Finite Group Databasebeta

← #14669833

Subgroups — #14669833

Order 2816.

422 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077387C211yesmaximal, characteristic
2C2×Dic11⋊C16C211yesmaximal, characteristic, complemented
3C2×#10622148C211yesmaximal, characteristic
4C2×#10622135C211yesmaximal, characteristic
5#13068786C211yesmaximal, characteristic, complemented
6#13066711C211yesmaximal, characteristic, complemented
7C11×#1382C211yesmaximal, characteristic, complemented
8C2×#66957C2211yescharacteristic
9#10623053—21no—
10C22×C11×C16C2211yescharacteristic
11C2×C11×#108C2211yescharacteristic
12C11×#427C2211yescharacteristic
13C2×#66886—21no—
14#10622731—21no—
15C2×#66883C2211yescharacteristic
16C2×C8×Dic11C2211yescharacteristic
17C22×C11⋊C16C2211yescharacteristic
18#10622615—21no—
19#10622486C411yescharacteristic
20#10622486C411yescharacteristic
21#10622485C411yescharacteristic
22#10622485C411yescharacteristic
23#10622465—21no—
24#10622465—21no—
25#10622148—22no—
26Dic11⋊C16—21no—
27Dic11⋊C16—21no—
28#10622135—22no—
29C2×#4339—21no—
30C2×C11×M16—21no—
31C22×C8×C11C2311yescharacteristic
32C11×#117—21no—
33C2×C4×Dic11D411yescharacteristic
34C2×#4318—21no—
35C22×C11⋊C8D411yescharacteristic
36C2×Dic44C2×C411yescharacteristic
37#66957—21no—
38#66957—21no—
39#66957D412yes—
40#66957Q812yes—
41C2×D88C2×C411yescharacteristic
42C2×#4314—21no—
43#66946—21no—
44#66946—21no—
45#66940—21no—
46#66940—21no—
47(C22⋊D11)⋊C4—41no—
48(C22⋊D11)⋊C4—41no—
49#66925—41no—
50C42×D11—41no—
51C2×C11×C16—21no—
52C2×C11×C16—21no—
53C2×C11×C16—21no—
54C11×#108—21no—
55C11×#108—21no—
56C11×#107C2×C411yescharacteristic
57C11×#107C2×C411yescharacteristic
58C11×#106—21no—
59#66886—42no—
60#66883—21no—
61#66883—21no—
62Dic11⋊C8—41no—
63Dic11⋊C8—41no—
64C8×Dic11C2×C411yescharacteristic
65C8×Dic11C2×C411yescharacteristic
66C8×Dic11D411yescharacteristic
67C8×Dic11D411yescharacteristic
68C2×C11⋊C16—21no—
69C2×C11⋊C16—21no—
70C2×C11⋊C16—21no—
71#66874—21no—
72#66874—21no—
73#66873—21no—
74#66873—21no—
75#12815—111nomaximal, Sylow
76C22×C4×C11C2×D411yescharacteristic
77C2×C22⋊D11—41no—
78C22×Dic11SD1611yescharacteristic
79C22×Dic11SD1611yescharacteristic
80#4339—22no—
81#4339—22no—
82#4339—41no—
83#4339—41no—
84C2×D44—21no—
85C2×C4×D11—41no—
86C2×C4×D11—41no—
87C2×C4×D11—41no—
88C2×Dic22—21no—
89C11×M16—41no—
90C11×M16—41no—
91C2×C8×C11—41no—
92C2×C8×C11C22×C411yescharacteristic
93C2×C8×C11C2×D411yescharacteristic
94C2×C8×C11C2×D411yescharacteristic
95C2×C8×C11C2×Q811yescharacteristic
96C2×C8×C11#4111yescharacteristic
97C2×C8×C11#4111yescharacteristic
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C22⋊C4—41no—
101C42×C11—41no—
102(C2×D11)⋊C4—41no—
103(C2×D11)⋊C4—41no—
104Dic11⋊C4—41no—
105Dic11⋊C4—41no—
106C4×Dic11—41no—
107C4×Dic11—41no—
108C4×Dic11C22⋊C411yescharacteristic
109C4×Dic11C22⋊C411yescharacteristic
110C4×Dic11D811yescharacteristic
111C4×Dic11D811yescharacteristic
112#4318—41no—
113#4318—41no—
114C2×C11⋊C8—21no—
115C2×C11⋊C8—21no—
116C2×C11⋊C8—41no—
117C2×C11⋊C8C22⋊C411yescharacteristic
118C2×C11⋊C8C22⋊C411yescharacteristic
119Dic44—21no—
120Dic44C4⋊C412yes—
121D88—21no—
122D88C4⋊C412yes—
123#4314—22no—
124#4314—22no—
125C11×C16—41no—
126C11⋊C16—41no—
127C4×#135—111no—
128C2×C4⋊C16—111no—
129C2×#359—111no—
130C2×#359—111no—
131#1848—111no—
132#1382—111no—
133#1382D1111yescharacteristic, complemented
134C23×C11C2×SD1611yescharacteristic
135C22×D11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11C2×C22⋊C411yescharacteristic
139C2×C4×C11#12111yescharacteristic
140C2×C4×C11C22⋊Q811yescharacteristic
141C2×C4×C11C2×D811yescharacteristic
142C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C11#13711yescharacteristic
144C22⋊D11—42no—
145C22⋊D11—42no—
146C2×Dic11—22no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11#10211yescharacteristic
150C2×Dic11#10211yescharacteristic
151C2×Dic11#10211yescharacteristic
152C2×Dic11#10211yescharacteristic
153D44—22no—
154D44—41no—
155C4×D11—42no—
156C4×D11—42no—
157C4×D11—82no—
158C4×D11—82no—
159Dic22—22no—
160Dic22—41no—
161C8×C11—81no—
162C8×C11C2×C4⋊C411yescharacteristic
163C8×C11#11711yescharacteristic
164C8×C11#12111yescharacteristic
165C8×C11C22⋊Q811yescharacteristic
166C11⋊C8—21no—
167C11⋊C8—21no—
168C11⋊C8—81no—
169C2×#135—111no—
170C4×#41—221no—
171C22×C16—111no—
172C22×C16C2×D1111yescharacteristic
173C4×Q16—111no—
174C4×Q16—111no—
175C4×SD16—221no—
176C4×SD16—221no—
177C4×D8—111no—
178C4×D8—111no—
179C2×#108—111no—
180C2×#108—221no—
181C2×#108C2×D1111yescharacteristic
182#427C2×D1111yescharacteristic
183#423—221no—
184#416—221no—
185C2×C4×C8—111no—
186C4⋊C16—221no—
187C4⋊C16—221no—
188#359—222no—
189#359—222no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11C2×#10211yescharacteristic
193C22×C11#46111yescharacteristic
194C22×C11#47611yescharacteristic
195C2×D11—42no—
196C2×D11—81no—
197C2×D11—81no—
198C4×C11—81no—
199C4×C11—81no—
200C4×C11#38011yescharacteristic
201C4×C11#41711yescharacteristic
202C4×C11#45911yescharacteristic
203C4×C11#47411yescharacteristic
204Dic11—21no—
205Dic11—21no—
206Dic11—21no—
207Dic11—42no—
208Dic11#35912yescomplemented
209C2×#41—221no—
210#135—112no—
211#135—112no—
212#135—221no—
213#135—221no—
214C2×Q16—111no—
215C2×SD16—221no—
216C2×D8—111no—
217C2×M16—21no—
218C2×M16—221no—
219C22×C8—111no—
220C22×C8C22×D1111yescharacteristic
221C4×Q8—221no—
222C4×Q8—221no—
223C4×D4—221no—
224C4×D4—221no—
225C4×D4—441no—
226C4×D4—441no—
227#117—21no—
228#117—441no—
229C2×C42—111no—
230C2×C42—441no—
231C2×C16—21no—
232C2×C16—21no—
233C2×C16—21no—
234C2×C16—221no—
235C2×C16—221no—
236C2×C16—221no—
237#108—21no—
238#108—21no—
239#108—221no—
240#108—221no—
241#108—442no—
242#107C4×D1111yescharacteristic
243#107C4×D1111yescharacteristic
244#106—21no—
245C4⋊C8—441no—
246C4⋊C8—441no—
247#103—221no—
248#103—221no—
249#102—221no—
250#102—221no—
251C4×C8—111no—
252C4×C8—111no—
253C4×C8—111no—
254C4×C8—111no—
255C2×C11—21no—
256C2×C11—21no—
257C2×C11#180211yescharacteristic
258C2×C11C2×#35911yescharacteristic
259C2×C11#214311yescharacteristic
260D11—82no—
261#41—222no—
262#41—222no—
263#41—441no—
264#41—441no—
265C2×Q8—221no—
266C2×D4—221no—
267C2×D4—441no—
268C22×C4—111no—
269C22×C4—111no—
270C22×C4—441no—
271C22×C4—441no—
272C22×C4—441no—
273C22×C4D4×D1111yescharacteristic
274Q16—112no—
275Q16—221no—
276SD16—222no—
277SD16—222no—
278D8—112no—
279D8—221no—
280M16—41no—
281M16—41no—
282M16—441no—
283M16—441no—
284C2×C8—41no—
285C2×C8—111no—
286C2×C8—111no—
287C2×C8—221no—
288C2×C8—221no—
289C2×C8—441no—
290C2×C8C2×C4×D1111yescharacteristic
291C2×C8#433911yescharacteristic
292C2×C8#433911yescharacteristic
293C2×C8D4×D1111yescharacteristic
294C2×C8D4×D1111yescharacteristic
295C2×C8Q8×D1111yescharacteristic
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—441no—
299C4⋊C4—441no—
300C22⋊C4—41no—
301C22⋊C4—441no—
302C22⋊C4—441no—
303C42—41no—
304C42—111no—
305C42—111no—
306C42—111no—
307C42—111no—
308C42—441no—
309C42—441no—
310C16—41no—
311C16—441no—
312C11#1281511yescharacteristic, complemented, Sylow
313C23—441no—
314C23SD16×D1111yescharacteristic
315Q8—222no—
316Q8—441no—
317D4—222no—
318D4—442no—
319D4—442no—
320D4—441no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—111no—
324C2×C4—111no—
325C2×C4—111no—
326C2×C4—111no—
327C2×C4—222no—
328C2×C4—441no—
329C2×C4—441no—
330C2×C4—442no—
331C2×C4—442no—
332C2×C4—882no—
333C2×C4—882no—
334C2×C4C22⋊C4×D1111yescharacteristic
335C2×C4#6693711yescharacteristic
336C2×C4#6694911yescharacteristic
337C2×C4D8×D1111yescharacteristic
338C2×C4#6696711yescharacteristic
339C2×C4#6697111yescharacteristic
340C8—81no—
341C8—221no—
342C8—221no—
343C8—881no—
344C8#6692511yescharacteristic
345C8#6693711yescharacteristic
346C8C4⋊C4×D1111yescharacteristic
347C8#6694911yescharacteristic
348C22—21no—
349C22—21no—
350C22—442no—
351C22—881no—
352C22—881no—
353C22D11×#10211yescharacteristic
354C22#1062243111yescharacteristic
355C22#1062248311yescharacteristic
356C4—81no—
357C4—81no—
358C4—112no—
359C4—221no—
360C4—221no—
361C4—221no—
362C4—442no—
363C4#1062228011yescharacteristic
364C4#1062239911yescharacteristic
365C4#1062241611yescharacteristic
366C4#1062250311yescharacteristic
367C2—21no—
368C2—21no—
369C2—882no—
370C2#1306861511yescharacteristic
371C2D11×#35911yescharacteristic
372C2#1307034211yescharacteristic
subgroupG/H
centerC2×C4D8×D11
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#1382C2
socleC22×C11C2×#102
prime radicalC2×#66957C22
cosocleC22×C8×C11C23
hypercenter#1382D11
hypocenterC11#12815
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ #1382

Complements

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

NH ≅ G/Ntype
2. C2×Dic11⋊C16C2semidirect
5. #13068786C2semidirect
6. #13066711C2semidirect
7. C11×#1382C2semidirect
133. #1382D11semidirect
208. Dic11#359semidirect
312. C11#12815semidirect

Maximal subgroups

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

subgroupindex
#130773872
C2×Dic11⋊C162
C2×#106221482
C2×#106221352
#130687862
#130667112
C11×#13822
#1281511