Finite Group Databasebeta

← #14802100

Subgroups — #14802100

Order 2816.

926 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622646C211yesmaximal, characteristic
2C2×#10622654C211yesmaximal, characteristic
3#13073101C211yesmaximal, characteristic, complemented
4#13070097C211yesmaximal, characteristic, complemented
5#13070029C211yesmaximal, characteristic, complemented
6#13070008C211yesmaximal, characteristic, complemented
7#13069933C211yesmaximal, characteristic, complemented
8#13069384C211yesmaximal, characteristic, complemented
9#13069257C211yesmaximal, characteristic, complemented
10#13068950C211yesmaximal, characteristic, complemented
11#13068923C211yesmaximal, characteristic, complemented
12#13068796C211yesmaximal, characteristic, complemented
13#13068626C211yesmaximal, characteristic, complemented
14C2×#10622167C211yesmaximal, characteristic, complemented
15C11×#2361C211yesmaximal, characteristic
16C2×C11×#121C2211yescharacteristic
17C2×C4×D4×C11—21no—
18C2×C4×D4×C11C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×#4324C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C2×#66977C2211yescharacteristic
23C23×C11⋊C8C2211yescharacteristic
24C11×#390C2211yescharacteristic
25C11×#389C2211yescharacteristic
26C11×#388—21no—
27C11×#386—21no—
28C11×#385—21no—
29C4×C11×C4⋊C4C2211yescharacteristic
30C4×C11×C22⋊C4C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35#10622654—24no—
36#10622646—24no—
37C2×#66874C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66872C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43#10622556—21no—
44#10622556—21no—
45#10622549C2211yescharacteristic
46#10622549C2211yescharacteristic
47#10622542C2211yescharacteristic
48#10622542C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51#10622272—21no—
52#10622272—21no—
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×D4×C11—21no—
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C23×C4×C11—21no—
65C23×C4×C11C2311yescharacteristic
66C23×Dic11—21no—
67C22×Dic22C2311yescharacteristic
68C11×#121—22no—
69C11×#121D414yes—
70C4×D4×C11—22no—
71C4×D4×C11—41no—
72C4×D4×C11—44no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—41no—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4D411yescharacteristic
85C2×C11×C22⋊C4D411yescharacteristic
86C2×C42×C11—21no—
87C2×C42×C11C2311yescharacteristic
88C2×C42×C11C2311yescharacteristic
89C2×C22⋊Dic11—21no—
90C2×#4324—22no—
91C2×#4324—22no—
92C2×#4324—41no—
93C2×C4⋊Dic11—22no—
94C2×C4⋊Dic11—22no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99#66977—22no—
100#66977—22no—
101C2×Dic11⋊C4—21no—
102C22×C11⋊C8—22no—
103C22×C11⋊C8—22no—
104C22×C11⋊C8—41no—
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C11×#95—21no—
110C11×#95—21no—
111C11×#95D411yescharacteristic
112C11×#95D411yescharacteristic
113#66896—22no—
114#66896—22no—
115#66896—22no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C22⋊(C11⋊C8)—22no—
125#66874—22no—
126#66874—22no—
127#66874—41no—
128#66872—22no—
129#66871—22no—
130#66871—22no—
131C4⋊(C11⋊C8)—22no—
132C4⋊(C11⋊C8)—41no—
133#25212—111nomaximal, Sylow
134C24×C11—21no—
135C24×C11C2×D411yescharacteristic
136C2×D4×C11—24no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—42no—
143C2×D4×C11—42no—
144C2×D4×C11C2×D412yes—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—42no—
153C22×C4×C11—42no—
154C22×C4×C11—42no—
155C22×C4×C11—42no—
156C22×C4×C11—81no—
157C22×C4×C11—81no—
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D412yes—
164C22×C4×C11#4112yes—
165C22×C4×C11C2411yescharacteristic
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—42no—
171C22×Dic11—42no—
172C22×Dic11—42no—
173C2×Dic22—21no—
174C2×Dic22—21no—
175C2×Dic22—21no—
176C2×Dic22—21no—
177C2×Dic22—21no—
178C2×Dic22—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—42no—
184C11×C4⋊C4—42no—
185C11×C4⋊C4C2×D412yes—
186C11×C4⋊C4#4112yes—
187C11×C22⋊C4—22no—
188C11×C22⋊C4—22no—
189C11×C22⋊C4—24no—
190C11×C22⋊C4—42no—
191C11×C22⋊C4—42no—
192C11×C22⋊C4—81no—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11—21no—
196C42×C11—21no—
197C42×C11—42no—
198C22⋊Dic11—42no—
199#4324—44no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—42no—
207Dic11⋊C4—42no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—44no—
220C2×C11⋊C8#4112yes—
221C2×#480—111no—
222C2×#465—111no—
223#2503—111no—
224#2361D1111yescharacteristic
225#2085—111no—
226#2073—111no—
227#2068—111no—
228#2055—111no—
229#1949—111no—
230#1928—111no—
231#1877—111no—
232#1872—111no—
233#1850—111no—
234#1804—111no—
235C2×#340—111no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—22no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11#12112yes—
248C23×C11#13512yes—
249C23×C11AGL(1,ℤ/8)12yes—
250C23×C11C22×D411yescharacteristic
251D4×C11—22no—
252D4×C11—22no—
253D4×C11—48no—
254D4×C11—41no—
255D4×C11—41no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—22no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—84no—
284C2×C4×C11—84no—
285C2×C4×C11#12112yes—
286C2×C4×C11C22×D411yescharacteristic
287C2×C4×C11C2×#4111yescharacteristic
288C2×C4×C11C2×#4111yescharacteristic
289C2×C4×C11C2×#4111yescharacteristic
290C2×C4×C11H(5,𝔽2)11yescharacteristic
291C2×C4×C112−1+411yescharacteristic
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11—41no—
304C2×Dic11—84no—
305Dic22—41no—
306Dic22—41no—
307Dic22—41no—
308Dic22—41no—
309C11⋊C8—22no—
310C11⋊C8—41no—
311C11⋊C8—41no—
312C11⋊C8—41no—
313C22×SD16—111no—
314C23×C8—111no—
315C2×C22⋊Q8—111no—
316C2×#121C2×D1111yescharacteristic
317C2×C4×D4—21no—
318C2×C4×D4C2×D1111yescharacteristic
319C22×C4⋊C4—111no—
320C22×C4⋊C4C2×D1111yescharacteristic
321#480—224no—
322#465—224no—
323C2×#107—111no—
324C2×#107—111no—
325C2×#106—111no—
326C2×C4⋊C8—111no—
327C2×C4⋊C8—111no—
328C2×#103—111no—
329C2×#103—111no—
330C2×#103—111no—
331C2×#102—111no—
332C2×#102—111no—
333C2×#102—111no—
334C2×C22⋊C8—111no—
335#400—221no—
336#400—221no—
337#391—111no—
338#391—111no—
339#390C2×D1111yescharacteristic
340#389C2×D1111yescharacteristic
341#388—21no—
342#386—21no—
343#385—21no—
344#382—111no—
345#382—111no—
346#381—221no—
347#381—221no—
348C4×C4⋊C4C2×D1111yescharacteristic
349C4×C22⋊C4C2×D1111yescharacteristic
350#340—111no—
351#340—111no—
352#340—111no—
353#340—111no—
354#340—111no—
355#340—111no—
356#336—111no—
357#336—111no—
358C22×C11—22no—
359C22×C11—22no—
360C22×C11—22no—
361C22×C11—22no—
362C22×C11—22no—
363C22×C11—22no—
364C22×C11—42no—
365C22×C11—42no—
366C22×C11—42no—
367C22×C11—81no—
368C22×C11—81no—
369C22×C11—81no—
370C22×C11—81no—
371C22×C11#46314yes—
372C22×C11C2×#12111yescharacteristic
373C22×C11#54611yescharacteristic
374C22×C11#54711yescharacteristic
375C22×C11C2×#13511yescharacteristic
376C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
377C22×C11#57711yescharacteristic
378C22×C11#57811yescharacteristic
379C4×C11—22no—
380C4×C11—41no—
381C4×C11—41no—
382C4×C11—42no—
383C4×C11—41no—
384C4×C11—41no—
385C4×C11—42no—
386C4×C11—81no—
387C4×C11#52911yescharacteristic
388C4×C11#53911yescharacteristic
389C4×C11#54611yescharacteristic
390C4×C11#54711yescharacteristic
391Dic11—81no—
392Dic11—81no—
393Dic11—81no—
394Dic11—81no—
395C22×Q8—111no—
396C22×D4—21no—
397C22×D4C22×D1111yescharacteristic
398C23×C4—21no—
399C23×C4—21no—
400C23×C4—221no—
401C23×C4C22×D1111yescharacteristic
402C2×SD16—222no—
403C2×SD16—222no—
404C2×SD16—441no—
405C22×C8—111no—
406C22×C8—111no—
407C22×C8—111no—
408C22×C8—111no—
409C22×C8—222no—
410C22×C8—222no—
411C22×C8—441no—
412C22⋊Q8—222no—
413C22⋊Q8—222no—
414#121—22no—
415#121D4414yes—
416C4×D4—22no—
417C4×D4—41no—
418C4×D4—44no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—41no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—111no—
425C2×C4⋊C4—111no—
426C2×C4⋊C4—222no—
427C2×C4⋊C4—222no—
428C2×C4⋊C4—221no—
429C2×C4⋊C4—221no—
430C2×C4⋊C4C22×D1111yescharacteristic
431C2×C4⋊C4C22×D1111yescharacteristic
432C2×C4⋊C4C22×D1111yescharacteristic
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—221no—
438C2×C22⋊C4C22⋊D1111yescharacteristic
439C2×C22⋊C4C22⋊D1111yescharacteristic
440C2×C42—21no—
441C2×C42C22×D1111yescharacteristic
442C2×C42C22×D1111yescharacteristic
443#107—222no—
444#107—222no—
445#106—222no—
446C4⋊C8—222no—
447C4⋊C8—441no—
448#103—222no—
449#103—222no—
450#103—441no—
451#102—222no—
452#102—222no—
453#102—222no—
454C22⋊C8—222no—
455#95—21no—
456#95—21no—
457#95—221no—
458#95—221no—
459#95—221no—
460#95—221no—
461#95—221no—
462#95—221no—
463#95—221no—
464#95—221no—
465#95C22⋊D1111yescharacteristic
466#95C22⋊D1111yescharacteristic
467C2×C11—24no—
468C2×C11—82no—
469C2×C11#242511yescharacteristic
470C2×C11C2×#46311yescharacteristic
471C2×C11#304611yescharacteristic
472C2×C11#330011yescharacteristic
473C2×C11#331011yescharacteristic
474C2×C11#333711yescharacteristic
475C2×C11#334311yescharacteristic
476C24—21no—
477C24C2×C22⋊D1111yescharacteristic
478C2×Q8—221no—
479C2×Q8—221no—
480C2×Q8—221no—
481C2×Q8—221no—
482C2×Q8—221no—
483C2×Q8—221no—
484C2×D4—24no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—42no—
491C2×D4—42no—
492C2×D4C2×D4412yes—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—81no—
505C22×C4—81no—
506C22×C4—221no—
507C22×C4—221no—
508C22×C4—221no—
509C22×C4—221no—
510C22×C4—442no—
511C22×C4—442no—
512C22×C4—442no—
513C22×C4C2×D4412yes—
514C22×C4#433912yes—
515C22×C4C2×C22⋊D1111yescharacteristic
516C22×C4C2×C22⋊D1111yescharacteristic
517C22×C4C2×C22⋊D1111yescharacteristic
518C22×C4C2×C22⋊D1111yescharacteristic
519C22×C4C2×C22⋊D1111yescharacteristic
520C22×C4C23×D1111yescharacteristic
521SD16—444no—
522C2×C8—112no—
523C2×C8—221no—
524C2×C8—221no—
525C2×C8—221no—
526C2×C8—221no—
527C2×C8—221no—
528C2×C8—221no—
529C2×C8—221no—
530C2×C8—221no—
531C2×C8—221no—
532C2×C8—221no—
533C2×C8—221no—
534C2×C8—444no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—42no—
540C4⋊C4—42no—
541C4⋊C4—221no—
542C4⋊C4—221no—
543C4⋊C4—221no—
544C4⋊C4—221no—
545C4⋊C4—221no—
546C4⋊C4—221no—
547C4⋊C4—442no—
548C4⋊C4—442no—
549C4⋊C4C2×D4412yes—
550C4⋊C4#434112yes—
551C22⋊C4—22no—
552C22⋊C4—22no—
553C22⋊C4—24no—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—81no—
557C22⋊C4—442no—
558C42—21no—
559C42—21no—
560C42—21no—
561C42—21no—
562C42—42no—
563C11#2521211yescharacteristic, complemented, Sylow
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—22no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23#6698312yes—
576C23#6698512yes—
577C23#6700312yes—
578C23C22×C22⋊D1111yescharacteristic
579Q8—441no—
580Q8—441no—
581Q8—441no—
582Q8—441no—
583D4—22no—
584D4—22no—
585D4—48no—
586D4—41no—
587D4—41no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—22no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—84no—
616C2×C4—84no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4—441no—
621C2×C4—441no—
622C2×C4—441no—
623C2×C4—441no—
624C2×C4—441no—
625C2×C4—441no—
626C2×C4—441no—
627C2×C4—441no—
628C2×C4—441no—
629C2×C4—884no—
630C2×C4#6698312yes—
631C2×C4C22×D4411yescharacteristic
632C2×C4C2×#433911yescharacteristic
633C2×C4C2×#434111yescharacteristic
634C2×C4#6703711yescharacteristic
635C2×C4#41×D1111yescharacteristic
636C2×C4#6704311yescharacteristic
637C8—222no—
638C8—441no—
639C8—441no—
640C8—441no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—22no—
646C22—22no—
647C22—42no—
648C22—42no—
649C22—42no—
650C22—81no—
651C22—81no—
652C22—81no—
653C22—81no—
654C22#1062262914yes—
655C22C2×#6698311yescharacteristic
656C22C2×#6698511yescharacteristic
657C22#1062333711yescharacteristic
658C22C2×#6700311yescharacteristic
659C22#1062335511yescharacteristic
660C22#1062336711yescharacteristic
661C22#1062336911yescharacteristic
662C4—22no—
663C4—42no—
664C4—41no—
665C4—42no—
666C4—41no—
667C4—41no—
668C4—41no—
669C4—81no—
670C4—881no—
671C4—881no—
672C4—881no—
673C4—881no—
674C4#1062306911yescharacteristic
675C4#1062308511yescharacteristic
676C4#1062308611yescharacteristic
677C4#1062309511yescharacteristic
678C2—24no—
679C2—82no—
680C2#1307216111yescharacteristic
681C2C2×#1062262911yescharacteristic
682C2#1307816611yescharacteristic
683C2#1308050311yescharacteristic
684C2#1308063711yescharacteristic
685C2#1308098911yescharacteristic
686C2#1308105011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2361C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenter#2361D11
hypocenterC11#25212
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2361

Complements

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

NH ≅ G/Ntype
3. #13073101C2semidirect
4. #13070097C2semidirect
5. #13070029C2semidirect
6. #13070008C2semidirect
7. #13069933C2semidirect
8. #13069384C2semidirect
9. #13069257C2semidirect
10. #13068950C2semidirect
11. #13068923C2semidirect
12. #13068796C2semidirect
13. #13068626C2semidirect
14. C2×#10622167C2semidirect
563. C11#25212semidirect

Maximal subgroups

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

subgroupindex
C2×#106226462
C2×#106226542
#130731012
#130700972
#130700292
#130700082
#130699332
#130693842
#130692572
#130689502
#130689232
#130687962
#130686262
C2×#106221672
C11×#23612
#2521211