Finite Group Databasebeta

← #14908890

Subgroups — #14908890

Order 2816.

558 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077493C211yesmaximal, characteristic, complemented
2#13070799C211yesmaximal, characteristic, complemented
3#13070794C211yesmaximal, characteristic, complemented
4#13070777C211yesmaximal, characteristic, complemented
5#13070770C211yesmaximal, characteristic, complemented
6#13070653C211yesmaximal, characteristic, complemented
7#13070648C211yesmaximal, characteristic, complemented
8#13070537C211yesmaximal, characteristic, complemented
9#13070537C211yesmaximal, characteristic, complemented
10#13070490C211yesmaximal, characteristic, complemented
11#13070480C211yesmaximal, characteristic, complemented
12C4×#66891C211yesmaximal, characteristic, complemented
13C4×#66890C211yesmaximal, characteristic, complemented
14#13070423C211yesmaximal, characteristic, complemented
15C11×#3176C211yesmaximal, characteristic, complemented
16C11×#540—21no—
17C2×#66957C2211yescharacteristic
18#10623054—21no—
19C11×#499C2211yescharacteristic
20C11×#493C2211yescharacteristic
21C11×#490—21no—
22C11×#469—21no—
23C11×#466C2211yescharacteristic
24C11×#466C2211yescharacteristic
25C11×#442—21no—
26C4×C11×D8C2211yescharacteristic
27C4×C11×D8C2211yescharacteristic
28C11×#405C2211yescharacteristic
29C2×#66891C2211yescharacteristic
30C2×#66891C2211yescharacteristic
31C2×#66890C2211yescharacteristic
32C2×#66890C2211yescharacteristic
33#10622746—21no—
34C2×#66882C2211yescharacteristic
35#10622323—21no—
36#10622323—21no—
37C4×Dic44C2211yescharacteristic
38C4×Dic44C2211yescharacteristic
39C4×D88C2211yescharacteristic
40C4×D88C2211yescharacteristic
41#10622200C2211yescharacteristic
42#10622200C2211yescharacteristic
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#10622127C2211yescharacteristic
54#10622127C2211yescharacteristic
55C4⋊(C11⋊C16)C2211yescharacteristic
56C4⋊(C11⋊C16)C2211yescharacteristic
57#10622099C2211yescharacteristic
58C4×C11⋊C16C2211yescharacteristic
59C2×#4339—21no—
60C2×C11×D8—21no—
61C2×C11×D8C2311yescharacteristic
62C2×C11×D8C2311yescharacteristic
63C2×C11×M16D411yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C11×#127—21no—
66C11×#125—21no—
67C11×#123—41no—
68C11×#123—41no—
69C11×#121—21no—
70C11×#121—21no—
71C11×#121—41no—
72C11×#121—41no—
73C4×D4×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×#107C2311yescharacteristic
91C11×#107C2311yescharacteristic
92C11×#106—21no—
93C11×#102—21no—
94C11×#102—21no—
95C11×#102—21no—
96C11×#102—21no—
97C11×#97D411yescharacteristic
98C11×#97D411yescharacteristic
99C4×C8×C11C2311yescharacteristic
100C4×C8×C11C2311yescharacteristic
101#66891—22no—
102#66891—22no—
103#66890—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#33679—111nomaximal, Sylow
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—41no—
120C2×D4×C11—41no—
121C2×D4×C11—41no—
122C2×D4×C11—41no—
123C22×C4×C11—41no—
124C22×C4×C11—41no—
125C22×C4×C11C2×D411yescharacteristic
126C2×C22⋊D11—41no—
127C22×Dic11—41no—
128#4339—24no—
129#4339—42no—
130C2×D44—21no—
131C2×C4×D11—41no—
132C2×C4×D11—41no—
133C2×C4×D11—41no—
134C2×Dic22—21no—
135C11×D8—21no—
136C11×D8—21no—
137C11×D8—21no—
138C11×D8—21no—
139C11×D8—42no—
140C11×M16—41no—
141C2×C8×C11—21no—
142C2×C8×C11—21no—
143C2×C8×C11C2×D411yescharacteristic
144C2×C8×C11C2×D411yescharacteristic
145C2×C8×C11C2×D411yescharacteristic
146C2×C8×C11C2411yescharacteristic
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—41no—
150C11×C4⋊C4—41no—
151C11×C4⋊C4D811yescharacteristic
152C11×C4⋊C4D811yescharacteristic
153C11×C22⋊C4—41no—
154C11×C22⋊C4—41no—
155C11×C22⋊C4—41no—
156C11×C22⋊C4—41no—
157C11×C22⋊C4D811yescharacteristic
158C11×C22⋊C4D811yescharacteristic
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#3176D1111yescharacteristic, complemented
180#2951—111no—
181#2233—111no—
182#2232—111no—
183#2229—111no—
184#2228—111no—
185#2207—111no—
186#2206—111no—
187#2186—111no—
188#2186—111no—
189#2177—111no—
190#2175—111no—
191C4×SD32—111no—
192C4×D16—111no—
193#2164—111no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11C2×D811yescharacteristic
197C22×D11—41no—
198D4×C11—41no—
199D4×C11—41no—
200D4×C11—41no—
201D4×C11—41no—
202D4×C11—161no—
203D4×C11—161no—
204D4×C11—161no—
205D4×C11—161no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—161no—
211C2×C4×C11—161no—
212C2×C4×C11C2×D811yescharacteristic
213C2×C4×C11C2×D811yescharacteristic
214C2×C4×C11C2×D811yescharacteristic
215C2×C4×C11C2×D811yescharacteristic
216C2×C4×C11C2×D811yescharacteristic
217C2×C4×C11C22×D411yescharacteristic
218C22⋊D11—44no—
219C2×Dic11—41no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222C2×Dic11—161no—
223D44—22no—
224D44—41no—
225C4×D11—44no—
226C4×D11—161no—
227C4×D11—161no—
228Dic22—22no—
229Dic22—41no—
230C8×C11—21no—
231C8×C11—21no—
232C8×C11—21no—
233C8×C11C2×#4111yescharacteristic
234C8×C11C2×#4111yescharacteristic
235C2×#135—111no—
236#540—21no—
237#520—221no—
238C2×SD32—111no—
239C2×SD32—111no—
240C2×D16—111no—
241C2×D16—111no—
242#499C2×D1111yescharacteristic
243#493C2×D1111yescharacteristic
244#490—21no—
245#469—21no—
246#466C2×D1111yescharacteristic
247#466C2×D1111yescharacteristic
248#442—21no—
249#440—221no—
250#440—221no—
251C4×Q16—111no—
252C4×Q16—111no—
253C4×D8—111no—
254C4×D8—111no—
255C4×D8C2×D1111yescharacteristic
256C4×D8C2×D1111yescharacteristic
257C2×#107—111no—
258#417—221no—
259#405C2×D1111yescharacteristic
260#367—111no—
261#367—111no—
262#366—111no—
263#366—111no—
264C4⋊C16—111no—
265C4⋊C16—111no—
266#358—111no—
267#358—111no—
268#357—111no—
269#357—111no—
270#357—111no—
271#357—111no—
272#357—111no—
273#357—111no—
274C22⋊C16—111no—
275C22⋊C16—111no—
276#346—111no—
277C4×C16—111no—
278C22×C11—21no—
279C22×C11—21no—
280C22×C11—21no—
281C22×C11—81no—
282C22×C11—81no—
283C22×C11—81no—
284C22×C11—81no—
285C22×C11—81no—
286C22×C11—81no—
287C22×C11C22×D811yescharacteristic
288C2×D11—42no—
289C2×D11—81no—
290C2×D11—81no—
291C4×C11—21no—
292C4×C11—21no—
293C4×C11—21no—
294C4×C11—21no—
295C4×C11—21no—
296C4×C11—81no—
297C4×C11—81no—
298C4×C11#52511yescharacteristic
299C4×C11#57511yescharacteristic
300Dic11—42no—
301Dic11—81no—
302Dic11—81no—
303C2×#41—221no—
304#135—222no—
305#135—222no—
306C2×Q16—111no—
307C2×SD16—221no—
308C2×D8—21no—
309C2×D8—111no—
310C2×D8C22×D1111yescharacteristic
311C2×D8C22×D1111yescharacteristic
312C2×M16C22⋊D1111yescharacteristic
313C22×C8C22×D1111yescharacteristic
314#127—21no—
315#125—21no—
316#123—41no—
317#123—41no—
318#121—21no—
319#121—21no—
320#121—41no—
321#121—41no—
322C4×Q8—221no—
323C4×Q8—221no—
324C4×D4—21no—
325C4×D4—21no—
326C4×D4—221no—
327C4×D4—221no—
328C4×D4—441no—
329C4×D4—441no—
330#117—441no—
331#117C22⋊D1111yescharacteristic
332C2×C4⋊C4—221no—
333C2×C4⋊C4—441no—
334SD32—222no—
335SD32—222no—
336D16—222no—
337D16—222no—
338C2×C16—111no—
339C2×C16—111no—
340C2×C16—111no—
341C2×C16—111no—
342#107—111no—
343#107—111no—
344#107—221no—
345#107C22×D1111yescharacteristic
346#107C22×D1111yescharacteristic
347#106—21no—
348#103—221no—
349#103—221no—
350#102—21no—
351#102—21no—
352#102—21no—
353#102—21no—
354#102—221no—
355#102—221no—
356#97C22⋊D1111yescharacteristic
357#97C22⋊D1111yescharacteristic
358C4×C8C22×D1111yescharacteristic
359C4×C8C22×D1111yescharacteristic
360C2×C11—41no—
361C2×C11—161no—
362C2×C11—161no—
363C2×C11#310011yescharacteristic
364C2×C11#341511yescharacteristic
365C2×C11#341611yescharacteristic
366D11—82no—
367#41—224no—
368#41—442no—
369C2×Q8—221no—
370C2×D4—21no—
371C2×D4—21no—
372C2×D4—41no—
373C2×D4—41no—
374C2×D4—41no—
375C2×D4—41no—
376C2×D4—221no—
377C2×D4—441no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—441no—
381C22×C4—441no—
382C22×C4—441no—
383C22×C4—441no—
384C22×C4C2×C22⋊D1111yescharacteristic
385Q16—112no—
386Q16—221no—
387SD16—224no—
388D8—21no—
389D8—21no—
390D8—21no—
391D8—21no—
392D8—42no—
393D8—112no—
394D8—221no—
395M16—41no—
396C2×C8—21no—
397C2×C8—21no—
398C2×C8C2×C22⋊D1111yescharacteristic
399C2×C8C2×C22⋊D1111yescharacteristic
400C2×C8C2×C22⋊D1111yescharacteristic
401C2×C8C23×D1111yescharacteristic
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—41no—
405C4⋊C4—41no—
406C4⋊C4—221no—
407C4⋊C4—221no—
408C4⋊C4—441no—
409C4⋊C4—441no—
410C4⋊C4—441no—
411C4⋊C4#432311yescharacteristic
412C4⋊C4#432311yescharacteristic
413C22⋊C4—41no—
414C22⋊C4—41no—
415C22⋊C4—41no—
416C22⋊C4—41no—
417C22⋊C4—441no—
418C22⋊C4—441no—
419C22⋊C4#432311yescharacteristic
420C22⋊C4#432311yescharacteristic
421C42—441no—
422C42—441no—
423C42C2×C22⋊D1111yescharacteristic
424C42C2×C22⋊D1111yescharacteristic
425C16—221no—
426C16—221no—
427C16—221no—
428C16—221no—
429C11#3367911yescharacteristic, complemented, Sylow
430C23—41no—
431C23—41no—
432C23—441no—
433C23C2×#432311yescharacteristic
434Q8—222no—
435Q8—441no—
436D4—41no—
437D4—41no—
438D4—41no—
439D4—41no—
440D4—161no—
441D4—161no—
442D4—161no—
443D4—161no—
444D4—222no—
445D4—444no—
446D4—441no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—161no—
452C2×C4—161no—
453C2×C4—444no—
454C2×C4—441no—
455C2×C4—441no—
456C2×C4—441no—
457C2×C4—1761no—
458C2×C4—1761no—
459C2×C4—1761no—
460C2×C4C2×#432311yescharacteristic
461C2×C4C2×#432311yescharacteristic
462C2×C4C2×#432311yescharacteristic
463C2×C4C2×#432311yescharacteristic
464C2×C4C2×#432311yescharacteristic
465C2×C4C22×C22⋊D1111yescharacteristic
466C8—21no—
467C8—21no—
468C8—21no—
469C8#41×D1111yescharacteristic
470C8#41×D1111yescharacteristic
471C22—21no—
472C22—21no—
473C22—21no—
474C22—81no—
475C22—81no—
476C22—81no—
477C22—81no—
478C22—81no—
479C22—81no—
480C22—442no—
481C22—881no—
482C22—881no—
483C22C22×#432311yescharacteristic
484C4—21no—
485C4—21no—
486C4—21no—
487C4—21no—
488C4—21no—
489C4—81no—
490C4—81no—
491C4—442no—
492C4—881no—
493C4—881no—
494C4#1062335311yescharacteristic
495C4#1062335911yescharacteristic
496C2—41no—
497C2—161no—
498C2—161no—
499C2—882no—
500C2#1307861211yescharacteristic
501C2#1308175511yescharacteristic
502C2#1308176311yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3176C2
socleC22×C11C22×D8
hypercenter#3176D11
hypocenterC11#33679
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #3176

Complements

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

NH ≅ G/Ntype
1. #13077493C2semidirect
2. #13070799C2semidirect
3. #13070794C2semidirect
4. #13070777C2semidirect
5. #13070770C2semidirect
6. #13070653C2semidirect
7. #13070648C2semidirect
8. #13070537C2semidirect
9. #13070537C2semidirect
10. #13070490C2semidirect
11. #13070480C2semidirect
12. C4×#66891C2semidirect
13. C4×#66890C2semidirect
14. #13070423C2semidirect
15. C11×#3176C2semidirect
179. #3176D11semidirect
429. C11#33679semidirect

Maximal subgroups

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

subgroupindex
#130774932
#130707992
#130707942
#130707772
#130707702
#130706532
#130706482
#130705372
#130704902
#130704802
C4×#668912
C4×#668902
#130704232
C11×#31762
#3367911