Finite Group Databasebeta

← #28399390

Subgroups — #28399390

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×#16813654C211yesmaximal, characteristic
2C4×#14268648C211yesmaximal, characteristic
3C4×Q8×D113C211yesmaximal, characteristic, complemented
4#20298703C211yesmaximal, characteristic, complemented
5#20298700C211yesmaximal, characteristic, complemented
6#20298696C211yesmaximal, characteristic, complemented
7Q16×Dic113C211yesmaximal, characteristic, complemented
8#20298690C211yesmaximal, characteristic, complemented
9#20298685C211yesmaximal, characteristic, complemented
10#20298683C211yesmaximal, characteristic, complemented
11#20298637C211yesmaximal, characteristic, complemented
12#20298605C211yesmaximal, characteristic, complemented
13#20298598C211yesmaximal, characteristic
14#20298550C211yesmaximal, characteristic, complemented
15#441×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×Q8×D113C2211yescharacteristic
18#16813654C418yescomplemented
19C2×#14268637C2211yescharacteristic
20C2×#14268636C2211yescharacteristic
21C2×#14268634C2211yescharacteristic
22C2×#14268630C2211yescharacteristic
23C2×#14268630C2211yescharacteristic
24Q8×Dic113C2211yescharacteristic
25Q8×Dic113C2211yescharacteristic
26C4×Dic226—21no—
27C4×Dic226C2211yescharacteristic
28#16813587—21no—
29#16813587C2211yescharacteristic
30C4×D452—21no—
31C4×D452C2211yescharacteristic
32#16813584—21no—
33#16813584C2211yescharacteristic
34#16813580—21no—
35#16813580C2211yescharacteristic
36C4⋊C4×D113—21no—
37C4⋊C4×D113C2211yescharacteristic
38C42×D113—21no—
39C42×D113—21no—
40C42×D113C2211yescharacteristic
41#16813556C2211yescharacteristic
42#16813555C2211yescharacteristic
43#16813553C2211yescharacteristic
44#16813547C2211yescharacteristic
45#16813546C2211yescharacteristic
46#16813546C2211yescharacteristic
47#16813545C2211yescharacteristic
48#16813544C2211yescharacteristic
49#16813542C2211yescharacteristic
50#16813533C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C8×Dic113C2211yescharacteristic
53C2×Q16×C113C2211yescharacteristic
54C4×Q8×C113C2211yescharacteristic
55C4×Q8×C113C2211yescharacteristic
56#106×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58#103×C113C2211yescharacteristic
59#97×C113C2211yescharacteristic
60#14268648—22no—
61#14268648C2×C414yes—
62C2×Dic226—21no—
63C2×Dic226C2311yescharacteristic
64Q8×D113—22no—
65Q8×D113C2×C414yescomplemented
66C2×D452—21no—
67C2×D452C2311yescharacteristic
68C2×C4×D113—21no—
69C2×C4×D113—21no—
70C2×C4×D113—21no—
71C2×C4×D113—21no—
72C2×C4×D113—21no—
73C2×C4×D113D411yescharacteristic
74C2×C4×D113D411yescharacteristic
75C2×C4×D113C2311yescharacteristic
76#14268637C2×C414yescomplemented
77#14268636C2×C414yescomplemented
78#14268634C2×C414yescomplemented
79#14268630—22no—
80#14268630C2×C414yescomplemented
81C2×#11744751C2311yescharacteristic
82C2×#11744751C2311yescharacteristic
83C4⋊Dic113—21no—
84C4⋊Dic113—21no—
85C4⋊Dic113C2311yescharacteristic
86C4⋊Dic113C2311yescharacteristic
87#14268626—21no—
88#14268626—21no—
89#14268626—21no—
90#14268624—21no—
91#14268624—21no—
92#14268624—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×Q8×C113C2311yescharacteristic
103Q16×C113C2×C414yescomplemented
104C2×C8×C113C2311yescharacteristic
105C2×C8×C113C2311yescharacteristic
106C4⋊C4×C113—21no—
107C4⋊C4×C113—21no—
108C4⋊C4×C113C2311yescharacteristic
109C4⋊C4×C113C2311yescharacteristic
110C42×C113—21no—
111C42×C113—21no—
112C42×C113C2311yescharacteristic
113C22×D113—21no—
114C22×D113C2×D411yescharacteristic
115Q8×C113—21no—
116Q8×C113—21no—
117Q8×C113C22×C412yes—
118Q8×C113C22×C412yes—
119C2×C4×C113—21no—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113C2×D411yescharacteristic
124C2×C4×C113C2×D411yescharacteristic
125C2×C4×C113C2411yescharacteristic
126C2×Dic113—21no—
127C2×Dic113—21no—
128C2×Dic113—21no—
129C2×Dic113C2×D411yescharacteristic
130C2×Dic113C2×D411yescharacteristic
131C2×Dic113C2×D411yescharacteristic
132D452—24no—
133D452—21no—
134D452C22×C412yes—
135C4×D113—24no—
136C4×D113—24no—
137C4×D113—22no—
138C4×D113—41no—
139C4×D113—42no—
140C4×D113—42no—
141C4×D113—42no—
142C4×D113C22×C412yes—
143C4×D113#4112yes—
144Dic226—21no—
145Dic226—24no—
146Dic226C22×C412yes—
147C8×C113—21no—
148C8×C113C22×C412yes—
149#11744751—21no—
150#11744751C22×C412yes—
151C22×C113C22×D411yescharacteristic
152C2×D113—21no—
153C2×D113—21no—
154C2×D113—22no—
155C2×D113—41no—
156C2×D113—41no—
157C2×D113C4×D412yes—
158C4×C113—22no—
159C4×C113—22no—
160C4×C113—21no—
161C4×C113—21no—
162C4×C113—41no—
163C4×C113—41no—
164C4×C113C23×C411yescharacteristic
165C4×C113C2×#4111yescharacteristic
166Dic113—22no—
167Dic113—21no—
168Dic113—41no—
169Dic113—41no—
170Dic113C4×D412yes—
171Dic113#13712yescomplemented
172C2×C113C2×C4×D411yescharacteristic
173C2×C113C2×#13711yescharacteristic
174C2×C113#57511yescharacteristic
175D113—22no—
176D113—42no—
177C4×#137—1131nomaximal, Sylow
178C113C4×#13711yescharacteristic, complemented, Sylow
179C2×#137—1131no—
180C4×#41—1131no—
181C2×C4×Q8—1131no—
182#441—1131no—
183#441D11311yescharacteristic, complemented
184#440—1131no—
185#440—1131no—
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×Q16C2×D11311yescharacteristic
199C2×SD16—1131no—
200C2×SD16—1131no—
201C2×M16—1131no—
202C2×M16—1131no—
203C4×Q8—1131no—
204C4×Q8—1131no—
205C4×Q8—1131no—
206C4×Q8—1131no—
207C4×Q8—2261no—
208C4×Q8—2261no—
209C4×Q8C2×D11311yescharacteristic
210C4×Q8C2×D11311yescharacteristic
211C4×D4—1131no—
212C4×D4—1131no—
213C4×D4—2261no—
214C4×D4—2261no—
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#107—1131no—
224#106—1131no—
225#106C2×D11311yescharacteristic
226#103—1131no—
227#103—1131no—
228#103—1131no—
229#103—1131no—
230#103C2×D11311yescharacteristic
231#103C2×D11311yescharacteristic
232#102—1131no—
233#102—1131no—
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—2261no—
243C2×Q8—2262no—
244C2×Q8C22×D11311yescharacteristic
245C2×Q8C22×D11311yescharacteristic
246C2×D4—1131no—
247C2×D4—2261no—
248C22×C4—1131no—
249C22×C4—1131no—
250C22×C4—1131no—
251C22×C4—2261no—
252C22×C4—2261no—
253C22×C4—2261no—
254C22×C4—2261no—
255C22×C4—2261no—
256Q16—1134no—
257Q16C4×D11314yescomplemented
258SD16—1134no—
259SD16—1134no—
260M16—1134no—
261M16—2262no—
262C2×C8—1131no—
263C2×C8—1131no—
264C2×C8C22×D11311yescharacteristic
265C2×C8C22×D11311yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—1131no—
269C4⋊C4—1131no—
270C4⋊C4—2261no—
271C4⋊C4—2261no—
272C4⋊C4—2261no—
273C4⋊C4—2261no—
274C4⋊C4—2261no—
275C4⋊C4C22×D11311yescharacteristic
276C4⋊C4C22×D11311yescharacteristic
277C22⋊C4—2261no—
278C22⋊C4—2261no—
279C22⋊C4—2261no—
280C42—21no—
281C42—21no—
282C42—1131no—
283C42—1131no—
284C42—1131no—
285C42—2261no—
286C42—2261no—
287C42—2261no—
288C42—2261no—
289C42—2261no—
290C42C22×D11311yescharacteristic
291C23—1131no—
292C23—2261no—
293Q8—21no—
294Q8—21no—
295Q8—1132no—
296Q8—2264no—
297Q8—2261no—
298Q8C2×C4×D11312yes—
299Q8C2×C4×D11312yes—
300D4—1132no—
301D4—2264no—
302D4—2261no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—1131no—
308C2×C4—1131no—
309C2×C4—1132no—
310C2×C4—1132no—
311C2×C4—1131no—
312C2×C4—4522no—
313C2×C4—4521no—
314C2×C4—4522no—
315C2×C4—4522no—
316C2×C4—2262no—
317C2×C4—2264no—
318C2×C4—2264no—
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—1132no—
330C22—4521no—
331C22—4521no—
332C22—2262no—
333C22—2261no—
334C22—2261no—
335C22C2×D4×D11311yescharacteristic
336C4—22no—
337C4—22no—
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—1132no—
343C4—1132no—
344C4—4521no—
345C4—4521no—
346C4—2262no—
347C4—2261no—
348C4C22×C4×D11311yescharacteristic
349C4#41×D11311yescharacteristic
350C2—4522no—
351C2—2262no—
352C2C4×D4×D11311yescharacteristic
353C2#137×D11311yescharacteristic
354C2#2029939711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutatorC4×C113C23×C4
FrattiniC2×C4C23×D113
Fitting#441×C113C2
socleC22×C113C22×D4
prime radicalC2×#14268648C22
cosocleC2×C4×C113C24
hypercenter#441D113
hypocenterC113C4×#137
LCSG ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
3. C4×Q8×D113C2semidirect
4. #20298703C2semidirect
5. #20298700C2semidirect
6. #20298696C2semidirect
7. Q16×Dic113C2semidirect
8. #20298690C2semidirect
9. #20298685C2semidirect
10. #20298683C2semidirect
11. #20298637C2semidirect
12. #20298605C2semidirect
14. #20298550C2semidirect
15. #441×C113C2semidirect
18. #16813654C4semidirect
65. Q8×D113C2×C4semidirect
76. #14268637C2×C4semidirect
77. #14268636C2×C4semidirect
78. #14268634C2×C4semidirect
80. #14268630C2×C4semidirect
103. Q16×C113C2×C4semidirect
171. Dic113#137semidirect
178. C113C4×#137semidirect
183. #441D113semidirect
257. Q16C4×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136542
C4×#142686482
C4×Q8×D1132
#202987032
#202987002
#202986962
Q16×Dic1132
#202986902
#202986852
#202986832
#202986372
#202986052
#202985982
#202985502
#441×C1132
C4×#137113