Finite Group Databasebeta

← #14802104

Subgroups — #14802104

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×#10622349C211yesmaximal, characteristic
2C2×#10622727C211yesmaximal, characteristic
3#13073101C211yesmaximal, characteristic, complemented
4#13071630C211yesmaximal, characteristic
5#13070099C211yesmaximal, characteristic, complemented
6#13070031C211yesmaximal, characteristic, complemented
7#13070010C211yesmaximal, characteristic, complemented
8#13069934C211yesmaximal, characteristic, complemented
9#13069386C211yesmaximal, characteristic, complemented
10#13069258C211yesmaximal, characteristic, complemented
11#13068949C211yesmaximal, characteristic, complemented
12#13068921C211yesmaximal, characteristic, complemented
13#13068627C211yesmaximal, characteristic, complemented
14C2×#10622189C211yesmaximal, characteristic, complemented
15C11×#1850C211yesmaximal, characteristic, complemented
16C23×C8×C11C2211yescharacteristic
17C2×#66983C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C2×#66977C2211yescharacteristic
21C22×#4314C2211yescharacteristic
22C2×(C22⋊D11)⋊C4—21no—
23C2×C4×D44C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27C4×C11×C22⋊C4C2211yescharacteristic
28#10622727—24no—
29C2×#66885C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×#66885C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33C2×#66882C2211yescharacteristic
34C2×#66881C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×#66880C2211yescharacteristic
37C2×#66880C2211yescharacteristic
38#10622571—21no—
39#10622556—21no—
40#10622556—21no—
41#10622552C2211yescharacteristic
42#10622549C2211yescharacteristic
43#10622549C2211yescharacteristic
44C4×C4⋊Dic11C2211yescharacteristic
45#10622542C2211yescharacteristic
46#10622542C2211yescharacteristic
47#10622541C2211yescharacteristic
48#10622349—24no—
49#10622283—21no—
50#10622281—21no—
51#10622272—21no—
52#10622272—21no—
53C11×#336C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11—21no—
63C23×Dic11—21no—
64C23×Dic11—21no—
65C22×D44C2311yescharacteristic
66C22×C4×D11—21no—
67C22×Dic22C2311yescharacteristic
68C22×C8×C11—22no—
69C22×C8×C11—22no—
70C22×C8×C11—41no—
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C2×C11×C22⋊C4D411yescharacteristic
76C2×C11×C22⋊C4D411yescharacteristic
77C2×C42×C11C2311yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C2×C22⋊Dic11—21no—
80#66983—22no—
81#66983D414yes—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×C4⋊Dic11—22no—
87C2×C4⋊Dic11—22no—
88C2×C4⋊Dic11—22no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—41no—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98#66977—22no—
99#66977—22no—
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×C4×Dic11—21no—
103C2×#4314—22no—
104C2×#4314—22no—
105C2×#4314—41no—
106(C22⋊D11)⋊C4—44no—
107C4×D44—22no—
108C4×D44—41no—
109C11×C4⋊C8—22no—
110C11×C4⋊C8—41no—
111C11×C22⋊C8—22no—
112C11×#95D411yescharacteristic
113C11×#95D411yescharacteristic
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124#66885—22no—
125#66885—22no—
126#66885—22no—
127#66882—22no—
128#66882—22no—
129#66881—22no—
130#66880—22no—
131#66880—22no—
132#66880—41no—
133#25212—111nomaximal, Sylow
134C24×C11C2×D411yescharacteristic
135C23×D11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D412yes—
146C22×C4×C11#4112yes—
147C22×C4×C11C2411yescharacteristic
148C2×C22⋊D11—24no—
149C2×C22⋊D11—42no—
150C2×C22⋊D11—42no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—42no—
159C22×Dic11—42no—
160C22×Dic11—42no—
161C22×Dic11—42no—
162C22×Dic11—42no—
163C22×Dic11—81no—
164C2×D44—21no—
165C2×D44—21no—
166C2×D44—21no—
167C2×D44—21no—
168C2×D44—21no—
169C2×D44C2×D412yes—
170C2×C4×D11—42no—
171C2×C4×D11—42no—
172C2×C4×D11—81no—
173C2×Dic22—21no—
174C2×Dic22—21no—
175C2×Dic22—21no—
176C2×Dic22—21no—
177C2×Dic22—21no—
178C2×Dic22—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—44no—
191C2×C8×C11#4112yes—
192C11×C22⋊C4—22no—
193C11×C22⋊C4—22no—
194C42×C11—21no—
195C42×C11—21no—
196C42×C11—21no—
197C42×C11—21no—
198C22⋊Dic11—42no—
199(C2×D11)⋊C4—24no—
200(C2×D11)⋊C4—42no—
201(C2×D11)⋊C4—42no—
202(C2×D11)⋊C4—81no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11—21no—
211C4⋊Dic11—21no—
212C4⋊Dic11—21no—
213C4⋊Dic11—42no—
214C4⋊Dic11—42no—
215C4⋊Dic11C2×D412yes—
216C4⋊Dic11#4112yes—
217Dic11⋊C4—42no—
218Dic11⋊C4—42no—
219C4×Dic11—42no—
220#4314—44no—
221C2×#480—111no—
222C2×#465—111no—
223#2503—111no—
224#2361—111no—
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#1850D1111yescharacteristic, complemented
234#1804—111no—
235C2×#340—111no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11#12112yes—
241C23×C11#13512yes—
242C23×C11AGL(1,ℤ/8)12yes—
243C23×C11C22×D411yescharacteristic
244C22×D11—22no—
245C22×D11—41no—
246C22×D11—41no—
247C22×D11—41no—
248C22×D11—41no—
249C22×D11—41no—
250C22×D11—41no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
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#12112yes—
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11H(5,𝔽2)11yescharacteristic
275C2×C4×C112−1+411yescharacteristic
276C22⋊D11—48no—
277C2×Dic11—22no—
278C2×Dic11—22no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—84no—
299C2×Dic11—84no—
300D44—22no—
301D44—22no—
302D44—41no—
303D44—41no—
304C4×D11—84no—
305Dic22—41no—
306Dic22—41no—
307Dic22—41no—
308Dic22—41no—
309C8×C11—22no—
310C8×C11—41no—
311C8×C11—41no—
312C8×C11—41no—
313C22×SD16—111no—
314C23×C8C2×D1111yescharacteristic
315C2×C22⋊Q8—111no—
316C2×#121—111no—
317C2×C4×D4—111no—
318C2×C4×D4—221no—
319C22×C4⋊C4—111no—
320C22×C4⋊C4—111no—
321#480—224no—
322#465—224no—
323C2×#107—111no—
324C2×#107—111no—
325C2×#106—111no—
326C2×C4⋊C8C2×D1111yescharacteristic
327C2×C4⋊C8C2×D1111yescharacteristic
328C2×#103—111no—
329C2×#103—111no—
330C2×#103—111no—
331C2×#102—111no—
332C2×#102—111no—
333C2×#102—111no—
334C2×C22⋊C8C2×D1111yescharacteristic
335#400—221no—
336#400—221no—
337#391—111no—
338#391—111no—
339#390—111no—
340#389—111no—
341#388—221no—
342#386—221no—
343#385—221no—
344#382—111no—
345#382—111no—
346#381—221no—
347#381—221no—
348C4×C4⋊C4—111no—
349C4×C22⋊C4C2×D1111yescharacteristic
350#340—111no—
351#340—111no—
352#340—111no—
353#340—111no—
354#340—111no—
355#340—111no—
356#336C2×D1111yescharacteristic
357#336C2×D1111yescharacteristic
358C22×C11—22no—
359C22×C11—22no—
360C22×C11—22no—
361C22×C11—22no—
362C22×C11—22no—
363C22×C11—22no—
364C22×C11#46314yes—
365C22×C11C2×#12111yescharacteristic
366C22×C11#54611yescharacteristic
367C22×C11#54711yescharacteristic
368C22×C11C2×#13511yescharacteristic
369C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
370C22×C11#57711yescharacteristic
371C22×C11#57811yescharacteristic
372C2×D11—42no—
373C2×D11—42no—
374C2×D11—42no—
375C2×D11—81no—
376C2×D11—81no—
377C2×D11—81no—
378C2×D11—81no—
379C4×C11—22no—
380C4×C11—41no—
381C4×C11—41no—
382C4×C11—41no—
383C4×C11—41no—
384C4×C11#52911yescharacteristic
385C4×C11#53911yescharacteristic
386C4×C11#54611yescharacteristic
387C4×C11#54711yescharacteristic
388Dic11—42no—
389Dic11—42no—
390Dic11—81no—
391Dic11—81no—
392Dic11—81no—
393Dic11—81no—
394Dic11—81no—
395C22×Q8—111no—
396C22×D4—111no—
397C22×D4—221no—
398C23×C4—221no—
399C23×C4—221no—
400C23×C4—221no—
401C23×C4C22×D1111yescharacteristic
402C2×SD16—222no—
403C2×SD16—222no—
404C2×SD16—441no—
405C22×C8—22no—
406C22×C8—22no—
407C22×C8—41no—
408C22×C8C22×D1111yescharacteristic
409C22×C8C22×D1111yescharacteristic
410C22×C8C22×D1111yescharacteristic
411C22×C8C22×D1111yescharacteristic
412C22⋊Q8—222no—
413C22⋊Q8—222no—
414#121—114no—
415#121—222no—
416C4×D4—222no—
417C4×D4—441no—
418C4×D4—444no—
419C2×C4⋊C4—111no—
420C2×C4⋊C4—111no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—111no—
425C2×C4⋊C4—222no—
426C2×C4⋊C4—222no—
427C2×C4⋊C4—222no—
428C2×C4⋊C4—221no—
429C2×C4⋊C4—221no—
430C2×C4⋊C4—221no—
431C2×C4⋊C4—221no—
432C2×C4⋊C4—441no—
433C2×C22⋊C4—221no—
434C2×C22⋊C4—221no—
435C2×C22⋊C4—221no—
436C2×C22⋊C4—221no—
437C2×C22⋊C4—221no—
438C2×C22⋊C4D4411yescharacteristic
439C2×C22⋊C4D4411yescharacteristic
440C2×C42—221no—
441C2×C42C22×D1111yescharacteristic
442C2×C42C22×D1111yescharacteristic
443#107—222no—
444#107—222no—
445#106—222no—
446C4⋊C8—22no—
447C4⋊C8—41no—
448#103—222no—
449#103—222no—
450#103—441no—
451#102—222no—
452#102—222no—
453#102—222no—
454C22⋊C8—22no—
455#95—221no—
456#95—221no—
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#95D4411yescharacteristic
466#95D4411yescharacteristic
467C2×C11—24no—
468C2×C11#242511yescharacteristic
469C2×C11C2×#46311yescharacteristic
470C2×C11#304611yescharacteristic
471C2×C11#330011yescharacteristic
472C2×C11#331011yescharacteristic
473C2×C11#333711yescharacteristic
474C2×C11#334311yescharacteristic
475D11—82no—
476C24—221no—
477C24C2×D4411yescharacteristic
478C2×Q8—221no—
479C2×Q8—221no—
480C2×Q8—221no—
481C2×Q8—221no—
482C2×Q8—221no—
483C2×Q8—221no—
484C2×D4—112no—
485C2×D4—224no—
486C2×D4—221no—
487C2×D4—221no—
488C2×D4—221no—
489C2×D4—221no—
490C2×D4—221no—
491C2×D4—442no—
492C2×D4—442no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4—221no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4—442no—
505C22×C4—442no—
506C22×C4—442no—
507C22×C4—442no—
508C22×C4—442no—
509C22×C4—442no—
510C22×C4—442no—
511C22×C4—881no—
512C22×C4—881no—
513C22×C4C2×D4411yescharacteristic
514C22×C4C2×D4411yescharacteristic
515C22×C4C2×D4411yescharacteristic
516C22×C4C2×D4411yescharacteristic
517C22×C4C2×D4411yescharacteristic
518C22×C4D4×D1112yes—
519C22×C4#434312yes—
520C22×C4C23×D1111yescharacteristic
521SD16—444no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—44no—
534C2×C8#434112yes—
535C4⋊C4—112no—
536C4⋊C4—112no—
537C4⋊C4—221no—
538C4⋊C4—221no—
539C4⋊C4—221no—
540C4⋊C4—221no—
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⋊C4—442no—
550C4⋊C4—442no—
551C22⋊C4—22no—
552C22⋊C4—22no—
553C22⋊C4—224no—
554C22⋊C4—442no—
555C22⋊C4—442no—
556C22⋊C4—442no—
557C22⋊C4—881no—
558C42—21no—
559C42—21no—
560C42—21no—
561C42—21no—
562C42—442no—
563C11#2521211yescharacteristic, complemented, Sylow
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—222no—
569C23—441no—
570C23—441no—
571C23—441no—
572C23—441no—
573C23—441no—
574C23—441no—
575C23#6694812yes—
576C23#6695712yes—
577C23#6696112yes—
578C23C22×D4411yescharacteristic
579Q8—441no—
580Q8—441no—
581Q8—441no—
582Q8—441no—
583D4—222no—
584D4—222no—
585D4—448no—
586D4—441no—
587D4—441no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—21no—
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—21no—
605C2×C4—21no—
606C2×C4—222no—
607C2×C4—222no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
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—884no—
628C2×C4—884no—
629C2×C4—884no—
630C2×C4#6694812yes—
631C2×C4C2×D4×D1111yescharacteristic
632C2×C4C2×#434111yescharacteristic
633C2×C4#6703711yescharacteristic
634C2×C4C2×#434311yescharacteristic
635C2×C4#41×D1111yescharacteristic
636C2×C4#6704311yescharacteristic
637C8—22no—
638C8—41no—
639C8—41no—
640C8—41no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—22no—
646C22—22no—
647C22—442no—
648C22—442no—
649C22—442no—
650C22—881no—
651C22—881no—
652C22—881no—
653C22—881no—
654C22#1062245714yes—
655C22C2×#6694811yescharacteristic
656C22#1062308511yescharacteristic
657C22#1062308611yescharacteristic
658C22C2×#6695711yescharacteristic
659C22C2×#6696111yescharacteristic
660C22#1062328211yescharacteristic
661C22#1062328411yescharacteristic
662C4—22no—
663C4—41no—
664C4—41no—
665C4—41no—
666C4—41no—
667C4—442no—
668C4—442no—
669C4—881no—
670C4—881no—
671C4—881no—
672C4—881no—
673C4—881no—
674C4#1062312211yescharacteristic
675C4#1062315511yescharacteristic
676C4#1062317611yescharacteristic
677C4#1062318611yescharacteristic
678C2—24no—
679C2—882no—
680C2#1307216511yescharacteristic
681C2C2×#1062245711yescharacteristic
682C2#1307816811yescharacteristic
683C2#1308050511yescharacteristic
684C2#1308063911yescharacteristic
685C2#1308099711yescharacteristic
686C2#1308105811yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1850C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenter#1850D11
hypocenterC11#25212
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1850

Complements

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

NH ≅ G/Ntype
3. #13073101C2semidirect
5. #13070099C2semidirect
6. #13070031C2semidirect
7. #13070010C2semidirect
8. #13069934C2semidirect
9. #13069386C2semidirect
10. #13069258C2semidirect
11. #13068949C2semidirect
12. #13068921C2semidirect
13. #13068627C2semidirect
14. C2×#10622189C2semidirect
15. C11×#1850C2semidirect
233. #1850D11semidirect
563. C11#25212semidirect

Maximal subgroups

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

subgroupindex
C2×#106223492
C2×#106227272
#130731012
#130716302
#130700992
#130700312
#130700102
#130699342
#130693862
#130692582
#130689492
#130689212
#130686272
C2×#106221892
C11×#18502
#2521211