Finite Group Databasebeta

← #14812585

Subgroups — #14812585

Order 2816.

774 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622296C211yesmaximal, characteristic, complemented
2C2×#10622734C211yesmaximal, characteristic
3#13072340C211yesmaximal, characteristic
4#13072329C211yesmaximal, characteristic
5#13070099C211yesmaximal, characteristic, complemented
6#13070094C211yesmaximal, characteristic, complemented
7#13069955C211yesmaximal, characteristic, complemented
8#13069955C211yesmaximal, characteristic, complemented
9#13069354C211yesmaximal, characteristic, complemented
10#13069344C211yesmaximal, characteristic, complemented
11#13068817C211yesmaximal, characteristic
12#13068811C211yesmaximal, characteristic
13#13068784C211yesmaximal, characteristic, complemented
14#13068649C211yesmaximal, characteristic
15C11×#1753C211yesmaximal, characteristic
16C22×C11×M16C2211yescharacteristic
17C2×#66979C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C2×#66923C2211yescharacteristic
20C2×#66923C2211yescharacteristic
21C2×C11×C22⋊C8C2211yescharacteristic
22C2×C11×#97C2211yescharacteristic
23C2×C4×C8×C11C2211yescharacteristic
24C4×C11×C22⋊C4C2211yescharacteristic
25#10622825C2211yescharacteristic
26#10622825C2211yescharacteristic
27#10622734—24no—
28C2×#66882C2211yescharacteristic
29C2×#66882C2211yescharacteristic
30C2×#66882C2211yescharacteristic
31C2×#66882C2211yescharacteristic
32C2×#66881C2211yescharacteristic
33C2×#66881C2211yescharacteristic
34C2×#66881C2211yescharacteristic
35C2×#66881C2211yescharacteristic
36C2×#66881C2211yescharacteristic
37C2×#66881C2211yescharacteristic
38#10622562—21no—
39#10622561—21no—
40#10622559—21no—
41#10622555—21no—
42#10622549C2211yescharacteristic
43#10622548C2211yescharacteristic
44#10622541C2211yescharacteristic
45#10622541C2211yescharacteristic
46#10622541C2211yescharacteristic
47#10622541C2211yescharacteristic
48#10622296—24no—
49#10622273—21no—
50#10622270—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—
63C2×C11×M16—22no—
64C2×C11×M16—22no—
65C2×C11×M16Q814yes—
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C2×C11×C22⋊C4D411yescharacteristic
71C2×C11×C22⋊C4D411yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11—21no—
77#66979—22no—
78#66979—41no—
79C2×C4⋊Dic11—22no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—41no—
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×C4×Dic11—21no—
101#66923—22no—
102#66923—22no—
103#66923—41no—
104#66923—41no—
105C11×C22⋊C8Q814yes—
106C11×#97—22no—
107C4×C8×C11—22no—
108C11×#95D411yescharacteristic
109C11×#95D411yescharacteristic
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118#66882—22no—
119#66882—22no—
120#66882—41no—
121#66882D414yes—
122#66881—22no—
123#66881—22no—
124#66881—22no—
125#66881—22no—
126#66881—22no—
127#66881—41no—
128#26075—111nomaximal, Sylow
129C24×C11C2×D411yescharacteristic
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×Q812yes—
140C22×C4×C11C2×Q812yes—
141C22×C4×C11C2411yescharacteristic
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—42no—
151C22×Dic11—42no—
152C22×Dic11—81no—
153C11×M16—28no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11C2×D412yes—
161C2×C8×C11C2×Q812yes—
162C2×C8×C11C2×Q812yes—
163C2×C8×C11C2×Q812yes—
164C2×C8×C11C2×Q812yes—
165C2×C8×C11#4112yes—
166C11×C22⋊C4—41no—
167C11×C22⋊C4—41no—
168C42×C11—21no—
169C42×C11—21no—
170C42×C11—21no—
171C42×C11—21no—
172C22⋊Dic11—42no—
173C22⋊Dic11—42no—
174C22⋊Dic11—81no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
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—42no—
190C4⋊Dic11—42no—
191C4⋊Dic11—81no—
192C4⋊Dic11C2×D412yes—
193C4⋊Dic11C2×D412yes—
194Dic11⋊C4—42no—
195Dic11⋊C4—42no—
196Dic11⋊C4—42no—
197Dic11⋊C4—42no—
198Dic11⋊C4—42no—
199Dic11⋊C4—81no—
200Dic11⋊C4—81no—
201Dic11⋊C4—81no—
202C4×Dic11—42no—
203C2×#499—111no—
204C2×#428—111no—
205#2442—111no—
206#2441—111no—
207#2085—111no—
208#2084—111no—
209#2059—111no—
210#2059—111no—
211#1943—111no—
212#1941—111no—
213#1854—111no—
214#1853—111no—
215#1847—111no—
216#1809—111no—
217#1753D1111yescharacteristic
218C23×C11—21no—
219C23×C11—21no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—21no—
224C23×C11C4⋊Q812yes—
225C23×C11C22×D411yescharacteristic
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
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×C11C4⋊Q812yes—
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C22×Q811yescharacteristic
247C2×C4×C11C22×Q811yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11H(5,𝔽2)11yescharacteristic
250C2×C4×C112−1+411yescharacteristic
251C2×Dic11—22no—
252C2×Dic11—22no—
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—
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—84no—
276C8×C11—22no—
277C8×C11—22no—
278C8×C11—22no—
279C8×C11C22⋊Q814yes—
280C22×M16C2×D1111yescharacteristic
281C2×#125—111no—
282C2×#125—111no—
283C2×#117—111no—
284C22×C4⋊C4—111no—
285#499—224no—
286#428—224no—
287C2×#107—111no—
288C2×#107—111no—
289C2×#107—111no—
290C2×#107—111no—
291C2×#106—111no—
292C2×#106—111no—
293C2×#106—111no—
294C2×#106—111no—
295C2×#106—111no—
296C2×#106—111no—
297C2×C22⋊C8C2×D1111yescharacteristic
298C2×#97C2×D1111yescharacteristic
299C2×C4×C8C2×D1111yescharacteristic
300#400—221no—
301#399—221no—
302#398—221no—
303#396—221no—
304#389—111no—
305#389—111no—
306#389—111no—
307#389—111no—
308#389—221no—
309#387—221no—
310#385—221no—
311#384—111no—
312#382—111no—
313#380—111no—
314#380—111no—
315#380—221no—
316C4×C22⋊C4C2×D1111yescharacteristic
317#340—111no—
318#340—111no—
319#340—111no—
320#340—111no—
321#340—111no—
322#340—111no—
323#336C2×D1111yescharacteristic
324#336C2×D1111yescharacteristic
325C22×C11—22no—
326C22×C11—22no—
327C22×C11—22no—
328C22×C11—41no—
329C22×C11—41no—
330C22×C11—41no—
331C22×C11—41no—
332C22×C11C2×C4⋊Q811yescharacteristic
333C22×C11D4211yescharacteristic
334C22×C11#54711yescharacteristic
335C22×C11#57511yescharacteristic
336C22×C11#57511yescharacteristic
337C22×C11#57711yescharacteristic
338C22×C11#57711yescharacteristic
339C4×C11—22no—
340C4×C11—41no—
341C4×C11—41no—
342C4×C11—41no—
343C4×C11—41no—
344C4×C11C2×C22⋊Q811yescharacteristic
345C4×C11#54411yescharacteristic
346C4×C11D4×Q811yescharacteristic
347C4×C11#55411yescharacteristic
348Dic11—42no—
349Dic11—42no—
350Dic11—81no—
351Dic11—81no—
352Dic11—81no—
353Dic11—81no—
354Dic11—81no—
355Dic11—81no—
356C23×C4—221no—
357C23×C4C22×D1111yescharacteristic
358C2×M16—22no—
359C2×M16—22no—
360C2×M16Dic2214yes—
361C22×C8C22×D1111yescharacteristic
362C22×C8C22×D1111yescharacteristic
363C22×C8C22×D1111yescharacteristic
364C22×C8C22×D1111yescharacteristic
365#125—222no—
366#125—222no—
367#125—441no—
368#125—441no—
369#117—222no—
370#117—441no—
371C2×C4⋊C4—111no—
372C2×C4⋊C4—111no—
373C2×C4⋊C4—111no—
374C2×C4⋊C4—111no—
375C2×C4⋊C4—111no—
376C2×C4⋊C4—111no—
377C2×C4⋊C4—111no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—222no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—441no—
392C2×C22⋊C4—221no—
393C2×C22⋊C4—221no—
394C2×C22⋊C4—221no—
395C2×C22⋊C4D4411yescharacteristic
396C2×C22⋊C4D4411yescharacteristic
397C2×C42—221no—
398C2×C42C22×D1111yescharacteristic
399C2×C42C22×D1111yescharacteristic
400#107—114no—
401#107—222no—
402#107—222no—
403#107—441no—
404#106—222no—
405#106—222no—
406#106—222no—
407#106—222no—
408#106—222no—
409#106—441no—
410C22⋊C8Dic2214yes—
411#97—22no—
412C4×C8—22no—
413#95—221no—
414#95—221no—
415#95—221no—
416#95—221no—
417#95—221no—
418#95—221no—
419#95—221no—
420#95—221no—
421#95D4411yescharacteristic
422#95D4411yescharacteristic
423C2×C11—42no—
424C2×C11#244011yescharacteristic
425C2×C11#316311yescharacteristic
426C2×C11#316611yescharacteristic
427C2×C11#326711yescharacteristic
428C2×C11#327111yescharacteristic
429C2×C11#335111yescharacteristic
430C2×C11#335111yescharacteristic
431C24C2×D4411yescharacteristic
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—221no—
437C22×C4—221no—
438C22×C4—221no—
439C22×C4—221no—
440C22×C4—221no—
441C22×C4—221no—
442C22×C4—221no—
443C22×C4—221no—
444C22×C4—442no—
445C22×C4—442no—
446C22×C4—881no—
447C22×C4C2×Dic2212yes—
448C22×C4C2×Dic2212yes—
449C22×C4C2×D4411yescharacteristic
450C22×C4C2×D4411yescharacteristic
451C22×C4C2×D4411yescharacteristic
452C22×C4C2×D4411yescharacteristic
453C22×C4C2×D4411yescharacteristic
454C22×C4C23×D1111yescharacteristic
455M16—28no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8C2×Dic2212yes—
463C2×C8C2×Dic2212yes—
464C2×C8C2×Dic2212yes—
465C2×C8C2×Dic2212yes—
466C2×C8D4×D1112yes—
467C2×C8#434112yes—
468C4⋊C4—112no—
469C4⋊C4—112no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—442no—
485C4⋊C4—442no—
486C4⋊C4—442no—
487C4⋊C4—442no—
488C4⋊C4—442no—
489C4⋊C4—442no—
490C4⋊C4—442no—
491C4⋊C4—881no—
492C4⋊C4—881no—
493C4⋊C4—881no—
494C4⋊C4—881no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4—442no—
498C22⋊C4—442no—
499C22⋊C4—881no—
500C42—21no—
501C42—21no—
502C42—21no—
503C42—21no—
504C42—442no—
505C11#2607511yescharacteristic, complemented, Sylow
506C23—21no—
507C23—21no—
508C23—21no—
509C23—21no—
510C23—21no—
511C23—21no—
512C23#6692212yes—
513C23C22×D4411yescharacteristic
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—222no—
533C2×C4—222no—
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—441no—
543C2×C4—441no—
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—884no—
557C2×C4#6692212yes—
558C2×C4C22×Dic2211yescharacteristic
559C2×C4C22×Dic2211yescharacteristic
560C2×C4C2×D4×D1111yescharacteristic
561C2×C4C2×#434111yescharacteristic
562C2×C4#6704211yescharacteristic
563C2×C4#6704311yescharacteristic
564C8—22no—
565C8—22no—
566C8—22no—
567C8#6693114yes—
568C22—22no—
569C22—22no—
570C22—22no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22C2×#6692211yescharacteristic
576C22D4×D4411yescharacteristic
577C22#1062308611yescharacteristic
578C22#1062327911yescharacteristic
579C22#1062327911yescharacteristic
580C22#1062328211yescharacteristic
581C22#1062328211yescharacteristic
582C4—22no—
583C4—41no—
584C4—41no—
585C4—41no—
586C4—41no—
587C4—442no—
588C4—442no—
589C4—881no—
590C4—881no—
591C4—881no—
592C4—881no—
593C4—881no—
594C4—881no—
595C4C2×#6693111yescharacteristic
596C4#1062305011yescharacteristic
597C4D4×Dic2211yescharacteristic
598C4#1062307411yescharacteristic
599C2—42no—
600C2#1307231811yescharacteristic
601C2#1307914711yescharacteristic
602C2#1307916811yescharacteristic
603C2#1308014611yescharacteristic
604C2#1308020611yescharacteristic
605C2#1308117811yescharacteristic
606C2#1308117811yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1753C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#1753D11
hypocenterC11#26075
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×#10622296C2semidirect
5. #13070099C2semidirect
6. #13070094C2semidirect
7. #13069955C2semidirect
8. #13069955C2semidirect
9. #13069354C2semidirect
10. #13069344C2semidirect
13. #13068784C2semidirect
505. C11#26075semidirect

Maximal subgroups

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

subgroupindex
C2×#106222962
C2×#106227342
#130723402
#130723292
#130700992
#130700942
#130699552
#130693542
#130693442
#130688172
#130688112
#130687842
#130686492
C11×#17532
#2607511