Finite Group Databasebeta

← #28400811

Subgroups — #28400811

Order 14464.

418 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299201C211yesmaximal, characteristic, complemented
2#20299073C211yesmaximal, characteristic, complemented
3#20298923C211yesmaximal, characteristic, complemented
4#20298919C211yesmaximal, characteristic, complemented
5#20298900C211yesmaximal, characteristic, complemented
6#20298896C211yesmaximal, characteristic, complemented
7#20298791C211yesmaximal, characteristic, complemented
8#20298791C211yesmaximal, characteristic, complemented
9#20298732C211yesmaximal, characteristic, complemented
10#20298710C211yesmaximal, characteristic, complemented
11#20298707C211yesmaximal, characteristic, complemented
12D8×Dic113C211yesmaximal, characteristic, complemented
13#20298678C211yesmaximal, characteristic, complemented
14#20298656C211yesmaximal, characteristic, complemented
15#447×C113C211yesmaximal, characteristic, complemented
16C2×#14268632C2211yescharacteristic
17C2×#14268632C2211yescharacteristic
18#16813618C2211yescharacteristic, complemented
19#16813613C2211yescharacteristic, complemented
20#16813606—21no—
21#16813604—21no—
22#16813596C2211yescharacteristic
23#16813594—21no—
24#16813593—21no—
25D4×Dic113—21no—
26D4×Dic113—21no—
27D4×Dic113C2211yescharacteristic
28D4×Dic113C2211yescharacteristic
29D4×Dic113C2211yescharacteristic
30D4×Dic113C2211yescharacteristic
31D4×Dic113C2211yescharacteristic, complemented
32#16813584C2211yescharacteristic, complemented
33#16813581C2211yescharacteristic
34#16813581C2211yescharacteristic
35C2×C22⋊Dic113—21no—
36C2×C22⋊Dic113—21no—
37#16813556C2211yescharacteristic, complemented
38#16813555C2211yescharacteristic, complemented
39#16813554C2211yescharacteristic, complemented
40#16813553C2211yescharacteristic, complemented
41#16813551C2211yescharacteristic, complemented
42#16813551C2211yescharacteristic, complemented
43#16813544C2211yescharacteristic, complemented
44#16813544C2211yescharacteristic, complemented
45#16813543C2211yescharacteristic
46#16813543C2211yescharacteristic
47#16813543C2211yescharacteristic, complemented
48#16813543C2211yescharacteristic, complemented
49C22⋊#11744751C2211yescharacteristic
50#16813532C2211yescharacteristic, complemented
51C8×Dic113C2211yescharacteristic, complemented
52C22×D4×C113C2211yescharacteristic
53C2×D8×C113C2211yescharacteristic
54C2×D8×C113C2211yescharacteristic
55#121×C113C2211yescharacteristic
56#102×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58C22⋊C8×C113C2211yescharacteristic
59C2×D452C2311yescharacteristic
60C2×C22⋊D113—21no—
61C2×C22⋊D113—21no—
62C2×C22⋊D113—21no—
63C22×Dic113—21no—
64C22×Dic113—21no—
65C22×Dic113—21no—
66C22×Dic113—21no—
67C22×Dic113—21no—
68C2×C4×D113—21no—
69#14268632—22no—
70#14268632—22no—
71C2×#11744751C2311yescharacteristic
72C2×#11744751C2311yescharacteristic
73C4⋊Dic113—21no—
74C4⋊Dic113D411yescharacteristic
75C4⋊Dic113D411yescharacteristic
76C4⋊Dic113C2311yescharacteristic
77C4⋊Dic113C2311yescharacteristic
78C4⋊Dic113C2311yescharacteristic
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
88#14268624—21no—
89#14268624—21no—
90C4×Dic113—21no—
91C4×Dic113C2311yescharacteristic
92C4×Dic113C2311yescharacteristic
93C24×C113—21no—
94C2×D4×C113—22no—
95C2×D4×C113—22no—
96C2×D4×C113—21no—
97C2×D4×C113—21no—
98C2×D4×C113C2311yescharacteristic
99C2×D4×C113C2311yescharacteristic
100C2×D4×C113C2311yescharacteristic
101C22×C4×C113C2311yescharacteristic
102D8×C113—22no—
103D8×C113—22no—
104C2×C8×C113C2311yescharacteristic
105C2×C8×C113C2311yescharacteristic
106C4⋊C4×C113C2311yescharacteristic
107C22⋊C4×C113—21no—
108C23×C113—24no—
109C23×C113—21no—
110C23×C113—21no—
111C23×C113—21no—
112C23×C113—81no—
113C23×C113—81no—
114C23×C113C2×D411yescharacteristic
115C22×D113—21no—
116D4×C113—24no—
117D4×C113—21no—
118D4×C113—21no—
119D4×C113—21no—
120D4×C113—21no—
121D4×C113—81no—
122D4×C113#4112yes—
123D4×C113#4112yes—
124C2×C4×C113—21no—
125C2×C4×C113—21no—
126C2×C4×C113—21no—
127C2×C4×C113C2×D411yescharacteristic
128C2×C4×C113C2411yescharacteristic
129C22⋊D113—81no—
130C22⋊D113—81no—
131C22⋊D113—81no—
132C2×Dic113—21no—
133C2×Dic113—21no—
134C2×Dic113—21no—
135C2×Dic113—81no—
136C2×Dic113—81no—
137C2×Dic113—81no—
138C2×Dic113—81no—
139C2×Dic113—81no—
140C2×Dic113C2×D411yescharacteristic
141C2×Dic113C2×D411yescharacteristic
142C2×Dic113C2×D411yescharacteristic
143C2×Dic113C2×D411yescharacteristic
144D452—21no—
145D452—21no—
146C4×D113—81no—
147C8×C113—21no—
148C8×C113—21no—
149#11744751—21no—
150#11744751—21no—
151C22×C113—21no—
152C22×C113—22no—
153C22×C113—22no—
154C22×C113—21no—
155C22×C113—21no—
156C22×C113—41no—
157C22×C113—41no—
158C22×C113—41no—
159C22×C113—41no—
160C22×C113—41no—
161C22×C113—41no—
162C22×C113—41no—
163C22×C113—84no—
164C22×C113C22×D411yescharacteristic
165C2×D113—41no—
166C2×D113—41no—
167C2×D113—41no—
168C4×C113—21no—
169C4×C113—41no—
170C4×C113C2×#4111yescharacteristic
171C4×C113C2×#4111yescharacteristic
172Dic113—21no—
173Dic113—21no—
174Dic113—21no—
175Dic113—21no—
176Dic113—41no—
177Dic113—41no—
178Dic113—41no—
179C2×C113—41no—
180C2×C113—42no—
181C2×C113—42no—
182C2×C113—81no—
183C2×C113#52511yescharacteristic
184C2×C113#57611yescharacteristic
185C2×C113#57611yescharacteristic
186D113—81no—
187#3122—1131nomaximal, Sylow
188C113#312211yescharacteristic, complemented, Sylow
189#540—1131no—
190#518—1131no—
191#482—1131no—
192#482—1131no—
193#478—1131no—
194#478—1131no—
195#459—1131no—
196#459—1131no—
197#447—1131no—
198#447D11311yescharacteristic, complemented
199#442—1131no—
200#442—1131no—
201C4×D8—1131no—
202C4×D8—1131no—
203#433—1131no—
204C22×D4C2×D11311yescharacteristic
205C2×D8—1131no—
206C2×D8—1131no—
207C2×D8C2×D11311yescharacteristic
208C2×D8C2×D11311yescharacteristic
209#127—1131no—
210#125—1131no—
211#123—2261no—
212#123—2261no—
213#121—1131no—
214#121—2261no—
215#121—2261no—
216#121C2×D11311yescharacteristic
217C4×D4—1131no—
218C4×D4—1131no—
219C4×D4—1131no—
220C4×D4—1131no—
221C4×D4—1131no—
222C4×D4—1131no—
223C4×D4—2261no—
224C4×D4—2261no—
225#117—1131no—
226#117—1131no—
227C2×C22⋊C4—2261no—
228C2×C22⋊C4—2261no—
229#107—1131no—
230#107—1131no—
231#106—1131no—
232#106—1131no—
233C4⋊C8—1131no—
234C4⋊C8—1131no—
235#102—1131no—
236#102—1131no—
237#102—1131no—
238#102—1131no—
239#102—1131no—
240#102—1131no—
241#102C2×D11311yescharacteristic
242#102C2×D11311yescharacteristic
243C22⋊C8—1131no—
244C22⋊C8C2×D11311yescharacteristic
245#97—1131no—
246C4×C8—1131no—
247C24—21no—
248C2×D4—22no—
249C2×D4—22no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—1131no—
253C2×D4—2261no—
254C2×D4—2261no—
255C2×D4—2261no—
256C2×D4C22×D11311yescharacteristic
257C2×D4C22×D11311yescharacteristic
258C2×D4C22×D11311yescharacteristic
259C22×C4—2261no—
260C22×C4—2261no—
261C22×C4—2261no—
262C22×C4—2261no—
263C22×C4—2261no—
264C22×C4—2261no—
265C22×C4C22×D11311yescharacteristic
266D8—22no—
267D8—22no—
268D8—2262no—
269D8—2262no—
270C2×C8—1131no—
271C2×C8—1131no—
272C2×C8C22×D11311yescharacteristic
273C2×C8C22×D11311yescharacteristic
274C4⋊C4—1131no—
275C4⋊C4—1131no—
276C4⋊C4—1131no—
277C4⋊C4—1131no—
278C4⋊C4—1131no—
279C4⋊C4—2261no—
280C4⋊C4—2261no—
281C4⋊C4C22×D11311yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—1131no—
284C22⋊C4—1131no—
285C22⋊C4—2261no—
286C22⋊C4—2261no—
287C22⋊C4—2261no—
288C22⋊C4—2261no—
289C22⋊C4—2261no—
290C22⋊C4—2261no—
291C22⋊C4—2261no—
292C22⋊C4—2261no—
293C42—1131no—
294C42—1131no—
295C42—2261no—
296C23—24no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—81no—
301C23—81no—
302C23—2261no—
303C23D4×D11311yescharacteristic
304D4—24no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—21no—
309D4—81no—
310D4—9041no—
311D4—9041no—
312D4—9041no—
313D4—2261no—
314D4—2261no—
315D4#1426864612yes—
316D4#1426864612yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—1131no—
321C2×C4—1131no—
322C2×C4—1131no—
323C2×C4—1131no—
324C2×C4—9041no—
325C2×C4—9041no—
326C2×C4—9041no—
327C2×C4—9041no—
328C2×C4—9041no—
329C2×C4—9041no—
330C2×C4—2261no—
331C2×C4—2261no—
332C2×C4—2261no—
333C2×C4D4×D11311yescharacteristic
334C2×C4C23×D11311yescharacteristic
335C8—21no—
336C8—21no—
337C8—2261no—
338C8—2261no—
339C22—21no—
340C22—22no—
341C22—22no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—84no—
352C22—4521no—
353C22—4521no—
354C22—4521no—
355C22C2×D4×D11311yescharacteristic
356C4—21no—
357C4—41no—
358C4—4521no—
359C4—4521no—
360C4—4521no—
361C4—2261no—
362C4—2261no—
363C4—2261no—
364C4—2261no—
365C4C2×#1426864611yescharacteristic
366C4C2×#1426864611yescharacteristic
367C2—41no—
368C2—42no—
369C2—42no—
370C2—81no—
371C2—9041no—
372C2#2029910411yescharacteristic
373C2#2029939911yescharacteristic
374C2#2029940211yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#447×C113C2
socleC22×C113C22×D4
hypercenter#447D113
hypocenterC113#3122
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #20299201C2semidirect
2. #20299073C2semidirect
3. #20298923C2semidirect
4. #20298919C2semidirect
5. #20298900C2semidirect
6. #20298896C2semidirect
7. #20298791C2semidirect
8. #20298791C2semidirect
9. #20298732C2semidirect
10. #20298710C2semidirect
11. #20298707C2semidirect
12. D8×Dic113C2semidirect
13. #20298678C2semidirect
14. #20298656C2semidirect
15. #447×C113C2semidirect
18. #16813618C22semidirect
19. #16813613C22semidirect
31. D4×Dic113C22semidirect
32. #16813584C22semidirect
37. #16813556C22semidirect
38. #16813555C22semidirect
39. #16813554C22semidirect
40. #16813553C22semidirect
41. #16813551C22semidirect
42. #16813551C22semidirect
43. #16813544C22semidirect
44. #16813544C22semidirect
47. #16813543C22semidirect
48. #16813543C22semidirect
50. #16813532C22semidirect
51. C8×Dic113C22semidirect
188. C113#3122semidirect
198. #447D113semidirect

Maximal subgroups

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

subgroupindex
#202992012
#202990732
#202989232
#202989192
#202989002
#202988962
#202987912
#202987322
#202987102
#202987072
D8×Dic1132
#202986782
#202986562
#447×C1132
#3122113