Finite Group Databasebeta

← #28403640

Subgroups — #28403640

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#20299333C211yesmaximal, characteristic, complemented
2#20298990C211yesmaximal, characteristic, complemented
3#20298988C211yesmaximal, characteristic
4#20298980C211yesmaximal, characteristic, complemented
5#20298820C211yesmaximal, characteristic, complemented
6#20298817C211yesmaximal, characteristic, complemented
7#20298813C211yesmaximal, characteristic, complemented
8#20298810C211yesmaximal, characteristic, complemented
9#20298800C211yesmaximal, characteristic, complemented
10#20298798C211yesmaximal, characteristic, complemented
11#20298729C211yesmaximal, characteristic, complemented
12#20298708C211yesmaximal, characteristic, complemented
13#20298703C211yesmaximal, characteristic, complemented
14C4×#14268634C211yesmaximal, characteristic, complemented
15#556×C113C211yesmaximal, characteristic, complemented
16C2×#14268637C2211yescharacteristic
17C2×#14268637C2211yescharacteristic
18C2×#14268635C2211yescharacteristic
19C2×#14268634C2211yescharacteristic
20C2×#14268634C2211yescharacteristic
21C2×#14268634C2211yescharacteristic
22C2×#14268634C2211yescharacteristic
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#16813553C2211yescharacteristic
36C4⋊#11744751C2211yescharacteristic
37C4⋊#11744751C2211yescharacteristic
38C4⋊#11744751C2211yescharacteristic
39#16813546C2211yescharacteristic
40#16813546C2211yescharacteristic
41#16813545C2211yescharacteristic
42#16813543C2211yescharacteristic
43#16813542C2211yescharacteristic
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×D452—21no—
61C2×D452—21no—
62C2×D452C2311yescharacteristic
63C2×D452C2311yescharacteristic
64C2×C4×D113—21no—
65C2×C4×D113—21no—
66#14268637—22no—
67#14268637—41no—
68#14268635—41no—
69#14268634—22no—
70#14268634—41no—
71#14268634—41no—
72#14268634—41no—
73#14268632—22no—
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×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—
113C22×D113—21no—
114Q8×C113—21no—
115Q8×C113—21no—
116Q8×C113—21no—
117Q8×C113—21no—
118Q8×C113—41no—
119D4×C113—21no—
120D4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113—21no—
124C2×C4×C113—42no—
125C2×C4×C113C2×D411yescharacteristic
126C2×C4×C113C2×D411yescharacteristic
127C2×C4×C113C2×D411yescharacteristic
128C2×C4×C113C2×D411yescharacteristic
129C2×C4×C113C2×D411yescharacteristic
130C2×C4×C113C2×D411yescharacteristic
131C2×C4×C113C2411yescharacteristic
132C2×Dic113—21no—
133C2×Dic113—21no—
134D452—21no—
135D452—21no—
136D452—21no—
137D452—21no—
138D452—42no—
139D452—81no—
140C4×D113—81no—
141C4×D113—81no—
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×C113C22×D411yescharacteristic
152C2×D113—41no—
153C2×D113—41no—
154C2×D113—41no—
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×C113—41no—
167C4×C113C2×#4111yescharacteristic
168C4×C113H(5,𝔽2)11yescharacteristic
169Dic113—41no—
170Dic113—41no—
171C2×C113—81no—
172C2×C113#55011yescharacteristic
173C2×C113#57511yescharacteristic
174C2×C113#57711yescharacteristic
175D113—81no—
176D113—81no—
177#3401—1131nomaximal, Sylow
178C113#340111yescharacteristic, complemented, Sylow
179#559—1131no—
180#556D11311yescharacteristic, complemented
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⋊Q8C2×D11311yescharacteristic
204#127—1131no—
205#126—21no—
206#126—21no—
207#124—1131no—
208#124—1131no—
209#124—2261no—
210#124C2×D11311yescharacteristic
211#124C2×D11311yescharacteristic
212#123—2261no—
213#123—2261no—
214C22⋊Q8—21no—
215C4×Q8—1131no—
216C4×Q8C2×D11311yescharacteristic
217C4×Q8C2×D11311yescharacteristic
218C4×Q8C2×D11311yescharacteristic
219C4×D4—1131no—
220C4×D4—1131no—
221C4×D4—2261no—
222C4×D4C2×D11311yescharacteristic
223#117—21no—
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×Q8C22⋊D11311yescharacteristic
239C2×Q8C22×D11311yescharacteristic
240C2×Q8C22×D11311yescharacteristic
241C2×D4—1131no—
242C2×D4—1131no—
243C2×D4—2261no—
244C2×D4—2261no—
245C2×D4C22×D11311yescharacteristic
246C22×C4—21no—
247C22×C4—2261no—
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—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—1131no—
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—2261no—
278C22⋊C4—2261no—
279C22⋊C4—2261no—
280C22⋊C4—2261no—
281C22⋊C4—2261no—
282C22⋊C4—2261no—
283C42—21no—
284C42—21no—
285C42—2261no—
286C42C22×D11311yescharacteristic
287C42C22×D11311yescharacteristic
288C42C22×D11311yescharacteristic
289C23—21no—
290C23—2261no—
291C23—2261no—
292Q8—21no—
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—41no—
297Q8—2261no—
298Q8—2261no—
299D4—21no—
300D4—21no—
301D4—9041no—
302D4—4522no—
303D4—2261no—
304D4—2261no—
305D4—2261no—
306D4—2261no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—42no—
311C2×C4—9041no—
312C2×C4—9041no—
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—4521no—
330C22—4521no—
331C22—4521no—
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—41no—
345C4—4521no—
346C4—4521no—
347C4#41×D11311yescharacteristic
348C4#1681366811yescharacteristic
349C2—81no—
350C2—9041no—
351C2—9041no—
352C2#2029926711yescharacteristic
353C2#2029939611yescharacteristic
354C2#2029940611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#556×C113C2
socleC22×C113C22×D4
prime radical#20298988C2
hypercenter#556D113
hypocenterC113#3401
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. #20299333C2semidirect
2. #20298990C2semidirect
4. #20298980C2semidirect
5. #20298820C2semidirect
6. #20298817C2semidirect
7. #20298813C2semidirect
8. #20298810C2semidirect
9. #20298800C2semidirect
10. #20298798C2semidirect
11. #20298729C2semidirect
12. #20298708C2semidirect
13. #20298703C2semidirect
14. C4×#14268634C2semidirect
15. #556×C113C2semidirect
178. C113#3401semidirect
180. #556D113semidirect

Maximal subgroups

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

subgroupindex
#202993332
#202989902
#202989882
#202989802
#202988202
#202988172
#202988132
#202988102
#202988002
#202987982
#202987292
#202987082
#202987032
C4×#142686342
#556×C1132
#3401113