Finite Group Databasebeta

← #14911307

Subgroups — #14911307

Order 2816.

464 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080985C211yesmaximal, characteristic
2#13070899C211yesmaximal, characteristic, complemented
3#13070824C211yesmaximal, characteristic, complemented
4#13070824C211yesmaximal, characteristic, complemented
5#13070821C211yesmaximal, characteristic, complemented
6#13070816C211yesmaximal, characteristic, complemented
7#13070780C211yesmaximal, characteristic, complemented
8#13070765C211yesmaximal, characteristic, complemented
9#13070722C211yesmaximal, characteristic, complemented
10#13070705C211yesmaximal, characteristic, complemented
11#13070485C211yesmaximal, characteristic, complemented
12#13070442C211yesmaximal, characteristic
13#13070405C211yesmaximal, characteristic, complemented
14#13070398C211yesmaximal, characteristic, complemented
15C11×#3342C211yesmaximal, characteristic
16C11×#556—21no—
17#10623072—21no—
18C11×#500C2211yescharacteristic
19C11×#485—21no—
20C11×#485—21no—
21C11×#475—21no—
22C11×#467C2211yescharacteristic
23C11×#467C2211yescharacteristic
24C4×C11×Q16C2211yescharacteristic
25C8×D4×C11C2211yescharacteristic
26C11×#427C2211yescharacteristic
27C11×#427C2211yescharacteristic
28C2×#66893C2211yescharacteristic
29#10622729C2211yescharacteristic
30#10622729C2211yescharacteristic
31#10622719C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33C2×#66876C2211yescharacteristic
34C22×C11⋊C16C2211yescharacteristic
35#10622442—21no—
36#10622336—21no—
37#10622334—21no—
38C4×Dic44C2211yescharacteristic
39#10622296C2211yescharacteristic
40#10622202C2211yescharacteristic
41#10622202C2211yescharacteristic
42#10622202C2211yescharacteristic
43C22⋊(C11⋊C16)C2211yescharacteristic
44C22⋊(C11⋊C16)C2211yescharacteristic
45#10622130C2211yescharacteristic
46#10622130C2211yescharacteristic
47#10622130C2211yescharacteristic
48#10622128C2211yescharacteristic
49#10622128C2211yescharacteristic
50#10622128C2211yescharacteristic
51#10622128C2211yescharacteristic
52#10622127C2211yescharacteristic
53#10622127C2211yescharacteristic
54#10622127C2211yescharacteristic
55#10622127C2211yescharacteristic
56#10622127C2211yescharacteristic
57C4⋊(C11⋊C16)C2211yescharacteristic
58#10622099C2211yescharacteristic
59C2×C11×Q16C2311yescharacteristic
60C22×C8×C11C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C11×C4⋊Q8—21no—
63C11×#126—41no—
64C11×#126—41no—
65C11×#124—41no—
66C11×C22⋊Q8—21no—
67C11×C22⋊Q8—21no—
68C4×Q8×C11—21no—
69C4×Q8×C11—41no—
70C4×D4×C11D411yescharacteristic
71C11×#117—21no—
72C11×#117—21no—
73#66988—41no—
74#66979—21no—
75C2×C4⋊Dic11—21no—
76#66977—21no—
77#66977—21no—
78C2×Dic44C2311yescharacteristic
79#66942—41no—
80#66932—41no—
81#66930—41no—
82#66923—21no—
83C4×Dic22—21no—
84C11×#107—21no—
85C11×#107C2311yescharacteristic
86C11×#107C2311yescharacteristic
87C11×#107C2311yescharacteristic
88C11×#106—21no—
89C11×#106—21no—
90C11×C4⋊C8D411yescharacteristic
91C11×#103—21no—
92C11×#103—21no—
93C11×#103—21no—
94C11×C22⋊C8D411yescharacteristic
95C11×C22⋊C8D411yescharacteristic
96C4×C8×C11C2311yescharacteristic
97#66893—22no—
98#66882—21no—
99#66882C2311yescharacteristic
100#66882C2311yescharacteristic
101#66882C2311yescharacteristic
102#66881—21no—
103#66881—21no—
104#66880—21no—
105#66880—21no—
106#66880—21no—
107#66876—22no—
108C2×C11⋊C16—22no—
109C2×C11⋊C16C2311yescharacteristic
110C2×C11⋊C16C2311yescharacteristic
111C2×C11⋊C16C2311yescharacteristic
112C2×C11⋊C16C2311yescharacteristic
113#33916—111nomaximal, Sylow
114C2×Q8×C11—21no—
115C2×Q8×C11—41no—
116C2×D4×C11D811yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×Dic11—41no—
120C2×Dic22—21no—
121C11×Q16—21no—
122C11×Q16—21no—
123C2×C8×C11—21no—
124C2×C8×C11—21no—
125C2×C8×C11—21no—
126C2×C8×C11—21no—
127C2×C8×C11C2×D411yescharacteristic
128C2×C8×C11C2×D411yescharacteristic
129C2×C8×C11C2×D411yescharacteristic
130C2×C8×C11C2411yescharacteristic
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—41no—
135C11×C4⋊C4—41no—
136C11×C4⋊C4—41no—
137C11×C4⋊C4—41no—
138C11×C4⋊C4D811yescharacteristic
139C11×C22⋊C4—41no—
140C11×C22⋊C4—41no—
141C11×C22⋊C4—41no—
142C11×C22⋊C4—41no—
143C11×C22⋊C4D811yescharacteristic
144C11×C22⋊C4D811yescharacteristic
145C42×C11—41no—
146C42×C11—41no—
147C42×C11—41no—
148C42×C11C2×D411yescharacteristic
149C22⋊Dic11—41no—
150C22⋊Dic11—41no—
151C22⋊Dic11—41no—
152C4⋊Dic11—21no—
153C4⋊Dic11—21no—
154C4⋊Dic11—21no—
155C4⋊Dic11—41no—
156Dic11⋊C4—41no—
157Dic11⋊C4—41no—
158Dic11⋊C4—41no—
159Dic11⋊C4—41no—
160Dic11⋊C4—41no—
161C4×Dic11—41no—
162C4×Dic11—41no—
163Dic44—21no—
164Dic44—21no—
165C11⋊C16—21no—
166C11⋊C16—21no—
167C11⋊C16—21no—
168C11⋊C16#4112yes—
169#3342D1111yescharacteristic
170#3336—111no—
171#2255—111no—
172#2237—111no—
173#2237—111no—
174#2237—111no—
175#2236—111no—
176#2229—111no—
177#2227—111no—
178#2219—111no—
179#2216—111no—
180#2176—111no—
181#2168—111no—
182#2159—111no—
183#2158—111no—
184C23×C11C2×D811yescharacteristic
185C23×C11C2×D811yescharacteristic
186Q8×C11—41no—
187Q8×C11—41no—
188Q8×C11—82no—
189D4×C11—41no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11C2×D811yescharacteristic
199C2×C4×C11C2×D811yescharacteristic
200C2×C4×C11C2×D811yescharacteristic
201C2×C4×C11C2×D811yescharacteristic
202C2×C4×C11C22×D411yescharacteristic
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—82no—
208Dic22—41no—
209Dic22—41no—
210C8×C11—21no—
211C8×C11—21no—
212C8×C11—21no—
213C8×C11C2×#4111yescharacteristic
214C8×C112−1+411yescharacteristic
215#556—21no—
216#552—221no—
217C2×Q32—111no—
218C2×M32—111no—
219C22×C16—111no—
220#500C2×D1111yescharacteristic
221#499—111no—
222#485—21no—
223#485—21no—
224#485—221no—
225#483—221no—
226#479—221no—
227#475—21no—
228#467—111no—
229#467—111no—
230#467C2×D1111yescharacteristic
231#467C2×D1111yescharacteristic
232C4×Q16—111no—
233C4×Q16C2×D1111yescharacteristic
234C8×D4C2×D1111yescharacteristic
235#427—111no—
236#427C2×D1111yescharacteristic
237#427C2×D1111yescharacteristic
238C2×#107—111no—
239#367—111no—
240#367—111no—
241#367—111no—
242#367—111no—
243#366—111no—
244#366—111no—
245#366—111no—
246#366—111no—
247#366—111no—
248C4⋊C16—111no—
249#358—111no—
250#358—111no—
251#358—111no—
252#358—111no—
253#358—111no—
254#358—111no—
255C22⋊C16—111no—
256C22⋊C16—111no—
257#346—111no—
258C22×C11—21no—
259C22×C11—21no—
260C22×C11—21no—
261C22×C11—21no—
262C22×C11—21no—
263C22×C11—21no—
264C22×C11C22×D811yescharacteristic
265C4×C11—21no—
266C4×C11—21no—
267C4×C11—21no—
268C4×C11—21no—
269C4×C11—81no—
270C4×C11—81no—
271C4×C11—81no—
272C4×C11—81no—
273C4×C11#54711yescharacteristic
274C4×C11#57811yescharacteristic
275Dic11—81no—
276Dic11—81no—
277Dic11—81no—
278Dic11—81no—
279C2×Q16—111no—
280C2×Q16C22×D1111yescharacteristic
281C22×C8C22×D1111yescharacteristic
282C22×C8C22×D1111yescharacteristic
283C4⋊Q8—21no—
284#126—41no—
285#126—41no—
286#126—441no—
287#125—221no—
288#125—441no—
289#124—41no—
290#123—441no—
291C22⋊Q8—21no—
292C22⋊Q8—21no—
293C22⋊Q8—221no—
294C22⋊Q8—221no—
295C4×Q8—21no—
296C4×Q8—41no—
297C4×Q8—221no—
298C4×D4C22⋊D1111yescharacteristic
299#117—21no—
300#117—21no—
301#117—221no—
302#117—441no—
303C2×C4⋊C4—221no—
304Q32—222no—
305M32—222no—
306C2×C16—111no—
307C2×C16—111no—
308C2×C16—111no—
309C2×C16—111no—
310C2×C16—222no—
311#107—21no—
312#107—111no—
313#107—111no—
314#107—111no—
315#107—221no—
316#107C22×D1111yescharacteristic
317#107C22×D1111yescharacteristic
318#107C22×D1111yescharacteristic
319#106—21no—
320#106—21no—
321#106—221no—
322#106—221no—
323C4⋊C8C22⋊D1111yescharacteristic
324#103—21no—
325#103—21no—
326#103—21no—
327#103—221no—
328#103—221no—
329#103—221no—
330C22⋊C8C22⋊D1111yescharacteristic
331C22⋊C8C22⋊D1111yescharacteristic
332C4×C8C22×D1111yescharacteristic
333C2×C11—41no—
334C2×C11—41no—
335C2×C11#333411yescharacteristic
336C2×C11#341411yescharacteristic
337C2×C11#341711yescharacteristic
338C2×Q8—21no—
339C2×Q8—41no—
340C2×Q8—221no—
341C2×D4#432311yescharacteristic
342C22×C4—441no—
343C22×C4C2×C22⋊D1111yescharacteristic
344C22×C4C2×C22⋊D1111yescharacteristic
345Q16—21no—
346Q16—21no—
347Q16—221no—
348Q16—221no—
349C2×C8—21no—
350C2×C8—21no—
351C2×C8—21no—
352C2×C8—21no—
353C2×C8C2×C22⋊D1111yescharacteristic
354C2×C8C2×C22⋊D1111yescharacteristic
355C2×C8C2×C22⋊D1111yescharacteristic
356C2×C8C23×D1111yescharacteristic
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—41no—
361C4⋊C4—41no—
362C4⋊C4—41no—
363C4⋊C4—41no—
364C4⋊C4—221no—
365C4⋊C4—221no—
366C4⋊C4—221no—
367C4⋊C4—441no—
368C4⋊C4—441no—
369C4⋊C4—441no—
370C4⋊C4—441no—
371C4⋊C4—441no—
372C4⋊C4—441no—
373C4⋊C4#432311yescharacteristic
374C22⋊C4—41no—
375C22⋊C4—41no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—441no—
379C22⋊C4—441no—
380C22⋊C4—441no—
381C22⋊C4#432311yescharacteristic
382C22⋊C4#432311yescharacteristic
383C42—41no—
384C42—41no—
385C42—41no—
386C42—441no—
387C42—441no—
388C42C2×C22⋊D1111yescharacteristic
389C16—112no—
390C16—221no—
391C16—221no—
392C16—221no—
393C11#3391611yescharacteristic, complemented, Sylow
394C23C2×#432311yescharacteristic
395C23C2×#432311yescharacteristic
396Q8—41no—
397Q8—41no—
398Q8—82no—
399Q8—441no—
400Q8—441no—
401D4—41no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—441no—
411C2×C4—441no—
412C2×C4—441no—
413C2×C4—441no—
414C2×C4—882no—
415C2×C4C2×#432311yescharacteristic
416C2×C4C2×#432311yescharacteristic
417C2×C4C2×#432311yescharacteristic
418C2×C4C2×#432311yescharacteristic
419C2×C4C22×C22⋊D1111yescharacteristic
420C8—21no—
421C8—21no—
422C8—21no—
423C8#41×D1111yescharacteristic
424C8#6704311yescharacteristic
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22C22×#432311yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—81no—
437C4—81no—
438C4—81no—
439C4—81no—
440C4—881no—
441C4—881no—
442C4—881no—
443C4—881no—
444C4#1062335511yescharacteristic
445C4#1062336911yescharacteristic
446C2—41no—
447C2—41no—
448C2#1308095911yescharacteristic
449C2#1308175011yescharacteristic
450C2#1308176711yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3342C2
socleC22×C11C22×D8
prime radicalC2×D4×C11D8
hypercenter#3342D11
hypocenterC11#33916
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3342

Complements

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

NH ≅ G/Ntype
2. #13070899C2semidirect
3. #13070824C2semidirect
4. #13070824C2semidirect
5. #13070821C2semidirect
6. #13070816C2semidirect
7. #13070780C2semidirect
8. #13070765C2semidirect
9. #13070722C2semidirect
10. #13070705C2semidirect
11. #13070485C2semidirect
13. #13070405C2semidirect
14. #13070398C2semidirect
393. C11#33916semidirect

Maximal subgroups

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

subgroupindex
#130809852
#130708992
#130708242
#130708212
#130708162
#130707802
#130707652
#130707222
#130707052
#130704852
#130704422
#130704052
#130703982
C11×#33422
#3391611