Finite Group Databasebeta

← #14826464

Subgroups — #14826464

Order 2816.

792 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073043C211yesmaximal, characteristic, complemented
2#13071631C211yesmaximal, characteristic
3#13070023C211yesmaximal, characteristic, complemented
4#13069991C211yesmaximal, characteristic, complemented
5#13069808C211yesmaximal, characteristic
6#13069807C211yesmaximal, characteristic
7#13069376C211yesmaximal, characteristic, complemented
8#13069341C211yesmaximal, characteristic, complemented
9#13069220C211yesmaximal, characteristic, complemented
10#13069200C211yesmaximal, characteristic, complemented
11#13068880C211yesmaximal, characteristic, complemented
12#13068810C211yesmaximal, characteristic, complemented
13#13068701C211yesmaximal, characteristic, complemented
14C4×#66873C211yesmaximal, characteristic, complemented
15C11×#1919C211yesmaximal, characteristic, complemented
16C2×#66948C2211yescharacteristic
17C2×#66946—21no—
18C2×C4⋊C4×D11C2211yescharacteristic
19C2×C4×D44C2211yescharacteristic
20C2×C11×#106C2211yescharacteristic
21C11×#389C2211yescharacteristic
22C4×C11×C4⋊C4C2211yescharacteristic
23C2×#66885C2211yescharacteristic
24C2×#66885C2211yescharacteristic
25C2×(C2×D11)⋊C8C2211yescharacteristic
26C2×(C2×D11)⋊C8C2211yescharacteristic
27C2×#66881C2211yescharacteristic
28C2×Dic11⋊C8C2211yescharacteristic
29#10622602—21no—
30#10622601C2211yescharacteristic
31#10622600C2211yescharacteristic
32#10622600C2211yescharacteristic
33#10622589C2211yescharacteristic
34C4⋊C4×Dic11C2211yescharacteristic
35#10622586C2211yescharacteristic
36C2×#66873C2211yescharacteristic
37C2×#66873C2211yescharacteristic
38C2×#66872C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40#10622553—21no—
41C4×(C2×D11)⋊C4C2211yescharacteristic
42#10622546—21no—
43#10622541C2211yescharacteristic
44C2×C4×C11⋊C8C2211yescharacteristic
45#10622289—21no—
46#10622282—21no—
47#10622278—21no—
48#10622271—21no—
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#336C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×D44—21no—
60C22×D44C2311yescharacteristic
61C22×C4×D11—21no—
62C22×C4×D11—21no—
63C22×C4×D11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
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×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4D411yescharacteristic
80C2×(C2×D11)⋊C4D411yescharacteristic
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×C4×Dic11—21no—
90C2×C4×Dic11C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93#66948—22no—
94#66948—22no—
95#66946—44no—
96C4⋊C4×D11—22no—
97C4⋊C4×D11—41no—
98C4×D44—22no—
99C4×D44—41no—
100C11×#106—22no—
101C11×#95—21no—
102C11×#95—21no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95D411yescharacteristic
109C11⋊#95D411yescharacteristic
110#66885—22no—
111#66885—41no—
112(C2×D11)⋊C8—22no—
113(C2×D11)⋊C8—41no—
114#66881—22no—
115Dic11⋊C8—22no—
116#66873—22no—
117#66873—22no—
118#66872—22no—
119#66872—41no—
120C4×C11⋊C8—41no—
121#27032—111nomaximal, Sylow
122C23×D11—21no—
123C23×D11C2×D411yescharacteristic
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×C11C2411yescharacteristic
131C22×Dic11—21no—
132C22×Dic11—21no—
133C22×Dic11—21no—
134C22×Dic11C2×D411yescharacteristic
135C22×Dic11C2×D411yescharacteristic
136C22×Dic11C2×D411yescharacteristic
137C2×D44—24no—
138C2×D44—21no—
139C2×D44—21no—
140C2×D44—21no—
141C2×D44—21no—
142C2×D44—21no—
143C2×D44—42no—
144C2×D44—42no—
145C2×D44#4112yes—
146C2×C4×D11—21no—
147C2×C4×D11—21no—
148C2×C4×D11—21no—
149C2×C4×D11—21no—
150C2×C4×D11—21no—
151C2×C4×D11—21no—
152C2×C4×D11—42no—
153C2×C4×D11—42no—
154C2×C4×D11—42no—
155C2×C4×D11—42no—
156C2×C4×D11—81no—
157C2×C4×D11—81no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—42no—
172C11×C4⋊C4#4112yes—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11—81no—
176(C2×D11)⋊C4—24no—
177(C2×D11)⋊C4—41no—
178(C2×D11)⋊C4—42no—
179(C2×D11)⋊C4—42no—
180(C2×D11)⋊C4—81no—
181(C2×D11)⋊C4—81no—
182(C2×D11)⋊C4—81no—
183(C2×D11)⋊C4SD1614yes—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11#4112yes—
190Dic11⋊C4—42no—
191Dic11⋊C4—42no—
192Dic11⋊C4—81no—
193Dic11⋊C4—81no—
194Dic11⋊C4—81no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C4×Dic11—42no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8#4112yes—
204#2497—111no—
205#2361—111no—
206#2071—111no—
207#2065—111no—
208#2034—111no—
209#2034—111no—
210#1948—111no—
211#1941—111no—
212#1923—111no—
213#1920—111no—
214#1919D1111yescharacteristic, complemented
215#1864—111no—
216#1853—111no—
217#1823—111no—
218C4×#102—111no—
219C23×C11C22×D411yescharacteristic
220C22×D11—21no—
221C22×D11—21no—
222C22×D11—21no—
223C22×D11—21no—
224C22×D11—21no—
225C22×D11—21no—
226C22×D11—22no—
227C22×D11—41no—
228C22×D11—41no—
229C22×D11—41no—
230C22×D11—41no—
231C22×D11—41no—
232C22×D11—41no—
233C22×D11C2×SD1612yes—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—22no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11C2×SD1612yes—
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11H(5,𝔽2)11yescharacteristic
257C2×C4×C112−1+411yescharacteristic
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—22no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11C2×SD1612yes—
276D44—22no—
277D44—22no—
278D44—48no—
279D44—41no—
280D44—41no—
281C4×D11—41no—
282C4×D11—41no—
283C4×D11—41no—
284C4×D11—41no—
285C4×D11—84no—
286C4×D11—84no—
287C8×C11—41no—
288C8×C11—41no—
289C11⋊C8—22no—
290C11⋊C8—41no—
291C2×#121—111no—
292C2×C4×D4—111no—
293C2×C4×D4—221no—
294C22×C4⋊C4—111no—
295C2×#106—111no—
296C2×#106—111no—
297C2×#106—111no—
298C2×#106C2×D1111yescharacteristic
299C2×C4⋊C8—111no—
300C2×#102—111no—
301C2×#102—111no—
302C2×#102—111no—
303C2×#102—111no—
304C2×C22⋊C8—111no—
305C2×C22⋊C8—111no—
306C2×C4×C8—111no—
307#400—221no—
308#396—221no—
309#390—111no—
310#389—111no—
311#389—111no—
312#389C2×D1111yescharacteristic
313#388—221no—
314#388—221no—
315#387—221no—
316#386—221no—
317#385—221no—
318#384—111no—
319#380—111no—
320#380—111no—
321C4×C4⋊C4—111no—
322C4×C4⋊C4C2×D1111yescharacteristic
323C4×C22⋊C4—111no—
324#340—111no—
325#340—111no—
326#340—111no—
327#340—111no—
328#340—111no—
329#340C2×D1111yescharacteristic
330#340C2×D1111yescharacteristic
331#340C2×D1111yescharacteristic
332#336—111no—
333#336C2×D1111yescharacteristic
334C22×C11#52511yescharacteristic
335C22×C11#54611yescharacteristic
336C22×C11#54711yescharacteristic
337C22×C11C22×SD1611yescharacteristic
338C22×C11#57511yescharacteristic
339C22×C11#57611yescharacteristic
340C22×C11#57711yescharacteristic
341C2×D11—22no—
342C2×D11—22no—
343C2×D11—22no—
344C2×D11—41no—
345C2×D11—41no—
346C2×D11—41no—
347C2×D11—41no—
348C2×D11—42no—
349C2×D11—42no—
350C2×D11—42no—
351C2×D11—81no—
352C2×D11—81no—
353C2×D11—81no—
354C2×D11—81no—
355C4×C11—22no—
356C4×C11—42no—
357C4×C11—41no—
358C4×C11—81no—
359C4×C11—81no—
360C4×C11—81no—
361C4×C11#52911yescharacteristic
362C4×C11#53911yescharacteristic
363C4×C11#55311yescharacteristic
364C4×C11#55611yescharacteristic
365Dic11—22no—
366Dic11—41no—
367Dic11—41no—
368Dic11—42no—
369Dic11—81no—
370Dic11—81no—
371C22×D4—111no—
372C22×D4—221no—
373C23×C4—111no—
374C23×C4—221no—
375C23×C4—221no—
376C22×C8—111no—
377C22×C8—111no—
378C22×C8C22×D1111yescharacteristic
379C22×C8C22×D1111yescharacteristic
380#121—222no—
381#121—222no—
382C4×D4—222no—
383C4×D4—441no—
384C4×D4—444no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—111no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—222no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4—441no—
396C2×C4⋊C4C22×D1111yescharacteristic
397C2×C4⋊C4C22×D1111yescharacteristic
398C2×C4⋊C4C22×D1111yescharacteristic
399C2×C4⋊C4C22×D1111yescharacteristic
400C2×C22⋊C4—111no—
401C2×C22⋊C4—111no—
402C2×C22⋊C4—221no—
403C2×C22⋊C4—221no—
404C2×C22⋊C4—221no—
405C2×C22⋊C4—221no—
406C2×C22⋊C4—221no—
407C2×C22⋊C4—221no—
408C2×C42—21no—
409C2×C42—111no—
410C2×C42—221no—
411C2×C42C22×D1111yescharacteristic
412#106—22no—
413#106—222no—
414#106—222no—
415#106—441no—
416C4⋊C8—222no—
417#102—222no—
418#102—222no—
419#102—222no—
420#102—441no—
421C22⋊C8—222no—
422C22⋊C8—441no—
423C4×C8—441no—
424#95—21no—
425#95—21no—
426#95—111no—
427#95—111no—
428#95—221no—
429#95—221no—
430#95—221no—
431#95—221no—
432#95—221no—
433C2×C11#246611yescharacteristic
434C2×C11#310111yescharacteristic
435C2×C11#311911yescharacteristic
436C2×C11#329511yescharacteristic
437C2×C11#332111yescharacteristic
438C2×C11#333511yescharacteristic
439C2×C11#335511yescharacteristic
440D11—42no—
441D11—82no—
442C24—111no—
443C24—221no—
444C2×D4—112no—
445C2×D4—224no—
446C2×D4—221no—
447C2×D4—221no—
448C2×D4—221no—
449C2×D4—221no—
450C2×D4—221no—
451C2×D4—442no—
452C2×D4—442no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—111no—
458C22×C4—111no—
459C22×C4—111no—
460C22×C4—221no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4—221no—
465C22×C4—221no—
466C22×C4—221no—
467C22×C4—221no—
468C22×C4—221no—
469C22×C4—442no—
470C22×C4—442no—
471C22×C4—442no—
472C22×C4—442no—
473C22×C4—881no—
474C22×C4—881no—
475C22×C4D4×D1111yescharacteristic
476C22×C4D4×D1111yescharacteristic
477C22×C4C23×D1111yescharacteristic
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—112no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8—221no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—42no—
498C4⋊C4—112no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4—221no—
504C4⋊C4—442no—
505C4⋊C4—442no—
506C4⋊C4—881no—
507C4⋊C4—881no—
508C4⋊C4—881no—
509C4⋊C4#433912yes—
510C22⋊C4—114no—
511C22⋊C4—224no—
512C22⋊C4—441no—
513C22⋊C4—442no—
514C22⋊C4—442no—
515C22⋊C4—881no—
516C22⋊C4—881no—
517C22⋊C4—881no—
518C42—21no—
519C42—21no—
520C42—81no—
521C42—221no—
522C42—221no—
523C42—442no—
524C11#2703211yescharacteristic, complemented, Sylow
525C23—112no—
526C23—221no—
527C23—221no—
528C23—221no—
529C23—221no—
530C23—221no—
531C23—221no—
532C23—222no—
533C23—441no—
534C23—441no—
535C23—441no—
536C23—441no—
537C23—441no—
538C23—441no—
539C23C2×D4×D1111yescharacteristic
540D4—222no—
541D4—222no—
542D4—448no—
543D4—441no—
544D4—441no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—112no—
563C2×C4—221no—
564C2×C4—221no—
565C2×C4—221no—
566C2×C4—221no—
567C2×C4—221no—
568C2×C4—221no—
569C2×C4—221no—
570C2×C4—222no—
571C2×C4—221no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—884no—
585C2×C4—884no—
586C2×C4SD16×D1112yes—
587C2×C4C2×#433911yescharacteristic
588C2×C4#6704011yescharacteristic
589C2×C4#41×D1111yescharacteristic
590C2×C4#41×D1111yescharacteristic
591C2×C4#41×D1111yescharacteristic
592C2×C4#6704211yescharacteristic
593C8—41no—
594C8—41no—
595C8—222no—
596C8—441no—
597C22—222no—
598C22—222no—
599C22—222no—
600C22—441no—
601C22—441no—
602C22—441no—
603C22—441no—
604C22—442no—
605C22—442no—
606C22—442no—
607C22—881no—
608C22—881no—
609C22—881no—
610C22—881no—
611C22#1062307811yescharacteristic
612C22#1062316211yescharacteristic
613C22#1062318511yescharacteristic
614C22C2×SD16×D1111yescharacteristic
615C22#1062329911yescharacteristic
616C22#1062330511yescharacteristic
617C22#1062330911yescharacteristic
618C4—22no—
619C4—42no—
620C4—41no—
621C4—81no—
622C4—81no—
623C4—81no—
624C4—222no—
625C4—441no—
626C4—442no—
627C4—441no—
628C4—881no—
629C4—881no—
630C4#1062306111yescharacteristic
631C4#1062309911yescharacteristic
632C4#1062322311yescharacteristic
633C4#1062323711yescharacteristic
634C2—442no—
635C2—882no—
636C2#1307265611yescharacteristic
637C2#1307862211yescharacteristic
638C2#1307881311yescharacteristic
639C2#1308043811yescharacteristic
640C2#1308080011yescharacteristic
641C2#1308097611yescharacteristic
642C2#1308121911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1919C2
socleC23×C11C22×D4
prime radicalC2×#66948C22
hypercenter#1919D11
hypocenterC11#27032
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1919

Complements

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

NH ≅ G/Ntype
1. #13073043C2semidirect
3. #13070023C2semidirect
4. #13069991C2semidirect
7. #13069376C2semidirect
8. #13069341C2semidirect
9. #13069220C2semidirect
10. #13069200C2semidirect
11. #13068880C2semidirect
12. #13068810C2semidirect
13. #13068701C2semidirect
14. C4×#66873C2semidirect
15. C11×#1919C2semidirect
214. #1919D11semidirect
524. C11#27032semidirect

Maximal subgroups

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

subgroupindex
#130730432
#130716312
#130700232
#130699912
#130698082
#130698072
#130693762
#130693412
#130692202
#130692002
#130688802
#130688102
#130687012
C4×#668732
C11×#19192
#2703211