Finite Group Databasebeta

← #14672478

Subgroups — #14672478

Order 2816.

618 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66864C211yesmaximal, characteristic, complemented
2C2×#10622500C211yesmaximal, characteristic, complemented
3C2×#10622496C211yesmaximal, characteristic
4C2×#10622130C211yesmaximal, characteristic, complemented
5C2×#10622129C211yesmaximal, characteristic, complemented
6C2×(C2×D11)⋊C16C211yesmaximal, characteristic, complemented
7C11×#1380C211yesmaximal, characteristic, complemented
8C22×Dic44C2211yescharacteristic
9C22×D88C2211yescharacteristic
10C22×C8×D11C2211yescharacteristic
11C2×#66950—21no—
12C2×#66948—21no—
13C22×C11×C16C2211yescharacteristic
14C2×C11×#107C2211yescharacteristic
15C2×C11×#107C2211yescharacteristic
16C22×C11⋊C16C2211yescharacteristic
17C2×#66874—21no—
18C2×#66873—21no—
19C2×#66864—22no—
20C2×#66864—22no—
21C2×#66864—22no—
22#10622500—22no—
23#10622500—22no—
24#10622496—22no—
25#10622496—22no—
26(C2×D11)⋊C16—22no—
27#10622130—22no—
28#10622129—22no—
29C22×D44—21no—
30C22×D44—41no—
31C22×C4×D11D411yescharacteristic
32C22×Dic22—21no—
33C22×C8×C11C2311yescharacteristic
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×(C2×D11)⋊C4—41no—
37C2×(C2×D11)⋊C4—41no—
38C2×C4⋊Dic11—41no—
39C22×C11⋊C8D411yescharacteristic
40C2×Dic44—21no—
41C2×Dic44—21no—
42C2×Dic44—21no—
43C2×Dic44—21no—
44C2×Dic44—21no—
45C2×Dic44D412yescomplemented
46C2×D88—21no—
47C2×D88—21no—
48C2×D88—21no—
49C2×D88—21no—
50C2×D88—21no—
51C2×D88D412yes—
52C2×C8×D11—21no—
53C2×C8×D11—21no—
54C2×C8×D11—21no—
55C2×C8×D11—21no—
56C2×C8×D11—21no—
57C2×C8×D11—21no—
58#66950—24no—
59#66950—42no—
60#66948—24no—
61#66948—42no—
62C2×C11×C16—21no—
63C2×C11×C16—21no—
64C2×C11×C16D412yescomplemented
65C11×#107—21no—
66C11×#107—21no—
67C11×#107D412yes—
68C11×#107D412yescomplemented
69C2×C11⋊C16—21no—
70C2×C11⋊C16—21no—
71C2×C11⋊C16—21no—
72#66874—24no—
73#66873—24no—
74#66864—28no—
75#13305—111nomaximal, Sylow
76C23×D11—41no—
77C23×D11D811yescharacteristic
78C22×C4×C11—41no—
79C22×C4×C11—41no—
80C22×C4×C11C2×D411yescharacteristic
81C22×Dic11—41no—
82C22×Dic11D811yescharacteristic
83C2×D44—22no—
84C2×D44—44no—
85C2×D44—41no—
86C2×D44—41no—
87C2×D44—41no—
88C2×D44—41no—
89C2×D44—41no—
90C2×D44—82no—
91C2×D44—82no—
92C2×C4×D11—21no—
93C2×C4×D11—21no—
94C2×C4×D11—21no—
95C2×C4×D11—21no—
96C2×C4×D11—21no—
97C2×C4×D11—21no—
98C2×Dic22—22no—
99C2×Dic22—41no—
100C2×Dic22—41no—
101C2×Dic22—41no—
102C2×Dic22—41no—
103C2×Dic22—41no—
104C2×C8×C11C2×D411yescharacteristic
105C2×C8×C11C2×D411yescharacteristic
106C2×C8×C11C2×D411yescharacteristic
107C2×C8×C11C2×D411yescharacteristic
108C2×C8×C11C2×D411yescharacteristic
109C2×C8×C11#4111yescharacteristic
110C11×C4⋊C4—22no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114(C2×D11)⋊C4—44no—
115(C2×D11)⋊C4—44no—
116C4⋊Dic11—44no—
117C2×C11⋊C8—21no—
118C2×C11⋊C8—21no—
119C2×C11⋊C8—21no—
120Dic44—22no—
121Dic44—22no—
122Dic44—41no—
123Dic44—41no—
124D88—22no—
125D88—22no—
126D88—41no—
127D88—41no—
128C8×D11—41no—
129C8×D11—41no—
130C8×D11—41no—
131C8×D11—41no—
132C11×C16—22no—
133C11⋊C16—41no—
134C22×SD32—111no—
135C2×#467—111no—
136C2×#466—111no—
137C2×#358—111no—
138C2×#357—111no—
139C2×C22⋊C16—111no—
140#1380D1111yescharacteristic, complemented
141C23×C11C2×D811yescharacteristic
142C22×D11—21no—
143C22×D11—21no—
144C22×D11—21no—
145C22×D11—21no—
146C22×D11—21no—
147C22×D11—21no—
148C22×D11—42no—
149C22×D11—81no—
150C22×D11—81no—
151C22×D11—81no—
152C22×D11—81no—
153C22×D11—81no—
154C22×D11—81no—
155C22×D11SD3212yescomplemented
156C2×C4×C11—42no—
157C2×C4×C11—42no—
158C2×C4×C11—81no—
159C2×C4×C11—81no—
160C2×C4×C11—81no—
161C2×C4×C11—81no—
162C2×C4×C11#12011yescharacteristic
163C2×C4×C11#12011yescharacteristic
164C2×C4×C11#12111yescharacteristic
165C2×C4×C11#13511yescharacteristic
166C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
168C2×Dic11—21no—
169C2×Dic11—21no—
170C2×Dic11—21no—
171C2×Dic11—42no—
172C2×Dic11—81no—
173C2×Dic11—81no—
174D44—42no—
175D44—42no—
176D44—88no—
177D44—81no—
178D44—81no—
179C4×D11—41no—
180C4×D11—41no—
181C4×D11—41no—
182C4×D11—41no—
183Dic22—42no—
184Dic22—42no—
185Dic22—81no—
186Dic22—81no—
187C8×C11#12011yescharacteristic
188C8×C11#12111yescharacteristic
189C8×C11#12111yescharacteristic
190C8×C11#12711yescharacteristic
191C11⋊C8—41no—
192C22×Q16—111no—
193C22×D8—111no—
194C23×C8—111no—
195C2×C22⋊Q8—221no—
196C2×#121—221no—
197C2×SD32—222no—
198C2×SD32—222no—
199C2×SD32—222no—
200C22×C16—111no—
201C22×C16C2×D1111yescharacteristic
202#467—222no—
203#467—222no—
204#466—222no—
205#466—222no—
206C2×#107C2×D1111yescharacteristic
207C2×#107C2×D1111yescharacteristic
208C2×#103—221no—
209C2×#102—221no—
210#358—222no—
211#357—222no—
212C22⋊C16—222no—
213C22×C11#44711yescharacteristic
214C22×C11#44711yescharacteristic
215C22×C11#46611yescharacteristic
216C22×C11C2×SD3211yescharacteristic
217C22×C11#50811yescharacteristic
218C22×C11#50911yescharacteristic
219C22×C11#51011yescharacteristic
220C2×D11—22no—
221C2×D11—22no—
222C2×D11—22no—
223C2×D11—41no—
224C2×D11—41no—
225C2×D11—41no—
226C2×D11—41no—
227C2×D11—82no—
228C2×D11—82no—
229C2×D11—82no—
230C2×D11—161no—
231C2×D11—161no—
232C2×D11—161no—
233C2×D11—161no—
234C4×C11—82no—
235C4×C11—82no—
236C4×C11#39211yescharacteristic
237C4×C11#44911yescharacteristic
238C4×C11#44911yescharacteristic
239C4×C11#46911yescharacteristic
240Dic11—41no—
241Dic11—82no—
242C22×Q8—221no—
243C22×D4—221no—
244C22×D4—441no—
245C23×C4—111no—
246C2×Q16—112no—
247C2×Q16—221no—
248C2×Q16—221no—
249C2×Q16—221no—
250C2×Q16—221no—
251C2×Q16—221no—
252C2×D8—112no—
253C2×D8—221no—
254C2×D8—221no—
255C2×D8—221no—
256C2×D8—221no—
257C2×D8—221no—
258C22×C8—111no—
259C22×C8—221no—
260C22×C8—221no—
261C22×C8—221no—
262C22×C8—221no—
263C22×C8—221no—
264C22×C8—221no—
265C22×C8C22×D1111yescharacteristic
266C22⋊Q8—224no—
267C22⋊Q8—442no—
268#121—224no—
269#121—442no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—441no—
273C2×C22⋊C4—441no—
274C2×C22⋊C4—441no—
275SD32—228no—
276C2×C16—21no—
277C2×C16—21no—
278C2×C16—221no—
279C2×C16—221no—
280C2×C16—221no—
281C2×C16D4412yescomplemented
282#107—21no—
283#107—21no—
284#107D4412yes—
285#107D4412yescomplemented
286#103—224no—
287#102—224no—
288C2×C11#199911yescharacteristic
289C2×C11#218511yescharacteristic
290C2×C11#218611yescharacteristic
291C2×C11#218711yescharacteristic
292C2×C11#218911yescharacteristic
293C2×C11#221711yescharacteristic
294C2×C11#222011yescharacteristic
295D11—42no—
296D11—162no—
297C24—111no—
298C24—441no—
299C2×Q8—222no—
300C2×Q8—441no—
301C2×Q8—441no—
302C2×Q8—441no—
303C2×Q8—441no—
304C2×Q8—441no—
305C2×D4—222no—
306C2×D4—444no—
307C2×D4—441no—
308C2×D4—441no—
309C2×D4—441no—
310C2×D4—441no—
311C2×D4—441no—
312C2×D4—882no—
313C2×D4—882no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—111no—
317C22×C4—221no—
318C22×C4—221no—
319C22×C4—221no—
320C22×C4—221no—
321C22×C4—221no—
322C22×C4—221no—
323C22×C4—441no—
324C22×C4D4×D1111yescharacteristic
325Q16—222no—
326Q16—222no—
327Q16—441no—
328Q16—441no—
329D8—222no—
330D8—222no—
331D8—441no—
332D8—441no—
333C2×C8—221no—
334C2×C8—221no—
335C2×C8—221no—
336C2×C8—441no—
337C2×C8—441no—
338C2×C8—441no—
339C2×C8—441no—
340C2×C8C2×D4411yescharacteristic
341C2×C8C2×D4411yescharacteristic
342C2×C8C2×D4411yescharacteristic
343C2×C8D4×D1111yescharacteristic
344C2×C8D4×D1111yescharacteristic
345C2×C8#434311yescharacteristic
346C4⋊C4—22no—
347C4⋊C4—22no—
348C4⋊C4—41no—
349C4⋊C4—41no—
350C4⋊C4—444no—
351C22⋊C4—444no—
352C22⋊C4—444no—
353C16—22no—
354C16—441no—
355C11#1330511yescharacteristic, complemented, Sylow
356C23—112no—
357C23—221no—
358C23—221no—
359C23—221no—
360C23—221no—
361C23—221no—
362C23—221no—
363C23—442no—
364C23—881no—
365C23—881no—
366C23—881no—
367C23—881no—
368C23—881no—
369C23—881no—
370C23D8×D1111yescharacteristic
371Q8—442no—
372Q8—442no—
373Q8—881no—
374Q8—881no—
375D4—442no—
376D4—442no—
377D4—888no—
378D4—881no—
379D4—881no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—221no—
387C2×C4—221no—
388C2×C4—221no—
389C2×C4—441no—
390C2×C4—441no—
391C2×C4—441no—
392C2×C4—441no—
393C2×C4—442no—
394C2×C4—881no—
395C2×C4—881no—
396C2×C4#6693511yescharacteristic
397C2×C4#6693511yescharacteristic
398C2×C4#6694811yescharacteristic
399C2×C4#6696711yescharacteristic
400C2×C4#6696711yescharacteristic
401C2×C4#6697211yescharacteristic
402C8—441no—
403C8#6692711yescharacteristic
404C8#6693511yescharacteristic
405C8#6694811yescharacteristic
406C8#6694811yescharacteristic
407C22—222no—
408C22—222no—
409C22—222no—
410C22—441no—
411C22—441no—
412C22—441no—
413C22—441no—
414C22—882no—
415C22—882no—
416C22—882no—
417C22—1761no—
418C22—1761no—
419C22—1761no—
420C22—1761no—
421C22#1062238611yescharacteristic
422C22#1062238611yescharacteristic
423C22#1062249611yescharacteristic
424C22#1062252411yescharacteristic
425C22D11×SD3211yescharacteristic
426C22#1062252911yescharacteristic
427C22#1062253111yescharacteristic
428C4—82no—
429C4—82no—
430C4—441no—
431C4—882no—
432C4#1062228411yescharacteristic
433C4#1062242411yescharacteristic
434C4#1062242411yescharacteristic
435C4#1062247811yescharacteristic
436C2—442no—
437C2—1762no—
438C2#1306961511yescharacteristic
439C2#1307053411yescharacteristic
440C2#1307054011yescharacteristic
441C2#1307054611yescharacteristic
442C2#1307055911yescharacteristic
443C2#1307071311yescharacteristic
444C2#1307073011yescharacteristic
subgroupG/H
centerC23D8×D11
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#1380C2
socleC23×C11C2×D8
prime radicalC2×#10622496C2
hypercenter#1380D11
hypocenterC11#13305
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ #1380

Complements

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

NH ≅ G/Ntype
1. C22×#66864C2semidirect
2. C2×#10622500C2semidirect
4. C2×#10622130C2semidirect
5. C2×#10622129C2semidirect
6. C2×(C2×D11)⋊C16C2semidirect
7. C11×#1380C2semidirect
45. C2×Dic44D4semidirect
64. C2×C11×C16D4semidirect
68. C11×#107D4semidirect
140. #1380D11semidirect
155. C22×D11SD32semidirect
281. C2×C16D44semidirect
285. #107D44semidirect
355. C11#13305semidirect

Maximal subgroups

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

subgroupindex
C22×#668642
C2×#106225002
C2×#106224962
C2×#106221302
C2×#106221292
C2×(C2×D11)⋊C162
C11×#13802
#1330511