Finite Group Databasebeta

← #14764160

Subgroups — #14764160

Order 2816.

862 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Dic11⋊C8C211yesmaximal, characteristic
2#13071018C211yesmaximal, characteristic
3#13071011C211yesmaximal, characteristic
4#13069383C212yesmaximal, complemented
5#13069381C212yesmaximal, complemented
6#13069378C212yesmaximal, complemented
7#13069371C212yesmaximal, complemented
8#13068643C211yesmaximal, characteristic
9#13068641C211yesmaximal, characteristic
10#13068639C211yesmaximal, characteristic
11C11×#1808C211yesmaximal, characteristic
12C23×C8×C11C2211yescharacteristic
13C22×C4×Dic11C2211yescharacteristic
14C23×C11⋊C8C2211yescharacteristic
15C2×#66930—21no—
16C2×C11×#107C2212yes—
17C11×#380C2211yescharacteristic
18C11×#380C2211yescharacteristic
19#10622825C2211yescharacteristic
20#10622825C2211yescharacteristic
21C2×#66881C2212yes—
22C2×Dic11⋊C8C418yescomplemented
23C2×Dic11⋊C8C2211yescharacteristic
24C2×Dic11⋊C8C2211yescharacteristic
25C2×Dic11⋊C8C2211yescharacteristic
26C2×Dic11⋊C8C2211yescharacteristic
27#10622590C2212yes—
28#10622589C2212yes—
29C4⋊C4×Dic11C2212yes—
30C4⋊C4×Dic11C2212yes—
31C2×#66872C2212yes—
32C2×#66871C2212yes—
33#10622556—21no—
34#10622555—21no—
35C22⋊C4×Dic11—21no—
36#10622264—21no—
37#10622263—21no—
38#10622262—21no—
39#10622261—21no—
40C11×#340C2212yes—
41#10622189C2212yes—
42#10622167C2212yes—
43#10622167C2212yes—
44C23×C4×C11C2311yescharacteristic
45C23×Dic11D411yescharacteristic
46C23×Dic11D411yescharacteristic
47C22×C8×C11—42no—
48C22×C8×C11C2×C414yes—
49C22×C8×C11C2311yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C2×C11×C4⋊C4C2312yes—
52C2×C11×C4⋊C4C2312yes—
53C2×C11×C22⋊C4—21no—
54C2×C11×C22⋊C4—21no—
55C2×C22⋊Dic11—21no—
56C2×C22⋊Dic11—21no—
57C2×C4⋊Dic11C2312yes—
58C2×C4⋊Dic11C2312yes—
59C2×Dic11⋊C4—22no—
60C2×Dic11⋊C4—22no—
61C2×C4×Dic11—22no—
62C2×C4×Dic11—22no—
63C2×C4×Dic11C2×C414yes—
64C2×C4×Dic11D411yescharacteristic
65C2×C4×Dic11D411yescharacteristic
66C2×C4×Dic11Q814yes—
67C2×C4×Dic11C2311yescharacteristic
68C2×C4×Dic11C2311yescharacteristic
69C22×C11⋊C8—42no—
70C22×C11⋊C8C2×C414yes—
71C22×C11⋊C8C2311yescharacteristic
72C22×C11⋊C8C2311yescharacteristic
73#66930—44no—
74C11×#107—42no—
75C11×#95—21no—
76C11×#95—21no—
77C11⋊#95—21no—
78C11⋊#95—21no—
79C11⋊#95—22no—
80C11⋊#95—22no—
81C11⋊#95—22no—
82C11⋊#95—22no—
83#66881—42no—
84Dic11⋊C8C2×C414yes—
85Dic11⋊C8C2×C414yes—
86Dic11⋊C8C2×C414yes—
87Dic11⋊C8C2×C414yes—
88#66872—42no—
89#66871—42no—
90#21962—111nomaximal, Sylow
91C24×C11C2×D411yescharacteristic
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11C22×C412yes—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×Q812yes—
99C22×C4×C11C2411yescharacteristic
100C22×Dic11—24no—
101C22×Dic11—22no—
102C22×Dic11—22no—
103C22×Dic11—22no—
104C22×Dic11—22no—
105C22×Dic11C4⋊C414yes—
106C22×Dic11C4⋊C414yes—
107C22×Dic11C2×D411yescharacteristic
108C22×Dic11C2×D411yescharacteristic
109C22×Dic11C2×D411yescharacteristic
110C22×Dic11C2×D411yescharacteristic
111C2×C8×C11—22no—
112C2×C8×C11—22no—
113C2×C8×C11—44no—
114C2×C8×C11C22×C412yes—
115C2×C8×C11C22×C412yes—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—22no—
120C11×C22⋊C4—42no—
121C11×C22⋊C4—42no—
122C22⋊Dic11—42no—
123C22⋊Dic11—42no—
124C4⋊Dic11—22no—
125C4⋊Dic11—22no—
126C4⋊Dic11—22no—
127C4⋊Dic11—22no—
128Dic11⋊C4—44no—
129Dic11⋊C4—44no—
130C4×Dic11—44no—
131C4×Dic11—44no—
132C4×Dic11C4⋊C414yes—
133C4×Dic11C4⋊C414yes—
134C4×Dic11C22×C412yes—
135C4×Dic11C22×C412yes—
136C4×Dic11C2×Q812yes—
137C4×Dic11C2×Q812yes—
138C2×C11⋊C8—22no—
139C2×C11⋊C8—22no—
140C2×C11⋊C8—44no—
141C2×C11⋊C8C22×C412yes—
142C2×C11⋊C8C22×C412yes—
143C22×C4⋊C8—111no—
144#2285—111no—
145#2283—111no—
146#1949—112no—
147#1949—112no—
148#1948—112no—
149#1947—112no—
150#1808—111no—
151#1808D1111yescharacteristic
152#1807—111no—
153#1807—111no—
154C23×C11—22no—
155C23×C11—22no—
156C23×C11C2×C4⋊C412yes—
157C23×C11AGL(1,ℤ/8)12yes—
158C23×C11#13712yes—
159C23×C11C22×D411yescharacteristic
160C2×C4×C11—22no—
161C2×C4×C11—22no—
162C2×C4×C11—22no—
163C2×C4×C11—24no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11—42no—
170C2×C4×C11C2×C4⋊C412yes—
171C2×C4×C11C23×C411yescharacteristic
172C2×C4×C11C22×Q811yescharacteristic
173C2×C4×C11H(5,𝔽2)12yes—
174C2×C4×C112−1+412yes—
175C2×Dic11—22no—
176C2×Dic11—21no—
177C2×Dic11—21no—
178C2×Dic11—21no—
179C2×Dic11—21no—
180C2×Dic11—28no—
181C2×Dic11—28no—
182C2×Dic11—42no—
183C2×Dic11—42no—
184C2×Dic11—42no—
185C2×Dic11—42no—
186C2×Dic11—42no—
187C2×Dic11—42no—
188C2×Dic11C2×C4⋊C412yes—
189C2×Dic11C2×C4⋊C412yes—
190C2×Dic11C2×C4⋊C412yes—
191C2×Dic11C2×C4⋊C412yes—
192C2×Dic11#13514yes—
193C8×C11—22no—
194C8×C11—22no—
195C11⋊C8—22no—
196C11⋊C8—22no—
197C23×C8—111no—
198C23×C8C2×D1111yescharacteristic
199C2×#117—221no—
200C22×C42—111no—
201C2×#107—112no—
202C2×#107C2×D1112yes—
203C2×#106—112no—
204C2×#106—112no—
205C2×C4⋊C8—111no—
206C2×C4⋊C8—111no—
207C2×C4⋊C8—111no—
208C2×C4⋊C8—111no—
209C2×C4⋊C8—118no—
210#384—112no—
211#383—221no—
212#382—112no—
213#382—221no—
214#381—221no—
215#380—111no—
216#380—111no—
217#380—221no—
218#380C2×D1111yescharacteristic
219#380C2×D1111yescharacteristic
220C4×C4⋊C4—112no—
221C4×C4⋊C4—112no—
222C4×C4⋊C4—221no—
223C4×C22⋊C4—221no—
224#376—221no—
225#340—112no—
226#340—112no—
227#340—112no—
228#340C2×D1112yes—
229C22×C11—22no—
230C22×C11—22no—
231C22×C11—24no—
232C22×C11—24no—
233C22×C11#42814yes—
234C22×C11C22×C4⋊C411yescharacteristic
235C22×C11#53712yes—
236C22×C11C2×#13512yes—
237C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
238C22×C11C2×#13711yescharacteristic
239C4×C11—22no—
240C4×C11—82no—
241C4×C11—82no—
242C4×C11#51811yescharacteristic
243C4×C11#51911yescharacteristic
244C4×C11#54412yes—
245Dic11—22no—
246Dic11—22no—
247Dic11—22no—
248Dic11—82no—
249Dic11—82no—
250Dic11#42714yes—
251C23×C4—111no—
252C23×C4—111no—
253C23×C4C22×D1111yescharacteristic
254C22×C8—42no—
255C22×C8—111no—
256C22×C8—111no—
257C22×C8—114no—
258C22×C8—442no—
259C22×C8C4×D1114yes—
260C22×C8C22×D1111yescharacteristic
261C22×C8C22×D1111yescharacteristic
262#117—444no—
263C2×C4⋊C4—112no—
264C2×C4⋊C4—112no—
265C2×C4⋊C4—222no—
266C2×C4⋊C4—222no—
267C2×C4⋊C4C22×D1112yes—
268C2×C4⋊C4C22×D1112yes—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—221no—
272C2×C22⋊C4—221no—
273C2×C42—114no—
274C2×C42—111no—
275C2×C42—111no—
276C2×C42—114no—
277C2×C42—111no—
278C2×C42—111no—
279C2×C42—222no—
280C2×C42—222no—
281#107—42no—
282#107—442no—
283#106—442no—
284#106—442no—
285C4⋊C8—114no—
286C4⋊C8—114no—
287C4⋊C8—114no—
288C4⋊C8—114no—
289#95—21no—
290#95—21no—
291#95—222no—
292#95—222no—
293#95—222no—
294#95—222no—
295#95—221no—
296#95—221no—
297C2×C11—24no—
298C2×C11#231611yescharacteristic
299C2×C11C2×#42711yescharacteristic
300C2×C11C2×#42811yescharacteristic
301C2×C11#324712yes—
302C2×C11#324812yes—
303C24D4×D1111yescharacteristic
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—111no—
309C22×C4—114no—
310C22×C4—114no—
311C22×C4—111no—
312C22×C4—111no—
313C22×C4—111no—
314C22×C4—224no—
315C22×C4—222no—
316C22×C4—222no—
317C22×C4—222no—
318C22×C4—222no—
319C22×C4C2×C4×D1112yes—
320C22×C4D4×D1111yescharacteristic
321C22×C4Q8×D1112yes—
322C22×C4C23×D1111yescharacteristic
323C2×C8—22no—
324C2×C8—22no—
325C2×C8—44no—
326C2×C8—112no—
327C2×C8—112no—
328C2×C8—222no—
329C2×C8—222no—
330C2×C8—444no—
331C2×C8C2×C4×D1112yes—
332C2×C8C2×C4×D1112yes—
333C4⋊C4—22no—
334C4⋊C4—22no—
335C4⋊C4—22no—
336C4⋊C4—22no—
337C4⋊C4—222no—
338C4⋊C4—222no—
339C4⋊C4—222no—
340C4⋊C4—222no—
341C4⋊C4—444no—
342C4⋊C4—444no—
343C22⋊C4—42no—
344C22⋊C4—42no—
345C22⋊C4—442no—
346C22⋊C4—442no—
347C42—114no—
348C42—114no—
349C42—112no—
350C42—112no—
351C42—112no—
352C42—112no—
353C42—444no—
354C42—444no—
355C11#2196211yescharacteristic, complemented, Sylow
356C23—22no—
357C23—22no—
358C23C4⋊C4×D1112yes—
359C23#6696412yes—
360C23#6697112yes—
361C23C2×D4×D1111yescharacteristic
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—24no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—112no—
373C2×C4—114no—
374C2×C4—112no—
375C2×C4—112no—
376C2×C4—112no—
377C2×C4—228no—
378C2×C4—228no—
379C2×C4—221no—
380C2×C4—221no—
381C2×C4—221no—
382C2×C4—221no—
383C2×C4—222no—
384C2×C4—442no—
385C2×C4—442no—
386C2×C4—442no—
387C2×C4—442no—
388C2×C4—442no—
389C2×C4—442no—
390C2×C4C4⋊C4×D1112yes—
391C2×C4C22×C4×D1111yescharacteristic
392C2×C4#6703712yes—
393C2×C4C2×Q8×D1111yescharacteristic
394C2×C4#6704312yes—
395C8—22no—
396C8—22no—
397C8—222no—
398C8—222no—
399C22—24no—
400C22—22no—
401C22—24no—
402C22—22no—
403C22#1062249414yes—
404C22C2×C4⋊C4×D1111yescharacteristic
405C22#1062312812yes—
406C22C2×#6696411yescharacteristic
407C22C2×#6697111yescharacteristic
408C22D11×#13512yes—
409C4—22no—
410C4—82no—
411C4—82no—
412C4—114no—
413C4—222no—
414C4—222no—
415C4—222no—
416C4—882no—
417C4—882no—
418C4#1062301711yescharacteristic
419C4#1062304711yescharacteristic
420C4#1062315412yes—
421C2—24no—
422C2#1307123311yescharacteristic
423C2D11×#42711yescharacteristic
424C2C2×#1062249411yescharacteristic
425C2#1307993512yes—
426C2#1307994812yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1808C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#1808D11
hypocenterC11#21962
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1808

Complements

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

NH ≅ G/Ntype
4. #13069383C2semidirect
5. #13069381C2semidirect
6. #13069378C2semidirect
7. #13069371C2semidirect
22. C2×Dic11⋊C8C4semidirect
355. C11#21962semidirect

Maximal subgroups

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

subgroupindex
C22×Dic11⋊C82
#130710182
#130710112
#130693832
#130693812
#130693782
#130693712
#130686432
#130686412
#130686392
C11×#18082
#2196211