Finite Group Databasebeta

← #28403196

Subgroups — #28403196

Order 14464.

354 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#20299311C211yesmaximal, characteristic
2#20299303C211yesmaximal, characteristic, complemented
3#20299002C211yesmaximal, characteristic, complemented
4#20298942C211yesmaximal, characteristic, complemented
5#20298939C211yesmaximal, characteristic, complemented
6#20298913C211yesmaximal, characteristic, complemented
7#20298911C211yesmaximal, characteristic, complemented
8#20298892C211yesmaximal, characteristic, complemented
9#20298887C211yesmaximal, characteristic, complemented
10#20298845C211yesmaximal, characteristic, complemented
11#20298844C211yesmaximal, characteristic, complemented
12#20298685C211yesmaximal, characteristic, complemented
13#20298674C211yesmaximal, characteristic, complemented
14#20298637C211yesmaximal, characteristic, complemented
15#428×C113C211yesmaximal, characteristic, complemented
16C2×#14268636C2211yescharacteristic
17C2×#14268630C2211yescharacteristic
18#16813621C2211yescharacteristic
19#16813621C2211yescharacteristic
20#16813612—21no—
21#16813610—21no—
22#16813608—21no—
23#16813602C2211yescharacteristic
24#16813601—21no—
25#16813601C2211yescharacteristic
26#16813600—21no—
27#16813597C2211yescharacteristic
28#16813596C2211yescharacteristic
29#16813595—21no—
30#16813587C2211yescharacteristic
31#16813584C2211yescharacteristic
32C4×C22⋊D113—21no—
33C4×C22⋊D113C2211yescharacteristic
34#16813580C2211yescharacteristic
35#16813579—21no—
36C4⋊C4×D113C2211yescharacteristic
37#16813556C2211yescharacteristic
38#16813555C2211yescharacteristic
39#16813555C2211yescharacteristic
40#16813555C2211yescharacteristic
41#16813553C2211yescharacteristic
42#16813551C2211yescharacteristic
43#16813547C2211yescharacteristic
44#16813545C2211yescharacteristic
45#16813545C2211yescharacteristic
46#16813544C2211yescharacteristic
47#16813542C2211yescharacteristic
48#16813542C2211yescharacteristic
49C22⋊#11744751C2211yescharacteristic
50#16813534C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C2×M16×C113C2211yescharacteristic
53#117×C113C2211yescharacteristic
54C2×C4⋊C4×C113C2211yescharacteristic
55#107×C113C2211yescharacteristic
56#107×C113C2211yescharacteristic
57#106×C113C2211yescharacteristic
58#106×C113C2211yescharacteristic
59C2×Dic226—21no—
60C2×Dic226—21no—
61C2×Dic226C2311yescharacteristic
62C2×D452—21no—
63C2×D452C2311yescharacteristic
64C2×C22⋊D113—21no—
65C2×C22⋊D113D411yescharacteristic
66C2×C4×D113—21no—
67C2×C4×D113—21no—
68C2×C4×D113C2311yescharacteristic
69#14268636—22no—
70#14268630—22no—
71C2×#11744751C2311yescharacteristic
72C2×#11744751C2311yescharacteristic
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×C113C2311yescharacteristic
95M16×C113—22no—
96C2×C8×C113C2311yescharacteristic
97C2×C8×C113C2311yescharacteristic
98C4⋊C4×C113—21no—
99C4⋊C4×C113C2311yescharacteristic
100C4⋊C4×C113C2311yescharacteristic
101C4⋊C4×C113C2311yescharacteristic
102C4⋊C4×C113C2311yescharacteristic
103C22⋊C4×C113—21no—
104C42×C113—21no—
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×C113C2×D411yescharacteristic
116C2×C4×C113C2411yescharacteristic
117C22⋊D113—22no—
118C22⋊D113—81no—
119C2×Dic113—21no—
120C2×Dic113—21no—
121C2×Dic113—21no—
122C2×Dic113C2×D411yescharacteristic
123C2×Dic113C2×D411yescharacteristic
124C2×Dic113C2×D411yescharacteristic
125D452—21no—
126D452—21no—
127D452—81no—
128C4×D113—21no—
129C4×D113—21no—
130C4×D113—42no—
131C4×D113—81no—
132Dic226—21no—
133Dic226—21no—
134Dic226—81no—
135Dic226—81no—
136C8×C113—21no—
137C8×C113#4112yes—
138#11744751—21no—
139#11744751—21no—
140C22×C113—21no—
141C22×C113—21no—
142C22×C113—21no—
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—41no—
160Dic113—41no—
161Dic113—41no—
162Dic113#13712yes—
163C2×C113—41no—
164C2×C113#54711yescharacteristic
165C2×C113C2×#13711yescharacteristic
166C2×C113#57611yescharacteristic
167D113—41no—
168D113—81no—
169#3357—1131nomaximal, Sylow
170C113#335711yescharacteristic, complemented, Sylow
171#555—1131no—
172#554—1131no—
173#500—1131no—
174#485—1131no—
175#485—1131no—
176#480—1131no—
177#480—1131no—
178#477—1131no—
179#476—1131no—
180#468—1131no—
181#468—1131no—
182C4×SD16—1131no—
183#436—1131no—
184#428—1131no—
185#428D11311yescharacteristic, complemented
186C2×SD16—1131no—
187C2×M16—1131no—
188C2×M16C2×D11311yescharacteristic
189C4⋊Q8—1131no—
190C4⋊Q8—1131no—
191#125—2261no—
192#124—2261no—
193#124—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—
205#117—1131no—
206#117—2261no—
207#117C2×D11311yescharacteristic
208C2×C4⋊C4—1131no—
209C2×C4⋊C4C2×D11311yescharacteristic
210#107—1131no—
211#107—1131no—
212#107—1131no—
213#107—1131no—
214#107C2×D11311yescharacteristic
215#107C2×D11311yescharacteristic
216#106—1131no—
217#106C2×D11311yescharacteristic
218#106C2×D11311yescharacteristic
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—
228C4×C8—1131no—
229C2×Q8—1131no—
230C2×Q8—2261no—
231C2×Q8—2261no—
232C2×D4—1131no—
233C2×D4—1131no—
234C2×D4—2261no—
235C2×D4—2261no—
236C22×C4—21no—
237C22×C4—1131no—
238C22×C4—2261no—
239C22×C4—2261no—
240C22×C4C22×D11311yescharacteristic
241SD16—2262no—
242M16—22no—
243M16—2262no—
244C2×C8—1131no—
245C2×C8—1131no—
246C2×C8C22×D11311yescharacteristic
247C2×C8C22×D11311yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—1131no—
250C4⋊C4—1131no—
251C4⋊C4—1131no—
252C4⋊C4—2261no—
253C4⋊C4—2261no—
254C4⋊C4—2261no—
255C4⋊C4—2261no—
256C4⋊C4—2261no—
257C4⋊C4—2261no—
258C4⋊C4C22×D11311yescharacteristic
259C4⋊C4C22×D11311yescharacteristic
260C4⋊C4C22×D11311yescharacteristic
261C4⋊C4C22×D11311yescharacteristic
262C22⋊C4—21no—
263C22⋊C4—1131no—
264C22⋊C4—1131no—
265C22⋊C4—2261no—
266C22⋊C4—2261no—
267C22⋊C4—2261no—
268C22⋊C4—2261no—
269C22⋊C4—2261no—
270C22⋊C4—2261no—
271C42—21no—
272C42—1131no—
273C42—2261no—
274C42—2261no—
275C23—1131no—
276C23—2261no—
277C23D4×D11311yescharacteristic
278Q8—9041no—
279Q8—9041no—
280Q8—2261no—
281Q8—2261no—
282D4—9041no—
283D4—9041no—
284D4—2262no—
285D4—2261no—
286D4—2261no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—81no—
294C2×C4—1131no—
295C2×C4—1131no—
296C2×C4—1131no—
297C2×C4—9041no—
298C2×C4—4522no—
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—21no—
313C22—4521no—
314C22—4521no—
315C22—4521no—
316C22—2261no—
317C22—2261no—
318C22—2261no—
319C22C2×D4×D11311yescharacteristic
320C4—21no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—41no—
325C4—1132no—
326C4—4521no—
327C4—4521no—
328C4—4521no—
329C4—2261no—
330C4—2261no—
331C4C2×#1426864711yescharacteristic
332C4#1681367011yescharacteristic
333C2—41no—
334C2—9041no—
335C2—4521no—
336C2#2029924911yescharacteristic
337C2#137×D11311yescharacteristic
338C2#2029940211yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#428×C113C2
socleC22×C113C22×D4
prime radical#20299311C2
hypercenter#428D113
hypocenterC113#3357
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
2. #20299303C2semidirect
3. #20299002C2semidirect
4. #20298942C2semidirect
5. #20298939C2semidirect
6. #20298913C2semidirect
7. #20298911C2semidirect
8. #20298892C2semidirect
9. #20298887C2semidirect
10. #20298845C2semidirect
11. #20298844C2semidirect
12. #20298685C2semidirect
13. #20298674C2semidirect
14. #20298637C2semidirect
15. #428×C113C2semidirect
170. C113#3357semidirect
185. #428D113semidirect

Maximal subgroups

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

subgroupindex
#202993112
#202993032
#202990022
#202989422
#202989392
#202989132
#202989112
#202988922
#202988872
#202988452
#202988442
#202986852
#202986742
#202986372
#428×C1132
#3357113