Finite Group Databasebeta

← #14908968

Subgroups — #14908968

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#13077493C211yesmaximal, characteristic, complemented
2#13070811C211yesmaximal, characteristic, complemented
3#13070799C211yesmaximal, characteristic, complemented
4#13070760C211yesmaximal, characteristic, complemented
5#13070755C211yesmaximal, characteristic, complemented
6#13070675C211yesmaximal, characteristic, complemented
7#13070668C211yesmaximal, characteristic, complemented
8#13070554C211yesmaximal, characteristic, complemented
9#13070537C211yesmaximal, characteristic
10#13070490C211yesmaximal, characteristic, complemented
11#13070485C211yesmaximal, characteristic, complemented
12C4×#66892C211yesmaximal, characteristic, complemented
13C4×#66891C211yesmaximal, characteristic, complemented
14#13070423C211yesmaximal, characteristic, complemented
15C11×#3175C211yesmaximal, characteristic, complemented
16C11×#542—21no—
17C2×#66957C2211yescharacteristic
18#10623054—21no—
19C11×#500C2211yescharacteristic
20C11×#495C2211yescharacteristic
21C11×#489—21no—
22C11×#468—21no—
23C11×#467C2211yescharacteristic
24C11×#466C2211yescharacteristic
25C11×#440—21no—
26C4×C11×Q16C2211yescharacteristic
27C4×C11×D8C2211yescharacteristic
28C11×#405C2211yescharacteristic
29C2×#66893C2211yescharacteristic
30C2×#66892C2211yescharacteristic
31C2×#66891C2211yescharacteristic
32C2×#66890C2211yescharacteristic
33#10622746—21no—
34C2×#66882C2211yescharacteristic
35#10622323—21no—
36#10622323—21no—
37C4×Dic44C2211yescharacteristic
38C4×Dic44C2211yescharacteristic
39C4×D88C2211yescharacteristic
40C4×D88C2211yescharacteristic
41#10622202C2211yescharacteristic
42#10622202C2211yescharacteristic
43#10622200C2211yescharacteristic
44#10622200C2211yescharacteristic
45C22⋊(C11⋊C16)C2211yescharacteristic
46C22⋊(C11⋊C16)C2211yescharacteristic
47#10622130C2211yescharacteristic
48#10622130C2211yescharacteristic
49#10622129C2211yescharacteristic
50#10622129C2211yescharacteristic
51#10622128C2211yescharacteristic
52#10622128C2211yescharacteristic
53#10622128C2211yescharacteristic
54#10622128C2211yescharacteristic
55C4⋊(C11⋊C16)C2211yescharacteristic
56C4⋊(C11⋊C16)C2211yescharacteristic
57#10622099C2211yescharacteristic
58C4×C11⋊C16C2211yescharacteristic
59C2×#4339—21no—
60C2×C11×Q16C2311yescharacteristic
61C2×C11×SD16—21no—
62C2×C11×D8C2311yescharacteristic
63C2×C11×M16D411yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C11×C4⋊Q8—21no—
66C11×#126—41no—
67C11×#124—21no—
68C11×#124—41no—
69C11×#123—41no—
70C11×C22⋊Q8—21no—
71C11×C22⋊Q8—41no—
72C11×#121—21no—
73C4×Q8×C11—21no—
74C4×D4×C11—21no—
75C11×#117D411yescharacteristic
76C2×C4⋊Dic11—21no—
77C2×Dic44C2311yescharacteristic
78#66957—22no—
79#66957—22no—
80C2×D88C2311yescharacteristic
81C2×#4314—21no—
82#66945—41no—
83C4⋊C4×D11—41no—
84(C22⋊D11)⋊C4—41no—
85(C22⋊D11)⋊C4—41no—
86C4×D44—21no—
87C4×D44—21no—
88C4×Dic22—21no—
89C4×Dic22—21no—
90C11×#107—21no—
91C11×#107C2311yescharacteristic
92C11×#107C2311yescharacteristic
93C11×#103—21no—
94C11×#103—21no—
95C11×#102—21no—
96C11×#102—21no—
97C11×#97D411yescharacteristic
98C11×#97D411yescharacteristic
99C4×C8×C11C2311yescharacteristic
100C4×C8×C11C2311yescharacteristic
101#66893—22no—
102#66892—22no—
103#66891—22no—
104#66890—22no—
105#66885—21no—
106#66885—21no—
107#66882—21no—
108#66882C2311yescharacteristic
109#66882C2311yescharacteristic
110#66880—21no—
111#66880—21no—
112C2×C11⋊C16C2311yescharacteristic
113C2×C11⋊C16C2311yescharacteristic
114C2×C11⋊C16C2311yescharacteristic
115C2×C11⋊C16C2311yescharacteristic
116#33685—111nomaximal, Sylow
117C2×Q8×C11—21no—
118C2×Q8×C11—41no—
119C2×D4×C11—21no—
120C2×D4×C11—41no—
121C22×C4×C11—41no—
122C22×C4×C11C2×D411yescharacteristic
123C2×C22⋊D11—41no—
124C22×Dic11—41no—
125#4339—24no—
126#4339—42no—
127C2×D44—21no—
128C2×C4×D11—41no—
129C2×C4×D11—41no—
130C2×C4×D11—41no—
131C2×Dic22—21no—
132C11×Q16—21no—
133C11×Q16—21no—
134C11×SD16—42no—
135C11×D8—21no—
136C11×D8—21no—
137C11×M16—41no—
138C2×C8×C11—21no—
139C2×C8×C11—21no—
140C2×C8×C11C2×D411yescharacteristic
141C2×C8×C11C2×D411yescharacteristic
142C2×C8×C11C2×D411yescharacteristic
143C2×C8×C11C2411yescharacteristic
144C11×C4⋊C4—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—41no—
147C11×C4⋊C4—41no—
148C11×C4⋊C4—41no—
149C11×C4⋊C4D811yescharacteristic
150C11×C4⋊C4D811yescharacteristic
151C11×C22⋊C4—41no—
152C11×C22⋊C4—41no—
153C11×C22⋊C4—41no—
154C11×C22⋊C4—41no—
155C11×C22⋊C4—41no—
156C11×C22⋊C4D811yescharacteristic
157C11×C22⋊C4D811yescharacteristic
158C42×C11—41no—
159C42×C11C2×D411yescharacteristic
160C42×C11C2×D411yescharacteristic
161(C2×D11)⋊C4—41no—
162(C2×D11)⋊C4—41no—
163C4⋊Dic11—21no—
164C4⋊Dic11—21no—
165C4⋊Dic11—41no—
166Dic11⋊C4—41no—
167Dic11⋊C4—41no—
168C4×Dic11—41no—
169C4×Dic11—41no—
170Dic44—21no—
171Dic44#4112yes—
172D88—21no—
173D88#4112yes—
174#4314—24no—
175C11⋊C16—21no—
176C11⋊C16—21no—
177C11⋊C16—21no—
178C11⋊C16—21no—
179#3175D1111yescharacteristic, complemented
180#2951—111no—
181#2235—111no—
182#2233—111no—
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—
197Q8×C11—41no—
198Q8×C11—41no—
199Q8×C11—161no—
200D4×C11—41no—
201D4×C11—41no—
202D4×C11—161no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—161no—
209C2×C4×C11C2×D811yescharacteristic
210C2×C4×C11C2×D811yescharacteristic
211C2×C4×C11C2×D811yescharacteristic
212C2×C4×C11C2×D811yescharacteristic
213C2×C4×C11C2×D811yescharacteristic
214C2×C4×C11C22×D411yescharacteristic
215C22⋊D11—44no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219C2×Dic11—161no—
220D44—22no—
221D44—41no—
222C4×D11—44no—
223C4×D11—161no—
224C4×D11—161no—
225Dic22—22no—
226Dic22—41no—
227C8×C11—21no—
228C8×C11—21no—
229C8×C11—21no—
230C8×C11C2×#4111yescharacteristic
231C8×C11C2×#4111yescharacteristic
232C2×#135—111no—
233#542—21no—
234#520—221no—
235C2×Q32—111no—
236C2×SD32—111no—
237C2×SD32—111no—
238C2×D16—111no—
239#500C2×D1111yescharacteristic
240#495C2×D1111yescharacteristic
241#489—21no—
242#468—21no—
243#467C2×D1111yescharacteristic
244#466C2×D1111yescharacteristic
245#440—21no—
246#440—221no—
247#440—221no—
248C4×Q16—111no—
249C4×Q16—111no—
250C4×Q16C2×D1111yescharacteristic
251C4×D8—111no—
252C4×D8—111no—
253C4×D8C2×D1111yescharacteristic
254C2×#107—111no—
255#417—221no—
256#405C2×D1111yescharacteristic
257#367—111no—
258#367—111no—
259#367—111no—
260#367—111no—
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#357—111no—
270#357—111no—
271C22⋊C16—111no—
272C22⋊C16—111no—
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—21no—
287C4×C11—21no—
288C4×C11—21no—
289C4×C11—21no—
290C4×C11—81no—
291C4×C11—81no—
292C4×C11—81no—
293C4×C11#52511yescharacteristic
294C4×C11#57511yescharacteristic
295Dic11—42no—
296Dic11—81no—
297Dic11—81no—
298C2×#41—221no—
299#135—222no—
300#135—222no—
301C2×Q16—111no—
302C2×Q16C22×D1111yescharacteristic
303C2×SD16—21no—
304C2×SD16—221no—
305C2×D8—111no—
306C2×D8C22×D1111yescharacteristic
307C2×M16C22⋊D1111yescharacteristic
308C22×C8C22×D1111yescharacteristic
309C4⋊Q8—21no—
310#126—41no—
311#124—21no—
312#124—41no—
313#123—41no—
314C22⋊Q8—21no—
315C22⋊Q8—41no—
316#121—21no—
317C4×Q8—21no—
318C4×Q8—221no—
319C4×Q8—221no—
320C4×D4—21no—
321C4×D4—221no—
322C4×D4—221no—
323C4×D4—441no—
324C4×D4—441no—
325#117—441no—
326#117C22⋊D1111yescharacteristic
327C2×C4⋊C4—221no—
328C2×C4⋊C4—441no—
329Q32—222no—
330SD32—222no—
331SD32—222no—
332D16—222no—
333C2×C16—111no—
334C2×C16—111no—
335C2×C16—111no—
336C2×C16—111no—
337#107—21no—
338#107—111no—
339#107—111no—
340#107—221no—
341#107C22×D1111yescharacteristic
342#107C22×D1111yescharacteristic
343#103—21no—
344#103—21no—
345#103—221no—
346#103—221no—
347#102—21no—
348#102—21no—
349#102—221no—
350#102—221no—
351#97C22⋊D1111yescharacteristic
352#97C22⋊D1111yescharacteristic
353C4×C8C22×D1111yescharacteristic
354C4×C8C22×D1111yescharacteristic
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—21no—
364C2×Q8—41no—
365C2×Q8—221no—
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×C4C2×C22⋊D1111yescharacteristic
376Q16—21no—
377Q16—21no—
378Q16—112no—
379Q16—221no—
380SD16—42no—
381SD16—224no—
382D8—21no—
383D8—21no—
384D8—112no—
385D8—221no—
386M16—41no—
387C2×C8—21no—
388C2×C8—21no—
389C2×C8C2×C22⋊D1111yescharacteristic
390C2×C8C2×C22⋊D1111yescharacteristic
391C2×C8C2×C22⋊D1111yescharacteristic
392C2×C8C23×D1111yescharacteristic
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—41no—
396C4⋊C4—41no—
397C4⋊C4—41no—
398C4⋊C4—221no—
399C4⋊C4—221no—
400C4⋊C4—441no—
401C4⋊C4—441no—
402C4⋊C4—441no—
403C4⋊C4#432311yescharacteristic
404C4⋊C4#432311yescharacteristic
405C22⋊C4—41no—
406C22⋊C4—41no—
407C22⋊C4—41no—
408C22⋊C4—41no—
409C22⋊C4—41no—
410C22⋊C4—441no—
411C22⋊C4—441no—
412C22⋊C4#432311yescharacteristic
413C22⋊C4#432311yescharacteristic
414C42—41no—
415C42—441no—
416C42—441no—
417C42C2×C22⋊D1111yescharacteristic
418C42C2×C22⋊D1111yescharacteristic
419C16—221no—
420C16—221no—
421C16—221no—
422C16—221no—
423C11#3368511yescharacteristic, complemented, Sylow
424C23—41no—
425C23—441no—
426C23C2×#432311yescharacteristic
427Q8—41no—
428Q8—41no—
429Q8—161no—
430Q8—222no—
431Q8—441no—
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—161no—
444C2×C4—444no—
445C2×C4—441no—
446C2×C4—441no—
447C2×C4—441no—
448C2×C4—1761no—
449C2×C4—1761no—
450C2×C4—1761no—
451C2×C4C2×#432311yescharacteristic
452C2×C4C2×#432311yescharacteristic
453C2×C4C2×#432311yescharacteristic
454C2×C4C2×#432311yescharacteristic
455C2×C4C2×#432311yescharacteristic
456C2×C4C22×C22⋊D1111yescharacteristic
457C8—21no—
458C8—21no—
459C8—21no—
460C8#41×D1111yescharacteristic
461C8#41×D1111yescharacteristic
462C22—21no—
463C22—21no—
464C22—21no—
465C22—81no—
466C22—81no—
467C22—81no—
468C22—442no—
469C22—881no—
470C22—881no—
471C22C22×#432311yescharacteristic
472C4—21no—
473C4—21no—
474C4—21no—
475C4—21no—
476C4—21no—
477C4—81no—
478C4—81no—
479C4—81no—
480C4—442no—
481C4—881no—
482C4—881no—
483C4#1062335311yescharacteristic
484C4#1062335911yescharacteristic
485C2—41no—
486C2—161no—
487C2—882no—
488C2#1307861211yescharacteristic
489C2#1308176011yescharacteristic
490C2#1308176311yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3175C2
socleC22×C11C22×D8
prime radical#13070537C2
hypercenter#3175D11
hypocenterC11#33685
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #3175

Complements

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

NH ≅ G/Ntype
1. #13077493C2semidirect
2. #13070811C2semidirect
3. #13070799C2semidirect
4. #13070760C2semidirect
5. #13070755C2semidirect
6. #13070675C2semidirect
7. #13070668C2semidirect
8. #13070554C2semidirect
10. #13070490C2semidirect
11. #13070485C2semidirect
12. C4×#66892C2semidirect
13. C4×#66891C2semidirect
14. #13070423C2semidirect
15. C11×#3175C2semidirect
179. #3175D11semidirect
423. C11#33685semidirect

Maximal subgroups

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

subgroupindex
#130774932
#130708112
#130707992
#130707602
#130707552
#130706752
#130706682
#130705542
#130705372
#130704902
#130704852
C4×#668922
C4×#668912
#130704232
C11×#31752
#3368511