Finite Group Databasebeta

← #28403658

Subgroups — #28403658

Order 14464.

380 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299333C211yesmaximal, characteristic, complemented
2#20298988C211yesmaximal, characteristic, complemented
3#20298985C211yesmaximal, characteristic, complemented
4#20298980C211yesmaximal, characteristic, complemented
5#20298820C211yesmaximal, characteristic, complemented
6#20298817C211yesmaximal, characteristic, complemented
7#20298813C211yesmaximal, characteristic, complemented
8#20298810C211yesmaximal, characteristic, complemented
9#20298793C211yesmaximal, characteristic, complemented
10#20298790C211yesmaximal, characteristic, complemented
11#20298729C211yesmaximal, characteristic, complemented
12#20298698C211yesmaximal, characteristic, complemented
13#20298696C211yesmaximal, characteristic, complemented
14C4×#14268632C211yesmaximal, characteristic, complemented
15#559×C113C211yesmaximal, characteristic, complemented
16C2×#14268637C2211yescharacteristic
17C2×#14268635C2211yescharacteristic
18C2×#14268635C2211yescharacteristic
19C2×#14268634C2211yescharacteristic
20C2×#14268634C2211yescharacteristic
21C2×#14268632C2211yescharacteristic
22C2×#14268632C2211yescharacteristic
23C2×#14268632C2211yescharacteristic
24C2×#14268632C2211yescharacteristic
25#16813619C2211yescharacteristic
26#16813611—21no—
27#16813610C2211yescharacteristic
28#16813610C2211yescharacteristic
29#16813607—21no—
30#16813607—21no—
31C4×Dic226C2211yescharacteristic
32C4×D452C2211yescharacteristic
33C4×D452C2211yescharacteristic
34#16813584—21no—
35#16813555C2211yescharacteristic
36C4⋊#11744751C2211yescharacteristic
37C4⋊#11744751C2211yescharacteristic
38C4⋊#11744751C2211yescharacteristic
39#16813546C2211yescharacteristic
40#16813545C2211yescharacteristic
41#16813543C2211yescharacteristic
42#16813543C2211yescharacteristic
43#16813542C2211yescharacteristic
44#16813542C2211yescharacteristic
45#16813533C2211yescharacteristic
46#16813533C2211yescharacteristic
47C4×#11744751C2211yescharacteristic
48#127×C113C2211yescharacteristic
49#124×C113—21no—
50#124×C113C2211yescharacteristic
51#124×C113C2211yescharacteristic
52#123×C113—21no—
53#123×C113—21no—
54C4×Q8×C113C2211yescharacteristic
55C4×Q8×C113C2211yescharacteristic
56C4×D4×C113—21no—
57C4×D4×C113C2211yescharacteristic
58C4×D4×C113C2211yescharacteristic
59C2×Dic226C2311yescharacteristic
60C2×D452—21no—
61C2×D452—21no—
62C2×D452C2311yescharacteristic
63C2×D452C2311yescharacteristic
64C2×C4×D113—21no—
65C2×C4×D113—21no—
66#14268637—41no—
67#14268635—22no—
68#14268635—41no—
69#14268634—22no—
70#14268634—41no—
71#14268632—22no—
72#14268632—41no—
73#14268632—41no—
74#14268632—41no—
75C2×#11744751C2311yescharacteristic
76C2×#11744751C2311yescharacteristic
77C2×#11744751C2311yescharacteristic
78C2×#11744751C2311yescharacteristic
79C4⋊Dic113C2311yescharacteristic
80#14268626—21no—
81#14268624—21no—
82#14268624—21no—
83#14268624—21no—
84#14268624—21no—
85#14268624—21no—
86#14268624—21no—
87C4×Dic113—21no—
88C2×Q8×C113D411yescharacteristic
89C2×Q8×C113C2311yescharacteristic
90C2×D4×C113—21no—
91C2×D4×C113—21no—
92C2×D4×C113C2311yescharacteristic
93C2×D4×C113C2311yescharacteristic
94C22×C4×C113—21no—
95C22×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—
106C22⋊C4×C113—21no—
107C42×C113—21no—
108C42×C113C2311yescharacteristic
109C42×C113C2311yescharacteristic
110C42×C113C2311yescharacteristic
111C23×C113—21no—
112C23×C113—21no—
113C22×D113—21no—
114C22×D113—21no—
115Q8×C113—21no—
116Q8×C113—21no—
117Q8×C113—41no—
118D4×C113—21no—
119D4×C113—21no—
120D4×C113—21no—
121D4×C113—21no—
122D4×C113—42no—
123D4×C113—81no—
124C2×C4×C113—21no—
125C2×C4×C113—21no—
126C2×C4×C113—81no—
127C2×C4×C113—81no—
128C2×C4×C113C2×D411yescharacteristic
129C2×C4×C113C2×D411yescharacteristic
130C2×C4×C113C2×D411yescharacteristic
131C2×C4×C113C2×D411yescharacteristic
132C2×C4×C113C2×D411yescharacteristic
133C2×C4×C113C2×D411yescharacteristic
134C2×C4×C113C2411yescharacteristic
135C2×Dic113—21no—
136C2×Dic113—21no—
137D452—21no—
138D452—21no—
139D452—21no—
140D452—21no—
141D452—42no—
142D452—81no—
143C4×D113—81no—
144C4×D113—81no—
145Dic226—21no—
146Dic226—21no—
147#11744751—21no—
148#11744751—21no—
149#11744751—21no—
150#11744751#4112yes—
151C22×C113—41no—
152C22×C113—41no—
153C22×C113—41no—
154C22×C113—41no—
155C22×C113—41no—
156C22×C113—41no—
157C22×C113C22×D411yescharacteristic
158C2×D113—41no—
159C2×D113—41no—
160C2×D113—41no—
161C2×D113—41no—
162C2×D113—41no—
163C2×D113—41no—
164C4×C113—21no—
165C4×C113—21no—
166C4×C113—21no—
167C4×C113—21no—
168C4×C113—21no—
169C4×C113—21no—
170C4×C113—41no—
171C4×C113—41no—
172C4×C113C2×#4111yescharacteristic
173C4×C113H(5,𝔽2)11yescharacteristic
174Dic113—41no—
175Dic113—41no—
176C2×C113—81no—
177C2×C113—81no—
178C2×C113#55011yescharacteristic
179C2×C113#57511yescharacteristic
180C2×C113#57611yescharacteristic
181D113—81no—
182D113—81no—
183#3403—1131nomaximal, Sylow
184C113#340311yescharacteristic, complemented, Sylow
185#559—1131no—
186#559D11311yescharacteristic, complemented
187#496—1131no—
188#496—1131no—
189#495—1131no—
190#464—1131no—
191#464—1131no—
192#463—1131no—
193#463—1131no—
194#459—1131no—
195#459—1131no—
196#446—1131no—
197#440—1131no—
198#440—1131no—
199C4×D8—1131no—
200C2×Q16—1131no—
201C2×SD16—1131no—
202C2×SD16—1131no—
203C2×SD16—1131no—
204C2×SD16—1131no—
205C2×D8—1131no—
206C2×D8—1131no—
207C2×D8—1131no—
208C2×D8—1131no—
209#127—1131no—
210#127C2×D11311yescharacteristic
211#124—21no—
212#124—1131no—
213#124—1131no—
214#124—2261no—
215#124C2×D11311yescharacteristic
216#124C2×D11311yescharacteristic
217#123—21no—
218#123—21no—
219#123—2261no—
220#123—2261no—
221C4×Q8—1131no—
222C4×Q8C2×D11311yescharacteristic
223C4×Q8C2×D11311yescharacteristic
224C4×D4—21no—
225C4×D4—1131no—
226C4×D4—1131no—
227C4×D4—2261no—
228C4×D4C2×D11311yescharacteristic
229C4×D4C2×D11311yescharacteristic
230#107—1131no—
231C4⋊C8—1131no—
232C4⋊C8—1131no—
233C4⋊C8—1131no—
234#103—1131no—
235#103—1131no—
236#102—1131no—
237#102—1131no—
238#102—1131no—
239#102—1131no—
240#97—1131no—
241#97—1131no—
242C4×C8—1131no—
243C2×Q8—1131no—
244C2×Q8C22⋊D11311yescharacteristic
245C2×Q8C22×D11311yescharacteristic
246C2×D4—21no—
247C2×D4—21no—
248C2×D4—1131no—
249C2×D4—1131no—
250C2×D4—2261no—
251C2×D4—2261no—
252C2×D4C22×D11311yescharacteristic
253C2×D4C22×D11311yescharacteristic
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—2261no—
257C22×C4—2261no—
258Q16—4521no—
259SD16—4521no—
260SD16—4521no—
261SD16—2262no—
262SD16—2262no—
263D8—4521no—
264D8—4521no—
265D8—4521no—
266D8—2262no—
267C2×C8—1131no—
268C2×C8—1131no—
269C2×C8—1131no—
270C2×C8—1131no—
271C4⋊C4—21no—
272C4⋊C4—1131no—
273C4⋊C4—2261no—
274C4⋊C4C22⋊D11311yescharacteristic
275C4⋊C4C22⋊D11311yescharacteristic
276C4⋊C4C22⋊D11311yescharacteristic
277C4⋊C4C22×D11311yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—2261no—
285C22⋊C4—2261no—
286C22⋊C4—2261no—
287C22⋊C4—2261no—
288C22⋊C4—2261no—
289C22⋊C4—2261no—
290C42—21no—
291C42—2261no—
292C42C22×D11311yescharacteristic
293C42C22×D11311yescharacteristic
294C42C22×D11311yescharacteristic
295C23—21no—
296C23—21no—
297C23—2261no—
298C23—2261no—
299Q8—21no—
300Q8—21no—
301Q8—41no—
302Q8—2261no—
303Q8—2261no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—42no—
309D4—81no—
310D4—9041no—
311D4—4522no—
312D4—2261no—
313D4—2261no—
314D4—2261no—
315D4—2261no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—9041no—
321C2×C4—9041no—
322C2×C4—2261no—
323C2×C4—2261no—
324C2×C4C2×C22⋊D11311yescharacteristic
325C2×C4C2×C22⋊D11311yescharacteristic
326C2×C4C2×C22⋊D11311yescharacteristic
327C2×C4C2×C22⋊D11311yescharacteristic
328C2×C4C2×C22⋊D11311yescharacteristic
329C2×C4C2×C22⋊D11311yescharacteristic
330C2×C4C23×D11311yescharacteristic
331C8—1132no—
332C8—2261no—
333C8—2261no—
334C8—2261no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—4521no—
342C22—4521no—
343C22—4521no—
344C22—4521no—
345C22—4521no—
346C22—4521no—
347C22C22×C22⋊D11311yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—4521no—
357C4—4521no—
358C4#41×D11311yescharacteristic
359C4#1681366811yescharacteristic
360C2—81no—
361C2—81no—
362C2—9041no—
363C2—9041no—
364C2#2029926711yescharacteristic
365C2#2029939611yescharacteristic
366C2#2029940111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#559×C113C2
socleC22×C113C22×D4
hypercenter#559D113
hypocenterC113#3403
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #559

Complements

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

NH ≅ G/Ntype
1. #20299333C2semidirect
2. #20298988C2semidirect
3. #20298985C2semidirect
4. #20298980C2semidirect
5. #20298820C2semidirect
6. #20298817C2semidirect
7. #20298813C2semidirect
8. #20298810C2semidirect
9. #20298793C2semidirect
10. #20298790C2semidirect
11. #20298729C2semidirect
12. #20298698C2semidirect
13. #20298696C2semidirect
14. C4×#14268632C2semidirect
15. #559×C113C2semidirect
184. C113#3403semidirect
186. #559D113semidirect

Maximal subgroups

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

subgroupindex
#202993332
#202989882
#202989852
#202989802
#202988202
#202988172
#202988132
#202988102
#202987932
#202987902
#202987292
#202986982
#202986962
C4×#142686322
#559×C1132
#3403113