Finite Group Databasebeta

← #14795134

Subgroups — #14795134

Order 2816.

746 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622463C211yesmaximal, characteristic, complemented
2#13074437C211yesmaximal, characteristic
3#13071298C211yesmaximal, characteristic
4#13070044C211yesmaximal, characteristic
5#13070039C211yesmaximal, characteristic
6#13069820C211yesmaximal, characteristic
7#13069813C211yesmaximal, characteristic
8#13069567C211yesmaximal, characteristic, complemented
9#13069386C211yesmaximal, characteristic, complemented
10#13069359C211yesmaximal, characteristic, complemented
11#13069349C211yesmaximal, characteristic, complemented
12#13069306C211yesmaximal, characteristic, complemented
13#13069292C211yesmaximal, characteristic, complemented
14#13068632C211yesmaximal, characteristic, complemented
15C2×C11×#433C211yesmaximal, characteristic
16C2×C11×#117C2211yescharacteristic
17C2×#66977C2211yescharacteristic
18C2×#66922C2211yescharacteristic
19C2×C4×Dic22C2211yescharacteristic
20C11×#433—24no—
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×C22⋊C8C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C2×C11×#97C2211yescharacteristic
26C2×C4×C8×C11C2211yescharacteristic
27#10622825C2211yescharacteristic
28#10622825C2211yescharacteristic
29#10622825C2211yescharacteristic
30C2×#66882C2211yescharacteristic
31C2×#66882C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33C2×#66881C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×#66880C2211yescharacteristic
37C2×#66880C2211yescharacteristic
38#10622599—21no—
39#10622592—21no—
40#10622591—21no—
41#10622585—21no—
42#10622562—21no—
43#10622560—21no—
44#10622558—21no—
45#10622557—21no—
46#10622549C2211yescharacteristic
47C4×C4⋊Dic11C2211yescharacteristic
48#10622542C2211yescharacteristic
49#10622541C2211yescharacteristic
50#10622541C2211yescharacteristic
51#10622541C2211yescharacteristic
52#10622463—24no—
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C22×Dic22—21no—
63C22×Dic22C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C11×#117—22no—
69C11×#117—22no—
70C2×C11×C4⋊C4D411yescharacteristic
71C2×C11×C4⋊C4D411yescharacteristic
72C2×C11×C22⋊C4D411yescharacteristic
73C2×C11×C22⋊C4D411yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88#66977—22no—
89#66977—22no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97#66922—22no—
98#66922—22no—
99C4×Dic22—22no—
100C4×Dic22—22no—
101C11×C4⋊C8—22no—
102C11×C4⋊C8D414yes—
103C11×C22⋊C8—22no—
104C11×C22⋊C8—22no—
105C11×#97—22no—
106C4×C8×C11—22no—
107C11⋊#95—21no—
108C11⋊#95—21no—
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—
118#66882—22no—
119#66882—22no—
120#66882—22no—
121#66881—22no—
122#66880—22no—
123#66880—22no—
124#66880—22no—
125#66880—22no—
126#24714—111nomaximal, Sylow
127C24×C11C2×D411yescharacteristic
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
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—42no—
154C2×Dic22—81no—
155C2×Dic22—81no—
156C2×Dic22#4112yes—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
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×C11C2×D412yes—
168C2×C8×C11C2×D412yes—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—22no—
171C11×C22⋊C4—22no—
172C11×C22⋊C4—22no—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11C2×D412yes—
176C42×C11#4112yes—
177C22⋊Dic11—24no—
178C22⋊Dic11—81no—
179C22⋊Dic11—81no—
180C22⋊Dic11—81no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—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—42no—
195C4⋊Dic11#4112yes—
196Dic11⋊C4—24no—
197Dic11⋊C4—42no—
198Dic11⋊C4—81no—
199Dic11⋊C4—81no—
200Dic11⋊C4—81no—
201C4×Dic11—42no—
202C4×Dic11—81no—
203C2×#477—111no—
204C2×#433D1111yescharacteristic
205#2628—111no—
206#2323—111no—
207#2076—111no—
208#2075—111no—
209#2036—111no—
210#2035—111no—
211#1988—111no—
212#1949—111no—
213#1944—111no—
214#1942—111no—
215#1935—111no—
216#1933—111no—
217#1805—111no—
218C23×C11—21no—
219C23×C11—21no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—21no—
224C23×C11—21no—
225C23×C11C22×D411yescharacteristic
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
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—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11#12112yes—
244C2×C4×C11#12112yes—
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C112−1+411yescharacteristic
250C2×C4×C112−1+411yescharacteristic
251C2×Dic11—22no—
252C2×Dic11—22no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
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—
275Dic22—22no—
276Dic22—22no—
277Dic22—41no—
278Dic22—41no—
279Dic22—84no—
280C8×C11—22no—
281C8×C11—22no—
282C8×C11—41no—
283C8×C11—41no—
284C2×C4⋊Q8—111no—
285C2×C22⋊Q8—111no—
286C2×C4×Q8—111no—
287C2×#117C2×D1111yescharacteristic
288#477—224no—
289#433—24no—
290C2×#107—111no—
291C2×#107—111no—
292C2×#107—111no—
293C2×#106—111no—
294C2×C4⋊C8C2×D1111yescharacteristic
295C2×C4⋊C8C2×D1111yescharacteristic
296C2×#103—111no—
297C2×#103—111no—
298C2×#103—111no—
299C2×#103—111no—
300C2×C22⋊C8C2×D1111yescharacteristic
301C2×C22⋊C8C2×D1111yescharacteristic
302C2×#97C2×D1111yescharacteristic
303C2×C4×C8C2×D1111yescharacteristic
304#400—221no—
305#399—221no—
306#395—221no—
307#393—221no—
308#391—111no—
309#389—111no—
310#389—111no—
311#389—111no—
312#389—221no—
313#388—221no—
314#388—221no—
315#387—221no—
316#382—111no—
317#380—111no—
318#380—111no—
319#380—111no—
320C4×C4⋊C4—111no—
321#340—111no—
322#340—111no—
323#340—111no—
324#340—111no—
325#340—111no—
326#340—111no—
327#340—111no—
328#340—111no—
329C22×C11—41no—
330C22×C11—41no—
331C22×C11—41no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11C2×#12111yescharacteristic
337C22×C11#52511yescharacteristic
338C22×C11#53611yescharacteristic
339C22×C11#57611yescharacteristic
340C22×C11#57711yescharacteristic
341C22×C11#57811yescharacteristic
342C22×C11#57811yescharacteristic
343C4×C11—22no—
344C4×C11—22no—
345C4×C11—41no—
346C4×C11—41no—
347C4×C11—41no—
348C4×C11#54711yescharacteristic
349C4×C11#54811yescharacteristic
350C4×C11#55211yescharacteristic
351C4×C11#55611yescharacteristic
352Dic11—42no—
353Dic11—42no—
354Dic11—81no—
355Dic11—81no—
356Dic11—81no—
357Dic11—81no—
358Dic11—81no—
359Dic11—81no—
360C22×Q8—111no—
361C22×Q8—221no—
362C23×C4C22×D1111yescharacteristic
363C22×C8C22×D1111yescharacteristic
364C22×C8C22×D1111yescharacteristic
365C22×C8C22×D1111yescharacteristic
366C22×C8C22×D1111yescharacteristic
367C4⋊Q8—222no—
368C4⋊Q8—222no—
369C22⋊Q8—222no—
370C22⋊Q8—222no—
371C4×Q8—222no—
372C4×Q8—222no—
373#117—22no—
374#117—22no—
375C2×C4⋊C4—111no—
376C2×C4⋊C4—111no—
377C2×C4⋊C4—111no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4D4411yescharacteristic
389C2×C4⋊C4D4411yescharacteristic
390C2×C22⋊C4—221no—
391C2×C22⋊C4—221no—
392C2×C22⋊C4—221no—
393C2×C22⋊C4—221no—
394C2×C22⋊C4D4411yescharacteristic
395C2×C22⋊C4D4411yescharacteristic
396C2×C42—221no—
397C2×C42—221no—
398C2×C42C22×D1111yescharacteristic
399C2×C42C22×D1111yescharacteristic
400#107—222no—
401#107—222no—
402#107—222no—
403#106—222no—
404C4⋊C8—22no—
405C4⋊C8C22⋊D1114yes—
406#103—222no—
407#103—222no—
408#103—222no—
409#103—222no—
410C22⋊C8—22no—
411C22⋊C8—22no—
412#97—22no—
413C4×C8—22no—
414#95—221no—
415#95—221no—
416#95—221no—
417#95—221no—
418#95—221no—
419#95—221no—
420#95—221no—
421#95—221no—
422#95—221no—
423#95—221no—
424#95—221no—
425C2×C11—81no—
426C2×C11#241511yescharacteristic
427C2×C11#305911yescharacteristic
428C2×C11#306211yescharacteristic
429C2×C11#312111yescharacteristic
430C2×C11#312411yescharacteristic
431C2×C11#324211yescharacteristic
432C2×C11#324311yescharacteristic
433C24C2×D4411yescharacteristic
434C2×Q8—112no—
435C2×Q8—221no—
436C2×Q8—221no—
437C2×Q8—221no—
438C2×Q8—221no—
439C2×Q8—221no—
440C2×Q8—442no—
441C2×Q8—881no—
442C2×Q8—881no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—221no—
450C22×C4—221no—
451C22×C4—221no—
452C22×C4—221no—
453C22×C4—221no—
454C22×C4—221no—
455C22×C4—221no—
456C22×C4—221no—
457C22×C4C2×D4411yescharacteristic
458C22×C4C2×D4411yescharacteristic
459C22×C4C2×D4411yescharacteristic
460C22×C4C2×D4411yescharacteristic
461C22×C4C2×D4411yescharacteristic
462C22×C4C23×D1111yescharacteristic
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8C2×C22⋊D1112yes—
474C2×C8C2×C22⋊D1112yes—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—112no—
478C4⋊C4—224no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4—442no—
493C4⋊C4—442no—
494C4⋊C4—881no—
495C4⋊C4—881no—
496C4⋊C4—881no—
497C22⋊C4—22no—
498C22⋊C4—22no—
499C22⋊C4—224no—
500C22⋊C4—881no—
501C22⋊C4—881no—
502C22⋊C4—881no—
503C42—21no—
504C42—21no—
505C42—442no—
506C42—881no—
507C42#433912yes—
508C42C2×C22⋊D1112yes—
509C11#2471411yescharacteristic, complemented, Sylow
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23C22×D4411yescharacteristic
518Q8—222no—
519Q8—222no—
520Q8—441no—
521Q8—441no—
522Q8—884no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—222no—
541C2×C4—222no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
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#6698312yes—
565C2×C4#6698312yes—
566C2×C4C2×#433911yescharacteristic
567C2×C4#41×D1111yescharacteristic
568C2×C4#41×D1111yescharacteristic
569C2×C4#6704311yescharacteristic
570C2×C4#6704311yescharacteristic
571C2×C4C22×C22⋊D1111yescharacteristic
572C8—22no—
573C8—22no—
574C8—41no—
575C8—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22#1062305511yescharacteristic
584C22#1062305711yescharacteristic
585C22#1062328211yescharacteristic
586C22#1062328311yescharacteristic
587C22#1062328411yescharacteristic
588C22#1062328411yescharacteristic
589C22C2×#6698311yescharacteristic
590C4—22no—
591C4—22no—
592C4—41no—
593C4—41no—
594C4—41no—
595C4—442no—
596C4—442no—
597C4—881no—
598C4—881no—
599C4—881no—
600C4—881no—
601C4—881no—
602C4—881no—
603C4#1062306011yescharacteristic
604C4#1062306411yescharacteristic
605C4#1062335511yescharacteristic
606C4#1062336211yescharacteristic
607C2—81no—
608C2#1307203911yescharacteristic
609C2#1307827111yescharacteristic
610C2#1307829611yescharacteristic
611C2#1307884711yescharacteristic
612C2#1307888011yescharacteristic
613C2#1307988611yescharacteristic
614C2#1307990111yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#433C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenterC2×#433D11
hypocenterC11#24714
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
1. C2×#10622463C2semidirect
8. #13069567C2semidirect
9. #13069386C2semidirect
10. #13069359C2semidirect
11. #13069349C2semidirect
12. #13069306C2semidirect
13. #13069292C2semidirect
14. #13068632C2semidirect
509. C11#24714semidirect

Maximal subgroups

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

subgroupindex
C2×#106224632
#130744372
#130712982
#130700442
#130700392
#130698202
#130698132
#130695672
#130693862
#130693592
#130693492
#130693062
#130692922
#130686322
C2×C11×#4332
#2471411