Finite Group Databasebeta

← #14782587

Subgroups — #14782587

Order 2816.

1010 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622845C211yesmaximal, characteristic
2#13071236C211yesmaximal, characteristic, complemented
3#13071208C211yesmaximal, characteristic
4#13070037C212yesmaximal, complemented
5#13070032C212yesmaximal, complemented
6#13070027C212yesmaximal, complemented
7#13070022C212yesmaximal, complemented
8#13068337C211yesmaximal, characteristic, complemented
9C2×#10622189C211yesmaximal, characteristic, complemented
10#13068312C211yesmaximal, characteristic, complemented
11C2×C11×#416C211yesmaximal, characteristic
12C22×C11×#41C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C2×#66979C2211yescharacteristic
16C22×C4⋊Dic11C2211yescharacteristic
17C22×C4⋊Dic11C2211yescharacteristic
18C22×#4318C2211yescharacteristic
19C11×#416—24no—
20C2×C11×#103C2211yescharacteristic
21C2×C11×#103C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24#10622845—24no—
25#10622843C2212yes—
26C2×#66899C2212yes—
27#10622834C2212yes—
28#10622833—22no—
29C2×#66896C2212yes—
30#10622825—21no—
31#10622825—21no—
32#10622590C2212yes—
33#10622589C2212yes—
34#10622559—22no—
35#10622541—21no—
36#10622541—21no—
37#10622189C2212yes—
38#10622189C2212yes—
39#10622188C2212yes—
40#10622188C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43C2×C11×#41—22no—
44C2×C11×#41—22no—
45C2×C11×#41—22no—
46C2×C11×#41—22no—
47C2×C11×#41—22no—
48C2×C11×#41D414yes—
49C22×Q8×C11C2311yescharacteristic
50C22×D4×C11—21no—
51C22×D4×C11C2311yescharacteristic
52C23×C4×C11—21no—
53C23×C4×C11C2311yescharacteristic
54C23×Dic11—21no—
55C23×Dic11—21no—
56C22×C8×C11—22no—
57C22×C8×C11—22no—
58C22×C8×C11—22no—
59C22×C8×C11C2311yescharacteristic
60C22×C8×C11C2311yescharacteristic
61C11×#117—22no—
62C11×#117—22no—
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C22⋊C4—21no—
66C2×C42×C11—21no—
67C2×C22⋊Dic11—22no—
68C2×C22⋊Dic11—22no—
69C2×C22⋊Dic11D412yes—
70#66979—22no—
71#66979—22no—
72C2×C4⋊Dic11—22no—
73C2×C4⋊Dic11—22no—
74C2×C4⋊Dic11—22no—
75C2×C4⋊Dic11—22no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11D411yescharacteristic
79C2×C4⋊Dic11D411yescharacteristic
80C2×C4⋊Dic11C2312yes—
81C2×C4⋊Dic11C2312yes—
82C2×Dic11⋊C4—22no—
83C2×Dic11⋊C4—22no—
84C2×C4×Dic11C2312yes—
85C2×#4318—22no—
86C2×#4318—22no—
87C2×#4318—22no—
88C22×C11⋊C8C2312yes—
89C11×#103—22no—
90C11×#103—22no—
91C11×#102—22no—
92C11×#102—22no—
93#66899—24no—
94#66896—24no—
95C11⋊#95—22no—
96C11⋊#95—22no—
97C11⋊#95—22no—
98C11⋊#95—22no—
99#23634—111nomaximal, Sylow
100C24×C11—21no—
101C24×C11C2×D411yescharacteristic
102C11×#41—28no—
103C11×#41—28no—
104C11×#41—44no—
105C11×#41—44no—
106C2×Q8×C11—21no—
107C2×Q8×C11—21no—
108C2×Q8×C11—21no—
109C2×Q8×C11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11C2×D412yes—
112C2×D4×C11—24no—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—42no—
119C2×D4×C11—42no—
120C2×D4×C11C2×D412yes—
121C22×C4×C11—21no—
122C22×C4×C11—24no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—42no—
126C22×C4×C11—42no—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D412yes—
129C22×C4×C11#4112yes—
130C22×C4×C11#4112yes—
131C22×C4×C11#4112yes—
132C22×C4×C11#4112yes—
133C22×C4×C11#4112yes—
134C22×C4×C11C2411yescharacteristic
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—42no—
138C22×Dic11—42no—
139C22×Dic11—81no—
140C22×Dic11—81no—
141C22×Dic11—81no—
142C22×Dic11—81no—
143C22×Dic11C2×D412yes—
144C22×Dic11C2×D412yes—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—44no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C22⋊C4—42no—
157C42×C11—42no—
158C22⋊Dic11—24no—
159C22⋊Dic11—82no—
160C22⋊Dic11—82no—
161C4⋊Dic11—22no—
162C4⋊Dic11—22no—
163C4⋊Dic11—22no—
164C4⋊Dic11—22no—
165C4⋊Dic11—22no—
166C4⋊Dic11—22no—
167C4⋊Dic11—42no—
168C4⋊Dic11—42no—
169Dic11⋊C4—82no—
170Dic11⋊C4—82no—
171C4×Dic11—22no—
172C4×Dic11—22no—
173#4318—44no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—22no—
177C2×#417—111no—
178C2×#416D1111yescharacteristic
179#2317—111no—
180#2311—111no—
181#2074—112no—
182#2073—112no—
183#2072—112no—
184#2071—112no—
185#1736—111no—
186C2×#340—111no—
187#1729—111no—
188C23×C11—21no—
189C23×C11—21no—
190C23×C11—21no—
191C23×C11—21no—
192C23×C11—22no—
193C23×C11—41no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11—41no—
198C23×C11—41no—
199C23×C11#12112yes—
200C23×C11#12312yes—
201C23×C11#12412yes—
202C23×C11C22×D411yescharacteristic
203Q8×C11—22no—
204Q8×C11—22no—
205Q8×C11—41no—
206Q8×C11—41no—
207D4×C11—22no—
208D4×C11—22no—
209D4×C11—48no—
210D4×C11—41no—
211D4×C11—41no—
212C2×C4×C11—22no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—48no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11#12112yes—
223C2×C4×C11#12312yes—
224C2×C4×C11#12314yes—
225C2×C4×C11#12314yes—
226C2×C4×C11#12412yes—
227C2×C4×C11#12614yes—
228C2×C4×C11#12614yes—
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C2×#4111yescharacteristic
231C2×C4×C11C2×#4111yescharacteristic
232C2×C4×C11C2×#4111yescharacteristic
233C2×C4×C11C2×#4111yescharacteristic
234C2×C4×C11C2×#4111yescharacteristic
235C2×Dic11—22no—
236C2×Dic11—22no—
237C2×Dic11—22no—
238C2×Dic11—22no—
239C2×Dic11—22no—
240C2×Dic11—22no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247C2×Dic11—84no—
248C2×Dic11—84no—
249C8×C11—41no—
250C8×C11—41no—
251C11⋊C8—42no—
252C22×#41C2×D1111yescharacteristic
253C22×M16—111no—
254C23×C8C2×D1111yescharacteristic
255C2×#117—111no—
256C2×#117C2×D1111yescharacteristic
257C22×C4⋊C4—111no—
258C22×C4⋊C4—111no—
259#417—224no—
260#416—24no—
261C2×#103—112no—
262C2×#103C2×D1111yescharacteristic
263C2×#103C2×D1111yescharacteristic
264C2×#102—112no—
265C2×#102C2×D1111yescharacteristic
266C2×#102C2×D1111yescharacteristic
267#391—112no—
268#390—112no—
269#389—221no—
270#389—221no—
271#386—222no—
272#385—222no—
273#384—112no—
274#382—112no—
275#380—221no—
276#380—221no—
277#340—112no—
278#340—112no—
279#340—112no—
280#340—112no—
281#336—112no—
282#336—112no—
283C22×C11—22no—
284C22×C11—22no—
285C22×C11—22no—
286C22×C11—22no—
287C22×C11—22no—
288C22×C11—22no—
289C22×C11—42no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11—81no—
293C22×C11—81no—
294C22×C11—81no—
295C22×C11—81no—
296C22×C11#39714yes—
297C22×C11C2×#12111yescharacteristic
298C22×C11C2×#12311yescharacteristic
299C22×C11C2×#12411yescharacteristic
300C22×C11#57611yescharacteristic
301C22×C11#57711yescharacteristic
302C22×C11#57711yescharacteristic
303C22×C11#57811yescharacteristic
304C4×C11—42no—
305C4×C11—81no—
306C4×C11—81no—
307C4×C11#39714yes—
308C4×C11C2×#12311yescharacteristic
309C4×C11C2×#12311yescharacteristic
310C4×C11C2×#12611yescharacteristic
311C4×C11C2×#12611yescharacteristic
312Dic11—42no—
313Dic11—42no—
314Dic11—82no—
315Dic11—82no—
316C2×#41—22no—
317C2×#41—22no—
318C2×#41—22no—
319C2×#41—22no—
320C2×#41—22no—
321C2×#41C22⋊D1114yes—
322C22×Q8C22×D1111yescharacteristic
323C22×D4—21no—
324C22×D4C22×D1111yescharacteristic
325C23×C4—21no—
326C23×C4—221no—
327C23×C4—221no—
328C23×C4C22×D1111yescharacteristic
329C2×M16—222no—
330C2×M16—222no—
331C2×M16—222no—
332C22×C8—22no—
333C22×C8—22no—
334C22×C8—22no—
335C22×C8—112no—
336C22×C8C22×D1111yescharacteristic
337C22×C8C22×D1111yescharacteristic
338#117—22no—
339#117—22no—
340#117—222no—
341#117—222no—
342C2×C4⋊C4—111no—
343C2×C4⋊C4—111no—
344C2×C4⋊C4—112no—
345C2×C4⋊C4—112no—
346C2×C4⋊C4—222no—
347C2×C4⋊C4—222no—
348C2×C4⋊C4—222no—
349C2×C4⋊C4—222no—
350C2×C4⋊C4—221no—
351C2×C4⋊C4—221no—
352C2×C4⋊C4—222no—
353C2×C4⋊C4—222no—
354C2×C4⋊C4C22×D1111yescharacteristic
355C2×C4⋊C4C22×D1111yescharacteristic
356C2×C22⋊C4—21no—
357C2×C22⋊C4—112no—
358C2×C22⋊C4—222no—
359C2×C22⋊C4—222no—
360C2×C42—21no—
361C2×C42—112no—
362#103—22no—
363#103—22no—
364#103—224no—
365#102—22no—
366#102—22no—
367#102—224no—
368#95—222no—
369#95—222no—
370#95—222no—
371#95—222no—
372C2×C11—24no—
373C2×C11—82no—
374C2×C11C2×#39711yescharacteristic
375C2×C11#304511yescharacteristic
376C2×C11#304611yescharacteristic
377C2×C11#309811yescharacteristic
378C2×C11#309911yescharacteristic
379C2×C11#313611yescharacteristic
380C2×C11#313711yescharacteristic
381C24—21no—
382C24D4×D1111yescharacteristic
383#41—28no—
384#41—28no—
385#41—44no—
386#41—44no—
387C2×Q8—21no—
388C2×Q8—21no—
389C2×Q8—21no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8C2×C22⋊D1112yes—
393C2×D4—24no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—21no—
398C2×D4—21no—
399C2×D4—42no—
400C2×D4—42no—
401C2×D4C2×C22⋊D1112yes—
402C22×C4—21no—
403C22×C4—24no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—42no—
407C22×C4—42no—
408C22×C4—112no—
409C22×C4—112no—
410C22×C4—222no—
411C22×C4—222no—
412C22×C4—442no—
413C22×C4—442no—
414C22×C4—881no—
415C22×C4—881no—
416C22×C4—881no—
417C22×C4—881no—
418C22×C4#433912yes—
419C22×C4#433912yes—
420C22×C4D4×D1111yescharacteristic
421C22×C4#434112yes—
422C22×C4#434112yes—
423C22×C4#434112yes—
424C22×C4C2×C22⋊D1112yes—
425C22×C4C23×D1111yescharacteristic
426M16—444no—
427C2×C8—21no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—44no—
434C2×C8—222no—
435C2×C8—222no—
436C2×C8—222no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—222no—
442C4⋊C4—222no—
443C4⋊C4—222no—
444C4⋊C4—222no—
445C4⋊C4—222no—
446C4⋊C4—222no—
447C4⋊C4—442no—
448C4⋊C4—442no—
449C4⋊C4—882no—
450C4⋊C4—882no—
451C22⋊C4—42no—
452C22⋊C4—224no—
453C22⋊C4—882no—
454C22⋊C4—882no—
455C42—42no—
456C42—222no—
457C42—222no—
458C11#2363411yescharacteristic, complemented, Sylow
459C23—21no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—22no—
464C23—41no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23—41no—
469C23—41no—
470C23#6693612yes—
471C23#6693812yes—
472C23#6699212yes—
473C23C2×D4×D1111yescharacteristic
474Q8—22no—
475Q8—22no—
476Q8—41no—
477Q8—41no—
478D4—22no—
479D4—22no—
480D4—48no—
481D4—41no—
482D4—41no—
483C2×C4—22no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—48no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—222no—
494C2×C4—222no—
495C2×C4—222no—
496C2×C4—222no—
497C2×C4—222no—
498C2×C4—222no—
499C2×C4—442no—
500C2×C4—442no—
501C2×C4—442no—
502C2×C4—442no—
503C2×C4—442no—
504C2×C4—442no—
505C2×C4—884no—
506C2×C4—884no—
507C2×C4#6693214yes—
508C2×C4#6693214yes—
509C2×C4#6693612yes—
510C2×C4#6693812yes—
511C2×C4#6698214yes—
512C2×C4#6698814yes—
513C2×C4#6699212yes—
514C2×C4C2×#433911yescharacteristic
515C2×C4C2×#433911yescharacteristic
516C2×C4C2×#434111yescharacteristic
517C2×C4C2×#434111yescharacteristic
518C2×C4C2×#434111yescharacteristic
519C2×C4C22×C22⋊D1111yescharacteristic
520C8—41no—
521C8—41no—
522C8—442no—
523C22—22no—
524C22—22no—
525C22—22no—
526C22—22no—
527C22—22no—
528C22—22no—
529C22—42no—
530C22—42no—
531C22—42no—
532C22—81no—
533C22—81no—
534C22—81no—
535C22—81no—
536C22#1062256514yes—
537C22C2×#6693611yescharacteristic
538C22C2×#6693811yescharacteristic
539C22#1062330011yescharacteristic
540C22#1062330111yescharacteristic
541C22#1062330111yescharacteristic
542C22#1062330211yescharacteristic
543C22C2×#6699211yescharacteristic
544C4—42no—
545C4—81no—
546C4—81no—
547C4—442no—
548C4—442no—
549C4—882no—
550C4—882no—
551C4#1062256514yes—
552C4C2×#6693211yescharacteristic
553C4C2×#6693211yescharacteristic
554C4C2×#6698211yescharacteristic
555C4C2×#6698811yescharacteristic
556C2—24no—
557C2—82no—
558C2C2×#1062256511yescharacteristic
559C2#1307815311yescharacteristic
560C2#1307816411yescharacteristic
561C2#1307859211yescharacteristic
562C2#1307860311yescharacteristic
563C2#1307897411yescharacteristic
564C2#1307898511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#416C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
hypercenterC2×#416D11
hypocenterC11#23634
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
2. #13071236C2semidirect
4. #13070037C2semidirect
5. #13070032C2semidirect
6. #13070027C2semidirect
7. #13070022C2semidirect
8. #13068337C2semidirect
9. C2×#10622189C2semidirect
10. #13068312C2semidirect
458. C11#23634semidirect

Maximal subgroups

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

subgroupindex
C2×#106228452
#130712362
#130712082
#130700372
#130700322
#130700272
#130700222
#130683372
C2×#106221892
#130683122
C2×C11×#4162
#2363411