Finite Group Databasebeta

← #14816690

Subgroups — #14816690

Order 2816.

896 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622679C211yesmaximal, characteristic, complemented
2C2×#10622608C211yesmaximal, characteristic, complemented
3#13071630C211yesmaximal, characteristic
4#13070150C211yesmaximal, characteristic, complemented
5#13070117C211yesmaximal, characteristic, complemented
6#13070001C211yesmaximal, characteristic, complemented
7#13069951C211yesmaximal, characteristic, complemented
8#13069377C211yesmaximal, characteristic, complemented
9#13069184C211yesmaximal, characteristic, complemented
10#13069052C211yesmaximal, characteristic
11#13068938C211yesmaximal, characteristic
12#13068876C211yesmaximal, characteristic, complemented
13#13068808C211yesmaximal, characteristic, complemented
14#13068801C211yesmaximal, characteristic, complemented
15C11×#2441C211yesmaximal, characteristic, complemented
16C2×C11×#125C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C2×#66983C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C22×#4318C2211yescharacteristic
21C2×(C22⋊D11)⋊C4—21no—
22C2×C4×D44C2211yescharacteristic
23C11×#399—21no—
24C11×#396—21no—
25C11×#389—21no—
26C11×#389C2211yescharacteristic
27C11×#389C2211yescharacteristic
28C11×#387—21no—
29C11×#384C2211yescharacteristic
30C11×#380C2211yescharacteristic
31C4×C11×C22⋊C4C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33#10622679—24no—
34#10622608—24no—
35C2×#66873C2211yescharacteristic
36C2×#66873C2211yescharacteristic
37C2×#66873C2211yescharacteristic
38C2×#66873C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40C2×#66872C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45#10622571—21no—
46#10622552C2211yescharacteristic
47C4×C4⋊Dic11C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51#10622283—21no—
52#10622281—21no—
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11—21no—
63C23×Dic11—21no—
64C22×D44C2311yescharacteristic
65C22×C4×D11—21no—
66C11×#125—22no—
67C11×#125—41no—
68C11×#117—22no—
69C11×#117—41no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4D411yescharacteristic
83C2×C11×C22⋊C4D411yescharacteristic
84C2×C42×C11—21no—
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2311yescharacteristic
87#66983—22no—
88#66983Q814yes—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93C2×C4⋊Dic11—22no—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11—41no—
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×Dic11⋊C4—21no—
100C2×C4×Dic11—21no—
101C2×#4318—22no—
102C2×#4318—22no—
103C2×#4318—22no—
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108(C22⋊D11)⋊C4—44no—
109C4×D44—22no—
110C4×D44—41no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95—21no—
114C11×#95D411yescharacteristic
115C11×#95D411yescharacteristic
116C11⋊#95—21no—
117C11⋊#95—21no—
118C22⋊(C11⋊C8)—22no—
119#66873—22no—
120#66873—22no—
121#66873—22no—
122#66873—41no—
123#66872—22no—
124#66872—22no—
125#66872—22no—
126#66872—41no—
127#66871—22no—
128#66871D414yescomplemented
129C4⋊(C11⋊C8)—22no—
130C4⋊(C11⋊C8)—22no—
131#26366—111nomaximal, Sylow
132C24×C11C2×D411yescharacteristic
133C23×D11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×Q812yes—
148C22×C4×C11#4112yes—
149C22×C4×C11C2411yescharacteristic
150C2×C22⋊D11—24no—
151C2×C22⋊D11—42no—
152C2×C22⋊D11—42no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—42no—
157C22×Dic11—42no—
158C22×Dic11—81no—
159C2×D44—21no—
160C2×D44—21no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44C2×Q812yes—
165C2×C4×D11—42no—
166C2×C4×D11—42no—
167C2×C4×D11—81no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—42no—
176C11×C4⋊C4—42no—
177C11×C4⋊C4—42no—
178C11×C4⋊C4—42no—
179C11×C4⋊C4—81no—
180C11×C4⋊C4—81no—
181C11×C4⋊C4C2×D412yes—
182C11×C22⋊C4—22no—
183C11×C22⋊C4—41no—
184C11×C22⋊C4—42no—
185C11×C22⋊C4—81no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—21no—
190C42×C11—42no—
191(C2×D11)⋊C4—24no—
192(C2×D11)⋊C4—42no—
193(C2×D11)⋊C4—42no—
194(C2×D11)⋊C4—81no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—42no—
200C4⋊Dic11C2×D412yes—
201C4⋊Dic11C2×Q812yes—
202Dic11⋊C4—42no—
203C4×Dic11—42no—
204#4318—28no—
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⋊C8—21no—
215C2×C11⋊C8C2×D412yes—
216C2×C11⋊C8#4112yes—
217C2×#478—111no—
218C2×#428—111no—
219#2441D1111yescharacteristic, complemented
220#2361—111no—
221#2094—111no—
222#2088—111no—
223#2067—111no—
224#2059—111no—
225#1948—111no—
226#1918—111no—
227#1895—111no—
228#1875—111no—
229#1864—111no—
230#1853—111no—
231#1851—111no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11C22⋊Q812yes—
239C23×C11C22×D411yescharacteristic
240C22×D11—22no—
241C22×D11—41no—
242C22×D11—41no—
243C22×D11—41no—
244C22×D11—41no—
245C22×D11—41no—
246C22×D11—41no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—22no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11C22⋊Q812yes—
277C2×C4×C11AGL(1,ℤ/8)12yes—
278C2×C4×C11C22×D411yescharacteristic
279C2×C4×C11C22×Q811yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11H(5,𝔽2)11yescharacteristic
283C2×C4×C112−1+411yescharacteristic
284C22⋊D11—48no—
285C2×Dic11—22no—
286C2×Dic11—22no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—84no—
295D44—22no—
296D44—22no—
297D44—41no—
298D44—41no—
299C4×D11—84no—
300C11⋊C8—22no—
301C11⋊C8—22no—
302C11⋊C8—41no—
303C11⋊C8—41no—
304C22×M16—111no—
305C2×#125C2×D1111yescharacteristic
306C2×#121—111no—
307C2×C4×D4—111no—
308C2×C4×D4—221no—
309C2×#117C2×D1111yescharacteristic
310C22×C4⋊C4—111no—
311#478—224no—
312#428—224no—
313C2×#107—111no—
314C2×#107—111no—
315C2×#106—111no—
316C2×#106—111no—
317C2×#106—111no—
318C2×#106—111no—
319C2×C4⋊C8—111no—
320C2×C4⋊C8—111no—
321C2×#102—111no—
322C2×#102—111no—
323C2×#102—111no—
324C2×#102—111no—
325C2×C22⋊C8—111no—
326#399—21no—
327#396—21no—
328#390—111no—
329#389—21no—
330#389—111no—
331#389C2×D1111yescharacteristic
332#389C2×D1111yescharacteristic
333#388—221no—
334#387—21no—
335#386—221no—
336#385—221no—
337#384C2×D1111yescharacteristic
338#380C2×D1111yescharacteristic
339C4×C4⋊C4—111no—
340C4×C22⋊C4C2×D1111yescharacteristic
341#340—111no—
342#340—111no—
343#340—111no—
344#340—111no—
345#340—111no—
346#340—111no—
347#336—111no—
348#336—111no—
349C22×C11—22no—
350C22×C11—22no—
351C22×C11—22no—
352C22×C11—41no—
353C22×C11—41no—
354C22×C11—41no—
355C22×C11—41no—
356C22×C11C2×C22⋊Q811yescharacteristic
357C22×C11D4211yescharacteristic
358C22×C11#54711yescharacteristic
359C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
360C22×C11#57511yescharacteristic
361C22×C11#57711yescharacteristic
362C22×C11#57711yescharacteristic
363C2×D11—42no—
364C2×D11—42no—
365C2×D11—42no—
366C2×D11—81no—
367C2×D11—81no—
368C2×D11—81no—
369C2×D11—81no—
370C4×C11—22no—
371C4×C11—22no—
372C4×C11—41no—
373C4×C11—41no—
374C4×C11—41no—
375C4×C11—42no—
376C4×C11—81no—
377C4×C11—81no—
378C4×C11—81no—
379C4×C11#52511yescharacteristic
380C4×C11#53911yescharacteristic
381C4×C11D4×Q811yescharacteristic
382C4×C11#55411yescharacteristic
383Dic11—42no—
384Dic11—42no—
385Dic11—81no—
386C22×D4—111no—
387C22×D4—221no—
388C23×C4—221no—
389C23×C4—221no—
390C23×C4C22×D1111yescharacteristic
391C2×M16—222no—
392C2×M16—222no—
393C2×M16—222no—
394C22×C8—111no—
395C22×C8—111no—
396C22×C8—111no—
397C22×C8—111no—
398#125—22no—
399#125—41no—
400#121—114no—
401#121—222no—
402C4×D4—222no—
403C4×D4—441no—
404C4×D4—444no—
405#117—22no—
406#117—41no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—222no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4—441no—
420C2×C4⋊C4C22×D1111yescharacteristic
421C2×C4⋊C4C22×D1111yescharacteristic
422C2×C4⋊C4C22×D1111yescharacteristic
423C2×C4⋊C4C22×D1111yescharacteristic
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—221no—
427C2×C22⋊C4—221no—
428C2×C22⋊C4—221no—
429C2×C22⋊C4—221no—
430C2×C22⋊C4C22⋊D1111yescharacteristic
431C2×C22⋊C4C22⋊D1111yescharacteristic
432C2×C42—21no—
433C2×C42—221no—
434C2×C42C22×D1111yescharacteristic
435C2×C42C22×D1111yescharacteristic
436#107—114no—
437#107—222no—
438#106—222no—
439#106—222no—
440#106—222no—
441#106—441no—
442C4⋊C8—222no—
443C4⋊C8—222no—
444#102—222no—
445#102—222no—
446#102—222no—
447#102—441no—
448C22⋊C8—222no—
449#95—21no—
450#95—21no—
451#95—21no—
452#95—221no—
453#95—221no—
454#95C22⋊D1111yescharacteristic
455#95C22⋊D1111yescharacteristic
456C2×C11—42no—
457C2×C11#244911yescharacteristic
458C2×C11#307711yescharacteristic
459C2×C11#308411yescharacteristic
460C2×C11#327111yescharacteristic
461C2×C11#327211yescharacteristic
462C2×C11#334511yescharacteristic
463C2×C11#335111yescharacteristic
464D11—82no—
465C24—221no—
466C24C2×C22⋊D1111yescharacteristic
467C2×D4—112no—
468C2×D4—224no—
469C2×D4—221no—
470C2×D4—221no—
471C2×D4—221no—
472C2×D4—221no—
473C2×D4—221no—
474C2×D4—442no—
475C2×D4—442no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4—442no—
488C22×C4—442no—
489C22×C4—442no—
490C22×C4—442no—
491C22×C4—881no—
492C22×C4—881no—
493C22×C4Q8×D1112yes—
494C22×C4#434312yes—
495C22×C4C2×C22⋊D1111yescharacteristic
496C22×C4C2×C22⋊D1111yescharacteristic
497C22×C4C2×C22⋊D1111yescharacteristic
498C22×C4C2×C22⋊D1111yescharacteristic
499C22×C4C2×C22⋊D1111yescharacteristic
500C22×C4C23×D1111yescharacteristic
501M16—228no—
502C2×C8—112no—
503C2×C8—112no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—221no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—221no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—42no—
522C4⋊C4—42no—
523C4⋊C4—42no—
524C4⋊C4—42no—
525C4⋊C4—81no—
526C4⋊C4—81no—
527C4⋊C4—112no—
528C4⋊C4—112no—
529C4⋊C4—221no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4—221no—
533C4⋊C4—442no—
534C4⋊C4—442no—
535C4⋊C4D4×D1112yes—
536C22⋊C4—22no—
537C22⋊C4—41no—
538C22⋊C4—42no—
539C22⋊C4—81no—
540C22⋊C4—224no—
541C22⋊C4—442no—
542C22⋊C4—442no—
543C22⋊C4—881no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—42no—
549C42—442no—
550C11#2636611yescharacteristic, complemented, Sylow
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—222no—
558C23—441no—
559C23—441no—
560C23—441no—
561C23—441no—
562C23—441no—
563C23—441no—
564C23#6699912yes—
565C23C22×C22⋊D1111yescharacteristic
566D4—222no—
567D4—222no—
568D4—448no—
569D4—441no—
570D4—441no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—22no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—222no—
601C2×C4—222no—
602C2×C4—441no—
603C2×C4—441no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—884no—
610C2×C4—884no—
611C2×C4#6699912yes—
612C2×C4#6700212yes—
613C2×C4C2×D4×D1111yescharacteristic
614C2×C4#6703711yescharacteristic
615C2×C4C2×Q8×D1111yescharacteristic
616C2×C4C2×#434311yescharacteristic
617C2×C4#41×D1111yescharacteristic
618C2×C4#6704311yescharacteristic
619C8—222no—
620C8—222no—
621C8—441no—
622C8—441no—
623C22—22no—
624C22—22no—
625C22—22no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22—41no—
630C22—442no—
631C22—442no—
632C22—442no—
633C22—881no—
634C22—881no—
635C22—881no—
636C22—881no—
637C22D4×C22⋊D1111yescharacteristic
638C22C2×#6699911yescharacteristic
639C22C2×#6700211yescharacteristic
640C22#1062335311yescharacteristic
641C22#1062335511yescharacteristic
642C22#1062336711yescharacteristic
643C22#1062336811yescharacteristic
644C4—22no—
645C4—22no—
646C4—41no—
647C4—41no—
648C4—41no—
649C4—42no—
650C4—81no—
651C4—81no—
652C4—81no—
653C4—442no—
654C4—442no—
655C4—881no—
656C4#1062315811yescharacteristic
657C4#1062316311yescharacteristic
658C4#1062316711yescharacteristic
659C4#1062317611yescharacteristic
660C2—42no—
661C2—882no—
662C2#1307242111yescharacteristic
663C2#1307840911yescharacteristic
664C2#1307847411yescharacteristic
665C2#1308019711yescharacteristic
666C2#1308021611yescharacteristic
667C2#1308108011yescharacteristic
668C2#1308117611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2441C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenter#2441D11
hypocenterC11#26366
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2441

Complements

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

NH ≅ G/Ntype
1. C2×#10622679C2semidirect
2. C2×#10622608C2semidirect
4. #13070150C2semidirect
5. #13070117C2semidirect
6. #13070001C2semidirect
7. #13069951C2semidirect
8. #13069377C2semidirect
9. #13069184C2semidirect
12. #13068876C2semidirect
13. #13068808C2semidirect
14. #13068801C2semidirect
15. C11×#2441C2semidirect
128. #66871D4semidirect
219. #2441D11semidirect
550. C11#26366semidirect

Maximal subgroups

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

subgroupindex
C2×#106226792
C2×#106226082
#130716302
#130701502
#130701172
#130700012
#130699512
#130693772
#130691842
#130690522
#130689382
#130688762
#130688082
#130688012
C11×#24412
#2636611