Finite Group Databasebeta

← #14723831

Subgroups — #14723831

Order 2816.

648 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#13078665C211yesmaximal, characteristic
2#13077761C211yesmaximal, characteristic, complemented
3#13077639C211yesmaximal, characteristic, complemented
4#13067479C211yesmaximal, characteristic, complemented
5#13067472C211yesmaximal, characteristic, complemented
6#13067451C211yesmaximal, characteristic, complemented
7#13067444C211yesmaximal, characteristic, complemented
8#13067439C211yesmaximal, characteristic, complemented
9#13067427C211yesmaximal, characteristic, complemented
10#13067415C211yesmaximal, characteristic, complemented
11#13067410C211yesmaximal, characteristic, complemented
12#13067040C211yesmaximal, characteristic, complemented
13#13067022C211yesmaximal, characteristic, complemented
14#13066916C211yesmaximal, characteristic, complemented
15C11×#1574C211yesmaximal, characteristic, complemented
16#10623010C2211yescharacteristic
17C2×C4×D44C2211yescharacteristic
18C11×#431C2211yescharacteristic
19C11×#431C2211yescharacteristic
20C11×#423C2211yescharacteristic
21#10622741—21no—
22#10622740—21no—
23#10622538C2211yescharacteristic
24#10622538C2211yescharacteristic
25#10622460C411yescharacteristic
26#10622460C411yescharacteristic
27#10622457C411yescharacteristic
28#10622457C411yescharacteristic
29#10622453—21no—
30#10622452—21no—
31#10622451C2211yescharacteristic, complemented
32#10622447C2211yescharacteristic
33#10622447C2211yescharacteristic
34#10622447C2211yescharacteristic
35#10622447C2211yescharacteristic
36#10622447C2211yescharacteristic, complemented
37#10622444C2211yescharacteristic, complemented
38#10622443C2211yescharacteristic, complemented
39#10622348C411yescharacteristic
40#10622345C411yescharacteristic
41#10622344C411yescharacteristic
42D11×C22⋊C8—21no—
43D11×C22⋊C8—21no—
44#10622335C411yescharacteristic
45C4×D88C2211yescharacteristic
46C4×D88C2211yescharacteristic
47C4×#4314C2211yescharacteristic
48C4×#4314C2211yescharacteristic
49C8×D44—21no—
50C8×D44—21no—
51C11×#335C2211yescharacteristic, complemented
52C11×#335C2211yescharacteristic, complemented
53C11×#334C2211yescharacteristic, complemented
54C11×#334C2211yescharacteristic, complemented
55#10622122C2211yescharacteristic, complemented
56#10622122C2211yescharacteristic, complemented
57#10622121C2211yescharacteristic
58#10622121C2211yescharacteristic
59#10622121C2211yescharacteristic
60#10622121C2211yescharacteristic
61#10622121C2211yescharacteristic, complemented
62#10622121C2211yescharacteristic, 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×C42×C11C2311yescharacteristic
71#66983C2×C411yescharacteristic
72#66982—21no—
73C4×C22⋊D11—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×C4⋊Dic11C2×C411yescharacteristic
76#66977C2×C411yescharacteristic
77C2×D88C2×C411yescharacteristic
78C2×D88C2×C411yescharacteristic
79C2×#4314C2×C411yescharacteristic
80C2×#4314C2×C411yescharacteristic
81C2×#4313—21no—
82C2×C8×D11—21no—
83C2×C8×D11—21no—
84C2×C8×D11—21no—
85C2×C8×D11—21no—
86C2×C8×D11—21no—
87#66929—21no—
88#66928C2×C411yescharacteristic
89C4×D44—21no—
90C4×D44—21no—
91C4×D44C2×C411yescharacteristic
92C4×D44C2×C411yescharacteristic
93C4×D44C2311yescharacteristic
94C4×D44C2311yescharacteristic
95C4×D44C2311yescharacteristic
96#66925—21no—
97#66923C2×C411yescharacteristic
98C4×Dic22C2311yescharacteristic
99C11×C4⋊C8—21no—
100C11×C4⋊C8C2×C411yescharacteristic
101C11×C4⋊C8C2×C411yescharacteristic
102C11×C4⋊C8C2311yescharacteristic
103C11×C4⋊C8C2311yescharacteristic
104C11×C4⋊C8C2311yescharacteristic
105C11×C4⋊C8C2311yescharacteristic
106C11×C22⋊C8—21no—
107C11×C22⋊C8C2×C411yescharacteristic
108C11×C22⋊C8C2×C411yescharacteristic
109C4×C8×C11—21no—
110C4×C8×C11C2311yescharacteristic
111C4×C8×C11C2311yescharacteristic
112C22⋊(C11⋊C8)—21no—
113C22⋊(C11⋊C8)D411yescharacteristic
114C22⋊(C11⋊C8)D411yescharacteristic
115#66885C2×C411yescharacteristic
116#66885C2×C411yescharacteristic
117#66885C2×C411yescharacteristic
118#66885C2×C411yescharacteristic
119#66885C2×C411yescharacteristic
120#66885C2×C411yescharacteristic
121(C2×D11)⋊C8—21no—
122(C2×D11)⋊C8—21no—
123(C2×D11)⋊C8—21no—
124(C2×D11)⋊C8—21no—
125(C2×D11)⋊C8—21no—
126(C2×D11)⋊C8—21no—
127#66882C2×C411yescharacteristic
128#66882C2×C411yescharacteristic
129#66881C2×C411yescharacteristic
130#66881C2×C411yescharacteristic
131#66880C2×C411yescharacteristic
132#66880C2×C411yescharacteristic
133#66879—21no—
134Dic11⋊C8—21no—
135Dic11⋊C8—21no—
136C8×Dic11—21no—
137C4⋊(C11⋊C8)—21no—
138C4⋊(C11⋊C8)D411yescharacteristic
139C4⋊(C11⋊C8)D411yescharacteristic
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#17918—111nomaximal, Sylow
145C23×D11—21no—
146C22×C4×C11C22×C411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11#4111yescharacteristic
149C2×C22⋊D11—21no—
150C22×Dic11—21no—
151C2×D44—22no—
152C2×D44—22no—
153C2×D44—21no—
154C2×D44C22×C411yescharacteristic
155C2×D44C22×C411yescharacteristic
156C2×D44C22×C411yescharacteristic
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—81no—
163C2×C4×D11—81no—
164C2×Dic22C22×C411yescharacteristic
165C11×M16—81no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11C22×C411yescharacteristic
171C2×C8×C11C22×C411yescharacteristic
172C2×C8×C11C22×C411yescharacteristic
173C2×C8×C11C22×C411yescharacteristic
174C42×C11C22×C411yescharacteristic
175C42×C11C2×D411yescharacteristic
176C42×C11#4111yescharacteristic
177C42×C11C2411yescharacteristic
178C22⋊Dic11—21no—
179(C2×D11)⋊C4—21no—
180(C2×D11)⋊C4—21no—
181(C2×D11)⋊C4—21no—
182(C2×D11)⋊C4—21no—
183(C2×D11)⋊C4—21no—
184(C2×D11)⋊C4—21no—
185(C2×D11)⋊C4—21no—
186(C2×D11)⋊C4—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11C22×C411yescharacteristic
189C4⋊Dic11C22×C411yescharacteristic
190C4⋊Dic11C22×C411yescharacteristic
191C4⋊Dic11C22×C411yescharacteristic
192Dic11⋊C4—21no—
193Dic11⋊C4—21no—
194Dic11⋊C4—21no—
195Dic11⋊C4—21no—
196C4×Dic11—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8C2×D411yescharacteristic
200C2×C11⋊C8C2×D411yescharacteristic
201C2×C11⋊C8C2×D411yescharacteristic
202C2×C11⋊C8C2×D411yescharacteristic
203D88—22no—
204D88—22no—
205#4314—22no—
206#4314—22no—
207#4313—81no—
208C8×D11—81no—
209C8×D11—81no—
210C8×D11—81no—
211C8×D11—81no—
212C8×D11—81no—
213#3105—111no—
214#2993—111no—
215#2972—111no—
216#1586—111no—
217#1585—111no—
218#1582—111no—
219#1581—111no—
220#1580—111no—
221SD16⋊C8—111no—
222C8×SD16—111no—
223C8×D8—111no—
224#1574D1111yescharacteristic, complemented
225#1486—111no—
226#1482—111no—
227#1454—111no—
228C23×C11C4×D411yescharacteristic
229C22×D11—21no—
230C22×D11—21no—
231C22×D11—24no—
232C22×D11—21no—
233C22×D11—81no—
234C22×D11—81no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—41no—
240C2×C4×C11C4×D411yescharacteristic
241C2×C4×C11C4×D411yescharacteristic
242C2×C4×C11C4×D411yescharacteristic
243C2×C4×C11C23×C411yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C22⋊D11—81no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—81no—
253D44—24no—
254D44—21no—
255D44—21no—
256D44—21no—
257D44—21no—
258D44#13112yes—
259D44#13112yes—
260C4×D11—41no—
261C4×D11—41no—
262C4×D11—41no—
263C4×D11—41no—
264C4×D11—41no—
265C4×D11—41no—
266C4×D11—81no—
267C4×D11—81no—
268Dic22—21no—
269Dic22—21no—
270C8×C11—21no—
271C8×C11—21no—
272C8×C11—21no—
273C8×C11—21no—
274C8×C11—41no—
275C8×C11—41no—
276C8×C11—41no—
277C8×C11—41no—
278C11⋊C8—21no—
279C11⋊C8—21no—
280C11⋊C8—21no—
281C11⋊C8—21no—
282C11⋊C8—41no—
283C11⋊C8—41no—
284#529—111no—
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#446—111no—
295C8×Q8—111no—
296C4×SD16—111no—
297C4×SD16—111no—
298C4×D8—111no—
299C4×D8—111no—
300#436—111no—
301#436—221no—
302#435—221no—
303C8×D4—111no—
304C8×D4—111no—
305C8×D4—111no—
306C8×D4—111no—
307C8×D4—111no—
308C8×D4—221no—
309C8×D4—221no—
310#433—221no—
311#431—111no—
312#431—111no—
313#431C2×D1111yescharacteristic
314#431C2×D1111yescharacteristic
315#424—221no—
316#423C2×D1111yescharacteristic
317C2×C22⋊C8—221no—
318C2×C22⋊C8—221no—
319#335C2×D1111yescharacteristic, complemented
320#335C2×D1111yescharacteristic, complemented
321#334C2×D1111yescharacteristic, complemented
322#334C2×D1111yescharacteristic, complemented
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×C11C2×C4×D411yescharacteristic
339C2×D11—22no—
340C2×D11—22no—
341C2×D11—41no—
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×C11C2×#13111yescharacteristic
354C4×C11C2×#13111yescharacteristic
355C4×C11#57611yescharacteristic
356C4×C11#57711yescharacteristic
357Dic11—41no—
358Dic11—41no—
359Dic11—41no—
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—221no—
370C22×C8—221no—
371C22×C8—221no—
372C22×C8—221no—
373C22×C8—221no—
374C22×C8—221no—
375#126—221no—
376#125—111no—
377#124—111no—
378#123—221no—
379C22⋊Q8—111no—
380#121—111no—
381C4×Q8—111no—
382C4×D4—111no—
383C4×D4—111no—
384C4×D4—111no—
385C4×D4—111no—
386C4×D4—111no—
387C4×D4—221no—
388C4×D4—221no—
389C4×D4—221no—
390#117—221no—
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—111no—
400C4⋊C8—111no—
401C4⋊C8—221no—
402C4⋊C8—221no—
403C4⋊C8—221no—
404C4⋊C8C4×D1111yescharacteristic
405C4⋊C8C4×D1111yescharacteristic
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—111no—
420C22⋊C8—111no—
421C22⋊C8—221no—
422C22⋊C8—221no—
423C22⋊C8—221no—
424C22⋊C8—221no—
425C22⋊C8—221no—
426C22⋊C8—221no—
427C22⋊C8—221no—
428C22⋊C8C4×D1111yescharacteristic
429C22⋊C8C4×D1111yescharacteristic
430#97—221no—
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#292911yescharacteristic
441C2×C11#294611yescharacteristic
442C2×C11#295711yescharacteristic
443D11—42no—
444D11—42no—
445D11—81no—
446C24—221no—
447C2×Q8—111no—
448C2×D4—111no—
449C2×D4—111no—
450C2×D4—111no—
451C2×D4—222no—
452C2×D4—222no—
453C2×D4—221no—
454C2×D4—221no—
455C22×C4—221no—
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×C4D4×D1111yescharacteristic
465C22×C4#434311yescharacteristic
466SD16—222no—
467SD16—222no—
468D8—222no—
469D8—222no—
470M16—81no—
471M16—881no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—111no—
477C2×C8—111no—
478C2×C8—111no—
479C2×C8—111no—
480C2×C8—221no—
481C2×C8—221no—
482C2×C8—881no—
483C2×C8—881no—
484C2×C8—881no—
485C2×C8—881no—
486C2×C8—881no—
487C2×C8C2×C4×D1111yescharacteristic
488C2×C8C2×C4×D1111yescharacteristic
489C2×C8C2×C4×D1111yescharacteristic
490C2×C8C2×C4×D1111yescharacteristic
491C4⋊C4—111no—
492C4⋊C4—111no—
493C4⋊C4—111no—
494C4⋊C4—111no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C22⋊C4—221no—
501C22⋊C4—221no—
502C22⋊C4—221no—
503C22⋊C4—221no—
504C22⋊C4—221no—
505C22⋊C4—221no—
506C22⋊C4—221no—
507C22⋊C4—221no—
508C22⋊C4—221no—
509C42—221no—
510C42C2×C4×D1111yescharacteristic
511C42D4×D1111yescharacteristic
512C42#434311yescharacteristic
513C42C23×D1111yescharacteristic
514C11#1791811yescharacteristic, complemented, Sylow
515C23—224no—
516C23—221no—
517C23—221no—
518C23—221no—
519C23—881no—
520C23—881no—
521C23#6694611yescharacteristic
522Q8—221no—
523Q8—221no—
524D4—112no—
525D4—112no—
526D4—224no—
527D4—221no—
528D4—221no—
529D4—221no—
530D4—221no—
531D4—881no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—221no—
538C2×C4—221no—
539C2×C4—221no—
540C2×C4—221no—
541C2×C4—221no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—881no—
549C2×C4—881no—
550C2×C4—881no—
551C2×C4#6694611yescharacteristic
552C2×C4#6694611yescharacteristic
553C2×C4#6694611yescharacteristic
554C2×C4C22×C4×D1111yescharacteristic
555C2×C4C2×D4×D1111yescharacteristic
556C2×C4C2×#434311yescharacteristic
557C8—21no—
558C8—21no—
559C8—21no—
560C8—21no—
561C8—41no—
562C8—41no—
563C8—41no—
564C8—41no—
565C8—221no—
566C8—221no—
567C8—221no—
568C8—221no—
569C8—441no—
570C8—441no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—222no—
575C22—222no—
576C22—441no—
577C22—441no—
578C22—441no—
579C22—441no—
580C22—441no—
581C22—441no—
582C22—441no—
583C22—884no—
584C22C2×#6694611yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—441no—
590C4—441no—
591C4—441no—
592C4—441no—
593C4—441no—
594C4D11×#13111yescharacteristic
595C4D11×#13111yescharacteristic
596C4#1062330511yescharacteristic
597C4#1062330911yescharacteristic
598C2—41no—
599C2—442no—
600C2—442no—
601C2—881no—
602C2#1307730911yescharacteristic
603C2#1307744611yescharacteristic
604C2#1307753211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1574C2
socleC22×C11C2×C4×D4
prime radical#10622345C4
cosocleC42×C11C24
hypercenter#1574D11
hypocenterC11#17918
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1574

Complements

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

NH ≅ G/Ntype
2. #13077761C2semidirect
3. #13077639C2semidirect
4. #13067479C2semidirect
5. #13067472C2semidirect
6. #13067451C2semidirect
7. #13067444C2semidirect
8. #13067439C2semidirect
9. #13067427C2semidirect
10. #13067415C2semidirect
11. #13067410C2semidirect
12. #13067040C2semidirect
13. #13067022C2semidirect
14. #13066916C2semidirect
15. C11×#1574C2semidirect
31. #10622451C22semidirect
36. #10622447C22semidirect
37. #10622444C22semidirect
38. #10622443C22semidirect
51. C11×#335C22semidirect
52. C11×#335C22semidirect
53. C11×#334C22semidirect
54. C11×#334C22semidirect
55. #10622122C22semidirect
56. #10622122C22semidirect
61. #10622121C22semidirect
62. #10622121C22semidirect
63. #10622093C22semidirect
64. #10622092C22semidirect
65. #10622092C22semidirect
66. C8×C11⋊C8C22semidirect
224. #1574D11semidirect
319. #335C2×D11semidirect
320. #335C2×D11semidirect
321. #334C2×D11semidirect
322. #334C2×D11semidirect
514. C11#17918semidirect

Maximal subgroups

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

subgroupindex
#130786652
#130777612
#130776392
#130674792
#130674722
#130674512
#130674442
#130674392
#130674272
#130674152
#130674102
#130670402
#130670222
#130669162
C11×#15742
#1791811