Finite Group Databasebeta

← #14720105

Subgroups — #14720105

Order 2816.

1016 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077651C212yesmaximal, complemented
2#13066968C212yesmaximal, complemented
3#13066964C214yesmaximal, complemented
4#13066960C211yesmaximal, characteristic, complemented
5#13066954C212yesmaximal, complemented
6#13066940C211yesmaximal, characteristic, complemented
7#13066934C212yesmaximal, complemented
8C2×C11×#559C211yesmaximal, characteristic
9C11×#559—22no—
10C11×#559—24no—
11C11×#559—22no—
12C2×C11×#127C411yescharacteristic
13C2×C11×#124C411yescharacteristic
14C2×C11×#124C412yes—
15C2×C11×#124C2211yescharacteristic
16C2×C11×#123C412yes—
17C2×C11×#123C2212yes—
18C2×C4×Q8×C11C411yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11C411yescharacteristic
21C2×C4×D4×C11C2212yes—
22C2×C4×D4×C11C2211yescharacteristic
23#10622820C2214yes—
24C2×C22⋊(C11⋊C8)C2214yes—
25#10622625—22no—
26#10622624—24no—
27D4×C11⋊C8—22no—
28#10622539C2212yes—
29#10622538C2212yes—
30#10622166C2211yescharacteristic
31#10622166C2212yes—
32#10622166C2211yescharacteristic
33#10622166C2212yes—
34#10622166C2212yes—
35#10622163C2214yes—
36#10622163C2214yes—
37C22×Q8×C11C2×C411yescharacteristic
38C22×Q8×C11C2×C411yescharacteristic
39C22×D4×C11C2×C412yes—
40C22×D4×C11C2×C411yescharacteristic
41C22×D4×C11C2×C412yes—
42C22×D4×C11C2×C411yescharacteristic
43C23×C4×C11C2×C412yes—
44C23×C4×C11C2312yes—
45C11×#127—22no—
46C11×#127—22no—
47C11×#124—22no—
48C11×#124—22no—
49C11×#124—24no—
50C11×#124—24no—
51C11×#124—22no—
52C11×#124—22no—
53C11×#123—24no—
54C11×#123—24no—
55C11×#123—24no—
56C11×#123—24no—
57C4×Q8×C11—22no—
58C4×Q8×C11—21no—
59C4×Q8×C11—21no—
60C4×Q8×C11—22no—
61C4×Q8×C11—22no—
62C4×D4×C11—24no—
63C4×D4×C11—24no—
64C4×D4×C11—22no—
65C4×D4×C11—21no—
66C4×D4×C11—21no—
67C4×D4×C11D412yes—
68C4×D4×C11D414yes—
69C4×D4×C11D412yes—
70C2×C11×C4⋊C4C2×C412yes—
71C2×C11×C4⋊C4C2×C411yescharacteristic
72C2×C11×C4⋊C4C2×C411yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4C2×C412yes—
76C2×C11×C22⋊C4C2×C412yes—
77C2×C11×C22⋊C4C2×C412yes—
78C2×C11×C22⋊C4C2×C412yes—
79C2×C11×C22⋊C4C2×C412yes—
80C2×C11×C22⋊C4C2312yes—
81C2×C42×C11C2×C411yescharacteristic
82C2×C42×C11C2×C412yes—
83C2×C42×C11C2×C411yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×#4318—24no—
86C22×C11⋊C8—24no—
87C22⋊(C11⋊C8)—24no—
88C22⋊(C11⋊C8)—24no—
89C22⋊(C11⋊C8)C2312yes—
90C22⋊(C11⋊C8)C2312yes—
91C22⋊(C11⋊C8)C2314yes—
92C4⋊(C11⋊C8)—22no—
93C4⋊(C11⋊C8)—22no—
94#66867—22no—
95C4×C11⋊C8—22no—
96#17429—111nomaximal, Sylow
97C24×C11C22×C412yes—
98C24×C11C22×C412yes—
99C2×Q8×C11—22no—
100C2×Q8×C11—21no—
101C2×Q8×C11—21no—
102C2×Q8×C11—22no—
103C2×Q8×C11—41no—
104C2×Q8×C11—42no—
105C2×D4×C11—24no—
106C2×D4×C11—24no—
107C2×D4×C11—21no—
108C2×D4×C11—21no—
109C2×D4×C11—24no—
110C2×D4×C11—42no—
111C2×D4×C11—42no—
112C2×D4×C11—42no—
113C2×D4×C11—82no—
114C2×D4×C11C22⋊C412yes—
115C2×D4×C11C22⋊C412yes—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—82no—
119C22×C4×C11—82no—
120C22×C4×C11C22×C411yescharacteristic
121C22×C4×C11C22×C411yescharacteristic
122C22×C4×C11C22×C411yescharacteristic
123C22×C4×C11C22×C411yescharacteristic
124C22×C4×C11C22×C412yes—
125C22×C4×C11C22×C411yescharacteristic
126C22×C4×C11C22×C411yescharacteristic
127C22×C4×C11C22×C412yes—
128C22×C4×C11C2×D414yes—
129C22×C4×C11C2×D414yes—
130C22×C4×C11C2411yescharacteristic
131C11×C4⋊C4—22no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4C22⋊C412yes—
137C11×C4⋊C4C22⋊C411yescharacteristic
138C11×C4⋊C4C22⋊C411yescharacteristic
139C11×C22⋊C4—24no—
140C11×C22⋊C4—24no—
141C11×C22⋊C4—22no—
142C11×C22⋊C4—22no—
143C11×C22⋊C4—24no—
144C11×C22⋊C4—24no—
145C11×C22⋊C4C22⋊C414yes—
146C11×C22⋊C4C22⋊C414yes—
147C42×C11—22no—
148C42×C11—22no—
149C42×C11—21no—
150C42×C11—21no—
151C42×C11—21no—
152C42×C11—21no—
153C42×C11C2×D412yes—
154C42×C11C2×D412yes—
155#4318—84no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8—22no—
158C2×C11⋊C8—24no—
159C2×C11⋊C8—84no—
160C2×#559D1111yescharacteristic
161#2974—112no—
162#1469—112no—
163#1468—114no—
164#1467—111no—
165#1465—112no—
166#1461—111no—
167#1459—112no—
168C23×C11—22no—
169C23×C11—22no—
170C23×C11—22no—
171C23×C11—22no—
172C23×C11—22no—
173C23×C11—42no—
174C23×C11—42no—
175C23×C11—42no—
176C23×C11—42no—
177C23×C11C2×C22⋊C414yes—
178C23×C11C23×C411yescharacteristic
179Q8×C11—44no—
180Q8×C11—42no—
181Q8×C11—42no—
182D4×C11—24no—
183D4×C11—42no—
184D4×C11—48no—
185D4×C11—42no—
186D4×C11—42no—
187D4×C11—84no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—22no—
193C2×C4×C11—21no—
194C2×C4×C11—22no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—44no—
200C2×C4×C11—44no—
201C2×C4×C11—42no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—42no—
206C2×C4×C11—82no—
207C2×C4×C11—82no—
208C2×C4×C11C2×C22⋊C411yescharacteristic
209C2×C4×C11C2×C22⋊C412yes—
210C2×C4×C11C2×C22⋊C412yes—
211C2×C4×C11C2×C22⋊C412yes—
212C2×C4×C11C2×C22⋊C411yescharacteristic
213C2×C4×C11#13112yes—
214C2×C4×C11C22×D412yes—
215C11⋊C8—42no—
216C11⋊C8—44no—
217C11⋊C8—42no—
218#559—22no—
219#559—24no—
220#559—22no—
221C2×#127Dic1111yescharacteristic
222C2×#124Dic1111yescharacteristic
223C2×#124Dic1112yes—
224C2×#124C2×D1111yescharacteristic
225C2×#123Dic1112yes—
226C2×#123C2×D1112yes—
227C2×C4×Q8Dic1111yescharacteristic
228C2×C4×Q8C2×D1111yescharacteristic
229C2×C4×D4Dic1111yescharacteristic
230C2×C4×D4C2×D1112yes—
231C2×C4×D4C2×D1111yescharacteristic
232#436—222no—
233#435—224no—
234C8×D4—222no—
235#432—112no—
236#431—112no—
237#407—114no—
238C2×C22⋊C8—114no—
239#324—111no—
240#324—112no—
241#324—111no—
242#324—112no—
243#324—112no—
244#323—114no—
245#323—114no—
246C22×C11—21no—
247C22×C11—21no—
248C22×C11—24no—
249C22×C11—24no—
250C22×C11—24no—
251C22×C11—42no—
252C22×C11—42no—
253C22×C11—42no—
254C22×C11—82no—
255C22×C11—82no—
256C22×C11—82no—
257C22×C11—82no—
258C22×C11C22×C22⋊C411yescharacteristic
259C22×C11C2×#13111yescharacteristic
260C22×C11#56811yescharacteristic
261C4×C11—22no—
262C4×C11—22no—
263C4×C11—22no—
264C4×C11—22no—
265C4×C11—22no—
266C4×C11—21no—
267C4×C11—41no—
268C4×C11—41no—
269C4×C11—41no—
270C4×C11—42no—
271C4×C11#41312yes—
272C22×Q8C2×Dic1111yescharacteristic
273C22×Q8C2×Dic1111yescharacteristic
274C22×D4C2×Dic1112yes—
275C22×D4C2×Dic1111yescharacteristic
276C22×D4C2×Dic1112yes—
277C22×D4C2×Dic1111yescharacteristic
278C23×C4C2×Dic1112yes—
279C23×C4C22×D1112yes—
280C2×M16—224no—
281C22×C8—224no—
282#127—22no—
283#127—22no—
284#124—22no—
285#124—22no—
286#124—24no—
287#124—24no—
288#124—22no—
289#124—22no—
290#123—24no—
291#123—24no—
292#123—24no—
293#123—24no—
294C4×Q8—22no—
295C4×Q8—21no—
296C4×Q8—21no—
297C4×Q8—22no—
298C4×Q8—22no—
299C4×D4—24no—
300C4×D4—24no—
301C4×D4—22no—
302C4×D4—21no—
303C4×D4—21no—
304C4×D4C22⋊D1112yes—
305C4×D4C22⋊D1114yes—
306C4×D4C22⋊D1112yes—
307C2×C4⋊C4C2×Dic1112yes—
308C2×C4⋊C4C2×Dic1111yescharacteristic
309C2×C4⋊C4C2×Dic1111yescharacteristic
310C2×C4⋊C4C22×D1111yescharacteristic
311C2×C4⋊C4C22×D1111yescharacteristic
312C2×C22⋊C4C2×Dic1112yes—
313C2×C22⋊C4C2×Dic1112yes—
314C2×C22⋊C4C2×Dic1112yes—
315C2×C22⋊C4C2×Dic1112yes—
316C2×C22⋊C4C2×Dic1112yes—
317C2×C22⋊C4C22×D1112yes—
318C2×C42C2×Dic1111yescharacteristic
319C2×C42C2×Dic1112yes—
320C2×C42C2×Dic1111yescharacteristic
321C2×C42C22×D1111yescharacteristic
322C4⋊C8—222no—
323C4⋊C8—222no—
324C22⋊C8—112no—
325C22⋊C8—114no—
326C22⋊C8—112no—
327C22⋊C8—224no—
328C22⋊C8—224no—
329#97—222no—
330C4×C8—222no—
331C2×C11—21no—
332C2×C11—21no—
333C2×C11—44no—
334C2×C11—82no—
335C2×C11#288011yescharacteristic
336C2×C11#288311yescharacteristic
337C2×C11C2×#41311yescharacteristic
338C24C22×Dic1112yes—
339C24C22×Dic1112yes—
340C2×Q8—22no—
341C2×Q8—22no—
342C2×Q8—21no—
343C2×Q8—21no—
344C2×Q8—41no—
345C2×Q8—42no—
346C2×D4—24no—
347C2×D4—24no—
348C2×D4—24no—
349C2×D4—21no—
350C2×D4—21no—
351C2×D4—42no—
352C2×D4—42no—
353C2×D4—42no—
354C2×D4—82no—
355C2×D4C22⋊Dic1112yes—
356C2×D4C22⋊Dic1112yes—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—82no—
360C22×C4—82no—
361C22×C4C22×Dic1111yescharacteristic
362C22×C4C22×Dic1111yescharacteristic
363C22×C4C22×Dic1111yescharacteristic
364C22×C4C22×Dic1111yescharacteristic
365C22×C4C22×Dic1112yes—
366C22×C4C22×Dic1111yescharacteristic
367C22×C4C22×Dic1111yescharacteristic
368C22×C4C22×Dic1112yes—
369C22×C4C2×C22⋊D1114yes—
370C22×C4C2×C22⋊D1114yes—
371C22×C4C23×D1111yescharacteristic
372M16—884no—
373C2×C8—222no—
374C2×C8—222no—
375C2×C8—224no—
376C2×C8—884no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4C22⋊Dic1112yes—
383C4⋊C4C22⋊Dic1111yescharacteristic
384C4⋊C4C22⋊Dic1111yescharacteristic
385C22⋊C4—24no—
386C22⋊C4—24no—
387C22⋊C4—22no—
388C22⋊C4—22no—
389C22⋊C4—24no—
390C22⋊C4—24no—
391C22⋊C4C22⋊Dic1114yes—
392C22⋊C4C22⋊Dic1114yes—
393C42—22no—
394C42—22no—
395C42—21no—
396C42—21no—
397C42—21no—
398C42—21no—
399C42C2×C22⋊D1112yes—
400C42C2×C22⋊D1112yes—
401C11#1742911yescharacteristic, complemented, Sylow
402C23—22no—
403C23—22no—
404C23—22no—
405C23—22no—
406C23—22no—
407C23—42no—
408C23—42no—
409C23—42no—
410C23—42no—
411C23C2×C22⋊Dic1114yes—
412C23C23×Dic1111yescharacteristic
413Q8—44no—
414Q8—42no—
415Q8—42no—
416D4—24no—
417D4—42no—
418D4—48no—
419D4—42no—
420D4—42no—
421D4—84no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—22no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—22no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—44no—
434C2×C4—44no—
435C2×C4—42no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—82no—
441C2×C4—82no—
442C2×C4#6700112yes—
443C2×C4C2×C22⋊Dic1111yescharacteristic
444C2×C4C2×C22⋊Dic1112yes—
445C2×C4C2×C22⋊Dic1112yes—
446C2×C4C2×C22⋊Dic1112yes—
447C2×C4C2×C22⋊Dic1111yescharacteristic
448C2×C4C22×C22⋊D1112yes—
449C8—442no—
450C8—444no—
451C8—442no—
452C22—21no—
453C22—21no—
454C22—24no—
455C22—24no—
456C22—24no—
457C22—42no—
458C22—42no—
459C22—42no—
460C22—82no—
461C22—82no—
462C22—82no—
463C22—82no—
464C22C2×#6700111yescharacteristic
465C22#1062335011yescharacteristic
466C22C22×C22⋊Dic1111yescharacteristic
467C4—22no—
468C4—22no—
469C4—22no—
470C4—22no—
471C4—22no—
472C4—21no—
473C4—41no—
474C4—41no—
475C4—41no—
476C4—42no—
477C4#1062285012yes—
478C2—21no—
479C2—21no—
480C2—44no—
481C2—82no—
482C2#1307706511yescharacteristic
483C2#1307707711yescharacteristic
484C2C2×#1062285011yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#559C2
socleC22×C11C22×C22⋊C4
prime radicalC2×C11×#127C4
cosocleC22×C4×C11C24
hypercenterC2×#559D11
hypocenterC11#17429
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
1. #13077651C2semidirect
2. #13066968C2semidirect
3. #13066964C2semidirect
4. #13066960C2semidirect
5. #13066954C2semidirect
6. #13066940C2semidirect
7. #13066934C2semidirect
401. C11#17429semidirect

Maximal subgroups

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

subgroupindex
#130776512
#130669682
#130669642
#130669602
#130669542
#130669402
#130669342
C2×C11×#5592
#1742911