Finite Group Databasebeta

← #14732287

Subgroups — #14732287

Order 2816.

986 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079557C211yesmaximal, characteristic
2#13078655C211yesmaximal, characteristic, complemented
3#13078421C211yesmaximal, characteristic, complemented
4#13067802C214yesmaximal, complemented
5#13067737C214yesmaximal, complemented
6#13067284C211yesmaximal, characteristic
7#13067045C211yesmaximal, characteristic, complemented
8#13067011C211yesmaximal, characteristic, complemented
9C2×C11×#559C211yesmaximal, characteristic
10C11×#559—22no—
11C11×#559—22no—
12C11×#559—22no—
13C11×#559C2214yes—
14C2×C11×#127C2211yescharacteristic
15C2×C11×#124—21no—
16C2×C11×#124—21no—
17C2×C11×#123—22no—
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11—21no—
21C2×C4×D4×C11—21no—
22#10623001C2211yescharacteristic
23#10622841—21no—
24#10622838—21no—
25#10622831—22no—
26#10622689C2212yes—
27#10622688—22no—
28#10622683C2212yes—
29#10622644C2212yescomplemented
30C4×#4326—22no—
31#10622635—22no—
32#10622634C2212yescomplemented
33#10622634C2212yescomplemented
34#10622633C2212yescomplemented
35#10622583—21no—
36#10622577—21no—
37#10622538C2211yescharacteristic
38#10622538C2211yescharacteristic
39#10622537C2211yescharacteristic
40#10622182C2214yes—
41Q8⋊(C11⋊C8)C2214yescomplemented
42Q8⋊(C11⋊C8)C2214yescomplemented
43C22×Q8×C11D411yescharacteristic
44C22×Q8×C11D411yescharacteristic
45C22×D4×C11—21no—
46C22×D4×C11—21no—
47C22×D4×C11D412yes—
48C23×C4×C11—22no—
49C11×#127—21no—
50C11×#127—21no—
51C11×#127D412yes—
52C11×#127C2312yes—
53C11×#124—24no—
54C11×#124—24no—
55C11×#124—24no—
56C11×#124—24no—
57C11×#123—28no—
58C11×#123—28no—
59C4×Q8×C11—21no—
60C4×Q8×C11—21no—
61C4×Q8×C11—21no—
62C4×Q8×C11—21no—
63C4×Q8×C11D412yes—
64C4×Q8×C11D412yes—
65C4×Q8×C11C2312yes—
66C4×Q8×C11C2312yes—
67C4×D4×C11—24no—
68C4×D4×C11—24no—
69C4×D4×C11—24no—
70C4×D4×C11—24no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C4⋊C4D411yescharacteristic
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—22no—
78C2×C42×C11—21no—
79C2×C42×C11—21no—
80C2×C42×C11C2311yescharacteristic
81C2×#4326—22no—
82C2×#4324—24no—
83#66979—21no—
84#66977—21no—
85#66977—21no—
86C2×#4318—21no—
87#66923—21no—
88#66922C2311yescharacteristic
89#66922C2311yescharacteristic
90C4×Dic22—21no—
91C4×Dic22—21no—
92#66899—22no—
93#66899—22no—
94#66899—22no—
95#66896—24no—
96C22⋊(C11⋊C8)—21no—
97C22⋊(C11⋊C8)—21no—
98#66874—22no—
99#66872—22no—
100#66871—22no—
101#66871—22no—
102C4⋊(C11⋊C8)—21no—
103C4⋊(C11⋊C8)—21no—
104C4⋊(C11⋊C8)C2312yes—
105C4⋊(C11⋊C8)C2312yes—
106C4×C11⋊C8—21no—
107C4×C11⋊C8C2312yes—
108#18751—111nomaximal, Sylow
109C24×C11—22no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11—42no—
115C2×Q8×C11C2×D412yes—
116C2×Q8×C11C2×D412yes—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—44no—
123C2×D4×C11—42no—
124C2×D4×C11—42no—
125C2×D4×C11—82no—
126C2×D4×C11C2×D414yes—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—28no—
132C22×C4×C11—84no—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C2×Dic22—21no—
137C2×Dic22—21no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4C2×D412yes—
145C11×C4⋊C4C2×D412yes—
146C11×C22⋊C4—28no—
147C11×C22⋊C4—28no—
148C11×C22⋊C4—28no—
149C42×C11—22no—
150C42×C11—22no—
151C42×C11—22no—
152C42×C11—22no—
153C42×C11C2×D411yescharacteristic
154C42×C11C2×D411yescharacteristic
155C42×C11C2×D411yescharacteristic
156C42×C11C2411yescharacteristic
157C22⋊Dic11—41no—
158#4326—44no—
159#4324—84no—
160C4⋊Dic11—21no—
161C4⋊Dic11—21no—
162C4⋊Dic11—21no—
163C4⋊Dic11—21no—
164Dic11⋊C4—41no—
165Dic11⋊C4—41no—
166C4×Dic11—41no—
167#4318—42no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—22no—
171C2×#559D1111yescharacteristic
172#3208—111no—
173#3104—111no—
174#3078—111no—
175#1640—114no—
176#1630—114no—
177#1545—111no—
178#1487—111no—
179#1479—111no—
180C23×C11—24no—
181C23×C11—44no—
182C23×C11—44no—
183C23×C11—44no—
184C23×C11#12011yescharacteristic
185Q8×C11—22no—
186Q8×C11—22no—
187Q8×C11—22no—
188Q8×C11—22no—
189Q8×C11—42no—
190Q8×C11—42no—
191D4×C11—44no—
192D4×C11—44no—
193D4×C11—42no—
194D4×C11—42no—
195D4×C11—44no—
196D4×C11—44no—
197D4×C11—82no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—41no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—88no—
209C2×C4×C11#12011yescharacteristic
210C2×C4×C11#12011yescharacteristic
211C2×C4×C11#12011yescharacteristic
212C2×C4×C11#13512yes—
213C2×C4×C11#13712yes—
214C2×C4×C11C22×D411yescharacteristic
215C2×C4×C11C22×D411yescharacteristic
216C2×C4×C11C22×D411yescharacteristic
217C2×Dic11—41no—
218C2×Dic11—41no—
219Dic22—42no—
220Dic22—42no—
221C11⋊C8—42no—
222C11⋊C8—42no—
223C11⋊C8—42no—
224#559—22no—
225#559—22no—
226#559—22no—
227#559C2×D1114yes—
228#533—111no—
229C2×#127C2×D1111yescharacteristic
230C2×#124—21no—
231C2×#124—21no—
232C2×#123—22no—
233C2×C4×Q8C2×D1111yescharacteristic
234C2×C4×Q8C2×D1111yescharacteristic
235C2×C4×D4—21no—
236C2×C4×D4—21no—
237#492—112no—
238#486—112no—
239#484—221no—
240#479—222no—
241#477—112no—
242#477—112no—
243#475—112no—
244#462—112no—
245#460—222no—
246#451—221no—
247#450—222no—
248C4×Q16—222no—
249#431—111no—
250#431—111no—
251#428—221no—
252#423—111no—
253#419—221no—
254#331—114no—
255Q8⋊C8—114no—
256Q8⋊C8—114no—
257C22×C11—21no—
258C22×C11—21no—
259C22×C11—44no—
260C22×C11—44no—
261C22×C11—44no—
262C22×C11—88no—
263C22×C11#45212yes—
264C22×C11C2×#12011yescharacteristic
265C4×C11—21no—
266C4×C11—21no—
267C4×C11—21no—
268C4×C11—42no—
269C4×C11—42no—
270C4×C11—42no—
271C4×C11—42no—
272C4×C11#45212yes—
273C4×C11C2×#13511yescharacteristic
274C4×C11C2×#13711yescharacteristic
275C4×C11#57512yes—
276Dic11—81no—
277Dic11—81no—
278C22×Q8C22⋊D1111yescharacteristic
279C22×Q8C22⋊D1111yescharacteristic
280C22×D4—21no—
281C22×D4—21no—
282C22×D4C22⋊D1112yes—
283C23×C4—22no—
284C2×Q16—222no—
285C2×SD16—224no—
286C2×M16—221no—
287C4⋊Q8—111no—
288C4⋊Q8—111no—
289#127—21no—
290#127—21no—
291#127C22⋊D1112yes—
292#127C22×D1112yes—
293#125—221no—
294#124—24no—
295#124—24no—
296#124—24no—
297#124—24no—
298#123—28no—
299#123—28no—
300C22⋊Q8—221no—
301C22⋊Q8—221no—
302C4×Q8—21no—
303C4×Q8—21no—
304C4×Q8—21no—
305C4×Q8—21no—
306C4×Q8—221no—
307C4×Q8—221no—
308C4×Q8C22⋊D1112yes—
309C4×Q8C22⋊D1112yes—
310C4×Q8C22×D1112yes—
311C4×Q8C22×D1112yes—
312C4×D4—24no—
313C4×D4—24no—
314C4×D4—24no—
315C4×D4—24no—
316#117—221no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4C22⋊D1111yescharacteristic
320C2×C4⋊C4C22⋊D1111yescharacteristic
321C2×C22⋊C4—22no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—22no—
324C2×C42—21no—
325C2×C42—21no—
326C2×C42C22×D1111yescharacteristic
327#107—222no—
328#107—222no—
329#106—222no—
330C4⋊C8—112no—
331C4⋊C8—112no—
332C4⋊C8—221no—
333C4⋊C8—221no—
334#103—222no—
335#103—222no—
336#103—222no—
337#103—222no—
338#102—224no—
339C22⋊C8—221no—
340C22⋊C8—221no—
341C4×C8—112no—
342C4×C8—221no—
343C2×C11—22no—
344C2×C11—84no—
345C2×C11C2×#45211yescharacteristic
346C2×C11#300511yescharacteristic
347C2×C11#301911yescharacteristic
348C24—22no—
349C2×Q8—21no—
350C2×Q8—21no—
351C2×Q8—22no—
352C2×Q8—22no—
353C2×Q8—42no—
354C2×Q8—221no—
355C2×Q8—221no—
356C2×Q8C2×C22⋊D1112yes—
357C2×Q8C2×C22⋊D1112yes—
358C2×D4—22no—
359C2×D4—22no—
360C2×D4—22no—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—44no—
364C2×D4—42no—
365C2×D4—42no—
366C2×D4—82no—
367C2×D4C2×C22⋊D1114yes—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—28no—
373C22×C4—84no—
374C22×C4C2×C22⋊D1111yescharacteristic
375C22×C4C2×C22⋊D1111yescharacteristic
376C22×C4C2×C22⋊D1111yescharacteristic
377Q16—444no—
378SD16—884no—
379M16—442no—
380C2×C8—222no—
381C2×C8—222no—
382C2×C8—222no—
383C4⋊C4—22no—
384C4⋊C4—22no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—22no—
388C4⋊C4—22no—
389C4⋊C4—221no—
390C4⋊C4—221no—
391C4⋊C4—221no—
392C4⋊C4—221no—
393C4⋊C4—441no—
394C4⋊C4—441no—
395C4⋊C4C2×C22⋊D1112yes—
396C4⋊C4C2×C22⋊D1112yes—
397C22⋊C4—28no—
398C22⋊C4—28no—
399C22⋊C4—28no—
400C22⋊C4—441no—
401C42—22no—
402C42—22no—
403C42—22no—
404C42—22no—
405C42—441no—
406C42C2×C22⋊D1111yescharacteristic
407C42C2×C22⋊D1111yescharacteristic
408C42C2×C22⋊D1111yescharacteristic
409C42C23×D1111yescharacteristic
410C11#1875111yescharacteristic, complemented, Sylow
411C23—24no—
412C23—44no—
413C23—44no—
414C23—44no—
415C23#6700611yescharacteristic
416Q8—22no—
417Q8—22no—
418Q8—22no—
419Q8—22no—
420Q8—42no—
421Q8—42no—
422Q8—442no—
423Q8—442no—
424D4—44no—
425D4—44no—
426D4—42no—
427D4—44no—
428D4—42no—
429D4—44no—
430D4—82no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—41no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—88no—
442C2×C4—441no—
443C2×C4—441no—
444C2×C4#6700312yes—
445C2×C4#6700412yes—
446C2×C4#6700611yescharacteristic
447C2×C4#6700611yescharacteristic
448C2×C4#6700611yescharacteristic
449C2×C4C22×C22⋊D1111yescharacteristic
450C2×C4C22×C22⋊D1111yescharacteristic
451C2×C4C22×C22⋊D1111yescharacteristic
452C8—442no—
453C8—442no—
454C8—442no—
455C22—21no—
456C22—21no—
457C22—44no—
458C22—44no—
459C22—44no—
460C22—88no—
461C22#1062285212yes—
462C22C2×#6700611yescharacteristic
463C4—21no—
464C4—21no—
465C4—21no—
466C4—42no—
467C4—42no—
468C4—42no—
469C4—42no—
470C4—881no—
471C4—881no—
472C4#1062285212yes—
473C4C2×#6700311yescharacteristic
474C4#1062335312yes—
475C4C2×#6700411yescharacteristic
476C2—22no—
477C2—84no—
478C2C2×#1062285211yescharacteristic
479C2#1307785811yescharacteristic
480C2#1307797311yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#559C2
socleC22×C11C2×#120
prime radicalC2×C11×#127C22
hypercenterC2×#559D11
hypocenterC11#18751
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
2. #13078655C2semidirect
3. #13078421C2semidirect
4. #13067802C2semidirect
5. #13067737C2semidirect
7. #13067045C2semidirect
8. #13067011C2semidirect
29. #10622644C22semidirect
32. #10622634C22semidirect
33. #10622634C22semidirect
34. #10622633C22semidirect
41. Q8⋊(C11⋊C8)C22semidirect
42. Q8⋊(C11⋊C8)C22semidirect
410. C11#18751semidirect

Maximal subgroups

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

subgroupindex
#130795572
#130786552
#130784212
#130678022
#130677372
#130672842
#130670452
#130670112
C2×C11×#5592
#1875111