Finite Group Databasebeta

← #28400702

Subgroups — #28400702

Order 14464.

380 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299152C211yesmaximal, characteristic
2C4×Q8×D113C211yesmaximal, characteristic
3#20298930C211yesmaximal, characteristic
4#20298927C211yesmaximal, characteristic
5#20298882C211yesmaximal, characteristic, complemented
6#20298881C211yesmaximal, characteristic, complemented
7#20298807C211yesmaximal, characteristic, complemented
8#20298806C211yesmaximal, characteristic, complemented
9#20298755C211yesmaximal, characteristic
10#20298752C211yesmaximal, characteristic
11#20298706C211yesmaximal, characteristic, complemented
12#20298703C211yesmaximal, characteristic, complemented
13#20298703C211yesmaximal, characteristic, complemented
14#20298653C211yesmaximal, characteristic
15#441×C113C211yesmaximal, characteristic, complemented
16C2×Q8×D113C2211yescharacteristic
17C2×Dic452C2211yescharacteristic
18C2×#14268637C2211yescharacteristic
19C2×#14268637C2211yescharacteristic
20#16813621C2211yescharacteristic
21#16813620C2211yescharacteristic
22#16813612—21no—
23#16813602C2211yescharacteristic
24#16813600—21no—
25#16813598C2211yescharacteristic
26Q8×Dic113C2211yescharacteristic
27C4×Dic226—21no—
28C4×Dic226—21no—
29C4×Dic226C2211yescharacteristic
30C4×Dic226C2211yescharacteristic
31#16813587—21no—
32#16813587C2211yescharacteristic
33#16813579—21no—
34C4⋊C4×D113—21no—
35C4⋊C4×D113C2211yescharacteristic
36C42×D113—21no—
37C42×D113C2211yescharacteristic
38#16813554C2211yescharacteristic
39#16813553C2211yescharacteristic
40#16813553C2211yescharacteristic
41#16813551C2211yescharacteristic
42#16813551C2211yescharacteristic
43#16813547C2211yescharacteristic
44#16813547C2211yescharacteristic
45#16813546C2211yescharacteristic
46#16813546C2211yescharacteristic
47#16813545C2211yescharacteristic
48#16813545C2211yescharacteristic
49#16813534C2211yescharacteristic
50#16813534C2211yescharacteristic
51#16813533C2211yescharacteristic
52C2×Q16×C113C2211yescharacteristic
53C4×Q8×C113C2211yescharacteristic
54C4×Q8×C113C2211yescharacteristic
55#106×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58#97×C113C2211yescharacteristic
59C2×Dic226—21no—
60C2×Dic226—21no—
61C2×Dic226C2311yescharacteristic
62C2×Dic226C2311yescharacteristic
63Q8×D113—22no—
64Q8×D113—22no—
65C2×C4×D113—21no—
66C2×C4×D113—21no—
67C2×C4×D113D411yescharacteristic
68C2×C4×D113D411yescharacteristic
69C2×C4×D113C2311yescharacteristic
70Dic452—22no—
71#14268637—22no—
72#14268637—22no—
73C2×#11744751C2311yescharacteristic
74C2×#11744751C2311yescharacteristic
75C4⋊Dic113—21no—
76C4⋊Dic113—21no—
77C4⋊Dic113C2311yescharacteristic
78C4⋊Dic113C2311yescharacteristic
79#14268626—21no—
80#14268626—21no—
81#14268626—21no—
82#14268626—21no—
83#14268626—21no—
84#14268626—21no—
85#14268626—21no—
86#14268626—21no—
87#14268624—21no—
88#14268624—21no—
89C4×Dic113—21no—
90C4×Dic113—21no—
91C4×Dic113—21no—
92C4×Dic113—21no—
93C4×Dic113D411yescharacteristic
94C4×Dic113D411yescharacteristic
95C4×Dic113C2311yescharacteristic
96C2×Q8×C113C2311yescharacteristic
97C2×Q8×C113C2311yescharacteristic
98Q16×C113—22no—
99C2×C8×C113C2311yescharacteristic
100C2×C8×C113C2311yescharacteristic
101C4⋊C4×C113—21no—
102C4⋊C4×C113—21no—
103C4⋊C4×C113C2311yescharacteristic
104C4⋊C4×C113C2311yescharacteristic
105C42×C113—21no—
106C42×C113—21no—
107C42×C113C2311yescharacteristic
108C22×D113C2×D411yescharacteristic
109Q8×C113—21no—
110Q8×C113—21no—
111Q8×C113—21no—
112Q8×C113#4112yes—
113C2×C4×C113—21no—
114C2×C4×C113—21no—
115C2×C4×C113—21no—
116C2×C4×C113—21no—
117C2×C4×C113C2×D411yescharacteristic
118C2×C4×C113C2×D411yescharacteristic
119C2×C4×C113C2411yescharacteristic
120C2×Dic113—21no—
121C2×Dic113—21no—
122C2×Dic113—21no—
123C2×Dic113—21no—
124C2×Dic113C2×D411yescharacteristic
125C2×Dic113C2×D411yescharacteristic
126C2×Dic113C2×D411yescharacteristic
127C4×D113—24no—
128C4×D113—22no—
129C4×D113—21no—
130C4×D113—21no—
131C4×D113—22no—
132C4×D113—42no—
133Dic226—24no—
134Dic226—21no—
135Dic226—21no—
136Dic226—21no—
137Dic226—42no—
138Dic226#4112yes—
139C8×C113—21no—
140C8×C113—21no—
141#11744751—21no—
142#11744751—21no—
143C22×C113C22×D411yescharacteristic
144C2×D113—21no—
145C2×D113—21no—
146C2×D113#13712yes—
147C4×C113—22no—
148C4×C113—21no—
149C4×C113—21no—
150C4×C113—41no—
151C4×C113—41no—
152C4×C113—41no—
153C4×C113C2×#4111yescharacteristic
154C4×C113C2×#4111yescharacteristic
155Dic113—21no—
156Dic113—22no—
157Dic113—21no—
158Dic113—41no—
159Dic113—41no—
160Dic113—41no—
161Dic113#13712yes—
162C2×C113#52511yescharacteristic
163C2×C113C2×#13711yescharacteristic
164C2×C113C2×#13711yescharacteristic
165D113—22no—
166#3113—1131nomaximal, Sylow
167C113#311311yescharacteristic, complemented, Sylow
168#533—1131no—
169C2×C4×Q8—1131no—
170#483—1131no—
171#483—1131no—
172#475—1131no—
173#475—1131no—
174#462—1131no—
175#462—1131no—
176#451—1131no—
177#451—1131no—
178#441—1131no—
179#441—1131no—
180#441—1131no—
181#441D11311yescharacteristic, complemented
182#432—1131no—
183C22×Q8—1131no—
184C2×Q16—1131no—
185C2×Q16—1131no—
186C2×Q16—1131no—
187C2×Q16C2×D11311yescharacteristic
188C4⋊Q8—1131no—
189C4⋊Q8—1131no—
190#125—2261no—
191C22⋊Q8—1131no—
192C22⋊Q8—1131no—
193C22⋊Q8—2261no—
194C4×Q8—1131no—
195C4×Q8—1131no—
196C4×Q8—1131no—
197C4×Q8—1131no—
198C4×Q8—2261no—
199C4×Q8—2261no—
200C4×Q8—2261no—
201C4×Q8C2×D11311yescharacteristic
202C4×Q8C2×D11311yescharacteristic
203#117—2261no—
204C2×C4⋊C4—1131no—
205C2×C4⋊C4—2261no—
206C2×C42—1131no—
207C2×C42—2261no—
208#106—1131no—
209#106—1131no—
210#106—1131no—
211#106C2×D11311yescharacteristic
212C4⋊C8—1131no—
213C4⋊C8—1131no—
214#103—1131no—
215#103—1131no—
216#103—1131no—
217#103—1131no—
218#103—1131no—
219#103—1131no—
220#103C2×D11311yescharacteristic
221#103C2×D11311yescharacteristic
222C22⋊C8—1131no—
223C22⋊C8—1131no—
224#97—1131no—
225#97C2×D11311yescharacteristic
226C2×Q8—1131no—
227C2×Q8—1131no—
228C2×Q8—2261no—
229C2×Q8—2261no—
230C2×Q8—2262no—
231C2×Q8—2262no—
232C2×Q8C22×D11311yescharacteristic
233C2×Q8C22×D11311yescharacteristic
234C22×C4—1131no—
235C22×C4—1131no—
236C22×C4—1131no—
237C22×C4—2261no—
238C22×C4—2261no—
239Q16—22no—
240Q16—2262no—
241Q16—2262no—
242Q16—2262no—
243C2×C8—1131no—
244C2×C8—1131no—
245C2×C8C22×D11311yescharacteristic
246C2×C8C22×D11311yescharacteristic
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—1131no—
250C4⋊C4—1131no—
251C4⋊C4—2261no—
252C4⋊C4—2261no—
253C4⋊C4—2261no—
254C4⋊C4—2261no—
255C4⋊C4—2261no—
256C4⋊C4—2261no—
257C4⋊C4—2261no—
258C4⋊C4—2261no—
259C4⋊C4—2261no—
260C4⋊C4—2261no—
261C4⋊C4C22×D11311yescharacteristic
262C4⋊C4C22×D11311yescharacteristic
263C22⋊C4—2261no—
264C22⋊C4—2261no—
265C42—21no—
266C42—21no—
267C42—1131no—
268C42—1131no—
269C42—1131no—
270C42—2261no—
271C42—2261no—
272C42—2261no—
273C42—2261no—
274C42C22×D11311yescharacteristic
275C23—1131no—
276Q8—21no—
277Q8—21no—
278Q8—21no—
279Q8—1132no—
280Q8—4522no—
281Q8—2264no—
282Q8—2261no—
283Q8—2261no—
284Q8—2261no—
285Q8#1426864712yes—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—1131no—
291C2×C4—1131no—
292C2×C4—1131no—
293C2×C4—4522no—
294C2×C4—2262no—
295C2×C4—2262no—
296C2×C4—2264no—
297C2×C4—2261no—
298C2×C4—2261no—
299C2×C4—2261no—
300C2×C4—2261no—
301C2×C4—2261no—
302C2×C4—2261no—
303C2×C4D4×D11311yescharacteristic
304C2×C4D4×D11311yescharacteristic
305C2×C4C23×D11311yescharacteristic
306C8—21no—
307C8—21no—
308C8—2261no—
309C8—2261no—
310C22—1132no—
311C22—2261no—
312C22—2261no—
313C22C2×D4×D11311yescharacteristic
314C4—22no—
315C4—21no—
316C4—21no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—1132no—
321C4—4521no—
322C4—4521no—
323C4—4521no—
324C4—2261no—
325C4—2262no—
326C4—2261no—
327C4#41×D11311yescharacteristic
328C4C2×#1426864711yescharacteristic
329C2—2262no—
330C2#2029910711yescharacteristic
331C2#137×D11311yescharacteristic
332C2#137×D11311yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#441×C113C2
socleC22×C113C22×D4
prime radicalC22×D113C2×D4
hypercenter#441D113
hypocenterC113#3113
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
5. #20298882C2semidirect
6. #20298881C2semidirect
7. #20298807C2semidirect
8. #20298806C2semidirect
11. #20298706C2semidirect
12. #20298703C2semidirect
13. #20298703C2semidirect
15. #441×C113C2semidirect
167. C113#3113semidirect
181. #441D113semidirect

Maximal subgroups

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

subgroupindex
#202991522
C4×Q8×D1132
#202989302
#202989272
#202988822
#202988812
#202988072
#202988062
#202987552
#202987522
#202987062
#202987032
#202986532
#441×C1132
#3113113