Finite Group Databasebeta

← #14810232

Subgroups — #14810232

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×#10622294C211yesmaximal, characteristic, complemented
3C2×#10622634C211yesmaximal, characteristic, complemented
4#13073785C211yesmaximal, characteristic
5#13069822C214yesmaximal, complemented
6#13069539C211yesmaximal, characteristic, complemented
7#13069410C211yesmaximal, characteristic
8#13068549C214yesmaximal, complemented
9C4×C11×#103C211yesmaximal, characteristic, complemented
10C22×Q8×D11C2212yes—
11C2×C4×Q8×C11C2211yescharacteristic
12Q8×D44—24no—
13Q8×D44—24no—
14C2×#66950—22no—
15C2×#66950C2212yes—
16C2×C4×D44—21no—
17C2×C4×D44C2211yescharacteristic
18C2×#66922—21no—
19C2×#66922C2211yescharacteristic
20C2×#66922C2211yescharacteristic
21C2×C11×#103C2212yes—
22C2×C4×C8×C11C2211yescharacteristic
23C4×C11×C4⋊C4C2211yescharacteristic
24C2×#66899C2212yes—
25C2×(C2×D11)⋊C8C2214yes—
26C2×#66880C2214yes—
27#10622634—24no—
28#10622600C2214yes—
29C2×#66874C2214yes—
30C2×#66871C2212yes—
31#10622552—21no—
32#10622549—21no—
33C2×C4⋊(C11⋊C8)C2211yescharacteristic
34#10622294—24no—
35#10622286—22no—
36C11×#340C2212yes—
37C22×Q8×C11C2311yescharacteristic
38C2×Q8×D11—24no—
39C2×Q8×D11—24no—
40C2×Q8×D11—28no—
41C2×Q8×D11—44no—
42C22×D44D411yescharacteristic
43C22×C4×D11—22no—
44C22×C4×D11C2312yes—
45C22×Dic22—22no—
46C22×Dic22—21no—
47C22×Dic22C2312yes—
48C22×C8×C11C2312yes—
49C4×Q8×C11—22no—
50C4×Q8×C11D414yes—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4C2312yes—
53C2×C11×C4⋊C4C2311yescharacteristic
54C2×C42×C11—21no—
55C2×C42×C11—21no—
56C2×C42×C11C2311yescharacteristic
57C2×(C2×D11)⋊C4—22no—
58C2×(C2×D11)⋊C4—24no—
59C2×(C2×D11)⋊C4D412yes—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11—22no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11D411yescharacteristic
65C2×C4⋊Dic11C2312yes—
66C22×C11⋊C8C2312yes—
67#66950—216no—
68#66950—24no—
69#66950—24no—
70C4×D44—28no—
71C4×D44—22no—
72C4×D44—22no—
73#66922—28no—
74#66922—22no—
75#66922—22no—
76#66922—22no—
77#66922D414yes—
78C11×#103—24no—
79C4×C8×C11—22no—
80C11×#95—21no—
81#66899—24no—
82C11⋊#95—24no—
83(C2×D11)⋊C8—44no—
84#66880—28no—
85#66874—44no—
86#66871—24no—
87C4⋊(C11⋊C8)—22no—
88#25888—111nomaximal, Sylow
89C23×D11C2×D412yes—
90C2×Q8×C11—21no—
91C2×Q8×C11—22no—
92C2×Q8×C11C2×D412yes—
93C2×Q8×C11#4114yes—
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—22no—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2411yescharacteristic
100C22×Dic11—22no—
101C22×Dic11—22no—
102C22×Dic11C2×D412yes—
103Q8×D11—416no—
104Q8×D11—48no—
105Q8×D11—48no—
106C2×D44—22no—
107C2×D44—22no—
108C2×D44Q1614yes—
109C2×C4×D11—28no—
110C2×C4×D11—22no—
111C2×C4×D11—22no—
112C2×C4×D11—24no—
113C2×C4×D11—24no—
114C2×C4×D11—48no—
115C2×Dic22—28no—
116C2×Dic22—22no—
117C2×Dic22—24no—
118C2×Dic22—24no—
119C2×Dic22—48no—
120C2×Dic22—42no—
121C2×Dic22—82no—
122C2×Dic22C2×D414yes—
123C2×C8×C11—22no—
124C2×C8×C11—22no—
125C2×C8×C11—22no—
126C11×C4⋊C4—24no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4C2×D412yes—
131C42×C11—24no—
132C42×C11—42no—
133C42×C11C2×D412yes—
134C42×C11C2×D412yes—
135(C2×D11)⋊C4—28no—
136(C2×D11)⋊C4—24no—
137(C2×D11)⋊C4—84no—
138C4⋊Dic11—28no—
139C4⋊Dic11—22no—
140C4⋊Dic11—24no—
141C4⋊Dic11—24no—
142C4⋊Dic11—22no—
143C4⋊Dic11—22no—
144C4⋊Dic11—42no—
145C2×C11⋊C8—22no—
146C2×C11⋊C8—24no—
147C2×D4×Q8—111no—
148C2×#487—111no—
149C2×#477—111no—
150#2563—111no—
151#2036—114no—
152#1981—111no—
153#1954—111no—
154#1787—114no—
155C4×#103D1111yescharacteristic, complemented
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#12414yes—
165C2×C4×C11—22no—
166C2×C4×C11—24no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—42no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
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—44no—
187D44—28no—
188C4×D11—416no—
189C4×D11—42no—
190C4×D11—42no—
191C4×D11—44no—
192Dic22—28no—
193Dic22—416no—
194Dic22—42no—
195Dic22—42no—
196Dic22—84no—
197C8×C11—42no—
198C11⋊C8—42no—
199C23×Q8—112no—
200D4×Q8—224no—
201D4×Q8—224no—
202C2×C4⋊Q8—111no—
203C2×C4⋊Q8—111no—
204C2×C4⋊Q8—221no—
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—224no—
212C2×#107—112no—
213C2×C4⋊C8—111no—
214C2×#103—112no—
215C2×#103—114no—
216C2×#103—114no—
217C2×#103C2×D1112yes—
218C2×C22⋊C8—114no—
219C2×C4×C8C2×D1111yescharacteristic
220#393—222no—
221#390—221no—
222#382—221no—
223#380—114no—
224C4×C4⋊C4C2×D1111yescharacteristic
225#340C2×D1112yes—
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—112no—
248C22×Q8—222no—
249C22×Q8—224no—
250C22×Q8—224no—
251C22×Q8—221no—
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—114no—
261C4⋊Q8—228no—
262C4⋊Q8—222no—
263C4⋊Q8—222no—
264C4⋊Q8—222no—
265C22⋊Q8—224no—
266C22⋊Q8—2216no—
267C22⋊Q8—224no—
268C4×Q8—22no—
269C4×Q8D4414yes—
270C4×D4—228no—
271C4×D4—222no—
272C4×D4—222no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—111no—
275C2×C4⋊C4—112no—
276C2×C4⋊C4—222no—
277C2×C4⋊C4—221no—
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—21no—
287C2×C42C22×D1111yescharacteristic
288#107—224no—
289C4⋊C8—222no—
290#103—24no—
291#103—228no—
292#103—224no—
293#103—444no—
294C22⋊C8—444no—
295C4×C8—22no—
296#95—21no—
297#95—224no—
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—114no—
308C2×Q8—228no—
309C2×Q8—222no—
310C2×Q8—224no—
311C2×Q8—224no—
312C2×Q8—448no—
313C2×Q8—4416no—
314C2×Q8—448no—
315C2×Q8—448no—
316C2×Q8—442no—
317C2×Q8—882no—
318C2×Q8C2×D4412yes—
319C2×Q8#433914yes—
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—222no—
332C22×C4—224no—
333C22×C4—222no—
334C22×C4—448no—
335C22×C4D4×D1111yescharacteristic
336C22×C4D4×D1111yescharacteristic
337C22×C4C23×D1111yescharacteristic
338C2×C8—22no—
339C2×C8—22no—
340C2×C8—22no—
341C2×C8—222no—
342C2×C8—224no—
343C4⋊C4—24no—
344C4⋊C4—21no—
345C4⋊C4—22no—
346C4⋊C4—22no—
347C4⋊C4—228no—
348C4⋊C4—222no—
349C4⋊C4—224no—
350C4⋊C4—224no—
351C4⋊C4—222no—
352C4⋊C4—222no—
353C4⋊C4—442no—
354C4⋊C4C2×D4412yes—
355C22⋊C4—228no—
356C22⋊C4—224no—
357C22⋊C4—884no—
358C42—24no—
359C42—42no—
360C42C2×D4412yes—
361C42D4×D1112yes—
362C11#2588811yescharacteristic, complemented, Sylow
363C23—114no—
364C23—222no—
365C23—222no—
366C23—224no—
367C23—224no—
368C23C2×D4×D1111yescharacteristic
369Q8—22no—
370Q8—24no—
371Q8—228no—
372Q8—4416no—
373Q8—442no—
374Q8—442no—
375Q8—884no—
376Q8#6692814yes—
377D4—228no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—24no—
381C2×C4—22no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—222no—
387C2×C4—224no—
388C2×C4—224no—
389C2×C4—4416no—
390C2×C4—444no—
391C2×C4—442no—
392C2×C4—442no—
393C2×C4—444no—
394C2×C4—442no—
395C2×C4—444no—
396C2×C4#6693512yes—
397C2×C4#6693512yes—
398C2×C4#6696812yes—
399C2×C4Q16×D1112yes—
400C2×C4C22×D4411yescharacteristic
401C2×C4C2×#433912yes—
402C2×C4C2×D4×D1111yescharacteristic
403C2×C4#6704212yes—
404C8—42no—
405C8—442no—
406C22—224no—
407C22—228no—
408C22—444no—
409C22—442no—
410C22—442no—
411C22C2×#6693511yescharacteristic
412C22#1062308112yes—
413C22C2×#6696811yescharacteristic
414C22C2×Q16×D1111yescharacteristic
415C22#1062330112yes—
416C4—24no—
417C4—22no—
418C4—42no—
419C4—82no—
420C4—442no—
421C4—444no—
422C4—882no—
423C4#1062242114yes—
424C4C2×#6692811yescharacteristic
425C4#1062305611yescharacteristic
426C4#1062308112yes—
427C2—444no—
428C2#1307226711yescharacteristic
429C2C2×#1062242111yescharacteristic
430C2#1307790511yescharacteristic
431C2#1308049412yes—
432C2#1308091212yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×#103C2
socleC23×C11C22×D4
prime radicalC22×D44D4
hypercenterC4×#103D11
hypocenterC11#25888
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#103

Complements

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

NH ≅ G/Ntype
2. C2×#10622294C2semidirect
3. C2×#10622634C2semidirect
5. #13069822C2semidirect
6. #13069539C2semidirect
8. #13068549C2semidirect
9. C4×C11×#103C2semidirect
155. C4×#103D11semidirect
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×#106222942
C2×#106226342
#130737852
#130698222
#130695392
#130694102
#130685492
C4×C11×#1032
#2588811