Finite Group Databasebeta

← #14646751

Subgroups — #14646751

Order 2816.

456 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077310C211yesmaximal, characteristic
2#13068645C211yesmaximal, characteristic, complemented
3#13067160C212yesmaximal
4#13066523C212yesmaximal, complemented
5C11×#1810C211yesmaximal, characteristic, complemented
6C23×C8×C11C2211yescharacteristic
7#10623322C2211yescharacteristic
8C2×#66954C411yescharacteristic, complemented
9C2×C11×#108—21no—
10C11×#407C2212yes—
11#10622825C2212yes—
12#10622820C2211yescharacteristic
13#10622724—21no—
14#10622724—21no—
15#10622723C411yescharacteristic, complemented
16C8×C22⋊D11—21no—
17C8×C22⋊D11—21no—
18C2×#66882—21no—
19#10622715C411yescharacteristic, complemented
20#10622714C411yescharacteristic, complemented
21C11×#341—21no—
22#10622189—21no—
23#10622108—22no—
24#10622105—22no—
25C23×C4×C11C2311yescharacteristic
26C2×#4339C2×C411yescharacteristic
27C2×C11×M16—22no—
28C22×C8×C11—42no—
29C22×C8×C11C2×C411yescharacteristic
30C22×C8×C11C2×C411yescharacteristic
31C22×C8×C11D411yescharacteristic
32C22×C8×C11D411yescharacteristic
33C22×C8×C11D411yescharacteristic
34C22×C8×C11D411yescharacteristic
35#67006—21no—
36C2×C22⋊Dic11—22no—
37#66983D411yescharacteristic
38#66983Q811yescharacteristic
39#66982—21no—
40C4×C22⋊D11—21no—
41C4×C22⋊D11—21no—
42#66979C2×C411yescharacteristic
43C2×C4⋊Dic11—22no—
44#66977D411yescharacteristic
45#66977Q811yescharacteristic
46C2×#4318C2×C411yescharacteristic
47C2×#4318C2×C411yescharacteristic
48#66954—42no—
49C2×#4313—21no—
50C2×C8×D11—21no—
51C11×#108—42no—
52C11×C22⋊C8—22no—
53C11×C22⋊C8—22no—
54C11⋊#95—22no—
55C22⋊(C11⋊C8)—21no—
56C22⋊(C11⋊C8)—21no—
57(C2×D11)⋊C8—21no—
58(C2×D11)⋊C8—21no—
59#66882—42no—
60#66879—21no—
61Dic11⋊C8—21no—
62Dic11⋊C8—21no—
63C8×Dic11—21no—
64#8627—111nomaximal, Sylow
65C24×C11#4111yescharacteristic
66C22×C4×C11—41no—
67C22×C4×C11—41no—
68C22×C4×C11C22×C411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×Q811yescharacteristic
73C22×C4×C11#4111yescharacteristic
74C2×C22⋊D11—21no—
75C2×C22⋊D11—21no—
76C2×C22⋊D11—21no—
77C22×Dic11—42no—
78#4339—41no—
79#4339—41no—
80C2×D44C4⋊C411yescharacteristic
81C2×C4×D11—21no—
82C2×Dic22C4⋊C411yescharacteristic
83C11×M16—42no—
84C11×M16—42no—
85C2×C8×C11—22no—
86C2×C8×C11—22no—
87C2×C8×C11—22no—
88C2×C8×C11—41no—
89C2×C8×C11—41no—
90C2×C8×C11—41no—
91C2×C8×C11—42no—
92C2×C8×C11C22⋊C411yescharacteristic
93C2×C8×C11C22⋊C411yescharacteristic
94C2×C8×C11C22⋊C411yescharacteristic
95C2×C8×C11C22⋊C411yescharacteristic
96C22⋊Dic11—21no—
97C22⋊Dic11—21no—
98C22⋊Dic11—21no—
99C22⋊Dic11—82no—
100(C2×D11)⋊C4—21no—
101(C2×D11)⋊C4—21no—
102C4⋊Dic11—42no—
103C4⋊Dic11—42no—
104C4⋊Dic11C4⋊C411yescharacteristic
105C4⋊Dic11C4⋊C411yescharacteristic
106Dic11⋊C4—21no—
107Dic11⋊C4—21no—
108C4×Dic11—21no—
109#4318—41no—
110#4318—41no—
111C2×C11⋊C8—21no—
112C2×C11⋊C8—21no—
113#4313—42no—
114C8×D11—42no—
115#2929—111no—
116#1810D1111yescharacteristic, complemented
117#1808—111no—
118#1513—112no—
119#1305—112no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—41no—
123C23×C11—41no—
124C23×C11#11711yescharacteristic
125C23×C11#12111yescharacteristic
126C23×C11C22⋊Q811yescharacteristic
127C22×D11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11C2×C22⋊C411yescharacteristic
138C2×C4×C11C2×C4⋊C411yescharacteristic
139C2×C4×C11#12111yescharacteristic
140C2×C4×C11C22⋊Q811yescharacteristic
141C22⋊D11—42no—
142C22⋊D11—42no—
143C22⋊D11—41no—
144C22⋊D11—41no—
145C2×Dic11—21no—
146C2×Dic11—21no—
147C2×Dic11—21no—
148C2×Dic11—82no—
149C2×Dic11—82no—
150C2×Dic11—82no—
151D44—41no—
152C4×D11—41no—
153C4×D11—41no—
154Dic22—41no—
155C8×C11—21no—
156C8×C11—21no—
157C8×C11—21no—
158C8×C11—82no—
159C8×C11#9912yes—
160C11⋊C8—41no—
161C11⋊C8—41no—
162C2×#131—111no—
163C23×C8C2×D1111yescharacteristic
164#525—111no—
165#435—221no—
166#435—221no—
167C8×D4—221no—
168C8×D4—221no—
169C2×#108—21no—
170C2×#107—221no—
171#424—111no—
172#408—111no—
173#407—111no—
174#407C2×D1112yes—
175#405—111no—
176#380—112no—
177#341—21no—
178#340—221no—
179#328—222no—
180#327—222no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—42no—
190C22×C11—42no—
191C22×C11#38011yescharacteristic
192C22×C11#47211yescharacteristic
193C22×C11#47311yescharacteristic
194C2×D11—41no—
195C2×D11—41no—
196C2×D11—41no—
197C4×C11—21no—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11C2×#9911yescharacteristic
201C4×C11#41011yescharacteristic
202Dic11—41no—
203Dic11—41no—
204Dic11—41no—
205Dic11—162no—
206C2×#41—111no—
207C23×C4C22×D1111yescharacteristic
208#131—442no—
209C2×M16—22no—
210C2×M16—111no—
211C2×M16—111no—
212C2×M16—221no—
213C22×C8—42no—
214C22×C8—221no—
215C22×C8C4×D1111yescharacteristic
216C22×C8C4×D1111yescharacteristic
217C22×C8D4411yescharacteristic
218C22×C8D4411yescharacteristic
219C22×C8C22⋊D1111yescharacteristic
220C22×C8C22⋊D1111yescharacteristic
221#123—221no—
222C22⋊Q8—111no—
223C22⋊Q8—111no—
224#121—111no—
225#121—111no—
226#120—221no—
227C4×D4—221no—
228C4×D4—221no—
229#117—111no—
230C2×C4⋊C4—222no—
231C2×C22⋊C4—222no—
232#108—42no—
233#107—442no—
234C4⋊C8—221no—
235C4⋊C8—221no—
236C22⋊C8—22no—
237C22⋊C8—22no—
238C22⋊C8—221no—
239C22⋊C8—221no—
240C22⋊C8—221no—
241C22⋊C8—221no—
242#97—221no—
243C4×C8—221no—
244#95—222no—
245C2×C11—21no—
246C2×C11—21no—
247C2×C11—41no—
248C2×C11—41no—
249C2×C11#179911yescharacteristic
250C2×C11#181411yescharacteristic
251C2×C11#181611yescharacteristic
252D11—81no—
253C24#434311yescharacteristic
254#41—441no—
255#41—441no—
256C2×Q8—111no—
257C2×D4—111no—
258C2×D4—221no—
259C2×D4—221no—
260C2×D4—221no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—221no—
264C22×C4—442no—
265C22×C4C2×C4×D1111yescharacteristic
266C22×C4C2×D4411yescharacteristic
267C22×C4D4×D1111yescharacteristic
268C22×C4#434111yescharacteristic
269C22×C4Q8×D1111yescharacteristic
270C22×C4C2×C22⋊D1111yescharacteristic
271M16—42no—
272M16—42no—
273M16—442no—
274M16—441no—
275M16—441no—
276C2×C8—22no—
277C2×C8—22no—
278C2×C8—22no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—42no—
283C2×C8—221no—
284C2×C8—221no—
285C2×C8—442no—
286C2×C8(C2×D11)⋊C411yescharacteristic
287C2×C8(C2×D11)⋊C411yescharacteristic
288C2×C8(C2×D11)⋊C411yescharacteristic
289C2×C8(C2×D11)⋊C411yescharacteristic
290C4⋊C4—111no—
291C4⋊C4—111no—
292C4⋊C4—221no—
293C4⋊C4—221no—
294C4⋊C4—442no—
295C4⋊C4—442no—
296C22⋊C4—221no—
297C22⋊C4—221no—
298C22⋊C4—221no—
299C22⋊C4—221no—
300C22⋊C4—221no—
301C22⋊C4—882no—
302C42—221no—
303C11#862711yescharacteristic, complemented, Sylow
304C23—21no—
305C23—21no—
306C23—41no—
307C23—41no—
308C23—221no—
309C23#6694511yescharacteristic
310C23#6694811yescharacteristic
311C23#6699911yescharacteristic
312Q8—441no—
313D4—441no—
314D4—442no—
315D4—442no—
316D4—441no—
317D4—441no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—221no—
328C2×C4—221no—
329C2×C4—221no—
330C2×C4—441no—
331C2×C4—441no—
332C2×C4—882no—
333C2×C4—882no—
334C2×C4—882no—
335C2×C4C4⋊C4×D1111yescharacteristic
336C2×C4#6695011yescharacteristic
337C2×C4C2×(C2×D11)⋊C411yescharacteristic
338C2×C4#6699111yescharacteristic
339C8—21no—
340C8—21no—
341C8—21no—
342C8—82no—
343C8—441no—
344C8—441no—
345C8#6687012yes—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—42no—
355C22—42no—
356C22—441no—
357C22—441no—
358C22—441no—
359C22#1062250911yescharacteristic
360C22#1062251011yescharacteristic
361C22#1062260011yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—441no—
366C4—441no—
367C4—441no—
368C4—1762no—
369C4C2×#6687011yescharacteristic
370C4#1062261911yescharacteristic
371C2—21no—
372C2—21no—
373C2—41no—
374C2—41no—
375C2—881no—
376C2#1306860111yescharacteristic
377C2#1306867111yescharacteristic
378C2#1306867711yescharacteristic
subgroupG/H
centerC22#10622600
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1810C2
socleC22×C11#380
prime radical#10623322C22
cosocleC23×C4×C11C23
hypercenter#1810D11
hypocenterC11#8627
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1810

Complements

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

NH ≅ G/Ntype
2. #13068645C2semidirect
4. #13066523C2semidirect
5. C11×#1810C2semidirect
8. C2×#66954C4semidirect
15. #10622723C4semidirect
19. #10622715C4semidirect
20. #10622714C4semidirect
116. #1810D11semidirect
303. C11#8627semidirect

Maximal subgroups

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

subgroupindex
#130773102
#130686452
#130671602
#130665232
C11×#18102
#862711