Finite Group Databasebeta

← #14908898

Subgroups — #14908898

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#13079266C211yesmaximal, characteristic, complemented
2#13077493C211yesmaximal, characteristic, complemented
3#13070802C211yesmaximal, characteristic, complemented
4#13070797C211yesmaximal, characteristic, complemented
5#13070781C211yesmaximal, characteristic, complemented
6#13070774C211yesmaximal, characteristic, complemented
7#13070657C211yesmaximal, characteristic, complemented
8#13070652C211yesmaximal, characteristic, complemented
9#13070541C211yesmaximal, characteristic, complemented
10#13070541C211yesmaximal, characteristic, complemented
11#13070493C211yesmaximal, characteristic, complemented
12#13070482C211yesmaximal, characteristic, complemented
13C4×#66864C211yesmaximal, characteristic, complemented
14C4×D176C211yesmaximal, characteristic, complemented
15C11×#2164C211yesmaximal, characteristic, complemented
16C2×#66957C2211yescharacteristic
17#10623066—21no—
18#10623054—21no—
19C11×#405C2211yescharacteristic
20#10622748—21no—
21#10622746—21no—
22#10622728C2211yescharacteristic
23#10622728C2211yescharacteristic
24C2×#66882C2211yescharacteristic
25C2×#66864C2211yescharacteristic
26C2×#66864C2211yescharacteristic
27C2×D176C2211yescharacteristic
28C2×D176C2211yescharacteristic
29#10622326—21no—
30#10622324—21no—
31#10622323—21no—
32#10622323—21no—
33C4×Dic44C2211yescharacteristic
34C4×Dic44C2211yescharacteristic
35#10622308C2211yescharacteristic
36C4×D88C2211yescharacteristic
37C4×D88C2211yescharacteristic
38C4×D88C2211yescharacteristic
39C4×D88C2211yescharacteristic
40#10622296C2211yescharacteristic
41C11×C4⋊C16C2211yescharacteristic
42C11×C4⋊C16C2211yescharacteristic
43C11×C22⋊C16C2211yescharacteristic
44C11×C22⋊C16C2211yescharacteristic
45C11×#346C2211yescharacteristic
46C4×C11×C16C2211yescharacteristic
47#10622147C2211yescharacteristic
48#10622147C2211yescharacteristic
49#10622147C2211yescharacteristic
50#10622147C2211yescharacteristic
51#10622147C2211yescharacteristic
52#10622147C2211yescharacteristic
53#10622143C2211yescharacteristic
54#10622143C2211yescharacteristic
55#10622142C2211yescharacteristic
56#10622142C2211yescharacteristic
57#10622141C2211yescharacteristic
58#10622141C2211yescharacteristic
59C2×#4339—21no—
60C2×C11×M16D411yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C11×#117D411yescharacteristic
63#66983—21no—
64#66983—21no—
65C2×C4⋊Dic11—21no—
66C2×Dic44C2311yescharacteristic
67#66957—22no—
68#66957—22no—
69C2×D88—21no—
70C2×D88C2311yescharacteristic
71C2×D88C2311yescharacteristic
72C2×D88C2311yescharacteristic
73C2×#4314—21no—
74#66947—41no—
75#66947—41no—
76#66945—41no—
77C4⋊C4×D11—41no—
78#66937—41no—
79#66937—41no—
80(C22⋊D11)⋊C4—41no—
81(C22⋊D11)⋊C4—41no—
82#66927—21no—
83C4×D44—21no—
84C4×D44—21no—
85C4×D44—21no—
86C4×D44—21no—
87#66923—21no—
88C4×Dic22—21no—
89C4×Dic22—21no—
90C2×C11×C16C2311yescharacteristic
91C2×C11×C16C2311yescharacteristic
92C2×C11×C16C2311yescharacteristic
93C2×C11×C16C2311yescharacteristic
94C11×#97D411yescharacteristic
95C11×#97D411yescharacteristic
96C4×C8×C11C2311yescharacteristic
97C4×C8×C11C2311yescharacteristic
98#66885—21no—
99#66885—21no—
100#66885—21no—
101#66885—21no—
102#66885—21no—
103#66885—21no—
104#66882—21no—
105#66882C2311yescharacteristic
106#66882C2311yescharacteristic
107#66882C2311yescharacteristic
108#66882C2311yescharacteristic
109#66881—21no—
110#66880—21no—
111#66880—21no—
112#66864—22no—
113#66864—22no—
114D176—22no—
115D176—22no—
116#33679—111nomaximal, Sylow
117C22×C4×C11C2×D411yescharacteristic
118C2×C22⋊D11—41no—
119C2×C22⋊D11—41no—
120C2×C22⋊D11—41no—
121C22×Dic11—41no—
122#4339—24no—
123#4339—42no—
124C2×D44—21no—
125C2×D44—21no—
126C2×D44—21no—
127C2×D44—41no—
128C2×D44—41no—
129C2×C4×D11—41no—
130C2×C4×D11—41no—
131C2×C4×D11—41no—
132C2×C4×D11—41no—
133C2×C4×D11—41no—
134C2×Dic22—21no—
135C11×M16—41no—
136C2×C8×C11—21no—
137C2×C8×C11—21no—
138C2×C8×C11C2×D411yescharacteristic
139C2×C8×C11C2×D411yescharacteristic
140C2×C8×C11C2×D411yescharacteristic
141C2×C8×C11C2411yescharacteristic
142C11×C4⋊C4D811yescharacteristic
143C11×C4⋊C4D811yescharacteristic
144C11×C22⋊C4D811yescharacteristic
145C11×C22⋊C4D811yescharacteristic
146C42×C11C2×D411yescharacteristic
147C42×C11C2×D411yescharacteristic
148(C2×D11)⋊C4—41no—
149(C2×D11)⋊C4—41no—
150(C2×D11)⋊C4—41no—
151(C2×D11)⋊C4—41no—
152(C2×D11)⋊C4—41no—
153(C2×D11)⋊C4—41no—
154C4⋊Dic11—21no—
155C4⋊Dic11—21no—
156C4⋊Dic11—21no—
157C4⋊Dic11—21no—
158C4⋊Dic11—41no—
159Dic11⋊C4—41no—
160Dic11⋊C4—41no—
161Dic11⋊C4—41no—
162Dic11⋊C4—41no—
163C4×Dic11—41no—
164C4×Dic11—41no—
165Dic44—21no—
166Dic44#4112yes—
167D88—21no—
168D88—21no—
169D88—21no—
170D88—21no—
171D88—21no—
172D88—42no—
173D88#4112yes—
174#4314—24no—
175C11×C16—21no—
176C11×C16—21no—
177C11×C16—21no—
178C11×C16—21no—
179#3176—111no—
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#2164D1111yescharacteristic, complemented
194C23×C11C2×D811yescharacteristic
195C22×D11—41no—
196C22×D11—41no—
197C22×D11—41no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11C2×D811yescharacteristic
201C2×C4×C11C2×D811yescharacteristic
202C2×C4×C11C2×D811yescharacteristic
203C2×C4×C11C2×D811yescharacteristic
204C2×C4×C11C2×D811yescharacteristic
205C2×C4×C11C22×D411yescharacteristic
206C22⋊D11—44no—
207C22⋊D11—161no—
208C22⋊D11—161no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—161no—
215D44—22no—
216D44—41no—
217D44—41no—
218D44—41no—
219D44—41no—
220D44—41no—
221D44—161no—
222D44—161no—
223C4×D11—44no—
224C4×D11—161no—
225C4×D11—161no—
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—221no—
237#520—221no—
238C2×SD32—111no—
239C2×SD32—111no—
240C2×D16—111no—
241C2×D16—111no—
242#499—111no—
243#493—111no—
244#490—221no—
245#469—221no—
246#466—111no—
247#466—111no—
248#442—221no—
249#440—221no—
250#440—221no—
251C4×Q16—111no—
252C4×Q16—111no—
253C4×D8—111no—
254C4×D8—111no—
255C4×D8—111no—
256C4×D8—111no—
257C2×#107—111no—
258#417—221no—
259#405C2×D1111yescharacteristic
260#367—111no—
261#367—111no—
262#366—111no—
263#366—111no—
264C4⋊C16C2×D1111yescharacteristic
265C4⋊C16C2×D1111yescharacteristic
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⋊C16C2×D1111yescharacteristic
275C22⋊C16C2×D1111yescharacteristic
276#346C2×D1111yescharacteristic
277C4×C16C2×D1111yescharacteristic
278C22×C11—21no—
279C22×C11—21no—
280C22×C11—21no—
281C22×C11C22×D811yescharacteristic
282C2×D11—42no—
283C2×D11—81no—
284C2×D11—81no—
285C2×D11—81no—
286C2×D11—81no—
287C2×D11—81no—
288C2×D11—81no—
289C2×D11—81no—
290C2×D11—81no—
291C4×C11—21no—
292C4×C11—21no—
293C4×C11—21no—
294C4×C11—21no—
295C4×C11—21no—
296C4×C11#52511yescharacteristic
297C4×C11#57511yescharacteristic
298Dic11—42no—
299Dic11—81no—
300Dic11—81no—
301Dic11—81no—
302Dic11—81no—
303C2×#41—221no—
304#135—222no—
305#135—222no—
306C2×Q16—111no—
307C2×SD16—221no—
308C2×D8—111no—
309C2×D8—111no—
310C2×D8—111no—
311C2×D8—221no—
312C2×M16D4411yescharacteristic
313C22×C8C22×D1111yescharacteristic
314#127—221no—
315#125—221no—
316#123—441no—
317#123—441no—
318#121—221no—
319#121—221no—
320#121—441no—
321#121—441no—
322C4×Q8—221no—
323C4×Q8—221no—
324C4×D4—221no—
325C4×D4—221no—
326C4×D4—221no—
327C4×D4—221no—
328C4×D4—441no—
329C4×D4—441no—
330#117—441no—
331#117D4411yescharacteristic
332C2×C4⋊C4—221no—
333C2×C4⋊C4—441no—
334SD32—222no—
335SD32—222no—
336D16—222no—
337D16—222no—
338C2×C16C22×D1111yescharacteristic
339C2×C16C22×D1111yescharacteristic
340C2×C16C22×D1111yescharacteristic
341C2×C16C22×D1111yescharacteristic
342#107—111no—
343#107—111no—
344#107—111no—
345#107—111no—
346#107—221no—
347#106—221no—
348#103—221no—
349#103—221no—
350#102—221no—
351#102—221no—
352#102—221no—
353#102—221no—
354#102—221no—
355#102—221no—
356#97D4411yescharacteristic
357#97D4411yescharacteristic
358C4×C8C22×D1111yescharacteristic
359C4×C8C22×D1111yescharacteristic
360C2×C11—41no—
361C2×C11#310011yescharacteristic
362C2×C11#341511yescharacteristic
363C2×C11#341611yescharacteristic
364D11—82no—
365D11—161no—
366D11—161no—
367#41—224no—
368#41—442no—
369C2×Q8—221no—
370C2×D4—221no—
371C2×D4—221no—
372C2×D4—221no—
373C2×D4—441no—
374C2×D4—441no—
375C2×D4—441no—
376C2×D4—441no—
377C2×D4—441no—
378C22×C4—441no—
379C22×C4—441no—
380C22×C4—441no—
381C22×C4—441no—
382C22×C4—441no—
383C22×C4—441no—
384C22×C4C2×D4411yescharacteristic
385Q16—112no—
386Q16—221no—
387SD16—224no—
388D8—112no—
389D8—221no—
390D8—221no—
391D8—221no—
392D8—221no—
393D8—221no—
394D8—442no—
395M16—41no—
396C2×C8—21no—
397C2×C8—21no—
398C2×C8C2×D4411yescharacteristic
399C2×C8C2×D4411yescharacteristic
400C2×C8C2×D4411yescharacteristic
401C2×C8C23×D1111yescharacteristic
402C4⋊C4—221no—
403C4⋊C4—221no—
404C4⋊C4—221no—
405C4⋊C4—221no—
406C4⋊C4—441no—
407C4⋊C4—441no—
408C4⋊C4—441no—
409C4⋊C4—441no—
410C4⋊C4—441no—
411C4⋊C4D8811yescharacteristic
412C4⋊C4D8811yescharacteristic
413C22⋊C4—441no—
414C22⋊C4—441no—
415C22⋊C4—441no—
416C22⋊C4—441no—
417C22⋊C4—441no—
418C22⋊C4—441no—
419C22⋊C4D8811yescharacteristic
420C22⋊C4D8811yescharacteristic
421C42—441no—
422C42—441no—
423C42C2×D4411yescharacteristic
424C42C2×D4411yescharacteristic
425C16—21no—
426C16—21no—
427C16—21no—
428C16—21no—
429C11#3367911yescharacteristic, complemented, Sylow
430C23—441no—
431C23—441no—
432C23—441no—
433C23C2×D8811yescharacteristic
434Q8—222no—
435Q8—441no—
436D4—222no—
437D4—444no—
438D4—441no—
439D4—441no—
440D4—441no—
441D4—441no—
442D4—441no—
443D4—1761no—
444D4—1761no—
445D4—1761no—
446D4—1761no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—444no—
450C2×C4—441no—
451C2×C4—441no—
452C2×C4—441no—
453C2×C4—441no—
454C2×C4—441no—
455C2×C4—1761no—
456C2×C4—1761no—
457C2×C4—1761no—
458C2×C4—1761no—
459C2×C4—1761no—
460C2×C4C2×D8811yescharacteristic
461C2×C4C2×D8811yescharacteristic
462C2×C4C2×D8811yescharacteristic
463C2×C4C2×D8811yescharacteristic
464C2×C4C2×D8811yescharacteristic
465C2×C4C22×D4411yescharacteristic
466C8—21no—
467C8—21no—
468C8—21no—
469C8#41×D1111yescharacteristic
470C8#41×D1111yescharacteristic
471C22—21no—
472C22—21no—
473C22—21no—
474C22—442no—
475C22—881no—
476C22—881no—
477C22—881no—
478C22—881no—
479C22—881no—
480C22—881no—
481C22—881no—
482C22—881no—
483C22C22×D8811yescharacteristic
484C4—21no—
485C4—21no—
486C4—21no—
487C4—21no—
488C4—21no—
489C4—442no—
490C4—881no—
491C4—881no—
492C4—881no—
493C4—881no—
494C4#1062305511yescharacteristic
495C4#1062327911yescharacteristic
496C2—41no—
497C2—882no—
498C2—1761no—
499C2—1761no—
500C2#1307861711yescharacteristic
501C2#1308175711yescharacteristic
502C2#1308176411yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2164C2
socleC22×C11C22×D8
hypercenter#2164D11
hypocenterC11#33679
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #2164

Complements

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

NH ≅ G/Ntype
1. #13079266C2semidirect
2. #13077493C2semidirect
3. #13070802C2semidirect
4. #13070797C2semidirect
5. #13070781C2semidirect
6. #13070774C2semidirect
7. #13070657C2semidirect
8. #13070652C2semidirect
9. #13070541C2semidirect
10. #13070541C2semidirect
11. #13070493C2semidirect
12. #13070482C2semidirect
13. C4×#66864C2semidirect
14. C4×D176C2semidirect
15. C11×#2164C2semidirect
193. #2164D11semidirect
429. C11#33679semidirect

Maximal subgroups

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

subgroupindex
#130792662
#130774932
#130708022
#130707972
#130707812
#130707742
#130706572
#130706522
#130705412
#130704932
#130704822
C4×#668642
C4×D1762
C11×#21642
#3367911