Finite Group Databasebeta

← #14853528

Subgroups — #14853528

Order 2816.

754 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074592C211yesmaximal, characteristic, complemented
2#13071342C211yesmaximal, characteristic
3#13070185C211yesmaximal, characteristic, complemented
4#13070184C211yesmaximal, characteristic, complemented
5#13069847C211yesmaximal, characteristic
6#13069315C211yesmaximal, characteristic, complemented
7#13069310C211yesmaximal, characteristic, complemented
8#13069301C211yesmaximal, characteristic, complemented
9#13069296C211yesmaximal, characteristic, complemented
10#13068624C211yesmaximal, characteristic, complemented
11#13068624C211yesmaximal, characteristic, complemented
12#13068614C211yesmaximal, characteristic, complemented
13#13068614C211yesmaximal, characteristic, complemented
14#13068472C211yesmaximal, characteristic, complemented
15C11×#2041C211yesmaximal, characteristic
16C2×C11×#127C2211yescharacteristic
17C2×D4×Dic11C2211yescharacteristic
18C2×D4×Dic11C2211yescharacteristic
19C2×C11×#102C2211yescharacteristic
20C2×C11×#102C2211yescharacteristic
21C2×C11×#102C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C11×#389C2211yescharacteristic
24#10622834C2211yescharacteristic
25#10622834C2211yescharacteristic
26#10622833—21no—
27#10622833—21no—
28#10622833—21no—
29#10622833—21no—
30C2×#66896C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34C2×#66879C2211yescharacteristic
35C2×Dic11⋊C8C2211yescharacteristic
36C2×Dic11⋊C8C2211yescharacteristic
37C2×C8×Dic11C2211yescharacteristic
38#10622598C2211yescharacteristic
39#10622597—21no—
40#10622593—21no—
41#10622590C2211yescharacteristic
42#10622589C2211yescharacteristic
43#10622586C2211yescharacteristic
44#10622549C2211yescharacteristic
45#10622545C2211yescharacteristic
46#10622541C2211yescharacteristic
47#10622272—21no—
48#10622271—21no—
49C11×#336C2211yescharacteristic
50#10622189C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D4×C11—21no—
60C22×D4×C11—21no—
61C22×D4×C11C2311yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×Dic11—21no—
64C23×Dic11—21no—
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C11×#127—22no—
68C11×#127—22no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×C22⋊Dic11—21no—
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79D4×Dic11—22no—
80D4×Dic11—22no—
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×Dic11C2311yescharacteristic
93C2×C4×Dic11C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C11×#102—22no—
97C11×#102—22no—
98C11×#102—41no—
99C11×#102—41no—
100C11×#95—21no—
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⋊#95—21no—
112C11⋊#95D411yescharacteristic
113C11⋊#95D411yescharacteristic
114C11⋊#95D411yescharacteristic
115C11⋊#95D411yescharacteristic
116#66879—41no—
117Dic11⋊C8—22no—
118Dic11⋊C8—22no—
119C8×Dic11—41no—
120#29133—111nomaximal, Sylow
121C24×C11—21no—
122C24×C11—21no—
123C2×D4×C11—24no—
124C2×D4×C11—24no—
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—21no—
135C2×D4×C11—81no—
136C2×D4×C11—81no—
137C2×D4×C11—81no—
138C2×D4×C11—81no—
139C2×D4×C11#4112yes—
140C2×D4×C11#4112yes—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2411yescharacteristic
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—42no—
151C22×Dic11—42no—
152C22×Dic11—81no—
153C22×Dic11—81no—
154C22×Dic11—81no—
155C22×Dic11—81no—
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—81no—
171C42×C11—21no—
172C42×C11—21no—
173C22⋊Dic11—42no—
174C22⋊Dic11—42no—
175C22⋊Dic11—81no—
176C22⋊Dic11—81no—
177C22⋊Dic11—81no—
178C22⋊Dic11—81no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—81no—
188Dic11⋊C4—81no—
189Dic11⋊C4—81no—
190Dic11⋊C4—81no—
191Dic11⋊C4—81no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11#4112yes—
195C4×Dic11#4112yes—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202#2647—111no—
203#2328—111no—
204#2101—111no—
205#2101—111no—
206#2041—111no—
207#2041D1111yescharacteristic
208#1936—111no—
209#1936—111no—
210#1934—111no—
211#1934—111no—
212#1804—111no—
213#1804—111no—
214#1802—111no—
215#1802—111no—
216#1768—111no—
217C23×C11—22no—
218C23×C11—22no—
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×C11—41no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11C22×D411yescharacteristic
232D4×C11—22no—
233D4×C11—22no—
234D4×C11—22no—
235D4×C11—22no—
236D4×C11—41no—
237D4×C11—41no—
238D4×C11—41no—
239D4×C11—41no—
240D4×C11—84no—
241D4×C11—84no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11H(5,𝔽2)11yescharacteristic
259C2×C4×C112−1+411yescharacteristic
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—21no—
269C2×Dic11—21no—
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—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—84no—
283C2×Dic11—84no—
284C2×Dic11#12412yes—
285C2×Dic11#12412yes—
286C8×C11—41no—
287C8×C11—41no—
288C11⋊C8—41no—
289C11⋊C8—41no—
290C2×#127C2×D1111yescharacteristic
291C2×C4×D4—111no—
292C2×C4×D4—111no—
293C2×C4⋊C8—111no—
294C2×C4⋊C8—111no—
295C2×#102—111no—
296C2×#102—111no—
297C2×#102—111no—
298C2×#102—111no—
299C2×#102C2×D1111yescharacteristic
300C2×#102C2×D1111yescharacteristic
301C2×#102C2×D1111yescharacteristic
302C2×#102C2×D1111yescharacteristic
303C2×#97—111no—
304C2×C4×C8—111no—
305#400—221no—
306#400—221no—
307#398—221no—
308#398—221no—
309#390—111no—
310#390—111no—
311#389—111no—
312#389—111no—
313#389—111no—
314#389C2×D1111yescharacteristic
315#386—221no—
316#386—221no—
317#386—221no—
318#386—221no—
319#384—111no—
320#382—111no—
321#382—111no—
322#376—111no—
323#340—111no—
324#340—111no—
325#340—111no—
326#340—111no—
327#340—111no—
328#340—111no—
329#340—111no—
330#340—111no—
331#336—111no—
332#336C2×D1111yescharacteristic
333C22×C11—42no—
334C22×C11—42no—
335C22×C11—42no—
336C22×C11—42no—
337C22×C11—42no—
338C22×C11—42no—
339C22×C11—81no—
340C22×C11—81no—
341C22×C11—81no—
342C22×C11—81no—
343C22×C11—81no—
344C22×C11—81no—
345C22×C11—81no—
346C22×C11—81no—
347C22×C11#52511yescharacteristic
348C22×C11C2×#12411yescharacteristic
349C22×C11#53711yescharacteristic
350C22×C11#57611yescharacteristic
351C22×C11#57611yescharacteristic
352C22×C11#57711yescharacteristic
353C22×C11#57711yescharacteristic
354C4×C11—41no—
355C4×C11—41no—
356C4×C11—81no—
357C4×C11—81no—
358C4×C11#55211yescharacteristic
359C4×C11#55211yescharacteristic
360C4×C11#55311yescharacteristic
361C4×C11#55311yescharacteristic
362Dic11—22no—
363Dic11—22no—
364Dic11—41no—
365Dic11—41no—
366Dic11—81no—
367Dic11—81no—
368Dic11—81no—
369Dic11—81no—
370C22×D4—21no—
371C22×D4—21no—
372C22×D4C22×D1111yescharacteristic
373C22×D4C22×D1111yescharacteristic
374C23×C4—221no—
375C23×C4—221no—
376C22×C8—111no—
377C22×C8—111no—
378C22×C8C22×D1111yescharacteristic
379C22×C8C22×D1111yescharacteristic
380#127—22no—
381#127—22no—
382C4×D4—222no—
383C4×D4—222no—
384C4×D4—222no—
385C4×D4—222no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—111no—
390C2×C4⋊C4—111no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4C22×D1111yescharacteristic
397C2×C4⋊C4C22×D1111yescharacteristic
398C2×C22⋊C4—221no—
399C2×C22⋊C4—221no—
400C2×C22⋊C4—221no—
401C2×C22⋊C4—221no—
402C2×C22⋊C4—221no—
403C2×C22⋊C4—221no—
404C2×C42—111no—
405C2×C42—111no—
406C2×C42C22×D1111yescharacteristic
407C4⋊C8—222no—
408C4⋊C8—222no—
409#102—22no—
410#102—22no—
411#102—41no—
412#102—41no—
413#102—222no—
414#102—222no—
415#102—441no—
416#102—441no—
417#97—441no—
418C4×C8—441no—
419#95—21no—
420#95—111no—
421#95—111no—
422#95—111no—
423#95—111no—
424#95—221no—
425#95—221no—
426#95—221no—
427#95—221no—
428#95—221no—
429#95—221no—
430#95—221no—
431C2×C11—82no—
432C2×C11—82no—
433C2×C11#256211yescharacteristic
434C2×C11#312211yescharacteristic
435C2×C11#312311yescharacteristic
436C2×C11#313611yescharacteristic
437C2×C11#313611yescharacteristic
438C2×C11#325711yescharacteristic
439C2×C11#325711yescharacteristic
440C24—21no—
441C24—21no—
442C2×D4—24no—
443C2×D4—24no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—81no—
455C2×D4—81no—
456C2×D4—81no—
457C2×D4—81no—
458C2×D4#434112yes—
459C2×D4#434112yes—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—111no—
463C22×C4—111no—
464C22×C4—111no—
465C22×C4—111no—
466C22×C4—221no—
467C22×C4—221no—
468C22×C4—221no—
469C22×C4—221no—
470C22×C4—442no—
471C22×C4—442no—
472C22×C4—881no—
473C22×C4—881no—
474C22×C4—881no—
475C22×C4—881no—
476C22×C4D4×D1111yescharacteristic
477C22×C4D4×D1111yescharacteristic
478C22×C4C23×D1111yescharacteristic
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8—221no—
490C2×C8—221no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—81no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4—221no—
504C4⋊C4—881no—
505C4⋊C4—881no—
506C4⋊C4—881no—
507C4⋊C4—881no—
508C4⋊C4—881no—
509C22⋊C4—442no—
510C22⋊C4—442no—
511C22⋊C4—881no—
512C22⋊C4—881no—
513C22⋊C4—881no—
514C22⋊C4—881no—
515C42—21no—
516C42—21no—
517C42—112no—
518C42—112no—
519C42—221no—
520C42—221no—
521C11#2913311yescharacteristic, complemented, Sylow
522C23—22no—
523C23—22no—
524C23—41no—
525C23—41no—
526C23—41no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23—41no—
536C23C2×D4×D1111yescharacteristic
537D4—22no—
538D4—22no—
539D4—22no—
540D4—22no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—41no—
545D4—84no—
546D4—84no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—112no—
560C2×C4—112no—
561C2×C4—221no—
562C2×C4—221no—
563C2×C4—221no—
564C2×C4—221no—
565C2×C4—221no—
566C2×C4—221no—
567C2×C4—221no—
568C2×C4—221no—
569C2×C4—221no—
570C2×C4—221no—
571C2×C4—441no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—884no—
584C2×C4—884no—
585C2×C4C2×#434111yescharacteristic
586C2×C4C2×#434111yescharacteristic
587C2×C4#6703711yescharacteristic
588C2×C4#41×D1111yescharacteristic
589C2×C4#41×D1111yescharacteristic
590C2×C4#6704311yescharacteristic
591C8—41no—
592C8—41no—
593C8—441no—
594C8—441no—
595C22—42no—
596C22—42no—
597C22—42no—
598C22—42no—
599C22—42no—
600C22—42no—
601C22—81no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22—81no—
608C22—81no—
609C22#1062311711yescharacteristic
610C22#1062313911yescharacteristic
611C22D11×#12411yescharacteristic
612C22#1062328811yescharacteristic
613C22#1062329311yescharacteristic
614C22#1062330511yescharacteristic
615C22#1062330611yescharacteristic
616C4—41no—
617C4—41no—
618C4—81no—
619C4—81no—
620C4—222no—
621C4—222no—
622C4—441no—
623C4—441no—
624C4—881no—
625C4—881no—
626C4—881no—
627C4—881no—
628C4#1062313211yescharacteristic
629C4#1062313211yescharacteristic
630C4#1062318111yescharacteristic
631C4#1062318111yescharacteristic
632C2—82no—
633C2—82no—
634C2#1307377611yescharacteristic
635C2#1307885311yescharacteristic
636C2#1307886211yescharacteristic
637C2#1307896511yescharacteristic
638C2#1307897111yescharacteristic
639C2#1308002311yescharacteristic
640C2#1308002511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2041C2
socleC23×C11C22×D4
prime radicalC2×C11×#127C22
hypercenter#2041D11
hypocenterC11#29133
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2041

Complements

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

NH ≅ G/Ntype
1. #13074592C2semidirect
3. #13070185C2semidirect
4. #13070184C2semidirect
6. #13069315C2semidirect
7. #13069310C2semidirect
8. #13069301C2semidirect
9. #13069296C2semidirect
10. #13068624C2semidirect
11. #13068624C2semidirect
12. #13068614C2semidirect
13. #13068614C2semidirect
14. #13068472C2semidirect
521. C11#29133semidirect

Maximal subgroups

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

subgroupindex
#130745922
#130713422
#130701852
#130701842
#130698472
#130693152
#130693102
#130693012
#130692962
#130686242
#130686142
#130684722
C11×#20412
#2913311