Finite Group Databasebeta

← #14764836

Subgroups — #14764836

Order 2816.

1008 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622624C211yesmaximal, characteristic, complemented
2C2×#10622847C211yesmaximal, characteristic, complemented
3#13069415C212yesmaximal, complemented
4#13069231C212yesmaximal, complemented
5#13069231C212yesmaximal, complemented
6#13068914C211yesmaximal, characteristic, complemented
7#13068914C212yesmaximal, complemented
8#13068801C211yesmaximal, characteristic, complemented
9#13068528C211yesmaximal, characteristic, complemented
10#13068394C211yesmaximal, characteristic, complemented
11C11×#2388C211yesmaximal, characteristic
12C22×C11×#41C2211yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14C2×C4×D4×C11C2212yes—
15C22×#4318C2211yescharacteristic
16C22×#4318C2211yescharacteristic
17C23×C11⋊C8C2211yescharacteristic
18C11×#395C411yescharacteristic
19C11×#394C412yes—
20C11×#394C411yescharacteristic
21C11×#393C411yescharacteristic
22C11×#392C411yescharacteristic
23C11×#392C412yes—
24C4×C11×C22⋊C4C2211yescharacteristic
25C4×C11×C22⋊C4C2212yes—
26#10622847—24no—
27C2×C22⋊(C11⋊C8)C2211yescharacteristic
28C2×C22⋊(C11⋊C8)C2211yescharacteristic
29C2×C22⋊(C11⋊C8)C2212yes—
30C2×C22⋊(C11⋊C8)C2212yes—
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2212yes—
33C2×C22⋊(C11⋊C8)C2212yes—
34C2×C22⋊(C11⋊C8)C2212yes—
35#10622624—24no—
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2212yes—
38C2×#66867C2211yescharacteristic
39C2×#66867C2212yes—
40#10622162C2212yes—
41#10622162C2212yes—
42#10622162C2212yes—
43C2×C11×#41—22no—
44C2×C11×#41—22no—
45C2×C11×#41—42no—
46C2×C11×#41—42no—
47C22×Q8×C11C2×C411yescharacteristic
48C22×D4×C11C2×C411yescharacteristic
49C22×D4×C11C2×C412yes—
50C22×D4×C11C2×C411yescharacteristic
51C22×D4×C11C2×C412yes—
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2312yes—
54C23×C4×C11C2311yescharacteristic
55C4×D4×C11—22no—
56C4×D4×C11—22no—
57C4×D4×C11—42no—
58C4×D4×C11—42no—
59C2×C11×C4⋊C4C2×C411yescharacteristic
60C2×C11×C4⋊C4C2×C412yes—
61C2×C11×C22⋊C4C2×C411yescharacteristic
62C2×C11×C22⋊C4C2×C411yescharacteristic
63C2×C11×C22⋊C4C2×C412yes—
64C2×C11×C22⋊C4C2×C412yes—
65C2×C11×C22⋊C4C2×C412yes—
66C2×C11×C22⋊C4C2×C412yes—
67C2×C11×C22⋊C4C2×C412yes—
68C2×C42×C11C2311yescharacteristic
69C2×C42×C11C2312yes—
70C2×#4318—22no—
71C2×#4318—22no—
72C2×#4318—42no—
73C2×#4318—42no—
74C22×C11⋊C8—42no—
75C22×C11⋊C8D414yescomplemented
76C22×C11⋊C8C2311yescharacteristic
77C22×C11⋊C8C2312yes—
78C22×C11⋊C8C2311yescharacteristic
79C22×C11⋊C8C2312yes—
80C22×C11⋊C8C2311yescharacteristic
81C22×C11⋊C8C2311yescharacteristic
82C11×#95C2×C412yes—
83C11×#95C2×C411yescharacteristic
84C11×#95C2×C412yes—
85C11×#95C2×C411yescharacteristic
86C22⋊(C11⋊C8)—22no—
87C22⋊(C11⋊C8)—22no—
88C22⋊(C11⋊C8)—24no—
89C22⋊(C11⋊C8)—24no—
90C22⋊(C11⋊C8)—22no—
91C22⋊(C11⋊C8)—42no—
92C22⋊(C11⋊C8)—42no—
93C22⋊(C11⋊C8)—42no—
94C4⋊(C11⋊C8)—22no—
95C4⋊(C11⋊C8)—42no—
96#66867—22no—
97#66867—42no—
98#22035—111nomaximal, Sylow
99C24×C11C22×C411yescharacteristic
100C24×C11C22×C412yes—
101C24×C11C22×C411yescharacteristic
102C11×#41—44no—
103C11×#41—44no—
104C11×#41—48no—
105C2×Q8×C11—22no—
106C2×Q8×C11—42no—
107C2×D4×C11—22no—
108C2×D4×C11—24no—
109C2×D4×C11—22no—
110C2×D4×C11—42no—
111C2×D4×C11—41no—
112C2×D4×C11—42no—
113C2×D4×C11—41no—
114C2×D4×C11—42no—
115C2×D4×C11—42no—
116C2×D4×C11—42no—
117C2×D4×C11—42no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11C22×C411yescharacteristic
131C22×C4×C11C22×C412yes—
132C22×C4×C11C22×C411yescharacteristic
133C22×C4×C11C22×C412yes—
134C22×C4×C11C22×C412yes—
135C22×C4×C11C22×C411yescharacteristic
136C22×C4×C11C22×C411yescharacteristic
137C22×C4×C11C2×D412yes—
138C22×C4×C11#4112yes—
139C22×C4×C11C2411yescharacteristic
140C11×C4⋊C4—22no—
141C11×C4⋊C4—42no—
142C11×C22⋊C4—22no—
143C11×C22⋊C4—22no—
144C11×C22⋊C4—42no—
145C11×C22⋊C4—42no—
146C11×C22⋊C4—42no—
147C11×C22⋊C4—42no—
148C11×C22⋊C4—42no—
149C42×C11—21no—
150C42×C11—21no—
151C42×C11—22no—
152C42×C11—22no—
153#4318—44no—
154#4318—44no—
155C2×C11⋊C8—21no—
156C2×C11⋊C8—21no—
157C2×C11⋊C8—22no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—22no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—44no—
168C2×C11⋊C8C2×D412yes—
169C2×C11⋊C8C2×D412yes—
170C2×#435—111no—
171C2×#408—111no—
172#2388D1111yescharacteristic
173#1955—112no—
174#1924—112no—
175#1924—112no—
176#1870—111no—
177#1870—112no—
178#1851—111no—
179#1780—111no—
180#1752—111no—
181C23×C11—22no—
182C23×C11—22no—
183C23×C11—21no—
184C23×C11—21no—
185C23×C11—21no—
186C23×C11—22no—
187C23×C11—22no—
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—21no—
193C23×C11—21no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11C4×D412yes—
198C23×C11C23×C411yescharacteristic
199Q8×C11—44no—
200D4×C11—44no—
201D4×C11—44no—
202D4×C11—48no—
203D4×C11—48no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—24no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—21no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—21no—
223C2×C4×C11—22no—
224C2×C4×C11—41no—
225C2×C4×C11—42no—
226C2×C4×C11—41no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11C4×D412yes—
232C2×C4×C11C22×D411yescharacteristic
233C2×C4×C11C2×#4111yescharacteristic
234C2×C4×C11H(5,𝔽2)12yes—
235C2×C4×C11H(5,𝔽2)12yes—
236C11⋊C8—22no—
237C11⋊C8—22no—
238C11⋊C8—41no—
239C11⋊C8—41no—
240C11⋊C8—42no—
241C11⋊C8—42no—
242C22×#41C2×D1111yescharacteristic
243C22×M16—111no—
244C22×M16—111no—
245C23×C8—111no—
246C2×C4×D4C2×D1111yescharacteristic
247C2×C4×D4C2×D1112yes—
248#435—224no—
249C2×C4⋊C8—111no—
250C2×C4⋊C8—112no—
251#408—224no—
252C2×C22⋊C8—111no—
253C2×C22⋊C8—112no—
254C2×C22⋊C8—112no—
255C2×C22⋊C8—111no—
256C2×C22⋊C8—111no—
257C2×C22⋊C8—112no—
258C2×C22⋊C8—112no—
259C2×C22⋊C8—112no—
260C2×#97—111no—
261C2×#97—112no—
262#395Dic1111yescharacteristic
263#394Dic1112yes—
264#394Dic1111yescharacteristic
265#393Dic1111yescharacteristic
266#392Dic1111yescharacteristic
267#392Dic1112yes—
268C4×C22⋊C4C2×D1111yescharacteristic
269C4×C22⋊C4C2×D1112yes—
270#336—112no—
271#336—112no—
272#336—112no—
273C22×C11—22no—
274C22×C11—22no—
275C22×C11—22no—
276C22×C11—42no—
277C22×C11—42no—
278C22×C11—42no—
279C22×C11—41no—
280C22×C11—41no—
281C22×C11—42no—
282C22×C11—41no—
283C22×C11—42no—
284C22×C11—42no—
285C22×C11—42no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11—42no—
289C22×C11—42no—
290C22×C11C2×C4×D411yescharacteristic
291C22×C11#51812yes—
292C22×C11#56811yescharacteristic
293C22×C11#56811yescharacteristic
294C22×C11#56812yes—
295C4×C11—22no—
296C4×C11—41no—
297C4×C11—42no—
298C4×C11—41no—
299C4×C11—41no—
300C4×C11—42no—
301C4×C11—42no—
302C4×C11#53411yescharacteristic
303C4×C11#53511yescharacteristic
304C4×C11#53812yes—
305C2×#41—22no—
306C2×#41—22no—
307C2×#41—42no—
308C2×#41—42no—
309C22×Q8C2×Dic1111yescharacteristic
310C22×D4C2×Dic1111yescharacteristic
311C22×D4C2×Dic1112yes—
312C22×D4C2×Dic1111yescharacteristic
313C22×D4C2×Dic1112yes—
314C23×C4C22×D1111yescharacteristic
315C23×C4C22×D1112yes—
316C23×C4C22×D1111yescharacteristic
317C2×M16—222no—
318C2×M16—222no—
319C2×M16—442no—
320C2×M16—442no—
321C22×C8—111no—
322C22×C8—111no—
323C22×C8—114no—
324C22×C8—112no—
325C22×C8—111no—
326C22×C8—112no—
327C22×C8—111no—
328C22×C8—442no—
329C4×D4—22no—
330C4×D4—22no—
331C4×D4—42no—
332C4×D4—42no—
333C2×C4⋊C4C2×Dic1111yescharacteristic
334C2×C4⋊C4C2×Dic1112yes—
335C2×C22⋊C4C2×Dic1111yescharacteristic
336C2×C22⋊C4C2×Dic1111yescharacteristic
337C2×C22⋊C4C2×Dic1112yes—
338C2×C22⋊C4C2×Dic1112yes—
339C2×C22⋊C4C2×Dic1112yes—
340C2×C22⋊C4C2×Dic1112yes—
341C2×C22⋊C4C2×Dic1112yes—
342C2×C42C22×D1111yescharacteristic
343C2×C42C22×D1112yes—
344C4⋊C8—222no—
345C4⋊C8—442no—
346C22⋊C8—224no—
347C22⋊C8—224no—
348C22⋊C8—222no—
349C22⋊C8—222no—
350C22⋊C8—222no—
351C22⋊C8—442no—
352C22⋊C8—442no—
353C22⋊C8—442no—
354#97—222no—
355#97—442no—
356#95C2×Dic1112yes—
357#95C2×Dic1111yescharacteristic
358#95C2×Dic1112yes—
359#95C2×Dic1111yescharacteristic
360C2×C11—42no—
361C2×C11—82no—
362C2×C11—81no—
363C2×C11#232111yescharacteristic
364C2×C11#293011yescharacteristic
365C2×C11#293211yescharacteristic
366C2×C11#297812yes—
367C2×C11#298012yes—
368C24C22×Dic1111yescharacteristic
369C24C22×Dic1112yes—
370C24C22×Dic1111yescharacteristic
371#41—44no—
372#41—44no—
373#41—48no—
374C2×Q8—22no—
375C2×Q8—42no—
376C2×D4—22no—
377C2×D4—24no—
378C2×D4—22no—
379C2×D4—42no—
380C2×D4—42no—
381C2×D4—42no—
382C2×D4—42no—
383C2×D4—41no—
384C2×D4—42no—
385C2×D4—41no—
386C2×D4—42no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4D4×D1112yes—
400C22×C4#434112yes—
401C22×C4C22×Dic1111yescharacteristic
402C22×C4C22×Dic1112yes—
403C22×C4C22×Dic1111yescharacteristic
404C22×C4C22×Dic1112yes—
405C22×C4C22×Dic1112yes—
406C22×C4C22×Dic1111yescharacteristic
407C22×C4C22×Dic1111yescharacteristic
408C22×C4C23×D1111yescharacteristic
409M16—444no—
410M16—444no—
411C2×C8—112no—
412C2×C8—112no—
413C2×C8—222no—
414C2×C8—222no—
415C2×C8—221no—
416C2×C8—222no—
417C2×C8—221no—
418C2×C8—222no—
419C2×C8—222no—
420C2×C8—222no—
421C2×C8—222no—
422C2×C8—222no—
423C2×C8—222no—
424C2×C8—222no—
425C2×C8—444no—
426C4⋊C4—22no—
427C4⋊C4—42no—
428C22⋊C4—22no—
429C22⋊C4—22no—
430C22⋊C4—42no—
431C22⋊C4—42no—
432C22⋊C4—42no—
433C22⋊C4—42no—
434C22⋊C4—42no—
435C42—21no—
436C42—21no—
437C42—22no—
438C42—22no—
439C11#2203511yescharacteristic, complemented, Sylow
440C23—22no—
441C23—22no—
442C23—21no—
443C23—21no—
444C23—21no—
445C23—22no—
446C23—22no—
447C23—22no—
448C23—22no—
449C23—22no—
450C23—22no—
451C23—21no—
452C23—21no—
453C23—22no—
454C23—22no—
455C23—22no—
456C23D4×Dic1112yes—
457C23C23×Dic1111yescharacteristic
458Q8—44no—
459D4—44no—
460D4—44no—
461D4—48no—
462D4—48no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—24no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—21no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—21no—
482C2×C4—22no—
483C2×C4—41no—
484C2×C4—42no—
485C2×C4—41no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4D4×Dic1112yes—
491C2×C4C2×D4×D1111yescharacteristic
492C2×C4C2×#434111yescharacteristic
493C2×C4#6703712yes—
494C2×C4#6703712yes—
495C8—222no—
496C8—222no—
497C8—441no—
498C8—442no—
499C8—441no—
500C8—442no—
501C22—22no—
502C22—22no—
503C22—22no—
504C22—42no—
505C22—42no—
506C22—41no—
507C22—42no—
508C22—41no—
509C22—42no—
510C22—42no—
511C22—41no—
512C22—42no—
513C22—42no—
514C22—42no—
515C22—42no—
516C22—42no—
517C22—42no—
518C22C2×D4×Dic1111yescharacteristic
519C22#1062332912yes—
520C22#1062335011yescharacteristic
521C22#1062335011yescharacteristic
522C22#1062335012yes—
523C4—22no—
524C4—41no—
525C4—41no—
526C4—42no—
527C4—41no—
528C4—42no—
529C4—42no—
530C4#1062312011yescharacteristic
531C4#1062312311yescharacteristic
532C4#1062312412yes—
533C2—42no—
534C2—81no—
535C2—82no—
536C2#1307127711yescharacteristic
537C2#1307732011yescharacteristic
538C2#1307733411yescharacteristic
539C2#1307767812yes—
540C2#1307768712yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
Fitting, prime radicalC11×#2388C2
cosocleC22×C4×C11C24
hypercenter#2388D11
hypocenterC11#22035
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2388

Complements

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

NH ≅ G/Ntype
1. C2×#10622624C2semidirect
2. C2×#10622847C2semidirect
3. #13069415C2semidirect
4. #13069231C2semidirect
5. #13069231C2semidirect
6. #13068914C2semidirect
7. #13068914C2semidirect
8. #13068801C2semidirect
9. #13068528C2semidirect
10. #13068394C2semidirect
75. C22×C11⋊C8D4semidirect
439. C11#22035semidirect

Maximal subgroups

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

subgroupindex
C2×#106226242
C2×#106228472
#130694152
#130692312
#130689142
#130688012
#130685282
#130683942
C11×#23882
#2203511