Finite Group Databasebeta

← #14684174

Subgroups — #14684174

Order 2816.

1246 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
1C2×#10622592C211yesmaximal, characteristic
2#13066886C212yesmaximal
3#13066871C212yesmaximal
4#13066851C212yesmaximal
5#13066848C211yesmaximal, characteristic
6#13066847C212yesmaximal
7Dic11⋊#95C212yesmaximal
8#13066842C212yesmaximal
9C11×#1445C211yesmaximal, characteristic
10C23×Dic22C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×Dic11⋊C4C2212yes—
13C22×Dic11⋊C4C2212yes—
14C22×C4×Dic11C2212yes—
15C22×C4×Dic11C2211yescharacteristic
16C2×C11×#95C2211yescharacteristic
17C2×C11×#95C2212yes—
18C2×C11×#95C2212yes—
19C2×C11×#95C2211yescharacteristic
20C2×C11⋊#95C2212yes—
21C2×C11⋊#95C2212yes—
22C2×C11⋊#95C2212yes—
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2211yescharacteristic
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2212yes—
31#10622592C418yescomplemented
32C23×C4×C11C2312yes—
33C23×C4×C11C2311yescharacteristic
34C23×C4×C11C2311yescharacteristic
35C23×C4×C11C2311yescharacteristic
36C23×C4×C11C2312yes—
37C23×Dic11C2312yes—
38C23×Dic11C2312yes—
39C23×Dic11C2312yes—
40C23×Dic11C2312yes—
41C22×Dic22—41no—
42C22×Dic22—41no—
43C22×Dic22—42no—
44C22×Dic22—42no—
45C22×Dic22C2×C414yes—
46C2×C11×C4⋊C4—41no—
47C2×C11×C4⋊C4—41no—
48C2×C11×C4⋊C4C2×C414yes—
49C2×Dic11⋊C4—24no—
50C2×Dic11⋊C4—24no—
51C2×Dic11⋊C4—42no—
52C2×Dic11⋊C4—42no—
53C2×Dic11⋊C4—42no—
54C2×Dic11⋊C4C2×C418yes—
55C2×C4×Dic11—24no—
56C2×C4×Dic11—24no—
57C2×C4×Dic11—42no—
58C2×C4×Dic11—42no—
59C2×C4×Dic11—41no—
60C11×#95—41no—
61C11×#95—42no—
62C11×#95—42no—
63C11×#95—41no—
64C11⋊#95—24no—
65C11⋊#95—24no—
66C11⋊#95—41no—
67C11⋊#95—42no—
68C11⋊#95—42no—
69C11⋊#95—42no—
70C11⋊#95—42no—
71C11⋊#95—42no—
72C11⋊#95C2×C418yes—
73C11⋊#95C2×C414yes—
74C11⋊#95Q818yescomplemented
75#14599—111nomaximal, Sylow
76C24×C11C2411yescharacteristic
77C22×C4×C11—22no—
78C22×C4×C11—22no—
79C22×C4×C11—22no—
80C22×C4×C11—22no—
81C22×C4×C11—22no—
82C22×C4×C11—21no—
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11—22no—
86C22×C4×C11—21no—
87C22×C4×C11—21no—
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11C22×C412yes—
103C22×C4×C11C22×C412yes—
104C22×C4×C11C22×C412yes—
105C22×C4×C11C2×Q814yes—
106C22×Dic11—22no—
107C22×Dic11—22no—
108C22×Dic11—22no—
109C22×Dic11—22no—
110C22×Dic11—22no—
111C22×Dic11—22no—
112C22×Dic11—22no—
113C22×Dic11—22no—
114C22×Dic11—22no—
115C22×Dic11—22no—
116C22×Dic11—22no—
117C22×Dic11—22no—
118C22×Dic11—22no—
119C22×Dic11—22no—
120C22×Dic11—22no—
121C22×Dic11—22no—
122C22×Dic11—22no—
123C22×Dic11—22no—
124C22×Dic11—22no—
125C22×Dic11—22no—
126C22×Dic11—22no—
127C22×Dic11—22no—
128C22×Dic11C22×C414yes—
129C22×Dic11C22×C414yes—
130C22×Dic11C2×Q814yes—
131C22×Dic11C2×Q814yes—
132C22×Dic11#4114yes—
133C22×Dic11#4114yes—
134C2×Dic22—44no—
135C2×Dic22—48no—
136C2×Dic22—44no—
137C2×Dic22—48no—
138C2×Dic22—44no—
139C11×C4⋊C4—44no—
140Dic11⋊C4—48no—
141Dic11⋊C4—48no—
142C4×Dic11—48no—
143C4×Dic11—44no—
144C2×#395—111no—
145#1446—112no—
146#1445D1111yescharacteristic
147#1442—112no—
148#1436—112no—
149#1436—112no—
150#1436—111no—
151C4⋊#95—112no—
152#1434—112no—
153C23×C11C23×C411yescharacteristic
154C23×C11C22×Q812yes—
155C23×C11C2×#4112yes—
156C23×C11C2×#4112yes—
157C23×C11H(5,𝔽2)11yescharacteristic
158C23×C11H(5,𝔽2)11yescharacteristic
159C23×C11H(5,𝔽2)12yes—
160C23×C11H(5,𝔽2)12yes—
161C23×C112−1+412yes—
162C2×C4×C11—22no—
163C2×C4×C11—24no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—24no—
168C2×C4×C11—22no—
169C2×C4×C11—24no—
170C2×C4×C11—24no—
171C2×C4×C11—24no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—41no—
178C2×C4×C11—42no—
179C2×C4×C11—41no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×Dic11—24no—
192C2×Dic11—24no—
193C2×Dic11—24no—
194C2×Dic11—24no—
195C2×Dic11—24no—
196C2×Dic11—24no—
197C2×Dic11—24no—
198C2×Dic11—24no—
199C2×Dic11—24no—
200C2×Dic11—24no—
201C2×Dic11—24no—
202C2×Dic11—24no—
203C2×Dic11—24no—
204C2×Dic11—24no—
205C2×Dic11—24no—
206C2×Dic11—42no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211C2×Dic11—42no—
212C2×Dic11—42no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215C2×Dic11—42no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218C2×Dic11C4×Q818yes—
219Dic22—416no—
220C23×Q8—111no—
221C22×C4⋊C4—112no—
222C22×C4⋊C4—112no—
223C22×C4⋊C4C2×D1111yescharacteristic
224C22×C42—112no—
225C22×C42—111no—
226#395—118no—
227C2×#95—112no—
228C2×#95—111no—
229C2×#95—112no—
230C2×#95—112no—
231C2×#95—112no—
232C2×#95—112no—
233C2×#95—112no—
234C2×#95—111no—
235C2×#95—112no—
236C2×#95—112no—
237C2×#95—112no—
238C2×#95C2×D1111yescharacteristic
239C2×#95C2×D1112yes—
240C2×#95C2×D1112yes—
241C2×#95C2×D1111yescharacteristic
242C22×C11C2×C4×Q812yes—
243C22×C11C4×#4111yescharacteristic
244C22×C11#51811yescharacteristic
245C22×C11#51812yes—
246C22×C11#51911yescharacteristic
247C22×C11#53912yes—
248C22×C11#54212yes—
249C22×C11#54212yes—
250C22×C11#54212yes—
251C22×C11#54412yes—
252C22×C11#54412yes—
253C22×C11#55112yes—
254C22×C11#55112yes—
255C22×C11#55412yes—
256C22×C11#55412yes—
257C22×C11#55412yes—
258C22×C11#55511yescharacteristic
259C22×C11Q8211yescharacteristic
260C22×C11#56011yescharacteristic
261C22×C11#56012yes—
262C22×C11H(3,𝔽4)11yescharacteristic
263C4×C11—42no—
264C4×C11—42no—
265C4×C11—42no—
266C4×C11—44no—
267C4×C11—82no—
268Dic11—28no—
269Dic11—44no—
270Dic11—44no—
271Dic11—44no—
272C22×Q8—114no—
273C22×Q8—442no—
274C22×Q8—441no—
275C22×Q8—441no—
276C22×Q8—442no—
277C23×C4—112no—
278C23×C4—112no—
279C23×C4—112no—
280C23×C4—112no—
281C23×C4C22×D1112yes—
282C23×C4C22×D1111yescharacteristic
283C23×C4C22×D1111yescharacteristic
284C23×C4C22×D1111yescharacteristic
285C23×C4C22×D1112yes—
286C2×C4⋊C4—41no—
287C2×C4⋊C4—41no—
288C2×C4⋊C4—118no—
289C2×C4⋊C4—224no—
290C2×C4⋊C4—224no—
291C2×C4⋊C4—442no—
292C2×C4⋊C4—442no—
293C2×C4⋊C4—442no—
294C2×C4⋊C4C4×D1114yes—
295C2×C42—224no—
296C2×C42—224no—
297C2×C42—442no—
298C2×C42—441no—
299C2×C42—442no—
300#95—41no—
301#95—42no—
302#95—42no—
303#95—41no—
304#95—114no—
305#95—118no—
306#95—118no—
307#95—224no—
308#95—224no—
309#95—442no—
310#95—442no—
311#95—441no—
312#95—442no—
313#95—442no—
314#95—442no—
315C2×C11#233112yes—
316C2×C11#233211yescharacteristic
317C2×C11#236812yes—
318C2×C11#236911yescharacteristic
319C2×C11#237511yescharacteristic
320C2×C11#273712yes—
321C2×C11#274212yes—
322C2×C11#276312yes—
323C2×C11#279212yes—
324C24C23×D1111yescharacteristic
325C2×Q8—444no—
326C2×Q8—448no—
327C2×Q8—444no—
328C2×Q8—448no—
329C2×Q8—444no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—114no—
356C22×C4—114no—
357C22×C4—114no—
358C22×C4—114no—
359C22×C4—114no—
360C22×C4—114no—
361C22×C4—222no—
362C22×C4—222no—
363C22×C4—222no—
364C22×C4—222no—
365C22×C4—222no—
366C22×C4—222no—
367C22×C4—222no—
368C22×C4—222no—
369C22×C4—222no—
370C22×C4—222no—
371C22×C4—222no—
372C22×C4—222no—
373C22×C4—222no—
374C22×C4—222no—
375C22×C4—222no—
376C22×C4—222no—
377C22×C4—222no—
378C22×C4—222no—
379C22×C4—222no—
380C22×C4—222no—
381C22×C4—222no—
382C22×C4—222no—
383C22×C4C2×C4×D1112yes—
384C22×C4C2×C4×D1112yes—
385C22×C4C2×C4×D1112yes—
386C22×C4Q8×D1114yes—
387C4⋊C4—44no—
388C4⋊C4—448no—
389C4⋊C4—448no—
390C42—448no—
391C42—444no—
392C11#1459911yescharacteristic, complemented, Sylow
393C23C22×C4×D1111yescharacteristic
394C23#6703711yescharacteristic
395C23#6703712yes—
396C23#6703711yescharacteristic
397C23C2×Q8×D1112yes—
398C23#41×D1112yes—
399C23#41×D1112yes—
400C23#6704212yes—
401C23#6704312yes—
402Q8—4416no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—24no—
409C2×C4—24no—
410C2×C4—24no—
411C2×C4—24no—
412C2×C4—24no—
413C2×C4—42no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—118no—
433C2×C4—224no—
434C2×C4—224no—
435C2×C4—224no—
436C2×C4—224no—
437C2×C4—224no—
438C2×C4—224no—
439C2×C4—224no—
440C2×C4—224no—
441C2×C4—224no—
442C2×C4—224no—
443C2×C4—224no—
444C2×C4—224no—
445C2×C4—224no—
446C2×C4—224no—
447C2×C4—224no—
448C2×C4—442no—
449C2×C4—442no—
450C2×C4—442no—
451C2×C4—442no—
452C2×C4—442no—
453C2×C4—442no—
454C2×C4—442no—
455C2×C4—442no—
456C2×C4—442no—
457C2×C4—442no—
458C2×C4—442no—
459C2×C4—442no—
460C22#1062301711yescharacteristic
461C22#1062304711yescharacteristic
462C22#1062305311yescharacteristic
463C22#1062307612yes—
464C22C4×Q8×D1112yes—
465C22#1062315112yes—
466C22#1062315412yes—
467C22#1062316712yes—
468C22#1062316712yes—
469C22#1062319012yes—
470C22#1062319112yes—
471C22#1062319312yes—
472C22#1062319312yes—
473C22#1062320111yescharacteristic
474C22#1062321411yescharacteristic
475C22#1062322012yes—
476C22#1062322112yes—
477C22#1062323612yes—
478C22#1062324112yes—
479C22#1062325111yescharacteristic
480C22#1062325311yescharacteristic
481C4—42no—
482C4—44no—
483C4—42no—
484C4—42no—
485C4—82no—
486C4—228no—
487C4—444no—
488C4—444no—
489C4—444no—
490C2#1307136112yes—
491C2#1307136911yescharacteristic
492C2#1307169312yes—
493C2#1307170411yescharacteristic
494C2#1307175311yescharacteristic
495C2#1307567612yes—
496C2#1307574612yes—
497C2#1307603112yes—
498C2#1307641412yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1445C2
socle, prime radical, cosocleC24×C11C24
hypercenter#1445D11
hypocenterC11#14599
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1445

Complements

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

NH ≅ G/Ntype
31. #10622592C4semidirect
74. C11⋊#95Q8semidirect
392. C11#14599semidirect

Maximal subgroups

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

subgroupindex
C2×#106225922
#130668862
#130668712
#130668512
#130668482
#130668472
Dic11⋊#952
#130668422
C11×#14452
#1459911