
9. #31826754C2semidirect
10. #31826712C2semidirect
11. #31826711C2semidirect
12. #31826552C2semidirect
13. #31826541C2semidirect
14. #31826504C2semidirect
15. #428×C283C2semidirect
169. C283#3357semidirect
185. #428D283semidirect

Maximal subgroups

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

subgroupindex
#318271782
#318271702
#318268692
#318268092
#318268062
#318267802
#318267782
#318267592
#318267542
#318267122
#318267112
#318265522
#318265412
#318265042
#428×C2832
#3357283