Finite Group Databasebeta

← #14826248

Subgroups — #14826248

Order 2816.

706 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072488C211yesmaximal, characteristic
2#13071705C211yesmaximal, characteristic, complemented
3#13070003C211yesmaximal, characteristic
4#13069955C211yesmaximal, characteristic, complemented
5#13069945C211yesmaximal, characteristic, complemented
6#13069753C211yesmaximal, characteristic
7#13069571C211yesmaximal, characteristic, complemented
8#13069354C211yesmaximal, characteristic, complemented
9#13069244C211yesmaximal, characteristic
10#13069237C211yesmaximal, characteristic
11#13069209C211yesmaximal, characteristic, complemented
12#13069188C211yesmaximal, characteristic, complemented
13#13068866C211yesmaximal, characteristic
14#13068442C211yesmaximal, characteristic
15C11×#1917C211yesmaximal, characteristic, complemented
16C2×C4×D44C2211yescharacteristic
17C2×#66923C2211yescharacteristic
18C2×#66922C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×#97C2211yescharacteristic
21C4×C11×C4⋊C4C2211yescharacteristic
22C2×#66885C2211yescharacteristic
23C2×#66885C2211yescharacteristic
24C2×#66885C2211yescharacteristic
25C2×#66885C2211yescharacteristic
26C2×#66882C2211yescharacteristic
27C2×#66882C2211yescharacteristic
28C2×#66882C2211yescharacteristic
29C2×#66881C2211yescharacteristic
30#10622605—21no—
31#10622602—21no—
32C4⋊C4×Dic11—21no—
33#10622586—21no—
34#10622552C2211yescharacteristic
35#10622552C2211yescharacteristic
36C4×C4⋊Dic11C2211yescharacteristic
37C4×C4⋊Dic11C2211yescharacteristic
38C4×C4⋊Dic11C2211yescharacteristic
39#10622541C2211yescharacteristic
40#10622541C2211yescharacteristic
41#10622541C2211yescharacteristic
42#10622541C2211yescharacteristic
43#10622289—21no—
44#10622280—21no—
45#10622259—21no—
46#10622259—21no—
47C11×#336C2211yescharacteristic
48C11×#336C2211yescharacteristic
49C11×#336C2211yescharacteristic
50C11×#336C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59C22×D44C2311yescharacteristic
60C22×C4×D11—21no—
61C22×Dic22—21no—
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C2×C11×C4⋊C4D411yescharacteristic
67C2×C11×C4⋊C4D411yescharacteristic
68C2×C42×C11C2311yescharacteristic
69C2×C42×C11C2311yescharacteristic
70C2×C42×C11C2311yescharacteristic
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C4×D44—22no—
94C4×D44—41no—
95#66923—22no—
96#66923—41no—
97#66922—22no—
98#66922—22no—
99C11×C4⋊C8—41no—
100C11×#97—41no—
101C11×#95D411yescharacteristic
102C11×#95D411yescharacteristic
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110#66885—22no—
111#66885—22no—
112#66885—41no—
113#66885Q814yescomplemented
114#66882—22no—
115#66882—22no—
116#66882—22no—
117#66881—41no—
118#27018—111nomaximal, Sylow
119C23×D11—21no—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2411yescharacteristic
127C22×Dic11—21no—
128C22×Dic11—21no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11—21no—
132C22×Dic11—21no—
133C22×Dic11—21no—
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×Dic22—24no—
144C2×Dic22—81no—
145C2×Dic22—81no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11C2×Q812yes—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—41no—
160C42×C11—21no—
161C42×C11—21no—
162C42×C11—21no—
163C42×C11—21no—
164C42×C11—21no—
165C42×C11—21no—
166(C2×D11)⋊C4—42no—
167(C2×D11)⋊C4—42no—
168(C2×D11)⋊C4—81no—
169(C2×D11)⋊C4—81no—
170(C2×D11)⋊C4—81no—
171C4⋊Dic11—24no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11C2×Q812yes—
183C4⋊Dic11#4112yes—
184C4⋊Dic11#4112yes—
185C4⋊Dic11#4112yes—
186Dic11⋊C4—42no—
187Dic11⋊C4—42no—
188Dic11⋊C4—81no—
189Dic11⋊C4—81no—
190Dic11⋊C4—81no—
191Dic11⋊C4—81no—
192C4×Dic11—42no—
193C4×Dic11—81no—
194C4×Dic11—81no—
195#2454—111no—
196#2369—111no—
197#2067—111no—
198#2059—111no—
199#2057—111no—
200#2023—111no—
201#1989—111no—
202#1943—111no—
203#1926—111no—
204#1925—111no—
205#1921—111no—
206#1918—111no—
207#1917D1111yescharacteristic, complemented
208#1862—111no—
209#1762—111no—
210C23×C11C22×D411yescharacteristic
211C22×D11—22no—
212C22×D11—41no—
213C22×D11—41no—
214C22×D11—41no—
215C22×D11—41no—
216C22×D11—41no—
217C22×D11—41no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
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—21no—
235C2×C4×C11#13712yes—
236C2×C4×C11C22×Q811yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C2×C4×C11H(5,𝔽2)11yescharacteristic
241C2×C4×C112−1+411yescharacteristic
242C2×Dic11—22no—
243C2×Dic11—22no—
244C2×Dic11—22no—
245C2×Dic11—22no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248C2×Dic11—41no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263D44—22no—
264D44—22no—
265D44—41no—
266D44—41no—
267C4×D11—84no—
268Dic22—84no—
269C8×C11—22no—
270C8×C11—41no—
271C8×C11—41no—
272C8×C11—41no—
273C2×C4⋊Q8—111no—
274C2×#125—111no—
275C2×C4×D4—111no—
276C2×#107—111no—
277C2×#107—111no—
278C2×#107—111no—
279C2×#106—111no—
280C2×C4⋊C8C2×D1111yescharacteristic
281C2×#102—111no—
282C2×#102—111no—
283C2×#102—111no—
284C2×#102—111no—
285C2×#97C2×D1111yescharacteristic
286#399—221no—
287#396—221no—
288#391—221no—
289#391—221no—
290#390—111no—
291#390—111no—
292#389—111no—
293#389—111no—
294#389—111no—
295#389—111no—
296#389—221no—
297#385—221no—
298#380—221no—
299C4×C4⋊C4—111no—
300C4×C4⋊C4—111no—
301C4×C4⋊C4—111no—
302C4×C4⋊C4—221no—
303C4×C4⋊C4C2×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#336C2×D1111yescharacteristic
313#336C2×D1111yescharacteristic
314#336C2×D1111yescharacteristic
315#336C2×D1111yescharacteristic
316C22×C11#52511yescharacteristic
317C22×C11#54611yescharacteristic
318C22×C11D4×Q811yescharacteristic
319C22×C11C2×#13711yescharacteristic
320C22×C11#57511yescharacteristic
321C22×C11#57611yescharacteristic
322C22×C11#57611yescharacteristic
323C2×D11—42no—
324C2×D11—42no—
325C2×D11—42no—
326C2×D11—81no—
327C2×D11—81no—
328C2×D11—81no—
329C2×D11—81no—
330C4×C11—22no—
331C4×C11—41no—
332C4×C11—41no—
333C4×C11—41no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11#53311yescharacteristic
337C4×C11#54211yescharacteristic
338C4×C11#55411yescharacteristic
339C4×C11#55611yescharacteristic
340Dic11—42no—
341Dic11—42no—
342Dic11—42no—
343Dic11—42no—
344Dic11—81no—
345Dic11—81no—
346Dic11—81no—
347C22×Q8—221no—
348C22×D4—111no—
349C23×C4—221no—
350C22×C8C22×D1111yescharacteristic
351C22×C8C22×D1111yescharacteristic
352C22×C8C22×D1111yescharacteristic
353C22×C8C22×D1111yescharacteristic
354C4⋊Q8—222no—
355C4⋊Q8—222no—
356#125—222no—
357#125—441no—
358C4×D4—222no—
359C4×D4—441no—
360C2×C4⋊C4—111no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—111no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—111no—
366C2×C4⋊C4—111no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4D4411yescharacteristic
375C2×C4⋊C4D4411yescharacteristic
376C2×C22⋊C4—221no—
377C2×C22⋊C4—221no—
378C2×C22⋊C4—221no—
379C2×C22⋊C4—221no—
380C2×C22⋊C4—221no—
381C2×C42—221no—
382C2×C42—221no—
383C2×C42—221no—
384C2×C42C22×D1111yescharacteristic
385C2×C42C22×D1111yescharacteristic
386C2×C42C22×D1111yescharacteristic
387#107—222no—
388#107—222no—
389#107—222no—
390#106—441no—
391C4⋊C8—41no—
392#102—114no—
393#102—222no—
394#102—222no—
395#102—441no—
396#97—41no—
397#95—221no—
398#95—221no—
399#95—221no—
400#95—221no—
401#95—221no—
402#95—221no—
403#95—221no—
404#95D4411yescharacteristic
405#95D4411yescharacteristic
406C2×C11#246511yescharacteristic
407C2×C11#311711yescharacteristic
408C2×C11#312211yescharacteristic
409C2×C11#331911yescharacteristic
410C2×C11#333311yescharacteristic
411C2×C11#338511yescharacteristic
412C2×C11#338911yescharacteristic
413D11—82no—
414C24—221no—
415C2×Q8—224no—
416C2×Q8—881no—
417C2×Q8—881no—
418C2×D4—112no—
419C2×D4—221no—
420C2×D4—221no—
421C2×D4—221no—
422C2×D4—221no—
423C2×D4—221no—
424C22×C4—221no—
425C22×C4—221no—
426C22×C4—221no—
427C22×C4—221no—
428C22×C4—221no—
429C22×C4—221no—
430C22×C4—221no—
431C22×C4—442no—
432C22×C4—442no—
433C22×C4—881no—
434C22×C4C2×D4411yescharacteristic
435C22×C4C2×D4411yescharacteristic
436C22×C4C2×D4411yescharacteristic
437C22×C4C2×D4411yescharacteristic
438C22×C4C2×D4411yescharacteristic
439C22×C4C2×D4411yescharacteristic
440C22×C4C23×D1111yescharacteristic
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8Q8×D1112yes—
453C4⋊C4—22no—
454C4⋊C4—41no—
455C4⋊C4—112no—
456C4⋊C4—112no—
457C4⋊C4—112no—
458C4⋊C4—112no—
459C4⋊C4—224no—
460C4⋊C4—221no—
461C4⋊C4—221no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C4⋊C4—221no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—442no—
471C4⋊C4—442no—
472C4⋊C4—881no—
473C4⋊C4—881no—
474C4⋊C4—881no—
475C4⋊C4—881no—
476C22⋊C4—442no—
477C22⋊C4—442no—
478C22⋊C4—881no—
479C22⋊C4—881no—
480C22⋊C4—881no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—442no—
488C42—881no—
489C42—881no—
490C11#2701811yescharacteristic, complemented, Sylow
491C23—222no—
492C23—441no—
493C23—441no—
494C23—441no—
495C23—441no—
496C23—441no—
497C23—441no—
498C23C22×D4411yescharacteristic
499Q8—884no—
500D4—222no—
501D4—222no—
502D4—441no—
503D4—441no—
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—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—222no—
522C2×C4—222no—
523C2×C4—222no—
524C2×C4—222no—
525C2×C4—441no—
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×C4—441no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4—441no—
540C2×C4—441no—
541C2×C4—441no—
542C2×C4—884no—
543C2×C4#6696212yes—
544C2×C4#6703711yescharacteristic
545C2×C4C2×Q8×D1111yescharacteristic
546C2×C4#41×D1111yescharacteristic
547C2×C4#41×D1111yescharacteristic
548C2×C4#41×D1111yescharacteristic
549C2×C4#6704311yescharacteristic
550C8—22no—
551C8—41no—
552C8—41no—
553C8—41no—
554C22—442no—
555C22—442no—
556C22—442no—
557C22—881no—
558C22—881no—
559C22—881no—
560C22—881no—
561C22#1062305511yescharacteristic
562C22#1062308511yescharacteristic
563C22Q8×D4411yescharacteristic
564C22C2×#6696211yescharacteristic
565C22#1062327911yescharacteristic
566C22#1062328311yescharacteristic
567C22#1062328311yescharacteristic
568C4—22no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—442no—
575C4—442no—
576C4—442no—
577C4—442no—
578C4—881no—
579C4—881no—
580C4—881no—
581C4#1062316711yescharacteristic
582C4#1062319311yescharacteristic
583C4#1062321911yescharacteristic
584C4#1062323311yescharacteristic
585C2—882no—
586C2#1307263511yescharacteristic
587C2#1307878911yescharacteristic
588C2#1307886011yescharacteristic
589C2#1308077411yescharacteristic
590C2#1308095511yescharacteristic
591C2#1308152811yescharacteristic
592C2#1308157611yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1917C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1917D11
hypocenterC11#27018
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1917

Complements

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

NH ≅ G/Ntype
2. #13071705C2semidirect
4. #13069955C2semidirect
5. #13069945C2semidirect
7. #13069571C2semidirect
8. #13069354C2semidirect
11. #13069209C2semidirect
12. #13069188C2semidirect
15. C11×#1917C2semidirect
113. #66885Q8semidirect
207. #1917D11semidirect
490. C11#27018semidirect

Maximal subgroups

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

subgroupindex
#130724882
#130717052
#130700032
#130699552
#130699452
#130697532
#130695712
#130693542
#130692442
#130692372
#130692092
#130691882
#130688662
#130684422
C11×#19172
#2701811