Finite Group Databasebeta

← #14675386

Subgroups — #14675386

Order 2816.

1630 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622594C212yesmaximal
2C2×C4⋊C4×Dic11C212yesmaximal
3#13066850C212yesmaximal
4#13066848C212yesmaximal
5#13066848C212yesmaximal
6C4×C11⋊#95C211yesmaximal, characteristic
7C4×C11⋊#95C211yesmaximal, characteristic
8#95×Dic11C212yesmaximal
9C2×C11×#389C211yesmaximal, characteristic
10C22×C11×C4⋊C4C2212yes—
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C22×C4⋊Dic11C2212yes—
15C22×C4×Dic11C2212yes—
16C22×C4×Dic11C2212yes—
17C22×C4×Dic11C2212yes—
18C22×C4×Dic11C2212yes—
19C11×#389C418yescomplemented
20C2×C11×#95C2212yes—
21C2×C11⋊#95C2212yes—
22C2×C11⋊#95C2211yescharacteristic
23C2×C11⋊#95C2211yescharacteristic
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2211yescharacteristic
32#10622594C4116yescomplemented
33C4⋊C4×Dic11—28no—
34C23×C4×C11C2312yes—
35C23×C4×C11C2312yes—
36C23×C4×C11C2311yescharacteristic
37C23×C4×C11C2311yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C23×Dic11C2312yes—
40C23×Dic11C2312yes—
41C23×Dic11C2312yes—
42C23×Dic11C2312yes—
43C2×C11×C4⋊C4—24no—
44C2×C11×C4⋊C4—24no—
45C2×C11×C4⋊C4—42no—
46C2×C11×C4⋊C4C2×C418yes—
47C2×C11×C4⋊C4C2×C418yes—
48C2×C11×C4⋊C4C2×C414yes—
49C2×C11×C4⋊C4C2×C414yes—
50C2×C42×C11—42no—
51C2×C42×C11C2×C414yes—
52C2×C4⋊Dic11—24no—
53C2×C4⋊Dic11—24no—
54C2×C4⋊Dic11C2×C418yes—
55C2×C4×Dic11—24no—
56C2×C4×Dic11—24no—
57C2×C4×Dic11—24no—
58C2×C4×Dic11—24no—
59C2×C4×Dic11—24no—
60C2×C4×Dic11—24no—
61C2×C4×Dic11—24no—
62C2×C4×Dic11—24no—
63C2×C4×Dic11—42no—
64C2×C4×Dic11—42no—
65C2×C4×Dic11—42no—
66C2×C4×Dic11C2×C418yes—
67C11×#95C2×C418yes—
68C11⋊#95—22no—
69C11⋊#95—22no—
70C11⋊#95—24no—
71C11⋊#95—24no—
72C11⋊#95—42no—
73C11⋊#95C2×C418yes—
74C11⋊#95C2×C418yes—
75C11⋊#95C2×C418yes—
76C11⋊#95C2×C418yes—
77C11⋊#95D414yes—
78C11⋊#95Q814yes—
79#13825—111nomaximal, Sylow
80C24×C11C2411yescharacteristic
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11—22no—
86C22×C4×C11—22no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
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×C11C22×C414yes—
99C22×C4×C11C22×C414yes—
100C22×C4×C11C22×C414yes—
101C22×C4×C11C22×C414yes—
102C22×C4×C11C22×C414yes—
103C22×C4×C11C22×C412yes—
104C22×C4×C11C22×C412yes—
105C22×C4×C11C22×C412yes—
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2×Q812yes—
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—22no—
125C22×Dic11—22no—
126C22×Dic11—22no—
127C22×Dic11—22no—
128C22×Dic11—22no—
129C22×Dic11—22no—
130C22×Dic11C22×C414yes—
131C22×Dic11C22×C414yes—
132C22×Dic11C22×C414yes—
133C22×Dic11C22×C414yes—
134C22×Dic11C2×D414yes—
135C22×Dic11C2×Q814yes—
136C22×Dic11#4114yes—
137C22×Dic11#4114yes—
138C11×C4⋊C4—216no—
139C11×C4⋊C4—44no—
140C11×C4⋊C4C42116yescomplemented
141C42×C11—44no—
142C4⋊Dic11—216no—
143C4×Dic11—216no—
144C4×Dic11—48no—
145C4×Dic11—48no—
146C4×Dic11—48no—
147C2×#389D1111yescharacteristic
148C2×#387—112no—
149C2×C4×C4⋊C4—112no—
150#1436—112no—
151#1436—112no—
152#1436—112no—
153C4×#95—111no—
154C4×#95—111no—
155C4×#95—112no—
156C23×C11C23×C412yes—
157C23×C11C23×C411yescharacteristic
158C23×C11C22×D411yescharacteristic
159C23×C11C22×Q811yescharacteristic
160C23×C11C2×#4111yescharacteristic
161C23×C11C2×#4111yescharacteristic
162C23×C11C2×#4112yes—
163C23×C11C2×#4112yes—
164C23×C11H(5,𝔽2)12yes—
165C23×C112−1+411yescharacteristic
166C23×C112−1+411yescharacteristic
167C2×C4×C11—24no—
168C2×C4×C11—24no—
169C2×C4×C11—24no—
170C2×C4×C11—24no—
171C2×C4×C11—24no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—24no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—24no—
180C2×C4×C11—24no—
181C2×C4×C11—24no—
182C2×C4×C11—24no—
183C2×C4×C11—24no—
184C2×C4×C11—24no—
185C2×C4×C11—24no—
186C2×C4×C11—24no—
187C2×C4×C11—24no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11C2×C4218yes—
193C2×C4×C11C2×C4214yes—
194C2×C4×C11C4×D414yes—
195C2×C4×C11C4×Q814yes—
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—24no—
207C2×Dic11—24no—
208C2×Dic11—24no—
209C2×Dic11—24no—
210C2×Dic11—24no—
211C2×Dic11—24no—
212C2×Dic11—24no—
213C2×Dic11—24no—
214C2×Dic11—42no—
215C2×Dic11—42no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11—42no—
222C2×Dic11C4×D418yes—
223C2×Dic11C4×Q818yes—
224C22×C4⋊C4—112no—
225C22×C4⋊C4C2×D1112yes—
226C22×C4⋊C4C2×D1111yescharacteristic
227C22×C4⋊C4C2×D1111yescharacteristic
228C22×C42—112no—
229C22×C42—112no—
230C22×C42—112no—
231C22×C42—112no—
232C22×C42C2×D1111yescharacteristic
233#389Dic1118yescomplemented
234#387—1116no—
235C4×C4⋊C4—228no—
236C2×#95—111no—
237C2×#95—112no—
238C2×#95—112no—
239C2×#95—112no—
240C2×#95—111no—
241C2×#95—112no—
242C2×#95—112no—
243C2×#95—111no—
244C2×#95—111no—
245C2×#95—112no—
246C2×#95—112no—
247C2×#95C2×D1112yes—
248C22×C11C22×C4211yescharacteristic
249C22×C11C2×C4×D411yescharacteristic
250C22×C11C2×C4×D412yes—
251C22×C11C2×C4×Q811yescharacteristic
252C22×C11C2×C4×Q812yes—
253C22×C11C4×#4112yes—
254C22×C11C4×#4111yescharacteristic
255C22×C11C4×#4111yescharacteristic
256C22×C11C4×#4112yes—
257C22×C11#51811yescharacteristic
258C22×C11#51911yescharacteristic
259C22×C11#52012yes—
260C22×C11#52012yes—
261C22×C11#54612yes—
262C22×C11#54711yescharacteristic
263C22×C11D4×Q811yescharacteristic
264C22×C11#55112yes—
265C22×C11#55212yes—
266C22×C11#55212yes—
267C22×C11#55312yes—
268C22×C11#55412yes—
269C22×C11#55611yescharacteristic
270C22×C11#55711yescharacteristic
271C4×C11—24no—
272C4×C11—24no—
273C4×C11—28no—
274C4×C11—24no—
275C4×C11—44no—
276Dic11—28no—
277Dic11—28no—
278Dic11—44no—
279Dic11—44no—
280C23×C4—112no—
281C23×C4—112no—
282C23×C4—112no—
283C23×C4—112no—
284C23×C4C22×D1112yes—
285C23×C4C22×D1112yes—
286C23×C4C22×D1111yescharacteristic
287C23×C4C22×D1111yescharacteristic
288C23×C4C22×D1111yescharacteristic
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—42no—
292C2×C4⋊C4—118no—
293C2×C4⋊C4—224no—
294C2×C4⋊C4—224no—
295C2×C4⋊C4C4×D1118yes—
296C2×C4⋊C4C2×Dic1118yes—
297C2×C4⋊C4C2×Dic1114yes—
298C2×C4⋊C4C2×Dic1114yes—
299C2×C42—42no—
300C2×C42—118no—
301C2×C42—224no—
302C2×C42—224no—
303C2×C42—224no—
304C2×C42—224no—
305C2×C42—224no—
306C2×C42—224no—
307C2×C42—224no—
308C2×C42—224no—
309C2×C42—442no—
310C2×C42—442no—
311C2×C42—442no—
312C2×C42C2×Dic1114yes—
313#95—118no—
314#95—118no—
315#95—118no—
316#95—118no—
317#95—114no—
318#95—114no—
319#95—224no—
320#95—224no—
321#95—222no—
322#95—222no—
323#95—442no—
324#95C2×Dic1118yes—
325C2×C11C42×D411yescharacteristic
326C2×C11C42×Q811yescharacteristic
327C2×C11#227411yescharacteristic
328C2×C11#235912yes—
329C2×C11#236012yes—
330C2×C11#236411yescharacteristic
331C2×C11#236511yescharacteristic
332C2×C11#236811yescharacteristic
333C2×C11#237012yes—
334C2×C11#237111yescharacteristic
335C2×C11#237312yes—
336C24C23×D1111yescharacteristic
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—21no—
343C22×C4—21no—
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—114no—
355C22×C4—114no—
356C22×C4—114no—
357C22×C4—114no—
358C22×C4—114no—
359C22×C4—114no—
360C22×C4—114no—
361C22×C4—114no—
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×C4C2×C4×D1114yes—
383C22×C4C2×C4×D1114yes—
384C22×C4C2×C4×D1114yes—
385C22×C4D4×D1112yes—
386C22×C4#434112yes—
387C22×C4Q8×D1112yes—
388C22×C4#434312yes—
389C22×C4C22×Dic1114yes—
390C22×C4C22×Dic1114yes—
391C22×C4C22×Dic1112yes—
392C22×C4C22×Dic1112yes—
393C22×C4C22×Dic1112yes—
394C4⋊C4—216no—
395C4⋊C4—44no—
396C4⋊C4—2216no—
397C4⋊C4C4×Dic11116yescomplemented
398C42—44no—
399C42—2216no—
400C42—448no—
401C42—448no—
402C42—448no—
403C11#1382511yescharacteristic, complemented, Sylow
404C23C22×C4×D1112yes—
405C23C2×D4×D1111yescharacteristic
406C23C2×#434111yescharacteristic
407C23#6703712yes—
408C23C2×Q8×D1111yescharacteristic
409C23C2×#434311yescharacteristic
410C23#6704011yescharacteristic
411C23#6704011yescharacteristic
412C23#41×D1112yes—
413C23#41×D1112yes—
414C23C23×Dic1111yescharacteristic
415C2×C4—24no—
416C2×C4—24no—
417C2×C4—24no—
418C2×C4—24no—
419C2×C4—24no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—24no—
424C2×C4—24no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—24no—
429C2×C4—24no—
430C2×C4—24no—
431C2×C4—24no—
432C2×C4—24no—
433C2×C4—24no—
434C2×C4—24no—
435C2×C4—24no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—118no—
441C2×C4—118no—
442C2×C4—224no—
443C2×C4—224no—
444C2×C4—224no—
445C2×C4—224no—
446C2×C4—224no—
447C2×C4—224no—
448C2×C4—224no—
449C2×C4—224no—
450C2×C4—224no—
451C2×C4—224no—
452C2×C4—224no—
453C2×C4—224no—
454C2×C4—224no—
455C2×C4—224no—
456C2×C4—224no—
457C2×C4—224no—
458C2×C4—224no—
459C2×C4—224no—
460C2×C4—442no—
461C2×C4—442no—
462C2×C4—442no—
463C2×C4—442no—
464C2×C4—442no—
465C2×C4—442no—
466C2×C4—442no—
467C2×C4—442no—
468C2×C4C2×C4×Dic1118yes—
469C2×C4C2×C4×Dic1114yes—
470C2×C4D4×Dic1114yes—
471C2×C4Q8×Dic1114yes—
472C22#1062303512yes—
473C22#1062303512yes—
474C22C4×#434112yes—
475C22C4×D4×D1112yes—
476C22C4×Q8×D1112yes—
477C22C4×#434312yes—
478C22#1062313212yes—
479C22#1062314112yes—
480C22#1062316712yes—
481C22#1062316812yes—
482C22#1062322412yes—
483C22#1062322412yes—
484C22#1062325211yescharacteristic
485C22#1062325711yescharacteristic
486C22#1062325811yescharacteristic
487C22#1062326311yescharacteristic
488C22C22×C4×Dic1111yescharacteristic
489C22C2×D4×Dic1111yescharacteristic
490C22#1062332911yescharacteristic
491C22C2×Q8×Dic1111yescharacteristic
492C22#1062334311yescharacteristic
493C22#41×Dic1111yescharacteristic
494C22#41×Dic1111yescharacteristic
495C4—24no—
496C4—24no—
497C4—28no—
498C4—24no—
499C4—44no—
500C4—228no—
501C4—228no—
502C4—444no—
503C4—444no—
504C2C4×D4×Dic1111yescharacteristic
505C2C4×Q8×Dic1111yescharacteristic
506C2#1307097311yescharacteristic
507C2#1307160312yes—
508C2#1307161812yes—
509C2#1307166811yescharacteristic
510C2#1307167611yescharacteristic
511C2#1307170111yescharacteristic
512C2#1307171512yes—
513C2#1307172211yescharacteristic
514C2#1307173912yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC22×C11C22×C42
FittingC2×C11×#389C2
socle, prime radical, cosocleC24×C11C24
hypercenterC2×#389D11
hypocenterC11#13825
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
19. C11×#389C4semidirect
32. #10622594C4semidirect
140. C11×C4⋊C4C42semidirect
233. #389Dic11semidirect
397. C4⋊C4C4×Dic11semidirect
403. C11#13825semidirect

Maximal subgroups

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

subgroupindex
C2×#106225942
C2×C4⋊C4×Dic112
#130668502
#130668482
C4×C11⋊#952
#95×Dic112
C2×C11×#3892
#1382511