Finite Group Databasebeta

← #14911274

Subgroups — #14911274

Order 2816.

484 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081021C211yesmaximal, characteristic
2#13081005C211yesmaximal, characteristic, complemented
3#13070901C211yesmaximal, characteristic, complemented
4#13070823C211yesmaximal, characteristic, complemented
5#13070816C211yesmaximal, characteristic, complemented
6#13070799C211yesmaximal, characteristic, complemented
7#13070795C211yesmaximal, characteristic, complemented
8#13070782C211yesmaximal, characteristic, complemented
9#13070751C211yesmaximal, characteristic, complemented
10#13070726C211yesmaximal, characteristic, complemented
11#13070481C211yesmaximal, characteristic, complemented
12#13070441C211yesmaximal, characteristic, complemented
13#13070403C211yesmaximal, characteristic, complemented
14C2×#10622142C211yesmaximal, characteristic, complemented
15C11×#2217C211yesmaximal, characteristic, complemented
16#10623166—21no—
17#10623149—21no—
18C2×C11×SD32C2211yescharacteristic
19C22×C11×C16C2211yescharacteristic
20C11×#467C2211yescharacteristic
21C11×#466C2211yescharacteristic
22#10622801C2211yescharacteristic
23Q16×Dic11C2211yescharacteristic
24#10622770C2211yescharacteristic
25D8×Dic11C2211yescharacteristic
26C8×C22⋊D11C2211yescharacteristic
27C2×#66882C2211yescharacteristic
28C2×#66882C2211yescharacteristic
29#10622657—21no—
30#10622647—21no—
31C2×#66862C2211yescharacteristic
32#10622493C2211yescharacteristic
33D11×#107C2211yescharacteristic
34#10622491C2211yescharacteristic
35#10622487C2211yescharacteristic
36#10622422—21no—
37#10622407—21no—
38#10622397—21no—
39#10622379—21no—
40C11×#367C2211yescharacteristic
41C11×#358C2211yescharacteristic
42C11×#357C2211yescharacteristic
43#10622202C2211yescharacteristic
44#10622202C2211yescharacteristic
45#10622200C2211yescharacteristic
46#10622200C2211yescharacteristic
47C22⋊(C11⋊C16)C2211yescharacteristic
48(C2×D11)⋊C16C2211yescharacteristic
49#10622142C2211yescharacteristic
50#10622142C2211yescharacteristic
51#10622142C2211yescharacteristic
52#10622142C2211yescharacteristic
53#10622140C2211yescharacteristic
54Dic11⋊C16C2211yescharacteristic
55#10622128C2211yescharacteristic
56#10622128C2211yescharacteristic
57#10622127C2211yescharacteristic
58#10622127C2211yescharacteristic
59C2×C11×Q16C2311yescharacteristic
60C2×C11×D8C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C11×C22⋊Q8—21no—
63C11×#121—21no—
64#66999—21no—
65Q8×Dic11—21no—
66#66992—41no—
67#66991—21no—
68D4×Dic11—21no—
69D4×Dic11—41no—
70C4×C22⋊D11D411yescharacteristic
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11—21no—
73C2×C8×D11C2311yescharacteristic
74#66950—41no—
75#66945—21no—
76C4⋊C4×D11—21no—
77#66943—21no—
78#66942—41no—
79#66941—21no—
80#66939—41no—
81(C22⋊D11)⋊C4—41no—
82#66932—41no—
83#66931—41no—
84C11×SD32—22no—
85C2×C11×C16—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#66882—21no—
100#66882C2311yescharacteristic
101#66882C2311yescharacteristic
102#66882C2311yescharacteristic
103#66882C2311yescharacteristic
104Dic11⋊C8D411yescharacteristic
105C8×Dic11C2311yescharacteristic
106C2×C11⋊C16C2311yescharacteristic
107C2×C11⋊C16C2311yescharacteristic
108#66872—21no—
109#66872—21no—
110#66871—21no—
111#66871—21no—
112#66862—22no—
113#33913—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—
122C22×Dic11—41no—
123C2×C4×D11—41no—
124C2×C4×D11C2×D411yescharacteristic
125C2×Dic22—41no—
126C11×Q16—21no—
127C11×Q16—21no—
128C11×D8—21no—
129C11×D8—21no—
130C2×C8×C11—21no—
131C2×C8×C11—21no—
132C2×C8×C11C2×D411yescharacteristic
133C2×C8×C11C2411yescharacteristic
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—41no—
137C11×C22⋊C4—41no—
138C11×C22⋊C4—41no—
139C22⋊Dic11—41no—
140C22⋊Dic11—41no—
141C22⋊Dic11D811yescharacteristic
142(C2×D11)⋊C4—41no—
143(C2×D11)⋊C4—41no—
144(C2×D11)⋊C4D811yescharacteristic
145C4⋊Dic11—21no—
146C4⋊Dic11—21no—
147C4⋊Dic11—21no—
148C4⋊Dic11—21no—
149C4⋊Dic11—41no—
150C4⋊Dic11—41no—
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×Dic11C2×D411yescharacteristic
161C2×C11⋊C8C2×D411yescharacteristic
162C2×C11⋊C8C2×D411yescharacteristic
163C8×D11—21no—
164C8×D11—21no—
165C11×C16—21no—
166C11×C16#4112yes—
167C11⋊C16—21no—
168C11⋊C16—21no—
169#3339—111no—
170#3338—111no—
171#2255—111no—
172#2237—111no—
173#2236—111no—
174#2233—111no—
175#2232—111no—
176#2229—111no—
177#2224—111no—
178#2220—111no—
179#2217D1111yescharacteristic, complemented
180#2175—111no—
181#2168—111no—
182#2159—111no—
183C2×#366—111no—
184C23×C11—41no—
185C23×C11C2×D811yescharacteristic
186C22×D11C2×D811yescharacteristic
187Q8×C11—41no—
188Q8×C11—41no—
189D4×C11—41no—
190D4×C11—41no—
191D4×C11—82no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11C2×D811yescharacteristic
198C2×C4×C11C22×D411yescharacteristic
199C22⋊D11—22no—
200C22⋊D11—161no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—161no—
206C2×Dic11—161no—
207C2×Dic11—161no—
208C2×Dic11C2×D811yescharacteristic
209C2×Dic11C2×D811yescharacteristic
210C2×Dic11C2×D811yescharacteristic
211C4×D11—21no—
212C4×D11—21no—
213C4×D11—161no—
214Dic22—161no—
215C8×C11—21no—
216C8×C11C2×#4111yescharacteristic
217C8×C112−1+411yescharacteristic
218C11⋊C8—21no—
219C11⋊C8—21no—
220#554—221no—
221#553—221no—
222C2×SD32C2×D1111yescharacteristic
223C2×M32—111no—
224C22×C16C2×D1111yescharacteristic
225#500—111no—
226#499—111no—
227#484—221no—
228#484—221no—
229#482—221no—
230#481—221no—
231#478—221no—
232#477—221no—
233#467—111no—
234#467C2×D1111yescharacteristic
235#466—111no—
236#466C2×D1111yescharacteristic
237C4×Q16—111no—
238C4×D8—111no—
239C8×D4—111no—
240#427—111no—
241C2×#107—111no—
242C2×#107—111no—
243C2×#107—111no—
244#367—111no—
245#367—111no—
246#367C2×D1111yescharacteristic
247#366—111no—
248#366—111no—
249#366—111no—
250#366—111no—
251#366—111no—
252#366—111no—
253C4⋊C16—111no—
254#358—111no—
255#358—111no—
256#358C2×D1111yescharacteristic
257#357—111no—
258#357—111no—
259#357C2×D1111yescharacteristic
260C22⋊C16—111no—
261C22⋊C16—111no—
262#346—111no—
263C22×C11—21no—
264C22×C11—21no—
265C22×C11—81no—
266C22×C11—81no—
267C22×C11—81no—
268C22×C11#51012yes—
269C22×C11C22×D811yescharacteristic
270C2×D11—21no—
271C2×D11—21no—
272C2×D11—21no—
273C4×C11—21no—
274C4×C11—81no—
275C4×C11—81no—
276C4×C11—81no—
277C4×C11#54711yescharacteristic
278C4×C11#57811yescharacteristic
279Dic11—21no—
280Dic11—21no—
281Dic11—21no—
282Dic11—81no—
283Dic11—81no—
284Dic11—81no—
285Dic11—81no—
286C2×Q16C22×D1111yescharacteristic
287C2×D8C22×D1111yescharacteristic
288C22×C8—111no—
289C22×C8C22×D1111yescharacteristic
290C4⋊Q8—221no—
291#126—441no—
292#125—221no—
293#125—441no—
294#123—441no—
295C22⋊Q8—21no—
296C22⋊Q8—221no—
297C22⋊Q8—441no—
298C22⋊Q8—441no—
299#121—21no—
300#121—221no—
301#121—441no—
302C4×Q8—221no—
303C4×D4—111no—
304C4×D4—221no—
305C4×D4—441no—
306C4×D4—441no—
307#117—221no—
308C2×C4⋊C4—221no—
309C2×C4⋊C4—221no—
310C2×C4⋊C4—221no—
311SD32—22no—
312M32—222no—
313C2×C16—22no—
314C2×C16—111no—
315C2×C16—111no—
316C2×C16C22×D1111yescharacteristic
317C2×C16C22×D1111yescharacteristic
318#107—111no—
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#106—221no—
329#106—221no—
330C4⋊C8—111no—
331#103—21no—
332#103—221no—
333#103—221no—
334#102—21no—
335#102—221no—
336#102—221no—
337C22⋊C8—111no—
338C22⋊C8—111no—
339C4×C8—111no—
340C2×C11—22no—
341C2×C11—161no—
342C2×C11#333411yescharacteristic
343C2×C11C2×#51011yescharacteristic
344C2×C11#341511yescharacteristic
345D11—41no—
346C2×Q8—21no—
347C2×Q8—441no—
348C2×D4—21no—
349C2×D4—41no—
350C2×D4—111no—
351C2×D4—441no—
352C22×C4—111no—
353C22×C4—441no—
354C22×C4—441no—
355C22×C4—441no—
356C22×C4—441no—
357C22×C4D4×D1111yescharacteristic
358Q16—21no—
359Q16—21no—
360D8—21no—
361D8—21no—
362C2×C8—21no—
363C2×C8—21no—
364C2×C8—111no—
365C2×C8—111no—
366C2×C8—221no—
367C2×C8—221no—
368C2×C8D4×D1111yescharacteristic
369C2×C8C23×D1111yescharacteristic
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—41no—
373C4⋊C4—111no—
374C4⋊C4—221no—
375C4⋊C4—221no—
376C4⋊C4—221no—
377C4⋊C4—221no—
378C4⋊C4—441no—
379C4⋊C4—441no—
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—
394C42—111no—
395C42—441no—
396C42—441no—
397C16—21no—
398C16—221no—
399C16—221no—
400C16#434112yes—
401C11#3391311yescharacteristic, complemented, Sylow
402C23—41no—
403C23—111no—
404C23D8×D1111yescharacteristic
405Q8—41no—
406Q8—41no—
407Q8—1761no—
408D4—41no—
409D4—41no—
410D4—82no—
411D4—222no—
412D4—1761no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—111no—
419C2×C4—111no—
420C2×C4—111no—
421C2×C4—221no—
422C2×C4—221no—
423C2×C4—441no—
424C2×C4—441no—
425C2×C4—441no—
426C2×C4—441no—
427C2×C4—1761no—
428C2×C4—1761no—
429C2×C4—1761no—
430C2×C4—1761no—
431C2×C4D8×D1111yescharacteristic
432C2×C4C2×D4×D1111yescharacteristic
433C8—21no—
434C8—221no—
435C8—221no—
436C8C2×#434111yescharacteristic
437C8#6704311yescharacteristic
438C22—21no—
439C22—21no—
440C22—81no—
441C22—81no—
442C22—81no—
443C22—221no—
444C22—221no—
445C22—221no—
446C22#1062252812yes—
447C22C2×D8×D1111yescharacteristic
448C4—21no—
449C4—81no—
450C4—81no—
451C4—81no—
452C4—221no—
453C4—221no—
454C4—221no—
455C4—881no—
456C4—881no—
457C4—881no—
458C4—881no—
459C4#1062314211yescharacteristic
460C4#1062330211yescharacteristic
461C2—22no—
462C2—161no—
463C2—441no—
464C2#1308096011yescharacteristic
465C2C2×#1062252811yescharacteristic
466C2#1308175411yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2217C2
socleC22×C11C22×D8
prime radical#13081021C2
hypercenter#2217D11
hypocenterC11#33913
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2217

Complements

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

NH ≅ G/Ntype
2. #13081005C2semidirect
3. #13070901C2semidirect
4. #13070823C2semidirect
5. #13070816C2semidirect
6. #13070799C2semidirect
7. #13070795C2semidirect
8. #13070782C2semidirect
9. #13070751C2semidirect
10. #13070726C2semidirect
11. #13070481C2semidirect
12. #13070441C2semidirect
13. #13070403C2semidirect
14. C2×#10622142C2semidirect
15. C11×#2217C2semidirect
179. #2217D11semidirect
401. C11#33913semidirect

Maximal subgroups

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

subgroupindex
#130810212
#130810052
#130709012
#130708232
#130708162
#130707992
#130707952
#130707822
#130707512
#130707262
#130704812
#130704412
#130704032
C2×#106221422
C11×#22172
#3391311