Finite Group Databasebeta

← #14826203

Subgroups — #14826203

Order 2816.

770 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072466C211yesmaximal, characteristic
2#13071674C211yesmaximal, characteristic, complemented
3#13070003C211yesmaximal, characteristic
4#13069950C211yesmaximal, characteristic, complemented
5#13069945C211yesmaximal, characteristic, complemented
6#13069753C211yesmaximal, characteristic
7#13069563C211yesmaximal, characteristic, complemented
8#13069354C211yesmaximal, characteristic, complemented
9#13069244C211yesmaximal, characteristic
10#13069237C211yesmaximal, characteristic
11#13069209C211yesmaximal, characteristic, complemented
12#13069195C211yesmaximal, characteristic, complemented
13#13068880C211yesmaximal, characteristic
14#13068442C211yesmaximal, characteristic
15C11×#1917C211yesmaximal, characteristic, complemented
16C2×#66949—21no—
17C2×#66940—21no—
18C2×C4×D44C2211yescharacteristic
19C2×#66922C2211yescharacteristic
20C2×#66922C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×#97C2211yescharacteristic
23C4×C11×C4⋊C4C2211yescharacteristic
24C2×#66885C2211yescharacteristic
25C2×#66885C2211yescharacteristic
26C2×#66885C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×#66882C2211yescharacteristic
29C2×#66882C2211yescharacteristic
30C2×#66881C2211yescharacteristic
31C2×#66881C2211yescharacteristic
32#10622607—21no—
33#10622587—21no—
34#10622552C2211yescharacteristic
35#10622552C2211yescharacteristic
36C4×C4⋊Dic11C2211yescharacteristic
37C4×C4⋊Dic11C2211yescharacteristic
38C4×C4⋊Dic11C2211yescharacteristic
39#10622541C2211yescharacteristic
40#10622541C2211yescharacteristic
41#10622541C2211yescharacteristic
42#10622541C2211yescharacteristic
43#10622286—21no—
44#10622281—21no—
45#10622266—21no—
46#10622266—21no—
47C11×#336C2211yescharacteristic
48C11×#336C2211yescharacteristic
49C11×#336C2211yescharacteristic
50C11×#336C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59C22×D44C2311yescharacteristic
60C22×C4×D11—21no—
61C22×Dic22—21no—
62C22×Dic22—21no—
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C2×C11×C4⋊C4D411yescharacteristic
68C2×C11×C4⋊C4D411yescharacteristic
69C2×C42×C11C2311yescharacteristic
70C2×C42×C11C2311yescharacteristic
71C2×C42×C11C2311yescharacteristic
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93#66949—44no—
94#66940—44no—
95C4×D44—22no—
96C4×D44—41no—
97#66922—22no—
98#66922—22no—
99#66922—22no—
100#66922—41no—
101C11×C4⋊C8—41no—
102C11×#97—41no—
103C11×#95D411yescharacteristic
104C11×#95D411yescharacteristic
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112#66885—22no—
113#66885—22no—
114#66885—41no—
115#66885Q814yescomplemented
116#66882—22no—
117#66882—22no—
118#66881—22no—
119#66881—41no—
120#27015—111nomaximal, Sylow
121C23×D11—21no—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2411yescharacteristic
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11—21no—
132C22×Dic11—21no—
133C22×Dic11—21no—
134C22×Dic11—21no—
135C22×Dic11—21no—
136C2×D44—21no—
137C2×D44—21no—
138C2×D44—21no—
139C2×D44—21no—
140C2×D44—21no—
141C2×D44C2×Q812yes—
142C2×C4×D11—42no—
143C2×C4×D11—42no—
144C2×C4×D11—81no—
145C2×Dic22—24no—
146C2×Dic22—42no—
147C2×Dic22—42no—
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—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11C2×Q812yes—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—22no—
165C42×C11—21no—
166C42×C11—21no—
167C42×C11—21no—
168C42×C11—21no—
169C42×C11—21no—
170C42×C11—21no—
171(C2×D11)⋊C4—42no—
172(C2×D11)⋊C4—42no—
173(C2×D11)⋊C4—42no—
174(C2×D11)⋊C4—42no—
175(C2×D11)⋊C4—81no—
176C4⋊Dic11—24no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
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—42no—
188C4⋊Dic11C2×Q812yes—
189C4⋊Dic11#4112yes—
190C4⋊Dic11#4112yes—
191C4⋊Dic11#4112yes—
192Dic11⋊C4—42no—
193Dic11⋊C4—42no—
194Dic11⋊C4—42no—
195Dic11⋊C4—42no—
196C4×Dic11—42no—
197C4×Dic11—42no—
198C4×Dic11—42no—
199#2452—111no—
200#2365—111no—
201#2067—111no—
202#2058—111no—
203#2057—111no—
204#2023—111no—
205#1987—111no—
206#1943—111no—
207#1926—111no—
208#1925—111no—
209#1921—111no—
210#1919—111no—
211#1917D1111yescharacteristic, complemented
212#1864—111no—
213#1762—111no—
214C23×C11C22×D411yescharacteristic
215C22×D11—22no—
216C22×D11—41no—
217C22×D11—41no—
218C22×D11—41no—
219C22×D11—41no—
220C22×D11—41no—
221C22×D11—41no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
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—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11AGL(1,ℤ/8)12yes—
239C2×C4×C11AGL(1,ℤ/8)12yes—
240C2×C4×C11C22×Q811yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C2×C4×C11H(5,𝔽2)11yescharacteristic
245C2×C4×C112−1+411yescharacteristic
246C2×Dic11—22no—
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—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267D44—22no—
268D44—22no—
269D44—41no—
270D44—41no—
271C4×D11—84no—
272Dic22—48no—
273Dic22—84no—
274C8×C11—22no—
275C8×C11—41no—
276C8×C11—41no—
277C8×C11—41no—
278C2×C4⋊Q8—111no—
279C2×C4⋊Q8—111no—
280C2×C22⋊Q8—221no—
281C2×C4×Q8—221no—
282C2×C4×D4—111no—
283C2×#107—111no—
284C2×#107—111no—
285C2×#106—111no—
286C2×#106—111no—
287C2×C4⋊C8C2×D1111yescharacteristic
288C2×#102—111no—
289C2×#102—111no—
290C2×#102—111no—
291C2×#102—111no—
292C2×#97C2×D1111yescharacteristic
293#396—221no—
294#393—221no—
295#391—221no—
296#390—111no—
297#390—111no—
298#389—111no—
299#389—111no—
300#389—111no—
301#389—111no—
302#387—221no—
303#387—221no—
304#385—221no—
305C4×C4⋊C4—111no—
306C4×C4⋊C4—111no—
307C4×C4⋊C4—111no—
308C4×C4⋊C4C2×D1111yescharacteristic
309#340—111no—
310#340—111no—
311#340—111no—
312#340—111no—
313#340—111no—
314#340—111no—
315#340—111no—
316#340—111no—
317#336C2×D1111yescharacteristic
318#336C2×D1111yescharacteristic
319#336C2×D1111yescharacteristic
320#336C2×D1111yescharacteristic
321C22×C11#52511yescharacteristic
322C22×C11#54611yescharacteristic
323C22×C11D4×Q811yescharacteristic
324C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
325C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
326C22×C11#57711yescharacteristic
327C22×C11#57811yescharacteristic
328C2×D11—42no—
329C2×D11—42no—
330C2×D11—42no—
331C2×D11—81no—
332C2×D11—81no—
333C2×D11—81no—
334C2×D11—81no—
335C4×C11—22no—
336C4×C11—22no—
337C4×C11—41no—
338C4×C11—41no—
339C4×C11—41no—
340C4×C11—41no—
341C4×C11#53311yescharacteristic
342C4×C11#54211yescharacteristic
343C4×C11#55411yescharacteristic
344C4×C11#55611yescharacteristic
345Dic11—42no—
346Dic11—42no—
347Dic11—42no—
348Dic11—42no—
349Dic11—81no—
350Dic11—81no—
351Dic11—81no—
352C22×Q8—221no—
353C22×Q8—221no—
354C22×D4—111no—
355C23×C4—221no—
356C22×C8C22×D1111yescharacteristic
357C22×C8C22×D1111yescharacteristic
358C22×C8C22×D1111yescharacteristic
359C22×C8C22×D1111yescharacteristic
360C4⋊Q8—222no—
361C4⋊Q8—222no—
362C4⋊Q8—222no—
363C4⋊Q8—441no—
364C22⋊Q8—444no—
365C4×Q8—444no—
366C4×D4—222no—
367C4×D4—441no—
368C2×C4⋊C4—111no—
369C2×C4⋊C4—111no—
370C2×C4⋊C4—111no—
371C2×C4⋊C4—111no—
372C2×C4⋊C4—111no—
373C2×C4⋊C4—111no—
374C2×C4⋊C4—111no—
375C2×C4⋊C4—221no—
376C2×C4⋊C4—221no—
377C2×C4⋊C4—221no—
378C2×C4⋊C4—221no—
379C2×C4⋊C4—221no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4D4411yescharacteristic
382C2×C4⋊C4D4411yescharacteristic
383C2×C22⋊C4—221no—
384C2×C22⋊C4—221no—
385C2×C22⋊C4—221no—
386C2×C22⋊C4—221no—
387C2×C22⋊C4—221no—
388C2×C42—221no—
389C2×C42—221no—
390C2×C42—221no—
391C2×C42C22×D1111yescharacteristic
392C2×C42C22×D1111yescharacteristic
393C2×C42C22×D1111yescharacteristic
394#107—222no—
395#107—222no—
396#106—222no—
397#106—441no—
398C4⋊C8—41no—
399#102—114no—
400#102—222no—
401#102—222no—
402#102—441no—
403#97—41no—
404#95—221no—
405#95—221no—
406#95—221no—
407#95—221no—
408#95—221no—
409#95—221no—
410#95—221no—
411#95D4411yescharacteristic
412#95D4411yescharacteristic
413C2×C11#246511yescharacteristic
414C2×C11#310911yescharacteristic
415C2×C11#312111yescharacteristic
416C2×C11#330811yescharacteristic
417C2×C11#332411yescharacteristic
418C2×C11#338411yescharacteristic
419C2×C11#338611yescharacteristic
420D11—82no—
421C24—221no—
422C2×Q8—224no—
423C2×Q8—442no—
424C2×Q8—442no—
425C2×Q8—442no—
426C2×Q8—442no—
427C2×Q8—881no—
428C2×D4—112no—
429C2×D4—221no—
430C2×D4—221no—
431C2×D4—221no—
432C2×D4—221no—
433C2×D4—221no—
434C22×C4—221no—
435C22×C4—221no—
436C22×C4—221no—
437C22×C4—221no—
438C22×C4—221no—
439C22×C4—221no—
440C22×C4—221no—
441C22×C4—442no—
442C22×C4—442no—
443C22×C4—881no—
444C22×C4C2×D4411yescharacteristic
445C22×C4C2×D4411yescharacteristic
446C22×C4C2×D4411yescharacteristic
447C22×C4C2×D4411yescharacteristic
448C22×C4C2×D4411yescharacteristic
449C22×C4C2×D4411yescharacteristic
450C22×C4C23×D1111yescharacteristic
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8Q8×D1112yes—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—112no—
466C4⋊C4—112no—
467C4⋊C4—112no—
468C4⋊C4—112no—
469C4⋊C4—224no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—442no—
481C4⋊C4—442no—
482C4⋊C4—442no—
483C4⋊C4—442no—
484C4⋊C4—442no—
485C22⋊C4—442no—
486C22⋊C4—442no—
487C22⋊C4—442no—
488C22⋊C4—442no—
489C22⋊C4—881no—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—442no—
497C42—442no—
498C42—442no—
499C11#2701511yescharacteristic, complemented, Sylow
500C23—222no—
501C23—441no—
502C23—441no—
503C23—441no—
504C23—441no—
505C23—441no—
506C23—441no—
507C23C22×D4411yescharacteristic
508Q8—448no—
509Q8—884no—
510D4—222no—
511D4—222no—
512D4—441no—
513D4—441no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—222no—
531C2×C4—222no—
532C2×C4—222no—
533C2×C4—222no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4—441no—
540C2×C4—441no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—884no—
552C2×C4#6696112yes—
553C2×C4#6696112yes—
554C2×C4#6703711yescharacteristic
555C2×C4C2×Q8×D1111yescharacteristic
556C2×C4#41×D1111yescharacteristic
557C2×C4#41×D1111yescharacteristic
558C2×C4#41×D1111yescharacteristic
559C2×C4#6704311yescharacteristic
560C8—22no—
561C8—41no—
562C8—41no—
563C8—41no—
564C22—442no—
565C22—442no—
566C22—442no—
567C22—881no—
568C22—881no—
569C22—881no—
570C22—881no—
571C22#1062305511yescharacteristic
572C22#1062308511yescharacteristic
573C22Q8×D4411yescharacteristic
574C22C2×#6696111yescharacteristic
575C22C2×#6696111yescharacteristic
576C22#1062328211yescharacteristic
577C22#1062328411yescharacteristic
578C4—22no—
579C4—22no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—41no—
584C4—442no—
585C4—442no—
586C4—442no—
587C4—442no—
588C4—881no—
589C4—881no—
590C4—881no—
591C4#1062316711yescharacteristic
592C4#1062319311yescharacteristic
593C4#1062321911yescharacteristic
594C4#1062323311yescharacteristic
595C2—882no—
596C2#1307263511yescharacteristic
597C2#1307870811yescharacteristic
598C2#1307884711yescharacteristic
599C2#1308060911yescharacteristic
600C2#1308084811yescharacteristic
601C2#1308151711yescharacteristic
602C2#1308153911yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1917C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1917D11
hypocenterC11#27015
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1917

Complements

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

NH ≅ G/Ntype
2. #13071674C2semidirect
4. #13069950C2semidirect
5. #13069945C2semidirect
7. #13069563C2semidirect
8. #13069354C2semidirect
11. #13069209C2semidirect
12. #13069195C2semidirect
15. C11×#1917C2semidirect
115. #66885Q8semidirect
211. #1917D11semidirect
499. C11#27015semidirect

Maximal subgroups

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

subgroupindex
#130724662
#130716742
#130700032
#130699502
#130699452
#130697532
#130695632
#130693542
#130692442
#130692372
#130692092
#130691952
#130688802
#130684422
C11×#19172
#2701511