Finite Group Databasebeta

← #14909529

Subgroups — #14909529

Order 2816.

594 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078195C211yesmaximal, characteristic
2C2×#10622801C211yesmaximal, characteristic, complemented
3#13070822C212yesmaximal, complemented
4#13070814C211yesmaximal, characteristic, complemented
5#13070794C211yesmaximal, characteristic, complemented
6#13070709C212yesmaximal, complemented
7#13070706C212yesmaximal, complemented
8#13070553C212yesmaximal, complemented
9#13070550C211yesmaximal, characteristic, complemented
10D11×C22⋊C16C211yesmaximal, characteristic, complemented
11C11×#2185C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2211yescharacteristic
13C2×#66999—21no—
14C2×#66965C2211yescharacteristic
15C22×C8×D11C2211yescharacteristic
16#10623137—21no—
17C2×C11×SD32C2212yescomplemented
18C11×#466C2211yescharacteristic
19C2×#66899—21no—
20#10622801—21no—
21#10622801—21no—
22#10622801C2212yes—
23#10622801C2212yes—
24C2×#66893C2212yescomplemented
25#10622770C2211yescharacteristic
26#10622729C2211yescharacteristic
27C2×#66882C2211yescharacteristic
28#10622654—21no—
29C2×C16×D11C2212yes—
30#10622500C2211yescharacteristic
31#10622493C2211yescharacteristic
32#10622391—21no—
33#10622385—21no—
34C11×#358C2212yescomplemented
35C11×C22⋊C16C2211yescharacteristic
36#10622202C2212yescomplemented
37#10622200C2212yescomplemented
38C22⋊(C11⋊C16)C2211yescharacteristic
39(C2×D11)⋊C16C2212yes—
40#10622143C2212yescomplemented
41#10622141C2212yescomplemented
42#10622127C2212yescomplemented
43C22×Q8×C11—21no—
44C2×#4341—21no—
45C22×C4×D11D411yescharacteristic
46C2×C11×Q16—21no—
47C2×C11×Q16—42no—
48C2×C11×Q16C2312yes—
49C2×C11×D8C2311yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C11×#121—21no—
52#66999—22no—
53#66999—22no—
54#66999—41no—
55#66999—41no—
56#66991—21no—
57#66990—41no—
58D4×Dic11—41no—
59C2×#4324—21no—
60C2×(C2×D11)⋊C4—41no—
61C2×C4⋊Dic11—21no—
62#66977—21no—
63C2×Dic11⋊C4—41no—
64C22×C11⋊C8D411yescharacteristic
65#66965—42no—
66C2×Dic44C2311yescharacteristic
67C2×C8×D11—42no—
68C2×C8×D11D411yescharacteristic
69C2×C8×D11D411yescharacteristic
70C2×C8×D11C2311yescharacteristic
71C2×C8×D11C2311yescharacteristic
72#66950—21no—
73#66945—21no—
74#66936—41no—
75(C22⋊D11)⋊C4—41no—
76C11×SD32—42no—
77C2×C11×C16C2312yes—
78C11×#107C2311yescharacteristic
79C11×#102—21no—
80#66899—22no—
81#66899—22no—
82#66896—21no—
83#66893—42no—
84#66882—21no—
85#66882C2311yescharacteristic
86#66882C2312yes—
87#66880—21no—
88C2×C11⋊C16C2312yes—
89#66874—21no—
90#66872—21no—
91C16×D11—42no—
92#33756—111nomaximal, Sylow
93C23×D11D811yescharacteristic
94C2×Q8×C11—22no—
95C2×Q8×C11—42no—
96C2×Q8×C11—42no—
97C2×Q8×C11—41no—
98C2×D4×C11—21no—
99C2×D4×C11—41no—
100C22×C4×C11—41no—
101C22×C4×C11C2×D411yescharacteristic
102C2×C22⋊D11—41no—
103C2×C22⋊D11—41no—
104C22×Dic11—41no—
105C22×Dic11—41no—
106C22×Dic11D811yescharacteristic
107#4341—42no—
108#4341—42no—
109C2×C4×D11—41no—
110C2×C4×D11—41no—
111C2×C4×D11D811yescharacteristic
112C2×C4×D11D811yescharacteristic
113C2×C4×D11C2×D411yescharacteristic
114C2×C4×D11C2×D411yescharacteristic
115C2×Dic22—21no—
116C11×Q16—22no—
117C11×Q16—22no—
118C11×Q16—42no—
119C11×D8—22no—
120C2×C8×C11—22no—
121C2×C8×C11C2×D411yescharacteristic
122C2×C8×C11C2411yescharacteristic
123C11×C4⋊C4—21no—
124C11×C22⋊C4—41no—
125C22⋊Dic11—41no—
126C22⋊Dic11—41no—
127#4324—42no—
128(C2×D11)⋊C4—41no—
129(C2×D11)⋊C4—41no—
130(C2×D11)⋊C4—42no—
131(C2×D11)⋊C4—42no—
132C4⋊Dic11—21no—
133C4⋊Dic11—22no—
134C4⋊Dic11—41no—
135C4⋊Dic11—41no—
136Dic11⋊C4—42no—
137Dic11⋊C4—42no—
138Dic11⋊C4—41no—
139C4×Dic11—41no—
140C2×C11⋊C8—41no—
141C2×C11⋊C8C2×D411yescharacteristic
142C2×C11⋊C8C2×D411yescharacteristic
143Dic44—22no—
144C8×D11—22no—
145C8×D11—22no—
146C8×D11—41no—
147C8×D11—41no—
148C11×C16—22no—
149C11⋊C16—22no—
150#3050—111no—
151C2×#467—111no—
152#2237—112no—
153#2235—111no—
154#2232—111no—
155#2217—112no—
156#2216—112no—
157#2189—112no—
158#2188—111no—
159#2185D1111yescharacteristic, complemented
160C2×C22⋊C16—111no—
161C23×C11—41no—
162C23×C11C2×D811yescharacteristic
163C22×D11—22no—
164C22×D11—22no—
165C22×D11—41no—
166C22×D11C2×D811yescharacteristic
167C22×D11C2×D811yescharacteristic
168Q8×C11—42no—
169Q8×C11—42no—
170Q8×C11—82no—
171D4×C11—41no—
172D4×C11—41no—
173D4×C11—82no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—41no—
177C2×C4×C11—42no—
178C2×C4×C11—82no—
179C2×C4×C11C2×D811yescharacteristic
180C2×C4×C11C22×D411yescharacteristic
181C22⋊D11—82no—
182C22⋊D11—82no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11—42no—
186C2×Dic11—41no—
187C2×Dic11—82no—
188C2×Dic11—82no—
189C2×Dic11C2×D811yescharacteristic
190C2×Dic11C2×D811yescharacteristic
191C4×D11—21no—
192C4×D11—21no—
193C4×D11—21no—
194C4×D11—21no—
195C4×D11—41no—
196C4×D11—41no—
197Dic22—41no—
198Dic22—41no—
199C8×C11—21no—
200C8×C11H(5,𝔽2)12yes—
201C11⋊C8—21no—
202C11⋊C8—21no—
203C2×#135—111no—
204C22×Q16C2×D1111yescharacteristic
205C23×C8—111no—
206#525—221no—
207C2×C22⋊Q8—221no—
208C2×Q32—112no—
209C2×SD32C2×D1112yescomplemented
210C22×C16—112no—
211#467—112no—
212#467—112no—
213#467—111no—
214#467—111no—
215#467—221no—
216#467—221no—
217#466—111no—
218#466C2×D1111yescharacteristic
219#465—221no—
220#465—221no—
221#427—111no—
222C2×#107—111no—
223#416—221no—
224C2×#103—221no—
225#367—112no—
226#366—112no—
227#358—112no—
228#358—112no—
229#358C2×D1112yescomplemented
230#357—112no—
231C22⋊C16—111no—
232C22⋊C16—112no—
233C22⋊C16C2×D1111yescharacteristic
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—81no—
237C22×C11—81no—
238C22×C11—81no—
239C22×C11#50812yes—
240C22×C11C22×D811yescharacteristic
241C2×D11—21no—
242C2×D11—21no—
243C2×D11—21no—
244C2×D11—21no—
245C2×D11—21no—
246C2×D11—44no—
247C2×D11#51012yes—
248C4×C11—21no—
249C4×C11—81no—
250C4×C11—82no—
251C4×C11#53411yescharacteristic
252C4×C11#57511yescharacteristic
253Dic11—21no—
254Dic11—21no—
255Dic11—82no—
256Dic11—81no—
257Dic11—81no—
258C2×#41—221no—
259C22×Q8—21no—
260C23×C4—111no—
261#135—442no—
262C2×Q16—21no—
263C2×Q16—42no—
264C2×Q16—111no—
265C2×Q16C22×D1112yes—
266C2×SD16—221no—
267C2×D8C22×D1111yescharacteristic
268C22×C8—111no—
269C22×C8—111no—
270C22×C8—111no—
271C22×C8—111no—
272C22×C8—111no—
273C22×C8—442no—
274C22×C8C22×D1111yescharacteristic
275#123—441no—
276C22⋊Q8—221no—
277C22⋊Q8—222no—
278C22⋊Q8—222no—
279C22⋊Q8—221no—
280C22⋊Q8—441no—
281C22⋊Q8—441no—
282#121—21no—
283#121—221no—
284#120—441no—
285C4×D4—441no—
286C4×D4—441no—
287#117—221no—
288C2×C4⋊C4—221no—
289C2×C4⋊C4—441no—
290C2×C22⋊C4—441no—
291Q32—442no—
292SD32—42no—
293C2×C16—112no—
294C2×C16—442no—
295C2×C16C22×D1112yes—
296#107—112no—
297#107—111no—
298#107—221no—
299#107C22×D1111yescharacteristic
300#106—221no—
301#103—221no—
302#103—222no—
303#103—222no—
304#103—221no—
305#102—21no—
306#102—221no—
307C2×C11—22no—
308C2×C11—161no—
309C2×C11#318611yescharacteristic
310C2×C11C2×#50811yescharacteristic
311C2×C11C2×#51011yescharacteristic
312D11—22no—
313D11—41no—
314C24—111no—
315#41—442no—
316#41—442no—
317C2×Q8—22no—
318C2×Q8—42no—
319C2×Q8—42no—
320C2×Q8—41no—
321C2×Q8—221no—
322C2×D4—21no—
323C2×D4—41no—
324C2×D4—441no—
325C2×D4—441no—
326C22×C4—41no—
327C22×C4—111no—
328C22×C4—111no—
329C22×C4—111no—
330C22×C4—111no—
331C22×C4—111no—
332C22×C4—441no—
333C22×C4—441no—
334C22×C4—441no—
335C22×C4—441no—
336C22×C4D4×D1111yescharacteristic
337Q16—22no—
338Q16—22no—
339Q16—42no—
340Q16—222no—
341SD16—442no—
342D8—22no—
343C2×C8—22no—
344C2×C8—111no—
345C2×C8—111no—
346C2×C8—222no—
347C2×C8—222no—
348C2×C8—441no—
349C2×C8—441no—
350C2×C8—441no—
351C2×C8D4×D1111yescharacteristic
352C2×C8C23×D1111yescharacteristic
353C4⋊C4—21no—
354C4⋊C4—221no—
355C4⋊C4—222no—
356C4⋊C4—442no—
357C4⋊C4—442no—
358C4⋊C4—441no—
359C4⋊C4—441no—
360C4⋊C4—441no—
361C22⋊C4—41no—
362C22⋊C4—442no—
363C22⋊C4—442no—
364C22⋊C4—441no—
365C22⋊C4—441no—
366C22⋊C4—441no—
367C22⋊C4—441no—
368C42—441no—
369C16—22no—
370C16—222no—
371C11#3375611yescharacteristic, complemented, Sylow
372C23—41no—
373C23—111no—
374C23—111no—
375C23—222no—
376C23—222no—
377C23—441no—
378C23D8×D1111yescharacteristic
379Q8—42no—
380Q8—42no—
381Q8—82no—
382Q8—441no—
383Q8—441no—
384D4—41no—
385D4—41no—
386D4—82no—
387D4—882no—
388D4—882no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—41no—
392C2×C4—42no—
393C2×C4—82no—
394C2×C4—111no—
395C2×C4—111no—
396C2×C4—221no—
397C2×C4—221no—
398C2×C4—221no—
399C2×C4—221no—
400C2×C4—441no—
401C2×C4—441no—
402C2×C4—441no—
403C2×C4—441no—
404C2×C4—442no—
405C2×C4—441no—
406C2×C4—882no—
407C2×C4—882no—
408C2×C4D8×D1111yescharacteristic
409C2×C4C2×D4×D1111yescharacteristic
410C8—21no—
411C8—221no—
412C8—221no—
413C8#6703712yes—
414C22—21no—
415C22—21no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22—112no—
420C22—221no—
421C22—221no—
422C22—221no—
423C22—221no—
424C22—221no—
425C22—444no—
426C22#1062252912yes—
427C22C2×D8×D1111yescharacteristic
428C4—21no—
429C4—82no—
430C4—81no—
431C4—221no—
432C4—221no—
433C4—881no—
434C4—882no—
435C4—881no—
436C4#1062312011yescharacteristic
437C4#1062330411yescharacteristic
438C2—22no—
439C2—161no—
440C2—222no—
441C2—441no—
442C2#1307936511yescharacteristic
443C2C2×#1062252911yescharacteristic
444C2D11×#51011yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2185C2
socleC22×C11C22×D8
prime radical#13078195C2
hypercenter#2185D11
hypocenterC11#33756
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2185

Complements

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

NH ≅ G/Ntype
2. C2×#10622801C2semidirect
3. #13070822C2semidirect
4. #13070814C2semidirect
5. #13070794C2semidirect
6. #13070709C2semidirect
7. #13070706C2semidirect
8. #13070553C2semidirect
9. #13070550C2semidirect
10. D11×C22⋊C16C2semidirect
11. C11×#2185C2semidirect
17. C2×C11×SD32C22semidirect
24. C2×#66893C22semidirect
34. C11×#358C22semidirect
36. #10622202C22semidirect
37. #10622200C22semidirect
40. #10622143C22semidirect
41. #10622141C22semidirect
42. #10622127C22semidirect
159. #2185D11semidirect
209. C2×SD32C2×D11semidirect
229. #358C2×D11semidirect
371. C11#33756semidirect

Maximal subgroups

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

subgroupindex
#130781952
C2×#106228012
#130708222
#130708142
#130707942
#130707092
#130707062
#130705532
#130705502
D11×C22⋊C162
C11×#21852
#3375611