Finite Group Databasebeta

← #28399396

Subgroups — #28399396

Order 14464.

484 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
1C2×#16813651C211yesmaximal, characteristic
2C4×#14268646C211yesmaximal, characteristic
3C4×Q8×D113C211yesmaximal, characteristic, complemented
4#20298706C211yesmaximal, characteristic, complemented
5#20298703C211yesmaximal, characteristic, complemented
6#20298698C211yesmaximal, characteristic, complemented
7#20298692C211yesmaximal, characteristic, complemented
8#20298690C211yesmaximal, characteristic, complemented
9#20298689C211yesmaximal, characteristic, complemented
10SD16×Dic113C211yesmaximal, characteristic, complemented
11#20298639C211yesmaximal, characteristic, complemented
12#20298605C211yesmaximal, characteristic, complemented
13#20298596C211yesmaximal, characteristic
14#20298550C211yesmaximal, characteristic, complemented
15#440×C113C211yesmaximal, characteristic, complemented
16C2×#14268646C2211yescharacteristic
17C2×Q8×D113C2211yescharacteristic
18#16813651C418yescomplemented
19C2×Dic452C2211yescharacteristic
20C2×#14268637C2211yescharacteristic
21C2×#14268635C2211yescharacteristic
22C2×#14268630C2211yescharacteristic
23C2×#14268630C2211yescharacteristic
24Q8×Dic113C2211yescharacteristic
25C4×Dic226—21no—
26C4×Dic226C2211yescharacteristic
27C4×Dic226C2211yescharacteristic
28#16813587—21no—
29#16813587C2211yescharacteristic
30#16813587C2211yescharacteristic
31D4×Dic113C2211yescharacteristic
32C4×C22⋊D113—21no—
33#16813582—21no—
34#16813580C2211yescharacteristic
35#16813578—21no—
36C4⋊C4×D113—21no—
37C4⋊C4×D113C2211yescharacteristic
38C2×C4×Dic113—21no—
39C42×D113—21no—
40C42×D113C2211yescharacteristic
41#16813555C2211yescharacteristic
42#16813554C2211yescharacteristic
43#16813553C2211yescharacteristic
44#16813547C2211yescharacteristic
45#16813547C2211yescharacteristic
46#16813546C2211yescharacteristic
47#16813545C2211yescharacteristic
48#16813545C2211yescharacteristic
49#16813543C2211yescharacteristic
50#16813533C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C8×Dic113C2211yescharacteristic
53C2×SD16×C113C2211yescharacteristic
54C4×Q8×C113C2211yescharacteristic
55C4×D4×C113C2211yescharacteristic
56#107×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58#102×C113C2211yescharacteristic
59#97×C113C2211yescharacteristic
60#14268646—22no—
61#14268646C2×C414yes—
62C2×Dic226—21no—
63C2×Dic226C2311yescharacteristic
64C2×Dic226C2311yescharacteristic
65Q8×D113—22no—
66Q8×D113C2×C414yescomplemented
67C2×C22⋊D113—21no—
68C22×Dic113—21no—
69C22×Dic113—21no—
70C2×C4×D113—21no—
71C2×C4×D113—21no—
72C2×C4×D113D411yescharacteristic
73C2×C4×D113D411yescharacteristic
74C2×C4×D113C2311yescharacteristic
75Dic452C2×C414yescomplemented
76#14268637C2×C414yescomplemented
77#14268635C2×C414yescomplemented
78#14268630—22no—
79#14268630C2×C414yescomplemented
80C2×#11744751C2311yescharacteristic
81C2×#11744751C2311yescharacteristic
82C4⋊Dic113—21no—
83C4⋊Dic113C2311yescharacteristic
84C4⋊Dic113C2311yescharacteristic
85#14268626—21no—
86#14268626—21no—
87#14268626—21no—
88#14268626—21no—
89#14268626—21no—
90C22⋊Dic113—21no—
91#14268624—21no—
92C4×Dic113—21no—
93C4×Dic113—21no—
94C4×Dic113—21no—
95C4×Dic113—21no—
96C4×Dic113—21no—
97C4×Dic113—21no—
98C4×Dic113D411yescharacteristic
99C4×Dic113D411yescharacteristic
100C4×Dic113C2311yescharacteristic
101C2×Q8×C113C2311yescharacteristic
102C2×D4×C113C2311yescharacteristic
103C22×C4×C113—21no—
104SD16×C113C2×C414yescomplemented
105C2×C8×C113C2311yescharacteristic
106C2×C8×C113C2311yescharacteristic
107C4⋊C4×C113—21no—
108C4⋊C4×C113C2311yescharacteristic
109C4⋊C4×C113C2311yescharacteristic
110C22⋊C4×C113—21no—
111C42×C113—21no—
112C42×C113C2311yescharacteristic
113C23×C113—21no—
114C22×D113C2×D411yescharacteristic
115Q8×C113—21no—
116Q8×C113C22×C412yes—
117D4×C113—21no—
118D4×C113C22×C412yes—
119C2×C4×C113—21no—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—42no—
123C2×C4×C113C2×D411yescharacteristic
124C2×C4×C113C2×D411yescharacteristic
125C2×C4×C113C2411yescharacteristic
126C22⋊D113—24no—
127C2×Dic113—21no—
128C2×Dic113—21no—
129C2×Dic113—24no—
130C2×Dic113—21no—
131C2×Dic113—21no—
132C2×Dic113—42no—
133C2×Dic113C2×D411yescharacteristic
134C2×Dic113C2×D411yescharacteristic
135C2×Dic113C2×D411yescharacteristic
136C4×D113—24no—
137C4×D113—22no—
138C4×D113—41no—
139C4×D113—42no—
140C4×D113C22×C412yes—
141C4×D113#4112yes—
142Dic226—21no—
143Dic226—21no—
144Dic226—24no—
145Dic226C22×C412yes—
146Dic226C22×C412yes—
147C8×C113—21no—
148C8×C113C22×C412yes—
149#11744751—21no—
150#11744751C22×C412yes—
151C22×C113—22no—
152C22×C113—41no—
153C22×C113—41no—
154C22×C113C22×D411yescharacteristic
155C2×D113—21no—
156C2×D113—21no—
157C2×D113C4×D412yes—
158C4×C113—22no—
159C4×C113—21no—
160C4×C113—21no—
161C4×C113—41no—
162C4×C113—41no—
163C4×C113C23×C411yescharacteristic
164C4×C113C2×#4111yescharacteristic
165Dic113—22no—
166Dic113—22no—
167Dic113—21no—
168Dic113—41no—
169Dic113—41no—
170Dic113C4×D412yes—
171Dic113#13712yescomplemented
172C2×C113—42no—
173C2×C113C2×C4×D411yescharacteristic
174C2×C113C2×#13711yescharacteristic
175C2×C113#57511yescharacteristic
176D113—22no—
177C4×#137—1131nomaximal, Sylow
178C113C4×#13711yescharacteristic, complemented, Sylow
179C2×#137—1131no—
180C4×#41—1131no—
181C2×C4×Q8—1131no—
182#441—1131no—
183#441—1131no—
184#440—1131no—
185#440D11311yescharacteristic, complemented
186C4×Q16—1131no—
187C4×Q16—1131no—
188C4×SD16—1131no—
189C4×SD16—1131no—
190#428—1131no—
191#419—1131no—
192#417—1131no—
193C4×M16—1131no—
194C2×#41—1131no—
195C22×Q8—1131no—
196#137—1138no—
197C2×Q16—1131no—
198C2×Q16—1131no—
199C2×SD16—1131no—
200C2×SD16C2×D11311yescharacteristic
201C2×M16—1131no—
202C2×M16—1131no—
203C4×Q8—1131no—
204C4×Q8—1131no—
205C4×Q8—1131no—
206C4×Q8—1131no—
207C4×Q8—1131no—
208C4×Q8—2261no—
209C4×Q8—2261no—
210C4×Q8C2×D11311yescharacteristic
211C4×D4—1131no—
212C4×D4—2261no—
213C4×D4—2261no—
214C4×D4C2×D11311yescharacteristic
215#117—1131no—
216#117—2261no—
217C2×C4⋊C4—1131no—
218C2×C4⋊C4—2261no—
219C2×C42—1131no—
220C2×C42—2261no—
221C2×C42—2261no—
222#107—1131no—
223#107C2×D11311yescharacteristic
224#106—1131no—
225#106—1131no—
226#103—1131no—
227#103—1131no—
228#103—1131no—
229#103—1131no—
230#103—1131no—
231#103C2×D11311yescharacteristic
232#102—1131no—
233#102C2×D11311yescharacteristic
234#97—1131no—
235#97C2×D11311yescharacteristic
236C4×C8—1131no—
237C4×C8—1131no—
238#41—1134no—
239#41—2262no—
240C2×Q8—1134no—
241C2×Q8—1131no—
242C2×Q8—1131no—
243C2×Q8—2261no—
244C2×Q8—2262no—
245C2×Q8C22×D11311yescharacteristic
246C2×D4—2261no—
247C2×D4C22×D11311yescharacteristic
248C22×C4—21no—
249C22×C4—1131no—
250C22×C4—1131no—
251C22×C4—1131no—
252C22×C4—2261no—
253C22×C4—2261no—
254C22×C4—2261no—
255C22×C4—2261no—
256Q16—1134no—
257Q16—1134no—
258SD16—1134no—
259SD16C4×D11314yescomplemented
260M16—1134no—
261M16—2262no—
262C2×C8—1131no—
263C2×C8—1131no—
264C2×C8C22×D11311yescharacteristic
265C2×C8C22×D11311yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—1131no—
268C4⋊C4—1131no—
269C4⋊C4—2261no—
270C4⋊C4—2261no—
271C4⋊C4—2261no—
272C4⋊C4—2261no—
273C4⋊C4—2261no—
274C4⋊C4—2261no—
275C4⋊C4C22×D11311yescharacteristic
276C4⋊C4C22×D11311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—2261no—
279C22⋊C4—2261no—
280C42—21no—
281C42—1131no—
282C42—1131no—
283C42—1131no—
284C42—2261no—
285C42—2261no—
286C42—2261no—
287C42—2261no—
288C42—2261no—
289C42—2261no—
290C42C22×D11311yescharacteristic
291C23—21no—
292C23—1131no—
293Q8—21no—
294Q8—1132no—
295Q8—1132no—
296Q8—2264no—
297Q8—2261no—
298Q8—2261no—
299Q8C2×C4×D11312yes—
300D4—21no—
301D4—2264no—
302D4C2×C4×D11312yes—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—42no—
307C2×C4—1131no—
308C2×C4—1131no—
309C2×C4—1132no—
310C2×C4—1132no—
311C2×C4—1131no—
312C2×C4—4521no—
313C2×C4—4522no—
314C2×C4—4522no—
315C2×C4—2262no—
316C2×C4—2264no—
317C2×C4—2264no—
318C2×C4—2261no—
319C2×C4—2261no—
320C2×C4—2261no—
321C2×C4—2261no—
322C2×C4D4×D11311yescharacteristic
323C2×C4D4×D11311yescharacteristic
324C2×C4C23×D11311yescharacteristic
325C8—21no—
326C8—1132no—
327C8—2261no—
328C8C2×C4×D11312yes—
329C22—22no—
330C22—41no—
331C22—41no—
332C22—1132no—
333C22—2261no—
334C22—2261no—
335C22C2×D4×D11311yescharacteristic
336C4—22no—
337C4—21no—
338C4—21no—
339C4—41no—
340C4—41no—
341C4—1132no—
342C4—1132no—
343C4—4521no—
344C4—4521no—
345C4—2262no—
346C4—2262no—
347C4—2261no—
348C4C22×C4×D11311yescharacteristic
349C4#41×D11311yescharacteristic
350C2—42no—
351C2—2262no—
352C2C4×D4×D11311yescharacteristic
353C2#137×D11311yescharacteristic
354C2#2029939411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutatorC4×C113C23×C4
FrattiniC2×C4C23×D113
Fitting#440×C113C2
socleC22×C113C22×D4
prime radicalC2×#14268646C22
cosocleC2×C4×C113C24
hypercenter#440D113
hypocenterC113C4×#137
LCSG ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
3. C4×Q8×D113C2semidirect
4. #20298706C2semidirect
5. #20298703C2semidirect
6. #20298698C2semidirect
7. #20298692C2semidirect
8. #20298690C2semidirect
9. #20298689C2semidirect
10. SD16×Dic113C2semidirect
11. #20298639C2semidirect
12. #20298605C2semidirect
14. #20298550C2semidirect
15. #440×C113C2semidirect
18. #16813651C4semidirect
66. Q8×D113C2×C4semidirect
75. Dic452C2×C4semidirect
76. #14268637C2×C4semidirect
77. #14268635C2×C4semidirect
79. #14268630C2×C4semidirect
104. SD16×C113C2×C4semidirect
171. Dic113#137semidirect
178. C113C4×#137semidirect
185. #440D113semidirect
259. SD16C4×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136512
C4×#142686462
C4×Q8×D1132
#202987062
#202987032
#202986982
#202986922
#202986902
#202986892
SD16×Dic1132
#202986392
#202986052
#202985962
#202985502
#440×C1132
C4×#137113