Finite Group Databasebeta

← #14680175

Subgroups — #14680175

Order 2816.

1382 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622542C211yesmaximal, characteristic
2C2×#10622542C211yesmaximal, characteristic
3C2×#10622542C211yesmaximal, characteristic
4C2×#10622541C211yesmaximal, characteristic
5#13066876C214yesmaximal
6#13066871C214yesmaximal
7#13066846C211yesmaximal, characteristic
8#13066846C211yesmaximal, characteristic
9C2×C11×#376C211yesmaximal, characteristic
10C23×Dic22C2211yescharacteristic
11C22×C42×C11C2211yescharacteristic
12C22×C42×C11C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C22×C4⋊Dic11C2211yescharacteristic
15C22×C4⋊Dic11C2211yescharacteristic
16C22×C4⋊Dic11C2211yescharacteristic
17C22×Dic11⋊C4C2212yes—
18C11×#376—24no—
19C2×C11×#95C2212yes—
20C2×C11×#95C2212yes—
21C2×C11⋊#95C2212yes—
22C2×C11⋊#95C2214yes—
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2214yes—
26C2×C11⋊#95C2214yes—
27C2×C11⋊#95C2214yes—
28#10622542—24no—
29#10622542—24no—
30#10622542C418yescomplemented
31#10622541—24no—
32C23×C4×C11C2312yes—
33C23×C4×C11C2311yescharacteristic
34C23×C4×C11C2311yescharacteristic
35C23×C4×C11C2312yes—
36C23×C4×C11C2311yescharacteristic
37C23×Dic11C2312yes—
38C23×Dic11C2312yes—
39C23×Dic11C2312yes—
40C23×Dic11C2312yes—
41C22×Dic22—22no—
42C22×Dic22—22no—
43C22×Dic22—22no—
44C22×Dic22—22no—
45C22×Dic22—22no—
46C22×Dic22—22no—
47C22×Dic22C2×C414yes—
48C2×C42×C11—22no—
49C2×C42×C11—22no—
50C2×C42×C11—22no—
51C2×C42×C11—22no—
52C2×C42×C11—22no—
53C2×C42×C11—22no—
54C2×C42×C11C2×C414yes—
55C2×C42×C11D414yes—
56C2×C42×C11D414yes—
57C2×C4⋊Dic11—22no—
58C2×C4⋊Dic11—22no—
59C2×C4⋊Dic11—22no—
60C2×C4⋊Dic11—22no—
61C2×C4⋊Dic11—22no—
62C2×C4⋊Dic11—22no—
63C2×C4⋊Dic11—22no—
64C2×C4⋊Dic11—22no—
65C2×C4⋊Dic11C2×C414yes—
66C2×Dic11⋊C4—24no—
67C2×Dic11⋊C4—44no—
68C11×#95—24no—
69C11×#95—24no—
70C11⋊#95—24no—
71C11⋊#95—24no—
72C11⋊#95—24no—
73C11⋊#95—28no—
74C11⋊#95—44no—
75C11⋊#95—44no—
76C11⋊#95C2×C4116yes—
77#14261—111nomaximal, Sylow
78C24×C11C2411yescharacteristic
79C22×C4×C11—22no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—22no—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—22no—
86C22×C4×C11—22no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
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×C11C22×C414yes—
100C22×C4×C11C22×C412yes—
101C22×C4×C11C2×D412yes—
102C22×C4×C11C2×D412yes—
103C22×C4×C11C2×D414yes—
104C22×C4×C11C2×D412yes—
105C22×C4×C11C2×D412yes—
106C22×C4×C11#4112yes—
107C22×C4×C11#4112yes—
108C22×C4×C11#4112yes—
109C22×C4×C11#4112yes—
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—24no—
125C22×Dic11—24no—
126C22×Dic11—24no—
127C22×Dic11—24no—
128C22×Dic11—24no—
129C22×Dic11—24no—
130C22×Dic11C22×C414yes—
131C22×Dic11C22×C414yes—
132C2×Dic22—28no—
133C2×Dic22—28no—
134C2×Dic22—28no—
135C2×Dic22—44no—
136C2×Dic22—44no—
137C2×Dic22—44no—
138C2×Dic22—44no—
139C42×C11—28no—
140C42×C11—28no—
141C42×C11—28no—
142C4⋊Dic11—28no—
143C4⋊Dic11—44no—
144C4⋊Dic11—44no—
145Dic11⋊C4—48no—
146C2×#391—111no—
147C2×#391—111no—
148C2×#391—111no—
149C2×#389—111no—
150C2×#376D1111yescharacteristic
151#1443—114no—
152#1442—114no—
153C4⋊#95—111no—
154C4⋊#95—111no—
155C23×C11C23×C411yescharacteristic
156C23×C11C22×D411yescharacteristic
157C23×C11C22×D411yescharacteristic
158C23×C11C2×#4111yescharacteristic
159C23×C11C2×#4111yescharacteristic
160C23×C11C2×#4111yescharacteristic
161C23×C11C2×#4111yescharacteristic
162C23×C11H(5,𝔽2)12yes—
163C23×C112−1+412yes—
164C23×C112−1+412yes—
165C23×C112−1+412yes—
166C2×C4×C11—24no—
167C2×C4×C11—24no—
168C2×C4×C11—24no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—24no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—24no—
177C2×C4×C11—24no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
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#11714yes—
191C2×C4×C11C4×D414yes—
192C2×C4×C11C4×D414yes—
193C2×C4×C11#12114yes—
194C2×C4×C11#12314yes—
195C2×C4×C11#12414yes—
196C2×C4×C11#12614yes—
197C2×Dic11—24no—
198C2×Dic11—24no—
199C2×Dic11—24no—
200C2×Dic11—24no—
201C2×Dic11—28no—
202C2×Dic11—42no—
203C2×Dic11—42no—
204C2×Dic11—42no—
205C2×Dic11—42no—
206C2×Dic11—42no—
207C2×Dic11—42no—
208C2×Dic11—44no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211C2×Dic11—42no—
212C2×Dic11—42no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215C2×Dic11—44no—
216C2×Dic11—44no—
217C2×Dic11—44no—
218C2×Dic11—44no—
219Dic22—416no—
220C23×Q8—111no—
221C22×C4⋊C4—111no—
222C22×C4⋊C4—111no—
223C22×C4⋊C4—111no—
224C22×C4⋊C4—112no—
225C22×C42C2×D1111yescharacteristic
226C22×C42C2×D1111yescharacteristic
227C22×C42C2×D1111yescharacteristic
228#391—118no—
229#391—224no—
230#391—224no—
231#389—224no—
232#376—24no—
233C2×#95—114no—
234C2×#95—112no—
235C2×#95—114no—
236C2×#95—112no—
237C2×#95—112no—
238C2×#95—114no—
239C2×#95—114no—
240C2×#95C2×D1112yes—
241C2×#95C2×D1112yes—
242C22×C11C2×#11711yescharacteristic
243C22×C11C2×C4×D411yescharacteristic
244C22×C11C2×C4×D411yescharacteristic
245C22×C11#51912yes—
246C22×C11#52012yes—
247C22×C11C2×#12111yescharacteristic
248C22×C11C2×#12311yescharacteristic
249C22×C11C2×#12411yescharacteristic
250C22×C11C2×#12611yescharacteristic
251C22×C11#53511yescharacteristic
252C22×C11#53611yescharacteristic
253C22×C11#53611yescharacteristic
254C22×C11#53611yescharacteristic
255C22×C11#53612yes—
256C22×C11#53712yes—
257C22×C11#54112yes—
258C22×C11#54112yes—
259C22×C11#54112yes—
260C22×C11#54112yes—
261C22×C11#54212yes—
262C22×C11#54212yes—
263C22×C11#54212yes—
264C22×C11#54212yes—
265C4×C11—44no—
266C4×C11—42no—
267C4×C11—42no—
268C4×C11—44no—
269C4×C11#38818yes—
270Dic11—44no—
271Dic11—44no—
272Dic11—82no—
273Dic11—82no—
274C22×Q8—114no—
275C22×Q8—222no—
276C22×Q8—222no—
277C22×Q8—222no—
278C22×Q8—222no—
279C22×Q8—222no—
280C22×Q8—222no—
281C23×C4—112no—
282C23×C4—112no—
283C23×C4—112no—
284C23×C4—112no—
285C23×C4C22×D1112yes—
286C23×C4C22×D1111yescharacteristic
287C23×C4C22×D1111yescharacteristic
288C23×C4C22×D1112yes—
289C23×C4C22×D1111yescharacteristic
290C2×C4⋊C4—114no—
291C2×C4⋊C4—222no—
292C2×C4⋊C4—222no—
293C2×C4⋊C4—224no—
294C2×C4⋊C4—222no—
295C2×C4⋊C4—222no—
296C2×C4⋊C4—222no—
297C2×C4⋊C4—222no—
298C2×C4⋊C4—222no—
299C2×C4⋊C4—222no—
300C2×C4⋊C4—444no—
301C2×C42—22no—
302C2×C42—22no—
303C2×C42—22no—
304C2×C42—22no—
305C2×C42—22no—
306C2×C42—22no—
307C2×C42C4×D1114yes—
308C2×C42D4414yes—
309C2×C42C22⋊D1114yes—
310#95—24no—
311#95—24no—
312#95—1116no—
313#95—224no—
314#95—224no—
315#95—224no—
316#95—228no—
317#95—444no—
318#95—444no—
319C2×C11C2×#38811yescharacteristic
320C2×C11#232012yes—
321C2×C11#232312yes—
322C2×C11#232611yescharacteristic
323C2×C11#232711yescharacteristic
324C2×C11#262011yescharacteristic
325C2×C11#262111yescharacteristic
326C2×C11#262512yes—
327C2×C11#264011yescharacteristic
328C2×C11#264211yescharacteristic
329C2×C11#264512yes—
330C24C23×D1111yescharacteristic
331C2×Q8—228no—
332C2×Q8—228no—
333C2×Q8—228no—
334C2×Q8—444no—
335C2×Q8—444no—
336C2×Q8—444no—
337C2×Q8—444no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—21no—
342C22×C4—21no—
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—22no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—114no—
359C22×C4—114no—
360C22×C4—222no—
361C22×C4—222no—
362C22×C4—222no—
363C22×C4—222no—
364C22×C4—222no—
365C22×C4—222no—
366C22×C4—222no—
367C22×C4—224no—
368C22×C4—224no—
369C22×C4—222no—
370C22×C4—222no—
371C22×C4—222no—
372C22×C4—222no—
373C22×C4—222no—
374C22×C4—222no—
375C22×C4—224no—
376C22×C4—224no—
377C22×C4—224no—
378C22×C4—224no—
379C22×C4—222no—
380C22×C4C2×C4×D1114yes—
381C22×C4C2×C4×D1112yes—
382C22×C4C2×D4412yes—
383C22×C4C2×D4412yes—
384C22×C4C2×D4412yes—
385C22×C4#433912yes—
386C22×C4#433912yes—
387C22×C4#433912yes—
388C22×C4#433912yes—
389C22×C4C2×C22⋊D1114yes—
390C22×C4C2×C22⋊D1112yes—
391C4⋊C4—228no—
392C4⋊C4—448no—
393C4⋊C4—444no—
394C4⋊C4—444no—
395C42—28no—
396C42—28no—
397C42—28no—
398C11#1426111yescharacteristic, complemented, Sylow
399C23C22×C4×D1111yescharacteristic
400C23C22×D4411yescharacteristic
401C23C2×#433911yescharacteristic
402C23C2×#433911yescharacteristic
403C23C2×#433911yescharacteristic
404C23C2×#433911yescharacteristic
405C23#6704212yes—
406C23#6704312yes—
407C23#6704312yes—
408C23#6704312yes—
409C23C22×C22⋊D1111yescharacteristic
410Q8—4416no—
411C2×C4—24no—
412C2×C4—24no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—24no—
418C2×C4—24no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—24no—
422C2×C4—24no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—224no—
436C2×C4—224no—
437C2×C4—224no—
438C2×C4—228no—
439C2×C4—224no—
440C2×C4—442no—
441C2×C4—442no—
442C2×C4—442no—
443C2×C4—442no—
444C2×C4—442no—
445C2×C4—444no—
446C2×C4—442no—
447C2×C4—442no—
448C2×C4—442no—
449C2×C4—442no—
450C2×C4—442no—
451C2×C4—442no—
452C2×C4—444no—
453C2×C4—444no—
454C2×C4—444no—
455C2×C4—442no—
456C2×C4—444no—
457C2×C4#6692514yes—
458C2×C4C4×D4414yes—
459C2×C4#6692814yes—
460C2×C4#6692914yes—
461C2×C4C4×C22⋊D1114yes—
462C2×C4#6698214yes—
463C2×C4#6698314yes—
464C22C2×#6692511yescharacteristic
465C22C2×C4×D4411yescharacteristic
466C22C2×#6692811yescharacteristic
467C22C2×#6692911yescharacteristic
468C22#1062304712yes—
469C22#1062304912yes—
470C22#1062304912yes—
471C22#1062304912yes—
472C22#1062304912yes—
473C22#1062305412yes—
474C22#1062305611yescharacteristic
475C22#1062305711yescharacteristic
476C22#1062305711yescharacteristic
477C22#1062305711yescharacteristic
478C22#1062306512yes—
479C22#1062306512yes—
480C22#1062306512yes—
481C22#1062306512yes—
482C22C2×C4×C22⋊D1111yescharacteristic
483C22C2×#6698211yescharacteristic
484C22C2×#6698311yescharacteristic
485C22#1062335612yes—
486C22#1062336412yes—
487C4—44no—
488C4—42no—
489C4—42no—
490C4—44no—
491C4—444no—
492C4—444no—
493C4—882no—
494C4—882no—
495C4#1062255318yes—
496C2C2×#1062255311yescharacteristic
497C2#1307126812yes—
498C2#1307129812yes—
499C2#1307132711yescharacteristic
500C2#1307133511yescharacteristic
501C2#1307437311yescharacteristic
502C2#1307438211yescharacteristic
503C2#1307441312yes—
504C2#1307455211yescharacteristic
505C2#1307456411yescharacteristic
506C2#1307458112yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#376C2
socle, prime radical, cosocleC24×C11C24
hypercenterC2×#376D11
hypocenterC11#14261
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#376

Complements

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

NH ≅ G/Ntype
30. #10622542C4semidirect
398. C11#14261semidirect

Maximal subgroups

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

subgroupindex
C2×#106225422
C2×#106225412
#130668762
#130668712
#130668462
C2×C11×#3762
#1426111