Finite Group Databasebeta

← #28400293

Subgroups — #28400293

Order 14464.

452 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#20299398C211yesmaximal, characteristic, complemented
2#20299396C211yesmaximal, characteristic, complemented
3C2×#16813642C211yesmaximal, characteristic, complemented
4C2×#16813630C211yesmaximal, characteristic, complemented
5#20298872C212yesmaximal, complemented
6#20298867C212yesmaximal, complemented
7#20298864C212yesmaximal, complemented
8#20298860C212yesmaximal, complemented
9C2×#16813557C211yesmaximal, characteristic, complemented
10#20298580C211yesmaximal, characteristic, complemented
11#413×C113C211yesmaximal, characteristic, complemented
12C2×#14268647C2211yescharacteristic
13C2×#14268647C2211yescharacteristic
14#16813655—21no—
15#16813655C2212yes—
16#16813653C2212yes—
17#16813652—21no—
18#16813650—21no—
19#16813650C2212yes—
20#16813648C2212yes—
21#16813647—21no—
22#16813644—22no—
23#16813642—22no—
24#16813642—21no—
25#16813642—21no—
26#16813642—21no—
27#16813642—21no—
28C2×#14268637C2211yescharacteristic, complemented
29C2×#14268635C2211yescharacteristic, complemented
30C2×#14268634C2211yescharacteristic, complemented
31C2×#14268632C2211yescharacteristic, complemented
32#16813630—21no—
33#16813630—21no—
34#16813630C2212yes—
35#16813630C2212yes—
36C2×#14268631C2211yescharacteristic
37C2×#14268630—21no—
38C22×#11744751C2211yescharacteristic
39C2×C8×D113—21no—
40#16813557C2212yescomplemented
41#16813557C2212yescomplemented
42#16813540C2212yescomplemented
43#16813538C2212yescomplemented
44C2×#41×C113C2211yescharacteristic
45C2×M16×C113C2211yescharacteristic
46C2×M16×C113C2211yescharacteristic
47#101×C113C2212yescomplemented
48#100×C113C2212yescomplemented
49#14268647—21no—
50#14268647—21no—
51#14268647—21no—
52#14268647—21no—
53#14268647—21no—
54#14268647—21no—
55#14268647D412yes—
56#14268647C2312yes—
57C2×Dic226D411yescharacteristic
58C2×Dic226C2311yescharacteristic
59C2×D452D411yescharacteristic
60C2×D452C2311yescharacteristic
61C2×C22⋊D113—21no—
62C2×C22⋊D113—21no—
63C2×C4×D113—21no—
64C2×C4×D113—21no—
65Dic452—22no—
66#14268637—22no—
67#14268637—21no—
68#14268637—21no—
69#14268636—22no—
70#14268636—22no—
71#14268635—22no—
72#14268635—21no—
73#14268635—21no—
74#14268634—22no—
75#14268634—21no—
76#14268634—21no—
77D904—22no—
78#14268632—22no—
79#14268632—21no—
80#14268632—21no—
81#14268631—21no—
82#14268631C2312yes—
83#14268630—22no—
84#14268630—22no—
85C2×#11744751—21no—
86C2×#11744751D411yescharacteristic
87C2×#11744751D411yescharacteristic
88C2×#11744751D411yescharacteristic
89C2×#11744751D411yescharacteristic
90C2×#11744751C2311yescharacteristic
91C2×#11744751C2311yescharacteristic
92C8×D113—22no—
93C8×D113—22no—
94#41×C113—21no—
95#41×C113—21no—
96#41×C113—21no—
97#41×C113—21no—
98C2×Q8×C113C2311yescharacteristic
99C2×D4×C113—21no—
100C2×D4×C113C2311yescharacteristic
101C22×C4×C113—21no—
102C22×C4×C113C2311yescharacteristic
103M16×C113—21no—
104M16×C113—21no—
105M16×C113C2312yes—
106M16×C113C2312yes—
107C2×C8×C113—21no—
108C2×C8×C113—21no—
109C23×C113—21no—
110C23×C113#4111yescharacteristic
111C22×D113—21no—
112C22×D113—21no—
113Q8×C113—21no—
114Q8×C113—21no—
115D4×C113—21no—
116D4×C113—21no—
117D4×C113—41no—
118D4×C113—41no—
119C2×C4×C113—21no—
120C2×C4×C113—41no—
121C2×C4×C113—41no—
122C2×C4×C113C2×D411yescharacteristic
123C2×C4×C113C2×D411yescharacteristic
124C2×C4×C113C2×D411yescharacteristic
125C2×C4×C113C2×D411yescharacteristic
126C2×C4×C113#4111yescharacteristic
127C2×C4×C113C2411yescharacteristic
128C22⋊D113—22no—
129C22⋊D113—22no—
130C22⋊D113—41no—
131C22⋊D113—41no—
132C2×Dic113—21no—
133C2×Dic113—21no—
134D452—21no—
135D452—21no—
136D452—21no—
137D452C2×D412yes—
138C4×D113—22no—
139C4×D113—22no—
140C4×D113—41no—
141C4×D113—41no—
142Dic226—21no—
143Dic226—21no—
144Dic226—21no—
145Dic226C2×D412yes—
146C8×C113—22no—
147C8×C113—22no—
148#11744751—22no—
149#11744751C2×D411yescharacteristic
150#11744751C2×D411yescharacteristic
151#11744751C2×D411yescharacteristic
152#11744751C2×D411yescharacteristic
153C22×C113—41no—
154C22×C113—41no—
155C22×C113—81no—
156C22×C113#12111yescharacteristic
157C22×C113#12111yescharacteristic
158C22×C113C2×#4111yescharacteristic
159C2×D113—22no—
160C2×D113—42no—
161C2×D113—41no—
162C2×D113—81no—
163C4×C113—41no—
164C4×C113#12111yescharacteristic
165C4×C113#12111yescharacteristic
166C4×C113C22×D411yescharacteristic
167C4×C113C22×D411yescharacteristic
168Dic113—22no—
169Dic113—41no—
170C2×C113—21no—
171C2×C113—21no—
172C2×C113—21no—
173C2×C113—81no—
174C2×C113C2×#12111yescharacteristic
175D113—42no—
176D113—81no—
177#3067—1131nomaximal, Sylow
178C113#306711yescharacteristic, complemented, Sylow
179#575—1131no—
180#575—1131no—
181C2×#135—1131no—
182C2×#131—1131no—
183#473—1132no—
184#472—1132no—
185#471—1132no—
186#471—1132no—
187C2×#108—1131no—
188#413—1131no—
189#413D11311yescharacteristic, complemented
190C2×#41—1131no—
191C2×#41—1131no—
192C2×#41C2×D11311yescharacteristic
193#137—1132no—
194#137—1132no—
195#137—2261no—
196#137—2261no—
197AGL(1,ℤ/8)—1132no—
198AGL(1,ℤ/8)—1132no—
199AGL(1,ℤ/8)—2261no—
200AGL(1,ℤ/8)—2261no—
201#135—2262no—
202#135—2261no—
203#135—2261no—
204#135—2261no—
205#135—2261no—
206#135—2262no—
207C2×Q16—1131no—
208C2×SD16—1131no—
209C2×SD16—1131no—
210C2×D8—1131no—
211#131—1132no—
212#131—1132no—
213#131—2261no—
214#131—2261no—
215C2×M16—1131no—
216C2×M16—2261no—
217C2×M16C2×D11311yescharacteristic
218C2×M16C2×D11311yescharacteristic
219C22×C8—1131no—
220C22×C8—2261no—
221#108—1132no—
222#108—1132no—
223#101—1132no—
224#101C2×D11312yescomplemented
225#100—1132no—
226#100C2×D11312yescomplemented
227#41—21no—
228#41—21no—
229#41—21no—
230#41—21no—
231#41—1132no—
232#41—1132no—
233#41—2261no—
234#41—2261no—
235#41—2261no—
236#41—2261no—
237#41—2261no—
238#41—2261no—
239C2×Q8—1131no—
240C2×Q8—1131no—
241C2×Q8C22×D11311yescharacteristic
242C2×D4—21no—
243C2×D4—1131no—
244C2×D4—1131no—
245C2×D4—2261no—
246C2×D4—2261no—
247C2×D4C22×D11311yescharacteristic
248C22×C4—21no—
249C22×C4—2261no—
250C22×C4—2261no—
251C22×C4C22×D11311yescharacteristic
252Q16—2262no—
253Q16—2261no—
254Q16—2261no—
255Q16—2262no—
256SD16—2262no—
257SD16—2262no—
258SD16—2261no—
259SD16—2261no—
260SD16—2261no—
261SD16—2261no—
262SD16—2262no—
263SD16—2262no—
264D8—2262no—
265D8—2261no—
266D8—2261no—
267D8—2262no—
268M16—21no—
269M16—21no—
270M16—1132no—
271M16—2262no—
272M16—2262no—
273M16—2261no—
274M16C22×D11312yes—
275M16C22×D11312yes—
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—1131no—
279C2×C8—1131no—
280C2×C8—1131no—
281C2×C8—1131no—
282C2×C8—1131no—
283C2×C8—1131no—
284C2×C8—2262no—
285C2×C8—2262no—
286C2×C8—2261no—
287C23—21no—
288C23—2261no—
289C23—2261no—
290C23#1426864711yescharacteristic
291Q8—21no—
292Q8—21no—
293Q8—1132no—
294Q8—2261no—
295Q8—2261no—
296Q8—2261no—
297D4—21no—
298D4—21no—
299D4—41no—
300D4—41no—
301D4—1132no—
302D4—4521no—
303D4—4521no—
304D4—2262no—
305D4—2262no—
306D4—2261no—
307D4—2261no—
308D4—2261no—
309C2×C4—21no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—4521no—
313C2×C4—4521no—
314C2×C4—2261no—
315C2×C4—2261no—
316C2×C4—2262no—
317C2×C4—2262no—
318C2×C4D4×D11311yescharacteristic
319C2×C4D4×D11311yescharacteristic
320C2×C4D4×D11311yescharacteristic
321C2×C4D4×D11311yescharacteristic
322C2×C4#1426864711yescharacteristic
323C2×C4C23×D11311yescharacteristic
324C8—22no—
325C8—22no—
326C8—1131no—
327C8—1131no—
328C8—1131no—
329C8—1131no—
330C8—2262no—
331C22—41no—
332C22—41no—
333C22—81no—
334C22—9041no—
335C22—4522no—
336C22—4521no—
337C22—2262no—
338C22#1681359511yescharacteristic
339C22#1681359511yescharacteristic
340C22C2×#1426864711yescharacteristic
341C4—41no—
342C4—4521no—
343C4—2262no—
344C4#1681359511yescharacteristic
345C4#1681359511yescharacteristic
346C4C2×D4×D11311yescharacteristic
347C4C2×D4×D11311yescharacteristic
348C2—21no—
349C2—21no—
350C2—21no—
351C2—81no—
352C2—9041no—
353C2—4522no—
354C2C2×#1681359511yescharacteristic
subgroupG/H
centerC4#16813595
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#413×C113C2
socleC2×C113C2×#121
hypercenter#413D113
hypocenterC113#3067
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C4 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
1. #20299398C2semidirect
2. #20299396C2semidirect
3. C2×#16813642C2semidirect
4. C2×#16813630C2semidirect
5. #20298872C2semidirect
6. #20298867C2semidirect
7. #20298864C2semidirect
8. #20298860C2semidirect
9. C2×#16813557C2semidirect
10. #20298580C2semidirect
11. #413×C113C2semidirect
28. C2×#14268637C22semidirect
29. C2×#14268635C22semidirect
30. C2×#14268634C22semidirect
31. C2×#14268632C22semidirect
40. #16813557C22semidirect
41. #16813557C22semidirect
42. #16813540C22semidirect
43. #16813538C22semidirect
47. #101×C113C22semidirect
48. #100×C113C22semidirect
178. C113#3067semidirect
189. #413D113semidirect
224. #101C2×D113semidirect
226. #100C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202993982
#202993962
C2×#168136422
C2×#168136302
#202988722
#202988672
#202988642
#202988602
C2×#168135572
#202985802
#413×C1132
#3067113