Finite Group Databasebeta

← #14672476

Subgroups — #14672476

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×#66891C211yesmaximal, characteristic, complemented
2C2×#10622500C211yesmaximal, characteristic, complemented
3C2×#10622770C211yesmaximal, characteristic
4C2×#10622141C211yesmaximal, characteristic, complemented
5C2×(C2×D11)⋊C16C211yesmaximal, characteristic, complemented
6#13066707C211yesmaximal, characteristic, complemented
7C2×C11×#357C211yesmaximal, characteristic, complemented
8C22×C11×D8C2211yescharacteristic
9C2×#66991—21no—
10C22×Dic44C2211yescharacteristic
11C22×C8×D11C2211yescharacteristic
12C2×#66950—21no—
13C22×C11×C16C2211yescharacteristic
14C2×C11×#107C2211yescharacteristic
15C2×#66896—21no—
16#10622770—22no—
17#10622770—22no—
18C2×#66891—22no—
19C2×#66891—22no—
20C2×#66891—22no—
21C2×#66882C2211yescharacteristic
22C22×C11⋊C16C2211yescharacteristic
23C2×#66874—21no—
24#10622500—22no—
25#10622500—22no—
26C11×#357—22no—
27(C2×D11)⋊C16—22no—
28#10622141—22no—
29C22×D4×C11—21no—
30C22×C22⋊D11—41no—
31C22×C4×D11D411yescharacteristic
32C22×Dic22—21no—
33C2×C11×D8—21no—
34C2×C11×D8—21no—
35C2×C11×D8—21no—
36C2×C11×D8—21no—
37C2×C11×D8—21no—
38C2×C11×D8D412yes—
39C22×C8×C11C2311yescharacteristic
40C2×C11×C4⋊C4—21no—
41C2×C22⋊Dic11—41no—
42#66991—24no—
43#66991—42no—
44C2×(C2×D11)⋊C4—41no—
45C2×C4⋊Dic11—21no—
46C2×C4⋊Dic11—41no—
47C22×C11⋊C8D411yescharacteristic
48C2×Dic44—21no—
49C2×Dic44—21no—
50C2×Dic44—21no—
51C2×Dic44—21no—
52C2×Dic44—21no—
53C2×Dic44D412yescomplemented
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×#107D412yescomplemented
67#66896—24no—
68#66891—28no—
69#66882—21no—
70#66882D412yes—
71C2×C11⋊C16—21no—
72C2×C11⋊C16—21no—
73C2×C11⋊C16D412yescomplemented
74#66874—24no—
75#13305—111nomaximal, Sylow
76C24×C11—41no—
77C23×D11D811yescharacteristic
78C2×D4×C11—22no—
79C2×D4×C11—41no—
80C2×D4×C11—41no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C22×C4×C11—41no—
85C22×C4×C11C2×D411yescharacteristic
86C2×C22⋊D11—44no—
87C2×C22⋊D11—82no—
88C2×C22⋊D11—82no—
89C22×Dic11—41no—
90C22×Dic11—41no—
91C22×Dic11D811yescharacteristic
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—
104C11×D8—22no—
105C11×D8—22no—
106C11×D8—41no—
107C11×D8—41no—
108C2×C8×C11C2×D411yescharacteristic
109C2×C8×C11C2×D411yescharacteristic
110C2×C8×C11C2×D411yescharacteristic
111C2×C8×C11C2×D411yescharacteristic
112C2×C8×C11C2×D411yescharacteristic
113C2×C8×C11#4111yescharacteristic
114C11×C4⋊C4—22no—
115C11×C4⋊C4—41no—
116C22⋊Dic11—44no—
117(C2×D11)⋊C4—44no—
118C4⋊Dic11—22no—
119C4⋊Dic11—44no—
120C4⋊Dic11—41no—
121C2×C11⋊C8—21no—
122C2×C11⋊C8—21no—
123C2×C11⋊C8—21no—
124Dic44—22no—
125Dic44—22no—
126Dic44—41no—
127Dic44—41no—
128C8×D11—41no—
129C8×D11—41no—
130C8×D11—41no—
131C8×D11—41no—
132C11×C16—41no—
133C11⋊C16—22no—
134C22×SD32—111no—
135C2×#467—111no—
136C2×#466—111no—
137C2×#358—111no—
138C2×#357D1111yescharacteristic, complemented
139C2×C22⋊C16—111no—
140#1380—111no—
141C23×C11—42no—
142C23×C11—81no—
143C23×C11—81no—
144C23×C11—81no—
145C23×C11—81no—
146C23×C11—81no—
147C23×C11—81no—
148C23×C11C2×D811yescharacteristic
149C22×D11—21no—
150C22×D11—21no—
151C22×D11—21no—
152C22×D11—21no—
153C22×D11—21no—
154C22×D11—21no—
155C22×D11SD3212yescomplemented
156D4×C11—42no—
157D4×C11—42no—
158D4×C11—81no—
159D4×C11—81no—
160C2×C4×C11—42no—
161C2×C4×C11—81no—
162C2×C4×C11—81no—
163C2×C4×C11#12011yescharacteristic
164C2×C4×C11#12011yescharacteristic
165C2×C4×C11#12111yescharacteristic
166C2×C4×C11#13511yescharacteristic
167C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
169C22⋊D11—88no—
170C2×Dic11—21no—
171C2×Dic11—21no—
172C2×Dic11—21no—
173C2×Dic11—42no—
174C2×Dic11—42no—
175C2×Dic11—81no—
176C2×Dic11—81no—
177C2×Dic11—81no—
178C2×Dic11—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×D8C2×D1111yescharacteristic
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×#107—111no—
207C2×#107C2×D1111yescharacteristic
208C2×#103—221no—
209C2×#102—221no—
210#358—222no—
211#357—22no—
212C22⋊C16—222no—
213C22×C11—82no—
214C22×C11—82no—
215C22×C11—82no—
216C22×C11—161no—
217C22×C11—161no—
218C22×C11—161no—
219C22×C11—161no—
220C22×C11#44711yescharacteristic
221C22×C11#44711yescharacteristic
222C22×C11#46611yescharacteristic
223C22×C11C2×SD3211yescharacteristic
224C22×C11#50811yescharacteristic
225C22×C11#50911yescharacteristic
226C22×C11#51011yescharacteristic
227C2×D11—22no—
228C2×D11—22no—
229C2×D11—22no—
230C2×D11—41no—
231C2×D11—41no—
232C2×D11—41no—
233C2×D11—41no—
234C4×C11—82no—
235C4×C11#39211yescharacteristic
236C4×C11#44911yescharacteristic
237C4×C11#44911yescharacteristic
238C4×C11#46911yescharacteristic
239Dic11—41no—
240Dic11—82no—
241Dic11—82no—
242C22×Q8—221no—
243C22×D4—21no—
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—21no—
253C2×D8—21no—
254C2×D8—21no—
255C2×D8—21no—
256C2×D8—21no—
257C2×D8D4412yes—
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—221no—
272C2×C4⋊C4—441no—
273C2×C22⋊C4—441no—
274C2×C22⋊C4—441no—
275SD32—228no—
276C2×C16—21no—
277C2×C16—21no—
278C2×C16—21no—
279C2×C16—112no—
280C2×C16—221no—
281C2×C16—221no—
282#107—21no—
283#107—112no—
284#107—221no—
285#107C22⋊D1112yescomplemented
286#103—224no—
287#102—224no—
288C2×C11—162no—
289C2×C11#199911yescharacteristic
290C2×C11#218511yescharacteristic
291C2×C11#218611yescharacteristic
292C2×C11#218711yescharacteristic
293C2×C11#218911yescharacteristic
294C2×C11#221711yescharacteristic
295C2×C11#222011yescharacteristic
296D11—42no—
297C24—41no—
298C24—111no—
299C2×Q8—222no—
300C2×Q8—441no—
301C2×Q8—441no—
302C2×Q8—441no—
303C2×Q8—441no—
304C2×Q8—441no—
305C2×D4—22no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—444no—
312C2×D4—882no—
313C2×D4—882no—
314C22×C4—41no—
315C22×C4—111no—
316C22×C4—221no—
317C22×C4—221no—
318C22×C4—221no—
319C22×C4—221no—
320C22×C4—221no—
321C22×C4—221no—
322C22×C4—441no—
323C22×C4—441no—
324C22×C4D4×D1111yescharacteristic
325Q16—222no—
326Q16—222no—
327Q16—441no—
328Q16—441no—
329D8—22no—
330D8—22no—
331D8—41no—
332D8—41no—
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×C8#433911yescharacteristic
342C2×C8D4×D1111yescharacteristic
343C2×C8D4×D1111yescharacteristic
344C2×C8D4×D1111yescharacteristic
345C2×C8C2×C22⋊D1111yescharacteristic
346C4⋊C4—22no—
347C4⋊C4—41no—
348C4⋊C4—222no—
349C4⋊C4—444no—
350C4⋊C4—441no—
351C22⋊C4—444no—
352C22⋊C4—444no—
353C16—41no—
354C16—222no—
355C11#1330511yescharacteristic, complemented, Sylow
356C23—42no—
357C23—81no—
358C23—81no—
359C23—81no—
360C23—81no—
361C23—81no—
362C23—81no—
363C23—112no—
364C23—221no—
365C23—221no—
366C23—221no—
367C23—221no—
368C23—221no—
369C23—221no—
370C23D8×D1111yescharacteristic
371Q8—442no—
372Q8—442no—
373Q8—881no—
374Q8—881no—
375D4—42no—
376D4—42no—
377D4—81no—
378D4—81no—
379D4—888no—
380C2×C4—42no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4—221no—
384C2×C4—221no—
385C2×C4—221no—
386C2×C4—441no—
387C2×C4—441no—
388C2×C4—441no—
389C2×C4—441no—
390C2×C4—442no—
391C2×C4—442no—
392C2×C4—881no—
393C2×C4—881no—
394C2×C4—881no—
395C2×C4—881no—
396C2×C4#6693511yescharacteristic
397C2×C4#6693711yescharacteristic
398C2×C4#6696411yescharacteristic
399C2×C4#6696711yescharacteristic
400C2×C4#6696911yescharacteristic
401C2×C4#6699011yescharacteristic
402C8—441no—
403C8#6693511yescharacteristic
404C8#6693711yescharacteristic
405C8#6698311yescharacteristic
406C8#6699311yescharacteristic
407C22—82no—
408C22—82no—
409C22—82no—
410C22—161no—
411C22—161no—
412C22—161no—
413C22—161no—
414C22—222no—
415C22—222no—
416C22—222no—
417C22—441no—
418C22—441no—
419C22—441no—
420C22—441no—
421C22#1062238611yescharacteristic
422C22#1062238811yescharacteristic
423C22#1062252411yescharacteristic
424C22#1062252511yescharacteristic
425C22D11×SD3211yescharacteristic
426C22#1062252811yescharacteristic
427C22#1062276911yescharacteristic
428C4—82no—
429C4—441no—
430C4—882no—
431C4—882no—
432C4#1062239411yescharacteristic
433C4#1062239511yescharacteristic
434C4#1062257311yescharacteristic
435C4#1062278511yescharacteristic
436C2—162no—
437C2—442no—
438C2#1306961311yescharacteristic
439C2#1307053111yescharacteristic
440C2#1307053611yescharacteristic
441C2#1307054611yescharacteristic
442C2#1307055711yescharacteristic
443C2#1307071111yescharacteristic
444C2#1307072811yescharacteristic
subgroupG/H
centerC23D8×D11
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC2×C11×#357C2
socleC23×C11C2×D8
prime radicalC2×#10622770C2
hypercenterC2×#357D11
hypocenterC11#13305
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

Complements

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

NH ≅ G/Ntype
1. C22×#66891C2semidirect
2. C2×#10622500C2semidirect
4. C2×#10622141C2semidirect
5. C2×(C2×D11)⋊C16C2semidirect
6. #13066707C2semidirect
7. C2×C11×#357C2semidirect
53. C2×Dic44D4semidirect
66. C11×#107D4semidirect
73. C2×C11⋊C16D4semidirect
138. C2×#357D11semidirect
155. C22×D11SD32semidirect
285. #107C22⋊D11semidirect
355. C11#13305semidirect

Maximal subgroups

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

subgroupindex
C22×#668912
C2×#106225002
C2×#106227702
C2×#106221412
C2×(C2×D11)⋊C162
#130667072
C2×C11×#3572
#1330511