Finite Group Databasebeta

← #14672011

Subgroups — #14672011

Order 2816.

490 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079040C211yesmaximal, characteristic
2C2×#10622148C211yesmaximal, characteristic, complemented
3C2×#10622205C211yesmaximal, characteristic, complemented
4C2×#10622135C211yesmaximal, characteristic, complemented
5C2×C16×Dic11C211yesmaximal, characteristic, complemented
6#13068786C211yesmaximal, characteristic, complemented
7C2×C11×#359C211yesmaximal, characteristic, complemented
8C2×C11×#135C2211yescharacteristic
9#10623363—21no—
10C2×#67003—21no—
11C2×#66957C2211yescharacteristic
12C22×C11×C16C2211yescharacteristic
13C2×C11×#108C2211yescharacteristic
14#10622804C411yescharacteristic
15#10622794C411yescharacteristic
16#10622788—21no—
17#10622781—21no—
18#10622768C411yescharacteristic
19#10622764C411yescharacteristic
20C2×#66886—21no—
21#10622731—21no—
22C2×#66883C2211yescharacteristic
23C2×C8×Dic11C2211yescharacteristic
24C22×C11⋊C16C2211yescharacteristic
25C11×#359—22no—
26#10622205—22no—
27#10622148—22no—
28C16×Dic11—21no—
29C16×Dic11—21no—
30#10622135—22no—
31C2×C11×#41—21no—
32C2×#4339—21no—
33C11×#135—21no—
34C11×#135—21no—
35C11×#135—21no—
36C11×#135—21no—
37C2×C11×Q16C2×C411yescharacteristic
38C2×C11×SD16—21no—
39C2×C11×D8C2×C411yescharacteristic
40C2×C11×M16—21no—
41C22×C8×C11C2311yescharacteristic
42#67003—42no—
43#67003—42no—
44#67000—21no—
45#66997—21no—
46C2×#4326—21no—
47C2×#4325—21no—
48#66993—21no—
49#66992—42no—
50#66989—21no—
51C2×#4324—21no—
52C2×#4323—21no—
53C4×C22⋊D11—42no—
54C2×C4×Dic11D411yescharacteristic
55C2×#4318—21no—
56C22×C11⋊C8D411yescharacteristic
57C2×Dic44C2×C411yescharacteristic
58#66957—21no—
59#66957—21no—
60#66957—21no—
61#66957—21no—
62C2×D88C2×C411yescharacteristic
63C2×#4314—21no—
64C2×C11×C16—21no—
65C2×C11×C16—21no—
66C2×C11×C16D412yescomplemented
67C11×#108—21no—
68C11×#108—21no—
69#66886—42no—
70#66883—21no—
71#66883—21no—
72Dic11⋊C8—42no—
73C8×Dic11C2×C411yescharacteristic
74C8×Dic11C2×C411yescharacteristic
75C8×Dic11D411yescharacteristic
76C8×Dic11D411yescharacteristic
77C2×C11⋊C16—21no—
78C2×C11⋊C16—21no—
79C2×C11⋊C16D412yescomplemented
80#13208—111nomaximal, Sylow
81C11×#41—41no—
82C11×#41—41no—
83C11×#41—41no—
84C11×#41—41no—
85C2×Q8×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11C2×D411yescharacteristic
90C2×C22⋊D11—42no—
91C2×C22⋊D11—41no—
92C22×Dic11SD1612yes—
93#4339—41no—
94#4339—41no—
95#4339—41no—
96#4339—41no—
97C2×D44—21no—
98C2×C4×D11—41no—
99C2×Dic22—21no—
100C11×Q16—21no—
101C11×Q16—21no—
102C11×SD16—41no—
103C11×SD16—41no—
104C11×D8—21no—
105C11×D8—21no—
106C11×M16—41no—
107C11×M16—41no—
108C2×C8×C11—41no—
109C2×C8×C11C22×C411yescharacteristic
110C2×C8×C11C2×D411yescharacteristic
111C2×C8×C11C2×D411yescharacteristic
112C2×C8×C11C2×D411yescharacteristic
113C2×C8×C11#4111yescharacteristic
114C2×C8×C11#4111yescharacteristic
115C22⋊Dic11—42no—
116#4326—42no—
117#4325—42no—
118#4324—42no—
119#4323—42no—
120(C2×D11)⋊C4—42no—
121Dic11⋊C4—42no—
122C4×Dic11C22⋊C411yescharacteristic
123C4×Dic11C22⋊C411yescharacteristic
124C4×Dic11D812yes—
125#4318—41no—
126#4318—41no—
127C2×C11⋊C8—41no—
128C2×C11⋊C8C22⋊C411yescharacteristic
129C2×C11⋊C8C22⋊C411yescharacteristic
130C2×C11⋊C8D812yes—
131C2×C11⋊C8SD1612yes—
132Dic44—21no—
133Dic44—21no—
134D88—21no—
135D88—21no—
136#4314—41no—
137#4314—41no—
138C11×C16—22no—
139C11⋊C16—22no—
140#3147—111no—
141C2×#359—111no—
142C2×#359—111no—
143C2×#359—111no—
144C2×#359D1111yescharacteristic, complemented
145C2×C4×C16—111no—
146#1848—111no—
147C23×C11—41no—
148C23×C11C2×SD1611yescharacteristic
149C22×D11—41no—
150Q8×C11—41no—
151Q8×C11—41no—
152D4×C11—41no—
153D4×C11—41no—
154D4×C11—81no—
155D4×C11—81no—
156C2×C4×C11—41no—
157C2×C4×C11—81no—
158C2×C4×C11—81no—
159C2×C4×C11C2×C22⋊C411yescharacteristic
160C2×C4×C11#12411yescharacteristic
161C2×C4×C11#12711yescharacteristic
162C2×C4×C11C2×D811yescharacteristic
163C2×C4×C11C2×D811yescharacteristic
164C2×C4×C11C2×SD1611yescharacteristic
165C22⋊D11—81no—
166C22⋊D11—81no—
167C22⋊D11—84no—
168C2×Dic11—24no—
169C2×Dic11—41no—
170C2×Dic11#10212yes—
171C2×Dic11#10212yes—
172D44—41no—
173D44—41no—
174C4×D11—81no—
175C4×D11—81no—
176Dic22—41no—
177Dic22—41no—
178C8×C11—81no—
179C8×C11C4×D411yescharacteristic
180C8×C11C4×D411yescharacteristic
181C8×C11#12111yescharacteristic
182C8×C11#12111yescharacteristic
183C11⋊C8—81no—
184C11⋊C8#10212yes—
185C11⋊C8#10212yes—
186C2×#135—111no—
187C2×#135—221no—
188C2×#135C2×D1111yescharacteristic
189#532—221no—
190C22×C16—111no—
191C22×C16C2×D1111yescharacteristic
192#495—111no—
193#495—111no—
194#495—221no—
195#494—111no—
196#493—111no—
197#492—221no—
198C2×#108—111no—
199C2×#108—221no—
200C2×#108C2×D1111yescharacteristic
201#423—221no—
202C2×C4×C8—111no—
203#359—22no—
204#359—222no—
205#359—222no—
206#359—222no—
207C4×C16—221no—
208C4×C16—221no—
209C22×C11—22no—
210C22×C11—82no—
211C22×C11—81no—
212C22×C11C2×#10211yescharacteristic
213C22×C11#48611yescharacteristic
214C22×C11#49211yescharacteristic
215C2×D11—82no—
216C2×D11—81no—
217C4×C11—81no—
218C4×C11#39011yescharacteristic
219C4×C11C2×#10211yescharacteristic
220C4×C11#48611yescharacteristic
221C4×C11#49311yescharacteristic
222Dic11—22no—
223Dic11—81no—
224Dic11#35914yescomplemented
225C2×#41—21no—
226C2×#41—221no—
227#135—21no—
228#135—21no—
229#135—21no—
230#135—21no—
231#135—221no—
232#135—221no—
233#135—221no—
234#135—221no—
235#135—442no—
236#135—442no—
237C2×Q16—111no—
238C2×Q16—221no—
239C2×Q16C4×D1111yescharacteristic
240C2×SD16—21no—
241C2×SD16—221no—
242C2×SD16—221no—
243C2×SD16—221no—
244C2×D8—111no—
245C2×D8—221no—
246C2×D8C4×D1111yescharacteristic
247C2×M16—21no—
248C2×M16—221no—
249C22×C8—111no—
250C22×C8C22×D1111yescharacteristic
251C4⋊Q8—221no—
252#127—221no—
253#124—221no—
254#124—221no—
255#121—442no—
256C4×D4—442no—
257C2×C42—111no—
258C2×C16—21no—
259C2×C16—21no—
260C2×C16—112no—
261C2×C16—221no—
262C2×C16—221no—
263C2×C16C22⋊D1112yescomplemented
264#108—21no—
265#108—21no—
266#108—221no—
267#108—221no—
268#108—442no—
269C4⋊C8—442no—
270C4×C8—111no—
271C4×C8—111no—
272C4×C8—111no—
273C4×C8—111no—
274C2×C11—21no—
275C2×C11—21no—
276C2×C11—161no—
277C2×C11#195711yescharacteristic
278C2×C11C2×#35912yes—
279D11—161no—
280#41—41no—
281#41—41no—
282#41—41no—
283#41—41no—
284#41—441no—
285#41—441no—
286#41—441no—
287#41—441no—
288C2×Q8—21no—
289C2×Q8—221no—
290C2×D4—21no—
291C2×D4—41no—
292C2×D4—221no—
293C2×D4—442no—
294C2×D4—441no—
295C22×C4—41no—
296C22×C4—112no—
297C22×C4—441no—
298C22×C4D4×D1111yescharacteristic
299Q16—21no—
300Q16—21no—
301Q16—221no—
302Q16—221no—
303Q16—442no—
304SD16—41no—
305SD16—41no—
306SD16—442no—
307SD16—442no—
308SD16—441no—
309SD16—441no—
310D8—21no—
311D8—21no—
312D8—221no—
313D8—221no—
314D8—442no—
315M16—41no—
316M16—41no—
317M16—441no—
318M16—441no—
319C2×C8—41no—
320C2×C8—111no—
321C2×C8—111no—
322C2×C8—112no—
323C2×C8—112no—
324C2×C8—441no—
325C2×C8C2×C4×D1111yescharacteristic
326C2×C8#433911yescharacteristic
327C2×C8D4×D1111yescharacteristic
328C2×C8D4×D1111yescharacteristic
329C2×C8#434111yescharacteristic
330C2×C8C2×C22⋊D1111yescharacteristic
331C4⋊C4—442no—
332C22⋊C4—442no—
333C22⋊C4—442no—
334C42—111no—
335C42—111no—
336C42—112no—
337C16—22no—
338C16—222no—
339C11#1320811yescharacteristic, complemented, Sylow
340C23—41no—
341C23—441no—
342C23SD16×D1111yescharacteristic
343Q8—41no—
344Q8—41no—
345Q8—441no—
346Q8—441no—
347D4—41no—
348D4—41no—
349D4—81no—
350D4—81no—
351D4—441no—
352D4—441no—
353D4—884no—
354D4—881no—
355D4—881no—
356C2×C4—41no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—112no—
360C2×C4—112no—
361C2×C4—224no—
362C2×C4—441no—
363C2×C4—881no—
364C2×C4—881no—
365C2×C4C22⋊C4×D1111yescharacteristic
366C2×C4#6693811yescharacteristic
367C2×C4D8×D1111yescharacteristic
368C2×C4D8×D1111yescharacteristic
369C2×C4SD16×D1111yescharacteristic
370C2×C4#6699311yescharacteristic
371C8—81no—
372C8—112no—
373C8—112no—
374C8—881no—
375C8(C22⋊D11)⋊C411yescharacteristic
376C8#6693711yescharacteristic
377C8C4×C22⋊D1111yescharacteristic
378C8#6699211yescharacteristic
379C22—22no—
380C22—82no—
381C22—81no—
382C22—882no—
383C22—881no—
384C22#1062237311yescharacteristic
385C22D11×#10211yescharacteristic
386C22#1062278811yescharacteristic
387C4—81no—
388C4—114no—
389C4—222no—
390C4—881no—
391C4#1062237311yescharacteristic
392C4D11×#10211yescharacteristic
393C4#1062257011yescharacteristic
394C4#1062276411yescharacteristic
395C2—21no—
396C2—21no—
397C2—161no—
398C2—1761no—
399C2#1306942011yescharacteristic
400C2D11×#35912yes—
subgroupG/H
centerC2×C4D8×D11
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC2×C11×#359C2
socleC22×C11C2×#102
prime radical#13079040C2
cosocleC22×C8×C11C23
hypercenterC2×#359D11
hypocenterC11#13208
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C2×#359

Complements

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

NH ≅ G/Ntype
2. C2×#10622148C2semidirect
3. C2×#10622205C2semidirect
4. C2×#10622135C2semidirect
5. C2×C16×Dic11C2semidirect
6. #13068786C2semidirect
7. C2×C11×#359C2semidirect
66. C2×C11×C16D4semidirect
79. C2×C11⋊C16D4semidirect
144. C2×#359D11semidirect
224. Dic11#359semidirect
263. C2×C16C22⋊D11semidirect
339. C11#13208semidirect

Maximal subgroups

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

subgroupindex
#130790402
C2×#106221482
C2×#106222052
C2×#106221352
C2×C16×Dic112
#130687862
C2×C11×#3592
#1320811