Finite Group Databasebeta

← #14813950

Subgroups — #14813950

Order 2816.

800 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622462C211yesmaximal, characteristic
2C2×C4×Dic44C211yesmaximal, characteristic
3#13072392C211yesmaximal, characteristic
4C4⋊C4×Dic22C211yesmaximal, characteristic
5#13070153C211yesmaximal, characteristic
6#13070109C211yesmaximal, characteristic
7#13070026C211yesmaximal, characteristic
8#13069863C211yesmaximal, characteristic
9#13069292C211yesmaximal, characteristic
10#13068956C211yesmaximal, characteristic
11#13068956C211yesmaximal, characteristic
12#13068956C211yesmaximal, characteristic
13#13068873C211yesmaximal, characteristic
14#13068873C211yesmaximal, characteristic
15C11×#1916C211yesmaximal, characteristic
16C22×Dic44C2211yescharacteristic
17C22×Dic44C2211yescharacteristic
18C2×#66922C2211yescharacteristic
19C2×C4×Dic22C2211yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C4×C8×C11C2211yescharacteristic
25C4×C11×C4⋊C4C2211yescharacteristic
26C2×#66882C2211yescharacteristic
27C2×#66882C2211yescharacteristic
28C2×#66880C2211yescharacteristic
29C2×#66880C2211yescharacteristic
30C2×#66880C2211yescharacteristic
31C2×#66880C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36#10622597—21no—
37#10622594—21no—
38#10622589—21no—
39C4⋊C4×Dic11—21no—
40#10622548C2211yescharacteristic
41#10622542C2211yescharacteristic
42#10622542C2211yescharacteristic
43#10622542C2211yescharacteristic
44#10622541C2211yescharacteristic
45#10622541C2211yescharacteristic
46#10622541C2211yescharacteristic
47#10622462—24no—
48C4×Dic44—24no—
49#10622273—21no—
50#10622268—21no—
51#10622260—21no—
52#10622260—21no—
53C11×#336C2211yescharacteristic
54C11×#336C2211yescharacteristic
55C11×#336C2211yescharacteristic
56C11×#336C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61C22×Dic22C2311yescharacteristic
62C22×Dic22C2311yescharacteristic
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×C4⋊Dic11—21no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C2×Dic44—22no—
94C2×Dic44—22no—
95C2×Dic44—22no—
96C2×Dic44—22no—
97C2×Dic44—22no—
98C2×Dic44D414yes—
99#66922—22no—
100#66922—41no—
101C4×Dic22—22no—
102C4×Dic22—22no—
103C4×Dic22—22no—
104C4×Dic22—22no—
105C4×Dic22—22no—
106C4×Dic22—41no—
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—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122#66882—22no—
123#66882—41no—
124#66880—22no—
125#66880—22no—
126#66880—22no—
127#66880—22no—
128#66880—22no—
129#66880—22no—
130#66880—22no—
131#66880—41no—
132#26171—111nomaximal, Sylow
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2411yescharacteristic
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C2×Dic22—21no—
149C2×Dic22—21no—
150C2×Dic22—21no—
151C2×Dic22—21no—
152C2×Dic22—21no—
153C2×Dic22—21no—
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22C2×D412yes—
163C2×Dic22C2×D412yes—
164C2×Dic22#4112yes—
165C2×Dic22#4112yes—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
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×C11C2×D412yes—
178C11×C4⋊C4—41no—
179C11×C4⋊C4Q1614yescomplemented
180C42×C11—21no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11—21no—
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—42no—
196C4⋊Dic11—42no—
197C4⋊Dic11—42no—
198C4⋊Dic11—81no—
199C4⋊Dic11#4112yes—
200Dic11⋊C4—24no—
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—
210C4×Dic11—42no—
211Dic44—28no—
212Dic44—44no—
213C2×#462—111no—
214C2×C4×Q16—111no—
215#2446—111no—
216Q8×C4⋊C4—111no—
217#2095—111no—
218#2087—111no—
219#2072—111no—
220#2043—111no—
221#1933—111no—
222#1916D1111yescharacteristic
223#1878—111no—
224#1878—111no—
225#1878—111no—
226#1863—111no—
227#1863—111no—
228C23×C11C22×D411yescharacteristic
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
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×C11C2×Q1612yes—
245C2×C4×C11C2×Q1612yes—
246C2×C4×C11C2×Q1612yes—
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11H(5,𝔽2)11yescharacteristic
252C2×C4×C112−1+411yescharacteristic
253C2×Dic11—22no—
254C2×Dic11—22no—
255C2×Dic11—22no—
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
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—
277Dic22—22no—
278Dic22—22no—
279Dic22—22no—
280Dic22—22no—
281Dic22—22no—
282Dic22—41no—
283Dic22—41no—
284Dic22—41no—
285Dic22—41no—
286Dic22—41no—
287Dic22—41no—
288Dic22#12314yes—
289C8×C11—22no—
290C8×C11—41no—
291C8×C11—41no—
292C8×C11—41no—
293C22×Q16—111no—
294C22×Q16—111no—
295C2×C4⋊Q8—111no—
296C2×C4×Q8—111no—
297C2×C4×Q8—111no—
298C2×C4×Q8—111no—
299C2×C4×Q8—111no—
300#462—224no—
301C4×Q16—224no—
302C2×#107—111no—
303C2×#107—111no—
304C2×C4⋊C8C2×D1111yescharacteristic
305C2×#103—111no—
306C2×#103—111no—
307C2×#103—111no—
308C2×#103—111no—
309C2×#103—111no—
310C2×#103—111no—
311C2×#103—111no—
312C2×#103—111no—
313C2×C4×C8C2×D1111yescharacteristic
314#400—221no—
315#398—221no—
316#391—111no—
317#391—111no—
318#391—111no—
319#389—111no—
320#389—111no—
321#389—111no—
322#389—221no—
323#389—221no—
324#387—221no—
325#387—221no—
326#384—111no—
327#384—221no—
328C4×C4⋊C4—221no—
329C4×C4⋊C4C2×D1111yescharacteristic
330#340—111no—
331#340—111no—
332#340—111no—
333#340—111no—
334#336C2×D1111yescharacteristic
335#336C2×D1111yescharacteristic
336#336C2×D1111yescharacteristic
337#336C2×D1111yescharacteristic
338C22×C11#52511yescharacteristic
339C22×C11D4211yescharacteristic
340C22×C11#54811yescharacteristic
341C22×C11C22×Q1611yescharacteristic
342C22×C11#57511yescharacteristic
343C22×C11#57711yescharacteristic
344C22×C11#57811yescharacteristic
345C4×C11—22no—
346C4×C11—22no—
347C4×C11—22no—
348C4×C11—41no—
349C4×C11—41no—
350C4×C11—41no—
351C4×C11C2×#12311yescharacteristic
352C4×C11#53911yescharacteristic
353C4×C11#54711yescharacteristic
354C4×C11#55311yescharacteristic
355Dic11—24no—
356Dic11—42no—
357Dic11—42no—
358Dic11—81no—
359Dic11—81no—
360Dic11—81no—
361Dic11—81no—
362Dic11—81no—
363C22×Q8—111no—
364C22×Q8—111no—
365C22×Q8—111no—
366C2×Q16—114no—
367C2×Q16—222no—
368C2×Q16—222no—
369C2×Q16—222no—
370C2×Q16—222no—
371C2×Q16—222no—
372C22×C8C22×D1111yescharacteristic
373C22×C8C22×D1111yescharacteristic
374C22×C8C22×D1111yescharacteristic
375C22×C8C22×D1111yescharacteristic
376C4⋊Q8—222no—
377C4⋊Q8—441no—
378C4×Q8—222no—
379C4×Q8—222no—
380C4×Q8—222no—
381C4×Q8—222no—
382C4×Q8—222no—
383C4×Q8—441no—
384C4×Q8—441no—
385C4×Q8—441no—
386C2×C4⋊C4—111no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—111no—
390C2×C4⋊C4—111no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—221no—
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⋊C4D4411yescharacteristic
403C2×C4⋊C4D4411yescharacteristic
404C2×C42—221no—
405C2×C42—221no—
406C2×C42—221no—
407C2×C42—221no—
408C2×C42C22×D1111yescharacteristic
409C2×C42C22×D1111yescharacteristic
410C2×C42C22×D1111yescharacteristic
411#107—222no—
412#107—441no—
413C4⋊C8—22no—
414#103—222no—
415#103—222no—
416#103—222no—
417#103—222no—
418#103—222no—
419#103—222no—
420#103—222no—
421#103—441no—
422C4×C8—22no—
423#95—221no—
424#95—221no—
425#95—221no—
426#95—221no—
427#95—221no—
428#95—221no—
429#95—221no—
430#95—221no—
431#95—221no—
432#95D4411yescharacteristic
433#95D4411yescharacteristic
434C2×C11#244311yescharacteristic
435C2×C11#310411yescharacteristic
436C2×C11#312011yescharacteristic
437C2×C11#327111yescharacteristic
438C2×C11D4×Q1611yescharacteristic
439C2×C11#336311yescharacteristic
440C2×C11#337711yescharacteristic
441C2×Q8—112no—
442C2×Q8—112no—
443C2×Q8—112no—
444C2×Q8—112no—
445C2×Q8—221no—
446C2×Q8—221no—
447C2×Q8—221no—
448C2×Q8—221no—
449C2×Q8—221no—
450C2×Q8—221no—
451C2×Q8—221no—
452C2×Q8—221no—
453C2×Q8—221no—
454C2×Q8—221no—
455C2×Q8—221no—
456C2×Q8—221no—
457C2×Q8—221no—
458C2×Q8—221no—
459C22×C4—221no—
460C22×C4—221no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4—221no—
465C22×C4—221no—
466C22×C4—221no—
467C22×C4C2×D4411yescharacteristic
468C22×C4C2×D4411yescharacteristic
469C22×C4C2×D4411yescharacteristic
470C22×C4C2×D4411yescharacteristic
471C22×C4C2×D4411yescharacteristic
472C22×C4C2×D4411yescharacteristic
473C22×C4C23×D1111yescharacteristic
474Q16—228no—
475Q16—444no—
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×C8—21no—
487C2×C8D4×D1112yes—
488C4⋊C4—41no—
489C4⋊C4—112no—
490C4⋊C4—224no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—442no—
501C4⋊C4—442no—
502C4⋊C4—442no—
503C4⋊C4—442no—
504C4⋊C4—442no—
505C4⋊C4—442no—
506C4⋊C4—442no—
507C4⋊C4—881no—
508C4⋊C4—881no—
509C4⋊C4—881no—
510C4⋊C4Dic4414yescomplemented
511C42—21no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—21no—
516C42—21no—
517C42—224no—
518C42—442no—
519C42—442no—
520C42—442no—
521C11#2617111yescharacteristic, complemented, Sylow
522C23C22×D4411yescharacteristic
523Q8—114no—
524Q8—222no—
525Q8—222no—
526Q8—222no—
527Q8—222no—
528Q8—222no—
529Q8—441no—
530Q8—441no—
531Q8—441no—
532Q8—441no—
533Q8—441no—
534Q8—441no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
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—222no—
551C2×C4—222no—
552C2×C4—222no—
553C2×C4—222no—
554C2×C4—222no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4—441no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—441no—
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×C4C2×Dic4412yes—
575C2×C4C2×Dic4412yes—
576C2×C4C2×Dic4412yes—
577C2×C4C2×D4×D1111yescharacteristic
578C2×C4#6704011yescharacteristic
579C2×C4#41×D1111yescharacteristic
580C2×C4#41×D1111yescharacteristic
581C2×C4#41×D1111yescharacteristic
582C2×C4#6704211yescharacteristic
583C8—22no—
584C8—41no—
585C8—41no—
586C8—41no—
587C22#1062305511yescharacteristic
588C22D4×D4411yescharacteristic
589C22#1062310711yescharacteristic
590C22C22×Dic4411yescharacteristic
591C22#1062327911yescharacteristic
592C22#1062328211yescharacteristic
593C22#1062328411yescharacteristic
594C4—22no—
595C4—22no—
596C4—22no—
597C4—41no—
598C4—41no—
599C4—41no—
600C4—224no—
601C4—442no—
602C4—442no—
603C4—881no—
604C4—881no—
605C4—881no—
606C4—881no—
607C4—881no—
608C4#1062316211yescharacteristic
609C4D11×#12311yescharacteristic
610C4#1062322311yescharacteristic
611C4#1062324011yescharacteristic
612C2#1307235611yescharacteristic
613C2#1307865611yescharacteristic
614C2#1307883211yescharacteristic
615C2#1308020611yescharacteristic
616C2D4×Dic4411yescharacteristic
617C2#1308129511yescharacteristic
618C2#1308146011yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1916C2
socle, prime radicalC23×C11C22×D4
hypercenter#1916D11
hypocenterC11#26171
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
179. C11×C4⋊C4Q16semidirect
510. C4⋊C4Dic44semidirect
521. C11#26171semidirect

Maximal subgroups

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

subgroupindex
C2×#106224622
C2×C4×Dic442
#130723922
C4⋊C4×Dic222
#130701532
#130701092
#130700262
#130698632
#130692922
#130689562
#130688732
C11×#19162
#2617111