Finite Group Databasebeta

← #14680441

Subgroups — #14680441

Order 2816.

2302 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66948C211yesmaximal, characteristic
2C2×#10622277C211yesmaximal, characteristic, complemented
3C2×#10622279C211yesmaximal, characteristic, complemented
4#13066884C211yesmaximal, characteristic, complemented
5#13066856C214yesmaximal, complemented
6#13066856C211yesmaximal, characteristic, complemented
7#13066856C211yesmaximal, characteristic, complemented
8#13066852C214yesmaximal, complemented
9C11×#1445C211yesmaximal, characteristic, complemented
10C23×D44C2212yes—
11C23×D44C2211yescharacteristic
12C23×C4×D11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×(C2×D11)⋊C4C2212yes—
15C22×(C2×D11)⋊C4C2212yes—
16C22×(C2×D11)⋊C4C2214yes—
17C22×(C2×D11)⋊C4C2214yes—
18C22×(C2×D11)⋊C4C2212yes—
19C22×C4×Dic11C2212yes—
20C2×#66948—24no—
21C2×#66948—24no—
22C2×#66948C418yescomplemented
23C2×C11×#95C2211yescharacteristic
24C2×C11×#95C2211yescharacteristic
25C2×C11×#95C2214yes—
26C2×C11⋊#95C2211yescharacteristic
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2211yescharacteristic
29C2×C11⋊#95C2214yes—
30#10622279—24no—
31#10622277—24no—
32C24×D11C2312yes—
33C24×D11C2311yescharacteristic
34C23×C4×C11C2312yes—
35C23×C4×C11C2312yes—
36C23×C4×C11C2312yes—
37C23×C4×C11C2311yescharacteristic
38C23×Dic11C2312yes—
39C23×Dic11C2312yes—
40C23×Dic11C2311yescharacteristic
41C22×D44—24no—
42C22×D44—24no—
43C22×D44—22no—
44C22×D44—22no—
45C22×D44—44no—
46C22×D44—44no—
47C22×D44—44no—
48C22×D44C2×C418yes—
49C22×D44C2×C414yes—
50C22×C4×D11—44no—
51C22×C4×D11C2×C414yes—
52C22×C4×D11D414yes—
53C22×C4×D11D414yes—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4C2×C414yes—
57C2×(C2×D11)⋊C4—24no—
58C2×(C2×D11)⋊C4—24no—
59C2×(C2×D11)⋊C4—24no—
60C2×(C2×D11)⋊C4—24no—
61C2×(C2×D11)⋊C4—24no—
62C2×(C2×D11)⋊C4—24no—
63C2×(C2×D11)⋊C4—28no—
64C2×(C2×D11)⋊C4—28no—
65C2×(C2×D11)⋊C4—44no—
66C2×(C2×D11)⋊C4—44no—
67C2×(C2×D11)⋊C4—44no—
68C2×(C2×D11)⋊C4—44no—
69C2×(C2×D11)⋊C4—44no—
70C2×(C2×D11)⋊C4C2×C418yes—
71C2×C4×Dic11—24no—
72C2×C4×Dic11—44no—
73#66948—232no—
74C11×#95—22no—
75C11×#95—22no—
76C11×#95—44no—
77C11⋊#95—22no—
78C11⋊#95—22no—
79C11⋊#95—24no—
80C11⋊#95—44no—
81#14290—111nomaximal, Sylow
82C24×C11C2411yescharacteristic
83C23×D11—22no—
84C23×D11—22no—
85C23×D11—24no—
86C23×D11—22no—
87C23×D11—22no—
88C23×D11—22no—
89C23×D11—22no—
90C23×D11—24no—
91C23×D11—24no—
92C23×D11—24no—
93C23×D11—24no—
94C23×D11—24no—
95C23×D11—24no—
96C23×D11C22×C414yes—
97C23×D11C22×C412yes—
98C23×D11C2×D412yes—
99C23×D11C2×D412yes—
100C22×C4×C11—24no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—24no—
106C22×C4×C11—24no—
107C22×C4×C11—24no—
108C22×C4×C11—24no—
109C22×C4×C11—22no—
110C22×C4×C11—24no—
111C22×C4×C11—22no—
112C22×C4×C11—24no—
113C22×C4×C11—22no—
114C22×C4×C11C22×C414yes—
115C22×C4×C11C22×C412yes—
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2×D412yes—
118C22×C4×C11#4114yes—
119C22×Dic11—22no—
120C22×Dic11—22no—
121C22×Dic11—22no—
122C22×Dic11—24no—
123C22×Dic11—24no—
124C22×Dic11—24no—
125C22×Dic11—24no—
126C22×Dic11—22no—
127C22×Dic11—22no—
128C22×Dic11—24no—
129C22×Dic11C22×C412yes—
130C22×Dic11C2×D412yes—
131C22×Dic11C2×D412yes—
132C22×Dic11#4114yes—
133C2×D44—216no—
134C2×D44—28no—
135C2×D44—48no—
136C2×D44—416no—
137C2×D44—48no—
138C2×D44—48no—
139C2×D44—48no—
140C2×D44—416no—
141C2×D44—48no—
142C2×C4×D11—48no—
143C2×C4×D11—48no—
144C2×C4×D11—48no—
145C2×C4×D11C22⋊C4116yescomplemented
146C11×C4⋊C4—28no—
147(C2×D11)⋊C4—216no—
148(C2×D11)⋊C4—216no—
149(C2×D11)⋊C4—416no—
150(C2×D11)⋊C4—48no—
151(C2×D11)⋊C4—416no—
152C4×Dic11—48no—
153C22×#121—111no—
154C2×#381—111no—
155C2×C4×C22⋊C4—111no—
156#1445—111no—
157#1445D1111yescharacteristic, complemented
158#1438—114no—
159#1438—111no—
160#1438—111no—
161#1437—114no—
162C23×C11C23×C411yescharacteristic
163C23×C11C22×D411yescharacteristic
164C23×C11C22×D411yescharacteristic
165C23×C11C2×#4112yes—
166C23×C11C2×#4112yes—
167C23×C11H(5,𝔽2)12yes—
168C23×C11H(5,𝔽2)14yes—
169C23×C11H(5,𝔽2)12yes—
170C22×D11—24no—
171C22×D11—24no—
172C22×D11—24no—
173C22×D11—24no—
174C22×D11—22no—
175C22×D11—22no—
176C22×D11—24no—
177C22×D11—24no—
178C22×D11—22no—
179C22×D11—24no—
180C22×D11—22no—
181C22×D11—24no—
182C22×D11—28no—
183C22×D11—24no—
184C22×D11—24no—
185C22×D11—28no—
186C22×D11—44no—
187C22×D11—44no—
188C22×D11—44no—
189C22×D11—44no—
190C22×D11—44no—
191C22×D11—42no—
192C22×D11—42no—
193C22×D11—44no—
194C22×D11—44no—
195C22×D11—42no—
196C22×D11—44no—
197C22×D11—42no—
198C22×D11—44no—
199C22×D11—44no—
200C22×D11—44no—
201C22×D11—44no—
202C22×D11—44no—
203C22×D11—44no—
204C22×D11—44no—
205C22×D11—44no—
206C22×D11C2×C22⋊C414yes—
207C2×C4×C11—24no—
208C2×C4×C11—24no—
209C2×C4×C11—24no—
210C2×C4×C11—24no—
211C2×C4×C11—28no—
212C2×C4×C11—24no—
213C2×C4×C11—28no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—44no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—44no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—44no—
224C2×C4×C11—44no—
225C2×C4×C11C2×C22⋊C414yes—
226C2×Dic11—24no—
227C2×Dic11—24no—
228C2×Dic11—24no—
229C2×Dic11—24no—
230C2×Dic11—28no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233C2×Dic11—44no—
234C2×Dic11—42no—
235C2×Dic11—42no—
236C2×Dic11—42no—
237C2×Dic11—44no—
238C2×Dic11—44no—
239C2×Dic11C2×C22⋊C414yes—
240D44—416no—
241D44—432no—
242C4×D11—416no—
243C23×D4—112no—
244C23×D4—111no—
245C24×C4—111no—
246C2×#121—118no—
247C2×#121—224no—
248C2×#121—224no—
249C22×C4⋊C4C2×D1111yescharacteristic
250C22×C22⋊C4—112no—
251C22×C22⋊C4—112no—
252C22×C22⋊C4—114no—
253C22×C22⋊C4—114no—
254C22×C22⋊C4—112no—
255C22×C42—112no—
256#381—224no—
257C4×C22⋊C4—224no—
258C2×#95—112no—
259C2×#95—111no—
260C2×#95—111no—
261C2×#95—114no—
262C2×#95C2×D1111yescharacteristic
263C2×#95C2×D1111yescharacteristic
264C2×#95C2×D1114yes—
265C22×C11C22×C22⋊C411yescharacteristic
266C22×C11C4×#4112yes—
267C22×C11#51812yes—
268C22×C11#51812yes—
269C22×C11#52512yes—
270C22×C11#53211yescharacteristic
271C22×C11#53211yescharacteristic
272C22×C11#53412yes—
273C22×C11#53412yes—
274C22×C11#53511yescharacteristic
275C22×C11#53512yes—
276C22×C11#53511yescharacteristic
277C22×C11#53814yes—
278C22×C11#53814yes—
279C22×C11#54014yes—
280C22×C11#54014yes—
281C2×D11—24no—
282C2×D11—24no—
283C2×D11—24no—
284C2×D11—48no—
285C2×D11—44no—
286C2×D11—44no—
287C2×D11—44no—
288C2×D11—44no—
289C2×D11—44no—
290C2×D11—44no—
291C2×D11—48no—
292C2×D11—48no—
293C2×D11—44no—
294C2×D11—84no—
295C2×D11—84no—
296C2×D11—84no—
297C2×D11—84no—
298C4×C11—24no—
299C4×C11—44no—
300C4×C11—44no—
301C4×C11—82no—
302Dic11—24no—
303Dic11—44no—
304Dic11—82no—
305C25—111no—
306C25—112no—
307C22×D4—118no—
308C22×D4—114no—
309C22×D4—224no—
310C22×D4—224no—
311C22×D4—222no—
312C22×D4—222no—
313C22×D4—444no—
314C22×D4—444no—
315C22×D4—444no—
316C23×C4—111no—
317C23×C4—114no—
318C23×C4—114no—
319C23×C4—114no—
320C23×C4—112no—
321C23×C4—112no—
322C23×C4—444no—
323C23×C4C22×D1112yes—
324C23×C4C22×D1112yes—
325C23×C4C22×D1112yes—
326C23×C4C22×D1111yescharacteristic
327#121—2232no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4C4×D1114yes—
331C2×C22⋊C4—118no—
332C2×C22⋊C4—224no—
333C2×C22⋊C4—224no—
334C2×C22⋊C4—224no—
335C2×C22⋊C4—224no—
336C2×C22⋊C4—224no—
337C2×C22⋊C4—228no—
338C2×C22⋊C4—224no—
339C2×C22⋊C4—228no—
340C2×C22⋊C4—444no—
341C2×C22⋊C4—444no—
342C2×C22⋊C4—444no—
343C2×C22⋊C4—444no—
344C2×C22⋊C4—444no—
345C2×C42—224no—
346C2×C42—444no—
347#95—22no—
348#95—22no—
349#95—44no—
350#95—224no—
351#95—222no—
352#95—222no—
353#95—444no—
354C2×C11#229711yescharacteristic
355C2×C11#230811yescharacteristic
356C2×C11#230911yescharacteristic
357C2×C11#233314yes—
358C2×C11#263512yes—
359C2×C11#263512yes—
360C2×C11#266112yes—
361C2×C11#266112yes—
362D11—44no—
363D11—84no—
364C24—112no—
365C24—112no—
366C24—112no—
367C24—114no—
368C24—222no—
369C24—222no—
370C24—222no—
371C24—224no—
372C24—222no—
373C24—222no—
374C24—222no—
375C24—224no—
376C24—224no—
377C24—224no—
378C24—224no—
379C24—224no—
380C24—224no—
381C24C23×D1111yescharacteristic
382C2×D4—2216no—
383C2×D4—228no—
384C2×D4—448no—
385C2×D4—4416no—
386C2×D4—448no—
387C2×D4—448no—
388C2×D4—448no—
389C2×D4—4416no—
390C2×D4—448no—
391C22×C4—24no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—24no—
396C22×C4—24no—
397C22×C4—22no—
398C22×C4—24no—
399C22×C4—24no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—24no—
403C22×C4—22no—
404C22×C4—24no—
405C22×C4—112no—
406C22×C4—112no—
407C22×C4—112no—
408C22×C4—1116no—
409C22×C4—114no—
410C22×C4—224no—
411C22×C4—222no—
412C22×C4—222no—
413C22×C4—224no—
414C22×C4—224no—
415C22×C4—222no—
416C22×C4—222no—
417C22×C4—224no—
418C22×C4—222no—
419C22×C4—224no—
420C22×C4—448no—
421C22×C4—448no—
422C22×C4—448no—
423C22×C4C2×C4×D1114yes—
424C22×C4C2×C4×D1112yes—
425C22×C4D4×D1112yes—
426C22×C4D4×D1112yes—
427C22×C4#434314yes—
428C4⋊C4—28no—
429C22⋊C4—2216no—
430C22⋊C4—2216no—
431C22⋊C4—4416no—
432C22⋊C4—4416no—
433C22⋊C4—448no—
434C42—448no—
435C11#1429011yescharacteristic, complemented, Sylow
436C23—114no—
437C23—222no—
438C23—222no—
439C23—224no—
440C23—224no—
441C23—224no—
442C23—224no—
443C23—224no—
444C23—224no—
445C23—224no—
446C23—222no—
447C23—222no—
448C23—224no—
449C23—224no—
450C23—224no—
451C23—228no—
452C23—228no—
453C23—444no—
454C23—444no—
455C23—444no—
456C23—444no—
457C23—444no—
458C23—444no—
459C23—442no—
460C23—442no—
461C23—444no—
462C23—444no—
463C23—444no—
464C23—444no—
465C23—444no—
466C23—444no—
467C23—444no—
468C23—444no—
469C23—442no—
470C23—442no—
471C23—444no—
472C23—444no—
473C23C22×C4×D1111yescharacteristic
474C23C2×D4×D1111yescharacteristic
475C23C2×D4×D1111yescharacteristic
476C23#6703712yes—
477C23C2×#434312yes—
478C23#41×D1112yes—
479C23#6704212yes—
480C23#6704214yes—
481D4—4416no—
482D4—4432no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—28no—
488C2×C4—24no—
489C2×C4—28no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—44no—
493C2×C4—42no—
494C2×C4—44no—
495C2×C4—42no—
496C2×C4—44no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—44no—
500C2×C4—42no—
501C2×C4—114no—
502C2×C4—224no—
503C2×C4—224no—
504C2×C4—224no—
505C2×C4—228no—
506C2×C4—224no—
507C2×C4—4416no—
508C2×C4—442no—
509C2×C4—442no—
510C2×C4—444no—
511C2×C4—442no—
512C2×C4—442no—
513C2×C4—444no—
514C2×C4—442no—
515C2×C4—444no—
516C2×C4C22⋊C4×D1114yes—
517C22—224no—
518C22—224no—
519C22—224no—
520C22—448no—
521C22—444no—
522C22—444no—
523C22—444no—
524C22—444no—
525C22—444no—
526C22—448no—
527C22—448no—
528C22—444no—
529C22—444no—
530C22—884no—
531C22—884no—
532C22—884no—
533C22—884no—
534C22C2×C22⋊C4×D1111yescharacteristic
535C22#1062305212yes—
536C22#1062307612yes—
537C22C4×#434312yes—
538C22#1062313812yes—
539C22#1062315812yes—
540C22#1062317514yes—
541C22#1062318412yes—
542C22#1062318412yes—
543C22#1062319414yes—
544C22#1062319911yescharacteristic
545C22#1062320511yescharacteristic
546C22#1062322914yes—
547C22#1062323514yes—
548C22#1062324611yescharacteristic
549C22#1062325611yescharacteristic
550C4—24no—
551C4—44no—
552C4—44no—
553C4—82no—
554C4—224no—
555C4—444no—
556C4—882no—
557C2—444no—
558C2—884no—
559C2#1307110511yescharacteristic
560C2#1307119311yescharacteristic
561C2#1307119511yescharacteristic
562C2#1307138014yes—
563C2#1307450612yes—
564C2#1307450912yes—
565C2#1307474912yes—
566C2#1307475012yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1445C2
socle, cosocleC24×C11C24
prime radicalC22×#66948C2
hypercenter#1445D11
hypocenterC11#14290
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1445

Complements

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

NH ≅ G/Ntype
2. C2×#10622277C2semidirect
3. C2×#10622279C2semidirect
4. #13066884C2semidirect
5. #13066856C2semidirect
6. #13066856C2semidirect
7. #13066856C2semidirect
8. #13066852C2semidirect
9. C11×#1445C2semidirect
22. C2×#66948C4semidirect
145. C2×C4×D11C22⋊C4semidirect
157. #1445D11semidirect
435. C11#14290semidirect

Maximal subgroups

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

subgroupindex
C22×#669482
C2×#106222772
C2×#106222792
#130668842
#130668562
#130668522
C11×#14452
#1429011