Finite Group Databasebeta

← #14911224

Subgroups — #14911224

Order 2816.

504 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080984C211yesmaximal, characteristic, complemented
2#13080961C211yesmaximal, characteristic
3#13070901C211yesmaximal, characteristic, complemented
4#13070818C211yesmaximal, characteristic, complemented
5#13070815C211yesmaximal, characteristic, complemented
6#13070807C211yesmaximal, characteristic, complemented
7#13070798C211yesmaximal, characteristic, complemented
8#13070772C211yesmaximal, characteristic, complemented
9#13070767C211yesmaximal, characteristic, complemented
10#13070729C211yesmaximal, characteristic, complemented
11#13070713C211yesmaximal, characteristic, complemented
12#13070479C211yesmaximal, characteristic, complemented
13#13070439C211yesmaximal, characteristic, complemented
14D11×#366C211yesmaximal, characteristic, complemented
15C11×#2159C211yesmaximal, characteristic, complemented
16#10623060—21no—
17#10623038—21no—
18C2×C11×M32C2211yescharacteristic
19C11×#427C2211yescharacteristic
20C2×C11×#107C2211yescharacteristic
21#10622729C2211yescharacteristic
22#10622728C2211yescharacteristic
23C8×C22⋊D11C2211yescharacteristic
24#10622609—21no—
25#10622580—21no—
26C2×#66864C2211yescharacteristic
27C2×C16×D11C2211yescharacteristic
28#10622503—21no—
29#10622500C2211yescharacteristic
30#10622496C2211yescharacteristic
31#10622495—21no—
32D11×#107C2211yescharacteristic
33D11×#107C2211yescharacteristic
34#10622491C2211yescharacteristic
35#10622487C2211yescharacteristic
36#10622486C2211yescharacteristic
37#10622485C2211yescharacteristic
38#10622475—21no—
39#10622470—21no—
40C11×#367C2211yescharacteristic
41C11×#367C2211yescharacteristic
42C11×#366C2211yescharacteristic
43C11×#366C2211yescharacteristic
44C22⋊(C11⋊C16)C2211yescharacteristic
45#10622147C2211yescharacteristic
46(C2×D11)⋊C16C2211yescharacteristic
47#10622142C2211yescharacteristic
48#10622141C2211yescharacteristic
49#10622140C2211yescharacteristic
50Dic11⋊C16C2211yescharacteristic
51#10622130C2211yescharacteristic
52#10622130C2211yescharacteristic
53#10622129C2211yescharacteristic
54#10622129C2211yescharacteristic
55#10622128C2211yescharacteristic
56#10622127C2211yescharacteristic
57#10622127C2211yescharacteristic
58#10622127C2211yescharacteristic
59C2×#4339—41no—
60C22×C8×C11C2311yescharacteristic
61C11×#117—21no—
62C2×C11×C4⋊C4—21no—
63#66983—21no—
64#66982—41no—
65C4×C22⋊D11D411yescharacteristic
66#66977—21no—
67C2×Dic44C2311yescharacteristic
68C2×D88C2311yescharacteristic
69C2×C8×D11C2311yescharacteristic
70#66950—21no—
71#66949—41no—
72#66948—21no—
73#66947—41no—
74#66946—21no—
75C4⋊C4×D11—21no—
76C4⋊C4×D11—21no—
77#66943—21no—
78#66941—21no—
79#66940—21no—
80#66936—41no—
81#66932—41no—
82#66925—41no—
83#66923—41no—
84C11×M32—22no—
85C2×C11×C16C2311yescharacteristic
86C2×C11×C16C2311yescharacteristic
87C11×#107—21no—
88C11×#107C2311yescharacteristic
89C11×#107C2311yescharacteristic
90C11×#107C2311yescharacteristic
91C11×#107C2311yescharacteristic
92C11×#106—21no—
93C22⋊(C11⋊C8)D411yescharacteristic
94#66885—21no—
95(C2×D11)⋊C8D411yescharacteristic
96#66882C2311yescharacteristic
97#66882C2311yescharacteristic
98#66880—21no—
99Dic11⋊C8D411yescharacteristic
100C8×Dic11C2311yescharacteristic
101C2×C11⋊C16C2311yescharacteristic
102C2×C11⋊C16C2311yescharacteristic
103#66874—21no—
104#66874—21no—
105#66873—21no—
106#66873—21no—
107#66872—21no—
108#66871—21no—
109#66871—21no—
110#66871—21no—
111#66864—22no—
112C16×D11—22no—
113#33910—111nomaximal, Sylow
114C22×C4×C11—41no—
115C22×C4×C11C2×D411yescharacteristic
116C2×C22⋊D11—41no—
117C2×C22⋊D11D811yescharacteristic
118#4339—84no—
119C2×D44—21no—
120C2×D44—41no—
121C2×C4×D11—41no—
122C2×C4×D11—41no—
123C2×C4×D11—41no—
124C2×C4×D11C2×D411yescharacteristic
125C2×Dic22—21no—
126C2×Dic22—41no—
127C2×C8×C11—21no—
128C2×C8×C11—21no—
129C2×C8×C11C2×D411yescharacteristic
130C2×C8×C11C2411yescharacteristic
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—41no—
136C11×C22⋊C4—41no—
137C42×C11—41no—
138C22⋊Dic11—41no—
139C22⋊Dic11D811yescharacteristic
140(C2×D11)⋊C4—41no—
141(C2×D11)⋊C4—41no—
142(C2×D11)⋊C4—41no—
143(C2×D11)⋊C4—41no—
144(C2×D11)⋊C4D811yescharacteristic
145C4⋊Dic11—21no—
146C4⋊Dic11—21no—
147C4⋊Dic11—41no—
148C4⋊Dic11—41no—
149Dic11⋊C4—41no—
150Dic11⋊C4—41no—
151Dic11⋊C4—41no—
152Dic11⋊C4—41no—
153Dic11⋊C4—41no—
154Dic11⋊C4—41no—
155Dic11⋊C4D811yescharacteristic
156C4×Dic11—41no—
157C4×Dic11C2×D411yescharacteristic
158C2×C11⋊C8C2×D411yescharacteristic
159C2×C11⋊C8C2×D411yescharacteristic
160Dic44—21no—
161Dic44—21no—
162D88—21no—
163D88—21no—
164C8×D11—21no—
165C8×D11—21no—
166C11×C16—21no—
167C11×C16#4112yescomplemented
168C11⋊C16—21no—
169C11⋊C16—21no—
170#3336—111no—
171#3334—111no—
172#2255—111no—
173#2236—111no—
174#2235—111no—
175#2234—111no—
176#2232—111no—
177#2228—111no—
178#2227—111no—
179#2220—111no—
180#2217—111no—
181#2175—111no—
182#2168—111no—
183#2159D1111yescharacteristic, complemented
184C2×#366—111no—
185C23×C11C2×D811yescharacteristic
186C22×D11—41no—
187C22×D11C2×D811yescharacteristic
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—82no—
195C2×C4×C11C2×D811yescharacteristic
196C2×C4×C11C22×D411yescharacteristic
197C22⋊D11—22no—
198C22⋊D11—82no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11C2×D811yescharacteristic
203C2×Dic11C2×D811yescharacteristic
204C2×Dic11C2×D811yescharacteristic
205D44—41no—
206D44—41no—
207D44—82no—
208C4×D11—21no—
209C4×D11—21no—
210C4×D11—82no—
211C4×D11—82no—
212C4×D11—82no—
213Dic22—41no—
214Dic22—41no—
215Dic22—82no—
216C8×C11—21no—
217C8×C11C2×#4111yescharacteristic
218C8×C112−1+411yescharacteristic
219C11⋊C8—21no—
220C11⋊C8—21no—
221#552—221no—
222#547—221no—
223C2×SD32—111no—
224C2×M32C2×D1111yescharacteristic
225C22×C16—111no—
226#500—111no—
227#499—111no—
228#485—221no—
229#483—221no—
230#480—221no—
231#480—221no—
232#479—221no—
233#474—221no—
234#467—111no—
235#467—111no—
236#466—111no—
237#466—111no—
238C4×Q16—111no—
239C4×D8—111no—
240C8×D4—111no—
241#427C2×D1111yescharacteristic
242C2×#107—111no—
243C2×#107—111no—
244C2×#107C2×D1111yescharacteristic
245#367—111no—
246#367C2×D1111yescharacteristic
247#367C2×D1111yescharacteristic
248#366—111no—
249#366—111no—
250#366—111no—
251#366—111no—
252#366C2×D1111yescharacteristic
253#366C2×D1111yescharacteristic
254C4⋊C16—111no—
255#358—111no—
256#358—111no—
257#358—111no—
258#357—111no—
259#357—111no—
260#357—111no—
261C22⋊C16—111no—
262C22⋊C16—111no—
263#346—111no—
264C22×C11—21no—
265C22×C11—21no—
266C22×C11—21no—
267C22×C11C22×D811yescharacteristic
268C2×D11—21no—
269C2×D11—21no—
270C2×D11—81no—
271C2×D11—81no—
272C2×D11—81no—
273C2×D11#50912yes—
274C4×C11—21no—
275C4×C11—81no—
276C4×C11—81no—
277C4×C11—81no—
278C4×C11—81no—
279C4×C11#54711yescharacteristic
280C4×C11#57811yescharacteristic
281Dic11—21no—
282Dic11—21no—
283Dic11—21no—
284Dic11—81no—
285Dic11—81no—
286Dic11—81no—
287C2×#41—441no—
288C2×Q16—111no—
289C2×D8—111no—
290C22×C8—111no—
291C22×C8C22×D1111yescharacteristic
292C4⋊Q8—221no—
293#126—441no—
294#125—221no—
295#125—441no—
296#123—441no—
297#123—441no—
298#123—441no—
299C22⋊Q8—221no—
300C22⋊Q8—221no—
301C22⋊Q8—441no—
302#121—221no—
303#121—221no—
304C4×Q8—221no—
305C4×D4—111no—
306C4×D4—221no—
307#117—21no—
308#117—441no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—221no—
311C2×C4⋊C4—221no—
312SD32—222no—
313M32—22no—
314C2×C16—111no—
315C2×C16—111no—
316C2×C16—222no—
317C2×C16C22×D1111yescharacteristic
318C2×C16C22×D1111yescharacteristic
319#107—21no—
320#107—111no—
321#107—111no—
322#107—221no—
323#107—221no—
324#107—221no—
325#107C22×D1111yescharacteristic
326#107C22×D1111yescharacteristic
327#107C22×D1111yescharacteristic
328#107C22×D1111yescharacteristic
329#106—21no—
330#106—221no—
331C4⋊C8—111no—
332#103—221no—
333#103—221no—
334#103—221no—
335#102—221no—
336#102—221no—
337#102—221no—
338C22⋊C8—111no—
339C22⋊C8—111no—
340C4×C8—111no—
341C2×C11—41no—
342C2×C11#333411yescharacteristic
343C2×C11C2×#50911yescharacteristic
344C2×C11#341711yescharacteristic
345D11—22no—
346D11—161no—
347#41—884no—
348C2×Q8—221no—
349C2×Q8—441no—
350C2×D4—111no—
351C2×D4—221no—
352C2×D4—441no—
353C2×D4—441no—
354C22×C4—41no—
355C22×C4—111no—
356C22×C4—441no—
357C22×C4—441no—
358C22×C4—441no—
359C22×C4D4×D1111yescharacteristic
360Q16—221no—
361Q16—221no—
362D8—221no—
363D8—221no—
364C2×C8—21no—
365C2×C8—21no—
366C2×C8—111no—
367C2×C8—111no—
368C2×C8—221no—
369C2×C8—221no—
370C2×C8D4×D1111yescharacteristic
371C2×C8C23×D1111yescharacteristic
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—41no—
377C4⋊C4—111no—
378C4⋊C4—221no—
379C4⋊C4—221no—
380C4⋊C4—441no—
381C4⋊C4—441no—
382C4⋊C4—441no—
383C4⋊C4—441no—
384C4⋊C4—441no—
385C4⋊C4—441no—
386C4⋊C4—441no—
387C4⋊C4—441no—
388C22⋊C4—41no—
389C22⋊C4—111no—
390C22⋊C4—111no—
391C22⋊C4—441no—
392C22⋊C4—441no—
393C22⋊C4—441no—
394C22⋊C4—441no—
395C22⋊C4—441no—
396C42—41no—
397C42—111no—
398C42—441no—
399C16—21no—
400C16—221no—
401C16—221no—
402C16#433912yescomplemented
403C11#3391011yescharacteristic, complemented, Sylow
404C23—111no—
405C23—441no—
406C23D8×D1111yescharacteristic
407Q8—441no—
408Q8—441no—
409Q8—882no—
410D4—222no—
411D4—441no—
412D4—441no—
413D4—882no—
414D4—882no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—82no—
422C2×C4—111no—
423C2×C4—111no—
424C2×C4—111no—
425C2×C4—221no—
426C2×C4—221no—
427C2×C4—441no—
428C2×C4—441no—
429C2×C4—441no—
430C2×C4—882no—
431C2×C4—882no—
432C2×C4—882no—
433C2×C4D8×D1111yescharacteristic
434C2×C4C2×D4×D1111yescharacteristic
435C8—21no—
436C8—221no—
437C8—221no—
438C8C2×#433911yescharacteristic
439C8#6704011yescharacteristic
440C22—21no—
441C22—21no—
442C22—21no—
443C22—112no—
444C22—221no—
445C22—221no—
446C22—881no—
447C22—881no—
448C22—881no—
449C22C2×D8×D1111yescharacteristic
450C4—21no—
451C4—81no—
452C4—81no—
453C4—81no—
454C4—81no—
455C4—221no—
456C4—221no—
457C4—221no—
458C4—881no—
459C4—881no—
460C4—881no—
461C4#1062303811yescharacteristic
462C4#1062329711yescharacteristic
463C2—41no—
464C2—222no—
465C2—1761no—
466C2#1308096111yescharacteristic
467C2D11×#50911yescharacteristic
468C2#1308176811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2159C2
socleC22×C11C22×D8
prime radical#13080961C2
hypercenter#2159D11
hypocenterC11#33910
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2159

Complements

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

NH ≅ G/Ntype
1. #13080984C2semidirect
3. #13070901C2semidirect
4. #13070818C2semidirect
5. #13070815C2semidirect
6. #13070807C2semidirect
7. #13070798C2semidirect
8. #13070772C2semidirect
9. #13070767C2semidirect
10. #13070729C2semidirect
11. #13070713C2semidirect
12. #13070479C2semidirect
13. #13070439C2semidirect
14. D11×#366C2semidirect
15. C11×#2159C2semidirect
167. C11×C16#41semidirect
183. #2159D11semidirect
402. C16#4339semidirect
403. C11#33910semidirect

Maximal subgroups

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

subgroupindex
#130809842
#130809612
#130709012
#130708182
#130708152
#130708072
#130707982
#130707722
#130707672
#130707292
#130707132
#130704792
#130704392
D11×#3662
C11×#21592
#3391011