Finite Group Databasebeta

← #14719990

Subgroups — #14719990

Order 2816.

1008 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077274C212yesmaximal, complemented
2#13066985C214yesmaximal, complemented
3#13066976C212yesmaximal, complemented
4#13066957C212yesmaximal, complemented
5#13066954C211yesmaximal, characteristic, complemented
6#13066937C212yesmaximal, complemented
7#13066934C211yesmaximal, characteristic, complemented
8C2×C11×#553C211yesmaximal, characteristic
9C11×#553—22no—
10C11×#553—22no—
11C11×#553—24no—
12C2×C11×#126C2212yes—
13C2×C11×#125C411yescharacteristic
14C2×C11×#123C412yes—
15C2×C11×#121C412yes—
16C2×C11×#121C411yescharacteristic
17C2×C11×#121C2211yescharacteristic
18C2×C4×D4×C11C411yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×C4×D4×C11C2212yes—
21C2×C11×#117C2211yescharacteristic
22C22×C11×C4⋊C4C411yescharacteristic
23#10622820C2212yes—
24C2×C22⋊(C11⋊C8)C2212yes—
25#10622613—24no—
26#10622612—22no—
27#10622610—22no—
28#10622539C2214yes—
29#10622538C2214yes—
30#10622166C2212yes—
31#10622166C2212yes—
32#10622163C2211yescharacteristic
33#10622163C2211yescharacteristic
34#10622163C2212yes—
35#10622163C2214yes—
36#10622163C2214yes—
37C22×D4×C11C2×C411yescharacteristic
38C22×D4×C11C2×C412yes—
39C22×D4×C11C2×C411yescharacteristic
40C22×D4×C11C2×C412yes—
41C23×C4×C11C2×C411yescharacteristic
42C23×C4×C11C2×C412yes—
43C23×C4×C11C2×C412yes—
44C23×C4×C11C2311yescharacteristic
45C11×#126—24no—
46C11×#126—24no—
47C11×#125—22no—
48C11×#125—22no—
49C11×#123—24no—
50C11×#123—24no—
51C11×#121—22no—
52C11×#121—22no—
53C11×#121—22no—
54C11×#121—22no—
55C11×#121—24no—
56C11×#121—24no—
57C4×D4×C11—22no—
58C4×D4×C11—22no—
59C4×D4×C11—22no—
60C4×D4×C11—21no—
61C4×D4×C11—21no—
62C4×D4×C11—24no—
63C4×D4×C11—24no—
64C11×#117D412yes—
65C11×#117D412yes—
66C11×#117D414yes—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4C2×C411yescharacteristic
71C2×C11×C4⋊C4C2×C412yes—
72C2×C11×C4⋊C4C2×C412yes—
73C2×C11×C4⋊C4C2×C412yes—
74C2×C11×C4⋊C4C2×C411yescharacteristic
75C2×C11×C4⋊C4C2×C411yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4C2×C412yes—
78C2×C11×C22⋊C4C2×C411yescharacteristic
79C2×C11×C22⋊C4C2×C412yes—
80C2×C11×C22⋊C4C2×C412yes—
81C2×C11×C22⋊C4C2311yescharacteristic
82C2×C11×C22⋊C4C2312yes—
83C2×C42×C11C2×C411yescharacteristic
84C2×C42×C11C2312yes—
85C2×#4318—22no—
86C22×C11⋊C8—22no—
87C22⋊(C11⋊C8)—22no—
88C22⋊(C11⋊C8)—22no—
89C22⋊(C11⋊C8)C2312yes—
90C22⋊(C11⋊C8)C2314yes—
91C22⋊(C11⋊C8)C2312yes—
92C4⋊(C11⋊C8)—24no—
93C4⋊(C11⋊C8)—24no—
94#66867—24no—
95C4×C11⋊C8—24no—
96#17415—111nomaximal, Sylow
97C24×C11C22×C412yes—
98C24×C11C22×C411yescharacteristic
99C24×C11C22×C411yescharacteristic
100C2×D4×C11—22no—
101C2×D4×C11—24no—
102C2×D4×C11—22no—
103C2×D4×C11—24no—
104C2×D4×C11—21no—
105C2×D4×C11—24no—
106C2×D4×C11—21no—
107C2×D4×C11—42no—
108C2×D4×C11—41no—
109C2×D4×C11—42no—
110C2×D4×C11—82no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—42no—
118C22×C4×C11—42no—
119C22×C4×C11—82no—
120C22×C4×C11—82no—
121C22×C4×C11C22×C411yescharacteristic
122C22×C4×C11C22×C411yescharacteristic
123C22×C4×C11C22×C412yes—
124C22×C4×C11C22×C411yescharacteristic
125C22×C4×C11C22×C411yescharacteristic
126C22×C4×C11C22×C412yes—
127C22×C4×C11C22×C412yes—
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2411yescharacteristic
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—24no—
136C11×C4⋊C4—24no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4C22⋊C412yes—
139C11×C4⋊C4C22⋊C411yescharacteristic
140C11×C4⋊C4C22⋊C411yescharacteristic
141C11×C4⋊C4C22⋊C412yes—
142C11×C4⋊C4C22⋊C412yes—
143C11×C22⋊C4—22no—
144C11×C22⋊C4—22no—
145C11×C22⋊C4—22no—
146C11×C22⋊C4—24no—
147C11×C22⋊C4—22no—
148C11×C22⋊C4—24no—
149C11×C22⋊C4C22⋊C414yes—
150C11×C22⋊C4C22⋊C414yes—
151C42×C11—21no—
152C42×C11—21no—
153C42×C11C2×D414yes—
154C42×C11C2×D414yes—
155#4318—44no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8—24no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—44no—
160C2×#553D1111yescharacteristic
161#2924—112no—
162#1473—114no—
163#1471—112no—
164#1466—112no—
165#1465—111no—
166#1460—112no—
167#1459—111no—
168C23×C11—21no—
169C23×C11—21no—
170C23×C11—21no—
171C23×C11—21no—
172C23×C11—22no—
173C23×C11—22no—
174C23×C11—22no—
175C23×C11—41no—
176C23×C11—41no—
177C23×C11—41no—
178C23×C11—41no—
179C23×C11—42no—
180C23×C11—42no—
181C23×C11C2×C22⋊C412yes—
182C23×C11#13112yes—
183C23×C11C23×C411yescharacteristic
184D4×C11—48no—
185D4×C11—42no—
186D4×C11—44no—
187D4×C11—42no—
188D4×C11—84no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—24no—
192C2×C4×C11—22no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—22no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—42no—
200C2×C4×C11—41no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—42no—
207C2×C4×C11—82no—
208C2×C4×C11—82no—
209C2×C4×C11—82no—
210C2×C4×C11—82no—
211C2×C4×C11C2×C22⋊C411yescharacteristic
212C2×C4×C11C2×C22⋊C414yes—
213C2×C4×C11C2×C22⋊C412yes—
214C2×C4×C11C2×C22⋊C412yes—
215C2×C4×C11C2×C22⋊C411yescharacteristic
216C2×C4×C11C22×D412yes—
217C11⋊C8—42no—
218C11⋊C8—42no—
219C11⋊C8—44no—
220#553—22no—
221#553—22no—
222#553—24no—
223C2×#126C2×D1112yes—
224C2×#125Dic1111yescharacteristic
225C2×#123Dic1112yes—
226C2×#121Dic1112yes—
227C2×#121Dic1111yescharacteristic
228C2×#121C2×D1111yescharacteristic
229C2×C4×D4Dic1111yescharacteristic
230C2×C4×D4C2×D1112yes—
231C2×C4×D4C2×D1111yescharacteristic
232C2×#117C2×D1111yescharacteristic
233C22×C4⋊C4Dic1111yescharacteristic
234#433—224no—
235#432—114no—
236#431—114no—
237#424—222no—
238#407—112no—
239C2×C22⋊C8—112no—
240#405—222no—
241#324—112no—
242#324—112no—
243#323—111no—
244#323—111no—
245#323—112no—
246#323—114no—
247#323—114no—
248C22×C11—21no—
249C22×C11—21no—
250C22×C11—22no—
251C22×C11—22no—
252C22×C11—22no—
253C22×C11—22no—
254C22×C11—42no—
255C22×C11—42no—
256C22×C11—41no—
257C22×C11—41no—
258C22×C11—42no—
259C22×C11—42no—
260C22×C11—42no—
261C22×C11—81no—
262C22×C11—81no—
263C22×C11—82no—
264C22×C11—82no—
265C22×C11C22×C22⋊C411yescharacteristic
266C22×C11C2×#13111yescharacteristic
267C22×C11#56811yescharacteristic
268C4×C11—24no—
269C4×C11—21no—
270C4×C11—22no—
271C4×C11—22no—
272C4×C11—22no—
273C4×C11—41no—
274C4×C11—41no—
275C4×C11—41no—
276C4×C11—42no—
277C4×C11#41012yes—
278C22×D4C2×Dic1111yescharacteristic
279C22×D4C2×Dic1112yes—
280C22×D4C2×Dic1111yescharacteristic
281C22×D4C2×Dic1112yes—
282C23×C4C2×Dic1111yescharacteristic
283C23×C4C2×Dic1112yes—
284C23×C4C2×Dic1112yes—
285C23×C4C22×D1111yescharacteristic
286C2×M16—222no—
287C22×C8—222no—
288#126—24no—
289#126—24no—
290#125—22no—
291#125—22no—
292#123—24no—
293#123—24no—
294#121—22no—
295#121—22no—
296#121—22no—
297#121—22no—
298#121—24no—
299#121—24no—
300C4×D4—22no—
301C4×D4—22no—
302C4×D4—22no—
303C4×D4—21no—
304C4×D4—21no—
305C4×D4—24no—
306C4×D4—24no—
307#117C22⋊D1112yes—
308#117C22⋊D1112yes—
309#117C22⋊D1114yes—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4C2×Dic1111yescharacteristic
314C2×C4⋊C4C2×Dic1112yes—
315C2×C4⋊C4C2×Dic1112yes—
316C2×C4⋊C4C2×Dic1112yes—
317C2×C4⋊C4C2×Dic1111yescharacteristic
318C2×C4⋊C4C2×Dic1111yescharacteristic
319C2×C4⋊C4C22×D1111yescharacteristic
320C2×C22⋊C4C2×Dic1112yes—
321C2×C22⋊C4C2×Dic1111yescharacteristic
322C2×C22⋊C4C2×Dic1112yes—
323C2×C22⋊C4C2×Dic1112yes—
324C2×C22⋊C4C22×D1111yescharacteristic
325C2×C22⋊C4C22×D1112yes—
326C2×C42C2×Dic1111yescharacteristic
327C2×C42C22×D1112yes—
328C4⋊C8—224no—
329C4⋊C8—224no—
330C22⋊C8—112no—
331C22⋊C8—112no—
332C22⋊C8—114no—
333C22⋊C8—222no—
334C22⋊C8—222no—
335#97—224no—
336C4×C8—224no—
337C2×C11—21no—
338C2×C11—21no—
339C2×C11—42no—
340C2×C11—42no—
341C2×C11—82no—
342C2×C11#288011yescharacteristic
343C2×C11C2×#41011yescharacteristic
344C2×C11#288811yescharacteristic
345C24C22×Dic1112yes—
346C24C22×Dic1111yescharacteristic
347C24C22×Dic1111yescharacteristic
348C2×D4—24no—
349C2×D4—22no—
350C2×D4—22no—
351C2×D4—24no—
352C2×D4—21no—
353C2×D4—24no—
354C2×D4—21no—
355C2×D4—42no—
356C2×D4—41no—
357C2×D4—42no—
358C2×D4—82no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—42no—
366C22×C4—42no—
367C22×C4—82no—
368C22×C4—82no—
369C22×C4C22×Dic1111yescharacteristic
370C22×C4C22×Dic1112yes—
371C22×C4C22×Dic1111yescharacteristic
372C22×C4C22×Dic1111yescharacteristic
373C22×C4C22×Dic1112yes—
374C22×C4C22×Dic1111yescharacteristic
375C22×C4C22×Dic1112yes—
376C22×C4C2×C22⋊D1112yes—
377C22×C4C2×C22⋊D1112yes—
378C22×C4C23×D1111yescharacteristic
379M16—444no—
380C2×C8—222no—
381C2×C8—224no—
382C2×C8—222no—
383C2×C8—444no—
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—24no—
389C4⋊C4—24no—
390C4⋊C4—22no—
391C4⋊C4C22⋊Dic1112yes—
392C4⋊C4C22⋊Dic1111yescharacteristic
393C4⋊C4C22⋊Dic1111yescharacteristic
394C4⋊C4C22⋊Dic1112yes—
395C4⋊C4C22⋊Dic1112yes—
396C22⋊C4—22no—
397C22⋊C4—22no—
398C22⋊C4—22no—
399C22⋊C4—24no—
400C22⋊C4—22no—
401C22⋊C4—24no—
402C22⋊C4C22⋊Dic1114yes—
403C22⋊C4C22⋊Dic1114yes—
404C42—21no—
405C42—21no—
406C42C2×C22⋊D1114yes—
407C42C2×C22⋊D1114yes—
408C11#1741511yescharacteristic, complemented, Sylow
409C23—21no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—22no—
414C23—22no—
415C23—22no—
416C23—41no—
417C23—41no—
418C23—41no—
419C23—41no—
420C23—42no—
421C23—42no—
422C23#6700112yes—
423C23C2×C22⋊Dic1112yes—
424C23C23×Dic1111yescharacteristic
425D4—48no—
426D4—42no—
427D4—44no—
428D4—42no—
429D4—84no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—24no—
433C2×C4—22no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—22no—
440C2×C4—42no—
441C2×C4—41no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—42no—
448C2×C4—82no—
449C2×C4—82no—
450C2×C4—82no—
451C2×C4—82no—
452C2×C4C2×C22⋊Dic1111yescharacteristic
453C2×C4C2×C22⋊Dic1114yes—
454C2×C4C2×C22⋊Dic1112yes—
455C2×C4C2×C22⋊Dic1112yes—
456C2×C4C2×C22⋊Dic1111yescharacteristic
457C2×C4C22×C22⋊D1112yes—
458C8—442no—
459C8—442no—
460C8—444no—
461C22—21no—
462C22—21no—
463C22—22no—
464C22—22no—
465C22—22no—
466C22—22no—
467C22—42no—
468C22—42no—
469C22—41no—
470C22—41no—
471C22—42no—
472C22—42no—
473C22—42no—
474C22—81no—
475C22—81no—
476C22—82no—
477C22—82no—
478C22C2×#6700111yescharacteristic
479C22#1062335011yescharacteristic
480C22C22×C22⋊Dic1111yescharacteristic
481C4—24no—
482C4—22no—
483C4—21no—
484C4—22no—
485C4—22no—
486C4—41no—
487C4—41no—
488C4—41no—
489C4—42no—
490C4#1062285312yes—
491C2—21no—
492C2—21no—
493C2—42no—
494C2—42no—
495C2—82no—
496C2#1307706511yescharacteristic
497C2C2×#1062285311yescharacteristic
498C2#1307709511yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#553C2
socleC22×C11C22×C22⋊C4
cosocleC22×C4×C11C24
hypercenterC2×#553D11
hypocenterC11#17415
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#117 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. #13077274C2semidirect
2. #13066985C2semidirect
3. #13066976C2semidirect
4. #13066957C2semidirect
5. #13066954C2semidirect
6. #13066937C2semidirect
7. #13066934C2semidirect
408. C11#17415semidirect

Maximal subgroups

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

subgroupindex
#130772742
#130669852
#130669762
#130669572
#130669542
#130669372
#130669342
C2×C11×#5532
#1741511