Finite Group Databasebeta

← #14810233

Subgroups — #14810233

Order 2816.

1282 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×D44C211yesmaximal, characteristic
2C2×#10622706C211yesmaximal, characteristic, complemented
3#13073790C211yesmaximal, characteristic
4#13069821C214yesmaximal, complemented
5#13069538C211yesmaximal, characteristic, complemented
6#13069409C211yesmaximal, characteristic
7#13068549C214yesmaximal, complemented
8C4×#66899C211yesmaximal, characteristic, complemented
9C2×C11×#477C211yesmaximal, characteristic, complemented
10C22×Q8×D11C2212yes—
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×C4×Q8×C11C2211yescharacteristic
13Q8×D44—24no—
14Q8×D44—24no—
15C2×#66950—22no—
16C2×#66950C2212yes—
17C2×C4×D44—21no—
18C2×C4×D44C2211yescharacteristic
19C2×#66922—21no—
20C2×#66922C2211yescharacteristic
21C11×#477—24no—
22C2×C11×#107C2212yes—
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×#103C2212yes—
25#10622844—22no—
26C2×#66899C2212yes—
27C2×(C2×D11)⋊C8C2214yes—
28C2×#66880C2214yes—
29#10622706—24no—
30#10622601—21no—
31#10622600C2214yes—
32#10622590—21no—
33C2×#66874C2214yes—
34C4×C4⋊Dic11C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36#10622167C2212yes—
37C22×Q8×C11—21no—
38C22×Q8×C11C2311yescharacteristic
39C2×Q8×D11—24no—
40C2×Q8×D11—24no—
41C2×Q8×D11—28no—
42C2×Q8×D11—44no—
43C22×D44D411yescharacteristic
44C22×C4×D11—22no—
45C22×C4×D11C2312yes—
46C22×Dic22—22no—
47C22×Dic22C2312yes—
48C22×C8×C11C2312yes—
49C11×C4⋊Q8—22no—
50C11×C4⋊Q8—22no—
51C4×Q8×C11—22no—
52C4×Q8×C11D414yes—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4C2312yes—
56C2×C11×C4⋊C4C2311yescharacteristic
57C2×C42×C11—21no—
58C2×C42×C11C2311yescharacteristic
59C2×(C2×D11)⋊C4—22no—
60C2×(C2×D11)⋊C4—24no—
61C2×(C2×D11)⋊C4D412yes—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11—22no—
65C2×C4⋊Dic11D411yescharacteristic
66C2×C4⋊Dic11C2312yes—
67C2×C4×Dic11—21no—
68C22×C11⋊C8C2312yes—
69#66950—216no—
70#66950—24no—
71#66950—24no—
72C4×D44—28no—
73C4×D44—22no—
74C4×D44—22no—
75#66922—28no—
76#66922—22no—
77#66922D414yes—
78C11×#107—24no—
79C11×C4⋊C8—22no—
80C11×#103—24no—
81#66899—24no—
82C11⋊#95—21no—
83C11⋊#95—24no—
84(C2×D11)⋊C8—44no—
85#66880—44no—
86#66874—28no—
87C4×C11⋊C8—22no—
88#25888—111nomaximal, Sylow
89C23×D11C2×D412yes—
90C2×Q8×C11—21no—
91C2×Q8×C11—22no—
92C2×Q8×C11—42no—
93C2×Q8×C11—82no—
94C2×Q8×C11C2×D412yes—
95C2×Q8×C11#4114yes—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—22no—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2411yescharacteristic
102C22×Dic11—22no—
103C22×Dic11—22no—
104C22×Dic11C2×D412yes—
105Q8×D11—416no—
106Q8×D11—48no—
107Q8×D11—48no—
108C2×D44—22no—
109C2×D44—22no—
110C2×D44Q1614yes—
111C2×C4×D11—28no—
112C2×C4×D11—22no—
113C2×C4×D11—22no—
114C2×C4×D11—24no—
115C2×C4×D11—24no—
116C2×C4×D11—48no—
117C2×Dic22—28no—
118C2×Dic22—22no—
119C2×Dic22—24no—
120C2×Dic22—24no—
121C2×Dic22—48no—
122C2×Dic22C2×D414yes—
123C2×C8×C11—22no—
124C2×C8×C11—24no—
125C11×C4⋊C4—24no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—42no—
130C11×C4⋊C4C2×D412yes—
131C42×C11—24no—
132C42×C11C2×D412yes—
133C42×C11C2×D412yes—
134(C2×D11)⋊C4—28no—
135(C2×D11)⋊C4—24no—
136(C2×D11)⋊C4—84no—
137C4⋊Dic11—28no—
138C4⋊Dic11—22no—
139C4⋊Dic11—24no—
140C4⋊Dic11—24no—
141C4⋊Dic11—22no—
142C4⋊Dic11—22no—
143C4×Dic11—42no—
144C2×C11⋊C8—22no—
145C2×C11⋊C8—22no—
146C2×C11⋊C8—22no—
147C2×D4×Q8—111no—
148C2×#487—111no—
149C2×#477D1111yescharacteristic, complemented
150#2563—111no—
151#2036—114no—
152#1981—111no—
153#1954—111no—
154#1787—114no—
155C4×#103—111no—
156C23×C11C22×D411yescharacteristic
157C22×D11—22no—
158C22×D11—24no—
159C22×D11—22no—
160C22×D11—24no—
161C22×D11C2×Q1614yes—
162Q8×C11—22no—
163Q8×C11—24no—
164Q8×C11—84no—
165Q8×C11#12414yes—
166C2×C4×C11—22no—
167C2×C4×C11—24no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—44no—
173C2×C4×C11#12012yes—
174C2×C4×C11#12012yes—
175C2×C4×C11C2×Q1612yes—
176C2×C4×C11#13712yes—
177C2×C4×C11C22×D411yescharacteristic
178C2×C4×C11C22×D411yescharacteristic
179C2×C4×C11C2×#4112yes—
180C2×C4×C11H(5,𝔽2)12yes—
181C2×Dic11—22no—
182C2×Dic11—24no—
183C2×Dic11—24no—
184C2×Dic11—44no—
185C2×Dic11—42no—
186C2×Dic11—42no—
187C2×Dic11—42no—
188D44—28no—
189C4×D11—416no—
190C4×D11—42no—
191C4×D11—42no—
192C4×D11—44no—
193Dic22—28no—
194Dic22—416no—
195Dic22—42no—
196Dic22—42no—
197C8×C11—42no—
198C11⋊C8—42no—
199C23×Q8—112no—
200D4×Q8—224no—
201D4×Q8—224no—
202C2×C4⋊Q8—111no—
203C2×C4⋊Q8—221no—
204C2×C4⋊Q8C2×D1111yescharacteristic
205C2×C22⋊Q8—112no—
206C2×C22⋊Q8—222no—
207C2×C4×Q8C2×D1111yescharacteristic
208C2×C4×D4—111no—
209C2×C4×D4—221no—
210#487—224no—
211#477—24no—
212C2×#107C2×D1112yes—
213C2×C4⋊C8C2×D1111yescharacteristic
214C2×#103—112no—
215C2×#103—114no—
216C2×#103—114no—
217C2×#103C2×D1112yes—
218C2×C22⋊C8—114no—
219C2×C4×C8—111no—
220#393—222no—
221#390—221no—
222#382—221no—
223#380—114no—
224C4×C4⋊C4—111no—
225#340—112no—
226C22×C11C2×#12011yescharacteristic
227C22×C11#54612yes—
228C22×C11C22×Q1611yescharacteristic
229C22×C11C2×#13711yescharacteristic
230C22×C11#57712yes—
231C2×D11—24no—
232C2×D11—28no—
233C2×D11—44no—
234C2×D11—42no—
235C2×D11—42no—
236C4×C11—24no—
237C4×C11—22no—
238C4×C11—42no—
239C4×C11—82no—
240C4×C11#45114yes—
241C4×C11C2×#12411yescharacteristic
242C4×C11#53511yescharacteristic
243C4×C11#54612yes—
244Dic11—44no—
245Dic11—42no—
246Dic11—82no—
247C22×Q8—21no—
248C22×Q8—112no—
249C22×Q8—222no—
250C22×Q8—224no—
251C22×Q8—224no—
252C22×Q8—228no—
253C22×Q8—444no—
254C22×Q8C22×D1111yescharacteristic
255C22×D4—111no—
256C23×C4—112no—
257C23×C4—222no—
258C22×C8—112no—
259C22×C8C22×D1112yes—
260C4⋊Q8—22no—
261C4⋊Q8—22no—
262C4⋊Q8—114no—
263C4⋊Q8—228no—
264C4⋊Q8—222no—
265C22⋊Q8—224no—
266C22⋊Q8—2216no—
267C22⋊Q8—224no—
268C4×Q8—22no—
269C4×Q8C22⋊D1114yes—
270C4×D4—228no—
271C4×D4—222no—
272C4×D4—222no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—111no—
276C2×C4⋊C4—112no—
277C2×C4⋊C4—222no—
278C2×C4⋊C4—221no—
279C2×C4⋊C4—221no—
280C2×C4⋊C4C22×D1112yes—
281C2×C4⋊C4C22×D1111yescharacteristic
282C2×C22⋊C4—112no—
283C2×C22⋊C4—222no—
284C2×C22⋊C4—224no—
285C2×C42—21no—
286C2×C42—221no—
287C2×C42C22×D1111yescharacteristic
288#107—24no—
289C4⋊C8—22no—
290#103—24no—
291#103—228no—
292#103—224no—
293#103—444no—
294C22⋊C8—444no—
295C4×C8—222no—
296#95—224no—
297#95—221no—
298C2×C11#243511yescharacteristic
299C2×C11C2×#45111yescharacteristic
300C2×C11#301011yescharacteristic
301C2×C11#329912yes—
302C2×C11#332912yes—
303D11—44no—
304C24—112no—
305C2×Q8—21no—
306C2×Q8—22no—
307C2×Q8—42no—
308C2×Q8—82no—
309C2×Q8—114no—
310C2×Q8—228no—
311C2×Q8—222no—
312C2×Q8—224no—
313C2×Q8—224no—
314C2×Q8—448no—
315C2×Q8—4416no—
316C2×Q8—448no—
317C2×Q8—448no—
318C2×Q8#434314yes—
319C2×Q8C2×C22⋊D1112yes—
320C2×D4—114no—
321C2×D4—222no—
322C2×D4—222no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—22no—
326C22×C4—112no—
327C22×C4—228no—
328C22×C4—222no—
329C22×C4—222no—
330C22×C4—224no—
331C22×C4—224no—
332C22×C4—222no—
333C22×C4—222no—
334C22×C4—448no—
335C22×C4D4×D1111yescharacteristic
336C22×C4D4×D1111yescharacteristic
337C22×C4C23×D1111yescharacteristic
338C2×C8—24no—
339C2×C8—22no—
340C2×C8—222no—
341C2×C8—222no—
342C2×C8—222no—
343C4⋊C4—24no—
344C4⋊C4—21no—
345C4⋊C4—22no—
346C4⋊C4—22no—
347C4⋊C4—42no—
348C4⋊C4—228no—
349C4⋊C4—222no—
350C4⋊C4—224no—
351C4⋊C4—224no—
352C4⋊C4—222no—
353C4⋊C4—222no—
354C4⋊C4C2×C22⋊D1112yes—
355C22⋊C4—228no—
356C22⋊C4—224no—
357C22⋊C4—884no—
358C42—24no—
359C42—442no—
360C42D4×D1112yes—
361C42C2×C22⋊D1112yes—
362C11#2588811yescharacteristic, complemented, Sylow
363C23—114no—
364C23—222no—
365C23—224no—
366C23—222no—
367C23—224no—
368C23C2×D4×D1111yescharacteristic
369Q8—22no—
370Q8—24no—
371Q8—84no—
372Q8—228no—
373Q8—4416no—
374Q8—442no—
375Q8—442no—
376Q8#6700014yes—
377D4—228no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—24no—
381C2×C4—22no—
382C2×C4—42no—
383C2×C4—44no—
384C2×C4—42no—
385C2×C4—222no—
386C2×C4—224no—
387C2×C4—224no—
388C2×C4—4416no—
389C2×C4—444no—
390C2×C4—442no—
391C2×C4—442no—
392C2×C4—444no—
393C2×C4—442no—
394C2×C4—442no—
395C2×C4—442no—
396C2×C4Q16×D1112yes—
397C2×C4#6697112yes—
398C2×C4#6699012yes—
399C2×C4#6699012yes—
400C2×C4C2×D4×D1111yescharacteristic
401C2×C4C2×#434312yes—
402C2×C4#6704212yes—
403C2×C4C22×C22⋊D1111yescharacteristic
404C8—42no—
405C8—442no—
406C22—224no—
407C22—228no—
408C22—444no—
409C22—442no—
410C22—442no—
411C22#1062316112yes—
412C22C2×Q16×D1111yescharacteristic
413C22C2×#6697111yescharacteristic
414C22#1062330612yes—
415C22C2×#6699011yescharacteristic
416C4—24no—
417C4—22no—
418C4—42no—
419C4—82no—
420C4—442no—
421C4—444no—
422C4—882no—
423C4#1062279914yes—
424C4#1062316112yes—
425C4C2×#6700011yescharacteristic
426C4#1062336111yescharacteristic
427C2—444no—
428C2#1307226811yescharacteristic
429C2C2×#1062279911yescharacteristic
430C2#1307790111yescharacteristic
431C2#1308048912yes—
432C2#1308090712yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#477C2
socleC23×C11C22×D4
prime radicalC22×D44D4
hypercenterC2×#477D11
hypocenterC11#25888
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
2. C2×#10622706C2semidirect
4. #13069821C2semidirect
5. #13069538C2semidirect
7. #13068549C2semidirect
8. C4×#66899C2semidirect
9. C2×C11×#477C2semidirect
149. C2×#477D11semidirect
362. C11#25888semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×D442
C2×#106227062
#130737902
#130698212
#130695382
#130694092
#130685492
C4×#668992
C2×C11×#4772
#2588811