Finite Group Databasebeta

← #14802010

Subgroups — #14802010

Order 2816.

858 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622657C211yesmaximal, characteristic
2C2×#10622664C211yesmaximal, characteristic
3#13073094C211yesmaximal, characteristic
4#13070087C211yesmaximal, characteristic, complemented
5#13070024C211yesmaximal, characteristic, complemented
6#13070008C211yesmaximal, characteristic, complemented
7#13069938C211yesmaximal, characteristic, complemented
8#13069374C211yesmaximal, characteristic, complemented
9#13069257C211yesmaximal, characteristic, complemented
10#13068957C211yesmaximal, characteristic, complemented
11#13068923C211yesmaximal, characteristic
12#13068796C211yesmaximal, characteristic
13#13068621C211yesmaximal, characteristic, complemented
14C2×#10622167C211yesmaximal, characteristic
15C11×#2360C211yesmaximal, characteristic
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×#4326C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C2×#66977C2211yescharacteristic
22C23×C11⋊C8C2211yescharacteristic
23C11×#391C2211yescharacteristic
24C11×#389—21no—
25C11×#389C2211yescharacteristic
26C11×#387—21no—
27C11×#385—21no—
28C4×C11×C4⋊C4C2211yescharacteristic
29C4×C11×C22⋊C4—21no—
30C4×C11×C22⋊C4C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35#10622664—24no—
36#10622657—24no—
37C2×#66874C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43#10622563—21no—
44#10622563—21no—
45#10622548C2211yescharacteristic
46#10622548C2211yescharacteristic
47#10622542C2211yescharacteristic
48#10622542C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51#10622274—21no—
52#10622274—21no—
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C23×C4×C11C2311yescharacteristic
64C23×Dic11—21no—
65C22×Dic22C2311yescharacteristic
66C11×C22⋊Q8—22no—
67C11×C22⋊Q8D414yes—
68C4×Q8×C11—22no—
69C4×Q8×C11—41no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—41no—
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4D411yescharacteristic
81C2×C11×C22⋊C4D411yescharacteristic
82C2×C42×C11—21no—
83C2×C42×C11—21no—
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C22⋊Dic11—21no—
87C2×#4326—22no—
88C2×#4326—22no—
89C2×#4326—41no—
90C2×C4⋊Dic11—22no—
91C2×C4⋊Dic11—22no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100#66977—22no—
101#66977—22no—
102C2×Dic11⋊C4—21no—
103C22×C11⋊C8—22no—
104C22×C11⋊C8—22no—
105C22×C11⋊C8—41no—
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C11×#95—21no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95—21no—
114C11×#95D411yescharacteristic
115C11×#95D411yescharacteristic
116#66899—22no—
117#66899—22no—
118#66899—22no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C22⋊(C11⋊C8)—22no—
124#66874—22no—
125#66874—22no—
126#66874—41no—
127#66871—22no—
128#66871—22no—
129#66871—22no—
130C4⋊(C11⋊C8)—22no—
131C4⋊(C11⋊C8)—41no—
132#25206—111nomaximal, Sylow
133C24×C11C2×D411yescharacteristic
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11C2×D412yes—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—42no—
149C22×C4×C11—42no—
150C22×C4×C11—81no—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11#4112yes—
158C22×C4×C11C2411yescharacteristic
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—42no—
164C22×Dic11—81no—
165C22×Dic11—81no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C11×C4⋊C4—24no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—42no—
178C11×C4⋊C4—42no—
179C11×C4⋊C4—81no—
180C11×C4⋊C4C2×D412yes—
181C11×C4⋊C4#4112yes—
182C11×C22⋊C4—24no—
183C11×C22⋊C4—22no—
184C11×C22⋊C4Q1614yescomplemented
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—42no—
190C42×C11—81no—
191C22⋊Dic11—42no—
192#4326—44no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—42no—
200C4⋊Dic11—81no—
201C4⋊Dic11—81no—
202C4⋊Dic11—81no—
203C4⋊Dic11—81no—
204Dic11⋊C4—42no—
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⋊C8—21no—
216C2×C11⋊C8—44no—
217C2×C11⋊C8#4112yes—
218C2×#484—111no—
219C2×#467—111no—
220#2502—111no—
221#2360D1111yescharacteristic
222#2083—111no—
223#2072—111no—
224#2068—111no—
225#2056—111no—
226#1947—111no—
227#1928—111no—
228#1878—111no—
229#1872—111no—
230#1850—111no—
231#1803—111no—
232C2×#340—111no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11#12112yes—
238C23×C11C2×Q1612yes—
239C23×C11#13712yes—
240C23×C11C22×D411yescharacteristic
241Q8×C11—22no—
242Q8×C11—22no—
243Q8×C11—41no—
244Q8×C11—41no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
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—22no—
256C2×C4×C11—22no—
257C2×C4×C11—21no—
258C2×C4×C11—22no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—41no—
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—84no—
274C2×C4×C11#12112yes—
275C2×C4×C11C2×Q1612yes—
276C2×C4×C11C2×Q1612yes—
277C2×C4×C11C22×D411yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C11C2×#4111yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11H(5,𝔽2)11yescharacteristic
282C2×C4×C112−1+411yescharacteristic
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—84no—
296Dic22—41no—
297Dic22—41no—
298Dic22—41no—
299Dic22—41no—
300C11⋊C8—22no—
301C11⋊C8—41no—
302C11⋊C8—41no—
303C11⋊C8—41no—
304C22×Q16—111no—
305C23×C8—111no—
306C2×C22⋊Q8—111no—
307C2×C22⋊Q8C2×D1111yescharacteristic
308C2×C4×Q8C2×D1111yescharacteristic
309C22×C4⋊C4—111no—
310C22×C4⋊C4C2×D1111yescharacteristic
311#484—224no—
312#467—224no—
313C2×#107—111no—
314C2×#107—111no—
315C2×#107—111no—
316C2×C4⋊C8—111no—
317C2×C4⋊C8—111no—
318C2×#103—111no—
319C2×#103—111no—
320C2×#103—111no—
321C2×#103—111no—
322C2×#103—111no—
323C2×#103—111no—
324C2×C22⋊C8—111no—
325#398—221no—
326#398—221no—
327#391—111no—
328#391—111no—
329#391C2×D1111yescharacteristic
330#389—21no—
331#389C2×D1111yescharacteristic
332#387—21no—
333#385—21no—
334#385—221no—
335#385—221no—
336#384—111no—
337#384—111no—
338C4×C4⋊C4C2×D1111yescharacteristic
339C4×C22⋊C4—21no—
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—22no—
353C22×C11—22no—
354C22×C11—22no—
355C22×C11#46214yes—
356C22×C11C2×#12111yescharacteristic
357C22×C11#54611yescharacteristic
358C22×C11#54711yescharacteristic
359C22×C11C22×Q1611yescharacteristic
360C22×C11C2×#13711yescharacteristic
361C22×C11#57611yescharacteristic
362C22×C11#57711yescharacteristic
363C4×C11—22no—
364C4×C11—22no—
365C4×C11—22no—
366C4×C11—41no—
367C4×C11—42no—
368C4×C11—42no—
369C4×C11—41no—
370C4×C11—42no—
371C4×C11—81no—
372C4×C11#52911yescharacteristic
373C4×C11#53911yescharacteristic
374C4×C11#54611yescharacteristic
375C4×C11#54711yescharacteristic
376Dic11—81no—
377Dic11—81no—
378Dic11—81no—
379Dic11—81no—
380C22×Q8—111no—
381C22×Q8C22×D1111yescharacteristic
382C23×C4—21no—
383C23×C4—221no—
384C23×C4C22×D1111yescharacteristic
385C2×Q16—222no—
386C2×Q16—222no—
387C2×Q16—441no—
388C22×C8—111no—
389C22×C8—111no—
390C22×C8—111no—
391C22×C8—111no—
392C22×C8—222no—
393C22×C8—222no—
394C22×C8—441no—
395C22⋊Q8—22no—
396C22⋊Q8—222no—
397C22⋊Q8—222no—
398C22⋊Q8D4414yes—
399C4×Q8—22no—
400C4×Q8—41no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—41no—
407C2×C4⋊C4—111no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—111no—
410C2×C4⋊C4—222no—
411C2×C4⋊C4—222no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4C22×D1111yescharacteristic
419C2×C4⋊C4C22×D1111yescharacteristic
420C2×C4⋊C4C22×D1111yescharacteristic
421C2×C22⋊C4—21no—
422C2×C22⋊C4—221no—
423C2×C22⋊C4C22⋊D1111yescharacteristic
424C2×C22⋊C4C22⋊D1111yescharacteristic
425C2×C42—21no—
426C2×C42—21no—
427C2×C42C22×D1111yescharacteristic
428C2×C42C22×D1111yescharacteristic
429#107—222no—
430#107—222no—
431#107—222no—
432C4⋊C8—222no—
433C4⋊C8—441no—
434#103—222no—
435#103—222no—
436#103—222no—
437#103—222no—
438#103—222no—
439#103—441no—
440C22⋊C8—222no—
441#95—21no—
442#95—21no—
443#95—21no—
444#95—21no—
445#95—221no—
446#95—221no—
447#95—221no—
448#95—221no—
449#95C22⋊D1111yescharacteristic
450#95C22⋊D1111yescharacteristic
451C2×C11—24no—
452C2×C11#242511yescharacteristic
453C2×C11C2×#46211yescharacteristic
454C2×C11#304511yescharacteristic
455C2×C11#329911yescharacteristic
456C2×C11#331411yescharacteristic
457C2×C11#333811yescharacteristic
458C2×C11#334411yescharacteristic
459C24C2×C22⋊D1111yescharacteristic
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—221no—
466C2×Q8—221no—
467C2×Q8—221no—
468C2×Q8—221no—
469C2×Q8—221no—
470C2×Q8—221no—
471C2×Q8C2×D4412yes—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—81no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4—442no—
488C22×C4—881no—
489C22×C4—881no—
490C22×C4C2×D4412yes—
491C22×C4#433912yes—
492C22×C4C2×C22⋊D1111yescharacteristic
493C22×C4C2×C22⋊D1111yescharacteristic
494C22×C4C2×C22⋊D1111yescharacteristic
495C22×C4C2×C22⋊D1111yescharacteristic
496C22×C4C2×C22⋊D1111yescharacteristic
497C22×C4C23×D1111yescharacteristic
498Q16—444no—
499C2×C8—112no—
500C2×C8—221no—
501C2×C8—221no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—221no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8—444no—
512C4⋊C4—24no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—42no—
518C4⋊C4—42no—
519C4⋊C4—81no—
520C4⋊C4—221no—
521C4⋊C4—221no—
522C4⋊C4—221no—
523C4⋊C4—221no—
524C4⋊C4—221no—
525C4⋊C4—221no—
526C4⋊C4—442no—
527C4⋊C4—442no—
528C4⋊C4—881no—
529C4⋊C4—881no—
530C4⋊C4—881no—
531C4⋊C4—881no—
532C4⋊C4C2×D4412yes—
533C4⋊C4#434112yes—
534C22⋊C4—24no—
535C22⋊C4—22no—
536C22⋊C4—442no—
537C22⋊C4#432614yescomplemented
538C42—21no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—42no—
543C42—81no—
544C11#2520611yescharacteristic, complemented, Sylow
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23#6698312yes—
550C23C2×#432612yes—
551C23#6700412yes—
552C23C22×C22⋊D1111yescharacteristic
553Q8—22no—
554Q8—22no—
555Q8—41no—
556Q8—41no—
557Q8—441no—
558Q8—441no—
559Q8—441no—
560Q8—441no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—21no—
574C2×C4—22no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—84no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—884no—
603C2×C4#6698312yes—
604C2×C4C2×#432612yes—
605C2×C4C2×#432612yes—
606C2×C4C22×D4411yescharacteristic
607C2×C4C2×#433911yescharacteristic
608C2×C4C2×#434111yescharacteristic
609C2×C4#6703711yescharacteristic
610C2×C4#41×D1111yescharacteristic
611C2×C4#6704311yescharacteristic
612C8—222no—
613C8—441no—
614C8—441no—
615C8—441no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—22no—
621C22—22no—
622C22#1062264414yes—
623C22C2×#6698311yescharacteristic
624C22#1062333711yescharacteristic
625C22C22×#432611yescharacteristic
626C22C2×#6700411yescharacteristic
627C22#1062335511yescharacteristic
628C22#1062336611yescharacteristic
629C22#1062336811yescharacteristic
630C4—22no—
631C4—22no—
632C4—22no—
633C4—42no—
634C4—41no—
635C4—42no—
636C4—42no—
637C4—41no—
638C4—81no—
639C4—881no—
640C4—881no—
641C4—881no—
642C4—881no—
643C4#1062306911yescharacteristic
644C4#1062308511yescharacteristic
645C4#1062308611yescharacteristic
646C4#1062309511yescharacteristic
647C2—24no—
648C2#1307216111yescharacteristic
649C2C2×#1062264411yescharacteristic
650C2#1307815511yescharacteristic
651C2#1308049211yescharacteristic
652C2#1308069711yescharacteristic
653C2#1308100411yescharacteristic
654C2#1308107111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2360C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#2360D11
hypocenterC11#25206
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2360

Complements

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

NH ≅ G/Ntype
4. #13070087C2semidirect
5. #13070024C2semidirect
6. #13070008C2semidirect
7. #13069938C2semidirect
8. #13069374C2semidirect
9. #13069257C2semidirect
10. #13068957C2semidirect
13. #13068621C2semidirect
184. C11×C22⋊C4Q16semidirect
537. C22⋊C4#4326semidirect
544. C11#25206semidirect

Maximal subgroups

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

subgroupindex
C2×#106226572
C2×#106226642
#130730942
#130700872
#130700242
#130700082
#130699382
#130693742
#130692572
#130689572
#130689232
#130687962
#130686212
C2×#106221672
C11×#23602
#2520611