Finite Group Databasebeta

← #14783712

Subgroups — #14783712

Order 2816.

858 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
1D11×#389C211yesmaximal, characteristic
2#13071022C211yesmaximal, characteristic
3#13070185C211yesmaximal, characteristic, complemented
4#13070184C211yesmaximal, characteristic, complemented
5#13070183C211yesmaximal, characteristic, complemented
6#13070182C211yesmaximal, characteristic, complemented
7#13070181C211yesmaximal, characteristic, complemented
8#13070177C211yesmaximal, characteristic, complemented
9#13070176C211yesmaximal, characteristic, complemented
10#13068334C211yesmaximal, characteristic
11#13068334C211yesmaximal, characteristic
12#13068334C211yesmaximal, characteristic
13#13068334C211yesmaximal, characteristic
14#13068308C211yesmaximal, characteristic
15C11×#2101C211yesmaximal, characteristic, complemented
16C22×#4313C2211yescharacteristic
17C22×#4313C2211yescharacteristic
18C2×#66945C2211yescharacteristic
19C2×#66945C2211yescharacteristic
20C2×C4⋊C4×D11—21no—
21C2×C4⋊C4×D11C2211yescharacteristic
22C2×C4⋊C4×D11C2211yescharacteristic
23C2×C42×D11C2211yescharacteristic
24C11×#389C2211yescharacteristic
25C11×#382C2211yescharacteristic
26#10622598C2211yescharacteristic
27#10622589C2211yescharacteristic
28#10622589C2211yescharacteristic
29#10622586C2211yescharacteristic
30#10622585—21no—
31#10622549C2211yescharacteristic
32#10622541C2211yescharacteristic
33#10622280—21no—
34#10622280—21no—
35D11×#95—21no—
36#10622262—21no—
37#10622262—21no—
38#10622260—21no—
39C11×#340C2211yescharacteristic
40C11×#340C2211yescharacteristic
41C11×#340C2211yescharacteristic
42C11×#340C2211yescharacteristic
43C11×#336C2211yescharacteristic
44#10622189C2211yescharacteristic
45#10622189C2211yescharacteristic
46#10622189C2211yescharacteristic
47#10622189C2211yescharacteristic
48#10622188C2211yescharacteristic
49#10622188C2211yescharacteristic
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×C4×D11—21no—
60C22×C4×D11—21no—
61C22×C4×D11D411yescharacteristic
62C22×C4×D11D411yescharacteristic
63C22×C4×D11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C42×C11C2311yescharacteristic
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×Dic11⋊C4—21no—
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11D411yescharacteristic
90C2×C4×Dic11D411yescharacteristic
91C2×C4×Dic11C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C2×#4313—22no—
95C2×#4313—22no—
96C2×#4313—22no—
97C2×#4313—22no—
98C2×#4313—22no—
99C2×#4313—22no—
100#66945—22no—
101#66945—22no—
102#66945—22no—
103#66945—22no—
104C4⋊C4×D11—22no—
105C4⋊C4×D11—22no—
106C4⋊C4×D11—22no—
107C4⋊C4×D11—44no—
108C4⋊C4×D11Q814yes—
109C42×D11—22no—
110C42×D11—22no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119#23747—111nomaximal, Sylow
120C23×D11C2×D411yescharacteristic
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2411yescharacteristic
128C22×Dic11—21no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11—21no—
132C22×Dic11C2×D411yescharacteristic
133C22×Dic11C2×D411yescharacteristic
134C22×Dic11C2×D411yescharacteristic
135C2×C4×D11—22no—
136C2×C4×D11—22no—
137C2×C4×D11—24no—
138C2×C4×D11—22no—
139C2×C4×D11—22no—
140C2×C4×D11—41no—
141C2×C4×D11—41no—
142C2×C4×D11—42no—
143C2×C4×D11—42no—
144C2×C4×D11—42no—
145C2×C4×D11—42no—
146C2×C4×D11—42no—
147C2×C4×D11C2×Q812yes—
148C2×C4×D11#4112yes—
149C2×C4×D11#4112yes—
150C2×C4×D11#4112yes—
151C2×C4×D11#4112yes—
152C2×C4×D11#4112yes—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—42no—
167C11×C4⋊C4C2×Q812yes—
168C42×C11—21no—
169C42×C11—21no—
170(C2×D11)⋊C4—42no—
171(C2×D11)⋊C4—42no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—42no—
180C4⋊Dic11C2×Q812yes—
181Dic11⋊C4—24no—
182Dic11⋊C4—42no—
183Dic11⋊C4—42no—
184Dic11⋊C4—42no—
185Dic11⋊C4—42no—
186Dic11⋊C4—42no—
187Dic11⋊C4—42no—
188Dic11⋊C4—42no—
189C4×Dic11—22no—
190C4×Dic11—22no—
191C4×Dic11—21no—
192C4×Dic11—21no—
193C4×Dic11—42no—
194C4×Dic11—42no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201#4313—44no—
202#4313—44no—
203C2×#389—111no—
204#2285—111no—
205#2101—111no—
206#2101—111no—
207#2101—111no—
208#2101D1111yescharacteristic, complemented
209#2100—111no—
210#2100—111no—
211#2099—111no—
212#2099—111no—
213#1736—111no—
214#1736—111no—
215#1736—111no—
216#1736—111no—
217#1728—111no—
218C23×C11C22×D411yescharacteristic
219C22×D11—21no—
220C22×D11—21no—
221C22×D11—21no—
222C22×D11—21no—
223C22×D11C22⋊Q812yes—
224C22×D11#12312yes—
225C22×D11#12412yes—
226C2×C4×C11—22no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11C22×Q811yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—22no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11C22⋊Q812yes—
267C2×Dic11#12312yes—
268C2×Dic11#12412yes—
269C2×Dic11AGL(1,ℤ/8)12yes—
270C2×Dic11#13712yes—
271C4×D11—44no—
272C4×D11—44no—
273C4×D11—48no—
274C4×D11—84no—
275C4×D11#12514yes—
276C4×D11#12514yes—
277C4×D11#12614yes—
278C4×D11#12614yes—
279C8×C11—41no—
280C8×C11—41no—
281C11⋊C8—41no—
282C11⋊C8—41no—
283C22×M16—111no—
284C22×M16—111no—
285C2×#117—111no—
286C2×#117—111no—
287C22×C4⋊C4—111no—
288C22×C4⋊C4—111no—
289C22×C4⋊C4—221no—
290C22×C42—111no—
291#389—111no—
292#389—111no—
293#389—111no—
294#389—221no—
295#389—221no—
296#389C2×D1111yescharacteristic
297#384—111no—
298#384—111no—
299#382—111no—
300#382C2×D1111yescharacteristic
301#380—221no—
302#380—221no—
303C4×C4⋊C4—221no—
304C4×C4⋊C4—221no—
305C2×#95—221no—
306#340—111no—
307#340—111no—
308#340—111no—
309#340—111no—
310#340—111no—
311#340—111no—
312#340—111no—
313#340—111no—
314#340—111no—
315#340—111no—
316#340—111no—
317#340—111no—
318#340C2×D1111yescharacteristic
319#340C2×D1111yescharacteristic
320#340C2×D1111yescharacteristic
321#340C2×D1111yescharacteristic
322#336—111no—
323#336—111no—
324#336—111no—
325#336C2×D1111yescharacteristic
326C22×C11C2×C22⋊Q811yescharacteristic
327C22×C11C2×#12311yescharacteristic
328C22×C11C2×#12411yescharacteristic
329C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
330C22×C11C2×#13711yescharacteristic
331C22×C11#57511yescharacteristic
332C22×C11#57511yescharacteristic
333C2×D11—22no—
334C2×D11—22no—
335C2×D11—22no—
336C2×D11—22no—
337C2×D11—22no—
338C2×D11—22no—
339C2×D11#40014yes—
340C4×C11—42no—
341C4×C11—41no—
342C4×C11—41no—
343C4×C11—81no—
344C4×C11—81no—
345C4×C11—81no—
346C4×C11C2×#12511yescharacteristic
347C4×C11C2×#12511yescharacteristic
348C4×C11C2×#12611yescharacteristic
349C4×C11C2×#12611yescharacteristic
350Dic11—22no—
351Dic11—22no—
352Dic11—42no—
353Dic11—81no—
354Dic11—81no—
355Dic11—81no—
356Dic11#40014yes—
357C23×C4—111no—
358C23×C4—111no—
359C23×C4—111no—
360C23×C4—221no—
361C23×C4—221no—
362C2×M16—222no—
363C2×M16—222no—
364C2×M16—222no—
365C2×M16—222no—
366C2×M16—222no—
367C2×M16—222no—
368C22×C8—111no—
369C22×C8—111no—
370C22×C8C22×D1111yescharacteristic
371C22×C8C22×D1111yescharacteristic
372#117—222no—
373#117—222no—
374#117—222no—
375#117—222no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—111no—
378C2×C4⋊C4—114no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—222no—
383C2×C4⋊C4—222no—
384C2×C4⋊C4—222no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4—444no—
395C2×C4⋊C4C22×D1111yescharacteristic
396C2×C4⋊C4C22×D1111yescharacteristic
397C2×C4⋊C4C22×D1111yescharacteristic
398C2×C4⋊C4C22×D1111yescharacteristic
399C2×C22⋊C4—221no—
400C2×C22⋊C4—221no—
401C2×C42—111no—
402C2×C42—111no—
403C2×C42—111no—
404C2×C42—222no—
405C2×C42—222no—
406C2×C42—221no—
407C2×C42—221no—
408C2×C42C22×D1111yescharacteristic
409#95—21no—
410#95—21no—
411#95—21no—
412#95—221no—
413#95—221no—
414#95—221no—
415#95—221no—
416#95—221no—
417C2×C11C2×#40011yescharacteristic
418C2×C11#307711yescharacteristic
419C2×C11#307811yescharacteristic
420C2×C11#309411yescharacteristic
421C2×C11#309511yescharacteristic
422C2×C11#314111yescharacteristic
423C2×C11#314211yescharacteristic
424D11—24no—
425C24—111no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—111no—
431C22×C4—112no—
432C22×C4—112no—
433C22×C4—112no—
434C22×C4—112no—
435C22×C4—112no—
436C22×C4—112no—
437C22×C4—111no—
438C22×C4—111no—
439C22×C4—222no—
440C22×C4—222no—
441C22×C4—222no—
442C22×C4—222no—
443C22×C4—224no—
444C22×C4—221no—
445C22×C4—221no—
446C22×C4—221no—
447C22×C4—221no—
448C22×C4—441no—
449C22×C4—441no—
450C22×C4—442no—
451C22×C4—442no—
452C22×C4—442no—
453C22×C4—442no—
454C22×C4—442no—
455C22×C4D4×D1111yescharacteristic
456C22×C4D4×D1111yescharacteristic
457C22×C4C23×D1111yescharacteristic
458M16—444no—
459M16—444no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—221no—
467C2×C8—221no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8—221no—
471C2×C8—221no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—42no—
480C4⋊C4—112no—
481C4⋊C4—224no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—442no—
490C4⋊C4—442no—
491C4⋊C4—442no—
492C4⋊C4—442no—
493C4⋊C4—442no—
494C4⋊C4—442no—
495C4⋊C4—442no—
496C4⋊C4—442no—
497C4⋊C4Q8×D1112yes—
498C22⋊C4—442no—
499C22⋊C4—442no—
500C42—21no—
501C42—21no—
502C42—222no—
503C42—222no—
504C42—221no—
505C42—221no—
506C42—442no—
507C42—442no—
508C11#2374711yescharacteristic, complemented, Sylow
509C23—112no—
510C23—112no—
511C23—112no—
512C23—221no—
513C23—221no—
514C23—221no—
515C23—221no—
516C23C2×D4×D1111yescharacteristic
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—22no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—112no—
536C2×C4—112no—
537C2×C4—112no—
538C2×C4—114no—
539C2×C4—114no—
540C2×C4—114no—
541C2×C4—114no—
542C2×C4—112no—
543C2×C4—112no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—221no—
547C2×C4—221no—
548C2×C4—222no—
549C2×C4—444no—
550C2×C4—444no—
551C2×C4—448no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4—441no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—884no—
564C2×C4C2×Q8×D1111yescharacteristic
565C2×C4#41×D1111yescharacteristic
566C2×C4#41×D1111yescharacteristic
567C2×C4#41×D1111yescharacteristic
568C2×C4#41×D1111yescharacteristic
569C2×C4#41×D1111yescharacteristic
570C8—41no—
571C8—41no—
572C8—441no—
573C8—441no—
574C22—114no—
575C22—222no—
576C22—222no—
577C22—222no—
578C22—222no—
579C22—222no—
580C22—222no—
581C22D11×C22⋊Q811yescharacteristic
582C22D11×#12311yescharacteristic
583C22D11×#12411yescharacteristic
584C22#1062329911yescharacteristic
585C22#1062329911yescharacteristic
586C22D11×AGL(1,ℤ/8)11yescharacteristic
587C22D11×#13711yescharacteristic
588C4—41no—
589C4—41no—
590C4—42no—
591C4—81no—
592C4—81no—
593C4—81no—
594C4—114no—
595C4—222no—
596C4—222no—
597C4—442no—
598C4—881no—
599C4—881no—
600C4—881no—
601C4D11×#12511yescharacteristic
602C4D11×#12511yescharacteristic
603C4D11×#12611yescharacteristic
604C4D11×#12611yescharacteristic
605C2—224no—
606C2D11×#40011yescharacteristic
607C2#1307841111yescharacteristic
608C2#1307841911yescharacteristic
609C2#1307855511yescharacteristic
610C2#1307856311yescharacteristic
611C2#1307900811yescharacteristic
612C2#1307901311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2101C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#2101D11
hypocenterC11#23747
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2101

Complements

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

NH ≅ G/Ntype
3. #13070185C2semidirect
4. #13070184C2semidirect
5. #13070183C2semidirect
6. #13070182C2semidirect
7. #13070181C2semidirect
8. #13070177C2semidirect
9. #13070176C2semidirect
15. C11×#2101C2semidirect
208. #2101D11semidirect
508. C11#23747semidirect

Maximal subgroups

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

subgroupindex
D11×#3892
#130710222
#130701852
#130701842
#130701832
#130701822
#130701812
#130701772
#130701762
#130683342
#130683082
C11×#21012
#2374711