Finite Group Databasebeta

← #14816789

Subgroups — #14816789

Order 2816.

864 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622459C211yesmaximal, characteristic
2C2×C4×#4314C211yesmaximal, characteristic
3#13072455C211yesmaximal, characteristic, complemented
4#13071527C211yesmaximal, characteristic
5#13070163C211yesmaximal, characteristic, complemented
6#13070099C211yesmaximal, characteristic, complemented
7#13070010C211yesmaximal, characteristic, complemented
8#13069950C211yesmaximal, characteristic, complemented
9#13069349C211yesmaximal, characteristic, complemented
10#13068949C211yesmaximal, characteristic
11#13068949C211yesmaximal, characteristic
12#13068880C211yesmaximal, characteristic
13#13068873C211yesmaximal, characteristic, complemented
14#13068866C211yesmaximal, characteristic
15C11×#1916C211yesmaximal, characteristic, complemented
16C22×#4314C2211yescharacteristic
17C2×C4×D44C2211yescharacteristic
18C2×C4×D44C2211yescharacteristic
19C2×C4×D44C2211yescharacteristic
20C2×#66922C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C4×C8×C11C2211yescharacteristic
24C4×C11×C4⋊C4C2211yescharacteristic
25C2×#66885C2211yescharacteristic
26C2×#66885C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×#66882C2211yescharacteristic
29C2×#66882C2211yescharacteristic
30C2×#66882C2211yescharacteristic
31C2×#66881C2211yescharacteristic
32C2×#66881C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36#10622602—21no—
37#10622602—21no—
38#10622594—21no—
39#10622592—21no—
40#10622549C2211yescharacteristic
41#10622542C2211yescharacteristic
42#10622542C2211yescharacteristic
43#10622541C2211yescharacteristic
44#10622541C2211yescharacteristic
45#10622541C2211yescharacteristic
46#10622541C2211yescharacteristic
47#10622459—24no—
48C4×#4314—24no—
49#10622280—21no—
50D11×#95—21no—
51#10622270—21no—
52#10622259—21no—
53C11×#336C2211yescharacteristic
54C11×#336C2211yescharacteristic
55C11×#336C2211yescharacteristic
56C11×#336C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61C22×D44C2311yescharacteristic
62C22×C4×D11—21no—
63C22×C4×D11—21no—
64C22×C4×D11—21no—
65C22×Dic22—21no—
66C22×Dic22C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C2×C11×C4⋊C4D411yescharacteristic
72C2×C11×C4⋊C4D411yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×C4⋊Dic11—21no—
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×Dic11⋊C4—21no—
91C2×C4×Dic11—21no—
92C2×#4314—22no—
93C2×#4314—22no—
94C2×#4314Q814yescomplemented
95C4×D44—22no—
96C4×D44—22no—
97C4×D44—22no—
98C4×D44—22no—
99C4×D44—41no—
100C4×D44—41no—
101#66922—22no—
102#66922—41no—
103C4×Dic22—22no—
104C4×Dic22—41no—
105C11×C4⋊C8—22no—
106C4×C8×C11—22no—
107C11×#95D411yescharacteristic
108C11×#95D411yescharacteristic
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119#66885—22no—
120#66885—22no—
121#66885D414yes—
122#66882—22no—
123#66882—22no—
124#66882—22no—
125#66881—22no—
126#66881—41no—
127#66880—22no—
128#66880—22no—
129#66880—41no—
130#26372—111nomaximal, Sylow
131C23×D11—21no—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2411yescharacteristic
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C2×D44—21no—
147C2×D44—21no—
148C2×D44—21no—
149C2×D44C2×D412yes—
150C2×D44C2×Q812yes—
151C2×D44#4112yes—
152C2×C4×D11—24no—
153C2×C4×D11—42no—
154C2×C4×D11—42no—
155C2×C4×D11—42no—
156C2×C4×D11—42no—
157C2×C4×D11—81no—
158C2×C4×D11—81no—
159C2×C4×D11—81no—
160C2×C4×D11—81no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22—42no—
167C2×Dic22—42no—
168C2×Dic22—81no—
169C2×Dic22C2×Q812yes—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11C2×D412yes—
181C2×C8×C11C2×Q812yes—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—22no—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—21no—
190(C2×D11)⋊C4—24no—
191(C2×D11)⋊C4—42no—
192(C2×D11)⋊C4—42no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—42no—
204C4⋊Dic11C2×D412yes—
205C4⋊Dic11#4112yes—
206Dic11⋊C4—42no—
207Dic11⋊C4—81no—
208Dic11⋊C4—81no—
209Dic11⋊C4—81no—
210Dic11⋊C4—81no—
211C4×Dic11—42no—
212#4314—28no—
213C2×#474—111no—
214C2×C4×SD16—111no—
215#2451—111no—
216#2349—111no—
217#2097—111no—
218#2085—111no—
219#2068—111no—
220#2058—111no—
221#1942—111no—
222#1916D1111yescharacteristic, complemented
223#1877—111no—
224#1877—111no—
225#1864—111no—
226#1863—111no—
227#1862—111no—
228C23×C11C22×D411yescharacteristic
229C22×D11—22no—
230C22×D11—22no—
231C22×D11—22no—
232C22×D11—41no—
233C22×D11—41no—
234C22×D11—41no—
235C22×D11—41no—
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—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11#13512yes—
253C2×C4×C11#13712yes—
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C22×Q811yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11H(5,𝔽2)11yescharacteristic
259C2×C4×C112−1+411yescharacteristic
260C2×Dic11—22no—
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—41no—
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—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281D44—22no—
282D44—22no—
283D44—22no—
284D44C22⋊Q814yes—
285C4×D11—84no—
286C4×D11—84no—
287C4×D11—84no—
288Dic22—22no—
289Dic22—22no—
290Dic22—41no—
291Dic22—41no—
292Dic22—84no—
293C8×C11—22no—
294C8×C11—22no—
295C8×C11—41no—
296C8×C11—41no—
297C22×SD16—111no—
298C2×C4⋊Q8—111no—
299C2×C4×Q8—111no—
300C2×C4×D4—111no—
301C2×C4×D4—111no—
302C2×C4×D4—111no—
303#474—224no—
304C4×SD16—224no—
305C2×#107—111no—
306C2×#107—111no—
307C2×#107—111no—
308C2×#106—111no—
309C2×#106—111no—
310C2×C4⋊C8C2×D1111yescharacteristic
311C2×#103—111no—
312C2×#103—111no—
313C2×#103—111no—
314C2×#102—111no—
315C2×#102—111no—
316C2×#102—111no—
317C2×C4×C8C2×D1111yescharacteristic
318#398—221no—
319#395—221no—
320#391—111no—
321#391—111no—
322#391—221no—
323#389—111no—
324#389—111no—
325#389—111no—
326#389—111no—
327#387—221no—
328#385—221no—
329#385—221no—
330#382—111no—
331#380—221no—
332C4×C4⋊C4C2×D1111yescharacteristic
333C2×#95—221no—
334#340—111no—
335#340—111no—
336#340—111no—
337#340—111no—
338#336C2×D1111yescharacteristic
339#336C2×D1111yescharacteristic
340#336C2×D1111yescharacteristic
341#336C2×D1111yescharacteristic
342C22×C11#52511yescharacteristic
343C22×C11D4211yescharacteristic
344C22×C11D4×Q811yescharacteristic
345C22×C11C2×#13511yescharacteristic
346C22×C11C2×#13711yescharacteristic
347C22×C11#57611yescharacteristic
348C22×C11#57711yescharacteristic
349C2×D11—24no—
350C2×D11—42no—
351C2×D11—42no—
352C2×D11—42no—
353C2×D11—42no—
354C2×D11—42no—
355C2×D11—42no—
356C4×C11—22no—
357C4×C11—22no—
358C4×C11—41no—
359C4×C11—41no—
360C4×C11—41no—
361C4×C11—41no—
362C4×C11C2×C22⋊Q811yescharacteristic
363C4×C11#53911yescharacteristic
364C4×C11#54711yescharacteristic
365C4×C11#55411yescharacteristic
366Dic11—42no—
367Dic11—42no—
368Dic11—42no—
369Dic11—81no—
370Dic11—81no—
371Dic11—81no—
372Dic11—81no—
373C22×Q8—111no—
374C22×Q8—221no—
375C22×D4—111no—
376C23×C4—221no—
377C23×C4—221no—
378C23×C4—221no—
379C2×SD16—114no—
380C2×SD16—222no—
381C2×SD16—222no—
382C22×C8C22×D1111yescharacteristic
383C22×C8C22×D1111yescharacteristic
384C22×C8C22×D1111yescharacteristic
385C22×C8C22×D1111yescharacteristic
386C4⋊Q8—222no—
387C4⋊Q8—441no—
388C4×Q8—222no—
389C4×Q8—441no—
390C4×D4—222no—
391C4×D4—222no—
392C4×D4—222no—
393C4×D4—222no—
394C4×D4—441no—
395C4×D4—441no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4D4411yescharacteristic
409C2×C4⋊C4D4411yescharacteristic
410C2×C22⋊C4—221no—
411C2×C22⋊C4—221no—
412C2×C22⋊C4—221no—
413C2×C42—221no—
414C2×C42C22×D1111yescharacteristic
415C2×C42C22×D1111yescharacteristic
416C2×C42C22×D1111yescharacteristic
417#107—222no—
418#107—222no—
419#107—222no—
420#106—222no—
421#106—441no—
422C4⋊C8—22no—
423#103—222no—
424#103—222no—
425#103—441no—
426#102—114no—
427#102—222no—
428#102—222no—
429C4×C8—22no—
430#95—221no—
431#95—221no—
432#95—221no—
433#95—221no—
434#95—221no—
435#95—221no—
436#95—221no—
437#95—221no—
438#95—221no—
439#95—221no—
440#95D4411yescharacteristic
441#95D4411yescharacteristic
442C2×C11#244911yescharacteristic
443C2×C11#310711yescharacteristic
444C2×C11#311811yescharacteristic
445C2×C11#326611yescharacteristic
446C2×C11#328011yescharacteristic
447C2×C11#338111yescharacteristic
448C2×C11#338511yescharacteristic
449D11—44no—
450C24—221no—
451C2×Q8—112no—
452C2×Q8—221no—
453C2×Q8—221no—
454C2×Q8—221no—
455C2×Q8—221no—
456C2×Q8—221no—
457C2×Q8—442no—
458C2×Q8—442no—
459C2×Q8—881no—
460C2×D4—112no—
461C2×D4—112no—
462C2×D4—112no—
463C2×D4—221no—
464C2×D4—221no—
465C2×D4—221no—
466C22×C4—224no—
467C22×C4—221no—
468C22×C4—221no—
469C22×C4—221no—
470C22×C4—221no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—221no—
474C22×C4—442no—
475C22×C4—442no—
476C22×C4—442no—
477C22×C4—442no—
478C22×C4—881no—
479C22×C4—881no—
480C22×C4—881no—
481C22×C4—881no—
482C22×C4C2×D4411yescharacteristic
483C22×C4C2×D4411yescharacteristic
484C22×C4C2×D4411yescharacteristic
485C22×C4C2×D4411yescharacteristic
486C22×C4C2×D4411yescharacteristic
487C22×C4C2×D4411yescharacteristic
488C22×C4C23×D1111yescharacteristic
489SD16—228no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8D4×D1112yes—
501C2×C8Q8×D1112yes—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—112no—
505C4⋊C4—112no—
506C4⋊C4—221no—
507C4⋊C4—221no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—221no—
511C4⋊C4—221no—
512C4⋊C4—221no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4—221no—
516C4⋊C4—442no—
517C4⋊C4—442no—
518C4⋊C4—881no—
519C4⋊C4—881no—
520C4⋊C4—881no—
521C4⋊C4—881no—
522C22⋊C4—224no—
523C22⋊C4—442no—
524C22⋊C4—442no—
525C42—21no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—21no—
531C42—442no—
532C11#2637211yescharacteristic, complemented, Sylow
533C23—222no—
534C23—222no—
535C23—222no—
536C23—441no—
537C23—441no—
538C23—441no—
539C23—441no—
540C23C22×D4411yescharacteristic
541Q8—222no—
542Q8—222no—
543Q8—441no—
544Q8—441no—
545Q8—884no—
546D4—114no—
547D4—222no—
548D4—222no—
549D4—222no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—222no—
567C2×C4—222no—
568C2×C4—222no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—884no—
588C2×C4—884no—
589C2×C4—884no—
590C2×C4#6695712yes—
591C2×C4#6696212yes—
592C2×C4C2×D4×D1111yescharacteristic
593C2×C4C2×Q8×D1111yescharacteristic
594C2×C4#41×D1111yescharacteristic
595C2×C4#41×D1111yescharacteristic
596C2×C4#6704211yescharacteristic
597C2×C4#6704311yescharacteristic
598C8—22no—
599C8—22no—
600C8—41no—
601C8—41no—
602C22—224no—
603C22—442no—
604C22—442no—
605C22—442no—
606C22—442no—
607C22—442no—
608C22—442no—
609C22#1062305511yescharacteristic
610C22D4×D4411yescharacteristic
611C22Q8×D4411yescharacteristic
612C22C2×#6695711yescharacteristic
613C22C2×#6696211yescharacteristic
614C22#1062328211yescharacteristic
615C22#1062328311yescharacteristic
616C4—22no—
617C4—22no—
618C4—41no—
619C4—41no—
620C4—41no—
621C4—41no—
622C4—442no—
623C4—442no—
624C4—442no—
625C4—881no—
626C4—881no—
627C4—881no—
628C4—881no—
629C4D11×C22⋊Q811yescharacteristic
630C4#1062318611yescharacteristic
631C4#1062322111yescharacteristic
632C4#1062323811yescharacteristic
633C2—444no—
634C2#1307243011yescharacteristic
635C2#1307868811yescharacteristic
636C2#1307880211yescharacteristic
637C2#1308013111yescharacteristic
638C2#1308030311yescharacteristic
639C2#1308149311yescharacteristic
640C2#1308152811yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1916C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1916D11
hypocenterC11#26372
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1916

Complements

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

NH ≅ G/Ntype
3. #13072455C2semidirect
5. #13070163C2semidirect
6. #13070099C2semidirect
7. #13070010C2semidirect
8. #13069950C2semidirect
9. #13069349C2semidirect
13. #13068873C2semidirect
15. C11×#1916C2semidirect
94. C2×#4314Q8semidirect
222. #1916D11semidirect
532. C11#26372semidirect

Maximal subgroups

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

subgroupindex
C2×#106224592
C2×C4×#43142
#130724552
#130715272
#130701632
#130700992
#130700102
#130699502
#130693492
#130689492
#130688802
#130688732
#130688662
C11×#19162
#2637211