Finite Group Databasebeta

← #14796394

Subgroups — #14796394

Order 2816.

998 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622372C211yesmaximal, characteristic, complemented
2C2×#10622369C211yesmaximal, characteristic
3#13073568C211yesmaximal, characteristic, complemented
4D4×Dic11⋊C4C211yesmaximal, characteristic, complemented
5#13070091C211yesmaximal, characteristic, complemented
6#13070088C211yesmaximal, characteristic, complemented
7#13070005C211yesmaximal, characteristic, complemented
8#13070003C211yesmaximal, characteristic, complemented
9#13069575C211yesmaximal, characteristic, complemented
10#13069331C211yesmaximal, characteristic, complemented
11#13068964C211yesmaximal, characteristic
12#13068962C211yesmaximal, characteristic
13#13068615C211yesmaximal, characteristic, complemented
14#13068614C211yesmaximal, characteristic, complemented
15C11×#1802C211yesmaximal, characteristic, complemented
16C2×C4×D4×C11C2211yescharacteristic
17C2×D4×Dic11C2211yescharacteristic
18C2×D4×Dic11C2211yescharacteristic
19C22×#4323C2211yescharacteristic
20C22×Dic11⋊C4—21no—
21C2×#66949—21no—
22C2×#66949—21no—
23C2×#66946C2211yescharacteristic
24C2×#66941C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28C11×#384C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30#10622823—21no—
31C2×#66885C2211yescharacteristic
32C2×#66885C2211yescharacteristic
33C2×#66882C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35C2×Dic11⋊C8C2211yescharacteristic
36C2×C8×Dic11C2211yescharacteristic
37#10622605—21no—
38#10622605—21no—
39#10622601C2211yescharacteristic
40#10622589C2211yescharacteristic
41#10622589C2211yescharacteristic
42#10622586C2211yescharacteristic
43C2×#66873C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46#10622559—21no—
47#10622555—21no—
48#10622552C2211yescharacteristic
49C4×Dic11⋊C4C2211yescharacteristic
50#10622541C2211yescharacteristic
51#10622372—24no—
52#10622369—24no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×D4×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C23×Dic11—21no—
64C23×Dic11—21no—
65C22×D44C2311yescharacteristic
66C22×C4×D11—21no—
67C22×Dic22—21no—
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C4×D4×C11—22no—
71C4×D4×C11—41no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C42×C11C2311yescharacteristic
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81D4×Dic11—22no—
82D4×Dic11—22no—
83D4×Dic11—41no—
84D4×Dic11D414yes—
85C2×#4323—22no—
86C2×#4323—22no—
87C2×#4323Q814yescomplemented
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
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⋊C4—21no—
103C2×Dic11⋊C4—44no—
104C2×Dic11⋊C4D411yescharacteristic
105C2×Dic11⋊C4D411yescharacteristic
106C2×C4×Dic11C2311yescharacteristic
107C2×C4×Dic11C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110#66949—44no—
111#66949—44no—
112#66946—22no—
113#66946—22no—
114#66941—22no—
115#66941—22no—
116C11×C4⋊C8—41no—
117C11×#102—22no—
118C11×#102—22no—
119#66896—22no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95D411yescharacteristic
123C11⋊#95D411yescharacteristic
124#66885—22no—
125#66885—41no—
126#66882—22no—
127Dic11⋊C8—22no—
128Dic11⋊C8—41no—
129C8×Dic11—22no—
130#66873—41no—
131#66871—22no—
132#66871—22no—
133#24811—111nomaximal, Sylow
134C24×C11—21no—
135C23×D11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11C2×D412yes—
140C2×D4×C11C2×Q812yes—
141C2×D4×C11#4112yes—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—42no—
146C22×C4×C11—42no—
147C22×C4×C11—81no—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C22×Dic11—24no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—42no—
156C22×Dic11—42no—
157C22×Dic11—42no—
158C22×Dic11—42no—
159C22×Dic11—81no—
160C22×Dic11C2×D411yescharacteristic
161C22×Dic11C2×D411yescharacteristic
162C22×Dic11C2×D411yescharacteristic
163C22×Dic11C2×D411yescharacteristic
164C2×D44—21no—
165C2×D44—21no—
166C2×D44—21no—
167C2×D44—21no—
168C2×D44—21no—
169C2×D44C2×Q812yes—
170C2×C4×D11—42no—
171C2×C4×D11—42no—
172C2×C4×D11—42no—
173C2×Dic22—42no—
174C2×Dic22—42no—
175C2×Dic22—42no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—42no—
189C11×C4⋊C4—42no—
190C11×C22⋊C4—42no—
191C42×C11—21no—
192C42×C11—21no—
193C22⋊Dic11—24no—
194C22⋊Dic11—42no—
195#4323—28no—
196(C2×D11)⋊C4—42no—
197(C2×D11)⋊C4—42no—
198(C2×D11)⋊C4—42no—
199(C2×D11)⋊C4—42no—
200(C2×D11)⋊C4—42no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11C2×D412yes—
207Dic11⋊C4—22no—
208Dic11⋊C4—42no—
209Dic11⋊C4—42no—
210Dic11⋊C4—42no—
211Dic11⋊C4—42no—
212Dic11⋊C4—42no—
213Dic11⋊C4—42no—
214Dic11⋊C4—81no—
215Dic11⋊C4D814yescomplemented
216C4×Dic11—21no—
217C4×Dic11—21no—
218C4×Dic11C2×D412yes—
219C4×Dic11#4112yes—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8C2×Q812yes—
226C2×#474—111no—
227C2×C4×D8—111no—
228#2542—111no—
229D4×C4⋊C4—111no—
230#2083—111no—
231#2083—111no—
232#2067—111no—
233#2067—111no—
234#1990—111no—
235#1939—111no—
236#1879—111no—
237#1879—111no—
238#1802—111no—
239#1802—111no—
240#1802D1111yescharacteristic, complemented
241C23×C11—22no—
242C23×C11—22no—
243C23×C11—22no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11C22×D411yescharacteristic
249C22×D11—22no—
250C22×D11—41no—
251C22×D11—41no—
252C22×D11—41no—
253C22×D11—41no—
254C22×D11—41no—
255C22×D11—41no—
256D4×C11—22no—
257D4×C11—22no—
258D4×C11—22no—
259D4×C11C22⋊Q814yescomplemented
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—84no—
275C2×C4×C11C2×D812yes—
276C2×C4×C11C22×D411yescharacteristic
277C2×C4×C11C22×Q811yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C11C2×#4111yescharacteristic
280C2×C4×C11H(5,𝔽2)11yescharacteristic
281C2×C4×C112−1+411yescharacteristic
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—22no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—48no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—84no—
300C2×Dic11#12112yes—
301C2×Dic11#12112yes—
302C2×Dic11C2×D812yes—
303C2×Dic11C2×D812yes—
304C2×Dic11AGL(1,ℤ/8)12yes—
305D44—22no—
306D44—22no—
307D44—41no—
308D44—41no—
309C4×D11—84no—
310Dic22—84no—
311C8×C11—41no—
312C8×C11—41no—
313C11⋊C8—22no—
314C11⋊C8—41no—
315C22×D8—111no—
316C2×C4⋊Q8—111no—
317C2×C22⋊Q8—221no—
318C2×C22⋊Q8—221no—
319C2×C4×D4—111no—
320C2×C4×D4—111no—
321C2×C4×D4—111no—
322C2×C4×D4C2×D1111yescharacteristic
323C22×C4⋊C4—221no—
324#474—224no—
325C4×D8—224no—
326C2×#107—111no—
327C2×#107—111no—
328C2×#107—111no—
329C2×C4⋊C8—111no—
330C2×C4⋊C8—111no—
331C2×C4⋊C8C2×D1111yescharacteristic
332C2×#102—111no—
333C2×#102—111no—
334C2×#102—111no—
335C2×#102—111no—
336C2×#102C2×D1111yescharacteristic
337C2×#102C2×D1111yescharacteristic
338C2×C4×C8—111no—
339#399—221no—
340#399—221no—
341#390—111no—
342#390—111no—
343#389—111no—
344#389—111no—
345#385—221no—
346#385—221no—
347#384—111no—
348#384—111no—
349#384C2×D1111yescharacteristic
350#380—221no—
351C4×C4⋊C4—111no—
352#340—111no—
353#340—111no—
354#340—111no—
355#340—111no—
356#340C2×D1111yescharacteristic
357#340C2×D1111yescharacteristic
358#336—111no—
359#336—111no—
360C22×C11—24no—
361C22×C11—42no—
362C22×C11—42no—
363C22×C11—42no—
364C22×C11—42no—
365C22×C11—42no—
366C22×C11—42no—
367C22×C11C2×#12111yescharacteristic
368C22×C11#54611yescharacteristic
369C22×C11D4×Q811yescharacteristic
370C22×C11C22×D811yescharacteristic
371C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
372C22×C11#57711yescharacteristic
373C22×C11#57811yescharacteristic
374C2×D11—42no—
375C2×D11—42no—
376C2×D11—42no—
377C2×D11—81no—
378C2×D11—81no—
379C2×D11—81no—
380C2×D11—81no—
381C4×C11—22no—
382C4×C11—41no—
383C4×C11—81no—
384C4×C11—81no—
385C4×C11—81no—
386C4×C11C2×C22⋊Q811yescharacteristic
387C4×C11#53711yescharacteristic
388C4×C11#55211yescharacteristic
389C4×C11#55411yescharacteristic
390Dic11—22no—
391Dic11—22no—
392Dic11—41no—
393Dic11—42no—
394Dic11—81no—
395Dic11—81no—
396Dic11#45914yes—
397C22×Q8—221no—
398C22×D4—111no—
399C22×D4C22×D1111yescharacteristic
400C23×C4—21no—
401C23×C4—221no—
402C23×C4—221no—
403C23×C4—221no—
404C2×D8—114no—
405C2×D8—222no—
406C2×D8—222no—
407C22×C8—111no—
408C22×C8—111no—
409C22×C8C22×D1111yescharacteristic
410C22×C8C22×D1111yescharacteristic
411C4⋊Q8—222no—
412C4⋊Q8—222no—
413C22⋊Q8—444no—
414C22⋊Q8—444no—
415C4×D4—22no—
416C4×D4—41no—
417C4×D4—114no—
418C4×D4—222no—
419C4×D4—222no—
420C4×D4—222no—
421C4×D4—222no—
422C4×D4—441no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—111no—
426C2×C4⋊C4—111no—
427C2×C4⋊C4—111no—
428C2×C4⋊C4—111no—
429C2×C4⋊C4—111no—
430C2×C4⋊C4—221no—
431C2×C4⋊C4—221no—
432C2×C4⋊C4—221no—
433C2×C4⋊C4—221no—
434C2×C4⋊C4—221no—
435C2×C4⋊C4—221no—
436C2×C4⋊C4—221no—
437C2×C4⋊C4—444no—
438C2×C4⋊C4C22×D1111yescharacteristic
439C2×C4⋊C4C22×D1111yescharacteristic
440C2×C4⋊C4C22×D1111yescharacteristic
441C2×C22⋊C4—21no—
442C2×C22⋊C4—221no—
443C2×C22⋊C4—221no—
444C2×C22⋊C4—221no—
445C2×C22⋊C4—221no—
446C2×C22⋊C4—221no—
447C2×C22⋊C4—221no—
448C2×C22⋊C4—221no—
449C2×C42—111no—
450C2×C42—111no—
451C2×C42C22×D1111yescharacteristic
452#107—222no—
453#107—222no—
454#107—222no—
455C4⋊C8—41no—
456C4⋊C8—222no—
457C4⋊C8—441no—
458#102—22no—
459#102—22no—
460#102—222no—
461#102—222no—
462#102—441no—
463#102—441no—
464C4×C8—222no—
465#95—111no—
466#95—111no—
467#95—221no—
468#95—221no—
469C2×C11—44no—
470C2×C11#241711yescharacteristic
471C2×C11C2×#45911yescharacteristic
472C2×C11#304611yescharacteristic
473C2×C11#329411yescharacteristic
474C2×C11#333011yescharacteristic
475C2×C11Q8×D811yescharacteristic
476C2×C11#338411yescharacteristic
477D11—82no—
478C24—21no—
479C24—221no—
480C2×Q8—442no—
481C2×Q8—442no—
482C2×Q8—442no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—112no—
487C2×D4—221no—
488C2×D4—221no—
489C2×D4—221no—
490C2×D4—221no—
491C2×D4—221no—
492C2×D4#433912yes—
493C2×D4D4×D1112yes—
494C2×D4Q8×D1112yes—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—42no—
499C22×C4—42no—
500C22×C4—81no—
501C22×C4—111no—
502C22×C4—111no—
503C22×C4—111no—
504C22×C4—111no—
505C22×C4—224no—
506C22×C4—221no—
507C22×C4—221no—
508C22×C4—221no—
509C22×C4—442no—
510C22×C4—442no—
511C22×C4—442no—
512C22×C4—442no—
513C22×C4—442no—
514C22×C4—442no—
515C22×C4—442no—
516C22×C4—881no—
517C22×C4D4×D1111yescharacteristic
518C22×C4D4×D1111yescharacteristic
519C22×C4C23×D1111yescharacteristic
520D8—228no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—112no—
528C2×C8—221no—
529C2×C8—221no—
530C2×C8—221no—
531C2×C8—221no—
532C2×C8—221no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—42no—
540C4⋊C4—42no—
541C4⋊C4—114no—
542C4⋊C4—112no—
543C4⋊C4—222no—
544C4⋊C4—221no—
545C4⋊C4—221no—
546C4⋊C4—221no—
547C4⋊C4—221no—
548C4⋊C4—221no—
549C4⋊C4—442no—
550C4⋊C4—442no—
551C4⋊C4—442no—
552C4⋊C4—442no—
553C4⋊C4—442no—
554C4⋊C4—442no—
555C4⋊C4—881no—
556C22⋊C4—42no—
557C22⋊C4—224no—
558C22⋊C4—442no—
559C22⋊C4—442no—
560C22⋊C4—442no—
561C22⋊C4—442no—
562C22⋊C4—442no—
563C22⋊C4—442no—
564C42—21no—
565C42—21no—
566C42—112no—
567C42—112no—
568C42—221no—
569C42—221no—
570C11#2481111yescharacteristic, complemented, Sylow
571C23—22no—
572C23—22no—
573C23—22no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—222no—
579C23—441no—
580C23—441no—
581C23—441no—
582C23—441no—
583C23—441no—
584C23—441no—
585C23C2×D4×D1111yescharacteristic
586Q8—884no—
587D4—22no—
588D4—22no—
589D4—22no—
590D4—222no—
591D4—222no—
592D4—441no—
593D4—441no—
594D4#6694914yescomplemented
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—84no—
610C2×C4—112no—
611C2×C4—112no—
612C2×C4—112no—
613C2×C4—112no—
614C2×C4—112no—
615C2×C4—221no—
616C2×C4—221no—
617C2×C4—221no—
618C2×C4—221no—
619C2×C4—221no—
620C2×C4—221no—
621C2×C4—221no—
622C2×C4—222no—
623C2×C4—448no—
624C2×C4—441no—
625C2×C4—441no—
626C2×C4—441no—
627C2×C4—441no—
628C2×C4—441no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4—884no—
633C2×C4—884no—
634C2×C4D8×D1112yes—
635C2×C4C2×#433911yescharacteristic
636C2×C4C2×D4×D1111yescharacteristic
637C2×C4#6703711yescharacteristic
638C2×C4C2×Q8×D1111yescharacteristic
639C2×C4#41×D1111yescharacteristic
640C2×C4#6704311yescharacteristic
641C8—41no—
642C8—41no—
643C8—222no—
644C8—441no—
645C22—24no—
646C22—42no—
647C22—42no—
648C22—42no—
649C22—42no—
650C22—42no—
651C22—42no—
652C22—442no—
653C22—442no—
654C22—442no—
655C22—881no—
656C22—881no—
657C22—881no—
658C22—881no—
659C22#1062302111yescharacteristic
660C22D11×#12111yescharacteristic
661C22#1062316311yescharacteristic
662C22C2×D8×D1111yescharacteristic
663C22#1062329311yescharacteristic
664C22D11×AGL(1,ℤ/8)11yescharacteristic
665C22#1062331011yescharacteristic
666C4—22no—
667C4—41no—
668C4—81no—
669C4—81no—
670C4—81no—
671C4—114no—
672C4—222no—
673C4—222no—
674C4—442no—
675C4—441no—
676C4—881no—
677C4—881no—
678C4C2×#6694911yescharacteristic
679C4#1062306211yescharacteristic
680C4#1062312811yescharacteristic
681C4#1062316711yescharacteristic
682C2—44no—
683C2—882no—
684C2#1307206611yescharacteristic
685C2D11×#45911yescharacteristic
686C2#1307816111yescharacteristic
687C2#1308042511yescharacteristic
688C2#1308091711yescharacteristic
689C2#1308146611yescharacteristic
690C2#1308151011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1802C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
hypercenter#1802D11
hypocenterC11#24811
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1802

Complements

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

NH ≅ G/Ntype
1. C2×#10622372C2semidirect
3. #13073568C2semidirect
4. D4×Dic11⋊C4C2semidirect
5. #13070091C2semidirect
6. #13070088C2semidirect
7. #13070005C2semidirect
8. #13070003C2semidirect
9. #13069575C2semidirect
10. #13069331C2semidirect
13. #13068615C2semidirect
14. #13068614C2semidirect
15. C11×#1802C2semidirect
87. C2×#4323Q8semidirect
215. Dic11⋊C4D8semidirect
240. #1802D11semidirect
259. D4×C11C22⋊Q8semidirect
570. C11#24811semidirect
594. D4#66949semidirect

Maximal subgroups

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

subgroupindex
C2×#106223722
C2×#106223692
#130735682
D4×Dic11⋊C42
#130700912
#130700882
#130700052
#130700032
#130695752
#130693312
#130689642
#130689622
#130686152
#130686142
C11×#18022
#2481111