Finite Group Databasebeta

← #14856927

Subgroups — #14856927

Order 2816.

708 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074576C211yesmaximal, characteristic, complemented
2#13070107C211yesmaximal, characteristic, complemented
3#13069990C211yesmaximal, characteristic, complemented
4#13069987C211yesmaximal, characteristic, complemented
5#13069926C211yesmaximal, characteristic
6#13069481C211yesmaximal, characteristic
7#13069341C211yesmaximal, characteristic, complemented
8#13069316C211yesmaximal, characteristic, complemented
9#13069312C211yesmaximal, characteristic, complemented
10#13069243C211yesmaximal, characteristic, complemented
11#13069187C211yesmaximal, characteristic, complemented
12#13068964C211yesmaximal, characteristic
13#13068877C211yesmaximal, characteristic, complemented
14#13068473C211yesmaximal, characteristic, complemented
15C11×#2319C211yesmaximal, characteristic, complemented
16C2×C4×D4×C11C2211yescharacteristic
17C22×#4323C2211yescharacteristic
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×#66873C2211yescharacteristic
32C2×#66873C2211yescharacteristic
33C2×#66873C2211yescharacteristic
34C2×#66872C2211yescharacteristic
35C2×#66872C2211yescharacteristic
36C2×#66871C2211yescharacteristic
37#10622552C2211yescharacteristic
38#10622552C2211yescharacteristic
39#10622552C2211yescharacteristic
40#10622541C2211yescharacteristic
41#10622541C2211yescharacteristic
42#10622541C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44C2×C4⋊(C11⋊C8)C2211yescharacteristic
45C2×#66867C2211yescharacteristic
46C2×C4×C11⋊C8C2211yescharacteristic
47#10622289—21no—
48#10622288—21no—
49#10622288—21no—
50#10622288—21no—
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D4×C11C2311yescharacteristic
60C23×C4×C11—21no—
61C22×D44C2311yescharacteristic
62C4×D4×C11—22no—
63C4×D4×C11—22no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4—21no—
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—21no—
73C2×C11×C22⋊C4—21no—
74C2×C42×C11—21no—
75C2×C42×C11C2311yescharacteristic
76C2×C42×C11C2311yescharacteristic
77C2×C42×C11C2311yescharacteristic
78C2×#4323—22no—
79C2×#4323—22no—
80C2×#4323—41no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C11×#95—21no—
98C11×#95—21no—
99C11×#95—21no—
100C11×#95D411yescharacteristic
101C11×#95D411yescharacteristic
102C11×#95D411yescharacteristic
103C11×#95D411yescharacteristic
104#66896—22no—
105#66896—22no—
106#66896—41no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110#66873—22no—
111#66873—22no—
112#66873—41no—
113#66872—22no—
114#66872—41no—
115#66871—22no—
116C4⋊(C11⋊C8)—22no—
117C4⋊(C11⋊C8)—22no—
118#66867—41no—
119C4×C11⋊C8—41no—
120#29437—111nomaximal, Sylow
121C24×C11—21no—
122C23×D11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11#4112yes—
129C22×C4×C11—21no—
130C22×C4×C11—24no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—81no—
134C22×C4×C11—81no—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2411yescharacteristic
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C2×D44—21no—
146C2×D44—21no—
147C2×D44—21no—
148C2×D44—21no—
149C2×D44—21no—
150C2×D44—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—81no—
157C11×C4⋊C4—81no—
158C11×C4⋊C4#4112yes—
159C11×C22⋊C4—24no—
160C11×C22⋊C4—81no—
161C11×C22⋊C4—81no—
162C11×C22⋊C4—81no—
163C11×C22⋊C4—81no—
164C42×C11—21no—
165C42×C11—21no—
166C42×C11—21no—
167C42×C11—21no—
168C42×C11—21no—
169C42×C11—21no—
170C42×C11—81no—
171#4323—44no—
172(C2×D11)⋊C4—81no—
173(C2×D11)⋊C4—81no—
174(C2×D11)⋊C4—81no—
175(C2×D11)⋊C4—81no—
176(C2×D11)⋊C4—81no—
177(C2×D11)⋊C4—81no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184Dic11⋊C4—81no—
185Dic11⋊C4—81no—
186Dic11⋊C4—81no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8#4112yes—
198C2×C11⋊C8#4112yes—
199#2644—111no—
200#2319D1111yescharacteristic, complemented
201#2086—111no—
202#2065—111no—
203#2065—111no—
204#2054—111no—
205#1970—111no—
206#1941—111no—
207#1936—111no—
208#1936—111no—
209#1926—111no—
210#1918—111no—
211#1879—111no—
212#1864—111no—
213#1768—111no—
214C23×C11—22no—
215C23×C11—41no—
216C23×C11—41no—
217C23×C11—41no—
218C23×C11—41no—
219C23×C11—41no—
220C23×C11—41no—
221C23×C11C22×D411yescharacteristic
222C22×D11—41no—
223C22×D11—41no—
224C22×D11—41no—
225C22×D11—41no—
226C22×D11—41no—
227C22×D11—41no—
228C22×D11—41no—
229D4×C11—22no—
230D4×C11—22no—
231D4×C11—41no—
232D4×C11—41no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—22no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—84no—
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11H(5,𝔽2)11yescharacteristic
266C2×C4×C112−1+411yescharacteristic
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×Dic11—41no—
276D44—41no—
277D44—41no—
278D44—41no—
279D44—41no—
280C11⋊C8—22no—
281C11⋊C8—22no—
282C11⋊C8—41no—
283C11⋊C8—41no—
284C22×D8—111no—
285C2×C4×D4C2×D1111yescharacteristic
286C2×#107—111no—
287C2×#106—111no—
288C2×#106—111no—
289C2×C4⋊C8—111no—
290C2×C4⋊C8—111no—
291C2×#102—111no—
292C2×#102—111no—
293C2×#102—111no—
294C2×#102—111no—
295C2×#102—111no—
296C2×#102—111no—
297C2×#97—111no—
298C2×C4×C8—111no—
299#397—221no—
300#397—221no—
301#397—221no—
302#396—221no—
303#390—111no—
304#390—111no—
305#390—111no—
306#390C2×D1111yescharacteristic
307#390C2×D1111yescharacteristic
308#389—111no—
309#389—111no—
310#389—111no—
311#389C2×D1111yescharacteristic
312#389C2×D1111yescharacteristic
313#388—21no—
314#388—21no—
315#381—21no—
316#380—21no—
317C4×C4⋊C4C2×D1111yescharacteristic
318#376C2×D1111yescharacteristic
319#340—111no—
320#340—111no—
321#340—111no—
322#340—111no—
323#340—111no—
324#340—111no—
325#336—111no—
326#336—111no—
327C22×C11—42no—
328C22×C11—42no—
329C22×C11—42no—
330C22×C11—81no—
331C22×C11—81no—
332C22×C11—81no—
333C22×C11—81no—
334C22×C11#52511yescharacteristic
335C22×C11#53211yescharacteristic
336C22×C11#53711yescharacteristic
337C22×C11#57611yescharacteristic
338C22×C11#57611yescharacteristic
339C22×C11#57711yescharacteristic
340C22×C11#57711yescharacteristic
341C2×D11—81no—
342C2×D11—81no—
343C2×D11—81no—
344C2×D11—81no—
345C2×D11—81no—
346C2×D11—81no—
347C2×D11—81no—
348C4×C11—41no—
349C4×C11—42no—
350C4×C11—41no—
351C4×C11—41no—
352C4×C11—41no—
353C4×C11—41no—
354C4×C11—41no—
355C4×C11—81no—
356C4×C11—81no—
357C4×C11#55111yescharacteristic
358C4×C11#55211yescharacteristic
359C4×C11#55311yescharacteristic
360C4×C11#55611yescharacteristic
361Dic11—81no—
362Dic11—81no—
363Dic11—81no—
364C22×D4—111no—
365C22×D4C22×D1111yescharacteristic
366C23×C4—21no—
367C2×D8—222no—
368C2×D8—222no—
369C2×D8—441no—
370C22×C8—111no—
371C22×C8—111no—
372C22×C8—111no—
373C22×C8—111no—
374C4×D4—22no—
375C4×D4—22no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4C22×D1111yescharacteristic
385C2×C4⋊C4C22×D1111yescharacteristic
386C2×C4⋊C4C22×D1111yescharacteristic
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—221no—
393C2×C22⋊C4—221no—
394C2×C22⋊C4—221no—
395C2×C22⋊C4—221no—
396C2×C22⋊C4—221no—
397C2×C22⋊C4—221no—
398C2×C42—21no—
399C2×C42C22×D1111yescharacteristic
400C2×C42C22×D1111yescharacteristic
401C2×C42C22×D1111yescharacteristic
402#107—222no—
403#106—222no—
404#106—441no—
405C4⋊C8—222no—
406C4⋊C8—222no—
407#102—222no—
408#102—222no—
409#102—222no—
410#102—222no—
411#102—441no—
412#102—441no—
413#97—441no—
414C4×C8—441no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—221no—
419#95—221no—
420#95—221no—
421#95C22⋊D1111yescharacteristic
422#95C22⋊D1111yescharacteristic
423#95C22⋊D1111yescharacteristic
424#95C22⋊D1111yescharacteristic
425C2×C11—82no—
426C2×C11#260111yescharacteristic
427C2×C11#311811yescharacteristic
428C2×C11#311911yescharacteristic
429C2×C11#317311yescharacteristic
430C2×C11#317611yescharacteristic
431C2×C11#325711yescharacteristic
432C2×C11#325711yescharacteristic
433D11—161no—
434C24—21no—
435C24—221no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—221no—
442C2×D4—221no—
443C2×D4—221no—
444C2×D4—221no—
445C2×D4—221no—
446C2×D4—221no—
447C2×D4#433912yes—
448C22×C4—21no—
449C22×C4—24no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—81no—
453C22×C4—81no—
454C22×C4—221no—
455C22×C4—221no—
456C22×C4—221no—
457C22×C4C2×C22⋊D1111yescharacteristic
458C22×C4C2×C22⋊D1111yescharacteristic
459C22×C4C2×C22⋊D1111yescharacteristic
460C22×C4C2×C22⋊D1111yescharacteristic
461C22×C4C2×C22⋊D1111yescharacteristic
462C22×C4C2×C22⋊D1111yescharacteristic
463C22×C4C23×D1111yescharacteristic
464D8—444no—
465C2×C8—112no—
466C2×C8—112no—
467C2×C8—221no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8—221no—
474C2×C8—221no—
475C2×C8—221no—
476C2×C8—221no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—81no—
483C4⋊C4—81no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4—881no—
491C4⋊C4—881no—
492C4⋊C4—881no—
493C4⋊C4#433912yes—
494C22⋊C4—24no—
495C22⋊C4—81no—
496C22⋊C4—81no—
497C22⋊C4—81no—
498C22⋊C4—81no—
499C22⋊C4—881no—
500C22⋊C4—881no—
501C22⋊C4—881no—
502C22⋊C4—881no—
503C22⋊C4—881no—
504C22⋊C4—881no—
505C42—21no—
506C42—21no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42—81no—
512C11#2943711yescharacteristic, complemented, Sylow
513C23—22no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—441no—
521C23—441no—
522C23—441no—
523C23—441no—
524C23—441no—
525C23—441no—
526C23—441no—
527C23C22×C22⋊D1111yescharacteristic
528D4—22no—
529D4—22no—
530D4—41no—
531D4—41no—
532D4—441no—
533D4—441no—
534D4—441no—
535D4—441no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—84no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—441no—
573C2×C4C2×#433911yescharacteristic
574C2×C4C2×#433911yescharacteristic
575C2×C4#41×D1111yescharacteristic
576C2×C4#41×D1111yescharacteristic
577C2×C4#6704211yescharacteristic
578C2×C4#6704311yescharacteristic
579C8—222no—
580C8—222no—
581C8—441no—
582C8—441no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—881no—
591C22—881no—
592C22—881no—
593C22—881no—
594C22—881no—
595C22—881no—
596C22—881no—
597C22#1062332211yescharacteristic
598C22#1062336311yescharacteristic
599C22#1062336411yescharacteristic
600C22#1062336611yescharacteristic
601C22#1062336611yescharacteristic
602C22#1062336711yescharacteristic
603C22#1062336811yescharacteristic
604C4—41no—
605C4—42no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4—81no—
612C4—81no—
613C4—881no—
614C4—881no—
615C4—881no—
616C4#1062305811yescharacteristic
617C4#1062306111yescharacteristic
618C4#1062306211yescharacteristic
619C4#1062306411yescharacteristic
620C2—82no—
621C2—1761no—
622C2#1307421311yescharacteristic
623C2#1307880011yescharacteristic
624C2#1307881511yescharacteristic
625C2#1307922711yescharacteristic
626C2#1307926011yescharacteristic
627C2#1308002111yescharacteristic
628C2#1308002711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2319C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
hypercenter#2319D11
hypocenterC11#29437
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ #376 ◁ #2319

Complements

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

NH ≅ G/Ntype
1. #13074576C2semidirect
2. #13070107C2semidirect
3. #13069990C2semidirect
4. #13069987C2semidirect
7. #13069341C2semidirect
8. #13069316C2semidirect
9. #13069312C2semidirect
10. #13069243C2semidirect
11. #13069187C2semidirect
13. #13068877C2semidirect
14. #13068473C2semidirect
15. C11×#2319C2semidirect
200. #2319D11semidirect
512. C11#29437semidirect

Maximal subgroups

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

subgroupindex
#130745762
#130701072
#130699902
#130699872
#130699262
#130694812
#130693412
#130693162
#130693122
#130692432
#130691872
#130689642
#130688772
#130684732
C11×#23192
#2943711