Finite Group Databasebeta

← #28400774

Subgroups — #28400774

Order 14464.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299201C211yesmaximal, characteristic, complemented
2#20299081C211yesmaximal, characteristic, complemented
3#20298917C211yesmaximal, characteristic, complemented
4#20298909C211yesmaximal, characteristic, complemented
5#20298903C211yesmaximal, characteristic, complemented
6#20298900C211yesmaximal, characteristic, complemented
7#20298796C211yesmaximal, characteristic, complemented
8#20298791C211yesmaximal, characteristic, complemented
9#20298743C211yesmaximal, characteristic, complemented
10#20298710C211yesmaximal, characteristic, complemented
11#20298701C211yesmaximal, characteristic, complemented
12SD16×Dic113C211yesmaximal, characteristic, complemented
13#20298678C211yesmaximal, characteristic, complemented
14#20298656C211yesmaximal, characteristic, complemented
15#449×C113C211yesmaximal, characteristic, complemented
16C2×#14268634C2211yescharacteristic
17C2×#14268632C2211yescharacteristic
18#16813618C2211yescharacteristic
19#16813613C2211yescharacteristic
20#16813606—21no—
21#16813604—21no—
22#16813596C2211yescharacteristic
23#16813594—21no—
24#16813593—21no—
25Q8×Dic113C2211yescharacteristic
26Q8×Dic113C2211yescharacteristic
27D4×Dic113—21no—
28D4×Dic113—21no—
29D4×Dic113C2211yescharacteristic
30D4×Dic113C2211yescharacteristic
31D4×Dic113C2211yescharacteristic
32#16813584C2211yescharacteristic
33#16813581—21no—
34#16813581C2211yescharacteristic
35C2×C4⋊Dic113—21no—
36C2×C4⋊Dic113C2211yescharacteristic
37#16813555C2211yescharacteristic
38#16813555C2211yescharacteristic
39#16813554C2211yescharacteristic
40#16813554C2211yescharacteristic
41#16813551C2211yescharacteristic
42#16813551C2211yescharacteristic
43#16813546C2211yescharacteristic
44#16813544C2211yescharacteristic
45#16813544C2211yescharacteristic
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×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—
67C2×C4×D113—21no—
68#14268634—22no—
69#14268632—22no—
70C2×#11744751C2311yescharacteristic
71C2×#11744751C2311yescharacteristic
72C4⋊Dic113—21no—
73C4⋊Dic113—21no—
74C4⋊Dic113—21no—
75C4⋊Dic113—21no—
76C4⋊Dic113D411yescharacteristic
77C4⋊Dic113D411yescharacteristic
78C4⋊Dic113C2311yescharacteristic
79C4⋊Dic113C2311yescharacteristic
80C4⋊Dic113C2311yescharacteristic
81#14268626—21no—
82C22⋊Dic113—21no—
83C22⋊Dic113—21no—
84C22⋊Dic113—21no—
85C22⋊Dic113D411yescharacteristic
86C22⋊Dic113D411yescharacteristic
87#14268624—21no—
88#14268624—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
111C22×D113—21no—
112Q8×C113—21no—
113Q8×C113#4112yes—
114D4×C113—24no—
115D4×C113—21no—
116D4×C113—21no—
117D4×C113—21no—
118D4×C113—81no—
119D4×C113#4112yes—
120C2×C4×C113—24no—
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113—21no—
124C2×C4×C113—21no—
125C2×C4×C113C2×D411yescharacteristic
126C2×C4×C113C2411yescharacteristic
127C22⋊D113—81no—
128C22⋊D113—81no—
129C22⋊D113—81no—
130C2×Dic113—21no—
131C2×Dic113—21no—
132C2×Dic113—21no—
133C2×Dic113—81no—
134C2×Dic113—81no—
135C2×Dic113—81no—
136C2×Dic113—81no—
137C2×Dic113C2×D411yescharacteristic
138C2×Dic113C2×D411yescharacteristic
139C2×Dic113C2×D411yescharacteristic
140C2×Dic113C2×D411yescharacteristic
141D452—21no—
142D452—21no—
143C4×D113—81no—
144C8×C113—21no—
145C8×C113—21no—
146#11744751—21no—
147#11744751—21no—
148C22×C113—21no—
149C22×C113—22no—
150C22×C113—21no—
151C22×C113—21no—
152C22×C113—41no—
153C22×C113—41no—
154C22×C113—41no—
155C22×C113—41no—
156C22×C113—41no—
157C22×C113C22×D411yescharacteristic
158C2×D113—41no—
159C2×D113—41no—
160C2×D113—41no—
161C4×C113—21no—
162C4×C113—22no—
163C4×C113—41no—
164C4×C113C2×#4111yescharacteristic
165C4×C113C2×#4111yescharacteristic
166Dic113—21no—
167Dic113—21no—
168Dic113—21no—
169Dic113—21no—
170Dic113—41no—
171Dic113—41no—
172Dic113—41no—
173C2×C113—41no—
174C2×C113—42no—
175C2×C113—81no—
176C2×C113#52511yescharacteristic
177C2×C113#57611yescharacteristic
178C2×C113#57711yescharacteristic
179D113—81no—
180#3119—1131nomaximal, Sylow
181C113#311911yescharacteristic, complemented, Sylow
182#540—1131no—
183#520—1131no—
184#481—1131no—
185#480—1131no—
186#479—1131no—
187#478—1131no—
188#460—1131no—
189#459—1131no—
190#449—1131no—
191#449D11311yescharacteristic, complemented
192#442—1131no—
193#440—1131no—
194C4×SD16—1131no—
195C4×D8—1131no—
196#433—1131no—
197C2×#41C2×D11311yescharacteristic
198C2×SD16—1131no—
199C2×SD16C2×D11311yescharacteristic
200C2×D8—1131no—
201C2×D8C2×D11311yescharacteristic
202#127—1131no—
203#125—1131no—
204#123—2261no—
205#123—2261no—
206#121—1131no—
207#121—2261no—
208#121—2261no—
209#121C2×D11311yescharacteristic
210C4×Q8—1131no—
211C4×Q8—1131no—
212C4×D4—1131no—
213C4×D4—1131no—
214C4×D4—1131no—
215C4×D4—1131no—
216C4×D4—2261no—
217C4×D4—2261no—
218#117—1131no—
219#117—2261no—
220C2×C4⋊C4—1131no—
221C2×C4⋊C4—2261no—
222#107—1131no—
223#107—1131no—
224#106—1131no—
225#106—1131no—
226C4⋊C8—1131no—
227C4⋊C8—1131no—
228#103—1131no—
229#103C2×D11311yescharacteristic
230#102—1131no—
231#102—1131no—
232#102—1131no—
233#102—1131no—
234#102—1131no—
235#102C2×D11311yescharacteristic
236C22⋊C8—1131no—
237C22⋊C8C2×D11311yescharacteristic
238#97—1131no—
239C4×C8—1131no—
240#41—22no—
241#41—22no—
242C2×Q8C22×D11311yescharacteristic
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—1131no—
246C2×D4—2261no—
247C2×D4—2261no—
248C2×D4—2261no—
249C2×D4C22×D11311yescharacteristic
250C2×D4C22×D11311yescharacteristic
251C22×C4—21no—
252C22×C4—2261no—
253C22×C4—2261no—
254C22×C4—2261no—
255C22×C4—2261no—
256C22×C4—2261no—
257C22×C4C22×D11311yescharacteristic
258SD16—22no—
259SD16—2262no—
260D8—22no—
261D8—2262no—
262C2×C8—1131no—
263C2×C8—1131no—
264C2×C8C22×D11311yescharacteristic
265C2×C8C22×D11311yescharacteristic
266C4⋊C4—1131no—
267C4⋊C4—1131no—
268C4⋊C4—1131no—
269C4⋊C4—1131no—
270C4⋊C4—1131no—
271C4⋊C4—2261no—
272C4⋊C4—2261no—
273C4⋊C4—2261no—
274C4⋊C4—2261no—
275C4⋊C4—2261no—
276C4⋊C4C22×D11311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—1131no—
279C22⋊C4—1131no—
280C22⋊C4—2261no—
281C22⋊C4—2261no—
282C22⋊C4—2261no—
283C22⋊C4—2261no—
284C22⋊C4—2261no—
285C42—1131no—
286C42—1131no—
287C42—2261no—
288C42—2261no—
289C23—21no—
290C23—21no—
291C23—2261no—
292C23D4×D11311yescharacteristic
293Q8—21no—
294Q8#1426864612yes—
295D4—24no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—81no—
300D4—9041no—
301D4—9041no—
302D4—9041no—
303D4—2261no—
304D4—2261no—
305D4#1426864612yes—
306C2×C4—24no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—1131no—
312C2×C4—1131no—
313C2×C4—1131no—
314C2×C4—1131no—
315C2×C4—9041no—
316C2×C4—9041no—
317C2×C4—9041no—
318C2×C4—9041no—
319C2×C4—9041no—
320C2×C4—2261no—
321C2×C4—2261no—
322C2×C4—2261no—
323C2×C4D4×D11311yescharacteristic
324C2×C4C23×D11311yescharacteristic
325C8—21no—
326C8—21no—
327C8—2261no—
328C8—2261no—
329C22—21no—
330C22—22no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—4521no—
339C22—4521no—
340C22—4521no—
341C22C2×D4×D11311yescharacteristic
342C4—21no—
343C4—22no—
344C4—41no—
345C4—4521no—
346C4—4521no—
347C4—4521no—
348C4—2261no—
349C4—2261no—
350C4—2261no—
351C4—2261no—
352C4C2×#1426864611yescharacteristic
353C4C2×#1426864611yescharacteristic
354C2—41no—
355C2—42no—
356C2—81no—
357C2—9041no—
358C2#2029910411yescharacteristic
359C2#2029940211yescharacteristic
360C2#2029940511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#449×C113C2
socleC22×C113C22×D4
hypercenter#449D113
hypocenterC113#3119
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. #20299201C2semidirect
2. #20299081C2semidirect
3. #20298917C2semidirect
4. #20298909C2semidirect
5. #20298903C2semidirect
6. #20298900C2semidirect
7. #20298796C2semidirect
8. #20298791C2semidirect
9. #20298743C2semidirect
10. #20298710C2semidirect
11. #20298701C2semidirect
12. SD16×Dic113C2semidirect
13. #20298678C2semidirect
14. #20298656C2semidirect
15. #449×C113C2semidirect
181. C113#3119semidirect
191. #449D113semidirect

Maximal subgroups

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

subgroupindex
#202992012
#202990812
#202989172
#202989092
#202989032
#202989002
#202987962
#202987912
#202987432
#202987102
#202987012
SD16×Dic1132
#202986782
#202986562
#449×C1132
#3119113