Finite Group Databasebeta

← #14775504

Subgroups — #14775504

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×#10622450C211yesmaximal, characteristic
3C4×#66949C211yesmaximal, characteristic
4#13069550C211yesmaximal, characteristic, complemented
5#13069335C211yesmaximal, characteristic, complemented
6#13069333C211yesmaximal, characteristic, complemented
7#13069331C211yesmaximal, characteristic, complemented
8#13069183C211yesmaximal, characteristic, complemented
9#13068800C211yesmaximal, characteristic
10#13068800C211yesmaximal, characteristic
11#13068477C211yesmaximal, characteristic, complemented
12#13068401C211yesmaximal, characteristic
13#13068396C211yesmaximal, characteristic
14#13068373C211yesmaximal, characteristic
15C11×#1917C211yesmaximal, characteristic, complemented
16C22×#4313C2211yescharacteristic
17C22×#4313C2211yescharacteristic
18C2×#66949C411yescharacteristic
19C2×C42×D11C2211yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×#97C2211yescharacteristic
23C4×C11×C4⋊C4C2211yescharacteristic
24C2×(C2×D11)⋊C8C2211yescharacteristic
25C2×(C2×D11)⋊C8C2211yescharacteristic
26C2×#66879C2211yescharacteristic
27C2×Dic11⋊C8C2211yescharacteristic
28C2×Dic11⋊C8C2211yescharacteristic
29C2×Dic11⋊C8C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31C2×C8×Dic11C2211yescharacteristic
32C2×C8×Dic11C2211yescharacteristic
33C2×C8×Dic11C2211yescharacteristic
34#10622602C411yescharacteristic
35#10622594C411yescharacteristic
36#10622585C411yescharacteristic
37C4×(C2×D11)⋊C4C2211yescharacteristic
38C4×(C2×D11)⋊C4C2211yescharacteristic
39C4×Dic11⋊C4C2211yescharacteristic
40C4×Dic11⋊C4C2211yescharacteristic
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44C2×C4×C11⋊C8C2211yescharacteristic
45#10622450—24no—
46#10622314—24no—
47#10622281C411yescharacteristic
48#10622280C411yescharacteristic
49#10622265C411yescharacteristic
50#10622259C411yescharacteristic
51C11×#336C2211yescharacteristic
52C11×#336C2211yescharacteristic
53C11×#336C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×C4×D11C2×C411yescharacteristic
62C22×C4×D11C2×C411yescharacteristic
63C22×C4×D11C2311yescharacteristic
64C22×Dic22C2×C411yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C2×C11×C4⋊C4C2×C411yescharacteristic
70C2×C11×C4⋊C4C2×C411yescharacteristic
71C2×C42×C11C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×(C2×D11)⋊C4C2×C411yescharacteristic
75C2×(C2×D11)⋊C4C2×C411yescharacteristic
76C2×(C2×D11)⋊C4C2×C411yescharacteristic
77C2×(C2×D11)⋊C4C2×C411yescharacteristic
78C2×C4⋊Dic11C2×C411yescharacteristic
79C2×Dic11⋊C4C2×C411yescharacteristic
80C2×Dic11⋊C4C2×C411yescharacteristic
81C2×Dic11⋊C4C2×C411yescharacteristic
82C2×Dic11⋊C4C2×C411yescharacteristic
83C2×Dic11⋊C4C2×C411yescharacteristic
84C2×Dic11⋊C4C2×C411yescharacteristic
85C2×C4×Dic11C2×C411yescharacteristic
86C2×C4×Dic11C2×C411yescharacteristic
87C2×C4×Dic11C2311yescharacteristic
88C2×C4×Dic11C2311yescharacteristic
89C2×C4×Dic11C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C2×#4313—22no—
95C2×#4313—22no—
96C2×#4313—22no—
97C2×#4313—22no—
98C2×#4313—41no—
99C2×#4313—41no—
100#66949—24no—
101C42×D11—22no—
102C42×D11—22no—
103C4×Dic22—22no—
104C4×Dic22—22no—
105C11×C4⋊C8—22no—
106C11×#97—22no—
107C11×#95C2×C411yescharacteristic
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
117(C2×D11)⋊C8—22no—
118(C2×D11)⋊C8Q814yescomplemented
119#66879—22no—
120Dic11⋊C8—22no—
121Dic11⋊C8—22no—
122Dic11⋊C8—41no—
123Dic11⋊C8D414yes—
124C8×Dic11—22no—
125C8×Dic11—22no—
126C8×Dic11—41no—
127C4⋊(C11⋊C8)—22no—
128C4⋊(C11⋊C8)—22no—
129C4⋊(C11⋊C8)—41no—
130C4×C11⋊C8—41no—
131#22957—111nomaximal, Sylow
132C23×D11C22×C411yescharacteristic
133C22×C4×C11C22×C411yescharacteristic
134C22×C4×C11C22×C411yescharacteristic
135C22×C4×C11C22×C411yescharacteristic
136C22×C4×C11C22×C411yescharacteristic
137C22×C4×C11C22×C411yescharacteristic
138C22×C4×C11C22×C411yescharacteristic
139C22×C4×C11C2411yescharacteristic
140C22×Dic11C22×C411yescharacteristic
141C22×Dic11C22×C411yescharacteristic
142C22×Dic11C22×C411yescharacteristic
143C22×Dic11C22×C411yescharacteristic
144C22×Dic11C22×C411yescharacteristic
145C22×Dic11C22×C411yescharacteristic
146C22×Dic11C22×C411yescharacteristic
147C2×C4×D11—22no—
148C2×C4×D11—22no—
149C2×C4×D11—22no—
150C2×C4×D11—22no—
151C2×C4×D11—22no—
152C2×C4×D11—21no—
153C2×C4×D11—21no—
154C2×C4×D11—21no—
155C2×C4×D11—21no—
156C2×C4×D11—41no—
157C2×C4×D11C2×Q812yes—
158C2×C4×D11#4112yes—
159C2×Dic22—22no—
160C2×Dic22—22no—
161C2×Dic22—22no—
162C2×C8×C11—21no—
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—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—22no—
176C42×C11—21no—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11—21no—
181C42×C11—21no—
182(C2×D11)⋊C4—22no—
183(C2×D11)⋊C4—22no—
184(C2×D11)⋊C4—41no—
185(C2×D11)⋊C4—41no—
186C4⋊Dic11—22no—
187Dic11⋊C4—22no—
188Dic11⋊C4—22no—
189Dic11⋊C4—22no—
190Dic11⋊C4—22no—
191Dic11⋊C4—22no—
192Dic11⋊C4M1614yescomplemented
193C4×Dic11—22no—
194C4×Dic11—22no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C4×Dic11—21no—
198C4×Dic11—21no—
199C4×Dic11C2×D412yes—
200C4×Dic11#4112yes—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
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⋊C8C2×D412yes—
212C2×C11⋊C8C2×Q812yes—
213#4313—44no—
214#4313—44no—
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#1917D1111yescharacteristic, complemented
224#1851—111no—
225#1851—111no—
226C8×C4⋊C4—111no—
227#1753—111no—
228#1753—111no—
229C4×C22⋊C8—111no—
230C23×C11C23×C411yescharacteristic
231C22×D11—21no—
232C22×D11—21no—
233C22×D11—21no—
234C22×D11—21no—
235C22×D11—21no—
236C22×D11—21no—
237C22×D11C4×Q812yes—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
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×C11C2×M1612yes—
255C2×C4×C11#13112yes—
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C22×Q811yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×C4×C11H(5,𝔽2)11yescharacteristic
261C2×C4×C112−1+411yescharacteristic
262C2×Dic11—21no—
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×Dic11C4×D412yes—
278C2×Dic11C4×D412yes—
279C2×Dic11C4×Q812yes—
280C2×Dic11C2×M1612yes—
281C2×Dic11C2×M1612yes—
282C2×Dic11#13112yes—
283C4×D11—22no—
284C4×D11—22no—
285C4×D11—22no—
286C4×D11—22no—
287C4×D11—44no—
288C4×D11—44no—
289Dic22—44no—
290C8×C11—22no—
291C8×C11—22no—
292C8×C11—41no—
293C8×C11—41no—
294C11⋊C8—22no—
295C11⋊C8—22no—
296C11⋊C8—41no—
297C11⋊C8—41no—
298C22×M16—111no—
299C22×M16—111no—
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⋊C8C2×D1111yescharacteristic
313C2×C22⋊C8—111no—
314C2×C22⋊C8—111no—
315C2×#97—111no—
316C2×#97C2×D1111yescharacteristic
317C2×C4×C8—111no—
318C2×C4×C8—111no—
319C2×C4×C8—111no—
320C2×C4×C8—111no—
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⋊C4C2×D1111yescharacteristic
331C4×C22⋊C4—111no—
332C4×C22⋊C4—111no—
333#336—111no—
334#336—111no—
335#336—111no—
336#336—111no—
337#336—111no—
338#336—111no—
339#336C2×D1111yescharacteristic
340#336C2×D1111yescharacteristic
341#336C2×D1111yescharacteristic
342#336C2×D1111yescharacteristic
343C22×C11C2×C4×D411yescharacteristic
344C22×C11C2×C4×Q811yescharacteristic
345C22×C11#52011yescharacteristic
346C22×C11C22×M1611yescharacteristic
347C22×C11C2×#13111yescharacteristic
348C22×C11C2×#13111yescharacteristic
349C22×C11#56811yescharacteristic
350C2×D11—22no—
351C2×D11—22no—
352C2×D11—22no—
353C2×D11—41no—
354C2×D11—41no—
355C2×D11—41no—
356C2×D11—41no—
357C4×C11—22no—
358C4×C11—22no—
359C4×C11—41no—
360C4×C11—41no—
361C4×C11—41no—
362C4×C11—41no—
363C4×C11#54611yescharacteristic
364C4×C11D4×Q811yescharacteristic
365C4×C11#55211yescharacteristic
366C4×C11#55411yescharacteristic
367Dic11—22no—
368Dic11—22no—
369Dic11—22no—
370Dic11—41no—
371Dic11—41no—
372Dic11—41no—
373Dic11#43614yes—
374C22×Q8—111no—
375C23×C4—111no—
376C23×C4—111no—
377C23×C4—111no—
378C2×M16—222no—
379C2×M16—222no—
380C2×M16—222no—
381C2×M16—222no—
382C2×M16—441no—
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⋊C4C4×D1111yescharacteristic
403C2×C4⋊C4C4×D1111yescharacteristic
404C2×C22⋊C4—111no—
405C2×C22⋊C4—111no—
406C2×C22⋊C4—111no—
407C2×C22⋊C4—111no—
408C2×C42—111no—
409C2×C42—111no—
410C2×C42—111no—
411C2×C42—111no—
412C2×C42—111no—
413C2×C42—222no—
414C2×C42—222no—
415C2×C42C22×D1111yescharacteristic
416C2×C42C22×D1111yescharacteristic
417C2×C42C22×D1111yescharacteristic
418C4⋊C8—22no—
419C4⋊C8—114no—
420C4⋊C8—222no—
421C4⋊C8—222no—
422C4⋊C8—222no—
423C4⋊C8—222no—
424C4⋊C8—441no—
425C4⋊C8—441no—
426C22⋊C8—114no—
427C22⋊C8—222no—
428#97—22no—
429#97—222no—
430C4×C8—222no—
431C4×C8—222no—
432C4×C8—441no—
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#236011yescharacteristic
445C2×C11C2×#43611yescharacteristic
446C2×C11#293311yescharacteristic
447C2×C11#296011yescharacteristic
448C2×C11Q8×M1611yescharacteristic
449C2×C11#299011yescharacteristic
450C2×C11#299311yescharacteristic
451D11—42no—
452C24—111no—
453C2×Q8—222no—
454C2×Q8—222no—
455C2×Q8—222no—
456C22×C4—111no—
457C22×C4—111no—
458C22×C4—111no—
459C22×C4—111no—
460C22×C4—112no—
461C22×C4—112no—
462C22×C4—111no—
463C22×C4—111no—
464C22×C4—111no—
465C22×C4—222no—
466C22×C4—222no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4—221no—
470C22×C4—221no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—222no—
474C22×C4—441no—
475C22×C4C2×C4×D1111yescharacteristic
476C22×C4C2×C4×D1111yescharacteristic
477C22×C4C2×C4×D1111yescharacteristic
478C22×C4C2×C4×D1111yescharacteristic
479C22×C4C2×C4×D1111yescharacteristic
480C22×C4C2×C4×D1111yescharacteristic
481C22×C4C23×D1111yescharacteristic
482M16—444no—
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—21no—
494C2×C8—112no—
495C2×C8—112no—
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×C8—221no—
506C2×C8D4×D1112yes—
507C2×C8Q8×D1112yes—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—114no—
511C4⋊C4—222no—
512C4⋊C4—222no—
513C4⋊C4—222no—
514C4⋊C4—222no—
515C4⋊C4—222no—
516C4⋊C4—222no—
517C22⋊C4—222no—
518C22⋊C4—222no—
519C22⋊C4—441no—
520C22⋊C4—441no—
521C42—21no—
522C42—21no—
523C42—21no—
524C42—21no—
525C42—21no—
526C42—21no—
527C42—112no—
528C42—112no—
529C42—222no—
530C42—222no—
531C42—221no—
532C42—221no—
533C42—221no—
534C42—221no—
535C11#2295711yescharacteristic, complemented, Sylow
536C23—112no—
537C23—221no—
538C23—221no—
539C23—221no—
540C23—221no—
541C23—221no—
542C23—221no—
543C23C22×C4×D1111yescharacteristic
544Q8—444no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
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—112no—
562C2×C4—112no—
563C2×C4—112no—
564C2×C4—112no—
565C2×C4—112no—
566C2×C4—112no—
567C2×C4—221no—
568C2×C4—221no—
569C2×C4—221no—
570C2×C4—221no—
571C2×C4—221no—
572C2×C4—221no—
573C2×C4—222no—
574C2×C4—222no—
575C2×C4—222no—
576C2×C4—222no—
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×C4M16×D1112yes—
589C2×C4#6696012yes—
590C2×C4C2×D4×D1111yescharacteristic
591C2×C4C2×Q8×D1111yescharacteristic
592C2×C4#41×D1111yescharacteristic
593C2×C4#41×D1111yescharacteristic
594C2×C4#6704211yescharacteristic
595C2×C4#6704311yescharacteristic
596C8—22no—
597C8—22no—
598C8—41no—
599C8—41no—
600C8—222no—
601C8—222no—
602C8—441no—
603C8—441no—
604C22—222no—
605C22—222no—
606C22—222no—
607C22—441no—
608C22—441no—
609C22—441no—
610C22—441no—
611C22#1062305411yescharacteristic
612C22C4×D4×D1111yescharacteristic
613C22C4×Q8×D1111yescharacteristic
614C22C2×M16×D1111yescharacteristic
615C22C2×#6696011yescharacteristic
616C22D11×#13111yescharacteristic
617C22#1062328111yescharacteristic
618C4—22no—
619C4—22no—
620C4—41no—
621C4—41no—
622C4—41no—
623C4—41no—
624C4—114no—
625C4—222no—
626C4—222no—
627C4—222no—
628C4—441no—
629C4—441no—
630C4—441no—
631C4#1062316311yescharacteristic
632C4#1062318511yescharacteristic
633C4#1062322111yescharacteristic
634C4#1062323911yescharacteristic
635C2—442no—
636C2#1307162411yescharacteristic
637C2D11×#43611yescharacteristic
638C2#1307734211yescharacteristic
639C2#1307754711yescharacteristic
640C2#1307756811yescharacteristic
641C2#1307774311yescharacteristic
642C2#1307775911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1917C2
prime radicalC23×D11C22×C4
cosocleC22×C4×C11C24
hypercenter#1917D11
hypocenterC11#22957
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1917

Complements

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

NH ≅ G/Ntype
1. C2×#10622314C2semidirect
4. #13069550C2semidirect
5. #13069335C2semidirect
6. #13069333C2semidirect
7. #13069331C2semidirect
8. #13069183C2semidirect
11. #13068477C2semidirect
15. C11×#1917C2semidirect
118. (C2×D11)⋊C8Q8semidirect
192. Dic11⋊C4M16semidirect
223. #1917D11semidirect
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×#106224502
C4×#669492
#130695502
#130693352
#130693332
#130693312
#130691832
#130688002
#130684772
#130684012
#130683962
#130683732
C11×#19172
#2295711