Finite Group Databasebeta

← #14812630

Subgroups — #14812630

Order 2816.

818 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622315C211yesmaximal, characteristic, complemented
2C2×#10622734C211yesmaximal, characteristic
3#13072329C211yesmaximal, characteristic
4#13072318C211yesmaximal, characteristic
5#13070094C211yesmaximal, characteristic, complemented
6#13070089C211yesmaximal, characteristic, complemented
7#13069955C211yesmaximal, characteristic, complemented
8#13069950C211yesmaximal, characteristic, complemented
9#13069354C211yesmaximal, characteristic, complemented
10#13069349C211yesmaximal, characteristic, complemented
11#13068817C211yesmaximal, characteristic
12#13068811C211yesmaximal, characteristic
13#13068773C211yesmaximal, characteristic, complemented
14#13068649C211yesmaximal, characteristic
15C11×#1753C211yesmaximal, characteristic
16C22×C11×M16C2211yescharacteristic
17C2×#66979C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C2×#66931—21no—
20C2×#66923C2211yescharacteristic
21C2×#66922C2211yescharacteristic
22C2×C11×C22⋊C8C2211yescharacteristic
23C2×C11×#97C2211yescharacteristic
24C2×C4×C8×C11C2211yescharacteristic
25C4×C11×C22⋊C4C2211yescharacteristic
26#10622825C2211yescharacteristic
27#10622825C2211yescharacteristic
28#10622734—24no—
29C2×#66882C2211yescharacteristic
30C2×#66882C2211yescharacteristic
31C2×#66882C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33C2×#66881C2211yescharacteristic
34C2×#66881C2211yescharacteristic
35C2×#66881C2211yescharacteristic
36C2×#66881C2211yescharacteristic
37C2×#66881C2211yescharacteristic
38C2×#66881C2211yescharacteristic
39#10622563—21no—
40#10622562—21no—
41#10622561—21no—
42#10622548C2211yescharacteristic
43#10622548C2211yescharacteristic
44#10622541C2211yescharacteristic
45#10622541C2211yescharacteristic
46#10622541C2211yescharacteristic
47#10622541C2211yescharacteristic
48#10622315—24no—
49#10622274—21no—
50#10622269—21no—
51#10622267—21no—
52#10622260—21no—
53C11×#336C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×Dic11—21no—
63C22×Dic22—21no—
64C2×C11×M16—22no—
65C2×C11×M16—22no—
66C2×C11×M16Q814yescomplemented
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C2×C11×C22⋊C4D411yescharacteristic
72C2×C11×C22⋊C4D411yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11—21no—
78#66979—22no—
79#66979—41no—
80C2×C4⋊Dic11—22no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—41no—
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×C4×Dic11—21no—
103#66931—44no—
104#66923—22no—
105#66923—41no—
106#66922—22no—
107#66922—41no—
108C11×C22⋊C8Q814yescomplemented
109C11×#97—22no—
110C4×C8×C11—22no—
111C11×#95D411yescharacteristic
112C11×#95D411yescharacteristic
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119#66882—22no—
120#66882—22no—
121#66882—22no—
122#66882D414yes—
123#66881—22no—
124#66881—22no—
125#66881—22no—
126#66881—22no—
127#66881—41no—
128#66881—41no—
129#26078—111nomaximal, Sylow
130C24×C11C2×D411yescharacteristic
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×Q812yes—
141C22×C4×C11C2×Q812yes—
142C22×C4×C11C2411yescharacteristic
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—42no—
152C22×Dic11—42no—
153C22×Dic11—81no—
154C2×Dic22—42no—
155C2×Dic22—42no—
156C2×Dic22—81no—
157C11×M16—28no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11C2×D412yes—
165C2×C8×C11C2×Q812yes—
166C2×C8×C11C2×Q812yes—
167C2×C8×C11C2×Q812yes—
168C2×C8×C11C2×Q812yes—
169C2×C8×C11#4112yes—
170C11×C22⋊C4—22no—
171C11×C22⋊C4—22no—
172C42×C11—21no—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11—21no—
176C22⋊Dic11—42no—
177C22⋊Dic11—42no—
178C22⋊Dic11—81no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—42no—
194C4⋊Dic11—42no—
195C4⋊Dic11—42no—
196C4⋊Dic11—42no—
197C4⋊Dic11—81no—
198C4⋊Dic11—81no—
199C4⋊Dic11C2×D412yes—
200C4⋊Dic11C2×D412yes—
201Dic11⋊C4—42no—
202Dic11⋊C4—42no—
203Dic11⋊C4—42no—
204Dic11⋊C4—42no—
205Dic11⋊C4—42no—
206Dic11⋊C4—81no—
207C4×Dic11—42no—
208C2×#501—111no—
209C2×#428—111no—
210#2441—111no—
211#2440—111no—
212#2084—111no—
213#2083—111no—
214#2059—111no—
215#2058—111no—
216#1943—111no—
217#1942—111no—
218#1854—111no—
219#1853—111no—
220#1844—111no—
221#1809—111no—
222#1753D1111yescharacteristic
223C23×C11—21no—
224C23×C11—21no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11—21no—
228C23×C11—21no—
229C23×C11C4⋊Q812yes—
230C23×C11C22×D411yescharacteristic
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
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×C11C4⋊Q812yes—
248C2×C4×C11AGL(1,ℤ/8)12yes—
249C2×C4×C11#13712yes—
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C22×Q811yescharacteristic
252C2×C4×C11C22×Q811yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11H(5,𝔽2)11yescharacteristic
255C2×C4×C112−1+411yescharacteristic
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
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—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—84no—
281Dic22—84no—
282C8×C11—22no—
283C8×C11—22no—
284C8×C11—22no—
285C8×C11C22⋊Q814yescomplemented
286C22×M16C2×D1111yescharacteristic
287C2×C4⋊Q8—111no—
288C2×#125—111no—
289C2×C22⋊Q8—221no—
290C2×#117—111no—
291C22×C4⋊C4—111no—
292#501—224no—
293#428—224no—
294C2×#107—111no—
295C2×#107—111no—
296C2×#107—111no—
297C2×#107—111no—
298C2×#106—111no—
299C2×#106—111no—
300C2×#106—111no—
301C2×#106—111no—
302C2×#106—111no—
303C2×#106—111no—
304C2×C22⋊C8C2×D1111yescharacteristic
305C2×#97C2×D1111yescharacteristic
306C2×C4×C8C2×D1111yescharacteristic
307#399—221no—
308#398—221no—
309#396—221no—
310#395—221no—
311#389—111no—
312#389—111no—
313#389—111no—
314#389—111no—
315#389—221no—
316#387—221no—
317#385—221no—
318#384—111no—
319#384—111no—
320#380—111no—
321#380—111no—
322C4×C22⋊C4C2×D1111yescharacteristic
323#340—111no—
324#340—111no—
325#340—111no—
326#340—111no—
327#340—111no—
328#340—111no—
329#336C2×D1111yescharacteristic
330#336C2×D1111yescharacteristic
331C22×C11—22no—
332C22×C11—22no—
333C22×C11—22no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11—41no—
338C22×C11C2×C4⋊Q811yescharacteristic
339C22×C11D4211yescharacteristic
340C22×C11#54711yescharacteristic
341C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
342C22×C11C2×#13711yescharacteristic
343C22×C11#57711yescharacteristic
344C22×C11#57711yescharacteristic
345C4×C11—22no—
346C4×C11—22no—
347C4×C11—22no—
348C4×C11—41no—
349C4×C11—41no—
350C4×C11C2×C22⋊Q811yescharacteristic
351C4×C11#54411yescharacteristic
352C4×C11D4×Q811yescharacteristic
353C4×C11#55411yescharacteristic
354Dic11—42no—
355Dic11—42no—
356Dic11—81no—
357Dic11—81no—
358Dic11—81no—
359Dic11—81no—
360Dic11—81no—
361Dic11—81no—
362C22×Q8—221no—
363C23×C4—221no—
364C23×C4C22×D1111yescharacteristic
365C2×M16—22no—
366C2×M16—22no—
367C2×M16Dic2214yescomplemented
368C22×C8C22×D1111yescharacteristic
369C22×C8C22×D1111yescharacteristic
370C22×C8C22×D1111yescharacteristic
371C22×C8C22×D1111yescharacteristic
372C4⋊Q8—222no—
373C4⋊Q8—441no—
374#125—222no—
375#125—441no—
376C22⋊Q8—444no—
377#117—222no—
378#117—441no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—111no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—111no—
387C2×C4⋊C4—222no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4—221no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4—221no—
400C2×C4⋊C4—441no—
401C2×C22⋊C4—221no—
402C2×C22⋊C4—221no—
403C2×C22⋊C4—221no—
404C2×C22⋊C4D4411yescharacteristic
405C2×C22⋊C4D4411yescharacteristic
406C2×C42—221no—
407C2×C42C22×D1111yescharacteristic
408C2×C42C22×D1111yescharacteristic
409#107—114no—
410#107—222no—
411#107—222no—
412#107—222no—
413#106—222no—
414#106—222no—
415#106—222no—
416#106—222no—
417#106—441no—
418#106—441no—
419C22⋊C8Dic2214yescomplemented
420#97—22no—
421C4×C8—22no—
422#95—221no—
423#95—221no—
424#95—221no—
425#95—221no—
426#95—221no—
427#95—221no—
428#95D4411yescharacteristic
429#95D4411yescharacteristic
430C2×C11—42no—
431C2×C11#244011yescharacteristic
432C2×C11#316311yescharacteristic
433C2×C11#316511yescharacteristic
434C2×C11#327211yescharacteristic
435C2×C11#327811yescharacteristic
436C2×C11#334411yescharacteristic
437C2×C11#334511yescharacteristic
438C24C2×D4411yescharacteristic
439C2×Q8—442no—
440C2×Q8—442no—
441C2×Q8—881no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—221no—
447C22×C4—221no—
448C22×C4—221no—
449C22×C4—221no—
450C22×C4—221no—
451C22×C4—221no—
452C22×C4—221no—
453C22×C4—221no—
454C22×C4—442no—
455C22×C4—442no—
456C22×C4—881no—
457C22×C4C2×Dic2212yes—
458C22×C4C2×Dic2212yes—
459C22×C4C2×D4411yescharacteristic
460C22×C4C2×D4411yescharacteristic
461C22×C4C2×D4411yescharacteristic
462C22×C4C2×D4411yescharacteristic
463C22×C4C2×D4411yescharacteristic
464C22×C4C23×D1111yescharacteristic
465M16—28no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8C2×Dic2212yes—
473C2×C8C2×Dic2212yes—
474C2×C8C2×Dic2212yes—
475C2×C8C2×Dic2212yes—
476C2×C8D4×D1112yes—
477C2×C8#434112yes—
478C4⋊C4—112no—
479C4⋊C4—112no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4—442no—
495C4⋊C4—442no—
496C4⋊C4—442no—
497C4⋊C4—442no—
498C4⋊C4—442no—
499C4⋊C4—442no—
500C4⋊C4—442no—
501C4⋊C4—442no—
502C4⋊C4—442no—
503C4⋊C4—881no—
504C4⋊C4—881no—
505C4⋊C4—881no—
506C22⋊C4—22no—
507C22⋊C4—22no—
508C22⋊C4—442no—
509C22⋊C4—442no—
510C22⋊C4—881no—
511C42—21no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—442no—
516C11#2607811yescharacteristic, complemented, Sylow
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23#6692212yes—
524C23C22×D4411yescharacteristic
525Q8—884no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—222no—
543C2×C4—222no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4—441no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—884no—
567C2×C4#6692212yes—
568C2×C4#6696112yes—
569C2×C4#6696212yes—
570C2×C4C22×Dic2211yescharacteristic
571C2×C4C22×Dic2211yescharacteristic
572C2×C4C2×D4×D1111yescharacteristic
573C2×C4C2×#434111yescharacteristic
574C2×C4#6704211yescharacteristic
575C2×C4#6704311yescharacteristic
576C8—22no—
577C8—22no—
578C8—22no—
579C8#6693114yescomplemented
580C22—22no—
581C22—22no—
582C22—22no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22C2×#6692211yescharacteristic
588C22D4×D4411yescharacteristic
589C22#1062308611yescharacteristic
590C22C2×#6696111yescharacteristic
591C22C2×#6696211yescharacteristic
592C22#1062328211yescharacteristic
593C22#1062328211yescharacteristic
594C4—22no—
595C4—22no—
596C4—22no—
597C4—41no—
598C4—41no—
599C4—442no—
600C4—442no—
601C4—881no—
602C4—881no—
603C4—881no—
604C4—881no—
605C4—881no—
606C4—881no—
607C4C2×#6693111yescharacteristic
608C4#1062305011yescharacteristic
609C4D4×Dic2211yescharacteristic
610C4#1062307411yescharacteristic
611C2—42no—
612C2#1307231811yescharacteristic
613C2#1307914711yescharacteristic
614C2#1307916211yescharacteristic
615C2#1308021811yescharacteristic
616C2#1308028411yescharacteristic
617C2#1308107311yescharacteristic
618C2#1308108811yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1753C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#1753D11
hypocenterC11#26078
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1753

Complements

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

NH ≅ G/Ntype
1. C2×#10622315C2semidirect
5. #13070094C2semidirect
6. #13070089C2semidirect
7. #13069955C2semidirect
8. #13069950C2semidirect
9. #13069354C2semidirect
10. #13069349C2semidirect
13. #13068773C2semidirect
66. C2×C11×M16Q8semidirect
108. C11×C22⋊C8Q8semidirect
285. C8×C11C22⋊Q8semidirect
367. C2×M16Dic22semidirect
419. C22⋊C8Dic22semidirect
516. C11#26078semidirect
579. C8#66931semidirect

Maximal subgroups

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

subgroupindex
C2×#106223152
C2×#106227342
#130723292
#130723182
#130700942
#130700892
#130699552
#130699502
#130693542
#130693492
#130688172
#130688112
#130687732
#130686492
C11×#17532
#2607811