Finite Group Databasebeta

← #14677234

Subgroups — #14677234

Order 2816.

2054 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66997C211yesmaximal, characteristic
2C2×#10622843C211yesmaximal, characteristic
3C2×#10622542C211yesmaximal, characteristic
4C2×#10622587C211yesmaximal, characteristic
5#13066866C214yesmaximal
6#13066849C214yesmaximal
7#13066845C211yesmaximal, characteristic
8C4×C11⋊#95C211yesmaximal, characteristic
9C22×C4×Q8×C11C211yesmaximal, characteristic
10C23×Q8×C11C2211yescharacteristic
11C23×Dic22C2211yescharacteristic
12C2×C4×Q8×C11—24no—
13C2×C4×Q8×C11—24no—
14C2×C4×Q8×C11—24no—
15C22×C11×C4⋊C4C2212yes—
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C42×C11C2212yes—
18C22×C42×C11C2211yescharacteristic
19C2×#66997—24no—
20C2×#66997—24no—
21C2×#66997C418yescomplemented
22C22×C4⋊Dic11C2211yescharacteristic
23C22×Dic11⋊C4C2214yes—
24C22×C4×Dic11C2211yescharacteristic
25C22×C4×Dic11C2211yescharacteristic
26#10622843—24no—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2214yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2214yes—
31C2×C11⋊#95C2214yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34#10622587—24no—
35#10622542—24no—
36C22×Q8×C11—22no—
37C22×Q8×C11—22no—
38C22×Q8×C11—22no—
39C22×Q8×C11—22no—
40C22×Q8×C11C2×C414yes—
41C22×Q8×C11D414yes—
42C22×Q8×C11D414yes—
43C23×C4×C11C2312yes—
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2312yes—
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C23×Dic11C2312yes—
49C23×Dic11C2312yes—
50C23×Dic11C2312yes—
51C23×Dic11C2312yes—
52C22×Dic22—22no—
53C22×Dic22—22no—
54C22×Dic22—22no—
55C22×Dic22—22no—
56C22×Dic22—22no—
57C22×Dic22—22no—
58C22×Dic22C2×C414yes—
59C4×Q8×C11—232no—
60C2×C11×C4⋊C4—24no—
61C2×C11×C4⋊C4—24no—
62C2×C11×C4⋊C4—24no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4D414yes—
66C2×C42×C11—24no—
67C2×C42×C11—24no—
68C2×C42×C11—24no—
69C2×C42×C11—22no—
70C2×C42×C11—22no—
71C2×C42×C11D414yes—
72#66997—232no—
73C2×C4⋊Dic11—22no—
74C2×C4⋊Dic11—22no—
75C2×C4⋊Dic11—22no—
76C2×Dic11⋊C4—28no—
77C2×Dic11⋊C4—28no—
78C2×Dic11⋊C4C2×C4116yes—
79C2×C4×Dic11—22no—
80C2×C4×Dic11—22no—
81C2×C4×Dic11—22no—
82C2×C4×Dic11—22no—
83C2×C4×Dic11—22no—
84C2×C4×Dic11C2×C414yes—
85C11⋊#95—24no—
86C11⋊#95—24no—
87C11⋊#95—28no—
88C11⋊#95—28no—
89C11⋊#95—24no—
90C11⋊#95—28no—
91C11⋊#95Q818yescomplemented
92#14024—111nomaximal, Sylow
93C24×C11C2411yescharacteristic
94C2×Q8×C11—28no—
95C2×Q8×C11—28no—
96C2×Q8×C11—28no—
97C2×Q8×C11—28no—
98C2×Q8×C11—28no—
99C2×Q8×C11—28no—
100C2×Q8×C11C22⋊C4116yes—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—21no—
110C22×C4×C11—22no—
111C22×C4×C11—21no—
112C22×C4×C11—22no—
113C22×C4×C11—24no—
114C22×C4×C11—22no—
115C22×C4×C11—24no—
116C22×C4×C11C22×C414yes—
117C22×C4×C11C22×C412yes—
118C22×C4×C11C2×D414yes—
119C22×C4×C11C2×D412yes—
120C22×C4×C11C2×D414yes—
121C22×C4×C11C2×D414yes—
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×Q814yes—
128C22×C4×C11#4112yes—
129C22×C4×C11#4112yes—
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—24no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—24no—
151C22×Dic11C22×C414yes—
152C22×Dic11C22×C414yes—
153C22×Dic11C2×Q814yes—
154C22×Dic11C2×Q814yes—
155C22×Dic11#4114yes—
156C2×Dic22—28no—
157C2×Dic22—28no—
158C2×Dic22—28no—
159C2×Dic22—44no—
160C2×Dic22—44no—
161C2×Dic22—44no—
162C2×Dic22—44no—
163C11×C4⋊C4—216no—
164C11×C4⋊C4—28no—
165C42×C11—216no—
166C42×C11—28no—
167C4⋊Dic11—44no—
168Dic11⋊C4—232no—
169C4×Dic11—28no—
170C4×Dic11—44no—
171C22×C4⋊Q8—111no—
172C22×C4×Q8D1111yescharacteristic
173C2×#391—111no—
174C2×#391—111no—
175C2×#391—111no—
176#1441—114no—
177#1436—114no—
178C4⋊#95—111no—
179C4×#95—111no—
180C23×C11C23×C411yescharacteristic
181C23×C11C22×D411yescharacteristic
182C23×C11C22×D411yescharacteristic
183C23×C11C22×D411yescharacteristic
184C23×C11C22×D411yescharacteristic
185C23×C11C22×Q812yes—
186C23×C11C2×#4111yescharacteristic
187C23×C11C2×#4111yescharacteristic
188C23×C11C2×#4112yes—
189C23×C112−1+412yes—
190C23×C112−1+412yes—
191Q8×C11—232no—
192C2×C4×C11—24no—
193C2×C4×C11—24no—
194C2×C4×C11—22no—
195C2×C4×C11—24no—
196C2×C4×C11—24no—
197C2×C4×C11—24no—
198C2×C4×C11—24no—
199C2×C4×C11—22no—
200C2×C4×C11—24no—
201C2×C4×C11—24no—
202C2×C4×C11—24no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—28no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—44no—
212C2×C4×C11C2×C22⋊C418yes—
213C2×C4×C11C2×C22⋊C414yes—
214C2×C4×C11C4×D414yes—
215C2×C4×C11C4×D414yes—
216C2×C4×C11#12014yes—
217C2×C4×C11#12114yes—
218C2×C4×C11#12114yes—
219C2×C4×C11#12314yes—
220C2×C4×C11C4⋊Q814yescomplemented
221C2×Dic11—24no—
222C2×Dic11—24no—
223C2×Dic11—24no—
224C2×Dic11—24no—
225C2×Dic11—24no—
226C2×Dic11—24no—
227C2×Dic11—24no—
228C2×Dic11—24no—
229C2×Dic11—24no—
230C2×Dic11—24no—
231C2×Dic11—24no—
232C2×Dic11—24no—
233C2×Dic11—42no—
234C2×Dic11—42no—
235C2×Dic11—42no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238C2×Dic11—42no—
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11—44no—
245C2×Dic11—44no—
246C2×Dic11C4×Q818yescomplemented
247Dic22—416no—
248C23×Q8—111no—
249C23×Q8C2×D1111yescharacteristic
250C2×C4⋊Q8—118no—
251C2×C4⋊Q8—224no—
252C2×C4⋊Q8—224no—
253C2×C4×Q8—24no—
254C2×C4×Q8—24no—
255C2×C4×Q8—24no—
256C22×C4⋊C4—114no—
257C22×C4⋊C4—111no—
258C22×C4⋊C4C2×D1112yes—
259C22×C4⋊C4C2×D1111yescharacteristic
260C22×C42—111no—
261C22×C42—111no—
262C22×C42C2×D1112yes—
263C22×C42C2×D1111yescharacteristic
264#391—224no—
265#391—224no—
266#391—224no—
267C2×#95—112no—
268C2×#95—112no—
269C2×#95—114no—
270C2×#95—112no—
271C2×#95—114no—
272C2×#95—114no—
273C2×#95—112no—
274C22×C11C22×C22⋊C411yescharacteristic
275C22×C11C2×C4×D411yescharacteristic
276C22×C11C2×C4×D411yescharacteristic
277C22×C11C2×C4×Q812yes—
278C22×C11#51912yes—
279C22×C11C2×#12011yescharacteristic
280C22×C11C2×#12111yescharacteristic
281C22×C11C2×#12111yescharacteristic
282C22×C11C2×#12311yescharacteristic
283C22×C11C2×C4⋊Q811yescharacteristic
284C22×C11#53211yescharacteristic
285C22×C11#53312yes—
286C22×C11#53611yescharacteristic
287C22×C11#53611yescharacteristic
288C22×C11#54112yes—
289C22×C11#54712yes—
290C22×C11#54812yes—
291C22×C11#54812yes—
292C22×C11D4×Q812yes—
293C22×C11D4×Q812yes—
294C22×C11D4×Q812yes—
295C22×C11#55612yes—
296C22×C11#55712yes—
297C4×C11—24no—
298C4×C11—28no—
299C4×C11—42no—
300C4×C11—44no—
301C4×C11#38618yes—
302Dic11—28no—
303Dic11—44no—
304Dic11—44no—
305Dic11—82no—
306C22×Q8—22no—
307C22×Q8—22no—
308C22×Q8—22no—
309C22×Q8—22no—
310C22×Q8—114no—
311C22×Q8—222no—
312C22×Q8—222no—
313C22×Q8—222no—
314C22×Q8—222no—
315C22×Q8—222no—
316C22×Q8—222no—
317C22×Q8C4×D1114yes—
318C22×Q8D4414yes—
319C22×Q8C22⋊D1114yes—
320C23×C4—112no—
321C23×C4—112no—
322C23×C4—112no—
323C23×C4—112no—
324C23×C4C22×D1112yes—
325C23×C4C22×D1111yescharacteristic
326C23×C4C22×D1112yes—
327C23×C4C22×D1111yescharacteristic
328C23×C4C22×D1111yescharacteristic
329C4⋊Q8—2232no—
330C4×Q8—232no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—1116no—
337C2×C4⋊C4—228no—
338C2×C4⋊C4—228no—
339C2×C4⋊C4—222no—
340C2×C4⋊C4—222no—
341C2×C4⋊C4—222no—
342C2×C4⋊C4C22⋊D1114yes—
343C2×C42—24no—
344C2×C42—24no—
345C2×C42—24no—
346C2×C42—22no—
347C2×C42—22no—
348C2×C42—114no—
349C2×C42—222no—
350C2×C42—222no—
351C2×C42—222no—
352C2×C42—222no—
353C2×C42—222no—
354C2×C42C22⋊D1114yes—
355#95—118no—
356#95—224no—
357#95—228no—
358#95—228no—
359#95—228no—
360#95—224no—
361#95—224no—
362C2×C11C2×#38611yescharacteristic
363C2×C11C4×C4⋊Q811yescharacteristic
364C2×C11#232711yescharacteristic
365C2×C11Q8×C22⋊C412yes—
366C2×C11#236512yes—
367C2×C11#242912yes—
368C2×C11#243211yescharacteristic
369C2×C11#243411yescharacteristic
370C2×C11#244612yes—
371C2×C11#254511yescharacteristic
372C2×C11#254611yescharacteristic
373C24C23×D1111yescharacteristic
374C2×Q8—28no—
375C2×Q8—28no—
376C2×Q8—28no—
377C2×Q8—28no—
378C2×Q8—28no—
379C2×Q8—28no—
380C2×Q8—228no—
381C2×Q8—228no—
382C2×Q8—228no—
383C2×Q8—444no—
384C2×Q8—444no—
385C2×Q8—444no—
386C2×Q8—444no—
387C2×Q8(C2×D11)⋊C4116yes—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—24no—
396C22×C4—22no—
397C22×C4—24no—
398C22×C4—22no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—21no—
403C22×C4—114no—
404C22×C4—114no—
405C22×C4—114no—
406C22×C4—114no—
407C22×C4—114no—
408C22×C4—222no—
409C22×C4—222no—
410C22×C4—222no—
411C22×C4—222no—
412C22×C4—222no—
413C22×C4—222no—
414C22×C4—222no—
415C22×C4—222no—
416C22×C4—222no—
417C22×C4—222no—
418C22×C4—222no—
419C22×C4—222no—
420C22×C4—222no—
421C22×C4—222no—
422C22×C4—222no—
423C22×C4—222no—
424C22×C4—222no—
425C22×C4—222no—
426C22×C4—224no—
427C22×C4—224no—
428C22×C4—222no—
429C22×C4C2×C4×D1114yes—
430C22×C4C2×C4×D1112yes—
431C22×C4C2×D4414yes—
432C22×C4C2×D4412yes—
433C22×C4#433912yes—
434C22×C4#433912yes—
435C22×C4Q8×D1114yes—
436C22×C4C2×C22⋊D1114yes—
437C22×C4C2×C22⋊D1112yes—
438C22×C4C2×C22⋊D1114yes—
439C22×C4C2×C22⋊D1112yes—
440C22×C4C2×C22⋊D1112yes—
441C22×C4C2×C22⋊D1112yes—
442C22×C4C2×C22⋊D1112yes—
443C4⋊C4—216no—
444C4⋊C4—28no—
445C4⋊C4—2232no—
446C4⋊C4—444no—
447C42—216no—
448C42—28no—
449C42—228no—
450C42—444no—
451C11#1402411yescharacteristic, complemented, Sylow
452C23C22×C4×D1111yescharacteristic
453C23C22×D4411yescharacteristic
454C23C2×#433911yescharacteristic
455C23C2×#433911yescharacteristic
456C23C2×Q8×D1112yes—
457C23#6704012yes—
458C23#41×D1112yes—
459C23#6704312yes—
460C23C22×C22⋊D1111yescharacteristic
461C23C22×C22⋊D1111yescharacteristic
462C23C22×C22⋊D1111yescharacteristic
463Q8—232no—
464Q8—4416no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—24no—
475C2×C4—28no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—24no—
479C2×C4—22no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—44no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—118no—
486C2×C4—224no—
487C2×C4—224no—
488C2×C4—224no—
489C2×C4—224no—
490C2×C4—224no—
491C2×C4—224no—
492C2×C4—224no—
493C2×C4—224no—
494C2×C4—224no—
495C2×C4—224no—
496C2×C4—224no—
497C2×C4—224no—
498C2×C4—442no—
499C2×C4—442no—
500C2×C4—442no—
501C2×C4—442no—
502C2×C4—442no—
503C2×C4—442no—
504C2×C4—442no—
505C2×C4—442no—
506C2×C4—442no—
507C2×C4—442no—
508C2×C4—444no—
509C2×C4—444no—
510C2×C4—442no—
511C2×C4C2×(C2×D11)⋊C418yes—
512C2×C4C2×(C2×D11)⋊C414yes—
513C2×C4C4×C22⋊D1114yes—
514C2×C4C4×C22⋊D1114yes—
515C2×C4#6698214yes—
516C2×C4#6698314yes—
517C2×C4#6698314yes—
518C2×C4#6699714yescomplemented
519C2×C4#6700614yes—
520C22#1062309812yes—
521C22#1062309912yes—
522C22C4×Q8×D1112yes—
523C22#1062310312yes—
524C22Q8×D4412yes—
525C22#1062310712yes—
526C22#1062310912yes—
527C22#1062311412yes—
528C22C22×(C2×D11)⋊C411yescharacteristic
529C22C2×C4×C22⋊D1111yescharacteristic
530C22C2×C4×C22⋊D1111yescharacteristic
531C22C2×#6698211yescharacteristic
532C22C2×#6698311yescharacteristic
533C22C2×#6698311yescharacteristic
534C22C2×#6699711yescharacteristic
535C22Q8×C22⋊D1112yes—
536C22Q8×C22⋊D1112yes—
537C22#1062334711yescharacteristic
538C22#1062335512yes—
539C22#1062335611yescharacteristic
540C22#1062336212yes—
541C22#1062336311yescharacteristic
542C22C2×#6700611yescharacteristic
543C4—24no—
544C4—28no—
545C4—44no—
546C4—42no—
547C4—228no—
548C4—444no—
549C4—444no—
550C4—882no—
551C4#1062282618yes—
552C2C2×#1062282611yescharacteristic
553C2C4×#6699711yescharacteristic
554C2#1307133211yescharacteristic
555C2Q8×(C2×D11)⋊C412yes—
556C2#1307167012yes—
557C2#1307220912yes—
558C2#1307224011yescharacteristic
559C2#1307225611yescharacteristic
560C2#1307238612yes—
561C2#1307359211yescharacteristic
562C2#1307360111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC22×C4×Q8×C11C2
socle, prime radical, cosocleC24×C11C24
hypercenterC22×C4×Q8D11
hypocenterC11#14024
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
21. C2×#66997C4semidirect
91. C11⋊#95Q8semidirect
220. C2×C4×C11C4⋊Q8semidirect
246. C2×Dic11C4×Q8semidirect
451. C11#14024semidirect
518. C2×C4#66997semidirect

Maximal subgroups

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

subgroupindex
C22×#669972
C2×#106228432
C2×#106225422
C2×#106225872
#130668662
#130668492
#130668452
C4×C11⋊#952
C22×C4×Q8×C112
#1402411