Finite Group Databasebeta

← #14908977

Subgroups — #14908977

Order 2816.

546 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079248C211yesmaximal, characteristic, complemented
2#13077490C211yesmaximal, characteristic, complemented
3#13070813C211yesmaximal, characteristic, complemented
4#13070762C211yesmaximal, characteristic, complemented
5#13070757C211yesmaximal, characteristic, complemented
6#13070677C211yesmaximal, characteristic, complemented
7#13070670C211yesmaximal, characteristic, complemented
8#13070558C211yesmaximal, characteristic, complemented
9#13070537C211yesmaximal, characteristic
10#13070489C211yesmaximal, characteristic, complemented
11#13070486C211yesmaximal, characteristic, complemented
12#13070471C211yesmaximal, characteristic, complemented
13#13070467C211yesmaximal, characteristic, complemented
14#13070420C211yesmaximal, characteristic, complemented
15C11×#2233C211yesmaximal, characteristic, complemented
16C2×#66957C2211yescharacteristic
17#10623134—21no—
18#10623035—21no—
19C11×#466C2211yescharacteristic
20C2×C11×#107C2211yescharacteristic
21#10622768C2211yescharacteristic
22D8×Dic11C2211yescharacteristic
23C2×#66891C2211yescharacteristic
24C2×#66890C2211yescharacteristic
25#10622729C2211yescharacteristic
26#10622714C2211yescharacteristic
27#10622655—21no—
28#10622579—21no—
29C2×Dic88C2211yescharacteristic
30C2×#66864C2211yescharacteristic
31#10622502—21no—
32#10622502—21no—
33#10622487C2211yescharacteristic
34#10622486C2211yescharacteristic
35#10622486C2211yescharacteristic
36#10622486C2211yescharacteristic
37#10622485C2211yescharacteristic
38#10622485C2211yescharacteristic
39#10622378—21no—
40#10622370—21no—
41C11×#367C2211yescharacteristic
42C11×#367C2211yescharacteristic
43C11×#357C2211yescharacteristic
44C11×#357C2211yescharacteristic
45C11×C22⋊C16C2211yescharacteristic
46C22⋊(C11⋊C16)C2211yescharacteristic
47#10622147C2211yescharacteristic
48#10622141C2211yescharacteristic
49#10622140C2211yescharacteristic
50Dic11⋊C16C2211yescharacteristic
51Dic11⋊C16C2211yescharacteristic
52C16×Dic11C2211yescharacteristic
53#10622130C2211yescharacteristic
54#10622130C2211yescharacteristic
55#10622130C2211yescharacteristic
56#10622129C2211yescharacteristic
57#10622128C2211yescharacteristic
58#10622128C2211yescharacteristic
59C2×#4339—21no—
60C2×C11×D8C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C11×#121—21no—
63C2×C11×C4⋊C4—21no—
64#66989—21no—
65#66989—41no—
66#66988—41no—
67D4×Dic11—21no—
68C2×#4324—21no—
69C4×C22⋊D11—41no—
70C4×C22⋊D11—41no—
71#66979D411yescharacteristic
72#66977—21no—
73C2×#4318D411yescharacteristic
74C2×Dic44C2311yescharacteristic
75C2×Dic44C2311yescharacteristic
76#66957—22no—
77#66957—22no—
78C2×D88C2311yescharacteristic
79C2×#4314—21no—
80#66946—21no—
81#66946—21no—
82#66945—41no—
83C4⋊C4×D11—41no—
84#66941—21no—
85#66940—21no—
86#66940—21no—
87#66940—21no—
88#66932—41no—
89#66931—41no—
90C2×C11×C16C2311yescharacteristic
91C2×C11×C16C2311yescharacteristic
92C11×#107—21no—
93C11×#107C2311yescharacteristic
94C11×#107C2311yescharacteristic
95C11×#107C2311yescharacteristic
96C11×#102—21no—
97#66896—21no—
98#66891—22no—
99#66890—22no—
100#66882C2311yescharacteristic
101#66880—21no—
102#66879D411yescharacteristic
103#66879D411yescharacteristic
104C8×Dic11C2311yescharacteristic
105C8×Dic11C2311yescharacteristic
106C2×C11⋊C16C2311yescharacteristic
107C2×C11⋊C16C2311yescharacteristic
108#66874—21no—
109#66874—21no—
110#66874—21no—
111#66873—21no—
112#66873—21no—
113#66871—21no—
114Dic88—22no—
115#66864—22no—
116#33685—111nomaximal, Sylow
117C2×D4×C11—21no—
118C2×D4×C11—41no—
119C22×C4×C11—41no—
120C22×C4×C11C2×D411yescharacteristic
121C2×C22⋊D11—41no—
122C22×Dic11—41no—
123#4339—24no—
124#4339—42no—
125C2×D44—21no—
126C2×C4×D11—41no—
127C2×C4×D11—41no—
128C2×C4×D11—41no—
129C2×Dic22—21no—
130C2×Dic22—21no—
131C2×Dic22—41no—
132C11×D8—21no—
133C11×D8—21no—
134C2×C8×C11—21no—
135C2×C8×C11—21no—
136C2×C8×C11C2×D411yescharacteristic
137C2×C8×C11C2411yescharacteristic
138C11×C4⋊C4—21no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—41no—
142C11×C22⋊C4—41no—
143C22⋊Dic11—41no—
144C22⋊Dic11—41no—
145C22⋊Dic11—41no—
146C22⋊Dic11—41no—
147C22⋊Dic11D811yescharacteristic
148C22⋊Dic11D811yescharacteristic
149#4324—42no—
150(C2×D11)⋊C4—41no—
151(C2×D11)⋊C4—41no—
152C4⋊Dic11—21no—
153C4⋊Dic11D811yescharacteristic
154C4⋊Dic11D811yescharacteristic
155Dic11⋊C4—41no—
156Dic11⋊C4—41no—
157Dic11⋊C4—41no—
158Dic11⋊C4—41no—
159Dic11⋊C4—41no—
160C4×Dic11—41no—
161C4×Dic11—41no—
162C4×Dic11—41no—
163C4×Dic11C2×D411yescharacteristic
164C4×Dic11C2×D411yescharacteristic
165#4318—41no—
166C2×C11⋊C8C2×D411yescharacteristic
167C2×C11⋊C8C2×D411yescharacteristic
168Dic44—21no—
169Dic44—21no—
170Dic44—21no—
171Dic44#4112yes—
172D88—21no—
173D88#4112yes—
174#4314—24no—
175C11×C16—21no—
176C11×C16—21no—
177C11⋊C16—21no—
178C11⋊C16—21no—
179#3175—111no—
180#2951—111no—
181#2235—111no—
182#2233D1111yescharacteristic, complemented
183#2226—111no—
184#2225—111no—
185#2211—111no—
186#2210—111no—
187#2189—111no—
188#2186—111no—
189#2177—111no—
190#2176—111no—
191C4×SD32—111no—
192C4×SD32—111no—
193#2164—111no—
194C23×C11—41no—
195C23×C11C2×D811yescharacteristic
196C22×D11—41no—
197D4×C11—41no—
198D4×C11—41no—
199D4×C11—161no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—161no—
206C2×C4×C11C2×D811yescharacteristic
207C2×C4×C11C22×D411yescharacteristic
208C22⋊D11—44no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—161no—
213C2×Dic11C2×D811yescharacteristic
214C2×Dic11C2×D811yescharacteristic
215C2×Dic11C2×D811yescharacteristic
216C2×Dic11C2×D811yescharacteristic
217D44—22no—
218D44—41no—
219C4×D11—44no—
220C4×D11—161no—
221C4×D11—161no—
222Dic22—22no—
223Dic22—41no—
224Dic22—41no—
225Dic22—41no—
226Dic22—161no—
227C8×C11—21no—
228C8×C11C2×#4111yescharacteristic
229C8×C11C2×#4111yescharacteristic
230C11⋊C8—21no—
231C11⋊C8—21no—
232C2×#135—111no—
233#542—221no—
234#520—221no—
235C2×Q32—111no—
236C2×SD32—111no—
237C2×SD32—111no—
238C2×D16—111no—
239#500—111no—
240#495—111no—
241#489—221no—
242#468—221no—
243#467—111no—
244#466C2×D1111yescharacteristic
245#440—221no—
246#440—221no—
247#440—221no—
248C4×Q16—111no—
249C4×Q16—111no—
250C4×Q16—111no—
251C4×D8—111no—
252C4×D8—111no—
253C4×D8—111no—
254C2×#107C2×D1111yescharacteristic
255#417—221no—
256#405—111no—
257#367—111no—
258#367—111no—
259#367C2×D1111yescharacteristic
260#367C2×D1111yescharacteristic
261C4⋊C16—111no—
262C4⋊C16—111no—
263#358—111no—
264#358—111no—
265#358—111no—
266#358—111no—
267#357—111no—
268#357—111no—
269#357C2×D1111yescharacteristic
270#357C2×D1111yescharacteristic
271C22⋊C16—111no—
272C22⋊C16C2×D1111yescharacteristic
273#346—111no—
274C4×C16—111no—
275C22×C11—21no—
276C22×C11—21no—
277C22×C11—21no—
278C22×C11—81no—
279C22×C11—81no—
280C22×C11—81no—
281C22×C11C22×D811yescharacteristic
282C2×D11—42no—
283C2×D11—81no—
284C2×D11—81no—
285C4×C11—21no—
286C4×C11—81no—
287C4×C11—81no—
288C4×C11—81no—
289C4×C11#52511yescharacteristic
290C4×C11#57511yescharacteristic
291Dic11—21no—
292Dic11—21no—
293Dic11—21no—
294Dic11—21no—
295Dic11—42no—
296Dic11—81no—
297Dic11—81no—
298C2×#41—221no—
299#135—222no—
300#135—222no—
301C2×Q16—111no—
302C2×Q16—111no—
303C2×SD16—221no—
304C2×SD16—221no—
305C2×D8—111no—
306C2×D8C22×D1111yescharacteristic
307C2×M16—111no—
308C22×C8C22×D1111yescharacteristic
309C4⋊Q8—221no—
310#126—441no—
311#124—221no—
312#124—441no—
313#123—441no—
314C22⋊Q8—221no—
315C22⋊Q8—441no—
316#121—21no—
317C4×Q8—221no—
318C4×Q8—221no—
319C4×Q8—221no—
320C4×D4—221no—
321C4×D4—221no—
322C4×D4—221no—
323C4×D4—441no—
324C4×D4—441no—
325#117—111no—
326#117—441no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—441no—
329Q32—222no—
330SD32—222no—
331SD32—222no—
332D16—222no—
333C2×C16—111no—
334C2×C16—111no—
335C2×C16C22×D1111yescharacteristic
336C2×C16C22×D1111yescharacteristic
337#107—21no—
338#107—111no—
339#107—221no—
340#107C22×D1111yescharacteristic
341#107C22×D1111yescharacteristic
342#107C22×D1111yescharacteristic
343#103—221no—
344#103—221no—
345#103—221no—
346#103—221no—
347#102—21no—
348#102—221no—
349#102—221no—
350#102—221no—
351#97—111no—
352#97—111no—
353C4×C8—111no—
354C4×C8—111no—
355C2×C11—41no—
356C2×C11—161no—
357C2×C11#310011yescharacteristic
358C2×C11#341611yescharacteristic
359C2×C11#341611yescharacteristic
360D11—82no—
361#41—224no—
362#41—442no—
363C2×Q8—221no—
364C2×Q8—221no—
365C2×Q8—441no—
366C2×D4—21no—
367C2×D4—41no—
368C2×D4—221no—
369C2×D4—441no—
370C22×C4—41no—
371C22×C4—441no—
372C22×C4—441no—
373C22×C4—441no—
374C22×C4—441no—
375C22×C4D4×D1111yescharacteristic
376Q16—112no—
377Q16—221no—
378Q16—221no—
379Q16—221no—
380SD16—224no—
381SD16—442no—
382D8—21no—
383D8—21no—
384D8—112no—
385D8—221no—
386M16—441no—
387C2×C8—21no—
388C2×C8—21no—
389C2×C8—111no—
390C2×C8—111no—
391C2×C8D4×D1111yescharacteristic
392C2×C8C23×D1111yescharacteristic
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—41no—
397C4⋊C4—111no—
398C4⋊C4—111no—
399C4⋊C4—221no—
400C4⋊C4—441no—
401C4⋊C4—441no—
402C4⋊C4—441no—
403C4⋊C4—441no—
404C4⋊C4—441no—
405C22⋊C4—41no—
406C22⋊C4—111no—
407C22⋊C4—111no—
408C22⋊C4—441no—
409C22⋊C4—441no—
410C22⋊C4—441no—
411C22⋊C4—441no—
412C22⋊C4—441no—
413C22⋊C4—441no—
414C42—111no—
415C42—111no—
416C42—441no—
417C42—441no—
418C42—441no—
419C16—21no—
420C16—21no—
421C16—221no—
422C16—221no—
423C11#3368511yescharacteristic, complemented, Sylow
424C23—41no—
425C23—441no—
426C23D8×D1111yescharacteristic
427Q8—222no—
428Q8—441no—
429Q8—441no—
430Q8—441no—
431Q8—1761no—
432D4—41no—
433D4—41no—
434D4—161no—
435D4—222no—
436D4—444no—
437D4—441no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—111no—
444C2×C4—111no—
445C2×C4—111no—
446C2×C4—111no—
447C2×C4—161no—
448C2×C4—444no—
449C2×C4—441no—
450C2×C4—441no—
451C2×C4—441no—
452C2×C4—1761no—
453C2×C4—1761no—
454C2×C4—1761no—
455C2×C4D8×D1111yescharacteristic
456C2×C4C2×D4×D1111yescharacteristic
457C8—21no—
458C8—221no—
459C8—221no—
460C8#41×D1111yescharacteristic
461C8#41×D1111yescharacteristic
462C22—21no—
463C22—21no—
464C22—21no—
465C22—81no—
466C22—81no—
467C22—81no—
468C22—442no—
469C22—881no—
470C22—881no—
471C22C2×D8×D1111yescharacteristic
472C4—21no—
473C4—81no—
474C4—81no—
475C4—81no—
476C4—221no—
477C4—221no—
478C4—221no—
479C4—221no—
480C4—442no—
481C4—881no—
482C4—881no—
483C4#1062318711yescharacteristic
484C4#1062330811yescharacteristic
485C2—41no—
486C2—161no—
487C2—882no—
488C2#1307861311yescharacteristic
489C2#1308175811yescharacteristic
490C2#1308176211yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2233C2
socleC22×C11C22×D8
prime radical#13070537C2
hypercenter#2233D11
hypocenterC11#33685
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2233

Complements

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

NH ≅ G/Ntype
1. #13079248C2semidirect
2. #13077490C2semidirect
3. #13070813C2semidirect
4. #13070762C2semidirect
5. #13070757C2semidirect
6. #13070677C2semidirect
7. #13070670C2semidirect
8. #13070558C2semidirect
10. #13070489C2semidirect
11. #13070486C2semidirect
12. #13070471C2semidirect
13. #13070467C2semidirect
14. #13070420C2semidirect
15. C11×#2233C2semidirect
182. #2233D11semidirect
423. C11#33685semidirect

Maximal subgroups

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

subgroupindex
#130792482
#130774902
#130708132
#130707622
#130707572
#130706772
#130706702
#130705582
#130705372
#130704892
#130704862
#130704712
#130704672
#130704202
C11×#22332
#3368511