Finite Group Databasebeta

← #14765969

Subgroups — #14765969

Order 2816.

740 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622697C211yesmaximal, characteristic
2#13071260C211yesmaximal, characteristic
3#13069569C211yesmaximal, characteristic, complemented
4#13069382C211yesmaximal, characteristic, complemented
5#13069356C211yesmaximal, characteristic, complemented
6#13069341C211yesmaximal, characteristic, complemented
7#13069312C211yesmaximal, characteristic
8#13069298C211yesmaximal, characteristic
9#13069243C211yesmaximal, characteristic
10#13069236C211yesmaximal, characteristic
11#13069201C211yesmaximal, characteristic, complemented
12#13069194C211yesmaximal, characteristic, complemented
13#13068623C211yesmaximal, characteristic
14#13068473C211yesmaximal, characteristic, complemented
15C11×#2331C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C4×D44C2211yescharacteristic
18C11×#391—21no—
19C11×#391—21no—
20C11×#389C2211yescharacteristic
21C11×#389C2211yescharacteristic
22C11×#387—21no—
23C11×#387—21no—
24C11×#382C2211yescharacteristic
25C4×C11×C4⋊C4C2211yescharacteristic
26C4×C11×C4⋊C4C2211yescharacteristic
27C11×#376C2211yescharacteristic
28#10622697C418yescomplemented
29C2×#66873C2211yescharacteristic
30C2×#66873C2211yescharacteristic
31C2×#66873C2211yescharacteristic
32C2×#66873C2211yescharacteristic
33C2×#66872C2211yescharacteristic
34C2×#66872C2211yescharacteristic
35C2×#66872C2211yescharacteristic
36C2×#66871C2211yescharacteristic
37#10622552C2211yescharacteristic
38#10622552C2211yescharacteristic
39C4×C4⋊Dic11C2211yescharacteristic
40#10622541C2211yescharacteristic
41#10622541C2211yescharacteristic
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44C2×#66867C2211yescharacteristic
45C2×C4×C11⋊C8C2211yescharacteristic
46#10622282—21no—
47#10622282—21no—
48#10622280—21no—
49#10622277—21no—
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×Q8×C11—21no—
61C22×D44C2311yescharacteristic
62C22×C4×D11—21no—
63C11×C4⋊Q8—22no—
64C11×C4⋊Q8C2×C414yes—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C42×C11—21no—
73C2×C42×C11—21no—
74C2×C42×C11C2311yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×C42×C11C2311yescharacteristic
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×C4×Dic11—21no—
88C22×C11⋊C8C2311yescharacteristic
89C22×C11⋊C8C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C4×D44—22no—
93C4×D44C2×C414yes—
94C11×#95—21no—
95C11×#95—21no—
96C11×#95—21no—
97C11×#95—21no—
98C11×#95—21no—
99C11×#95—21no—
100C11×#95D411yescharacteristic
101C11×#95D411yescharacteristic
102C11×#95D411yescharacteristic
103C11×#95D411yescharacteristic
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107#66873—41no—
108#66873—41no—
109#66873C2×C414yes—
110#66873C2×C414yes—
111#66872—41no—
112#66872C2×C414yes—
113#66872C2×C414yes—
114#66871—41no—
115C4⋊(C11⋊C8)—22no—
116C4⋊(C11⋊C8)C2×C414yes—
117#66867—41no—
118C4×C11⋊C8—41no—
119#22123—111nomaximal, Sylow
120C23×D11—21no—
121C2×Q8×C11—24no—
122C2×Q8×C11—81no—
123C2×Q8×C11—81no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2411yescharacteristic
135C22×Dic11—21no—
136C22×Dic11—21no—
137C22×Dic11—21no—
138C2×D44—21no—
139C2×D44—21no—
140C2×D44—21no—
141C2×D44—21no—
142C2×D44—21no—
143C2×D44C22×C412yes—
144C2×C4×D11—24no—
145C2×C4×D11—81no—
146C2×C4×D11—81no—
147C11×C4⋊C4—24no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—81no—
155C11×C4⋊C4—81no—
156C11×C4⋊C4C22×C412yes—
157C11×C4⋊C4C22×C412yes—
158C42×C11—21no—
159C42×C11—21no—
160C42×C11—21no—
161C42×C11—21no—
162C42×C11—81no—
163C42×C11—81no—
164C42×C11C22×C412yes—
165C42×C11#4112yes—
166(C2×D11)⋊C4—24no—
167(C2×D11)⋊C4—81no—
168(C2×D11)⋊C4—81no—
169(C2×D11)⋊C4—81no—
170(C2×D11)⋊C4—81no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11C22×C412yes—
177Dic11⋊C4—81no—
178Dic11⋊C4—81no—
179C4×Dic11—81no—
180C2×C11⋊C8—21no—
181C2×C11⋊C8—21no—
182C2×C11⋊C8—21no—
183C2×C11⋊C8—21no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8—21no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8C22×C412yes—
191C2×C11⋊C8C22×C412yes—
192C2×#476—111no—
193#2331D1111yescharacteristic, complemented
194#2319—111no—
195#1988—111no—
196#1949—111no—
197#1944—111no—
198#1941—111no—
199#1936—111no—
200#1934—111no—
201#1926—111no—
202#1925—111no—
203#1920—111no—
204#1919—111no—
205#1804—111no—
206#1768—111no—
207C23×C11C22×D411yescharacteristic
208C22×D11—22no—
209C22×D11—41no—
210C22×D11—41no—
211C22×D11—41no—
212C22×D11—41no—
213C22×D11—41no—
214C22×D11—41no—
215Q8×C11—84no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
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—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11C4×D412yes—
245C2×C4×C11C4×D412yes—
246C2×C4×C11C23×C411yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C2×C4×C11H(5,𝔽2)11yescharacteristic
249C2×C4×C112−1+411yescharacteristic
250C2×C4×C112−1+411yescharacteristic
251C2×C4×C112−1+411yescharacteristic
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—
261D44—22no—
262D44—22no—
263D44—41no—
264D44—41no—
265C4×D11—84no—
266C11⋊C8—22no—
267C11⋊C8—22no—
268C11⋊C8—41no—
269C11⋊C8—41no—
270C2×C4⋊Q8C2×D1111yescharacteristic
271C2×C4×D4—111no—
272#476—118no—
273C2×#107—111no—
274C2×#106—111no—
275C2×#106—111no—
276C2×#106—111no—
277C2×C4⋊C8—111no—
278C2×C4⋊C8—111no—
279C2×#102—111no—
280C2×#102—111no—
281C2×#102—111no—
282C2×#102—111no—
283C2×#97—111no—
284C2×C4×C8—111no—
285#391—21no—
286#391—21no—
287#390—111no—
288#390—111no—
289#389—111no—
290#389—111no—
291#389C2×D1111yescharacteristic
292#389C2×D1111yescharacteristic
293#388—221no—
294#388—221no—
295#387—21no—
296#387—21no—
297#382C2×D1111yescharacteristic
298#381—221no—
299#380—221no—
300C4×C4⋊C4—111no—
301C4×C4⋊C4C2×D1111yescharacteristic
302C4×C4⋊C4C2×D1111yescharacteristic
303#376C2×D1111yescharacteristic
304#340—111no—
305#340—111no—
306#340—111no—
307#340—111no—
308#340—111no—
309#340—111no—
310#340—111no—
311#340—111no—
312#336—111no—
313#336—111no—
314C22×C11C2×C4×D411yescharacteristic
315C22×C11#53611yescharacteristic
316C22×C11#53711yescharacteristic
317C22×C11#57611yescharacteristic
318C22×C11#57711yescharacteristic
319C22×C11#57711yescharacteristic
320C22×C11#57711yescharacteristic
321C2×D11—42no—
322C2×D11—42no—
323C2×D11—42no—
324C2×D11—81no—
325C2×D11—81no—
326C2×D11—81no—
327C2×D11—81no—
328C4×C11—22no—
329C4×C11—22no—
330C4×C11—42no—
331C4×C11—42no—
332C4×C11—41no—
333C4×C11—41no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11—81no—
337C4×C11—81no—
338C4×C11#51911yescharacteristic
339C4×C11#52011yescharacteristic
340C4×C11#54111yescharacteristic
341C4×C11#54211yescharacteristic
342Dic11—42no—
343Dic11—81no—
344Dic11—81no—
345C22×Q8—21no—
346C22×D4—111no—
347C23×C4—221no—
348C22×C8—111no—
349C22×C8—111no—
350C22×C8—111no—
351C22×C8—111no—
352C4⋊Q8—22no—
353C4⋊Q8C4×D1114yes—
354C4×D4—114no—
355C4×D4—222no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—111no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—221no—
363C2×C4⋊C4—221no—
364C2×C4⋊C4C22×D1111yescharacteristic
365C2×C4⋊C4C22×D1111yescharacteristic
366C2×C4⋊C4C22×D1111yescharacteristic
367C2×C4⋊C4C22×D1111yescharacteristic
368C2×C22⋊C4—221no—
369C2×C22⋊C4—221no—
370C2×C22⋊C4—221no—
371C2×C22⋊C4—221no—
372C2×C22⋊C4—221no—
373C2×C42—21no—
374C2×C42—21no—
375C2×C42—221no—
376C2×C42C22×D1111yescharacteristic
377C2×C42C22×D1111yescharacteristic
378C2×C42C22×D1111yescharacteristic
379#107—441no—
380#106—114no—
381#106—114no—
382#106—441no—
383C4⋊C8—114no—
384C4⋊C8—222no—
385#102—114no—
386#102—114no—
387#102—441no—
388#102—441no—
389#97—441no—
390C4×C8—441no—
391#95—21no—
392#95—21no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95—221no—
398#95—221no—
399#95—221no—
400#95C22⋊D1111yescharacteristic
401#95C22⋊D1111yescharacteristic
402#95C22⋊D1111yescharacteristic
403#95C22⋊D1111yescharacteristic
404C2×C11#232311yescharacteristic
405C2×C11#294611yescharacteristic
406C2×C11#294911yescharacteristic
407C2×C11#324111yescharacteristic
408C2×C11#324411yescharacteristic
409C2×C11#325711yescharacteristic
410C2×C11#326311yescharacteristic
411D11—82no—
412C24—221no—
413C2×Q8—24no—
414C2×Q8—81no—
415C2×Q8—81no—
416C2×D4—112no—
417C2×D4—221no—
418C2×D4—221no—
419C2×D4—221no—
420C2×D4—221no—
421C2×D4—221no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—221no—
427C22×C4—224no—
428C22×C4—221no—
429C22×C4—221no—
430C22×C4—881no—
431C22×C4—881no—
432C22×C4C2×C22⋊D1111yescharacteristic
433C22×C4C2×C22⋊D1111yescharacteristic
434C22×C4C2×C22⋊D1111yescharacteristic
435C22×C4C2×C22⋊D1111yescharacteristic
436C22×C4C2×C22⋊D1111yescharacteristic
437C22×C4C2×C22⋊D1111yescharacteristic
438C22×C4C23×D1111yescharacteristic
439C2×C8—112no—
440C2×C8—112no—
441C2×C8—221no—
442C2×C8—221no—
443C2×C8—221no—
444C2×C8—221no—
445C2×C8—221no—
446C2×C8—221no—
447C2×C8—221no—
448C2×C8—221no—
449C2×C8—221no—
450C2×C8—221no—
451C4⋊C4—24no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—81no—
459C4⋊C4—81no—
460C4⋊C4—112no—
461C4⋊C4—221no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C4⋊C4—221no—
465C4⋊C4—221no—
466C4⋊C4—881no—
467C4⋊C4—881no—
468C4⋊C4C2×C4×D1112yes—
469C4⋊C4C2×C4×D1112yes—
470C22⋊C4—224no—
471C22⋊C4—881no—
472C22⋊C4—881no—
473C22⋊C4—881no—
474C22⋊C4—881no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—81no—
480C42—81no—
481C42—881no—
482C42C2×C4×D1112yes—
483C42#433912yes—
484C11#2212311yescharacteristic, complemented, Sylow
485C23—222no—
486C23—441no—
487C23—441no—
488C23—441no—
489C23—441no—
490C23—441no—
491C23—441no—
492C23C22×C22⋊D1111yescharacteristic
493Q8—84no—
494D4—222no—
495D4—222no—
496D4—441no—
497D4—441no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
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—884no—
536C2×C4C4×C22⋊D1112yes—
537C2×C4C4×C22⋊D1112yes—
538C2×C4C22×C4×D1111yescharacteristic
539C2×C4C2×#433911yescharacteristic
540C2×C4#6704011yescharacteristic
541C2×C4#6704011yescharacteristic
542C2×C4#6704211yescharacteristic
543C2×C4#6704311yescharacteristic
544C8—222no—
545C8—222no—
546C8—441no—
547C8—441no—
548C22—442no—
549C22—442no—
550C22—442no—
551C22—881no—
552C22—881no—
553C22—881no—
554C22—881no—
555C22C2×C4×C22⋊D1111yescharacteristic
556C22#1062334711yescharacteristic
557C22#1062336411yescharacteristic
558C22#1062336611yescharacteristic
559C22#1062336711yescharacteristic
560C22#1062336811yescharacteristic
561C22#1062336811yescharacteristic
562C4—22no—
563C4—22no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—42no—
568C4—42no—
569C4—41no—
570C4—81no—
571C4—81no—
572C4—442no—
573C4—881no—
574C4—881no—
575C4#1062310311yescharacteristic
576C4#1062310511yescharacteristic
577C4#1062311311yescharacteristic
578C4#1062311411yescharacteristic
579C2—882no—
580C2#1307129211yescharacteristic
581C2#1307744811yescharacteristic
582C2#1307747511yescharacteristic
583C2#1307986911yescharacteristic
584C2#1307991411yescharacteristic
585C2#1308002711yescharacteristic
586C2#1308008111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2331C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#2331D11
hypocenterC11#22123
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ #376 ◁ #2331

Complements

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

NH ≅ G/Ntype
3. #13069569C2semidirect
4. #13069382C2semidirect
5. #13069356C2semidirect
6. #13069341C2semidirect
11. #13069201C2semidirect
12. #13069194C2semidirect
14. #13068473C2semidirect
15. C11×#2331C2semidirect
28. #10622697C4semidirect
193. #2331D11semidirect
484. C11#22123semidirect

Maximal subgroups

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

subgroupindex
C2×#106226972
#130712602
#130695692
#130693822
#130693562
#130693412
#130693122
#130692982
#130692432
#130692362
#130692012
#130691942
#130686232
#130684732
C11×#23312
#2212311