Finite Group Databasebeta

← #14775502

Subgroups — #14775502

Order 2816.

860 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622314C211yesmaximal, characteristic, complemented
2C2×#10622731C211yesmaximal, characteristic
3C4×#66931C211yesmaximal, characteristic
4#13069550C211yesmaximal, characteristic, complemented
5#13069334C211yesmaximal, characteristic, complemented
6#13069333C211yesmaximal, characteristic, complemented
7#13069333C211yesmaximal, characteristic, complemented
8#13069180C211yesmaximal, characteristic, complemented
9#13069179C211yesmaximal, characteristic, complemented
10#13068801C211yesmaximal, characteristic
11#13068799C211yesmaximal, characteristic
12C8×Dic11⋊C4C211yesmaximal, characteristic, complemented
13#13068402C211yesmaximal, characteristic
14C22⋊C8×Dic11C211yesmaximal, characteristic
15C11×#1753C211yesmaximal, characteristic
16C22×C11×M16C2211yescharacteristic
17C22×C4×Dic11C2211yescharacteristic
18C22×#4318C2211yescharacteristic
19C2×#66931C411yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21C2×C11×C22⋊C8C2211yescharacteristic
22C2×C11×#97C2211yescharacteristic
23C2×C4×C8×C11C2211yescharacteristic
24C4×C11×C22⋊C4C2211yescharacteristic
25C4×C22⋊Dic11C2211yescharacteristic
26C2×C22⋊(C11⋊C8)C2211yescharacteristic
27#10622731—24no—
28C2×#66879C2211yescharacteristic
29C2×Dic11⋊C8C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31C2×Dic11⋊C8C2211yescharacteristic
32C2×Dic11⋊C8C2211yescharacteristic
33C2×Dic11⋊C8C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35C2×C8×Dic11C2211yescharacteristic
36C2×C8×Dic11C2211yescharacteristic
37C2×C8×Dic11C2211yescharacteristic
38#10622563C411yescharacteristic
39#10622559C411yescharacteristic
40#10622555C411yescharacteristic
41C4×C4⋊Dic11C2211yescharacteristic
42C4×Dic11⋊C4C2211yescharacteristic
43C4×Dic11⋊C4C2211yescharacteristic
44C2×C4⋊(C11⋊C8)C2211yescharacteristic
45C2×C4⋊(C11⋊C8)C2211yescharacteristic
46#10622314—24no—
47#10622268C411yescharacteristic
48#10622267C411yescharacteristic
49#10622260C411yescharacteristic
50#10622259C411yescharacteristic
51C11×#336C2211yescharacteristic
52C11×#336C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×Dic11C2×C411yescharacteristic
63C23×Dic11C2×C411yescharacteristic
64C22×Dic22C2×C411yescharacteristic
65C2×C11×M16—22no—
66C2×C11×M16—22no—
67C2×C11×M16—41no—
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C2×C11×C22⋊C4C2×C411yescharacteristic
73C2×C11×C22⋊C4C2×C411yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×C22⋊Dic11C2×C411yescharacteristic
77C2×C22⋊Dic11C2×C411yescharacteristic
78C2×C4⋊Dic11C2×C411yescharacteristic
79C2×C4⋊Dic11C2×C411yescharacteristic
80C2×C4⋊Dic11C2×C411yescharacteristic
81C2×Dic11⋊C4C2×C411yescharacteristic
82C2×Dic11⋊C4C2×C411yescharacteristic
83C2×Dic11⋊C4C2×C411yescharacteristic
84C2×Dic11⋊C4C2×C411yescharacteristic
85C2×Dic11⋊C4C2×C411yescharacteristic
86C2×Dic11⋊C4C2×C411yescharacteristic
87C2×C4×Dic11—22no—
88C2×C4×Dic11—22no—
89C2×C4×Dic11C2×C411yescharacteristic
90C2×C4×Dic11C2×C411yescharacteristic
91C2×C4×Dic11C2311yescharacteristic
92C2×C4×Dic11C2311yescharacteristic
93C2×C4×Dic11C2311yescharacteristic
94C2×C4×Dic11C2311yescharacteristic
95C2×#4318—22no—
96C2×#4318—22no—
97C2×#4318—41no—
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102#66931—24no—
103C4×Dic22—22no—
104C4×Dic22—22no—
105C11×C22⋊C8Q814yescomplemented
106C11×#97—22no—
107C4×C8×C11—41no—
108C11×#95C2×C411yescharacteristic
109C11×#95C2×C411yescharacteristic
110C11⋊#95C2×C411yescharacteristic
111C11⋊#95C2×C411yescharacteristic
112C11⋊#95C2×C411yescharacteristic
113C11⋊#95C2×C411yescharacteristic
114C11⋊#95C2×C411yescharacteristic
115C11⋊#95C2×C411yescharacteristic
116C11⋊#95C2×C411yescharacteristic
117C11⋊#95C2×C411yescharacteristic
118C22⋊(C11⋊C8)—22no—
119#66879—22no—
120Dic11⋊C8—22no—
121Dic11⋊C8—22no—
122Dic11⋊C8—22no—
123Dic11⋊C8—22no—
124Dic11⋊C8—41no—
125Dic11⋊C8D414yes—
126C8×Dic11—22no—
127C8×Dic11—22no—
128C8×Dic11—41no—
129C4⋊(C11⋊C8)—22no—
130C4⋊(C11⋊C8)—41no—
131#22957—111nomaximal, Sylow
132C24×C11C22×C411yescharacteristic
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11C22×C411yescharacteristic
138C22×C4×C11C22×C411yescharacteristic
139C22×C4×C11C22×C411yescharacteristic
140C22×C4×C11C22×C411yescharacteristic
141C22×C4×C11C22×C411yescharacteristic
142C22×C4×C11C2×Q812yes—
143C22×C4×C11#4112yes—
144C22×C4×C11C2411yescharacteristic
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—41no—
151C22×Dic11C22×C411yescharacteristic
152C22×Dic11C22×C411yescharacteristic
153C22×Dic11C22×C411yescharacteristic
154C22×Dic11C22×C411yescharacteristic
155C22×Dic11C22×C411yescharacteristic
156C22×Dic11C22×C411yescharacteristic
157C22×Dic11C22×C411yescharacteristic
158C22×Dic11C22×C411yescharacteristic
159C2×Dic22—22no—
160C2×Dic22—22no—
161C2×Dic22—22no—
162C11×M16—44no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11C2×D412yes—
173C2×C8×C11C2×Q812yes—
174C2×C8×C11C2×Q812yes—
175C11×C22⋊C4—22no—
176C11×C22⋊C4—41no—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11—21no—
181C22⋊Dic11—22no—
182C22⋊Dic11—41no—
183C4⋊Dic11—22no—
184C4⋊Dic11—22no—
185C4⋊Dic11—22no—
186Dic11⋊C4—22no—
187Dic11⋊C4—22no—
188Dic11⋊C4—22no—
189Dic11⋊C4—22no—
190Dic11⋊C4—22no—
191Dic11⋊C4M1614yescomplemented
192C4×Dic11—22no—
193C4×Dic11—22no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C4×Dic11—21no—
198C4×Dic11—21no—
199C4×Dic11—21no—
200C4×Dic11C2×D412yes—
201C4×Dic11#4112yes—
202#4318—44no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8C2×D412yes—
215C2×#446—111no—
216C2×#423—111no—
217C4×C22⋊Q8—111no—
218#1984—111no—
219#1939—111no—
220#1939—111no—
221#1939—111no—
222#1917—111no—
223#1917—111no—
224#1851—111no—
225#1851—111no—
226C8×C4⋊C4—111no—
227#1753—111no—
228#1753D1111yescharacteristic
229C4×C22⋊C8—111no—
230C23×C11—21no—
231C23×C11—21no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11C4×Q812yes—
237C23×C11C23×C411yescharacteristic
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11C4×Q812yes—
256C2×C4×C11C2×M1612yes—
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C22×Q811yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11H(5,𝔽2)11yescharacteristic
262C2×C4×C112−1+411yescharacteristic
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—44no—
282C2×Dic11—44no—
283C2×Dic11C4×D412yes—
284C2×Dic11C4×D412yes—
285C2×Dic11C2×M1612yes—
286C2×Dic11C2×M1612yes—
287C2×Dic11#13112yes—
288C2×Dic11#13112yes—
289Dic22—44no—
290C8×C11—22no—
291C8×C11—22no—
292C8×C11—22no—
293C8×C11—41no—
294C11⋊C8—22no—
295C11⋊C8—41no—
296C11⋊C8—41no—
297C11⋊C8—41no—
298C22×M16—111no—
299C22×M16C2×D1111yescharacteristic
300C2×C22⋊Q8—111no—
301C2×C4×Q8—111no—
302C22×C42—111no—
303#446—224no—
304#423—224no—
305C2×C4⋊C8—111no—
306C2×C4⋊C8—111no—
307C2×C4⋊C8—111no—
308C2×C4⋊C8—111no—
309C2×C4⋊C8—111no—
310C2×C4⋊C8—111no—
311C2×C4⋊C8—111no—
312C2×C4⋊C8—111no—
313C2×C22⋊C8—111no—
314C2×C22⋊C8C2×D1111yescharacteristic
315C2×#97—111no—
316C2×#97C2×D1111yescharacteristic
317C2×C4×C8—111no—
318C2×C4×C8—111no—
319C2×C4×C8—111no—
320C2×C4×C8C2×D1111yescharacteristic
321#391—111no—
322#389—111no—
323#387—111no—
324#387—111no—
325#385—111no—
326#385—111no—
327#380—111no—
328C4×C4⋊C4—111no—
329C4×C4⋊C4—111no—
330C4×C4⋊C4—111no—
331C4×C22⋊C4—111no—
332C4×C22⋊C4C2×D1111yescharacteristic
333#336—111no—
334#336—111no—
335#336—111no—
336#336—111no—
337#336—111no—
338#336—111no—
339#336—111no—
340#336—111no—
341#336C2×D1111yescharacteristic
342#336C2×D1111yescharacteristic
343C22×C11—22no—
344C22×C11—22no—
345C22×C11—22no—
346C22×C11—41no—
347C22×C11—41no—
348C22×C11—41no—
349C22×C11—41no—
350C22×C11C2×C4×D411yescharacteristic
351C22×C11C2×C4×Q811yescharacteristic
352C22×C11#52011yescharacteristic
353C22×C11C22×M1611yescharacteristic
354C22×C11C2×#13111yescharacteristic
355C22×C11C2×#13111yescharacteristic
356C22×C11#56811yescharacteristic
357C4×C11—22no—
358C4×C11—22no—
359C4×C11—41no—
360C4×C11—41no—
361C4×C11—41no—
362C4×C11#54611yescharacteristic
363C4×C11D4×Q811yescharacteristic
364C4×C11#55211yescharacteristic
365C4×C11#55411yescharacteristic
366Dic11—22no—
367Dic11—22no—
368Dic11—22no—
369Dic11—41no—
370Dic11—41no—
371Dic11—41no—
372Dic11—41no—
373Dic11#43614yes—
374C22×Q8—111no—
375C23×C4—111no—
376C23×C4—111no—
377C23×C4C22×D1111yescharacteristic
378C2×M16—22no—
379C2×M16—22no—
380C2×M16—41no—
381C2×M16—222no—
382C2×M16—222no—
383C2×M16—441no—
384C22×C8—111no—
385C22×C8—111no—
386C22×C8—111no—
387C22×C8—111no—
388C22×C8C22×D1111yescharacteristic
389C22×C8C22×D1111yescharacteristic
390C22×C8C22×D1111yescharacteristic
391C22×C8C22×D1111yescharacteristic
392C22⋊Q8—224no—
393C4×Q8—222no—
394C4×Q8—222no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—111no—
403C2×C4⋊C4—111no—
404C2×C22⋊C4—111no—
405C2×C22⋊C4—111no—
406C2×C22⋊C4C4×D1111yescharacteristic
407C2×C22⋊C4C4×D1111yescharacteristic
408C2×C42—111no—
409C2×C42—111no—
410C2×C42—111no—
411C2×C42—111no—
412C2×C42—111no—
413C2×C42—111no—
414C2×C42—222no—
415C2×C42—222no—
416C2×C42C22×D1111yescharacteristic
417C2×C42C22×D1111yescharacteristic
418C4⋊C8—114no—
419C4⋊C8—222no—
420C4⋊C8—222no—
421C4⋊C8—222no—
422C4⋊C8—222no—
423C4⋊C8—222no—
424C4⋊C8—441no—
425C4⋊C8—441no—
426C22⋊C8—222no—
427C22⋊C8Dic2214yescomplemented
428#97—22no—
429#97—222no—
430C4×C8—41no—
431C4×C8—222no—
432C4×C8—222no—
433C4×C8—441no—
434#95—111no—
435#95—111no—
436#95—111no—
437#95—111no—
438#95—111no—
439#95—111no—
440#95—111no—
441#95—111no—
442#95C4×D1111yescharacteristic
443#95C4×D1111yescharacteristic
444C2×C11—42no—
445C2×C11#236011yescharacteristic
446C2×C11C2×#43611yescharacteristic
447C2×C11#293311yescharacteristic
448C2×C11#296011yescharacteristic
449C2×C11Q8×M1611yescharacteristic
450C2×C11#299011yescharacteristic
451C2×C11#299311yescharacteristic
452C24C2×C4×D1111yescharacteristic
453C2×Q8—222no—
454C2×Q8—222no—
455C2×Q8—222no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—111no—
461C22×C4—111no—
462C22×C4—111no—
463C22×C4—111no—
464C22×C4—111no—
465C22×C4—111no—
466C22×C4—111no—
467C22×C4—111no—
468C22×C4—222no—
469C22×C4—222no—
470C22×C4—222no—
471C22×C4—222no—
472C22×C4—222no—
473C22×C4—441no—
474C22×C4C2×Dic2212yes—
475C22×C4C2×C4×D1111yescharacteristic
476C22×C4C2×C4×D1111yescharacteristic
477C22×C4C2×C4×D1111yescharacteristic
478C22×C4C2×C4×D1111yescharacteristic
479C22×C4C2×C4×D1111yescharacteristic
480C22×C4#433912yes—
481C22×C4C23×D1111yescharacteristic
482M16—44no—
483M16—444no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—112no—
494C2×C8—221no—
495C2×C8—221no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8—221no—
500C2×C8—221no—
501C2×C8—221no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8C2×Dic2212yes—
506C2×C8C2×Dic2212yes—
507C2×C8D4×D1112yes—
508C4⋊C4—114no—
509C4⋊C4—222no—
510C4⋊C4—222no—
511C4⋊C4—222no—
512C4⋊C4—222no—
513C4⋊C4—222no—
514C4⋊C4—222no—
515C4⋊C4—222no—
516C4⋊C4—222no—
517C22⋊C4—22no—
518C22⋊C4—41no—
519C22⋊C4—222no—
520C22⋊C4—441no—
521C42—21no—
522C42—21no—
523C42—21no—
524C42—21no—
525C42—112no—
526C42—112no—
527C42—222no—
528C42—222no—
529C42—221no—
530C42—221no—
531C42—221no—
532C42—221no—
533C42—221no—
534C42—221no—
535C11#2295711yescharacteristic, complemented, Sylow
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—21no—
542C23C4×Dic2212yes—
543C23C22×C4×D1111yescharacteristic
544Q8—444no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—112no—
563C2×C4—112no—
564C2×C4—112no—
565C2×C4—112no—
566C2×C4—112no—
567C2×C4—112no—
568C2×C4—221no—
569C2×C4—221no—
570C2×C4—221no—
571C2×C4—221no—
572C2×C4—221no—
573C2×C4—221no—
574C2×C4—221no—
575C2×C4—221no—
576C2×C4—221no—
577C2×C4—221no—
578C2×C4—221no—
579C2×C4—221no—
580C2×C4—221no—
581C2×C4—221no—
582C2×C4—221no—
583C2×C4—221no—
584C2×C4—221no—
585C2×C4—221no—
586C2×C4—444no—
587C2×C4—444no—
588C2×C4C4×Dic2212yes—
589C2×C4M16×D1112yes—
590C2×C4C22×Dic2211yescharacteristic
591C2×C4C2×#433911yescharacteristic
592C2×C4C2×D4×D1111yescharacteristic
593C2×C4#6703711yescharacteristic
594C2×C4#41×D1111yescharacteristic
595C2×C4#6704311yescharacteristic
596C8—22no—
597C8—22no—
598C8—22no—
599C8—41no—
600C8—222no—
601C8—441no—
602C8—441no—
603C8—441no—
604C22—22no—
605C22—22no—
606C22—22no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22C2×C4×Dic2211yescharacteristic
612C22C4×D4×D1111yescharacteristic
613C22#1062307711yescharacteristic
614C22C2×M16×D1111yescharacteristic
615C22#1062327611yescharacteristic
616C22D11×#13111yescharacteristic
617C22D11×#13111yescharacteristic
618C4—22no—
619C4—22no—
620C4—41no—
621C4—41no—
622C4—41no—
623C4—114no—
624C4—222no—
625C4—222no—
626C4—222no—
627C4—441no—
628C4—441no—
629C4—441no—
630C4—441no—
631C4#1062302111yescharacteristic
632C4#1062306211yescharacteristic
633C4D4×Dic2211yescharacteristic
634C4#1062307011yescharacteristic
635C2—42no—
636C2#1307162211yescharacteristic
637C2D11×#43611yescharacteristic
638C2#1307734511yescharacteristic
639C2#1307754811yescharacteristic
640C2M16×Dic2211yescharacteristic
641C2#1307773611yescharacteristic
642C2#1307775811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1753C2
prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenter#1753D11
hypocenterC11#22957
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1753

Complements

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

NH ≅ G/Ntype
1. C2×#10622314C2semidirect
4. #13069550C2semidirect
5. #13069334C2semidirect
6. #13069333C2semidirect
7. #13069333C2semidirect
8. #13069180C2semidirect
9. #13069179C2semidirect
12. C8×Dic11⋊C4C2semidirect
105. C11×C22⋊C8Q8semidirect
191. Dic11⋊C4M16semidirect
427. C22⋊C8Dic22semidirect
535. C11#22957semidirect

Maximal subgroups

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

subgroupindex
C2×#106223142
C2×#106227312
C4×#669312
#130695502
#130693342
#130693332
#130691802
#130691792
#130688012
#130687992
C8×Dic11⋊C42
#130684022
C22⋊C8×Dic112
C11×#17532
#2295711