Finite Group Databasebeta

← #49132668

Subgroups — #49132668

Order 36224.

358 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827080C211yesmaximal, characteristic, complemented
2#31827069C211yesmaximal, characteristic, complemented
3#31826773C211yesmaximal, characteristic, complemented
4#31826765C211yesmaximal, characteristic, complemented
5#31826753C211yesmaximal, characteristic, complemented
6#31826743C211yesmaximal, characteristic, complemented
7#31826715C211yesmaximal, characteristic, complemented
8#31826710C211yesmaximal, characteristic, complemented
9#31826698C211yesmaximal, characteristic, complemented
10#31826693C211yesmaximal, characteristic, complemented
11#31826678C211yesmaximal, characteristic, complemented
12#31826678C211yesmaximal, characteristic, complemented
13#31826662C211yesmaximal, characteristic, complemented
14#31826490C211yesmaximal, characteristic, complemented
15#459×C283C211yesmaximal, characteristic, complemented
16C2×#17985380C2211yescharacteristic
17C2×#17985380C2211yescharacteristic
18C2×#17985375C2211yescharacteristic
19C2×C8×D283C2211yescharacteristic
20#22583609C2211yescharacteristic
21#22583603—21no—
22#22583602C2211yescharacteristic
23#22583597C2211yescharacteristic
24#22583596—21no—
25#22583593—21no—
26#22583591—21no—
27#22583591—21no—
28#22583590C2211yescharacteristic
29#22583589—21no—
30#22583582—21no—
31#22583582—21no—
32#22583581C2211yescharacteristic
33#22583581C2211yescharacteristic
34#22583581C2211yescharacteristic
35C4×Dic566C2211yescharacteristic
36D4×Dic283C2211yescharacteristic
37D4×Dic283C2211yescharacteristic
38#22583567C2211yescharacteristic
39#22583544C2211yescharacteristic
40#22583543C2211yescharacteristic
41#22583542C2211yescharacteristic
42#22583541C2211yescharacteristic
43C4⋊(C283⋊C8)C2211yescharacteristic
44Dic283⋊C8C2211yescharacteristic
45Dic283⋊C8C2211yescharacteristic
46#22583535C2211yescharacteristic
47#22583535C2211yescharacteristic
48#22583531C2211yescharacteristic
49#22583531C2211yescharacteristic
50#22583531C2211yescharacteristic
51#22583531C2211yescharacteristic
52C2×D8×C283C2211yescharacteristic
53C2×D8×C283C2211yescharacteristic
54#127×C283C2211yescharacteristic
55C4×D4×C283C2211yescharacteristic
56C4⋊C8×C283C2211yescharacteristic
57#102×C283C2211yescharacteristic
58#102×C283C2211yescharacteristic
59C2×Dic566—21no—
60C2×Dic566C2311yescharacteristic
61C2×C22⋊D283—21no—
62C2×C22⋊D283—21no—
63C2×C22⋊D283—21no—
64C22×Dic283—21no—
65C22×Dic283—21no—
66C2×C4×D283C2311yescharacteristic
67#17985380—41no—
68#17985380—41no—
69#17985375—41no—
70C2×C283⋊C8C2311yescharacteristic
71C2×C283⋊C8C2311yescharacteristic
72C8×D283—41no—
73C4⋊Dic283—21no—
74C4⋊Dic283C2311yescharacteristic
75C4⋊Dic283C2311yescharacteristic
76C4⋊Dic283C2311yescharacteristic
77Dic283⋊C4—21no—
78Dic283⋊C4—21no—
79Dic283⋊C4—21no—
80Dic283⋊C4—21no—
81Dic283⋊C4D411yescharacteristic
82Dic283⋊C4D411yescharacteristic
83C22⋊Dic283—21no—
84C22⋊Dic283—21no—
85C22⋊Dic283—21no—
86C22⋊Dic283—21no—
87C22⋊Dic283—21no—
88C22⋊Dic283—21no—
89C22⋊Dic283—21no—
90(C2×D283)⋊C4—21no—
91(C2×D283)⋊C4D411yescharacteristic
92(C2×D283)⋊C4D411yescharacteristic
93C4×Dic283—21no—
94C4×Dic283C2311yescharacteristic
95C2×D4×C283—21no—
96C2×D4×C283—21no—
97C2×D4×C283C2311yescharacteristic
98C2×D4×C283C2311yescharacteristic
99C2×D4×C283C2311yescharacteristic
100C22×C4×C283—21no—
101D8×C283—41no—
102D8×C283—41no—
103C2×C8×C283C2311yescharacteristic
104C2×C8×C283C2311yescharacteristic
105C4⋊C4×C283C2311yescharacteristic
106C22⋊C4×C283—21no—
107C42×C283C2311yescharacteristic
108C22×D283C2×D411yescharacteristic
109Dic566—21no—
110Dic566—21no—
111Dic566—81no—
112C22⋊D283—81no—
113C22⋊D283—81no—
114C22⋊D283—81no—
115C2×Dic283—21no—
116C2×Dic283—21no—
117C2×Dic283—21no—
118C2×Dic283—21no—
119C2×Dic283—81no—
120C2×Dic283—81no—
121C2×Dic283C2×D411yescharacteristic
122C2×Dic283C2×D411yescharacteristic
123C2×Dic283C2×D411yescharacteristic
124C4×D283—21no—
125C4×D283—21no—
126C283⋊C8—21no—
127C283⋊C8—21no—
128C23×C283—21no—
129C23×C283—21no—
130C23×C283—21no—
131D4×C283—21no—
132D4×C283—21no—
133D4×C283—21no—
134D4×C283—21no—
135D4×C283—21no—
136D4×C283—21no—
137D4×C283—81no—
138D4×C283—81no—
139C2×C4×C283—21no—
140C2×C4×C283—81no—
141C2×C4×C283C2×D411yescharacteristic
142C2×C4×C283C2×D411yescharacteristic
143C2×C4×C283C2411yescharacteristic
144C8×C283—21no—
145C8×C283—21no—
146C22×C283—41no—
147C22×C283—41no—
148C22×C283—41no—
149C22×C283—41no—
150C22×C283—41no—
151C22×C283—41no—
152C22×C283—41no—
153C22×C283—41no—
154C22×C283—41no—
155C22×C283C22×D411yescharacteristic
156C2×D283—21no—
157C2×D283—21no—
158C2×D283—21no—
159C4×C283—21no—
160C4×C283—21no—
161C4×C283—41no—
162C4×C283H(5,𝔽2)11yescharacteristic
163C4×C2832−1+411yescharacteristic
164Dic283—21no—
165Dic283—21no—
166Dic283—21no—
167Dic283—41no—
168Dic283—41no—
169Dic283—41no—
170Dic283—41no—
171C2×C283—81no—
172C2×C283—81no—
173C2×C283—81no—
174C2×C283#53711yescharacteristic
175C2×C283#57611yescharacteristic
176C2×C283#57711yescharacteristic
177D283—41no—
178C283#325711yescharacteristic, complemented, Sylow
179#3257—2831nomaximal, Sylow
180#542—2831no—
181#540—2831no—
182#479—2831no—
183#478—2831no—
184#476—2831no—
185#474—2831no—
186#469—2831no—
187#468—2831no—
188#466—2831no—
189#465—2831no—
190#463—2831no—
191#463—2831no—
192#460—2831no—
193#459D28311yescharacteristic, complemented
194#424—2831no—
195C2×SD16—2831no—
196C2×SD16—2831no—
197C2×D8C2×D28311yescharacteristic
198C2×D8C2×D28311yescharacteristic
199C2×M16—2831no—
200C22×C8—2831no—
201C4⋊Q8—2831no—
202#127C2×D28311yescharacteristic
203#126—5661no—
204#125—2831no—
205#124—2831no—
206#124—5661no—
207#123—5661no—
208#123—5661no—
209#123—5661no—
210C22⋊Q8—2831no—
211C22⋊Q8—5661no—
212#121—2831no—
213#121—2831no—
214#121—2831no—
215#121—5661no—
216#121—5661no—
217C4×Q8—2831no—
218C4×D4—2831no—
219C4×D4—2831no—
220C4×D4C2×D28311yescharacteristic
221#117—2831no—
222#107—2831no—
223#107—2831no—
224#106—2831no—
225#106—2831no—
226C4⋊C8—2831no—
227C4⋊C8—2831no—
228C4⋊C8—2831no—
229C4⋊C8C2×D28311yescharacteristic
230#103—2831no—
231#103—2831no—
232#102—2831no—
233#102—2831no—
234#102—2831no—
235#102—2831no—
236#102C2×D28311yescharacteristic
237#102C2×D28311yescharacteristic
238C2×Q8—2831no—
239C2×Q8—5661no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—5661no—
243C2×D4—5661no—
244C2×D4—5661no—
245C2×D4C22×D28311yescharacteristic
246C2×D4C22×D28311yescharacteristic
247C2×D4C22×D28311yescharacteristic
248C22×C4—21no—
249C22×C4—2831no—
250C22×C4—5661no—
251C22×C4—5661no—
252SD16—11321no—
253SD16—11321no—
254D8—41no—
255D8—41no—
256M16—11321no—
257C2×C8—2831no—
258C2×C8—2831no—
259C2×C8—11321no—
260C2×C8C22×D28311yescharacteristic
261C2×C8C22×D28311yescharacteristic
262C4⋊C4—2831no—
263C4⋊C4—2831no—
264C4⋊C4—2831no—
265C4⋊C4—2831no—
266C4⋊C4—2831no—
267C4⋊C4—5661no—
268C4⋊C4—5661no—
269C4⋊C4—5661no—
270C4⋊C4—5661no—
271C4⋊C4—5661no—
272C4⋊C4C22×D28311yescharacteristic
273C22⋊C4—21no—
274C22⋊C4—2831no—
275C22⋊C4—2831no—
276C22⋊C4—5661no—
277C22⋊C4—5661no—
278C22⋊C4—5661no—
279C22⋊C4—5661no—
280C22⋊C4—5661no—
281C22⋊C4—5661no—
282C22⋊C4—5661no—
283C22⋊C4—5661no—
284C42—2831no—
285C42—5661no—
286C42C22×D28311yescharacteristic
287C23—21no—
288C23—21no—
289C23—21no—
290C23—2831no—
291Q8—5661no—
292Q8—5661no—
293Q8—22641no—
294D4—21no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—21no—
300D4—81no—
301D4—81no—
302D4—22641no—
303D4—22641no—
304D4—22641no—
305C2×C4—21no—
306C2×C4—81no—
307C2×C4—2831no—
308C2×C4—2831no—
309C2×C4—2831no—
310C2×C4—5661no—
311C2×C4—5661no—
312C2×C4—5661no—
313C2×C4—5661no—
314C2×C4—5661no—
315C2×C4—5661no—
316C2×C4—22641no—
317C2×C4—22641no—
318C2×C4D4×D28311yescharacteristic
319C2×C4D4×D28311yescharacteristic
320C2×C4C23×D28311yescharacteristic
321C8—21no—
322C8—21no—
323C8—5661no—
324C8—5661no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—5661no—
335C22—5661no—
336C22—5661no—
337C22C2×D4×D28311yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—5661no—
342C4—5661no—
343C4—5661no—
344C4—11321no—
345C4—11321no—
346C4—11321no—
347C4—11321no—
348C4#2258365511yescharacteristic
349C4#2258365711yescharacteristic
350C2—81no—
351C2—81no—
352C2—81no—
353C2—11321no—
354C2#3182704411yescharacteristic
355C2#3182726611yescharacteristic
356C2#3182727511yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#459×C283C2
socleC22×C283C22×D4
hypercenter#459D283
hypocenterC283#3257
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #31827080C2semidirect
2. #31827069C2semidirect
3. #31826773C2semidirect
4. #31826765C2semidirect
5. #31826753C2semidirect
6. #31826743C2semidirect
7. #31826715C2semidirect
8. #31826710C2semidirect
9. #31826698C2semidirect
10. #31826693C2semidirect
11. #31826678C2semidirect
12. #31826678C2semidirect
13. #31826662C2semidirect
14. #31826490C2semidirect
15. #459×C283C2semidirect
178. C283#3257semidirect
193. #459D283semidirect

Maximal subgroups

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

subgroupindex
#318270802
#318270692
#318267732
#318267652
#318267532
#318267432
#318267152
#318267102
#318266982
#318266932
#318266782
#318266622
#318264902
#459×C2832
#3257283