Finite Group Databasebeta

← #14811762

Subgroups — #14811762

Order 2816.

732 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071483C211yesmaximal, characteristic
2#13070178C211yesmaximal, characteristic, complemented
3#13070117C211yesmaximal, characteristic, complemented
4#13070107C211yesmaximal, characteristic, complemented
5#13069951C211yesmaximal, characteristic, complemented
6#13069574C211yesmaximal, characteristic, complemented
7#13069377C211yesmaximal, characteristic, complemented
8#13069205C211yesmaximal, characteristic, complemented
9#13069184C211yesmaximal, characteristic, complemented
10#13068815C211yesmaximal, characteristic
11#13068801C211yesmaximal, characteristic
12#13068704C211yesmaximal, characteristic
13#13068647C211yesmaximal, characteristic
14#13068337C211yesmaximal, characteristic
15C11×#2441C211yesmaximal, characteristic
16C2×C11×#125C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C22×#4318C2211yescharacteristic
20C2×#66930—21no—
21C11×#399—21no—
22C11×#396—21no—
23C11×#389—21no—
24C11×#389C2211yescharacteristic
25C11×#389C2211yescharacteristic
26C11×#387—21no—
27C11×#384C2211yescharacteristic
28C11×#380C2211yescharacteristic
29C4×C11×C22⋊C4C2211yescharacteristic
30#10622825C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32C2×#66872C2211yescharacteristic
33C2×#66872C2211yescharacteristic
34C2×#66871C2211yescharacteristic
35C2×#66871C2211yescharacteristic
36#10622556—21no—
37C4×C4⋊Dic11C2211yescharacteristic
38C4×C4⋊Dic11C2211yescharacteristic
39#10622541C2211yescharacteristic
40#10622541C2211yescharacteristic
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43#10622266—21no—
44#10622266—21no—
45#10622167C2211yescharacteristic
46#10622167C2211yescharacteristic
47#10622167C2211yescharacteristic
48#10622167C2211yescharacteristic
49#10622167C2211yescharacteristic
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×Dic11—21no—
61C11×#125—22no—
62C11×#125—41no—
63C11×#117—22no—
64C11×#117—41no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4D411yescharacteristic
78C2×C11×C22⋊C4D411yescharacteristic
79C2×C42×C11—21no—
80C2×C42×C11C2311yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C2×C22⋊Dic11—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—22no—
85C2×C4⋊Dic11Q814yes—
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11—21no—
94C2×#4318—22no—
95C2×#4318—22no—
96C2×#4318—41no—
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101#66930—44no—
102C11×#95—21no—
103C11×#95—21no—
104C11×#95—21no—
105C11×#95D411yescharacteristic
106C11×#95D411yescharacteristic
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C22⋊(C11⋊C8)—22no—
113#66872—41no—
114#66872—41no—
115#66871—22no—
116#66871—22no—
117C4⋊(C11⋊C8)—22no—
118C4⋊(C11⋊C8)—41no—
119#26014—111nomaximal, Sylow
120C24×C11C2×D411yescharacteristic
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×Q812yes—
135C22×C4×C11#4112yes—
136C22×C4×C11C2411yescharacteristic
137C22×Dic11—24no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—42no—
143C22×Dic11—42no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—42no—
152C11×C4⋊C4—42no—
153C11×C4⋊C4—42no—
154C11×C4⋊C4—42no—
155C11×C4⋊C4—81no—
156C11×C4⋊C4—81no—
157C11×C4⋊C4#4112yes—
158C11×C22⋊C4—22no—
159C11×C22⋊C4—41no—
160C11×C22⋊C4—42no—
161C11×C22⋊C4—81no—
162C42×C11—21no—
163C42×C11—21no—
164C42×C11—21no—
165C42×C11—21no—
166C42×C11—42no—
167C22⋊Dic11—42no—
168C4⋊Dic11—24no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11C2×Q812yes—
176C4⋊Dic11C2×Q812yes—
177Dic11⋊C4—42no—
178Dic11⋊C4—42no—
179C4×Dic11—42no—
180C4×Dic11—42no—
181#4318—44no—
182C2×C11⋊C8—21no—
183C2×C11⋊C8—21no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8—21no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8#4112yes—
194#2441D1111yescharacteristic
195#2344—111no—
196#2100—111no—
197#2088—111no—
198#2086—111no—
199#2059—111no—
200#1989—111no—
201#1948—111no—
202#1921—111no—
203#1918—111no—
204#1854—111no—
205#1851—111no—
206#1824—111no—
207#1809—111no—
208#1736—111no—
209C23×C11—21no—
210C23×C11—21no—
211C23×C11—21no—
212C23×C11—21no—
213C23×C11—21no—
214C23×C11—21no—
215C23×C11C22⋊Q812yes—
216C23×C11C22×D411yescharacteristic
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—22no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
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×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11C22⋊Q812yes—
247C2×C4×C11AGL(1,ℤ/8)12yes—
248C2×C4×C11C22×Q811yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11H(5,𝔽2)11yescharacteristic
253C2×C4×C112−1+411yescharacteristic
254C2×Dic11—22no—
255C2×Dic11—22no—
256C2×Dic11—48no—
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—
267C11⋊C8—22no—
268C11⋊C8—41no—
269C11⋊C8—41no—
270C11⋊C8—41no—
271C22×M16—111no—
272C2×#125C2×D1111yescharacteristic
273C2×#117—221no—
274C2×#117C2×D1111yescharacteristic
275C22×C4⋊C4—111no—
276C2×#107—111no—
277C2×#107—111no—
278C2×#106—111no—
279C2×#106—111no—
280C2×C4⋊C8—111no—
281C2×C4⋊C8—111no—
282C2×C22⋊C8—111no—
283#399—21no—
284#396—21no—
285#389—21no—
286#389—111no—
287#389—111no—
288#389C2×D1111yescharacteristic
289#389C2×D1111yescharacteristic
290#387—21no—
291#387—221no—
292#387—221no—
293#384C2×D1111yescharacteristic
294#381—221no—
295#380—111no—
296#380C2×D1111yescharacteristic
297C4×C4⋊C4—111no—
298C4×C4⋊C4—111no—
299C4×C22⋊C4C2×D1111yescharacteristic
300#340—111no—
301#340—111no—
302#340—111no—
303#340—111no—
304#340—111no—
305#340—111no—
306#340—111no—
307#340—111no—
308#340—111no—
309#340—111no—
310#340—111no—
311#340—111no—
312#336—111no—
313#336—111no—
314C22×C11—22no—
315C22×C11—22no—
316C22×C11—22no—
317C22×C11—41no—
318C22×C11—41no—
319C22×C11—41no—
320C22×C11—41no—
321C22×C11C2×C22⋊Q811yescharacteristic
322C22×C11#54611yescharacteristic
323C22×C11#54711yescharacteristic
324C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
325C22×C11#57511yescharacteristic
326C22×C11#57711yescharacteristic
327C22×C11#57811yescharacteristic
328C4×C11—22no—
329C4×C11—22no—
330C4×C11—41no—
331C4×C11—42no—
332C4×C11—41no—
333C4×C11—41no—
334C4×C11—81no—
335C4×C11—81no—
336C4×C11—81no—
337C4×C11#53311yescharacteristic
338C4×C11#54411yescharacteristic
339C4×C11#55111yescharacteristic
340C4×C11#55211yescharacteristic
341Dic11—42no—
342Dic11—42no—
343Dic11—81no—
344Dic11—81no—
345C23×C4—221no—
346C23×C4C22×D1111yescharacteristic
347C2×M16—222no—
348C2×M16—222no—
349C2×M16—441no—
350C22×C8—111no—
351C22×C8—111no—
352C22×C8—111no—
353C22×C8—111no—
354#125—22no—
355#125—41no—
356#117—22no—
357#117—41no—
358#117—444no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—114no—
366C2×C4⋊C4—111no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—111no—
369C2×C4⋊C4—111no—
370C2×C4⋊C4—222no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4C22×D1111yescharacteristic
375C2×C4⋊C4C22×D1111yescharacteristic
376C2×C4⋊C4C22×D1111yescharacteristic
377C2×C4⋊C4C22×D1111yescharacteristic
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—221no—
381C2×C22⋊C4C22⋊D1111yescharacteristic
382C2×C22⋊C4C22⋊D1111yescharacteristic
383C2×C42—21no—
384C2×C42—221no—
385C2×C42—221no—
386C2×C42C22×D1111yescharacteristic
387C2×C42C22×D1111yescharacteristic
388#107—222no—
389#107—222no—
390#106—441no—
391#106—441no—
392C4⋊C8—222no—
393C4⋊C8—441no—
394C22⋊C8—222no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—221no—
399#95—221no—
400#95—221no—
401#95—221no—
402#95—221no—
403#95C22⋊D1111yescharacteristic
404#95C22⋊D1111yescharacteristic
405C2×C11—42no—
406C2×C11#243811yescharacteristic
407C2×C11#307711yescharacteristic
408C2×C11#308211yescharacteristic
409C2×C11#331711yescharacteristic
410C2×C11#333011yescharacteristic
411C2×C11#334511yescharacteristic
412C2×C11#335211yescharacteristic
413C24C2×C22⋊D1111yescharacteristic
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—224no—
423C22×C4—221no—
424C22×C4—221no—
425C22×C4—221no—
426C22×C4—221no—
427C22×C4—442no—
428C22×C4—442no—
429C22×C4Q8×D1112yes—
430C22×C4#434312yes—
431C22×C4C2×C22⋊D1111yescharacteristic
432C22×C4C2×C22⋊D1111yescharacteristic
433C22×C4C2×C22⋊D1111yescharacteristic
434C22×C4C2×C22⋊D1111yescharacteristic
435C22×C4C2×C22⋊D1111yescharacteristic
436C22×C4C23×D1111yescharacteristic
437M16—444no—
438C2×C8—112no—
439C2×C8—221no—
440C2×C8—221no—
441C2×C8—221no—
442C2×C8—221no—
443C2×C8—221no—
444C2×C8—221no—
445C2×C8—221no—
446C2×C8—221no—
447C2×C8—221no—
448C2×C8—221no—
449C2×C8—221no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—42no—
458C4⋊C4—42no—
459C4⋊C4—42no—
460C4⋊C4—42no—
461C4⋊C4—81no—
462C4⋊C4—81no—
463C4⋊C4—112no—
464C4⋊C4—112no—
465C4⋊C4—224no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—442no—
473C4⋊C4—442no—
474C4⋊C4#434112yes—
475C22⋊C4—22no—
476C22⋊C4—41no—
477C22⋊C4—42no—
478C22⋊C4—81no—
479C22⋊C4—442no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—42no—
485C42—442no—
486C42—442no—
487C11#2601411yescharacteristic, complemented, Sylow
488C23—21no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23—21no—
493C23—21no—
494C23#6699912yes—
495C23C22×C22⋊D1111yescharacteristic
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—22no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—222no—
526C2×C4—222no—
527C2×C4—448no—
528C2×C4—441no—
529C2×C4—441no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4#6699912yes—
539C2×C4#6700212yes—
540C2×C4C2×#434111yescharacteristic
541C2×C4#6703711yescharacteristic
542C2×C4C2×Q8×D1111yescharacteristic
543C2×C4C2×#434311yescharacteristic
544C2×C4#41×D1111yescharacteristic
545C2×C4#6704311yescharacteristic
546C8—222no—
547C8—441no—
548C8—441no—
549C8—441no—
550C22—22no—
551C22—22no—
552C22—22no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22#1062333711yescharacteristic
558C22C2×#6699911yescharacteristic
559C22C2×#6700211yescharacteristic
560C22#1062335311yescharacteristic
561C22#1062335511yescharacteristic
562C22#1062336711yescharacteristic
563C22#1062336911yescharacteristic
564C4—22no—
565C4—22no—
566C4—41no—
567C4—42no—
568C4—41no—
569C4—41no—
570C4—81no—
571C4—81no—
572C4—81no—
573C4—442no—
574C4—442no—
575C4—881no—
576C4—881no—
577C4#1062315311yescharacteristic
578C4#1062315411yescharacteristic
579C4#1062316811yescharacteristic
580C4#1062317311yescharacteristic
581C2—42no—
582C2#1307228811yescharacteristic
583C2#1307840911yescharacteristic
584C2#1307845211yescharacteristic
585C2#1308074211yescharacteristic
586C2#1308092111yescharacteristic
587C2#1308108011yescharacteristic
588C2#1308118511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2441C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#2441D11
hypocenterC11#26014
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2441

Complements

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

NH ≅ G/Ntype
2. #13070178C2semidirect
3. #13070117C2semidirect
4. #13070107C2semidirect
5. #13069951C2semidirect
6. #13069574C2semidirect
7. #13069377C2semidirect
8. #13069205C2semidirect
9. #13069184C2semidirect
487. C11#26014semidirect

Maximal subgroups

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

subgroupindex
#130714832
#130701782
#130701172
#130701072
#130699512
#130695742
#130693772
#130692052
#130691842
#130688152
#130688012
#130687042
#130686472
#130683372
C11×#24412
#2601411