Finite Group Databasebeta

← #28403634

Subgroups — #28403634

Order 14464.

368 conjugacy classes of subgroups.

The subgroup lattice has 356 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#20298985C211yesmaximal, characteristic
4#20298980C211yesmaximal, characteristic, complemented
5#20298820C211yesmaximal, characteristic, complemented
6#20298817C211yesmaximal, characteristic, complemented
7#20298813C211yesmaximal, characteristic, complemented
8#20298810C211yesmaximal, characteristic, complemented
9#20298803C211yesmaximal, characteristic, complemented
10#20298795C211yesmaximal, characteristic, complemented
11#20298729C211yesmaximal, characteristic, complemented
12#20298708C211yesmaximal, characteristic, complemented
13#20298703C211yesmaximal, characteristic, complemented
14C4×#14268635C211yesmaximal, characteristic, complemented
15#559×C113C211yesmaximal, characteristic, complemented
16C2×#14268637C2211yescharacteristic
17C2×#14268637C2211yescharacteristic
18C2×#14268635C2211yescharacteristic
19C2×#14268635C2211yescharacteristic
20C2×#14268635C2211yescharacteristic
21C2×#14268635C2211yescharacteristic
22C2×#14268634C2211yescharacteristic
23C2×#14268632C2211yescharacteristic
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#16813553C2211yescharacteristic
36C4⋊#11744751C2211yescharacteristic
37C4⋊#11744751C2211yescharacteristic
38C4⋊#11744751C2211yescharacteristic
39#16813546C2211yescharacteristic
40#16813545C2211yescharacteristic
41#16813545C2211yescharacteristic
42#16813543C2211yescharacteristic
43#16813543C2211yescharacteristic
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×Dic226C2311yescharacteristic
61C2×D452C2311yescharacteristic
62C2×C4×D113—21no—
63#14268637—22no—
64#14268637—41no—
65#14268635—22no—
66#14268635—41no—
67#14268635—41no—
68#14268635—41no—
69#14268634—41no—
70#14268632—22no—
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×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—
114Q8×C113—21no—
115Q8×C113—21no—
116Q8×C113—41no—
117D4×C113—21no—
118D4×C113—21no—
119D4×C113—21no—
120D4×C113—21no—
121D4×C113—42no—
122D4×C113—81no—
123C2×C4×C113—21no—
124C2×C4×C113—21no—
125C2×C4×C113—81no—
126C2×C4×C113—81no—
127C2×C4×C113C2×D411yescharacteristic
128C2×C4×C113C2×D411yescharacteristic
129C2×C4×C113C2×D411yescharacteristic
130C2×C4×C113C2×D411yescharacteristic
131C2×C4×C113C2×D411yescharacteristic
132C2×C4×C113C2×D411yescharacteristic
133C2×C4×C113C2411yescharacteristic
134C2×Dic113—21no—
135C2×Dic113—21no—
136C2×Dic113—21no—
137D452—21no—
138D452—21no—
139C4×D113—42no—
140Dic226—21no—
141Dic226—21no—
142Dic226—21no—
143Dic226—21no—
144#11744751—21no—
145#11744751—21no—
146#11744751—21no—
147#11744751#4112yes—
148C22×C113—41no—
149C22×C113—41no—
150C22×C113—41no—
151C22×C113—41no—
152C22×C113—41no—
153C22×C113—41no—
154C22×C113C22×D411yescharacteristic
155C2×D113—41no—
156C2×D113—41no—
157C2×D113—41no—
158C4×C113—21no—
159C4×C113—21no—
160C4×C113—21no—
161C4×C113—21no—
162C4×C113—21no—
163C4×C113—21no—
164C4×C113—41no—
165C4×C113—41no—
166C4×C113C2×#4111yescharacteristic
167C4×C113H(5,𝔽2)11yescharacteristic
168Dic113—41no—
169Dic113—41no—
170Dic113—41no—
171C2×C113—81no—
172C2×C113—81no—
173C2×C113#55011yescharacteristic
174C2×C113#57511yescharacteristic
175C2×C113#57711yescharacteristic
176D113—81no—
177#3401—1131nomaximal, Sylow
178C113#340111yescharacteristic, complemented, Sylow
179#559D11311yescharacteristic, complemented
180#556—1131no—
181#497—1131no—
182#496—1131no—
183#495—1131no—
184#464—1131no—
185#464—1131no—
186#463—1131no—
187#463—1131no—
188#461—1131no—
189#460—1131no—
190#446—1131no—
191#442—1131no—
192#441—1131no—
193C4×SD16—1131no—
194C2×Q16—1131no—
195C2×Q16—1131no—
196C2×SD16—1131no—
197C2×SD16—1131no—
198C2×SD16—1131no—
199C2×SD16—1131no—
200C2×SD16—1131no—
201C2×D8—1131no—
202C2×D8—1131no—
203C4⋊Q8—1131no—
204#127C2×D11311yescharacteristic
205#126—2261no—
206#126—2261no—
207#124—21no—
208#124—1131no—
209#124—1131no—
210#124C2×D11311yescharacteristic
211#124C2×D11311yescharacteristic
212#123—21no—
213#123—21no—
214C22⋊Q8—2261no—
215C4×Q8—1131no—
216C4×Q8—1131no—
217C4×Q8C2×D11311yescharacteristic
218C4×Q8C2×D11311yescharacteristic
219C4×D4—21no—
220C4×D4—1131no—
221C4×D4C2×D11311yescharacteristic
222C4×D4C2×D11311yescharacteristic
223#117—2261no—
224#106—1131no—
225C4⋊C8—1131no—
226C4⋊C8—1131no—
227C4⋊C8—1131no—
228#103—1131no—
229#103—1131no—
230#103—1131no—
231#102—1131no—
232#102—1131no—
233#102—1131no—
234#97—1131no—
235#97—1131no—
236C4×C8—1131no—
237C2×Q8—1131no—
238C2×Q8—1131no—
239C2×Q8C22⋊D11311yescharacteristic
240C2×Q8C22×D11311yescharacteristic
241C2×D4—21no—
242C2×D4—21no—
243C2×D4—1131no—
244C2×D4C22×D11311yescharacteristic
245C2×D4C22×D11311yescharacteristic
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—2261no—
249Q16—4521no—
250Q16—2262no—
251SD16—4521no—
252SD16—4521no—
253SD16—4521no—
254SD16—4521no—
255SD16—2262no—
256D8—4521no—
257D8—2262no—
258C2×C8—1131no—
259C2×C8—1131no—
260C2×C8—1131no—
261C2×C8—1131no—
262C4⋊C4—21no—
263C4⋊C4—1131no—
264C4⋊C4—2261no—
265C4⋊C4—2261no—
266C4⋊C4—2261no—
267C4⋊C4—2261no—
268C4⋊C4C22⋊D11311yescharacteristic
269C4⋊C4C22⋊D11311yescharacteristic
270C4⋊C4C22⋊D11311yescharacteristic
271C4⋊C4C22×D11311yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—2261no—
279C22⋊C4—2261no—
280C22⋊C4—2261no—
281C22⋊C4—2261no—
282C22⋊C4—2261no—
283C42—21no—
284C42—2261no—
285C42—2261no—
286C42C22×D11311yescharacteristic
287C42C22×D11311yescharacteristic
288C42C22×D11311yescharacteristic
289C23—21no—
290C23—21no—
291C23—2261no—
292Q8—21no—
293Q8—21no—
294Q8—41no—
295Q8—2261no—
296Q8—2261no—
297Q8—2261no—
298Q8—2261no—
299D4—21no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—42no—
304D4—81no—
305D4—2261no—
306D4—2261no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—4522no—
312C2×C4—2261no—
313C2×C4—2261no—
314C2×C4—2261no—
315C2×C4C2×C22⋊D11311yescharacteristic
316C2×C4C2×C22⋊D11311yescharacteristic
317C2×C4C2×C22⋊D11311yescharacteristic
318C2×C4C2×C22⋊D11311yescharacteristic
319C2×C4C2×C22⋊D11311yescharacteristic
320C2×C4C2×C22⋊D11311yescharacteristic
321C2×C4C23×D11311yescharacteristic
322C8—1132no—
323C8—2261no—
324C8—2261no—
325C8—2261no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—4521no—
333C22—4521no—
334C22—4521no—
335C22C22×C22⋊D11311yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—4521no—
345C4—4521no—
346C4—4521no—
347C4#41×D11311yescharacteristic
348C4#1681366811yescharacteristic
349C2—81no—
350C2—81no—
351C2—9041no—
352C2#2029926711yescharacteristic
353C2#2029939611yescharacteristic
354C2#2029940911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#559×C113C2
socleC22×C113C22×D4
prime radical#20298985C2
hypercenter#559D113
hypocenterC113#3401
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. #20299321C2semidirect
2. #20298993C2semidirect
4. #20298980C2semidirect
5. #20298820C2semidirect
6. #20298817C2semidirect
7. #20298813C2semidirect
8. #20298810C2semidirect
9. #20298803C2semidirect
10. #20298795C2semidirect
11. #20298729C2semidirect
12. #20298708C2semidirect
13. #20298703C2semidirect
14. C4×#14268635C2semidirect
15. #559×C113C2semidirect
178. C113#3401semidirect
179. #559D113semidirect

Maximal subgroups

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

subgroupindex
#202993212
#202989932
#202989852
#202989802
#202988202
#202988172
#202988132
#202988102
#202988032
#202987952
#202987292
#202987082
#202987032
C4×#142686352
#559×C1132
#3401113