Finite Group Databasebeta

← #14764348

Subgroups — #14764348

Order 2816.

786 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622332C211yesmaximal, characteristic
2#13071019C211yesmaximal, characteristic
3#13071011C211yesmaximal, characteristic
4#13069387C211yesmaximal, characteristic, complemented
5#13069385C211yesmaximal, characteristic, complemented
6#13069383C211yesmaximal, characteristic, complemented
7#13069381C211yesmaximal, characteristic, complemented
8#13068817C211yesmaximal, characteristic
9#13068815C211yesmaximal, characteristic
10#13068813C211yesmaximal, characteristic
11#13068783C211yesmaximal, characteristic, complemented
12#13068781C211yesmaximal, characteristic, complemented
13#13068748C211yesmaximal, characteristic, complemented
14#13068748C211yesmaximal, characteristic, complemented
15C11×#1854C211yesmaximal, characteristic
16C2×C11×#117C2211yescharacteristic
17C2×#66979C2211yescharacteristic
18C22×C4×Dic11C2211yescharacteristic
19C2×C11×#107C2211yescharacteristic
20C2×C11×#106C2211yescharacteristic
21C2×C11×C22⋊C8C2211yescharacteristic
22C11×#380C2211yescharacteristic
23#10622825C2211yescharacteristic
24C2×C22⋊(C11⋊C8)C2211yescharacteristic
25C2×#66882C2211yescharacteristic
26C2×#66881C2211yescharacteristic
27C2×#66879C2211yescharacteristic
28C2×#66879C2211yescharacteristic
29C2×Dic11⋊C8C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31#10622590C2211yescharacteristic
32#10622590C2211yescharacteristic
33#10622590C2211yescharacteristic
34#10622590C2211yescharacteristic
35#10622589C2211yescharacteristic
36#10622589C2211yescharacteristic
37C4⋊C4×Dic11C2211yescharacteristic
38C4⋊C4×Dic11C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40C2×#66872C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43#10622556—21no—
44#10622555—21no—
45#10622555—21no—
46C22⋊C4×Dic11—21no—
47C4×Dic11⋊C4—21no—
48C4×Dic11⋊C4—21no—
49#10622332C418yescomplemented
50#10622264—21no—
51#10622261—21no—
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×Dic11D411yescharacteristic
62C23×Dic11D411yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C11×#117—41no—
66C11×#117—41no—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—21no—
73C2×C42×C11—21no—
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—21no—
76#66979—41no—
77#66979—41no—
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11C2×C414yes—
90C2×C4×Dic11D411yescharacteristic
91C2×C4×Dic11D411yescharacteristic
92C2×C4×Dic11Q814yes—
93C2×C4×Dic11C2311yescharacteristic
94C2×C4×Dic11C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C11×#107—41no—
98C11×#106—41no—
99C11×C22⋊C8C2×C414yes—
100C11×#95—21no—
101C11⋊#95—21no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C22⋊(C11⋊C8)C2×C414yes—
113#66882—41no—
114#66881—41no—
115#66879C2×C414yes—
116#66879C2×C414yes—
117Dic11⋊C8C2×C414yes—
118Dic11⋊C8C2×C414yes—
119#66872—41no—
120#66872—41no—
121#66871—41no—
122#66871—41no—
123#21989—111nomaximal, Sylow
124C24×C11C2×D411yescharacteristic
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11C22×C412yes—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×Q812yes—
136C22×C4×C11C2411yescharacteristic
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—41no—
142C22×Dic11—41no—
143C22×Dic11—41no—
144C22×Dic11—41no—
145C22×Dic11C4⋊C414yes—
146C22×Dic11C4⋊C414yes—
147C22×Dic11C2×D411yescharacteristic
148C22×Dic11C2×D411yescharacteristic
149C22×Dic11C2×D411yescharacteristic
150C22×Dic11C2×D411yescharacteristic
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11C22×C412yes—
156C2×C8×C11C22×C412yes—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—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×C22⋊C4—42no—
166C11×C22⋊C4—42no—
167C42×C11—42no—
168C22⋊Dic11—42no—
169C22⋊Dic11—42no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178Dic11⋊C4—42no—
179Dic11⋊C4—42no—
180Dic11⋊C4—42no—
181Dic11⋊C4—42no—
182C4×Dic11—42no—
183C4×Dic11—42no—
184C4×Dic11—42no—
185C4×Dic11C4⋊C414yes—
186C4×Dic11C4⋊C414yes—
187C4×Dic11C22×C412yes—
188C4×Dic11C22×C412yes—
189C4×Dic11C2×Q812yes—
190C4×Dic11C2×Q812yes—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8C22×C412yes—
196C2×C11⋊C8C22×C412yes—
197C2×#432—111no—
198#2285—111no—
199#2283—111no—
200#1949—111no—
201#1949—111no—
202#1949—111no—
203#1949—111no—
204#1854—111no—
205#1854—111no—
206#1854—111no—
207#1854D1111yescharacteristic
208#1847—111no—
209#1847—111no—
210#1836—111no—
211#1836—111no—
212C23×C11—21no—
213C23×C11—21no—
214C23×C11—21no—
215C23×C11—21no—
216C23×C11—21no—
217C23×C11—21no—
218C23×C11C2×C4⋊C412yes—
219C23×C11C22×D411yescharacteristic
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11C2×C4⋊C412yes—
239C2×C4×C11C23×C411yescharacteristic
240C2×C4×C11C22×Q811yescharacteristic
241C2×C4×C11H(5,𝔽2)11yescharacteristic
242C2×C4×C11H(5,𝔽2)11yescharacteristic
243C2×C4×C112−1+411yescharacteristic
244C2×C4×C112−1+411yescharacteristic
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—44no—
254C2×Dic11—44no—
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×Dic11—41no—
267C2×Dic11C2×C4⋊C412yes—
268C2×Dic11C2×C4⋊C412yes—
269C2×Dic11C2×C4⋊C412yes—
270C2×Dic11C2×C4⋊C412yes—
271C8×C11—22no—
272C8×C11—22no—
273C11⋊C8—22no—
274C11⋊C8—22no—
275C2×#117—111no—
276C2×#117C2×D1111yescharacteristic
277C22×C42—111no—
278#432—118no—
279C2×#107—111no—
280C2×#107—111no—
281C2×#107—111no—
282C2×#107C2×D1111yescharacteristic
283C2×#106—111no—
284C2×#106—111no—
285C2×#106—111no—
286C2×#106C2×D1111yescharacteristic
287C2×C4⋊C8—111no—
288C2×C4⋊C8—111no—
289C2×C22⋊C8—111no—
290C2×C22⋊C8C2×D1111yescharacteristic
291C2×#97—111no—
292C2×#97—111no—
293#384—111no—
294#384—111no—
295#383—221no—
296#382—111no—
297#382—111no—
298#382—111no—
299#382—111no—
300#381—221no—
301#380—111no—
302#380—221no—
303#380—221no—
304#380C2×D1111yescharacteristic
305C4×C4⋊C4—111no—
306C4×C4⋊C4—111no—
307C4×C4⋊C4—221no—
308C4×C4⋊C4—221no—
309C4×C22⋊C4—221no—
310#376—221no—
311#340—111no—
312#340—111no—
313#340—111no—
314#340—111no—
315#340—111no—
316#340—111no—
317#340C2×D1111yescharacteristic
318#340C2×D1111yescharacteristic
319C22×C11—22no—
320C22×C11—22no—
321C22×C11—22no—
322C22×C11—41no—
323C22×C11—41no—
324C22×C11—41no—
325C22×C11—41no—
326C22×C11C22×C4⋊C411yescharacteristic
327C22×C11#53511yescharacteristic
328C22×C11#53611yescharacteristic
329C22×C11#57511yescharacteristic
330C22×C11#57511yescharacteristic
331C22×C11#57511yescharacteristic
332C22×C11#57511yescharacteristic
333C4×C11—22no—
334C4×C11—81no—
335C4×C11—81no—
336C4×C11—81no—
337C4×C11—81no—
338C4×C11#52011yescharacteristic
339C4×C11#52011yescharacteristic
340C4×C11#54411yescharacteristic
341C4×C11#54411yescharacteristic
342Dic11—22no—
343Dic11—22no—
344Dic11—22no—
345Dic11—22no—
346Dic11—81no—
347Dic11—81no—
348Dic11—81no—
349Dic11—81no—
350C23×C4—111no—
351C23×C4—111no—
352C23×C4C22×D1111yescharacteristic
353C22×C8—111no—
354C22×C8—111no—
355C22×C8C22×D1111yescharacteristic
356C22×C8C22×D1111yescharacteristic
357#117—41no—
358#117—41no—
359#117—441no—
360#117—441no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—111no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4C22×D1111yescharacteristic
370C2×C4⋊C4C22×D1111yescharacteristic
371C2×C4⋊C4C22×D1111yescharacteristic
372C2×C4⋊C4C22×D1111yescharacteristic
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—221no—
376C2×C22⋊C4—221no—
377C2×C42—21no—
378C2×C42—114no—
379C2×C42—111no—
380C2×C42—111no—
381C2×C42—114no—
382C2×C42—111no—
383C2×C42—111no—
384C2×C42—221no—
385C2×C42—221no—
386C2×C42—221no—
387#107—41no—
388#107—441no—
389#107—441no—
390#107—441no—
391#106—41no—
392#106—441no—
393#106—441no—
394#106—441no—
395C4⋊C8—114no—
396C4⋊C8—114no—
397C22⋊C8—114no—
398C22⋊C8C4×D1114yes—
399#97—114no—
400#97—114no—
401#95—21no—
402#95—221no—
403#95—221no—
404#95—221no—
405#95—221no—
406#95—221no—
407#95—221no—
408#95—221no—
409#95—221no—
410#95—221no—
411#95—221no—
412#95—221no—
413C2×C11—42no—
414C2×C11#231711yescharacteristic
415C2×C11#291111yescharacteristic
416C2×C11#291111yescharacteristic
417C2×C11#321911yescharacteristic
418C2×C11#321911yescharacteristic
419C2×C11#324011yescharacteristic
420C2×C11#324011yescharacteristic
421C24D4×D1111yescharacteristic
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—111no—
431C22×C4—111no—
432C22×C4—111no—
433C22×C4—111no—
434C22×C4—114no—
435C22×C4—114no—
436C22×C4—221no—
437C22×C4—221no—
438C22×C4—221no—
439C22×C4—221no—
440C22×C4—441no—
441C22×C4—441no—
442C22×C4—441no—
443C22×C4—441no—
444C22×C4C2×C4×D1112yes—
445C22×C4D4×D1111yescharacteristic
446C22×C4Q8×D1112yes—
447C22×C4C23×D1111yescharacteristic
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—112no—
453C2×C8—112no—
454C2×C8—221no—
455C2×C8—221no—
456C2×C8—221no—
457C2×C8—221no—
458C2×C8C2×C4×D1112yes—
459C2×C8C2×C4×D1112yes—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—442no—
477C4⋊C4—442no—
478C4⋊C4—442no—
479C4⋊C4—442no—
480C22⋊C4—42no—
481C22⋊C4—42no—
482C22⋊C4—442no—
483C22⋊C4—442no—
484C42—42no—
485C42—114no—
486C42—114no—
487C42—112no—
488C42—112no—
489C42—112no—
490C42—112no—
491C42—442no—
492C42—442no—
493C42—442no—
494C11#2198911yescharacteristic, complemented, Sylow
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23—21no—
501C23C4⋊C4×D1112yes—
502C23C2×D4×D1111yescharacteristic
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—112no—
522C2×C4—112no—
523C2×C4—112no—
524C2×C4—112no—
525C2×C4—221no—
526C2×C4—221no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—221no—
533C2×C4—444no—
534C2×C4—444no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4—441no—
540C2×C4—441no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4C4⋊C4×D1112yes—
548C2×C4C22×C4×D1111yescharacteristic
549C2×C4#6703711yescharacteristic
550C2×C4#6703711yescharacteristic
551C2×C4C2×Q8×D1111yescharacteristic
552C2×C4#6704311yescharacteristic
553C2×C4#6704311yescharacteristic
554C8—22no—
555C8—22no—
556C8—222no—
557C8—222no—
558C22—22no—
559C22—22no—
560C22—22no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22C2×C4⋊C4×D1111yescharacteristic
566C22#1062312311yescharacteristic
567C22#1062317911yescharacteristic
568C22#1062329911yescharacteristic
569C22#1062329911yescharacteristic
570C22#1062330411yescharacteristic
571C22#1062330811yescharacteristic
572C4—22no—
573C4—81no—
574C4—81no—
575C4—81no—
576C4—81no—
577C4—222no—
578C4—222no—
579C4—222no—
580C4—222no—
581C4—881no—
582C4—881no—
583C4—881no—
584C4—881no—
585C4#1062307711yescharacteristic
586C4#1062307711yescharacteristic
587C4#1062315411yescharacteristic
588C4#1062315411yescharacteristic
589C2—42no—
590C2#1307123511yescharacteristic
591C2#1307720311yescharacteristic
592C2#1307720411yescharacteristic
593C2#1307965111yescharacteristic
594C2#1307965711yescharacteristic
595C2#1307985411yescharacteristic
596C2#1307986011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1854C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#1854D11
hypocenterC11#21989
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1854

Complements

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

NH ≅ G/Ntype
4. #13069387C2semidirect
5. #13069385C2semidirect
6. #13069383C2semidirect
7. #13069381C2semidirect
11. #13068783C2semidirect
12. #13068781C2semidirect
13. #13068748C2semidirect
14. #13068748C2semidirect
49. #10622332C4semidirect
494. C11#21989semidirect

Maximal subgroups

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

subgroupindex
C2×#106223322
#130710192
#130710112
#130693872
#130693852
#130693832
#130693812
#130688172
#130688152
#130688132
#130687832
#130687812
#130687482
C11×#18542
#2198911