Finite Group Databasebeta

← #14790086

Subgroups — #14790086

Order 2816.

988 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#13078417C211yesmaximal, characteristic, complemented
2C4×#67004C211yesmaximal, characteristic
3#13073832C211yesmaximal, characteristic, complemented
4#13069963C212yesmaximal, complemented
5#13069774C212yesmaximal, complemented
6#13069606C211yesmaximal, characteristic, complemented
7#13069561C211yesmaximal, characteristic, complemented
8#13068985C212yesmaximal
9#13068849C212yesmaximal
10#13068636C211yesmaximal, characteristic
11C11×#3503C211yesmaximal, characteristic
12Q82×C11—21no—
13C11×#557—21no—
14C11×#554—21no—
15C11×#554—22no—
16D4×Q8×C11—22no—
17D4×Q8×C11—21no—
18C11×#544—22no—
19C11×#544C2212yes—
20C11×#533—21no—
21C11×#533C2211yescharacteristic
22C2×C11×C4⋊Q8—21no—
23C2×C11×C4⋊Q8C2211yescharacteristic
24C11×#520C2212yes—
25C4×C11×#41C2211yescharacteristic
26C2×#67004C2211yescharacteristic
27C2×C4×Dic22C2211yescharacteristic
28C2×#66901C2212yes—
29#10622845C2211yescharacteristic
30#10622843—22no—
31#10622707—21no—
32#10622704—21no—
33#10622676—22no—
34#10622643—21no—
35C4×#4326—21no—
36#10622631—21no—
37C4×#4324—21no—
38#10622617C2212yes—
39#10622617C2211yescharacteristic
40#10622608C2212yes—
41#10622608C2211yescharacteristic
42#10622595—22no—
43#10622590C2212yes—
44#10622587C2212yes—
45C4×C4⋊Dic11C2211yescharacteristic
46#10622537C2211yescharacteristic
47C4×#4318C2211yescharacteristic
48#10622170C2212yes—
49#10622170C2212yes—
50#10622170C2212yes—
51#10622168C2212yes—
52#10622168C2212yes—
53C2×C11×#41C2311yescharacteristic
54C22×Q8×C11—22no—
55C22×Q8×C11D412yes—
56C22×Dic22C2311yescharacteristic
57C11×C4⋊Q8—22no—
58C11×C4⋊Q8—22no—
59C11×C4⋊Q8—24no—
60C11×C4⋊Q8—22no—
61C11×C4⋊Q8—22no—
62C11×C4⋊Q8—21no—
63C11×C4⋊Q8—21no—
64C11×C4⋊Q8—21no—
65C11×C4⋊Q8—21no—
66C11×C4⋊Q8D411yescharacteristic
67C11×C4⋊Q8D411yescharacteristic
68C11×#125—24no—
69C11×#125—22no—
70C11×#125—22no—
71C11×#125D412yes—
72C11×C22⋊Q8—22no—
73C11×C22⋊Q8—22no—
74C11×C22⋊Q8—24no—
75C11×C22⋊Q8—24no—
76C11×C22⋊Q8—21no—
77C11×C22⋊Q8—21no—
78C11×C22⋊Q8—24no—
79C4×Q8×C11—22no—
80C4×Q8×C11—22no—
81C4×Q8×C11—22no—
82C4×Q8×C11—21no—
83C4×Q8×C11—21no—
84C4×Q8×C11D411yescharacteristic
85C4×Q8×C11D411yescharacteristic
86C4×D4×C11—22no—
87C4×D4×C11—21no—
88C4×D4×C11—21no—
89C4×D4×C11—24no—
90C4×D4×C11D411yescharacteristic
91C4×D4×C11D411yescharacteristic
92C11×#117—22no—
93C11×#117—21no—
94C11×#117C2311yescharacteristic
95C11×#117C2312yes—
96C2×C11×C4⋊C4—22no—
97C2×C11×C4⋊C4—22no—
98C2×C11×C4⋊C4D412yes—
99C2×C11×C4⋊C4C2312yes—
100C2×C42×C11—21no—
101C2×C42×C11C2311yescharacteristic
102#67004—22no—
103#67004Q814yescomplemented
104C2×#4326—21no—
105C2×#4324—21no—
106C2×C4⋊Dic11—21no—
107C2×C4⋊Dic11C2311yescharacteristic
108C2×Dic11⋊C4—21no—
109C2×C4×Dic11—21no—
110C2×C4×Dic11C2312yes—
111C2×#4318C2311yescharacteristic
112C2×#4318C2312yes—
113C2×#4318C2311yescharacteristic
114C4×Dic22—21no—
115C4×Dic22—21no—
116C4×Dic22—21no—
117C4×Dic22—21no—
118#66901—24no—
119#66899—21no—
120#66896—21no—
121C11⋊#95—21no—
122C11⋊#95—24no—
123C11⋊#95—24no—
124#66874—21no—
125#66874—21no—
126#66874—22no—
127#66874—22no—
128#66872—21no—
129#66872—22no—
130#66871—21no—
131#66871—22no—
132C4⋊(C11⋊C8)—21no—
133C4⋊(C11⋊C8)—21no—
134#66867—21no—
135C4×C11⋊C8—21no—
136#24322—111nomaximal, Sylow
137C11×#41—21no—
138C11×#41—21no—
139C11×#41C2×Q812yes—
140C11×#41#4112yes—
141C2×Q8×C11—24no—
142C2×Q8×C11—21no—
143C2×Q8×C11—22no—
144C2×Q8×C11—21no—
145C2×Q8×C11—22no—
146C2×Q8×C11—44no—
147C2×Q8×C11—84no—
148C2×Q8×C11C2×D411yescharacteristic
149C2×D4×C11—21no—
150C2×D4×C11C2×D411yescharacteristic
151C22×C4×C11—21no—
152C22×C4×C11—24no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D414yes—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2411yescharacteristic
159C22×Dic11—21no—
160C22×Dic11—22no—
161C22×Dic11—21no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22C2×Q812yescomplemented
168C11×C4⋊C4—24no—
169C11×C4⋊C4—24no—
170C11×C4⋊C4—24no—
171C11×C4⋊C4—24no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4C2×D412yes—
183C11×C4⋊C4C2×D411yescharacteristic
184C11×C4⋊C4C2×D412yes—
185C11×C4⋊C4C2×D411yescharacteristic
186C11×C22⋊C4—24no—
187C11×C22⋊C4—22no—
188C11×C22⋊C4—21no—
189C11×C22⋊C4—21no—
190C11×C22⋊C4—21no—
191C42×C11—24no—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11—22no—
196C42×C11C2×D411yescharacteristic
197C42×C11C2×D411yescharacteristic
198C42×C11C2×D411yescharacteristic
199C42×C11C2×D411yescharacteristic
200#4326—24no—
201#4324—24no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—42no—
205Dic11⋊C4—41no—
206Dic11⋊C4—41no—
207C4×Dic11—22no—
208C4×Dic11—22no—
209C4×Dic11—41no—
210C4×Dic11—41no—
211#4318—21no—
212#4318—22no—
213#4318—21no—
214#4318—22no—
215#4318—21no—
216#4318C2×Q812yescomplemented
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—22no—
220#3503D1111yescharacteristic
221#3078—111no—
222C4×#137—111no—
223#2568—111no—
224#2061—112no—
225#2028—112no—
226#1997—111no—
227#1986—111no—
228#1882—112no—
229#1860—112no—
230#1806—111no—
231C23×C11—21no—
232C23×C11C22×D411yescharacteristic
233Q8×C11—21no—
234Q8×C11—42no—
235Q8×C11—44no—
236Q8×C11—42no—
237Q8×C11—82no—
238Q8×C11—84no—
239Q8×C11C22⋊Q812yes—
240D4×C11—22no—
241D4×C11—22no—
242D4×C11—21no—
243D4×C11C22⋊Q812yes—
244C2×C4×C11—21no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—24no—
252C2×C4×C11—22no—
253C2×C4×C11—41no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11—44no—
257C2×C4×C11—84no—
258C2×C4×C11#12011yescharacteristic
259C2×C4×C11#12011yescharacteristic
260C2×C4×C11#12011yescharacteristic
261C2×C4×C11#12011yescharacteristic
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11C22×Q811yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C112−1+411yescharacteristic
267C2×C4×C112−1+411yescharacteristic
268C2×Dic11—22no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—42no—
272C2×Dic11—42no—
273C2×Dic11—42no—
274C2×Dic11—41no—
275C2×Dic11—42no—
276Dic22—22no—
277Dic22—22no—
278Dic22—41no—
279Dic22—41no—
280C11⋊C8—22no—
281C11⋊C8—41no—
282C11⋊C8—42no—
283C2×#137—111no—
284Q82—21no—
285#557—21no—
286#554—21no—
287#554—22no—
288D4×Q8—22no—
289D4×Q8—21no—
290#544—22no—
291#544C2×D1112yes—
292#533—21no—
293#533C2×D1111yescharacteristic
294C2×C4⋊Q8—21no—
295C2×C4⋊Q8C2×D1111yescharacteristic
296#520C2×D1112yes—
297C4×#41C2×D1111yescharacteristic
298C2×C4×Q8—111no—
299#479—222no—
300#477—221no—
301#475—221no—
302#441—221no—
303#440—221no—
304C4×Q16—221no—
305C4×SD16—221no—
306#428—112no—
307#428—111no—
308#423—111no—
309C2×#104—112no—
310#419—112no—
311#419—111no—
312#417—111no—
313C4×M16—111no—
314#400—222no—
315#391—112no—
316#391—222no—
317#382—112no—
318C4×C4⋊C4—111no—
319#343—112no—
320#343—112no—
321#339—112no—
322#339—112no—
323#339—112no—
324C22×C11—21no—
325C22×C11—21no—
326C22×C11—22no—
327C22×C11—41no—
328C22×C11—41no—
329C22×C11C2×#12011yescharacteristic
330C22×C11#54811yescharacteristic
331C22×C11D4×Q811yescharacteristic
332C4×C11—22no—
333C4×C11—21no—
334C4×C11—21no—
335C4×C11—21no—
336C4×C11—41no—
337C4×C11—44no—
338C4×C11—42no—
339C4×C11—41no—
340C4×C11—42no—
341C4×C11#45512yes—
342C4×C11C2×C22⋊Q811yescharacteristic
343C4×C11#53611yescharacteristic
344C4×C11#54811yescharacteristic
345C4×C11D4×Q811yescharacteristic
346Dic11—42no—
347Dic11—82no—
348Dic11—81no—
349C2×#41C22×D1111yescharacteristic
350C22×Q8—22no—
351C22×Q8—111no—
352C22×Q8C22⋊D1112yes—
353#137—114no—
354#137—222no—
355C2×Q16—221no—
356C2×SD16—221no—
357C2×M16—111no—
358C2×M16—111no—
359C2×M16—112no—
360C4⋊Q8—22no—
361C4⋊Q8—22no—
362C4⋊Q8—24no—
363C4⋊Q8—22no—
364C4⋊Q8—22no—
365C4⋊Q8—21no—
366C4⋊Q8—21no—
367C4⋊Q8—21no—
368C4⋊Q8—21no—
369C4⋊Q8C22⋊D1111yescharacteristic
370C4⋊Q8C22⋊D1111yescharacteristic
371#125—24no—
372#125—22no—
373#125—22no—
374#125C22⋊D1112yes—
375C22⋊Q8—22no—
376C22⋊Q8—22no—
377C22⋊Q8—24no—
378C22⋊Q8—24no—
379C22⋊Q8—21no—
380C22⋊Q8—21no—
381C22⋊Q8—24no—
382C4×Q8—22no—
383C4×Q8—22no—
384C4×Q8—22no—
385C4×Q8—21no—
386C4×Q8—21no—
387C4×Q8—221no—
388C4×Q8—221no—
389C4×Q8—221no—
390C4×Q8—221no—
391C4×Q8C22⋊D1111yescharacteristic
392C4×Q8C22⋊D1111yescharacteristic
393C4×D4—22no—
394C4×D4—21no—
395C4×D4—21no—
396C4×D4—24no—
397C4×D4C22⋊D1111yescharacteristic
398C4×D4C22⋊D1111yescharacteristic
399#117—22no—
400#117—21no—
401#117C22×D1111yescharacteristic
402#117C22×D1112yes—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4C22⋊D1112yes—
409C2×C4⋊C4C22×D1112yes—
410C2×C42—21no—
411C2×C42—112no—
412C2×C42—221no—
413C2×C42C22×D1111yescharacteristic
414#107—221no—
415#107—222no—
416#106—221no—
417#106—222no—
418C4⋊C8—221no—
419C4⋊C8—221no—
420#104—224no—
421#103—221no—
422#103—221no—
423#103—221no—
424#103—222no—
425#103—222no—
426#102—221no—
427#97—221no—
428C4×C8—221no—
429#95—221no—
430#95—224no—
431#95—224no—
432C2×C11—21no—
433C2×C11—21no—
434C2×C11—42no—
435C2×C11#240911yescharacteristic
436C2×C11C2×#45511yescharacteristic
437C2×C11#302011yescharacteristic
438#41—21no—
439#41—21no—
440#41Q8×D1112yes—
441#41#434312yes—
442C2×Q8—24no—
443C2×Q8—21no—
444C2×Q8—22no—
445C2×Q8—21no—
446C2×Q8—22no—
447C2×Q8—44no—
448C2×Q8—84no—
449C2×Q8—112no—
450C2×Q8—221no—
451C2×Q8—221no—
452C2×Q8—221no—
453C2×Q8—221no—
454C2×Q8—221no—
455C2×Q8C2×C22⋊D1111yescharacteristic
456C2×D4—21no—
457C2×D4C2×C22⋊D1111yescharacteristic
458C22×C4—21no—
459C22×C4—24no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—221no—
463C22×C4—222no—
464C22×C4—221no—
465C22×C4C2×C22⋊D1111yescharacteristic
466C22×C4C2×C22⋊D1114yes—
467C22×C4C2×C22⋊D1111yescharacteristic
468C22×C4C23×D1111yescharacteristic
469Q16—224no—
470SD16—224no—
471M16—112no—
472M16—221no—
473M16—222no—
474M16—221no—
475M16—221no—
476M16—222no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8—222no—
480C4⋊C4—24no—
481C4⋊C4—24no—
482C4⋊C4—24no—
483C4⋊C4—24no—
484C4⋊C4—21no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—442no—
497C4⋊C4—441no—
498C4⋊C4—441no—
499C4⋊C4C2×C22⋊D1112yes—
500C4⋊C4C2×C22⋊D1111yescharacteristic
501C4⋊C4C2×C22⋊D1112yes—
502C4⋊C4C2×C22⋊D1111yescharacteristic
503C22⋊C4—24no—
504C22⋊C4—22no—
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C42—24no—
509C42—21no—
510C42—21no—
511C42—21no—
512C42—22no—
513C42—222no—
514C42—222no—
515C42—441no—
516C42—441no—
517C42C2×C22⋊D1111yescharacteristic
518C42C2×C22⋊D1111yescharacteristic
519C42C2×C22⋊D1111yescharacteristic
520C42C2×C22⋊D1111yescharacteristic
521C11#2432211yescharacteristic, complemented, Sylow
522C23—21no—
523C23C22×C22⋊D1111yescharacteristic
524Q8—21no—
525Q8—42no—
526Q8—44no—
527Q8—42no—
528Q8—82no—
529Q8—84no—
530Q8—222no—
531Q8—222no—
532Q8—441no—
533Q8—441no—
534Q8#6699912yes—
535D4—22no—
536D4—22no—
537D4—21no—
538D4#6699912yes—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—24no—
547C2×C4—22no—
548C2×C4—41no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—44no—
552C2×C4—84no—
553C2×C4—222no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—442no—
557C2×C4—442no—
558C2×C4—442no—
559C2×C4—442no—
560C2×C4—441no—
561C2×C4#6700611yescharacteristic
562C2×C4#6700611yescharacteristic
563C2×C4#6700611yescharacteristic
564C2×C4#6700611yescharacteristic
565C2×C4C2×Q8×D1111yescharacteristic
566C2×C4C2×#434311yescharacteristic
567C2×C4#6704011yescharacteristic
568C2×C4#6704011yescharacteristic
569C2×C4C22×C22⋊D1111yescharacteristic
570C2×C4C22×C22⋊D1111yescharacteristic
571C8—222no—
572C8—441no—
573C8—442no—
574C22—21no—
575C22—21no—
576C22—22no—
577C22—41no—
578C22—41no—
579C22Q8×C22⋊D1111yescharacteristic
580C22#1062334811yescharacteristic
581C22C2×#6700611yescharacteristic
582C4—22no—
583C4—21no—
584C4—21no—
585C4—21no—
586C4—41no—
587C4—44no—
588C4—42no—
589C4—41no—
590C4—42no—
591C4—442no—
592C4—882no—
593C4—881no—
594C4#1062285512yes—
595C4C2×#6699911yescharacteristic
596C4Q8×C22⋊D1111yescharacteristic
597C4#1062334711yescharacteristic
598C4#1062334811yescharacteristic
599C2—21no—
600C2—21no—
601C2—42no—
602C2#1307197511yescharacteristic
603C2C2×#1062285511yescharacteristic
604C2#1307798011yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3503C2
socleC22×C11C2×#120
prime radicalC2×C11×#41C23
hypercenter#3503D11
hypocenterC11#24322
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3503

Complements

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

NH ≅ G/Ntype
1. #13078417C2semidirect
3. #13073832C2semidirect
4. #13069963C2semidirect
5. #13069774C2semidirect
6. #13069606C2semidirect
7. #13069561C2semidirect
103. #67004Q8semidirect
167. C2×Dic22C2×Q8semidirect
216. #4318C2×Q8semidirect
521. C11#24322semidirect

Maximal subgroups

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

subgroupindex
#130784172
C4×#670042
#130738322
#130699632
#130697742
#130696062
#130695612
#130689852
#130688492
#130686362
C11×#35032
#2432211