Finite Group Databasebeta

← #14762854

Subgroups — #14762854

Order 2816.

1466 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×#10622820C211yesmaximal, characteristic
2#13070999C211yesmaximal, characteristic
3#13069050C214yesmaximal, complemented
4#13068929C214yesmaximal, complemented
5#13068706C212yesmaximal, complemented
6#13068551C212yesmaximal, complemented
7C22×C11×C22⋊Q8C211yesmaximal, characteristic
8C23×Q8×C11C2211yescharacteristic
9C24×C4×C11C2211yescharacteristic
10C2×C11×C22⋊Q8—24no—
11C2×C11×C22⋊Q8—21no—
12C2×C11×C22⋊Q8—21no—
13C2×C11×C22⋊Q8C418yescomplemented
14C2×C11×C22⋊Q8C2212yes—
15C2×C11×C22⋊Q8C2212yes—
16C22×C11×C4⋊C4—21no—
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4—21no—
19C2×#66979C2212yes—
20C22×#4318C2212yes—
21#10622860—21no—
22C2×#66899C2218yescomplemented
23#10622825C2212yes—
24#10622825C2212yes—
25#10622824—21no—
26C4×C22⋊Dic11—21no—
27C4×C22⋊Dic11—21no—
28#10622820—24no—
29C2×C22⋊(C11⋊C8)C2212yes—
30C2×C22⋊(C11⋊C8)C2212yes—
31#10622167C2218yescomplemented
32C25×C11D411yescharacteristic
33C22×Q8×C11—22no—
34C22×Q8×C11—21no—
35C22×Q8×C11—44no—
36C22×Q8×C11C2×C414yes—
37C22×Q8×C11C2312yes—
38C23×C4×C11—21no—
39C23×C4×C11—21no—
40C23×C4×C11—44no—
41C23×C4×C11C2×C414yes—
42C23×C4×C11D411yescharacteristic
43C23×C4×C11D411yescharacteristic
44C23×C4×C11D411yescharacteristic
45C23×C4×C11D414yes—
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C11×C22⋊Q8—28no—
50C11×C22⋊Q8—28no—
51C11×C22⋊Q8—24no—
52C11×C22⋊Q8—24no—
53C11×C22⋊Q8C2×C418yes—
54C11×C22⋊Q8C2×C418yes—
55C2×C11×C4⋊C4—28no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4C2×C414yes—
61C2×C11×C4⋊C4C2312yes—
62C2×C11×C22⋊C4—28no—
63C2×C11×C22⋊C4—22no—
64C2×C11×C22⋊C4—22no—
65C2×C22⋊Dic11—22no—
66C2×C22⋊Dic11—22no—
67C2×C22⋊Dic11—22no—
68#66979—44no—
69C2×C4⋊Dic11C2314yes—
70C2×C4×Dic11—22no—
71C2×#4318—24no—
72C2×#4318—44no—
73C22×C11⋊C8C2314yes—
74#66899—48no—
75C11⋊#95—22no—
76C11⋊#95—22no—
77C22⋊(C11⋊C8)—24no—
78C22⋊(C11⋊C8)—24no—
79#21768—111nomaximal, Sylow
80C24×C11—24no—
81C24×C11—42no—
82C24×C11—42no—
83C24×C11C22⋊C414yes—
84C24×C11C2×D411yescharacteristic
85C24×C11C2×D411yescharacteristic
86C24×C11C2×D411yescharacteristic
87C2×Q8×C11—24no—
88C2×Q8×C11—22no—
89C2×Q8×C11—28no—
90C2×Q8×C11—48no—
91C2×Q8×C11—44no—
92C2×Q8×C11—48no—
93C2×Q8×C11C22×C414yes—
94C22×C4×C11—24no—
95C22×C4×C11—24no—
96C22×C4×C11—24no—
97C22×C4×C11—24no—
98C22×C4×C11—24no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—48no—
102C22×C4×C11—48no—
103C22×C4×C11—42no—
104C22×C4×C11—42no—
105C22×C4×C11—42no—
106C22×C4×C11—44no—
107C22×C4×C11—44no—
108C22×C4×C11C22⋊C414yes—
109C22×C4×C11C22⋊C414yes—
110C22×C4×C11C22⋊C414yes—
111C22×C4×C11C22×C412yes—
112C22×C4×C11C22×C412yes—
113C22×C4×C11C22×C412yes—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2×D412yes—
119C22×C4×C11C2×D412yes—
120C22×C4×C11C2411yescharacteristic
121C22×Dic11—24no—
122C11×C4⋊C4—28no—
123C11×C4⋊C4—28no—
124C11×C4⋊C4—24no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4C22×C414yes—
127C11×C22⋊C4—28no—
128C11×C22⋊C4—28no—
129C22⋊Dic11—44no—
130C22⋊Dic11—44no—
131C22⋊Dic11—44no—
132C4⋊Dic11—28no—
133C4×Dic11—44no—
134#4318—48no—
135C2×C11⋊C8—24no—
136C2×C11⋊C8—28no—
137C22×C22⋊Q8D1111yescharacteristic
138C2×#407—111no—
139#2280—111no—
140#1894—114no—
141#1873—114no—
142#1824—112no—
143#1787—112no—
144C23×C11—22no—
145C23×C11—22no—
146C23×C11—22no—
147C23×C11—22no—
148C23×C11—22no—
149C23×C11—22no—
150C23×C11—22no—
151C23×C11—22no—
152C23×C11—28no—
153C23×C11—44no—
154C23×C11—44no—
155C23×C11—416no—
156C23×C11C2×C22⋊C412yes—
157C23×C11C2×C22⋊C412yes—
158C23×C11C2×C22⋊C412yes—
159C23×C11#13714yes—
160C23×C11C22×D411yescharacteristic
161Q8×C11—28no—
162Q8×C11—48no—
163Q8×C11—44no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—24no—
168C2×C4×C11—24no—
169C2×C4×C11—24no—
170C2×C4×C11—24no—
171C2×C4×C11—24no—
172C2×C4×C11—24no—
173C2×C4×C11—24no—
174C2×C4×C11—24no—
175C2×C4×C11—44no—
176C2×C4×C11—44no—
177C2×C4×C11—44no—
178C2×C4×C11—48no—
179C2×C4×C11—48no—
180C2×C4×C11—44no—
181C2×C4×C11—44no—
182C2×C4×C11C2×C22⋊C412yes—
183C2×C4×C11C2×C22⋊C412yes—
184C2×C4×C11C2×C22⋊C412yes—
185C2×C4×C11C23×C411yescharacteristic
186C2×C4×C11C22×D411yescharacteristic
187C2×C4×C11H(5,𝔽2)14yes—
188C2×Dic11—44no—
189C2×Dic11—44no—
190C2×Dic11—44no—
191C11⋊C8—44no—
192C23×Q8C2×D1111yescharacteristic
193C24×C4C2×D1111yescharacteristic
194C22×M16—112no—
195C2×C22⋊Q8—24no—
196C2×C22⋊Q8—21no—
197C2×C22⋊Q8—21no—
198C2×C22⋊Q8Dic1118yescomplemented
199C2×C22⋊Q8C2×D1112yes—
200C2×C22⋊Q8C2×D1112yes—
201C2×#117—112no—
202C22×C4⋊C4—21no—
203C22×C4⋊C4C2×D1111yescharacteristic
204C22×C22⋊C4—21no—
205C2×#103—118no—
206#407—224no—
207C2×C22⋊C8—112no—
208C2×C22⋊C8—112no—
209#381—221no—
210#380—112no—
211#380—112no—
212#379—221no—
213C4×C22⋊C4—221no—
214C4×C22⋊C4—221no—
215#340—118no—
216C22×C11—22no—
217C22×C11—22no—
218C22×C11—28no—
219C22×C11—22no—
220C22×C11—22no—
221C22×C11—22no—
222C22×C11—22no—
223C22×C11—22no—
224C22×C11—22no—
225C22×C11—416no—
226C22×C11—44no—
227C22×C11—44no—
228C22×C11#41914yes—
229C22×C11C22×C22⋊C411yescharacteristic
230C22×C11#53412yes—
231C22×C11C2×#13712yes—
232C22×C11#57512yes—
233C4×C11—22no—
234C4×C11—22no—
235C4×C11—22no—
236C4×C11—44no—
237C4×C11—44no—
238C4×C11#51812yes—
239C4×C11#53412yes—
240Dic11—84no—
241C25C22⋊D1111yescharacteristic
242C22×Q8—22no—
243C22×Q8—21no—
244C22×Q8—44no—
245C22×Q8C2×Dic1114yes—
246C22×Q8C22×D1112yes—
247C23×C4—21no—
248C23×C4—21no—
249C23×C4—44no—
250C23×C4C2×Dic1114yes—
251C23×C4C22⋊D1111yescharacteristic
252C23×C4C22⋊D1111yescharacteristic
253C23×C4C22⋊D1111yescharacteristic
254C23×C4C22⋊D1114yes—
255C23×C4C22×D1111yescharacteristic
256C23×C4C22×D1111yescharacteristic
257C23×C4C22×D1111yescharacteristic
258C2×M16—224no—
259C2×M16—444no—
260C22×C8—114no—
261C22⋊Q8—28no—
262C22⋊Q8—28no—
263C22⋊Q8—24no—
264C22⋊Q8—24no—
265C22⋊Q8C2×Dic1118yes—
266C22⋊Q8C2×Dic1118yes—
267#117—444no—
268C2×C4⋊C4—28no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—114no—
274C2×C4⋊C4C2×Dic1114yes—
275C2×C4⋊C4C22×D1112yes—
276C2×C22⋊C4—28no—
277C2×C22⋊C4—22no—
278C2×C22⋊C4—22no—
279C2×C22⋊C4—222no—
280C2×C22⋊C4—222no—
281C2×C22⋊C4—222no—
282C2×C42—222no—
283#103—448no—
284C22⋊C8—224no—
285C22⋊C8—224no—
286#95—222no—
287#95—222no—
288C2×C11—24no—
289C2×C11—42no—
290C2×C11—42no—
291C2×C11#230811yescharacteristic
292C2×C11C2×#41911yescharacteristic
293C2×C11#289611yescharacteristic
294C2×C11#319614yes—
295C24—24no—
296C24—42no—
297C24—42no—
298C24C22⋊Dic1114yes—
299C24C2×C22⋊D1111yescharacteristic
300C24C2×C22⋊D1111yescharacteristic
301C24C2×C22⋊D1111yescharacteristic
302C2×Q8—24no—
303C2×Q8—22no—
304C2×Q8—28no—
305C2×Q8—48no—
306C2×Q8—44no—
307C2×Q8—48no—
308C2×Q8C22×Dic1114yes—
309C22×C4—24no—
310C22×C4—24no—
311C22×C4—24no—
312C22×C4—24no—
313C22×C4—24no—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—48no—
317C22×C4—48no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—44no—
322C22×C4—44no—
323C22×C4—224no—
324C22×C4C22⋊Dic1114yes—
325C22×C4C22⋊Dic1114yes—
326C22×C4C22⋊Dic1114yes—
327C22×C4C22×Dic1112yes—
328C22×C4C22×Dic1112yes—
329C22×C4C22×Dic1112yes—
330C22×C4C2×C22⋊D1111yescharacteristic
331C22×C4C2×C22⋊D1111yescharacteristic
332C22×C4C2×C22⋊D1111yescharacteristic
333C22×C4C2×C22⋊D1112yes—
334C22×C4C2×C22⋊D1112yes—
335C22×C4C2×C22⋊D1112yes—
336C22×C4C23×D1111yescharacteristic
337M16—448no—
338C2×C8—228no—
339C2×C8—224no—
340C4⋊C4—28no—
341C4⋊C4—28no—
342C4⋊C4—24no—
343C4⋊C4—22no—
344C4⋊C4—228no—
345C4⋊C4C22×Dic1114yes—
346C22⋊C4—28no—
347C22⋊C4—28no—
348C22⋊C4—444no—
349C22⋊C4—444no—
350C22⋊C4—444no—
351C42—444no—
352C11#2176811yescharacteristic, complemented, Sylow
353C23—22no—
354C23—22no—
355C23—22no—
356C23—22no—
357C23—22no—
358C23—22no—
359C23—28no—
360C23—22no—
361C23—22no—
362C23—44no—
363C23—44no—
364C23—416no—
365C23#6699514yes—
366C23C2×C22⋊Dic1112yes—
367C23C2×C22⋊Dic1112yes—
368C23C2×C22⋊Dic1112yes—
369C23C22×C22⋊D1111yescharacteristic
370Q8—28no—
371Q8—48no—
372Q8—44no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—24no—
377C2×C4—24no—
378C2×C4—24no—
379C2×C4—24no—
380C2×C4—24no—
381C2×C4—24no—
382C2×C4—24no—
383C2×C4—24no—
384C2×C4—44no—
385C2×C4—44no—
386C2×C4—44no—
387C2×C4—48no—
388C2×C4—48no—
389C2×C4—44no—
390C2×C4—44no—
391C2×C4—444no—
392C2×C4—444no—
393C2×C4—444no—
394C2×C4C2×C22⋊Dic1112yes—
395C2×C4C2×C22⋊Dic1112yes—
396C2×C4C2×C22⋊Dic1112yes—
397C2×C4#6703714yes—
398C2×C4C23×Dic1111yescharacteristic
399C2×C4C22×C22⋊D1111yescharacteristic
400C8—444no—
401C22—22no—
402C22—22no—
403C22—28no—
404C22—22no—
405C22—22no—
406C22—22no—
407C22—22no—
408C22—22no—
409C22—22no—
410C22—416no—
411C22—44no—
412C22—44no—
413C22#1062283814yes—
414C22#1062333512yes—
415C22C2×#6699512yes—
416C22#1062335312yes—
417C22C22×C22⋊Dic1111yescharacteristic
418C4—22no—
419C4—22no—
420C4—22no—
421C4—44no—
422C4—44no—
423C4—884no—
424C4#1062332912yes—
425C4#1062333512yes—
426C2—24no—
427C2—42no—
428C2—42no—
429C2#1307119411yescharacteristic
430C2C2×#1062283811yescharacteristic
431C2#1307713511yescharacteristic
432C2#1307944614yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×C22⋊Q8C2
socleC23×C11C22×D4
prime radicalC25×C11D4
cosocleC22×C4×C11C24
hypercenterC22×C22⋊Q8D11
hypocenterC11#21768
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #13069050C2semidirect
4. #13068929C2semidirect
5. #13068706C2semidirect
6. #13068551C2semidirect
13. C2×C11×C22⋊Q8C4semidirect
22. C2×#66899C22semidirect
31. #10622167C22semidirect
198. C2×C22⋊Q8Dic11semidirect
352. C11#21768semidirect

Maximal subgroups

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

subgroupindex
C2×#106228202
#130709992
#130690502
#130689292
#130687062
#130685512
C22×C11×C22⋊Q82
#2176811