Finite Group Databasebeta

← #28401260

Subgroups — #28401260

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#20299215C211yesmaximal, characteristic, complemented
2#20299201C211yesmaximal, characteristic, complemented
3#20299006C211yesmaximal, characteristic, complemented
4#20298986C211yesmaximal, characteristic, complemented
5#20298951C211yesmaximal, characteristic, complemented
6#20298943C211yesmaximal, characteristic, complemented
7#20298849C211yesmaximal, characteristic, complemented
8#20298842C211yesmaximal, characteristic, complemented
9#20298827C211yesmaximal, characteristic, complemented
10#20298710C211yesmaximal, characteristic, complemented
11#20298697C211yesmaximal, characteristic, complemented
12#20298689C211yesmaximal, characteristic, complemented
13#20298678C211yesmaximal, characteristic, complemented
14#20298553C211yesmaximal, characteristic, complemented
15#466×C113C211yesmaximal, characteristic, complemented
16C2×#14268636C2211yescharacteristic
17C2×#14268635C2211yescharacteristic
18C2×#14268632C2211yescharacteristic
19C2×#14268631C2211yescharacteristic
20#16813621C2211yescharacteristic
21#16813618C2211yescharacteristic
22#16813615—21no—
23#16813613C2211yescharacteristic
24#16813609—21no—
25#16813609C2211yescharacteristic
26#16813606—21no—
27#16813604—21no—
28#16813603—21no—
29#16813601C2211yescharacteristic
30#16813599—21no—
31#16813596C2211yescharacteristic
32#16813594—21no—
33#16813593—21no—
34#16813587C2211yescharacteristic
35D4×Dic113C2211yescharacteristic
36D4×Dic113C2211yescharacteristic
37#16813584C2211yescharacteristic
38#16813581C2211yescharacteristic
39#16813555C2211yescharacteristic
40#16813554C2211yescharacteristic
41#16813553C2211yescharacteristic
42#16813547C2211yescharacteristic
43#16813545C2211yescharacteristic
44#16813544C2211yescharacteristic
45#16813543C2211yescharacteristic
46#16813543C2211yescharacteristic
47#16813542C2211yescharacteristic
48#16813532C2211yescharacteristic
49#16813532C2211yescharacteristic
50C8×Dic113C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C2×D8×C113C2211yescharacteristic
53C22×C8×C113C2211yescharacteristic
54#121×C113C2211yescharacteristic
55#121×C113C2211yescharacteristic
56#107×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58#102×C113C2211yescharacteristic
59C2×Dic226—21no—
60C2×Dic226C2311yescharacteristic
61C2×D452C2311yescharacteristic
62C2×C22⋊D113—21no—
63C2×C22⋊D113—21no—
64C2×C22⋊D113—21no—
65C22×Dic113—21no—
66C22×Dic113—21no—
67C2×C4×D113—21no—
68#14268636—22no—
69#14268635—22no—
70#14268632—22no—
71#14268631—22no—
72C2×#11744751C2311yescharacteristic
73C2×#11744751C2311yescharacteristic
74C4⋊Dic113—21no—
75C4⋊Dic113D411yescharacteristic
76C4⋊Dic113D411yescharacteristic
77C4⋊Dic113C2311yescharacteristic
78C4⋊Dic113C2311yescharacteristic
79#14268626—21no—
80#14268626—21no—
81#14268626—21no—
82#14268626—21no—
83C22⋊Dic113—21no—
84C22⋊Dic113—21no—
85C22⋊Dic113—21no—
86C22⋊Dic113—21no—
87C22⋊Dic113—21no—
88C22⋊Dic113D411yescharacteristic
89C22⋊Dic113D411yescharacteristic
90#14268624—21no—
91#14268624—21no—
92C4×Dic113—21no—
93C4×Dic113C2311yescharacteristic
94C4×Dic113C2311yescharacteristic
95C2×D4×C113—21no—
96C2×D4×C113—21no—
97C2×D4×C113C2311yescharacteristic
98C2×D4×C113C2311yescharacteristic
99C22×C4×C113C2311yescharacteristic
100D8×C113—22no—
101C2×C8×C113—22no—
102C2×C8×C113C2311yescharacteristic
103C2×C8×C113C2311yescharacteristic
104C4⋊C4×C113C2311yescharacteristic
105C4⋊C4×C113C2311yescharacteristic
106C22⋊C4×C113—21no—
107C22⋊C4×C113—21no—
108C23×C113—21no—
109C23×C113—21no—
110C23×C113C2×D411yescharacteristic
111C22×D113—21no—
112D4×C113—21no—
113D4×C113—21no—
114D4×C113—21no—
115D4×C113—21no—
116D4×C113—81no—
117D4×C113—81no—
118C2×C4×C113—21no—
119C2×C4×C113—21no—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113C2×D411yescharacteristic
123C2×C4×C113C2411yescharacteristic
124C22⋊D113—81no—
125C22⋊D113—81no—
126C22⋊D113—81no—
127C2×Dic113—21no—
128C2×Dic113—21no—
129C2×Dic113—21no—
130C2×Dic113—81no—
131C2×Dic113—81no—
132C2×Dic113C2×D411yescharacteristic
133C2×Dic113C2×D411yescharacteristic
134C2×Dic113C2×D411yescharacteristic
135C2×Dic113C2×D411yescharacteristic
136D452—21no—
137D452—21no—
138C4×D113—81no—
139Dic226—21no—
140Dic226—21no—
141Dic226—81no—
142C8×C113—21no—
143C8×C113#4112yes—
144#11744751—21no—
145#11744751#4112yes—
146C22×C113—21no—
147C22×C113—21no—
148C22×C113—21no—
149C22×C113—41no—
150C22×C113—41no—
151C22×C113—41no—
152C22×C113—41no—
153C22×C113—41no—
154C22×C113—41no—
155C22×C113C22×D411yescharacteristic
156C2×D113—41no—
157C2×D113—41no—
158C2×D113—41no—
159C4×C113—21no—
160C4×C113—41no—
161C4×C113—41no—
162C4×C113C2×#4111yescharacteristic
163C4×C113C2×#4111yescharacteristic
164Dic113—21no—
165Dic113—21no—
166Dic113—21no—
167Dic113—21no—
168Dic113—41no—
169Dic113—41no—
170Dic113—41no—
171C2×C113—41no—
172C2×C113—81no—
173C2×C113—81no—
174C2×C113#53211yescharacteristic
175C2×C113#57611yescharacteristic
176C2×C113#57711yescharacteristic
177D113—81no—
178#3179—1131nomaximal, Sylow
179C113#317911yescharacteristic, complemented, Sylow
180#542—1131no—
181#540—1131no—
182#501—1131no—
183#496—1131no—
184#488—1131no—
185#486—1131no—
186#469—1131no—
187#468—1131no—
188#466D11311yescharacteristic, complemented
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×D8C2×D11311yescharacteristic
199C2×M16—1131no—
200C22×C8C2×D11311yescharacteristic
201C4⋊Q8—1131no—
202#127—1131no—
203#126—2261no—
204#125—1131no—
205#124—1131no—
206#124—2261no—
207#123—2261no—
208#123—2261no—
209#123—2261no—
210C22⋊Q8—1131no—
211C22⋊Q8—2261no—
212#121—1131no—
213#121—2261no—
214#121—2261no—
215#121C2×D11311yescharacteristic
216#121C2×D11311yescharacteristic
217C4×Q8—1131no—
218C4×D4—1131no—
219C4×D4—1131no—
220C4×D4—1131no—
221#117—1131no—
222#107—1131no—
223#107C2×D11311yescharacteristic
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#102C2×D11311yescharacteristic
233#102C2×D11311yescharacteristic
234#97—1131no—
235#97—1131no—
236C4×C8—1131no—
237C4×C8—1131no—
238C2×Q8—1131no—
239C2×Q8—2261no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—1131no—
243C2×D4—2261no—
244C2×D4—2261no—
245C2×D4—2261no—
246C2×D4C22×D11311yescharacteristic
247C2×D4C22×D11311yescharacteristic
248C22×C4—2261no—
249C22×C4—2261no—
250C22×C4—2261no—
251C22×C4C22×D11311yescharacteristic
252SD16—2262no—
253SD16—2262no—
254D8—22no—
255D8—2262no—
256M16—2262no—
257C2×C8—22no—
258C2×C8—1131no—
259C2×C8—1131no—
260C2×C8C22×D11311yescharacteristic
261C2×C8C22×D11311yescharacteristic
262C4⋊C4—1131no—
263C4⋊C4—1131no—
264C4⋊C4—1131no—
265C4⋊C4—1131no—
266C4⋊C4—2261no—
267C4⋊C4—2261no—
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—1131no—
286C42—2261no—
287C23—21no—
288C23—21no—
289C23—2261no—
290C23D4×D11311yescharacteristic
291Q8—9041no—
292Q8—2261no—
293Q8—2261no—
294D4—21no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—81no—
299D4—81no—
300D4—9041no—
301D4—9041no—
302D4—9041no—
303D4—2261no—
304D4—2261no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—1131no—
310C2×C4—1131no—
311C2×C4—1131no—
312C2×C4—1131no—
313C2×C4—9041no—
314C2×C4—9041no—
315C2×C4—9041no—
316C2×C4—2261no—
317C2×C4—2261no—
318C2×C4—2261no—
319C2×C4D4×D11311yescharacteristic
320C2×C4C23×D11311yescharacteristic
321C8—21no—
322C8—1132no—
323C8—2261no—
324C8#1426864612yes—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—4521no—
335C22—4521no—
336C22—4521no—
337C22C2×D4×D11311yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—4521no—
342C4—4521no—
343C4—4521no—
344C4—2261no—
345C4—2261no—
346C4—2261no—
347C4—2261no—
348C4#41×D11311yescharacteristic
349C4C2×#1426864611yescharacteristic
350C2—41no—
351C2—81no—
352C2—81no—
353C2—9041no—
354C2#2029914311yescharacteristic
355C2#2029939911yescharacteristic
356C2#2029940511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#466×C113C2
socleC22×C113C22×D4
hypercenter#466D113
hypocenterC113#3179
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #20299215C2semidirect
2. #20299201C2semidirect
3. #20299006C2semidirect
4. #20298986C2semidirect
5. #20298951C2semidirect
6. #20298943C2semidirect
7. #20298849C2semidirect
8. #20298842C2semidirect
9. #20298827C2semidirect
10. #20298710C2semidirect
11. #20298697C2semidirect
12. #20298689C2semidirect
13. #20298678C2semidirect
14. #20298553C2semidirect
15. #466×C113C2semidirect
179. C113#3179semidirect
188. #466D113semidirect

Maximal subgroups

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

subgroupindex
#202992152
#202992012
#202990062
#202989862
#202989512
#202989432
#202988492
#202988422
#202988272
#202987102
#202986972
#202986892
#202986782
#202985532
#466×C1132
#3179113