Finite Group Databasebeta

← #14909618

Subgroups — #14909618

Order 2816.

584 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078264C211yesmaximal, characteristic
2#13070821C212yesmaximal, complemented
3#13070807C212yesmaximal, complemented
4#13070731C212yesmaximal, complemented
5#13070714C212yesmaximal, complemented
6#13070544C212yesmaximal, complemented
7#13070533C212yesmaximal, complemented
8#13070230C211yesmaximal, characteristic, complemented
9C11×#3059C211yesmaximal, characteristic, complemented
10C22×C11×Q16C2211yescharacteristic, complemented
11C2×C11×#131C2211yescharacteristic
12C11×#536—21no—
13#10623361—21no—
14C22×D88C2211yescharacteristic
15C11×#470—21no—
16C11×#470—21no—
17C11×#467C2212yes—
18C11×#467C2212yescomplemented
19C11×#427C2211yescharacteristic, complemented
20C11×#419—21no—
21C2×#66892C2212yes—
22C2×#66892C2212yes—
23#10622748—21no—
24#10622748—21no—
25#10622744—21no—
26#10622728C2212yes—
27#10622728C2212yes—
28#10622719C2211yescharacteristic
29C2×#66876C2211yescharacteristic, complemented
30C22×C11⋊C16C2211yescharacteristic, complemented
31#10622202C2212yescomplemented
32#10622202C2212yescomplemented
33C22⋊(C11⋊C16)C2212yes—
34C22⋊(C11⋊C16)C2212yescomplemented
35#10622129C2212yes—
36#10622129C2212yes—
37#10622128C2212yescomplemented
38#10622127C2212yescomplemented
39C2×C11×#41D411yescharacteristic
40C22×Q8×C11—21no—
41C22×D44—21no—
42C2×C11×Q16—21no—
43C2×C11×Q16—41no—
44C2×C11×Q16—41no—
45C2×C11×Q16C2312yes—
46C11×#131—41no—
47C11×#131—41no—
48C2×C11×M16D411yescharacteristic
49C2×C11×M16D411yescharacteristic
50C2×C11×M16D411yescharacteristic
51C22×C8×C11C2311yescharacteristic
52C22×C8×C11C2311yescharacteristic
53C22×C8×C11C2311yescharacteristic
54C11×C4⋊Q8—41no—
55C11×#124—41no—
56C11×#123—41no—
57C11×#123—41no—
58C11×C22⋊Q8—22no—
59C11×C22⋊Q8—22no—
60C11×#117—21no—
61#67000—41no—
62#66993—41no—
63#66990—41no—
64#66990—41no—
65#66983—22no—
66#66983—22no—
67#66979—21no—
68C2×D88—21no—
69C2×D88—41no—
70C2×D88—41no—
71C2×D88C2312yes—
72C11×#107C2312yes—
73C11×#106—21no—
74C11×#103—22no—
75C11×#103—22no—
76#66892—42no—
77#66892—42no—
78#66885—22no—
79#66885—22no—
80#66882C2312yes—
81#66881—21no—
82#66876—41no—
83C2×C11⋊C16—41no—
84C2×C11⋊C16C2312yes—
85C2×C11⋊C16C2312yes—
86#33766—111nomaximal, Sylow
87C23×D11—41no—
88C11×#41—41no—
89C11×#41—41no—
90C2×Q8×C11—22no—
91C2×Q8×C11—42no—
92C2×Q8×C11—42no—
93C2×Q8×C11—41no—
94C2×Q8×C11D811yescharacteristic
95C2×D4×C11D811yescharacteristic
96C2×D4×C11D811yescharacteristic
97C2×D4×C11D811yescharacteristic
98C22×C4×C11—41no—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C2×C22⋊D11—42no—
103C2×C22⋊D11—42no—
104C2×D44—22no—
105C2×D44—42no—
106C2×D44—42no—
107C2×D44—41no—
108C11×Q16—22no—
109C11×Q16—22no—
110C11×Q16—42no—
111C11×M16—41no—
112C11×M16—41no—
113C11×M16—41no—
114C2×C8×C11—21no—
115C2×C8×C11—21no—
116C2×C8×C11—21no—
117C2×C8×C11—21no—
118C2×C8×C11—21no—
119C2×C8×C11—21no—
120C2×C8×C11C2×D411yescharacteristic
121C2×C8×C11C2×D411yescharacteristic
122C2×C8×C11C2×D411yescharacteristic
123C2×C8×C11C2411yescharacteristic
124C11×C4⋊C4—22no—
125C11×C4⋊C4—42no—
126C11×C4⋊C4—42no—
127C11×C22⋊C4—41no—
128C11×C22⋊C4—42no—
129C11×C22⋊C4—42no—
130C42×C11—41no—
131C22⋊Dic11—41no—
132(C2×D11)⋊C4—42no—
133(C2×D11)⋊C4—42no—
134C4⋊Dic11—22no—
135C4×Dic11—41no—
136D88—22no—
137D88—22no—
138D88—42no—
139C11⋊C16—22no—
140C11⋊C16—22no—
141#3059D1111yescharacteristic, complemented
142#3058—111no—
143#2237—112no—
144#2234—112no—
145#2220—112no—
146#2217—112no—
147#2187—112no—
148#2185—112no—
149#2113—111no—
150C23×C11C2×D811yescharacteristic
151C23×C11C2×D811yescharacteristic
152C23×C11C2×D811yescharacteristic
153C22×D11—42no—
154C22×D11—82no—
155C22×D11—162no—
156Q8×C11—41no—
157Q8×C11—42no—
158Q8×C11—42no—
159Q8×C11—82no—
160D4×C11—41no—
161D4×C11—41no—
162D4×C11—41no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—42no—
170C2×C4×C11—42no—
171C2×C4×C11—82no—
172C2×C4×C11C2×D811yescharacteristic
173C2×C4×C11C2×D811yescharacteristic
174C2×C4×C11C2×D811yescharacteristic
175C2×C4×C11C22×D411yescharacteristic
176C22⋊D11—162no—
177C22⋊D11—162no—
178C2×Dic11—42no—
179D44—42no—
180D44—42no—
181D44—82no—
182C8×C11—21no—
183C8×C11—21no—
184C8×C11—21no—
185C8×C11H(5,𝔽2)11yescharacteristic
186C8×C11H(5,𝔽2)11yescharacteristic
187C22×Q16C2×D1111yescharacteristic, complemented
188C22×D8—111no—
189C2×#131C2×D1111yescharacteristic
190#536—21no—
191#535—221no—
192C2×SD32—112no—
193C2×SD32—112no—
194C2×M32—111no—
195C22×C16—111no—
196#470—21no—
197#470—21no—
198#469—221no—
199#469—221no—
200#467C2×D1112yes—
201#467C2×D1112yescomplemented
202#466—112no—
203#466—112no—
204#427—111no—
205#427C2×D1111yescharacteristic, complemented
206#419—21no—
207#418—221no—
208#367—112no—
209#366—112no—
210#358—112no—
211#358—112no—
212#357—112no—
213#357—112no—
214C22⋊C16—112no—
215C22⋊C16—112no—
216C22×C11—22no—
217C22×C11—22no—
218C22×C11—22no—
219C22×C11—21no—
220C22×C11—21no—
221C22×C11—21no—
222C22×C11C22×D811yescharacteristic
223C2×D11—82no—
224C2×D11—82no—
225C2×D11—82no—
226C2×D11—164no—
227C4×C11—21no—
228C4×C11—21no—
229C4×C11—21no—
230C4×C11—82no—
231C4×C11—82no—
232C4×C11#53411yescharacteristic
233C4×C11#57511yescharacteristic
234Dic11—82no—
235C2×#41C22⋊D1111yescharacteristic
236C22×Q8—21no—
237C22×D4—221no—
238C2×Q16—21no—
239C2×Q16—41no—
240C2×Q16—41no—
241C2×Q16C22×D1112yes—
242C2×D8—112no—
243C2×D8—221no—
244C2×D8—441no—
245C2×D8—441no—
246#131—41no—
247#131—41no—
248C2×M16C22⋊D1111yescharacteristic
249C2×M16C22⋊D1111yescharacteristic
250C2×M16C22⋊D1111yescharacteristic
251C22×C8C22×D1111yescharacteristic
252C22×C8C22×D1111yescharacteristic
253C22×C8C22×D1111yescharacteristic
254C4⋊Q8—41no—
255#127—441no—
256#124—41no—
257#124—441no—
258#123—41no—
259#123—41no—
260C22⋊Q8—22no—
261C22⋊Q8—22no—
262#121—222no—
263#121—222no—
264#120—441no—
265#120—441no—
266#117—21no—
267#117—221no—
268SD32—442no—
269SD32—442no—
270M32—441no—
271C2×C16—112no—
272C2×C16—112no—
273C2×C16—441no—
274#107—112no—
275#107C22×D1112yes—
276#106—21no—
277#106—221no—
278#103—22no—
279#103—22no—
280#102—222no—
281#102—222no—
282C2×C11—41no—
283C2×C11—41no—
284C2×C11—41no—
285C2×C11#318611yescharacteristic
286C2×C11#341612yes—
287D11—162no—
288C24—441no—
289#41—41no—
290#41—41no—
291C2×Q8—22no—
292C2×Q8—42no—
293C2×Q8—42no—
294C2×Q8—41no—
295C2×Q8#432311yescharacteristic
296C2×D4—222no—
297C2×D4—442no—
298C2×D4—442no—
299C2×D4—442no—
300C2×D4—442no—
301C2×D4—441no—
302C2×D4#432311yescharacteristic
303C2×D4#432311yescharacteristic
304C2×D4#432311yescharacteristic
305C22×C4—41no—
306C22×C4C2×C22⋊D1111yescharacteristic
307C22×C4C2×C22⋊D1111yescharacteristic
308C22×C4C2×C22⋊D1111yescharacteristic
309Q16—22no—
310Q16—22no—
311Q16—42no—
312D8—222no—
313D8—222no—
314D8—442no—
315M16—41no—
316M16—41no—
317M16—41no—
318C2×C8—21no—
319C2×C8—21no—
320C2×C8—21no—
321C2×C8—21no—
322C2×C8—21no—
323C2×C8—21no—
324C2×C8C2×C22⋊D1111yescharacteristic
325C2×C8C2×C22⋊D1111yescharacteristic
326C2×C8C2×C22⋊D1111yescharacteristic
327C2×C8C23×D1111yescharacteristic
328C4⋊C4—22no—
329C4⋊C4—42no—
330C4⋊C4—42no—
331C4⋊C4—222no—
332C22⋊C4—41no—
333C22⋊C4—42no—
334C22⋊C4—42no—
335C22⋊C4—441no—
336C22⋊C4—442no—
337C22⋊C4—442no—
338C42—41no—
339C42—441no—
340C16—222no—
341C16—222no—
342C11#3376611yescharacteristic, complemented, Sylow
343C23—442no—
344C23—882no—
345C23—1762no—
346C23C2×#432311yescharacteristic
347C23C2×#432311yescharacteristic
348C23C2×#432311yescharacteristic
349Q8—41no—
350Q8—42no—
351Q8—42no—
352Q8—82no—
353D4—41no—
354D4—41no—
355D4—41no—
356D4—442no—
357D4—442no—
358D4—882no—
359D4—1762no—
360D4—1762no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—82no—
370C2×C4—442no—
371C2×C4C2×#432311yescharacteristic
372C2×C4C2×#432311yescharacteristic
373C2×C4C2×#432311yescharacteristic
374C2×C4C22×C22⋊D1111yescharacteristic
375C8—21no—
376C8—21no—
377C8—21no—
378C8#6703711yescharacteristic
379C8#6703711yescharacteristic
380C22—21no—
381C22—21no—
382C22—21no—
383C22—22no—
384C22—22no—
385C22—22no—
386C22—882no—
387C22—882no—
388C22—882no—
389C22—1764no—
390C22C22×#432311yescharacteristic
391C4—21no—
392C4—21no—
393C4—21no—
394C4—82no—
395C4—82no—
396C4—882no—
397C4#1062333511yescharacteristic
398C4#1062335311yescharacteristic
399C2—41no—
400C2—41no—
401C2—41no—
402C2—1762no—
403C2#1307936411yescharacteristic
404C2#1308176012yes—
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3059C2
socleC22×C11C22×D8
prime radical#13078264C2
hypercenter#3059D11
hypocenterC11#33766
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131 ◁ #3059

Complements

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

NH ≅ G/Ntype
2. #13070821C2semidirect
3. #13070807C2semidirect
4. #13070731C2semidirect
5. #13070714C2semidirect
6. #13070544C2semidirect
7. #13070533C2semidirect
8. #13070230C2semidirect
9. C11×#3059C2semidirect
10. C22×C11×Q16C22semidirect
18. C11×#467C22semidirect
19. C11×#427C22semidirect
29. C2×#66876C22semidirect
30. C22×C11⋊C16C22semidirect
31. #10622202C22semidirect
32. #10622202C22semidirect
34. C22⋊(C11⋊C16)C22semidirect
37. #10622128C22semidirect
38. #10622127C22semidirect
141. #3059D11semidirect
187. C22×Q16C2×D11semidirect
201. #467C2×D11semidirect
205. #427C2×D11semidirect
342. C11#33766semidirect

Maximal subgroups

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

subgroupindex
#130782642
#130708212
#130708072
#130707312
#130707142
#130705442
#130705332
#130702302
C11×#30592
#3376611