Finite Group Databasebeta

← #28400829

Subgroups — #28400829

Order 14464.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299215C211yesmaximal, characteristic, complemented
2#20299081C211yesmaximal, characteristic, complemented
3#20298934C211yesmaximal, characteristic, complemented
4#20298909C211yesmaximal, characteristic, complemented
5#20298891C211yesmaximal, characteristic, complemented
6#20298876C211yesmaximal, characteristic, complemented
7#20298818C211yesmaximal, characteristic, complemented
8#20298811C211yesmaximal, characteristic, complemented
9#20298760C211yesmaximal, characteristic, complemented
10#20298699C211yesmaximal, characteristic, complemented
11#20298695C211yesmaximal, characteristic, complemented
12#20298690C211yesmaximal, characteristic, complemented
13D8×Dic113C211yesmaximal, characteristic, complemented
14#20298656C211yesmaximal, characteristic, complemented
15#449×C113C211yesmaximal, characteristic
16C2×#14268637C2211yescharacteristic
17C2×#14268635C2211yescharacteristic
18#16813621C2211yescharacteristic
19#16813615—21no—
20#16813609—21no—
21#16813609C2211yescharacteristic
22#16813603—21no—
23#16813601C2211yescharacteristic
24#16813599—21no—
25Q8×Dic113C2211yescharacteristic
26Q8×Dic113C2211yescharacteristic
27#16813587C2211yescharacteristic
28D4×Dic113—21no—
29D4×Dic113—21no—
30D4×Dic113C2211yescharacteristic
31D4×Dic113C2211yescharacteristic
32D4×Dic113C2211yescharacteristic
33#16813581—21no—
34#16813581C2211yescharacteristic
35C2×C4⋊Dic113—21no—
36C2×C4⋊Dic113C2211yescharacteristic
37#16813556C2211yescharacteristic
38#16813556C2211yescharacteristic
39#16813555C2211yescharacteristic
40#16813555C2211yescharacteristic
41#16813551C2211yescharacteristic
42#16813551C2211yescharacteristic
43#16813547C2211yescharacteristic
44#16813547C2211yescharacteristic
45#16813546C2211yescharacteristic
46#16813543C2211yescharacteristic
47#16813543C2211yescharacteristic
48#16813543C2211yescharacteristic
49C22⋊#11744751C2211yescharacteristic
50#16813532C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C2×#41×C113C2211yescharacteristic
53C2×SD16×C113C2211yescharacteristic
54C2×D8×C113C2211yescharacteristic
55#121×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58C22⋊C8×C113C2211yescharacteristic
59C2×Dic226—21no—
60C2×Dic226C2311yescharacteristic
61C22×Dic113—21no—
62C22×Dic113—21no—
63C22×Dic113—21no—
64C22×Dic113—21no—
65#14268637—22no—
66#14268635—22no—
67C2×#11744751C2311yescharacteristic
68C2×#11744751C2311yescharacteristic
69C4⋊Dic113—21no—
70C4⋊Dic113—21no—
71C4⋊Dic113—21no—
72C4⋊Dic113D411yescharacteristic
73C4⋊Dic113D411yescharacteristic
74C4⋊Dic113C2311yescharacteristic
75C4⋊Dic113C2311yescharacteristic
76C4⋊Dic113C2311yescharacteristic
77#14268626—21no—
78#14268626—21no—
79#14268626—21no—
80C22⋊Dic113—21no—
81C22⋊Dic113—21no—
82C22⋊Dic113—21no—
83C22⋊Dic113—21no—
84C22⋊Dic113—21no—
85C22⋊Dic113—21no—
86C22⋊Dic113D411yescharacteristic
87C22⋊Dic113D411yescharacteristic
88C4×Dic113—21no—
89C4×Dic113—21no—
90C4×Dic113—21no—
91C4×Dic113C2311yescharacteristic
92C4×Dic113C2311yescharacteristic
93#41×C113—22no—
94#41×C113—22no—
95C2×Q8×C113C2311yescharacteristic
96C2×D4×C113—21no—
97C2×D4×C113—21no—
98C2×D4×C113C2311yescharacteristic
99C2×D4×C113C2311yescharacteristic
100C22×C4×C113—21no—
101C22×C4×C113C2311yescharacteristic
102SD16×C113—22no—
103D8×C113—22no—
104C2×C8×C113C2311yescharacteristic
105C2×C8×C113C2311yescharacteristic
106C4⋊C4×C113C2311yescharacteristic
107C22⋊C4×C113—21no—
108C23×C113—21no—
109C23×C113—21no—
110C23×C113C2×D411yescharacteristic
111Q8×C113—21no—
112Q8×C113#4112yes—
113D4×C113—24no—
114D4×C113—21no—
115D4×C113—21no—
116D4×C113—21no—
117D4×C113—81no—
118D4×C113#4112yes—
119C2×C4×C113—24no—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113—21no—
124C2×C4×C113C2×D411yescharacteristic
125C2×C4×C113C2411yescharacteristic
126C2×Dic113—21no—
127C2×Dic113—21no—
128C2×Dic113—21no—
129C2×Dic113—21no—
130C2×Dic113—81no—
131C2×Dic113—81no—
132C2×Dic113—81no—
133C2×Dic113—81no—
134C2×Dic113C2×D411yescharacteristic
135C2×Dic113C2×D411yescharacteristic
136C2×Dic113C2×D411yescharacteristic
137C2×Dic113C2×D411yescharacteristic
138Dic226—21no—
139Dic226—21no—
140Dic226—81no—
141C8×C113—21no—
142C8×C113—21no—
143#11744751—21no—
144#11744751—21no—
145C22×C113—21no—
146C22×C113—22no—
147C22×C113—21no—
148C22×C113—21no—
149C22×C113—41no—
150C22×C113—41no—
151C22×C113—41no—
152C22×C113—41no—
153C22×C113—41no—
154C22×C113C22×D411yescharacteristic
155C4×C113—21no—
156C4×C113—22no—
157C4×C113—41no—
158C4×C113C2×#4111yescharacteristic
159C4×C113C2×#4111yescharacteristic
160Dic113—21no—
161Dic113—21no—
162Dic113—21no—
163Dic113—21no—
164Dic113—41no—
165Dic113—41no—
166Dic113—41no—
167Dic113—41no—
168C2×C113—41no—
169C2×C113—42no—
170C2×C113—81no—
171C2×C113#52511yescharacteristic
172C2×C113#57611yescharacteristic
173C2×C113#57811yescharacteristic
174#3124—1131nomaximal, Sylow
175C113#312411yescharacteristic, complemented, Sylow
176#542—1131no—
177#520—1131no—
178#484—1131no—
179#480—1131no—
180#477—1131no—
181#474—1131no—
182#464—1131no—
183#463—1131no—
184#452—1131no—
185#449D11311yescharacteristic
186#440—1131no—
187#440—1131no—
188C4×Q16—1131no—
189C4×D8—1131no—
190#433—1131no—
191C2×#41C2×D11311yescharacteristic
192C2×Q16—1131no—
193C2×SD16—1131no—
194C2×SD16C2×D11311yescharacteristic
195C2×D8C2×D11311yescharacteristic
196C4⋊Q8—1131no—
197#126—2261no—
198#124—1131no—
199#124—2261no—
200#123—2261no—
201C22⋊Q8—1131no—
202C22⋊Q8—2261no—
203#121C2×D11311yescharacteristic
204C4×Q8—1131no—
205C4×Q8—1131no—
206C4×Q8—1131no—
207C4×D4—1131no—
208C4×D4—1131no—
209C4×D4—1131no—
210C4×D4—2261no—
211C4×D4—2261no—
212#117—1131no—
213#117—2261no—
214C2×C4⋊C4—1131no—
215C2×C4⋊C4—2261no—
216#107—1131no—
217#107—1131no—
218#107—1131no—
219#107—1131no—
220C4⋊C8—1131no—
221C4⋊C8—1131no—
222#103—1131no—
223#103—1131no—
224#103—1131no—
225#103C2×D11311yescharacteristic
226#102—1131no—
227#102—1131no—
228#102—1131no—
229#102C2×D11311yescharacteristic
230C22⋊C8—1131no—
231C22⋊C8C2×D11311yescharacteristic
232#97—1131no—
233C4×C8—1131no—
234#41—22no—
235#41—22no—
236C2×Q8—1131no—
237C2×Q8—2261no—
238C2×Q8C22×D11311yescharacteristic
239C2×D4—21no—
240C2×D4—21no—
241C2×D4C22×D11311yescharacteristic
242C2×D4C22×D11311yescharacteristic
243C22×C4—21no—
244C22×C4—2261no—
245C22×C4—2261no—
246C22×C4—2261no—
247C22×C4—2261no—
248C22×C4C22×D11311yescharacteristic
249Q16—2262no—
250SD16—22no—
251SD16—2262no—
252D8—22no—
253C2×C8—1131no—
254C2×C8—1131no—
255C2×C8C22×D11311yescharacteristic
256C2×C8C22×D11311yescharacteristic
257C4⋊C4—1131no—
258C4⋊C4—1131no—
259C4⋊C4—1131no—
260C4⋊C4—1131no—
261C4⋊C4—1131no—
262C4⋊C4—2261no—
263C4⋊C4—2261no—
264C4⋊C4—2261no—
265C4⋊C4—2261no—
266C4⋊C4—2261no—
267C4⋊C4—2261no—
268C4⋊C4C22×D11311yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—1131no—
271C22⋊C4—1131no—
272C22⋊C4—2261no—
273C22⋊C4—2261no—
274C22⋊C4—2261no—
275C22⋊C4—2261no—
276C22⋊C4—2261no—
277C22⋊C4—2261no—
278C42—1131no—
279C42—1131no—
280C42—2261no—
281C42—2261no—
282C42—2261no—
283C23—21no—
284C23—21no—
285C23D4×D11311yescharacteristic
286Q8—21no—
287Q8—9041no—
288Q8—2261no—
289Q8—2261no—
290Q8#1426864612yes—
291D4—24no—
292D4—21no—
293D4—21no—
294D4—21no—
295D4—81no—
296D4#1426864612yes—
297C2×C4—24no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—1131no—
303C2×C4—1131no—
304C2×C4—1131no—
305C2×C4—1131no—
306C2×C4—9041no—
307C2×C4—9041no—
308C2×C4—9041no—
309C2×C4—9041no—
310C2×C4—2261no—
311C2×C4—2261no—
312C2×C4—2261no—
313C2×C4—2261no—
314C2×C4D4×D11311yescharacteristic
315C2×C4C23×D11311yescharacteristic
316C8—21no—
317C8—21no—
318C8—2261no—
319C8—2261no—
320C22—21no—
321C22—22no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22C2×D4×D11311yescharacteristic
330C4—21no—
331C4—22no—
332C4—41no—
333C4—4521no—
334C4—4521no—
335C4—4521no—
336C4—4521no—
337C4—2261no—
338C4—2261no—
339C4—2261no—
340C4—2261no—
341C4C2×#1426864611yescharacteristic
342C4C2×#1426864611yescharacteristic
343C2—41no—
344C2—42no—
345C2—81no—
346C2#2029910411yescharacteristic
347C2#2029940211yescharacteristic
348C2#2029941211yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting, prime radical#449×C113C2
socleC22×C113C22×D4
hypercenter#449D113
hypocenterC113#3124
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #20299215C2semidirect
2. #20299081C2semidirect
3. #20298934C2semidirect
4. #20298909C2semidirect
5. #20298891C2semidirect
6. #20298876C2semidirect
7. #20298818C2semidirect
8. #20298811C2semidirect
9. #20298760C2semidirect
10. #20298699C2semidirect
11. #20298695C2semidirect
12. #20298690C2semidirect
13. D8×Dic113C2semidirect
14. #20298656C2semidirect
175. C113#3124semidirect

Maximal subgroups

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

subgroupindex
#202992152
#202990812
#202989342
#202989092
#202988912
#202988762
#202988182
#202988112
#202987602
#202986992
#202986952
#202986902
D8×Dic1132
#202986562
#449×C1132
#3124113