Finite Group Databasebeta

← #14911348

Subgroups — #14911348

Order 2816.

476 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081020C211yesmaximal, characteristic
2#13080986C211yesmaximal, characteristic, complemented
3#13070895C211yesmaximal, characteristic, complemented
4#13070822C211yesmaximal, characteristic, complemented
5#13070812C211yesmaximal, characteristic, complemented
6#13070806C211yesmaximal, characteristic, complemented
7#13070800C211yesmaximal, characteristic, complemented
8#13070780C211yesmaximal, characteristic, complemented
9#13070773C211yesmaximal, characteristic, complemented
10#13070726C211yesmaximal, characteristic, complemented
11#13070726C211yesmaximal, characteristic, complemented
12#13070449C211yesmaximal, characteristic, complemented
13#13070403C211yesmaximal, characteristic, complemented
14#13070403C211yesmaximal, characteristic, complemented
15C4×C11×SD32C211yesmaximal, characteristic, complemented
16#10623112—21no—
17#10623089—21no—
18C2×C11×SD32C2211yescharacteristic
19C4×C11×Q16C2211yescharacteristic
20C4×C11×D8C2211yescharacteristic
21#10622801C2211yescharacteristic
22#10622801C2211yescharacteristic
23#10622770C2211yescharacteristic
24#10622770C2211yescharacteristic
25#10622635—21no—
26#10622622—21no—
27C2×#66862C2211yescharacteristic
28C2×#66862C2211yescharacteristic
29#10622493C2211yescharacteristic
30#10622493C2211yescharacteristic
31D11×#107C2211yescharacteristic
32D11×#107C2211yescharacteristic
33#10622428—21no—
34#10622418—21no—
35#10622392—21no—
36#10622390—21no—
37C8×D44C2211yescharacteristic
38#10622296C2211yescharacteristic
39#10622296C2211yescharacteristic
40C11×#367C2211yescharacteristic
41C11×#358C2211yescharacteristic
42C11×#357C2211yescharacteristic
43C4×C11×C16C2211yescharacteristic
44#10622202C2211yescharacteristic
45#10622202C2211yescharacteristic
46#10622200C2211yescharacteristic
47#10622200C2211yescharacteristic
48(C2×D11)⋊C16C2211yescharacteristic
49(C2×D11)⋊C16C2211yescharacteristic
50#10622143C2211yescharacteristic
51#10622143C2211yescharacteristic
52#10622142C2211yescharacteristic
53#10622142C2211yescharacteristic
54#10622128C2211yescharacteristic
55#10622128C2211yescharacteristic
56#10622127C2211yescharacteristic
57#10622127C2211yescharacteristic
58C4⋊(C11⋊C16)C2211yescharacteristic
59C2×C11×Q16C2311yescharacteristic
60C2×C11×D8C2311yescharacteristic
61C4×Q8×C11—21no—
62C4×D4×C11—21no—
63#66999—21no—
64#66999—21no—
65#66991—21no—
66#66991—21no—
67#66982—41no—
68C4×C22⋊D11—41no—
69C2×C8×D11C2311yescharacteristic
70C2×C8×D11C2311yescharacteristic
71#66947—41no—
72#66945—21no—
73#66945—21no—
74C4⋊C4×D11—21no—
75C4⋊C4×D11—21no—
76#66942—41no—
77#66937—41no—
78#66932—41no—
79#66929—41no—
80C4×D44D411yescharacteristic
81#66925—41no—
82#66923—21no—
83#66923—21no—
84C11×SD32—22no—
85C2×C11×C16C2311yescharacteristic
86C2×C11×C16C2311yescharacteristic
87C11×#107C2311yescharacteristic
88C11×#107C2311yescharacteristic
89C11×#103—21no—
90C11×#102—21no—
91C4×C8×C11C2311yescharacteristic
92#66899—21no—
93#66899—21no—
94#66896—21no—
95#66896—21no—
96(C2×D11)⋊C8D411yescharacteristic
97(C2×D11)⋊C8D411yescharacteristic
98#66882C2311yescharacteristic
99#66882C2311yescharacteristic
100#66882C2311yescharacteristic
101#66882C2311yescharacteristic
102#66881—21no—
103#66881—21no—
104C2×C11⋊C16C2311yescharacteristic
105C2×C11⋊C16C2311yescharacteristic
106#66872—21no—
107#66872—21no—
108#66871—21no—
109#66871—21no—
110C4⋊(C11⋊C8)D411yescharacteristic
111#66862—22no—
112#66862—22no—
113#33918—111nomaximal, Sylow
114C2×Q8×C11—21no—
115C2×D4×C11—21no—
116C22×C4×C11—41no—
117C2×C22⋊D11—41no—
118C2×C22⋊D11—41no—
119C2×D44D811yescharacteristic
120C2×C4×D11—41no—
121C2×C4×D11—41no—
122C2×C4×D11C2×D411yescharacteristic
123C2×C4×D11C2×D411yescharacteristic
124C11×Q16—21no—
125C11×Q16—21no—
126C11×D8—21no—
127C11×D8—21no—
128C2×C8×C11C2×D411yescharacteristic
129C2×C8×C11C2411yescharacteristic
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—41no—
133C11×C22⋊C4—41no—
134C42×C11—41no—
135C42×C11C2×D411yescharacteristic
136C22⋊Dic11—41no—
137C22⋊Dic11—41no—
138(C2×D11)⋊C4—41no—
139(C2×D11)⋊C4—41no—
140(C2×D11)⋊C4—41no—
141(C2×D11)⋊C4—41no—
142(C2×D11)⋊C4D811yescharacteristic
143(C2×D11)⋊C4D811yescharacteristic
144C4⋊Dic11—21no—
145C4⋊Dic11—21no—
146C4⋊Dic11—21no—
147C4⋊Dic11—21no—
148C4⋊Dic11D811yescharacteristic
149Dic11⋊C4—41no—
150Dic11⋊C4—41no—
151Dic11⋊C4—41no—
152Dic11⋊C4—41no—
153Dic11⋊C4—41no—
154Dic11⋊C4—41no—
155Dic11⋊C4—41no—
156Dic11⋊C4—41no—
157C4×Dic11—41no—
158C4×Dic11—41no—
159C2×C11⋊C8C2×D411yescharacteristic
160C2×C11⋊C8C2×D411yescharacteristic
161C8×D11—21no—
162C8×D11—21no—
163C8×D11—21no—
164C8×D11—21no—
165C11×C16—21no—
166C11×C16#4112yes—
167C11⋊C16—21no—
168C11⋊C16—21no—
169#3339—111no—
170#3336—111no—
171#2253—111no—
172#2237—111no—
173#2235—111no—
174#2234—111no—
175#2233—111no—
176#2229—111no—
177#2228—111no—
178#2220—111no—
179#2220—111no—
180C4×SD32D1111yescharacteristic, complemented
181#2169—111no—
182#2159—111no—
183#2159—111no—
184C23×C11—41no—
185C22×D11C2×D811yescharacteristic
186C22×D11C2×D811yescharacteristic
187Q8×C11—41no—
188Q8×C11—41no—
189D4×C11—41no—
190D4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—161no—
195C2×C4×C11C2×D811yescharacteristic
196C2×C4×C11C2×D811yescharacteristic
197C2×C4×C11C22×D411yescharacteristic
198C22⋊D11—82no—
199C22⋊D11—161no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11C2×D811yescharacteristic
205C2×Dic11C2×D811yescharacteristic
206D44—41no—
207C4×D11—21no—
208C4×D11—21no—
209C4×D11—21no—
210C4×D11—21no—
211C4×D11—82no—
212C4×D11—161no—
213C8×C11—21no—
214C8×C11C2×#4111yescharacteristic
215C8×C112−1+411yescharacteristic
216C11⋊C8—21no—
217C11⋊C8—21no—
218#553—221no—
219#552—221no—
220C2×SD32C2×D1111yescharacteristic
221C2×M32—111no—
222C2×M32—111no—
223#499—111no—
224#499—111no—
225#485—221no—
226#483—221no—
227#482—221no—
228#481—221no—
229#479—221no—
230#478—221no—
231#467—111no—
232#467—111no—
233#466—111no—
234#466—111no—
235C4×Q16C2×D1111yescharacteristic
236C4×D8C2×D1111yescharacteristic
237C8×D4—111no—
238#427—111no—
239#427—111no—
240C2×#107—111no—
241C2×#107—111no—
242#367—111no—
243#367—111no—
244#367—111no—
245#367—111no—
246#367C2×D1111yescharacteristic
247#366—111no—
248#366—111no—
249#366—111no—
250#366—111no—
251C4⋊C16—111no—
252#358—111no—
253#358—111no—
254#358C2×D1111yescharacteristic
255#357—111no—
256#357—111no—
257#357C2×D1111yescharacteristic
258C22⋊C16—111no—
259C22⋊C16—111no—
260C4×C16C2×D1111yescharacteristic
261C22×C11—81no—
262C22×C11—81no—
263C22×C11—81no—
264C22×C11C22×D811yescharacteristic
265C2×D11—21no—
266C2×D11—21no—
267C2×D11—21no—
268C2×D11—21no—
269C2×D11—21no—
270C2×D11—21no—
271C4×C11—21no—
272C4×C11—21no—
273C4×C11—81no—
274C4×C11—81no—
275C4×C11—81no—
276C4×C11#54711yescharacteristic
277C4×C11#57811yescharacteristic
278Dic11—21no—
279Dic11—21no—
280Dic11—81no—
281Dic11—81no—
282Dic11—81no—
283Dic11—81no—
284C2×Q16C22×D1111yescharacteristic
285C2×D8C22×D1111yescharacteristic
286C22×C8—111no—
287C22×C8—111no—
288#126—441no—
289#126—441no—
290#125—221no—
291#125—221no—
292#125—441no—
293#123—441no—
294#123—441no—
295C22⋊Q8—221no—
296C22⋊Q8—221no—
297#121—221no—
298#121—221no—
299#121—441no—
300C4×Q8—21no—
301C4×D4—21no—
302C4×D4—111no—
303C4×D4—441no—
304#117—221no—
305#117—221no—
306#117—441no—
307C2×C4⋊C4—221no—
308C2×C4⋊C4—221no—
309SD32—22no—
310M32—222no—
311M32—222no—
312C2×C16—111no—
313C2×C16—111no—
314C2×C16C22×D1111yescharacteristic
315C2×C16C22×D1111yescharacteristic
316#107—111no—
317#107—111no—
318#107—111no—
319#107—111no—
320#107—221no—
321#107—221no—
322#107C22×D1111yescharacteristic
323#107C22×D1111yescharacteristic
324#106—221no—
325#106—221no—
326#106—221no—
327#106—221no—
328C4⋊C8—111no—
329#103—21no—
330#103—221no—
331#103—221no—
332#102—21no—
333#102—221no—
334#102—221no—
335C22⋊C8—111no—
336C22⋊C8—111no—
337C4×C8C22×D1111yescharacteristic
338C2×C11—161no—
339C2×C11#333411yescharacteristic
340C2×C11#341411yescharacteristic
341C2×C11#341611yescharacteristic
342D11—41no—
343D11—41no—
344C2×Q8—21no—
345C2×D4—21no—
346C2×D4—111no—
347C2×D4—441no—
348C2×D4—441no—
349C22×C4—41no—
350C22×C4—111no—
351C22×C4—111no—
352C22×C4—441no—
353C22×C4—441no—
354Q16—21no—
355Q16—21no—
356D8—21no—
357D8—21no—
358C2×C8—111no—
359C2×C8—111no—
360C2×C8—221no—
361C2×C8—221no—
362C2×C8—221no—
363C2×C8—221no—
364C2×C8D4×D1111yescharacteristic
365C2×C8C23×D1111yescharacteristic
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—41no—
369C4⋊C4—111no—
370C4⋊C4—221no—
371C4⋊C4—221no—
372C4⋊C4—221no—
373C4⋊C4—221no—
374C4⋊C4—441no—
375C4⋊C4—441no—
376C4⋊C4—441no—
377C4⋊C4—441no—
378C4⋊C4—441no—
379C4⋊C4—441no—
380C4⋊C4—441no—
381C4⋊C4—441no—
382C22⋊C4—41no—
383C22⋊C4—111no—
384C22⋊C4—111no—
385C22⋊C4—441no—
386C22⋊C4—441no—
387C22⋊C4—441no—
388C22⋊C4—441no—
389C22⋊C4—441no—
390C22⋊C4—441no—
391C42—41no—
392C42—441no—
393C42—441no—
394C42D4×D1111yescharacteristic
395C16—21no—
396C16—221no—
397C16—221no—
398C16#433912yes—
399C11#3391811yescharacteristic, complemented, Sylow
400C23—41no—
401C23—111no—
402C23—111no—
403Q8—41no—
404Q8—41no—
405D4—41no—
406D4—41no—
407D4—441no—
408D4—882no—
409D4—1761no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—111no—
414C2×C4—111no—
415C2×C4—161no—
416C2×C4—221no—
417C2×C4—221no—
418C2×C4—221no—
419C2×C4—221no—
420C2×C4—441no—
421C2×C4—441no—
422C2×C4—441no—
423C2×C4—441no—
424C2×C4—882no—
425C2×C4—1761no—
426C2×C4D8×D1111yescharacteristic
427C2×C4D8×D1111yescharacteristic
428C2×C4C2×D4×D1111yescharacteristic
429C8—21no—
430C8—221no—
431C8—221no—
432C8C2×#433911yescharacteristic
433C8#6704311yescharacteristic
434C22—81no—
435C22—81no—
436C22—81no—
437C22—221no—
438C22—221no—
439C22—221no—
440C22—221no—
441C22—221no—
442C22—221no—
443C22C2×D8×D1111yescharacteristic
444C4—21no—
445C4—21no—
446C4—81no—
447C4—81no—
448C4—81no—
449C4—221no—
450C4—221no—
451C4—881no—
452C4—881no—
453C4—881no—
454C4—881no—
455C4#1062308211yescharacteristic
456C4#1062330211yescharacteristic
457C2—161no—
458C2—441no—
459C2—441no—
460C2#1308096511yescharacteristic
461C2#1308174911yescharacteristic
462C2#1308175811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC4×C11×SD32C2
socleC22×C11C22×D8
prime radical#13081020C2
hypercenterC4×SD32D11
hypocenterC11#33918
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×SD32

Complements

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

NH ≅ G/Ntype
2. #13080986C2semidirect
3. #13070895C2semidirect
4. #13070822C2semidirect
5. #13070812C2semidirect
6. #13070806C2semidirect
7. #13070800C2semidirect
8. #13070780C2semidirect
9. #13070773C2semidirect
10. #13070726C2semidirect
11. #13070726C2semidirect
12. #13070449C2semidirect
13. #13070403C2semidirect
14. #13070403C2semidirect
15. C4×C11×SD32C2semidirect
180. C4×SD32D11semidirect
399. C11#33918semidirect

Maximal subgroups

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

subgroupindex
#130810202
#130809862
#130708952
#130708222
#130708122
#130708062
#130708002
#130707802
#130707732
#130707262
#130704492
#130704032
C4×C11×SD322
#3391811