Finite Group Databasebeta

← #14805643

Subgroups — #14805643

Order 2816.

770 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622404C211yesmaximal, characteristic
2C2×#10622443C211yesmaximal, characteristic
3#13073987C211yesmaximal, characteristic
4#13073603C211yesmaximal, characteristic
5#13070119C211yesmaximal, characteristic
6#13070114C211yesmaximal, characteristic
7#13069993C211yesmaximal, characteristic
8#13069575C211yesmaximal, characteristic
9#13069376C211yesmaximal, characteristic
10#13069345C211yesmaximal, characteristic
11#13069341C211yesmaximal, characteristic
12#13069295C211yesmaximal, characteristic
13#13069289C211yesmaximal, characteristic
14#103×Dic11C211yesmaximal, characteristic
15C11×#2066C211yesmaximal, characteristic
16C2×Q8×Dic11C2211yescharacteristic
17C2×#66941—21no—
18C2×#66941C2211yescharacteristic
19C2×C4×Dic22C2211yescharacteristic
20C2×C11×#106C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×#103C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C11×#391C2211yescharacteristic
25C11×#389C2211yescharacteristic
26#10622843C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66881C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31C2×Dic11⋊C8C2211yescharacteristic
32C2×C8×Dic11C2211yescharacteristic
33C2×C8×Dic11C2211yescharacteristic
34#10622598C2211yescharacteristic
35#10622598C2211yescharacteristic
36#10622597—21no—
37#10622589C2211yescharacteristic
38C4⋊C4×Dic11C2211yescharacteristic
39#10622586C2211yescharacteristic
40C2×#66872C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42#10622541C2211yescharacteristic
43#10622541C2211yescharacteristic
44C2×C4×C11⋊C8C2211yescharacteristic
45#10622443—24no—
46#10622404—24no—
47#10622274—21no—
48#10622270—21no—
49#10622270—21no—
50#10622260—21no—
51#10622259—21no—
52#10622259—21no—
53C11×#340C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×Dic22—21no—
63C22×Dic22D411yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C42×C11C2311yescharacteristic
71Q8×Dic11—22no—
72Q8×Dic11—22no—
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11D411yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4D411yescharacteristic
88C2×Dic11⋊C4D411yescharacteristic
89C2×C4×Dic11—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11C2311yescharacteristic
92C2×C4×Dic11C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95#66941—22no—
96#66941—22no—
97#66941—44no—
98C4×Dic22—22no—
99C4×Dic22—22no—
100C11×#106—22no—
101C11×C4⋊C8—22no—
102C11×#103—22no—
103C11×#103—22no—
104C11×#95—21no—
105C11×#95—21no—
106C11×#95—21no—
107#66899—22no—
108#66899Q814yescomplemented
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117#66881—22no—
118Dic11⋊C8—22no—
119Dic11⋊C8D414yes—
120C8×Dic11—22no—
121C8×Dic11—22no—
122#66872—22no—
123#66872—22no—
124C4×C11⋊C8—22no—
125#25472—111nomaximal, Sylow
126C2×Q8×C11—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11C2×Q812yes—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2411yescharacteristic
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11C2×D411yescharacteristic
144C22×Dic11C2×D411yescharacteristic
145C22×Dic11C2×D411yescharacteristic
146C22×Dic11C2×D411yescharacteristic
147C2×Dic22—22no—
148C2×Dic22—22no—
149C2×Dic22—42no—
150C2×Dic22—42no—
151C2×Dic22—42no—
152C2×Dic22SD1614yes—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11C2×D412yes—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—42no—
165C11×C4⋊C4#4112yes—
166C42×C11—21no—
167C42×C11—21no—
168C4⋊Dic11—22no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—42no—
177C4⋊Dic11—42no—
178C4⋊Dic11—81no—
179C4⋊Dic11C2×Q812yes—
180Dic11⋊C4—22no—
181Dic11⋊C4—22no—
182Dic11⋊C4—42no—
183Dic11⋊C4—42no—
184Dic11⋊C4—42no—
185Dic11⋊C4—42no—
186Dic11⋊C4—81no—
187Dic11⋊C4—81no—
188C4×Dic11—21no—
189C4×Dic11—21no—
190C4×Dic11—42no—
191C4×Dic11—42no—
192C4×Dic11C2×D412yes—
193C4×Dic11#4112yes—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8C2×D412yes—
199C2×C11⋊C8C2×Q812yes—
200C2×#475—111no—
201C2×C8×Q8—111no—
202#2582—111no—
203#2546—111no—
204#2088—111no—
205#2088—111no—
206#2066—111no—
207#2066D1111yescharacteristic
208#1990—111no—
209#1948—111no—
210#1941—111no—
211#1941—111no—
212#1933—111no—
213#1933—111no—
214C4×#103—111no—
215C23×C11C22×D411yescharacteristic
216Q8×C11—22no—
217Q8×C11—22no—
218Q8×C11—41no—
219Q8×C11—41no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11C2×SD1612yes—
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C22×Q811yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C112−1+411yescharacteristic
243C2×C4×C112−1+411yescharacteristic
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—22no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—41no—
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#12112yes—
264C2×Dic11#12112yes—
265C2×Dic11C2×SD1612yes—
266C2×Dic11C2×SD1612yes—
267C2×Dic11#13512yes—
268Dic22—28no—
269Dic22—84no—
270C8×C11—22no—
271C8×C11—41no—
272C11⋊C8—22no—
273C11⋊C8—22no—
274C2×C4⋊Q8—111no—
275C2×C4⋊Q8—221no—
276C2×C4×Q8—111no—
277C2×C4×Q8—111no—
278#475—224no—
279C8×Q8—224no—
280C2×#106—111no—
281C2×#106—111no—
282C2×#106—111no—
283C2×#106C2×D1111yescharacteristic
284C2×C4⋊C8—111no—
285C2×C4⋊C8—111no—
286C2×C4⋊C8C2×D1111yescharacteristic
287C2×#103—111no—
288C2×#103—111no—
289C2×#103C2×D1111yescharacteristic
290C2×#103C2×D1111yescharacteristic
291C2×C4×C8—111no—
292C2×C4×C8—111no—
293C2×C4×C8—111no—
294#398—221no—
295#398—221no—
296#398—221no—
297#398—221no—
298#391—111no—
299#391—221no—
300#391—221no—
301#391C2×D1111yescharacteristic
302#389—111no—
303#389—111no—
304#389—111no—
305#389—111no—
306#389—111no—
307#389—221no—
308#389C2×D1111yescharacteristic
309#384—111no—
310C4×C4⋊C4—111no—
311#340—111no—
312#340—111no—
313#340—111no—
314#340—111no—
315#340—111no—
316#340—111no—
317#340—111no—
318#340C2×D1111yescharacteristic
319C22×C11C2×#12111yescharacteristic
320C22×C11#54811yescharacteristic
321C22×C11D4×Q811yescharacteristic
322C22×C11C22×SD1611yescharacteristic
323C22×C11C2×#13511yescharacteristic
324C22×C11#57711yescharacteristic
325C22×C11#57811yescharacteristic
326C4×C11—22no—
327C4×C11—42no—
328C4×C11—42no—
329C4×C11—41no—
330C4×C11—81no—
331C4×C11—81no—
332C4×C11#53311yescharacteristic
333C4×C11#54111yescharacteristic
334C4×C11#54711yescharacteristic
335C4×C11D4×Q811yescharacteristic
336Dic11—22no—
337Dic11—22no—
338Dic11—42no—
339Dic11—41no—
340Dic11—81no—
341Dic11—81no—
342Dic11—81no—
343Dic11#46514yes—
344C22×Q8—111no—
345C22×Q8—221no—
346C22×Q8C22×D1111yescharacteristic
347C22×C8—111no—
348C22×C8—111no—
349C22×C8C22×D1111yescharacteristic
350C22×C8C22×D1111yescharacteristic
351C4⋊Q8—222no—
352C4⋊Q8—222no—
353C4⋊Q8—444no—
354C4×Q8—222no—
355C4×Q8—222no—
356C4×Q8—222no—
357C4×Q8—222no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—111no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—111no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—111no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4—221no—
375C2×C4⋊C4C22×D1111yescharacteristic
376C2×C4⋊C4C22×D1111yescharacteristic
377C2×C4⋊C4C22×D1111yescharacteristic
378C2×C42—111no—
379C2×C42—111no—
380C2×C42—221no—
381C2×C42—221no—
382C2×C42C22×D1111yescharacteristic
383#106—22no—
384#106—222no—
385#106—222no—
386#106—222no—
387C4⋊C8—22no—
388C4⋊C8—114no—
389C4⋊C8—222no—
390#103—22no—
391#103—22no—
392#103—114no—
393#103—222no—
394C4×C8—222no—
395C4×C8—222no—
396C4×C8—222no—
397#95—21no—
398#95—21no—
399#95—21no—
400#95—221no—
401#95—221no—
402#95—221no—
403#95—221no—
404#95—221no—
405#95—221no—
406#95—221no—
407#95—221no—
408C2×C11#242911yescharacteristic
409C2×C11C2×#46511yescharacteristic
410C2×C11#306311yescharacteristic
411C2×C11#335911yescharacteristic
412C2×C11#336511yescharacteristic
413C2×C11Q8×SD1611yescharacteristic
414C2×C11#338311yescharacteristic
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—114no—
421C2×Q8—222no—
422C2×Q8—222no—
423C2×Q8—442no—
424C2×Q8—442no—
425C2×Q8—442no—
426C2×Q8Q8×D1112yes—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—111no—
432C22×C4—111no—
433C22×C4—111no—
434C22×C4—111no—
435C22×C4—221no—
436C22×C4—221no—
437C22×C4—221no—
438C22×C4—221no—
439C22×C4D4×D1111yescharacteristic
440C22×C4D4×D1111yescharacteristic
441C22×C4C23×D1111yescharacteristic
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—112no—
448C2×C8—112no—
449C2×C8—221no—
450C2×C8—221no—
451C2×C8—221no—
452C2×C8—221no—
453C2×C8D4×D1112yes—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—42no—
460C4⋊C4—112no—
461C4⋊C4—222no—
462C4⋊C4—222no—
463C4⋊C4—222no—
464C4⋊C4—221no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4—442no—
472C4⋊C4—442no—
473C4⋊C4—442no—
474C4⋊C4—442no—
475C4⋊C4—442no—
476C4⋊C4—442no—
477C4⋊C4—881no—
478C4⋊C4—881no—
479C4⋊C4—881no—
480C4⋊C4#434112yes—
481C42—21no—
482C42—21no—
483C42—112no—
484C42—112no—
485C42—221no—
486C42—221no—
487C42—442no—
488C42—442no—
489C11#2547211yescharacteristic, complemented, Sylow
490C23C2×D4×D1111yescharacteristic
491Q8—22no—
492Q8—22no—
493Q8—41no—
494Q8—41no—
495Q8—228no—
496Q8—884no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—22no—
502C2×C4—21no—
503C2×C4—22no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—112no—
515C2×C4—112no—
516C2×C4—112no—
517C2×C4—112no—
518C2×C4—112no—
519C2×C4—221no—
520C2×C4—221no—
521C2×C4—221no—
522C2×C4—221no—
523C2×C4—221no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—222no—
527C2×C4—441no—
528C2×C4—441no—
529C2×C4—441no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4SD16×D1112yes—
539C2×C4C2×D4×D1111yescharacteristic
540C2×C4C2×#434111yescharacteristic
541C2×C4C2×Q8×D1111yescharacteristic
542C2×C4#41×D1111yescharacteristic
543C2×C4#6704311yescharacteristic
544C2×C4#6704311yescharacteristic
545C8—22no—
546C8—41no—
547C8—222no—
548C8—222no—
549C22#1062312911yescharacteristic
550C22D11×#12111yescharacteristic
551C22#1062316311yescharacteristic
552C22C2×SD16×D1111yescharacteristic
553C22D11×#13511yescharacteristic
554C22#1062330911yescharacteristic
555C22#1062331011yescharacteristic
556C4—22no—
557C4—41no—
558C4—42no—
559C4—42no—
560C4—81no—
561C4—81no—
562C4—114no—
563C4—222no—
564C4—222no—
565C4—441no—
566C4—442no—
567C4—881no—
568C4—881no—
569C4—881no—
570C4#1062314211yescharacteristic
571C4#1062315311yescharacteristic
572C4#1062316311yescharacteristic
573C4#1062323211yescharacteristic
574C2#1307220811yescharacteristic
575C2D11×#46511yescharacteristic
576C2#1307830411yescharacteristic
577C2#1308125311yescharacteristic
578C2#1308130711yescharacteristic
579C2#1308147511yescharacteristic
580C2#1308150211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2066C2
socle, prime radicalC23×C11C22×D4
hypercenter#2066D11
hypocenterC11#25472
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2066

Complements

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

NH ≅ G/Ntype
108. #66899Q8semidirect
489. C11#25472semidirect

Maximal subgroups

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

subgroupindex
C2×#106224042
C2×#106224432
#130739872
#130736032
#130701192
#130701142
#130699932
#130695752
#130693762
#130693452
#130693412
#130692952
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