Finite Group Databasebeta

← #14826392

Subgroups — #14826392

Order 2816.

690 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
1#13072484C211yesmaximal, characteristic
2#13071714C211yesmaximal, characteristic, complemented
3#13070003C211yesmaximal, characteristic
4#13069957C211yesmaximal, characteristic, complemented
5#13069951C211yesmaximal, characteristic, complemented
6#13069761C211yesmaximal, characteristic
7#13069358C211yesmaximal, characteristic, complemented
8#13069243C211yesmaximal, characteristic
9#13069234C211yesmaximal, characteristic
10#13069197C211yesmaximal, characteristic, complemented
11#13069186C211yesmaximal, characteristic, complemented
12#13069177C211yesmaximal, characteristic, complemented
13#13068878C211yesmaximal, characteristic
14#13068440C211yesmaximal, characteristic
15C11×#1989C211yesmaximal, characteristic, complemented
16C2×C11×#125C2211yescharacteristic
17C2×#66946C2211yescharacteristic
18C2×#66943C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20C4×C11×C4⋊C4C2211yescharacteristic
21C2×#66885C2211yescharacteristic
22C2×#66885C2211yescharacteristic
23C2×#66882C2211yescharacteristic
24C2×#66879C2211yescharacteristic
25#10622607—21no—
26#10622605—21no—
27#10622602—21no—
28#10622601C2211yescharacteristic
29#10622600—21no—
30#10622598C2211yescharacteristic
31#10622598C2211yescharacteristic
32C4⋊C4×Dic11C2211yescharacteristic
33C4⋊C4×Dic11C2211yescharacteristic
34#10622586C2211yescharacteristic
35C2×#66873C2211yescharacteristic
36C2×#66873C2211yescharacteristic
37C2×#66872C2211yescharacteristic
38C2×#66872C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40#10622552C2211yescharacteristic
41C4×C4⋊Dic11—21no—
42#10622546—21no—
43C4×Dic11⋊C4C2211yescharacteristic
44#10622541C2211yescharacteristic
45#10622267—21no—
46#10622260—21no—
47C11×#340C2211yescharacteristic
48C11×#340C2211yescharacteristic
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D44C2311yescharacteristic
60C22×C4×D11—21no—
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C11×#125—22no—
64C11×#125—41no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C42×C11—21no—
72C2×C42×C11C2311yescharacteristic
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4D411yescharacteristic
88C2×Dic11⋊C4D411yescharacteristic
89C2×C4×Dic11—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11C2311yescharacteristic
92C2×C4×Dic11C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95#66946—22no—
96#66946—41no—
97#66943—22no—
98#66943—22no—
99C11×C4⋊C8—41no—
100C11×#95—21no—
101C11⋊#95—21no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95D411yescharacteristic
108C11⋊#95D411yescharacteristic
109#66885—22no—
110#66885—41no—
111#66882—22no—
112#66879—41no—
113#66873—22no—
114#66873Q814yes—
115#66872—22no—
116#66872—22no—
117#66871—41no—
118#27027—111nomaximal, Sylow
119C23×D11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2411yescharacteristic
127C22×Dic11—21no—
128C22×Dic11—21no—
129C22×Dic11—21no—
130C22×Dic11C2×D411yescharacteristic
131C22×Dic11C2×D411yescharacteristic
132C22×Dic11C2×D411yescharacteristic
133C22×Dic11C2×D411yescharacteristic
134C2×D44—21no—
135C2×D44—21no—
136C2×D44—21no—
137C2×D44—21no—
138C2×D44—21no—
139C2×D44C2×Q812yes—
140C2×C4×D11—42no—
141C2×C4×D11—42no—
142C2×C4×D11—81no—
143C2×C8×C11—21no—
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—42no—
155C11×C4⋊C4—42no—
156C11×C4⋊C4C2×Q812yes—
157C11×C4⋊C4#4112yes—
158C11×C4⋊C4#4112yes—
159C42×C11—21no—
160C42×C11—21no—
161C42×C11—42no—
162(C2×D11)⋊C4—42no—
163(C2×D11)⋊C4—42no—
164(C2×D11)⋊C4—81no—
165(C2×D11)⋊C4—81no—
166(C2×D11)⋊C4—81no—
167C4⋊Dic11—24no—
168C4⋊Dic11—21no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—42no—
174C4⋊Dic11—81no—
175C4⋊Dic11#4112yes—
176Dic11⋊C4—24no—
177Dic11⋊C4—41no—
178Dic11⋊C4—41no—
179Dic11⋊C4—81no—
180Dic11⋊C4—81no—
181C4×Dic11—21no—
182C4×Dic11—21no—
183C4×Dic11—21no—
184C4×Dic11—21no—
185C4×Dic11—81no—
186C4×Dic11—81no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8C2×Q812yes—
193#2454—111no—
194#2370—111no—
195#2067—111no—
196#2059—111no—
197#2059—111no—
198#2025—111no—
199#1989D1111yescharacteristic, complemented
200#1944—111no—
201#1926—111no—
202#1925—111no—
203#1919—111no—
204#1918—111no—
205#1917—111no—
206#1864—111no—
207#1762—111no—
208C23×C11C22×D411yescharacteristic
209C22×D11—22no—
210C22×D11—41no—
211C22×D11—41no—
212C22×D11—41no—
213C22×D11—41no—
214C22×D11—41no—
215C22×D11—41no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—22no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
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—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11C22×Q811yescharacteristic
235C2×C4×C11C2×#4111yescharacteristic
236C2×C4×C11C2×#4111yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C2×C4×C11H(5,𝔽2)11yescharacteristic
239C2×C4×C112−1+411yescharacteristic
240C2×Dic11—21no—
241C2×Dic11—21no—
242C2×Dic11—22no—
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—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—
266C8×C11—41no—
267C8×C11—41no—
268C11⋊C8—22no—
269C11⋊C8—41no—
270C2×#125—111no—
271C2×#125C2×D1111yescharacteristic
272C2×C4×D4—111no—
273C2×#107—111no—
274C2×#107—111no—
275C2×#106—111no—
276C2×#106—111no—
277C2×C4⋊C8C2×D1111yescharacteristic
278C2×#102—111no—
279C2×#102—111no—
280C2×#102—111no—
281C2×#102—111no—
282C2×#97—111no—
283#399—221no—
284#396—221no—
285#390—111no—
286#390—111no—
287#389—111no—
288#389—111no—
289#389—111no—
290#389—111no—
291#389—221no—
292#387—221no—
293#387—221no—
294#385—221no—
295#380—221no—
296C4×C4⋊C4—111no—
297C4×C4⋊C4—111no—
298C4×C4⋊C4—111no—
299C4×C4⋊C4—221no—
300C4×C4⋊C4C2×D1111yescharacteristic
301#340—111no—
302#340—111no—
303#340—111no—
304#340—111no—
305#340C2×D1111yescharacteristic
306#340C2×D1111yescharacteristic
307#340C2×D1111yescharacteristic
308#340C2×D1111yescharacteristic
309#336—111no—
310#336—111no—
311#336—111no—
312#336—111no—
313C22×C11#52511yescharacteristic
314C22×C11#54611yescharacteristic
315C22×C11D4×Q811yescharacteristic
316C22×C11#57511yescharacteristic
317C22×C11#57511yescharacteristic
318C22×C11#57611yescharacteristic
319C22×C11#57711yescharacteristic
320C2×D11—42no—
321C2×D11—42no—
322C2×D11—42no—
323C2×D11—81no—
324C2×D11—81no—
325C2×D11—81no—
326C2×D11—81no—
327C4×C11—42no—
328C4×C11—42no—
329C4×C11—41no—
330C4×C11—41no—
331C4×C11—42no—
332C4×C11—81no—
333C4×C11#53311yescharacteristic
334C4×C11#54211yescharacteristic
335C4×C11#55411yescharacteristic
336C4×C11#55611yescharacteristic
337Dic11—41no—
338Dic11—41no—
339Dic11—42no—
340Dic11—41no—
341Dic11—41no—
342Dic11—81no—
343Dic11—81no—
344C22×D4—111no—
345C23×C4—221no—
346C22×C8—111no—
347C22×C8—111no—
348C22×C8C22×D1111yescharacteristic
349C22×C8C22×D1111yescharacteristic
350#125—22no—
351#125—41no—
352#125—222no—
353#125—222no—
354C4×D4—222no—
355C4×D4—441no—
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—111no—
363C2×C4⋊C4—221no—
364C2×C4⋊C4—221no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4C22×D1111yescharacteristic
370C2×C4⋊C4C22×D1111yescharacteristic
371C2×C4⋊C4C22×D1111yescharacteristic
372C2×C4⋊C4C22×D1111yescharacteristic
373C2×C22⋊C4—221no—
374C2×C22⋊C4—221no—
375C2×C22⋊C4—221no—
376C2×C22⋊C4—221no—
377C2×C22⋊C4—221no—
378C2×C42—21no—
379C2×C42—111no—
380C2×C42—111no—
381C2×C42—221no—
382C2×C42—221no—
383C2×C42C22×D1111yescharacteristic
384#107—222no—
385#107—441no—
386#106—222no—
387#106—222no—
388C4⋊C8—41no—
389#102—114no—
390#102—222no—
391#102—222no—
392#102—441no—
393#97—441no—
394#95—21no—
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#246511yescharacteristic
404C2×C11#311111yescharacteristic
405C2×C11#311911yescharacteristic
406C2×C11#330911yescharacteristic
407C2×C11#332311yescharacteristic
408C2×C11#338811yescharacteristic
409C2×C11#338911yescharacteristic
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—442no—
430C22×C4—442no—
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—21no—
440C2×C8—21no—
441C2×C8—112no—
442C2×C8—221no—
443C2×C8—221no—
444C2×C8—221no—
445C2×C8—221no—
446C2×C8—221no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—42no—
453C4⋊C4—42no—
454C4⋊C4—112no—
455C4⋊C4—224no—
456C4⋊C4—224no—
457C4⋊C4—221no—
458C4⋊C4—221no—
459C4⋊C4—221no—
460C4⋊C4—221no—
461C4⋊C4—221no—
462C4⋊C4—441no—
463C4⋊C4—441no—
464C4⋊C4—442no—
465C4⋊C4—881no—
466C4⋊C4—881no—
467C4⋊C4—881no—
468C4⋊C4#433912yes—
469C4⋊C4Q8×D1112yes—
470C4⋊C4#434312yes—
471C22⋊C4—442no—
472C22⋊C4—442no—
473C22⋊C4—881no—
474C22⋊C4—881no—
475C22⋊C4—881no—
476C42—21no—
477C42—21no—
478C42—42no—
479C42—221no—
480C42—221no—
481C42—221no—
482C42—221no—
483C42—881no—
484C42—881no—
485C11#2702711yescharacteristic, complemented, Sylow
486C23—222no—
487C23—441no—
488C23—441no—
489C23—441no—
490C23—441no—
491C23—441no—
492C23—441no—
493C23C2×D4×D1111yescharacteristic
494D4—222no—
495D4—222no—
496D4—441no—
497D4—441no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—22no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—221no—
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—221no—
528C2×C4—222no—
529C2×C4—441no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4—884no—
538C2×C4C2×#433911yescharacteristic
539C2×C4#6703711yescharacteristic
540C2×C4C2×Q8×D1111yescharacteristic
541C2×C4C2×#434311yescharacteristic
542C2×C4#41×D1111yescharacteristic
543C2×C4#6704311yescharacteristic
544C8—41no—
545C8—41no—
546C8—222no—
547C8—441no—
548C22—442no—
549C22—442no—
550C22—442no—
551C22—881no—
552C22—881no—
553C22—881no—
554C22—881no—
555C22#1062302111yescharacteristic
556C22#1062315811yescharacteristic
557C22#1062316311yescharacteristic
558C22#1062329911yescharacteristic
559C22#1062330011yescharacteristic
560C22#1062330411yescharacteristic
561C22#1062330911yescharacteristic
562C4—41no—
563C4—42no—
564C4—41no—
565C4—42no—
566C4—42no—
567C4—81no—
568C4—441no—
569C4—441no—
570C4—442no—
571C4—441no—
572C4—441no—
573C4—881no—
574C4—881no—
575C4#1062310911yescharacteristic
576C4#1062311511yescharacteristic
577C4#1062320011yescharacteristic
578C4#1062326111yescharacteristic
579C2—882no—
580C2#1307264411yescharacteristic
581C2#1307873011yescharacteristic
582C2#1307882211yescharacteristic
583C2#1308061811yescharacteristic
584C2#1308083311yescharacteristic
585C2#1308155911yescharacteristic
586C2#1308157311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1989C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1989D11
hypocenterC11#27027
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1989

Complements

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

NH ≅ G/Ntype
2. #13071714C2semidirect
4. #13069957C2semidirect
5. #13069951C2semidirect
7. #13069358C2semidirect
10. #13069197C2semidirect
11. #13069186C2semidirect
12. #13069177C2semidirect
15. C11×#1989C2semidirect
199. #1989D11semidirect
485. C11#27027semidirect

Maximal subgroups

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

subgroupindex
#130724842
#130717142
#130700032
#130699572
#130699512
#130697612
#130693582
#130692432
#130692342
#130691972
#130691862
#130691772
#130688782
#130684402
C11×#19892
#2702711