Finite Group Databasebeta

← #14911362

Subgroups — #14911362

Order 2816.

502 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#13081043C211yesmaximal, characteristic, complemented
2#13080960C211yesmaximal, characteristic
3#13070890C211yesmaximal, characteristic, complemented
4#13070817C211yesmaximal, characteristic, complemented
5#13070816C211yesmaximal, characteristic, complemented
6#13070806C211yesmaximal, characteristic, complemented
7#13070804C211yesmaximal, characteristic, complemented
8#13070756C211yesmaximal, characteristic, complemented
9#13070751C211yesmaximal, characteristic, complemented
10#13070726C211yesmaximal, characteristic, complemented
11SD32×Dic11C211yesmaximal, characteristic, complemented
12#13070446C211yesmaximal, characteristic, complemented
13#13070404C211yesmaximal, characteristic, complemented
14#13070401C211yesmaximal, characteristic, complemented
15C11×#2220C211yesmaximal, characteristic, complemented
16#10623172—21no—
17#10623142—21no—
18C2×C11×SD32C2211yescharacteristic
19C2×C11×M32C2211yescharacteristic
20C11×#467C2211yescharacteristic
21C11×#466C2211yescharacteristic
22#10622801C2211yescharacteristic
23Q16×Dic11C2211yescharacteristic
24#10622770C2211yescharacteristic
25D8×Dic11C2211yescharacteristic
26C8×C22⋊D11C2211yescharacteristic
27#10622719C2211yescharacteristic
28C2×#66882C2211yescharacteristic
29#10622658—21no—
30#10622646—21no—
31C2×#66862C2211yescharacteristic
32#10622493C2211yescharacteristic
33D11×#107C2211yescharacteristic
34#10622487C2211yescharacteristic
35#10622487C2211yescharacteristic
36#10622428—21no—
37#10622404—21no—
38#10622387—21no—
39#10622372—21no—
40C11×#366C2211yescharacteristic
41C11×#358C2211yescharacteristic
42C11×#357C2211yescharacteristic
43#10622202C2211yescharacteristic
44#10622202C2211yescharacteristic
45#10622200C2211yescharacteristic
46#10622200C2211yescharacteristic
47C22⋊(C11⋊C16)C2211yescharacteristic
48(C2×D11)⋊C16C2211yescharacteristic
49#10622143C2211yescharacteristic
50#10622143C2211yescharacteristic
51#10622142C2211yescharacteristic
52#10622142C2211yescharacteristic
53Dic11⋊C16C2211yescharacteristic
54C16×Dic11C2211yescharacteristic
55#10622128C2211yescharacteristic
56#10622127C2211yescharacteristic
57#10622127C2211yescharacteristic
58#10622127C2211yescharacteristic
59C2×#4341—41no—
60C2×C11×Q16C2311yescharacteristic
61C2×C11×D8C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C11×C22⋊Q8—21no—
64C11×#121—21no—
65#66999—21no—
66Q8×Dic11—21no—
67#66991—21no—
68#66988—41no—
69D4×Dic11—21no—
70C4×C22⋊D11D411yescharacteristic
71#66979—21no—
72C2×C4⋊Dic11—21no—
73C2×C8×D11C2311yescharacteristic
74#66951—41no—
75#66945—21no—
76C4⋊C4×D11—21no—
77#66941—21no—
78#66941—21no—
79#66940—41no—
80#66938—41no—
81#66936—41no—
82#66932—41no—
83#66931—41no—
84C11×SD32—22no—
85C11×M32—22no—
86C2×C11×C16C2311yescharacteristic
87C2×C11×C16C2311yescharacteristic
88C11×#107C2311yescharacteristic
89C11×#107C2311yescharacteristic
90C11×#103—21no—
91C11×#102—21no—
92#66899—21no—
93#66899—21no—
94#66896—21no—
95#66896—21no—
96C22⋊(C11⋊C8)D411yescharacteristic
97(C2×D11)⋊C8D411yescharacteristic
98#66882—21no—
99#66882C2311yescharacteristic
100#66882C2311yescharacteristic
101#66882C2311yescharacteristic
102#66882C2311yescharacteristic
103#66881—21no—
104Dic11⋊C8D411yescharacteristic
105C8×Dic11C2311yescharacteristic
106C2×C11⋊C16C2311yescharacteristic
107C2×C11⋊C16C2311yescharacteristic
108#66872—21no—
109#66871—21no—
110#66871—21no—
111#66871—21no—
112#66862—22no—
113#33920—111nomaximal, Sylow
114C2×Q8×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—41no—
117C22×C4×C11C2×D411yescharacteristic
118C2×C22⋊D11—41no—
119C2×C22⋊D11D811yescharacteristic
120C22×Dic11—41no—
121C22×Dic11—41no—
122#4341—84no—
123C2×C4×D11—41no—
124C2×C4×D11C2×D411yescharacteristic
125C2×Dic22—41no—
126C2×Dic22—41no—
127C11×Q16—21no—
128C11×Q16—21no—
129C11×D8—21no—
130C11×D8—21no—
131C2×C8×C11—21no—
132C2×C8×C11—21no—
133C2×C8×C11C2×D411yescharacteristic
134C2×C8×C11C2411yescharacteristic
135C11×C4⋊C4—21no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—41no—
138C11×C22⋊C4—41no—
139C11×C22⋊C4—41no—
140C22⋊Dic11—41no—
141C22⋊Dic11—41no—
142C22⋊Dic11—41no—
143C22⋊Dic11D811yescharacteristic
144(C2×D11)⋊C4—41no—
145(C2×D11)⋊C4—41no—
146(C2×D11)⋊C4D811yescharacteristic
147C4⋊Dic11—21no—
148C4⋊Dic11—21no—
149C4⋊Dic11—21no—
150C4⋊Dic11—21no—
151C4⋊Dic11—41no—
152C4⋊Dic11—41no—
153Dic11⋊C4—41no—
154Dic11⋊C4—41no—
155Dic11⋊C4—41no—
156Dic11⋊C4—41no—
157Dic11⋊C4D811yescharacteristic
158C4×Dic11—41no—
159C4×Dic11—41no—
160C4×Dic11—41no—
161C4×Dic11C2×D411yescharacteristic
162C2×C11⋊C8C2×D411yescharacteristic
163C2×C11⋊C8C2×D411yescharacteristic
164C8×D11—21no—
165C8×D11—21no—
166C11×C16—21no—
167C11×C16#4112yescomplemented
168C11⋊C16—21no—
169C11⋊C16—21no—
170#3342—111no—
171#3334—111no—
172#2252—111no—
173#2236—111no—
174#2236—111no—
175#2234—111no—
176#2234—111no—
177#2225—111no—
178#2224—111no—
179#2220—111no—
180#2220D1111yescharacteristic, complemented
181C4×SD32—111no—
182#2169—111no—
183#2159—111no—
184#2159—111no—
185C23×C11—41no—
186C23×C11C2×D811yescharacteristic
187C22×D11C2×D811yescharacteristic
188Q8×C11—41no—
189Q8×C11—41no—
190D4×C11—41no—
191D4×C11—41no—
192D4×C11—82no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11C2×D811yescharacteristic
199C2×C4×C11C22×D411yescharacteristic
200C22⋊D11—22no—
201C22⋊D11—82no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—82no—
207C2×Dic11—82no—
208C2×Dic11C2×D811yescharacteristic
209C2×Dic11C2×D811yescharacteristic
210C2×Dic11C2×D811yescharacteristic
211C4×D11—21no—
212C4×D11—21no—
213C4×D11—82no—
214Dic22—82no—
215Dic22—82no—
216C8×C11—21no—
217C8×C11C2×#4111yescharacteristic
218C8×C112−1+411yescharacteristic
219C11⋊C8—21no—
220C11⋊C8—21no—
221#556—221no—
222#547—221no—
223C2×SD32C2×D1111yescharacteristic
224C2×M32—111no—
225C2×M32C2×D1111yescharacteristic
226#500—111no—
227#500—111no—
228#485—221no—
229#485—221no—
230#480—221no—
231#480—221no—
232#475—221no—
233#474—221no—
234#467—111no—
235#467C2×D1111yescharacteristic
236#466—111no—
237#466C2×D1111yescharacteristic
238C4×Q16—111no—
239C4×D8—111no—
240C8×D4—111no—
241#427—111no—
242#427—111no—
243C2×#107—111no—
244C2×#107—111no—
245#367—111no—
246#367—111no—
247#367—111no—
248#366—111no—
249#366—111no—
250#366—111no—
251#366—111no—
252#366—111no—
253#366C2×D1111yescharacteristic
254C4⋊C16—111no—
255#358—111no—
256#358—111no—
257#358C2×D1111yescharacteristic
258#357—111no—
259#357—111no—
260#357C2×D1111yescharacteristic
261C22⋊C16—111no—
262C22⋊C16—111no—
263C4×C16—111no—
264C22×C11—21no—
265C22×C11—21no—
266C22×C11—21no—
267C22×C11—81no—
268C22×C11—81no—
269C22×C11—81no—
270C22×C11C22×D811yescharacteristic
271C2×D11—21no—
272C2×D11—21no—
273C2×D11—21no—
274C4×C11—21no—
275C4×C11—81no—
276C4×C11—81no—
277C4×C11—81no—
278C4×C11#54711yescharacteristic
279C4×C11#57811yescharacteristic
280Dic11—21no—
281Dic11—21no—
282Dic11—81no—
283Dic11—81no—
284Dic11—81no—
285Dic11—81no—
286Dic11#50912yes—
287C2×#41—441no—
288C2×Q16C22×D1111yescharacteristic
289C2×D8C22×D1111yescharacteristic
290C22×C8—111no—
291C22×C8C22×D1111yescharacteristic
292C4⋊Q8—221no—
293C4⋊Q8—221no—
294#126—441no—
295#126—441no—
296#124—441no—
297#123—441no—
298#123—441no—
299C22⋊Q8—21no—
300C22⋊Q8—221no—
301C22⋊Q8—441no—
302#121—21no—
303#121—221no—
304C4×Q8—221no—
305C4×Q8—441no—
306C4×D4—111no—
307C4×D4—221no—
308#117—221no—
309#117—221no—
310C2×C4⋊C4—221no—
311C2×C4⋊C4—221no—
312SD32—22no—
313M32—22no—
314M32—222no—
315C2×C16—111no—
316C2×C16—111no—
317C2×C16C22×D1111yescharacteristic
318C2×C16C22×D1111yescharacteristic
319#107—111no—
320#107—111no—
321#107—111no—
322#107—111no—
323#107—221no—
324#107—221no—
325#107—221no—
326#107—221no—
327#107C22×D1111yescharacteristic
328#107C22×D1111yescharacteristic
329#106—221no—
330#106—221no—
331C4⋊C8—111no—
332#103—21no—
333#103—221no—
334#103—221no—
335#102—21no—
336#102—221no—
337#102—221no—
338C22⋊C8—111no—
339C22⋊C8—111no—
340C4×C8—111no—
341C2×C11—41no—
342C2×C11—161no—
343C2×C11#333411yescharacteristic
344C2×C11C2×#50911yescharacteristic
345C2×C11#341711yescharacteristic
346D11—41no—
347#41—884no—
348C2×Q8—21no—
349C2×Q8—441no—
350C2×Q8—441no—
351C2×D4—21no—
352C2×D4—41no—
353C2×D4—111no—
354C2×D4—441no—
355C22×C4—111no—
356C22×C4—441no—
357C22×C4—441no—
358C22×C4—441no—
359C22×C4D4×D1111yescharacteristic
360Q16—21no—
361Q16—21no—
362D8—21no—
363D8—21no—
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—41no—
375C4⋊C4—111no—
376C4⋊C4—221no—
377C4⋊C4—221no—
378C4⋊C4—221no—
379C4⋊C4—221no—
380C4⋊C4—441no—
381C4⋊C4—441no—
382C4⋊C4—441no—
383C4⋊C4—441no—
384C4⋊C4—441no—
385C4⋊C4—441no—
386C22⋊C4—41no—
387C22⋊C4—41no—
388C22⋊C4—111no—
389C22⋊C4—111no—
390C22⋊C4—441no—
391C22⋊C4—441no—
392C22⋊C4—441no—
393C22⋊C4—441no—
394C22⋊C4—441no—
395C42—111no—
396C42—441no—
397C42—441no—
398C42—441no—
399C16—21no—
400C16—221no—
401C16—221no—
402C16#434112yescomplemented
403C11#3392011yescharacteristic, complemented, Sylow
404C23—41no—
405C23—111no—
406C23D8×D1111yescharacteristic
407Q8—41no—
408Q8—41no—
409Q8—882no—
410Q8—882no—
411D4—41no—
412D4—41no—
413D4—82no—
414D4—222no—
415D4—882no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—111no—
422C2×C4—111no—
423C2×C4—111no—
424C2×C4—221no—
425C2×C4—221no—
426C2×C4—441no—
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×#434111yescharacteristic
439C8#6704311yescharacteristic
440C22—21no—
441C22—21no—
442C22—21no—
443C22—81no—
444C22—81no—
445C22—81no—
446C22—221no—
447C22—221no—
448C22—221no—
449C22C2×D8×D1111yescharacteristic
450C4—21no—
451C4—81no—
452C4—81no—
453C4—81no—
454C4—112no—
455C4—221no—
456C4—221no—
457C4—881no—
458C4—881no—
459C4—881no—
460C4—881no—
461C4#1062314211yescharacteristic
462C4#1062330211yescharacteristic
463C2—41no—
464C2—161no—
465C2—441no—
466C2#1308096011yescharacteristic
467C2D11×#50911yescharacteristic
468C2#1308176811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2220C2
socleC22×C11C22×D8
prime radical#13080960C2
hypercenter#2220D11
hypocenterC11#33920
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2220

Complements

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

NH ≅ G/Ntype
1. #13081043C2semidirect
3. #13070890C2semidirect
4. #13070817C2semidirect
5. #13070816C2semidirect
6. #13070806C2semidirect
7. #13070804C2semidirect
8. #13070756C2semidirect
9. #13070751C2semidirect
10. #13070726C2semidirect
11. SD32×Dic11C2semidirect
12. #13070446C2semidirect
13. #13070404C2semidirect
14. #13070401C2semidirect
15. C11×#2220C2semidirect
167. C11×C16#41semidirect
180. #2220D11semidirect
402. C16#4341semidirect
403. C11#33920semidirect

Maximal subgroups

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

subgroupindex
#130810432
#130809602
#130708902
#130708172
#130708162
#130708062
#130708042
#130707562
#130707512
#130707262
SD32×Dic112
#130704462
#130704042
#130704012
C11×#22202
#3392011