Finite Group Databasebeta

← #14720078

Subgroups — #14720078

Order 2816.

996 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077651C212yesmaximal
2#13066980C214yesmaximal, complemented
3#13066972C212yesmaximal, complemented
4#13066960C211yesmaximal, characteristic, complemented
5#13066946C212yesmaximal, complemented
6#13066940C211yesmaximal, characteristic, complemented
7C2×#10622166C212yesmaximal, complemented
8C2×C11×#554C211yesmaximal, characteristic
9C11×#554—22no—
10C11×#554—24no—
11C11×#554—22no—
12C2×C11×C4⋊Q8C411yescharacteristic
13C2×C11×#125C411yescharacteristic
14C2×C11×#125C2211yescharacteristic
15C2×C11×C22⋊Q8C412yes—
16C2×C11×C22⋊Q8C412yes—
17C2×C11×C22⋊Q8C2212yes—
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×D4×C11C411yescharacteristic
20C2×C4×D4×C11C411yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C22×C11×C4⋊C4C2212yes—
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#10622166C2214yes—
33#10622166C2211yescharacteristic
34#10622166C2212yes—
35#10622166C2214yes—
36#10622166C2212yes—
37C22×Q8×C11C2×C411yescharacteristic
38C22×Q8×C11C2×C412yes—
39C22×D4×C11C2×C411yescharacteristic
40C23×C4×C11C2×C412yes—
41C23×C4×C11C2×C412yes—
42C23×C4×C11C2312yes—
43C11×C4⋊Q8—22no—
44C11×C4⋊Q8—22no—
45C11×#125—22no—
46C11×#125—22no—
47C11×#125—22no—
48C11×#125—22no—
49C11×C22⋊Q8—24no—
50C11×C22⋊Q8—24no—
51C11×C22⋊Q8—24no—
52C11×C22⋊Q8—24no—
53C11×C22⋊Q8—24no—
54C11×C22⋊Q8—24no—
55C4×Q8×C11—22no—
56C4×Q8×C11—22no—
57C4×D4×C11—22no—
58C4×D4×C11—21no—
59C4×D4×C11—21no—
60C4×D4×C11—22no—
61C4×D4×C11—21no—
62C4×D4×C11—21no—
63C4×D4×C11D412yes—
64C4×D4×C11D414yes—
65C4×D4×C11D412yes—
66C2×C11×C4⋊C4—24no—
67C2×C11×C4⋊C4—24no—
68C2×C11×C4⋊C4C2×C412yes—
69C2×C11×C4⋊C4C2×C412yes—
70C2×C11×C4⋊C4C2×C411yescharacteristic
71C2×C11×C4⋊C4C2×C411yescharacteristic
72C2×C11×C4⋊C4C2×C411yescharacteristic
73C2×C11×C4⋊C4C2×C412yes—
74C2×C11×C4⋊C4C2×C412yes—
75C2×C11×C4⋊C4C2×C411yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2312yes—
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C22⋊C4C2×C412yes—
80C2×C11×C22⋊C4C2×C412yes—
81C2×C11×C22⋊C4C2×C412yes—
82C2×C42×C11C2×C411yescharacteristic
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#17426—111nomaximal, Sylow
97C24×C11C22×C412yes—
98C2×Q8×C11—22no—
99C2×Q8×C11—24no—
100C2×Q8×C11—22no—
101C2×Q8×C11—41no—
102C2×Q8×C11—82no—
103C2×D4×C11—24no—
104C2×D4×C11C22⋊C412yes—
105C2×D4×C11C22⋊C411yescharacteristic
106C2×D4×C11C22⋊C411yescharacteristic
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—24no—
112C22×C4×C11—42no—
113C22×C4×C11—82no—
114C22×C4×C11—82no—
115C22×C4×C11C22×C411yescharacteristic
116C22×C4×C11C22×C412yes—
117C22×C4×C11C22×C411yescharacteristic
118C22×C4×C11C22×C411yescharacteristic
119C22×C4×C11C22×C411yescharacteristic
120C22×C4×C11C22×C411yescharacteristic
121C22×C4×C11C22×C411yescharacteristic
122C22×C4×C11C22×C412yes—
123C22×C4×C11C22×C412yes—
124C22×C4×C11C2×D414yes—
125C22×C4×C11C2×D414yes—
126C22×C4×C11C2411yescharacteristic
127C11×C4⋊C4—24no—
128C11×C4⋊C4—24no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—24no—
135C11×C4⋊C4—24no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—24no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4C22⋊C412yes—
140C11×C4⋊C4C22⋊C412yes—
141C11×C22⋊C4—22no—
142C11×C22⋊C4—22no—
143C11×C22⋊C4—22no—
144C11×C22⋊C4—22no—
145C11×C22⋊C4C22⋊C414yes—
146C11×C22⋊C4C22⋊C414yes—
147C42×C11—21no—
148C42×C11—21no—
149C42×C11—21no—
150C42×C11—21no—
151C42×C11C2×D412yes—
152C42×C11C2×D412yes—
153#4318—84no—
154C2×C11⋊C8—22no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—24no—
157C2×C11⋊C8—84no—
158C2×#554D1111yescharacteristic
159#2974—112no—
160#1472—114no—
161#1470—112no—
162#1467—111no—
163#1463—112no—
164#1461—111no—
165C2×#324—112no—
166C23×C11—22no—
167C23×C11—22no—
168C23×C11—24no—
169C23×C11—42no—
170C23×C11C2×C22⋊C412yes—
171C23×C11C2×C22⋊C412yes—
172C23×C11C23×C411yescharacteristic
173Q8×C11—44no—
174Q8×C11—84no—
175D4×C11—24no—
176D4×C11—22no—
177D4×C11#10114yes—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—22no—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—21no—
190C2×C4×C11—22no—
191C2×C4×C11—21no—
192C2×C4×C11—44no—
193C2×C4×C11—44no—
194C2×C4×C11—41no—
195C2×C4×C11—42no—
196C2×C4×C11—44no—
197C2×C4×C11—44no—
198C2×C4×C11—41no—
199C2×C4×C11—42no—
200C2×C4×C11—41no—
201C2×C4×C11—82no—
202C2×C4×C11—82no—
203C2×C4×C11C2×C22⋊C411yescharacteristic
204C2×C4×C11C2×C22⋊C412yes—
205C2×C4×C11C2×C22⋊C414yes—
206C2×C4×C11C2×C22⋊C411yescharacteristic
207C2×C4×C11#13112yes—
208C2×C4×C11C22×D412yes—
209C11⋊C8—42no—
210C11⋊C8—44no—
211C11⋊C8—42no—
212#554—22no—
213#554—24no—
214#554—22no—
215C2×C4⋊Q8Dic1111yescharacteristic
216C2×#125Dic1111yescharacteristic
217C2×#125C2×D1111yescharacteristic
218C2×C22⋊Q8Dic1112yes—
219C2×C22⋊Q8Dic1112yes—
220C2×C22⋊Q8C2×D1112yes—
221C2×C4×Q8C2×D1111yescharacteristic
222C2×C4×D4Dic1111yescharacteristic
223C2×C4×D4Dic1111yescharacteristic
224C2×C4×D4C2×D1111yescharacteristic
225C22×C4⋊C4C2×D1112yes—
226#436—222no—
227#435—224no—
228C8×D4—222no—
229#432—112no—
230#431—112no—
231#407—114no—
232C2×C22⋊C8—114no—
233#324—111no—
234#324—112no—
235#324—114no—
236#324—111no—
237#324—112no—
238#324—114no—
239#324—112no—
240C22×C11—22no—
241C22×C11—21no—
242C22×C11—22no—
243C22×C11—21no—
244C22×C11—22no—
245C22×C11—22no—
246C22×C11—22no—
247C22×C11—44no—
248C22×C11—44no—
249C22×C11C2×#10114yes—
250C22×C11C22×C22⋊C411yescharacteristic
251C22×C11C2×#13111yescharacteristic
252C22×C11#56811yescharacteristic
253C4×C11—22no—
254C4×C11—22no—
255C4×C11—22no—
256C4×C11—24no—
257C4×C11—21no—
258C4×C11—42no—
259C4×C11—41no—
260C4×C11—41no—
261C4×C11—42no—
262C4×C11—41no—
263C4×C11C2×#10112yes—
264C22×Q8C2×Dic1111yescharacteristic
265C22×Q8C2×Dic1112yes—
266C22×D4C2×Dic1111yescharacteristic
267C23×C4C2×Dic1112yes—
268C23×C4C2×Dic1112yes—
269C23×C4C22×D1112yes—
270C2×M16—224no—
271C22×C8—224no—
272C4⋊Q8—22no—
273C4⋊Q8—22no—
274#125—22no—
275#125—22no—
276#125—22no—
277#125—22no—
278C22⋊Q8—24no—
279C22⋊Q8—24no—
280C22⋊Q8—24no—
281C22⋊Q8—24no—
282C22⋊Q8—24no—
283C22⋊Q8—24no—
284C4×Q8—22no—
285C4×Q8—22no—
286C4×D4—22no—
287C4×D4—21no—
288C4×D4—21no—
289C4×D4—22no—
290C4×D4—21no—
291C4×D4—21no—
292C4×D4C22⋊D1112yes—
293C4×D4C22⋊D1114yes—
294C4×D4C22⋊D1112yes—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4C2×Dic1112yes—
298C2×C4⋊C4C2×Dic1112yes—
299C2×C4⋊C4C2×Dic1111yescharacteristic
300C2×C4⋊C4C2×Dic1111yescharacteristic
301C2×C4⋊C4C2×Dic1111yescharacteristic
302C2×C4⋊C4C2×Dic1112yes—
303C2×C4⋊C4C2×Dic1112yes—
304C2×C4⋊C4C2×Dic1111yescharacteristic
305C2×C4⋊C4C22×D1111yescharacteristic
306C2×C4⋊C4C22×D1112yes—
307C2×C4⋊C4C22×D1111yescharacteristic
308C2×C22⋊C4C2×Dic1112yes—
309C2×C22⋊C4C2×Dic1112yes—
310C2×C22⋊C4C2×Dic1112yes—
311C2×C42C2×Dic1111yescharacteristic
312C2×C42C2×Dic1111yescharacteristic
313C2×C42C22×D1111yescharacteristic
314C4⋊C8—222no—
315C4⋊C8—222no—
316C22⋊C8—112no—
317C22⋊C8—114no—
318C22⋊C8—112no—
319C22⋊C8—224no—
320C22⋊C8—224no—
321#97—222no—
322C4×C8—222no—
323C2×C11—21no—
324C2×C11—21no—
325C2×C11—24no—
326C2×C11—42no—
327C2×C11#288011yescharacteristic
328C2×C11#288311yescharacteristic
329C2×C11C22×#10111yescharacteristic
330C24C22×Dic1112yes—
331C2×Q8—22no—
332C2×Q8—22no—
333C2×Q8—24no—
334C2×Q8—41no—
335C2×Q8—82no—
336C2×D4—24no—
337C2×D4C22⋊Dic1112yes—
338C2×D4C22⋊Dic1111yescharacteristic
339C2×D4C22⋊Dic1111yescharacteristic
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—24no—
345C22×C4—42no—
346C22×C4—82no—
347C22×C4—82no—
348C22×C4C22×Dic1111yescharacteristic
349C22×C4C22×Dic1112yes—
350C22×C4C22×Dic1111yescharacteristic
351C22×C4C22×Dic1111yescharacteristic
352C22×C4C22×Dic1111yescharacteristic
353C22×C4C22×Dic1111yescharacteristic
354C22×C4C22×Dic1111yescharacteristic
355C22×C4C22×Dic1112yes—
356C22×C4C22×Dic1112yes—
357C22×C4C2×C22⋊D1114yes—
358C22×C4C2×C22⋊D1114yes—
359C22×C4C23×D1111yescharacteristic
360M16—884no—
361C2×C8—222no—
362C2×C8—222no—
363C2×C8—224no—
364C2×C8—884no—
365C4⋊C4—24no—
366C4⋊C4—24no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—22no—
372C4⋊C4—24no—
373C4⋊C4—24no—
374C4⋊C4—22no—
375C4⋊C4—24no—
376C4⋊C4—22no—
377C4⋊C4C22⋊Dic1112yes—
378C4⋊C4C22⋊Dic1112yes—
379C22⋊C4—22no—
380C22⋊C4—22no—
381C22⋊C4—22no—
382C22⋊C4—22no—
383C22⋊C4C22⋊Dic1114yes—
384C22⋊C4C22⋊Dic1114yes—
385C42—21no—
386C42—21no—
387C42—21no—
388C42—21no—
389C42C2×C22⋊D1112yes—
390C42C2×C22⋊D1112yes—
391C11#1742611yescharacteristic, complemented, Sylow
392C23—22no—
393C23—22no—
394C23—24no—
395C23—42no—
396C23C2×C22⋊Dic1112yes—
397C23C2×C22⋊Dic1112yes—
398C23C23×Dic1111yescharacteristic
399Q8—44no—
400Q8—84no—
401D4—24no—
402D4—22no—
403D4#6690014yes—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—21no—
411C2×C4—22no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—44no—
419C2×C4—44no—
420C2×C4—41no—
421C2×C4—42no—
422C2×C4—44no—
423C2×C4—44no—
424C2×C4—41no—
425C2×C4—42no—
426C2×C4—41no—
427C2×C4—82no—
428C2×C4—82no—
429C2×C4#6700112yes—
430C2×C4C2×C22⋊Dic1111yescharacteristic
431C2×C4C2×C22⋊Dic1112yes—
432C2×C4C2×C22⋊Dic1114yes—
433C2×C4C2×C22⋊Dic1111yescharacteristic
434C2×C4C22×C22⋊D1112yes—
435C8—442no—
436C8—444no—
437C8—442no—
438C22—22no—
439C22—21no—
440C22—22no—
441C22—21no—
442C22—22no—
443C22—22no—
444C22—22no—
445C22—44no—
446C22—44no—
447C22C2×#6690014yes—
448C22C2×#6700111yescharacteristic
449C22#1062335011yescharacteristic
450C22C22×C22⋊Dic1111yescharacteristic
451C4—22no—
452C4—22no—
453C4—22no—
454C4—24no—
455C4—21no—
456C4—42no—
457C4—41no—
458C4—41no—
459C4—42no—
460C4—41no—
461C4C2×#6690012yes—
462C2—21no—
463C2—21no—
464C2—24no—
465C2—42no—
466C2#1307706511yescharacteristic
467C2#1307707711yescharacteristic
468C2C22×#6690011yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#554C2
socleC22×C11C22×C22⋊C4
prime radicalC22×D4×C11C2×C4
cosocleC22×C4×C11C24
hypercenterC2×#554D11
hypocenterC11#17426
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
2. #13066980C2semidirect
3. #13066972C2semidirect
4. #13066960C2semidirect
5. #13066946C2semidirect
6. #13066940C2semidirect
7. C2×#10622166C2semidirect
391. C11#17426semidirect

Maximal subgroups

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

subgroupindex
#130776512
#130669802
#130669722
#130669602
#130669462
#130669402
C2×#106221662
C2×C11×#5542
#1742611