Finite Group Databasebeta

← #14910761

Subgroups — #14910761

Order 2816.

554 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081019C211yesmaximal, characteristic, complemented
2#13080338C211yesmaximal, characteristic, complemented
3#13070862C211yesmaximal, characteristic, complemented
4#13070825C211yesmaximal, characteristic, complemented
5#13070814C211yesmaximal, characteristic, complemented
6#13070774C211yesmaximal, characteristic, complemented
7#13070729C211yesmaximal, characteristic, complemented
8#13070712C211yesmaximal, characteristic, complemented
9#13070662C211yesmaximal, characteristic, complemented
10#13070541C211yesmaximal, characteristic, complemented
11#13070541C211yesmaximal, characteristic, complemented
12#13070493C211yesmaximal, characteristic, complemented
13#13070329C211yesmaximal, characteristic, complemented
14#13070324C211yesmaximal, characteristic, complemented
15C11×#2168C211yesmaximal, characteristic, complemented
16C2×#66957C2211yescharacteristic
17C2×#66957C2211yescharacteristic
18#10623096—21no—
19#10623082—21no—
20C2×C11×M32C2211yescharacteristic
21C22×C11×C16C2211yescharacteristic
22C8×D4×C11C2211yescharacteristic
23#10622729C2211yescharacteristic
24#10622729C2211yescharacteristic
25#10622728C2211yescharacteristic
26#10622728C2211yescharacteristic
27#10622719C2211yescharacteristic
28C2×#66882C2211yescharacteristic
29C2×#66864C2211yescharacteristic
30C2×#66864C2211yescharacteristic
31C2×D176C2211yescharacteristic
32#10622460—21no—
33#10622454—21no—
34#10622350—21no—
35#10622348—21no—
36#10622346—21no—
37#10622346—21no—
38#10622312C2211yescharacteristic
39C4×D88C2211yescharacteristic
40C4×D88C2211yescharacteristic
41#10622296C2211yescharacteristic
42C11×C4⋊C16C2211yescharacteristic
43C11×C22⋊C16C2211yescharacteristic
44C11×C22⋊C16C2211yescharacteristic
45C11×#346C2211yescharacteristic
46#10622147C2211yescharacteristic
47#10622147C2211yescharacteristic
48#10622147C2211yescharacteristic
49#10622147C2211yescharacteristic
50#10622143C2211yescharacteristic
51#10622143C2211yescharacteristic
52#10622142C2211yescharacteristic
53#10622141C2211yescharacteristic
54#10622141C2211yescharacteristic
55#10622141C2211yescharacteristic
56#10622141C2211yescharacteristic
57#10622141C2211yescharacteristic
58#10622141C2211yescharacteristic
59C2×#4339—21no—
60C2×#4339—21no—
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C4×D4×C11D411yescharacteristic
64#66992—41no—
65#66991—41no—
66#66983—21no—
67#66983—21no—
68#66979—21no—
69C2×C4⋊Dic11—21no—
70#66977—21no—
71#66977—21no—
72C2×Dic44—21no—
73C2×Dic44C2311yescharacteristic
74C2×Dic44C2311yescharacteristic
75#66957—22no—
76#66957—22no—
77#66957—41no—
78#66957—41no—
79C2×D88C2311yescharacteristic
80C2×D88C2311yescharacteristic
81C2×#4314—21no—
82C2×#4314—21no—
83#66951—41no—
84C4⋊C4×D11—41no—
85#66936—41no—
86#66936—41no—
87#66936—41no—
88(C22⋊D11)⋊C4—41no—
89C4×D44—21no—
90C4×D44—21no—
91#66923—21no—
92#66922—21no—
93C11×M32—41no—
94C2×C11×C16—41no—
95C2×C11×C16C2311yescharacteristic
96C2×C11×C16C2311yescharacteristic
97C2×C11×C16C2311yescharacteristic
98C2×C11×C16C2311yescharacteristic
99C11×C4⋊C8D411yescharacteristic
100C11×C22⋊C8D411yescharacteristic
101C11×C22⋊C8D411yescharacteristic
102C4×C8×C11C2311yescharacteristic
103#66885—21no—
104#66885—21no—
105#66885—21no—
106#66885—21no—
107#66882—21no—
108#66882C2311yescharacteristic
109#66882C2311yescharacteristic
110#66882C2311yescharacteristic
111#66882C2311yescharacteristic
112#66881—21no—
113#66881—21no—
114#66880—21no—
115#66880—21no—
116#66864—41no—
117#66864—41no—
118D176—22no—
119#33874—111nomaximal, Sylow
120C2×D4×C11D811yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C2×C22⋊D11—41no—
124C2×C22⋊D11—41no—
125C2×C22⋊D11—41no—
126C2×C22⋊D11—41no—
127C22×Dic11—41no—
128#4339—42no—
129#4339—42no—
130#4339—81no—
131#4339—81no—
132C2×D44—21no—
133C2×D44—21no—
134C2×C4×D11—41no—
135C2×C4×D11—41no—
136C2×C4×D11—41no—
137C2×C4×D11—41no—
138C2×Dic22—21no—
139C2×Dic22—21no—
140C2×C8×C11—21no—
141C2×C8×C11—21no—
142C2×C8×C11—21no—
143C2×C8×C11—21no—
144C2×C8×C11C2×D411yescharacteristic
145C2×C8×C11C2×D411yescharacteristic
146C2×C8×C11C2×D411yescharacteristic
147C2×C8×C11C2411yescharacteristic
148C11×C4⋊C4D811yescharacteristic
149C11×C22⋊C4D811yescharacteristic
150C11×C22⋊C4D811yescharacteristic
151C42×C11C2×D411yescharacteristic
152C22⋊Dic11—41no—
153C22⋊Dic11—41no—
154C22⋊Dic11—41no—
155(C2×D11)⋊C4—41no—
156(C2×D11)⋊C4—41no—
157(C2×D11)⋊C4—41no—
158(C2×D11)⋊C4—41no—
159C4⋊Dic11—21no—
160C4⋊Dic11—21no—
161C4⋊Dic11—21no—
162C4⋊Dic11—21no—
163C4⋊Dic11—41no—
164C4⋊Dic11—41no—
165C4⋊Dic11—41no—
166Dic11⋊C4—41no—
167Dic11⋊C4—41no—
168Dic11⋊C4—41no—
169Dic11⋊C4—41no—
170C4×Dic11—41no—
171Dic44—21no—
172Dic44—21no—
173Dic44—21no—
174Dic44—21no—
175Dic44—81no—
176D88—21no—
177D88—21no—
178D88—21no—
179D88#4112yes—
180#4314—42no—
181#4314—42no—
182C11×C16—21no—
183C11×C16—21no—
184C11×C16—21no—
185C11×C16—21no—
186#3339—111no—
187#3283—111no—
188#2245—111no—
189#2237—111no—
190#2235—111no—
191#2228—111no—
192#2220—111no—
193#2217—111no—
194#2208—111no—
195#2186—111no—
196#2186—111no—
197#2177—111no—
198#2168D1111yescharacteristic, complemented
199#2139—111no—
200#2138—111no—
201C23×C11C2×D811yescharacteristic
202C23×C11C2×D811yescharacteristic
203C22×D11—41no—
204C22×D11—41no—
205D4×C11—41no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11C2×D811yescharacteristic
211C2×C4×C11C2×D811yescharacteristic
212C2×C4×C11C2×D811yescharacteristic
213C2×C4×C11C2×D811yescharacteristic
214C2×C4×C11C22×D411yescharacteristic
215C22⋊D11—82no—
216C22⋊D11—82no—
217C22⋊D11—82no—
218C22⋊D11—161no—
219C2×Dic11—41no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—161no—
226D44—22no—
227D44—41no—
228D44—41no—
229D44—41no—
230C4×D11—82no—
231C4×D11—82no—
232C4×D11—82no—
233C4×D11—161no—
234Dic22—41no—
235Dic22—41no—
236Dic22—41no—
237Dic22—41no—
238C8×C11—21no—
239C8×C11—21no—
240C8×C11—21no—
241C8×C11C2×#4111yescharacteristic
242C8×C11H(5,𝔽2)11yescharacteristic
243C2×#135—111no—
244C2×#135—111no—
245#553—221no—
246#547—221no—
247C2×SD32—111no—
248C2×SD32—111no—
249C2×D16—111no—
250C2×M32C2×D1111yescharacteristic
251C22×C16C2×D1111yescharacteristic
252#499—111no—
253#494—111no—
254#482—221no—
255#481—221no—
256#478—221no—
257#467—111no—
258#467—111no—
259#466—111no—
260#466—111no—
261#461—221no—
262#452—221no—
263#452—221no—
264C4×D8—111no—
265C4×D8—111no—
266C8×D4C2×D1111yescharacteristic
267#427—111no—
268C2×#107—111no—
269#367—111no—
270#367—111no—
271#366—111no—
272C4⋊C16C2×D1111yescharacteristic
273#358—111no—
274#358—111no—
275#358—111no—
276#358—111no—
277#358—111no—
278#358—111no—
279#357—111no—
280#357—111no—
281#357—111no—
282#357—111no—
283C22⋊C16C2×D1111yescharacteristic
284C22⋊C16C2×D1111yescharacteristic
285#346C2×D1111yescharacteristic
286C22×C11—21no—
287C22×C11—21no—
288C22×C11—21no—
289C22×C11—21no—
290C22×C11—21no—
291C22×C11—21no—
292C22×C11C22×D811yescharacteristic
293C2×D11—42no—
294C2×D11—81no—
295C2×D11—81no—
296C2×D11—81no—
297C2×D11—81no—
298C2×D11—81no—
299C4×C11—21no—
300C4×C11—21no—
301C4×C11—21no—
302C4×C11—21no—
303C4×C11#54611yescharacteristic
304C4×C11#57711yescharacteristic
305Dic11—81no—
306Dic11—81no—
307Dic11—81no—
308Dic11—81no—
309Dic11—81no—
310Dic11—81no—
311C2×#41—221no—
312C2×#41—221no—
313#135—222no—
314#135—222no—
315#135—441no—
316#135—441no—
317C2×Q16—111no—
318C2×Q16—111no—
319C2×Q16—221no—
320C2×SD16—221no—
321C2×SD16—221no—
322C2×D8—111no—
323C2×D8—111no—
324C22×C8C22×D1111yescharacteristic
325C22×C8C22×D1111yescharacteristic
326C4⋊Q8—221no—
327#126—441no—
328#125—221no—
329#123—441no—
330#123—441no—
331#123—441no—
332C22⋊Q8—221no—
333C22⋊Q8—221no—
334#121—221no—
335#121—221no—
336#121—441no—
337#121—441no—
338C4×D4—221no—
339C4×D4—221no—
340C4×D4—441no—
341C4×D4D4411yescharacteristic
342#117—221no—
343C2×C4⋊C4—221no—
344C2×C4⋊C4—441no—
345SD32—441no—
346SD32—441no—
347D16—222no—
348M32—41no—
349C2×C16—41no—
350C2×C16C22×D1111yescharacteristic
351C2×C16C22×D1111yescharacteristic
352C2×C16C22×D1111yescharacteristic
353C2×C16C22×D1111yescharacteristic
354#107—111no—
355#107—111no—
356#107—111no—
357#107—111no—
358#107—221no—
359#106—221no—
360#106—221no—
361C4⋊C8D4411yescharacteristic
362#103—221no—
363#103—221no—
364#102—221no—
365#102—221no—
366#102—221no—
367#102—221no—
368C22⋊C8D4411yescharacteristic
369C22⋊C8D4411yescharacteristic
370C4×C8C22×D1111yescharacteristic
371C2×C11—41no—
372C2×C11—41no—
373C2×C11#329411yescharacteristic
374C2×C11#341411yescharacteristic
375C2×C11#341611yescharacteristic
376D11—82no—
377D11—161no—
378#41—442no—
379#41—442no—
380#41—881no—
381#41—881no—
382C2×Q8—221no—
383C2×Q8—221no—
384C2×D4—221no—
385C2×D4—221no—
386C2×D4—441no—
387C2×D4—441no—
388C2×D4—441no—
389C2×D4—441no—
390C2×D4D8811yescharacteristic
391C22×C4—441no—
392C22×C4—441no—
393C22×C4—441no—
394C22×C4—441no—
395C22×C4—441no—
396C22×C4C2×D4411yescharacteristic
397C22×C4C2×D4411yescharacteristic
398Q16—221no—
399Q16—221no—
400Q16—221no—
401Q16—221no—
402Q16—881no—
403SD16—442no—
404SD16—442no—
405D8—112no—
406D8—221no—
407D8—221no—
408D8—221no—
409C2×C8—21no—
410C2×C8—21no—
411C2×C8—21no—
412C2×C8—21no—
413C2×C8C2×D4411yescharacteristic
414C2×C8C2×D4411yescharacteristic
415C2×C8C2×D4411yescharacteristic
416C2×C8C23×D1111yescharacteristic
417C4⋊C4—221no—
418C4⋊C4—221no—
419C4⋊C4—221no—
420C4⋊C4—221no—
421C4⋊C4—441no—
422C4⋊C4—441no—
423C4⋊C4—441no—
424C4⋊C4—441no—
425C4⋊C4—441no—
426C4⋊C4—441no—
427C4⋊C4—441no—
428C4⋊C4D8811yescharacteristic
429C22⋊C4—441no—
430C22⋊C4—441no—
431C22⋊C4—441no—
432C22⋊C4—441no—
433C22⋊C4—441no—
434C22⋊C4—441no—
435C22⋊C4—441no—
436C22⋊C4D8811yescharacteristic
437C22⋊C4D8811yescharacteristic
438C42—441no—
439C42C2×D4411yescharacteristic
440C16—21no—
441C16—21no—
442C16—21no—
443C16—21no—
444C11#3387411yescharacteristic, complemented, Sylow
445C23—441no—
446C23—441no—
447C23C2×D8811yescharacteristic
448C23C2×D8811yescharacteristic
449Q8—441no—
450Q8—441no—
451Q8—441no—
452Q8—441no—
453D4—41no—
454D4—222no—
455D4—441no—
456D4—441no—
457D4—441no—
458D4—882no—
459D4—882no—
460D4—882no—
461D4—1761no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—441no—
467C2×C4—441no—
468C2×C4—441no—
469C2×C4—441no—
470C2×C4—441no—
471C2×C4—441no—
472C2×C4—882no—
473C2×C4—882no—
474C2×C4—882no—
475C2×C4—1761no—
476C2×C4—1761no—
477C2×C4C2×D8811yescharacteristic
478C2×C4C2×D8811yescharacteristic
479C2×C4C2×D8811yescharacteristic
480C2×C4C2×D8811yescharacteristic
481C2×C4C22×D4411yescharacteristic
482C8—21no—
483C8—21no—
484C8—21no—
485C8#6703711yescharacteristic
486C8#41×D1111yescharacteristic
487C22—21no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—442no—
494C22—881no—
495C22—881no—
496C22—881no—
497C22—881no—
498C22—881no—
499C22C22×D8811yescharacteristic
500C4—21no—
501C4—21no—
502C4—21no—
503C4—21no—
504C4—881no—
505C4—881no—
506C4—881no—
507C4—881no—
508C4—881no—
509C4—881no—
510C4#1062308511yescharacteristic
511C4#1062328211yescharacteristic
512C2—41no—
513C2—41no—
514C2—882no—
515C2—1761no—
516C2#1308043011yescharacteristic
517C2#1308175211yescharacteristic
518C2#1308176411yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2168C2
socleC22×C11C22×D8
hypercenter#2168D11
hypocenterC11#33874
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #2168

Complements

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

NH ≅ G/Ntype
1. #13081019C2semidirect
2. #13080338C2semidirect
3. #13070862C2semidirect
4. #13070825C2semidirect
5. #13070814C2semidirect
6. #13070774C2semidirect
7. #13070729C2semidirect
8. #13070712C2semidirect
9. #13070662C2semidirect
10. #13070541C2semidirect
11. #13070541C2semidirect
12. #13070493C2semidirect
13. #13070329C2semidirect
14. #13070324C2semidirect
15. C11×#2168C2semidirect
198. #2168D11semidirect
444. C11#33874semidirect

Maximal subgroups

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

subgroupindex
#130810192
#130803382
#130708622
#130708252
#130708142
#130707742
#130707292
#130707122
#130706622
#130705412
#130704932
#130703292
#130703242
C11×#21682
#3387411