Finite Group Databasebeta

← #14856924

Subgroups — #14856924

Order 2816.

708 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074577C211yesmaximal, characteristic, complemented
2#13071253C211yesmaximal, characteristic, complemented
3#13070105C211yesmaximal, characteristic, complemented
4#13069988C211yesmaximal, characteristic, complemented
5#13069988C211yesmaximal, characteristic, complemented
6#13069924C211yesmaximal, characteristic
7#13069344C211yesmaximal, characteristic, complemented
8#13069316C211yesmaximal, characteristic, complemented
9#13069316C211yesmaximal, characteristic, complemented
10#13069245C211yesmaximal, characteristic, complemented
11#13069189C211yesmaximal, characteristic, complemented
12#13068966C211yesmaximal, characteristic
13#13068879C211yesmaximal, characteristic, complemented
14#13068474C211yesmaximal, characteristic, complemented
15C11×#1970C211yesmaximal, characteristic
16C22×C11×D8C2211yescharacteristic
17C2×D4×Dic11C2211yescharacteristic
18C2×C11×#107C2211yescharacteristic
19C2×C11×#102C2211yescharacteristic
20C2×C11×#102C2211yescharacteristic
21C2×C4×C8×C11C2211yescharacteristic
22C11×#390C2211yescharacteristic
23C11×#390C2211yescharacteristic
24#10622834C2211yescharacteristic
25#10622834C2211yescharacteristic
26#10622834C2211yescharacteristic
27C2×#66896C2211yescharacteristic
28C2×#66896C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31C2×#66881C2211yescharacteristic
32C2×#66881C2211yescharacteristic
33C2×Dic11⋊C8C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35#10622598C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37#10622586C2211yescharacteristic
38#10622586C2211yescharacteristic
39#10622566—21no—
40#10622565—21no—
41#10622565—21no—
42#10622561—21no—
43#10622558—21no—
44#10622557—21no—
45#10622556—21no—
46#10622555—21no—
47#10622545C2211yescharacteristic
48#10622541C2211yescharacteristic
49#10622541C2211yescharacteristic
50C2×#66867C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×D4×C11C2311yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×Dic11—21no—
62C2×C11×D8—22no—
63C2×C11×D8—22no—
64C2×C11×D8—41no—
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4—21no—
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—21no—
73C2×C42×C11C2311yescharacteristic
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81D4×Dic11—22no—
82D4×Dic11—22no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11C2311yescharacteristic
94C2×C4×Dic11C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C11×#107—22no—
98C11×#102—22no—
99C11×#102—22no—
100C4×C8×C11—41no—
101#66896—22no—
102#66896—22no—
103#66896—41no—
104#66896—41no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95D411yescharacteristic
112C11⋊#95D411yescharacteristic
113C11⋊#95D411yescharacteristic
114C11⋊#95D411yescharacteristic
115#66881—22no—
116#66881—41no—
117Dic11⋊C8—22no—
118Dic11⋊C8—22no—
119#66867—41no—
120#29437—111nomaximal, Sylow
121C24×C11—21no—
122C24×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11#4112yes—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2411yescharacteristic
140C22×Dic11—24no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—81no—
146C22×Dic11—81no—
147C22×Dic11C2×D411yescharacteristic
148C22×Dic11C2×D411yescharacteristic
149C22×Dic11C2×D411yescharacteristic
150C22×Dic11C2×D411yescharacteristic
151C11×D8—44no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11#4112yes—
157C2×C8×C11#4112yes—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C22⋊C4—81no—
163C11×C22⋊C4—81no—
164C11×C22⋊C4—81no—
165C11×C22⋊C4—81no—
166C42×C11—21no—
167C42×C11—21no—
168C22⋊Dic11—24no—
169C22⋊Dic11—81no—
170C22⋊Dic11—81no—
171C22⋊Dic11—81no—
172C22⋊Dic11—81no—
173C22⋊Dic11—81no—
174C22⋊Dic11—81no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—81no—
183C4⋊Dic11#4112yes—
184Dic11⋊C4—81no—
185Dic11⋊C4—81no—
186Dic11⋊C4—81no—
187Dic11⋊C4—81no—
188C4×Dic11—21no—
189C4×Dic11—21no—
190C4×Dic11—21no—
191C4×Dic11—21no—
192C4×Dic11—81no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199#2644—111no—
200#2319—111no—
201#2086—111no—
202#2065—111no—
203#2065—111no—
204#2054—111no—
205#1970D1111yescharacteristic
206#1941—111no—
207#1936—111no—
208#1936—111no—
209#1926—111no—
210#1918—111no—
211#1879—111no—
212#1864—111no—
213#1768—111no—
214C23×C11—22no—
215C23×C11—41no—
216C23×C11—41no—
217C23×C11—41no—
218C23×C11—41no—
219C23×C11—41no—
220C23×C11—41no—
221C23×C11—41no—
222C23×C11—41no—
223C23×C11—41no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11—41no—
228C23×C11C22×D411yescharacteristic
229D4×C11—22no—
230D4×C11—22no—
231D4×C11—41no—
232D4×C11—41no—
233D4×C11—41no—
234D4×C11—41no—
235D4×C11—41no—
236D4×C11—41no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11H(5,𝔽2)11yescharacteristic
254C2×C4×C112−1+411yescharacteristic
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—22no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—84no—
280C8×C11—22no—
281C8×C11—22no—
282C11⋊C8—41no—
283C11⋊C8—41no—
284C22×D8C2×D1111yescharacteristic
285C2×C4×D4—111no—
286C2×#107C2×D1111yescharacteristic
287C2×#106—111no—
288C2×#106—111no—
289C2×C4⋊C8—111no—
290C2×C4⋊C8—111no—
291C2×#102—111no—
292C2×#102—111no—
293C2×#102—111no—
294C2×#102—111no—
295C2×#102C2×D1111yescharacteristic
296C2×#102C2×D1111yescharacteristic
297C2×#97—111no—
298C2×C4×C8C2×D1111yescharacteristic
299#397—221no—
300#397—221no—
301#397—221no—
302#396—221no—
303#390—111no—
304#390—111no—
305#390—111no—
306#390C2×D1111yescharacteristic
307#390C2×D1111yescharacteristic
308#389—111no—
309#389—111no—
310#389—111no—
311#389—111no—
312#389—111no—
313#388—221no—
314#388—221no—
315#381—221no—
316#380—221no—
317C4×C4⋊C4—111no—
318#376—111no—
319#340—111no—
320#340—111no—
321#340—111no—
322#340—111no—
323#340—111no—
324#340—111no—
325#336—111no—
326#336—111no—
327C22×C11—42no—
328C22×C11—42no—
329C22×C11—42no—
330C22×C11—81no—
331C22×C11—81no—
332C22×C11—81no—
333C22×C11—81no—
334C22×C11—81no—
335C22×C11—81no—
336C22×C11—81no—
337C22×C11—81no—
338C22×C11—81no—
339C22×C11—81no—
340C22×C11—81no—
341C22×C11#52511yescharacteristic
342C22×C11#53211yescharacteristic
343C22×C11#53711yescharacteristic
344C22×C11#57611yescharacteristic
345C22×C11#57611yescharacteristic
346C22×C11#57711yescharacteristic
347C22×C11#57711yescharacteristic
348C4×C11—41no—
349C4×C11—41no—
350C4×C11—81no—
351C4×C11—81no—
352C4×C11#55111yescharacteristic
353C4×C11#55211yescharacteristic
354C4×C11#55311yescharacteristic
355C4×C11#55611yescharacteristic
356Dic11—41no—
357Dic11—42no—
358Dic11—41no—
359Dic11—41no—
360Dic11—41no—
361Dic11—81no—
362Dic11—81no—
363Dic11—81no—
364C22×D4C22×D1111yescharacteristic
365C22×D4C22×D1111yescharacteristic
366C23×C4—221no—
367C2×D8—22no—
368C2×D8—22no—
369C2×D8—41no—
370C22×C8—111no—
371C22×C8—111no—
372C22×C8C22×D1111yescharacteristic
373C22×C8C22×D1111yescharacteristic
374C4×D4—222no—
375C4×D4—222no—
376C2×C4⋊C4—111no—
377C2×C4⋊C4—111no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4C22×D1111yescharacteristic
386C2×C4⋊C4C22×D1111yescharacteristic
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—221no—
392C2×C22⋊C4—221no—
393C2×C22⋊C4—221no—
394C2×C22⋊C4—221no—
395C2×C22⋊C4—221no—
396C2×C22⋊C4—221no—
397C2×C22⋊C4—221no—
398C2×C42—111no—
399C2×C42—111no—
400C2×C42—221no—
401C2×C42C22×D1111yescharacteristic
402#107—22no—
403#106—222no—
404#106—441no—
405C4⋊C8—222no—
406C4⋊C8—222no—
407#102—22no—
408#102—22no—
409#102—222no—
410#102—222no—
411#102—441no—
412#102—441no—
413#97—441no—
414C4×C8—41no—
415#95—111no—
416#95—111no—
417#95—111no—
418#95—111no—
419#95—221no—
420#95—221no—
421#95—221no—
422#95—221no—
423#95—221no—
424#95—221no—
425C2×C11—82no—
426C2×C11—161no—
427C2×C11#260111yescharacteristic
428C2×C11#311811yescharacteristic
429C2×C11#311911yescharacteristic
430C2×C11#317311yescharacteristic
431C2×C11#317611yescharacteristic
432C2×C11#325711yescharacteristic
433C2×C11#325711yescharacteristic
434C24—21no—
435C24—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4#433912yes—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—111no—
451C22×C4—111no—
452C22×C4—111no—
453C22×C4—111no—
454C22×C4—221no—
455C22×C4—224no—
456C22×C4—221no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4—881no—
460C22×C4—881no—
461C22×C4D4×D1111yescharacteristic
462C22×C4D4×D1111yescharacteristic
463C22×C4C23×D1111yescharacteristic
464D8—44no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—221no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8—221no—
474C2×C8—221no—
475C2×C8#434112yes—
476C2×C8#434112yes—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—112no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—881no—
490C4⋊C4—881no—
491C4⋊C4—881no—
492C4⋊C4—881no—
493C4⋊C4—881no—
494C22⋊C4—81no—
495C22⋊C4—81no—
496C22⋊C4—81no—
497C22⋊C4—81no—
498C22⋊C4—224no—
499C22⋊C4—881no—
500C22⋊C4—881no—
501C22⋊C4—881no—
502C22⋊C4—881no—
503C22⋊C4—881no—
504C22⋊C4—881no—
505C42—21no—
506C42—21no—
507C42—221no—
508C42—221no—
509C42—221no—
510C42—221no—
511C42—881no—
512C11#2943711yescharacteristic, complemented, Sylow
513C23—22no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23—41no—
527C23C2×D4×D1111yescharacteristic
528D4—22no—
529D4—22no—
530D4—41no—
531D4—41no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—41no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—221no—
555C2×C4—221no—
556C2×C4—221no—
557C2×C4—221no—
558C2×C4—221no—
559C2×C4—221no—
560C2×C4—222no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—884no—
573C2×C4C2×#433911yescharacteristic
574C2×C4C2×#434111yescharacteristic
575C2×C4C2×#434111yescharacteristic
576C2×C4#6703711yescharacteristic
577C2×C4#41×D1111yescharacteristic
578C2×C4#6704311yescharacteristic
579C8—22no—
580C8—22no—
581C8—441no—
582C8—441no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22—81no—
592C22—81no—
593C22—81no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22#1062307811yescharacteristic
598C22#1062312811yescharacteristic
599C22#1062324711yescharacteristic
600C22#1062328811yescharacteristic
601C22#1062328811yescharacteristic
602C22#1062330111yescharacteristic
603C22#1062330111yescharacteristic
604C4—41no—
605C4—41no—
606C4—81no—
607C4—81no—
608C4—441no—
609C4—442no—
610C4—441no—
611C4—441no—
612C4—441no—
613C4—881no—
614C4—881no—
615C4—881no—
616C4#1062302611yescharacteristic
617C4#1062307211yescharacteristic
618C4#1062313211yescharacteristic
619C4#1062320211yescharacteristic
620C2—82no—
621C2—161no—
622C2#1307421011yescharacteristic
623C2#1307879611yescharacteristic
624C2#1307881111yescharacteristic
625C2#1307923011yescharacteristic
626C2#1307926311yescharacteristic
627C2#1308002011yescharacteristic
628C2#1308002011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1970C2
socleC23×C11C22×D4
prime radicalC22×C11×D8C22
hypercenter#1970D11
hypocenterC11#29437
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1970

Complements

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

NH ≅ G/Ntype
1. #13074577C2semidirect
2. #13071253C2semidirect
3. #13070105C2semidirect
4. #13069988C2semidirect
5. #13069988C2semidirect
7. #13069344C2semidirect
8. #13069316C2semidirect
9. #13069316C2semidirect
10. #13069245C2semidirect
11. #13069189C2semidirect
13. #13068879C2semidirect
14. #13068474C2semidirect
512. C11#29437semidirect

Maximal subgroups

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

subgroupindex
#130745772
#130712532
#130701052
#130699882
#130699242
#130693442
#130693162
#130692452
#130691892
#130689662
#130688792
#130684742
C11×#19702
#2943711