Finite Group Databasebeta

← #14719625

Subgroups — #14719625

Order 2816.

1322 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077249C212yesmaximal, complemented
2#13066950C214yesmaximal, complemented
3#13066946C212yesmaximal, complemented
4#13066943C212yesmaximal
5#13066930C214yesmaximal, complemented
6C22×C11×#117C211yesmaximal, characteristic
7C24×C4×C11C411yescharacteristic
8C2×C11×#117—22no—
9C2×C11×#117—22no—
10C2×C11×#117—22no—
11C2×C11×#117—22no—
12C2×C11×#117C412yes—
13C2×C11×#117C412yes—
14C2×C11×#117C2212yes—
15C2×C11×#117C2212yes—
16C22×C11×C4⋊C4C411yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C411yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C42×C11C411yescharacteristic
21C22×C42×C11C2211yescharacteristic
22#10622820C2214yes—
23#10622539—22no—
24#10622539C2214yescomplemented
25#10622538—22no—
26#10622538C2214yescomplemented
27#10622537—22no—
28C4×#4318—22no—
29#10622166C2218yescomplemented
30#10622163C2218yes—
31C25×C11C2×C411yescharacteristic
32C23×C4×C11—21no—
33C23×C4×C11—21no—
34C23×C4×C11—21no—
35C23×C4×C11—21no—
36C23×C4×C11—28no—
37C23×C4×C11C2×C411yescharacteristic
38C23×C4×C11C2×C412yes—
39C23×C4×C11C2×C411yescharacteristic
40C23×C4×C11C2×C412yes—
41C23×C4×C11C2×C411yescharacteristic
42C23×C4×C11C2×C411yescharacteristic
43C23×C4×C11C2×C411yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C11×#117—24no—
46C11×#117—24no—
47C11×#117—24no—
48C11×#117—24no—
49C11×#117—24no—
50C11×#117—24no—
51C11×#117—24no—
52C11×#117—24no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4C2×C412yes—
58C2×C11×C4⋊C4C2×C412yes—
59C2×C11×C4⋊C4C2×C412yes—
60C2×C11×C4⋊C4C2312yes—
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4—22no—
63C2×C11×C22⋊C4—22no—
64C2×C11×C22⋊C4—22no—
65C2×C11×C22⋊C4C2×C412yes—
66C2×C11×C22⋊C4C2×C412yes—
67C2×C11×C22⋊C4C2×C412yes—
68C2×C11×C22⋊C4C2312yes—
69C2×C42×C11—21no—
70C2×C42×C11—21no—
71C2×C42×C11—21no—
72C2×C42×C11—21no—
73C2×C42×C11C2×C412yes—
74C2×C42×C11C2×C412yes—
75C2×C42×C11C2×C411yescharacteristic
76C2×C42×C11C2×C411yescharacteristic
77C2×C42×C11D412yes—
78C2×C42×C11D412yes—
79C2×C42×C11D412yes—
80C2×C42×C11D412yes—
81C2×C42×C11C2311yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C2×#4318—24no—
84C22⋊(C11⋊C8)—24no—
85C22⋊(C11⋊C8)C2318yes—
86C4⋊(C11⋊C8)—24no—
87C4⋊(C11⋊C8)—24no—
88#66867—24no—
89C4×C11⋊C8—24no—
90#17357—111nomaximal, Sylow
91C24×C11—21no—
92C24×C11—21no—
93C24×C11—24no—
94C24×C11—42no—
95C24×C11—42no—
96C24×C11C22×C411yescharacteristic
97C24×C11C22×C412yes—
98C22×C4×C11—28no—
99C22×C4×C11—28no—
100C22×C4×C11—28no—
101C22×C4×C11—28no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—24no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—24no—
110C22×C4×C11—24no—
111C22×C4×C11—24no—
112C22×C4×C11—24no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—42no—
118C22×C4×C11—42no—
119C22×C4×C11—42no—
120C22×C4×C11—42no—
121C22×C4×C11C22⋊C411yescharacteristic
122C22×C4×C11C22⋊C411yescharacteristic
123C22×C4×C11C22⋊C411yescharacteristic
124C22×C4×C11C22⋊C411yescharacteristic
125C22×C4×C11C22⋊C412yes—
126C22×C4×C11C22⋊C412yes—
127C22×C4×C11M1618yescomplemented
128C22×C4×C11C22×C411yescharacteristic
129C22×C4×C11C22×C412yes—
130C22×C4×C11C22×C412yes—
131C22×C4×C11C22×C412yes—
132C22×C4×C11C22×C411yescharacteristic
133C22×C4×C11C22×C411yescharacteristic
134C22×C4×C11C22×C411yescharacteristic
135C22×C4×C11C22×C411yescharacteristic
136C22×C4×C11C2×D412yes—
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2411yescharacteristic
139C11×C4⋊C4—24no—
140C11×C4⋊C4—24no—
141C11×C4⋊C4—24no—
142C11×C4⋊C4—24no—
143C11×C22⋊C4—24no—
144C11×C22⋊C4—24no—
145C11×C22⋊C4—24no—
146C11×C22⋊C4—24no—
147C42×C11—22no—
148C42×C11—22no—
149C42×C11—22no—
150C42×C11—22no—
151C42×C11C22⋊C412yes—
152C42×C11C22⋊C412yes—
153C42×C11C22⋊C412yes—
154C42×C11C22⋊C412yes—
155C42×C11C2×D412yes—
156C42×C11C2×D412yes—
157C42×C11C2×D412yes—
158C42×C11C2×D412yes—
159#4318—48no—
160C2×C11⋊C8—28no—
161C22×#117D1111yescharacteristic
162#2920—112no—
163#1464—114no—
164#1463—112no—
165#1462—112no—
166#1458—114no—
167C23×C11—22no—
168C23×C11—22no—
169C23×C11—22no—
170C23×C11—24no—
171C23×C11—24no—
172C23×C11—22no—
173C23×C11—22no—
174C23×C11—42no—
175C23×C11—42no—
176C23×C11—416no—
177C23×C11—42no—
178C23×C11—42no—
179C23×C11—42no—
180C23×C11—42no—
181C23×C11C2×C22⋊C411yescharacteristic
182C23×C11C2×C22⋊C411yescharacteristic
183C23×C11C2×M1614yes—
184C23×C11C23×C411yescharacteristic
185C2×C4×C11—28no—
186C2×C4×C11—28no—
187C2×C4×C11—24no—
188C2×C4×C11—24no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—24no—
193C2×C4×C11—24no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—28no—
199C2×C4×C11—28no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—42no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—42no—
207C2×C4×C11—41no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11C2×C22⋊C411yescharacteristic
215C2×C4×C11C2×C22⋊C411yescharacteristic
216C2×C4×C11C2×C22⋊C412yes—
217C2×C4×C11C2×C22⋊C412yes—
218C2×C4×C11C2×C22⋊C412yes—
219C2×C4×C11C2×C22⋊C411yescharacteristic
220C2×C4×C11C2×C22⋊C411yescharacteristic
221C2×C4×C11C2×M1614yes—
222C2×C4×C11C2×M1614yes—
223C2×C4×C11C22×D412yes—
224C11⋊C8—48no—
225C24×C4Dic1111yescharacteristic
226C2×#117—22no—
227C2×#117—22no—
228C2×#117—22no—
229C2×#117—22no—
230C2×#117Dic1112yes—
231C2×#117Dic1112yes—
232C2×#117C2×D1112yes—
233C2×#117C2×D1112yes—
234C22×C4⋊C4Dic1111yescharacteristic
235C22×C4⋊C4C2×D1111yescharacteristic
236C22×C22⋊C4Dic1111yescharacteristic
237C22×C22⋊C4C2×D1111yescharacteristic
238C22×C42Dic1111yescharacteristic
239C22×C42C2×D1111yescharacteristic
240#432—114no—
241#432—222no—
242#431—114no—
243#431—222no—
244#423—222no—
245#407—114no—
246C4×M16—222no—
247#324—118no—
248#323—118no—
249C22×C11—28no—
250C22×C11—21no—
251C22×C11—21no—
252C22×C11—21no—
253C22×C11—21no—
254C22×C11—21no—
255C22×C11—21no—
256C22×C11—24no—
257C22×C11—44no—
258C22×C11—44no—
259C22×C11—48no—
260C22×C11—48no—
261C22×C11—42no—
262C22×C11—42no—
263C22×C11#41012yes—
264C22×C11#41312yes—
265C22×C11C22×C22⋊C411yescharacteristic
266C22×C11C22×M1612yes—
267C4×C11—21no—
268C4×C11—21no—
269C4×C11—24no—
270C4×C11—22no—
271C4×C11—22no—
272C4×C11—22no—
273C4×C11—22no—
274C4×C11—42no—
275C4×C11—42no—
276C4×C11#40712yes—
277C4×C11#40712yes—
278C25C2×Dic1111yescharacteristic
279C23×C4—28no—
280C23×C4—21no—
281C23×C4—21no—
282C23×C4—21no—
283C23×C4—21no—
284C23×C4C2×Dic1111yescharacteristic
285C23×C4C2×Dic1112yes—
286C23×C4C2×Dic1112yes—
287C23×C4C2×Dic1111yescharacteristic
288C23×C4C2×Dic1111yescharacteristic
289C23×C4C2×Dic1111yescharacteristic
290C23×C4C2×Dic1111yescharacteristic
291C23×C4C22×D1111yescharacteristic
292C2×M16—224no—
293#117—24no—
294#117—24no—
295#117—24no—
296#117—24no—
297#117—24no—
298#117—24no—
299#117—24no—
300#117—24no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4C2×Dic1112yes—
306C2×C4⋊C4C2×Dic1112yes—
307C2×C4⋊C4C2×Dic1112yes—
308C2×C4⋊C4C22×D1112yes—
309C2×C22⋊C4—22no—
310C2×C22⋊C4—22no—
311C2×C22⋊C4—22no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4C2×Dic1112yes—
314C2×C22⋊C4C2×Dic1112yes—
315C2×C22⋊C4C2×Dic1112yes—
316C2×C22⋊C4C22×D1112yes—
317C2×C42—21no—
318C2×C42—21no—
319C2×C42—21no—
320C2×C42—21no—
321C2×C42C2×Dic1112yes—
322C2×C42C2×Dic1112yes—
323C2×C42C2×Dic1111yescharacteristic
324C2×C42C2×Dic1111yescharacteristic
325C2×C42C22⋊D1112yes—
326C2×C42C22⋊D1112yes—
327C2×C42C22⋊D1112yes—
328C2×C42C22⋊D1112yes—
329C2×C42C22×D1111yescharacteristic
330C2×C42C22×D1111yescharacteristic
331C4⋊C8—224no—
332C4⋊C8—224no—
333C22⋊C8—118no—
334C22⋊C8—224no—
335#97—224no—
336C4×C8—224no—
337C2×C11—22no—
338C2×C11—22no—
339C2×C11—22no—
340C2×C11—44no—
341C2×C11C2×#40711yescharacteristic
342C2×C11C2×#41011yescharacteristic
343C2×C11C2×#41311yescharacteristic
344C24—24no—
345C24—21no—
346C24—21no—
347C24—42no—
348C24—42no—
349C24C22×Dic1111yescharacteristic
350C24C22×Dic1112yes—
351C22×C4—28no—
352C22×C4—28no—
353C22×C4—28no—
354C22×C4—28no—
355C22×C4—24no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—24no—
359C22×C4—24no—
360C22×C4—24no—
361C22×C4—24no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—42no—
371C22×C4—42no—
372C22×C4—42no—
373C22×C4—42no—
374C22×C4#431818yescomplemented
375C22×C4C22⋊Dic1111yescharacteristic
376C22×C4C22⋊Dic1111yescharacteristic
377C22×C4C22⋊Dic1112yes—
378C22×C4C22⋊Dic1111yescharacteristic
379C22×C4C22⋊Dic1111yescharacteristic
380C22×C4C22⋊Dic1112yes—
381C22×C4C22×Dic1112yes—
382C22×C4C22×Dic1111yescharacteristic
383C22×C4C22×Dic1112yes—
384C22×C4C22×Dic1112yes—
385C22×C4C22×Dic1111yescharacteristic
386C22×C4C22×Dic1111yescharacteristic
387C22×C4C22×Dic1111yescharacteristic
388C22×C4C22×Dic1111yescharacteristic
389C22×C4C2×C22⋊D1112yes—
390C22×C4C2×C22⋊D1112yes—
391C22×C4C23×D1111yescharacteristic
392M16—448no—
393C2×C8—228no—
394C4⋊C4—24no—
395C4⋊C4—24no—
396C4⋊C4—24no—
397C4⋊C4—24no—
398C22⋊C4—24no—
399C22⋊C4—24no—
400C22⋊C4—24no—
401C22⋊C4—24no—
402C42—22no—
403C42—22no—
404C42—22no—
405C42—22no—
406C42C22⋊Dic1112yes—
407C42C22⋊Dic1112yes—
408C42C22⋊Dic1112yes—
409C42C22⋊Dic1112yes—
410C42C2×C22⋊D1112yes—
411C42C2×C22⋊D1112yes—
412C42C2×C22⋊D1112yes—
413C42C2×C22⋊D1112yes—
414C11#1735711yescharacteristic, complemented, Sylow
415C23—22no—
416C23—22no—
417C23—22no—
418C23—24no—
419C23—24no—
420C23—22no—
421C23—22no—
422C23—42no—
423C23—42no—
424C23—416no—
425C23—42no—
426C23—42no—
427C23—42no—
428C23—42no—
429C23C2×#431814yes—
430C23C2×C22⋊Dic1111yescharacteristic
431C23C2×C22⋊Dic1111yescharacteristic
432C23C23×Dic1111yescharacteristic
433C2×C4—24no—
434C2×C4—24no—
435C2×C4—28no—
436C2×C4—28no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—24no—
440C2×C4—24no—
441C2×C4—22no—
442C2×C4—28no—
443C2×C4—28no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—42no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—42no—
455C2×C4—41no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4C2×#431814yes—
463C2×C4C2×#431814yes—
464C2×C4C2×C22⋊Dic1111yescharacteristic
465C2×C4C2×C22⋊Dic1111yescharacteristic
466C2×C4C2×C22⋊Dic1112yes—
467C2×C4C2×C22⋊Dic1112yes—
468C2×C4C2×C22⋊Dic1112yes—
469C2×C4C2×C22⋊Dic1111yescharacteristic
470C2×C4C2×C22⋊Dic1111yescharacteristic
471C2×C4C22×C22⋊D1112yes—
472C8—448no—
473C22—28no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—21no—
480C22—24no—
481C22—44no—
482C22—44no—
483C22—48no—
484C22—48no—
485C22—42no—
486C22—42no—
487C22#1062285012yes—
488C22#1062285312yes—
489C22C22×#431812yes—
490C22C22×C22⋊Dic1111yescharacteristic
491C4—24no—
492C4—21no—
493C4—21no—
494C4—22no—
495C4—22no—
496C4—22no—
497C4—22no—
498C4—42no—
499C4—42no—
500C4#1062282012yes—
501C4#1062282012yes—
502C2—22no—
503C2—22no—
504C2—22no—
505C2—44no—
506C2C2×#1062282011yescharacteristic
507C2C2×#1062285311yescharacteristic
508C2C2×#1062285011yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊Dic11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×#117C2
socleC22×C11C22×C22⋊C4
prime radicalC25×C11C2×C4
cosocleC22×C4×C11C24
hypercenterC22×#117D11
hypocenterC11#17357
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
1. #13077249C2semidirect
2. #13066950C2semidirect
3. #13066946C2semidirect
5. #13066930C2semidirect
24. #10622539C22semidirect
26. #10622538C22semidirect
29. #10622166C22semidirect
127. C22×C4×C11M16semidirect
374. C22×C4#4318semidirect
414. C11#17357semidirect

Maximal subgroups

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

subgroupindex
#130772492
#130669502
#130669462
#130669432
#130669302
C22×C11×#1172
#1735711