Finite Group Databasebeta

← #14967710

Subgroups — #14967710

Order 2816.

1810 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076947C212yesmaximal, complemented
2#13076155C214yesmaximal, complemented
3#13076092C214yesmaximal, complemented
4#13075889C214yesmaximal, complemented
5#13075301C214yesmaximal, complemented
6#13074718C211yesmaximal, characteristic
7#13074586C211yesmaximal, characteristic, complemented
8#13072351C214yesmaximal, complemented
9#13072167C214yesmaximal, complemented
10#13071319C212yesmaximal, complemented
11C2×C11×#382C211yesmaximal, characteristic, complemented
12C22×C11×C4⋊C4C2212yes—
13C22×C42×C11C2211yescharacteristic
14C2×#66983C2212yes—
15C2×#66983C2214yes—
16C2×#66982C2214yes—
17C2×C4×C22⋊D11C2214yes—
18C2×#66947C2214yes—
19C11×#382C2214yes—
20C11×#382C2214yes—
21C2×C11×#95C2211yescharacteristic
22C2×C11×#95C2212yes—
23C2×C11×#95C2211yescharacteristic
24#10622826C2214yes—
25#10622826C2214yes—
26#10622825C2212yes—
27#10622823C2214yes—
28#10622606C2214yes—
29#10622605C2214yes—
30#10622604C2214yes—
31#10622603C2214yes—
32#10622602C2214yes—
33#10622597C2214yes—
34#10622594C2214yes—
35#10622553C2214yes—
36#10622553C2214yes—
37#10622552C2212yes—
38#10622552C2212yes—
39#10622541C2212yes—
40#10622541C2212yes—
41#10622290C2214yes—
42#10622289C2214yes—
43#10622288C2214yes—
44#10622285C2214yes—
45#10622284C2214yes—
46#10622283C2214yes—
47#10622282C2214yes—
48#10622281C2214yes—
49#10622280C2214yes—
50#10622278C2214yes—
51#10622278C2214yes—
52#10622273C2214yes—
53#10622270C2214yes—
54#10622270C2214yes—
55#10622266C2214yes—
56#10622260C2214yes—
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2312yes—
60C23×C4×C11C2312yes—
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11C2314yes—
63C22×D44C2312yes—
64C22×D44C2314yes—
65C22×C4×D11C2314yes—
66C2×C11×C4⋊C4—44no—
67C2×C11×C4⋊C4C2314yes—
68C2×C11×C4⋊C4C2314yes—
69C2×C42×C11—24no—
70C2×C42×C11C2312yes—
71C2×C42×C11C2312yes—
72C2×C22⋊Dic11C2314yes—
73#66983—28no—
74#66983—48no—
75#66982—48no—
76C4×C22⋊D11—48no—
77C2×(C2×D11)⋊C4C2314yes—
78C2×(C2×D11)⋊C4C2314yes—
79C2×(C2×D11)⋊C4C2314yes—
80C2×(C2×D11)⋊C4C2314yes—
81C2×(C2×D11)⋊C4C2314yes—
82C2×(C2×D11)⋊C4C2314yes—
83C2×(C2×D11)⋊C4C2314yes—
84C2×(C2×D11)⋊C4C2314yes—
85C2×(C2×D11)⋊C4C2314yes—
86C2×(C2×D11)⋊C4C2314yes—
87C2×C4⋊Dic11C2312yes—
88C2×C4⋊Dic11C2314yes—
89C2×C4⋊Dic11C2312yes—
90C2×C4⋊Dic11C2312yes—
91C2×Dic11⋊C4C2314yes—
92C2×Dic11⋊C4C2314yes—
93C2×Dic11⋊C4C2314yes—
94C2×Dic11⋊C4C2314yes—
95C2×Dic11⋊C4C2314yes—
96C2×C4×Dic11C2314yes—
97#66947—48no—
98C11×#95C2314yes—
99C11×#95C2314yes—
100C11×#95C2314yes—
101C11×#95C2314yes—
102C11⋊#95C2314yes—
103C11⋊#95C2314yes—
104C11⋊#95C2314yes—
105C11⋊#95C2314yes—
106C11⋊#95C2314yes—
107C11⋊#95C2314yes—
108C11⋊#95C2314yes—
109#36976—111nomaximal, Sylow
110C24×C11C2411yescharacteristic
111C23×D11C2414yes—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—24no—
117C22×C4×C11—24no—
118C22×C4×C11—24no—
119C22×C4×C11—42no—
120C22×C4×C11—42no—
121C22×C4×C11—42no—
122C22×C4×C11—42no—
123C22×C4×C11—42no—
124C22×C4×C11#4114yes—
125C22×C4×C11C2414yes—
126C22×C4×C11C2414yes—
127C22×C4×C11C2412yes—
128C22×C4×C11C2412yes—
129C22×C4×C11C2411yescharacteristic
130C22×C4×C11C2411yescharacteristic
131C2×C22⋊D11—28no—
132C2×C22⋊D11—28no—
133C2×C22⋊D11—28no—
134C22×Dic11C2414yes—
135C22×Dic11C2414yes—
136C22×Dic11C2414yes—
137C2×D44—24no—
138C2×D44—44no—
139C2×D44—44no—
140C2×D44—42no—
141C2×D44—42no—
142C2×D44—44no—
143C2×C4×D11—44no—
144C2×C4×D11—44no—
145C2×C4×D11—44no—
146C11×C4⋊C4—28no—
147C11×C4⋊C4—44no—
148C42×C11—24no—
149C42×C11—24no—
150C22⋊Dic11—28no—
151(C2×D11)⋊C4—28no—
152(C2×D11)⋊C4—28no—
153(C2×D11)⋊C4—28no—
154(C2×D11)⋊C4—44no—
155(C2×D11)⋊C4—44no—
156(C2×D11)⋊C4—44no—
157(C2×D11)⋊C4—44no—
158(C2×D11)⋊C4—44no—
159(C2×D11)⋊C4—44no—
160(C2×D11)⋊C4—44no—
161C4⋊Dic11—24no—
162C4⋊Dic11—42no—
163C4⋊Dic11—42no—
164C4⋊Dic11—44no—
165Dic11⋊C4—44no—
166Dic11⋊C4—44no—
167Dic11⋊C4—44no—
168Dic11⋊C4—44no—
169Dic11⋊C4—44no—
170C4×Dic11—44no—
171#2854—112no—
172#2773—114no—
173#2768—114no—
174#2753—114no—
175#2706—114no—
176#2656—111no—
177#2646—111no—
178#2443—114no—
179#2425—114no—
180#2325—112no—
181C2×#382D1111yescharacteristic, complemented
182C23×C11—21no—
183C23×C11—21no—
184C23×C11—22no—
185C23×C11C2×#4112yes—
186C23×C11H(5,𝔽2)14yes—
187C23×C11C2511yescharacteristic
188C22×D11—24no—
189C22×D11—24no—
190C22×D11—24no—
191C22×D11—24no—
192C22×D11—24no—
193C22×D11—24no—
194C22×D11—24no—
195C2×C4×C11—28no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—24no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—24no—
207C2×C4×C11—24no—
208C2×C4×C11—24no—
209C2×C4×C11—24no—
210C2×C4×C11—24no—
211C2×C4×C11—44no—
212C2×C4×C11—44no—
213C2×C4×C11—84no—
214C2×C4×C11—84no—
215C2×C4×C11C2×#4114yes—
216C2×C4×C11H(5,𝔽2)12yes—
217C2×C4×C112−1+412yes—
218C22⋊D11—416no—
219C2×Dic11—24no—
220C2×Dic11—24no—
221C2×Dic11—24no—
222C2×Dic11—24no—
223C2×Dic11—24no—
224C2×Dic11—24no—
225C2×Dic11—24no—
226C2×Dic11—24no—
227C2×Dic11—24no—
228D44—84no—
229D44—88no—
230C4×D11—88no—
231C2×#123—114no—
232C2×#123—114no—
233C2×#121—112no—
234C2×#121—114no—
235C2×C4×D4—114no—
236C22×C4⋊C4C2×D1112yes—
237C22×C42C2×D1111yescharacteristic
238#400—114no—
239#399—114no—
240#399—114no—
241#398—114no—
242#398—114no—
243#398—114no—
244#397—114no—
245#397—114no—
246#396—114no—
247#394—114no—
248#394—114no—
249#392—114no—
250#390—112no—
251#390—112no—
252#389—112no—
253#389—112no—
254#389—114no—
255#388—114no—
256#388—114no—
257#388—114no—
258#388—114no—
259#388—114no—
260#387—114no—
261#387—114no—
262#386—114no—
263#386—114no—
264#386—114no—
265#386—114no—
266#385—114no—
267#385—114no—
268#385—114no—
269#382C2×D1114yes—
270#382C2×D1114yes—
271#380—112no—
272#380—114no—
273C2×#95C2×D1111yescharacteristic
274C2×#95C2×D1111yescharacteristic
275C2×#95C2×D1112yes—
276C22×C11—22no—
277C22×C11—22no—
278C22×C11—24no—
279C22×C11—24no—
280C22×C11#54014yes—
281C22×C11C22×#4111yescharacteristic
282C22×C11C2×H(5,𝔽2)11yescharacteristic
283C22×C11C2×H(5,𝔽2)12yes—
284C22×C11C2×2−1+411yescharacteristic
285C22×C11#58512yes—
286C2×D11—44no—
287C2×D11—44no—
288C2×D11—44no—
289C2×D11—44no—
290C2×D11—44no—
291C2×D11—44no—
292C2×D11—44no—
293C4×C11—24no—
294C4×C11—22no—
295C4×C11—22no—
296C4×C11—42no—
297C4×C11—44no—
298C4×C11—44no—
299Dic11—44no—
300Dic11—44no—
301Dic11—44no—
302C22×D4—114no—
303C22×D4—112no—
304C22×D4—114no—
305C23×C4—114no—
306C23×C4C22×D1111yescharacteristic
307C23×C4C22×D1111yescharacteristic
308C23×C4C22×D1112yes—
309C23×C4C22×D1112yes—
310C23×C4C22×D1111yescharacteristic
311#123—448no—
312#123—448no—
313#121—228no—
314#121—448no—
315C4×D4—448no—
316C2×C4⋊C4—44no—
317C2×C4⋊C4—112no—
318C2×C4⋊C4—114no—
319C2×C4⋊C4—114no—
320C2×C4⋊C4—114no—
321C2×C4⋊C4—114no—
322C2×C4⋊C4—114no—
323C2×C4⋊C4—112no—
324C2×C4⋊C4—112no—
325C2×C4⋊C4—114no—
326C2×C4⋊C4C22×D1114yes—
327C2×C4⋊C4C22×D1114yes—
328C2×C22⋊C4—114no—
329C2×C22⋊C4—114no—
330C2×C22⋊C4—114no—
331C2×C22⋊C4—114no—
332C2×C22⋊C4—114no—
333C2×C22⋊C4—114no—
334C2×C22⋊C4—114no—
335C2×C22⋊C4—114no—
336C2×C22⋊C4—114no—
337C2×C22⋊C4—114no—
338C2×C22⋊C4—114no—
339C2×C42—24no—
340C2×C42—114no—
341C2×C42C22×D1112yes—
342C2×C42C22×D1112yes—
343#95—114no—
344#95—114no—
345#95—114no—
346#95—114no—
347#95—114no—
348#95—114no—
349#95—114no—
350#95C22×D1114yes—
351#95C22×D1114yes—
352#95C22×D1114yes—
353#95C22×D1114yes—
354C2×C11—24no—
355C2×C11C2×#54011yescharacteristic
356C2×C11#349111yescharacteristic
357C2×C11#349211yescharacteristic
358C2×C11#355812yes—
359C2×C11#355912yes—
360D11—84no—
361C24—114no—
362C24C23×D1111yescharacteristic
363C2×D4—228no—
364C2×D4—228no—
365C2×D4—228no—
366C2×D4—224no—
367C2×D4—444no—
368C2×D4—444no—
369C2×D4—442no—
370C2×D4—442no—
371C2×D4—444no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—24no—
377C22×C4—24no—
378C22×C4—24no—
379C22×C4—42no—
380C22×C4—42no—
381C22×C4—42no—
382C22×C4—42no—
383C22×C4—42no—
384C22×C4—114no—
385C22×C4—114no—
386C22×C4—114no—
387C22×C4—444no—
388C22×C4—444no—
389C22×C4—444no—
390C22×C4#433914yes—
391C22×C4C23×D1114yes—
392C22×C4C23×D1114yes—
393C22×C4C23×D1112yes—
394C22×C4C23×D1112yes—
395C22×C4C23×D1111yescharacteristic
396C22×C4C23×D1111yescharacteristic
397C4⋊C4—28no—
398C4⋊C4—44no—
399C4⋊C4—224no—
400C4⋊C4—444no—
401C4⋊C4—444no—
402C4⋊C4—444no—
403C4⋊C4—444no—
404C4⋊C4—444no—
405C4⋊C4—444no—
406C4⋊C4—442no—
407C4⋊C4—442no—
408C22⋊C4—228no—
409C22⋊C4—228no—
410C22⋊C4—228no—
411C22⋊C4—228no—
412C22⋊C4—444no—
413C22⋊C4—444no—
414C22⋊C4—444no—
415C22⋊C4—444no—
416C22⋊C4—444no—
417C22⋊C4—444no—
418C22⋊C4—444no—
419C42—24no—
420C42—24no—
421C42—444no—
422C11#3697611yescharacteristic, complemented, Sylow
423C23—21no—
424C23—21no—
425C23—22no—
426C23—224no—
427C23—224no—
428C23—224no—
429C23—224no—
430C23—224no—
431C23—224no—
432C23—224no—
433C23C2×#433912yes—
434C23#6704214yes—
435C23C24×D1111yescharacteristic
436D4—4416no—
437D4—884no—
438D4—888no—
439C2×C4—28no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—24no—
448C2×C4—24no—
449C2×C4—24no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—24no—
453C2×C4—24no—
454C2×C4—24no—
455C2×C4—44no—
456C2×C4—44no—
457C2×C4—84no—
458C2×C4—84no—
459C2×C4—224no—
460C2×C4—224no—
461C2×C4—224no—
462C2×C4—224no—
463C2×C4—224no—
464C2×C4—224no—
465C2×C4—224no—
466C2×C4—224no—
467C2×C4—224no—
468C2×C4—888no—
469C2×C4C2×#433914yes—
470C2×C4#6703712yes—
471C2×C4#6704012yes—
472C22—24no—
473C22—22no—
474C22—22no—
475C22—24no—
476C22—444no—
477C22—444no—
478C22—444no—
479C22—444no—
480C22—444no—
481C22—444no—
482C22—444no—
483C22#1062306614yes—
484C22C22×#433911yescharacteristic
485C22C2×#6703711yescharacteristic
486C22C2×#6704011yescharacteristic
487C22C2×#6704212yes—
488C22#1062345312yes—
489C4—24no—
490C4—22no—
491C4—22no—
492C4—42no—
493C4—44no—
494C4—44no—
495C4—444no—
496C4—444no—
497C4—444no—
498C2—24no—
499C2—884no—
500C2C2×#1062306611yescharacteristic
501C2#1308231411yescharacteristic
502C2#1308232511yescharacteristic
503C2#1308313512yes—
504C2#1308315012yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC2×C11×#382C2
prime radical#13074718C2
hypercenterC2×#382D11
hypocenterC11#36976
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
1. #13076947C2semidirect
2. #13076155C2semidirect
3. #13076092C2semidirect
4. #13075889C2semidirect
5. #13075301C2semidirect
7. #13074586C2semidirect
8. #13072351C2semidirect
9. #13072167C2semidirect
10. #13071319C2semidirect
11. C2×C11×#382C2semidirect
181. C2×#382D11semidirect
422. C11#36976semidirect

Maximal subgroups

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

subgroupindex
#130769472
#130761552
#130760922
#130758892
#130753012
#130747182
#130745862
#130723512
#130721672
#130713192
C2×C11×#3822
#3697611