Finite Group Databasebeta

← #14766018

Subgroups — #14766018

Order 2816.

732 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622460C211yesmaximal, characteristic
2#13071355C211yesmaximal, characteristic, complemented
3#13071254C211yesmaximal, characteristic
4#13069573C211yesmaximal, characteristic, complemented
5#13069357C211yesmaximal, characteristic, complemented
6#13069347C211yesmaximal, characteristic, complemented
7#13069311C211yesmaximal, characteristic
8#13069297C211yesmaximal, characteristic
9#13069235C211yesmaximal, characteristic
10#13069235C211yesmaximal, characteristic
11#13069207C211yesmaximal, characteristic, complemented
12#13069193C211yesmaximal, characteristic, complemented
13#13068613C211yesmaximal, characteristic
14#13068475C211yesmaximal, characteristic, complemented
15C11×#1947C211yesmaximal, characteristic, complemented
16C2×C4×D44C2211yescharacteristic
17C2×#66923C2211yescharacteristic
18C2×C11×#107C2211yescharacteristic
19C2×C11×#107C2211yescharacteristic
20C2×C11×C4⋊C8C2211yescharacteristic
21C11×#384C2211yescharacteristic
22C4×C11×C4⋊C4C2211yescharacteristic
23C2×#66885C2211yescharacteristic
24C2×#66885C2211yescharacteristic
25C2×#66882C2211yescharacteristic
26C2×#66881C2211yescharacteristic
27C2×#66879C2211yescharacteristic
28C2×C8×Dic11C2211yescharacteristic
29#10622601C2211yescharacteristic
30#10622601C2211yescharacteristic
31#10622591—21no—
32#10622591—21no—
33C4⋊C4×Dic11C2211yescharacteristic
34C4⋊C4×Dic11C2211yescharacteristic
35#10622586C2211yescharacteristic
36#10622586C2211yescharacteristic
37#10622586C2211yescharacteristic
38#10622586C2211yescharacteristic
39#10622585—21no—
40#10622585—21no—
41C2×#66873C2211yescharacteristic
42C2×#66873C2211yescharacteristic
43#10622553—21no—
44#10622553—21no—
45#10622545C2211yescharacteristic
46C2×C4⋊(C11⋊C8)C2211yescharacteristic
47#10622460C418yescomplemented
48#10622280—21no—
49#10622277—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×D44C2311yescharacteristic
61C22×C4×D11—21no—
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C42×C11—21no—
71C2×C42×C11C2311yescharacteristic
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11C2311yescharacteristic
89C2×C4×Dic11C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C4×D44—22no—
93C4×D44C2×C414yes—
94#66923—22no—
95#66923C2×C414yes—
96C11×#107—41no—
97C11×#107—41no—
98C11×C4⋊C8C2×C414yes—
99C11×#95—21no—
100C11⋊#95—21no—
101C11⋊#95—21no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95D411yescharacteristic
107C11⋊#95D411yescharacteristic
108C11⋊#95D411yescharacteristic
109C11⋊#95D411yescharacteristic
110#66885C2×C414yes—
111#66885C2×C414yes—
112#66882C2×C414yes—
113#66881C2×C414yes—
114#66879—41no—
115C8×Dic11—41no—
116#66873—41no—
117#66873—41no—
118C4⋊(C11⋊C8)—22no—
119#22126—111nomaximal, Sylow
120C23×D11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2411yescharacteristic
128C22×Dic11—21no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11C2×D411yescharacteristic
132C22×Dic11C2×D411yescharacteristic
133C22×Dic11C2×D411yescharacteristic
134C22×Dic11C2×D411yescharacteristic
135C2×D44—21no—
136C2×D44—21no—
137C2×D44—21no—
138C2×D44—21no—
139C2×D44—21no—
140C2×D44C22×C412yes—
141C2×C4×D11—24no—
142C2×C4×D11—81no—
143C2×C4×D11—81no—
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11C22×C412yes—
149C2×C8×C11C22×C412yes—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—81no—
159C11×C4⋊C4—81no—
160C42×C11—81no—
161C42×C11C22×C412yes—
162C42×C11#4112yes—
163(C2×D11)⋊C4—24no—
164(C2×D11)⋊C4—81no—
165(C2×D11)⋊C4—81no—
166(C2×D11)⋊C4—81no—
167(C2×D11)⋊C4—81no—
168C4⋊Dic11—21no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11C22×C412yes—
172C4⋊Dic11C22×C412yes—
173C4⋊Dic11C22×C412yes—
174Dic11⋊C4—24no—
175Dic11⋊C4—24no—
176Dic11⋊C4—81no—
177Dic11⋊C4—81no—
178Dic11⋊C4—81no—
179Dic11⋊C4—81no—
180C4×Dic11—21no—
181C4×Dic11—21no—
182C4×Dic11—21no—
183C4×Dic11—21no—
184C4×Dic11—81no—
185C4×Dic11—81no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×#478—111no—
193#2330—111no—
194#2319—111no—
195#1989—111no—
196#1947D1111yescharacteristic, complemented
197#1944—111no—
198#1942—111no—
199#1936—111no—
200#1934—111no—
201#1925—111no—
202#1925—111no—
203#1921—111no—
204#1919—111no—
205#1802—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—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
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×C11C4×D412yes—
232C2×C4×C11C4×D412yes—
233C2×C4×C11C23×C411yescharacteristic
234C2×C4×C11C2×#4111yescharacteristic
235C2×C4×C11H(5,𝔽2)11yescharacteristic
236C2×C4×C112−1+411yescharacteristic
237C2×C4×C112−1+411yescharacteristic
238C2×C4×C112−1+411yescharacteristic
239C2×Dic11—22no—
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260D44—22no—
261D44—22no—
262D44—41no—
263D44—41no—
264C4×D11—84no—
265C8×C11—22no—
266C8×C11—22no—
267C11⋊C8—41no—
268C11⋊C8—41no—
269C2×#125—111no—
270C2×C4×D4—111no—
271#478—118no—
272C2×#107—111no—
273C2×#107C2×D1111yescharacteristic
274C2×#107C2×D1111yescharacteristic
275C2×#106—111no—
276C2×C4⋊C8—111no—
277C2×C4⋊C8C2×D1111yescharacteristic
278C2×#102—111no—
279C2×#102—111no—
280C2×#102—111no—
281C2×#102—111no—
282C2×#97—111no—
283C2×C4×C8—111no—
284#390—111no—
285#390—111no—
286#389—111no—
287#389—111no—
288#389—111no—
289#389—111no—
290#389—221no—
291#389—221no—
292#388—221no—
293#388—221no—
294#387—221no—
295#387—221no—
296#384C2×D1111yescharacteristic
297#381—221no—
298#380—221no—
299C4×C4⋊C4—111no—
300C4×C4⋊C4—111no—
301C4×C4⋊C4C2×D1111yescharacteristic
302#376—111no—
303#340—111no—
304#340—111no—
305#340—111no—
306#340—111no—
307#340—111no—
308#340—111no—
309#340C2×D1111yescharacteristic
310#340C2×D1111yescharacteristic
311#336—111no—
312#336—111no—
313C22×C11C2×C4×D411yescharacteristic
314C22×C11#53611yescharacteristic
315C22×C11#53711yescharacteristic
316C22×C11#57611yescharacteristic
317C22×C11#57611yescharacteristic
318C22×C11#57711yescharacteristic
319C22×C11#57811yescharacteristic
320C2×D11—42no—
321C2×D11—42no—
322C2×D11—42no—
323C2×D11—81no—
324C2×D11—81no—
325C2×D11—81no—
326C2×D11—81no—
327C4×C11—22no—
328C4×C11—22no—
329C4×C11—81no—
330C4×C11—81no—
331C4×C11—81no—
332C4×C11—81no—
333C4×C11#51911yescharacteristic
334C4×C11#52011yescharacteristic
335C4×C11#54111yescharacteristic
336C4×C11#54211yescharacteristic
337Dic11—42no—
338Dic11—42no—
339Dic11—42no—
340Dic11—41no—
341Dic11—41no—
342Dic11—41no—
343Dic11—41no—
344C22×D4—111no—
345C23×C4—221no—
346C22×C8—111no—
347C22×C8—111no—
348C22×C8C22×D1111yescharacteristic
349C22×C8C22×D1111yescharacteristic
350#125—114no—
351#125—222no—
352C4×D4—114no—
353C4×D4—222no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—111no—
357C2×C4⋊C4—111no—
358C2×C4⋊C4—111no—
359C2×C4⋊C4—221no—
360C2×C4⋊C4—221no—
361C2×C4⋊C4—221no—
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×C4⋊C4C22×D1111yescharacteristic
369C2×C22⋊C4—221no—
370C2×C22⋊C4—221no—
371C2×C22⋊C4—221no—
372C2×C22⋊C4—221no—
373C2×C22⋊C4—221no—
374C2×C42—21no—
375C2×C42—111no—
376C2×C42—111no—
377C2×C42—221no—
378C2×C42—221no—
379C2×C42C22×D1111yescharacteristic
380#107—41no—
381#107—41no—
382#107—114no—
383#106—114no—
384C4⋊C8—222no—
385C4⋊C8C4×D1114yes—
386#102—114no—
387#102—114no—
388#102—441no—
389#102—441no—
390#97—441no—
391C4×C8—441no—
392#95—21no—
393#95—111no—
394#95—111no—
395#95—111no—
396#95—111no—
397#95—221no—
398#95—221no—
399#95—221no—
400#95—221no—
401#95—221no—
402#95—221no—
403C2×C11#232311yescharacteristic
404C2×C11#294611yescharacteristic
405C2×C11#295111yescharacteristic
406C2×C11#324111yescharacteristic
407C2×C11#324311yescharacteristic
408C2×C11#325811yescharacteristic
409C2×C11#325911yescharacteristic
410D11—82no—
411C24—221no—
412C2×D4—112no—
413C2×D4—221no—
414C2×D4—221no—
415C2×D4—221no—
416C2×D4—221no—
417C2×D4—221no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—111no—
423C22×C4—111no—
424C22×C4—111no—
425C22×C4—111no—
426C22×C4—221no—
427C22×C4—221no—
428C22×C4—221no—
429C22×C4—224no—
430C22×C4—881no—
431C22×C4—881no—
432C22×C4D4×D1111yescharacteristic
433C22×C4D4×D1111yescharacteristic
434C22×C4C23×D1111yescharacteristic
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—221no—
440C2×C8—221no—
441C2×C8—221no—
442C2×C8—221no—
443C2×C8—221no—
444C2×C8—221no—
445C2×C8C2×C4×D1112yes—
446C2×C8C2×C4×D1112yes—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—81no—
456C4⋊C4—81no—
457C4⋊C4—112no—
458C4⋊C4—112no—
459C4⋊C4—112no—
460C4⋊C4—224no—
461C4⋊C4—224no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C4⋊C4—221no—
465C4⋊C4—881no—
466C4⋊C4—881no—
467C4⋊C4—881no—
468C4⋊C4—881no—
469C22⋊C4—224no—
470C22⋊C4—881no—
471C22⋊C4—881no—
472C22⋊C4—881no—
473C22⋊C4—881no—
474C42—81no—
475C42—221no—
476C42—221no—
477C42—221no—
478C42—221no—
479C42—881no—
480C42—881no—
481C42C2×C4×D1112yes—
482C42#434312yes—
483C11#2212611yescharacteristic, complemented, Sylow
484C23—222no—
485C23—441no—
486C23—441no—
487C23—441no—
488C23—441no—
489C23—441no—
490C23—441no—
491C23C2×D4×D1111yescharacteristic
492D4—222no—
493D4—222no—
494D4—441no—
495D4—441no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
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—221no—
513C2×C4—221no—
514C2×C4—222no—
515C2×C4—222no—
516C2×C4—222no—
517C2×C4—221no—
518C2×C4—221no—
519C2×C4—221no—
520C2×C4—221no—
521C2×C4—221no—
522C2×C4—221no—
523C2×C4—221no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—221no—
527C2×C4—441no—
528C2×C4—441no—
529C2×C4—441no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4—884no—
534C2×C4#6694612yes—
535C2×C4#6694612yes—
536C2×C4C22×C4×D1111yescharacteristic
537C2×C4#6703711yescharacteristic
538C2×C4C2×#434311yescharacteristic
539C2×C4#6704011yescharacteristic
540C2×C4#6704311yescharacteristic
541C2×C4#6704311yescharacteristic
542C8—22no—
543C8—22no—
544C8—441no—
545C8—441no—
546C22—442no—
547C22—442no—
548C22—442no—
549C22—881no—
550C22—881no—
551C22—881no—
552C22—881no—
553C22C2×#6694611yescharacteristic
554C22#1062313911yescharacteristic
555C22#1062315911yescharacteristic
556C22#1062328811yescharacteristic
557C22#1062329711yescharacteristic
558C22#1062330511yescharacteristic
559C22#1062330911yescharacteristic
560C4—22no—
561C4—22no—
562C4—81no—
563C4—81no—
564C4—81no—
565C4—81no—
566C4—441no—
567C4—441no—
568C4—442no—
569C4—442no—
570C4—441no—
571C4—442no—
572C4—441no—
573C4#1062307711yescharacteristic
574C4#1062310311yescharacteristic
575C4#1062322811yescharacteristic
576C4#1062326411yescharacteristic
577C2—882no—
578C2#1307129611yescharacteristic
579C2#1307744611yescharacteristic
580C2#1307749011yescharacteristic
581C2#1307987611yescharacteristic
582C2#1307990411yescharacteristic
583C2#1308004011yescharacteristic
584C2#1308005311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1947C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1947D11
hypocenterC11#22126
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1947

Complements

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

NH ≅ G/Ntype
2. #13071355C2semidirect
4. #13069573C2semidirect
5. #13069357C2semidirect
6. #13069347C2semidirect
11. #13069207C2semidirect
12. #13069193C2semidirect
14. #13068475C2semidirect
15. C11×#1947C2semidirect
47. #10622460C4semidirect
196. #1947D11semidirect
483. C11#22126semidirect

Maximal subgroups

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

subgroupindex
C2×#106224602
#130713552
#130712542
#130695732
#130693572
#130693472
#130693112
#130692972
#130692352
#130692072
#130691932
#130686132
#130684752
C11×#19472
#2212611