Finite Group Databasebeta

← #28401992

Subgroups — #28401992

Order 14464.

358 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#20299222C211yesmaximal, characteristic, complemented
2#20299199C211yesmaximal, characteristic, complemented
3#20298904C211yesmaximal, characteristic, complemented
4#20298901C211yesmaximal, characteristic, complemented
5#20298885C211yesmaximal, characteristic, complemented
6#20298850C211yesmaximal, characteristic, complemented
7#20298845C211yesmaximal, characteristic, complemented
8#20298835C211yesmaximal, characteristic, complemented
9#20298826C211yesmaximal, characteristic, complemented
10#20298814C211yesmaximal, characteristic, complemented
11#20298813C211yesmaximal, characteristic, complemented
12#20298797C211yesmaximal, characteristic, complemented
13#20298792C211yesmaximal, characteristic, complemented
14#20298623C211yesmaximal, characteristic, complemented
15#474×C113C211yesmaximal, characteristic, complemented
16C2×#14268636C2211yescharacteristic
17C2×#14268635C2211yescharacteristic
18C2×D904C2211yescharacteristic
19C2×#14268632C2211yescharacteristic
20C2×#14268630C2211yescharacteristic
21C2×C8×D113C2211yescharacteristic
22#16813618C2211yescharacteristic
23#16813617—21no—
24#16813613C2211yescharacteristic
25#16813611—21no—
26#16813610C2211yescharacteristic
27#16813607—21no—
28#16813605—21no—
29#16813604—21no—
30#16813602C2211yescharacteristic
31#16813598—21no—
32#16813597C2211yescharacteristic
33#16813597C2211yescharacteristic
34#16813596—21no—
35#16813595—21no—
36#16813593C2211yescharacteristic
37#16813587C2211yescharacteristic
38C4×D452C2211yescharacteristic
39#16813584C2211yescharacteristic
40#16813579C2211yescharacteristic
41#16813553C2211yescharacteristic
42#16813553C2211yescharacteristic
43C4⋊#11744751C2211yescharacteristic
44#16813551C2211yescharacteristic
45#16813551C2211yescharacteristic
46#16813547C2211yescharacteristic
47#16813545C2211yescharacteristic
48#16813544C2211yescharacteristic
49#16813542C2211yescharacteristic
50#16813542C2211yescharacteristic
51#16813542C2211yescharacteristic
52C4⋊Q8×C113C2211yescharacteristic
53C4×D4×C113C2211yescharacteristic
54#107×C113C2211yescharacteristic
55#107×C113C2211yescharacteristic
56C4⋊C8×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58#102×C113C2211yescharacteristic
59C2×Dic226C2311yescharacteristic
60C2×D452—21no—
61C2×D452—21no—
62C2×D452C2311yescharacteristic
63C2×D452C2311yescharacteristic
64C2×C22⋊D113—21no—
65C2×C22⋊D113—21no—
66C2×C22⋊D113—21no—
67C2×C4×D113—21no—
68C2×C4×D113—21no—
69C2×C4×D113C2311yescharacteristic
70#14268636—41no—
71#14268635—41no—
72D904—41no—
73#14268632—41no—
74#14268630—41no—
75C2×#11744751C2311yescharacteristic
76C2×#11744751C2311yescharacteristic
77C8×D113—41no—
78C4⋊Dic113—21no—
79C4⋊Dic113—21no—
80C4⋊Dic113C2311yescharacteristic
81#14268626—21no—
82#14268626—21no—
83#14268626D411yescharacteristic
84#14268626D411yescharacteristic
85C22⋊Dic113—21no—
86#14268624—21no—
87#14268624—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×C113—21no—
98C2×D4×C113C2311yescharacteristic
99C22×C4×C113—21no—
100C2×C8×C113C2311yescharacteristic
101C2×C8×C113C2311yescharacteristic
102C4⋊C4×C113—21no—
103C4⋊C4×C113C2311yescharacteristic
104C4⋊C4×C113C2311yescharacteristic
105C4⋊C4×C113C2311yescharacteristic
106C22⋊C4×C113—21no—
107C42×C113C2311yescharacteristic
108C23×C113—21no—
109C22×D113—21no—
110C22×D113—21no—
111C22×D113C2×D411yescharacteristic
112Q8×C113—81no—
113D4×C113—21no—
114D4×C113—21no—
115C2×C4×C113—21no—
116C2×C4×C113—21no—
117C2×C4×C113—21no—
118C2×C4×C113—81no—
119C2×C4×C113C2×D411yescharacteristic
120C2×C4×C113C2×D411yescharacteristic
121C2×C4×C113C2411yescharacteristic
122C22⋊D113—81no—
123C22⋊D113—81no—
124C22⋊D113—81no—
125C2×Dic113—21no—
126C2×Dic113—21no—
127C2×Dic113C2×D411yescharacteristic
128C2×Dic113C2×D411yescharacteristic
129C2×Dic113C2×D411yescharacteristic
130D452—21no—
131D452—21no—
132D452—21no—
133D452—21no—
134D452—81no—
135D452—81no—
136C4×D113—21no—
137C4×D113—21no—
138C4×D113—81no—
139C4×D113—81no—
140Dic226—21no—
141Dic226—21no—
142C8×C113—21no—
143C8×C113—21no—
144#11744751—21no—
145#11744751—21no—
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×C113H(5,𝔽2)11yescharacteristic
165C4×C1132−1+411yescharacteristic
166Dic113—21no—
167Dic113—21no—
168Dic113—21no—
169Dic113—41no—
170Dic113—41no—
171C2×C113—81no—
172C2×C113#53711yescharacteristic
173C2×C113#57611yescharacteristic
174C2×C113#57711yescharacteristic
175D113—41no—
176D113—81no—
177D113—81no—
178#3257—1131nomaximal, Sylow
179C113#325711yescharacteristic, complemented, Sylow
180#542—1131no—
181#540—1131no—
182#479—1131no—
183#478—1131no—
184#476—1131no—
185#474D11311yescharacteristic, complemented
186#469—1131no—
187#468—1131no—
188#466—1131no—
189#465—1131no—
190#463—1131no—
191#463—1131no—
192#460—1131no—
193#459—1131no—
194#424—1131no—
195C2×SD16—1131no—
196C2×SD16—1131no—
197C2×D8—1131no—
198C2×D8—1131no—
199C2×M16—1131no—
200C22×C8—1131no—
201C4⋊Q8C2×D11311yescharacteristic
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—1131no—
214#121—1131no—
215#121—2261no—
216#121—2261no—
217C4×Q8—1131no—
218C4×D4—1131no—
219C4×D4—1131no—
220C4×D4C2×D11311yescharacteristic
221#117—1131no—
222#107C2×D11311yescharacteristic
223#107C2×D11311yescharacteristic
224#106—1131no—
225#106—1131no—
226C4⋊C8—1131no—
227C4⋊C8—1131no—
228C4⋊C8—1131no—
229C4⋊C8C2×D11311yescharacteristic
230#103—1131no—
231#103—1131no—
232#102—1131no—
233#102—1131no—
234#102—1131no—
235#102—1131no—
236#102C2×D11311yescharacteristic
237#102C2×D11311yescharacteristic
238C2×Q8—21no—
239C2×Q8—1131no—
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—21no—
249C22×C4—1131no—
250C22×C4—2261no—
251C22×C4—2261no—
252SD16—4521no—
253SD16—4521no—
254D8—4521no—
255D8—4521no—
256M16—4521no—
257C2×C8—1131no—
258C2×C8—1131no—
259C2×C8—4521no—
260C2×C8C22×D11311yescharacteristic
261C2×C8C22×D11311yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—1131no—
264C4⋊C4—1131no—
265C4⋊C4—1131no—
266C4⋊C4—2261no—
267C4⋊C4—2261no—
268C4⋊C4—2261no—
269C4⋊C4—2261no—
270C4⋊C4C22×D11311yescharacteristic
271C4⋊C4C22×D11311yescharacteristic
272C4⋊C4C22×D11311yescharacteristic
273C22⋊C4—21no—
274C22⋊C4—1131no—
275C22⋊C4—1131no—
276C22⋊C4—2261no—
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—81no—
292Q8—2261no—
293Q8—2261no—
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—81no—
309C2×C4—1131no—
310C2×C4—1131no—
311C2×C4—1131no—
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—2261no—
324C8—2261no—
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#1681366811yescharacteristic
349C4#1681367011yescharacteristic
350C2—81no—
351C2—9041no—
352C2—9041no—
353C2—4521no—
354C2#2029917811yescharacteristic
355C2#2029939911yescharacteristic
356C2#2029940711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#474×C113C2
socleC22×C113C22×D4
hypercenter#474D113
hypocenterC113#3257
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #20299222C2semidirect
2. #20299199C2semidirect
3. #20298904C2semidirect
4. #20298901C2semidirect
5. #20298885C2semidirect
6. #20298850C2semidirect
7. #20298845C2semidirect
8. #20298835C2semidirect
9. #20298826C2semidirect
10. #20298814C2semidirect
11. #20298813C2semidirect
12. #20298797C2semidirect
13. #20298792C2semidirect
14. #20298623C2semidirect
15. #474×C113C2semidirect
179. C113#3257semidirect
185. #474D113semidirect

Maximal subgroups

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

subgroupindex
#202992222
#202991992
#202989042
#202989012
#202988852
#202988502
#202988452
#202988352
#202988262
#202988142
#202988132
#202987972
#202987922
#202986232
#474×C1132
#3257113