Finite Group Databasebeta

← #49134332

Subgroups — #49134332

Order 36224.

368 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827198C211yesmaximal, characteristic, complemented
2#31827185C211yesmaximal, characteristic, complemented
3#31826859C211yesmaximal, characteristic, complemented
4#31826853C211yesmaximal, characteristic
5#31826848C211yesmaximal, characteristic, complemented
6#31826686C211yesmaximal, characteristic, complemented
7#31826686C211yesmaximal, characteristic, complemented
8#31826680C211yesmaximal, characteristic, complemented
9#31826679C211yesmaximal, characteristic, complemented
10#31826670C211yesmaximal, characteristic, complemented
11#31826664C211yesmaximal, characteristic, complemented
12#31826593C211yesmaximal, characteristic, complemented
13#31826571C211yesmaximal, characteristic, complemented
14#31826552C211yesmaximal, characteristic, complemented
15#442×C283C211yesmaximal, characteristic, complemented
16C2×Dic1132C2211yescharacteristic
17C2×Dic1132C2211yescharacteristic
18C2×#17985381C2211yescharacteristic
19C2×#17985381C2211yescharacteristic
20C2×#17985380C2211yescharacteristic
21C2×#17985380C2211yescharacteristic
22C2×#17985380C2211yescharacteristic
23C2×#17985377C2211yescharacteristic
24#22583610C2211yescharacteristic
25#22583606C2211yescharacteristic
26#22583603—21no—
27#22583603—21no—
28#22583598C2211yescharacteristic
29#22583597C2211yescharacteristic
30#22583597C2211yescharacteristic
31#22583597C2211yescharacteristic
32#22583596—21no—
33#22583593—21no—
34#22583592—21no—
35#22583589—21no—
36C4×Dic566C2211yescharacteristic
37#22583575C2211yescharacteristic
38#22583575C2211yescharacteristic
39#22583575C2211yescharacteristic
40#22583572C2211yescharacteristic
41C4×C22⋊D283—21no—
42#22583569—21no—
43C4⋊(C283⋊C8)C2211yescharacteristic
44Dic283⋊C8C2211yescharacteristic
45Dic283⋊C8C2211yescharacteristic
46#22583533C2211yescharacteristic
47#22583533C2211yescharacteristic
48#22583533C2211yescharacteristic
49#22583530C2211yescharacteristic
50#22583520C2211yescharacteristic
51C8×Dic283C2211yescharacteristic
52C2×D8×C283C2211yescharacteristic
53C4×D4×C283C2211yescharacteristic
54C4×D4×C283C2211yescharacteristic
55#106×C283C2211yescharacteristic
56#102×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#17985381—22no—
70#17985381—41no—
71#17985380—41no—
72#17985380—41no—
73#17985380—41no—
74#17985377—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⋊C4D411yescharacteristic
84Dic283⋊C4D411yescharacteristic
85C22⋊Dic283—21no—
86C22⋊Dic283—21no—
87C22⋊Dic283—21no—
88C22⋊Dic283—21no—
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×D4×C283C2311yescharacteristic
100C2×D4×C283C2311yescharacteristic
101C22×C4×C283—21no—
102C22×C4×C283—21no—
103D8×C283—22no—
104C2×C8×C283C2311yescharacteristic
105C2×C8×C283C2311yescharacteristic
106C4⋊C4×C283C2311yescharacteristic
107C4⋊C4×C283C2311yescharacteristic
108C22⋊C4×C283—21no—
109C22⋊C4×C283—21no—
110C42×C283C2311yescharacteristic
111C22×D283—21no—
112Dic566—21no—
113Dic566—21no—
114Dic566—21no—
115Dic566—21no—
116Dic566—21no—
117Dic566—21no—
118Dic566—41no—
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—
134C23×C283—21no—
135D4×C283—21no—
136D4×C283—21no—
137D4×C283—21no—
138D4×C283—21no—
139C2×C4×C283—21no—
140C2×C4×C283—21no—
141C2×C4×C283—42no—
142C2×C4×C283—81no—
143C2×C4×C283C2×D411yescharacteristic
144C2×C4×C283C2×D411yescharacteristic
145C2×C4×C283C2411yescharacteristic
146C8×C283—21no—
147C8×C283#4112yes—
148C22×C283—41no—
149C22×C283—41no—
150C22×C283—41no—
151C22×C283—41no—
152C22×C283—41no—
153C22×C283—41no—
154C22×C283C22×D411yescharacteristic
155C2×D283—41no—
156C2×D283—41no—
157C2×D283—41no—
158C4×C283—21no—
159C4×C283—21no—
160C4×C283—41no—
161C4×C283—41no—
162C4×C283C2×#4111yescharacteristic
163C4×C283H(5,𝔽2)11yescharacteristic
164Dic283—21no—
165Dic283—21no—
166Dic283—21no—
167Dic283—21no—
168Dic283—41no—
169Dic283—41no—
170Dic283—41no—
171C2×C283—81no—
172C2×C283—81no—
173C2×C283#55011yescharacteristic
174C2×C283#57511yescharacteristic
175C2×C283#57711yescharacteristic
176D283—81no—
177C283#340111yescharacteristic, complemented, Sylow
178#3401—2831nomaximal, Sylow
179#559—2831no—
180#556—2831no—
181#497—2831no—
182#496—2831no—
183#495—2831no—
184#464—2831no—
185#464—2831no—
186#463—2831no—
187#463—2831no—
188#461—2831no—
189#460—2831no—
190#446—2831no—
191#442D28311yescharacteristic, complemented
192#441—2831no—
193C4×SD16—2831no—
194C2×Q16—2831no—
195C2×Q16—2831no—
196C2×SD16—2831no—
197C2×SD16—2831no—
198C2×SD16—2831no—
199C2×SD16—2831no—
200C2×SD16—2831no—
201C2×D8—2831no—
202C2×D8C2×D28311yescharacteristic
203C4⋊Q8—2831no—
204#127—2831no—
205#126—5661no—
206#126—5661no—
207#124—2831no—
208#124—2831no—
209#124—2831no—
210#124—2831no—
211#124—5661no—
212#123—5661no—
213#123—5661no—
214C22⋊Q8—5661no—
215C4×Q8—2831no—
216C4×Q8—2831no—
217C4×Q8—2831no—
218C4×Q8—2831no—
219C4×D4—2831no—
220C4×D4—5661no—
221C4×D4C2×D28311yescharacteristic
222C4×D4C2×D28311yescharacteristic
223#117—5661no—
224#106C2×D28311yescharacteristic
225C4⋊C8—2831no—
226C4⋊C8—2831no—
227C4⋊C8—2831no—
228#103—2831no—
229#103—2831no—
230#103—2831no—
231#102—2831no—
232#102C2×D28311yescharacteristic
233#102C2×D28311yescharacteristic
234#97—2831no—
235#97C2×D28311yescharacteristic
236C4×C8—2831no—
237C2×Q8—2831no—
238C2×Q8—2831no—
239C2×Q8—2831no—
240C2×Q8—2831no—
241C2×D4—2831no—
242C2×D4—5661no—
243C2×D4—5661no—
244C2×D4C22×D28311yescharacteristic
245C2×D4C22×D28311yescharacteristic
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—5661no—
249Q16—5662no—
250Q16—11321no—
251SD16—5662no—
252SD16—11321no—
253SD16—11321no—
254SD16—11321no—
255SD16—11321no—
256D8—22no—
257D8—11321no—
258C2×C8—2831no—
259C2×C8—2831no—
260C2×C8C22×D28311yescharacteristic
261C2×C8C22×D28311yescharacteristic
262C4⋊C4—2831no—
263C4⋊C4—2831no—
264C4⋊C4—2831no—
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—21no—
274C22⋊C4—5661no—
275C22⋊C4—5661no—
276C22⋊C4—5661no—
277C22⋊C4—5661no—
278C22⋊C4—5661no—
279C22⋊C4—5661no—
280C22⋊C4—5661no—
281C22⋊C4—5661no—
282C22⋊C4—5661no—
283C42—2831no—
284C42—2831no—
285C42—5661no—
286C42—5661no—
287C42—5661no—
288C42C22×D28311yescharacteristic
289C23—21no—
290C23—21no—
291C23—5661no—
292Q8—5661no—
293Q8—5661no—
294Q8—5661no—
295Q8—5661no—
296Q8—5661no—
297Q8—5661no—
298Q8—11321no—
299D4—21no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—5661no—
304D4—5661no—
305D4—11322no—
306D4—22641no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—81no—
311C2×C4—2831no—
312C2×C4—2831no—
313C2×C4—2831no—
314C2×C4—2831no—
315C2×C4—5661no—
316C2×C4—5661no—
317C2×C4—5661no—
318C2×C4—22641no—
319C2×C4D4×D28311yescharacteristic
320C2×C4D4×D28311yescharacteristic
321C2×C4C23×D28311yescharacteristic
322C8—21no—
323C8—5661no—
324C8—5661no—
325C8#1798539212yes—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—11321no—
333C22—11321no—
334C22—11321no—
335C22C2×D4×D28311yescharacteristic
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—5661no—
341C4—5661no—
342C4—5661no—
343C4—5661no—
344C4—11321no—
345C4—11321no—
346C4—11321no—
347C4C2×#1798539211yescharacteristic
348C4#2258365611yescharacteristic
349C2—81no—
350C2—81no—
351C2—22641no—
352C2#3182713611yescharacteristic
353C2#3182726111yescharacteristic
354C2#3182727511yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#442×C283C2
socleC22×C283C22×D4
prime radical#31826853C2
hypercenter#442D283
hypocenterC283#3401
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #31827198C2semidirect
2. #31827185C2semidirect
3. #31826859C2semidirect
5. #31826848C2semidirect
6. #31826686C2semidirect
7. #31826686C2semidirect
8. #31826680C2semidirect
9. #31826679C2semidirect
10. #31826670C2semidirect
11. #31826664C2semidirect
12. #31826593C2semidirect
13. #31826571C2semidirect
14. #31826552C2semidirect
15. #442×C283C2semidirect
177. C283#3401semidirect
191. #442D283semidirect

Maximal subgroups

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

subgroupindex
#318271982
#318271852
#318268592
#318268532
#318268482
#318266862
#318266802
#318266792
#318266702
#318266642
#318265932
#318265712
#318265522
#442×C2832
#3401283