Finite Group Databasebeta

← #49131454

Subgroups — #49131454

Order 36224.

396 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#31826945C211yesmaximal, characteristic, complemented
2#31826781C211yesmaximal, characteristic, complemented
3#31826776C211yesmaximal, characteristic, complemented
4#31826769C211yesmaximal, characteristic, complemented
5#31826762C211yesmaximal, characteristic, complemented
6#31826662C211yesmaximal, characteristic, complemented
7#31826657C211yesmaximal, characteristic, complemented
8#31826608C211yesmaximal, characteristic, complemented
9#31826608C211yesmaximal, characteristic, complemented
10#31826575C211yesmaximal, characteristic, complemented
11#31826565C211yesmaximal, characteristic, complemented
12C4×#17985380C211yesmaximal, characteristic, complemented
13C4×#17985377C211yesmaximal, characteristic, complemented
14#31826526C211yesmaximal, characteristic, complemented
15#540×C283C211yesmaximal, characteristic, complemented
16C2×#17985392C2211yescharacteristic
17C2×#17985380C2211yescharacteristic
18C2×#17985380C2211yescharacteristic
19C2×#17985377C2211yescharacteristic
20C2×#17985377C2211yescharacteristic
21C4×Dic566C2211yescharacteristic
22C4×Dic566C2211yescharacteristic
23C4×D1132C2211yescharacteristic
24C4×D1132C2211yescharacteristic
25(C22⋊D283)⋊C4—21no—
26(C22⋊D283)⋊C4—21no—
27#22583568—21no—
28C2×C4⋊Dic283C2211yescharacteristic
29C4⋊C4×D283—21no—
30#22583543C2211yescharacteristic
31#22583543C2211yescharacteristic
32#22583541C2211yescharacteristic
33#22583541C2211yescharacteristic
34C4⋊(C283⋊C8)C2211yescharacteristic
35C4⋊(C283⋊C8)C2211yescharacteristic
36#22583533C2211yescharacteristic
37#22583533C2211yescharacteristic
38#22583531C2211yescharacteristic
39#22583531C2211yescharacteristic
40#22583531C2211yescharacteristic
41#22583531C2211yescharacteristic
42#22583530C2211yescharacteristic
43#22583530C2211yescharacteristic
44C22⋊(C283⋊C8)C2211yescharacteristic
45C22⋊(C283⋊C8)C2211yescharacteristic
46#22583521C2211yescharacteristic
47C4×C283⋊C8C2211yescharacteristic
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
59#17985392—22no—
60#17985392—22no—
61C2×Dic566C2311yescharacteristic
62C2×D1132C2311yescharacteristic
63C2×C22⋊D283—21no—
64C22×Dic283—21no—
65C2×C4×D283—21no—
66C2×C4×D283—21no—
67C2×C4×D283—21no—
68#17985380—22no—
69#17985380—22no—
70#17985377—22no—
71#17985377—22no—
72C2×C283⋊C8C2311yescharacteristic
73C2×C283⋊C8C2311yescharacteristic
74C2×C283⋊C8C2311yescharacteristic
75C2×C283⋊C8C2311yescharacteristic
76C4⋊Dic283—21no—
77C4⋊Dic283C2311yescharacteristic
78C4⋊Dic283C2311yescharacteristic
79Dic283⋊C4—21no—
80Dic283⋊C4—21no—
81(C2×D283)⋊C4—21no—
82(C2×D283)⋊C4—21no—
83C4×Dic283—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#4112yes—
111D1132—21no—
112D1132#4112yes—
113C22⋊D283—24no—
114C2×Dic283—21no—
115C2×Dic283—21no—
116C2×Dic283—21no—
117C2×Dic283—81no—
118C4×D283—24no—
119C4×D283—81no—
120C4×D283—81no—
121C283⋊C8—21no—
122C283⋊C8—21no—
123C283⋊C8—21no—
124C283⋊C8—21no—
125C23×C283—21no—
126C23×C283—21no—
127C23×C283C2×D411yescharacteristic
128D4×C283—21no—
129D4×C283—21no—
130D4×C283—21no—
131D4×C283—21no—
132D4×C283—81no—
133D4×C283—81no—
134D4×C283—81no—
135D4×C283—81no—
136C2×C4×C283—21no—
137C2×C4×C283—21no—
138C2×C4×C283—21no—
139C2×C4×C283—21no—
140C2×C4×C283—81no—
141C2×C4×C283—81no—
142C2×C4×C283C2×D411yescharacteristic
143C2×C4×C283C2×D411yescharacteristic
144C2×C4×C283C2×D411yescharacteristic
145C2×C4×C283C2×D411yescharacteristic
146C2×C4×C283C2×D411yescharacteristic
147C2×C4×C283C2411yescharacteristic
148C22×C283—21no—
149C22×C283—21no—
150C22×C283—21no—
151C22×C283—41no—
152C22×C283—41no—
153C22×C283—41no—
154C22×C283—41no—
155C22×C283—41no—
156C22×C283—41no—
157C22×C283C22×D411yescharacteristic
158C2×D283—22no—
159C2×D283—41no—
160C2×D283—41no—
161C4×C283—21no—
162C4×C283—21no—
163C4×C283—21no—
164C4×C283—21no—
165C4×C283—21no—
166C4×C283—41no—
167C4×C283—41no—
168C4×C283C2×#4111yescharacteristic
169C4×C283C2×#4111yescharacteristic
170Dic283—22no—
171Dic283—41no—
172Dic283—41no—
173C2×C283—41no—
174C2×C283—81no—
175C2×C283—81no—
176C2×C283#52511yescharacteristic
177C2×C283#57611yescharacteristic
178C2×C283#57711yescharacteristic
179D283—42no—
180C283#311911yescharacteristic, complemented, Sylow
181#3119—2831nomaximal, Sylow
182#540D28311yescharacteristic, complemented
183#520—2831no—
184#481—2831no—
185#480—2831no—
186#479—2831no—
187#478—2831no—
188#460—2831no—
189#459—2831no—
190#449—2831no—
191#449—2831no—
192#442—2831no—
193#440—2831no—
194C4×SD16—2831no—
195C4×D8—2831no—
196#433—2831no—
197C2×#41—2831no—
198C2×SD16—2831no—
199C2×SD16—2831no—
200C2×D8—2831no—
201C2×D8—2831no—
202#127C2×D28311yescharacteristic
203#125C2×D28311yescharacteristic
204#123—21no—
205#123—21no—
206#121—21no—
207#121—21no—
208#121C2×D28311yescharacteristic
209#121C2×D28311yescharacteristic
210C4×Q8—2831no—
211C4×Q8—2831no—
212C4×D4—2831no—
213C4×D4—2831no—
214C4×D4—5661no—
215C4×D4—5661no—
216C4×D4C2×D28311yescharacteristic
217C4×D4C2×D28311yescharacteristic
218#117—5661no—
219#117C2×D28311yescharacteristic
220C2×C4⋊C4—2831no—
221C2×C4⋊C4—5661no—
222#107—2831no—
223#107—2831no—
224#106—2831no—
225#106—2831no—
226C4⋊C8—2831no—
227C4⋊C8—2831no—
228#103—2831no—
229#103—2831no—
230#102—2831no—
231#102—2831no—
232#102—2831no—
233#102—2831no—
234#102—2831no—
235#102—2831no—
236C22⋊C8—2831no—
237C22⋊C8—2831no—
238#97—2831no—
239C4×C8—2831no—
240#41—5662no—
241#41—5662no—
242C2×Q8—2831no—
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—2831no—
248C2×D4—5661no—
249C2×D4C22×D28311yescharacteristic
250C2×D4C22×D28311yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—5661no—
254C22×C4—5661no—
255C22×C4—5661no—
256C22×C4—5661no—
257C22×C4C22×D28311yescharacteristic
258SD16—5662no—
259SD16—5662no—
260D8—5662no—
261D8—5662no—
262C2×C8—2831no—
263C2×C8—2831no—
264C2×C8—2831no—
265C2×C8—2831no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—2831no—
269C4⋊C4—2831no—
270C4⋊C4—5661no—
271C4⋊C4—5661no—
272C4⋊C4—5661no—
273C4⋊C4C22⋊D28311yescharacteristic
274C4⋊C4C22⋊D28311yescharacteristic
275C4⋊C4C22×D28311yescharacteristic
276C4⋊C4C22×D28311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—5661no—
282C22⋊C4—5661no—
283C22⋊C4C22⋊D28311yescharacteristic
284C22⋊C4C22⋊D28311yescharacteristic
285C42—5661no—
286C42—5661no—
287C42C22×D28311yescharacteristic
288C42C22×D28311yescharacteristic
289C23—21no—
290C23—21no—
291C23—5661no—
292C23C2×C22⋊D28311yescharacteristic
293Q8—2832no—
294Q8—5661no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—81no—
300D4—81no—
301D4—81no—
302D4—81no—
303D4—2832no—
304D4—5664no—
305D4—5661no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—5664no—
313C2×C4—5661no—
314C2×C4—5661no—
315C2×C4—5661no—
316C2×C4—22641no—
317C2×C4—22641no—
318C2×C4—22641no—
319C2×C4C2×C22⋊D28311yescharacteristic
320C2×C4C2×C22⋊D28311yescharacteristic
321C2×C4C2×C22⋊D28311yescharacteristic
322C2×C4C2×C22⋊D28311yescharacteristic
323C2×C4C2×C22⋊D28311yescharacteristic
324C2×C4C23×D28311yescharacteristic
325C8—5661no—
326C8—5661no—
327C8—5661no—
328C8—5661no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—5662no—
339C22—11321no—
340C22—11321no—
341C22C22×C22⋊D28311yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—41no—
348C4—41no—
349C4—5662no—
350C4—11321no—
351C4—11321no—
352C4#41×D28311yescharacteristic
353C4#41×D28311yescharacteristic
354C2—41no—
355C2—81no—
356C2—81no—
357C2—11322no—
358C2#3182697211yescharacteristic
359C2#3182726811yescharacteristic
360C2#3182727611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#540×C283C2
socleC22×C283C22×D4
hypercenter#540D283
hypocenterC283#3119
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. #31826945C2semidirect
2. #31826781C2semidirect
3. #31826776C2semidirect
4. #31826769C2semidirect
5. #31826762C2semidirect
6. #31826662C2semidirect
7. #31826657C2semidirect
8. #31826608C2semidirect
9. #31826608C2semidirect
10. #31826575C2semidirect
11. #31826565C2semidirect
12. C4×#17985380C2semidirect
13. C4×#17985377C2semidirect
14. #31826526C2semidirect
15. #540×C283C2semidirect
180. C283#3119semidirect
182. #540D283semidirect

Maximal subgroups

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

subgroupindex
#318269452
#318267812
#318267762
#318267692
#318267622
#318266622
#318266572
#318266082
#318265752
#318265652
C4×#179853802
C4×#179853772
#318265262
#540×C2832
#3119283