Finite Group Databasebeta

← #28401985

Subgroups — #28401985

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#20299203C211yesmaximal, characteristic, complemented
2#20298905C211yesmaximal, characteristic, complemented
3#20298898C211yesmaximal, characteristic, complemented
4#20298885C211yesmaximal, characteristic, complemented
5#20298875C211yesmaximal, characteristic, complemented
6#20298849C211yesmaximal, characteristic, complemented
7#20298846C211yesmaximal, characteristic, complemented
8#20298832C211yesmaximal, characteristic, complemented
9#20298829C211yesmaximal, characteristic, complemented
10#20298810C211yesmaximal, characteristic, complemented
11#20298810C211yesmaximal, characteristic, complemented
12#20298798C211yesmaximal, characteristic, complemented
13#20298793C211yesmaximal, characteristic, complemented
14#20298625C211yesmaximal, characteristic, complemented
15#542×C113C211yesmaximal, characteristic, complemented
16C2×#14268634C2211yescharacteristic
17C2×#14268634C2211yescharacteristic
18C2×#14268632C2211yescharacteristic
19C2×#14268632C2211yescharacteristic
20C2×#14268631C2211yescharacteristic
21C22×#11744751C2211yescharacteristic
22#16813619C2211yescharacteristic
23#16813614C2211yescharacteristic
24#16813607—21no—
25#16813607—21no—
26#16813596C2211yescharacteristic
27#16813596C2211yescharacteristic
28#16813595—21no—
29#16813595—21no—
30C4×D452C2211yescharacteristic
31C4×D452C2211yescharacteristic
32#16813555C2211yescharacteristic
33#16813555C2211yescharacteristic
34#16813553C2211yescharacteristic
35#16813553C2211yescharacteristic
36C4⋊#11744751C2211yescharacteristic
37C4⋊#11744751C2211yescharacteristic
38C4⋊#11744751C2211yescharacteristic
39C4⋊#11744751C2211yescharacteristic
40#16813546C2211yescharacteristic
41#16813546C2211yescharacteristic
42#16813543C2211yescharacteristic
43#16813543C2211yescharacteristic
44#16813542C2211yescharacteristic
45#16813542C2211yescharacteristic
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×D452—21no—
60C2×D452—21no—
61C2×D452C2311yescharacteristic
62C2×D452C2311yescharacteristic
63C2×C22⋊D113—21no—
64C2×C22⋊D113—21no—
65C2×C4×D113—21no—
66C2×C4×D113—21no—
67#14268634—41no—
68#14268634—41no—
69#14268632—41no—
70#14268632—41no—
71#14268631—41no—
72C2×#11744751—41no—
73C2×#11744751C2311yescharacteristic
74C2×#11744751C2311yescharacteristic
75C2×#11744751C2311yescharacteristic
76C2×#11744751C2311yescharacteristic
77C4⋊Dic113C2311yescharacteristic
78C4⋊Dic113C2311yescharacteristic
79#14268626—21no—
80#14268626—21no—
81#14268624—21no—
82#14268624—21no—
83#14268624—21no—
84#14268624—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—
111C22×D113—21no—
112Q8×C113—21no—
113Q8×C113—21no—
114Q8×C113—81no—
115D4×C113—21no—
116D4×C113—21no—
117D4×C113—81no—
118C2×C4×C113—21no—
119C2×C4×C113—21no—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113—81no—
124C2×C4×C113C2×D411yescharacteristic
125C2×C4×C113C2×D411yescharacteristic
126C2×C4×C113C2×D411yescharacteristic
127C2×C4×C113C2×D411yescharacteristic
128C2×C4×C113C2×D411yescharacteristic
129C2×C4×C113C2411yescharacteristic
130C22⋊D113—81no—
131C22⋊D113—81no—
132C2×Dic113—21no—
133C2×Dic113—21no—
134D452—21no—
135D452—21no—
136D452—21no—
137D452—21no—
138D452—81no—
139D452—81no—
140C4×D113—81no—
141C4×D113—81no—
142#11744751—21no—
143#11744751—21no—
144#11744751—21no—
145#11744751—21no—
146C22×C113—21no—
147C22×C113—21no—
148C22×C113—21no—
149C22×C113—41no—
150C22×C113—41no—
151C22×C113—41no—
152C22×C113C22×D411yescharacteristic
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—21no—
162C4×C113—21no—
163C4×C113—21no—
164C4×C113—41no—
165C4×C113—41no—
166C4×C113—41no—
167C4×C113H(5,𝔽2)11yescharacteristic
168C4×C1132−1+411yescharacteristic
169Dic113—41no—
170Dic113—41no—
171C2×C113—41no—
172C2×C113—81no—
173C2×C113#53711yescharacteristic
174C2×C113#57611yescharacteristic
175C2×C113#57711yescharacteristic
176D113—81no—
177D113—81no—
178#3257—1131nomaximal, Sylow
179C113#325711yescharacteristic, complemented, Sylow
180#542D11311yescharacteristic, complemented
181#540—1131no—
182#479—1131no—
183#478—1131no—
184#476—1131no—
185#474—1131no—
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—21no—
204#125—1131no—
205#124—21no—
206#124C2×D11311yescharacteristic
207#123—21no—
208#123—2261no—
209#123—2261no—
210C22⋊Q8—21no—
211C22⋊Q8C2×D11311yescharacteristic
212#121—1131no—
213#121—1131no—
214#121—2261no—
215#121—2261no—
216#121C2×D11311yescharacteristic
217C4×Q8C2×D11311yescharacteristic
218C4×D4—1131no—
219C4×D4—1131no—
220C4×D4C2×D11311yescharacteristic
221#117C2×D11311yescharacteristic
222#107—1131no—
223#107—1131no—
224#106—1131no—
225#106—1131no—
226C4⋊C8—1131no—
227C4⋊C8—1131no—
228C4⋊C8—1131no—
229C4⋊C8—1131no—
230#103—1131no—
231#103—1131no—
232#102—1131no—
233#102—1131no—
234#102—1131no—
235#102—1131no—
236#102—1131no—
237#102—1131no—
238C2×Q8—21no—
239C2×Q8C22×D11311yescharacteristic
240C2×D4—21no—
241C2×D4—1131no—
242C2×D4—1131no—
243C2×D4—2261no—
244C2×D4—2261no—
245C2×D4—2261no—
246C2×D4—2261no—
247C2×D4C22×D11311yescharacteristic
248C22×C4—21no—
249C22×C4—2261no—
250C22×C4—2261no—
251C22×C4C22×D11311yescharacteristic
252SD16—4521no—
253SD16—4521no—
254D8—4521no—
255D8—4521no—
256M16—4521no—
257C2×C8—1131no—
258C2×C8—1131no—
259C2×C8—1131no—
260C2×C8—1131no—
261C2×C8—4521no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—1131no—
266C4⋊C4—1131no—
267C4⋊C4—2261no—
268C4⋊C4—2261no—
269C4⋊C4C22⋊D11311yescharacteristic
270C4⋊C4C22⋊D11311yescharacteristic
271C4⋊C4C22×D11311yescharacteristic
272C4⋊C4C22×D11311yescharacteristic
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—2261no—
279C22⋊C4—2261no—
280C22⋊C4—2261no—
281C22⋊C4—2261no—
282C22⋊C4C22⋊D11311yescharacteristic
283C22⋊C4C22⋊D11311yescharacteristic
284C42—21no—
285C42C22×D11311yescharacteristic
286C42C22×D11311yescharacteristic
287C23—21no—
288C23—2261no—
289C23—2261no—
290C23C2×C22⋊D11311yescharacteristic
291Q8—21no—
292Q8—21no—
293Q8—81no—
294D4—21no—
295D4—21no—
296D4—81no—
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—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—9041no—
312C2×C4—9041no—
313C2×C4—2261no—
314C2×C4—2261no—
315C2×C4C2×C22⋊D11311yescharacteristic
316C2×C4C2×C22⋊D11311yescharacteristic
317C2×C4C2×C22⋊D11311yescharacteristic
318C2×C4C2×C22⋊D11311yescharacteristic
319C2×C4C2×C22⋊D11311yescharacteristic
320C2×C4C23×D11311yescharacteristic
321C8—2261no—
322C8—2261no—
323C8—2261no—
324C8—2261no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—4521no—
332C22—4521no—
333C22—4521no—
334C22—4521no—
335C22—4521no—
336C22—4521no—
337C22C22×C22⋊D11311yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—4521no—
347C4—4521no—
348C4#1681366811yescharacteristic
349C4#1681366911yescharacteristic
350C2—41no—
351C2—81no—
352C2—9041no—
353C2—9041no—
354C2#2029917611yescharacteristic
355C2#2029940111yescharacteristic
356C2#2029940611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#542×C113C2
socleC22×C113C22×D4
hypercenter#542D113
hypocenterC113#3257
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. #20299203C2semidirect
2. #20298905C2semidirect
3. #20298898C2semidirect
4. #20298885C2semidirect
5. #20298875C2semidirect
6. #20298849C2semidirect
7. #20298846C2semidirect
8. #20298832C2semidirect
9. #20298829C2semidirect
10. #20298810C2semidirect
11. #20298810C2semidirect
12. #20298798C2semidirect
13. #20298793C2semidirect
14. #20298625C2semidirect
15. #542×C113C2semidirect
179. C113#3257semidirect
180. #542D113semidirect

Maximal subgroups

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

subgroupindex
#202992032
#202989052
#202988982
#202988852
#202988752
#202988492
#202988462
#202988322
#202988292
#202988102
#202987982
#202987932
#202986252
#542×C1132
#3257113