Finite Group Databasebeta

← #28401254

Subgroups — #28401254

Order 14464.

374 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299217C211yesmaximal, characteristic, complemented
2#20299202C211yesmaximal, characteristic, complemented
3#20299007C211yesmaximal, characteristic, complemented
4#20298952C211yesmaximal, characteristic, complemented
5#20298944C211yesmaximal, characteristic, complemented
6#20298848C211yesmaximal, characteristic, complemented
7#20298841C211yesmaximal, characteristic, complemented
8#20298831C211yesmaximal, characteristic, complemented
9#20298824C211yesmaximal, characteristic, complemented
10#20298710C211yesmaximal, characteristic, complemented
11#20298699C211yesmaximal, characteristic, complemented
12SD16×Dic113C211yesmaximal, characteristic, complemented
13D8×Dic113C211yesmaximal, characteristic, complemented
14#20298555C211yesmaximal, characteristic, complemented
15#496×C113C211yesmaximal, characteristic, complemented
16C2×#14268630C2211yescharacteristic
17C2×C8×D113C2211yescharacteristic
18#16813622C2211yescharacteristic
19#16813615—21no—
20#16813614C2211yescharacteristic
21#16813608—21no—
22#16813606—21no—
23#16813603—21no—
24#16813603—21no—
25#16813599—21no—
26#16813598C2211yescharacteristic
27#16813594—21no—
28#16813594—21no—
29#16813593C2211yescharacteristic
30#16813593C2211yescharacteristic
31#16813593C2211yescharacteristic
32Q8×Dic113C2211yescharacteristic
33D4×Dic113C2211yescharacteristic
34D4×Dic113C2211yescharacteristic
35D4×Dic113C2211yescharacteristic
36#16813579C2211yescharacteristic
37#16813556C2211yescharacteristic
38#16813556C2211yescharacteristic
39#16813554C2211yescharacteristic
40#16813554C2211yescharacteristic
41#16813546C2211yescharacteristic
42#16813546C2211yescharacteristic
43#16813543C2211yescharacteristic
44#16813543C2211yescharacteristic
45#16813543C2211yescharacteristic
46#16813543C2211yescharacteristic
47#16813543C2211yescharacteristic
48#16813543C2211yescharacteristic
49#16813532C2211yescharacteristic
50C4×#11744751C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C2×SD16×C113C2211yescharacteristic
53C2×SD16×C113C2211yescharacteristic
54C2×D8×C113C2211yescharacteristic
55C2×D8×C113C2211yescharacteristic
56#127×C113C2211yescharacteristic
57#124×C113C2211yescharacteristic
58#97×C113C2211yescharacteristic
59C2×Dic226—21no—
60C2×C22⋊D113—21no—
61C2×C22⋊D113—21no—
62C2×C22⋊D113—21no—
63C22×Dic113—21no—
64C22×Dic113—21no—
65C22×Dic113—21no—
66C2×C4×D113C2311yescharacteristic
67#14268630—22no—
68C2×#11744751C2311yescharacteristic
69C2×#11744751C2311yescharacteristic
70C8×D113—22no—
71C4⋊Dic113—21no—
72C4⋊Dic113—21no—
73C4⋊Dic113C2311yescharacteristic
74C4⋊Dic113C2311yescharacteristic
75C4⋊Dic113C2311yescharacteristic
76C4⋊Dic113C2311yescharacteristic
77#14268626—21no—
78#14268626—21no—
79#14268626—21no—
80#14268626D411yescharacteristic
81#14268626D411yescharacteristic
82C22⋊Dic113—21no—
83C22⋊Dic113—21no—
84C22⋊Dic113—21no—
85C22⋊Dic113—21no—
86C22⋊Dic113—21no—
87C22⋊Dic113—21no—
88#14268624—21no—
89#14268624D411yescharacteristic
90#14268624D411yescharacteristic
91C4×Dic113—21no—
92C4×Dic113C2311yescharacteristic
93C2×Q8×C113C2311yescharacteristic
94C2×D4×C113—21no—
95C2×D4×C113—21no—
96C2×D4×C113C2311yescharacteristic
97C2×D4×C113C2311yescharacteristic
98C2×D4×C113C2311yescharacteristic
99SD16×C113—22no—
100SD16×C113—22no—
101D8×C113—22no—
102D8×C113—22no—
103C2×C8×C113C2311yescharacteristic
104C2×C8×C113C2311yescharacteristic
105C22⋊C4×C113—21no—
106C22⋊C4×C113—21no—
107C42×C113C2311yescharacteristic
108C23×C113—21no—
109C23×C113—21no—
110C23×C113—21no—
111C22×D113C2×D411yescharacteristic
112Q8×C113—21no—
113Q8×C113—21no—
114D4×C113—21no—
115D4×C113—21no—
116D4×C113—21no—
117D4×C113—21no—
118D4×C113—21no—
119D4×C113—21no—
120D4×C113—81no—
121D4×C113—81no—
122C2×C4×C113—21no—
123C2×C4×C113C2×D411yescharacteristic
124C2×C4×C113C2×D411yescharacteristic
125C2×C4×C113C2411yescharacteristic
126C22⋊D113—81no—
127C22⋊D113—81no—
128C22⋊D113—81no—
129C2×Dic113—21no—
130C2×Dic113—21no—
131C2×Dic113—21no—
132C2×Dic113—21no—
133C2×Dic113—81no—
134C2×Dic113—81no—
135C2×Dic113—81no—
136C2×Dic113C2×D411yescharacteristic
137C2×Dic113C2×D411yescharacteristic
138C2×Dic113C2×D411yescharacteristic
139C4×D113—21no—
140C4×D113—21no—
141Dic226—81no—
142C8×C113#4112yes—
143C8×C113#4112yes—
144#11744751—21no—
145#11744751—21no—
146C22×C113—41no—
147C22×C113—41no—
148C22×C113—41no—
149C22×C113—41no—
150C22×C113—41no—
151C22×C113—41no—
152C22×C113—41no—
153C22×C113—41no—
154C22×C113—41no—
155C22×C113C22×D411yescharacteristic
156C2×D113—21no—
157C2×D113—21no—
158C2×D113—21no—
159C4×C113—21no—
160C4×C113—21no—
161C4×C113—41no—
162C4×C113C2×#4111yescharacteristic
163C4×C113C2×#4111yescharacteristic
164Dic113—21no—
165Dic113—21no—
166Dic113—21no—
167Dic113—41no—
168Dic113—41no—
169Dic113—41no—
170Dic113—41no—
171C2×C113—81no—
172C2×C113—81no—
173C2×C113—81no—
174C2×C113#53211yescharacteristic
175C2×C113#57611yescharacteristic
176C2×C113#57711yescharacteristic
177D113—41no—
178#3179—1131nomaximal, Sylow
179C113#317911yescharacteristic, complemented, Sylow
180#542—1131no—
181#540—1131no—
182#501—1131no—
183#496D11311yescharacteristic, complemented
184#488—1131no—
185#486—1131no—
186#469—1131no—
187#468—1131no—
188#466—1131no—
189#465—1131no—
190#442—1131no—
191#440—1131no—
192C4×SD16—1131no—
193C4×D8—1131no—
194#405—1131no—
195C2×SD16C2×D11311yescharacteristic
196C2×SD16C2×D11311yescharacteristic
197C2×D8C2×D11311yescharacteristic
198C2×D8C2×D11311yescharacteristic
199C2×M16—1131no—
200C22×C8—1131no—
201C4⋊Q8—1131no—
202#127C2×D11311yescharacteristic
203#126—2261no—
204#125—1131no—
205#124—2261no—
206#124C2×D11311yescharacteristic
207#123—2261no—
208#123—2261no—
209#123—2261no—
210C22⋊Q8—1131no—
211C22⋊Q8—2261no—
212#121—1131no—
213#121—1131no—
214#121—1131no—
215#121—2261no—
216#121—2261no—
217C4×Q8—1131no—
218C4×D4—1131no—
219C4×D4—1131no—
220C4×D4—1131no—
221#117—1131no—
222#107—1131no—
223#107—1131no—
224#106—1131no—
225#106—1131no—
226#103—1131no—
227#103—1131no—
228#102—1131no—
229#102—1131no—
230#102—1131no—
231#102—1131no—
232#102—1131no—
233#102—1131no—
234#97—1131no—
235#97C2×D11311yescharacteristic
236C4×C8—1131no—
237C4×C8—1131no—
238C2×Q8—2261no—
239C2×Q8C22×D11311yescharacteristic
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—2261no—
243C2×D4—2261no—
244C2×D4—2261no—
245C2×D4C22×D11311yescharacteristic
246C2×D4C22×D11311yescharacteristic
247C2×D4C22×D11311yescharacteristic
248C22×C4—1131no—
249C22×C4—2261no—
250C22×C4—2261no—
251C22×C4—2261no—
252SD16—22no—
253SD16—22no—
254D8—22no—
255D8—22no—
256M16—2262no—
257C2×C8—1131no—
258C2×C8—1131no—
259C2×C8—2262no—
260C2×C8C22×D11311yescharacteristic
261C2×C8C22×D11311yescharacteristic
262C4⋊C4—1131no—
263C4⋊C4—1131no—
264C4⋊C4—1131no—
265C4⋊C4—1131no—
266C4⋊C4—1131no—
267C4⋊C4—1131no—
268C4⋊C4—2261no—
269C4⋊C4—2261no—
270C4⋊C4—2261no—
271C4⋊C4—2261no—
272C4⋊C4—2261no—
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—1131no—
276C22⋊C4—1131no—
277C22⋊C4—2261no—
278C22⋊C4—2261no—
279C22⋊C4—2261no—
280C22⋊C4—2261no—
281C22⋊C4—2261no—
282C22⋊C4—2261no—
283C22⋊C4—2261no—
284C42—1131no—
285C42—2261no—
286C42C22×D11311yescharacteristic
287C23—21no—
288C23—21no—
289C23—21no—
290C23—1131no—
291Q8—21no—
292Q8—21no—
293Q8—9041no—
294D4—21no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—21no—
300D4—81no—
301D4—81no—
302D4—9041no—
303D4—9041no—
304D4—9041no—
305C2×C4—21no—
306C2×C4—1131no—
307C2×C4—1131no—
308C2×C4—1131no—
309C2×C4—9041no—
310C2×C4—9041no—
311C2×C4—9041no—
312C2×C4—2261no—
313C2×C4—2261no—
314C2×C4—2261no—
315C2×C4—2261no—
316C2×C4—2261no—
317C2×C4—2261no—
318C2×C4D4×D11311yescharacteristic
319C2×C4D4×D11311yescharacteristic
320C2×C4C23×D11311yescharacteristic
321C8—2261no—
322C8—2261no—
323C8#1426864612yes—
324C8#1426864612yes—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—2261no—
335C22—2261no—
336C22—2261no—
337C22C2×D4×D11311yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—4521no—
342C4—4521no—
343C4—4521no—
344C4—4521no—
345C4—2261no—
346C4—2261no—
347C4—2261no—
348C4C2×#1426864611yescharacteristic
349C4C2×#1426864611yescharacteristic
350C2—81no—
351C2—81no—
352C2—81no—
353C2—4521no—
354C2#2029914611yescharacteristic
355C2#2029940211yescharacteristic
356C2#2029940811yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#496×C113C2
socleC22×C113C22×D4
hypercenter#496D113
hypocenterC113#3179
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #20299217C2semidirect
2. #20299202C2semidirect
3. #20299007C2semidirect
4. #20298952C2semidirect
5. #20298944C2semidirect
6. #20298848C2semidirect
7. #20298841C2semidirect
8. #20298831C2semidirect
9. #20298824C2semidirect
10. #20298710C2semidirect
11. #20298699C2semidirect
12. SD16×Dic113C2semidirect
13. D8×Dic113C2semidirect
14. #20298555C2semidirect
15. #496×C113C2semidirect
179. C113#3179semidirect
183. #496D113semidirect

Maximal subgroups

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

subgroupindex
#202992172
#202992022
#202990072
#202989522
#202989442
#202988482
#202988412
#202988312
#202988242
#202987102
#202986992
SD16×Dic1132
D8×Dic1132
#202985552
#496×C1132
#3179113