Finite Group Databasebeta

← #14788157

Subgroups — #14788157

Order 2816.

1114 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623001C211yesmaximal, characteristic
2C2×#10622633C211yesmaximal, characteristic, complemented
3C2×#10622644C211yesmaximal, characteristic, complemented
4#13069812C212yesmaximal
5#13069624C212yesmaximal
6#13069568C211yesmaximal, characteristic, complemented
7#13069539C211yesmaximal, characteristic, complemented
8#13068960C212yesmaximal, complemented
9#13068883C212yesmaximal, complemented
10#13068596C211yesmaximal, characteristic
11C4×C11×C22⋊Q8C211yesmaximal, characteristic
12C2×C11×C22⋊Q8C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C22×#4326C2212yes—
16C2×#66979—21no—
17C2×#66977—21no—
18C2×#66977C2212yes—
19#10623001—24no—
20#10623001—24no—
21C2×#66923—21no—
22C2×#66922C2211yescharacteristic
23C2×#66922C2211yescharacteristic
24C2×C4×Dic22—21no—
25C2×C4×Dic22C2212yes—
26C11×#391C2211yescharacteristic
27C11×#389C2211yescharacteristic
28C11×#387—21no—
29C11×#385—21no—
30C11×#380C2211yescharacteristic
31C4×C11×C4⋊C4—21no—
32C4×C11×C4⋊C4C2211yescharacteristic
33C4×C11×C22⋊C4—21no—
34C2×#66899C2212yes—
35C2×C22⋊(C11⋊C8)C2212yes—
36#10622644—24no—
37#10622633—24no—
38C2×#66874C2212yes—
39C2×#66874C2212yes—
40C2×#66874C2212yes—
41C2×#66872C2212yes—
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44#10622167C2212yes—
45#10622167C2212yes—
46#10622162C2212yes—
47C22×Q8×C11C2311yescharacteristic
48C23×C4×C11D411yescharacteristic
49C23×C4×C11D411yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C22×Dic22—21no—
52C22×Dic22C2312yes—
53C11×C22⋊Q8—22no—
54C11×C22⋊Q8—22no—
55C4×Q8×C11—22no—
56C4×Q8×C11—22no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C11×C4⋊C4C2311yescharacteristic
62C2×C11×C4⋊C4C2311yescharacteristic
63C2×C11×C22⋊C4—21no—
64C2×C11×C22⋊C4—21no—
65C2×C42×C11—22no—
66C2×C42×C11—22no—
67C2×C42×C11—21no—
68C2×C42×C11—21no—
69C2×C42×C11D411yescharacteristic
70C2×C42×C11D411yescharacteristic
71C2×C42×C11C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×C22⋊Dic11—22no—
74C2×#4326—24no—
75C2×#4326—24no—
76C2×#4326—42no—
77#66979—28no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11C2312yes—
82#66977—28no—
83#66977—24no—
84#66977—24no—
85C2×Dic11⋊C4—22no—
86C2×Dic11⋊C4—22no—
87C2×C4×Dic11—22no—
88C22×C11⋊C8C2312yes—
89C22×C11⋊C8C2312yes—
90#66923—28no—
91#66922—22no—
92#66922—22no—
93#66922D414yes—
94#66922D414yes—
95C4×Dic22—28no—
96C4×Dic22—24no—
97C4×Dic22—24no—
98C11×#95—21no—
99C11×#95—21no—
100C11×#95—21no—
101C11×#95—21no—
102C11×#95—21no—
103#66899—24no—
104C22⋊(C11⋊C8)—42no—
105#66874—24no—
106#66874—24no—
107#66874—42no—
108#66872—24no—
109C4⋊(C11⋊C8)—22no—
110C4⋊(C11⋊C8)—22no—
111#24157—111nomaximal, Sylow
112C24×C11C2×D411yescharacteristic
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11—21no—
118C2×Q8×C11#4112yes—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—21no—
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×C11—21no—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2411yescharacteristic
141C22×Dic11—22no—
142C22×Dic11—22no—
143C2×Dic22—24no—
144C2×Dic22—22no—
145C2×Dic22—22no—
146C2×Dic22—22no—
147C2×Dic22—22no—
148C2×Dic22—22no—
149C2×Dic22—42no—
150C2×Dic22—42no—
151C2×Dic22C2×D414yes—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—42no—
159C11×C4⋊C4—42no—
160C11×C4⋊C4#4112yes—
161C11×C22⋊C4—24no—
162C11×C22⋊C4—42no—
163C42×C11—22no—
164C42×C11—22no—
165C42×C11—21no—
166C42×C11—21no—
167C42×C11—42no—
168C42×C11—42no—
169C42×C11C2×D412yes—
170C42×C11C2×D412yes—
171C22⋊Dic11—28no—
172#4326—48no—
173C4⋊Dic11—24no—
174C4⋊Dic11—24no—
175C4⋊Dic11—24no—
176C4⋊Dic11—22no—
177C4⋊Dic11C2×D414yes—
178Dic11⋊C4—28no—
179Dic11⋊C4—28no—
180C4×Dic11—28no—
181C2×C11⋊C8—22no—
182C2×C11⋊C8—22no—
183C2×C11⋊C8—22no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8—22no—
187C2×#533—111no—
188C2×#475—111no—
189C2×#462—111no—
190C4×C22⋊Q8D1111yescharacteristic
191#2035—112no—
192#2001—112no—
193#1988—111no—
194#1981—111no—
195#1878—112no—
196#1865—112no—
197#1797—111no—
198C23×C11—21no—
199C23×C11—21no—
200C23×C11—21no—
201C23×C11—21no—
202C23×C11—21no—
203C23×C11—21no—
204C23×C11#13712yes—
205C23×C11C22×D411yescharacteristic
206Q8×C11—22no—
207Q8×C11—22no—
208Q8×C11—41no—
209Q8×C11—41no—
210C2×C4×C11—28no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—44no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11#12012yes—
239C2×C4×C11#12012yes—
240C2×C4×C11#13512yes—
241C2×C4×C11#13712yes—
242C2×C4×C11#13712yes—
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C2×C4×C11H(5,𝔽2)11yescharacteristic
248C2×C4×C112−1+411yescharacteristic
249C2×Dic11—24no—
250C2×Dic11—24no—
251C2×Dic11—42no—
252C2×Dic11—42no—
253C2×Dic11—42no—
254C2×Dic11—42no—
255Dic22—24no—
256Dic22—24no—
257Dic22—42no—
258Dic22—42no—
259Dic22—48no—
260C11⋊C8—42no—
261C11⋊C8—42no—
262C22×Q16—112no—
263#533—224no—
264#533—224no—
265C2×C4⋊Q8—111no—
266C2×C4⋊Q8—111no—
267C2×#125—221no—
268C2×C22⋊Q8—112no—
269C2×C22⋊Q8—221no—
270C2×C22⋊Q8C2×D1111yescharacteristic
271C2×C4×Q8—112no—
272C2×C4×Q8—221no—
273C2×C4×Q8C2×D1111yescharacteristic
274C2×#117—221no—
275C22×C42C2×D1111yescharacteristic
276#475—224no—
277#462—224no—
278C2×#106—112no—
279C2×C4⋊C8—111no—
280C2×C4⋊C8—111no—
281C2×#103—112no—
282C2×#103—112no—
283C2×#103—112no—
284C2×#103—112no—
285C2×C22⋊C8—112no—
286#391C2×D1111yescharacteristic
287#389C2×D1111yescharacteristic
288#387—21no—
289#385—21no—
290#380C2×D1111yescharacteristic
291C4×C4⋊C4—21no—
292C4×C4⋊C4C2×D1111yescharacteristic
293C4×C22⋊C4—21no—
294#340—112no—
295#340—112no—
296#336—112no—
297C22×C11—22no—
298C22×C11—22no—
299C22×C11—22no—
300C22×C11—41no—
301C22×C11—41no—
302C22×C11—41no—
303C22×C11—41no—
304C22×C11C2×#12011yescharacteristic
305C22×C11#52511yescharacteristic
306C22×C11#53711yescharacteristic
307C22×C11C2×#13511yescharacteristic
308C22×C11C2×#13711yescharacteristic
309C22×C11C2×#13711yescharacteristic
310C22×C11C2×#13711yescharacteristic
311C4×C11—22no—
312C4×C11—22no—
313C4×C11—42no—
314C4×C11—41no—
315C4×C11—42no—
316C4×C11—41no—
317C4×C11—81no—
318C4×C11—81no—
319C4×C11#45214yes—
320C4×C11#54611yescharacteristic
321C4×C11#54711yescharacteristic
322C4×C11#54811yescharacteristic
323C4×C11#55011yescharacteristic
324Dic11—44no—
325Dic11—44no—
326C22×Q8—112no—
327C22×Q8—221no—
328C22×Q8C22×D1111yescharacteristic
329C23×C4C22⋊D1111yescharacteristic
330C23×C4C22⋊D1111yescharacteristic
331C23×C4C22×D1111yescharacteristic
332C2×Q16—224no—
333C2×Q16—224no—
334C2×Q16—442no—
335C22×C8—112no—
336C22×C8—112no—
337C4⋊Q8—114no—
338C4⋊Q8—114no—
339C4⋊Q8—222no—
340C4⋊Q8—222no—
341#125—228no—
342C22⋊Q8—22no—
343C22⋊Q8—22no—
344C22⋊Q8—224no—
345C22⋊Q8—224no—
346C22⋊Q8—228no—
347C4×Q8—22no—
348C4×Q8—22no—
349C4×Q8—224no—
350C4×Q8—224no—
351C4×Q8—228no—
352#117—228no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—112no—
357C2×C4⋊C4—221no—
358C2×C4⋊C4—221no—
359C2×C4⋊C4—222no—
360C2×C4⋊C4—222no—
361C2×C4⋊C4—221no—
362C2×C4⋊C4C22×D1111yescharacteristic
363C2×C4⋊C4C22×D1111yescharacteristic
364C2×C4⋊C4C22×D1111yescharacteristic
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—222no—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—21no—
371C2×C42—21no—
372C2×C42—222no—
373C2×C42C22⋊D1111yescharacteristic
374C2×C42C22⋊D1111yescharacteristic
375C2×C42C22×D1111yescharacteristic
376C2×C42C22×D1111yescharacteristic
377#106—224no—
378C4⋊C8—222no—
379C4⋊C8—222no—
380#103—224no—
381#103—224no—
382#103—224no—
383#103—442no—
384C22⋊C8—442no—
385#95—21no—
386#95—21no—
387#95—21no—
388#95—21no—
389#95—21no—
390C2×C11—42no—
391C2×C11#240711yescharacteristic
392C2×C11C2×#45211yescharacteristic
393C2×C11#300411yescharacteristic
394C2×C11#310711yescharacteristic
395C2×C11#311311yescharacteristic
396C2×C11#324811yescharacteristic
397C2×C11#325511yescharacteristic
398C24C2×C22⋊D1111yescharacteristic
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—21no—
402C2×Q8—21no—
403C2×Q8—21no—
404C2×Q8—114no—
405C2×Q8—224no—
406C2×Q8—222no—
407C2×Q8—222no—
408C2×Q8—222no—
409C2×Q8—222no—
410C2×Q8—222no—
411C2×Q8—442no—
412C2×Q8—442no—
413C2×Q8#433912yes—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—222no—
431C22×C4—222no—
432C22×C4C2×C22⋊D1111yescharacteristic
433C22×C4C2×C22⋊D1111yescharacteristic
434C22×C4C2×C22⋊D1111yescharacteristic
435C22×C4C2×C22⋊D1111yescharacteristic
436C22×C4C2×C22⋊D1111yescharacteristic
437C22×C4C23×D1111yescharacteristic
438Q16—448no—
439C2×C8—222no—
440C2×C8—222no—
441C2×C8—222no—
442C2×C8—222no—
443C2×C8—222no—
444C2×C8—222no—
445C4⋊C4—24no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—42no—
452C4⋊C4—42no—
453C4⋊C4—114no—
454C4⋊C4—228no—
455C4⋊C4—228no—
456C4⋊C4—224no—
457C4⋊C4—224no—
458C4⋊C4—224no—
459C4⋊C4—222no—
460C4⋊C4#433912yes—
461C22⋊C4—24no—
462C22⋊C4—42no—
463C22⋊C4—228no—
464C42—22no—
465C42—22no—
466C42—21no—
467C42—21no—
468C42—42no—
469C42—42no—
470C42—228no—
471C42D4×D1112yes—
472C42D4×D1112yes—
473C11#2415711yescharacteristic, complemented, Sylow
474C23—21no—
475C23—21no—
476C23—21no—
477C23—21no—
478C23—21no—
479C23—21no—
480C23#6700412yes—
481C23C22×C22⋊D1111yescharacteristic
482Q8—22no—
483Q8—22no—
484Q8—41no—
485Q8—41no—
486Q8—224no—
487Q8—224no—
488Q8—442no—
489Q8—442no—
490Q8—448no—
491C2×C4—28no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
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—44no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—224no—
520C2×C4—224no—
521C2×C4—442no—
522C2×C4—442no—
523C2×C4—442no—
524C2×C4—442no—
525C2×C4#6699012yes—
526C2×C4#6699012yes—
527C2×C4#6699512yes—
528C2×C4#6700312yes—
529C2×C4#6700412yes—
530C2×C4C2×#433911yescharacteristic
531C2×C4C2×#433911yescharacteristic
532C2×C4C2×D4×D1111yescharacteristic
533C2×C4C2×D4×D1111yescharacteristic
534C2×C4#6704211yescharacteristic
535C2×C4#6704311yescharacteristic
536C8—442no—
537C8—442no—
538C22—22no—
539C22—22no—
540C22—22no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22#1062332211yescharacteristic
546C22C2×#6699011yescharacteristic
547C22C2×#6699511yescharacteristic
548C22C2×#6700311yescharacteristic
549C22C2×#6700411yescharacteristic
550C22C2×#6700411yescharacteristic
551C22#1062336411yescharacteristic
552C4—22no—
553C4—22no—
554C4—41no—
555C4—41no—
556C4—42no—
557C4—42no—
558C4—81no—
559C4—81no—
560C4—444no—
561C4—444no—
562C4#1062266014yes—
563C4#1062308111yescharacteristic
564C4#1062308211yescharacteristic
565C4#1062308311yescharacteristic
566C4#1062308411yescharacteristic
567C2—42no—
568C2#1307196111yescharacteristic
569C2C2×#1062266011yescharacteristic
570C2#1307784911yescharacteristic
571C2#1307868711yescharacteristic
572C2#1307874611yescharacteristic
573C2#1307995311yescharacteristic
574C2#1308000711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×C22⋊Q8C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenterC4×C22⋊Q8D11
hypocenterC11#24157
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#10622633C2semidirect
3. C2×#10622644C2semidirect
6. #13069568C2semidirect
7. #13069539C2semidirect
8. #13068960C2semidirect
9. #13068883C2semidirect
473. C11#24157semidirect

Maximal subgroups

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

subgroupindex
C2×#106230012
C2×#106226332
C2×#106226442
#130698122
#130696242
#130695682
#130695392
#130689602
#130688832
#130685962
C4×C11×C22⋊Q82
#2415711