Finite Group Databasebeta

← #14909612

Subgroups — #14909612

Order 2816.

616 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078264C211yesmaximal, characteristic, complemented
2#13070807C212yesmaximal, complemented
3#13070804C212yesmaximal, complemented
4#13070717C212yesmaximal, complemented
5#13070700C212yesmaximal, complemented
6#13070528C212yesmaximal, complemented
7#13070527C212yesmaximal, complemented
8#13070230C211yesmaximal, characteristic, complemented
9C11×#3058C211yesmaximal, characteristic, complemented
10C22×C11×D8C2211yescharacteristic, complemented
11C2×C11×#131C2211yescharacteristic
12C11×#535—21no—
13#10623361—21no—
14C22×D88C2211yescharacteristic, complemented
15C11×#469—21no—
16C11×#469—21no—
17C11×#466C2212yes—
18C11×#466C2212yescomplemented
19C11×#427C2211yescharacteristic, complemented
20C11×#418—21no—
21C2×#66890C2212yes—
22C2×#66890C2212yes—
23#10622748—21no—
24#10622748—21no—
25#10622744—21no—
26#10622728C2212yes—
27#10622728C2212yescomplemented
28#10622719C2211yescharacteristic, complemented
29C2×#66876C2211yescharacteristic, complemented
30C22×C11⋊C16C2211yescharacteristic, complemented
31#10622200C2212yescomplemented
32#10622200C2212yescomplemented
33C22⋊(C11⋊C16)C2212yescomplemented
34C22⋊(C11⋊C16)C2212yescomplemented
35#10622129C2212yescomplemented
36#10622129C2212yescomplemented
37#10622128C2212yescomplemented
38#10622127C2212yescomplemented
39C2×C11×#41D411yescharacteristic
40C22×D4×C11—21no—
41C22×D44—21no—
42C2×C11×D8—21no—
43C2×C11×D8—41no—
44C2×C11×D8—41no—
45C2×C11×D8C2312yes—
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×#127—41no—
55C11×#124—41no—
56C11×#121—22no—
57C11×#121—22no—
58C11×#120—41no—
59C11×#120—41no—
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×#102—22no—
75C11×#102—22no—
76#66890—42no—
77#66890—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#33765—111nomaximal, Sylow
87C24×C11—41no—
88C23×D11—41no—
89C11×#41—41no—
90C11×#41—41no—
91C2×Q8×C11D811yescharacteristic
92C2×D4×C11—22no—
93C2×D4×C11—42no—
94C2×D4×C11—42no—
95C2×D4×C11—42no—
96C2×D4×C11—42no—
97C2×D4×C11—41no—
98C2×D4×C11D811yescharacteristic
99C2×D4×C11D811yescharacteristic
100C2×D4×C11D811yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C2×C22⋊D11—42no—
105C2×C22⋊D11—42no—
106C2×D44—22no—
107C2×D44—42no—
108C2×D44—42no—
109C2×D44—41no—
110C11×D8—22no—
111C11×D8—22no—
112C11×D8—42no—
113C11×M16—41no—
114C11×M16—41no—
115C11×M16—41no—
116C2×C8×C11—21no—
117C2×C8×C11—21no—
118C2×C8×C11—21no—
119C2×C8×C11—21no—
120C2×C8×C11—21no—
121C2×C8×C11—21no—
122C2×C8×C11C2×D411yescharacteristic
123C2×C8×C11C2×D411yescharacteristic
124C2×C8×C11C2×D411yescharacteristic
125C2×C8×C11C2411yescharacteristic
126C11×C4⋊C4—22no—
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#3058—111no—
142#3058D1111yescharacteristic, complemented
143#2234—112no—
144#2234—112no—
145#2218—112no—
146#2215—112no—
147#2184—112no—
148#2184—112no—
149#2113—111no—
150C23×C11—42no—
151C23×C11—82no—
152C23×C11—162no—
153C23×C11C2×D811yescharacteristic
154C23×C11C2×D811yescharacteristic
155C23×C11C2×D811yescharacteristic
156C22×D11—42no—
157C22×D11—82no—
158C22×D11—162no—
159Q8×C11—41no—
160D4×C11—41no—
161D4×C11—41no—
162D4×C11—41no—
163D4×C11—42no—
164D4×C11—42no—
165D4×C11—82no—
166D4×C11—162no—
167D4×C11—162no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—42no—
175C2×C4×C11C2×D811yescharacteristic
176C2×C4×C11C2×D811yescharacteristic
177C2×C4×C11C2×D811yescharacteristic
178C2×C4×C11C22×D411yescharacteristic
179C22⋊D11—162no—
180C22⋊D11—162no—
181C2×Dic11—42no—
182D44—42no—
183D44—42no—
184D44—82no—
185C8×C11—21no—
186C8×C11—21no—
187C8×C11—21no—
188C8×C11H(5,𝔽2)11yescharacteristic
189C8×C11H(5,𝔽2)11yescharacteristic
190C22×D8—111no—
191C22×D8C2×D1111yescharacteristic, complemented
192C2×#131C2×D1111yescharacteristic
193#535—21no—
194#535—221no—
195C2×D16—112no—
196C2×D16—112no—
197C2×M32—111no—
198C22×C16—111no—
199#469—21no—
200#469—21no—
201#469—221no—
202#469—221no—
203#466—112no—
204#466—112no—
205#466C2×D1112yes—
206#466C2×D1112yescomplemented
207#427—111no—
208#427C2×D1111yescharacteristic, complemented
209#418—21no—
210#418—221no—
211#367—112no—
212#366—112no—
213#357—112no—
214#357—112no—
215#357—112no—
216#357—112no—
217C22⋊C16—112no—
218C22⋊C16—112no—
219C22×C11—22no—
220C22×C11—22no—
221C22×C11—22no—
222C22×C11—21no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—82no—
226C22×C11—82no—
227C22×C11—82no—
228C22×C11—164no—
229C22×C11C22×D811yescharacteristic
230C2×D11—82no—
231C2×D11—82no—
232C2×D11—82no—
233C2×D11—164no—
234C4×C11—21no—
235C4×C11—21no—
236C4×C11—21no—
237C4×C11—82no—
238C4×C11#53411yescharacteristic
239C4×C11#57511yescharacteristic
240Dic11—82no—
241C2×#41C22⋊D1111yescharacteristic
242C22×D4—21no—
243C22×D4—221no—
244C2×D8—21no—
245C2×D8—41no—
246C2×D8—41no—
247C2×D8—112no—
248C2×D8—221no—
249C2×D8—441no—
250C2×D8—441no—
251C2×D8C22×D1112yes—
252#131—41no—
253#131—41no—
254C2×M16C22⋊D1111yescharacteristic
255C2×M16C22⋊D1111yescharacteristic
256C2×M16C22⋊D1111yescharacteristic
257C22×C8C22×D1111yescharacteristic
258C22×C8C22×D1111yescharacteristic
259C22×C8C22×D1111yescharacteristic
260#127—41no—
261#127—441no—
262#124—41no—
263#124—441no—
264#121—22no—
265#121—22no—
266#121—222no—
267#121—222no—
268#120—41no—
269#120—41no—
270#120—441no—
271#120—441no—
272#117—21no—
273#117—221no—
274D16—442no—
275D16—442no—
276M32—441no—
277C2×C16—112no—
278C2×C16—112no—
279C2×C16—441no—
280#107—112no—
281#107C22×D1112yes—
282#106—21no—
283#106—221no—
284#102—22no—
285#102—22no—
286#102—222no—
287#102—222no—
288C2×C11—41no—
289C2×C11—41no—
290C2×C11—41no—
291C2×C11—162no—
292C2×C11#318611yescharacteristic
293C2×C11#341512yes—
294D11—162no—
295C24—41no—
296C24—441no—
297#41—41no—
298#41—41no—
299C2×Q8#432311yescharacteristic
300C2×D4—22no—
301C2×D4—42no—
302C2×D4—42no—
303C2×D4—42no—
304C2×D4—42no—
305C2×D4—41no—
306C2×D4—222no—
307C2×D4—442no—
308C2×D4—442no—
309C2×D4—442no—
310C2×D4—442no—
311C2×D4—441no—
312C2×D4#432311yescharacteristic
313C2×D4#432311yescharacteristic
314C2×D4#432311yescharacteristic
315C22×C4C2×C22⋊D1111yescharacteristic
316C22×C4C2×C22⋊D1111yescharacteristic
317C22×C4C2×C22⋊D1111yescharacteristic
318D8—22no—
319D8—22no—
320D8—42no—
321D8—222no—
322D8—222no—
323D8—442no—
324M16—41no—
325M16—41no—
326M16—41no—
327C2×C8—21no—
328C2×C8—21no—
329C2×C8—21no—
330C2×C8—21no—
331C2×C8—21no—
332C2×C8—21no—
333C2×C8C2×C22⋊D1111yescharacteristic
334C2×C8C2×C22⋊D1111yescharacteristic
335C2×C8C2×C22⋊D1111yescharacteristic
336C2×C8C23×D1111yescharacteristic
337C4⋊C4—22no—
338C4⋊C4—222no—
339C22⋊C4—41no—
340C22⋊C4—42no—
341C22⋊C4—42no—
342C22⋊C4—441no—
343C22⋊C4—442no—
344C22⋊C4—442no—
345C42—41no—
346C42—441no—
347C16—222no—
348C16—222no—
349C11#3376511yescharacteristic, complemented, Sylow
350C23—42no—
351C23—82no—
352C23—162no—
353C23—442no—
354C23—882no—
355C23—1762no—
356C23C2×#432311yescharacteristic
357C23C2×#432311yescharacteristic
358C23C2×#432311yescharacteristic
359Q8—41no—
360D4—41no—
361D4—41no—
362D4—41no—
363D4—42no—
364D4—42no—
365D4—82no—
366D4—162no—
367D4—162no—
368D4—442no—
369D4—442no—
370D4—882no—
371D4—1762no—
372D4—1762no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—42no—
380C2×C4—442no—
381C2×C4C2×#432311yescharacteristic
382C2×C4C2×#432311yescharacteristic
383C2×C4C2×#432311yescharacteristic
384C2×C4C22×C22⋊D1111yescharacteristic
385C8—21no—
386C8—21no—
387C8—21no—
388C8#6703711yescharacteristic
389C8#6703711yescharacteristic
390C22—21no—
391C22—21no—
392C22—21no—
393C22—22no—
394C22—22no—
395C22—22no—
396C22—82no—
397C22—82no—
398C22—82no—
399C22—164no—
400C22—882no—
401C22—882no—
402C22—882no—
403C22—1764no—
404C22C22×#432311yescharacteristic
405C4—21no—
406C4—21no—
407C4—21no—
408C4—82no—
409C4—882no—
410C4#1062333511yescharacteristic
411C4#1062335311yescharacteristic
412C2—41no—
413C2—41no—
414C2—41no—
415C2—162no—
416C2—1762no—
417C2#1307936411yescharacteristic
418C2#1308175512yes—
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3058C2
socleC22×C11C22×D8
hypercenter#3058D11
hypocenterC11#33765
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131 ◁ #3058

Complements

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

NH ≅ G/Ntype
1. #13078264C2semidirect
2. #13070807C2semidirect
3. #13070804C2semidirect
4. #13070717C2semidirect
5. #13070700C2semidirect
6. #13070528C2semidirect
7. #13070527C2semidirect
8. #13070230C2semidirect
9. C11×#3058C2semidirect
10. C22×C11×D8C22semidirect
14. C22×D88C22semidirect
18. C11×#466C22semidirect
19. C11×#427C22semidirect
27. #10622728C22semidirect
28. #10622719C22semidirect
29. C2×#66876C22semidirect
30. C22×C11⋊C16C22semidirect
31. #10622200C22semidirect
32. #10622200C22semidirect
33. C22⋊(C11⋊C16)C22semidirect
34. C22⋊(C11⋊C16)C22semidirect
35. #10622129C22semidirect
36. #10622129C22semidirect
37. #10622128C22semidirect
38. #10622127C22semidirect
142. #3058D11semidirect
191. C22×D8C2×D11semidirect
206. #466C2×D11semidirect
208. #427C2×D11semidirect
349. C11#33765semidirect

Maximal subgroups

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

subgroupindex
#130782642
#130708072
#130708042
#130707172
#130707002
#130705282
#130705272
#130702302
C11×#30582
#3376511