Finite Group Databasebeta

← #14764277

Subgroups — #14764277

Order 2816.

774 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622333C211yesmaximal, characteristic
2C2×#10622732C211yesmaximal, characteristic
3#13071112C211yesmaximal, characteristic
4#13069336C211yesmaximal, characteristic, complemented
5#13069336C211yesmaximal, characteristic, complemented
6#13069333C211yesmaximal, characteristic, complemented
7#13069333C211yesmaximal, characteristic, complemented
8#13068799C211yesmaximal, characteristic
9#13068796C211yesmaximal, characteristic
10#13068793C211yesmaximal, characteristic
11#13068769C211yesmaximal, characteristic, complemented
12#13068767C211yesmaximal, characteristic, complemented
13#13068734C211yesmaximal, characteristic, complemented
14#13068731C211yesmaximal, characteristic, complemented
15C11×#1851C211yesmaximal, characteristic
16C22×C11×M16C2211yescharacteristic
17C2×#66979C2211yescharacteristic
18C23×C11⋊C8C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×C22⋊C8C2211yescharacteristic
22C4×C11×C22⋊C4C2211yescharacteristic
23C4×C22⋊Dic11C2211yescharacteristic
24C2×C22⋊(C11⋊C8)C2211yescharacteristic
25#10622732—24no—
26C2×#66879C2211yescharacteristic
27C2×Dic11⋊C8C2211yescharacteristic
28C2×Dic11⋊C8C2211yescharacteristic
29C2×Dic11⋊C8C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31C2×Dic11⋊C8C2211yescharacteristic
32C2×Dic11⋊C8C2211yescharacteristic
33C2×Dic11⋊C8C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35C2×Dic11⋊C8C2211yescharacteristic
36C2×Dic11⋊C8C2211yescharacteristic
37C2×C8×Dic11C2211yescharacteristic
38#10622558C411yescharacteristic
39#10622558C411yescharacteristic
40#10622557C411yescharacteristic
41#10622557C411yescharacteristic
42#10622545C2211yescharacteristic
43C4×Dic11⋊C4C2211yescharacteristic
44C4×Dic11⋊C4C2211yescharacteristic
45C42×Dic11C2211yescharacteristic
46C2×C4⋊(C11⋊C8)C2211yescharacteristic
47C2×C4⋊(C11⋊C8)C2211yescharacteristic
48#10622333—24no—
49#10622267C411yescharacteristic
50#10622267C411yescharacteristic
51#10622266C411yescharacteristic
52#10622266C411yescharacteristic
53C11×#336C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C2×C11×M16—22no—
63C2×C11×M16—41no—
64C2×C11×M16—41no—
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C2×C11×C22⋊C4C2×C411yescharacteristic
70C2×C11×C22⋊C4C2×C411yescharacteristic
71C2×C42×C11C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×C22⋊Dic11C2×C411yescharacteristic
74C2×C22⋊Dic11C2×C411yescharacteristic
75C2×C22⋊Dic11C2×C411yescharacteristic
76C2×C22⋊Dic11C2×C411yescharacteristic
77#66979D414yes—
78#66979Q814yes—
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×C4×Dic11C2×C411yescharacteristic
86C2×C4×Dic11C2×C411yescharacteristic
87C2×C4×Dic11C2×C411yescharacteristic
88C2×C4×Dic11C2×C411yescharacteristic
89C2×C4×Dic11C2311yescharacteristic
90C2×C4×Dic11C2311yescharacteristic
91C2×C4×Dic11C2311yescharacteristic
92C2×C4×Dic11C2311yescharacteristic
93C22×C11⋊C8—22no—
94C22×C11⋊C8—41no—
95C22×C11⋊C8—41no—
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C11×C4⋊C8—41no—
101C11×C4⋊C8—41no—
102C11×C22⋊C8—22no—
103C11×#95C2×C411yescharacteristic
104C11×#95C2×C411yescharacteristic
105C11⋊#95C2×C411yescharacteristic
106C11⋊#95C2×C411yescharacteristic
107C11⋊#95C2×C411yescharacteristic
108C11⋊#95C2×C411yescharacteristic
109C11⋊#95C2×C411yescharacteristic
110C11⋊#95C2×C411yescharacteristic
111C11⋊#95C2×C411yescharacteristic
112C11⋊#95C2×C411yescharacteristic
113C11⋊#95C2×C411yescharacteristic
114C11⋊#95C2×C411yescharacteristic
115C22⋊(C11⋊C8)—22no—
116#66879—22no—
117Dic11⋊C8—22no—
118Dic11⋊C8—22no—
119Dic11⋊C8—22no—
120Dic11⋊C8—22no—
121Dic11⋊C8—22no—
122Dic11⋊C8—22no—
123Dic11⋊C8—41no—
124Dic11⋊C8—41no—
125Dic11⋊C8—41no—
126Dic11⋊C8—41no—
127C8×Dic11—22no—
128C4⋊(C11⋊C8)—41no—
129C4⋊(C11⋊C8)—41no—
130#21980—111nomaximal, Sylow
131C24×C11C22×C411yescharacteristic
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11C22×C411yescharacteristic
137C22×C4×C11C22×C411yescharacteristic
138C22×C4×C11C22×C411yescharacteristic
139C22×C4×C11C22×C411yescharacteristic
140C22×C4×C11C22×C411yescharacteristic
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2×Q812yes—
143C22×C4×C11C2411yescharacteristic
144C22×Dic11C22×C411yescharacteristic
145C22×Dic11C22×C411yescharacteristic
146C22×Dic11C22×C411yescharacteristic
147C22×Dic11C22×C411yescharacteristic
148C22×Dic11C22×C411yescharacteristic
149C22×Dic11C22×C411yescharacteristic
150C22×Dic11C22×C411yescharacteristic
151C22×Dic11C22×C411yescharacteristic
152C11×M16—44no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C11×C22⋊C4—22no—
166C11×C22⋊C4—41no—
167C42×C11—21no—
168C42×C11—21no—
169C42×C11—21no—
170C42×C11—21no—
171C22⋊Dic11—22no—
172C22⋊Dic11—41no—
173C22⋊Dic11C4⋊C414yes—
174C22⋊Dic11C4⋊C414yes—
175C4⋊Dic11C4⋊C414yes—
176C4⋊Dic11C4⋊C414yes—
177Dic11⋊C4—22no—
178Dic11⋊C4—22no—
179Dic11⋊C4—41no—
180Dic11⋊C4—41no—
181C4×Dic11—22no—
182C4×Dic11—22no—
183C4×Dic11—21no—
184C4×Dic11—21no—
185C4×Dic11—21no—
186C4×Dic11—21no—
187C4×Dic11—41no—
188C4×Dic11—41no—
189C4×Dic11C2×D412yes—
190C4×Dic11C2×D412yes—
191C4×Dic11C2×Q812yes—
192C4×Dic11C2×Q812yes—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—44no—
206C2×#433—111no—
207C2×#424—111no—
208#2298—111no—
209#1940—111no—
210#1940—111no—
211#1939—111no—
212#1939—111no—
213#1851—111no—
214#1851D1111yescharacteristic
215#1850—111no—
216#1850—111no—
217#1843—111no—
218#1842—111no—
219#1832—111no—
220#1831—111no—
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—21no—
224C23×C11—21no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11C2×C4⋊C412yes—
228C23×C11C23×C411yescharacteristic
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—21no—
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×C11C2×C4⋊C412yes—
247C2×C4×C11#13112yes—
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C22×Q811yescharacteristic
250C2×C4×C11H(5,𝔽2)11yescharacteristic
251C2×C4×C11H(5,𝔽2)11yescharacteristic
252C2×C4×C112−1+411yescharacteristic
253C2×C4×C112−1+411yescharacteristic
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
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×Dic11C2×C4⋊C412yes—
274C2×Dic11C2×C4⋊C412yes—
275C2×Dic11C2×C4⋊C412yes—
276C2×Dic11C2×C4⋊C412yes—
277C2×Dic11#13112yes—
278C8×C11—41no—
279C8×C11—41no—
280C8×C11—41no—
281C8×C11—41no—
282C11⋊C8—41no—
283C11⋊C8—41no—
284C11⋊C8—41no—
285C11⋊C8—41no—
286C22×M16C2×D1111yescharacteristic
287C23×C8—111no—
288C2×#117—111no—
289#433—224no—
290#424—224no—
291C2×C4⋊C8—111no—
292C2×C4⋊C8—111no—
293C2×C4⋊C8—111no—
294C2×C4⋊C8—111no—
295C2×C4⋊C8—111no—
296C2×C4⋊C8—111no—
297C2×C4⋊C8—111no—
298C2×C4⋊C8—111no—
299C2×C4⋊C8—111no—
300C2×C4⋊C8—111no—
301C2×C4⋊C8—111no—
302C2×C4⋊C8—111no—
303C2×C4⋊C8C2×D1111yescharacteristic
304C2×C4⋊C8C2×D1111yescharacteristic
305C2×C22⋊C8—111no—
306C2×C22⋊C8C2×D1111yescharacteristic
307C2×#97—111no—
308C2×C4×C8—111no—
309#388—111no—
310#388—111no—
311#388—111no—
312#388—111no—
313#387—111no—
314#387—111no—
315#387—111no—
316#387—111no—
317C4×C4⋊C4—111no—
318C4×C4⋊C4—111no—
319C4×C22⋊C4—111no—
320C4×C22⋊C4C2×D1111yescharacteristic
321#376—111no—
322C43—111no—
323#336—111no—
324#336—111no—
325#336—111no—
326#336—111no—
327#336—111no—
328#336—111no—
329#336C2×D1111yescharacteristic
330#336C2×D1111yescharacteristic
331C22×C11—22no—
332C22×C11—22no—
333C22×C11—22no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11—41no—
338C22×C11C22×C4⋊C411yescharacteristic
339C22×C11#52011yescharacteristic
340C22×C11#52011yescharacteristic
341C22×C11C2×#13111yescharacteristic
342C22×C11C2×#13111yescharacteristic
343C22×C11#56811yescharacteristic
344C22×C11#56811yescharacteristic
345C4×C11—22no—
346C4×C11—22no—
347C4×C11—41no—
348C4×C11—41no—
349C4×C11—41no—
350C4×C11#53511yescharacteristic
351C4×C11#53611yescharacteristic
352C4×C11#54411yescharacteristic
353C4×C11#54411yescharacteristic
354Dic11—22no—
355Dic11—22no—
356Dic11—22no—
357Dic11—22no—
358Dic11—22no—
359Dic11—41no—
360Dic11—41no—
361Dic11—41no—
362C23×C4C22×D1111yescharacteristic
363C2×M16—22no—
364C2×M16—41no—
365C2×M16—41no—
366C22×C8—111no—
367C22×C8—111no—
368C22×C8—111no—
369C22×C8—111no—
370C22×C8—222no—
371C22×C8—441no—
372C22×C8—441no—
373C22×C8C22×D1111yescharacteristic
374C22×C8C22×D1111yescharacteristic
375C22×C8C22×D1111yescharacteristic
376C22×C8C22×D1111yescharacteristic
377#117—114no—
378#117—114no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—111no—
384C2×C4⋊C4—111no—
385C2×C22⋊C4—111no—
386C2×C22⋊C4—111no—
387C2×C22⋊C4—111no—
388C2×C22⋊C4—111no—
389C2×C22⋊C4C4×D1111yescharacteristic
390C2×C22⋊C4C4×D1111yescharacteristic
391C2×C42—111no—
392C2×C42—111no—
393C2×C42—111no—
394C2×C42—111no—
395C2×C42—111no—
396C2×C42—111no—
397C2×C42—111no—
398C2×C42—111no—
399C2×C42C22×D1111yescharacteristic
400C2×C42C22×D1111yescharacteristic
401C4⋊C8—41no—
402C4⋊C8—41no—
403C4⋊C8—222no—
404C4⋊C8—222no—
405C4⋊C8—222no—
406C4⋊C8—222no—
407C4⋊C8—222no—
408C4⋊C8—222no—
409C4⋊C8—441no—
410C4⋊C8—441no—
411C4⋊C8—441no—
412C4⋊C8—441no—
413C4⋊C8—441no—
414C4⋊C8—441no—
415C22⋊C8—22no—
416C22⋊C8—222no—
417#97—222no—
418C4×C8—222no—
419#95—111no—
420#95—111no—
421#95—111no—
422#95—111no—
423#95—111no—
424#95—111no—
425#95—111no—
426#95—111no—
427#95—111no—
428#95—111no—
429#95C4×D1111yescharacteristic
430#95C4×D1111yescharacteristic
431C2×C11—42no—
432C2×C11#231711yescharacteristic
433C2×C11#290611yescharacteristic
434C2×C11#290611yescharacteristic
435C2×C11#299211yescharacteristic
436C2×C11#299311yescharacteristic
437C2×C11#299411yescharacteristic
438C2×C11#299511yescharacteristic
439C24C2×C4×D1111yescharacteristic
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—111no—
445C22×C4—111no—
446C22×C4—111no—
447C22×C4—111no—
448C22×C4—111no—
449C22×C4—111no—
450C22×C4—111no—
451C22×C4—111no—
452C22×C4C2×C4×D1111yescharacteristic
453C22×C4C2×C4×D1111yescharacteristic
454C22×C4C2×C4×D1111yescharacteristic
455C22×C4C2×C4×D1111yescharacteristic
456C22×C4C2×C4×D1111yescharacteristic
457C22×C4D4×D1112yes—
458C22×C4Q8×D1112yes—
459C22×C4C23×D1111yescharacteristic
460M16—44no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—221no—
474C2×C8—221no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8—221no—
480C2×C8—221no—
481C2×C8—221no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8—444no—
486C4⋊C4—114no—
487C4⋊C4—114no—
488C4⋊C4—222no—
489C4⋊C4—222no—
490C4⋊C4—441no—
491C4⋊C4—441no—
492C22⋊C4—22no—
493C22⋊C4—41no—
494C22⋊C4—114no—
495C22⋊C4—114no—
496C22⋊C4—222no—
497C22⋊C4—441no—
498C42—21no—
499C42—21no—
500C42—21no—
501C42—21no—
502C42—112no—
503C42—112no—
504C42—112no—
505C42—112no—
506C42—222no—
507C42—222no—
508C42—221no—
509C42—221no—
510C42—221no—
511C42—221no—
512C42—441no—
513C42—441no—
514C11#2198011yescharacteristic, complemented, Sylow
515C23—21no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23C4⋊C4×D1112yes—
522C23C22×C4×D1111yescharacteristic
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—112no—
541C2×C4—112no—
542C2×C4—112no—
543C2×C4—112no—
544C2×C4—112no—
545C2×C4—221no—
546C2×C4—221no—
547C2×C4—221no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—221no—
555C2×C4—221no—
556C2×C4—221no—
557C2×C4—221no—
558C2×C4—221no—
559C2×C4—221no—
560C2×C4—221no—
561C2×C4—221no—
562C2×C4—221no—
563C2×C4—221no—
564C2×C4C4⋊C4×D1112yes—
565C2×C4#6696012yes—
566C2×C4C2×D4×D1111yescharacteristic
567C2×C4#6703711yescharacteristic
568C2×C4#6703711yescharacteristic
569C2×C4C2×Q8×D1111yescharacteristic
570C2×C4#6704311yescharacteristic
571C2×C4#6704311yescharacteristic
572C8—41no—
573C8—41no—
574C8—41no—
575C8—41no—
576C8—441no—
577C8—441no—
578C8—441no—
579C8—441no—
580C22—22no—
581C22—22no—
582C22—22no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22C2×C4⋊C4×D1111yescharacteristic
588C22#1062307711yescharacteristic
589C22#1062307711yescharacteristic
590C22C2×#6696011yescharacteristic
591C22#1062327611yescharacteristic
592C22D11×#13111yescharacteristic
593C22#1062328111yescharacteristic
594C4—22no—
595C4—22no—
596C4—41no—
597C4—41no—
598C4—41no—
599C4—222no—
600C4—222no—
601C4—222no—
602C4—222no—
603C4—222no—
604C4—441no—
605C4—441no—
606C4—441no—
607C4#1062312311yescharacteristic
608C4#1062315411yescharacteristic
609C4#1062315411yescharacteristic
610C4#1062317911yescharacteristic
611C2—42no—
612C2#1307123511yescharacteristic
613C2#1307718311yescharacteristic
614C2#1307718511yescharacteristic
615C2#1307775611yescharacteristic
616C2#1307776211yescharacteristic
617C2#1307777711yescharacteristic
618C2#1307778211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1851C2
prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenter#1851D11
hypocenterC11#21980
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1851

Complements

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

NH ≅ G/Ntype
4. #13069336C2semidirect
5. #13069336C2semidirect
6. #13069333C2semidirect
7. #13069333C2semidirect
11. #13068769C2semidirect
12. #13068767C2semidirect
13. #13068734C2semidirect
14. #13068731C2semidirect
514. C11#21980semidirect

Maximal subgroups

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

subgroupindex
C2×#106223332
C2×#106227322
#130711122
#130693362
#130693332
#130687992
#130687962
#130687932
#130687692
#130687672
#130687342
#130687312
C11×#18512
#2198011