Finite Group Databasebeta

← #14765975

Subgroups — #14765975

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×#10622621C211yesmaximal, characteristic
2#13071364C211yesmaximal, characteristic, complemented
3#13069568C211yesmaximal, characteristic, complemented
4#13069384C211yesmaximal, characteristic, complemented
5#13069356C211yesmaximal, characteristic, complemented
6#13069341C211yesmaximal, characteristic, complemented
7#13069316C211yesmaximal, characteristic
8#13069302C211yesmaximal, characteristic
9#13069240C211yesmaximal, characteristic
10#13069233C211yesmaximal, characteristic
11#13069198C211yesmaximal, characteristic, complemented
12#13069191C211yesmaximal, characteristic, complemented
13#13068626C211yesmaximal, characteristic
14#13068473C211yesmaximal, characteristic, complemented
15C11×#2319C211yesmaximal, characteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×#66922C2211yescharacteristic
18C11×#390C2211yescharacteristic
19C11×#390C2211yescharacteristic
20C11×#389C2211yescharacteristic
21C11×#389C2211yescharacteristic
22C11×#388—21no—
23C11×#388—21no—
24C11×#381—21no—
25C11×#380—21no—
26C4×C11×C4⋊C4C2211yescharacteristic
27C11×#376C2211yescharacteristic
28C2×#66896C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32#10622621C418yescomplemented
33C2×#66872C2211yescharacteristic
34C2×#66872C2211yescharacteristic
35C2×#66872C2211yescharacteristic
36C2×#66871C2211yescharacteristic
37#10622549C2211yescharacteristic
38C4×C4⋊Dic11C2211yescharacteristic
39C4×C4⋊Dic11C2211yescharacteristic
40#10622541C2211yescharacteristic
41#10622541C2211yescharacteristic
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44C2×#66867C2211yescharacteristic
45C2×C4×C11⋊C8C2211yescharacteristic
46#10622267—21no—
47#10622267—21no—
48#10622259—21no—
49#10622259—21no—
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C22×Dic22—21no—
63C4×D4×C11—22no—
64C4×D4×C11C2×C414yes—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C22⋊C4—21no—
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—21no—
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—21no—
75C2×C42×C11—21no—
76C2×C42×C11C2311yescharacteristic
77C2×C42×C11C2311yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11—21no—
88C22×C11⋊C8C2311yescharacteristic
89C22×C11⋊C8C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92#66922—22no—
93#66922C2×C414yes—
94C11×#95—21no—
95C11×#95—21no—
96C11×#95—21no—
97C11×#95D411yescharacteristic
98C11×#95D411yescharacteristic
99C11×#95D411yescharacteristic
100C11×#95D411yescharacteristic
101#66896—41no—
102#66896—41no—
103#66896C2×C414yes—
104#66896C2×C414yes—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
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
120C24×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11C22×C412yes—
127C22×C4×C11—21no—
128C22×C4×C11—24no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—81no—
132C22×C4×C11—81no—
133C22×C4×C11C2×D411yescharacteristic
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—
144C2×Dic22—24no—
145C2×Dic22—81no—
146C2×Dic22—81no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—81no—
153C11×C4⋊C4—81no—
154C11×C4⋊C4C22×C412yes—
155C11×C22⋊C4—24no—
156C11×C22⋊C4—81no—
157C11×C22⋊C4—81no—
158C11×C22⋊C4—81no—
159C11×C22⋊C4—81no—
160C42×C11—21no—
161C42×C11—21no—
162C42×C11—21no—
163C42×C11—21no—
164C42×C11—81no—
165C42×C11C22×C412yes—
166C42×C11#4112yes—
167C4⋊Dic11—24no—
168C4⋊Dic11—21no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11C22×C412yes—
175C4⋊Dic11C22×C412yes—
176Dic11⋊C4—81no—
177Dic11⋊C4—81no—
178C4×Dic11—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#2331—111no—
194#2319D1111yescharacteristic
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×C11—22no—
208C23×C11—41no—
209C23×C11—41no—
210C23×C11—41no—
211C23×C11—41no—
212C23×C11—41no—
213C23×C11—41no—
214C23×C11C22×D411yescharacteristic
215D4×C11—22no—
216D4×C11—22no—
217D4×C11—41no—
218D4×C11—41no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—22no—
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—21no—
235C2×C4×C11—21no—
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×C11—84no—
245C2×C4×C11C4×D412yes—
246C2×C4×C11C4×D412yes—
247C2×C4×C11C23×C411yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11H(5,𝔽2)11yescharacteristic
250C2×C4×C112−1+411yescharacteristic
251C2×C4×C112−1+411yescharacteristic
252C2×C4×C112−1+411yescharacteristic
253C2×Dic11—22no—
254C2×Dic11—22no—
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—
265Dic22—84no—
266C11⋊C8—22no—
267C11⋊C8—22no—
268C11⋊C8—41no—
269C11⋊C8—41no—
270C2×C4⋊Q8—111no—
271C2×C4×D4C2×D1111yescharacteristic
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—221no—
286#391—221no—
287#390C2×D1111yescharacteristic
288#390C2×D1111yescharacteristic
289#389—111no—
290#389—111no—
291#389C2×D1111yescharacteristic
292#389C2×D1111yescharacteristic
293#388—21no—
294#388—21no—
295#387—221no—
296#387—221no—
297#382—111no—
298#381—21no—
299#380—21no—
300C4×C4⋊C4—111no—
301C4×C4⋊C4—111no—
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×C11—42no—
315C22×C11—42no—
316C22×C11—42no—
317C22×C11—81no—
318C22×C11—81no—
319C22×C11—81no—
320C22×C11—81no—
321C22×C11C2×C4×D411yescharacteristic
322C22×C11#53611yescharacteristic
323C22×C11#53711yescharacteristic
324C22×C11#57611yescharacteristic
325C22×C11#57711yescharacteristic
326C22×C11#57711yescharacteristic
327C22×C11#57711yescharacteristic
328C4×C11—22no—
329C4×C11—22no—
330C4×C11—42no—
331C4×C11—41no—
332C4×C11—41no—
333C4×C11—41no—
334C4×C11—41no—
335C4×C11—81no—
336C4×C11—81no—
337C4×C11#51911yescharacteristic
338C4×C11#52011yescharacteristic
339C4×C11#54111yescharacteristic
340C4×C11#54211yescharacteristic
341Dic11—42no—
342Dic11—42no—
343Dic11—81no—
344Dic11—81no—
345C22×Q8—221no—
346C22×D4C22×D1111yescharacteristic
347C23×C4—21no—
348C22×C8—111no—
349C22×C8—111no—
350C22×C8—111no—
351C22×C8—111no—
352C4⋊Q8—114no—
353C4⋊Q8—222no—
354C4×D4—22no—
355C4×D4C4×D1114yes—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—111no—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—111no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—221no—
363C2×C4⋊C4—221no—
364C2×C4⋊C4—221no—
365C2×C4⋊C4C22×D1111yescharacteristic
366C2×C4⋊C4C22×D1111yescharacteristic
367C2×C4⋊C4C22×D1111yescharacteristic
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C42—21no—
374C2×C42—221no—
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—221no—
395#95—221no—
396#95—221no—
397#95—221no—
398#95—221no—
399#95—221no—
400#95C22⋊D1111yescharacteristic
401#95C22⋊D1111yescharacteristic
402#95C22⋊D1111yescharacteristic
403#95C22⋊D1111yescharacteristic
404C2×C11—82no—
405C2×C11#232311yescharacteristic
406C2×C11#294611yescharacteristic
407C2×C11#294911yescharacteristic
408C2×C11#324111yescharacteristic
409C2×C11#324411yescharacteristic
410C2×C11#325711yescharacteristic
411C2×C11#326311yescharacteristic
412C24—21no—
413C2×Q8—224no—
414C2×Q8—881no—
415C2×Q8—881no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4C2×C4×D1112yes—
422C22×C4—21no—
423C22×C4—24no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—81no—
427C22×C4—81no—
428C22×C4—221no—
429C22×C4—221no—
430C22×C4—221no—
431C22×C4—221no—
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—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—81no—
457C4⋊C4—81no—
458C4⋊C4—112no—
459C4⋊C4—112no—
460C4⋊C4—224no—
461C4⋊C4—221no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C4⋊C4—221no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—881no—
468C4⋊C4—881no—
469C4⋊C4C2×C4×D1112yes—
470C22⋊C4—24no—
471C22⋊C4—81no—
472C22⋊C4—81no—
473C22⋊C4—81no—
474C22⋊C4—81no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—81no—
480C42—881no—
481C42—881no—
482C42C2×C4×D1112yes—
483C42#433912yes—
484C11#2212311yescharacteristic, complemented, Sylow
485C23—22no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23C22×C22⋊D1111yescharacteristic
493Q8—884no—
494D4—22no—
495D4—22no—
496D4—41no—
497D4—41no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—21no—
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—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—84no—
524C2×C4—222no—
525C2×C4—222no—
526C2×C4—441no—
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×C4C4×C22⋊D1112yes—
537C2×C4C4×C22⋊D1112yes—
538C2×C4C22×C4×D1111yescharacteristic
539C2×C4C2×#433911yescharacteristic
540C2×C4#6704211yescharacteristic
541C2×C4#6704311yescharacteristic
542C2×C4#6704311yescharacteristic
543C2×C4#6704311yescharacteristic
544C8—222no—
545C8—222no—
546C8—441no—
547C8—441no—
548C22—42no—
549C22—42no—
550C22—42no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22—81no—
555C22C2×C4×C22⋊D1111yescharacteristic
556C22#1062335611yescharacteristic
557C22#1062336411yescharacteristic
558C22#1062336611yescharacteristic
559C22#1062336711yescharacteristic
560C22#1062336711yescharacteristic
561C22#1062336811yescharacteristic
562C4—22no—
563C4—22no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—42no—
569C4—81no—
570C4—81no—
571C4—442no—
572C4—442no—
573C4—881no—
574C4—881no—
575C4#1062304711yescharacteristic
576C4#1062304911yescharacteristic
577C4#1062305411yescharacteristic
578C4#1062306511yescharacteristic
579C2—82no—
580C2#1307129811yescharacteristic
581C2#1307744411yescharacteristic
582C2#1307747311yescharacteristic
583C2#1307986311yescharacteristic
584C2#1307990811yescharacteristic
585C2#1308002111yescharacteristic
586C2#1308008111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2319C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenter#2319D11
hypocenterC11#22123
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ #376 ◁ #2319

Complements

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

NH ≅ G/Ntype
2. #13071364C2semidirect
3. #13069568C2semidirect
4. #13069384C2semidirect
5. #13069356C2semidirect
6. #13069341C2semidirect
11. #13069198C2semidirect
12. #13069191C2semidirect
14. #13068473C2semidirect
32. #10622621C4semidirect
484. C11#22123semidirect

Maximal subgroups

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

subgroupindex
C2×#106226212
#130713642
#130695682
#130693842
#130693562
#130693412
#130693162
#130693022
#130692402
#130692332
#130691982
#130691912
#130686262
#130684732
C11×#23192
#2212311