Finite Group Databasebeta

← #14796434

Subgroups — #14796434

Order 2816.

910 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622483C211yesmaximal, characteristic
2C2×#10622465C211yesmaximal, characteristic
3#13073822C211yesmaximal, characteristic, complemented
4#13071517C211yesmaximal, characteristic
5#13070095C211yesmaximal, characteristic, complemented
6#13069994C211yesmaximal, characteristic, complemented
7#13069992C211yesmaximal, characteristic, complemented
8#13069575C211yesmaximal, characteristic, complemented
9#13069333C211yesmaximal, characteristic, complemented
10#13068951C211yesmaximal, characteristic
11#13068949C211yesmaximal, characteristic
12#13068620C211yesmaximal, characteristic, complemented
13#13068615C211yesmaximal, characteristic
14#13068613C211yesmaximal, characteristic
15C11×#2084C211yesmaximal, characteristic, complemented
16C22×#4314C2211yescharacteristic
17C2×#66946C2211yescharacteristic
18C2×#66946C2211yescharacteristic
19C2×C4⋊C4×D11—21no—
20C2×#66941C2211yescharacteristic
21C2×#66940C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×#106C2211yescharacteristic
25C11×#389C2211yescharacteristic
26C11×#384C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×#66880C2211yescharacteristic
29C2×Dic11⋊C8C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31C2×C8×Dic11C2211yescharacteristic
32#10622602—21no—
33#10622598C2211yescharacteristic
34#10622592—21no—
35#10622592—21no—
36#10622589C2211yescharacteristic
37#10622589C2211yescharacteristic
38#10622587C2211yescharacteristic
39#10622585—21no—
40#10622585—21no—
41C2×#66874C2211yescharacteristic
42C2×#66874C2211yescharacteristic
43C2×#66873C2211yescharacteristic
44C2×#66873C2211yescharacteristic
45C2×#66872C2211yescharacteristic
46C4×Dic11⋊C4C2211yescharacteristic
47#10622542C2211yescharacteristic
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49#10622483—24no—
50#10622465—24no—
51#10622281—21no—
52#10622280—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#336C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×D44C2311yescharacteristic
62C22×C4×D11—21no—
63C22×C4×D11—21no—
64C22×C4×D11—21no—
65C22×Dic22—21no—
66C22×Dic22C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C42×C11C2311yescharacteristic
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4D411yescharacteristic
90C2×Dic11⋊C4D411yescharacteristic
91C2×C4×Dic11—21no—
92C2×C4×Dic11C2311yescharacteristic
93C2×C4×Dic11C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C2×#4314—22no—
97C2×#4314—22no—
98C2×#4314Q814yescomplemented
99#66946—22no—
100#66946—22no—
101#66946—41no—
102#66946D414yes—
103C4⋊C4×D11—44no—
104#66941—22no—
105#66941—22no—
106#66940—22no—
107#66940—22no—
108C4×D44—22no—
109C4×D44—41no—
110C11×#106—22no—
111C11×#106—22no—
112C11×#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95D411yescharacteristic
119C11⋊#95D411yescharacteristic
120#66885—22no—
121#66880—41no—
122Dic11⋊C8—22no—
123Dic11⋊C8—41no—
124C8×Dic11—22no—
125#66874—22no—
126#66874—41no—
127#66873—22no—
128#66873—22no—
129#66872—22no—
130C4⋊(C11⋊C8)—41no—
131#24815—111nomaximal, Sylow
132C23×D11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2411yescharacteristic
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11C2×D411yescharacteristic
144C22×Dic11C2×D411yescharacteristic
145C22×Dic11C2×D411yescharacteristic
146C22×Dic11C2×D411yescharacteristic
147C2×D44—21no—
148C2×D44—21no—
149C2×D44—21no—
150C2×D44C2×D412yes—
151C2×D44C2×Q812yes—
152C2×D44#4112yes—
153C2×C4×D11—24no—
154C2×C4×D11—42no—
155C2×C4×D11—42no—
156C2×C4×D11—42no—
157C2×C4×D11—42no—
158C2×C4×D11—42no—
159C2×C4×D11—42no—
160C2×C4×D11—81no—
161C2×C4×D11—81no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22—42no—
168C2×Dic22—81no—
169C2×Dic22—81no—
170C2×Dic22C2×Q812yes—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11C2×Q812yes—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—42no—
185C11×C4⋊C4—81no—
186C11×C4⋊C4—81no—
187C11×C4⋊C4C2×D412yes—
188C42×C11—21no—
189C42×C11—21no—
190(C2×D11)⋊C4—24no—
191(C2×D11)⋊C4—42no—
192(C2×D11)⋊C4—42no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—42no—
198Dic11⋊C4—22no—
199Dic11⋊C4—42no—
200Dic11⋊C4—42no—
201Dic11⋊C4—42no—
202Dic11⋊C4—81no—
203Dic11⋊C4—81no—
204Dic11⋊C4—81no—
205Dic11⋊C4SD1614yescomplemented
206C4×Dic11—21no—
207C4×Dic11—21no—
208C4×Dic11—42no—
209C4×Dic11C2×D412yes—
210C4×Dic11#4112yes—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217#4314—28no—
218C2×#476—111no—
219C2×C4×SD16—111no—
220#2567—111no—
221D4×C4⋊C4—111no—
222#2084—111no—
223#2084D1111yescharacteristic, complemented
224#2066—111no—
225#2066—111no—
226#1990—111no—
227#1939—111no—
228#1877—111no—
229#1877—111no—
230#1803—111no—
231#1802—111no—
232#1802—111no—
233C23×C11C22×D411yescharacteristic
234C22×D11—22no—
235C22×D11—22no—
236C22×D11—22no—
237C22×D11—41no—
238C22×D11—41no—
239C22×D11—41no—
240C22×D11—41no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—22no—
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×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11C2×SD1612yes—
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C22×Q811yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11H(5,𝔽2)11yescharacteristic
264C2×C4×C112−1+411yescharacteristic
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—22no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11#12112yes—
282C2×Dic11#12112yes—
283C2×Dic11C2×SD1612yes—
284C2×Dic11C2×SD1612yes—
285C2×Dic11#13712yes—
286D44—22no—
287D44—22no—
288D44—22no—
289D44C22⋊Q814yes—
290C4×D11—48no—
291C4×D11—84no—
292C4×D11—84no—
293Dic22—22no—
294Dic22—22no—
295Dic22—41no—
296Dic22—41no—
297Dic22—84no—
298C8×C11—22no—
299C8×C11—41no—
300C11⋊C8—41no—
301C11⋊C8—41no—
302C22×SD16—111no—
303C2×C4⋊Q8—111no—
304C2×C4×Q8—111no—
305C2×C4×D4—111no—
306C2×C4×D4—111no—
307C2×C4×D4—111no—
308C22×C4⋊C4—221no—
309#476—224no—
310C4×SD16—224no—
311C2×#106—111no—
312C2×#106C2×D1111yescharacteristic
313C2×#106C2×D1111yescharacteristic
314C2×C4⋊C8—111no—
315C2×C4⋊C8—111no—
316C2×C4⋊C8—111no—
317C2×#103—111no—
318C2×#103—111no—
319C2×#103—111no—
320C2×#102—111no—
321C2×#102—111no—
322C2×#102—111no—
323C2×C4×C8—111no—
324#395—221no—
325#395—221no—
326#391—111no—
327#391—111no—
328#389—111no—
329#389—221no—
330#389—221no—
331#389C2×D1111yescharacteristic
332#385—221no—
333#385—221no—
334#384—111no—
335#384—111no—
336#384C2×D1111yescharacteristic
337#380—221no—
338C4×C4⋊C4—111no—
339#340—111no—
340#340—111no—
341#340—111no—
342#340—111no—
343#340C2×D1111yescharacteristic
344#340C2×D1111yescharacteristic
345#336—111no—
346#336C2×D1111yescharacteristic
347C22×C11C2×#12111yescharacteristic
348C22×C11#54611yescharacteristic
349C22×C11D4×Q811yescharacteristic
350C22×C11C22×SD1611yescharacteristic
351C22×C11C2×#13711yescharacteristic
352C22×C11#57611yescharacteristic
353C22×C11#57711yescharacteristic
354C2×D11—24no—
355C2×D11—42no—
356C2×D11—42no—
357C2×D11—42no—
358C2×D11—42no—
359C2×D11—42no—
360C2×D11—42no—
361C4×C11—22no—
362C4×C11—41no—
363C4×C11—42no—
364C4×C11—81no—
365C4×C11—81no—
366C4×C11—81no—
367C4×C11C2×C22⋊Q811yescharacteristic
368C4×C11#53711yescharacteristic
369C4×C11#55211yescharacteristic
370C4×C11#55411yescharacteristic
371Dic11—22no—
372Dic11—22no—
373Dic11—41no—
374Dic11—42no—
375Dic11—81no—
376Dic11—81no—
377Dic11#46114yes—
378C22×Q8—111no—
379C22×Q8—221no—
380C22×D4—111no—
381C23×C4—221no—
382C23×C4—221no—
383C23×C4—221no—
384C2×SD16—114no—
385C2×SD16—222no—
386C2×SD16—222no—
387C22×C8—111no—
388C22×C8—111no—
389C22×C8C22×D1111yescharacteristic
390C22×C8C22×D1111yescharacteristic
391C4⋊Q8—222no—
392C4⋊Q8—222no—
393C4×Q8—222no—
394C4×Q8—222no—
395C4×D4—114no—
396C4×D4—222no—
397C4×D4—222no—
398C4×D4—222no—
399C4×D4—441no—
400C4×D4—441no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—111no—
407C2×C4⋊C4—111no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4—444no—
416C2×C4⋊C4C22×D1111yescharacteristic
417C2×C4⋊C4C22×D1111yescharacteristic
418C2×C4⋊C4C22×D1111yescharacteristic
419C2×C4⋊C4C22×D1111yescharacteristic
420C2×C22⋊C4—221no—
421C2×C22⋊C4—221no—
422C2×C22⋊C4—221no—
423C2×C42—111no—
424C2×C42—111no—
425C2×C42—221no—
426C2×C42C22×D1111yescharacteristic
427#106—22no—
428#106—22no—
429#106—222no—
430C4⋊C8—222no—
431C4⋊C8—441no—
432C4⋊C8—441no—
433#103—222no—
434#103—441no—
435#103—441no—
436#102—222no—
437#102—222no—
438#102—222no—
439C4×C8—222no—
440#95—21no—
441#95—111no—
442#95—111no—
443#95—221no—
444#95—221no—
445#95—221no—
446#95—221no—
447#95—221no—
448C2×C11#241711yescharacteristic
449C2×C11C2×#46111yescharacteristic
450C2×C11#304511yescharacteristic
451C2×C11#329511yescharacteristic
452C2×C11#333111yescharacteristic
453C2×C11Q8×SD1611yescharacteristic
454C2×C11#338511yescharacteristic
455D11—44no—
456C24—221no—
457C2×Q8—112no—
458C2×Q8—221no—
459C2×Q8—221no—
460C2×Q8—221no—
461C2×Q8—221no—
462C2×Q8—221no—
463C2×Q8—442no—
464C2×Q8—881no—
465C2×Q8—881no—
466C2×D4—112no—
467C2×D4—112no—
468C2×D4—112no—
469C2×D4—221no—
470C2×D4—221no—
471C2×D4—221no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—111no—
477C22×C4—111no—
478C22×C4—111no—
479C22×C4—111no—
480C22×C4—224no—
481C22×C4—221no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4—442no—
485C22×C4—442no—
486C22×C4—442no—
487C22×C4—442no—
488C22×C4—442no—
489C22×C4—442no—
490C22×C4—881no—
491C22×C4—881no—
492C22×C4D4×D1111yescharacteristic
493C22×C4D4×D1111yescharacteristic
494C22×C4C23×D1111yescharacteristic
495SD16—228no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—221no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8Q8×D1112yes—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—42no—
516C4⋊C4—81no—
517C4⋊C4—81no—
518C4⋊C4—114no—
519C4⋊C4—222no—
520C4⋊C4—221no—
521C4⋊C4—221no—
522C4⋊C4—221no—
523C4⋊C4—221no—
524C4⋊C4—442no—
525C4⋊C4—442no—
526C4⋊C4—442no—
527C4⋊C4—442no—
528C4⋊C4—881no—
529C4⋊C4—881no—
530C4⋊C4—881no—
531C4⋊C4D4×D1112yes—
532C22⋊C4—224no—
533C22⋊C4—442no—
534C22⋊C4—442no—
535C42—21no—
536C42—21no—
537C42—112no—
538C42—112no—
539C42—221no—
540C42—221no—
541C42—442no—
542C11#2481511yescharacteristic, complemented, Sylow
543C23—222no—
544C23—222no—
545C23—222no—
546C23—441no—
547C23—441no—
548C23—441no—
549C23—441no—
550C23C2×D4×D1111yescharacteristic
551Q8—222no—
552Q8—222no—
553Q8—441no—
554Q8—441no—
555Q8—884no—
556D4—114no—
557D4—222no—
558D4—222no—
559D4—222no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—21no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—112no—
578C2×C4—112no—
579C2×C4—112no—
580C2×C4—112no—
581C2×C4—112no—
582C2×C4—221no—
583C2×C4—221no—
584C2×C4—221no—
585C2×C4—221no—
586C2×C4—222no—
587C2×C4—221no—
588C2×C4—221no—
589C2×C4—221no—
590C2×C4—448no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—884no—
600C2×C4—884no—
601C2×C4SD16×D1112yes—
602C2×C4C2×D4×D1111yescharacteristic
603C2×C4C2×Q8×D1111yescharacteristic
604C2×C4#6704011yescharacteristic
605C2×C4#41×D1111yescharacteristic
606C2×C4#41×D1111yescharacteristic
607C2×C4#6704211yescharacteristic
608C8—22no—
609C8—41no—
610C8—441no—
611C8—441no—
612C22—224no—
613C22—442no—
614C22—442no—
615C22—442no—
616C22—442no—
617C22—442no—
618C22—442no—
619C22D11×#12111yescharacteristic
620C22#1062318511yescharacteristic
621C22#1062325811yescharacteristic
622C22C2×SD16×D1111yescharacteristic
623C22#1062329311yescharacteristic
624C22#1062330511yescharacteristic
625C22D11×#13711yescharacteristic
626C4—22no—
627C4—42no—
628C4—41no—
629C4—81no—
630C4—81no—
631C4—81no—
632C4—114no—
633C4—222no—
634C4—222no—
635C4—441no—
636C4—442no—
637C4—881no—
638C4—881no—
639C4D11×C22⋊Q811yescharacteristic
640C4#1062316011yescharacteristic
641C4#1062322111yescharacteristic
642C4#1062322411yescharacteristic
643C2—444no—
644C2#1307206211yescharacteristic
645C2D11×#46111yescharacteristic
646C2#1307815211yescharacteristic
647C2#1308043811yescharacteristic
648C2#1308093011yescharacteristic
649C2#1308147311yescharacteristic
650C2#1308152311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2084C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#2084D11
hypocenterC11#24815
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2084

Complements

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

NH ≅ G/Ntype
3. #13073822C2semidirect
5. #13070095C2semidirect
6. #13069994C2semidirect
7. #13069992C2semidirect
8. #13069575C2semidirect
9. #13069333C2semidirect
12. #13068620C2semidirect
15. C11×#2084C2semidirect
98. C2×#4314Q8semidirect
205. Dic11⋊C4SD16semidirect
223. #2084D11semidirect
542. C11#24815semidirect

Maximal subgroups

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

subgroupindex
C2×#106224832
C2×#106224652
#130738222
#130715172
#130700952
#130699942
#130699922
#130695752
#130693332
#130689512
#130689492
#130686202
#130686152
#130686132
C11×#20842
#2481511