Finite Group Databasebeta

← #14672481

Subgroups — #14672481

Order 2816.

566 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66893C211yesmaximal, characteristic, complemented
2C2×#10622500C211yesmaximal, characteristic
3C2×#10622801C211yesmaximal, characteristic
4C2×#10622141C211yesmaximal, characteristic, complemented
5C2×(C2×D11)⋊C16C211yesmaximal, characteristic
6#13066707C211yesmaximal, characteristic, complemented
7C2×C11×#358C211yesmaximal, characteristic, complemented
8C22×C11×Q16C2211yescharacteristic
9C2×#66999—21no—
10C22×Dic44C2211yescharacteristic
11C22×C8×D11C2211yescharacteristic
12C2×#66950—21no—
13C22×C11×C16C2211yescharacteristic
14C2×C11×#107C2211yescharacteristic
15C2×#66899—21no—
16#10622801—22no—
17#10622801—22no—
18C2×#66893—22no—
19C2×#66893—22no—
20C2×#66893—22no—
21C2×#66882C2211yescharacteristic
22C22×C11⋊C16C2211yescharacteristic
23C2×#66874—21no—
24#10622500—22no—
25#10622500—22no—
26C11×#358—22no—
27(C2×D11)⋊C16—22no—
28#10622141—22no—
29C22×Q8×C11—21no—
30C22×C4×D11D411yescharacteristic
31C22×Dic22—21no—
32C2×C11×Q16—21no—
33C2×C11×Q16—21no—
34C2×C11×Q16—21no—
35C2×C11×Q16—21no—
36C2×C11×Q16—21no—
37C2×C11×Q16D412yes—
38C22×C8×C11C2311yescharacteristic
39C2×C11×C4⋊C4—21no—
40#66999—24no—
41#66999—42no—
42C2×(C2×D11)⋊C4—41no—
43C2×(C2×D11)⋊C4—41no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11—41no—
46C2×Dic11⋊C4—41no—
47C22×C11⋊C8D411yescharacteristic
48C2×Dic44—21no—
49C2×Dic44—21no—
50C2×Dic44—21no—
51C2×Dic44—21no—
52C2×Dic44—21no—
53C2×Dic44D412yes—
54C2×C8×D11—21no—
55C2×C8×D11—21no—
56C2×C8×D11—21no—
57C2×C8×D11—21no—
58C2×C8×D11—21no—
59C2×C8×D11—21no—
60#66950—24no—
61#66950—42no—
62C2×C11×C16—21no—
63C2×C11×C16—21no—
64C2×C11×C16—21no—
65C11×#107—21no—
66C11×#107D412yes—
67#66899—24no—
68#66893—28no—
69#66882—21no—
70#66882D412yes—
71C2×C11⋊C16—21no—
72C2×C11⋊C16—21no—
73C2×C11⋊C16D412yes—
74#66874—24no—
75#13306—111nomaximal, Sylow
76C23×D11D811yescharacteristic
77C2×Q8×C11—22no—
78C2×Q8×C11—41no—
79C2×Q8×C11—41no—
80C2×Q8×C11—41no—
81C2×Q8×C11—41no—
82C2×Q8×C11—41no—
83C22×C4×C11—41no—
84C22×C4×C11—41no—
85C22×C4×C11C2×D411yescharacteristic
86C22×Dic11—41no—
87C22×Dic11—41no—
88C22×Dic11D811yescharacteristic
89C2×C4×D11—21no—
90C2×C4×D11—21no—
91C2×C4×D11—21no—
92C2×C4×D11—21no—
93C2×C4×D11—21no—
94C2×C4×D11—21no—
95C2×Dic22—22no—
96C2×Dic22—41no—
97C2×Dic22—41no—
98C2×Dic22—41no—
99C2×Dic22—41no—
100C2×Dic22—41no—
101C11×Q16—22no—
102C11×Q16—22no—
103C11×Q16—41no—
104C11×Q16—41no—
105C2×C8×C11C2×D411yescharacteristic
106C2×C8×C11C2×D411yescharacteristic
107C2×C8×C11C2×D411yescharacteristic
108C2×C8×C11C2×D411yescharacteristic
109C2×C8×C11C2×D411yescharacteristic
110C2×C8×C11#4111yescharacteristic
111C11×C4⋊C4—22no—
112C11×C4⋊C4—41no—
113(C2×D11)⋊C4—44no—
114(C2×D11)⋊C4—44no—
115C4⋊Dic11—22no—
116C4⋊Dic11—44no—
117C4⋊Dic11—41no—
118Dic11⋊C4—44no—
119C2×C11⋊C8—21no—
120C2×C11⋊C8—21no—
121C2×C11⋊C8—21no—
122Dic44—22no—
123Dic44—22no—
124Dic44—41no—
125Dic44—41no—
126C8×D11—41no—
127C8×D11—41no—
128C8×D11—41no—
129C8×D11—41no—
130C11×C16—41no—
131C11⋊C16—22no—
132C22×Q32—111no—
133C2×#467—111no—
134C2×#467—111no—
135C2×#358—111no—
136C2×#358D1111yescharacteristic, complemented
137C2×C22⋊C16—111no—
138#1380—111no—
139C23×C11C2×D811yescharacteristic
140C22×D11—21no—
141C22×D11—21no—
142C22×D11—21no—
143C22×D11—21no—
144C22×D11—21no—
145C22×D11—21no—
146C22×D11Q3212yescomplemented
147Q8×C11—42no—
148Q8×C11—42no—
149Q8×C11—81no—
150Q8×C11—81no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—81no—
154C2×C4×C11—81no—
155C2×C4×C11—81no—
156C2×C4×C11—81no—
157C2×C4×C11#12011yescharacteristic
158C2×C4×C11#12011yescharacteristic
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11#13511yescharacteristic
161C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
163C2×Dic11—21no—
164C2×Dic11—21no—
165C2×Dic11—21no—
166C2×Dic11—42no—
167C2×Dic11—42no—
168C2×Dic11—81no—
169C2×Dic11—81no—
170C2×Dic11—81no—
171C2×Dic11—81no—
172C4×D11—41no—
173C4×D11—41no—
174C4×D11—41no—
175C4×D11—41no—
176Dic22—42no—
177Dic22—42no—
178Dic22—81no—
179Dic22—81no—
180C8×C11#12011yescharacteristic
181C8×C11#12111yescharacteristic
182C8×C11#12111yescharacteristic
183C8×C11#12711yescharacteristic
184C11⋊C8—41no—
185C22×Q16—111no—
186C22×Q16C2×D1111yescharacteristic
187C23×C8—111no—
188C2×C22⋊Q8—221no—
189C2×C22⋊Q8—221no—
190C2×Q32—222no—
191C2×Q32—222no—
192C2×Q32—222no—
193C22×C16—111no—
194C22×C16C2×D1111yescharacteristic
195#467—222no—
196#467—222no—
197#467—222no—
198#467—222no—
199C2×#107—111no—
200C2×#107C2×D1111yescharacteristic
201C2×#103—221no—
202C2×#103—221no—
203#358—22no—
204#358—222no—
205C22⋊C16—222no—
206C22×C11#44711yescharacteristic
207C22×C11#44711yescharacteristic
208C22×C11#46611yescharacteristic
209C22×C11C2×Q3211yescharacteristic
210C22×C11#50811yescharacteristic
211C22×C11#51011yescharacteristic
212C22×C11#51011yescharacteristic
213C2×D11—22no—
214C2×D11—22no—
215C2×D11—22no—
216C2×D11—41no—
217C2×D11—41no—
218C2×D11—41no—
219C2×D11—41no—
220C4×C11—82no—
221C4×C11—82no—
222C4×C11#39211yescharacteristic
223C4×C11#44911yescharacteristic
224C4×C11#44911yescharacteristic
225C4×C11#46911yescharacteristic
226Dic11—41no—
227Dic11—82no—
228Dic11—82no—
229C22×Q8—21no—
230C22×Q8—221no—
231C23×C4—111no—
232C2×Q16—21no—
233C2×Q16—21no—
234C2×Q16—21no—
235C2×Q16—21no—
236C2×Q16—21no—
237C2×Q16—112no—
238C2×Q16—221no—
239C2×Q16—221no—
240C2×Q16—221no—
241C2×Q16—221no—
242C2×Q16—221no—
243C2×Q16D4412yes—
244C22×C8—111no—
245C22×C8—221no—
246C22×C8—221no—
247C22×C8—221no—
248C22×C8—221no—
249C22×C8—221no—
250C22×C8—221no—
251C22×C8C22×D1111yescharacteristic
252C22⋊Q8—224no—
253C22⋊Q8—224no—
254C22⋊Q8—442no—
255C22⋊Q8—442no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—221no—
258C2×C4⋊C4—441no—
259C2×C4⋊C4—441no—
260C2×C22⋊C4—441no—
261C2×C22⋊C4—441no—
262Q32—228no—
263C2×C16—21no—
264C2×C16—21no—
265C2×C16—21no—
266C2×C16—112no—
267C2×C16—221no—
268C2×C16—221no—
269#107—21no—
270#107—112no—
271#107—221no—
272#107C22⋊D1112yes—
273#103—224no—
274#103—224no—
275C2×C11#199911yescharacteristic
276C2×C11#218811yescharacteristic
277C2×C11#218811yescharacteristic
278C2×C11#218911yescharacteristic
279C2×C11#218911yescharacteristic
280C2×C11#221611yescharacteristic
281C2×C11#221911yescharacteristic
282D11—42no—
283C24—111no—
284C2×Q8—22no—
285C2×Q8—41no—
286C2×Q8—41no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×Q8—222no—
291C2×Q8—441no—
292C2×Q8—441no—
293C2×Q8—441no—
294C2×Q8—441no—
295C2×Q8—441no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4—111no—
299C22×C4—221no—
300C22×C4—221no—
301C22×C4—221no—
302C22×C4—221no—
303C22×C4—221no—
304C22×C4—221no—
305C22×C4—441no—
306C22×C4—441no—
307C22×C4D4×D1111yescharacteristic
308Q16—22no—
309Q16—22no—
310Q16—41no—
311Q16—41no—
312Q16—222no—
313Q16—222no—
314Q16—441no—
315Q16—441no—
316C2×C8—221no—
317C2×C8—221no—
318C2×C8—221no—
319C2×C8—441no—
320C2×C8—441no—
321C2×C8—441no—
322C2×C8—441no—
323C2×C8C2×D4411yescharacteristic
324C2×C8#433911yescharacteristic
325C2×C8D4×D1111yescharacteristic
326C2×C8D4×D1111yescharacteristic
327C2×C8D4×D1111yescharacteristic
328C2×C8C2×C22⋊D1111yescharacteristic
329C4⋊C4—22no—
330C4⋊C4—41no—
331C4⋊C4—222no—
332C4⋊C4—444no—
333C4⋊C4—444no—
334C4⋊C4—441no—
335C22⋊C4—444no—
336C22⋊C4—444no—
337C16—41no—
338C16—222no—
339C11#1330611yescharacteristic, complemented, Sylow
340C23—112no—
341C23—221no—
342C23—221no—
343C23—221no—
344C23—221no—
345C23—221no—
346C23—221no—
347C23D8×D1111yescharacteristic
348Q8—42no—
349Q8—42no—
350Q8—81no—
351Q8—81no—
352Q8—442no—
353Q8—442no—
354Q8—881no—
355Q8—881no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4—221no—
363C2×C4—221no—
364C2×C4—221no—
365C2×C4—441no—
366C2×C4—441no—
367C2×C4—441no—
368C2×C4—441no—
369C2×C4—442no—
370C2×C4—442no—
371C2×C4—881no—
372C2×C4—881no—
373C2×C4—881no—
374C2×C4—881no—
375C2×C4#6693511yescharacteristic
376C2×C4#6693711yescharacteristic
377C2×C4#6696411yescharacteristic
378C2×C4#6696711yescharacteristic
379C2×C4#6696911yescharacteristic
380C2×C4#6699011yescharacteristic
381C8—441no—
382C8#6693511yescharacteristic
383C8#6693711yescharacteristic
384C8#6698311yescharacteristic
385C8#6699311yescharacteristic
386C22—222no—
387C22—222no—
388C22—222no—
389C22—441no—
390C22—441no—
391C22—441no—
392C22—441no—
393C22#1062238611yescharacteristic
394C22#1062238811yescharacteristic
395C22#1062252811yescharacteristic
396C22#1062252911yescharacteristic
397C22D11×Q3211yescharacteristic
398C22#1062253111yescharacteristic
399C22#1062276911yescharacteristic
400C4—82no—
401C4—82no—
402C4—441no—
403C4—882no—
404C4—882no—
405C4#1062239411yescharacteristic
406C4#1062239511yescharacteristic
407C4#1062257311yescharacteristic
408C4#1062278511yescharacteristic
409C2—442no—
410C2#1306961311yescharacteristic
411C2#1307054811yescharacteristic
412C2#1307055111yescharacteristic
413C2#1307055311yescharacteristic
414C2#1307055911yescharacteristic
415C2#1307070611yescharacteristic
416C2#1307072311yescharacteristic
subgroupG/H
centerC23D8×D11
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC2×C11×#358C2
socleC23×C11C2×D8
prime radicalC23×D11D8
hypercenterC2×#358D11
hypocenterC11#13306
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#358

Complements

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

NH ≅ G/Ntype
1. C22×#66893C2semidirect
4. C2×#10622141C2semidirect
6. #13066707C2semidirect
7. C2×C11×#358C2semidirect
136. C2×#358D11semidirect
146. C22×D11Q32semidirect
339. C11#13306semidirect

Maximal subgroups

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

subgroupindex
C22×#668932
C2×#106225002
C2×#106228012
C2×#106221412
C2×(C2×D11)⋊C162
#130667072
C2×C11×#3582
#1330611