Finite Group Databasebeta

← #14810235

Subgroups — #14810235

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×D4×Dic22C211yesmaximal, characteristic
2C2×#10622706C211yesmaximal, characteristic, complemented
3C2×#10622704C211yesmaximal, characteristic, complemented
4#13069819C214yesmaximal, complemented
5#13069539C211yesmaximal, characteristic, complemented
6#13069411C211yesmaximal, characteristic
7#13068550C214yesmaximal, complemented
8C4×#66874C211yesmaximal, characteristic, complemented
9C11×#2563C211yesmaximal, characteristic
10C23×Dic22C2212yes—
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×C4×D4×C11C2211yescharacteristic
13C2×D4×Dic11—21no—
14C2×#66977C2212yes—
15D4×Dic22—24no—
16D4×Dic22—24no—
17C2×#66941—21no—
18C2×#66931—22no—
19C2×#66922C2211yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21C11×#393—22no—
22C11×#390—21no—
23C11×#382—21no—
24C11×#380C2214yes—
25C4×C11×C4⋊C4C2211yescharacteristic
26C2×C22⋊(C11⋊C8)C2214yes—
27#10622706—24no—
28#10622704—24no—
29C2×#66874C2212yes—
30C2×#66874C2212yes—
31C2×#66874C2214yes—
32C2×#66874C2214yes—
33C2×#66871C2212yes—
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36#10622167C2212yes—
37C22×Q8×C11—21no—
38C22×D4×C11D411yescharacteristic
39C23×C4×C11C2312yes—
40C23×Dic11—22no—
41C22×Dic22—22no—
42C22×Dic22—24no—
43C22×Dic22—24no—
44C22×Dic22—28no—
45C22×Dic22—44no—
46C22×Dic22C2312yes—
47C22×Dic22C2311yescharacteristic
48C11×C4⋊Q8—22no—
49C11×C4⋊Q8—22no—
50C4×D4×C11—22no—
51C4×D4×C11—22no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4D411yescharacteristic
54C2×C11×C4⋊C4C2312yes—
55C2×C11×C4⋊C4C2312yes—
56C2×C11×C22⋊C4—24no—
57C2×C11×C22⋊C4D412yes—
58C2×C42×C11—21no—
59C2×C42×C11C2311yescharacteristic
60C2×C22⋊Dic11—22no—
61D4×Dic11—28no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11C2311yescharacteristic
65#66977—24no—
66#66977—24no—
67C2×Dic11⋊C4—21no—
68C2×Dic11⋊C4—22no—
69C2×C4×Dic11—21no—
70C22×C11⋊C8C2312yes—
71C22×C11⋊C8C2312yes—
72#66941—28no—
73#66931—216no—
74#66922—22no—
75#66922D414yes—
76C4×Dic22—22no—
77C4×Dic22D414yes—
78C11×#95—21no—
79C11×#95—24no—
80C22⋊(C11⋊C8)—44no—
81#66874—24no—
82#66874—28no—
83#66874—24no—
84#66874—44no—
85#66871—24no—
86C4⋊(C11⋊C8)—22no—
87C4×C11⋊C8—22no—
88#25888—111nomaximal, Sylow
89C24×C11C2×D412yes—
90C2×Q8×C11—42no—
91C2×Q8×C11—82no—
92C2×D4×C11—22no—
93C2×D4×C11—22no—
94C2×D4×C11Q1614yes—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—24no—
98C22×C4×C11—24no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11C2×D412yes—
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2411yescharacteristic
105C22×Dic11—28no—
106C22×Dic11—21no—
107C22×Dic11—21no—
108C22×Dic11—22no—
109C22×Dic11—48no—
110C2×Dic22—28no—
111C2×Dic22—21no—
112C2×Dic22—22no—
113C2×Dic22—24no—
114C2×Dic22—22no—
115C2×Dic22—24no—
116C2×Dic22—48no—
117C2×Dic22—416no—
118C2×Dic22—48no—
119C2×Dic22—48no—
120C2×Dic22C2×D414yes—
121C2×Dic22C2×D412yes—
122C2×Dic22#4114yes—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—42no—
129C11×C22⋊C4—24no—
130C11×C22⋊C4—84no—
131C42×C11—42no—
132C42×C11C2×D412yes—
133C42×C11C2×D412yes—
134C22⋊Dic11—28no—
135C4⋊Dic11—24no—
136C4⋊Dic11—24no—
137C4⋊Dic11—21no—
138C4⋊Dic11C2×D412yes—
139Dic11⋊C4—28no—
140Dic11⋊C4—24no—
141C4×Dic11—24no—
142C2×C11⋊C8—22no—
143C2×C11⋊C8—22no—
144C2×C11⋊C8—22no—
145C2×C11⋊C8—24no—
146C2×C11⋊C8—22no—
147C2×D4×Q8—111no—
148C2×#487—111no—
149C2×#477—111no—
150#2563D1111yescharacteristic
151#2036—114no—
152#1981—111no—
153#1954—111no—
154#1787—114no—
155C4×#103—111no—
156C23×C11—22no—
157C23×C11—24no—
158C23×C11—22no—
159C23×C11—24no—
160C23×C11C2×Q1614yes—
161C23×C11C22×D411yescharacteristic
162Q8×C11—84no—
163D4×C11—28no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—24no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11—44no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—44no—
175C2×C4×C11#12012yes—
176C2×C4×C11#12012yes—
177C2×C4×C11C2×Q1612yes—
178C2×C4×C11#13712yes—
179C2×C4×C11C22×D411yescharacteristic
180C2×C4×C11C22×D411yescharacteristic
181C2×C4×C11C2×#4112yes—
182C2×C4×C11H(5,𝔽2)12yes—
183C2×Dic11—22no—
184C2×Dic11—24no—
185C2×Dic11—22no—
186C2×Dic11—24no—
187C2×Dic11—416no—
188C2×Dic11—44no—
189C2×Dic11—42no—
190Dic22—22no—
191Dic22—24no—
192Dic22—28no—
193Dic22—416no—
194Dic22—42no—
195Dic22—42no—
196Dic22#12414yes—
197C11⋊C8—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×Q8—111no—
208C2×C4×D4—221no—
209C2×C4×D4C2×D1111yescharacteristic
210#487—224no—
211#477—224no—
212C2×#107—112no—
213C2×C4⋊C8—111no—
214C2×#103—112no—
215C2×#103—114no—
216C2×#103—112no—
217C2×#103—114no—
218C2×C22⋊C8—114no—
219C2×C4×C8—111no—
220#393—22no—
221#390—21no—
222#382—21no—
223#380C2×D1114yes—
224C4×C4⋊C4C2×D1111yescharacteristic
225#340—112no—
226C22×C11—24no—
227C22×C11—28no—
228C22×C11—44no—
229C22×C11—42no—
230C22×C11—42no—
231C22×C11C2×#12011yescharacteristic
232C22×C11#54612yes—
233C22×C11C22×Q1611yescharacteristic
234C22×C11C2×#13711yescharacteristic
235C22×C11#57712yes—
236C4×C11—22no—
237C4×C11—42no—
238C4×C11—82no—
239C4×C11—82no—
240C4×C11#45114yes—
241C4×C11C2×#12411yescharacteristic
242C4×C11#53511yescharacteristic
243C4×C11#54612yes—
244Dic11—24no—
245Dic11—44no—
246Dic11—42no—
247C22×Q8—21no—
248C22×Q8—111no—
249C22×Q8—112no—
250C22×Q8—224no—
251C22×Q8—224no—
252C22×Q8—228no—
253C22×Q8—222no—
254C22×Q8—444no—
255C22×D4C22⋊D1111yescharacteristic
256C23×C4—222no—
257C23×C4C22×D1112yes—
258C22×C8—112no—
259C22×C8—112no—
260C4⋊Q8—22no—
261C4⋊Q8—22no—
262C4⋊Q8—114no—
263C4⋊Q8—228no—
264C4⋊Q8—222no—
265C22⋊Q8—2216no—
266C22⋊Q8—224no—
267C22⋊Q8—224no—
268C4×Q8—114no—
269C4×Q8—222no—
270C4×D4—22no—
271C4×D4—22no—
272C4×D4—228no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—111no—
275C2×C4⋊C4—221no—
276C2×C4⋊C4—221no—
277C2×C4⋊C4—222no—
278C2×C4⋊C4—221no—
279C2×C4⋊C4C22⋊D1111yescharacteristic
280C2×C4⋊C4C22×D1112yes—
281C2×C4⋊C4C22×D1112yes—
282C2×C22⋊C4—24no—
283C2×C22⋊C4—222no—
284C2×C22⋊C4C22⋊D1112yes—
285C2×C42—21no—
286C2×C42—221no—
287C2×C42C22×D1111yescharacteristic
288#107—224no—
289C4⋊C8—222no—
290#103—224no—
291#103—224no—
292#103—228no—
293#103—444no—
294C22⋊C8—444no—
295C4×C8—222no—
296#95—21no—
297#95—24no—
298C2×C11—44no—
299C2×C11#243511yescharacteristic
300C2×C11C2×#45111yescharacteristic
301C2×C11#301011yescharacteristic
302C2×C11#329912yes—
303C2×C11#332912yes—
304C24C2×C22⋊D1112yes—
305C2×Q8—42no—
306C2×Q8—82no—
307C2×Q8—112no—
308C2×Q8—114no—
309C2×Q8—114no—
310C2×Q8—228no—
311C2×Q8—221no—
312C2×Q8—222no—
313C2×Q8—222no—
314C2×Q8—224no—
315C2×Q8—224no—
316C2×Q8—448no—
317C2×Q8—448no—
318C2×Q8—4416no—
319C2×Q8—448no—
320C2×D4—22no—
321C2×D4—22no—
322C2×D4#432614yes—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—24no—
326C22×C4—24no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—221no—
330C22×C4—228no—
331C22×C4—221no—
332C22×C4—222no—
333C22×C4—448no—
334C22×C4C2×C22⋊D1112yes—
335C22×C4C2×C22⋊D1111yescharacteristic
336C22×C4C2×C22⋊D1111yescharacteristic
337C22×C4C23×D1111yescharacteristic
338C2×C8—222no—
339C2×C8—222no—
340C2×C8—222no—
341C2×C8—222no—
342C2×C8—224no—
343C4⋊C4—22no—
344C4⋊C4—22no—
345C4⋊C4—22no—
346C4⋊C4—22no—
347C4⋊C4—22no—
348C4⋊C4—42no—
349C4⋊C4—112no—
350C4⋊C4—228no—
351C4⋊C4—224no—
352C4⋊C4—224no—
353C4⋊C4—224no—
354C4⋊C4—221no—
355C22⋊C4—24no—
356C22⋊C4—84no—
357C22⋊C4—228no—
358C42—42no—
359C42—224no—
360C42D4×D1112yes—
361C42D4×D1112yes—
362C11#2588811yescharacteristic, complemented, Sylow
363C23—22no—
364C23—22no—
365C23—24no—
366C23—24no—
367C23C2×#432614yes—
368C23C22×C22⋊D1111yescharacteristic
369Q8—84no—
370Q8—114no—
371Q8—222no—
372Q8—224no—
373Q8—228no—
374Q8—4416no—
375Q8—442no—
376Q8—442no—
377D4—28no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—24no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—44no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—44no—
389C2×C4—222no—
390C2×C4—224no—
391C2×C4—222no—
392C2×C4—224no—
393C2×C4—4416no—
394C2×C4—444no—
395C2×C4—442no—
396C2×C4#6699012yes—
397C2×C4#6699012yes—
398C2×C4C2×#432612yes—
399C2×C4#6700412yes—
400C2×C4C2×D4×D1111yescharacteristic
401C2×C4C2×D4×D1111yescharacteristic
402C2×C4#41×D1112yes—
403C2×C4#6704212yes—
404C8—442no—
405C8—442no—
406C22—24no—
407C22—28no—
408C22—44no—
409C22—42no—
410C22—42no—
411C22C2×#6699011yescharacteristic
412C22C22×#432611yescharacteristic
413C22C2×#6700411yescharacteristic
414C22#1062336012yes—
415C22#1062336712yes—
416C4—22no—
417C4—42no—
418C4—82no—
419C4—82no—
420C4—224no—
421C4—444no—
422C4—442no—
423C4#1062266314yes—
424C4D11×#12411yescharacteristic
425C4#1062320511yescharacteristic
426C4#1062320712yes—
427C2—44no—
428C2#1307226411yescharacteristic
429C2C2×#1062266311yescharacteristic
430C2#1307790011yescharacteristic
431C2#1308048612yes—
432C2#1308090412yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2563C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
hypercenter#2563D11
hypocenterC11#25888
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2563

Complements

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

NH ≅ G/Ntype
2. C2×#10622706C2semidirect
3. C2×#10622704C2semidirect
4. #13069819C2semidirect
5. #13069539C2semidirect
7. #13068550C2semidirect
8. C4×#66874C2semidirect
362. C11#25888semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic222
C2×#106227062
C2×#106227042
#130698192
#130695392
#130694112
#130685502
C4×#668742
C11×#25632
#2588811