Finite Group Databasebeta

← #14811849

Subgroups — #14811849

Order 2816.

786 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073643C211yesmaximal, characteristic, complemented
2#13071564C211yesmaximal, characteristic
3#13070004C211yesmaximal, characteristic
4#13070002C211yesmaximal, characteristic
5#13069750C211yesmaximal, characteristic
6#13069569C211yesmaximal, characteristic, complemented
7#13069566C211yesmaximal, characteristic, complemented
8#13069373C211yesmaximal, characteristic, complemented
9#13069333C211yesmaximal, characteristic, complemented
10#13069188C211yesmaximal, characteristic, complemented
11#13069185C211yesmaximal, characteristic, complemented
12#13068742C211yesmaximal, characteristic, complemented
13#13068614C211yesmaximal, characteristic
14#102×Dic11C211yesmaximal, characteristic
15C11×#2023C211yesmaximal, characteristic
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×#66997—21no—
18C2×D4×Dic11C2211yescharacteristic
19C2×#66941C2211yescharacteristic
20C2×#66930—21no—
21C2×C11×#102C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C11×#390C2211yescharacteristic
24#10622842—21no—
25#10622834C2211yescharacteristic
26C2×#66896C2211yescharacteristic
27C2×#66896C2211yescharacteristic
28C2×#66882C2211yescharacteristic
29C2×Dic11⋊C8C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31C2×C8×Dic11C2211yescharacteristic
32#10622592—21no—
33#10622589C2211yescharacteristic
34#10622589C2211yescharacteristic
35C4⋊C4×Dic11C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37#10622586C2211yescharacteristic
38#10622585—21no—
39C2×#66871C2211yescharacteristic
40#10622558—21no—
41#10622557—21no—
42#10622555—21no—
43C4×C4⋊Dic11C2211yescharacteristic
44C4×Dic11⋊C4C2211yescharacteristic
45#10622541C2211yescharacteristic
46C2×C4⋊(C11⋊C8)C2211yescharacteristic
47C11×#340C2211yescharacteristic
48C11×#340C2211yescharacteristic
49C11×#336C2211yescharacteristic
50#10622189C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×Q8×C11—21no—
60C22×D4×C11C2311yescharacteristic
61C23×Dic11—21no—
62C22×Dic22—21no—
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C11×C4⋊Q8—22no—
66C11×C4⋊Q8—41no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
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—
77#66997—44no—
78D4×Dic11—22no—
79D4×Dic11Q814yescomplemented
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4D411yescharacteristic
92C2×Dic11⋊C4D411yescharacteristic
93C2×C4×Dic11—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11C2311yescharacteristic
97C2×C4×Dic11C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100#66941—22no—
101#66941—41no—
102#66930—44no—
103C11×#102—22no—
104C11×#102—41no—
105#66896—22no—
106#66896—41no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95D411yescharacteristic
113C11⋊#95D411yescharacteristic
114#66882—22no—
115Dic11⋊C8—22no—
116Dic11⋊C8—41no—
117C8×Dic11—22no—
118#66871—22no—
119C4⋊(C11⋊C8)—41no—
120#26020—111nomaximal, Sylow
121C24×C11—21no—
122C2×Q8×C11—42no—
123C2×Q8×C11—42no—
124C2×Q8×C11—81no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11C2×Q812yes—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2411yescharacteristic
137C22×Dic11—24no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—42no—
143C22×Dic11—42no—
144C22×Dic11C2×D411yescharacteristic
145C22×Dic11C2×D411yescharacteristic
146C22×Dic11C2×D411yescharacteristic
147C22×Dic11C2×D411yescharacteristic
148C2×Dic22—42no—
149C2×Dic22—42no—
150C2×Dic22—81no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—42no—
163C11×C4⋊C4#4112yes—
164C11×C22⋊C4—42no—
165C11×C22⋊C4—81no—
166C42×C11—21no—
167C42×C11—21no—
168C22⋊Dic11—24no—
169C22⋊Dic11—42no—
170C22⋊Dic11—81no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11C2×Q812yes—
178C4⋊Dic11#4112yes—
179Dic11⋊C4—22no—
180Dic11⋊C4—42no—
181Dic11⋊C4—42no—
182Dic11⋊C4—42no—
183Dic11⋊C4—42no—
184Dic11⋊C4—42no—
185Dic11⋊C4—81no—
186Dic11⋊C4—81no—
187Dic11⋊C4D814yes—
188C4×Dic11—21no—
189C4×Dic11—21no—
190C4×Dic11—42no—
191C4×Dic11—42no—
192C4×Dic11—42no—
193C4×Dic11C2×Q812yes—
194C4×Dic11#4112yes—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201#2551—111no—
202#2354—111no—
203#2067—111no—
204#2067—111no—
205#2023—111no—
206#2023D1111yescharacteristic
207#1988—111no—
208#1988—111no—
209#1947—111no—
210#1939—111no—
211#1918—111no—
212#1918—111no—
213#1834—111no—
214#1802—111no—
215C4×#102—111no—
216C23×C11—22no—
217C23×C11—41no—
218C23×C11—41no—
219C23×C11—41no—
220C23×C11—41no—
221C23×C11—41no—
222C23×C11—41no—
223C23×C11C22×D411yescharacteristic
224Q8×C11—84no—
225D4×C11—22no—
226D4×C11—22no—
227D4×C11—41no—
228D4×C11—41no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—22no—
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×C11C2×D812yes—
244C2×C4×C11C22×Q811yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C2×C4×C11H(5,𝔽2)11yescharacteristic
249C2×C4×C112−1+411yescharacteristic
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—22no—
255C2×Dic11—21no—
256C2×Dic11—22no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—48no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11C22⋊Q812yes—
271C2×Dic11C22⋊Q812yes—
272C2×Dic11C2×D812yes—
273C2×Dic11C2×D812yes—
274C2×Dic11#13712yes—
275Dic22—84no—
276C8×C11—41no—
277C8×C11—41no—
278C11⋊C8—41no—
279C11⋊C8—41no—
280C2×C4⋊Q8—111no—
281C2×C4⋊Q8—221no—
282C2×C4⋊Q8C2×D1111yescharacteristic
283C2×C4×D4—111no—
284C2×#117—221no—
285C2×#107—111no—
286C2×#107—111no—
287C2×C4⋊C8—111no—
288C2×C4⋊C8—111no—
289C2×C4⋊C8—111no—
290C2×#102—111no—
291C2×#102—111no—
292C2×#102C2×D1111yescharacteristic
293C2×#102C2×D1111yescharacteristic
294C2×C4×C8—111no—
295#395—221no—
296#395—221no—
297#390—111no—
298#390C2×D1111yescharacteristic
299#389—111no—
300#389—111no—
301#389—221no—
302#388—221no—
303#388—221no—
304#384—111no—
305#384—111no—
306#380—221no—
307C4×C4⋊C4—111no—
308C4×C4⋊C4—111no—
309C4×C4⋊C4—111no—
310C4×C4⋊C4—111no—
311#340—111no—
312#340—111no—
313#340—111no—
314#340—111no—
315#340—111no—
316#340—111no—
317#340—111no—
318#340—111no—
319#340C2×D1111yescharacteristic
320#340C2×D1111yescharacteristic
321#336—111no—
322#336C2×D1111yescharacteristic
323C22×C11—42no—
324C22×C11—42no—
325C22×C11—42no—
326C22×C11—81no—
327C22×C11—81no—
328C22×C11—81no—
329C22×C11—81no—
330C22×C11C2×C22⋊Q811yescharacteristic
331C22×C11#54611yescharacteristic
332C22×C11#54811yescharacteristic
333C22×C11C22×D811yescharacteristic
334C22×C11C2×#13711yescharacteristic
335C22×C11#57711yescharacteristic
336C22×C11#57711yescharacteristic
337C4×C11—22no—
338C4×C11—41no—
339C4×C11—42no—
340C4×C11—81no—
341C4×C11—81no—
342C4×C11#53311yescharacteristic
343C4×C11#54411yescharacteristic
344C4×C11#55511yescharacteristic
345C4×C11#55611yescharacteristic
346Dic11—22no—
347Dic11—22no—
348Dic11—41no—
349Dic11—42no—
350Dic11—42no—
351Dic11—81no—
352Dic11—81no—
353Dic11#47414yes—
354C22×Q8—21no—
355C22×Q8—221no—
356C22×D4C22×D1111yescharacteristic
357C23×C4—221no—
358C22×C8—111no—
359C22×C8—111no—
360C22×C8C22×D1111yescharacteristic
361C22×C8C22×D1111yescharacteristic
362C4⋊Q8—22no—
363C4⋊Q8—41no—
364C4⋊Q8—222no—
365C4⋊Q8—441no—
366C4⋊Q8—444no—
367C4×D4—114no—
368C4×D4—222no—
369#117—444no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—111no—
372C2×C4⋊C4—111no—
373C2×C4⋊C4—111no—
374C2×C4⋊C4—111no—
375C2×C4⋊C4—111no—
376C2×C4⋊C4—111no—
377C2×C4⋊C4—221no—
378C2×C4⋊C4—221no—
379C2×C4⋊C4—221no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4C22×D1111yescharacteristic
385C2×C4⋊C4C22×D1111yescharacteristic
386C2×C4⋊C4C22×D1111yescharacteristic
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—221no—
390C2×C22⋊C4—221no—
391C2×C22⋊C4—221no—
392C2×C42—111no—
393C2×C42—111no—
394C2×C42—221no—
395C2×C42—221no—
396C2×C42—221no—
397C2×C42C22×D1111yescharacteristic
398#107—222no—
399#107—222no—
400C4⋊C8—222no—
401C4⋊C8—441no—
402C4⋊C8—441no—
403#102—22no—
404#102—41no—
405#102—222no—
406#102—441no—
407C4×C8—222no—
408#95—111no—
409#95—111no—
410#95—221no—
411#95—221no—
412#95—221no—
413#95—221no—
414#95—221no—
415C2×C11—82no—
416C2×C11#243911yescharacteristic
417C2×C11C2×#47411yescharacteristic
418C2×C11#308411yescharacteristic
419C2×C11#329411yescharacteristic
420C2×C11#332911yescharacteristic
421C2×C11#335811yescharacteristic
422C2×C11#336911yescharacteristic
423C24—21no—
424C2×Q8—42no—
425C2×Q8—42no—
426C2×Q8—81no—
427C2×Q8—442no—
428C2×Q8—442no—
429C2×Q8—881no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4Q8×D1112yes—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—111no—
440C22×C4—111no—
441C22×C4—111no—
442C22×C4—111no—
443C22×C4—224no—
444C22×C4—221no—
445C22×C4—221no—
446C22×C4—221no—
447C22×C4—221no—
448C22×C4—442no—
449C22×C4—442no—
450C22×C4D4×D1111yescharacteristic
451C22×C4D4×D1111yescharacteristic
452C22×C4C23×D1111yescharacteristic
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8—221no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—42no—
471C4⋊C4—114no—
472C4⋊C4—112no—
473C4⋊C4—112no—
474C4⋊C4—222no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—442no—
482C4⋊C4—442no—
483C4⋊C4—442no—
484C4⋊C4—442no—
485C4⋊C4—442no—
486C4⋊C4—881no—
487C4⋊C4—881no—
488C4⋊C4#434112yes—
489C22⋊C4—42no—
490C22⋊C4—81no—
491C22⋊C4—224no—
492C22⋊C4—442no—
493C22⋊C4—881no—
494C42—21no—
495C42—21no—
496C42—112no—
497C42—112no—
498C42—221no—
499C42—221no—
500C42—442no—
501C42—442no—
502C42—442no—
503C11#2602011yescharacteristic, complemented, Sylow
504C23—22no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23C2×D4×D1111yescharacteristic
512Q8—84no—
513Q8—884no—
514D4—22no—
515D4—22no—
516D4—41no—
517D4—41no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—22no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—112no—
533C2×C4—112no—
534C2×C4—112no—
535C2×C4—112no—
536C2×C4—112no—
537C2×C4—221no—
538C2×C4—221no—
539C2×C4—221no—
540C2×C4—221no—
541C2×C4—221no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—222no—
545C2×C4—222no—
546C2×C4—448no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4D8×D1112yes—
558C2×C4C2×#434111yescharacteristic
559C2×C4#6703711yescharacteristic
560C2×C4C2×Q8×D1111yescharacteristic
561C2×C4#41×D1111yescharacteristic
562C2×C4#41×D1111yescharacteristic
563C2×C4#6704311yescharacteristic
564C8—41no—
565C8—41no—
566C8—441no—
567C8—441no—
568C22—42no—
569C22—42no—
570C22—42no—
571C22—81no—
572C22—81no—
573C22—81no—
574C22—81no—
575C22#1062312211yescharacteristic
576C22D11×C22⋊Q811yescharacteristic
577C22#1062320811yescharacteristic
578C22C2×D8×D1111yescharacteristic
579C22#1062329311yescharacteristic
580C22#1062330611yescharacteristic
581C22D11×#13711yescharacteristic
582C4—22no—
583C4—41no—
584C4—42no—
585C4—81no—
586C4—81no—
587C4—114no—
588C4—222no—
589C4—222no—
590C4—441no—
591C4—442no—
592C4—442no—
593C4—881no—
594C4—881no—
595C4#1062315311yescharacteristic
596C4#1062315411yescharacteristic
597C4#1062320111yescharacteristic
598C4#1062320211yescharacteristic
599C2—82no—
600C2#1307230011yescharacteristic
601C2D11×#47411yescharacteristic
602C2#1307847311yescharacteristic
603C2#1308042211yescharacteristic
604C2#1308090311yescharacteristic
605C2#1308124811yescharacteristic
606C2#1308135311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2023C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#2023D11
hypocenterC11#26020
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2023

Complements

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

NH ≅ G/Ntype
1. #13073643C2semidirect
6. #13069569C2semidirect
7. #13069566C2semidirect
8. #13069373C2semidirect
9. #13069333C2semidirect
10. #13069188C2semidirect
11. #13069185C2semidirect
12. #13068742C2semidirect
79. D4×Dic11Q8semidirect
503. C11#26020semidirect

Maximal subgroups

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

subgroupindex
#130736432
#130715642
#130700042
#130700022
#130697502
#130695692
#130695662
#130693732
#130693332
#130691882
#130691852
#130687422
#130686142
#102×Dic112
C11×#20232
#2602011