Finite Group Databasebeta

← #14685189

Subgroups — #14685189

Order 2816.

2494 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×Dic11⋊C4C211yesmaximal, characteristic
2C2×#10622842C212yesmaximal, complemented
3C2×#10622559C212yesmaximal
4#13066879C214yesmaximal, complemented
5#13066866C212yesmaximal, complemented
6#13066839C211yesmaximal, characteristic
7#13066838C212yesmaximal
8C22×C11×C22⋊Q8C211yesmaximal, characteristic
9C23×Q8×C11C2211yescharacteristic
10C24×C4×C11C2211yescharacteristic
11C24×Dic11C2211yescharacteristic
12C24×Dic11C2211yescharacteristic
13C2×C11×C22⋊Q8—24no—
14C2×C11×C22⋊Q8—28no—
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C4⋊C4C2212yes—
17C22×C11×C22⋊C4C2212yes—
18C22×C22⋊Dic11C2212yes—
19C22×Dic11⋊C4—24no—
20C22×Dic11⋊C4—28no—
21C22×Dic11⋊C4C2212yes—
22C22×Dic11⋊C4C2214yes—
23C22×Dic11⋊C4C2212yes—
24#10622842—28no—
25C2×C11⋊#95C2214yes—
26C2×C11⋊#95C2214yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2214yes—
29C2×C11⋊#95C2212yes—
30#10622559—28no—
31C25×C11C2311yescharacteristic
32C22×Q8×C11—24no—
33C22×Q8×C11—22no—
34C22×Q8×C11—24no—
35C22×Q8×C11—42no—
36C23×C4×C11—24no—
37C23×C4×C11—24no—
38C23×C4×C11—42no—
39C23×C4×C11D414yes—
40C23×C4×C11C2312yes—
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C23×Dic11—22no—
45C23×Dic11—22no—
46C23×Dic11—24no—
47C23×Dic11—24no—
48C23×Dic11—22no—
49C23×Dic11—24no—
50C23×Dic11—24no—
51C23×Dic11—42no—
52C23×Dic11Q814yescomplemented
53C23×Dic11C2312yes—
54C23×Dic11C2314yes—
55C23×Dic11C2312yes—
56C11×C22⋊Q8—232no—
57C2×C11×C4⋊C4—24no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—24no—
60C2×C11×C4⋊C4—24no—
61C2×C11×C4⋊C4—24no—
62C2×C11×C22⋊C4—24no—
63C2×C11×C22⋊C4—24no—
64C2×C11×C22⋊C4D418yes—
65C2×C22⋊Dic11—24no—
66C2×C22⋊Dic11—24no—
67C2×C22⋊Dic11Q818yescomplemented
68C2×Dic11⋊C4—232no—
69C2×Dic11⋊C4—24no—
70C2×Dic11⋊C4—24no—
71C2×Dic11⋊C4—24no—
72C2×Dic11⋊C4—24no—
73C2×Dic11⋊C4—24no—
74C2×Dic11⋊C4—28no—
75C2×Dic11⋊C4—28no—
76C2×Dic11⋊C4—44no—
77C2×Dic11⋊C4D418yes—
78C11⋊#95—28no—
79C11⋊#95—24no—
80C11⋊#95—28no—
81C11⋊#95—28no—
82C11⋊#95—42no—
83#14720—111nomaximal, Sylow
84C24×C11—22no—
85C24×C11—22no—
86C24×C11—22no—
87C24×C11—22no—
88C24×C11C2×D414yes—
89C24×C11C2×D412yes—
90C24×C11C2×Q814yes—
91C24×C11C2×Q812yes—
92C24×C11#4112yes—
93C24×C11C2411yescharacteristic
94C2×Q8×C11—28no—
95C2×Q8×C11—416no—
96C2×Q8×C11—44no—
97C2×Q8×C11—44no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—28no—
101C22×C4×C11—24no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—24no—
109C22×C4×C11—22no—
110C22×C4×C11—24no—
111C22×C4×C11—24no—
112C22×C4×C11—28no—
113C22×C4×C11—44no—
114C22×C4×C11—416no—
115C22×C4×C11C2×D414yes—
116C22×C4×C11C2×D414yes—
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2×D414yes—
119C22×C4×C11C2×D412yes—
120C22×Dic11—28no—
121C22×Dic11—28no—
122C22×Dic11—216no—
123C22×Dic11—216no—
124C22×Dic11—28no—
125C22×Dic11—28no—
126C22×Dic11—22no—
127C22×Dic11—22no—
128C22×Dic11—24no—
129C22×Dic11—24no—
130C22×Dic11—24no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—24no—
136C22×Dic11—24no—
137C22×Dic11—24no—
138C22×Dic11—24no—
139C22×Dic11—24no—
140C22×Dic11—416no—
141C22×Dic11—44no—
142C22×Dic11—44no—
143C22×Dic11C2×D414yes—
144C22×Dic11C2×D414yes—
145C22×Dic11C2×Q818yes—
146C22×Dic11C2×Q814yes—
147C22×Dic11#4114yes—
148C11×C4⋊C4—28no—
149C11×C4⋊C4—216no—
150C11×C22⋊C4—216no—
151C22⋊Dic11—216no—
152Dic11⋊C4—216no—
153Dic11⋊C4—216no—
154Dic11⋊C4—416no—
155C22×C22⋊Q8D1111yescharacteristic
156C23×C4⋊C4—111no—
157C2×#395—112no—
158C2×#385—112no—
159#1444—114no—
160#1441—112no—
161C22⋊#95—111no—
162C22⋊#95—112no—
163C23×C11—22no—
164C23×C11—24no—
165C23×C11—22no—
166C23×C11—24no—
167C23×C11—22no—
168C23×C11—22no—
169C23×C11—24no—
170C23×C11—24no—
171C23×C11—28no—
172C23×C11—28no—
173C23×C11—28no—
174C23×C11—28no—
175C23×C11#12014yes—
176C23×C11C22⋊Q818yes—
177C23×C11C22⋊Q814yes—
178C23×C11C4⋊Q814yes—
179C23×C11C4⋊Q818yes—
180C23×C11C22×D412yes—
181C23×C11C22×D411yescharacteristic
182C23×C11C22×D412yes—
183C23×C11C22×Q811yescharacteristic
184C23×C11C22×Q812yes—
185C23×C11C2×#4111yescharacteristic
186C23×C11C2×#4112yes—
187C23×C11H(5,𝔽2)12yes—
188C23×C112−1+412yes—
189Q8×C11—416no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—28no—
193C2×C4×C11—22no—
194C2×C4×C11—24no—
195C2×C4×C11—24no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—28no—
199C2×C4×C11—28no—
200C2×C4×C11—416no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—44no—
206C2×C4×C11—44no—
207C2×C4×C11—44no—
208C2×C4×C11#12014yes—
209C2×Dic11—232no—
210C2×Dic11—24no—
211C2×Dic11—24no—
212C2×Dic11—24no—
213C2×Dic11—24no—
214C2×Dic11—24no—
215C2×Dic11—24no—
216C2×Dic11—24no—
217C2×Dic11—28no—
218C2×Dic11—28no—
219C2×Dic11—28no—
220C2×Dic11—28no—
221C2×Dic11—416no—
222C2×Dic11—42no—
223C2×Dic11—44no—
224C2×Dic11—42no—
225C2×Dic11—44no—
226C2×Dic11—44no—
227C2×Dic11—44no—
228C2×Dic11—44no—
229C2×Dic11C22⋊Q818yescomplemented
230C23×Q8C2×D1111yescharacteristic
231C24×C4—111no—
232C24×C4—111no—
233C24×C4C2×D1111yescharacteristic
234C2×C22⋊Q8—24no—
235C2×C22⋊Q8—28no—
236C22×C4⋊C4—112no—
237C22×C4⋊C4—112no—
238C22×C4⋊C4—114no—
239C22×C4⋊C4—228no—
240C22×C4⋊C4—224no—
241C22×C4⋊C4C2×D1111yescharacteristic
242C22×C4⋊C4C2×D1112yes—
243C22×C22⋊C4—112no—
244C22×C22⋊C4C2×D1112yes—
245#395—228no—
246#385—228no—
247C2×#95—112no—
248C2×#95—114no—
249C2×#95—114no—
250C2×#95—114no—
251C2×#95—112no—
252C22×C11—24no—
253C22×C11—24no—
254C22×C11—24no—
255C22×C11—24no—
256C22×C11—24no—
257C22×C11—24no—
258C22×C11—216no—
259C22×C11—216no—
260C22×C11#39518yescomplemented
261C22×C11C2×#12011yescharacteristic
262C22×C11C2×#12011yescharacteristic
263C22×C11C2×C22⋊Q811yescharacteristic
264C22×C11C2×C22⋊Q812yes—
265C22×C11C2×C22⋊Q812yes—
266C22×C11#52511yescharacteristic
267C22×C11#52512yes—
268C22×C11C2×C4⋊Q811yescharacteristic
269C22×C11C2×C4⋊Q812yes—
270C22×C11#53411yescharacteristic
271C22×C11#53611yescharacteristic
272C22×C11#53912yes—
273C22×C11#54412yes—
274C22×C11D4214yes—
275C22×C11#54714yes—
276C22×C11D4×Q814yes—
277C22×C11#55414yes—
278C4×C11—24no—
279C4×C11—42no—
280C4×C11—44no—
281C4×C11—44no—
282Dic11—28no—
283Dic11—44no—
284Dic11—48no—
285C25C22×D1111yescharacteristic
286C22×Q8—24no—
287C22×Q8—24no—
288C22×Q8—22no—
289C22×Q8—42no—
290C23×C4—24no—
291C23×C4—24no—
292C23×C4—42no—
293C23×C4—112no—
294C23×C4—114no—
295C23×C4—114no—
296C23×C4—112no—
297C23×C4—224no—
298C23×C4—224no—
299C23×C4—224no—
300C23×C4—222no—
301C23×C4—222no—
302C23×C4—222no—
303C23×C4—224no—
304C23×C4—442no—
305C23×C4C22⋊D1114yes—
306C23×C4C22×D1112yes—
307C23×C4C22×D1112yes—
308C23×C4C22×D1111yescharacteristic
309C23×C4C22×D1111yescharacteristic
310C22⋊Q8—232no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—118no—
317C2×C4⋊C4—224no—
318C2×C4⋊C4—224no—
319C2×C4⋊C4—2232no—
320C2×C4⋊C4—224no—
321C2×C4⋊C4—224no—
322C2×C4⋊C4—224no—
323C2×C4⋊C4—228no—
324C2×C4⋊C4—228no—
325C2×C4⋊C4—444no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—118no—
329C2×C22⋊C4—224no—
330C2×C22⋊C4—224no—
331C2×C22⋊C4C22⋊D1118yes—
332#95—228no—
333#95—228no—
334#95—224no—
335#95—228no—
336#95—442no—
337C2×C11—28no—
338C2×C11C2×#39511yescharacteristic
339C2×C11#240311yescharacteristic
340C2×C11#240611yescharacteristic
341C2×C11#243411yescharacteristic
342C2×C11#244014yes—
343C2×C11#244914yes—
344C2×C11#258311yescharacteristic
345C2×C11#262711yescharacteristic
346C2×C11#284811yescharacteristic
347C24—22no—
348C24—22no—
349C24—22no—
350C24—22no—
351C24Q8×D1114yes—
352C24Q8×D1112yes—
353C24#434312yes—
354C24C2×C22⋊D1112yes—
355C24C2×C22⋊D1114yes—
356C24C23×D1111yescharacteristic
357C2×Q8—28no—
358C2×Q8—416no—
359C2×Q8—44no—
360C2×Q8—44no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—28no—
364C22×C4—24no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—24no—
368C22×C4—24no—
369C22×C4—24no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—28no—
376C22×C4—44no—
377C22×C4—416no—
378C22×C4—114no—
379C22×C4—114no—
380C22×C4—114no—
381C22×C4—114no—
382C22×C4—118no—
383C22×C4—2216no—
384C22×C4—228no—
385C22×C4—228no—
386C22×C4—2216no—
387C22×C4—228no—
388C22×C4—222no—
389C22×C4—222no—
390C22×C4—222no—
391C22×C4—222no—
392C22×C4—228no—
393C22×C4—224no—
394C22×C4—222no—
395C22×C4—224no—
396C22×C4—224no—
397C22×C4—224no—
398C22×C4—224no—
399C22×C4—224no—
400C22×C4—224no—
401C22×C4—224no—
402C22×C4—222no—
403C22×C4—4416no—
404C22×C4—444no—
405C22×C4—444no—
406C22×C4D4×D1114yes—
407C22×C4C2×C22⋊D1114yes—
408C22×C4C2×C22⋊D1114yes—
409C22×C4C2×C22⋊D1112yes—
410C22×C4C2×C22⋊D1112yes—
411C4⋊C4—28no—
412C4⋊C4—216no—
413C4⋊C4—2216no—
414C4⋊C4—2216no—
415C4⋊C4—4416no—
416C22⋊C4—216no—
417C22⋊C4—2216no—
418C11#1472011yescharacteristic, complemented, Sylow
419C23—22no—
420C23—28no—
421C23—22no—
422C23—28no—
423C23—22no—
424C23—22no—
425C23—24no—
426C23—24no—
427C23—24no—
428C23—28no—
429C23—28no—
430C23—24no—
431C23#6699714yes—
432C23#6699718yes—
433C23#6699918yes—
434C23#6699914yes—
435C23#6700614yes—
436C23C2×D4×D1112yes—
437C23#6703712yes—
438C23C2×Q8×D1111yescharacteristic
439C23C2×Q8×D1112yes—
440C23C2×#434311yescharacteristic
441C23#41×D1112yes—
442C23#6704312yes—
443C23C22×C22⋊D1111yescharacteristic
444C23C22×C22⋊D1112yes—
445Q8—416no—
446C2×C4—28no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—28no—
451C2×C4—22no—
452C2×C4—28no—
453C2×C4—24no—
454C2×C4—24no—
455C2×C4—22no—
456C2×C4—416no—
457C2×C4—42no—
458C2×C4—44no—
459C2×C4—44no—
460C2×C4—42no—
461C2×C4—44no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—118no—
465C2×C4—2232no—
466C2×C4—224no—
467C2×C4—224no—
468C2×C4—224no—
469C2×C4—224no—
470C2×C4—224no—
471C2×C4—224no—
472C2×C4—224no—
473C2×C4—228no—
474C2×C4—228no—
475C2×C4—228no—
476C2×C4—228no—
477C2×C4—4416no—
478C2×C4—444no—
479C2×C4—444no—
480C2×C4—442no—
481C2×C4—444no—
482C2×C4—442no—
483C2×C4—444no—
484C2×C4—444no—
485C2×C4#6699014yes—
486C22—216no—
487C22—24no—
488C22—24no—
489C22—24no—
490C22—24no—
491C22—24no—
492C22—216no—
493C22—24no—
494C22#1062284218yescomplemented
495C22#1062315412yes—
496C22D11×C22⋊Q812yes—
497C22#1062315812yes—
498C22#1062316314yes—
499C22#1062316714yes—
500C22#1062317612yes—
501C22C2×#6699011yescharacteristic
502C22D4×C22⋊D1114yes—
503C22#1062333511yescharacteristic
504C22C2×#6699711yescharacteristic
505C22C2×#6699712yes—
506C22C2×#6699912yes—
507C22C2×#6699911yescharacteristic
508C22#1062335514yes—
509C22#1062335611yescharacteristic
510C22#1062335911yescharacteristic
511C22C2×#6700611yescharacteristic
512C4—24no—
513C4—42no—
514C4—44no—
515C4—44no—
516C4—228no—
517C4—448no—
518C4—444no—
519C2—28no—
520C2C2×#1062284211yescharacteristic
521C2#1307192611yescharacteristic
522C2#1307194711yescharacteristic
523C2#1307226111yescharacteristic
524C2#1307231514yes—
525C2#1307242114yes—
526C2#1307399711yescharacteristic
527C2#1307443111yescharacteristic
528C2#1307690011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, cosocleC24×C11C24
FittingC22×C11×C22⋊Q8C2
prime radicalC25×C11C23
hypercenterC22×C22⋊Q8D11
hypocenterC11#14720
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#10622842C2semidirect
4. #13066879C2semidirect
5. #13066866C2semidirect
52. C23×Dic11Q8semidirect
67. C2×C22⋊Dic11Q8semidirect
229. C2×Dic11C22⋊Q8semidirect
260. C22×C11#395semidirect
418. C11#14720semidirect
494. C22#10622842semidirect

Maximal subgroups

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

subgroupindex
C23×Dic11⋊C42
C2×#106228422
C2×#106225592
#130668792
#130668662
#130668392
#130668382
C22×C11×C22⋊Q82
#1472011