Finite Group Databasebeta

← #14826201

Subgroups — #14826201

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#13071674C211yesmaximal, characteristic, complemented
2#13070004C211yesmaximal, characteristic
3#13069946C211yesmaximal, characteristic, complemented
4#13069944C211yesmaximal, characteristic, complemented
5#13069752C211yesmaximal, characteristic
6#13069565C211yesmaximal, characteristic, complemented
7#13069351C211yesmaximal, characteristic, complemented
8#13069240C211yesmaximal, characteristic
9#13069233C211yesmaximal, characteristic
10#13069205C211yesmaximal, characteristic, complemented
11#13069191C211yesmaximal, characteristic, complemented
12#13069182C211yesmaximal, characteristic, complemented
13#13068877C211yesmaximal, characteristic
14#13068441C211yesmaximal, characteristic
15C11×#2452C211yesmaximal, characteristic
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×C22⋊Q8—21no—
18C2×C4×D4×C11C2211yescharacteristic
19C2×#66940—21no—
20C2×#66922C2211yescharacteristic
21C11×#396—21no—
22C11×#393—21no—
23C11×#390C2211yescharacteristic
24C11×#390C2211yescharacteristic
25C11×#389C2211yescharacteristic
26C11×#389C2211yescharacteristic
27C11×#385—21no—
28C4×C11×C4⋊C4C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33#10622587—21no—
34C2×#66872C2211yescharacteristic
35C2×#66872C2211yescharacteristic
36C2×#66871C2211yescharacteristic
37C2×#66871C2211yescharacteristic
38C4×C4⋊Dic11C2211yescharacteristic
39C4×C4⋊Dic11C2211yescharacteristic
40C4×C4⋊Dic11C2211yescharacteristic
41#10622541C2211yescharacteristic
42#10622541C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44C2×#66867C2211yescharacteristic
45#10622266—21no—
46#10622266—21no—
47#10622167C2211yescharacteristic
48#10622167C2211yescharacteristic
49#10622167C2211yescharacteristic
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×Q8×C11—21no—
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C22×Dic22—21no—
63C11×C4⋊Q8—22no—
64C11×C4⋊Q8—41no—
65C11×C22⋊Q8—44no—
66C4×D4×C11—22no—
67C4×D4×C11—41no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4D411yescharacteristic
72C2×C11×C4⋊C4D411yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C42×C11C2311yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11—21no—
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98#66940—44no—
99#66922—22no—
100#66922—22no—
101C11×#95—21no—
102C11×#95—21no—
103C11×#95D411yescharacteristic
104C11×#95D411yescharacteristic
105#66896—22no—
106#66896—22no—
107#66896—41no—
108#66896Q814yescomplemented
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114#66872—22no—
115#66872—41no—
116#66871—22no—
117#66871—22no—
118C4⋊(C11⋊C8)—41no—
119#66867—41no—
120#27015—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×C11—42no—
135C22×C4×C11—42no—
136C22×C4×C11—81no—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2411yescharacteristic
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C2×Dic22—24no—
149C2×Dic22—42no—
150C2×Dic22—42no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—42no—
159C11×C4⋊C4—42no—
160C11×C4⋊C4—42no—
161C11×C4⋊C4#4112yes—
162C11×C22⋊C4—42no—
163C11×C22⋊C4—42no—
164C11×C22⋊C4—42no—
165C11×C22⋊C4—42no—
166C11×C22⋊C4—81no—
167C42×C11—21no—
168C42×C11—21no—
169C42×C11—21no—
170C42×C11—21no—
171C42×C11—21no—
172C42×C11—21no—
173C4⋊Dic11—24no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11C2×Q812yes—
180C4⋊Dic11#4112yes—
181C4⋊Dic11#4112yes—
182Dic11⋊C4—42no—
183Dic11⋊C4—42no—
184C4×Dic11—42no—
185C4×Dic11—42no—
186C4×Dic11—42no—
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—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8C2×Q812yes—
199#2452D1111yescharacteristic
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#1917—111no—
212#1864—111no—
213#1762—111no—
214C23×C11—22no—
215C23×C11—41no—
216C23×C11—41no—
217C23×C11—41no—
218C23×C11—41no—
219C23×C11—41no—
220C23×C11—41no—
221C23×C11C22×D411yescharacteristic
222Q8×C11—84no—
223D4×C11—22no—
224D4×C11—22no—
225D4×C11—41no—
226D4×C11—41no—
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—22no—
236C2×C4×C11—21no—
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—21no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—84no—
253C2×C4×C11AGL(1,ℤ/8)12yes—
254C2×C4×C11AGL(1,ℤ/8)12yes—
255C2×C4×C11C22×Q811yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11H(5,𝔽2)11yescharacteristic
260C2×C4×C112−1+411yescharacteristic
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—22no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273Dic22—48no—
274C11⋊C8—22no—
275C11⋊C8—41no—
276C11⋊C8—41no—
277C11⋊C8—41no—
278C2×C4⋊Q8—111no—
279C2×C4⋊Q8C2×D1111yescharacteristic
280C2×C22⋊Q8—21no—
281C2×C4×Q8—221no—
282C2×C4×D4C2×D1111yescharacteristic
283C2×#107—111no—
284C2×#107—111no—
285C2×#106—111no—
286C2×#106—111no—
287C2×C4⋊C8—111no—
288C2×#102—111no—
289C2×#102—111no—
290C2×#102—111no—
291C2×#102—111no—
292C2×#97—111no—
293#396—21no—
294#393—21no—
295#391—221no—
296#390C2×D1111yescharacteristic
297#390C2×D1111yescharacteristic
298#389—111no—
299#389—111no—
300#389C2×D1111yescharacteristic
301#389C2×D1111yescharacteristic
302#387—221no—
303#387—221no—
304#385—21no—
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#336—111no—
318#336—111no—
319#336—111no—
320#336—111no—
321C22×C11—42no—
322C22×C11—42no—
323C22×C11—42no—
324C22×C11—81no—
325C22×C11—81no—
326C22×C11—81no—
327C22×C11—81no—
328C22×C11#52511yescharacteristic
329C22×C11#54611yescharacteristic
330C22×C11D4×Q811yescharacteristic
331C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
332C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
333C22×C11#57711yescharacteristic
334C22×C11#57811yescharacteristic
335C4×C11—22no—
336C4×C11—22no—
337C4×C11—41no—
338C4×C11—41no—
339C4×C11—41no—
340C4×C11—41no—
341C4×C11—42no—
342C4×C11—81no—
343C4×C11—81no—
344C4×C11#53311yescharacteristic
345C4×C11#54211yescharacteristic
346C4×C11#55411yescharacteristic
347C4×C11#55611yescharacteristic
348Dic11—42no—
349Dic11—42no—
350Dic11—42no—
351Dic11—81no—
352C22×Q8—21no—
353C22×Q8—221no—
354C22×D4C22×D1111yescharacteristic
355C23×C4—21no—
356C22×C8—111no—
357C22×C8—111no—
358C22×C8—111no—
359C22×C8—111no—
360C4⋊Q8—22no—
361C4⋊Q8—41no—
362C4⋊Q8—222no—
363C4⋊Q8—222no—
364C22⋊Q8—44no—
365C4×Q8—444no—
366C4×D4—22no—
367C4×D4—41no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
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⋊C4C22⋊D1111yescharacteristic
379C2×C4⋊C4C22⋊D1111yescharacteristic
380C2×C4⋊C4C22×D1111yescharacteristic
381C2×C4⋊C4C22×D1111yescharacteristic
382C2×C4⋊C4C22×D1111yescharacteristic
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
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—441no—
399#102—114no—
400#102—222no—
401#102—222no—
402#102—441no—
403#97—441no—
404#95—21no—
405#95—21no—
406#95—221no—
407#95—221no—
408#95—221no—
409#95—221no—
410#95—221no—
411#95C22⋊D1111yescharacteristic
412#95C22⋊D1111yescharacteristic
413C2×C11—82no—
414C2×C11#246511yescharacteristic
415C2×C11#310911yescharacteristic
416C2×C11#312111yescharacteristic
417C2×C11#330811yescharacteristic
418C2×C11#332411yescharacteristic
419C2×C11#338411yescharacteristic
420C2×C11#338611yescharacteristic
421C24—21no—
422C2×Q8—42no—
423C2×Q8—42no—
424C2×Q8—81no—
425C2×Q8—224no—
426C2×Q8—442no—
427C2×Q8—442no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4Q8×D1112yes—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—81no—
440C22×C4—221no—
441C22×C4—221no—
442C22×C4—221no—
443C22×C4—221no—
444C22×C4C2×C22⋊D1111yescharacteristic
445C22×C4C2×C22⋊D1111yescharacteristic
446C22×C4C2×C22⋊D1111yescharacteristic
447C22×C4C2×C22⋊D1111yescharacteristic
448C22×C4C2×C22⋊D1111yescharacteristic
449C22×C4C2×C22⋊D1111yescharacteristic
450C22×C4C23×D1111yescharacteristic
451C2×C8—112no—
452C2×C8—221no—
453C2×C8—221no—
454C2×C8—221no—
455C2×C8—221no—
456C2×C8—221no—
457C2×C8—221no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—221no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—42no—
471C4⋊C4—42no—
472C4⋊C4—42no—
473C4⋊C4—112no—
474C4⋊C4—112no—
475C4⋊C4—112no—
476C4⋊C4—224no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—442no—
483C4⋊C4—442no—
484C4⋊C4#434112yes—
485C22⋊C4—42no—
486C22⋊C4—42no—
487C22⋊C4—42no—
488C22⋊C4—42no—
489C22⋊C4—81no—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—442no—
497C42—442no—
498C42—442no—
499C11#2701511yescharacteristic, complemented, Sylow
500C23—22no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23C22×C22⋊D1111yescharacteristic
508Q8—84no—
509Q8—448no—
510D4—22no—
511D4—22no—
512D4—41no—
513D4—41no—
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—22no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—84no—
540C2×C4—222no—
541C2×C4—222no—
542C2×C4—222no—
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—441no—
552C2×C4#6698512yes—
553C2×C4#6700212yes—
554C2×C4C2×#434111yescharacteristic
555C2×C4#6703711yescharacteristic
556C2×C4C2×Q8×D1111yescharacteristic
557C2×C4#6704011yescharacteristic
558C2×C4#41×D1111yescharacteristic
559C2×C4#41×D1111yescharacteristic
560C8—222no—
561C8—441no—
562C8—441no—
563C8—441no—
564C22—42no—
565C22—42no—
566C22—42no—
567C22—81no—
568C22—81no—
569C22—81no—
570C22—81no—
571C22C2×#6698511yescharacteristic
572C22#1062333711yescharacteristic
573C22Q8×C22⋊D1111yescharacteristic
574C22C2×#6700211yescharacteristic
575C22#1062335911yescharacteristic
576C22#1062336711yescharacteristic
577C22#1062336911yescharacteristic
578C4—22no—
579C4—22no—
580C4—41no—
581C4—41no—
582C4—42no—
583C4—41no—
584C4—41no—
585C4—81no—
586C4—81no—
587C4—442no—
588C4—442no—
589C4—442no—
590C4—881no—
591C4#1062315311yescharacteristic
592C4#1062316711yescharacteristic
593C4#1062317111yescharacteristic
594C4#1062317211yescharacteristic
595C2—82no—
596C2#1307263311yescharacteristic
597C2#1307870311yescharacteristic
598C2#1307883911yescharacteristic
599C2#1308060711yescharacteristic
600C2#1308084711yescharacteristic
601C2#1308151511yescharacteristic
602C2#1308153711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2452C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#2452D11
hypocenterC11#27015
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2452

Complements

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

NH ≅ G/Ntype
1. #13071674C2semidirect
3. #13069946C2semidirect
4. #13069944C2semidirect
6. #13069565C2semidirect
7. #13069351C2semidirect
10. #13069205C2semidirect
11. #13069191C2semidirect
12. #13069182C2semidirect
108. #66896Q8semidirect
499. C11#27015semidirect

Maximal subgroups

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

subgroupindex
#130716742
#130700042
#130699462
#130699442
#130697522
#130695652
#130693512
#130692402
#130692332
#130692052
#130691912
#130691822
#130688772
#130684412
C11×#24522
#2701511