Finite Group Databasebeta

← #49133371

Subgroups — #49133371

Order 36224.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827176C211yesmaximal, characteristic, complemented
2#31827123C211yesmaximal, characteristic
3#31826794C211yesmaximal, characteristic, complemented
4#31826782C211yesmaximal, characteristic, complemented
5#31826747C211yesmaximal, characteristic, complemented
6#31826722C211yesmaximal, characteristic, complemented
7#31826693C211yesmaximal, characteristic, complemented
8#31826684C211yesmaximal, characteristic, complemented
9#31826628C211yesmaximal, characteristic, complemented
10#31826622C211yesmaximal, characteristic, complemented
11#31826573C211yesmaximal, characteristic, complemented
12#31826538C211yesmaximal, characteristic, complemented
13#31826463C211yesmaximal, characteristic, complemented
14#103×D283C211yesmaximal, characteristic, complemented
15#489×C283C211yesmaximal, characteristic, complemented
16C2×#17985391C2211yescharacteristic
17C2×Q8×D283C2211yescharacteristic
18C2×Dic1132C2211yescharacteristic
19C2×#17985382C2211yescharacteristic
20C2×#17985380C2211yescharacteristic
21C2×#17985375C2211yescharacteristic
22C2×C8×D283C2211yescharacteristic
23#22583601—21no—
24#22583596—21no—
25#22583590C2211yescharacteristic
26#22583590C2211yescharacteristic
27#22583587—21no—
28#22583586—21no—
29#22583586—21no—
30#22583586C2211yescharacteristic
31#22583583—21no—
32#22583581C2211yescharacteristic
33C4×Dic566C2211yescharacteristic
34C4×Dic566C2211yescharacteristic
35C4×D1132C2211yescharacteristic
36#22583572—21no—
37(C22⋊D283)⋊C4—21no—
38C4⋊C4×D283C2211yescharacteristic
39C4⋊C4×D283C2211yescharacteristic
40#22583542C2211yescharacteristic
41#22583541C2211yescharacteristic
42#22583541C2211yescharacteristic
43C4⋊(C283⋊C8)C2211yescharacteristic
44#22583535C2211yescharacteristic
45#22583535C2211yescharacteristic
46#22583534C2211yescharacteristic
47#22583533C2211yescharacteristic
48#22583533C2211yescharacteristic
49#22583531C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51(C2×D283)⋊C8C2211yescharacteristic
52C4⋊Q8×C283C2211yescharacteristic
53#124×C283C2211yescharacteristic
54#103×C283C2211yescharacteristic
55#103×C283C2211yescharacteristic
56#102×C283C2211yescharacteristic
57#102×C283C2211yescharacteristic
58#97×C283C2211yescharacteristic
59#17985391—22no—
60#17985391—41no—
61C2×Dic566—21no—
62C2×Dic566C2311yescharacteristic
63C2×Dic566C2311yescharacteristic
64Q8×D283—22no—
65Q8×D283—41no—
66C2×D1132D411yescharacteristic
67C2×C22⋊D283—21no—
68C2×C22⋊D283—21no—
69C22×Dic283—21no—
70C2×C4×D283—21no—
71C2×C4×D283—21no—
72C2×C4×D283—21no—
73C2×C4×D283C2311yescharacteristic
74C2×C4×D283C2311yescharacteristic
75Dic1132—22no—
76#17985382—41no—
77#17985380—41no—
78#17985375—41no—
79C2×C283⋊C8C2311yescharacteristic
80C2×C283⋊C8C2311yescharacteristic
81C8×D283—41no—
82C4⋊Dic283—21no—
83C4⋊Dic283—21no—
84C4⋊Dic283D411yescharacteristic
85C4⋊Dic283C2311yescharacteristic
86C4⋊Dic283C2311yescharacteristic
87Dic283⋊C4—21no—
88Dic283⋊C4—21no—
89Dic283⋊C4—21no—
90Dic283⋊C4—21no—
91Dic283⋊C4—21no—
92C22⋊Dic283—21no—
93(C2×D283)⋊C4—21no—
94(C2×D283)⋊C4—21no—
95(C2×D283)⋊C4—21no—
96(C2×D283)⋊C4D411yescharacteristic
97(C2×D283)⋊C4D411yescharacteristic
98C4×Dic283—21no—
99C4×Dic283—21no—
100C2×Q8×C283—21no—
101C2×Q8×C283C2311yescharacteristic
102C2×D4×C283C2311yescharacteristic
103C2×C8×C283C2311yescharacteristic
104C2×C8×C283C2311yescharacteristic
105C4⋊C4×C283—21no—
106C4⋊C4×C283C2311yescharacteristic
107C4⋊C4×C283C2311yescharacteristic
108C22⋊C4×C283—21no—
109C22⋊C4×C283—21no—
110C42×C283C2311yescharacteristic
111C22×D283C2×D411yescharacteristic
112C22×D283C2×D411yescharacteristic
113Dic566—21no—
114Dic566—21no—
115Dic566—21no—
116Dic566—42no—
117Dic566#4112yes—
118D1132—22no—
119C22⋊D283—42no—
120C22⋊D283—42no—
121C2×Dic283—21no—
122C2×Dic283—21no—
123C2×Dic283—21no—
124C2×Dic283—21no—
125C2×Dic283—42no—
126C2×Dic283C2×D411yescharacteristic
127C2×Dic283C2×D411yescharacteristic
128C4×D283—21no—
129C4×D283—21no—
130C4×D283—21no—
131C4×D283—21no—
132C4×D283—42no—
133C4×D283—81no—
134C4×D283—81no—
135C283⋊C8—21no—
136C283⋊C8—21no—
137C23×C283—21no—
138Q8×C283—21no—
139Q8×C283—21no—
140Q8×C283—81no—
141D4×C283—21no—
142D4×C283—21no—
143C2×C4×C283—21no—
144C2×C4×C283—21no—
145C2×C4×C283—21no—
146C2×C4×C283C2×D411yescharacteristic
147C2×C4×C283C2×D411yescharacteristic
148C2×C4×C283C2411yescharacteristic
149C8×C283—21no—
150C8×C283—21no—
151C22×C283—41no—
152C22×C283—41no—
153C22×C283—41no—
154C22×C283C22×D411yescharacteristic
155C2×D283—21no—
156C2×D283—21no—
157C2×D283—21no—
158C2×D283—21no—
159C2×D283—21no—
160C2×D283#13712yes—
161C4×C283—21no—
162C4×C283—21no—
163C4×C283—41no—
164C4×C283—41no—
165C4×C283—41no—
166C4×C283C2×#4111yescharacteristic
167C4×C283H(5,𝔽2)11yescharacteristic
168Dic283—21no—
169Dic283—21no—
170Dic283—22no—
171Dic283—41no—
172Dic283—41no—
173Dic283—41no—
174C2×C283—81no—
175C2×C283#54611yescharacteristic
176C2×C283C2×#13711yescharacteristic
177C2×C283#57711yescharacteristic
178D283—22no—
179D283—41no—
180C283#331611yescharacteristic, complemented, Sylow
181#3316—2831nomaximal, Sylow
182#554—2831no—
183#548—2831no—
184#489D28311yescharacteristic, complemented
185#483—2831no—
186#481—2831no—
187#475—2831no—
188#470—2831no—
189#465—2831no—
190#464—2831no—
191#452—2831no—
192#451—2831no—
193#441—2831no—
194#435—2831no—
195#417—2831no—
196C2×#103—2831no—
197C2×#41—2831no—
198C22×Q8—2831no—
199C2×Q16—2831no—
200C2×Q16—2831no—
201C2×SD16—2831no—
202C2×M16—2831no—
203C22×C8—2831no—
204C4⋊Q8C2×D28311yescharacteristic
205#125—5661no—
206#124—5661no—
207#124C2×D28311yescharacteristic
208C22⋊Q8—2831no—
209C22⋊Q8—2831no—
210C22⋊Q8—2831no—
211C22⋊Q8—5661no—
212C22⋊Q8—5661no—
213C22⋊Q8—5661no—
214#121—2831no—
215#121—5661no—
216C4×Q8—2831no—
217C4×Q8—2831no—
218C4×D4—2831no—
219C4×D4—5661no—
220C4×D4—5661no—
221C2×C4⋊C4—2831no—
222C2×C4⋊C4—2831no—
223#106—2831no—
224#106—2831no—
225#106—2831no—
226C4⋊C8—2831no—
227#103—2831no—
228#103—2831no—
229#103—2831no—
230#103—2831no—
231#103—2831no—
232#103C2×D28311yescharacteristic
233#103C2×D28311yescharacteristic
234#102—2831no—
235#102C2×D28311yescharacteristic
236#102C2×D28311yescharacteristic
237C22⋊C8—2831no—
238C22⋊C8—2831no—
239#97C2×D28311yescharacteristic
240#41—5662no—
241#41—11321no—
242C2×Q8—21no—
243C2×Q8—2831no—
244C2×Q8—2831no—
245C2×Q8—5661no—
246C2×Q8—5662no—
247C2×Q8—11321no—
248C2×Q8C22×D28311yescharacteristic
249C2×D4—2831no—
250C2×D4—5661no—
251C2×D4—5661no—
252C2×D4C22×D28311yescharacteristic
253C22×C4—2831no—
254C22×C4—2831no—
255C22×C4—5661no—
256C22×C4—5661no—
257C22×C4—5661no—
258C22×C4—5661no—
259Q16—5662no—
260Q16—11321no—
261SD16—11321no—
262M16—11321no—
263C2×C8—2831no—
264C2×C8—2831no—
265C2×C8—11321no—
266C2×C8C22×D28311yescharacteristic
267C2×C8C22×D28311yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—2831no—
270C4⋊C4—2831no—
271C4⋊C4—2831no—
272C4⋊C4—5661no—
273C4⋊C4—5661no—
274C4⋊C4—5661no—
275C4⋊C4—5661no—
276C4⋊C4—5661no—
277C4⋊C4—5661no—
278C4⋊C4—5661no—
279C4⋊C4C22×D28311yescharacteristic
280C4⋊C4C22×D28311yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—2831no—
284C22⋊C4—2831no—
285C22⋊C4—5661no—
286C22⋊C4—5661no—
287C22⋊C4—5661no—
288C22⋊C4—5661no—
289C42—5661no—
290C42—5661no—
291C42C22×D28311yescharacteristic
292C23—21no—
293C23—2831no—
294C23—2831no—
295Q8—21no—
296Q8—21no—
297Q8—81no—
298Q8—2832no—
299Q8—5661no—
300Q8—5661no—
301Q8—5661no—
302Q8—11322no—
303D4—21no—
304D4—21no—
305D4—5662no—
306D4—11322no—
307D4—11322no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—2831no—
312C2×C4—2831no—
313C2×C4—5661no—
314C2×C4—5661no—
315C2×C4—5661no—
316C2×C4—5661no—
317C2×C4—5661no—
318C2×C4—5661no—
319C2×C4—5661no—
320C2×C4—5661no—
321C2×C4—11322no—
322C2×C4—11322no—
323C2×C4—22641no—
324C2×C4—22641no—
325C2×C4D4×D28311yescharacteristic
326C2×C4D4×D28311yescharacteristic
327C2×C4C23×D28311yescharacteristic
328C8—21no—
329C8—21no—
330C8—5661no—
331C8—5661no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—2832no—
336C22—5661no—
337C22—5661no—
338C22—5661no—
339C22—5661no—
340C22—5661no—
341C22C2×D4×D28311yescharacteristic
342C4—21no—
343C4—21no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—5661no—
348C4—5661no—
349C4—5662no—
350C4—11321no—
351C4—11321no—
352C4—11321no—
353C4#41×D28311yescharacteristic
354C4#2258365611yescharacteristic
355C2—81no—
356C2—5662no—
357C2—11321no—
358C2#3182710811yescharacteristic
359C2#137×D28311yescharacteristic
360C2#3182727511yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#489×C283C2
socleC22×C283C22×D4
prime radical#31827123C2
hypercenter#489D283
hypocenterC283#3316
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #31827176C2semidirect
3. #31826794C2semidirect
4. #31826782C2semidirect
5. #31826747C2semidirect
6. #31826722C2semidirect
7. #31826693C2semidirect
8. #31826684C2semidirect
9. #31826628C2semidirect
10. #31826622C2semidirect
11. #31826573C2semidirect
12. #31826538C2semidirect
13. #31826463C2semidirect
14. #103×D283C2semidirect
15. #489×C283C2semidirect
180. C283#3316semidirect
184. #489D283semidirect

Maximal subgroups

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

subgroupindex
#318271762
#318271232
#318267942
#318267822
#318267472
#318267222
#318266932
#318266842
#318266282
#318266222
#318265732
#318265382
#318264632
#103×D2832
#489×C2832
#3316283