Finite Group Databasebeta

← #14810414

Subgroups — #14810414

Order 2816.

1116 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#125C211yesmaximal, characteristic, complemented
2C2×#10622413C212yesmaximal, complemented
3#13076920C211yesmaximal, characteristic
4#13069767C211yesmaximal, characteristic, complemented
5#13069763C211yesmaximal, characteristic, complemented
6#13069759C211yesmaximal, characteristic, complemented
7#13069579C212yesmaximal, complemented
8#13068932C212yesmaximal
9#13068920C212yesmaximal, complemented
10#13068373C211yesmaximal, characteristic, complemented
11C11×#2026C211yesmaximal, characteristic, complemented
12C2×C11×#125C2211yescharacteristic
13C2×#67000C2211yescharacteristic
14C2×#66999C2211yescharacteristic
15D11×#125—28no—
16C2×#66948C2211yescharacteristic
17C2×C4⋊C4×D11—22no—
18C2×C4⋊C4×D11C2212yes—
19C2×#66943C2212yes—
20C2×#66942—22no—
21C2×C42×D11C2211yescharacteristic
22C2×#66923C2211yescharacteristic
23C2×C11×#103C2212yes—
24C11×#391C2211yescharacteristic
25C2×#66899C2212yes—
26C2×#66885C2212yes—
27C2×(C2×D11)⋊C8C2212yes—
28C2×C8×Dic11C2212yes—
29#10622590C2211yescharacteristic
30C2×#66873C2212yes—
31#10622552C2211yescharacteristic
32#10622413—28no—
33#10622282—22no—
34#10622278—22no—
35C11×#340C2212yes—
36C11×#336C2211yescharacteristic
37#10622189C2212yes—
38#10622167C2212yes—
39#10622167C2212yes—
40#10622162C2211yescharacteristic
41C22×Q8×C11C2311yescharacteristic
42C22×D44—21no—
43C22×D44C2311yescharacteristic
44C22×C4×D11—22no—
45C22×C4×D11D412yes—
46C22×C4×D11C2311yescharacteristic
47C22×C8×C11C2312yes—
48C11×#125—24no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4C2311yescharacteristic
51C2×C11×C4⋊C4C2312yes—
52C2×C42×C11C2311yescharacteristic
53#67000—24no—
54#66999—24no—
55C2×(C2×D11)⋊C4—21no—
56C2×(C2×D11)⋊C4—22no—
57C2×(C2×D11)⋊C4—21no—
58C2×(C2×D11)⋊C4—22no—
59C2×C4⋊Dic11—22no—
60C2×C4⋊Dic11C2311yescharacteristic
61C2×C4⋊Dic11C2312yes—
62C2×Dic11⋊C4—22no—
63C2×Dic11⋊C4—22no—
64C2×Dic11⋊C4—22no—
65C2×Dic11⋊C4—21no—
66C2×C4×Dic11D412yes—
67C2×C4×Dic11C2311yescharacteristic
68C22×C11⋊C8C2312yes—
69#66948—24no—
70C4⋊C4×D11—216no—
71C4⋊C4×D11—24no—
72C4⋊C4×D11—24no—
73#66943—24no—
74#66943D418yescomplemented
75#66942—216no—
76C42×D11—24no—
77#66923—24no—
78C11×#103—24no—
79C11×#95—22no—
80#66899—24no—
81C11⋊#95—22no—
82#66885—24no—
83(C2×D11)⋊C8—24no—
84C8×Dic11—24no—
85#66873—24no—
86#25907—111nomaximal, Sylow
87C23×D11—21no—
88C23×D11C2×D411yescharacteristic
89C2×Q8×C11—22no—
90C2×Q8×C11—22no—
91C2×Q8×C11—21no—
92C2×Q8×C11—21no—
93C22×C4×C11—22no—
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11C2×D412yes—
97C22×C4×C11C2411yescharacteristic
98C22×Dic11—22no—
99C22×Dic11—21no—
100C22×Dic11C2×D412yes—
101C22×Dic11C2×D411yescharacteristic
102C2×D44—22no—
103C2×D44—22no—
104C2×D44—21no—
105C2×D44—21no—
106C2×D44—42no—
107C2×D44—44no—
108C2×C4×D11—28no—
109C2×C4×D11—24no—
110C2×C4×D11—24no—
111C2×C4×D11—22no—
112C2×C4×D11—21no—
113C2×C4×D11—21no—
114C2×C4×D11—42no—
115C2×C4×D11—44no—
116C2×C4×D11—44no—
117C2×C4×D11#4114yes—
118C2×C8×C11—22no—
119C2×C8×C11—22no—
120C2×C8×C11—22no—
121C11×C4⋊C4—28no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4C2×D414yes—
125C42×C11—22no—
126(C2×D11)⋊C4—44no—
127(C2×D11)⋊C4—44no—
128(C2×D11)⋊C4—42no—
129(C2×D11)⋊C4—42no—
130C4⋊Dic11—28no—
131C4⋊Dic11—22no—
132C4⋊Dic11—22no—
133C4⋊Dic11C2×D414yes—
134Dic11⋊C4—28no—
135Dic11⋊C4—28no—
136Dic11⋊C4—28no—
137Dic11⋊C4—42no—
138C4×Dic11—24no—
139C4×Dic11C2×D414yes—
140C2×C11⋊C8—22no—
141C2×C11⋊C8—22no—
142C2×C11⋊C8—22no—
143C22×#125—111no—
144C2×#488—112no—
145#2850—111no—
146#2026—111no—
147#2026D1111yescharacteristic, complemented
148#2025—111no—
149#2025—111no—
150#1991—112no—
151#1874—112no—
152#1872—112no—
153C4×C22⋊C8—111no—
154C23×C11C22×D411yescharacteristic
155C22×D11—21no—
156C22×D11—21no—
157C22×D11—22no—
158C22×D11—41no—
159C22×D11—41no—
160C22×D11—41no—
161C22×D11—42no—
162C22×D11—42no—
163C22×D11#12412yes—
164C22×D11#13514yes—
165Q8×C11—42no—
166Q8×C11—42no—
167C2×C4×C11—22no—
168C2×C4×C11—24no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—42no—
178C2×C4×C11C22×D412yes—
179C2×C4×C11C2×#4112yes—
180C2×C4×C112−1+411yescharacteristic
181C2×C4×C112−1+411yescharacteristic
182C2×Dic11—21no—
183C2×Dic11—21no—
184C2×Dic11—22no—
185C2×Dic11—22no—
186C2×Dic11—24no—
187C2×Dic11—42no—
188C2×Dic11—42no—
189C2×Dic11—41no—
190C2×Dic11—42no—
191C2×Dic11#12014yes—
192C2×Dic11#12412yes—
193D44—42no—
194D44—42no—
195D44—84no—
196C4×D11—24no—
197C4×D11—24no—
198C4×D11—48no—
199C4×D11—416no—
200C8×C11—42no—
201C11⋊C8—42no—
202C2×#125—112no—
203C2×#125—111no—
204C2×#125—222no—
205C2×#125—228no—
206C2×#125C2×D1111yescharacteristic
207C2×#124—111no—
208C2×C22⋊Q8—111no—
209C2×#121—111no—
210C22×C4⋊C4—112no—
211C22×C4⋊C4—222no—
212C22×C42—111no—
213#488—228no—
214C2×#103—112no—
215C2×#103C2×D1112yes—
216C2×#102—112no—
217C2×#102—112no—
218C2×C22⋊C8—112no—
219C2×C4×C8—112no—
220#391C2×D1111yescharacteristic
221#390—111no—
222#388—222no—
223#386—222no—
224#382—111no—
225#340—112no—
226#340—112no—
227#340—112no—
228#340C2×D1112yes—
229#336—111no—
230#336C2×D1111yescharacteristic
231C22×C11C2×#12011yescharacteristic
232C22×C11C2×#12411yescharacteristic
233C22×C11#53611yescharacteristic
234C22×C11C2×#13512yes—
235C22×C11#57512yes—
236C2×D11—22no—
237C2×D11—22no—
238C2×D11—24no—
239C2×D11—24no—
240C2×D11—81no—
241C2×D11—81no—
242C2×D11—81no—
243C2×D11—82no—
244C2×D11—82no—
245C2×D11#48814yescomplemented
246C4×C11—42no—
247C4×C11—44no—
248C4×C11—81no—
249C4×C11—81no—
250C4×C11#54812yes—
251C4×C11#54812yes—
252Dic11—22no—
253Dic11—24no—
254Dic11—44no—
255Dic11—81no—
256C22×Q8C22×D1111yescharacteristic
257C22×D4—111no—
258C22×D4—221no—
259C23×C4—111no—
260C23×C4—112no—
261C23×C4—222no—
262C22×C8—112no—
263C22×C8C22×D1112yes—
264#125—24no—
265#125—118no—
266#125—224no—
267#125—224no—
268#125—2216no—
269#124—224no—
270C22⋊Q8—224no—
271#121—224no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—112no—
274C2×C4⋊C4—111no—
275C2×C4⋊C4—224no—
276C2×C4⋊C4—2216no—
277C2×C4⋊C4—222no—
278C2×C4⋊C4—222no—
279C2×C4⋊C4—222no—
280C2×C4⋊C4—222no—
281C2×C4⋊C4—224no—
282C2×C4⋊C4—221no—
283C2×C4⋊C4C22×D1111yescharacteristic
284C2×C4⋊C4C22×D1112yes—
285C2×C22⋊C4—221no—
286C2×C22⋊C4—222no—
287C2×C22⋊C4—221no—
288C2×C22⋊C4—222no—
289C2×C42—111no—
290C2×C42—112no—
291C2×C42—224no—
292C2×C42C22×D1111yescharacteristic
293#103—24no—
294#103—224no—
295#102—224no—
296#102—224no—
297C22⋊C8—224no—
298C4×C8—224no—
299#95—22no—
300#95—222no—
301C2×C11#243611yescharacteristic
302C2×C11#300212yes—
303C2×C11C2×#48811yescharacteristic
304C2×C11#314211yescharacteristic
305C2×C11#323212yes—
306D11—24no—
307D11—161no—
308C24—111no—
309C24—221no—
310C2×Q8—22no—
311C2×Q8—21no—
312C2×Q8—22no—
313C2×Q8—21no—
314C2×D4—222no—
315C2×D4—221no—
316C2×D4—222no—
317C2×D4—221no—
318C2×D4—442no—
319C2×D4—444no—
320C22×C4—22no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—112no—
324C22×C4—111no—
325C22×C4—114no—
326C22×C4—224no—
327C22×C4—224no—
328C22×C4—228no—
329C22×C4—222no—
330C22×C4—221no—
331C22×C4—221no—
332C22×C4—222no—
333C22×C4—221no—
334C22×C4—442no—
335C22×C4—444no—
336C22×C4—444no—
337C22×C4D4×D1112yes—
338C22×C4C23×D1111yescharacteristic
339C2×C8—22no—
340C2×C8—22no—
341C2×C8—22no—
342C2×C8—222no—
343C2×C8—222no—
344C2×C8—222no—
345C4⋊C4—28no—
346C4⋊C4—22no—
347C4⋊C4—22no—
348C4⋊C4—114no—
349C4⋊C4—228no—
350C4⋊C4—228no—
351C4⋊C4—228no—
352C4⋊C4—228no—
353C4⋊C4—222no—
354C4⋊C4—222no—
355C4⋊C4—442no—
356C4⋊C4D4×D1114yes—
357C22⋊C4—444no—
358C22⋊C4—442no—
359C22⋊C4—444no—
360C22⋊C4—442no—
361C42—22no—
362C42—114no—
363C42—224no—
364C11#2590711yescharacteristic, complemented, Sylow
365C23—114no—
366C23—112no—
367C23—222no—
368C23—221no—
369C23—221no—
370C23—442no—
371C23—442no—
372C23—441no—
373C23—441no—
374C23—441no—
375C23C2×D4×D1111yescharacteristic
376Q8—42no—
377Q8—42no—
378D4—442no—
379D4—442no—
380D4—884no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—24no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—114no—
393C2×C4—112no—
394C2×C4—222no—
395C2×C4—222no—
396C2×C4—221no—
397C2×C4—221no—
398C2×C4—224no—
399C2×C4—224no—
400C2×C4—224no—
401C2×C4—448no—
402C2×C4—4416no—
403C2×C4—442no—
404C2×C4—442no—
405C2×C4—442no—
406C2×C4—441no—
407C2×C4C2×D4×D1112yes—
408C2×C4#6704011yescharacteristic
409C2×C4#41×D1112yes—
410C2×C4#6704311yescharacteristic
411C8—42no—
412C8—442no—
413C22—114no—
414C22—224no—
415C22—222no—
416C22—222no—
417C22—224no—
418C22—882no—
419C22—881no—
420C22—881no—
421C22—881no—
422C22—882no—
423C22D11×#12011yescharacteristic
424C22#1062315911yescharacteristic
425C22D11×#12411yescharacteristic
426C22D11×#13512yes—
427C22#1062330812yes—
428C4—42no—
429C4—44no—
430C4—81no—
431C4—81no—
432C4—224no—
433C4—222no—
434C4—444no—
435C4—881no—
436C4#1062316412yes—
437C4#1062320812yes—
438C2—224no—
439C2—1761no—
440C2#1307226911yescharacteristic
441C2#1307783712yes—
442C2D11×#48811yescharacteristic
443C2#1307901811yescharacteristic
444C2#1307978812yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2026C2
socleC23×C11C22×D4
prime radicalC2×#66948C22
hypercenter#2026D11
hypocenterC11#25907
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2026

Complements

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

NH ≅ G/Ntype
1. C2×D11×#125C2semidirect
2. C2×#10622413C2semidirect
4. #13069767C2semidirect
5. #13069763C2semidirect
6. #13069759C2semidirect
7. #13069579C2semidirect
9. #13068920C2semidirect
10. #13068373C2semidirect
11. C11×#2026C2semidirect
74. #66943D4semidirect
147. #2026D11semidirect
245. C2×D11#488semidirect
364. C11#25907semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1252
C2×#106224132
#130769202
#130697672
#130697632
#130697592
#130695792
#130689322
#130689202
#130683732
C11×#20262
#2590711