Finite Group Databasebeta

← #14910579

Subgroups — #14910579

Order 2816.

646 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081769C211yesmaximal, characteristic, complemented
2#13081757C211yesmaximal, characteristic, complemented
3#13080403C212yesmaximal, complemented
4#13070877C211yesmaximal, characteristic, complemented
5#13070741C211yesmaximal, characteristic, complemented
6#13070736C211yesmaximal, characteristic, complemented
7#13070686C212yesmaximal, complemented
8#13070589C212yesmaximal, complemented
9#13070582C212yesmaximal, complemented
10#13070498C211yesmaximal, characteristic, complemented
11C11×#2170C211yesmaximal, characteristic, complemented
12#10623301—22no—
13#10623284C2212yescomplemented
14#10623283C2212yes—
15C11×#504C2211yescharacteristic
16C11×#504C2211yescharacteristic, complemented
17C11×#443C2211yescharacteristic
18#10622756C2212yes—
19#10622755C2212yescomplemented
20#10622522—22no—
21#10622522C2212yescomplemented
22#10622521—22no—
23#10622521C2212yes—
24C2×Dic88—21no—
25C2×Dic88C2211yescharacteristic, complemented
26#10622517—21no—
27#10622517—21no—
28#10622517C2211yescharacteristic
29C2×#66864C2212yescomplemented
30C2×D176—21no—
31C2×D176C2211yescharacteristic
32#10622511—22no—
33#10622440—22no—
34#10622438—22no—
35#10622313C2212yescomplemented
36#10622309C2212yescomplemented
37C11×#364C2211yescharacteristic, complemented
38C11×#350C2211yescharacteristic
39C11×#350C2211yescharacteristic, complemented
40C4×C11×C16C2211yescharacteristic, complemented
41#10622155C2212yescomplemented
42#10622154C2212yescomplemented
43#10622148C2212yescomplemented
44#10622144C2211yescharacteristic, complemented
45#67043—22no—
46#67042—22no—
47C11×#135D411yescharacteristic
48C11×#131C2311yescharacteristic
49C11×#131C2311yescharacteristic
50#67004—22no—
51#67002—22no—
52#66971—42no—
53#66969—42no—
54SD16×D11—42no—
55#66964—42no—
56#66962—22no—
57#66962—42no—
58#66961—22no—
59#66961—42no—
60C2×Dic44—22no—
61C2×Dic44C2312yes—
62#66957—22no—
63#66957—22no—
64#66957C2312yes—
65C2×D88—22no—
66C2×D88C2312yes—
67C2×#4314—22no—
68#66954—22no—
69#66928—22no—
70C11×M32—21no—
71C11×M32—21no—
72C11×M32C2311yescharacteristic
73C11×M32C2311yescharacteristic
74C2×C11×C16—21no—
75C2×C11×C16—21no—
76C2×C11×C16C2311yescharacteristic
77C2×C11×C16C2311yescharacteristic
78C11×#108D411yescharacteristic
79C11×#104D411yescharacteristic
80C11×#104D411yescharacteristic
81C4×C8×C11C2311yescharacteristic
82#66888—22no—
83#66887—22no—
84#66883C2312yes—
85#66869—22no—
86Dic88—22no—
87Dic88—21no—
88Dic88—21no—
89Dic88D411yescharacteristic
90#66864—22no—
91#66864—22no—
92#66864—42no—
93#66864D412yes—
94D176—22no—
95D176—21no—
96D176—21no—
97D176D411yescharacteristic
98#33859—111nomaximal, Sylow
99C11×#41C2×D411yescharacteristic
100C11×#41C2×D411yescharacteristic
101#4343—42no—
102Q8×D11—42no—
103#4341—42no—
104#4341—82no—
105D4×D11—42no—
106D4×D11—82no—
107#4339—22no—
108#4339—42no—
109#4339—42no—
110C2×D44—22no—
111C2×D44—42no—
112C2×Dic22—22no—
113C2×Dic22—42no—
114C11×Q16D811yescharacteristic
115C11×SD16D811yescharacteristic
116C11×SD16D811yescharacteristic
117C11×D8D811yescharacteristic
118C11×M16—21no—
119C11×M16—21no—
120C11×M16C2×D411yescharacteristic
121C11×M16C2×D411yescharacteristic
122C2×C8×C11—21no—
123C2×C8×C11—21no—
124C2×C8×C11C2×D411yescharacteristic
125C2×C8×C11C2411yescharacteristic
126C42×C11C2×D411yescharacteristic
127#4326—42no—
128#4325—42no—
129#4324—42no—
130#4323—42no—
131(C2×D11)⋊C4—82no—
132#4318—22no—
133Dic44—22no—
134Dic44—22no—
135Dic44—42no—
136Dic44C2×D412yes—
137D88—22no—
138D88—22no—
139D88—42no—
140D88C2×D412yes—
141#4314—22no—
142#4314—42no—
143#4314—42no—
144#4314—42no—
145#4314—42no—
146#4313—42no—
147C8×D11—42no—
148C11×C16—21no—
149C11×C16—21no—
150C11×C16—21no—
151C11×C16C2×D411yescharacteristic
152C11×C16C2×D411yescharacteristic
153#3417—111no—
154#3415—111no—
155#3290—112no—
156#2249—111no—
157#2222—111no—
158#2221—111no—
159#2212—112no—
160#2194—112no—
161#2193—112no—
162#2178—111no—
163#2170D1111yescharacteristic, complemented
164C22×D11—42no—
165C22×D11—82no—
166Q8×C11C2×D811yescharacteristic
167Q8×C11C2×D811yescharacteristic
168D4×C11—21no—
169D4×C11—21no—
170D4×C11C2×D811yescharacteristic
171D4×C11C2×D811yescharacteristic
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11C22×D411yescharacteristic
176C22⋊D11—42no—
177C22⋊D11—82no—
178C22⋊D11—82no—
179C2×Dic11—42no—
180C2×Dic11—82no—
181D44—22no—
182D44—42no—
183D44—42no—
184D44—82no—
185C4×D11—42no—
186C4×D11—82no—
187C4×D11—82no—
188Dic22—22no—
189Dic22—42no—
190Dic22—42no—
191Dic22—82no—
192C8×C11—21no—
193C8×C11—21no—
194C8×C11C2×D811yescharacteristic
195C8×C11C2×D811yescharacteristic
196C8×C11C22×D411yescharacteristic
197C8×C11H(5,𝔽2)11yescharacteristic
198C11⋊C8—42no—
199#578—112no—
200#577—222no—
201#576—112no—
202#510—112no—
203#510—222no—
204#509—112no—
205#509—222no—
206#508—111no—
207#508—221no—
208#508—221no—
209C2×Q32—111no—
210C2×Q32—221no—
211C2×SD32—112no—
212C2×D16—111no—
213C2×D16—221no—
214#504C2×D1111yescharacteristic
215#504C2×D1111yescharacteristic, complemented
216#495—112no—
217#473—112no—
218#472—112no—
219#471—222no—
220#455—222no—
221#454—222no—
222#443—112no—
223#443C2×D1111yescharacteristic
224#368—111no—
225#364C2×D1111yescharacteristic, complemented
226#362—112no—
227#361—112no—
228#359—112no—
229#350C2×D1111yescharacteristic
230#350C2×D1111yescharacteristic, complemented
231C4×C16C2×D1111yescharacteristic, complemented
232C22×C11—21no—
233C22×C11—21no—
234C22×C11#57611yescharacteristic
235C2×D11—42no—
236C2×D11—82no—
237C2×D11—162no—
238C2×D11—322no—
239C4×C11—21no—
240C4×C11—21no—
241C4×C11—41no—
242C4×C11D4211yescharacteristic
243C4×C11C22×D811yescharacteristic
244Dic11—42no—
245Dic11—82no—
2462−1+4—222no—
247H(5,𝔽2)—222no—
248#137—222no—
249#137—222no—
250#137—442no—
251#137—442no—
252AGL(1,ℤ/8)—222no—
253AGL(1,ℤ/8)—222no—
254AGL(1,ℤ/8)—442no—
255AGL(1,ℤ/8)—442no—
256#135—112no—
257#135—222no—
258#135—222no—
259#135—442no—
260#135D4411yescharacteristic
261C2×Q16—112no—
262C2×Q16—222no—
263C2×SD16—222no—
264C2×SD16—442no—
265C2×D8—112no—
266C2×D8—222no—
267#131—222no—
268#131C22×D1111yescharacteristic
269#131C22×D1111yescharacteristic
270#124—222no—
271Q32—111no—
272Q32—222no—
273Q32—221no—
274Q32—221no—
275SD32—112no—
276SD32—222no—
277SD32—222no—
278SD32—442no—
279D16—111no—
280D16—222no—
281D16—221no—
282D16—221no—
283M32—21no—
284M32—21no—
285M32C22×D1111yescharacteristic
286M32C22×D1111yescharacteristic
287C2×C16—21no—
288C2×C16—21no—
289C2×C16C22×D1111yescharacteristic
290C2×C16C22×D1111yescharacteristic
291#108—112no—
292#108D4411yescharacteristic
293#104—222no—
294#104D4411yescharacteristic
295#104D4411yescharacteristic
296#101—222no—
297#100—222no—
298C4×C8C22×D1111yescharacteristic
299C2×C11—21no—
300C2×C11—41no—
301C2×C11—41no—
302C2×C11D4×D811yescharacteristic
303D11—82no—
304D11—162no—
305#41—222no—
306#41—442no—
307#41—442no—
308#41—442no—
309#41—442no—
310#41—882no—
311#41C2×D4411yescharacteristic
312#41C2×D4411yescharacteristic
313C2×Q8—222no—
314C2×Q8—442no—
315C2×Q8—442no—
316C2×D4—222no—
317C2×D4—442no—
318C2×D4—442no—
319C2×D4—882no—
320Q16—112no—
321Q16—222no—
322Q16—222no—
323Q16—442no—
324Q16—442no—
325Q16D8811yescharacteristic
326SD16—222no—
327SD16—442no—
328SD16—442no—
329SD16—442no—
330SD16—442no—
331SD16—442no—
332SD16—442no—
333SD16D8811yescharacteristic
334SD16D8811yescharacteristic
335D8—112no—
336D8—222no—
337D8—222no—
338D8—442no—
339D8—442no—
340D8D8811yescharacteristic
341M16—21no—
342M16—21no—
343M16—222no—
344M16—442no—
345M16C2×D4411yescharacteristic
346M16C2×D4411yescharacteristic
347C2×C8—21no—
348C2×C8—21no—
349C2×C8—442no—
350C2×C8C2×D4411yescharacteristic
351C2×C8C23×D1111yescharacteristic
352C22⋊C4—882no—
353C42C2×D4411yescharacteristic
354C16—21no—
355C16—21no—
356C16—21no—
357C16D4×D1111yescharacteristic
358C16D4×D1111yescharacteristic
359C11#3385911yescharacteristic, complemented, Sylow
360C23—442no—
361C23—882no—
362Q8—222no—
363Q8—442no—
364Q8—442no—
365Q8—882no—
366Q8C2×D8811yescharacteristic
367Q8C2×D8811yescharacteristic
368D4—21no—
369D4—21no—
370D4—222no—
371D4—442no—
372D4—442no—
373D4—442no—
374D4—882no—
375D4—882no—
376D4—882no—
377D4C2×D8811yescharacteristic
378D4C2×D8811yescharacteristic
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—442no—
383C2×C4—442no—
384C2×C4—882no—
385C2×C4—882no—
386C2×C4—882no—
387C2×C4C22×D4411yescharacteristic
388C8—21no—
389C8—21no—
390C8—442no—
391C8C2×D8811yescharacteristic
392C8C2×D8811yescharacteristic
393C8C2×D4×D1111yescharacteristic
394C8#6704211yescharacteristic
395C22—21no—
396C22—21no—
397C22—442no—
398C22—882no—
399C22—3522no—
400C22—1762no—
401C22#1062328311yescharacteristic
402C4—21no—
403C4—21no—
404C4—41no—
405C4—442no—
406C4—882no—
407C4D4×D4411yescharacteristic
408C4C22×D8811yescharacteristic
409C2—21no—
410C2—41no—
411C2—41no—
412C2—882no—
413C2—1762no—
414C2D4×D8811yescharacteristic
subgroupG/H
centerC2D4×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2170C2
socleC2×C11D4×D8
hypercenter#2170D11
hypocenterC11#33859
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ #443 ◁ #2170

Complements

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

NH ≅ G/Ntype
1. #13081769C2semidirect
2. #13081757C2semidirect
3. #13080403C2semidirect
4. #13070877C2semidirect
5. #13070741C2semidirect
6. #13070736C2semidirect
7. #13070686C2semidirect
8. #13070589C2semidirect
9. #13070582C2semidirect
10. #13070498C2semidirect
11. C11×#2170C2semidirect
13. #10623284C22semidirect
16. C11×#504C22semidirect
19. #10622755C22semidirect
21. #10622522C22semidirect
25. C2×Dic88C22semidirect
29. C2×#66864C22semidirect
35. #10622313C22semidirect
36. #10622309C22semidirect
37. C11×#364C22semidirect
39. C11×#350C22semidirect
40. C4×C11×C16C22semidirect
41. #10622155C22semidirect
42. #10622154C22semidirect
43. #10622148C22semidirect
44. #10622144C22semidirect
163. #2170D11semidirect
215. #504C2×D11semidirect
225. #364C2×D11semidirect
230. #350C2×D11semidirect
231. C4×C16C2×D11semidirect
359. C11#33859semidirect

Maximal subgroups

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

subgroupindex
#130817692
#130817572
#130804032
#130708772
#130707412
#130707362
#130706862
#130705892
#130705822
#130704982
C11×#21702
#3385911