Finite Group Databasebeta

← #14660265

Subgroups — #14660265

Order 2816.

3098 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66898C212yesmaximal, complemented
2C2×#10622860C212yesmaximal, complemented
3C2×#10622164C212yesmaximal, complemented
4C22×C11×#120C211yesmaximal, characteristic
5C26×C11C2211yescharacteristic
6C23×D4×C11C412yescomplemented
7C23×D4×C11C2211yescharacteristic
8C2×C11×#120—24no—
9C2×C11×#120—24no—
10C2×C11×#120—24no—
11C22×C11×C22⋊C4C412yescomplemented
12C22×C11×C22⋊C4C2211yescharacteristic
13C22×C22⋊Dic11—24no—
14C22×C22⋊Dic11C2214yes—
15#10622860—28no—
16C2×#66898—24no—
17C2×#66898—28no—
18#10622164—24no—
19C25×C11—24no—
20C25×C11—22no—
21C25×C11—22no—
22C25×C11—24no—
23C25×C11—48no—
24C25×C11C2×C412yes—
25C25×C11C2×C411yescharacteristic
26C25×C11D414yes—
27C25×C11C2311yescharacteristic
28C22×D4×C11—24no—
29C22×D4×C11—24no—
30C22×D4×C11—24no—
31C22×D4×C11—22no—
32C22×D4×C11—22no—
33C22×D4×C11—24no—
34C22×D4×C11—24no—
35C22×D4×C11—48no—
36C22×D4×C11D414yes—
37C23×C4×C11C2×C411yescharacteristic
38C23×C4×C11C2×C412yes—
39C23×Dic11—24no—
40C11×#120—232no—
41C2×C11×C22⋊C4—24no—
42C2×C11×C22⋊C4—22no—
43C2×C11×C22⋊C4—22no—
44C2×C11×C22⋊C4—24no—
45C2×C11×C22⋊C4—24no—
46C2×C11×C22⋊C4D414yes—
47C2×C22⋊Dic11—24no—
48C2×C22⋊Dic11—24no—
49C2×C22⋊Dic11—24no—
50C2×C22⋊Dic11—24no—
51C2×C22⋊Dic11—216no—
52C2×C22⋊Dic11—24no—
53C2×C22⋊Dic11—416no—
54C2×C22⋊Dic11D418yescomplemented
55#66898—216no—
56#10965—111nomaximal, Sylow
57C24×C11—216no—
58C24×C11—28no—
59C24×C11—22no—
60C24×C11—22no—
61C24×C11—24no—
62C24×C11—24no—
63C24×C11—21no—
64C24×C11—21no—
65C24×C11—28no—
66C24×C11—28no—
67C24×C11—28no—
68C24×C11—24no—
69C24×C11—44no—
70C24×C11—48no—
71C24×C11—44no—
72C24×C11—432no—
73C24×C11—416no—
74C24×C11—416no—
75C24×C11—432no—
76C24×C11—44no—
77C24×C11—42no—
78C24×C11—44no—
79C24×C11—44no—
80C24×C11—42no—
81C24×C11—42no—
82C24×C11—42no—
83C24×C11C22⋊C414yes—
84C24×C11C22⋊C412yescomplemented
85C24×C11C22×C411yescharacteristic
86C24×C11C2×D412yes—
87C24×C11C2×D412yes—
88C24×C11C2×D412yes—
89C24×C11C2×D414yes—
90C24×C11#4114yes—
91C2×D4×C11—216no—
92C2×D4×C11—24no—
93C2×D4×C11—28no—
94C2×D4×C11—28no—
95C2×D4×C11—24no—
96C2×D4×C11—416no—
97C2×D4×C11—48no—
98C2×D4×C11—416no—
99C2×D4×C11—48no—
100C2×D4×C11—42no—
101C2×D4×C11—44no—
102C2×D4×C11—44no—
103C2×D4×C11—42no—
104C2×D4×C11—42no—
105C2×D4×C11—42no—
106C22×C4×C11—22no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—22no—
110C22×C4×C11—24no—
111C22×C4×C11—44no—
112C22×C4×C11C22⋊C412yescomplemented
113C22×C4×C11C22⋊C414yescomplemented
114C22×Dic11—28no—
115C22×Dic11—416no—
116C22×Dic11—44no—
117C22×Dic11—44no—
118C11×C22⋊C4—216no—
119C11×C22⋊C4—28no—
120C22⋊Dic11—28no—
121C22⋊Dic11—28no—
122C22⋊Dic11—432no—
123C22⋊Dic11—44no—
124C22⋊Dic11—44no—
125C22×#120D1111yescharacteristic
126C22×#99—112no—
127C2×#379—112no—
128C2×#342—112no—
129C23×C11—28no—
130C23×C11—24no—
131C23×C11—216no—
132C23×C11—28no—
133C23×C11—28no—
134C23×C11—216no—
135C23×C11—24no—
136C23×C11—28no—
137C23×C11—24no—
138C23×C11—28no—
139C23×C11—22no—
140C23×C11—24no—
141C23×C11—48no—
142C23×C11—44no—
143C23×C11—44no—
144C23×C11—48no—
145C23×C11—432no—
146C23×C11—432no—
147C23×C11—432no—
148C23×C11—48no—
149C23×C11—48no—
150C23×C11—44no—
151C23×C11—44no—
152C23×C11—44no—
153C23×C11—44no—
154C23×C11—416no—
155C23×C11—432no—
156C23×C11—432no—
157C23×C11—416no—
158C23×C11—416no—
159C23×C11—416no—
160C23×C11—44no—
161C23×C11—44no—
162C23×C11—48no—
163C23×C11—48no—
164C23×C11—42no—
165C23×C11—42no—
166C23×C11—44no—
167C23×C11—88no—
168C23×C11#9918yescomplemented
169C23×C11C2×C22⋊C411yescharacteristic
170C23×C11C2×C22⋊C411yescharacteristic
171C23×C11C2×C22⋊C411yescharacteristic
172C23×C11C4×D414yes—
173C23×C11#12012yes—
174C23×C11#12012yes—
175C23×C11#12014yes—
176C23×C11#12114yes—
177C23×C11#12114yes—
178C23×C11#12114yes—
179C23×C11#12312yes—
180C23×C11#12312yes—
181C23×C11#12412yes—
182C23×C11#12712yes—
183D4×C11—432no—
184D4×C11—48no—
185D4×C11—48no—
186C2×C4×C11—22no—
187C2×C4×C11—24no—
188C2×C4×C11—24no—
189C2×C4×C11—44no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—44no—
193C2×C4×C11—44no—
194C2×Dic11—416no—
195C2×Dic11—48no—
196C2×Dic11—88no—
197C2×Dic11—88no—
198C26C2×D1111yescharacteristic
199C23×D4Dic1112yescomplemented
200C23×D4C2×D1111yescharacteristic
201C2×#120—24no—
202C2×#120—24no—
203C2×#120—24no—
204C22×C22⋊C4—114no—
205C22×C22⋊C4—224no—
206C22×C22⋊C4Dic1112yescomplemented
207C22×C22⋊C4C2×D1111yescharacteristic
208C2×#99—228no—
209C2×#99—224no—
210#379—228no—
211#342—224no—
212C22×C11—24no—
213C22×C11—24no—
214C22×C11—28no—
215C22×C11—28no—
216C22×C11—22no—
217C22×C11—22no—
218C22×C11—28no—
219C22×C11—216no—
220C22×C11—28no—
221C22×C11—42no—
222C22×C11—44no—
223C22×C11—44no—
224C22×C11—42no—
225C22×C11—42no—
226C22×C11—42no—
227C22×C11—432no—
228C22×C11—416no—
229C22×C11—416no—
230C22×C11—432no—
231C22×C11—48no—
232C22×C11—44no—
233C22×C11—44no—
234C22×C11—42no—
235C22×C11—44no—
236C22×C11—84no—
237C22×C11—84no—
238C22×C11—84no—
239C22×C11#37911yescharacteristic
240C22×C11#38612yes—
241C22×C11#38612yes—
242C22×C11#39012yes—
243C22×C11#39214yes—
244C22×C11#39414yes—
245C22×C11C2×#9914yes—
246C4×C11—42no—
247C4×C11—44no—
248Dic11—88no—
249C25—24no—
250C25—24no—
251C25—22no—
252C25—22no—
253C25—48no—
254C25C2×Dic1112yes—
255C25C2×Dic1111yescharacteristic
256C25C22⋊D1114yes—
257C25C22×D1111yescharacteristic
258C22×D4—24no—
259C22×D4—24no—
260C22×D4—24no—
261C22×D4—24no—
262C22×D4—22no—
263C22×D4—22no—
264C22×D4—24no—
265C22×D4—48no—
266C22×D4C22⋊D1114yes—
267C23×C4—224no—
268C23×C4C2×Dic1111yescharacteristic
269C23×C4C2×Dic1112yes—
270#120—232no—
271C2×C22⋊C4—24no—
272C2×C22⋊C4—22no—
273C2×C22⋊C4—22no—
274C2×C22⋊C4—24no—
275C2×C22⋊C4—24no—
276C2×C22⋊C4—118no—
277C2×C22⋊C4—224no—
278C2×C22⋊C4—224no—
279C2×C22⋊C4—224no—
280C2×C22⋊C4—224no—
281C2×C22⋊C4—2216no—
282C2×C22⋊C4—224no—
283C2×C22⋊C4—4416no—
284C2×C22⋊C4C22⋊D1114yes—
285#99—2216no—
286C2×C11—24no—
287C2×C11—22no—
288C2×C11—22no—
289C2×C11—24no—
290C2×C11—48no—
291C2×C11—82no—
292C2×C11#143811yescharacteristic
293C2×C11#178112yes—
294C2×C11#189814yes—
295C24—216no—
296C24—28no—
297C24—24no—
298C24—24no—
299C24—22no—
300C24—22no—
301C24—28no—
302C24—28no—
303C24—21no—
304C24—21no—
305C24—28no—
306C24—24no—
307C24—44no—
308C24—44no—
309C24—48no—
310C24—432no—
311C24—416no—
312C24—416no—
313C24—432no—
314C24—44no—
315C24—42no—
316C24—42no—
317C24—42no—
318C24—44no—
319C24—44no—
320C24—42no—
321C24C22⋊Dic1114yes—
322C24C22⋊Dic1112yescomplemented
323C24D4×D1114yes—
324C24#434114yes—
325C24C22×Dic1111yescharacteristic
326C24C2×C22⋊D1112yes—
327C24C2×C22⋊D1112yes—
328C24C2×C22⋊D1112yes—
329C2×D4—216no—
330C2×D4—24no—
331C2×D4—24no—
332C2×D4—28no—
333C2×D4—28no—
334C2×D4—416no—
335C2×D4—48no—
336C2×D4—416no—
337C2×D4—48no—
338C2×D4—42no—
339C2×D4—42no—
340C2×D4—42no—
341C2×D4—44no—
342C2×D4—44no—
343C2×D4—42no—
344C22×C4—24no—
345C22×C4—22no—
346C22×C4—21no—
347C22×C4—22no—
348C22×C4—21no—
349C22×C4—44no—
350C22×C4—228no—
351C22×C4—4416no—
352C22×C4—444no—
353C22×C4—444no—
354C22×C4C22⋊Dic1112yescomplemented
355C22×C4C22⋊Dic1114yescomplemented
356C22⋊C4—216no—
357C22⋊C4—28no—
358C22⋊C4—228no—
359C22⋊C4—228no—
360C22⋊C4—4432no—
361C22⋊C4—444no—
362C22⋊C4—444no—
363C11#1096511yescharacteristic, complemented, Sylow
364C23—24no—
365C23—28no—
366C23—216no—
367C23—28no—
368C23—28no—
369C23—216no—
370C23—24no—
371C23—28no—
372C23—28no—
373C23—24no—
374C23—22no—
375C23—24no—
376C23—48no—
377C23—48no—
378C23—44no—
379C23—44no—
380C23—432no—
381C23—432no—
382C23—432no—
383C23—48no—
384C23—48no—
385C23—44no—
386C23—44no—
387C23—44no—
388C23—44no—
389C23—416no—
390C23—416no—
391C23—416no—
392C23—432no—
393C23—432no—
394C23—416no—
395C23—44no—
396C23—44no—
397C23—48no—
398C23—48no—
399C23—44no—
400C23—42no—
401C23—42no—
402C23—88no—
403C23#6689818yescomplemented
404C23D4×Dic1114yes—
405C23#6698812yes—
406C23#6698812yes—
407C23#6698912yes—
408C23#6699012yes—
409C23#6699012yes—
410C23#6699114yes—
411C23#6699214yes—
412C23#6699214yes—
413C23#6699312yes—
414C23C2×C22⋊Dic1111yescharacteristic
415C23C2×C22⋊Dic1111yescharacteristic
416C23C2×C22⋊Dic1111yescharacteristic
417C23#6700614yes—
418D4—432no—
419D4—48no—
420D4—48no—
421C2×C4—24no—
422C2×C4—22no—
423C2×C4—24no—
424C2×C4—44no—
425C2×C4—44no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—44no—
429C2×C4—4416no—
430C2×C4—448no—
431C2×C4—888no—
432C2×C4—888no—
433C22—24no—
434C22—28no—
435C22—24no—
436C22—28no—
437C22—22no—
438C22—22no—
439C22—28no—
440C22—216no—
441C22—28no—
442C22—42no—
443C22—42no—
444C22—42no—
445C22—44no—
446C22—44no—
447C22—42no—
448C22—432no—
449C22—416no—
450C22—416no—
451C22—432no—
452C22—48no—
453C22—44no—
454C22—44no—
455C22—42no—
456C22—44no—
457C22—84no—
458C22—84no—
459C22—84no—
460C22C2×#6689814yes—
461C22#1062283312yes—
462C22#1062283312yes—
463C22#1062283412yes—
464C22#1062283514yes—
465C22#1062283614yes—
466C22#1062286011yescharacteristic
467C4—42no—
468C4—44no—
469C4—888no—
470C2—24no—
471C2—22no—
472C2—22no—
473C2—24no—
474C2—48no—
475C2—82no—
476C2#1306685711yescharacteristic
477C2#1306853112yes—
478C2#1306907014yes—
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC24×C11C22×C4
FrattiniC25C22×D11
Fitting, prime radicalC22×C11×#120C2
socleC23×C11C2×C22⋊C4
cosocleC25×C11C23
hypercenterC22×#120D11
hypocenterC11#10965
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C26 ◁ C22×#120

Complements

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

NH ≅ G/Ntype
1. C22×#66898C2semidirect
2. C2×#10622860C2semidirect
3. C2×#10622164C2semidirect
6. C23×D4×C11C4semidirect
11. C22×C11×C22⋊C4C4semidirect
54. C2×C22⋊Dic11D4semidirect
84. C24×C11C22⋊C4semidirect
112. C22×C4×C11C22⋊C4semidirect
113. C22×C4×C11C22⋊C4semidirect
168. C23×C11#99semidirect
199. C23×D4Dic11semidirect
206. C22×C22⋊C4Dic11semidirect
322. C24C22⋊Dic11semidirect
354. C22×C4C22⋊Dic11semidirect
355. C22×C4C22⋊Dic11semidirect
363. C11#10965semidirect
403. C23#66898semidirect

Maximal subgroups

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

subgroupindex
C22×#668982
C2×#106228602
C2×#106221642
C22×C11×#1202
#1096511