Finite Group Databasebeta

← #14672473

Subgroups — #14672473

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×#66892C211yesmaximal, characteristic, complemented
2C2×#10622728C211yesmaximal, characteristic
3C2×#10622202C211yesmaximal, characteristic, complemented
4C2×#10622129C211yesmaximal, characteristic, complemented
5C2×C22⋊(C11⋊C16)C211yesmaximal, characteristic, complemented
6#13066707C211yesmaximal, characteristic, complemented
7C2×C11×#467C211yesmaximal, characteristic, complemented
8C22×C11×Q16C2211yescharacteristic
9C23×C8×C11C2211yescharacteristic
10C2×C11×C22⋊Q8—21no—
11C2×#66983—21no—
12C22×D88C2211yescharacteristic
13C11×#467—22no—
14C11×#467—22no—
15C2×C11×#107C2211yescharacteristic
16C2×C11×#103—21no—
17C2×#66892—22no—
18C2×#66892—22no—
19C2×#66892—22no—
20#10622728—22no—
21#10622728—22no—
22C2×#66885—21no—
23C2×#66882C2211yescharacteristic
24C22×C11⋊C16C2211yescharacteristic
25C22×C11⋊C16C2211yescharacteristic
26#10622202—22no—
27C22⋊(C11⋊C16)—22no—
28#10622129—22no—
29C22×Q8×C11—21no—
30C23×C4×C11D411yescharacteristic
31C22×C22⋊D11—41no—
32C22×D44—21no—
33C2×C11×Q16—21no—
34C2×C11×Q16—21no—
35C2×C11×Q16—21no—
36C2×C11×Q16—21no—
37C2×C11×Q16—21no—
38C2×C11×Q16D412yescomplemented
39C22×C8×C11—21no—
40C22×C8×C11—21no—
41C22×C8×C11—21no—
42C22×C8×C11—21no—
43C22×C8×C11—21no—
44C22×C8×C11—21no—
45C22×C8×C11D411yescharacteristic
46C22×C8×C11C2311yescharacteristic
47C11×C22⋊Q8—24no—
48C11×C22⋊Q8—42no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—41no—
51C2×C11×C22⋊C4—41no—
52#66983—24no—
53#66983—42no—
54C2×(C2×D11)⋊C4—41no—
55C2×C4⋊Dic11—21no—
56C2×D88—21no—
57C2×D88—21no—
58C2×D88—21no—
59C2×D88—21no—
60C2×D88—21no—
61C2×D88D412yes—
62C11×#107—21no—
63C11×#107D412yescomplemented
64C11×#103—24no—
65#66892—28no—
66#66885—24no—
67#66882—21no—
68#66882D412yes—
69C2×C11⋊C16—21no—
70C2×C11⋊C16—21no—
71C2×C11⋊C16—21no—
72C2×C11⋊C16—21no—
73C2×C11⋊C16—21no—
74C2×C11⋊C16D412yescomplemented
75#13305—111nomaximal, Sylow
76C24×C11D811yescharacteristic
77C23×D11—41no—
78C2×Q8×C11—22no—
79C2×Q8×C11—41no—
80C2×Q8×C11—41no—
81C2×Q8×C11—41no—
82C2×Q8×C11—41no—
83C2×Q8×C11—41no—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11—21no—
90C22×C4×C11—41no—
91C22×C4×C11—41no—
92C22×C4×C11D811yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C2×C22⋊D11—44no—
95C2×C22⋊D11—82no—
96C2×C22⋊D11—82no—
97C22×Dic11—41no—
98C2×D44—22no—
99C2×D44—41no—
100C2×D44—41no—
101C2×D44—41no—
102C2×D44—41no—
103C2×D44—41no—
104C11×Q16—22no—
105C11×Q16—22no—
106C11×Q16—41no—
107C11×Q16—41no—
108C2×C8×C11—21no—
109C2×C8×C11—21no—
110C2×C8×C11—21no—
111C2×C8×C11—41no—
112C2×C8×C11—41no—
113C2×C8×C11—41no—
114C2×C8×C11—41no—
115C2×C8×C11C2×D411yescharacteristic
116C2×C8×C11C2×D411yescharacteristic
117C2×C8×C11C2×D411yescharacteristic
118C2×C8×C11C2×D411yescharacteristic
119C2×C8×C11C2×D411yescharacteristic
120C2×C8×C11#4111yescharacteristic
121C11×C4⋊C4—22no—
122C11×C4⋊C4—44no—
123C11×C4⋊C4—41no—
124C11×C22⋊C4—44no—
125(C2×D11)⋊C4—44no—
126C4⋊Dic11—22no—
127C4⋊Dic11—41no—
128D88—22no—
129D88—22no—
130D88—41no—
131D88—41no—
132C11⋊C16—22no—
133C11⋊C16—41no—
134C22×SD32—111no—
135C2×#467D1111yescharacteristic, complemented
136C2×#466—111no—
137C2×#358—111no—
138C2×#357—111no—
139C2×C22⋊C16—111no—
140#1380—111no—
141C23×C11—21no—
142C23×C11—21no—
143C23×C11—21no—
144C23×C11—21no—
145C23×C11—21no—
146C23×C11—21no—
147C23×C11SD3212yescomplemented
148C23×C11C2×D811yescharacteristic
149C22×D11—42no—
150C22×D11—81no—
151C22×D11—81no—
152C22×D11—81no—
153C22×D11—81no—
154C22×D11—81no—
155C22×D11—81no—
156Q8×C11—42no—
157Q8×C11—42no—
158Q8×C11—81no—
159Q8×C11—81no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11—81no—
170C2×C4×C11—81no—
171C2×C4×C11—81no—
172C2×C4×C11—81no—
173C2×C4×C11#12011yescharacteristic
174C2×C4×C11#12011yescharacteristic
175C2×C4×C11#12111yescharacteristic
176C2×C4×C11#13511yescharacteristic
177C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
178C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
179C22⋊D11—88no—
180C2×Dic11—42no—
181C2×Dic11—81no—
182C2×Dic11—81no—
183D44—42no—
184D44—42no—
185D44—81no—
186D44—81no—
187C8×C11—41no—
188C8×C11#12011yescharacteristic
189C8×C11#12111yescharacteristic
190C8×C11#12111yescharacteristic
191C8×C11#12711yescharacteristic
192C22×Q16C2×D1111yescharacteristic
193C22×D8—111no—
194C23×C8C2×D1111yescharacteristic
195C2×C22⋊Q8—21no—
196C2×#121—221no—
197C2×SD32—222no—
198C2×SD32—222no—
199C2×SD32—222no—
200C22×C16—111no—
201C22×C16—111no—
202#467—22no—
203#467—22no—
204#466—222no—
205#466—222no—
206C2×#107—111no—
207C2×#107C2×D1111yescharacteristic
208C2×#103—21no—
209C2×#102—221no—
210#358—222no—
211#357—222no—
212C22⋊C16—222no—
213C22×C11—22no—
214C22×C11—22no—
215C22×C11—22no—
216C22×C11—41no—
217C22×C11—41no—
218C22×C11—41no—
219C22×C11—41no—
220C22×C11#44711yescharacteristic
221C22×C11#44711yescharacteristic
222C22×C11#46611yescharacteristic
223C22×C11C2×SD3211yescharacteristic
224C22×C11#50811yescharacteristic
225C22×C11#50911yescharacteristic
226C22×C11#51011yescharacteristic
227C2×D11—82no—
228C2×D11—82no—
229C2×D11—82no—
230C2×D11—161no—
231C2×D11—161no—
232C2×D11—161no—
233C2×D11—161no—
234C4×C11—41no—
235C4×C11—82no—
236C4×C11—82no—
237C4×C11#39211yescharacteristic
238C4×C11#44911yescharacteristic
239C4×C11#44911yescharacteristic
240C4×C11#46911yescharacteristic
241Dic11—82no—
242C22×Q8—21no—
243C22×D4—221no—
244C22×D4—441no—
245C23×C4C22⋊D1111yescharacteristic
246C2×Q16—21no—
247C2×Q16—21no—
248C2×Q16—21no—
249C2×Q16—21no—
250C2×Q16—21no—
251C2×Q16C22⋊D1112yescomplemented
252C2×D8—112no—
253C2×D8—221no—
254C2×D8—221no—
255C2×D8—221no—
256C2×D8—221no—
257C2×D8—221no—
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—21no—
264C22×C8C22⋊D1111yescharacteristic
265C22×C8C22×D1111yescharacteristic
266C22⋊Q8—24no—
267C22⋊Q8—42no—
268#121—224no—
269#121—442no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—41no—
272C2×C4⋊C4—221no—
273C2×C22⋊C4—41no—
274C2×C22⋊C4—441no—
275SD32—228no—
276C2×C16—112no—
277C2×C16—221no—
278C2×C16—221no—
279C2×C16—221no—
280C2×C16—221no—
281C2×C16—221no—
282#107—21no—
283#107—112no—
284#107—221no—
285#107C22⋊D1112yescomplemented
286#103—24no—
287#102—224no—
288C2×C11—42no—
289C2×C11#199911yescharacteristic
290C2×C11#218511yescharacteristic
291C2×C11#218611yescharacteristic
292C2×C11#218711yescharacteristic
293C2×C11#218911yescharacteristic
294C2×C11#221711yescharacteristic
295C2×C11#222011yescharacteristic
296D11—162no—
297C24—441no—
298C24#432311yescharacteristic
299C2×Q8—22no—
300C2×Q8—41no—
301C2×Q8—41no—
302C2×Q8—41no—
303C2×Q8—41no—
304C2×Q8—41no—
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—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—441no—
323C22×C4#432311yescharacteristic
324C22×C4C2×C22⋊D1111yescharacteristic
325Q16—22no—
326Q16—22no—
327Q16—41no—
328Q16—41no—
329D8—222no—
330D8—222no—
331D8—441no—
332D8—441no—
333C2×C8—21no—
334C2×C8—21no—
335C2×C8—21no—
336C2×C8—41no—
337C2×C8—41no—
338C2×C8—41no—
339C2×C8—41no—
340C2×C8D4×D1111yescharacteristic
341C2×C8D4×D1111yescharacteristic
342C2×C8D4×D1111yescharacteristic
343C2×C8#434111yescharacteristic
344C2×C8C2×C22⋊D1111yescharacteristic
345C2×C8C2×C22⋊D1111yescharacteristic
346C4⋊C4—22no—
347C4⋊C4—44no—
348C4⋊C4—41no—
349C4⋊C4—222no—
350C4⋊C4—441no—
351C22⋊C4—44no—
352C22⋊C4—444no—
353C16—222no—
354C16—441no—
355C11#1330511yescharacteristic, complemented, Sylow
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—442no—
363C23—881no—
364C23—881no—
365C23—881no—
366C23—881no—
367C23—881no—
368C23—881no—
369C23#6689212yescomplemented
370C23C2×#432311yescharacteristic
371Q8—42no—
372Q8—42no—
373Q8—81no—
374Q8—81no—
375D4—442no—
376D4—442no—
377D4—888no—
378D4—881no—
379D4—881no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—81no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—442no—
394C2×C4—881no—
395C2×C4—881no—
396C2×C4#6698511yescharacteristic
397C2×C4#6699011yescharacteristic
398C2×C4#6699211yescharacteristic
399C2×C4#6700211yescharacteristic
400C2×C4#6700311yescharacteristic
401C2×C4#6700611yescharacteristic
402C8—41no—
403C8#6699011yescharacteristic
404C8#6699111yescharacteristic
405C8#6699211yescharacteristic
406C8#6699311yescharacteristic
407C22—22no—
408C22—22no—
409C22—22no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—882no—
415C22—882no—
416C22—882no—
417C22—1761no—
418C22—1761no—
419C22—1761no—
420C22—1761no—
421C22#1062264911yescharacteristic
422C22#1062265111yescharacteristic
423C22C2×#6689211yescharacteristic
424C22#1062279211yescharacteristic
425C22#1062280611yescharacteristic
426C22#1062280711yescharacteristic
427C22#1062283011yescharacteristic
428C4—41no—
429C4—82no—
430C4—82no—
431C4—882no—
432C4#1062265011yescharacteristic
433C4#1062265211yescharacteristic
434C4#1062283611yescharacteristic
435C4#1062285111yescharacteristic
436C2—42no—
437C2—1762no—
438C2#1306961211yescharacteristic
439C2#1307053311yescharacteristic
440C2#1307053911yescharacteristic
441C2#1307054411yescharacteristic
442C2#1307055411yescharacteristic
443C2#1307071411yescharacteristic
444C2#1307073111yescharacteristic
subgroupG/H
centerC23C2×#4323
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC2×C11×#467C2
socleC23×C11C2×D8
prime radicalC2×#10622728C2
hypercenterC2×#467D11
hypocenterC11#13305
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
1. C22×#66892C2semidirect
3. C2×#10622202C2semidirect
4. C2×#10622129C2semidirect
5. C2×C22⋊(C11⋊C16)C2semidirect
6. #13066707C2semidirect
7. C2×C11×#467C2semidirect
38. C2×C11×Q16D4semidirect
63. C11×#107D4semidirect
74. C2×C11⋊C16D4semidirect
135. C2×#467D11semidirect
147. C23×C11SD32semidirect
251. C2×Q16C22⋊D11semidirect
285. #107C22⋊D11semidirect
355. C11#13305semidirect
369. C23#66892semidirect

Maximal subgroups

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

subgroupindex
C22×#668922
C2×#106227282
C2×#106222022
C2×#106221292
C2×C22⋊(C11⋊C16)2
#130667072
C2×C11×#4672
#1330511