Finite Group Databasebeta

← #28403649

Subgroups — #28403649

Order 14464.

356 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299321C211yesmaximal, characteristic, complemented
2#20298993C211yesmaximal, characteristic, complemented
3#20298990C211yesmaximal, characteristic, complemented
4#20298980C211yesmaximal, characteristic
5#20298820C211yesmaximal, characteristic, complemented
6#20298817C211yesmaximal, characteristic, complemented
7#20298813C211yesmaximal, characteristic
8#20298810C211yesmaximal, characteristic
9#20298808C211yesmaximal, characteristic, complemented
10#20298805C211yesmaximal, characteristic, complemented
11#20298729C211yesmaximal, characteristic, complemented
12#20298698C211yesmaximal, characteristic, complemented
13#20298696C211yesmaximal, characteristic, complemented
14C4×#14268637C211yesmaximal, characteristic, complemented
15#556×C113C211yesmaximal, characteristic, complemented
16C2×#14268637C2211yescharacteristic
17C2×#14268637C2211yescharacteristic
18C2×#14268637C2211yescharacteristic
19C2×#14268637C2211yescharacteristic
20C2×#14268635C2211yescharacteristic
21C2×#14268635C2211yescharacteristic
22C2×#14268634C2211yescharacteristic
23C2×#14268634C2211yescharacteristic
24C2×#14268632C2211yescharacteristic
25#16813622C2211yescharacteristic
26#16813617—21no—
27#16813617—21no—
28#16813610C2211yescharacteristic
29#16813610C2211yescharacteristic
30#16813598—21no—
31C4×Dic226C2211yescharacteristic
32C4×Dic226C2211yescharacteristic
33C4×D452C2211yescharacteristic
34#16813580—21no—
35#16813555C2211yescharacteristic
36C4⋊#11744751C2211yescharacteristic
37C4⋊#11744751C2211yescharacteristic
38C4⋊#11744751C2211yescharacteristic
39#16813546C2211yescharacteristic
40#16813546C2211yescharacteristic
41#16813545C2211yescharacteristic
42#16813545C2211yescharacteristic
43#16813543C2211yescharacteristic
44#16813542C2211yescharacteristic
45#16813533C2211yescharacteristic
46#16813533C2211yescharacteristic
47C4×#11744751C2211yescharacteristic
48C4⋊Q8×C113C2211yescharacteristic
49#126×C113—21no—
50#126×C113—21no—
51#124×C113C2211yescharacteristic
52#124×C113C2211yescharacteristic
53C22⋊Q8×C113—21no—
54C4×Q8×C113C2211yescharacteristic
55C4×Q8×C113C2211yescharacteristic
56C4×Q8×C113C2211yescharacteristic
57C4×D4×C113C2211yescharacteristic
58#117×C113—21no—
59C2×Dic226C2311yescharacteristic
60C2×Dic226C2311yescharacteristic
61C2×D452C2311yescharacteristic
62C2×C4×D113—21no—
63#14268637—22no—
64#14268637—41no—
65#14268637—41no—
66#14268637—41no—
67#14268635—22no—
68#14268635—41no—
69#14268634—22no—
70#14268634—41no—
71#14268632—41no—
72C2×#11744751C2311yescharacteristic
73C2×#11744751C2311yescharacteristic
74C2×#11744751C2311yescharacteristic
75C2×#11744751C2311yescharacteristic
76C4⋊Dic113—21no—
77C4⋊Dic113—21no—
78C4⋊Dic113C2311yescharacteristic
79#14268626—21no—
80#14268626—21no—
81#14268624—21no—
82#14268624—21no—
83#14268624—21no—
84#14268624—21no—
85#14268624—21no—
86C4×Dic113—21no—
87C4×Dic113—21no—
88C2×Q8×C113D411yescharacteristic
89C2×Q8×C113C2311yescharacteristic
90C2×Q8×C113C2311yescharacteristic
91C2×D4×C113C2311yescharacteristic
92C22×C4×C113—21no—
93C4⋊C4×C113—21no—
94C4⋊C4×C113—21no—
95C4⋊C4×C113—21no—
96C4⋊C4×C113—21no—
97C4⋊C4×C113D411yescharacteristic
98C4⋊C4×C113D411yescharacteristic
99C4⋊C4×C113D411yescharacteristic
100C4⋊C4×C113C2311yescharacteristic
101C22⋊C4×C113—21no—
102C22⋊C4×C113—21no—
103C22⋊C4×C113—21no—
104C22⋊C4×C113—21no—
105C22⋊C4×C113—21no—
106C42×C113—21no—
107C42×C113—21no—
108C42×C113C2311yescharacteristic
109C42×C113C2311yescharacteristic
110C42×C113C2311yescharacteristic
111C23×C113—21no—
112C22×D113—21no—
113Q8×C113—21no—
114Q8×C113—21no—
115Q8×C113—21no—
116Q8×C113—21no—
117Q8×C113—41no—
118D4×C113—21no—
119D4×C113—21no—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113—42no—
124C2×C4×C113C2×D411yescharacteristic
125C2×C4×C113C2×D411yescharacteristic
126C2×C4×C113C2×D411yescharacteristic
127C2×C4×C113C2×D411yescharacteristic
128C2×C4×C113C2×D411yescharacteristic
129C2×C4×C113C2×D411yescharacteristic
130C2×C4×C113C2411yescharacteristic
131C2×Dic113—21no—
132C2×Dic113—21no—
133C2×Dic113—21no—
134D452—21no—
135D452—21no—
136C4×D113—42no—
137Dic226—21no—
138Dic226—21no—
139Dic226—21no—
140Dic226—21no—
141#11744751—21no—
142#11744751—21no—
143#11744751—21no—
144#11744751#4112yes—
145C22×C113—41no—
146C22×C113—41no—
147C22×C113—41no—
148C22×C113C22×D411yescharacteristic
149C2×D113—41no—
150C2×D113—41no—
151C2×D113—41no—
152C4×C113—21no—
153C4×C113—21no—
154C4×C113—21no—
155C4×C113—21no—
156C4×C113—21no—
157C4×C113—21no—
158C4×C113—41no—
159C4×C113—41no—
160C4×C113—41no—
161C4×C113C2×#4111yescharacteristic
162C4×C113H(5,𝔽2)11yescharacteristic
163Dic113—41no—
164Dic113—41no—
165Dic113—41no—
166C2×C113—81no—
167C2×C113#55011yescharacteristic
168C2×C113#57511yescharacteristic
169C2×C113#57811yescharacteristic
170D113—81no—
171#3402—1131nomaximal, Sylow
172C113#340211yescharacteristic, complemented, Sylow
173#556—1131no—
174#556D11311yescharacteristic, complemented
175#497—1131no—
176#497—1131no—
177#495—1131no—
178#464—1131no—
179#464—1131no—
180#463—1131no—
181#463—1131no—
182#462—1131no—
183#462—1131no—
184#446—1131no—
185#440—1131no—
186#440—1131no—
187C4×Q16—1131no—
188C2×Q16—1131no—
189C2×Q16—1131no—
190C2×Q16—1131no—
191C2×Q16—1131no—
192C2×SD16—1131no—
193C2×SD16—1131no—
194C2×SD16—1131no—
195C2×SD16—1131no—
196C2×D8—1131no—
197C4⋊Q8—1131no—
198C4⋊Q8C2×D11311yescharacteristic
199#126—21no—
200#126—21no—
201#126—2261no—
202#126—2261no—
203#124—1131no—
204#124—1131no—
205#124C2×D11311yescharacteristic
206#124C2×D11311yescharacteristic
207C22⋊Q8—21no—
208C22⋊Q8—2261no—
209C4×Q8—1131no—
210C4×Q8—1131no—
211C4×Q8C2×D11311yescharacteristic
212C4×Q8C2×D11311yescharacteristic
213C4×Q8C2×D11311yescharacteristic
214C4×D4—1131no—
215C4×D4C2×D11311yescharacteristic
216#117—21no—
217#117—2261no—
218#107—1131no—
219C4⋊C8—1131no—
220C4⋊C8—1131no—
221C4⋊C8—1131no—
222#103—1131no—
223#103—1131no—
224#103—1131no—
225#103—1131no—
226#102—1131no—
227#102—1131no—
228#97—1131no—
229#97—1131no—
230C4×C8—1131no—
231C2×Q8—1131no—
232C2×Q8—1131no—
233C2×Q8C22⋊D11311yescharacteristic
234C2×Q8C22×D11311yescharacteristic
235C2×Q8C22×D11311yescharacteristic
236C2×D4—1131no—
237C2×D4C22×D11311yescharacteristic
238C22×C4—21no—
239C22×C4—2261no—
240Q16—4521no—
241Q16—4521no—
242Q16—4521no—
243Q16—2262no—
244SD16—4521no—
245SD16—4521no—
246SD16—2262no—
247SD16—2262no—
248D8—4521no—
249C2×C8—1131no—
250C2×C8—1131no—
251C2×C8—1131no—
252C2×C8—1131no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—1131no—
258C4⋊C4—2261no—
259C4⋊C4—2261no—
260C4⋊C4—2261no—
261C4⋊C4—2261no—
262C4⋊C4C22⋊D11311yescharacteristic
263C4⋊C4C22⋊D11311yescharacteristic
264C4⋊C4C22⋊D11311yescharacteristic
265C4⋊C4C22×D11311yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—2261no—
272C22⋊C4—2261no—
273C22⋊C4—2261no—
274C22⋊C4—2261no—
275C22⋊C4—2261no—
276C42—21no—
277C42—21no—
278C42—2261no—
279C42—2261no—
280C42C22×D11311yescharacteristic
281C42C22×D11311yescharacteristic
282C42C22×D11311yescharacteristic
283C23—21no—
284C23—2261no—
285Q8—21no—
286Q8—21no—
287Q8—21no—
288Q8—21no—
289Q8—41no—
290Q8—2261no—
291Q8—2261no—
292Q8—2261no—
293Q8—2261no—
294D4—21no—
295D4—21no—
296D4—2261no—
297D4—2261no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—42no—
302C2×C4—4522no—
303C2×C4—2261no—
304C2×C4—2261no—
305C2×C4—2261no—
306C2×C4C2×C22⋊D11311yescharacteristic
307C2×C4C2×C22⋊D11311yescharacteristic
308C2×C4C2×C22⋊D11311yescharacteristic
309C2×C4C2×C22⋊D11311yescharacteristic
310C2×C4C2×C22⋊D11311yescharacteristic
311C2×C4C2×C22⋊D11311yescharacteristic
312C2×C4C23×D11311yescharacteristic
313C8—1132no—
314C8—2261no—
315C8—2261no—
316C8—2261no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—4521no—
321C22—4521no—
322C22—4521no—
323C22C22×C22⋊D11311yescharacteristic
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—4521no—
334C4—4521no—
335C4—4521no—
336C4#41×D11311yescharacteristic
337C4#1681366811yescharacteristic
338C2—81no—
339C2—9041no—
340C2#2029926711yescharacteristic
341C2#2029939611yescharacteristic
342C2#2029941311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#556×C113C2
socleC22×C113C22×D4
prime radicalC2×#14268632C22
hypercenter#556D113
hypocenterC113#3402
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #556

Complements

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

NH ≅ G/Ntype
1. #20299321C2semidirect
2. #20298993C2semidirect
3. #20298990C2semidirect
5. #20298820C2semidirect
6. #20298817C2semidirect
9. #20298808C2semidirect
10. #20298805C2semidirect
11. #20298729C2semidirect
12. #20298698C2semidirect
13. #20298696C2semidirect
14. C4×#14268637C2semidirect
15. #556×C113C2semidirect
172. C113#3402semidirect
174. #556D113semidirect

Maximal subgroups

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

subgroupindex
#202993212
#202989932
#202989902
#202989802
#202988202
#202988172
#202988132
#202988102
#202988082
#202988052
#202987292
#202986982
#202986962
C4×#142686372
#556×C1132
#3402113