Finite Group Databasebeta

← #14783523

Subgroups — #14783523

Order 2816.

972 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622737C212yesmaximal, complemented
2#13077060C211yesmaximal, characteristic
3#13077060C212yesmaximal
4#13070131C218yesmaximal, complemented
5C2×C11⋊#338C211yesmaximal, characteristic, complemented
6C2×C11×#430C211yesmaximal, characteristic, complemented
7C22×#4339C2211yescharacteristic
8C22×C11×M16C2212yes—
9C22×C11×M16C2211yescharacteristic
10C22×#4318C2211yescharacteristic
11C22×#4318C2212yes—
12C11×#430—22no—
13C11×#430C2214yes—
14C2×C11×#108—22no—
15#10622742—22no—
16#10622742—24no—
17#10622739C2214yes—
18#10622739C2218yes—
19#10622737—24no—
20#10622737C2218yes—
21C2×#66886—24no—
22#10622723—22no—
23#10622723—24no—
24C11⋊#338C2214yes—
25C23×C4×C11C2311yescharacteristic
26C22×C22⋊D11Q812yes—
27C2×#4339—22no—
28C2×#4339—21no—
29C2×#4339—22no—
30C2×#4339—21no—
31C2×#4339—22no—
32C2×#4339—22no—
33C2×#4339—21no—
34C2×#4339—21no—
35C22×D44Q811yescharacteristic
36C22×C4×D11C2312yes—
37C22×Dic22Q811yescharacteristic
38C2×C11×M16—22no—
39C2×C11×M16—22no—
40C2×C11×M16—22no—
41C2×C11×M16—22no—
42C2×C11×M16—22no—
43C2×C11×M16—22no—
44C2×C11×M16—22no—
45C2×C11×M16D412yes—
46C2×C11×M16C2314yes—
47C2×C11×M16C2312yes—
48C22×C8×C11—22no—
49C22×C8×C11D412yes—
50C2×#4318—22no—
51C2×#4318—22no—
52C2×#4318—22no—
53C2×#4318—22no—
54C2×#4318—21no—
55C2×#4318—22no—
56C2×#4318—22no—
57C2×#4318D414yes—
58C2×#4318C2312yes—
59C2×#4318C2314yes—
60C22×C11⋊C8—21no—
61C22×C11⋊C8D414yes—
62C11×#108—28no—
63#66886—216no—
64(C2×D11)⋊C8—28no—
65(C2×D11)⋊C8—216no—
66#23723—111nomaximal, Sylow
67C24×C11C2×Q811yescharacteristic
68C23×D11C2×Q812yes—
69C22×C4×C11C2×D412yes—
70C22×C4×C11C2×D412yes—
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×Q811yescharacteristic
74C22×C4×C11#4112yes—
75C22×C4×C11#4112yes—
76C22×C4×C11#4111yescharacteristic
77C22×C4×C11#4111yescharacteristic
78C22×C4×C11C2411yescharacteristic
79C2×C22⋊D11—24no—
80C2×C22⋊D11—24no—
81C2×C22⋊D11—22no—
82C2×C22⋊D11—22no—
83C22×Dic11C2×Q812yes—
84#4339—42no—
85#4339—42no—
86#4339—42no—
87#4339—42no—
88#4339—41no—
89#4339—41no—
90#4339—42no—
91#4339—42no—
92#4339—41no—
93#4339—41no—
94C2×D44—22no—
95C2×D44—22no—
96C2×D44—21no—
97C2×D44—21no—
98C2×C4×D11—24no—
99C2×C4×D11—22no—
100C2×C4×D11—24no—
101C2×C4×D11—22no—
102C2×Dic22—22no—
103C2×Dic22—22no—
104C2×Dic22—21no—
105C2×Dic22—21no—
106C11×M16—24no—
107C11×M16—24no—
108C11×M16—24no—
109C11×M16—24no—
110C11×M16—42no—
111C11×M16—42no—
112C2×C8×C11—22no—
113C2×C8×C11—22no—
114C2×C8×C11—24no—
115C2×C8×C11—42no—
116C2×C8×C11—42no—
117C2×C8×C11C2×D414yes—
118#4318—24no—
119#4318—24no—
120#4318—24no—
121#4318—24no—
122#4318—24no—
123#4318—41no—
124#4318—41no—
125C2×C11⋊C8—24no—
126C2×C11⋊C8—24no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—42no—
129C2×C11⋊C8C2×D418yes—
130C2×#430—112no—
131C2×#430D1111yescharacteristic, complemented
132#2879—112no—
133#2879—111no—
134#2091—118no—
135C2×#338—111no—
136C23×C11—81no—
137C23×C11C22⋊Q812yes—
138C23×C11C22⋊Q812yes—
139C23×C11C22⋊Q811yescharacteristic
140C23×C11C22⋊Q811yescharacteristic
141C23×C11C22×Q811yescharacteristic
142C22×D11—24no—
143C22×D11—22no—
144C22×D11—82no—
145C2×C4×C11C22⋊Q812yes—
146C2×C4×C11C22⋊Q812yes—
147C2×C4×C11C22⋊Q811yescharacteristic
148C2×C4×C11C22⋊Q811yescharacteristic
149C2×C4×C11#12312yes—
150C2×C4×C11#12312yes—
151C2×C4×C11#12312yes—
152C2×C4×C11#12312yes—
153C2×C4×C11#12311yescharacteristic
154C2×C4×C11#12311yescharacteristic
155C2×C4×C11#12312yes—
156C2×C4×C11#12712yes—
157C2×C4×C11#12711yescharacteristic
158C2×C4×C11#12711yescharacteristic
159C2×C4×C11C22×D412yes—
160C2×C4×C11C22×D411yescharacteristic
161C2×C4×C11C2×#4112yes—
162C2×C4×C11C2×#4111yescharacteristic
163C22⋊D11—42no—
164C22⋊D11—44no—
165C22⋊D11—42no—
166C2×Dic11—24no—
167C2×Dic11—22no—
168D44—41no—
169D44—42no—
170D44—41no—
171C4×D11—44no—
172C4×D11—42no—
173C4×D11—42no—
174Dic22—41no—
175Dic22—42no—
176Dic22—41no—
177C8×C11—24no—
178C8×C11—44no—
179C11⋊C8—28no—
180C11⋊C8—42no—
181C22×#41—111no—
182C22×M16—112no—
183C22×M16—111no—
184C22×M16C2×D1112yes—
185C22×M16C2×D1111yescharacteristic
186#430—22no—
187#430—118no—
188#430—224no—
189#430C2×D1114yes—
190C2×#108—22no—
191C2×#108—224no—
192#408—224no—
193#408—224no—
194#408—222no—
195#408—222no—
196#407—118no—
197#407—114no—
198#338—114no—
199C22×C11—41no—
200C22×C11—42no—
201C22×C11—42no—
202C22×C11—41no—
203C22×C11—41no—
204C22×C11#39911yescharacteristic
205C22×C11#39912yes—
206C22×C11#39911yescharacteristic
207C22×C11C2×C22⋊Q812yes—
208C22×C11C2×C22⋊Q811yescharacteristic
209C2×D11—48no—
210C2×D11—44no—
211C2×D11—42no—
212C4×C11#39911yescharacteristic
213C4×C11#39912yes—
214C4×C11#39911yescharacteristic
215C4×C11C2×#12312yes—
216C4×C11C2×#12311yescharacteristic
217C4×C11C2×#12711yescharacteristic
218Dic11—42no—
219C2×#41—222no—
220C2×#41—222no—
221C2×#41—222no—
222C2×#41—222no—
223C2×#41—221no—
224C2×#41—221no—
225C2×#41—221no—
226C2×#41—221no—
227C22×Q8—111no—
228C22×D4—112no—
229C22×D4—111no—
230C23×C4—112no—
231C23×C4C22×D1111yescharacteristic
232C2×M16—22no—
233C2×M16—22no—
234C2×M16—22no—
235C2×M16—22no—
236C2×M16—22no—
237C2×M16—22no—
238C2×M16—22no—
239C2×M16—114no—
240C2×M16—114no—
241C2×M16—112no—
242C2×M16—222no—
243C2×M16—222no—
244C2×M16—222no—
245C2×M16—222no—
246C2×M16—221no—
247C2×M16—222no—
248C2×M16—222no—
249C2×M16C22⋊D1112yes—
250C2×M16C22×D1114yes—
251C2×M16C22×D1112yes—
252C22×C8—22no—
253C22×C8—114no—
254C22×C8—221no—
255C22×C8C22⋊D1112yes—
256#108—28no—
257#108—2216no—
258C22⋊C8—2216no—
259C22⋊C8—228no—
260C2×C11—22no—
261C2×C11—21no—
262C2×C11—21no—
263C2×C11—22no—
264C2×C11—21no—
265C2×C11C2×#39911yescharacteristic
266D11—82no—
267C24—112no—
268C24Q8×D1111yescharacteristic
269#41—442no—
270#41—442no—
271#41—442no—
272#41—442no—
273#41—441no—
274#41—441no—
275#41—442no—
276#41—441no—
277#41—442no—
278#41—441no—
279C2×Q8—222no—
280C2×Q8—222no—
281C2×Q8—221no—
282C2×Q8—221no—
283C2×D4—224no—
284C2×D4—224no—
285C2×D4—222no—
286C2×D4—222no—
287C2×D4—222no—
288C2×D4—222no—
289C2×D4—221no—
290C2×D4—221no—
291C22×C4—112no—
292C22×C4—224no—
293C22×C4—224no—
294C22×C4—222no—
295C22×C4—222no—
296C22×C4#433912yes—
297C22×C4#433912yes—
298C22×C4D4×D1112yes—
299C22×C4D4×D1112yes—
300C22×C4Q8×D1111yescharacteristic
301C22×C4#434311yescharacteristic
302C22×C4#434311yescharacteristic
303C22×C4C2×C22⋊D1111yescharacteristic
304C22×C4C2×C22⋊D1111yescharacteristic
305C22×C4C23×D1111yescharacteristic
306M16—24no—
307M16—24no—
308M16—24no—
309M16—24no—
310M16—42no—
311M16—42no—
312M16—224no—
313M16—224no—
314M16—224no—
315M16—224no—
316M16—224no—
317M16—441no—
318M16—441no—
319C2×C8—22no—
320C2×C8—22no—
321C2×C8—24no—
322C2×C8—42no—
323C2×C8—42no—
324C2×C8—118no—
325C2×C8—224no—
326C2×C8—224no—
327C2×C8—222no—
328C2×C8—442no—
329C2×C8C2×C22⋊D1114yes—
330C11#2372311yescharacteristic, complemented, Sylow
331C23—81no—
332C23—224no—
333C23—222no—
334C23—882no—
335C23#6694912yes—
336C23#6694912yes—
337C23#6699911yescharacteristic
338C23#6699911yescharacteristic
339C23C2×Q8×D1111yescharacteristic
340Q8—441no—
341Q8—442no—
342Q8—441no—
343D4—442no—
344D4—444no—
345D4—442no—
346D4—441no—
347D4—442no—
348D4—441no—
349C2×C4—224no—
350C2×C4—222no—
351C2×C4—444no—
352C2×C4—442no—
353C2×C4—442no—
354C2×C4#6694712yes—
355C2×C4#6694712yes—
356C2×C4#6694712yes—
357C2×C4#6694712yes—
358C2×C4#6694912yes—
359C2×C4#6694912yes—
360C2×C4#6698211yescharacteristic
361C2×C4#6698211yescharacteristic
362C2×C4#6698212yes—
363C2×C4#6699311yescharacteristic
364C2×C4#6699312yes—
365C2×C4#6699311yescharacteristic
366C2×C4#6699911yescharacteristic
367C2×C4#6699911yescharacteristic
368C2×C4C2×#433912yes—
369C2×C4C2×D4×D1112yes—
370C2×C4C2×#434311yescharacteristic
371C2×C4C22×C22⋊D1111yescharacteristic
372C8—24no—
373C8—44no—
374C8—228no—
375C8—442no—
376C22—41no—
377C22—42no—
378C22—42no—
379C22—41no—
380C22—41no—
381C22—448no—
382C22—444no—
383C22—442no—
384C22#1062260511yescharacteristic
385C22#1062260512yes—
386C22#1062260511yescharacteristic
387C22C2×#6694912yes—
388C22C2×#6699911yescharacteristic
389C4—442no—
390C4#1062260511yescharacteristic
391C4#1062260512yes—
392C4#1062260511yescharacteristic
393C4C2×#6694712yes—
394C4C2×#6698211yescharacteristic
395C4C2×#6699311yescharacteristic
396C2—22no—
397C2—21no—
398C2—21no—
399C2—22no—
400C2—21no—
401C2—882no—
402C2C2×#1062260511yescharacteristic
subgroupG/H
centerC4C2×#66993
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#430C2
socleC2×C11C2×#399
prime radicalC22×#4339C22
hypercenterC2×#430D11
hypocenterC11#23723
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#430

Complements

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

NH ≅ G/Ntype
1. C2×#10622737C2semidirect
4. #13070131C2semidirect
5. C2×C11⋊#338C2semidirect
6. C2×C11×#430C2semidirect
131. C2×#430D11semidirect
330. C11#23723semidirect

Maximal subgroups

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

subgroupindex
C2×#106227372
#130770602
#130701312
C2×C11⋊#3382
C2×C11×#4302
#2372311