Finite Group Databasebeta

← #14772147

Subgroups — #14772147

Order 2816.

906 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622797C211yesmaximal, characteristic
2C2×Q16×Dic11C211yesmaximal, characteristic
3#13071534C211yesmaximal, characteristic
4Q8×Dic11⋊C4C211yesmaximal, characteristic
5#13069359C211yesmaximal, characteristic
6#13069342C211yesmaximal, characteristic
7#13068884C211yesmaximal, characteristic
8#13068882C211yesmaximal, characteristic
9#13068870C211yesmaximal, characteristic
10#13068868C211yesmaximal, characteristic
11#13068781C211yesmaximal, characteristic
12#13068629C211yesmaximal, characteristic
13#13068619C211yesmaximal, characteristic
14#13068492C211yesmaximal, characteristic
15C2×C11×#441C211yesmaximal, characteristic
16C22×C11×Q16C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×Q8×Dic11C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21C2×Q8×Dic11C2211yescharacteristic
22C2×Q8×Dic11C2211yescharacteristic
23C11×#441—24no—
24C2×C11×#106C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×#97C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32#10622797C418yescomplemented
33Q16×Dic11—24no—
34C2×#66882C2211yescharacteristic
35C2×#66881C2211yescharacteristic
36C2×#66879C2211yescharacteristic
37C2×Dic11⋊C8C2211yescharacteristic
38C2×C8×Dic11C2211yescharacteristic
39#10622590—21no—
40#10622590C2211yescharacteristic
41#10622589—21no—
42#10622589C2211yescharacteristic
43#10622586—21no—
44#10622586—21no—
45#10622586C2211yescharacteristic
46#10622586C2211yescharacteristic
47C2×#66872C2211yescharacteristic
48C2×#66871C2211yescharacteristic
49C4×Dic11⋊C4—21no—
50C4×Dic11⋊C4—21no—
51C4×Dic11⋊C4C2211yescharacteristic
52#10622541—21no—
53#10622541—21no—
54#10622541C2211yescharacteristic
55#10622541C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622162C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C2×C11×Q16C2×C414yes—
65C2×C11×Q16D414yes—
66C2×C11×Q16Q814yes—
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C4×Q8×C11—22no—
70C4×Q8×C11—22no—
71C4×Q8×C11—41no—
72C4×Q8×C11—41no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C42×C11—21no—
78C2×C42×C11—21no—
79C2×C42×C11C2311yescharacteristic
80Q8×Dic11—22no—
81Q8×Dic11—22no—
82Q8×Dic11—22no—
83Q8×Dic11—22no—
84Q8×Dic11—41no—
85Q8×Dic11—41no—
86Q8×Dic11C2×C414yes—
87Q8×Dic11C2×C414yes—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4D411yescharacteristic
103C2×Dic11⋊C4D411yescharacteristic
104C2×C4×Dic11—21no—
105C2×C4×Dic11—21no—
106C2×C4×Dic11—21no—
107C2×C4×Dic11—21no—
108C2×C4×Dic11C2311yescharacteristic
109C2×C4×Dic11C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112C11×#106—22no—
113C11×#103—22no—
114C11×#103—22no—
115C11×#97—22no—
116#66899—22no—
117#66899—22no—
118#66899C2×C414yes—
119#66899C2×C414yes—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95D411yescharacteristic
127C11⋊#95D411yescharacteristic
128#66882—22no—
129#66881C2×C414yes—
130#66879C2×C414yes—
131Dic11⋊C8—22no—
132C8×Dic11—22no—
133#66872—41no—
134#66871—41no—
135#22679—111nomaximal, Sylow
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11C22×C412yes—
143C2×Q8×C11C22×C412yes—
144C2×Q8×C11C2×D412yes—
145C2×Q8×C11C2×D412yes—
146C2×Q8×C11C2×Q812yes—
147C2×Q8×C11C2×Q812yes—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2411yescharacteristic
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11C2×D411yescharacteristic
160C22×Dic11C2×D411yescharacteristic
161C22×Dic11C2×D411yescharacteristic
162C22×Dic11C2×D411yescharacteristic
163C11×Q16C4⋊C4116yescomplemented
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11C22×C412yes—
168C2×C8×C11C2×D412yes—
169C2×C8×C11C2×Q812yes—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—42no—
175C11×C4⋊C4—42no—
176C42×C11—21no—
177C42×C11—21no—
178C42×C11—42no—
179C42×C11—42no—
180C4⋊Dic11—24no—
181C4⋊Dic11—24no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—42no—
189C4⋊Dic11—42no—
190C4⋊Dic11C22×C412yes—
191C4⋊Dic11C22×C412yes—
192Dic11⋊C4—22no—
193Dic11⋊C4—41no—
194Dic11⋊C4—42no—
195Dic11⋊C4—42no—
196Dic11⋊C4—42no—
197Dic11⋊C4—81no—
198Dic11⋊C4—81no—
199Dic11⋊C4—81no—
200C4×Dic11—24no—
201C4×Dic11—24no—
202C4×Dic11—21no—
203C4×Dic11—21no—
204C4×Dic11—42no—
205C4×Dic11—42no—
206C4×Dic11C22×C412yes—
207C4×Dic11#4112yes—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8C22×C412yes—
214C2×#441—111no—
215C2×#441D1111yescharacteristic
216C2×C4×Q16—111no—
217#2351—111no—
218Q8×C4⋊C4—111no—
219#1944—111no—
220#1941—111no—
221#1865—111no—
222#1865—111no—
223#1863—111no—
224#1863—111no—
225#1847—111no—
226#1805—111no—
227#1803—111no—
228#1771—111no—
229C23×C11C22×D411yescharacteristic
230Q8×C11—22no—
231Q8×C11—22no—
232Q8×C11—22no—
233Q8×C11—22no—
234Q8×C11—22no—
235Q8×C11—22no—
236Q8×C11C2×C4⋊C414yes—
237Q8×C11C2×C4⋊C414yes—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
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—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11C23×C411yescharacteristic
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C22×Q811yescharacteristic
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—22no—
269C2×Dic11—22no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11C4×D412yes—
284C2×Dic11C4×D412yes—
285C2×Dic11#13712yes—
286C8×C11—41no—
287C8×C11C2×C4⋊C414yes—
288C11⋊C8—22no—
289C11⋊C8—41no—
290C22×Q16C2×D1111yescharacteristic
291C2×C4×Q8—111no—
292C2×C4×Q8—111no—
293C2×C4×Q8—111no—
294C2×C4×Q8—111no—
295C2×C4×Q8C2×D1111yescharacteristic
296C2×C4×Q8C2×D1111yescharacteristic
297#441—24no—
298#441—118no—
299C4×Q16—224no—
300C2×#107—111no—
301C2×#107—111no—
302C2×#106—111no—
303C2×#106—111no—
304C2×#106C2×D1111yescharacteristic
305C2×C4⋊C8—111no—
306C2×#103—111no—
307C2×#103—111no—
308C2×#103—111no—
309C2×#103—111no—
310C2×#103C2×D1111yescharacteristic
311C2×#103C2×D1111yescharacteristic
312C2×#97—111no—
313C2×#97C2×D1111yescharacteristic
314C2×C4×C8—111no—
315#389—111no—
316#389—111no—
317#389—111no—
318#389—111no—
319#389—221no—
320#389—221no—
321#389—221no—
322#389—221no—
323#384—111no—
324#384—221no—
325#382—111no—
326#382—221no—
327C4×C4⋊C4—111no—
328C4×C4⋊C4—221no—
329C4×C4⋊C4—221no—
330#340—111no—
331#340—111no—
332#340—111no—
333#340—111no—
334#336—111no—
335#336—111no—
336C22×C11C2×C4×D411yescharacteristic
337C22×C11D4211yescharacteristic
338C22×C11D4×Q811yescharacteristic
339C22×C11C2×#13711yescharacteristic
340C22×C11#57511yescharacteristic
341C22×C11#57711yescharacteristic
342C22×C11#57811yescharacteristic
343C4×C11—24no—
344C4×C11—24no—
345C4×C11—41no—
346C4×C11—41no—
347C4×C11—81no—
348C4×C11—81no—
349C4×C11C22×C4⋊C411yescharacteristic
350C4×C11#52011yescharacteristic
351C4×C11#54711yescharacteristic
352C4×C11#55411yescharacteristic
353Dic11—22no—
354Dic11—22no—
355Dic11—22no—
356Dic11—42no—
357Dic11—42no—
358Dic11—41no—
359Dic11—81no—
360Dic11—81no—
361C22×Q8C22×D1111yescharacteristic
362C22×Q8C22×D1111yescharacteristic
363C2×Q16Dic2214yes—
364C2×Q16C4×D1114yes—
365C2×Q16C22⋊D1114yes—
366C22×C8—111no—
367C22×C8—111no—
368C22×C8C22×D1111yescharacteristic
369C22×C8C22×D1111yescharacteristic
370C4×Q8—22no—
371C4×Q8—22no—
372C4×Q8—41no—
373C4×Q8—41no—
374C4×Q8—114no—
375C4×Q8—114no—
376C4×Q8—222no—
377C4×Q8—222no—
378C4×Q8—222no—
379C4×Q8—222no—
380C4×Q8—441no—
381C4×Q8—441no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—111no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—111no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4—221no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4—221no—
400C2×C4⋊C4C22×D1111yescharacteristic
401C2×C4⋊C4C22×D1111yescharacteristic
402C2×C42—21no—
403C2×C42—21no—
404C2×C42—111no—
405C2×C42—111no—
406C2×C42—221no—
407C2×C42—221no—
408C2×C42—221no—
409C2×C42—221no—
410C2×C42C22×D1111yescharacteristic
411#107—222no—
412#107—441no—
413#106—22no—
414#106—114no—
415#106—441no—
416C4⋊C8—222no—
417#103—22no—
418#103—22no—
419#103—114no—
420#103—114no—
421#103—222no—
422#103—222no—
423#97—22no—
424#97—114no—
425C4×C8—222no—
426#95—111no—
427#95—111no—
428#95—221no—
429#95—221no—
430#95—221no—
431#95—221no—
432#95—221no—
433#95—221no—
434C2×C11D4×C4⋊C411yescharacteristic
435C2×C11C4×#13711yescharacteristic
436C2×C11#294711yescharacteristic
437C2×C11#327011yescharacteristic
438C2×C11#327111yescharacteristic
439C2×C11#338711yescharacteristic
440C2×C11#339011yescharacteristic
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8C2×Dic2212yes—
448C2×Q8C2×Dic2212yes—
449C2×Q8C2×C4×D1112yes—
450C2×Q8C2×C4×D1112yes—
451C2×Q8C2×C22⋊D1112yes—
452C2×Q8C2×C22⋊D1112yes—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—111no—
458C22×C4—111no—
459C22×C4—111no—
460C22×C4—111no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4—221no—
465C22×C4D4×D1111yescharacteristic
466C22×C4D4×D1111yescharacteristic
467C22×C4C23×D1111yescharacteristic
468Q16Dic11⋊C4116yescomplemented
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—112no—
473C2×C8—221no—
474C2×C8—221no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8C2×Dic2212yes—
479C2×C8C2×C4×D1112yes—
480C2×C8C2×C22⋊D1112yes—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—42no—
486C4⋊C4—42no—
487C4⋊C4—112no—
488C4⋊C4—112no—
489C4⋊C4—222no—
490C4⋊C4—224no—
491C4⋊C4—224no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—441no—
499C4⋊C4—442no—
500C4⋊C4—442no—
501C4⋊C4—442no—
502C4⋊C4—442no—
503C4⋊C4—442no—
504C4⋊C4—881no—
505C4⋊C4—881no—
506C4⋊C4—881no—
507C42—21no—
508C42—21no—
509C42—42no—
510C42—42no—
511C42—112no—
512C42—112no—
513C42—224no—
514C42—224no—
515C42—221no—
516C42—221no—
517C42—442no—
518C42—442no—
519C11#2267911yescharacteristic, complemented, Sylow
520C23C2×D4×D1111yescharacteristic
521Q8—22no—
522Q8—22no—
523Q8—22no—
524Q8—22no—
525Q8—22no—
526Q8—22no—
527Q8C2×Dic11⋊C414yes—
528Q8C2×Dic11⋊C414yes—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—112no—
548C2×C4—112no—
549C2×C4—112no—
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—222no—
559C2×C4—222no—
560C2×C4—221no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4C22×Dic2211yescharacteristic
572C2×C4C22×C4×D1111yescharacteristic
573C2×C4#6703711yescharacteristic
574C2×C4#41×D1111yescharacteristic
575C2×C4#6704311yescharacteristic
576C2×C4C22×C22⋊D1111yescharacteristic
577C8—41no—
578C8—222no—
579C8—441no—
580C8C2×Dic11⋊C414yes—
581C22D4×Dic2211yescharacteristic
582C22C4×D4×D1111yescharacteristic
583C22D11×#13711yescharacteristic
584C22#1062330811yescharacteristic
585C22#1062330911yescharacteristic
586C22#1062331011yescharacteristic
587C22D4×C22⋊D1111yescharacteristic
588C4—24no—
589C4—24no—
590C4—41no—
591C4—41no—
592C4—81no—
593C4—81no—
594C4—222no—
595C4—222no—
596C4—222no—
597C4—441no—
598C4—442no—
599C4—442no—
600C4—881no—
601C4—881no—
602C4#1062307011yescharacteristic
603C4#1062307711yescharacteristic
604C4C22×Dic11⋊C411yescharacteristic
605C4#1062335511yescharacteristic
606C2D4×Dic11⋊C411yescharacteristic
607C2#1307743211yescharacteristic
608C2#1307745811yescharacteristic
609C2#1308018011yescharacteristic
610C2#1308019511yescharacteristic
611C2#1308154911yescharacteristic
612C2#1308158411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#441C2
socle, prime radicalC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenterC2×#441D11
hypocenterC11#22679
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
32. #10622797C4semidirect
163. C11×Q16C4⋊C4semidirect
468. Q16Dic11⋊C4semidirect
519. C11#22679semidirect

Maximal subgroups

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

subgroupindex
C2×#106227972
C2×Q16×Dic112
#130715342
Q8×Dic11⋊C42
#130693592
#130693422
#130688842
#130688822
#130688702
#130688682
#130687812
#130686292
#130686192
#130684922
C2×C11×#4412
#2267911