Finite Group Databasebeta

← #14911355

Subgroups — #14911355

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#13080986C211yesmaximal, characteristic
2#13080983C211yesmaximal, characteristic
3#13070892C211yesmaximal, characteristic, complemented
4#13070827C211yesmaximal, characteristic, complemented
5#13070822C211yesmaximal, characteristic, complemented
6#13070820C211yesmaximal, characteristic, complemented
7#13070817C211yesmaximal, characteristic, complemented
8#13070781C211yesmaximal, characteristic, complemented
9#13070723C211yesmaximal, characteristic, complemented
10#13070723C211yesmaximal, characteristic, complemented
11C4×#66893C211yesmaximal, characteristic, complemented
12#13070447C211yesmaximal, characteristic
13#13070403C211yesmaximal, characteristic, complemented
14#13070401C211yesmaximal, characteristic, complemented
15C11×#2229C211yesmaximal, characteristic, complemented
16#10623225—21no—
17#10623112—21no—
18C11×#499C2211yescharacteristic
19C4×C11×Q16C2211yescharacteristic
20#10622801C2211yescharacteristic
21#10622801C2211yescharacteristic
22C2×#66893C2211yescharacteristic
23#10622676—21no—
24#10622635—21no—
25C2×#66862C2211yescharacteristic
26C2×#66862C2211yescharacteristic
27#10622500C2211yescharacteristic
28#10622500C2211yescharacteristic
29#10622493C2211yescharacteristic
30#10622493C2211yescharacteristic
31D11×#107C2211yescharacteristic
32D11×#107C2211yescharacteristic
33#10622480—21no—
34#10622475—21no—
35#10622428—21no—
36#10622418—21no—
37C4×Dic44C2211yescharacteristic
38C8×D44C2211yescharacteristic
39#10622296C2211yescharacteristic
40C11×#367C2211yescharacteristic
41C11×#366C2211yescharacteristic
42C11×C4⋊C16C2211yescharacteristic
43C11×#358C2211yescharacteristic
44C11×#358C2211yescharacteristic
45#10622202C2211yescharacteristic
46(C2×D11)⋊C16C2211yescharacteristic
47(C2×D11)⋊C16C2211yescharacteristic
48#10622143C2211yescharacteristic
49#10622142C2211yescharacteristic
50#10622141C2211yescharacteristic
51#10622141C2211yescharacteristic
52#10622130C2211yescharacteristic
53#10622128C2211yescharacteristic
54#10622128C2211yescharacteristic
55#10622127C2211yescharacteristic
56#10622127C2211yescharacteristic
57#10622127C2211yescharacteristic
58C4×C11⋊C16C2211yescharacteristic
59C2×C11×Q16C2311yescharacteristic
60C11×#125—21no—
61C4×Q8×C11—21no—
62#66999—21no—
63#66999—21no—
64C2×Dic44C2311yescharacteristic
65C2×C8×D11C2311yescharacteristic
66C2×C8×D11C2311yescharacteristic
67#66951—41no—
68#66950—21no—
69#66950—21no—
70#66947—41no—
71#66947—41no—
72#66945—21no—
73#66945—21no—
74#66945—41no—
75C4⋊C4×D11—21no—
76C4⋊C4×D11—21no—
77#66943—41no—
78#66942—41no—
79#66929—41no—
80C4×D44D411yescharacteristic
81#66925—41no—
82#66923—21no—
83C4×Dic22—21no—
84C2×C11×C16C2311yescharacteristic
85C2×C11×C16C2311yescharacteristic
86C11×#107C2311yescharacteristic
87C11×#107C2311yescharacteristic
88C11×#107C2311yescharacteristic
89C11×#106—21no—
90C11×#103—21no—
91C4×C8×C11C2311yescharacteristic
92#66899—21no—
93#66899—21no—
94#66893—22no—
95(C2×D11)⋊C8D411yescharacteristic
96(C2×D11)⋊C8D411yescharacteristic
97#66882C2311yescharacteristic
98#66882C2311yescharacteristic
99#66882C2311yescharacteristic
100#66881—21no—
101#66880—21no—
102C2×C11⋊C16C2311yescharacteristic
103C2×C11⋊C16C2311yescharacteristic
104#66874—21no—
105#66874—21no—
106#66872—21no—
107#66872—21no—
108#66871—21no—
109#66871—21no—
110C4⋊(C11⋊C8)D411yescharacteristic
111#66862—22no—
112#66862—22no—
113#33919—111nomaximal, Sylow
114C2×Q8×C11—21no—
115C2×D44D811yescharacteristic
116C2×C4×D11—41no—
117C2×C4×D11—41no—
118C2×C4×D11C2×D411yescharacteristic
119C2×C4×D11C2×D411yescharacteristic
120C2×Dic22—21no—
121C11×Q16—21no—
122C11×Q16—21no—
123C2×C8×C11C2×D411yescharacteristic
124C2×C8×C11C2411yescharacteristic
125C11×C4⋊C4—21no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—41no—
129C11×C4⋊C4—41no—
130C11×C4⋊C4—41no—
131C42×C11—41no—
132C42×C11C2×D411yescharacteristic
133(C2×D11)⋊C4—41no—
134(C2×D11)⋊C4—41no—
135(C2×D11)⋊C4—41no—
136(C2×D11)⋊C4—41no—
137(C2×D11)⋊C4—41no—
138(C2×D11)⋊C4—41no—
139(C2×D11)⋊C4D811yescharacteristic
140(C2×D11)⋊C4D811yescharacteristic
141C4⋊Dic11—21no—
142C4⋊Dic11—21no—
143C4⋊Dic11—21no—
144C4⋊Dic11—41no—
145C4⋊Dic11—41no—
146C4⋊Dic11D811yescharacteristic
147Dic11⋊C4—41no—
148Dic11⋊C4—41no—
149Dic11⋊C4—41no—
150Dic11⋊C4—41no—
151Dic11⋊C4—41no—
152Dic11⋊C4—41no—
153Dic11⋊C4—41no—
154C4×Dic11—41no—
155C4×Dic11—41no—
156C4×Dic11—41no—
157C2×C11⋊C8C2×D411yescharacteristic
158C2×C11⋊C8C2×D411yescharacteristic
159Dic44—21no—
160Dic44—21no—
161C8×D11—21no—
162C8×D11—21no—
163C8×D11—21no—
164C8×D11—21no—
165C11×C16—21no—
166C11×C16—21no—
167C11⋊C16—21no—
168C11⋊C16#4112yes—
169#3336—111no—
170#3336—111no—
171#2253—111no—
172#2237—111no—
173#2237—111no—
174#2236—111no—
175#2236—111no—
176#2229—111no—
177#2229D1111yescharacteristic, complemented
178#2219—111no—
179#2219—111no—
180C4×Q32—111no—
181#2169—111no—
182#2159—111no—
183#2159—111no—
184C22×D11C2×D811yescharacteristic
185C22×D11C2×D811yescharacteristic
186Q8×C11—41no—
187Q8×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11C2×D811yescharacteristic
193C2×C4×C11C2×D811yescharacteristic
194C2×C4×C11C22×D411yescharacteristic
195C2×Dic11—41no—
196C2×Dic11—41no—
197C2×Dic11—41no—
198C2×Dic11—41no—
199C2×Dic11C2×D811yescharacteristic
200C2×Dic11C2×D811yescharacteristic
201D44—41no—
202C4×D11—21no—
203C4×D11—21no—
204C4×D11—21no—
205C4×D11—21no—
206C4×D11—82no—
207C4×D11—82no—
208Dic22—41no—
209Dic22—41no—
210C8×C11—21no—
211C8×C11C2×#4111yescharacteristic
212C8×C112−1+411yescharacteristic
213C11⋊C8—21no—
214C11⋊C8—21no—
215#552—221no—
216#552—221no—
217C2×Q32—111no—
218C2×M32—111no—
219C2×M32—111no—
220#499—111no—
221#499C2×D1111yescharacteristic
222#485—221no—
223#485—221no—
224#483—221no—
225#483—221no—
226#479—221no—
227#479—221no—
228#467—111no—
229#467—111no—
230#467—111no—
231#467—111no—
232C4×Q16—111no—
233C4×Q16C2×D1111yescharacteristic
234C8×D4—111no—
235#427—111no—
236#427—111no—
237C2×#107—111no—
238C2×#107—111no—
239#367—111no—
240#367—111no—
241#367—111no—
242#367C2×D1111yescharacteristic
243#366—111no—
244#366—111no—
245#366—111no—
246#366—111no—
247#366C2×D1111yescharacteristic
248C4⋊C16C2×D1111yescharacteristic
249#358—111no—
250#358—111no—
251#358—111no—
252#358—111no—
253#358C2×D1111yescharacteristic
254#358C2×D1111yescharacteristic
255C22⋊C16—111no—
256C22⋊C16—111no—
257C4×C16—111no—
258C22×C11C22×D811yescharacteristic
259C2×D11—21no—
260C2×D11—21no—
261C2×D11—21no—
262C2×D11—21no—
263C2×D11—21no—
264C2×D11—21no—
265C4×C11—21no—
266C4×C11—21no—
267C4×C11—81no—
268C4×C11—81no—
269C4×C11—81no—
270C4×C11—81no—
271C4×C11#54711yescharacteristic
272C4×C11#57811yescharacteristic
273Dic11—21no—
274Dic11—21no—
275Dic11—81no—
276Dic11—81no—
277Dic11—81no—
278Dic11—81no—
279C2×Q16—111no—
280C2×Q16C22×D1111yescharacteristic
281C22×C8—111no—
282C22×C8—111no—
283#126—441no—
284#126—441no—
285#125—21no—
286#125—221no—
287#125—441no—
288#125—441no—
289#123—441no—
290#123—441no—
291C22⋊Q8—221no—
292C22⋊Q8—221no—
293C22⋊Q8—221no—
294C22⋊Q8—221no—
295C4×Q8—21no—
296C4×Q8—221no—
297C4×D4—111no—
298#117—221no—
299#117—221no—
300#117—441no—
301#117—441no—
302C2×C4⋊C4—221no—
303C2×C4⋊C4—221no—
304Q32—222no—
305M32—222no—
306M32—222no—
307C2×C16—111no—
308C2×C16—111no—
309C2×C16C22×D1111yescharacteristic
310C2×C16C22×D1111yescharacteristic
311#107—111no—
312#107—111no—
313#107—111no—
314#107—221no—
315#107—221no—
316#107C22×D1111yescharacteristic
317#107C22×D1111yescharacteristic
318#107C22×D1111yescharacteristic
319#106—21no—
320#106—221no—
321#106—221no—
322#106—221no—
323C4⋊C8—111no—
324#103—21no—
325#103—221no—
326#103—221no—
327#103—221no—
328#103—221no—
329#103—221no—
330C22⋊C8—111no—
331C22⋊C8—111no—
332C4×C8C22×D1111yescharacteristic
333C2×C11#333411yescharacteristic
334C2×C11#341411yescharacteristic
335C2×C11#341711yescharacteristic
336D11—41no—
337D11—41no—
338C2×Q8—21no—
339C2×Q8—221no—
340C2×D4—111no—
341C22×C4—111no—
342C22×C4—111no—
343C22×C4—441no—
344C22×C4—441no—
345Q16—21no—
346Q16—21no—
347Q16—221no—
348Q16—221no—
349C2×C8—111no—
350C2×C8—111no—
351C2×C8—221no—
352C2×C8—221no—
353C2×C8—221no—
354C2×C8—221no—
355C2×C8D4×D1111yescharacteristic
356C2×C8C23×D1111yescharacteristic
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—41no—
361C4⋊C4—41no—
362C4⋊C4—41no—
363C4⋊C4—111no—
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—441no—
374C4⋊C4—441no—
375C4⋊C4—441no—
376C22⋊C4—111no—
377C22⋊C4—111no—
378C22⋊C4—441no—
379C22⋊C4—441no—
380C22⋊C4—441no—
381C22⋊C4—441no—
382C22⋊C4—441no—
383C22⋊C4—441no—
384C42—41no—
385C42—441no—
386C42—441no—
387C42—441no—
388C42D4×D1111yescharacteristic
389C16—21no—
390C16—21no—
391C16—112no—
392C16—221no—
393C11#3391911yescharacteristic, complemented, Sylow
394C23—111no—
395C23—111no—
396Q8—41no—
397Q8—41no—
398Q8—441no—
399Q8—441no—
400D4—441no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—111no—
406C2×C4—111no—
407C2×C4—221no—
408C2×C4—221no—
409C2×C4—221no—
410C2×C4—221no—
411C2×C4—441no—
412C2×C4—441no—
413C2×C4—441no—
414C2×C4—441no—
415C2×C4—882no—
416C2×C4—882no—
417C2×C4D8×D1111yescharacteristic
418C2×C4D8×D1111yescharacteristic
419C2×C4C2×D4×D1111yescharacteristic
420C8—21no—
421C8—221no—
422C8—221no—
423C8#6704011yescharacteristic
424C8#41×D1111yescharacteristic
425C22—221no—
426C22—221no—
427C22—221no—
428C22—221no—
429C22—221no—
430C22—221no—
431C22C2×D8×D1111yescharacteristic
432C4—21no—
433C4—21no—
434C4—81no—
435C4—81no—
436C4—81no—
437C4—81no—
438C4—221no—
439C4—221no—
440C4—881no—
441C4—881no—
442C4—881no—
443C4—881no—
444C4#1062316211yescharacteristic
445C4#1062331011yescharacteristic
446C2—441no—
447C2—441no—
448C2#1308096211yescharacteristic
449C2#1308174911yescharacteristic
450C2#1308176811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2229C2
socleC22×C11C22×D8
prime radicalC2×D44D8
hypercenter#2229D11
hypocenterC11#33919
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2229

Complements

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

NH ≅ G/Ntype
3. #13070892C2semidirect
4. #13070827C2semidirect
5. #13070822C2semidirect
6. #13070820C2semidirect
7. #13070817C2semidirect
8. #13070781C2semidirect
9. #13070723C2semidirect
10. #13070723C2semidirect
11. C4×#66893C2semidirect
13. #13070403C2semidirect
14. #13070401C2semidirect
15. C11×#2229C2semidirect
177. #2229D11semidirect
393. C11#33919semidirect

Maximal subgroups

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

subgroupindex
#130809862
#130809832
#130708922
#130708272
#130708222
#130708202
#130708172
#130707812
#130707232
C4×#668932
#130704472
#130704032
#130704012
C11×#22292
#3391911