Finite Group Databasebeta

← #28403055

Subgroups — #28403055

Order 14464.

356 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299303C211yesmaximal, characteristic, complemented
2#20299296C211yesmaximal, characteristic
3#20299006C211yesmaximal, characteristic, complemented
4#20298941C211yesmaximal, characteristic, complemented
5#20298933C211yesmaximal, characteristic, complemented
6#20298916C211yesmaximal, characteristic, complemented
7#20298913C211yesmaximal, characteristic, complemented
8#20298904C211yesmaximal, characteristic, complemented
9#20298877C211yesmaximal, characteristic, complemented
10#20298845C211yesmaximal, characteristic, complemented
11#20298827C211yesmaximal, characteristic, complemented
12#20298697C211yesmaximal, characteristic, complemented
13#20298669C211yesmaximal, characteristic, complemented
14#20298639C211yesmaximal, characteristic, complemented
15C2×#107×C113C211yesmaximal, characteristic, complemented
16C2×#14268636C2211yescharacteristic
17C2×#14268630C2211yescharacteristic
18#16813621C2211yescharacteristic
19#16813617—21no—
20#16813613C2211yescharacteristic
21#16813612—21no—
22#16813607—21no—
23#16813602C2211yescharacteristic
24#16813601—21no—
25#16813601C2211yescharacteristic
26#16813600—21no—
27#16813597C2211yescharacteristic
28#16813596—21no—
29#16813596C2211yescharacteristic
30#16813587C2211yescharacteristic
31#16813584C2211yescharacteristic
32C4×C22⋊D113—21no—
33C4×C22⋊D113—21no—
34C4×C22⋊D113C2211yescharacteristic
35#16813580C2211yescharacteristic
36C4⋊C4×D113C2211yescharacteristic
37#16813555C2211yescharacteristic
38#16813555C2211yescharacteristic
39#16813554C2211yescharacteristic
40#16813553C2211yescharacteristic
41#16813553C2211yescharacteristic
42#16813551C2211yescharacteristic
43#16813547C2211yescharacteristic
44#16813545C2211yescharacteristic
45#16813545C2211yescharacteristic
46#16813544C2211yescharacteristic
47#16813542C2211yescharacteristic
48#16813542C2211yescharacteristic
49C22⋊#11744751C2211yescharacteristic
50#16813534C2211yescharacteristic
51#16813532C2211yescharacteristic
52C22×C8×C113C2211yescharacteristic
53C2×C4⋊C4×C113C2211yescharacteristic
54C2×C4⋊C4×C113C2211yescharacteristic
55#107×C113C2211yescharacteristic
56#107×C113C2211yescharacteristic
57#107×C113C2211yescharacteristic
58#107×C113C2211yescharacteristic
59C2×Dic226—21no—
60C2×Dic226C2311yescharacteristic
61C2×D452—21no—
62C2×D452C2311yescharacteristic
63C2×C22⋊D113—21no—
64C2×C22⋊D113D411yescharacteristic
65C2×C4×D113—21no—
66C2×C4×D113—21no—
67C2×C4×D113C2311yescharacteristic
68#14268636—22no—
69#14268630—22no—
70C2×#11744751C2311yescharacteristic
71C2×#11744751C2311yescharacteristic
72C4⋊Dic113—21no—
73C4⋊Dic113—21no—
74C4⋊Dic113C2311yescharacteristic
75C4⋊Dic113C2311yescharacteristic
76#14268626—21no—
77#14268626—21no—
78#14268626—21no—
79#14268626—21no—
80#14268626—21no—
81#14268626D411yescharacteristic
82C22⋊Dic113—21no—
83C22⋊Dic113D411yescharacteristic
84#14268624—21no—
85#14268624—21no—
86#14268624—21no—
87#14268624—21no—
88#14268624—21no—
89#14268624D411yescharacteristic
90C4×Dic113—21no—
91C4×Dic113—21no—
92C4×Dic113C2311yescharacteristic
93C22×C4×C113—21no—
94C22×C4×C113—21no—
95C22×C4×C113C2311yescharacteristic
96C2×C8×C113—22no—
97C2×C8×C113C2311yescharacteristic
98C2×C8×C113C2311yescharacteristic
99C4⋊C4×C113—21no—
100C4⋊C4×C113—21no—
101C4⋊C4×C113C2311yescharacteristic
102C4⋊C4×C113C2311yescharacteristic
103C4⋊C4×C113C2311yescharacteristic
104C4⋊C4×C113C2311yescharacteristic
105C23×C113C2×D411yescharacteristic
106C22×D113—21no—
107C22×D113C2×D411yescharacteristic
108C2×C4×C113—21no—
109C2×C4×C113—21no—
110C2×C4×C113—21no—
111C2×C4×C113—21no—
112C2×C4×C113—21no—
113C2×C4×C113—21no—
114C2×C4×C113—81no—
115C2×C4×C113—81no—
116C2×C4×C113C2×D411yescharacteristic
117C2×C4×C113C2411yescharacteristic
118C22⋊D113—22no—
119C22⋊D113—42no—
120C2×Dic113—21no—
121C2×Dic113—21no—
122C2×Dic113—21no—
123C2×Dic113C2×D411yescharacteristic
124C2×Dic113C2×D411yescharacteristic
125C2×Dic113C2×D411yescharacteristic
126D452—21no—
127D452—21no—
128D452—81no—
129C4×D113—21no—
130C4×D113—21no—
131C4×D113—81no—
132C4×D113—81no—
133Dic226—21no—
134Dic226—21no—
135Dic226—81no—
136C8×C113—21no—
137C8×C113#4112yes—
138#11744751—21no—
139#11744751—21no—
140C22×C113—21no—
141C22×C113—21no—
142C22×C113#13712yes—
143C22×C113C22×D411yescharacteristic
144C2×D113—21no—
145C2×D113—21no—
146C2×D113—21no—
147C2×D113—41no—
148C2×D113—41no—
149C2×D113—41no—
150C4×C113—21no—
151C4×C113—41no—
152C4×C113—41no—
153C4×C113—41no—
154C4×C113—41no—
155C4×C113C2×#4111yescharacteristic
156C4×C1132−1+411yescharacteristic
157Dic113—21no—
158Dic113—21no—
159Dic113—21no—
160Dic113—41no—
161Dic113—41no—
162Dic113—41no—
163C2×C113—22no—
164C2×C113#54711yescharacteristic
165C2×C113C2×#13711yescharacteristic
166C2×C113#57611yescharacteristic
167D113—41no—
168D113—81no—
169#3346—1131nomaximal, Sylow
170C113#334611yescharacteristic, complemented, Sylow
171#554—1131no—
172#553—1131no—
173#501—1131no—
174#485—1131no—
175#484—1131no—
176#481—1131no—
177#480—1131no—
178#479—1131no—
179#474—1131no—
180#468—1131no—
181#465—1131no—
182#440—1131no—
183#435—1131no—
184#428—1131no—
185C2×#107D11311yescharacteristic, complemented
186C2×SD16—1131no—
187C2×M16—1131no—
188C22×C8C2×D11311yescharacteristic
189C4⋊Q8—1131no—
190#126—2261no—
191#125—1131no—
192#125—2261no—
193#123—2261no—
194C22⋊Q8—1131no—
195C22⋊Q8—1131no—
196C22⋊Q8—2261no—
197C22⋊Q8—2261no—
198#121—1131no—
199#121—1131no—
200#121—2261no—
201C4×Q8—1131no—
202C4×D4—1131no—
203C4×D4—1131no—
204C4×D4—2261no—
205C4×D4—2261no—
206#117—1131no—
207C2×C4⋊C4—1131no—
208C2×C4⋊C4C2×D11311yescharacteristic
209C2×C4⋊C4C2×D11311yescharacteristic
210#107—1131no—
211#107—1131no—
212#107C2×D11311yescharacteristic
213#107C2×D11311yescharacteristic
214#107C2×D11311yescharacteristic
215#107C2×D11311yescharacteristic
216#106—1131no—
217#106—1131no—
218#106—1131no—
219C4⋊C8—1131no—
220#103—1131no—
221#103—1131no—
222#103—1131no—
223#102—1131no—
224#102—1131no—
225#102—1131no—
226C22⋊C8—1131no—
227C22⋊C8—1131no—
228#97—1131no—
229C2×Q8—1131no—
230C2×Q8—2261no—
231C2×D4—1131no—
232C2×D4—1131no—
233C2×D4—2261no—
234C2×D4—2261no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—1131no—
238C22×C4—2261no—
239C22×C4—2261no—
240C22×C4C22×D11311yescharacteristic
241SD16—2262no—
242M16—2262no—
243C2×C8—22no—
244C2×C8—1131no—
245C2×C8—1131no—
246C2×C8C22×D11311yescharacteristic
247C2×C8C22×D11311yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—1131no—
251C4⋊C4—1131no—
252C4⋊C4—1131no—
253C4⋊C4—2261no—
254C4⋊C4—2261no—
255C4⋊C4—2261no—
256C4⋊C4—2261no—
257C4⋊C4—2261no—
258C4⋊C4—2261no—
259C4⋊C4—2261no—
260C4⋊C4C22×D11311yescharacteristic
261C4⋊C4C22×D11311yescharacteristic
262C4⋊C4C22×D11311yescharacteristic
263C4⋊C4C22×D11311yescharacteristic
264C22⋊C4—1131no—
265C22⋊C4—1131no—
266C22⋊C4—2261no—
267C22⋊C4—2261no—
268C22⋊C4—2261no—
269C22⋊C4—2261no—
270C22⋊C4—2261no—
271C22⋊C4—2261no—
272C42—1131no—
273C42—2261no—
274C42—2261no—
275C23—1131no—
276C23—2261no—
277C23D4×D11311yescharacteristic
278Q8—9041no—
279Q8—2261no—
280Q8—2261no—
281D4—9041no—
282D4—4522no—
283D4—2262no—
284D4—2261no—
285D4—2261no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4—1131no—
295C2×C4—1131no—
296C2×C4—1131no—
297C2×C4—9041no—
298C2×C4—9041no—
299C2×C4—2261no—
300C2×C4—2261no—
301C2×C4—2261no—
302C2×C4—2261no—
303C2×C4—2261no—
304C2×C4D4×D11311yescharacteristic
305C2×C4C23×D11311yescharacteristic
306C8—21no—
307C8—2261no—
308C8—2261no—
309C8#1426864712yes—
310C22—21no—
311C22—21no—
312C22—4521no—
313C22—4521no—
314C22—4521no—
315C22—2261no—
316C22—2261no—
317C22—2261no—
318C22#1681365412yes—
319C22C2×D4×D11311yescharacteristic
320C4—21no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—41no—
325C4—4521no—
326C4—4521no—
327C4—4521no—
328C4—2261no—
329C4—2261no—
330C4—2261no—
331C4C2×#1426864711yescharacteristic
332C4#1681367011yescharacteristic
333C2—22no—
334C2—9041no—
335C2—4521no—
336C2#2029924911yescharacteristic
337C2C2×#1681365411yescharacteristic
338C2#2029939911yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×#107×C113C2
socleC22×C113C22×D4
prime radical#20299296C2
hypercenterC2×#107D113
hypocenterC113#3346
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
1. #20299303C2semidirect
3. #20299006C2semidirect
4. #20298941C2semidirect
5. #20298933C2semidirect
6. #20298916C2semidirect
7. #20298913C2semidirect
8. #20298904C2semidirect
9. #20298877C2semidirect
10. #20298845C2semidirect
11. #20298827C2semidirect
12. #20298697C2semidirect
13. #20298669C2semidirect
14. #20298639C2semidirect
15. C2×#107×C113C2semidirect
170. C113#3346semidirect
185. C2×#107D113semidirect

Maximal subgroups

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

subgroupindex
#202993032
#202992962
#202990062
#202989412
#202989332
#202989162
#202989132
#202989042
#202988772
#202988452
#202988272
#202986972
#202986692
#202986392
C2×#107×C1132
#3346113