Finite Group Databasebeta

← #14722367

Subgroups — #14722367

Order 2816.

1178 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077249C211yesmaximal, characteristic
2#13077249C211yesmaximal, characteristic
3#13067333C214yesmaximal, complemented
4#13067301C214yesmaximal, complemented
5#13067288C214yesmaximal, complemented
6C22×C11×C4⋊Q8C211yesmaximal, characteristic
7C23×Q8×C11—21no—
8C2×C11×C4⋊Q8—21no—
9C2×C11×C4⋊Q8—21no—
10C2×C11×C4⋊Q8—21no—
11C2×C11×C4⋊Q8—21no—
12C2×C11×C4⋊Q8—21no—
13C2×C11×C4⋊Q8—21no—
14C2×C11×C4⋊Q8C412yes—
15C2×C11×C4⋊Q8C412yes—
16C2×C11×C4⋊Q8C412yes—
17C2×C11×C4⋊Q8C2212yes—
18C2×C11×C4⋊Q8C2212yes—
19C2×C11×C4⋊Q8C2212yes—
20C22×C11×C4⋊C4—21no—
21C22×C11×C4⋊C4C412yes—
22C22×C42×C11C2211yescharacteristic
23#10622820—21no—
24#10622820—21no—
25#10622539—21no—
26#10622539—21no—
27#10622539C2212yes—
28#10622539C2212yes—
29#10622538—21no—
30#10622538—21no—
31#10622538C2212yes—
32#10622538C2212yes—
33#10622537C2212yes—
34#10622537C2212yes—
35C4×#4318—21no—
36C4×#4318—21no—
37#10622185C22116yescomplemented
38C22×Q8×C11—22no—
39C22×Q8×C11—22no—
40C22×Q8×C11—22no—
41C22×Q8×C11—22no—
42C22×Q8×C11—22no—
43C22×Q8×C11—22no—
44C22×Q8×C11—48no—
45C23×C4×C11—22no—
46C23×C4×C11C2×C411yescharacteristic
47C23×C4×C11D411yescharacteristic
48C23×C4×C11D411yescharacteristic
49C11×C4⋊Q8—22no—
50C11×C4⋊Q8—22no—
51C11×C4⋊Q8—22no—
52C11×C4⋊Q8—22no—
53C11×C4⋊Q8—22no—
54C11×C4⋊Q8—22no—
55C11×C4⋊Q8—22no—
56C11×C4⋊Q8—22no—
57C11×C4⋊Q8—22no—
58C11×C4⋊Q8—22no—
59C11×C4⋊Q8—22no—
60C11×C4⋊Q8—22no—
61C11×C4⋊Q8C2×C414yes—
62C11×C4⋊Q8C2×C414yes—
63C11×C4⋊Q8C2×C414yes—
64C11×C4⋊Q8C2314yes—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4—22no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4C2×C414yes—
75C2×C11×C4⋊C4C2×C414yes—
76C2×C11×C4⋊C4C2×C414yes—
77C2×C42×C11C2×C411yescharacteristic
78C2×C42×C11C2×C411yescharacteristic
79C2×C42×C11C2×C411yescharacteristic
80C2×C42×C11D411yescharacteristic
81C2×C42×C11D411yescharacteristic
82C2×C42×C11D411yescharacteristic
83C2×C42×C11D411yescharacteristic
84C2×C42×C11D411yescharacteristic
85C2×C42×C11D411yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C2×C42×C11C2311yescharacteristic
89C2×#4318—22no—
90C2×#4318—22no—
91C22⋊(C11⋊C8)—22no—
92C22⋊(C11⋊C8)—22no—
93C22⋊(C11⋊C8)—22no—
94C22⋊(C11⋊C8)—22no—
95C4⋊(C11⋊C8)—22no—
96C4⋊(C11⋊C8)—22no—
97C4⋊(C11⋊C8)C2314yes—
98C4⋊(C11⋊C8)C2314yes—
99#66867—22no—
100#66867—22no—
101C4×C11⋊C8—22no—
102C4×C11⋊C8—22no—
103#17742—111nomaximal, Sylow
104C24×C11C22⋊C411yescharacteristic
105C2×Q8×C11—24no—
106C2×Q8×C11—24no—
107C2×Q8×C11—24no—
108C2×Q8×C11—24no—
109C2×Q8×C11—48no—
110C2×Q8×C11—48no—
111C2×Q8×C11—48no—
112C2×Q8×C11—48no—
113C2×Q8×C11—48no—
114C2×Q8×C11—48no—
115C22×C4×C11—24no—
116C22×C4×C11—24no—
117C22×C4×C11—24no—
118C22×C4×C11—24no—
119C22×C4×C11—24no—
120C22×C4×C11—24no—
121C22×C4×C11—48no—
122C22×C4×C11C22⋊C411yescharacteristic
123C22×C4×C11C22⋊C411yescharacteristic
124C22×C4×C11C22⋊C411yescharacteristic
125C22×C4×C11C22⋊C411yescharacteristic
126C22×C4×C11C22⋊C411yescharacteristic
127C22×C4×C11C22⋊C411yescharacteristic
128C22×C4×C11C22⋊C411yescharacteristic
129C22×C4×C11C22⋊C411yescharacteristic
130C22×C4×C11C22⋊C411yescharacteristic
131C22×C4×C11C22×C411yescharacteristic
132C22×C4×C11C22×C411yescharacteristic
133C22×C4×C11C22×C411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C11×C4⋊C4—24no—
141C11×C4⋊C4—24no—
142C11×C4⋊C4—24no—
143C11×C4⋊C4—24no—
144C11×C4⋊C4—24no—
145C11×C4⋊C4—24no—
146C11×C4⋊C4—24no—
147C11×C4⋊C4C22×C418yes—
148C42×C11C22⋊C411yescharacteristic
149C42×C11C22⋊C411yescharacteristic
150C42×C11C22⋊C411yescharacteristic
151C42×C11C22⋊C411yescharacteristic
152C42×C11C22⋊C411yescharacteristic
153C42×C11C22⋊C411yescharacteristic
154C42×C11C22×C411yescharacteristic
155C42×C11C22×C411yescharacteristic
156C42×C11C22×C411yescharacteristic
157C42×C11C2×D411yescharacteristic
158C42×C11C2×D411yescharacteristic
159C42×C11C2×D411yescharacteristic
160C42×C11C2×D411yescharacteristic
161C42×C11C2×D411yescharacteristic
162C42×C11C2×D411yescharacteristic
163C42×C11C2411yescharacteristic
164#4318—44no—
165#4318—44no—
166C2×C11⋊C8—24no—
167C2×C11⋊C8—24no—
168C22×C4⋊Q8D1111yescharacteristic
169#2920—111no—
170#2920—111no—
171#1556—114no—
172#1549—114no—
173#1546—114no—
174C23×C11—22no—
175C23×C11—22no—
176C23×C11—22no—
177C23×C11C2×C22⋊C411yescharacteristic
178C23×C11C2×C22⋊C411yescharacteristic
179C23×C11C2×C22⋊C411yescharacteristic
180Q8×C11—48no—
181Q8×C11—48no—
182Q8×C11—48no—
183Q8×C11—48no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—28no—
200C2×C4×C11—48no—
201C2×C4×C11—48no—
202C2×C4×C11—48no—
203C2×C4×C11#10114yes—
204C2×C4×C11C2×C22⋊C411yescharacteristic
205C2×C4×C11C2×C22⋊C411yescharacteristic
206C2×C4×C11C2×C22⋊C411yescharacteristic
207C2×C4×C11C2×C22⋊C411yescharacteristic
208C2×C4×C11C2×C22⋊C411yescharacteristic
209C2×C4×C11C2×C22⋊C411yescharacteristic
210C2×C4×C11C2×C22⋊C411yescharacteristic
211C2×C4×C11C2×C22⋊C411yescharacteristic
212C2×C4×C11C2×C22⋊C411yescharacteristic
213C2×C4×C11AGL(1,ℤ/8)14yes—
214C2×C4×C11#13714yes—
215C2×C4×C11C23×C411yescharacteristic
216C2×C4×C11C22×D411yescharacteristic
217C2×C4×C11C22×D411yescharacteristic
218C11⋊C8—44no—
219C11⋊C8—44no—
220C23×Q8—21no—
221C2×C4⋊Q8—21no—
222C2×C4⋊Q8—21no—
223C2×C4⋊Q8—21no—
224C2×C4⋊Q8—21no—
225C2×C4⋊Q8—21no—
226C2×C4⋊Q8—21no—
227C2×C4⋊Q8Dic1112yes—
228C2×C4⋊Q8Dic1112yes—
229C2×C4⋊Q8Dic1112yes—
230C2×C4⋊Q8C2×D1112yes—
231C2×C4⋊Q8C2×D1112yes—
232C2×C4⋊Q8C2×D1112yes—
233C22×C4⋊C4—21no—
234C22×C4⋊C4Dic1112yes—
235C22×C42C2×D1111yescharacteristic
236#432—112no—
237#432—112no—
238#432—221no—
239#432—221no—
240#431—112no—
241#431—112no—
242#431—221no—
243#431—221no—
244#423—112no—
245#423—112no—
246#407—221no—
247#407—221no—
248C4×M16—221no—
249C4×M16—221no—
250#332—1116no—
251C22×C11—28no—
252C22×C11—21no—
253C22×C11—21no—
254C22×C11—21no—
255C22×C11—21no—
256C22×C11—21no—
257C22×C11—21no—
258C22×C11C2×#10112yes—
259C22×C11#41812yes—
260C22×C11#41912yes—
261C22×C11C22×C22⋊C411yescharacteristic
262C4×C11—21no—
263C4×C11—21no—
264C4×C11—21no—
265C4×C11—21no—
266C4×C11—21no—
267C4×C11—21no—
268C4×C11—48no—
269C4×C11C2×#10112yes—
270C4×C11C2×#10112yes—
271C4×C11#41812yes—
272C4×C11#41912yes—
273C4×C11C2×AGL(1,ℤ/8)12yes—
274C4×C11C2×#13712yes—
275C22×Q8—22no—
276C22×Q8—22no—
277C22×Q8—22no—
278C22×Q8—22no—
279C22×Q8—22no—
280C22×Q8—22no—
281C22×Q8—48no—
282C23×C4—22no—
283C23×C4C2×Dic1111yescharacteristic
284C23×C4C22⋊D1111yescharacteristic
285C23×C4C22⋊D1111yescharacteristic
286C2×M16—222no—
287C2×M16—222no—
288C4⋊Q8—22no—
289C4⋊Q8—22no—
290C4⋊Q8—22no—
291C4⋊Q8—22no—
292C4⋊Q8—22no—
293C4⋊Q8—22no—
294C4⋊Q8—22no—
295C4⋊Q8—22no—
296C4⋊Q8—22no—
297C4⋊Q8—22no—
298C4⋊Q8—22no—
299C4⋊Q8—22no—
300C4⋊Q8C2×Dic1114yes—
301C4⋊Q8C2×Dic1114yes—
302C4⋊Q8C2×Dic1114yes—
303C4⋊Q8C22×D1114yes—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4C2×Dic1114yes—
314C2×C4⋊C4C2×Dic1114yes—
315C2×C4⋊C4C2×Dic1114yes—
316C2×C42C2×Dic1111yescharacteristic
317C2×C42C2×Dic1111yescharacteristic
318C2×C42C2×Dic1111yescharacteristic
319C2×C42C22⋊D1111yescharacteristic
320C2×C42C22⋊D1111yescharacteristic
321C2×C42C22⋊D1111yescharacteristic
322C2×C42C22⋊D1111yescharacteristic
323C2×C42C22⋊D1111yescharacteristic
324C2×C42C22⋊D1111yescharacteristic
325C2×C42C22×D1111yescharacteristic
326C2×C42C22×D1111yescharacteristic
327C2×C42C22×D1111yescharacteristic
328C4⋊C8—114no—
329C4⋊C8—114no—
330C4⋊C8—222no—
331C4⋊C8—222no—
332C22⋊C8—222no—
333C22⋊C8—222no—
334C22⋊C8—222no—
335C22⋊C8—222no—
336#97—222no—
337#97—222no—
338C4×C8—222no—
339C4×C8—222no—
340C2×C11—22no—
341C2×C11—22no—
342C2×C11—22no—
343C2×C11C22×#10111yescharacteristic
344C2×C11C2×#41811yescharacteristic
345C2×C11C2×#41911yescharacteristic
346C24C22⋊Dic1111yescharacteristic
347C2×Q8—24no—
348C2×Q8—24no—
349C2×Q8—24no—
350C2×Q8—24no—
351C2×Q8—48no—
352C2×Q8—48no—
353C2×Q8—48no—
354C2×Q8—48no—
355C2×Q8—48no—
356C2×Q8—48no—
357C22×C4—24no—
358C22×C4—24no—
359C22×C4—24no—
360C22×C4—24no—
361C22×C4—24no—
362C22×C4—24no—
363C22×C4—48no—
364C22×C4C22⋊Dic1111yescharacteristic
365C22×C4C22⋊Dic1111yescharacteristic
366C22×C4C22⋊Dic1111yescharacteristic
367C22×C4C22⋊Dic1111yescharacteristic
368C22×C4C22⋊Dic1111yescharacteristic
369C22×C4C22⋊Dic1111yescharacteristic
370C22×C4C22⋊Dic1111yescharacteristic
371C22×C4C22⋊Dic1111yescharacteristic
372C22×C4C22⋊Dic1111yescharacteristic
373C22×C4C22×Dic1111yescharacteristic
374C22×C4C22×Dic1111yescharacteristic
375C22×C4C22×Dic1111yescharacteristic
376C22×C4C2×C22⋊D1111yescharacteristic
377C22×C4C2×C22⋊D1111yescharacteristic
378C22×C4C2×C22⋊D1111yescharacteristic
379C22×C4C2×C22⋊D1111yescharacteristic
380C22×C4C2×C22⋊D1111yescharacteristic
381C22×C4C2×C22⋊D1111yescharacteristic
382M16—444no—
383M16—444no—
384C2×C8—224no—
385C2×C8—224no—
386C4⋊C4—24no—
387C4⋊C4—24no—
388C4⋊C4—24no—
389C4⋊C4—24no—
390C4⋊C4—24no—
391C4⋊C4—24no—
392C4⋊C4—24no—
393C4⋊C4C22×Dic1118yes—
394C42C22⋊Dic1111yescharacteristic
395C42C22⋊Dic1111yescharacteristic
396C42C22⋊Dic1111yescharacteristic
397C42C22⋊Dic1111yescharacteristic
398C42C22⋊Dic1111yescharacteristic
399C42C22⋊Dic1111yescharacteristic
400C42C22×Dic1111yescharacteristic
401C42C22×Dic1111yescharacteristic
402C42C22×Dic1111yescharacteristic
403C42C2×C22⋊D1111yescharacteristic
404C42C2×C22⋊D1111yescharacteristic
405C42C2×C22⋊D1111yescharacteristic
406C42C2×C22⋊D1111yescharacteristic
407C42C2×C22⋊D1111yescharacteristic
408C42C2×C22⋊D1111yescharacteristic
409C42C23×D1111yescharacteristic
410C11#1774211yescharacteristic, complemented, Sylow
411C23—22no—
412C23—22no—
413C23—22no—
414C23C2×C22⋊Dic1111yescharacteristic
415C23C2×C22⋊Dic1111yescharacteristic
416C23C2×C22⋊Dic1111yescharacteristic
417Q8—48no—
418Q8—48no—
419Q8—48no—
420Q8—48no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—28no—
437C2×C4—48no—
438C2×C4—48no—
439C2×C4—48no—
440C2×C4#6690014yes—
441C2×C4#6698514yes—
442C2×C4#6699514yes—
443C2×C4C2×C22⋊Dic1111yescharacteristic
444C2×C4C2×C22⋊Dic1111yescharacteristic
445C2×C4C2×C22⋊Dic1111yescharacteristic
446C2×C4C2×C22⋊Dic1111yescharacteristic
447C2×C4C2×C22⋊Dic1111yescharacteristic
448C2×C4C2×C22⋊Dic1111yescharacteristic
449C2×C4C2×C22⋊Dic1111yescharacteristic
450C2×C4C2×C22⋊Dic1111yescharacteristic
451C2×C4C2×C22⋊Dic1111yescharacteristic
452C2×C4C23×Dic1111yescharacteristic
453C2×C4C22×C22⋊D1111yescharacteristic
454C2×C4C22×C22⋊D1111yescharacteristic
455C8—444no—
456C8—444no—
457C22—28no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22#1062282812yes—
465C22#1062283812yes—
466C22C2×#6690012yes—
467C22C22×C22⋊Dic1111yescharacteristic
468C4—21no—
469C4—21no—
470C4—21no—
471C4—21no—
472C4—21no—
473C4—21no—
474C4—48no—
475C4#1062282812yes—
476C4#1062283812yes—
477C4C2×#6690012yes—
478C4C2×#6690012yes—
479C4C2×#6698512yes—
480C4C2×#6699512yes—
481C2—22no—
482C2—22no—
483C2—22no—
484C2C22×#6690011yescharacteristic
485C2C2×#1062282811yescharacteristic
486C2C2×#1062283811yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC22×C11×C4⋊Q8C2
socleC22×C11C22×C22⋊C4
prime radicalC24×C11C22⋊C4
cosocleC42×C11C24
hypercenterC22×C4⋊Q8D11
hypocenterC11#17742
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C42 ◁ C22×C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. #13067333C2semidirect
4. #13067301C2semidirect
5. #13067288C2semidirect
37. #10622185C22semidirect
410. C11#17742semidirect

Maximal subgroups

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

subgroupindex
#130772492
#130673332
#130673012
#130672882
C22×C11×C4⋊Q82
#1774211