Finite Group Databasebeta

← #44408802

Subgroups — #44408802

Order 29056.

394 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#28409579C211yesmaximal, characteristic
2#28409106C211yesmaximal, characteristic, complemented
3#28409105C211yesmaximal, characteristic, complemented
4#28409104C211yesmaximal, characteristic, complemented
5#28409103C211yesmaximal, characteristic, complemented
6#28409102C211yesmaximal, characteristic, complemented
7#28409101C211yesmaximal, characteristic, complemented
8#28409100C211yesmaximal, characteristic, complemented
9#28409088C211yesmaximal, characteristic, complemented
10#28409087C211yesmaximal, characteristic, complemented
11#28409000C211yesmaximal, characteristic, complemented
12#28408998C211yesmaximal, characteristic, complemented
13#28408997C211yesmaximal, characteristic, complemented
14#28408997C211yesmaximal, characteristic, complemented
15#435×C227C211yesmaximal, characteristic, complemented
16C2×#16813884C2211yescharacteristic
17C2×#16813884C2211yescharacteristic
18C2×#16813868C2211yescharacteristic
19C2×#16813867C2211yescharacteristic
20C2×#16813867C2211yescharacteristic
21C22×C227⋊C8C2211yescharacteristic
22C2×C8×D227C2211yescharacteristic
23C2×C8×D227C2211yescharacteristic
24#20300287C411yescharacteristic
25#20300284C411yescharacteristic
26#20300274C411yescharacteristic
27#20300274C411yescharacteristic
28#20300263C411yescharacteristic
29#20300261C411yescharacteristic
30#20300261C411yescharacteristic
31#20300259C411yescharacteristic
32C4×D908C2211yescharacteristic
33C4×C22⋊D227C2211yescharacteristic
34C4×C22⋊D227C2211yescharacteristic
35C42×D227C2211yescharacteristic
36C4⋊(C227⋊C8)C2211yescharacteristic
37Dic227⋊C8C2211yescharacteristic
38Dic227⋊C8C2211yescharacteristic
39C22⋊(C227⋊C8)C2211yescharacteristic
40C22⋊(C227⋊C8)C2211yescharacteristic
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
48(C2×D227)⋊C8C2211yescharacteristic
49#20300199C2211yescharacteristic
50#20300198C2211yescharacteristic
51#20300198C2211yescharacteristic
52C2×M16×C227C2211yescharacteristic
53C22×C8×C227C2211yescharacteristic
54C4×D4×C227C2211yescharacteristic
55C4⋊C8×C227C2211yescharacteristic
56C22⋊C8×C227C2211yescharacteristic
57C22⋊C8×C227C2211yescharacteristic
58#97×C227C2211yescharacteristic
59#16813884—41no—
60#16813884—41no—
61#16813884—41no—
62#16813884—41no—
63C2×Dic454C2×C411yescharacteristic
64C2×Dic454C2×C411yescharacteristic
65C2×D908C2×C411yescharacteristic
66C2×D908C2×C411yescharacteristic
67C2×D908C2×C411yescharacteristic
68C2×C22⋊D227C2×C411yescharacteristic
69C2×C22⋊D227C2×C411yescharacteristic
70C2×C22⋊D227C2×C411yescharacteristic
71C2×C22⋊D227C2×C411yescharacteristic
72C2×C22⋊D227C2×C411yescharacteristic
73C2×C22⋊D227C2×C411yescharacteristic
74C2×C4×D227C2×C411yescharacteristic
75C2×C4×D227C2×C411yescharacteristic
76C2×C4×D227C2311yescharacteristic
77C2×C4×D227C2311yescharacteristic
78C2×C4×D227C2311yescharacteristic
79#16813868—41no—
80#16813867—41no—
81#16813867—41no—
82C2×C227⋊C8—41no—
83C2×C227⋊C8C2311yescharacteristic
84C2×C227⋊C8C2311yescharacteristic
85C2×C227⋊C8C2311yescharacteristic
86C2×C227⋊C8C2311yescharacteristic
87C8×D227—41no—
88C8×D227—41no—
89C4⋊Dic227C2×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
98C4×Dic227C2×C411yescharacteristic
99C4×Dic227C2×C411yescharacteristic
100C4×Dic227C2311yescharacteristic
101C2×D4×C227C2×C411yescharacteristic
102C22×C4×C227C2311yescharacteristic
103C22×C4×C227C2311yescharacteristic
104M16×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×D227C22×C411yescharacteristic
115C22×D227C22×C411yescharacteristic
116C22×D227C22×C411yescharacteristic
117Dic454—41no—
118Dic454—41no—
119D908—41no—
120D908—41no—
121D908—41no—
122C22⋊D227—41no—
123C22⋊D227—41no—
124C22⋊D227—41no—
125C22⋊D227—41no—
126C22⋊D227—41no—
127C22⋊D227—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—41no—
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—21no—
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—
177C4×C227—21no—
178C4×C227—21no—
179C4×C227—21no—
180C4×C227—21no—
181C4×C227H(5,𝔽2)11yescharacteristic
182C4×C227H(5,𝔽2)11yescharacteristic
183Dic227—21no—
184Dic227—21no—
185Dic227—21no—
186Dic227—21no—
187Dic227—21no—
188C2×C227—41no—
189C2×C227—41no—
190C2×C227#51811yescharacteristic
191C2×C227#56811yescharacteristic
192C2×C227#56811yescharacteristic
193D227—41no—
194D227—41no—
195D227—41no—
196C227#298011yescharacteristic, complemented, Sylow
197#2980—2271nomaximal, Sylow
198#532—2271no—
199#435—2271no—
200#435—2271no—
201#435—2271no—
202#435—2271no—
203#435—2271no—
204#435—2271no—
205#435—2271no—
206#435D22711yescharacteristic, complemented
207#432—2271no—
208#432—2271no—
209#408—2271no—
210#408—2271no—
211#408—2271no—
212#408—2271no—
213C2×#41—2271no—
214C2×#41—2271no—
215C2×M16—2271no—
216C2×M16—2271no—
217C2×M16—2271no—
218C2×M16C2×D22711yescharacteristic
219C22×C8—2271no—
220C22×C8—2271no—
221C22×C8—2271no—
222C22×C8C2×D22711yescharacteristic
223C4⋊Q8—2271no—
224#127—2271no—
225#124—2271no—
226#124—2271no—
227#121—2271no—
228#121—2271no—
229#121—2271no—
230#121—2271no—
231C4×D4—2271no—
232C4×D4—2271no—
233C4×D4—2271no—
234C4×D4C2×D22711yescharacteristic
235C2×C42—2271no—
236C4⋊C8—2271no—
237C4⋊C8—2271no—
238C4⋊C8—2271no—
239C4⋊C8C2×D22711yescharacteristic
240C22⋊C8—2271no—
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⋊C8C2×D22711yescharacteristic
251C22⋊C8C2×D22711yescharacteristic
252#97—2271no—
253#97—2271no—
254#97—2271no—
255#97C2×D22711yescharacteristic
256#41—9081no—
257#41—9081no—
258#41—9081no—
259#41—9081no—
260C2×Q8—2271no—
261C2×Q8—2271no—
262C2×D4—2271no—
263C2×D4—2271no—
264C2×D4—2271no—
265C2×D4—2271no—
266C2×D4—2271no—
267C2×D4—2271no—
268C2×D4—2271no—
269C2×D4—2271no—
270C2×D4—2271no—
271C2×D4C4×D22711yescharacteristic
272C22×C4—2271no—
273C22×C4—2271no—
274C22×C4—2271no—
275C22×C4—2271no—
276C22×C4—2271no—
277C22×C4C22×D22711yescharacteristic
278C22×C4C22×D22711yescharacteristic
279M16—41no—
280M16—9081no—
281M16—9081no—
282M16—9081no—
283C2×C8—41no—
284C2×C8—9081no—
285C2×C8—9081no—
286C2×C8—9081no—
287C2×C8—2271no—
288C2×C8—2271no—
289C2×C8—2271no—
290C2×C8—2271no—
291C2×C8C22×D22711yescharacteristic
292C2×C8C22×D22711yescharacteristic
293C2×C8C22×D22711yescharacteristic
294C2×C8C22×D22711yescharacteristic
295C4⋊C4—2271no—
296C4⋊C4—2271no—
297C4⋊C4—2271no—
298C4⋊C4C4×D22711yescharacteristic
299C22⋊C4—2271no—
300C22⋊C4—2271no—
301C22⋊C4—2271no—
302C22⋊C4—2271no—
303C22⋊C4—2271no—
304C22⋊C4—2271no—
305C22⋊C4C4×D22711yescharacteristic
306C22⋊C4C4×D22711yescharacteristic
307C42—2271no—
308C42—2271no—
309C42—2271no—
310C42C22×D22711yescharacteristic
311C23—2271no—
312C23—2271no—
313C23—2271no—
314C23C2×C4×D22711yescharacteristic
315C23C2×C4×D22711yescharacteristic
316Q8—9081no—
317Q8—9081no—
318D4—41no—
319D4—9081no—
320D4—9081no—
321D4—9081no—
322D4—9081no—
323D4—9081no—
324D4—9081no—
325D4—9081no—
326D4—9081no—
327D4—9081no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—9081no—
333C2×C4—9081no—
334C2×C4—4541no—
335C2×C4—4541no—
336C2×C4—4541no—
337C2×C4—4541no—
338C2×C4—4541no—
339C2×C4—4541no—
340C2×C4—2271no—
341C2×C4—2271no—
342C2×C4—2271no—
343C2×C4—2271no—
344C2×C4—2271no—
345C2×C4C2×C4×D22711yescharacteristic
346C2×C4C2×C4×D22711yescharacteristic
347C2×C4C2×C4×D22711yescharacteristic
348C2×C4C2×C4×D22711yescharacteristic
349C2×C4C23×D22711yescharacteristic
350C8—21no—
351C8—21no—
352C8—21no—
353C8—21no—
354C8—4541no—
355C8—4541no—
356C8—4541no—
357C8—4541no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—4541no—
365C22—4541no—
366C22—4541no—
367C22—4541no—
368C22—4541no—
369C22—4541no—
370C22—4541no—
371C22—4541no—
372C22—4541no—
373C22C22×C4×D22711yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—4541no—
379C4—4541no—
380C4—4541no—
381C4—4541no—
382C4—4541no—
383C4#2030033311yescharacteristic
384C4#2030033411yescharacteristic
385C2—41no—
386C2—41no—
387C2—9081no—
388C2—9081no—
389C2—9081no—
390C2#2840950411yescharacteristic
391C2#2840979711yescharacteristic
392C2#2840979811yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D227
commutator, socleC22×C227C23×C4
Fitting#435×C227C2
prime radical#28409579C2
cosocleC2×C4×C227C24
hypercenter#435D227
hypocenterC227#2980
LCSG ▷ C22×C227 ▷ C227
UCSC1 ◁ C2×C4 ◁ #435

Complements

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

NH ≅ G/Ntype
2. #28409106C2semidirect
3. #28409105C2semidirect
4. #28409104C2semidirect
5. #28409103C2semidirect
6. #28409102C2semidirect
7. #28409101C2semidirect
8. #28409100C2semidirect
9. #28409088C2semidirect
10. #28409087C2semidirect
11. #28409000C2semidirect
12. #28408998C2semidirect
13. #28408997C2semidirect
14. #28408997C2semidirect
15. #435×C227C2semidirect
196. C227#2980semidirect
206. #435D227semidirect

Maximal subgroups

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

subgroupindex
#284095792
#284091062
#284091052
#284091042
#284091032
#284091022
#284091012
#284091002
#284090882
#284090872
#284090002
#284089982
#284089972
#435×C2272
#2980227