Finite Group Databasebeta

← #49134315

Subgroups — #49134315

Order 36224.

362 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827198C211yesmaximal, characteristic
2#31827193C211yesmaximal, characteristic, complemented
3#31826859C211yesmaximal, characteristic, complemented
4#31826856C211yesmaximal, characteristic, complemented
5#31826836C211yesmaximal, characteristic
6#31826687C211yesmaximal, characteristic, complemented
7#31826686C211yesmaximal, characteristic, complemented
8#31826674C211yesmaximal, characteristic, complemented
9#31826670C211yesmaximal, characteristic, complemented
10#31826669C211yesmaximal, characteristic, complemented
11#31826664C211yesmaximal, characteristic
12#31826593C211yesmaximal, characteristic, complemented
13#31826564C211yesmaximal, characteristic, complemented
14#31826559C211yesmaximal, characteristic, complemented
15#440×C283C211yesmaximal, characteristic, complemented
16C2×Dic1132C2211yescharacteristic
17C2×Dic1132C2211yescharacteristic
18C2×#17985382C2211yescharacteristic
19C2×#17985381C2211yescharacteristic
20C2×#17985381C2211yescharacteristic
21C2×#17985380C2211yescharacteristic
22C2×#17985380C2211yescharacteristic
23C2×#17985379C2211yescharacteristic
24#22583610C2211yescharacteristic
25#22583608C2211yescharacteristic
26#22583608C2211yescharacteristic
27#22583606C2211yescharacteristic
28#22583602—21no—
29#22583600—21no—
30#22583600—21no—
31#22583598C2211yescharacteristic
32#22583597C2211yescharacteristic
33#22583596—21no—
34#22583593—21no—
35#22583592—21no—
36C4×Dic566—21no—
37C4×Dic566C2211yescharacteristic
38#22583575C2211yescharacteristic
39#22583575C2211yescharacteristic
40#22583575C2211yescharacteristic
41#22583572C2211yescharacteristic
42C4×C22⋊D283—21no—
43C4⋊(C283⋊C8)C2211yescharacteristic
44Dic283⋊C8C2211yescharacteristic
45Dic283⋊C8C2211yescharacteristic
46#22583533C2211yescharacteristic
47#22583533C2211yescharacteristic
48#22583533C2211yescharacteristic
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×Dic566D411yescharacteristic
60C2×Dic566C2311yescharacteristic
61C2×Dic566C2311yescharacteristic
62C2×Dic566C2311yescharacteristic
63C2×D1132C2311yescharacteristic
64C2×C22⋊D283—21no—
65C2×C22⋊D283—21no—
66C2×C4×D283—21no—
67Dic1132—22no—
68Dic1132—41no—
69#17985382—41no—
70#17985381—22no—
71#17985381—41no—
72#17985380—41no—
73#17985380—41no—
74#17985379—41no—
75C2×C283⋊C8C2311yescharacteristic
76C2×C283⋊C8C2311yescharacteristic
77C4⋊Dic283—21no—
78C4⋊Dic283—21no—
79C4⋊Dic283D411yescharacteristic
80Dic283⋊C4—21no—
81Dic283⋊C4—21no—
82Dic283⋊C4—21no—
83Dic283⋊C4—21no—
84Dic283⋊C4—21no—
85Dic283⋊C4—21no—
86Dic283⋊C4—21no—
87Dic283⋊C4D411yescharacteristic
88Dic283⋊C4D411yescharacteristic
89C22⋊Dic283—21no—
90C22⋊Dic283—21no—
91(C2×D283)⋊C4—21no—
92(C2×D283)⋊C4—21no—
93(C2×D283)⋊C4—21no—
94C4×Dic283—21no—
95C4×Dic283—21no—
96C4×Dic283—21no—
97C4×Dic283C2311yescharacteristic
98C4×Dic283C2311yescharacteristic
99C2×Q8×C283C2311yescharacteristic
100C2×D4×C283C2311yescharacteristic
101C22×C4×C283—21no—
102SD16×C283—22no—
103C2×C8×C283C2311yescharacteristic
104C2×C8×C283C2311yescharacteristic
105C4⋊C4×C283—21no—
106C4⋊C4×C283C2311yescharacteristic
107C4⋊C4×C283C2311yescharacteristic
108C22⋊C4×C283—21no—
109C42×C283—21no—
110C42×C283C2311yescharacteristic
111C22×D283—21no—
112Dic566—22no—
113Dic566—21no—
114Dic566—21no—
115Dic566—21no—
116Dic566—21no—
117Dic566—21no—
118Dic566—21no—
119D1132—21no—
120D1132—21no—
121C22⋊D283—42no—
122C22⋊D283—81no—
123C2×Dic283—21no—
124C2×Dic283—21no—
125C2×Dic283—21no—
126C2×Dic283C2×D411yescharacteristic
127C2×Dic283C2×D411yescharacteristic
128C2×Dic283C2×D411yescharacteristic
129C2×Dic283C2×D411yescharacteristic
130C4×D283—81no—
131C283⋊C8—21no—
132C283⋊C8—21no—
133C23×C283—21no—
134Q8×C283—21no—
135Q8×C283—21no—
136D4×C283—21no—
137D4×C283—21no—
138C2×C4×C283—21no—
139C2×C4×C283—21no—
140C2×C4×C283—21no—
141C2×C4×C283—81no—
142C2×C4×C283C2×D411yescharacteristic
143C2×C4×C283C2×D411yescharacteristic
144C2×C4×C283C2411yescharacteristic
145C8×C283—21no—
146C8×C283#4112yes—
147C22×C283—41no—
148C22×C283—41no—
149C22×C283—41no—
150C22×C283C22×D411yescharacteristic
151C2×D283—41no—
152C2×D283—41no—
153C2×D283—41no—
154C4×C283—21no—
155C4×C283—21no—
156C4×C283—41no—
157C4×C283—41no—
158C4×C283—41no—
159C4×C283C2×#4111yescharacteristic
160C4×C283H(5,𝔽2)11yescharacteristic
161Dic283—21no—
162Dic283—21no—
163Dic283—21no—
164Dic283—41no—
165Dic283—41no—
166Dic283—41no—
167Dic283#13712yes—
168C2×C283—81no—
169C2×C283#55011yescharacteristic
170C2×C283C2×#13711yescharacteristic
171C2×C283#57711yescharacteristic
172D283—81no—
173C283#340011yescharacteristic, complemented, Sylow
174#3400—2831nomaximal, Sylow
175#559—2831no—
176#557—2831no—
177#497—2831no—
178#497—2831no—
179#492—2831no—
180#464—2831no—
181#464—2831no—
182#462—2831no—
183#461—2831no—
184#461—2831no—
185#460—2831no—
186#446—2831no—
187#440—2831no—
188#440D28311yescharacteristic, complemented
189C4×Q16—2831no—
190C2×Q16—2831no—
191C2×Q16—2831no—
192C2×Q16—2831no—
193C2×SD16—2831no—
194C2×SD16—2831no—
195C2×SD16—2831no—
196C2×SD16—2831no—
197C2×SD16—2831no—
198C2×SD16C2×D28311yescharacteristic
199C4⋊Q8—2831no—
200C4⋊Q8—2831no—
201C4⋊Q8—2831no—
202#127—2831no—
203#125—5661no—
204#125—5661no—
205#125—5661no—
206#124—2831no—
207#124—2831no—
208#124—5661no—
209#123—5661no—
210#123—5661no—
211C4×Q8—2831no—
212C4×Q8—2831no—
213C4×Q8—2831no—
214C4×Q8—2831no—
215C4×Q8—5661no—
216C4×Q8C2×D28311yescharacteristic
217C4×D4—2831no—
218C4×D4—5661no—
219C4×D4C2×D28311yescharacteristic
220#107C2×D28311yescharacteristic
221C4⋊C8—2831no—
222C4⋊C8—2831no—
223C4⋊C8—2831no—
224#103—2831no—
225#103—2831no—
226#103—2831no—
227#103C2×D28311yescharacteristic
228#102—2831no—
229#102C2×D28311yescharacteristic
230#97—2831no—
231#97C2×D28311yescharacteristic
232C4×C8—2831no—
233C2×Q8—2831no—
234C2×Q8—2831no—
235C2×Q8—2831no—
236C2×Q8—2831no—
237C2×Q8C22×D28311yescharacteristic
238C2×D4—2831no—
239C2×D4—5661no—
240C2×D4—5661no—
241C2×D4C22×D28311yescharacteristic
242C22×C4—21no—
243C22×C4—5661no—
244Q16—5662no—
245Q16—11321no—
246Q16—11321no—
247SD16—22no—
248SD16—5662no—
249SD16—11321no—
250SD16—11321no—
251SD16—11321no—
252SD16—11321no—
253C2×C8—2831no—
254C2×C8—2831no—
255C2×C8C22×D28311yescharacteristic
256C2×C8C22×D28311yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—2831no—
259C4⋊C4—2831no—
260C4⋊C4—2831no—
261C4⋊C4—5661no—
262C4⋊C4—5661no—
263C4⋊C4—5661no—
264C4⋊C4—5661no—
265C4⋊C4—5661no—
266C4⋊C4—5661no—
267C4⋊C4—5661no—
268C4⋊C4—5661no—
269C4⋊C4—5661no—
270C4⋊C4C22×D28311yescharacteristic
271C4⋊C4C22×D28311yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—5661no—
274C22⋊C4—5661no—
275C22⋊C4—5661no—
276C22⋊C4—5661no—
277C22⋊C4—5661no—
278C42—21no—
279C42—2831no—
280C42—2831no—
281C42—5661no—
282C42—5661no—
283C42—5661no—
284C42C22×D28311yescharacteristic
285C23—21no—
286C23—5661no—
287Q8—21no—
288Q8—21no—
289Q8—5662no—
290Q8—5661no—
291Q8—5661no—
292Q8—5661no—
293Q8—5661no—
294Q8—5661no—
295Q8—5661no—
296D4—21no—
297D4—21no—
298D4—5661no—
299D4—5661no—
300D4—11322no—
301D4—22641no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—81no—
306C2×C4—2831no—
307C2×C4—2831no—
308C2×C4—2831no—
309C2×C4—2831no—
310C2×C4—5661no—
311C2×C4—5661no—
312C2×C4—5661no—
313C2×C4—22641no—
314C2×C4D4×D28311yescharacteristic
315C2×C4D4×D28311yescharacteristic
316C2×C4C23×D28311yescharacteristic
317C8—21no—
318C8—5661no—
319C8—5661no—
320C8#1798539212yes—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—11321no—
325C22—11321no—
326C22—11321no—
327C22C2×D4×D28311yescharacteristic
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—2832no—
334C4—5661no—
335C4—5661no—
336C4—5661no—
337C4—11321no—
338C4—11321no—
339C4—11321no—
340C4C2×#1798539211yescharacteristic
341C4#2258365611yescharacteristic
342C2—81no—
343C2—22641no—
344C2#3182713611yescharacteristic
345C2#137×D28311yescharacteristic
346C2#3182727511yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#440×C283C2
socleC22×C283C22×D4
prime radical#22583606C22
hypercenter#440D283
hypocenterC283#3400
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
2. #31827193C2semidirect
3. #31826859C2semidirect
4. #31826856C2semidirect
6. #31826687C2semidirect
7. #31826686C2semidirect
8. #31826674C2semidirect
9. #31826670C2semidirect
10. #31826669C2semidirect
12. #31826593C2semidirect
13. #31826564C2semidirect
14. #31826559C2semidirect
15. #440×C283C2semidirect
173. C283#3400semidirect
188. #440D283semidirect

Maximal subgroups

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

subgroupindex
#318271982
#318271932
#318268592
#318268562
#318268362
#318266872
#318266862
#318266742
#318266702
#318266692
#318266642
#318265932
#318265642
#318265592
#440×C2832
#3400283