Finite Group Databasebeta

← #28403174

Subgroups — #28403174

Order 14464.

360 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299294C211yesmaximal, characteristic, complemented
2#20298997C211yesmaximal, characteristic, complemented
3#20298922C211yesmaximal, characteristic, complemented
4#20298919C211yesmaximal, characteristic, complemented
5#20298911C211yesmaximal, characteristic, complemented
6#20298909C211yesmaximal, characteristic, complemented
7#20298898C211yesmaximal, characteristic, complemented
8#20298895C211yesmaximal, characteristic, complemented
9#20298849C211yesmaximal, characteristic, complemented
10#20298849C211yesmaximal, characteristic, complemented
11C4×#14268632C211yesmaximal, characteristic, complemented
12#20298676C211yesmaximal, characteristic, complemented
13#20298641C211yesmaximal, characteristic, complemented
14#20298638C211yesmaximal, characteristic, complemented
15#553×C113C211yesmaximal, characteristic, complemented
16C2×#14268632C2211yescharacteristic
17C2×#14268631C2211yescharacteristic
18C2×#14268631C2211yescharacteristic
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#16813553C2211yescharacteristic
35#16813553C2211yescharacteristic
36#16813553C2211yescharacteristic
37#16813553C2211yescharacteristic
38C4⋊#11744751C2211yescharacteristic
39#16813543C2211yescharacteristic
40#16813543C2211yescharacteristic
41#16813543C2211yescharacteristic
42#16813542C2211yescharacteristic
43#16813542C2211yescharacteristic
44#16813542C2211yescharacteristic
45C22⋊#11744751C2211yescharacteristic
46C22⋊#11744751C2211yescharacteristic
47C4×#11744751C2211yescharacteristic
48#126×C113—21no—
49#125×C113C2211yescharacteristic
50#123×C113—21no—
51#121×C113—21no—
52#121×C113C2211yescharacteristic
53#121×C113C2211yescharacteristic
54C4×D4×C113—21no—
55C4×D4×C113C2211yescharacteristic
56C4×D4×C113C2211yescharacteristic
57#117×C113C2211yescharacteristic
58C2×C4⋊C4×C113C2211yescharacteristic
59C2×D452C2311yescharacteristic
60C2×C22⋊D113—21no—
61C2×C22⋊D113—21no—
62C22×Dic113—21no—
63C2×C4×D113—21no—
64#14268632—22no—
65#14268631—22no—
66#14268631—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×D4×C113—21no—
83C2×D4×C113—21no—
84C2×D4×C113D411yescharacteristic
85C2×D4×C113C2311yescharacteristic
86C22×C4×C113—21no—
87C22×C4×C113—21no—
88C22×C4×C113C2311yescharacteristic
89C22×C4×C113C2311yescharacteristic
90C4⋊C4×C113—21no—
91C4⋊C4×C113—21no—
92C4⋊C4×C113—21no—
93C4⋊C4×C113D411yescharacteristic
94C4⋊C4×C113C2311yescharacteristic
95C4⋊C4×C113C2311yescharacteristic
96C4⋊C4×C113C2311yescharacteristic
97C22⋊C4×C113—21no—
98C22⋊C4×C113—21no—
99C22⋊C4×C113—21no—
100C22⋊C4×C113—21no—
101C22⋊C4×C113D411yescharacteristic
102C22⋊C4×C113D411yescharacteristic
103C42×C113—21no—
104C42×C113C2311yescharacteristic
105C23×C113—21no—
106C23×C113C2×D411yescharacteristic
107C23×C113C2×D411yescharacteristic
108C22×D113—21no—
109D4×C113—21no—
110D4×C113—21no—
111D4×C113—41no—
112D4×C113—42no—
113D4×C113—81no—
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—21no—
121C2×C4×C113—81no—
122C2×C4×C113—81no—
123C2×C4×C113C2×D411yescharacteristic
124C2×C4×C113C2×D411yescharacteristic
125C2×C4×C113C2×D411yescharacteristic
126C2×C4×C113C2×D411yescharacteristic
127C2×C4×C113C2411yescharacteristic
128C22⋊D113—42no—
129C22⋊D113—81no—
130C2×Dic113—21no—
131C2×Dic113—21no—
132C2×Dic113—21no—
133C2×Dic113—81no—
134D452—21no—
135D452—21no—
136C4×D113—81no—
137#11744751—21no—
138#11744751—21no—
139#11744751—21no—
140#11744751#4112yes—
141C22×C113—21no—
142C22×C113—21no—
143C22×C113—21no—
144C22×C113—21no—
145C22×C113—21no—
146C22×C113—21no—
147C22×C113—41no—
148C22×C113—41no—
149C22×C113—41no—
150C22×C113C22×D411yescharacteristic
151C2×D113—41no—
152C2×D113—41no—
153C2×D113—41no—
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×C1132−1+411yescharacteristic
163Dic113—41no—
164Dic113—41no—
165Dic113—41no—
166C2×C113—41no—
167C2×C113—41no—
168C2×C113—81no—
169C2×C113#54711yescharacteristic
170C2×C113#57511yescharacteristic
171C2×C113#57611yescharacteristic
172D113—81no—
173#3355—1131nomaximal, Sylow
174C113#335511yescharacteristic, complemented, Sylow
175#553—1131no—
176#553D11311yescharacteristic, complemented
177#499—1131no—
178#482—1131no—
179#482—1131no—
180#480—1131no—
181#480—1131no—
182#478—1131no—
183#478—1131no—
184#469—1131no—
185#469—1131no—
186C4×D8—1131no—
187#436—1131no—
188#428—1131no—
189#428—1131no—
190C2×D8—1131no—
191C2×M16—1131no—
192C2×M16—1131no—
193#126—21no—
194#126—2261no—
195#125—1131no—
196#125C2×D11311yescharacteristic
197#123—21no—
198#123—2261no—
199#121—21no—
200#121—1131no—
201#121—1131no—
202#121—2261no—
203#121C2×D11311yescharacteristic
204#121C2×D11311yescharacteristic
205C4×D4—21no—
206C4×D4—1131no—
207C4×D4—2261no—
208C4×D4C2×D11311yescharacteristic
209C4×D4C2×D11311yescharacteristic
210#117—1131no—
211#117C2×D11311yescharacteristic
212C2×C4⋊C4—1131no—
213C2×C4⋊C4C2×D11311yescharacteristic
214#107—1131no—
215#107—1131no—
216#107—1131no—
217#107—1131no—
218#107—1131no—
219#106—1131no—
220#106—1131no—
221#106—1131no—
222#106—1131no—
223C4⋊C8—1131no—
224#102—1131no—
225#102—1131no—
226#102—1131no—
227#102—1131no—
228#102—1131no—
229#102—1131no—
230C22⋊C8—1131no—
231C22⋊C8—1131no—
232C4×C8—1131no—
233C2×D4—21no—
234C2×D4—21no—
235C2×D4—1131no—
236C2×D4—2261no—
237C2×D4—2261no—
238C2×D4C22⋊D11311yescharacteristic
239C2×D4C22×D11311yescharacteristic
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—2261no—
243C22×C4—2261no—
244C22×C4C22×D11311yescharacteristic
245C22×C4C22×D11311yescharacteristic
246D8—2262no—
247M16—2262no—
248M16—2262no—
249C2×C8—1131no—
250C2×C8—1131no—
251C2×C8—1131no—
252C2×C8—1131no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—1131no—
257C4⋊C4—1131no—
258C4⋊C4—1131no—
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—2261no—
271C22⋊C4—2261no—
272C22⋊C4—2261no—
273C22⋊C4—2261no—
274C22⋊C4C22⋊D11311yescharacteristic
275C22⋊C4C22⋊D11311yescharacteristic
276C42—21no—
277C42—2261no—
278C42C22×D11311yescharacteristic
279C23—21no—
280C23—2261no—
281C23C2×C22⋊D11311yescharacteristic
282C23C2×C22⋊D11311yescharacteristic
283D4—21no—
284D4—21no—
285D4—41no—
286D4—42no—
287D4—81no—
288D4—9041no—
289D4—4522no—
290D4—2261no—
291D4—2261no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—9041no—
302C2×C4—9041no—
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×C4C23×D11311yescharacteristic
311C8—1132no—
312C8—2261no—
313C8—2261no—
314C8—2261no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—4521no—
325C22—4521no—
326C22—4521no—
327C22C22×C22⋊D11311yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—4521no—
336C4—4521no—
337C4—4521no—
338C4#41×D11311yescharacteristic
339C4#1681366911yescharacteristic
340C2—41no—
341C2—41no—
342C2—81no—
343C2—9041no—
344C2#2029924711yescharacteristic
345C2#2029939611yescharacteristic
346C2#2029940111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#553×C113C2
socleC22×C113C22×D4
hypercenter#553D113
hypocenterC113#3355
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #20299294C2semidirect
2. #20298997C2semidirect
3. #20298922C2semidirect
4. #20298919C2semidirect
5. #20298911C2semidirect
6. #20298909C2semidirect
7. #20298898C2semidirect
8. #20298895C2semidirect
9. #20298849C2semidirect
10. #20298849C2semidirect
11. C4×#14268632C2semidirect
12. #20298676C2semidirect
13. #20298641C2semidirect
14. #20298638C2semidirect
15. #553×C113C2semidirect
174. C113#3355semidirect
176. #553D113semidirect

Maximal subgroups

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

subgroupindex
#202992942
#202989972
#202989222
#202989192
#202989112
#202989092
#202988982
#202988952
#202988492
C4×#142686322
#202986762
#202986412
#202986382
#553×C1132
#3355113