Finite Group Databasebeta

← #28401256

Subgroups — #28401256

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#20299204C211yesmaximal, characteristic, complemented
3#20299008C211yesmaximal, characteristic, complemented
4#20298988C211yesmaximal, characteristic, complemented
5#20298945C211yesmaximal, characteristic, complemented
6#20298850C211yesmaximal, characteristic, complemented
7#20298847C211yesmaximal, characteristic, complemented
8#20298833C211yesmaximal, characteristic, complemented
9#20298830C211yesmaximal, characteristic, complemented
10#20298707C211yesmaximal, characteristic, complemented
11#20298701C211yesmaximal, characteristic, complemented
12#20298683C211yesmaximal, characteristic, complemented
13#20298678C211yesmaximal, characteristic, complemented
14#20298552C211yesmaximal, characteristic, complemented
15#488×C113C211yesmaximal, characteristic, complemented
16C2×#14268634C2211yescharacteristic
17C2×#14268634C2211yescharacteristic
18C2×#14268632C2211yescharacteristic
19C2×#14268632C2211yescharacteristic
20C2×#14268630C2211yescharacteristic
21C2×C8×D113C2211yescharacteristic
22#16813622C2211yescharacteristic
23#16813619C2211yescharacteristic
24#16813615—21no—
25#16813608—21no—
26#16813607—21no—
27#16813607—21no—
28#16813606—21no—
29#16813599—21no—
30#16813598C2211yescharacteristic
31#16813597—21no—
32#16813597—21no—
33#16813597C2211yescharacteristic
34#16813597C2211yescharacteristic
35#16813593C2211yescharacteristic
36Q8×Dic113C2211yescharacteristic
37D4×Dic113C2211yescharacteristic
38#16813584C2211yescharacteristic
39#16813584C2211yescharacteristic
40#16813579C2211yescharacteristic
41#16813555C2211yescharacteristic
42#16813555C2211yescharacteristic
43#16813553C2211yescharacteristic
44#16813553C2211yescharacteristic
45#16813544C2211yescharacteristic
46#16813544C2211yescharacteristic
47#16813544C2211yescharacteristic
48#16813544C2211yescharacteristic
49#16813533C2211yescharacteristic
50#16813532C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52#125×C113C2211yescharacteristic
53#124×C113C2211yescharacteristic
54#103×C113C2211yescharacteristic
55#103×C113C2211yescharacteristic
56#102×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58C4×C8×C113C2211yescharacteristic
59C2×Dic226—21no—
60C2×D452—21no—
61C2×D452—21no—
62C2×D452—21no—
63C2×D452—21no—
64C2×D452C2311yescharacteristic
65C2×D452C2311yescharacteristic
66C2×C22⋊D113—21no—
67C22×Dic113—21no—
68C2×C4×D113—21no—
69C2×C4×D113—21no—
70C2×C4×D113C2311yescharacteristic
71#14268634—22no—
72#14268634—22no—
73#14268632—22no—
74#14268632—22no—
75#14268630—22no—
76C2×#11744751C2311yescharacteristic
77C2×#11744751C2311yescharacteristic
78C8×D113—22no—
79C4⋊Dic113—21no—
80C4⋊Dic113—21no—
81C4⋊Dic113C2311yescharacteristic
82C4⋊Dic113C2311yescharacteristic
83#14268626—21no—
84#14268626D411yescharacteristic
85#14268626D411yescharacteristic
86C22⋊Dic113—21no—
87C22⋊Dic113—21no—
88#14268624—21no—
89#14268624—21no—
90#14268624—21no—
91#14268624—21no—
92#14268624—21no—
93#14268624D411yescharacteristic
94#14268624D411yescharacteristic
95C4×Dic113—21no—
96C4×Dic113C2311yescharacteristic
97C2×Q8×C113C2311yescharacteristic
98C2×D4×C113C2311yescharacteristic
99C2×C8×C113C2311yescharacteristic
100C2×C8×C113C2311yescharacteristic
101C4⋊C4×C113—21no—
102C4⋊C4×C113—21no—
103C4⋊C4×C113C2311yescharacteristic
104C4⋊C4×C113C2311yescharacteristic
105C22⋊C4×C113—21no—
106C22⋊C4×C113—21no—
107C42×C113C2311yescharacteristic
108C23×C113—21no—
109C22×D113—21no—
110C22×D113—21no—
111C22×D113C2×D411yescharacteristic
112Q8×C113—21no—
113Q8×C113—21no—
114D4×C113—21no—
115D4×C113—21no—
116C2×C4×C113—21no—
117C2×C4×C113—21no—
118C2×C4×C113—21no—
119C2×C4×C113C2×D411yescharacteristic
120C2×C4×C113C2×D411yescharacteristic
121C2×C4×C113C2411yescharacteristic
122C22⋊D113—81no—
123C2×Dic113—21no—
124C2×Dic113—21no—
125C2×Dic113—81no—
126C2×Dic113C2×D411yescharacteristic
127C2×Dic113C2×D411yescharacteristic
128C2×Dic113C2×D411yescharacteristic
129D452—21no—
130D452—21no—
131D452—21no—
132D452—21no—
133D452—81no—
134D452—81no—
135D452—81no—
136D452—81no—
137C4×D113—21no—
138C4×D113—21no—
139C4×D113—81no—
140C4×D113—81no—
141Dic226—81no—
142C8×C113—21no—
143C8×C113—21no—
144#11744751#4112yes—
145#11744751#4112yes—
146C22×C113—41no—
147C22×C113—41no—
148C22×C113—41no—
149C22×C113C22×D411yescharacteristic
150C2×D113—21no—
151C2×D113—21no—
152C2×D113—21no—
153C2×D113—41no—
154C2×D113—41no—
155C2×D113—41no—
156C2×D113—41no—
157C2×D113—41no—
158C2×D113—41no—
159C4×C113—21no—
160C4×C113—21no—
161C4×C113—41no—
162C4×C113—41no—
163C4×C113—41no—
164C4×C113C2×#4111yescharacteristic
165C4×C113C2×#4111yescharacteristic
166Dic113—21no—
167Dic113—21no—
168Dic113—21no—
169Dic113—41no—
170Dic113—41no—
171C2×C113—81no—
172C2×C113#53211yescharacteristic
173C2×C113#57611yescharacteristic
174C2×C113#57711yescharacteristic
175D113—41no—
176D113—81no—
177D113—81no—
178#3179—1131nomaximal, Sylow
179C113#317911yescharacteristic, complemented, Sylow
180#542—1131no—
181#540—1131no—
182#501—1131no—
183#496—1131no—
184#488D11311yescharacteristic, complemented
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×SD16—1131no—
196C2×SD16—1131no—
197C2×D8—1131no—
198C2×D8—1131no—
199C2×M16—1131no—
200C22×C8—1131no—
201C4⋊Q8—1131no—
202#127—1131no—
203#126—2261no—
204#125C2×D11311yescharacteristic
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#103C2×D11311yescharacteristic
227#103C2×D11311yescharacteristic
228#102—1131no—
229#102—1131no—
230#102—1131no—
231#102—1131no—
232#102C2×D11311yescharacteristic
233#102C2×D11311yescharacteristic
234#97—1131no—
235#97—1131no—
236C4×C8—1131no—
237C4×C8C2×D11311yescharacteristic
238C2×Q8—2261no—
239C2×Q8C22×D11311yescharacteristic
240C2×D4—1131no—
241C2×D4—1131no—
242C2×D4—2261no—
243C2×D4—2261no—
244C2×D4—2261no—
245C2×D4—2261no—
246C2×D4—2261no—
247C2×D4C22×D11311yescharacteristic
248C22×C4—1131no—
249C22×C4—2261no—
250C22×C4—2261no—
251C22×C4—2261no—
252SD16—2262no—
253SD16—2262no—
254D8—2262no—
255D8—2262no—
256M16—2262no—
257C2×C8—1131no—
258C2×C8—1131no—
259C2×C8—2262no—
260C2×C8C22×D11311yescharacteristic
261C2×C8C22×D11311yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—1131no—
265C4⋊C4—1131no—
266C4⋊C4—1131no—
267C4⋊C4—1131no—
268C4⋊C4—2261no—
269C4⋊C4—2261no—
270C4⋊C4—2261no—
271C4⋊C4C22×D11311yescharacteristic
272C4⋊C4C22×D11311yescharacteristic
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—1131no—
289C23—2261no—
290C23—2261no—
291Q8—21no—
292Q8—21no—
293Q8—9041no—
294D4—21no—
295D4—21no—
296D4—9041no—
297D4—9041no—
298D4—9041no—
299D4—9041no—
300D4—9041no—
301D4—2261no—
302D4—2261no—
303D4—2261no—
304D4—2261no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—1131no—
309C2×C4—1131no—
310C2×C4—1131no—
311C2×C4—9041no—
312C2×C4—9041no—
313C2×C4—9041no—
314C2×C4—2261no—
315C2×C4—2261no—
316C2×C4—2261no—
317C2×C4—2261no—
318C2×C4D4×D11311yescharacteristic
319C2×C4D4×D11311yescharacteristic
320C2×C4C23×D11311yescharacteristic
321C8—21no—
322C8—21no—
323C8—1132no—
324C8—1132no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—4521no—
329C22—4521no—
330C22—4521no—
331C22—4521no—
332C22—4521no—
333C22—4521no—
334C22—2261no—
335C22—2261no—
336C22—2261no—
337C22C2×D4×D11311yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—4521no—
344C4—4521no—
345C4—2261no—
346C4—2261no—
347C4—2261no—
348C4#41×D11311yescharacteristic
349C4#41×D11311yescharacteristic
350C2—81no—
351C2—9041no—
352C2—9041no—
353C2—4521no—
354C2#2029914711yescharacteristic
355C2#2029940011yescharacteristic
356C2#2029940511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#488×C113C2
socleC22×C113C22×D4
hypercenter#488D113
hypocenterC113#3179
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #20299217C2semidirect
2. #20299204C2semidirect
3. #20299008C2semidirect
4. #20298988C2semidirect
5. #20298945C2semidirect
6. #20298850C2semidirect
7. #20298847C2semidirect
8. #20298833C2semidirect
9. #20298830C2semidirect
10. #20298707C2semidirect
11. #20298701C2semidirect
12. #20298683C2semidirect
13. #20298678C2semidirect
14. #20298552C2semidirect
15. #488×C113C2semidirect
179. C113#3179semidirect
184. #488D113semidirect

Maximal subgroups

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

subgroupindex
#202992172
#202992042
#202990082
#202989882
#202989452
#202988502
#202988472
#202988332
#202988302
#202987072
#202987012
#202986832
#202986782
#202985522
#488×C1132
#3179113