Finite Group Databasebeta

← #14802162

Subgroups — #14802162

Order 2816.

900 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622616C211yesmaximal, characteristic
2C2×#10622662C211yesmaximal, characteristic
3#13071630C211yesmaximal, characteristic
4#13070088C211yesmaximal, characteristic, complemented
5#13070030C211yesmaximal, characteristic, complemented
6#13069997C211yesmaximal, characteristic, complemented
7#13069931C211yesmaximal, characteristic, complemented
8#13069382C211yesmaximal, characteristic, complemented
9#13069254C211yesmaximal, characteristic, complemented
10#13068953C211yesmaximal, characteristic, complemented
11#13068924C211yesmaximal, characteristic, complemented
12#13068801C211yesmaximal, characteristic, complemented
13#13068613C211yesmaximal, characteristic, complemented
14#13068337C211yesmaximal, characteristic, complemented
15C11×#2499C211yesmaximal, characteristic, complemented
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×#4325C2211yescharacteristic
19C2×#66983C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C22×#4318C2211yescharacteristic
22C2×(C22⋊D11)⋊C4—21no—
23C2×C4×D44C2211yescharacteristic
24C11×#397—21no—
25C11×#397—21no—
26C11×#391C2211yescharacteristic
27C11×#391C2211yescharacteristic
28C11×#387—21no—
29C11×#387—21no—
30C11×#384C2211yescharacteristic
31C11×#382C2211yescharacteristic
32C4×C11×C22⋊C4C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2211yescharacteristic
37#10622662—24no—
38#10622616—24no—
39C2×#66873C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45#10622571—21no—
46#10622552C2211yescharacteristic
47C4×C4⋊Dic11C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51#10622283—21no—
52#10622281—21no—
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11—21no—
64C23×Dic11—21no—
65C22×D44C2311yescharacteristic
66C22×C4×D11—21no—
67C11×C22⋊Q8—22no—
68C11×C22⋊Q8—22no—
69C11×#117—22no—
70C11×#117—22no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4D411yescharacteristic
80C2×C11×C22⋊C4D411yescharacteristic
81C2×C42×C11—21no—
82C2×C42×C11C2311yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×#4325—22no—
85C2×#4325—22no—
86C2×#4325—41no—
87#66983—22no—
88#66983D414yes—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93C2×C4⋊Dic11—22no—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11—41no—
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×Dic11⋊C4—21no—
100C2×C4×Dic11—21no—
101C2×#4318—22no—
102C2×#4318—22no—
103C2×#4318—41no—
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108(C22⋊D11)⋊C4—44no—
109C4×D44—22no—
110C4×D44—41no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95—21no—
114C11×#95—21no—
115C11×#95—21no—
116C11×#95—21no—
117C11×#95D411yescharacteristic
118C11×#95D411yescharacteristic
119#66899—22no—
120#66899—22no—
121#66899—41no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C22⋊(C11⋊C8)—22no—
125#66873—22no—
126#66873—22no—
127#66873—22no—
128#66872—22no—
129#66871—22no—
130#66871—22no—
131C4⋊(C11⋊C8)—22no—
132C4⋊(C11⋊C8)—41no—
133#25216—111nomaximal, Sylow
134C24×C11C2×D411yescharacteristic
135C23×D11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11#4112yes—
157C22×C4×C11C2411yescharacteristic
158C2×C22⋊D11—24no—
159C2×C22⋊D11—42no—
160C2×C22⋊D11—42no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—42no—
165C22×Dic11—42no—
166C22×Dic11—81no—
167C2×D44—21no—
168C2×D44—21no—
169C2×D44—21no—
170C2×D44—21no—
171C2×D44—21no—
172C2×D44C2×D412yes—
173C2×C4×D11—42no—
174C2×C4×D11—42no—
175C2×C4×D11—81no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—42no—
183C11×C4⋊C4—42no—
184C11×C4⋊C4—42no—
185C11×C22⋊C4—22no—
186C11×C22⋊C4—41no—
187C11×C22⋊C4—42no—
188C11×C22⋊C4—42no—
189C42×C11—21no—
190C42×C11—21no—
191C42×C11—21no—
192C42×C11—21no—
193C42×C11—42no—
194#4325—44no—
195(C2×D11)⋊C4—24no—
196(C2×D11)⋊C4—42no—
197(C2×D11)⋊C4—42no—
198(C2×D11)⋊C4—81no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—42no—
204C4⋊Dic11C2×D412yes—
205C4⋊Dic11#4112yes—
206Dic11⋊C4—42no—
207C4×Dic11—42no—
208#4318—44no—
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—21no—
220C2×C11⋊C8#4112yes—
221C2×#482—111no—
222C2×#468—111no—
223#2499D1111yescharacteristic, complemented
224#2361—111no—
225#2083—111no—
226#2073—111no—
227#2066—111no—
228#2055—111no—
229#1949—111no—
230#1928—111no—
231#1877—111no—
232#1872—111no—
233#1851—111no—
234#1802—111no—
235#1736—111no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11#12112yes—
243C23×C11C22×D411yescharacteristic
244C22×D11—22no—
245C22×D11—41no—
246C22×D11—41no—
247C22×D11—41no—
248C22×D11—41no—
249C22×D11—41no—
250C22×D11—41no—
251Q8×C11—41no—
252Q8×C11—41no—
253Q8×C11—41no—
254Q8×C11—41no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
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—21no—
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—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
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—41no—
284C2×C4×C11#12112yes—
285C2×C4×C11AGL(1,ℤ/8)12yes—
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
292C22⋊D11—48no—
293C2×Dic11—22no—
294C2×Dic11—22no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—84no—
303D44—22no—
304D44—22no—
305D44—41no—
306D44—41no—
307C4×D11—84no—
308C11⋊C8—22no—
309C11⋊C8—41no—
310C11⋊C8—41no—
311C11⋊C8—41no—
312C22×SD16—111no—
313C22×M16—111no—
314C2×C22⋊Q8C2×D1111yescharacteristic
315C2×#121—111no—
316C2×C4×D4—111no—
317C2×C4×D4—221no—
318C2×#117C2×D1111yescharacteristic
319C22×C4⋊C4—111no—
320#482—224no—
321#468—224no—
322C2×#107—111no—
323C2×#107—111no—
324C2×#106—111no—
325C2×C4⋊C8—111no—
326C2×C4⋊C8—111no—
327C2×#103—111no—
328C2×#103—111no—
329C2×#103—111no—
330C2×#102—111no—
331C2×#102—111no—
332C2×#102—111no—
333C2×C22⋊C8—111no—
334#397—21no—
335#397—21no—
336#391C2×D1111yescharacteristic
337#391C2×D1111yescharacteristic
338#390—111no—
339#389—111no—
340#388—221no—
341#387—21no—
342#387—21no—
343#386—221no—
344#385—221no—
345#384C2×D1111yescharacteristic
346#382C2×D1111yescharacteristic
347C4×C4⋊C4—111no—
348C4×C22⋊C4C2×D1111yescharacteristic
349#340—111no—
350#340—111no—
351#340—111no—
352#340—111no—
353#340—111no—
354#340—111no—
355#336—111no—
356#336—111no—
357C22×C11—22no—
358C22×C11—22no—
359C22×C11—22no—
360C22×C11—41no—
361C22×C11—41no—
362C22×C11—41no—
363C22×C11—41no—
364C22×C11C2×#12111yescharacteristic
365C22×C11#54611yescharacteristic
366C22×C11#54711yescharacteristic
367C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
368C22×C11#57511yescharacteristic
369C22×C11#57711yescharacteristic
370C22×C11#57811yescharacteristic
371C2×D11—42no—
372C2×D11—42no—
373C2×D11—42no—
374C2×D11—81no—
375C2×D11—81no—
376C2×D11—81no—
377C2×D11—81no—
378C4×C11—22no—
379C4×C11—22no—
380C4×C11—41no—
381C4×C11—41no—
382C4×C11—41no—
383C4×C11—81no—
384C4×C11—81no—
385C4×C11—81no—
386C4×C11—81no—
387C4×C11#52911yescharacteristic
388C4×C11#53911yescharacteristic
389C4×C11#54611yescharacteristic
390C4×C11#54711yescharacteristic
391Dic11—42no—
392Dic11—42no—
393Dic11—81no—
394C22×Q8C22×D1111yescharacteristic
395C22×D4—111no—
396C22×D4—221no—
397C23×C4—221no—
398C23×C4—221no—
399C23×C4C22×D1111yescharacteristic
400C2×SD16—222no—
401C2×SD16—222no—
402C2×SD16—441no—
403C2×M16—222no—
404C2×M16—222no—
405C2×M16—441no—
406C22×C8—111no—
407C22×C8—111no—
408C22×C8—111no—
409C22×C8—111no—
410C22⋊Q8—22no—
411C22⋊Q8—22no—
412#121—114no—
413#121—222no—
414C4×D4—222no—
415C4×D4—441no—
416C4×D4—444no—
417#117—22no—
418#117—22no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—111no—
425C2×C4⋊C4—222no—
426C2×C4⋊C4—221no—
427C2×C4⋊C4—221no—
428C2×C4⋊C4—441no—
429C2×C4⋊C4C22×D1111yescharacteristic
430C2×C4⋊C4C22×D1111yescharacteristic
431C2×C4⋊C4C22×D1111yescharacteristic
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—221no—
435C2×C22⋊C4—221no—
436C2×C22⋊C4—221no—
437C2×C22⋊C4—221no—
438C2×C22⋊C4C22⋊D1111yescharacteristic
439C2×C22⋊C4C22⋊D1111yescharacteristic
440C2×C42—21no—
441C2×C42—221no—
442C2×C42C22×D1111yescharacteristic
443C2×C42C22×D1111yescharacteristic
444#107—222no—
445#107—222no—
446#106—222no—
447C4⋊C8—222no—
448C4⋊C8—441no—
449#103—222no—
450#103—222no—
451#103—441no—
452#102—222no—
453#102—222no—
454#102—222no—
455C22⋊C8—222no—
456#95—21no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—221no—
463#95—221no—
464#95C22⋊D1111yescharacteristic
465#95C22⋊D1111yescharacteristic
466C2×C11—42no—
467C2×C11#242511yescharacteristic
468C2×C11#303611yescharacteristic
469C2×C11#304611yescharacteristic
470C2×C11#331011yescharacteristic
471C2×C11#332711yescharacteristic
472C2×C11#335011yescharacteristic
473C2×C11#335311yescharacteristic
474D11—82no—
475C24—221no—
476C24C2×C22⋊D1111yescharacteristic
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×D4—112no—
484C2×D4—224no—
485C2×D4—221no—
486C2×D4—221no—
487C2×D4—221no—
488C2×D4—221no—
489C2×D4—221no—
490C2×D4—442no—
491C2×D4—442no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4—442no—
504C22×C4—442no—
505C22×C4—442no—
506C22×C4—442no—
507C22×C4—881no—
508C22×C4—881no—
509C22×C4D4×D1112yes—
510C22×C4#434112yes—
511C22×C4C2×C22⋊D1111yescharacteristic
512C22×C4C2×C22⋊D1111yescharacteristic
513C22×C4C2×C22⋊D1111yescharacteristic
514C22×C4C2×C22⋊D1111yescharacteristic
515C22×C4C2×C22⋊D1111yescharacteristic
516C22×C4C23×D1111yescharacteristic
517SD16—444no—
518M16—444no—
519C2×C8—112no—
520C2×C8—221no—
521C2×C8—221no—
522C2×C8—221no—
523C2×C8—221no—
524C2×C8—221no—
525C2×C8—221no—
526C2×C8—221no—
527C2×C8—221no—
528C2×C8—221no—
529C2×C8—221no—
530C2×C8—221no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—42no—
538C4⋊C4—42no—
539C4⋊C4—42no—
540C4⋊C4—112no—
541C4⋊C4—112no—
542C4⋊C4—221no—
543C4⋊C4—221no—
544C4⋊C4—221no—
545C4⋊C4—221no—
546C4⋊C4—442no—
547C4⋊C4—442no—
548C22⋊C4—22no—
549C22⋊C4—41no—
550C22⋊C4—42no—
551C22⋊C4—42no—
552C22⋊C4—224no—
553C22⋊C4—442no—
554C22⋊C4—442no—
555C22⋊C4—881no—
556C42—21no—
557C42—21no—
558C42—21no—
559C42—21no—
560C42—42no—
561C42—442no—
562C11#2521611yescharacteristic, complemented, Sylow
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—222no—
570C23—441no—
571C23—441no—
572C23—441no—
573C23—441no—
574C23—441no—
575C23—441no—
576C23#6699112yes—
577C23C22×C22⋊D1111yescharacteristic
578Q8—41no—
579Q8—41no—
580Q8—41no—
581Q8—41no—
582D4—222no—
583D4—222no—
584D4—448no—
585D4—441no—
586D4—441no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
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—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—222no—
617C2×C4—222no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4—441no—
621C2×C4—441no—
622C2×C4—441no—
623C2×C4—441no—
624C2×C4—441no—
625C2×C4—884no—
626C2×C4—884no—
627C2×C4#6699112yes—
628C2×C4#6700212yes—
629C2×C4C2×D4×D1111yescharacteristic
630C2×C4C2×#434111yescharacteristic
631C2×C4#41×D1111yescharacteristic
632C2×C4#41×D1111yescharacteristic
633C2×C4#6704211yescharacteristic
634C2×C4#6704311yescharacteristic
635C8—222no—
636C8—441no—
637C8—441no—
638C8—441no—
639C22—22no—
640C22—22no—
641C22—22no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—442no—
647C22—442no—
648C22—442no—
649C22—881no—
650C22—881no—
651C22—881no—
652C22—881no—
653C22C2×#6699111yescharacteristic
654C22C2×#6700211yescharacteristic
655C22#1062335311yescharacteristic
656C22#1062335511yescharacteristic
657C22#1062336011yescharacteristic
658C22#1062336811yescharacteristic
659C22#1062336911yescharacteristic
660C4—22no—
661C4—22no—
662C4—41no—
663C4—41no—
664C4—41no—
665C4—81no—
666C4—81no—
667C4—81no—
668C4—81no—
669C4—442no—
670C4—442no—
671C4—881no—
672C4#1062318011yescharacteristic
673C4#1062318511yescharacteristic
674C4#1062318611yescharacteristic
675C4#1062319611yescharacteristic
676C2—42no—
677C2—882no—
678C2#1307216311yescharacteristic
679C2#1307807611yescharacteristic
680C2#1307816211yescharacteristic
681C2#1308063111yescharacteristic
682C2#1308087811yescharacteristic
683C2#1308116111yescharacteristic
684C2#1308119411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2499C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenter#2499D11
hypocenterC11#25216
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2499

Complements

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

NH ≅ G/Ntype
4. #13070088C2semidirect
5. #13070030C2semidirect
6. #13069997C2semidirect
7. #13069931C2semidirect
8. #13069382C2semidirect
9. #13069254C2semidirect
10. #13068953C2semidirect
11. #13068924C2semidirect
12. #13068801C2semidirect
13. #13068613C2semidirect
14. #13068337C2semidirect
15. C11×#2499C2semidirect
223. #2499D11semidirect
562. C11#25216semidirect

Maximal subgroups

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

subgroupindex
C2×#106226162
C2×#106226622
#130716302
#130700882
#130700302
#130699972
#130699312
#130693822
#130692542
#130689532
#130689242
#130688012
#130686132
#130683372
C11×#24992
#2521611