Finite Group Databasebeta

← #14764180

Subgroups — #14764180

Order 2816.

754 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622612C211yesmaximal, characteristic
2#13071225C211yesmaximal, characteristic
3#13069384C211yesmaximal, characteristic, complemented
4#13069384C211yesmaximal, characteristic, complemented
5#13069382C211yesmaximal, characteristic, complemented
6#13069382C211yesmaximal, characteristic, complemented
7#13069379C211yesmaximal, characteristic, complemented
8#13069377C211yesmaximal, characteristic, complemented
9#13069374C211yesmaximal, characteristic, complemented
10#13069372C211yesmaximal, characteristic, complemented
11#13068647C211yesmaximal, characteristic
12#13068647C211yesmaximal, characteristic
13#13068643C211yesmaximal, characteristic
14#13068639C211yesmaximal, characteristic
15C11×#2314C211yesmaximal, characteristic
16C2×C11×#117C2211yescharacteristic
17C22×#4318C2211yescharacteristic
18C23×C11⋊C8C2211yescharacteristic
19C11×#388—21no—
20C11×#388—21no—
21C11×#387—21no—
22C11×#387—21no—
23C11×#384C2211yescharacteristic
24C11×#382C2211yescharacteristic
25C11×#380C2211yescharacteristic
26C11×#380C2211yescharacteristic
27C4×C11×C4⋊C4C2211yescharacteristic
28C4×C11×C4⋊C4C2211yescharacteristic
29#10622825C2211yescharacteristic
30#10622825C2211yescharacteristic
31#10622612C418yescomplemented
32#10622594—21no—
33#10622594—21no—
34C2×#66872C2211yescharacteristic
35C2×#66872C2211yescharacteristic
36C2×#66872C2211yescharacteristic
37C2×#66872C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42#10622564—21no—
43#10622564—21no—
44#10622549C2211yescharacteristic
45#10622548C2211yescharacteristic
46C4×C4⋊Dic11C2211yescharacteristic
47C4×C4⋊Dic11C2211yescharacteristic
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C11×#117C2×C414yes—
62C11×#117Q814yes—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4D411yescharacteristic
66C2×C11×C4⋊C4D411yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—21no—
73C2×C11×C22⋊C4D411yescharacteristic
74C2×C11×C22⋊C4D411yescharacteristic
75C2×C42×C11—21no—
76C2×C42×C11—21no—
77C2×C42×C11C2311yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4×Dic11—21no—
88C2×C4×Dic11—21no—
89C2×#4318—41no—
90C2×#4318—41no—
91C2×#4318C2×C414yes—
92C22×C11⋊C8—41no—
93C22×C11⋊C8—41no—
94C22×C11⋊C8C2×C414yes—
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C11×#95—21no—
100C11×#95—21no—
101C11×#95—21no—
102C11×#95—21no—
103C11×#95—21no—
104C11×#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111#66872—41no—
112#66872—41no—
113#66872—41no—
114#66872—41no—
115#66871—41no—
116#66871—41no—
117#66871—41no—
118#66871—41no—
119C4⋊(C11⋊C8)C2×C414yes—
120C4⋊(C11⋊C8)C2×C414yes—
121C4⋊(C11⋊C8)C2×C414yes—
122C4⋊(C11⋊C8)C2×C414yes—
123#21966—111nomaximal, Sylow
124C24×C11C2×D411yescharacteristic
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11C22×C412yes—
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×C11C2411yescharacteristic
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—81no—
154C11×C4⋊C4—81no—
155C11×C4⋊C4C4⋊C414yes—
156C11×C4⋊C4C4⋊C414yes—
157C11×C22⋊C4—81no—
158C11×C22⋊C4—81no—
159C11×C22⋊C4C4⋊C414yes—
160C11×C22⋊C4C4⋊C414yes—
161C42×C11—81no—
162C42×C11—81no—
163C42×C11C22×C412yes—
164C42×C11C22×C412yes—
165C42×C11C2×Q812yes—
166C42×C11C2×Q812yes—
167C22⋊Dic11—81no—
168C22⋊Dic11—81no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—81no—
178C4⋊Dic11—81no—
179C4×Dic11—81no—
180C4×Dic11—81no—
181#4318—44no—
182C2×C11⋊C8—21no—
183C2×C11⋊C8—21no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8—21no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—44no—
191C2×C11⋊C8C22×C412yes—
192C2×C11⋊C8C22×C412yes—
193C2×C11⋊C8C22×C412yes—
194C2×C11⋊C8C22×C412yes—
195C2×#424—111no—
196#2314—111no—
197#2314D1111yescharacteristic
198#1949—111no—
199#1949—111no—
200#1949—111no—
201#1949—111no—
202#1948—111no—
203#1948—111no—
204#1947—111no—
205#1947—111no—
206#1809—111no—
207#1809—111no—
208#1808—111no—
209#1807—111no—
210C23×C11—21no—
211C23×C11—21no—
212C23×C11—21no—
213C23×C11—21no—
214C23×C11—21no—
215C23×C11—21no—
216C23×C11C2×C4⋊C412yes—
217C23×C11C22×D411yescharacteristic
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—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11C2×C4⋊C412yes—
245C2×C4×C11C2×C4⋊C412yes—
246C2×C4×C11C2×C4⋊C412yes—
247C2×C4×C11C2×C4⋊C412yes—
248C2×C4×C11C2×C4⋊C412yes—
249C2×C4×C11C23×C411yescharacteristic
250C2×C4×C11C22×Q811yescharacteristic
251C2×C4×C11H(5,𝔽2)11yescharacteristic
252C2×C4×C11H(5,𝔽2)11yescharacteristic
253C2×C4×C112−1+411yescharacteristic
254C2×C4×C112−1+411yescharacteristic
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—
267C11⋊C8—22no—
268C11⋊C8—22no—
269C11⋊C8—22no—
270C11⋊C8—22no—
271C22×M16—111no—
272C23×C8—111no—
273C2×#117C2×D1111yescharacteristic
274C2×#107—111no—
275C2×#107—111no—
276C2×#107—111no—
277C2×#107—111no—
278C2×#106—111no—
279C2×#106—111no—
280C2×#106—111no—
281C2×#106—111no—
282#424—118no—
283C2×C4⋊C8—111no—
284C2×C4⋊C8—111no—
285C2×C4⋊C8—111no—
286C2×C4⋊C8—111no—
287#388—21no—
288#388—21no—
289#388—221no—
290#388—221no—
291#387—21no—
292#387—21no—
293#387—221no—
294#387—221no—
295#384—111no—
296#384C2×D1111yescharacteristic
297#382—111no—
298#382C2×D1111yescharacteristic
299#380—111no—
300#380—111no—
301#380C2×D1111yescharacteristic
302#380C2×D1111yescharacteristic
303C4×C4⋊C4—111no—
304C4×C4⋊C4—111no—
305C4×C4⋊C4C2×D1111yescharacteristic
306C4×C4⋊C4C2×D1111yescharacteristic
307#340—111no—
308#340—111no—
309#340—111no—
310#340—111no—
311#340—111no—
312#340—111no—
313#340—111no—
314#340—111no—
315C22×C11—22no—
316C22×C11—22no—
317C22×C11—22no—
318C22×C11—41no—
319C22×C11—41no—
320C22×C11—41no—
321C22×C11—41no—
322C22×C11C22×C4⋊C411yescharacteristic
323C22×C11#53711yescharacteristic
324C22×C11#53711yescharacteristic
325C22×C11#57611yescharacteristic
326C22×C11#57711yescharacteristic
327C22×C11#57711yescharacteristic
328C22×C11#57811yescharacteristic
329C4×C11—22no—
330C4×C11—22no—
331C4×C11—22no—
332C4×C11—22no—
333C4×C11—22no—
334C4×C11—81no—
335C4×C11—81no—
336C4×C11—81no—
337C4×C11—81no—
338C4×C11#51811yescharacteristic
339C4×C11#51911yescharacteristic
340C4×C11#54411yescharacteristic
341C4×C11#54411yescharacteristic
342Dic11—81no—
343Dic11—81no—
344Dic11—81no—
345Dic11—81no—
346C23×C4C22×D1111yescharacteristic
347C2×M16—114no—
348C2×M16—441no—
349C2×M16—441no—
350C22×C8—111no—
351C22×C8—111no—
352C22×C8—111no—
353C22×C8—111no—
354C22×C8—114no—
355C22×C8—441no—
356C22×C8—441no—
357#117Dic2214yes—
358#117C4×D1114yes—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—111no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4C22⋊D1111yescharacteristic
368C2×C4⋊C4C22⋊D1111yescharacteristic
369C2×C4⋊C4C22×D1111yescharacteristic
370C2×C4⋊C4C22×D1111yescharacteristic
371C2×C4⋊C4C22×D1111yescharacteristic
372C2×C4⋊C4C22×D1111yescharacteristic
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—221no—
376C2×C22⋊C4—221no—
377C2×C22⋊C4C22⋊D1111yescharacteristic
378C2×C22⋊C4C22⋊D1111yescharacteristic
379C2×C42—21no—
380C2×C42—21no—
381C2×C42—221no—
382C2×C42—221no—
383C2×C42C22×D1111yescharacteristic
384C2×C42C22×D1111yescharacteristic
385#107—441no—
386#107—441no—
387#107—441no—
388#107—441no—
389#106—441no—
390#106—441no—
391#106—441no—
392#106—441no—
393C4⋊C8—114no—
394C4⋊C8—114no—
395C4⋊C8—114no—
396C4⋊C8—114no—
397#95—21no—
398#95—21no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—221no—
404#95—221no—
405#95—221no—
406#95—221no—
407#95—221no—
408#95—221no—
409C2×C11—42no—
410C2×C11#231611yescharacteristic
411C2×C11#291211yescharacteristic
412C2×C11#291311yescharacteristic
413C2×C11#325711yescharacteristic
414C2×C11#325711yescharacteristic
415C2×C11#325811yescharacteristic
416C2×C11#325811yescharacteristic
417C24C2×C22⋊D1111yescharacteristic
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—221no—
427C22×C4—221no—
428C22×C4—221no—
429C22×C4—221no—
430C22×C4C2×Dic2212yes—
431C22×C4C2×C4×D1112yes—
432C22×C4C2×C22⋊D1111yescharacteristic
433C22×C4C2×C22⋊D1111yescharacteristic
434C22×C4C2×C22⋊D1111yescharacteristic
435C22×C4C2×C22⋊D1111yescharacteristic
436C22×C4C2×C22⋊D1111yescharacteristic
437C22×C4C23×D1111yescharacteristic
438M16—444no—
439C2×C8—112no—
440C2×C8—112no—
441C2×C8—112no—
442C2×C8—112no—
443C2×C8—221no—
444C2×C8—221no—
445C2×C8—221no—
446C2×C8—221no—
447C2×C8—221no—
448C2×C8—221no—
449C2×C8—221no—
450C2×C8—221no—
451C2×C8—444no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—81no—
461C4⋊C4—81no—
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—881no—
471C4⋊C4—881no—
472C4⋊C4Dic11⋊C414yes—
473C4⋊C4Dic11⋊C414yes—
474C22⋊C4—81no—
475C22⋊C4—81no—
476C22⋊C4—881no—
477C22⋊C4—881no—
478C22⋊C4Dic11⋊C414yes—
479C22⋊C4Dic11⋊C414yes—
480C42—81no—
481C42—81no—
482C42—881no—
483C42—881no—
484C42C2×Dic2212yes—
485C42C2×Dic2212yes—
486C42C2×C4×D1112yes—
487C42C2×C4×D1112yes—
488C11#2196611yescharacteristic, complemented, Sylow
489C23—21no—
490C23—21no—
491C23—21no—
492C23—21no—
493C23—21no—
494C23—21no—
495C23C2×Dic11⋊C412yes—
496C23C22×C22⋊D1111yescharacteristic
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—441no—
524C2×C4—441no—
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×C4C2×Dic11⋊C412yes—
536C2×C4C2×Dic11⋊C412yes—
537C2×C4C2×Dic11⋊C412yes—
538C2×C4C2×Dic11⋊C412yes—
539C2×C4C2×Dic11⋊C412yes—
540C2×C4C22×Dic2211yescharacteristic
541C2×C4C22×C4×D1111yescharacteristic
542C2×C4#6704211yescharacteristic
543C2×C4#6704211yescharacteristic
544C2×C4#6704311yescharacteristic
545C2×C4#6704311yescharacteristic
546C8—222no—
547C8—222no—
548C8—222no—
549C8—222no—
550C22—22no—
551C22—22no—
552C22—22no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22C22×Dic11⋊C411yescharacteristic
558C22#1062336411yescharacteristic
559C22#1062336411yescharacteristic
560C22#1062336611yescharacteristic
561C22#1062336711yescharacteristic
562C22#1062336811yescharacteristic
563C22#1062336911yescharacteristic
564C4—22no—
565C4—22no—
566C4—22no—
567C4—22no—
568C4—22no—
569C4—81no—
570C4—81no—
571C4—81no—
572C4—81no—
573C4—881no—
574C4—881no—
575C4—881no—
576C4—881no—
577C4#1062304711yescharacteristic
578C4#1062305011yescharacteristic
579C4#1062305011yescharacteristic
580C4#1062305211yescharacteristic
581C2—42no—
582C2#1307123211yescharacteristic
583C2#1307720911yescharacteristic
584C2#1307721411yescharacteristic
585C2#1308002111yescharacteristic
586C2#1308002711yescharacteristic
587C2#1308003611yescharacteristic
588C2#1308004211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2314C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#2314D11
hypocenterC11#21966
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2314

Complements

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

NH ≅ G/Ntype
3. #13069384C2semidirect
4. #13069384C2semidirect
5. #13069382C2semidirect
6. #13069382C2semidirect
7. #13069379C2semidirect
8. #13069377C2semidirect
9. #13069374C2semidirect
10. #13069372C2semidirect
31. #10622612C4semidirect
488. C11#21966semidirect

Maximal subgroups

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

subgroupindex
C2×#106226122
#130712252
#130693842
#130693822
#130693792
#130693772
#130693742
#130693722
#130686472
#130686432
#130686392
C11×#23142
#2196611