Finite Group Databasebeta

← #14763218

Subgroups — #14763218

Order 2816.

1474 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13070999C212yesmaximal
2#13069602C218yesmaximal, complemented
3#13068690C214yesmaximal
4C22×C11×C22⋊Q8C211yesmaximal, characteristic
5C23×Q8×C11C411yescharacteristic, complemented
6C24×C4×C11C2211yescharacteristic
7C2×C11×C22⋊Q8—22no—
8C2×C11×C22⋊Q8—22no—
9C2×C11×C22⋊Q8—22no—
10C2×C11×C22⋊Q8—22no—
11C2×C11×C22⋊Q8C414yescomplemented
12C2×C11×C22⋊Q8C2214yes—
13C22×C11×C4⋊C4C411yescharacteristic, complemented
14C22×C11×C4⋊C4C412yescomplemented
15C22×C11×C22⋊C4C2212yes—
16C2×#66979—22no—
17#10622860C2214yes—
18#10622825—22no—
19#10622825C2214yes—
20#10622824—22no—
21C4×C22⋊Dic11—22no—
22C4×C22⋊Dic11C2214yes—
23#10622164C22116yes—
24C25×C11C2311yescharacteristic
25C22×Q8×C11—22no—
26C22×Q8×C11—21no—
27C22×Q8×C11—21no—
28C22×Q8×C11—44no—
29C22×Q8×C11C2×C414yes—
30C23×C4×C11—44no—
31C23×C4×C11C2×C411yescharacteristic
32C23×C4×C11C2×C412yes—
33C23×C4×C11C2×C412yes—
34C23×C4×C11C2×C411yescharacteristic
35C23×C4×C11C2×C412yes—
36C23×C4×C11D412yes—
37C23×C4×C11D412yes—
38C23×C4×C11D412yes—
39C23×C4×C11D412yes—
40C23×C4×C11C2312yes—
41C11×C22⋊Q8—24no—
42C11×C22⋊Q8—24no—
43C11×C22⋊Q8—24no—
44C11×C22⋊Q8—24no—
45C11×C22⋊Q8—24no—
46C11×C22⋊Q8—24no—
47C11×C22⋊Q8—24no—
48C11×C22⋊Q8—24no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—24no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4C2×C414yes—
56C2×C11×C4⋊C4C2×C418yes—
57C2×C11×C22⋊C4—24no—
58C2×C11×C22⋊C4—24no—
59C2×C11×C22⋊C4C2×C414yes—
60C2×C11×C22⋊C4C2314yes—
61C2×C22⋊Dic11—24no—
62C2×C22⋊Dic11—24no—
63C2×C22⋊Dic11C2318yes—
64#66979—48no—
65C2×C4⋊Dic11—24no—
66C2×C4×Dic11—24no—
67C11⋊#95—24no—
68C11⋊#95—24no—
69#21825—111nomaximal, Sylow
70C24×C11—24no—
71C24×C11—42no—
72C24×C11—42no—
73C24×C11C22×C411yescharacteristic
74C24×C11C22×C411yescharacteristic
75C24×C11C2×D412yes—
76C24×C11C2×D412yes—
77C24×C11C2411yescharacteristic
78C2×Q8×C11—24no—
79C2×Q8×C11—24no—
80C2×Q8×C11—44no—
81C2×Q8×C11—48no—
82C2×Q8×C11—48no—
83C2×Q8×C11—44no—
84C22×C4×C11—28no—
85C22×C4×C11—24no—
86C22×C4×C11—22no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—44no—
91C22×C4×C11—44no—
92C22×C4×C11—44no—
93C22×C4×C11—44no—
94C22×C4×C11—42no—
95C22×C4×C11—44no—
96C22×C4×C11—44no—
97C22×C4×C11—44no—
98C22×C4×C11C22⋊C412yes—
99C22×C4×C11C22⋊C411yescharacteristic
100C22×C4×C11C22⋊C412yes—
101C22×C4×C11C22⋊C412yes—
102C22×C4×C11C22⋊C412yes—
103C22×C4×C11C22⋊C411yescharacteristic
104C22×C4×C11C22⋊C411yescharacteristic
105C22×C4×C11C22⋊C412yes—
106C22×C4×C11C22⋊C412yes—
107C22×C4×C11C22⋊C411yescharacteristic
108C22×C4×C11C22×C412yes—
109C22×C4×C11C22×C414yes—
110C22×C4×C11C22×C414yes—
111C22×C4×C11C22×C412yes—
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2×D412yes—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D412yes—
116C22×Dic11—28no—
117C11×C4⋊C4—24no—
118C11×C4⋊C4—24no—
119C11×C4⋊C4—28no—
120C11×C4⋊C4—28no—
121C11×C22⋊C4—28no—
122C11×C22⋊C4—28no—
123C22⋊Dic11—216no—
124C22⋊Dic11—48no—
125C22⋊Dic11—48no—
126C4⋊Dic11—48no—
127C4×Dic11—48no—
128C22×C22⋊Q8D1111yescharacteristic
129#2280—112no—
130#1996—118no—
131#1819—114no—
132C23×C11—22no—
133C23×C11—22no—
134C23×C11—22no—
135C23×C11—22no—
136C23×C11—24no—
137C23×C11—24no—
138C23×C11—24no—
139C23×C11—24no—
140C23×C11—41no—
141C23×C11—42no—
142C23×C11—41no—
143C23×C11—41no—
144C23×C11—42no—
145C23×C11—41no—
146C23×C11—416no—
147C23×C11C2×C22⋊C412yes—
148C23×C11C2×C22⋊C411yescharacteristic
149C23×C11C2×C22⋊C411yescharacteristic
150C23×C11C23×C411yescharacteristic
151C23×C11C22×D412yes—
152C23×C112−1+414yes—
153Q8×C11—48no—
154Q8×C11—48no—
155C2×C4×C11—24no—
156C2×C4×C11—22no—
157C2×C4×C11—24no—
158C2×C4×C11—24no—
159C2×C4×C11—24no—
160C2×C4×C11—24no—
161C2×C4×C11—24no—
162C2×C4×C11—24no—
163C2×C4×C11—24no—
164C2×C4×C11—24no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11—42no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—44no—
173C2×C4×C11—44no—
174C2×C4×C11—44no—
175C2×C4×C11—44no—
176C2×C4×C11—44no—
177C2×C4×C11—44no—
178C2×C4×C11#9914yes—
179C2×C4×C11C2×C22⋊C412yes—
180C2×C4×C11C2×C22⋊C412yes—
181C2×C4×C11C2×C22⋊C412yes—
182C2×C4×C11C2×C22⋊C412yes—
183C2×Dic11—48no—
184C2×Dic11—48no—
185C2×Dic11—48no—
186C23×Q8Dic1111yescharacteristic, complemented
187C24×C4C2×D1111yescharacteristic
188C2×C22⋊Q8—22no—
189C2×C22⋊Q8—22no—
190C2×C22⋊Q8—22no—
191C2×C22⋊Q8—22no—
192C2×C22⋊Q8Dic1114yescomplemented
193C2×C22⋊Q8C2×D1114yes—
194C2×#117—222no—
195C22×C4⋊C4Dic1111yescharacteristic, complemented
196C22×C4⋊C4Dic1112yescomplemented
197C22×C22⋊C4C2×D1112yes—
198#381—222no—
199#380—114no—
200#380—222no—
201#379—114no—
202C4×C22⋊C4—114no—
203C4×C22⋊C4—222no—
204#342—1116no—
205C22×C11—28no—
206C22×C11—21no—
207C22×C11—21no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—22no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—22no—
214C22×C11—22no—
215C22×C11—22no—
216C22×C11—22no—
217C22×C11—44no—
218C22×C11—48no—
219C22×C11—48no—
220C22×C11—44no—
221C22×C11C2×#9912yes—
222C22×C11#41012yes—
223C22×C11C22×C22⋊C411yescharacteristic
224C22×C11#51912yes—
225C22×C11#53614yes—
226C4×C11—22no—
227C4×C11—22no—
228C4×C11—22no—
229C4×C11—44no—
230C4×C11—44no—
231C4×C11C2×#9914yes—
232Dic11—88no—
233C25C22×D1111yescharacteristic
234C22×Q8—22no—
235C22×Q8—21no—
236C22×Q8—21no—
237C22×Q8—44no—
238C22×Q8C2×Dic1114yes—
239C23×C4—44no—
240C23×C4C2×Dic1111yescharacteristic
241C23×C4C2×Dic1112yes—
242C23×C4C2×Dic1112yes—
243C23×C4C2×Dic1111yescharacteristic
244C23×C4C2×Dic1112yes—
245C23×C4C22⋊D1112yes—
246C23×C4C22⋊D1112yes—
247C23×C4C22⋊D1112yes—
248C23×C4C22⋊D1112yes—
249C23×C4C22×D1112yes—
250C22⋊Q8—24no—
251C22⋊Q8—24no—
252C22⋊Q8—24no—
253C22⋊Q8—24no—
254C22⋊Q8—24no—
255C22⋊Q8—24no—
256C22⋊Q8—24no—
257C22⋊Q8—24no—
258#117—448no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—24no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—224no—
266C2×C4⋊C4C2×Dic1114yes—
267C2×C4⋊C4C2×Dic1118yes—
268C2×C22⋊C4—24no—
269C2×C22⋊C4—24no—
270C2×C22⋊C4—118no—
271C2×C22⋊C4—224no—
272C2×C22⋊C4—224no—
273C2×C22⋊C4C2×Dic1114yes—
274C2×C22⋊C4C22×D1114yes—
275C2×C42—224no—
276#95—224no—
277#95—224no—
278C2×C11—24no—
279C2×C11—22no—
280C2×C11—22no—
281C2×C11—22no—
282C2×C11—42no—
283C2×C11#231011yescharacteristic
284C2×C11C22×#9911yescharacteristic
285C2×C11C2×#41011yescharacteristic
286C24—24no—
287C24—42no—
288C24—42no—
289C24C22×Dic1111yescharacteristic
290C24C22×Dic1111yescharacteristic
291C24C2×C22⋊D1112yes—
292C24C2×C22⋊D1112yes—
293C24C23×D1111yescharacteristic
294C2×Q8—24no—
295C2×Q8—24no—
296C2×Q8—48no—
297C2×Q8—44no—
298C2×Q8—48no—
299C2×Q8—44no—
300C22×C4—28no—
301C22×C4—24no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—44no—
307C22×C4—44no—
308C22×C4—44no—
309C22×C4—44no—
310C22×C4—42no—
311C22×C4—44no—
312C22×C4—44no—
313C22×C4—44no—
314C22×C4—228no—
315C22×C4C22⋊Dic1112yes—
316C22×C4C22⋊Dic1111yescharacteristic
317C22×C4C22⋊Dic1112yes—
318C22×C4C22⋊Dic1112yes—
319C22×C4C22⋊Dic1112yes—
320C22×C4C22⋊Dic1111yescharacteristic
321C22×C4C22⋊Dic1111yescharacteristic
322C22×C4C22⋊Dic1112yes—
323C22×C4C22⋊Dic1112yes—
324C22×C4C22⋊Dic1111yescharacteristic
325C22×C4C22×Dic1112yes—
326C22×C4C22×Dic1114yes—
327C22×C4C22×Dic1114yes—
328C22×C4C22×Dic1112yes—
329C22×C4C2×C22⋊D1112yes—
330C22×C4C2×C22⋊D1112yes—
331C22×C4C2×C22⋊D1112yes—
332C22×C4C2×C22⋊D1112yes—
333C4⋊C4—24no—
334C4⋊C4—24no—
335C4⋊C4—28no—
336C4⋊C4—28no—
337C4⋊C4—448no—
338C22⋊C4—28no—
339C22⋊C4—28no—
340C22⋊C4—2216no—
341C22⋊C4—448no—
342C22⋊C4—448no—
343C42—448no—
344C11#2182511yescharacteristic, complemented, Sylow
345C23—22no—
346C23—22no—
347C23—22no—
348C23—22no—
349C23—24no—
350C23—24no—
351C23—24no—
352C23—24no—
353C23—41no—
354C23—42no—
355C23—41no—
356C23—41no—
357C23—42no—
358C23—41no—
359C23—416no—
360C23C2×C22⋊Dic1112yes—
361C23C2×C22⋊Dic1111yescharacteristic
362C23C2×C22⋊Dic1111yescharacteristic
363C23#6704014yes—
364C23C23×Dic1111yescharacteristic
365C23C22×C22⋊D1112yes—
366Q8—48no—
367Q8—48no—
368C2×C4—24no—
369C2×C4—22no—
370C2×C4—24no—
371C2×C4—24no—
372C2×C4—24no—
373C2×C4—24no—
374C2×C4—24no—
375C2×C4—24no—
376C2×C4—24no—
377C2×C4—24no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—44no—
386C2×C4—44no—
387C2×C4—44no—
388C2×C4—44no—
389C2×C4—44no—
390C2×C4—44no—
391C2×C4—448no—
392C2×C4—448no—
393C2×C4—448no—
394C2×C4#6689814yes—
395C2×C4C2×C22⋊Dic1112yes—
396C2×C4C2×C22⋊Dic1112yes—
397C2×C4C2×C22⋊Dic1112yes—
398C2×C4C2×C22⋊Dic1112yes—
399C22—28no—
400C22—21no—
401C22—21no—
402C22—22no—
403C22—21no—
404C22—21no—
405C22—22no—
406C22—21no—
407C22—21no—
408C22—22no—
409C22—22no—
410C22—22no—
411C22—44no—
412C22—48no—
413C22—48no—
414C22—44no—
415C22C2×#6689812yes—
416C22#1062285312yes—
417C22#1062334312yes—
418C22#1062334714yes—
419C22C22×C22⋊Dic1111yescharacteristic
420C4—22no—
421C4—22no—
422C4—22no—
423C4—44no—
424C4—44no—
425C4—888no—
426C4C2×#6689814yes—
427C2—24no—
428C2—22no—
429C2—22no—
430C2—22no—
431C2—42no—
432C2#1307120211yescharacteristic
433C2C22×#6689811yescharacteristic
434C2C2×#1062285311yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC22×C11×C22⋊Q8C2
socleC22×C11C22×C22⋊C4
prime radicalC25×C11C23
cosocleC24×C11C24
hypercenterC22×C22⋊Q8D11
hypocenterC11#21825
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24×C4 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #13069602C2semidirect
5. C23×Q8×C11C4semidirect
11. C2×C11×C22⋊Q8C4semidirect
13. C22×C11×C4⋊C4C4semidirect
14. C22×C11×C4⋊C4C4semidirect
186. C23×Q8Dic11semidirect
192. C2×C22⋊Q8Dic11semidirect
195. C22×C4⋊C4Dic11semidirect
196. C22×C4⋊C4Dic11semidirect
344. C11#21825semidirect

Maximal subgroups

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

subgroupindex
#130709992
#130696022
#130686902
C22×C11×C22⋊Q82
#2182511