Finite Group Databasebeta

← #28403053

Subgroups — #28403053

Order 14464.

356 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299294C211yesmaximal, characteristic
2#20299004C211yesmaximal, characteristic, complemented
3#20298936C211yesmaximal, characteristic, complemented
4#20298931C211yesmaximal, characteristic, complemented
5#20298916C211yesmaximal, characteristic, complemented
6#20298911C211yesmaximal, characteristic, complemented
7#20298905C211yesmaximal, characteristic, complemented
8#20298875C211yesmaximal, characteristic, complemented
9#20298846C211yesmaximal, characteristic, complemented
10#20298829C211yesmaximal, characteristic, complemented
11#20298696C211yesmaximal, characteristic, complemented
12#20298670C211yesmaximal, characteristic, complemented
13#20298638C211yesmaximal, characteristic, complemented
14C2×#16813555C211yesmaximal, characteristic, complemented
15#554×C113C211yesmaximal, characteristic, complemented
16C2×#14268634C2211yescharacteristic
17C2×#14268631C2211yescharacteristic
18C22×#11744751C2211yescharacteristic
19#16813617—21no—
20#16813614C2211yescharacteristic
21#16813604—21no—
22#16813596C2211yescharacteristic
23#16813596C2211yescharacteristic
24#16813594—21no—
25C4×D452C2211yescharacteristic
26#16813582—21no—
27#16813581C2211yescharacteristic
28C2×C4⋊Dic113C2211yescharacteristic
29#16813555C2211yescharacteristic
30#16813555C2211yescharacteristic
31#16813555C2211yescharacteristic
32#16813555C2211yescharacteristic
33#16813555C2211yescharacteristic
34#16813555C2211yescharacteristic
35#16813553C2211yescharacteristic
36#16813553C2211yescharacteristic
37#16813553C2211yescharacteristic
38C4⋊#11744751C2211yescharacteristic
39#16813546C2211yescharacteristic
40#16813546C2211yescharacteristic
41#16813546C2211yescharacteristic
42#16813542C2211yescharacteristic
43#16813542C2211yescharacteristic
44#16813542C2211yescharacteristic
45C22⋊#11744751C2211yescharacteristic
46C22⋊#11744751C2211yescharacteristic
47#16813533C2211yescharacteristic
48C4⋊Q8×C113C2211yescharacteristic
49#125×C113—21no—
50C22⋊Q8×C113—21no—
51C22⋊Q8×C113—21no—
52C22⋊Q8×C113C2211yescharacteristic
53C22⋊Q8×C113C2211yescharacteristic
54C4×Q8×C113C2211yescharacteristic
55C4×D4×C113—21no—
56C4×D4×C113C2211yescharacteristic
57C2×C4⋊C4×C113C2211yescharacteristic
58C2×C4⋊C4×C113C2211yescharacteristic
59C2×D452C2311yescharacteristic
60C2×C22⋊D113—21no—
61C2×C22⋊D113—21no—
62C22×Dic113—21no—
63C2×C4×D113—21no—
64#14268634—22no—
65#14268631—22no—
66C2×#11744751—22no—
67C2×#11744751C2311yescharacteristic
68C2×#11744751C2311yescharacteristic
69C2×#11744751C2311yescharacteristic
70C2×#11744751C2311yescharacteristic
71C4⋊Dic113—21no—
72C4⋊Dic113C2311yescharacteristic
73C4⋊Dic113C2311yescharacteristic
74C4⋊Dic113C2311yescharacteristic
75#14268626—21no—
76#14268626—21no—
77C22⋊Dic113—21no—
78#14268624—21no—
79#14268624—21no—
80#14268624—21no—
81C4×Dic113—21no—
82C2×Q8×C113—21no—
83C2×Q8×C113C2311yescharacteristic
84C2×D4×C113D411yescharacteristic
85C22×C4×C113—21no—
86C22×C4×C113—21no—
87C22×C4×C113C2311yescharacteristic
88C22×C4×C113C2311yescharacteristic
89C4⋊C4×C113—21no—
90C4⋊C4×C113—21no—
91C4⋊C4×C113—21no—
92C4⋊C4×C113—21no—
93C4⋊C4×C113—21no—
94C4⋊C4×C113—21no—
95C4⋊C4×C113D411yescharacteristic
96C4⋊C4×C113C2311yescharacteristic
97C4⋊C4×C113C2311yescharacteristic
98C4⋊C4×C113C2311yescharacteristic
99C22⋊C4×C113—21no—
100C22⋊C4×C113—21no—
101C22⋊C4×C113D411yescharacteristic
102C22⋊C4×C113D411yescharacteristic
103C42×C113—21no—
104C42×C113C2311yescharacteristic
105C23×C113C2×D411yescharacteristic
106C23×C113C2×D411yescharacteristic
107C22×D113—21no—
108Q8×C113—21no—
109Q8×C113—21no—
110Q8×C113—81no—
111D4×C113—22no—
112C2×C4×C113—21no—
113C2×C4×C113—21no—
114C2×C4×C113—21no—
115C2×C4×C113—21no—
116C2×C4×C113—21no—
117C2×C4×C113—21no—
118C2×C4×C113—21no—
119C2×C4×C113—21no—
120C2×C4×C113—81no—
121C2×C4×C113—81no—
122C2×C4×C113C2×D411yescharacteristic
123C2×C4×C113C2×D411yescharacteristic
124C2×C4×C113C2×D411yescharacteristic
125C2×C4×C113C2×D411yescharacteristic
126C2×C4×C113C2411yescharacteristic
127C22⋊D113—42no—
128C22⋊D113—81no—
129C2×Dic113—21no—
130C2×Dic113—21no—
131C2×Dic113—21no—
132C2×Dic113—81no—
133D452—21no—
134D452—21no—
135C4×D113—81no—
136#11744751—21no—
137#11744751—21no—
138#11744751—21no—
139#11744751#4112yes—
140C22×C113—21no—
141C22×C113—21no—
142C22×C113—21no—
143C22×C113—21no—
144C22×C113—21no—
145C22×C113#13712yes—
146C22×C113C22×D411yescharacteristic
147C2×D113—41no—
148C2×D113—41no—
149C2×D113—41no—
150C4×C113—21no—
151C4×C113—21no—
152C4×C113—21no—
153C4×C113—21no—
154C4×C113—41no—
155C4×C113—41no—
156C4×C113—41no—
157C4×C113—41no—
158C4×C113C2×#4111yescharacteristic
159C4×C1132−1+411yescharacteristic
160Dic113—41no—
161Dic113—41no—
162Dic113—41no—
163C2×C113—22no—
164C2×C113—41no—
165C2×C113#54711yescharacteristic
166C2×C113C2×#13711yescharacteristic
167C2×C113#57611yescharacteristic
168D113—81no—
169#3346—1131nomaximal, Sylow
170C113#334611yescharacteristic, complemented, Sylow
171#554D11311yescharacteristic, complemented
172#553—1131no—
173#501—1131no—
174#485—1131no—
175#484—1131no—
176#481—1131no—
177#480—1131no—
178#479—1131no—
179#474—1131no—
180#468—1131no—
181#465—1131no—
182#440—1131no—
183#435—1131no—
184#428—1131no—
185C2×#107—1131no—
186C2×SD16—1131no—
187C2×M16—1131no—
188C22×C8—1131no—
189C4⋊Q8C2×D11311yescharacteristic
190#126—2261no—
191#125—21no—
192#125—1131no—
193#123—2261no—
194C22⋊Q8—21no—
195C22⋊Q8—21no—
196C22⋊Q8C2×D11311yescharacteristic
197C22⋊Q8C2×D11311yescharacteristic
198#121—1131no—
199#121—1131no—
200#121—2261no—
201C4×Q8C2×D11311yescharacteristic
202C4×D4—21no—
203C4×D4—1131no—
204C4×D4—2261no—
205C4×D4C2×D11311yescharacteristic
206#117—1131no—
207C2×C4⋊C4—1131no—
208C2×C4⋊C4C2×D11311yescharacteristic
209C2×C4⋊C4C2×D11311yescharacteristic
210#107—1131no—
211#107—1131no—
212#107—1131no—
213#107—1131no—
214#107—1131no—
215#107—1131no—
216#106—1131no—
217#106—1131no—
218#106—1131no—
219C4⋊C8—1131no—
220#103—1131no—
221#103—1131no—
222#103—1131no—
223#102—1131no—
224#102—1131no—
225#102—1131no—
226C22⋊C8—1131no—
227C22⋊C8—1131no—
228#97—1131no—
229C2×Q8—21no—
230C2×Q8C22×D11311yescharacteristic
231C2×D4—1131no—
232C2×D4—2261no—
233C2×D4—2261no—
234C2×D4C22⋊D11311yescharacteristic
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—2261no—
238C22×C4—2261no—
239C22×C4C22×D11311yescharacteristic
240C22×C4C22×D11311yescharacteristic
241SD16—2262no—
242M16—2262no—
243C2×C8—1131no—
244C2×C8—1131no—
245C2×C8—1131no—
246C2×C8—1131no—
247C2×C8—2262no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—1131no—
255C4⋊C4—1131no—
256C4⋊C4—1131no—
257C4⋊C4—2261no—
258C4⋊C4—2261no—
259C4⋊C4—2261no—
260C4⋊C4C22⋊D11311yescharacteristic
261C4⋊C4C22×D11311yescharacteristic
262C4⋊C4C22×D11311yescharacteristic
263C4⋊C4C22×D11311yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—2261no—
267C22⋊C4—2261no—
268C22⋊C4—2261no—
269C22⋊C4—2261no—
270C22⋊C4C22⋊D11311yescharacteristic
271C22⋊C4C22⋊D11311yescharacteristic
272C42—21no—
273C42—2261no—
274C42C22×D11311yescharacteristic
275C23—2261no—
276C23C2×C22⋊D11311yescharacteristic
277C23C2×C22⋊D11311yescharacteristic
278Q8—21no—
279Q8—21no—
280Q8—81no—
281D4—22no—
282D4—9041no—
283D4—4522no—
284D4—2261no—
285D4—2261no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—9041no—
297C2×C4—9041no—
298C2×C4—2261no—
299C2×C4—2261no—
300C2×C4—2261no—
301C2×C4C2×C22⋊D11311yescharacteristic
302C2×C4C2×C22⋊D11311yescharacteristic
303C2×C4C2×C22⋊D11311yescharacteristic
304C2×C4C2×C22⋊D11311yescharacteristic
305C2×C4C23×D11311yescharacteristic
306C8—1132no—
307C8—2261no—
308C8—2261no—
309C8—2261no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—4521no—
316C22—4521no—
317C22—4521no—
318C22#1681365312yes—
319C22C22×C22⋊D11311yescharacteristic
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—4521no—
329C4—4521no—
330C4—4521no—
331C4#41×D11311yescharacteristic
332C4#1681366911yescharacteristic
333C2—22no—
334C2—41no—
335C2—9041no—
336C2#2029924711yescharacteristic
337C2C2×#1681365311yescharacteristic
338C2#2029940111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#554×C113C2
socleC22×C113C22×D4
prime radical#20299294C2
hypercenter#554D113
hypocenterC113#3346
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4 ◁ #554

Complements

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

NH ≅ G/Ntype
2. #20299004C2semidirect
3. #20298936C2semidirect
4. #20298931C2semidirect
5. #20298916C2semidirect
6. #20298911C2semidirect
7. #20298905C2semidirect
8. #20298875C2semidirect
9. #20298846C2semidirect
10. #20298829C2semidirect
11. #20298696C2semidirect
12. #20298670C2semidirect
13. #20298638C2semidirect
14. C2×#16813555C2semidirect
15. #554×C113C2semidirect
170. C113#3346semidirect
171. #554D113semidirect

Maximal subgroups

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

subgroupindex
#202992942
#202990042
#202989362
#202989312
#202989162
#202989112
#202989052
#202988752
#202988462
#202988292
#202986962
#202986702
#202986382
C2×#168135552
#554×C1132
#3346113