Finite Group Databasebeta

← #14822340

Subgroups — #14822340

Order 2816.

692 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071672C211yesmaximal, characteristic
2#13070025C211yesmaximal, characteristic
3#13069994C211yesmaximal, characteristic
4#13069862C211yesmaximal, characteristic
5#13069862C211yesmaximal, characteristic
6#13069291C211yesmaximal, characteristic
7#13069250C211yesmaximal, characteristic
8#13069191C211yesmaximal, characteristic
9#13069191C211yesmaximal, characteristic
10#13069175C211yesmaximal, characteristic
11#13068883C211yesmaximal, characteristic
12#13068883C211yesmaximal, characteristic
13#13068618C211yesmaximal, characteristic
14C4×#66874C211yesmaximal, characteristic
15C11×#2506C211yesmaximal, characteristic
16C2×C11×#125—21no—
17C2×#66922C2211yescharacteristic
18C2×C4×Dic22C2211yescharacteristic
19C2×C4×Dic22C2211yescharacteristic
20C11×#400—21no—
21C11×#398—21no—
22C11×#389C2211yescharacteristic
23C11×#389C2211yescharacteristic
24C11×#389C2211yescharacteristic
25C11×#389C2211yescharacteristic
26C11×#387—21no—
27C11×#384C2211yescharacteristic
28C4×C11×C4⋊C4C2211yescharacteristic
29C4×C11×C4⋊C4C2211yescharacteristic
30C4⋊C4×Dic11—21no—
31#10622586—21no—
32C2×#66874C2211yescharacteristic
33C2×#66874C2211yescharacteristic
34C2×#66874C2211yescharacteristic
35C2×#66874C2211yescharacteristic
36C2×#66874C2211yescharacteristic
37C2×#66874C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66872C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C4×C4⋊Dic11C2211yescharacteristic
43#10622542C2211yescharacteristic
44#10622542C2211yescharacteristic
45C2×C4⋊(C11⋊C8)C2211yescharacteristic
46C2×C4×C11⋊C8C2211yescharacteristic
47#10622267—21no—
48#10622267—21no—
49#10622167C2211yescharacteristic
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×Dic22C2311yescharacteristic
60C22×Dic22C2311yescharacteristic
61C11×#125—44no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4D411yescharacteristic
69C2×C11×C4⋊C4D411yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C42×C11—21no—
75C2×C42×C11C2311yescharacteristic
76C2×C42×C11C2311yescharacteristic
77C2×C42×C11C2311yescharacteristic
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×C4×Dic11—21no—
85C2×C4×Dic11—21no—
86C2×C4×Dic11—21no—
87C22×C11⋊C8C2311yescharacteristic
88C22×C11⋊C8C2311yescharacteristic
89C22×C11⋊C8C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91#66922—22no—
92#66922—22no—
93C4×Dic22—22no—
94C4×Dic22—22no—
95C4×Dic22—41no—
96C4×Dic22—41no—
97C11×#95—21no—
98C11×#95—21no—
99C11×#95—21no—
100C11×#95—21no—
101C11×#95—21no—
102C11×#95D411yescharacteristic
103C11×#95D411yescharacteristic
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109#66874—22no—
110#66874—22no—
111#66874—22no—
112#66874—22no—
113#66874—22no—
114#66874—22no—
115#66874—41no—
116#66874—41no—
117#66872—22no—
118#66872—22no—
119C4⋊(C11⋊C8)—41no—
120C4×C11⋊C8—41no—
121#26756—111nomaximal, Sylow
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2411yescharacteristic
133C22×Dic11—21no—
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11—21no—
137C2×Dic22—21no—
138C2×Dic22—21no—
139C2×Dic22—21no—
140C2×Dic22—21no—
141C2×Dic22—21no—
142C2×Dic22—21no—
143C2×Dic22—21no—
144C2×Dic22—21no—
145C2×Dic22—21no—
146C2×Dic22—21no—
147C2×Dic22#4112yes—
148C2×Dic22#4112yes—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—41no—
157C11×C4⋊C4—42no—
158C11×C4⋊C4—42no—
159C11×C4⋊C4—42no—
160C11×C4⋊C4—42no—
161C11×C4⋊C4—42no—
162C11×C4⋊C4—42no—
163C11×C4⋊C4SD1614yes—
164C11×C4⋊C4#4112yes—
165C42×C11—21no—
166C42×C11—21no—
167C42×C11—21no—
168C42×C11—21no—
169C42×C11—21no—
170C42×C11—21no—
171C42×C11—42no—
172C4⋊Dic11—24no—
173C4⋊Dic11—24no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11#4112yes—
178Dic11⋊C4—42no—
179Dic11⋊C4—42no—
180C4×Dic11—42no—
181C4×Dic11—42no—
182C4×Dic11—42no—
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—21no—
194C2×C11⋊C8—21no—
195#2506D1111yescharacteristic
196#2365—111no—
197#2072—111no—
198#2066—111no—
199#2043—111no—
200#2043—111no—
201#1933—111no—
202#1927—111no—
203#1919—111no—
204#1919—111no—
205#1916—111no—
206#1865—111no—
207#1865—111no—
208#1803—111no—
209C4×#103—111no—
210C23×C11C22×D411yescharacteristic
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—22no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
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×SD1612yes—
239C2×C4×C11C2×SD1612yes—
240C2×C4×C11C2×SD1612yes—
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C2×C4×C11H(5,𝔽2)11yescharacteristic
246C2×C4×C112−1+411yescharacteristic
247C2×Dic11—22no—
248C2×Dic11—22no—
249C2×Dic11—22no—
250C2×Dic11—41no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259Dic22—22no—
260Dic22—22no—
261Dic22—22no—
262Dic22—22no—
263Dic22—41no—
264Dic22—41no—
265Dic22—41no—
266Dic22—41no—
267C11⋊C8—41no—
268C11⋊C8—41no—
269C11⋊C8—41no—
270C11⋊C8—41no—
271C2×C4⋊Q8—111no—
272C2×#125—21no—
273C2×C4×Q8—111no—
274C2×C4×Q8—111no—
275C2×#106—111no—
276C2×#106—111no—
277C2×C4⋊C8—111no—
278C2×#103—111no—
279C2×#103—111no—
280C2×#103—111no—
281C2×#103—111no—
282C2×#103—111no—
283C2×#103—111no—
284C2×#103—111no—
285C2×#103—111no—
286C2×C4×C8—111no—
287#400—21no—
288#398—21no—
289#391—111no—
290#391—111no—
291#389—221no—
292#389C2×D1111yescharacteristic
293#389C2×D1111yescharacteristic
294#389C2×D1111yescharacteristic
295#389C2×D1111yescharacteristic
296#387—21no—
297#387—221no—
298#387—221no—
299#384C2×D1111yescharacteristic
300C4×C4⋊C4—111no—
301C4×C4⋊C4—221no—
302C4×C4⋊C4C2×D1111yescharacteristic
303C4×C4⋊C4C2×D1111yescharacteristic
304#340—111no—
305#340—111no—
306#340—111no—
307#340—111no—
308#340—111no—
309#340—111no—
310#336—111no—
311#336—111no—
312#336—111no—
313#336—111no—
314C22×C11#52511yescharacteristic
315C22×C11#54611yescharacteristic
316C22×C11#54811yescharacteristic
317C22×C11C22×SD1611yescharacteristic
318C22×C11#57511yescharacteristic
319C22×C11#57811yescharacteristic
320C22×C11#57811yescharacteristic
321C4×C11—22no—
322C4×C11—22no—
323C4×C11—22no—
324C4×C11—42no—
325C4×C11—41no—
326C4×C11—41no—
327C4×C11—41no—
328C4×C11—81no—
329C4×C11—81no—
330C4×C11—81no—
331C4×C11#52911yescharacteristic
332C4×C11#53911yescharacteristic
333C4×C11#55211yescharacteristic
334C4×C11#55311yescharacteristic
335Dic11—42no—
336Dic11—42no—
337Dic11—42no—
338Dic11—81no—
339C22×Q8—111no—
340C22×Q8—111no—
341C22×C8—111no—
342C22×C8—111no—
343C22×C8—111no—
344C22×C8—111no—
345C4⋊Q8—222no—
346C4⋊Q8—222no—
347#125—44no—
348C4×Q8—222no—
349C4×Q8—222no—
350C4×Q8—441no—
351C4×Q8—441no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—111no—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—221no—
361C2×C4⋊C4—221no—
362C2×C4⋊C4—221no—
363C2×C4⋊C4—221no—
364C2×C4⋊C4C22⋊D1111yescharacteristic
365C2×C4⋊C4C22⋊D1111yescharacteristic
366C2×C4⋊C4C22×D1111yescharacteristic
367C2×C4⋊C4C22×D1111yescharacteristic
368C2×C4⋊C4C22×D1111yescharacteristic
369C2×C4⋊C4C22×D1111yescharacteristic
370C2×C42—21no—
371C2×C42—221no—
372C2×C42—221no—
373C2×C42—221no—
374C2×C42C22×D1111yescharacteristic
375C2×C42C22×D1111yescharacteristic
376C2×C42C22×D1111yescharacteristic
377#106—222no—
378#106—222no—
379C4⋊C8—441no—
380#103—222no—
381#103—222no—
382#103—222no—
383#103—222no—
384#103—222no—
385#103—222no—
386#103—441no—
387#103—441no—
388C4×C8—441no—
389#95—21no—
390#95—21no—
391#95—21no—
392#95—21no—
393#95—21no—
394#95—221no—
395#95—221no—
396#95—221no—
397#95—221no—
398#95—221no—
399#95C22⋊D1111yescharacteristic
400#95C22⋊D1111yescharacteristic
401C2×C11#246011yescharacteristic
402C2×C11#310311yescharacteristic
403C2×C11#312711yescharacteristic
404C2×C11#329811yescharacteristic
405C2×C11#331511yescharacteristic
406C2×C11#335911yescharacteristic
407C2×C11#337711yescharacteristic
408C2×Q8—112no—
409C2×Q8—112no—
410C2×Q8—221no—
411C2×Q8—221no—
412C2×Q8—221no—
413C2×Q8—221no—
414C2×Q8—221no—
415C2×Q8—221no—
416C2×Q8—221no—
417C2×Q8—221no—
418C2×Q8—221no—
419C2×Q8—221no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—221no—
425C22×C4—221no—
426C22×C4—221no—
427C22×C4—221no—
428C22×C4C2×C22⋊D1111yescharacteristic
429C22×C4C2×C22⋊D1111yescharacteristic
430C22×C4C2×C22⋊D1111yescharacteristic
431C22×C4C2×C22⋊D1111yescharacteristic
432C22×C4C2×C22⋊D1111yescharacteristic
433C22×C4C2×C22⋊D1111yescharacteristic
434C22×C4C23×D1111yescharacteristic
435C2×C8—221no—
436C2×C8—221no—
437C2×C8—221no—
438C2×C8—221no—
439C2×C8—221no—
440C2×C8—221no—
441C2×C8—221no—
442C2×C8—221no—
443C2×C8—221no—
444C2×C8—221no—
445C2×C8—221no—
446C2×C8—221no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—41no—
455C4⋊C4—42no—
456C4⋊C4—42no—
457C4⋊C4—42no—
458C4⋊C4—42no—
459C4⋊C4—42no—
460C4⋊C4—42no—
461C4⋊C4—112no—
462C4⋊C4—224no—
463C4⋊C4—224no—
464C4⋊C4—221no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—442no—
468C4⋊C4—442no—
469C4⋊C4#432414yes—
470C4⋊C4#434312yes—
471C42—21no—
472C42—21no—
473C42—21no—
474C42—21no—
475C42—21no—
476C42—21no—
477C42—42no—
478C42—442no—
479C42—442no—
480C42—442no—
481C11#2675611yescharacteristic, complemented, Sylow
482C23C22×C22⋊D1111yescharacteristic
483Q8—222no—
484Q8—222no—
485Q8—222no—
486Q8—222no—
487Q8—441no—
488Q8—441no—
489Q8—441no—
490Q8—441no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—22no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—41no—
508C2×C4—41no—
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—222no—
519C2×C4—222no—
520C2×C4—222no—
521C2×C4—441no—
522C2×C4—441no—
523C2×C4—441no—
524C2×C4—441no—
525C2×C4—441no—
526C2×C4—441no—
527C2×C4—441no—
528C2×C4—441no—
529C2×C4—441no—
530C2×C4C2×#432412yes—
531C2×C4C2×#432412yes—
532C2×C4C2×#432412yes—
533C2×C4C2×#434311yescharacteristic
534C2×C4#6704011yescharacteristic
535C2×C4#41×D1111yescharacteristic
536C2×C4#41×D1111yescharacteristic
537C2×C4#41×D1111yescharacteristic
538C2×C4#6704211yescharacteristic
539C8—441no—
540C8—441no—
541C8—441no—
542C8—441no—
543C22C22×#432411yescharacteristic
544C22#1062334811yescharacteristic
545C22#1062335311yescharacteristic
546C22#1062335911yescharacteristic
547C22#1062336011yescharacteristic
548C22#1062336911yescharacteristic
549C22#1062336911yescharacteristic
550C4—22no—
551C4—22no—
552C4—22no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—42no—
557C4—81no—
558C4—81no—
559C4—81no—
560C4—442no—
561C4—442no—
562C4—442no—
563C4—881no—
564C4#1062322211yescharacteristic
565C4#1062322311yescharacteristic
566C4#1062322411yescharacteristic
567C4#1062322611yescharacteristic
568C2#1307256411yescharacteristic
569C2#1307864311yescharacteristic
570C2#1307891111yescharacteristic
571C2#1308047511yescharacteristic
572C2#1308070611yescharacteristic
573C2#1308125811yescharacteristic
574C2#1308145811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2506C2
socle, prime radicalC23×C11C22×D4
hypercenter#2506D11
hypocenterC11#26756
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2506

Complements

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

NH ≅ G/Ntype
481. C11#26756semidirect

Maximal subgroups

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

subgroupindex
#130716722
#130700252
#130699942
#130698622
#130692912
#130692502
#130691912
#130691752
#130688832
#130686182
C4×#668742
C11×#25062
#2675611