Finite Group Databasebeta

← #28401130

Subgroups — #28401130

Order 14464.

412 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#20299152C211yesmaximal, characteristic, complemented
2#20299145C211yesmaximal, characteristic
3#20298995C211yesmaximal, characteristic, complemented
4#20298969C211yesmaximal, characteristic, complemented
5#20298947C211yesmaximal, characteristic, complemented
6#20298943C211yesmaximal, characteristic, complemented
7#20298830C211yesmaximal, characteristic, complemented
8#20298828C211yesmaximal, characteristic, complemented
9#20298826C211yesmaximal, characteristic, complemented
10#20298824C211yesmaximal, characteristic, complemented
11C4×#14268636C211yesmaximal, characteristic, complemented
12C4×#14268634C211yesmaximal, characteristic, complemented
13C4×#14268635C211yesmaximal, characteristic, complemented
14C4×C8×D113C211yesmaximal, characteristic, complemented
15C4×SD16×C113C211yesmaximal, characteristic, complemented
16C2×#14268647—21no—
17C2×#14268636C2211yescharacteristic
18C2×#14268635C2211yescharacteristic
19C2×#14268634C2211yescharacteristic
20C2×C8×D113C2211yescharacteristic
21C2×C8×D113C2211yescharacteristic
22#16813621C2211yescharacteristic
23#16813621C2211yescharacteristic
24#16813620C2211yescharacteristic
25#16813618C2211yescharacteristic
26#16813612—21no—
27#16813608—21no—
28#16813602C2211yescharacteristic
29#16813600—21no—
30#16813598C2211yescharacteristic
31#16813597C2211yescharacteristic
32#16813595—21no—
33#16813593C2211yescharacteristic
34C4×Dic226—21no—
35C4×Dic226C2211yescharacteristic
36C4×D452C2211yescharacteristic
37C4×C22⋊D113—21no—
38#16813579—21no—
39C42×D113C2211yescharacteristic
40#16813554C2211yescharacteristic
41#16813553C2211yescharacteristic
42#16813553C2211yescharacteristic
43#16813547C2211yescharacteristic
44#16813546C2211yescharacteristic
45#16813545C2211yescharacteristic
46#16813544C2211yescharacteristic
47#16813543C2211yescharacteristic
48#16813542C2211yescharacteristic
49C4×#11744751C2211yescharacteristic
50C8×Dic113C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C2×SD16×C113C2211yescharacteristic
53C4×Q8×C113C2211yescharacteristic
54C4×D4×C113C2211yescharacteristic
55#106×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58C4×C8×C113C2211yescharacteristic
59#14268647—44no—
60C2×Dic226—21no—
61C2×Dic226—21no—
62C2×Dic226C2311yescharacteristic
63C2×D452—21no—
64C2×D452C2311yescharacteristic
65C2×C22⋊D113—21no—
66C2×C22⋊D113—21no—
67C2×C22⋊D113—21no—
68C2×C4×D113—21no—
69C2×C4×D113D411yescharacteristic
70C2×C4×D113D411yescharacteristic
71C2×C4×D113C2311yescharacteristic
72#14268636—22no—
73#14268635—22no—
74#14268634—22no—
75C2×#11744751C2311yescharacteristic
76C2×#11744751C2311yescharacteristic
77C8×D113—22no—
78C8×D113—22no—
79C4⋊Dic113—21no—
80C4⋊Dic113C2311yescharacteristic
81C4⋊Dic113C2311yescharacteristic
82#14268626—21no—
83#14268626—21no—
84#14268626—21no—
85#14268626—21no—
86#14268626—21no—
87#14268626—21no—
88C22⋊Dic113—21no—
89#14268624—21no—
90#14268624—21no—
91#14268624—21no—
92#14268624—21no—
93C4×Dic113—21no—
94C4×Dic113D411yescharacteristic
95C4×Dic113D411yescharacteristic
96C4×Dic113C2311yescharacteristic
97C2×Q8×C113C2311yescharacteristic
98C2×D4×C113C2311yescharacteristic
99C22×C4×C113—21no—
100SD16×C113—22no—
101C2×C8×C113C2311yescharacteristic
102C2×C8×C113C2311yescharacteristic
103C4⋊C4×C113—21no—
104C4⋊C4×C113C2311yescharacteristic
105C4⋊C4×C113C2311yescharacteristic
106C22⋊C4×C113—21no—
107C42×C113—21no—
108C42×C113C2311yescharacteristic
109C23×C113—21no—
110C22×D113—21no—
111C22×D113C2×D411yescharacteristic
112Q8×C113—21no—
113Q8×C113—21no—
114D4×C113—21no—
115D4×C113—21no—
116C2×C4×C113—21no—
117C2×C4×C113—21no—
118C2×C4×C113—21no—
119C2×C4×C113—42no—
120C2×C4×C113C2×D411yescharacteristic
121C2×C4×C113C2×D411yescharacteristic
122C2×C4×C113C2411yescharacteristic
123C22⋊D113—42no—
124C22⋊D113—42no—
125C22⋊D113—42no—
126C2×Dic113—21no—
127C2×Dic113—21no—
128C2×Dic113—21no—
129C2×Dic113C2×D411yescharacteristic
130C2×Dic113C2×D411yescharacteristic
131C2×Dic113C2×D411yescharacteristic
132D452—21no—
133D452—21no—
134D452—42no—
135C4×D113—21no—
136C4×D113—21no—
137C4×D113—22no—
138C4×D113—42no—
139C4×D113SD1614yescomplemented
140Dic226—21no—
141Dic226—21no—
142Dic226—42no—
143Dic226—42no—
144C8×C113—21no—
145C8×C113#4112yescomplemented
146#11744751—21no—
147#11744751#4112yescomplemented
148C22×C113—41no—
149C22×C113—41no—
150C22×C113—41no—
151C22×C113C22×D411yescharacteristic
152C2×D113—21no—
153C2×D113—21no—
154C2×D113—41no—
155C2×D113—41no—
156C2×D113—41no—
157C2×D113C2×SD1612yes—
158C4×C113—21no—
159C4×C113—41no—
160C4×C113—41no—
161C4×C113—41no—
162C4×C113C2×SD1612yes—
163C4×C113C2×#4111yescharacteristic
164C4×C113C2×#4111yescharacteristic
165Dic113—21no—
166Dic113—41no—
167Dic113—41no—
168Dic113—41no—
169Dic113C2×SD1612yes—
170Dic113#13512yes—
171C2×C113—81no—
172C2×C113#53211yescharacteristic
173C2×C113C22×SD1611yescharacteristic
174C2×C113C2×#13511yescharacteristic
175D113—22no—
176D113—81no—
177#3167—1131nomaximal, Sylow
178C113#316711yescharacteristic, complemented, Sylow
179#533—1131no—
180#532—1131no—
181#498—1131no—
182#492—1131no—
183#487—1131no—
184#486—1131no—
185#465—1131no—
186#465—1131no—
187#465—1131no—
188#465—1131no—
189C4×SD16—1131no—
190C4×SD16—1131no—
191C4×SD16—1131no—
192C4×SD16D11311yescharacteristic, complemented
193C2×C4×C8—1131no—
194C2×#41—2261no—
195C2×SD16—1131no—
196C2×SD16—1131no—
197C2×SD16—1131no—
198C2×SD16C2×D11311yescharacteristic
199C22×C8—1131no—
200C22×C8—1131no—
201C4⋊Q8—1131no—
202C4⋊Q8—1131no—
203C4⋊Q8—1131no—
204#127—1131no—
205#125—2261no—
206#124—2261no—
207C22⋊Q8—1131no—
208C22⋊Q8—1131no—
209C22⋊Q8—2261no—
210#121—1131no—
211#121—1131no—
212#121—2261no—
213C4×Q8—1131no—
214C4×Q8—2261no—
215C4×Q8C2×D11311yescharacteristic
216C4×D4—1131no—
217C4×D4—2261no—
218C4×D4C2×D11311yescharacteristic
219#117—2261no—
220C2×C42—1131no—
221#106—1131no—
222#106—1131no—
223#106—1131no—
224#106C2×D11311yescharacteristic
225#103—1131no—
226#103—1131no—
227#103—1131no—
228#103C2×D11311yescharacteristic
229#102—1131no—
230#102—1131no—
231#102—1131no—
232#102C2×D11311yescharacteristic
233C4×C8—1131no—
234C4×C8—1131no—
235C4×C8—1131no—
236C4×C8C2×D11311yescharacteristic
237#41—4524no—
238C2×Q8—1131no—
239C2×Q8—2261no—
240C2×Q8—2261no—
241C2×Q8C22×D11311yescharacteristic
242C2×D4—1131no—
243C2×D4—2261no—
244C2×D4—2261no—
245C2×D4—2261no—
246C2×D4—2261no—
247C2×D4C22×D11311yescharacteristic
248C22×C4—21no—
249C22×C4—1131no—
250C22×C4—1131no—
251C22×C4—1131no—
252C22×C4—2261no—
253SD16—22no—
254SD16—2262no—
255SD16—2262no—
256SD16—2262no—
257C2×C8—1131no—
258C2×C8—1131no—
259C2×C8—2262no—
260C2×C8—2262no—
261C2×C8C22×D11311yescharacteristic
262C2×C8C22×D11311yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—1131no—
265C4⋊C4—1131no—
266C4⋊C4—2261no—
267C4⋊C4—2261no—
268C4⋊C4—2261no—
269C4⋊C4—2261no—
270C4⋊C4—2261no—
271C4⋊C4—2261no—
272C4⋊C4—2261no—
273C4⋊C4C22×D11311yescharacteristic
274C4⋊C4C22×D11311yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—2261no—
277C22⋊C4—2261no—
278C22⋊C4—2261no—
279C22⋊C4—2261no—
280C22⋊C4—2261no—
281C42—21no—
282C42—1131no—
283C42—1131no—
284C42—1131no—
285C42—2261no—
286C42C22×D11311yescharacteristic
287C23—21no—
288C23—1131no—
289C23—2261no—
290Q8—21no—
291Q8—21no—
292Q8—4522no—
293Q8—4522no—
294Q8—2261no—
295Q8—2261no—
296D4—21no—
297D4—21no—
298D4—4522no—
299D4—4522no—
300D4—4522no—
301D4—4522no—
302D4—2261no—
303D4—2261no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—42no—
308C2×C4—1131no—
309C2×C4—1131no—
310C2×C4—1134no—
311C2×C4—1131no—
312C2×C4—4522no—
313C2×C4—2262no—
314C2×C4—2261no—
315C2×C4—2261no—
316C2×C4—2261no—
317C2×C4—2261no—
318C2×C4—2261no—
319C2×C4D4×D11311yescharacteristic
320C2×C4D4×D11311yescharacteristic
321C2×C4C23×D11311yescharacteristic
322C8—21no—
323C8—1132no—
324C8—2261no—
325C8#1426864712yescomplemented
326C22—41no—
327C22—41no—
328C22—41no—
329C22—1132no—
330C22—4521no—
331C22—4521no—
332C22—4521no—
333C22—2261no—
334C22—2261no—
335C22C2×D4×D11311yescharacteristic
336C4—21no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—1132no—
341C4—1132no—
342C4—4521no—
343C4—4521no—
344C4—4521no—
345C4—2261no—
346C4SD16×D11312yes—
347C4#41×D11311yescharacteristic
348C4C2×#1426864711yescharacteristic
349C2—81no—
350C2—9041no—
351C2—2262no—
352C2#2029914511yescharacteristic
353C2C2×SD16×D11311yescharacteristic
354C2#135×D11311yescharacteristic
subgroupG/H
centerC2×C4D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC4×SD16×C113C2
socleC22×C113C22×D4
prime radical#20299145C2
hypercenterC4×SD16D113
hypocenterC113#3167
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #20299152C2semidirect
3. #20298995C2semidirect
4. #20298969C2semidirect
5. #20298947C2semidirect
6. #20298943C2semidirect
7. #20298830C2semidirect
8. #20298828C2semidirect
9. #20298826C2semidirect
10. #20298824C2semidirect
11. C4×#14268636C2semidirect
12. C4×#14268634C2semidirect
13. C4×#14268635C2semidirect
14. C4×C8×D113C2semidirect
15. C4×SD16×C113C2semidirect
139. C4×D113SD16semidirect
145. C8×C113#41semidirect
147. #11744751#41semidirect
178. C113#3167semidirect
192. C4×SD16D113semidirect
325. C8#14268647semidirect

Maximal subgroups

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

subgroupindex
#202991522
#202991452
#202989952
#202989692
#202989472
#202989432
#202988302
#202988282
#202988262
#202988242
C4×#142686362
C4×#142686342
C4×#142686352
C4×C8×D1132
C4×SD16×C1132
#3167113