Finite Group Databasebeta

← #49132666

Subgroups — #49132666

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#31827086C211yesmaximal, characteristic, complemented
2#31826769C211yesmaximal, characteristic, complemented
3#31826762C211yesmaximal, characteristic, complemented
4#31826755C211yesmaximal, characteristic, complemented
5#31826745C211yesmaximal, characteristic, complemented
6#31826716C211yesmaximal, characteristic, complemented
7#31826709C211yesmaximal, characteristic, complemented
8#31826699C211yesmaximal, characteristic, complemented
9#31826692C211yesmaximal, characteristic, complemented
10#31826680C211yesmaximal, characteristic, complemented
11#31826680C211yesmaximal, characteristic, complemented
12#31826662C211yesmaximal, characteristic, complemented
13#31826657C211yesmaximal, characteristic, complemented
14#31826492C211yesmaximal, characteristic, complemented
15#540×C283C211yesmaximal, characteristic, complemented
16C2×#17985380C2211yescharacteristic
17C2×#17985380C2211yescharacteristic
18C2×#17985377C2211yescharacteristic
19C2×#17985377C2211yescharacteristic
20C2×#17985376C2211yescharacteristic
21C22×C283⋊C8C2211yescharacteristic
22#22583610C2211yescharacteristic
23#22583605—21no—
24#22583598C2211yescharacteristic
25#22583596—21no—
26#22583592—21no—
27#22583589C2211yescharacteristic
28#22583588—21no—
29#22583584C2211yescharacteristic
30C4×Dic566C2211yescharacteristic
31C4×D1132C2211yescharacteristic
32#22583543C2211yescharacteristic
33#22583543C2211yescharacteristic
34#22583541C2211yescharacteristic
35#22583541C2211yescharacteristic
36C4⋊(C283⋊C8)C2211yescharacteristic
37C4⋊(C283⋊C8)C2211yescharacteristic
38C4⋊(C283⋊C8)C2211yescharacteristic
39C4⋊(C283⋊C8)C2211yescharacteristic
40#22583533C2211yescharacteristic
41#22583533C2211yescharacteristic
42#22583531C2211yescharacteristic
43#22583531C2211yescharacteristic
44#22583531C2211yescharacteristic
45#22583531C2211yescharacteristic
46#22583530C2211yescharacteristic
47#22583530C2211yescharacteristic
48#127×C283C2211yescharacteristic
49#125×C283C2211yescharacteristic
50#123×C283—21no—
51#123×C283—21no—
52#121×C283—21no—
53#121×C283—21no—
54#121×C283C2211yescharacteristic
55#121×C283C2211yescharacteristic
56C4×D4×C283C2211yescharacteristic
57C4×D4×C283C2211yescharacteristic
58#117×C283C2211yescharacteristic
59C2×Dic566—21no—
60C2×Dic566C2311yescharacteristic
61C2×D1132C2311yescharacteristic
62C2×C22⋊D283—21no—
63C2×C4×D283—21no—
64#17985380—41no—
65#17985380—41no—
66#17985377—41no—
67#17985377—41no—
68#17985376—41no—
69C2×C283⋊C8—41no—
70C2×C283⋊C8C2311yescharacteristic
71C2×C283⋊C8C2311yescharacteristic
72C2×C283⋊C8C2311yescharacteristic
73C2×C283⋊C8C2311yescharacteristic
74C4⋊Dic283—21no—
75C4⋊Dic283C2311yescharacteristic
76C4⋊Dic283C2311yescharacteristic
77Dic283⋊C4—21no—
78Dic283⋊C4—21no—
79C22⋊Dic283—21no—
80(C2×D283)⋊C4—21no—
81(C2×D283)⋊C4—21no—
82(C2×D283)⋊C4—21no—
83(C2×D283)⋊C4—21no—
84C4×Dic283—21no—
85C2×D4×C283—21no—
86C2×D4×C283—21no—
87C2×D4×C283—21no—
88C2×D4×C283—21no—
89C2×D4×C283C2311yescharacteristic
90C2×D4×C283C2311yescharacteristic
91C22×C4×C283—21no—
92C22×C4×C283—21no—
93C22×C4×C283C2311yescharacteristic
94C4⋊C4×C283—21no—
95C4⋊C4×C283—21no—
96C4⋊C4×C283D411yescharacteristic
97C4⋊C4×C283D411yescharacteristic
98C4⋊C4×C283C2311yescharacteristic
99C4⋊C4×C283C2311yescharacteristic
100C22⋊C4×C283—21no—
101C22⋊C4×C283—21no—
102C22⋊C4×C283—21no—
103C22⋊C4×C283—21no—
104C22⋊C4×C283D411yescharacteristic
105C22⋊C4×C283D411yescharacteristic
106C42×C283C2311yescharacteristic
107C42×C283C2311yescharacteristic
108C22×D283—21no—
109Dic566—21no—
110Dic566—21no—
111Dic566—81no—
112D1132—21no—
113D1132—21no—
114C22⋊D283—81no—
115C2×Dic283—21no—
116C2×Dic283—21no—
117C2×Dic283—21no—
118C4×D283—81no—
119C283⋊C8—21no—
120C283⋊C8—21no—
121C283⋊C8—21no—
122C283⋊C8—21no—
123C23×C283—21no—
124C23×C283—21no—
125C23×C283C2×D411yescharacteristic
126D4×C283—21no—
127D4×C283—21no—
128D4×C283—21no—
129D4×C283—21no—
130D4×C283—81no—
131D4×C283—81no—
132D4×C283—81no—
133D4×C283—81no—
134C2×C4×C283—21no—
135C2×C4×C283—21no—
136C2×C4×C283—21no—
137C2×C4×C283—21no—
138C2×C4×C283—81no—
139C2×C4×C283—81no—
140C2×C4×C283C2×D411yescharacteristic
141C2×C4×C283C2×D411yescharacteristic
142C2×C4×C283C2×D411yescharacteristic
143C2×C4×C283C2×D411yescharacteristic
144C2×C4×C283C2×D411yescharacteristic
145C2×C4×C283C2411yescharacteristic
146C22×C283—21no—
147C22×C283—21no—
148C22×C283—21no—
149C22×C283—41no—
150C22×C283—41no—
151C22×C283—41no—
152C22×C283—41no—
153C22×C283—41no—
154C22×C283—41no—
155C22×C283C22×D411yescharacteristic
156C2×D283—41no—
157C2×D283—41no—
158C2×D283—41no—
159C4×C283—21no—
160C4×C283—21no—
161C4×C283—21no—
162C4×C283—21no—
163C4×C283—21no—
164C4×C283—41no—
165C4×C283—41no—
166C4×C283H(5,𝔽2)11yescharacteristic
167C4×C2832−1+411yescharacteristic
168Dic283—41no—
169Dic283—41no—
170Dic283—41no—
171C2×C283—41no—
172C2×C283—81no—
173C2×C283—81no—
174C2×C283#53711yescharacteristic
175C2×C283#57611yescharacteristic
176C2×C283#57711yescharacteristic
177D283—81no—
178C283#325711yescharacteristic, complemented, Sylow
179#3257—2831nomaximal, Sylow
180#542—2831no—
181#540D28311yescharacteristic, complemented
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#459—2831no—
194#424—2831no—
195C2×SD16—2831no—
196C2×SD16—2831no—
197C2×D8—2831no—
198C2×D8—2831no—
199C2×M16—2831no—
200C22×C8—2831no—
201C4⋊Q8—2831no—
202#127C2×D28311yescharacteristic
203#126—5661no—
204#125C2×D28311yescharacteristic
205#124—2831no—
206#124—5661no—
207#123—21no—
208#123—21no—
209#123—5661no—
210C22⋊Q8—2831no—
211C22⋊Q8—5661no—
212#121—21no—
213#121—21no—
214#121—2831no—
215#121C2×D28311yescharacteristic
216#121C2×D28311yescharacteristic
217C4×Q8—2831no—
218C4×D4—2831no—
219C4×D4C2×D28311yescharacteristic
220C4×D4C2×D28311yescharacteristic
221#117C2×D28311yescharacteristic
222#107—2831no—
223#107—2831no—
224#106—2831no—
225#106—2831no—
226C4⋊C8—2831no—
227C4⋊C8—2831no—
228C4⋊C8—2831no—
229C4⋊C8—2831no—
230#103—2831no—
231#103—2831no—
232#102—2831no—
233#102—2831no—
234#102—2831no—
235#102—2831no—
236#102—2831no—
237#102—2831no—
238C2×Q8—2831no—
239C2×Q8—5661no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—2831no—
245C2×D4—5661no—
246C2×D4C22×D28311yescharacteristic
247C2×D4C22×D28311yescharacteristic
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—5661no—
251C22×C4C22×D28311yescharacteristic
252SD16—11321no—
253SD16—11321no—
254D8—11321no—
255D8—11321no—
256M16—11321no—
257C2×C8—2831no—
258C2×C8—2831no—
259C2×C8—2831no—
260C2×C8—2831no—
261C2×C8—11321no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—2831no—
265C4⋊C4—2831no—
266C4⋊C4—5661no—
267C4⋊C4—5661no—
268C4⋊C4—5661no—
269C4⋊C4C22⋊D28311yescharacteristic
270C4⋊C4C22⋊D28311yescharacteristic
271C4⋊C4C22×D28311yescharacteristic
272C4⋊C4C22×D28311yescharacteristic
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—5661no—
278C22⋊C4—5661no—
279C22⋊C4—5661no—
280C22⋊C4—5661no—
281C22⋊C4—5661no—
282C22⋊C4C22⋊D28311yescharacteristic
283C22⋊C4C22⋊D28311yescharacteristic
284C42—5661no—
285C42C22×D28311yescharacteristic
286C42C22×D28311yescharacteristic
287C23—21no—
288C23—21no—
289C23—5661no—
290C23C2×C22⋊D28311yescharacteristic
291Q8—5661no—
292Q8—5661no—
293Q8—22641no—
294D4—21no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—81no—
299D4—81no—
300D4—81no—
301D4—81no—
302D4—5661no—
303D4—5661no—
304D4—22641no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—5661no—
312C2×C4—5661no—
313C2×C4—5661no—
314C2×C4—22641no—
315C2×C4C2×C22⋊D28311yescharacteristic
316C2×C4C2×C22⋊D28311yescharacteristic
317C2×C4C2×C22⋊D28311yescharacteristic
318C2×C4C2×C22⋊D28311yescharacteristic
319C2×C4C2×C22⋊D28311yescharacteristic
320C2×C4C23×D28311yescharacteristic
321C8—5661no—
322C8—5661no—
323C8—5661no—
324C8—5661no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—11321no—
335C22—11321no—
336C22—11321no—
337C22C22×C22⋊D28311yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—11321no—
346C4—11321no—
347C4—11321no—
348C4#2258365611yescharacteristic
349C4#2258365711yescharacteristic
350C2—41no—
351C2—81no—
352C2—81no—
353C2—22641no—
354C2#3182704311yescharacteristic
355C2#3182726811yescharacteristic
356C2#3182727611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#540×C283C2
socleC22×C283C22×D4
hypercenter#540D283
hypocenterC283#3257
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #31827086C2semidirect
2. #31826769C2semidirect
3. #31826762C2semidirect
4. #31826755C2semidirect
5. #31826745C2semidirect
6. #31826716C2semidirect
7. #31826709C2semidirect
8. #31826699C2semidirect
9. #31826692C2semidirect
10. #31826680C2semidirect
11. #31826680C2semidirect
12. #31826662C2semidirect
13. #31826657C2semidirect
14. #31826492C2semidirect
15. #540×C283C2semidirect
178. C283#3257semidirect
181. #540D283semidirect

Maximal subgroups

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

subgroupindex
#318270862
#318267692
#318267622
#318267552
#318267452
#318267162
#318267092
#318266992
#318266922
#318266802
#318266622
#318266572
#318264922
#540×C2832
#3257283