Finite Group Databasebeta

← #14724153

Subgroups — #14724153

Order 2816.

616 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078659C211yesmaximal, characteristic
2#13077656C211yesmaximal, characteristic, complemented
3#13067528C211yesmaximal, characteristic, complemented
4#13067516C211yesmaximal, characteristic, complemented
5#13067506C211yesmaximal, characteristic, complemented
6#13067499C211yesmaximal, characteristic, complemented
7#13067494C211yesmaximal, characteristic, complemented
8#13067480C211yesmaximal, characteristic, complemented
9#13067459C211yesmaximal, characteristic, complemented
10#13067445C211yesmaximal, characteristic, complemented
11#13067407C211yesmaximal, characteristic, complemented
12#13067040C211yesmaximal, characteristic, complemented
13#13067024C211yesmaximal, characteristic, complemented
14#13066916C211yesmaximal, characteristic, complemented
15C11×#2993C211yesmaximal, characteristic, complemented
16C11×#529C2211yescharacteristic
17C2×C4×D44C2211yescharacteristic
18C11×#446C2211yescharacteristic, complemented
19C8×Q8×C11C2211yescharacteristic, complemented
20C11×#436—21no—
21C11×#436C2211yescharacteristic, complemented
22C11×#435—21no—
23C8×D4×C11C2211yescharacteristic, complemented
24C11×#433—21no—
25C11×#431C2211yescharacteristic
26C11×#424—21no—
27C11×#423C2211yescharacteristic
28#10622679C411yescharacteristic
29#10622679C411yescharacteristic
30#10622670C411yescharacteristic
31#10622670C411yescharacteristic
32#10622659C411yescharacteristic
33#10622657C411yescharacteristic
34#10622649C411yescharacteristic
35#10622647C411yescharacteristic
36C4×#4325C2211yescharacteristic
37C4×#4325C2211yescharacteristic
38C4×#4323C2211yescharacteristic
39C4×#4323C2211yescharacteristic
40#10622538C2211yescharacteristic
41#10622538C2211yescharacteristic
42#10622538C2211yescharacteristic
43#10622451—21no—
44#10622451—21no—
45#10622339—21no—
46#10622339—21no—
47#10622301C2211yescharacteristic
48#10622301C2211yescharacteristic
49#10622301C2211yescharacteristic
50#10622301C2211yescharacteristic
51Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
52Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
53D4⋊(C11⋊C8)C2211yescharacteristic, complemented
54D4⋊(C11⋊C8)C2211yescharacteristic, complemented
55#10622121C2211yescharacteristic
56#10622121C2211yescharacteristic
57#10622121C2211yescharacteristic
58#10622121C2211yescharacteristic
59#10622118C2211yescharacteristic, complemented
60#10622118C2211yescharacteristic, complemented
61#10622117C2211yescharacteristic, complemented
62#10622117C2211yescharacteristic, complemented
63#10622093C2211yescharacteristic, complemented
64#10622092C2211yescharacteristic, complemented
65#10622092C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, complemented
67C22×D44C2×C411yescharacteristic
68C22×C4×D11—21no—
69C2×C11×M16—21no—
70C2×C11×M16—21no—
71C22×C8×C11—21no—
72C11×#126—21no—
73C11×#125C2×C411yescharacteristic
74C11×#124C2×C411yescharacteristic
75C11×#123—21no—
76C11×C22⋊Q8C2×C411yescharacteristic
77C11×#121C2×C411yescharacteristic
78C4×Q8×C11C2311yescharacteristic
79C4×D4×C11—21no—
80C4×D4×C11C2311yescharacteristic
81C11×#117—21no—
82C2×C42×C11C2311yescharacteristic
83C2×#4325C2×C411yescharacteristic
84C2×#4325C2×C411yescharacteristic
85C2×#4323C2×C411yescharacteristic
86C2×#4323C2×C411yescharacteristic
87C2×(C2×D11)⋊C4—21no—
88C2×C4⋊Dic11C2×C411yescharacteristic
89C2×#4313—21no—
90C2×#4313—21no—
91C2×#4313—21no—
92C2×#4313—21no—
93C4×D44—21no—
94C4×D44—21no—
95C4×D44C2×C411yescharacteristic
96C4×D44C2×C411yescharacteristic
97C4×D44C2311yescharacteristic
98C4×D44C2311yescharacteristic
99C11×C4⋊C8—21no—
100C11×C4⋊C8—21no—
101C11×C4⋊C8—21no—
102C11×C4⋊C8D411yescharacteristic
103C11×C4⋊C8D411yescharacteristic
104C11×C4⋊C8C2311yescharacteristic
105C11×C4⋊C8C2311yescharacteristic
106C11×C22⋊C8—21no—
107C11×C22⋊C8—21no—
108C11×C22⋊C8D411yescharacteristic
109C11×C22⋊C8D411yescharacteristic
110C11×#97—21no—
111C4×C8×C11—21no—
112C4×C8×C11C2311yescharacteristic
113C4×C8×C11C2311yescharacteristic
114#66899C2×C411yescharacteristic
115#66899C2×C411yescharacteristic
116#66896C2×C411yescharacteristic
117#66896C2×C411yescharacteristic
118C22⋊(C11⋊C8)—21no—
119C22⋊(C11⋊C8)—21no—
120C22⋊(C11⋊C8)C2×C411yescharacteristic
121C22⋊(C11⋊C8)C2×C411yescharacteristic
122(C2×D11)⋊C8—21no—
123(C2×D11)⋊C8—21no—
124(C2×D11)⋊C8—21no—
125(C2×D11)⋊C8—21no—
126#66873C2×C411yescharacteristic
127#66873C2×C411yescharacteristic
128#66873C2×C411yescharacteristic
129#66873C2×C411yescharacteristic
130#66872C2×C411yescharacteristic
131#66872C2×C411yescharacteristic
132#66871C2×C411yescharacteristic
133#66871C2×C411yescharacteristic
134C4⋊(C11⋊C8)—21no—
135C4⋊(C11⋊C8)C2×C411yescharacteristic
136C4⋊(C11⋊C8)C2×C411yescharacteristic
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4×C11⋊C8—21no—
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#17946—111nomaximal, Sylow
145C23×D11—21no—
146C2×Q8×C11C22×C411yescharacteristic
147C2×D4×C11—21no—
148C2×D4×C11C22×C411yescharacteristic
149C22×C4×C11—21no—
150C22×C4×C11C22×C411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11#4111yescharacteristic
153C22×Dic11—21no—
154C2×D44—21no—
155C2×D44—41no—
156C2×D44—41no—
157C2×D44C22×C411yescharacteristic
158C2×D44C22×C411yescharacteristic
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11—81no—
164C2×C4×D11—81no—
165C11×M16—81no—
166C11×M16—81no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—81no—
170C2×C8×C11C2×D411yescharacteristic
171C2×C8×C11C2×D411yescharacteristic
172C2×C8×C11C2×D411yescharacteristic
173C2×C8×C11C2×D411yescharacteristic
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4C22×C411yescharacteristic
179C11×C4⋊C4C22×C411yescharacteristic
180C11×C22⋊C4—21no—
181C11×C22⋊C4—21no—
182C11×C22⋊C4—21no—
183C11×C22⋊C4—21no—
184C11×C22⋊C4—21no—
185C42×C11—21no—
186C42×C11C22×C411yescharacteristic
187C42×C11C2×D411yescharacteristic
188C42×C11#4111yescharacteristic
189C42×C11C2411yescharacteristic
190#4325—41no—
191#4325—41no—
192#4323—41no—
193#4323—41no—
194(C2×D11)⋊C4—21no—
195(C2×D11)⋊C4—21no—
196(C2×D11)⋊C4—21no—
197(C2×D11)⋊C4—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11C22×C411yescharacteristic
200C4⋊Dic11C22×C411yescharacteristic
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8C22×C411yescharacteristic
206C2×C11⋊C8C22×C411yescharacteristic
207C2×C11⋊C8C22×C411yescharacteristic
208C2×C11⋊C8C22×C411yescharacteristic
209#4313—81no—
210#4313—81no—
211#4313—81no—
212#4313—81no—
213#3105—111no—
214#2993D1111yescharacteristic, complemented
215#2975—111no—
216#1594—111no—
217#1592—111no—
218#1590—111no—
219#1589—111no—
220#1588—111no—
221#1586—111no—
222#1583—111no—
223#1581—111no—
224#1574—111no—
225#1486—111no—
226#1482—111no—
227#1454—111no—
228C23×C11—21no—
229C23×C11C4×D411yescharacteristic
230C22×D11—21no—
231C22×D11—21no—
232C22×D11—42no—
233C22×D11—81no—
234C22×D11—81no—
235Q8×C11—21no—
236Q8×C11—21no—
237D4×C11—21no—
238D4×C11—21no—
239D4×C11—81no—
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—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11C4×D411yescharacteristic
251C2×C4×C11C4×D411yescharacteristic
252C2×C4×C11C4×D411yescharacteristic
253C2×C4×C11C23×C411yescharacteristic
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—81no—
259D44—21no—
260D44—21no—
261D44—21no—
262D44—21no—
263D44—42no—
264C4×D11—41no—
265C4×D11—41no—
266C4×D11—41no—
267C4×D11—41no—
268C4×D11—81no—
269C4×D11—81no—
270C8×C11—21no—
271C8×C11—21no—
272C8×C11—21no—
273C8×C11—21no—
274C8×C11—41no—
275C8×C11—41no—
276C11⋊C8—21no—
277C11⋊C8—21no—
278C11⋊C8—21no—
279C11⋊C8—21no—
280C11⋊C8—41no—
281C11⋊C8—41no—
282C11⋊C8—41no—
283C11⋊C8—41no—
284#529C2×D1111yescharacteristic
285C2×C4×D4—111no—
286#484—111no—
287#481—111no—
288#478—111no—
289#478—111no—
290#463—111no—
291#463—111no—
292#450—111no—
293#447—111no—
294#446C2×D1111yescharacteristic, complemented
295C8×Q8C2×D1111yescharacteristic, complemented
296C4×SD16—111no—
297C4×SD16—111no—
298C4×D8—111no—
299C4×D8—111no—
300#436—21no—
301#436—111no—
302#436—111no—
303#436—111no—
304#436—111no—
305#436—221no—
306#436—221no—
307#436C2×D1111yescharacteristic, complemented
308#435—21no—
309C8×D4C2×D1111yescharacteristic, complemented
310#433—21no—
311#431—111no—
312#431—111no—
313#431—111no—
314#431C2×D1111yescharacteristic
315#424—21no—
316#423C2×D1111yescharacteristic
317#407—221no—
318#407—221no—
319#335—111no—
320#335—111no—
321#334—111no—
322#334—111no—
323Q8⋊C8—111no—
324Q8⋊C8—111no—
325D4⋊C8—111no—
326D4⋊C8—111no—
327D4⋊C8—111no—
328D4⋊C8—111no—
329D4⋊C8—111no—
330D4⋊C8—111no—
331#322—111no—
332#322—111no—
333#322—111no—
334C82—111no—
335C22×C11—21no—
336C22×C11—21no—
337C22×C11—21no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11—41no—
341C22×C11C2×C4×D411yescharacteristic
342C2×D11—41no—
343C2×D11—41no—
344C2×D11—41no—
345C2×D11—41no—
346C2×D11—41no—
347C2×D11—41no—
348C2×D11—84no—
349C4×C11—21no—
350C4×C11—21no—
351C4×C11—21no—
352C4×C11—21no—
353C4×C11—41no—
354C4×C11—41no—
355C4×C11—41no—
356C4×C11#56811yescharacteristic
357C4×C11#56811yescharacteristic
358C4×C11#57611yescharacteristic
359C4×C11#57711yescharacteristic
360Dic11—41no—
361Dic11—41no—
362C22×D4—111no—
363C23×C4—221no—
364C2×SD16—111no—
365C2×SD16—111no—
366C2×D8—111no—
367C2×D8—111no—
368C2×M16—21no—
369C2×M16—21no—
370C2×M16—221no—
371C2×M16—221no—
372C2×M16—221no—
373C2×M16—221no—
374C22×C8—21no—
375#126—21no—
376#125C4×D1111yescharacteristic
377#124C4×D1111yescharacteristic
378#123—21no—
379C22⋊Q8C4×D1111yescharacteristic
380#121C4×D1111yescharacteristic
381C4×Q8C22×D1111yescharacteristic
382C4×D4—21no—
383C4×D4—111no—
384C4×D4—111no—
385C4×D4—111no—
386C4×D4—111no—
387C4×D4—221no—
388C4×D4—221no—
389C4×D4C22×D1111yescharacteristic
390#117—21no—
391C2×C4⋊C4—111no—
392C2×C22⋊C4—221no—
393C2×C42C22×D1111yescharacteristic
394#107—111no—
395#107—111no—
396#106—111no—
397#106—111no—
398C4⋊C8—21no—
399C4⋊C8—21no—
400C4⋊C8—21no—
401C4⋊C8—111no—
402C4⋊C8—111no—
403C4⋊C8—111no—
404C4⋊C8—111no—
405C4⋊C8—221no—
406C4⋊C8C22⋊D1111yescharacteristic
407C4⋊C8C22⋊D1111yescharacteristic
408C4⋊C8C22×D1111yescharacteristic
409C4⋊C8C22×D1111yescharacteristic
410#103—111no—
411#103—111no—
412#102—111no—
413#102—111no—
414#102—111no—
415#102—111no—
416#102—111no—
417#102—111no—
418C22⋊C8—21no—
419C22⋊C8—21no—
420C22⋊C8—111no—
421C22⋊C8—111no—
422C22⋊C8—221no—
423C22⋊C8—221no—
424C22⋊C8—221no—
425C22⋊C8—221no—
426C22⋊C8—221no—
427C22⋊C8—221no—
428C22⋊C8C22⋊D1111yescharacteristic
429C22⋊C8C22⋊D1111yescharacteristic
430#97—21no—
431C4×C8—21no—
432C4×C8—111no—
433C4×C8—111no—
434C4×C8—111no—
435C4×C8—111no—
436C4×C8—221no—
437C4×C8C22×D1111yescharacteristic
438C4×C8C22×D1111yescharacteristic
439C2×C11—41no—
440C2×C11—81no—
441C2×C11#293011yescharacteristic
442C2×C11#294611yescharacteristic
443C2×C11#295711yescharacteristic
444D11—81no—
445D11—81no—
446C24—221no—
447C2×Q8C2×C4×D1111yescharacteristic
448C2×D4—21no—
449C2×D4—111no—
450C2×D4—111no—
451C2×D4—221no—
452C2×D4—441no—
453C2×D4—441no—
454C2×D4C2×C4×D1111yescharacteristic
455C22×C4—21no—
456C22×C4—221no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4—221no—
460C22×C4—221no—
461C22×C4—881no—
462C22×C4—881no—
463C22×C4C2×C4×D1111yescharacteristic
464C22×C4#433911yescharacteristic
465C22×C4C2×C22⋊D1111yescharacteristic
466SD16—441no—
467SD16—441no—
468D8—441no—
469D8—441no—
470M16—81no—
471M16—81no—
472M16—881no—
473M16—881no—
474M16—881no—
475M16—881no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—81no—
479C2×C8—111no—
480C2×C8—111no—
481C2×C8—111no—
482C2×C8—111no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8C2×C22⋊D1111yescharacteristic
488C2×C8C2×C22⋊D1111yescharacteristic
489C2×C8C2×C22⋊D1111yescharacteristic
490C2×C8C2×C22⋊D1111yescharacteristic
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—111no—
496C4⋊C4—111no—
497C4⋊C4—221no—
498C4⋊C4C2×C4×D1111yescharacteristic
499C4⋊C4C2×C4×D1111yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—221no—
506C22⋊C4—221no—
507C22⋊C4—221no—
508C22⋊C4—221no—
509C42—21no—
510C42C2×C4×D1111yescharacteristic
511C42#433911yescharacteristic
512C42C2×C22⋊D1111yescharacteristic
513C42C23×D1111yescharacteristic
514C11#1794611yescharacteristic, complemented, Sylow
515C23—21no—
516C23—221no—
517C23—221no—
518C23—442no—
519C23—881no—
520C23—881no—
521C23C4×C22⋊D1111yescharacteristic
522Q8—21no—
523Q8—21no—
524D4—21no—
525D4—21no—
526D4—81no—
527D4—221no—
528D4—221no—
529D4—221no—
530D4—221no—
531D4—442no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—881no—
549C2×C4—881no—
550C2×C4—881no—
551C2×C4C4×C22⋊D1111yescharacteristic
552C2×C4C4×C22⋊D1111yescharacteristic
553C2×C4C4×C22⋊D1111yescharacteristic
554C2×C4C22×C4×D1111yescharacteristic
555C2×C4C2×#433911yescharacteristic
556C2×C4C22×C22⋊D1111yescharacteristic
557C8—21no—
558C8—21no—
559C8—21no—
560C8—21no—
561C8—41no—
562C8—41no—
563C8—221no—
564C8—221no—
565C8—221no—
566C8—221no—
567C8—441no—
568C8—441no—
569C8—441no—
570C8—441no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—441no—
578C22—441no—
579C22—441no—
580C22—441no—
581C22—441no—
582C22—441no—
583C22—884no—
584C22C2×C4×C22⋊D1111yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—441no—
593C4—441no—
594C4#1062328111yescharacteristic
595C4#1062328111yescharacteristic
596C4#1062336611yescharacteristic
597C4#1062336811yescharacteristic
598C2—41no—
599C2—81no—
600C2—881no—
601C2—881no—
602C2#1307731711yescharacteristic
603C2#1307744411yescharacteristic
604C2#1307753111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2993C2
socleC22×C11C2×C4×D4
prime radical#10622649C4
cosocleC42×C11C24
hypercenter#2993D11
hypocenterC11#17946
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2993

Complements

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

NH ≅ G/Ntype
2. #13077656C2semidirect
3. #13067528C2semidirect
4. #13067516C2semidirect
5. #13067506C2semidirect
6. #13067499C2semidirect
7. #13067494C2semidirect
8. #13067480C2semidirect
9. #13067459C2semidirect
10. #13067445C2semidirect
11. #13067407C2semidirect
12. #13067040C2semidirect
13. #13067024C2semidirect
14. #13066916C2semidirect
15. C11×#2993C2semidirect
18. C11×#446C22semidirect
19. C8×Q8×C11C22semidirect
21. C11×#436C22semidirect
23. C8×D4×C11C22semidirect
51. Q8⋊(C11⋊C8)C22semidirect
52. Q8⋊(C11⋊C8)C22semidirect
53. D4⋊(C11⋊C8)C22semidirect
54. D4⋊(C11⋊C8)C22semidirect
59. #10622118C22semidirect
60. #10622118C22semidirect
61. #10622117C22semidirect
62. #10622117C22semidirect
63. #10622093C22semidirect
64. #10622092C22semidirect
65. #10622092C22semidirect
66. C8×C11⋊C8C22semidirect
214. #2993D11semidirect
294. #446C2×D11semidirect
295. C8×Q8C2×D11semidirect
307. #436C2×D11semidirect
309. C8×D4C2×D11semidirect
514. C11#17946semidirect

Maximal subgroups

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

subgroupindex
#130786592
#130776562
#130675282
#130675162
#130675062
#130674992
#130674942
#130674802
#130674592
#130674452
#130674072
#130670402
#130670242
#130669162
C11×#29932
#1794611