Finite Group Databasebeta

← #14816834

Subgroups — #14816834

Order 2816.

820 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622442C211yesmaximal, characteristic, complemented
2C2×C4×#4314C211yesmaximal, characteristic
3#13072488C211yesmaximal, characteristic
4#13071536C211yesmaximal, characteristic, complemented
5#13070136C211yesmaximal, characteristic
6#13070099C211yesmaximal, characteristic, complemented
7#13069989C211yesmaximal, characteristic
8#13069955C211yesmaximal, characteristic, complemented
9#13069344C211yesmaximal, characteristic, complemented
10#13068970C211yesmaximal, characteristic
11#13068970C211yesmaximal, characteristic
12#13068887C211yesmaximal, characteristic, complemented
13#13068873C211yesmaximal, characteristic, complemented
14#13068866C211yesmaximal, characteristic
15C11×#1916C211yesmaximal, characteristic, complemented
16C22×#4314C2211yescharacteristic
17C2×C4×D44C2211yescharacteristic
18C2×#66923C2211yescharacteristic
19C2×C4×Dic22C2211yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
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×#66881C2211yescharacteristic
31C2×#66881C2211yescharacteristic
32C2×#66881C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36#10622605—21no—
37#10622602—21no—
38#10622585—21no—
39#10622585—21no—
40#10622552C2211yescharacteristic
41#10622552C2211yescharacteristic
42#10622549C2211yescharacteristic
43#10622541C2211yescharacteristic
44#10622541C2211yescharacteristic
45#10622541C2211yescharacteristic
46#10622541C2211yescharacteristic
47#10622442—24no—
48C4×#4314—24no—
49#10622289—21no—
50#10622280—21no—
51#10622263—21no—
52#10622262—21no—
53C11×#336C2211yescharacteristic
54C11×#336C2211yescharacteristic
55C11×#336C2211yescharacteristic
56C11×#336C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61C22×D44C2311yescharacteristic
62C22×C4×D11—21no—
63C22×Dic22C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C2×C11×C4⋊C4D411yescharacteristic
69C2×C11×C4⋊C4D411yescharacteristic
70C2×C42×C11C2311yescharacteristic
71C2×C42×C11C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×#4314—22no—
97C2×#4314—22no—
98C2×#4314Q814yes—
99C4×D44—22no—
100C4×D44—41no—
101#66923—22no—
102#66923—41no—
103C4×Dic22—22no—
104C4×Dic22—22no—
105C4×Dic22—22no—
106C4×Dic22—22no—
107C4×Dic22—41no—
108C4×Dic22—41no—
109C11×C4⋊C8—22no—
110C4×C8×C11—22no—
111C11×#95D411yescharacteristic
112C11×#95D411yescharacteristic
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#66885—41no—
122#66882—22no—
123#66882—41no—
124#66881—22no—
125#66881—22no—
126#66881—22no—
127#66880—22no—
128#66880—22no—
129#66880D414yes—
130#26375—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×D44—21no—
150C2×D44—21no—
151C2×D44C2×Q812yes—
152C2×C4×D11—42no—
153C2×C4×D11—42no—
154C2×C4×D11—81no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22C2×D412yes—
159C2×Dic22C2×Q812yes—
160C2×Dic22#4112yes—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11C2×D412yes—
172C2×C8×C11C2×Q812yes—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—41no—
175C42×C11—21no—
176C42×C11—21no—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11—21no—
181(C2×D11)⋊C4—42no—
182(C2×D11)⋊C4—42no—
183(C2×D11)⋊C4—81no—
184(C2×D11)⋊C4—81no—
185(C2×D11)⋊C4—81no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11C2×D412yes—
197C4⋊Dic11#4112yes—
198Dic11⋊C4—24no—
199Dic11⋊C4—42no—
200Dic11⋊C4—42no—
201Dic11⋊C4—42no—
202Dic11⋊C4—42no—
203Dic11⋊C4—42no—
204Dic11⋊C4—42no—
205Dic11⋊C4—81no—
206Dic11⋊C4—81no—
207C4×Dic11—24no—
208C4×Dic11—42no—
209C4×Dic11—42no—
210#4314—28no—
211C2×#479—111no—
212C2×C4×SD16—111no—
213#2454—111no—
214#2351—111no—
215#2092—111no—
216#2085—111no—
217#2065—111no—
218#2059—111no—
219#1941—111no—
220#1916D1111yescharacteristic, complemented
221#1880—111no—
222#1880—111no—
223#1865—111no—
224#1863—111no—
225#1862—111no—
226C23×C11C22×D411yescharacteristic
227C22×D11—22no—
228C22×D11—41no—
229C22×D11—41no—
230C22×D11—41no—
231C22×D11—41no—
232C22×D11—41no—
233C22×D11—41no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
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#13512yes—
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C22×Q811yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11H(5,𝔽2)11yescharacteristic
257C2×C4×C112−1+411yescharacteristic
258C2×Dic11—22no—
259C2×Dic11—22no—
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—
279D44—22no—
280D44—22no—
281D44—41no—
282D44—41no—
283C4×D11—84no—
284Dic22—22no—
285Dic22—22no—
286Dic22—22no—
287Dic22C22⋊Q814yes—
288C8×C11—22no—
289C8×C11—22no—
290C8×C11—41no—
291C8×C11—41no—
292C22×SD16—111no—
293C2×#125—111no—
294C2×C4×Q8—111no—
295C2×C4×Q8—111no—
296C2×C4×Q8—111no—
297C2×C4×D4—111no—
298#479—224no—
299C4×SD16—224no—
300C2×#107—111no—
301C2×#107—111no—
302C2×#106—111no—
303C2×#106—111no—
304C2×#106—111no—
305C2×C4⋊C8C2×D1111yescharacteristic
306C2×#103—111no—
307C2×#103—111no—
308C2×#103—111no—
309C2×#102—111no—
310C2×#102—111no—
311C2×#102—111no—
312C2×C4×C8C2×D1111yescharacteristic
313#399—221no—
314#396—221no—
315#390—111no—
316#390—111no—
317#389—111no—
318#389—111no—
319#389—111no—
320#389—111no—
321#389—221no—
322#389—221no—
323#385—221no—
324#382—111no—
325#382—221no—
326#380—221no—
327C4×C4⋊C4—221no—
328C4×C4⋊C4C2×D1111yescharacteristic
329#340—111no—
330#340—111no—
331#340—111no—
332#340—111no—
333#336C2×D1111yescharacteristic
334#336C2×D1111yescharacteristic
335#336C2×D1111yescharacteristic
336#336C2×D1111yescharacteristic
337C22×C11#52511yescharacteristic
338C22×C11D4211yescharacteristic
339C22×C11D4×Q811yescharacteristic
340C22×C11C2×#13511yescharacteristic
341C22×C11#57511yescharacteristic
342C22×C11#57711yescharacteristic
343C22×C11#57711yescharacteristic
344C2×D11—42no—
345C2×D11—42no—
346C2×D11—42no—
347C2×D11—81no—
348C2×D11—81no—
349C2×D11—81no—
350C2×D11—81no—
351C4×C11—22no—
352C4×C11—41no—
353C4×C11—41no—
354C4×C11—41no—
355C4×C11—41no—
356C4×C11—41no—
357C4×C11C2×C22⋊Q811yescharacteristic
358C4×C11#53911yescharacteristic
359C4×C11#54711yescharacteristic
360C4×C11#55411yescharacteristic
361Dic11—24no—
362Dic11—42no—
363Dic11—42no—
364Dic11—81no—
365Dic11—81no—
366Dic11—81no—
367Dic11—81no—
368C22×Q8—111no—
369C22×D4—111no—
370C23×C4—221no—
371C2×SD16—114no—
372C2×SD16—222no—
373C2×SD16—222no—
374C22×C8C22×D1111yescharacteristic
375C22×C8C22×D1111yescharacteristic
376C22×C8C22×D1111yescharacteristic
377C22×C8C22×D1111yescharacteristic
378#125—222no—
379#125—441no—
380C4×Q8—222no—
381C4×Q8—222no—
382C4×Q8—222no—
383C4×Q8—222no—
384C4×Q8—441no—
385C4×Q8—441no—
386C4×D4—222no—
387C4×D4—441no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—111no—
390C2×C4⋊C4—111no—
391C2×C4⋊C4—111no—
392C2×C4⋊C4—111no—
393C2×C4⋊C4—111no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4—221no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4—221no—
400C2×C4⋊C4—221no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4D4411yescharacteristic
404C2×C4⋊C4D4411yescharacteristic
405C2×C22⋊C4—221no—
406C2×C22⋊C4—221no—
407C2×C22⋊C4—221no—
408C2×C22⋊C4—221no—
409C2×C22⋊C4—221no—
410C2×C42—221no—
411C2×C42—221no—
412C2×C42—221no—
413C2×C42C22×D1111yescharacteristic
414C2×C42C22×D1111yescharacteristic
415C2×C42C22×D1111yescharacteristic
416#107—222no—
417#107—441no—
418#106—222no—
419#106—222no—
420#106—222no—
421C4⋊C8—22no—
422#103—114no—
423#103—222no—
424#103—222no—
425#102—222no—
426#102—222no—
427#102—441no—
428C4×C8—22no—
429#95—221no—
430#95—221no—
431#95—221no—
432#95—221no—
433#95—221no—
434#95—221no—
435#95D4411yescharacteristic
436#95D4411yescharacteristic
437C2×C11#244911yescharacteristic
438C2×C11#310211yescharacteristic
439C2×C11#312611yescharacteristic
440C2×C11#327111yescharacteristic
441C2×C11#328211yescharacteristic
442C2×C11#338111yescharacteristic
443C2×C11#338811yescharacteristic
444D11—82no—
445C24—221no—
446C2×Q8—112no—
447C2×Q8—112no—
448C2×Q8—112no—
449C2×Q8—221no—
450C2×Q8—221no—
451C2×Q8—221no—
452C2×D4—112no—
453C2×D4—221no—
454C2×D4—221no—
455C2×D4—221no—
456C2×D4—221no—
457C2×D4—221no—
458C22×C4—221no—
459C22×C4—221no—
460C22×C4—221no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4—221no—
465C22×C4—442no—
466C22×C4—442no—
467C22×C4—881no—
468C22×C4C2×D4411yescharacteristic
469C22×C4C2×D4411yescharacteristic
470C22×C4C2×D4411yescharacteristic
471C22×C4C2×D4411yescharacteristic
472C22×C4C2×D4411yescharacteristic
473C22×C4C2×D4411yescharacteristic
474C22×C4C23×D1111yescharacteristic
475SD16—228no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8D4×D1112yes—
487C2×C8Q8×D1112yes—
488C4⋊C4—22no—
489C4⋊C4—41no—
490C4⋊C4—112no—
491C4⋊C4—112no—
492C4⋊C4—224no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4—442no—
504C4⋊C4—442no—
505C4⋊C4—442no—
506C4⋊C4—442no—
507C4⋊C4—442no—
508C4⋊C4—442no—
509C4⋊C4—881no—
510C4⋊C4—881no—
511C22⋊C4—442no—
512C22⋊C4—442no—
513C22⋊C4—881no—
514C22⋊C4—881no—
515C22⋊C4—881no—
516C42—21no—
517C42—21no—
518C42—21no—
519C42—21no—
520C42—21no—
521C42—21no—
522C42—224no—
523C42—442no—
524C42—442no—
525C11#2637511yescharacteristic, complemented, Sylow
526C23—222no—
527C23—441no—
528C23—441no—
529C23—441no—
530C23—441no—
531C23—441no—
532C23—441no—
533C23C22×D4411yescharacteristic
534Q8—114no—
535Q8—222no—
536Q8—222no—
537Q8—222no—
538D4—222no—
539D4—222no—
540D4—441no—
541D4—441no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
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—222no—
560C2×C4—222no—
561C2×C4—222no—
562C2×C4—222no—
563C2×C4—222no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—441no—
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—884no—
581C2×C4#6695712yes—
582C2×C4C2×D4×D1111yescharacteristic
583C2×C4C2×Q8×D1111yescharacteristic
584C2×C4#41×D1111yescharacteristic
585C2×C4#41×D1111yescharacteristic
586C2×C4#6704211yescharacteristic
587C2×C4#6704311yescharacteristic
588C8—22no—
589C8—22no—
590C8—41no—
591C8—41no—
592C22—442no—
593C22—442no—
594C22—442no—
595C22—881no—
596C22—881no—
597C22—881no—
598C22—881no—
599C22#1062305511yescharacteristic
600C22D4×D4411yescharacteristic
601C22Q8×D4411yescharacteristic
602C22C2×#6695711yescharacteristic
603C22#1062327911yescharacteristic
604C22#1062328211yescharacteristic
605C22#1062328211yescharacteristic
606C4—22no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4—41no—
612C4—224no—
613C4—442no—
614C4—442no—
615C4—881no—
616C4—881no—
617C4—881no—
618C4—881no—
619C4D11×C22⋊Q811yescharacteristic
620C4#1062318611yescharacteristic
621C4#1062322111yescharacteristic
622C4#1062323811yescharacteristic
623C2—882no—
624C2#1307243011yescharacteristic
625C2#1307863611yescharacteristic
626C2#1307890811yescharacteristic
627C2#1308020611yescharacteristic
628C2#1308032811yescharacteristic
629C2#1308149311yescharacteristic
630C2#1308156311yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1916C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1916D11
hypocenterC11#26375
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
1. C2×#10622442C2semidirect
4. #13071536C2semidirect
6. #13070099C2semidirect
8. #13069955C2semidirect
9. #13069344C2semidirect
12. #13068887C2semidirect
13. #13068873C2semidirect
15. C11×#1916C2semidirect
220. #1916D11semidirect
525. C11#26375semidirect

Maximal subgroups

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

subgroupindex
C2×#106224422
C2×C4×#43142
#130724882
#130715362
#130701362
#130700992
#130699892
#130699552
#130693442
#130689702
#130688872
#130688732
#130688662
C11×#19162
#2637511