Finite Group Databasebeta

← #44408776

Subgroups — #44408776

Order 29056.

412 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#28409541C211yesmaximal, characteristic
2#28409111C211yesmaximal, characteristic, complemented
3#28409107C211yesmaximal, characteristic, complemented
4#28409104C211yesmaximal, characteristic, complemented
5#28409103C211yesmaximal, characteristic, complemented
6#28409102C211yesmaximal, characteristic, complemented
7#28409100C211yesmaximal, characteristic, complemented
8C8×C22⋊D227C211yesmaximal, characteristic, complemented
9#28409092C211yesmaximal, characteristic, complemented
10#28409091C211yesmaximal, characteristic, complemented
11#28408998C211yesmaximal, characteristic, complemented
12#28408997C211yesmaximal, characteristic, complemented
13#28408994C211yesmaximal, characteristic, complemented
14C2×(C2×D227)⋊C8C211yesmaximal, characteristic, complemented
15C8×D4×C227C211yesmaximal, characteristic, complemented
16C2×#16813884C2211yescharacteristic
17C22×C4×D227C2211yescharacteristic
18C2×#16813868C2211yescharacteristic, complemented
19C2×#16813867C2211yescharacteristic
20C2×#16813867C2211yescharacteristic
21C2×#16813867C2211yescharacteristic, complemented
22C22×C227⋊C8C2211yescharacteristic
23C2×C8×D227C2211yescharacteristic, complemented
24#20300273C411yescharacteristic
25#20300270C411yescharacteristic
26#20300266C411yescharacteristic
27#20300265C411yescharacteristic
28#20300261C411yescharacteristic
29#20300260C411yescharacteristic
30#20300258C411yescharacteristic
31#20300256C411yescharacteristic
32C4×D908C2211yescharacteristic
33C4×C22⋊D227C2211yescharacteristic
34C4×C22⋊D227C2211yescharacteristic
35#20300245C2211yescharacteristic
36C4⋊(C227⋊C8)C2211yescharacteristic, complemented
37Dic227⋊C8C2211yescharacteristic, complemented
38Dic227⋊C8C2211yescharacteristic, complemented
39C22⋊(C227⋊C8)C2211yescharacteristic
40C22⋊(C227⋊C8)C2211yescharacteristic, complemented
41(C2×D227)⋊C8C2211yescharacteristic
42(C2×D227)⋊C8C2211yescharacteristic
43(C2×D227)⋊C8C2211yescharacteristic
44(C2×D227)⋊C8C2211yescharacteristic
45(C2×D227)⋊C8C2211yescharacteristic
46(C2×D227)⋊C8C2211yescharacteristic
47(C2×D227)⋊C8C2211yescharacteristic, complemented
48(C2×D227)⋊C8C2211yescharacteristic, complemented
49#20300199C2211yescharacteristic, complemented
50#20300198C2211yescharacteristic, complemented
51C8×Dic227C2211yescharacteristic, complemented
52C22×C8×C227C2211yescharacteristic
53C22×C8×C227C2211yescharacteristic, complemented
54C4×D4×C227C2211yescharacteristic
55C4⋊C8×C227C2211yescharacteristic, complemented
56C22⋊C8×C227C2211yescharacteristic
57C22⋊C8×C227C2211yescharacteristic, complemented
58C4×C8×C227C2211yescharacteristic, complemented
59C23×D227C2×C411yescharacteristic
60#16813884—41no—
61#16813884—41no—
62C2×Dic454C2×C411yescharacteristic
63C2×D908C2×C411yescharacteristic
64C2×D908C2×C411yescharacteristic
65C2×C22⋊D227C2×C411yescharacteristic
66C2×C22⋊D227C2×C411yescharacteristic
67C2×C22⋊D227C2×C411yescharacteristic
68C2×C22⋊D227C2×C411yescharacteristic
69C22×Dic227C2×C411yescharacteristic
70C2×C4×D227—41no—
71C2×C4×D227—41no—
72C2×C4×D227C2×C411yescharacteristic
73C2×C4×D227C2×C411yescharacteristic
74C2×C4×D227C2311yescharacteristic
75C2×C4×D227C2311yescharacteristic
76C2×C4×D227C2311yescharacteristic
77#16813868—41no—
78#16813867—41no—
79#16813867—41no—
80#16813867—41no—
81C2×C227⋊C8—41no—
82C2×C227⋊C8C2311yescharacteristic
83C2×C227⋊C8C2311yescharacteristic
84C2×C227⋊C8C2311yescharacteristic
85C2×C227⋊C8C2311yescharacteristic
86C8×D227—41no—
87C4⋊Dic227C2×C411yescharacteristic
88Dic227⋊C4C2×C411yescharacteristic
89Dic227⋊C4C2×C411yescharacteristic
90Dic227⋊C4C2×C411yescharacteristic
91Dic227⋊C4C2×C411yescharacteristic
92C22⋊Dic227C2×C411yescharacteristic
93C22⋊Dic227C2×C411yescharacteristic
94(C2×D227)⋊C4C2×C411yescharacteristic
95(C2×D227)⋊C4C2×C411yescharacteristic
96(C2×D227)⋊C4C2×C411yescharacteristic
97(C2×D227)⋊C4C2×C411yescharacteristic
98(C2×D227)⋊C4C2×C411yescharacteristic
99(C2×D227)⋊C4C2×C411yescharacteristic
100C4×Dic227C2311yescharacteristic
101C2×D4×C227C2×C411yescharacteristic
102C22×C4×C227C2311yescharacteristic
103C22×C4×C227C2311yescharacteristic
104C2×C8×C227—41no—
105C2×C8×C227—41no—
106C2×C8×C227C2311yescharacteristic
107C2×C8×C227C2311yescharacteristic
108C2×C8×C227C2311yescharacteristic
109C2×C8×C227C2311yescharacteristic
110C4⋊C4×C227C2×C411yescharacteristic
111C22⋊C4×C227C2×C411yescharacteristic
112C22⋊C4×C227C2×C411yescharacteristic
113C42×C227C2311yescharacteristic
114C22×D227—22no—
115C22×D227—41no—
116C22×D227—41no—
117C22×D227C22×C411yescharacteristic
118C22×D227C22×C411yescharacteristic
119C22×D227C22×C411yescharacteristic
120Dic454—41no—
121D908—41no—
122D908—41no—
123C22⋊D227—22no—
124C22⋊D227—41no—
125C22⋊D227—41no—
126C22⋊D227—41no—
127C2×Dic227—41no—
128C2×Dic227C22×C411yescharacteristic
129C2×Dic227C22×C411yescharacteristic
130C2×Dic227C22×C411yescharacteristic
131C2×Dic227C22×C411yescharacteristic
132C2×Dic227C22×C411yescharacteristic
133C4×D227—21no—
134C4×D227—21no—
135C4×D227—21no—
136C4×D227—21no—
137C4×D227—21no—
138C4×D227—21no—
139C4×D227—41no—
140C4×D227—41no—
141C227⋊C8—21no—
142C227⋊C8—21no—
143C227⋊C8—21no—
144C227⋊C8—21no—
145C23×C227C22×C411yescharacteristic
146C23×C227C22×C411yescharacteristic
147D4×C227—22no—
148C2×C4×C227—21no—
149C2×C4×C227—21no—
150C2×C4×C227—21no—
151C2×C4×C227—21no—
152C2×C4×C227C22×C411yescharacteristic
153C2×C4×C227C22×C411yescharacteristic
154C2×C4×C227C22×C411yescharacteristic
155C2×C4×C227C22×C411yescharacteristic
156C2×C4×C227C2411yescharacteristic
157C8×C227—21no—
158C8×C227—21no—
159C8×C227—21no—
160C8×C227—21no—
161C22×C227—21no—
162C22×C227—21no—
163C22×C227—21no—
164C22×C227—21no—
165C22×C227—21no—
166C22×C227#13112yes—
167C22×C227C23×C411yescharacteristic
168C2×D227—21no—
169C2×D227—21no—
170C2×D227—21no—
171C2×D227—21no—
172C2×D227—21no—
173C2×D227—21no—
174C2×D227—21no—
175C2×D227—21no—
176C2×D227—21no—
177C2×D227—44no—
178C4×C227—21no—
179C4×C227—21no—
180C4×C227—21no—
181C4×C227—21no—
182C4×C227H(5,𝔽2)11yescharacteristic
183C4×C227H(5,𝔽2)11yescharacteristic
184Dic227—21no—
185Dic227—21no—
186Dic227—21no—
187Dic227—21no—
188Dic227—21no—
189C2×C227—22no—
190C2×C227—41no—
191C2×C227#51811yescharacteristic
192C2×C227C2×#13111yescharacteristic
193C2×C227#56811yescharacteristic
194D227—41no—
195D227—41no—
196D227—41no—
197C227#297611yescharacteristic, complemented, Sylow
198#2976—2271nomaximal, Sylow
199#525—2271no—
200#436—2271no—
201#436—2271no—
202#435—2271no—
203#435—2271no—
204#435—2271no—
205#435—2271no—
206C8×D4—2271no—
207C8×D4D22711yescharacteristic, complemented
208#433—2271no—
209#433—2271no—
210#408—2271no—
211#408—2271no—
212#407—2271no—
213C2×C22⋊C8—2271no—
214C2×#41—2271no—
215C23×C4—2271no—
216C2×M16—2271no—
217C2×M16—2271no—
218C2×M16—2271no—
219C2×M16—2271no—
220C22×C8—2271no—
221C22×C8—2271no—
222C22×C8C2×D22711yescharacteristic
223C22×C8C2×D22711yescharacteristic, complemented
224#123—2271no—
225#123—2271no—
226C22⋊Q8—2271no—
227C22⋊Q8—2271no—
228#121—2271no—
229#121—2271no—
230#120—2271no—
231#120—2271no—
232C4×D4—2271no—
233C4×D4—2271no—
234C4×D4—2271no—
235C4×D4C2×D22711yescharacteristic
236#117—2271no—
237C4⋊C8—2271no—
238C4⋊C8—2271no—
239C4⋊C8—2271no—
240C4⋊C8C2×D22711yescharacteristic, complemented
241C22⋊C8—2271no—
242C22⋊C8—2271no—
243C22⋊C8—2271no—
244C22⋊C8—2271no—
245C22⋊C8—2271no—
246C22⋊C8—2271no—
247C22⋊C8—2271no—
248C22⋊C8—2271no—
249C22⋊C8—2271no—
250C22⋊C8—2271no—
251C22⋊C8C2×D22711yescharacteristic
252C22⋊C8C2×D22711yescharacteristic, complemented
253#97—2271no—
254#97—2271no—
255C4×C8—2271no—
256C4×C8C2×D22711yescharacteristic, complemented
257C24—2271no—
258#41—9081no—
259#41—9081no—
260C2×Q8—2271no—
261C2×D4—2271no—
262C2×D4—2271no—
263C2×D4—2271no—
264C2×D4—2271no—
265C2×D4—2271no—
266C2×D4—2271no—
267C2×D4C4×D22711yescharacteristic
268C22×C4—9081no—
269C22×C4—9081no—
270C22×C4—2271no—
271C22×C4—2271no—
272C22×C4—2271no—
273C22×C4—2271no—
274C22×C4—2271no—
275C22×C4—2271no—
276C22×C4C22×D22711yescharacteristic
277C22×C4C22×D22711yescharacteristic
278M16—9081no—
279M16—9081no—
280M16—9081no—
281M16—9081no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—9081no—
285C2×C8—9081no—
286C2×C8—2271no—
287C2×C8—2271no—
288C2×C8—2271no—
289C2×C8—2271no—
290C2×C8C22×D22711yescharacteristic
291C2×C8C22×D22711yescharacteristic
292C2×C8C22×D22711yescharacteristic
293C2×C8C22×D22711yescharacteristic
294C4⋊C4—2271no—
295C4⋊C4—2271no—
296C4⋊C4—2271no—
297C4⋊C4—2271no—
298C4⋊C4—2271no—
299C4⋊C4C4×D22711yescharacteristic
300C22⋊C4—2271no—
301C22⋊C4—2271no—
302C22⋊C4—2271no—
303C22⋊C4—2271no—
304C22⋊C4—2271no—
305C22⋊C4—2271no—
306C22⋊C4—2271no—
307C22⋊C4—2271no—
308C22⋊C4C4×D22711yescharacteristic
309C22⋊C4C4×D22711yescharacteristic
310C42—2271no—
311C42C22×D22711yescharacteristic
312C23—9081no—
313C23—9081no—
314C23—4542no—
315C23—2271no—
316C23—2271no—
317C23—2271no—
318C23C2×C4×D22711yescharacteristic
319C23C2×C4×D22711yescharacteristic
320Q8—9081no—
321D4—22no—
322D4—9081no—
323D4—9081no—
324D4—9081no—
325D4—9081no—
326D4—9081no—
327D4—4542no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—9081no—
333C2×C4—9081no—
334C2×C4—9081no—
335C2×C4—4541no—
336C2×C4—4541no—
337C2×C4—4541no—
338C2×C4—4541no—
339C2×C4—4541no—
340C2×C4—4541no—
341C2×C4—2271no—
342C2×C4—2271no—
343C2×C4—2271no—
344C2×C4—2271no—
345C2×C4—2271no—
346C2×C4C2×C4×D22711yescharacteristic
347C2×C4C2×C4×D22711yescharacteristic
348C2×C4C2×C4×D22711yescharacteristic
349C2×C4C2×C4×D22711yescharacteristic
350C2×C4C23×D22711yescharacteristic
351C8—21no—
352C8—21no—
353C8—21no—
354C8—21no—
355C8—4541no—
356C8—4541no—
357C8—4541no—
358C8—4541no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—9084no—
365C22—4541no—
366C22—4541no—
367C22—4541no—
368C22—4541no—
369C22—4541no—
370C22—4541no—
371C22—4541no—
372C22—4541no—
373C22—4541no—
374C22#2030029412yes—
375C22C22×C4×D22711yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—4541no—
381C4—4541no—
382C4—4541no—
383C4—4541no—
384C4—4541no—
385C4#2030033311yescharacteristic
386C4#2030033411yescharacteristic
387C2—22no—
388C2—41no—
389C2—9081no—
390C2—9081no—
391C2—9081no—
392C2#2840950411yescharacteristic
393C2C2×#2030029411yescharacteristic
394C2#2840979711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D227
commutator, socleC22×C227C23×C4
FittingC8×D4×C227C2
prime radical#28409541C2
cosocleC2×C4×C227C24
hypercenterC8×D4D227
hypocenterC227#2976
LCSG ▷ C22×C227 ▷ C227
UCSC1 ◁ C2×C4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
2. #28409111C2semidirect
3. #28409107C2semidirect
4. #28409104C2semidirect
5. #28409103C2semidirect
6. #28409102C2semidirect
7. #28409100C2semidirect
8. C8×C22⋊D227C2semidirect
9. #28409092C2semidirect
10. #28409091C2semidirect
11. #28408998C2semidirect
12. #28408997C2semidirect
13. #28408994C2semidirect
14. C2×(C2×D227)⋊C8C2semidirect
15. C8×D4×C227C2semidirect
18. C2×#16813868C22semidirect
21. C2×#16813867C22semidirect
23. C2×C8×D227C22semidirect
36. C4⋊(C227⋊C8)C22semidirect
37. Dic227⋊C8C22semidirect
38. Dic227⋊C8C22semidirect
40. C22⋊(C227⋊C8)C22semidirect
47. (C2×D227)⋊C8C22semidirect
48. (C2×D227)⋊C8C22semidirect
49. #20300199C22semidirect
50. #20300198C22semidirect
51. C8×Dic227C22semidirect
53. C22×C8×C227C22semidirect
55. C4⋊C8×C227C22semidirect
57. C22⋊C8×C227C22semidirect
58. C4×C8×C227C22semidirect
197. C227#2976semidirect
207. C8×D4D227semidirect
223. C22×C8C2×D227semidirect
240. C4⋊C8C2×D227semidirect
252. C22⋊C8C2×D227semidirect
256. C4×C8C2×D227semidirect

Maximal subgroups

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

subgroupindex
#284095412
#284091112
#284091072
#284091042
#284091032
#284091022
#284091002
C8×C22⋊D2272
#284090922
#284090912
#284089982
#284089972
#284089942
C2×(C2×D227)⋊C82
C8×D4×C2272
#2976227