Finite Group Databasebeta

← #14911230

Subgroups — #14911230

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#13080983C211yesmaximal, characteristic, complemented
2#13080965C211yesmaximal, characteristic
3#13070903C211yesmaximal, characteristic, complemented
4#13070820C211yesmaximal, characteristic, complemented
5#13070815C211yesmaximal, characteristic, complemented
6#13070805C211yesmaximal, characteristic, complemented
7#13070795C211yesmaximal, characteristic, complemented
8#13070769C211yesmaximal, characteristic, complemented
9#13070728C211yesmaximal, characteristic, complemented
10#13070711C211yesmaximal, characteristic, complemented
11#13070480C211yesmaximal, characteristic, complemented
12#13070440C211yesmaximal, characteristic, complemented
13#13070403C211yesmaximal, characteristic, complemented
14D11×#366C211yesmaximal, characteristic, complemented
15C11×#2228C211yesmaximal, characteristic, complemented
16#10623225—21no—
17#10623082—21no—
18C11×#499C2211yescharacteristic
19C4×C11×D8C2211yescharacteristic
20#10622770C2211yescharacteristic
21#10622770C2211yescharacteristic
22C2×#66891C2211yescharacteristic
23#10622676—21no—
24#10622620—21no—
25C2×#66862C2211yescharacteristic
26C2×C16×D11C2211yescharacteristic
27#10622500C2211yescharacteristic
28#10622500C2211yescharacteristic
29#10622493C2211yescharacteristic
30D11×#107C2211yescharacteristic
31D11×#107C2211yescharacteristic
32D11×#107C2211yescharacteristic
33#10622480—21no—
34#10622475—21no—
35#10622387—21no—
36#10622387—21no—
37C4×Dic44C2211yescharacteristic
38C8×D44C2211yescharacteristic
39#10622295C2211yescharacteristic
40C11×#367C2211yescharacteristic
41C11×#366C2211yescharacteristic
42C11×C4⋊C16C2211yescharacteristic
43C11×#357C2211yescharacteristic
44C11×#357C2211yescharacteristic
45#10622200C2211yescharacteristic
46(C2×D11)⋊C16C2211yescharacteristic
47(C2×D11)⋊C16C2211yescharacteristic
48#10622142C2211yescharacteristic
49#10622142C2211yescharacteristic
50#10622141C2211yescharacteristic
51#10622141C2211yescharacteristic
52#10622130C2211yescharacteristic
53#10622128C2211yescharacteristic
54#10622128C2211yescharacteristic
55#10622127C2211yescharacteristic
56#10622127C2211yescharacteristic
57#10622127C2211yescharacteristic
58#10622099C2211yescharacteristic
59C2×#4339—41no—
60C2×C11×D8C2311yescharacteristic
61C11×#125—21no—
62C4×D4×C11—21no—
63#66991—21no—
64#66991—21no—
65#66977—41no—
66C2×Dic44C2311yescharacteristic
67C2×C8×D11C2311yescharacteristic
68C2×C8×D11C2311yescharacteristic
69#66951—41no—
70#66950—21no—
71#66950—21no—
72#66947—41no—
73#66945—21no—
74#66945—41no—
75C4⋊C4×D11—21no—
76C4⋊C4×D11—21no—
77C4⋊C4×D11—21no—
78#66943—41no—
79#66936—41no—
80#66936—41no—
81C4×D44D411yescharacteristic
82#66922—21no—
83C4×Dic22—21no—
84C2×C11×C16C2311yescharacteristic
85C2×C11×C16C2311yescharacteristic
86C11×#107C2311yescharacteristic
87C11×#107C2311yescharacteristic
88C11×#107C2311yescharacteristic
89C11×#106—21no—
90C11×#102—21no—
91C4×C8×C11C2311yescharacteristic
92#66896—21no—
93#66896—21no—
94#66891—22no—
95(C2×D11)⋊C8D411yescharacteristic
96(C2×D11)⋊C8D411yescharacteristic
97#66882—21no—
98#66882C2311yescharacteristic
99#66882C2311yescharacteristic
100#66882C2311yescharacteristic
101#66880—21no—
102C2×C11⋊C16C2311yescharacteristic
103C2×C11⋊C16C2311yescharacteristic
104#66874—21no—
105#66874—21no—
106#66872—21no—
107#66871—21no—
108#66871—21no—
109#66871—21no—
110C4⋊(C11⋊C8)D411yescharacteristic
111#66862—22no—
112C16×D11—22no—
113#33910—111nomaximal, Sylow
114C2×D4×C11—21no—
115C22×C4×C11—41no—
116C2×C22⋊D11—41no—
117C2×C22⋊D11—41no—
118#4339—84no—
119C2×D44D811yescharacteristic
120C2×C4×D11—41no—
121C2×C4×D11—41no—
122C2×C4×D11—41no—
123C2×C4×D11C2×D411yescharacteristic
124C2×C4×D11C2×D411yescharacteristic
125C2×Dic22—21no—
126C2×Dic22—41no—
127C11×D8—21no—
128C11×D8—21no—
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×C22⋊C4—41no—
137C42×C11C2×D411yescharacteristic
138C22⋊Dic11—41no—
139C22⋊Dic11—41no—
140(C2×D11)⋊C4—41no—
141(C2×D11)⋊C4—41no—
142(C2×D11)⋊C4—41no—
143(C2×D11)⋊C4D811yescharacteristic
144(C2×D11)⋊C4D811yescharacteristic
145C4⋊Dic11—21no—
146C4⋊Dic11—21no—
147C4⋊Dic11—21no—
148C4⋊Dic11—41no—
149C4⋊Dic11—41no—
150C4⋊Dic11—41no—
151C4⋊Dic11D811yescharacteristic
152Dic11⋊C4—41no—
153Dic11⋊C4—41no—
154Dic11⋊C4—41no—
155Dic11⋊C4—41no—
156C4×Dic11—41no—
157C4×Dic11—41no—
158C2×C11⋊C8C2×D411yescharacteristic
159C2×C11⋊C8C2×D411yescharacteristic
160Dic44—21no—
161Dic44—21no—
162C8×D11—21no—
163C8×D11—21no—
164C8×D11—21no—
165C8×D11—21no—
166C11×C16—21no—
167C11×C16—21no—
168C11⋊C16—21no—
169C11⋊C16#4112yescomplemented
170#3336—111no—
171#3334—111no—
172#2255—111no—
173#2236—111no—
174#2235—111no—
175#2234—111no—
176#2232—111no—
177#2228D1111yescharacteristic, complemented
178#2227—111no—
179#2220—111no—
180#2217—111no—
181#2175—111no—
182#2168—111no—
183#2159—111no—
184C2×#366—111no—
185C23×C11—41no—
186C22×D11C2×D811yescharacteristic
187C22×D11C2×D811yescharacteristic
188D4×C11—41no—
189D4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—82no—
194C2×C4×C11C2×D811yescharacteristic
195C2×C4×C11C2×D811yescharacteristic
196C2×C4×C11C22×D411yescharacteristic
197C22⋊D11—82no—
198C22⋊D11—82no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11C2×D811yescharacteristic
204C2×Dic11C2×D811yescharacteristic
205D44—22no—
206C4×D11—21no—
207C4×D11—21no—
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×M32—111no—
225C22×C16—111no—
226#500—111no—
227#499C2×D1111yescharacteristic
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×D8C2×D1111yescharacteristic
240C8×D4—111no—
241#427—111no—
242C2×#107—111no—
243C2×#107—111no—
244C2×#107—111no—
245#367—111no—
246#367—111no—
247#367C2×D1111yescharacteristic
248#366—111no—
249#366—111no—
250#366—111no—
251#366—111no—
252#366—111no—
253#366C2×D1111yescharacteristic
254C4⋊C16C2×D1111yescharacteristic
255#358—111no—
256#358—111no—
257#358—111no—
258#357—111no—
259#357C2×D1111yescharacteristic
260#357C2×D1111yescharacteristic
261C22⋊C16—111no—
262C22⋊C16—111no—
263#346—111no—
264C22×C11—81no—
265C22×C11—81no—
266C22×C11—81no—
267C22×C11C22×D811yescharacteristic
268C2×D11—21no—
269C2×D11—21no—
270C2×D11—21no—
271C2×D11—21no—
272C2×D11—21no—
273C2×D11#50912yes—
274C4×C11—21no—
275C4×C11—21no—
276C4×C11—81no—
277C4×C11—81no—
278C4×C11—81no—
279C4×C11#54711yescharacteristic
280C4×C11#57811yescharacteristic
281Dic11—21no—
282Dic11—21no—
283Dic11—81no—
284Dic11—81no—
285Dic11—81no—
286Dic11—81no—
287C2×#41—441no—
288C2×Q16—111no—
289C2×D8C22×D1111yescharacteristic
290C22×C8—111no—
291C22×C8—111no—
292C4⋊Q8—221no—
293#126—441no—
294#125—21no—
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—21no—
306C4×D4—111no—
307#117—221no—
308#117—441no—
309C2×C4⋊C4—221no—
310C2×C4⋊C4—221no—
311C2×C4⋊C4—221no—
312SD32—222no—
313M32—222no—
314C2×C16—111no—
315C2×C16—111no—
316C2×C16—222no—
317C2×C16C22×D1111yescharacteristic
318C2×C16C22×D1111yescharacteristic
319#107—111no—
320#107—111no—
321#107—111no—
322#107—221no—
323#107—221no—
324#107—221no—
325#107—221no—
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—21no—
336#102—221no—
337#102—221no—
338C22⋊C8—111no—
339C22⋊C8—111no—
340C4×C8C22×D1111yescharacteristic
341C2×C11—161no—
342C2×C11#333411yescharacteristic
343C2×C11C2×#50911yescharacteristic
344C2×C11#341711yescharacteristic
345D11—22no—
346D11—41no—
347#41—884no—
348C2×Q8—221no—
349C2×Q8—441no—
350C2×D4—21no—
351C2×D4—111no—
352C2×D4—441no—
353C2×D4—441no—
354C22×C4—41no—
355C22×C4—111no—
356C22×C4—111no—
357C22×C4—441no—
358C22×C4—441no—
359C22×C4—441no—
360Q16—221no—
361Q16—221no—
362D8—21no—
363D8—21no—
364C2×C8—111no—
365C2×C8—111no—
366C2×C8—221no—
367C2×C8—221no—
368C2×C8—221no—
369C2×C8—221no—
370C2×C8D4×D1111yescharacteristic
371C2×C8C23×D1111yescharacteristic
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—41no—
376C4⋊C4—41no—
377C4⋊C4—111no—
378C4⋊C4—221no—
379C4⋊C4—221no—
380C4⋊C4—221no—
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—441no—
397C42—441no—
398C42D4×D1111yescharacteristic
399C16—21no—
400C16—21no—
401C16—112no—
402C16—221no—
403C11#3391011yescharacteristic, complemented, Sylow
404C23—41no—
405C23—111no—
406C23—111no—
407Q8—441no—
408Q8—441no—
409Q8—882no—
410D4—41no—
411D4—41no—
412D4—222no—
413D4—882no—
414D4—882no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—82no—
419C2×C4—111no—
420C2×C4—111no—
421C2×C4—221no—
422C2×C4—221no—
423C2×C4—221no—
424C2×C4—221no—
425C2×C4—441no—
426C2×C4—441no—
427C2×C4—441no—
428C2×C4—441no—
429C2×C4—882no—
430C2×C4—882no—
431C2×C4—882no—
432C2×C4D8×D1111yescharacteristic
433C2×C4D8×D1111yescharacteristic
434C2×C4C2×D4×D1111yescharacteristic
435C8—21no—
436C8—221no—
437C8—221no—
438C8#6704011yescharacteristic
439C8#41×D1111yescharacteristic
440C22—81no—
441C22—81no—
442C22—81no—
443C22—112no—
444C22—221no—
445C22—221no—
446C22—221no—
447C22—221no—
448C22—221no—
449C22C2×D8×D1111yescharacteristic
450C4—21no—
451C4—21no—
452C4—81no—
453C4—81no—
454C4—81no—
455C4—221no—
456C4—221no—
457C4—881no—
458C4—881no—
459C4—881no—
460C4—881no—
461C4#1062316211yescharacteristic
462C4#1062331011yescharacteristic
463C2—161no—
464C2—222no—
465C2—441no—
466C2#1308096211yescharacteristic
467C2D11×#50911yescharacteristic
468C2#1308176611yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2228C2
socleC22×C11C22×D8
prime radical#13080965C2
hypercenter#2228D11
hypocenterC11#33910
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2228

Complements

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

NH ≅ G/Ntype
1. #13080983C2semidirect
3. #13070903C2semidirect
4. #13070820C2semidirect
5. #13070815C2semidirect
6. #13070805C2semidirect
7. #13070795C2semidirect
8. #13070769C2semidirect
9. #13070728C2semidirect
10. #13070711C2semidirect
11. #13070480C2semidirect
12. #13070440C2semidirect
13. #13070403C2semidirect
14. D11×#366C2semidirect
15. C11×#2228C2semidirect
169. C11⋊C16#41semidirect
177. #2228D11semidirect
403. C11#33910semidirect

Maximal subgroups

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

subgroupindex
#130809832
#130809652
#130709032
#130708202
#130708152
#130708052
#130707952
#130707692
#130707282
#130707112
#130704802
#130704402
#130704032
D11×#3662
C11×#22282
#3391011