Finite Group Databasebeta

← #28402039

Subgroups — #28402039

Order 14464.

346 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299219C211yesmaximal, characteristic, complemented
2#20298888C211yesmaximal, characteristic, complemented
3#20298885C211yesmaximal, characteristic, complemented
4#20298883C211yesmaximal, characteristic, complemented
5#20298880C211yesmaximal, characteristic, complemented
6#20298854C211yesmaximal, characteristic, complemented
7#20298849C211yesmaximal, characteristic
8#20298829C211yesmaximal, characteristic, complemented
9#20298825C211yesmaximal, characteristic, complemented
10#20298820C211yesmaximal, characteristic, complemented
11#20298817C211yesmaximal, characteristic, complemented
12#20298813C211yesmaximal, characteristic, complemented
13#20298810C211yesmaximal, characteristic, complemented
14#20298625C211yesmaximal, characteristic, complemented
15#542×C113C211yesmaximal, characteristic, complemented
16C2×#14268637C2211yescharacteristic
17C2×#14268635C2211yescharacteristic
18C2×#14268634C2211yescharacteristic
19C2×#14268632C2211yescharacteristic
20C2×#14268631C2211yescharacteristic
21C22×#11744751C2211yescharacteristic
22#16813622C2211yescharacteristic
23#16813617—21no—
24#16813610C2211yescharacteristic
25#16813608—21no—
26#16813604—21no—
27#16813601C2211yescharacteristic
28#16813600—21no—
29#16813596C2211yescharacteristic
30C4×Dic226C2211yescharacteristic
31C4×D452C2211yescharacteristic
32#16813553C2211yescharacteristic
33#16813553C2211yescharacteristic
34#16813553C2211yescharacteristic
35#16813553C2211yescharacteristic
36C4⋊#11744751C2211yescharacteristic
37C4⋊#11744751C2211yescharacteristic
38C4⋊#11744751C2211yescharacteristic
39C4⋊#11744751C2211yescharacteristic
40#16813546C2211yescharacteristic
41#16813546C2211yescharacteristic
42#16813545C2211yescharacteristic
43#16813545C2211yescharacteristic
44#16813543C2211yescharacteristic
45#16813543C2211yescharacteristic
46#16813542C2211yescharacteristic
47#16813542C2211yescharacteristic
48C4⋊Q8×C113C2211yescharacteristic
49#126×C113—21no—
50#124×C113—21no—
51#124×C113C2211yescharacteristic
52#123×C113—21no—
53C22⋊Q8×C113—21no—
54C22⋊Q8×C113C2211yescharacteristic
55#121×C113C2211yescharacteristic
56C4×Q8×C113C2211yescharacteristic
57C4×D4×C113C2211yescharacteristic
58#117×C113C2211yescharacteristic
59C2×Dic226—21no—
60C2×Dic226C2311yescharacteristic
61C2×D452C2311yescharacteristic
62C2×C22⋊D113—21no—
63C2×C4×D113—21no—
64#14268637—41no—
65#14268635—41no—
66#14268634—41no—
67#14268632—41no—
68#14268631—41no—
69C2×#11744751—41no—
70C2×#11744751C2311yescharacteristic
71C2×#11744751C2311yescharacteristic
72C2×#11744751C2311yescharacteristic
73C2×#11744751C2311yescharacteristic
74C4⋊Dic113—21no—
75C4⋊Dic113C2311yescharacteristic
76C4⋊Dic113C2311yescharacteristic
77#14268626—21no—
78#14268626—21no—
79C22⋊Dic113—21no—
80#14268624—21no—
81#14268624—21no—
82#14268624—21no—
83#14268624—21no—
84C4×Dic113—21no—
85C2×Q8×C113—21no—
86C2×Q8×C113C2311yescharacteristic
87C2×D4×C113—21no—
88C2×D4×C113C2311yescharacteristic
89C22×C4×C113—21no—
90C22×C4×C113C2311yescharacteristic
91C4⋊C4×C113—21no—
92C4⋊C4×C113—21no—
93C4⋊C4×C113—21no—
94C4⋊C4×C113D411yescharacteristic
95C4⋊C4×C113D411yescharacteristic
96C4⋊C4×C113C2311yescharacteristic
97C4⋊C4×C113C2311yescharacteristic
98C22⋊C4×C113—21no—
99C22⋊C4×C113—21no—
100C22⋊C4×C113—21no—
101C22⋊C4×C113—21no—
102C22⋊C4×C113—21no—
103C22⋊C4×C113D411yescharacteristic
104C22⋊C4×C113D411yescharacteristic
105C42×C113—21no—
106C42×C113C2311yescharacteristic
107C42×C113C2311yescharacteristic
108C23×C113—21no—
109C23×C113C2×D411yescharacteristic
110C22×D113—21no—
111Q8×C113—21no—
112Q8×C113—21no—
113Q8×C113—81no—
114D4×C113—21no—
115D4×C113—21no—
116D4×C113—81no—
117C2×C4×C113—21no—
118C2×C4×C113—21no—
119C2×C4×C113—21no—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—81no—
123C2×C4×C113C2×D411yescharacteristic
124C2×C4×C113C2×D411yescharacteristic
125C2×C4×C113C2×D411yescharacteristic
126C2×C4×C113C2×D411yescharacteristic
127C2×C4×C113C2×D411yescharacteristic
128C2×C4×C113C2411yescharacteristic
129C22⋊D113—81no—
130C2×Dic113—21no—
131C2×Dic113—21no—
132C2×Dic113—21no—
133D452—21no—
134D452—21no—
135C4×D113—81no—
136Dic226—21no—
137Dic226—21no—
138Dic226—81no—
139#11744751—21no—
140#11744751—21no—
141#11744751—21no—
142#11744751—21no—
143C22×C113—21no—
144C22×C113—21no—
145C22×C113—21no—
146C22×C113—41no—
147C22×C113—41no—
148C22×C113—41no—
149C22×C113C22×D411yescharacteristic
150C2×D113—41no—
151C2×D113—41no—
152C2×D113—41no—
153C4×C113—21no—
154C4×C113—21no—
155C4×C113—21no—
156C4×C113—21no—
157C4×C113—21no—
158C4×C113—41no—
159C4×C113—41no—
160C4×C113—41no—
161C4×C113H(5,𝔽2)11yescharacteristic
162C4×C1132−1+411yescharacteristic
163Dic113—41no—
164Dic113—41no—
165Dic113—41no—
166C2×C113—41no—
167C2×C113—81no—
168C2×C113#53711yescharacteristic
169C2×C113#57711yescharacteristic
170C2×C113#57711yescharacteristic
171D113—81no—
172#3263—1131nomaximal, Sylow
173C113#326311yescharacteristic, complemented, Sylow
174#542—1131no—
175#542D11311yescharacteristic, complemented
176#476—1131no—
177#476—1131no—
178#475—1131no—
179#475—1131no—
180#470—1131no—
181#469—1131no—
182#465—1131no—
183#465—1131no—
184#464—1131no—
185#464—1131no—
186#463—1131no—
187#463—1131no—
188#424—1131no—
189C2×Q16—1131no—
190C2×SD16—1131no—
191C2×SD16—1131no—
192C2×D8—1131no—
193C2×M16—1131no—
194C22×C8—1131no—
195C4⋊Q8—1131no—
196C4⋊Q8C2×D11311yescharacteristic
197#126—21no—
198#126—2261no—
199#124—21no—
200#124—1131no—
201#124—2261no—
202#124C2×D11311yescharacteristic
203#123—21no—
204#123—2261no—
205C22⋊Q8—21no—
206C22⋊Q8—1131no—
207C22⋊Q8—2261no—
208C22⋊Q8C2×D11311yescharacteristic
209#121—1131no—
210#121C2×D11311yescharacteristic
211C4×Q8—1131no—
212C4×Q8C2×D11311yescharacteristic
213C4×D4—1131no—
214C4×D4C2×D11311yescharacteristic
215#117C2×D11311yescharacteristic
216#106—1131no—
217#106—1131no—
218#106—1131no—
219#106—1131no—
220C4⋊C8—1131no—
221C4⋊C8—1131no—
222C4⋊C8—1131no—
223C4⋊C8—1131no—
224#103—1131no—
225#103—1131no—
226#103—1131no—
227#103—1131no—
228#102—1131no—
229#102—1131no—
230#102—1131no—
231#102—1131no—
232C2×Q8—21no—
233C2×Q8—1131no—
234C2×Q8—2261no—
235C2×Q8C22×D11311yescharacteristic
236C2×D4—21no—
237C2×D4—1131no—
238C2×D4—2261no—
239C2×D4C22×D11311yescharacteristic
240C22×C4—21no—
241C22×C4—2261no—
242C22×C4C22×D11311yescharacteristic
243Q16—4521no—
244SD16—4521no—
245SD16—4521no—
246D8—4521no—
247M16—4521no—
248C2×C8—1131no—
249C2×C8—1131no—
250C2×C8—1131no—
251C2×C8—1131no—
252C2×C8—4521no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—1131no—
257C4⋊C4—1131no—
258C4⋊C4—2261no—
259C4⋊C4—2261no—
260C4⋊C4—2261no—
261C4⋊C4C22⋊D11311yescharacteristic
262C4⋊C4C22⋊D11311yescharacteristic
263C4⋊C4C22×D11311yescharacteristic
264C4⋊C4C22×D11311yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—2261no—
271C22⋊C4—2261no—
272C22⋊C4—2261no—
273C22⋊C4—2261no—
274C22⋊C4—2261no—
275C22⋊C4C22⋊D11311yescharacteristic
276C22⋊C4C22⋊D11311yescharacteristic
277C42—21no—
278C42—2261no—
279C42C22×D11311yescharacteristic
280C42C22×D11311yescharacteristic
281C23—21no—
282C23—2261no—
283C23C2×C22⋊D11311yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—81no—
287Q8—9041no—
288Q8—2261no—
289Q8—2261no—
290D4—21no—
291D4—21no—
292D4—81no—
293D4—9041no—
294D4—2261no—
295D4—2261no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—81no—
302C2×C4—9041no—
303C2×C4—2261no—
304C2×C4—2261no—
305C2×C4—2261no—
306C2×C4C2×C22⋊D11311yescharacteristic
307C2×C4C2×C22⋊D11311yescharacteristic
308C2×C4C2×C22⋊D11311yescharacteristic
309C2×C4C2×C22⋊D11311yescharacteristic
310C2×C4C2×C22⋊D11311yescharacteristic
311C2×C4C23×D11311yescharacteristic
312C8—2261no—
313C8—2261no—
314C8—2261no—
315C8—2261no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—4521no—
323C22—4521no—
324C22—4521no—
325C22C22×C22⋊D11311yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—4521no—
335C4—4521no—
336C4—4521no—
337C4#1681366811yescharacteristic
338C4#1681366911yescharacteristic
339C2—41no—
340C2—81no—
341C2—9041no—
342C2#2029917611yescharacteristic
343C2#2029940611yescharacteristic
344C2#2029940911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#542×C113C2
socleC22×C113C22×D4
prime radical#20298849C2
hypercenter#542D113
hypocenterC113#3263
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #20299219C2semidirect
2. #20298888C2semidirect
3. #20298885C2semidirect
4. #20298883C2semidirect
5. #20298880C2semidirect
6. #20298854C2semidirect
8. #20298829C2semidirect
9. #20298825C2semidirect
10. #20298820C2semidirect
11. #20298817C2semidirect
12. #20298813C2semidirect
13. #20298810C2semidirect
14. #20298625C2semidirect
15. #542×C113C2semidirect
173. C113#3263semidirect
175. #542D113semidirect

Maximal subgroups

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

subgroupindex
#202992192
#202988882
#202988852
#202988832
#202988802
#202988542
#202988492
#202988292
#202988252
#202988202
#202988172
#202988132
#202988102
#202986252
#542×C1132
#3263113