Finite Group Databasebeta

← #14797712

Subgroups — #14797712

Order 2816.

940 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622841C211yesmaximal, characteristic
2C2×#10622403C211yesmaximal, characteristic, complemented
3#13072143C211yesmaximal, characteristic
4Q8×C22⋊Dic11C211yesmaximal, characteristic
5#13070152C211yesmaximal, characteristic, complemented
6#13070047C211yesmaximal, characteristic
7#13069937C211yesmaximal, characteristic, complemented
8#13069820C211yesmaximal, characteristic
9#13069294C211yesmaximal, characteristic, complemented
10#13069225C211yesmaximal, characteristic
11#13068955C211yesmaximal, characteristic, complemented
12#13068954C211yesmaximal, characteristic, complemented
13#13068872C211yesmaximal, characteristic, complemented
14#13068619C211yesmaximal, characteristic, complemented
15C11×#1787C211yesmaximal, characteristic
16C23×Q8×C11C2211yescharacteristic
17C2×Q8×Dic11C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C22×#4326C2211yescharacteristic
20C22×#4326C2211yescharacteristic
21C2×#66977C2211yescharacteristic
22C2×#66940C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×C22⋊C8C2211yescharacteristic
28C11×#380C2211yescharacteristic
29#10622843—21no—
30#10622843—21no—
31#10622843C2211yescharacteristic
32#10622843C2211yescharacteristic
33#10622841—24no—
34C2×#66899C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36#10622825—21no—
37#10622825C2211yescharacteristic
38C4×C22⋊Dic11—21no—
39C4×C22⋊Dic11C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C2×#66882C2211yescharacteristic
42C2×#66880C2211yescharacteristic
43C2×#66880C2211yescharacteristic
44C2×Dic11⋊C8C2211yescharacteristic
45C2×C8×Dic11C2211yescharacteristic
46#10622598C2211yescharacteristic
47#10622589C2211yescharacteristic
48#10622587C2211yescharacteristic
49C2×#66871C2211yescharacteristic
50#10622562—21no—
51#10622558—21no—
52#10622403—24no—
53#10622270—21no—
54#10622265—21no—
55#10622189C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11—22no—
62C22×Q8×C11—22no—
63C22×Q8×C11—21no—
64C22×Q8×C11—22no—
65C22×Q8×C11—22no—
66C22×Q8×C11—41no—
67C22×Q8×C11—41no—
68C22×Q8×C11C2311yescharacteristic
69C22×Q8×C11C2311yescharacteristic
70C23×C4×C11—21no—
71C23×C4×C11C2311yescharacteristic
72C22×Dic22C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11D411yescharacteristic
81C2×C22⋊Dic11D411yescharacteristic
82Q8×Dic11—22no—
83Q8×Dic11—22no—
84Q8×Dic11—41no—
85Q8×Dic11—41no—
86C2×#4326—22no—
87C2×#4326—22no—
88C2×#4326—22no—
89C2×#4326—22no—
90C2×#4326—41no—
91C2×#4326D414yes—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98#66977—22no—
99#66977—41no—
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4—21no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11—21no—
106C2×C4×Dic11—21no—
107C2×C4×Dic11C2311yescharacteristic
108C2×C4×Dic11C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111#66940—22no—
112#66940—41no—
113C11×#103—22no—
114C11×#103—22no—
115C11×#103—22no—
116C11×#103—41no—
117C11×C22⋊C8—41no—
118C11×#95—21no—
119#66899—22no—
120#66899—22no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129C11⋊#95D411yescharacteristic
130C11⋊#95D411yescharacteristic
131C22⋊(C11⋊C8)—22no—
132#66882—41no—
133#66880—22no—
134#66880—41no—
135Dic11⋊C8—41no—
136C8×Dic11—22no—
137#66871—22no—
138#24906—111nomaximal, Sylow
139C24×C11C2×D411yescharacteristic
140C2×Q8×C11—24no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—42no—
150C2×Q8×C11—42no—
151C2×Q8×C11—44no—
152C2×Q8×C11—44no—
153C2×Q8×C11—44no—
154C2×Q8×C11—44no—
155C2×Q8×C11C2×D412yes—
156C2×Q8×C11#4112yes—
157C2×Q8×C11#4112yes—
158C2×Q8×C11#4112yes—
159C22×C4×C11—21no—
160C22×C4×C11—24no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—42no—
171C22×C4×C11—42no—
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2411yescharacteristic
174C22×Dic11—21no—
175C22×Dic11—21no—
176C22×Dic11—21no—
177C22×Dic11—21no—
178C22×Dic11C2×D411yescharacteristic
179C22×Dic11C2×D411yescharacteristic
180C22×Dic11C2×D411yescharacteristic
181C22×Dic11C2×D411yescharacteristic
182C2×Dic22—21no—
183C2×Dic22—21no—
184C2×Dic22—21no—
185C2×Dic22—21no—
186C2×Dic22—21no—
187C2×Dic22C2×D412yes—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C22⋊C4—81no—
199C22⋊Dic11—41no—
200C22⋊Dic11—42no—
201C22⋊Dic11—42no—
202C22⋊Dic11Q1614yescomplemented
203#4326—28no—
204#4326—44no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11—21no—
211C4⋊Dic11—42no—
212C4⋊Dic11—42no—
213C4⋊Dic11—81no—
214Dic11⋊C4—42no—
215Dic11⋊C4—42no—
216Dic11⋊C4—42no—
217Dic11⋊C4—81no—
218C4×Dic11—21no—
219C4×Dic11—21no—
220C4×Dic11—21no—
221C4×Dic11—21no—
222C4×Dic11—42no—
223C4×Dic11—42no—
224C4×Dic11—42no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8C2×D412yes—
231C2×#451—111no—
232C2×C4×Q16—111no—
233#2423—111no—
234Q8×C22⋊C4—111no—
235#2095—111no—
236#2076—111no—
237#2056—111no—
238#2036—111no—
239#1933—111no—
240#1923—111no—
241#1878—111no—
242#1878—111no—
243#1863—111no—
244#1803—111no—
245#1787D1111yescharacteristic
246C23×C11—21no—
247C23×C11—21no—
248C23×C11—21no—
249C23×C11—21no—
250C23×C11—21no—
251C23×C11—21no—
252C23×C11C2×Q1612yes—
253C23×C11C22×D411yescharacteristic
254Q8×C11—22no—
255Q8×C11—22no—
256Q8×C11—22no—
257Q8×C11—22no—
258Q8×C11—22no—
259Q8×C11—48no—
260Q8×C11—41no—
261Q8×C11—41no—
262Q8×C11#12314yes—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—48no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11C22×D411yescharacteristic
284C2×C4×C11C2×#4111yescharacteristic
285C2×C4×C11C2×#4111yescharacteristic
286C2×C4×C11C2×#4111yescharacteristic
287C2×C4×C11H(5,𝔽2)11yescharacteristic
288C2×C4×C11H(5,𝔽2)11yescharacteristic
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—21no—
293C2×Dic11—21no—
294C2×Dic11—22no—
295C2×Dic11—21no—
296C2×Dic11—21no—
297C2×Dic11—21no—
298C2×Dic11—21no—
299C2×Dic11—21no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11—41no—
304C2×Dic11—41no—
305C2×Dic11—41no—
306C2×Dic11—41no—
307C2×Dic11—41no—
308C2×Dic11—41no—
309C2×Dic11—41no—
310C2×Dic11—41no—
311C2×Dic11C2×Q1612yes—
312C2×Dic11C2×Q1612yes—
313Dic22—22no—
314Dic22—22no—
315Dic22—41no—
316Dic22—41no—
317C8×C11—41no—
318C8×C11—41no—
319C11⋊C8—22no—
320C11⋊C8—41no—
321C23×Q8C2×D1111yescharacteristic
322C22×Q16—111no—
323C22×Q16—111no—
324C2×C22⋊Q8—111no—
325C2×C4×Q8—111no—
326C2×C4×Q8—111no—
327C2×C4×Q8—111no—
328#451—224no—
329C4×Q16—224no—
330C2×#107—111no—
331C2×#107—111no—
332C2×C4⋊C8—111no—
333C2×#103—111no—
334C2×#103—111no—
335C2×#103—111no—
336C2×#103—111no—
337C2×#103C2×D1111yescharacteristic
338C2×#103C2×D1111yescharacteristic
339C2×#103C2×D1111yescharacteristic
340C2×#103C2×D1111yescharacteristic
341C2×C22⋊C8—111no—
342C2×C22⋊C8C2×D1111yescharacteristic
343C2×C4×C8—111no—
344#399—221no—
345#398—221no—
346#391—111no—
347#391—111no—
348#391—111no—
349#391—221no—
350#391—221no—
351#389—111no—
352#388—221no—
353#387—221no—
354#384—111no—
355#380—111no—
356#380—221no—
357#380C2×D1111yescharacteristic
358C4×C22⋊C4—111no—
359C4×C22⋊C4—221no—
360#340—111no—
361#340—111no—
362#340—111no—
363#340—111no—
364#336—111no—
365#336—111no—
366C22×C11—22no—
367C22×C11—22no—
368C22×C11—22no—
369C22×C11—41no—
370C22×C11—41no—
371C22×C11—41no—
372C22×C11—41no—
373C22×C11#52511yescharacteristic
374C22×C11D4211yescharacteristic
375C22×C11#54611yescharacteristic
376C22×C11C22×Q1611yescharacteristic
377C22×C11#57511yescharacteristic
378C22×C11#57711yescharacteristic
379C22×C11#57811yescharacteristic
380C4×C11—24no—
381C4×C11—41no—
382C4×C11—42no—
383C4×C11—81no—
384C4×C11—81no—
385C4×C11C2×#12311yescharacteristic
386C4×C11#53811yescharacteristic
387C4×C11#54611yescharacteristic
388C4×C11#55111yescharacteristic
389Dic11—22no—
390Dic11—22no—
391Dic11—42no—
392Dic11—41no—
393Dic11—41no—
394Dic11—81no—
395Dic11—81no—
396Dic11—81no—
397C22×Q8—22no—
398C22×Q8—22no—
399C22×Q8—21no—
400C22×Q8—22no—
401C22×Q8—22no—
402C22×Q8—41no—
403C22×Q8—41no—
404C22×Q8—111no—
405C22×Q8C22×D1111yescharacteristic
406C22×Q8C22×D1111yescharacteristic
407C23×C4—21no—
408C23×C4C22×D1111yescharacteristic
409C2×Q16—114no—
410C2×Q16—222no—
411C2×Q16—222no—
412C2×Q16—222no—
413C2×Q16—222no—
414C2×Q16—441no—
415C22×C8—111no—
416C22×C8—111no—
417C22×C8C22×D1111yescharacteristic
418C22×C8C22×D1111yescharacteristic
419C22⋊Q8—222no—
420C22⋊Q8—441no—
421C4×Q8—222no—
422C4×Q8—222no—
423C4×Q8—222no—
424C4×Q8—441no—
425C4×Q8—441no—
426C4×Q8—441no—
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⋊C4C22×D1111yescharacteristic
438C2×C4⋊C4C22×D1111yescharacteristic
439C2×C22⋊C4—21no—
440C2×C22⋊C4—111no—
441C2×C22⋊C4—111no—
442C2×C22⋊C4—221no—
443C2×C22⋊C4—221no—
444C2×C42—111no—
445C2×C42—111no—
446C2×C42—221no—
447C2×C42—221no—
448C2×C42—221no—
449#107—222no—
450#107—441no—
451C4⋊C8—441no—
452#103—22no—
453#103—22no—
454#103—22no—
455#103—41no—
456#103—222no—
457#103—222no—
458#103—222no—
459#103—441no—
460C22⋊C8—41no—
461C22⋊C8—222no—
462C4×C8—222no—
463#95—21no—
464#95—111no—
465#95—111no—
466#95—221no—
467#95—221no—
468#95—221no—
469#95—221no—
470#95—221no—
471#95—221no—
472#95—221no—
473#95—221no—
474C2×C11—42no—
475C2×C11#241811yescharacteristic
476C2×C11#310411yescharacteristic
477C2×C11#312111yescharacteristic
478C2×C11#327111yescharacteristic
479C2×C11D4×Q1611yescharacteristic
480C2×C11#329911yescharacteristic
481C2×C11#332711yescharacteristic
482C24D4×D1111yescharacteristic
483C2×Q8—24no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—42no—
493C2×Q8—42no—
494C2×Q8—44no—
495C2×Q8—44no—
496C2×Q8—44no—
497C2×Q8—44no—
498C2×Q8—112no—
499C2×Q8—221no—
500C2×Q8—221no—
501C2×Q8—221no—
502C2×Q8—221no—
503C2×Q8—221no—
504C2×Q8#433912yes—
505C2×Q8D4×D1112yes—
506C2×Q8#434112yes—
507C2×Q8#434112yes—
508C22×C4—21no—
509C22×C4—24no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—111no—
522C22×C4—111no—
523C22×C4—111no—
524C22×C4—111no—
525C22×C4—221no—
526C22×C4—221no—
527C22×C4—221no—
528C22×C4—221no—
529C22×C4D4×D1111yescharacteristic
530C22×C4C23×D1111yescharacteristic
531Q16—228no—
532Q16—444no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—112no—
540C2×C8—221no—
541C2×C8—221no—
542C2×C8—221no—
543C2×C8—221no—
544C2×C8—221no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—221no—
550C4⋊C4—221no—
551C4⋊C4—221no—
552C4⋊C4—221no—
553C4⋊C4—221no—
554C4⋊C4—221no—
555C4⋊C4—442no—
556C4⋊C4—442no—
557C4⋊C4—442no—
558C4⋊C4—442no—
559C4⋊C4—442no—
560C4⋊C4—881no—
561C4⋊C4—881no—
562C22⋊C4—81no—
563C22⋊C4—114no—
564C22⋊C4—441no—
565C22⋊C4—442no—
566C22⋊C4—442no—
567C42—221no—
568C42—221no—
569C42—221no—
570C42—221no—
571C42—442no—
572C42—442no—
573C42—442no—
574C11#2490611yescharacteristic, complemented, Sylow
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23Q16×D1112yes—
582C23C2×D4×D1111yescharacteristic
583Q8—22no—
584Q8—22no—
585Q8—22no—
586Q8—22no—
587Q8—22no—
588Q8—48no—
589Q8—41no—
590Q8—41no—
591Q8—222no—
592Q8—222no—
593Q8—441no—
594Q8—441no—
595Q8#6693614yes—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—21no—
600C2×C4—22no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—48no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—112no—
617C2×C4—112no—
618C2×C4—221no—
619C2×C4—221no—
620C2×C4—221no—
621C2×C4—221no—
622C2×C4—221no—
623C2×C4—221no—
624C2×C4—221no—
625C2×C4—221no—
626C2×C4—221no—
627C2×C4—221no—
628C2×C4—222no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4—441no—
633C2×C4—441no—
634C2×C4—441no—
635C2×C4—441no—
636C2×C4—441no—
637C2×C4—441no—
638C2×C4—441no—
639C2×C4—441no—
640C2×C4C2×#433911yescharacteristic
641C2×C4C2×D4×D1111yescharacteristic
642C2×C4C2×#434111yescharacteristic
643C2×C4C2×#434111yescharacteristic
644C2×C4#6703711yescharacteristic
645C2×C4#6703711yescharacteristic
646C8—41no—
647C8—41no—
648C8—222no—
649C8—441no—
650C22—22no—
651C22—22no—
652C22—22no—
653C22—41no—
654C22—41no—
655C22—41no—
656C22—41no—
657C22#1062302111yescharacteristic
658C22#1062311711yescharacteristic
659C22#1062312111yescharacteristic
660C22#1062329311yescharacteristic
661C22C2×Q16×D1111yescharacteristic
662C22#1062330811yescharacteristic
663C22#1062331011yescharacteristic
664C4—24no—
665C4—41no—
666C4—42no—
667C4—81no—
668C4—81no—
669C4—222no—
670C4—222no—
671C4—441no—
672C4—441no—
673C4—442no—
674C4—881no—
675C4—881no—
676C4—881no—
677C4C2×#6693611yescharacteristic
678C4#1062302611yescharacteristic
679C4#1062312211yescharacteristic
680C4#1062312411yescharacteristic
681C2—42no—
682C2#1307208211yescharacteristic
683C2#1307865011yescharacteristic
684C2#1307883811yescharacteristic
685C2#1308020411yescharacteristic
686C2#1308036111yescharacteristic
687C2#1308048811yescharacteristic
688C2#1308088011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1787C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#1787D11
hypocenterC11#24906
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1787

Complements

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

NH ≅ G/Ntype
2. C2×#10622403C2semidirect
5. #13070152C2semidirect
7. #13069937C2semidirect
9. #13069294C2semidirect
11. #13068955C2semidirect
12. #13068954C2semidirect
13. #13068872C2semidirect
14. #13068619C2semidirect
202. C22⋊Dic11Q16semidirect
574. C11#24906semidirect

Maximal subgroups

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

subgroupindex
C2×#106228412
C2×#106224032
#130721432
Q8×C22⋊Dic112
#130701522
#130700472
#130699372
#130698202
#130692942
#130692252
#130689552
#130689542
#130688722
#130686192
C11×#17872
#2490611