Finite Group Databasebeta

← #14788663

Subgroups — #14788663

Order 2816.

1116 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622696C211yesmaximal, characteristic, complemented
2C2×#10622627C211yesmaximal, characteristic
3#13073974C211yesmaximal, characteristic, complemented
4#13069852C212yesmaximal, complemented
5#13069693C212yesmaximal
6#13069557C211yesmaximal, characteristic, complemented
7#13069437C211yesmaximal, characteristic, complemented
8#13068971C212yesmaximal, complemented
9#13068884C212yesmaximal, complemented
10#13068626C211yesmaximal, characteristic, complemented
11C2×C11×#556C211yesmaximal, characteristic, complemented
12C11×#556—24no—
13C11×#556—24no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#126—22no—
16C2×C11×#124C2212yes—
17C2×C11×C22⋊Q8—21no—
18C2×C4×Q8×C11C2212yes—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×C11×#117—21no—
22C22×#4325C2212yes—
23C22×#4323C2211yescharacteristic
24C2×C4×D44C2211yescharacteristic
25#10622844—21no—
26C2×#66899C2212yes—
27C2×#66899C2212yes—
28C2×#66899C2212yes—
29C2×#66896C2211yescharacteristic
30C2×#66896C2212yes—
31#10622696—24no—
32#10622627—24no—
33#10622605—21no—
34#10622602—22no—
35C2×#66873C2211yescharacteristic
36C2×#66872C2211yescharacteristic
37#10622552C2212yes—
38#10622549C2211yescharacteristic
39#10622541C2212yes—
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×#66867C2211yescharacteristic
42#10622167C2212yes—
43#10622162C2212yes—
44#10622162C2212yes—
45C22×Q8×C11D411yescharacteristic
46C22×Q8×C11C2312yes—
47C22×D4×C11C2311yescharacteristic
48C23×C4×C11—21no—
49C22×D44C2311yescharacteristic
50C22×C4×D11—21no—
51C11×C4⋊Q8—22no—
52C11×C4⋊Q8D414yes—
53C11×#126—216no—
54C11×#124—24no—
55C11×#124—24no—
56C11×C22⋊Q8—28no—
57C4×Q8×C11—24no—
58C4×Q8×C11—24no—
59C4×Q8×C11—22no—
60C4×Q8×C11—22no—
61C4×D4×C11—22no—
62C4×D4×C11D414yes—
63C11×#117—28no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4D412yes—
68C2×C11×C4⋊C4D411yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—22no—
73C2×C42×C11—22no—
74C2×C42×C11C2312yes—
75C2×C42×C11C2311yescharacteristic
76C2×#4325—24no—
77C2×#4325—24no—
78C2×#4325—42no—
79C2×#4323—22no—
80C2×#4323—22no—
81C2×#4323—22no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—22no—
84C2×(C2×D11)⋊C4—22no—
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2312yes—
87C2×Dic11⋊C4—22no—
88C22×C11⋊C8C2311yescharacteristic
89C22×C11⋊C8C2312yes—
90C22×C11⋊C8C2311yescharacteristic
91C4×D44—22no—
92C4×D44—22no—
93#66899—24no—
94#66899—24no—
95#66899—42no—
96#66896—22no—
97#66896—42no—
98C11⋊#95—22no—
99C11⋊#95—21no—
100C11⋊#95—21no—
101#66873—22no—
102#66872—22no—
103C4⋊(C11⋊C8)—22no—
104#66867—22no—
105#24197—111nomaximal, Sylow
106C24×C11—21no—
107C23×D11—21no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11—42no—
115C2×Q8×C11C2×D414yes—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11C2×D412yes—
122C22×C4×C11—21no—
123C22×C4×C11—22no—
124C22×C4×C11—24no—
125C22×C4×C11—44no—
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2411yescharacteristic
131C22×Dic11—22no—
132C22×Dic11—21no—
133C2×D44—21no—
134C2×D44—21no—
135C2×D44—21no—
136C2×D44—21no—
137C2×D44—21no—
138C2×D44#4112yes—
139C2×C4×D11—42no—
140C2×C4×D11—82no—
141C11×C4⋊C4—28no—
142C11×C4⋊C4—24no—
143C11×C4⋊C4—24no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—24no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4C2×D412yes—
148C11×C22⋊C4—28no—
149C11×C22⋊C4—28no—
150C11×C22⋊C4—24no—
151C42×C11—28no—
152C42×C11—22no—
153C42×C11—22no—
154C42×C11C2×D412yes—
155C42×C11C2×D412yes—
156#4325—48no—
157#4323—28no—
158(C2×D11)⋊C4—44no—
159(C2×D11)⋊C4—42no—
160(C2×D11)⋊C4—82no—
161C4⋊Dic11—21no—
162C4⋊Dic11—21no—
163C4⋊Dic11—22no—
164C4⋊Dic11—22no—
165Dic11⋊C4—82no—
166C2×C11⋊C8—21no—
167C2×C11⋊C8—21no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—21no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—21no—
173C2×C11⋊C8—21no—
174C2×C11⋊C8#4112yes—
175C2×#556D1111yescharacteristic, complemented
176C2×#461—111no—
177C2×#442—111no—
178#2580—111no—
179#2042—112no—
180#2012—112no—
181#1985—111no—
182#1960—111no—
183#1880—112no—
184#1865—112no—
185#1804—111no—
186C23×C11—22no—
187C23×C11—41no—
188C23×C11—41no—
189C23×C11—42no—
190C23×C11—42no—
191C23×C11C22×D411yescharacteristic
192C22×D11—22no—
193C22×D11—41no—
194C22×D11—41no—
195C22×D11—42no—
196C22×D11—42no—
197Q8×C11—24no—
198Q8×C11—24no—
199Q8×C11—44no—
200Q8×C11—42no—
201Q8×C11—42no—
202D4×C11—22no—
203D4×C11—22no—
204D4×C11—41no—
205D4×C11—41no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—24no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—48no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11#12012yes—
221C2×C4×C11#12012yes—
222C2×C4×C11C22×D411yescharacteristic
223C2×C4×C11C22×D411yescharacteristic
224C2×C4×C11C2×#4111yescharacteristic
225C2×C4×C11C2×#4111yescharacteristic
226C2×C4×C11H(5,𝔽2)11yescharacteristic
227C2×C4×C112−1+411yescharacteristic
228C2×Dic11—41no—
229C2×Dic11—42no—
230C2×Dic11—42no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233D44—22no—
234D44—22no—
235D44—41no—
236D44—41no—
237C4×D11—84no—
238C11⋊C8—22no—
239C11⋊C8—41no—
240C11⋊C8—42no—
241C22×SD16—112no—
242C22×D8—111no—
243#556—24no—
244#556—24no—
245C2×C4⋊Q8C2×D1111yescharacteristic
246C2×#126—22no—
247C2×#124C2×D1112yes—
248C2×C22⋊Q8—21no—
249C2×C4×Q8C2×D1112yes—
250C2×C4×Q8C2×D1111yescharacteristic
251C2×C4×D4—111no—
252C2×C4×D4C2×D1111yescharacteristic
253C2×#117—21no—
254#461—224no—
255#442—224no—
256C2×#106—111no—
257C2×C4⋊C8—111no—
258C2×#103—112no—
259C2×#103—112no—
260C2×#103—112no—
261C2×#102—111no—
262C2×#102—111no—
263C2×#102—112no—
264C2×#97—111no—
265#399—221no—
266#393—221no—
267#390—112no—
268#389—112no—
269#385—222no—
270#382—111no—
271#340—112no—
272#336—112no—
273#336—112no—
274C22×C11—42no—
275C22×C11—42no—
276C22×C11—42no—
277C22×C11—82no—
278C22×C11—82no—
279C22×C11C2×#12011yescharacteristic
280C22×C11#54811yescharacteristic
281C22×C11#55011yescharacteristic
282C22×C11#57512yes—
283C22×C11#57712yes—
284C2×D11—44no—
285C2×D11—42no—
286C2×D11—82no—
287C2×D11—81no—
288C2×D11—81no—
289C4×C11—22no—
290C4×C11—22no—
291C4×C11—44no—
292C4×C11—42no—
293C4×C11—42no—
294C4×C11—42no—
295C4×C11#52511yescharacteristic
296C4×C11#53711yescharacteristic
297C4×C11#54611yescharacteristic
298C4×C11#54711yescharacteristic
299Dic11—82no—
300Dic11—81no—
301C22×Q8C22⋊D1111yescharacteristic
302C22×Q8C22×D1112yes—
303C22×D4—111no—
304C22×D4C22×D1111yescharacteristic
305C23×C4—21no—
306C23×C4—221no—
307C2×SD16—224no—
308C2×SD16—224no—
309C2×SD16—442no—
310C2×D8—222no—
311C2×D8—222no—
312C2×D8—222no—
313C22×C8—111no—
314C22×C8—112no—
315C22×C8—111no—
316C4⋊Q8—22no—
317C4⋊Q8C22⋊D1114yes—
318#126—216no—
319#124—24no—
320#124—24no—
321C22⋊Q8—28no—
322C4×Q8—24no—
323C4×Q8—24no—
324C4×Q8—22no—
325C4×Q8—22no—
326C4×D4—22no—
327C4×D4—222no—
328C4×D4—222no—
329C4×D4C22⋊D1114yes—
330#117—28no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—111no—
335C2×C4⋊C4—112no—
336C2×C4⋊C4—222no—
337C2×C4⋊C4C22⋊D1111yescharacteristic
338C2×C4⋊C4C22⋊D1112yes—
339C2×C4⋊C4C22×D1111yescharacteristic
340C2×C22⋊C4—22no—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—221no—
344C2×C22⋊C4—222no—
345C2×C22⋊C4—222no—
346C2×C42—22no—
347C2×C42C22×D1112yes—
348C2×C42C22×D1111yescharacteristic
349#106—222no—
350C4⋊C8—222no—
351#103—224no—
352#103—224no—
353#103—442no—
354#102—222no—
355#102—222no—
356#102—442no—
357#97—222no—
358#95—221no—
359#95—221no—
360#95—222no—
361C2×C11—82no—
362C2×C11#240711yescharacteristic
363C2×C11#300511yescharacteristic
364C2×C11#301011yescharacteristic
365C2×C11#337612yes—
366C2×C11#340112yes—
367D11—82no—
368C24—21no—
369C24—221no—
370C2×Q8—22no—
371C2×Q8—22no—
372C2×Q8—22no—
373C2×Q8—22no—
374C2×Q8—22no—
375C2×Q8—22no—
376C2×Q8—42no—
377C2×Q8C2×C22⋊D1114yes—
378C2×D4—21no—
379C2×D4—21no—
380C2×D4—21no—
381C2×D4—21no—
382C2×D4—21no—
383C2×D4—112no—
384C2×D4—221no—
385C2×D4—221no—
386C2×D4—221no—
387C2×D4—221no—
388C2×D4—221no—
389C2×D4C2×C22⋊D1112yes—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—24no—
393C22×C4—44no—
394C22×C4—222no—
395C22×C4—221no—
396C22×C4—442no—
397C22×C4—882no—
398C22×C4C2×C22⋊D1112yes—
399C22×C4C2×C22⋊D1112yes—
400C22×C4C2×C22⋊D1111yescharacteristic
401C22×C4C2×C22⋊D1111yescharacteristic
402C22×C4C23×D1111yescharacteristic
403SD16—448no—
404D8—228no—
405C2×C8—112no—
406C2×C8—221no—
407C2×C8—221no—
408C2×C8—222no—
409C2×C8—222no—
410C2×C8—221no—
411C2×C8—221no—
412C2×C8—221no—
413C2×C8—222no—
414C4⋊C4—28no—
415C4⋊C4—24no—
416C4⋊C4—24no—
417C4⋊C4—22no—
418C4⋊C4—24no—
419C4⋊C4—21no—
420C4⋊C4—222no—
421C4⋊C4—222no—
422C4⋊C4—221no—
423C4⋊C4—221no—
424C4⋊C4—882no—
425C4⋊C4C2×C22⋊D1112yes—
426C22⋊C4—28no—
427C22⋊C4—28no—
428C22⋊C4—24no—
429C22⋊C4—444no—
430C22⋊C4—442no—
431C22⋊C4—882no—
432C42—28no—
433C42—22no—
434C42—22no—
435C42C2×C22⋊D1112yes—
436C42C2×C22⋊D1112yes—
437C11#2419711yescharacteristic, complemented, Sylow
438C23—22no—
439C23—42no—
440C23—41no—
441C23—41no—
442C23—42no—
443C23—222no—
444C23—442no—
445C23—441no—
446C23—442no—
447C23—441no—
448C23C22×C22⋊D1111yescharacteristic
449Q8—24no—
450Q8—24no—
451Q8—44no—
452Q8—42no—
453Q8—42no—
454D4—22no—
455D4—22no—
456D4—41no—
457D4—41no—
458D4—222no—
459D4—222no—
460D4—441no—
461D4—441no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—24no—
471C2×C4—22no—
472C2×C4—48no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—442no—
477C2×C4—442no—
478C2×C4—442no—
479C2×C4—442no—
480C2×C4—441no—
481C2×C4—884no—
482C2×C4#6700612yes—
483C2×C4#6700612yes—
484C2×C4#41×D1111yescharacteristic
485C2×C4#41×D1111yescharacteristic
486C2×C4#6704211yescharacteristic
487C2×C4#6704311yescharacteristic
488C2×C4C22×C22⋊D1111yescharacteristic
489C2×C4C22×C22⋊D1111yescharacteristic
490C8—222no—
491C8—442no—
492C8—441no—
493C22—42no—
494C22—42no—
495C22—42no—
496C22—82no—
497C22—82no—
498C22—442no—
499C22—444no—
500C22—882no—
501C22—881no—
502C22—881no—
503C22#1062335312yes—
504C22#1062336211yescharacteristic
505C22#1062336511yescharacteristic
506C22#1062336812yes—
507C22C2×#6700611yescharacteristic
508C4—22no—
509C4—22no—
510C4—44no—
511C4—42no—
512C4—42no—
513C4—42no—
514C4—882no—
515C4—881no—
516C4#1062335511yescharacteristic
517C4#1062335911yescharacteristic
518C4#1062336011yescharacteristic
519C4#1062336411yescharacteristic
520C2—82no—
521C2—882no—
522C2#1307195511yescharacteristic
523C2#1307785811yescharacteristic
524C2#1307790211yescharacteristic
525C2#1308143712yes—
526C2#1308168212yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#556C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
hypercenterC2×#556D11
hypocenterC11#24197
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. C2×#10622696C2semidirect
3. #13073974C2semidirect
4. #13069852C2semidirect
6. #13069557C2semidirect
7. #13069437C2semidirect
8. #13068971C2semidirect
9. #13068884C2semidirect
10. #13068626C2semidirect
11. C2×C11×#556C2semidirect
175. C2×#556D11semidirect
437. C11#24197semidirect

Maximal subgroups

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

subgroupindex
C2×#106226962
C2×#106226272
#130739742
#130698522
#130696932
#130695572
#130694372
#130689712
#130688842
#130686262
C2×C11×#5562
#2419711