Finite Group Databasebeta

← #14908170

Subgroups — #14908170

Order 2816.

706 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081750C211yesmaximal, characteristic, complemented
2C2×#10622760C211yesmaximal, characteristic, complemented
3#13077534C211yesmaximal, characteristic, complemented
4#13070689C214yesmaximal, complemented
5#13070682C214yesmaximal, complemented
6#13070382C211yesmaximal, characteristic, complemented
7#13070365C211yesmaximal, characteristic, complemented
8C2×#10622201C211yesmaximal, characteristic, complemented
9C11×#3155C211yesmaximal, characteristic, complemented
10C2×C11×AGL(1,ℤ/8)—21no—
11C2×C11×#135C2211yescharacteristic
12C22×C11×D8C2211yescharacteristic
13C11×#535—21no—
14#10623276—21no—
15C2×#66957C2211yescharacteristic
16C11×#496—22no—
17C11×#495C2212yescomplemented
18C11×#493C2212yescomplemented
19C11×#405C2211yescharacteristic
20#10622808—21no—
21#10622807—22no—
22#10622806—21no—
23#10622792C2212yescomplemented
24C2×#66891—21no—
25#10622760—22no—
26#10622760C2214yes—
27#10622760C2212yescomplemented
28C2×#66890—21no—
29C2×#66883C2211yescharacteristic
30C2×#66876C2211yescharacteristic
31C2×#66876C2211yescharacteristic
32#10622618—21no—
33#10622330—22no—
34#10622313C2214yescomplemented
35#10622203C2212yescomplemented
36#10622201C2214yescomplemented
37#10622201C2212yescomplemented
38#10622101C2214yescomplemented
39C2×C11×#41—21no—
40C22×D4×C11—21no—
41C2×#4339—21no—
42C11×AGL(1,ℤ/8)—42no—
43C11×AGL(1,ℤ/8)—42no—
44C11×#135—21no—
45C11×#135—21no—
46C11×#135—21no—
47C11×#135—21no—
48C2×C11×Q16C2311yescharacteristic
49C2×C11×SD16—22no—
50C2×C11×SD16—21no—
51C2×C11×D8—21no—
52C2×C11×D8—21no—
53C2×C11×D8—22no—
54C2×C11×D8—21no—
55C2×C11×D8—21no—
56C2×C11×D8—21no—
57C2×C11×D8C2311yescharacteristic
58C2×C11×D8C2312yes—
59C2×C11×M16D411yescharacteristic
60C22×C8×C11C2311yescharacteristic
61C11×#127—22no—
62C11×#124—22no—
63C11×#121—42no—
64C11×#120—42no—
65C11×#117D411yescharacteristic
66C2×#4318—21no—
67#66960—42no—
68M16×D11—42no—
69C2×Dic44D411yescharacteristic, complemented
70#66957—21no—
71#66957—21no—
72#66957D412yescomplemented
73#66957C2312yes—
74C2×D88D411yescharacteristic, complemented
75C2×#4314—21no—
76#66954—24no—
77C11×#97D412yes—
78C4×C8×C11C2312yes—
79#66893—22no—
80#66892—22no—
81#66891—24no—
82#66891—22no—
83#66890—24no—
84#66890—22no—
85#66883—21no—
86#66883C2312yes—
87#66876—21no—
88#66876—21no—
89#66876C2312yes—
90#66876C2312yes—
91C2×C11⋊C16—21no—
92C2×C11⋊C16—21no—
93#66869—24no—
94#33595—111nomaximal, Sylow
95C24×C11—41no—
96C11×#41—41no—
97C11×#41—41no—
98C11×#41—41no—
99C11×#41—41no—
100C2×Q8×C11—21no—
101C2×D4×C11—22no—
102C2×D4×C11—21no—
103C2×D4×C11—44no—
104C2×D4×C11—41no—
105C2×D4×C11—41no—
106C2×D4×C11—41no—
107C2×D4×C11—41no—
108C2×D4×C11—41no—
109C2×D4×C11—41no—
110C22×C4×C11—41no—
111C22×C4×C11C2×D411yescharacteristic
112C2×C22⋊D11—41no—
113#4339—22no—
114#4339—22no—
115#4339—41no—
116#4339—41no—
117C2×D44—21no—
118C2×C4×D11—41no—
119C2×Dic22—21no—
120C11×Q16—21no—
121C11×Q16—21no—
122C11×SD16—41no—
123C11×SD16—41no—
124C11×SD16—44no—
125C11×D8—22no—
126C11×D8—21no—
127C11×D8—22no—
128C11×D8—21no—
129C11×D8—41no—
130C11×D8—41no—
131C11×D8—44no—
132C11×M16D812yes—
133C11×M16D812yes—
134C2×C8×C11C2×D411yescharacteristic
135C2×C8×C11C2×D411yescharacteristic
136C2×C8×C11C2×D411yescharacteristic
137C2×C8×C11C2×D412yes—
138C2×C8×C11#4111yescharacteristic
139C2×C8×C11#4111yescharacteristic
140C2×C8×C11C2411yescharacteristic
141C11×C4⋊C4—21no—
142C11×C22⋊C4—21no—
143C11×C22⋊C4—44no—
144C42×C11C2×D412yes—
145#4318—22no—
146#4318—41no—
147C2×C11⋊C8—41no—
148Dic44—21no—
149Dic44C2×D412yes—
150D88—21no—
151D88C2×D412yes—
152#4314—22no—
153#4314—22no—
154#4313—44no—
155C8×D11—44no—
156C11⋊C16—22no—
157C11⋊C16—22no—
158#3414—111no—
159C2×#509—111no—
160#3155D1111yescharacteristic, complemented
161#2957—111no—
162#2213—114no—
163#2212—114no—
164#2153—111no—
165#2148—111no—
166C2×#361—111no—
167C23×C11—42no—
168C23×C11—41no—
169C23×C11—81no—
170C23×C11—81no—
171C23×C11—162no—
172C23×C11AGL(1,ℤ/8)11yescharacteristic
173C22×D11—41no—
174Q8×C11—41no—
175Q8×C11—41no—
176D4×C11—42no—
177D4×C11—41no—
178D4×C11—41no—
179D4×C11—42no—
180D4×C11—81no—
181D4×C11—81no—
182D4×C11—81no—
183D4×C11—81no—
184D4×C11—164no—
185C2×C4×C11—22no—
186C2×C4×C11—41no—
187C2×C4×C11—81no—
188C2×C4×C11—81no—
189C2×C4×C11#12111yescharacteristic
190C2×C4×C11#12111yescharacteristic
191C2×C4×C11C2×D811yescharacteristic
192C2×C4×C11C2×D811yescharacteristic
193C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
194C2×C4×C11C22×D411yescharacteristic
195C22⋊D11—42no—
196C22⋊D11—42no—
197C2×Dic11—41no—
198D44—22no—
199D44—41no—
200C4×D11—42no—
201C4×D11—42no—
202Dic22—22no—
203Dic22—41no—
204C8×C11#12111yescharacteristic
205C8×C11#12111yescharacteristic
206C8×C11C2×D814yes—
207C8×C11C22×D411yescharacteristic
208C8×C11C2×#4111yescharacteristic
209C11⋊C8—42no—
210C2×AGL(1,ℤ/8)—21no—
211C2×#135—111no—
212C2×#135C2×D1111yescharacteristic
213C22×D8C2×D1111yescharacteristic
214#568—221no—
215#535—21no—
216#510—112no—
217#510—221no—
218#509—114no—
219#509—112no—
220#509—222no—
221#509—221no—
222#508—222no—
223C2×SD32—221no—
224C2×D16—221no—
225C2×M32—111no—
226C2×M32—111no—
227#496—22no—
228#495C2×D1112yescomplemented
229#493C2×D1112yescomplemented
230#444—222no—
231#443—114no—
232C2×#108—111no—
233#421—221no—
234#405C2×D1111yescharacteristic
235#364—114no—
236#362—112no—
237#361—114no—
238#361—112no—
239C22×C11—41no—
240C22×C11—82no—
241C22×C11—84no—
242C22×C11—81no—
243C22×C11—82no—
244C22×C11—162no—
245C22×C11—162no—
246C22×C11#45911yescharacteristic
247C22×C11#45911yescharacteristic
248C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
249C2×D11—42no—
250C2×D11—161no—
251C4×C11—42no—
252C4×C11—81no—
253C4×C11#45911yescharacteristic
254C4×C11#45911yescharacteristic
255C4×C11C2×#12111yescharacteristic
256C4×C11C22×D811yescharacteristic
257Dic11—42no—
258C2×#41—21no—
259C2×#41—221no—
260C22×D4—21no—
261AGL(1,ℤ/8)—42no—
262AGL(1,ℤ/8)—42no—
263#135—21no—
264#135—21no—
265#135—21no—
266#135—21no—
267#135—112no—
268#135—112no—
269#135—221no—
270#135—221no—
271C2×Q16—111no—
272C2×Q16C22×D1111yescharacteristic
273C2×SD16—21no—
274C2×SD16—22no—
275C2×SD16—221no—
276C2×D8—21no—
277C2×D8—21no—
278C2×D8—21no—
279C2×D8—21no—
280C2×D8—21no—
281C2×D8—22no—
282C2×D8—111no—
283C2×D8C22×D1112yes—
284C2×D8C22×D1111yescharacteristic
285#131—224no—
286#131—442no—
287C2×M16—221no—
288C2×M16—442no—
289C2×M16C22⋊D1111yescharacteristic
290C22×C8C22×D1111yescharacteristic
291#127—22no—
292#124—22no—
293#121—42no—
294#120—42no—
295#117C22⋊D1111yescharacteristic
296Q32—222no—
297SD32—224no—
298SD32—222no—
299SD32—222no—
300D16—224no—
301D16—222no—
302M32—112no—
303M32—112no—
304M32—221no—
305M32—221no—
306C2×C16—221no—
307C2×C16—221no—
308#108—112no—
309#108—221no—
310#104—224no—
311#97C22⋊D1112yes—
312C4×C8C22×D1112yes—
313C2×C11—21no—
314C2×C11—21no—
315C2×C11—21no—
316C2×C11—161no—
317C2×C11—162no—
318C2×C11C2×#45911yescharacteristic
319D11—82no—
320C24—41no—
321#41—41no—
322#41—41no—
323#41—41no—
324#41—41no—
325#41—222no—
326#41—222no—
327#41—441no—
328#41—441no—
329C2×Q8—21no—
330C2×Q8—221no—
331C2×D4—22no—
332C2×D4—21no—
333C2×D4—44no—
334C2×D4—41no—
335C2×D4—41no—
336C2×D4—41no—
337C2×D4—41no—
338C2×D4—41no—
339C2×D4—41no—
340C2×D4—221no—
341C2×D4—441no—
342C22×C4—41no—
343C22×C4—441no—
344C22×C4C2×C22⋊D1111yescharacteristic
345Q16—21no—
346Q16—21no—
347Q16—112no—
348Q16—221no—
349SD16—44no—
350SD16—41no—
351SD16—41no—
352SD16—222no—
353SD16—222no—
354D8—22no—
355D8—21no—
356D8—22no—
357D8—21no—
358D8—44no—
359D8—41no—
360D8—41no—
361D8—112no—
362D8—221no—
363M16—222no—
364M16—441no—
365M16—444no—
366M16#432312yes—
367M16#432312yes—
368C2×C8—441no—
369C2×C8—444no—
370C2×C8D4×D1111yescharacteristic
371C2×C8D4×D1111yescharacteristic
372C2×C8#434111yescharacteristic
373C2×C8#434111yescharacteristic
374C2×C8C2×C22⋊D1112yes—
375C2×C8C2×C22⋊D1111yescharacteristic
376C2×C8C23×D1111yescharacteristic
377C4⋊C4—21no—
378C22⋊C4—21no—
379C22⋊C4—44no—
380C42C2×C22⋊D1112yes—
381C16—222no—
382C16—222no—
383C11#3359511yescharacteristic, complemented, Sylow
384C23—42no—
385C23—41no—
386C23—81no—
387C23—81no—
388C23—162no—
389C23—441no—
390C23#6698511yescharacteristic
391Q8—41no—
392Q8—41no—
393Q8—222no—
394Q8—441no—
395D4—41no—
396D4—42no—
397D4—42no—
398D4—41no—
399D4—81no—
400D4—81no—
401D4—81no—
402D4—81no—
403D4—164no—
404D4—222no—
405D4—442no—
406D4—442no—
407D4—441no—
408C2×C4—22no—
409C2×C4—41no—
410C2×C4—81no—
411C2×C4—81no—
412C2×C4—441no—
413C2×C4—442no—
414C2×C4—442no—
415C2×C4C2×#432311yescharacteristic
416C2×C4C2×#432311yescharacteristic
417C2×C4#6698511yescharacteristic
418C2×C4#6699111yescharacteristic
419C2×C4#6699111yescharacteristic
420C2×C4C22×C22⋊D1111yescharacteristic
421C8—442no—
422C8C2×#432314yes—
423C8#6699111yescharacteristic
424C8#6699111yescharacteristic
425C8C2×D4×D1111yescharacteristic
426C8C2×#434111yescharacteristic
427C22—41no—
428C22—82no—
429C22—84no—
430C22—81no—
431C22—82no—
432C22—162no—
433C22—162no—
434C22—442no—
435C22—1761no—
436C22#1062268511yescharacteristic
437C22#1062268511yescharacteristic
438C22C2×#6698511yescharacteristic
439C4—42no—
440C4—81no—
441C4—442no—
442C4#1062268511yescharacteristic
443C4#1062268511yescharacteristic
444C4C22×#432311yescharacteristic
445C4C2×#6699111yescharacteristic
446C2—21no—
447C2—21no—
448C2—21no—
449C2—162no—
450C2—161no—
451C2—882no—
452C2C2×#1062268511yescharacteristic
subgroupG/H
centerC2C2×#10622685
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3155C2
socleC2×C11C2×#459
hypercenter#3155D11
hypocenterC11#33595
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ #405 ◁ #3155

Complements

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

NH ≅ G/Ntype
1. #13081750C2semidirect
2. C2×#10622760C2semidirect
3. #13077534C2semidirect
4. #13070689C2semidirect
5. #13070682C2semidirect
6. #13070382C2semidirect
7. #13070365C2semidirect
8. C2×#10622201C2semidirect
9. C11×#3155C2semidirect
17. C11×#495C22semidirect
18. C11×#493C22semidirect
23. #10622792C22semidirect
27. #10622760C22semidirect
34. #10622313C22semidirect
35. #10622203C22semidirect
36. #10622201C22semidirect
37. #10622201C22semidirect
38. #10622101C22semidirect
69. C2×Dic44D4semidirect
72. #66957D4semidirect
74. C2×D88D4semidirect
160. #3155D11semidirect
228. #495C2×D11semidirect
229. #493C2×D11semidirect
383. C11#33595semidirect

Maximal subgroups

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

subgroupindex
#130817502
C2×#106227602
#130775342
#130706892
#130706822
#130703822
#130703652
C2×#106222012
C11×#31552
#3359511