Finite Group Databasebeta

← #14645121

Subgroups — #14645121

Order 2816.

1238 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 1238 conjugacy classes of subgroups — too many to draw. Only its 171 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068526C212yesmaximal, complemented
2C2×#10622166C212yesmaximal, complemented
3C2×#10622163C212yesmaximal, complemented
4C22×C11×#123C211yesmaximal, characteristic
5C23×D4×C11C411yescharacteristic
6C24×C4×C11C2211yescharacteristic
7C2×C11×#123—24no—
8C2×C11×#123—24no—
9C2×C11×#123—24no—
10C22×C11×C4⋊C4C411yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C11×C22⋊C4C411yescharacteristic
13C22×C11×C22⋊C4C411yescharacteristic
14C22×C11×C22⋊C4C2211yescharacteristic
15C2×C22⋊(C11⋊C8)—24no—
16C2×C22⋊(C11⋊C8)C2214yes—
17#10622166—24no—
18#10622163—24no—
19C25×C11C2×C411yescharacteristic
20C25×C11C2×C411yescharacteristic
21C22×D4×C11—22no—
22C22×D4×C11—22no—
23C22×D4×C11—22no—
24C22×D4×C11—44no—
25C23×C4×C11—22no—
26C23×C4×C11—22no—
27C23×C4×C11—44no—
28C23×C4×C11C2×C411yescharacteristic
29C23×C4×C11C2×C411yescharacteristic
30C23×C4×C11C2×C411yescharacteristic
31C23×C4×C11C2×C411yescharacteristic
32C23×C4×C11D414yes—
33C23×C4×C11C2311yescharacteristic
34C11×#123—232no—
35C2×C11×C4⋊C4—22no—
36C2×C11×C4⋊C4—22no—
37C2×C11×C4⋊C4—22no—
38C2×C11×C4⋊C4—22no—
39C2×C11×C4⋊C4—22no—
40C2×C11×C4⋊C4D414yes—
41C2×C11×C22⋊C4—22no—
42C2×C11×C22⋊C4—22no—
43C2×C11×C22⋊C4—22no—
44C2×C11×C22⋊C4—22no—
45C2×C11×C22⋊C4—22no—
46C2×C11×C22⋊C4—22no—
47C2×C11×C22⋊C4—22no—
48C2×C11×C22⋊C4—22no—
49C2×C11×C22⋊C4D414yes—
50C22×C11⋊C8—24no—
51C22⋊(C11⋊C8)—24no—
52C22⋊(C11⋊C8)—24no—
53C22⋊(C11⋊C8)—48no—
54#8304—111nomaximal, Sylow
55C24×C11—24no—
56C24×C11—21no—
57C24×C11—21no—
58C24×C11—21no—
59C24×C11—21no—
60C24×C11—24no—
61C24×C11—24no—
62C24×C11—42no—
63C24×C11—42no—
64C24×C11—42no—
65C24×C11C22⋊C412yes—
66C24×C11C22⋊C412yes—
67C24×C11C22×C411yescharacteristic
68C2×D4×C11—28no—
69C2×D4×C11—48no—
70C2×D4×C11—44no—
71C2×D4×C11—48no—
72C2×D4×C11—44no—
73C22×C4×C11—28no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—24no—
83C22×C4×C11—28no—
84C22×C4×C11—42no—
85C22×C4×C11—44no—
86C22×C4×C11—42no—
87C22×C4×C11—48no—
88C22×C4×C11—48no—
89C22×C4×C11—42no—
90C22×C4×C11—42no—
91C22×C4×C11C22⋊C412yes—
92C22×C4×C11C22⋊C412yes—
93C22×C4×C11C22⋊C412yes—
94C22×C4×C11C22⋊C412yes—
95C22×C4×C11C2×D412yes—
96C22×C4×C11C2×D412yes—
97C22×C4×C11C2×D412yes—
98C11×C4⋊C4—28no—
99C11×C4⋊C4—28no—
100C11×C22⋊C4—28no—
101C11×C22⋊C4—28no—
102C11×C22⋊C4—28no—
103C2×C11⋊C8—48no—
104C2×C11⋊C8—44no—
105C22×#123D1111yescharacteristic
106#1779—112no—
107C2×#324—112no—
108C2×#323—112no—
109C23×C11—22no—
110C23×C11—22no—
111C23×C11—24no—
112C23×C11—24no—
113C23×C11—22no—
114C23×C11—24no—
115C23×C11—22no—
116C23×C11—24no—
117C23×C11—22no—
118C23×C11—24no—
119C23×C11—416no—
120C23×C11—42no—
121C23×C11—42no—
122C23×C11—42no—
123C23×C11—42no—
124C23×C11—42no—
125C23×C11—42no—
126C23×C11—42no—
127C23×C11—42no—
128C23×C11—42no—
129C23×C11—42no—
130C23×C11—42no—
131C23×C11—42no—
132C23×C11—88no—
133C23×C11#9914yes—
134C23×C11C2×C22⋊C411yescharacteristic
135C23×C11C2×C22⋊C411yescharacteristic
136C23×C11C2×C22⋊C411yescharacteristic
137C23×C11#13114yes—
138D4×C11—416no—
139C2×C4×C11—24no—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—22no—
143C2×C4×C11—22no—
144C2×C4×C11—24no—
145C2×C4×C11—24no—
146C2×C4×C11—42no—
147C2×C4×C11—42no—
148C2×C4×C11—416no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11—42no—
156C2×C4×C11—42no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11#12014yes—
160C11⋊C8—84no—
161C23×D4Dic1111yescharacteristic
162C24×C4C2×D1111yescharacteristic
163C2×#123—24no—
164C2×#123—24no—
165C2×#123—24no—
166C22×C4⋊C4Dic1111yescharacteristic
167C22×C4⋊C4C2×D1111yescharacteristic
168C22×C22⋊C4Dic1111yescharacteristic
169C22×C22⋊C4Dic1111yescharacteristic
170C22×C22⋊C4C2×D1111yescharacteristic
171C2×C22⋊C8—114no—
172C2×C22⋊C8—224no—
173#324—224no—
174#323—224no—
175C22×C11—28no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11—28no—
181C22×C11—24no—
182C22×C11—48no—
183C22×C11—48no—
184C22×C11—44no—
185C22×C11—42no—
186C22×C11—42no—
187C22×C11—42no—
188C22×C11—42no—
189C22×C11—42no—
190C22×C11—84no—
191C22×C11—84no—
192C22×C11—84no—
193C22×C11#37911yescharacteristic
194C22×C11#40812yes—
195C22×C11#40812yes—
196C22×C11#40812yes—
197C22×C11C2×#9912yes—
198C22×C11#41312yes—
199C4×C11—24no—
200C4×C11—42no—
201C4×C11—42no—
202C4×C11—42no—
203C4×C11—42no—
204C25C2×Dic1111yescharacteristic
205C25C2×Dic1111yescharacteristic
206C22×D4—22no—
207C22×D4—22no—
208C22×D4—22no—
209C22×D4—44no—
210C23×C4—22no—
211C23×C4—22no—
212C23×C4—44no—
213C23×C4C2×Dic1111yescharacteristic
214C23×C4C2×Dic1111yescharacteristic
215C23×C4C2×Dic1111yescharacteristic
216C23×C4C2×Dic1111yescharacteristic
217C23×C4C22⋊D1114yes—
218C23×C4C22×D1111yescharacteristic
219C22×C8—224no—
220#123—232no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4—22no—
223C2×C4⋊C4—22no—
224C2×C4⋊C4—22no—
225C2×C4⋊C4—22no—
226C2×C4⋊C4C22⋊D1114yes—
227C2×C22⋊C4—22no—
228C2×C22⋊C4—22no—
229C2×C22⋊C4—22no—
230C2×C22⋊C4—22no—
231C2×C22⋊C4—22no—
232C2×C22⋊C4—22no—
233C2×C22⋊C4—22no—
234C2×C22⋊C4—22no—
235C2×C22⋊C4C22⋊D1114yes—
236C22⋊C8—224no—
237C22⋊C8—224no—
238C22⋊C8—448no—
239C2×C11—22no—
240C2×C11—22no—
241C2×C11—44no—
242C2×C11—82no—
243C2×C11#146814yes—
244C2×C11#178011yescharacteristic
245C2×C11#178111yescharacteristic
246C2×C11#178511yescharacteristic
247C24—24no—
248C24—21no—
249C24—21no—
250C24—24no—
251C24—21no—
252C24—21no—
253C24—24no—
254C24—42no—
255C24—42no—
256C24—42no—
257C24C22⋊Dic1112yes—
258C24C22⋊Dic1112yes—
259C24C22×Dic1111yescharacteristic
260C2×D4—28no—
261C2×D4—48no—
262C2×D4—44no—
263C2×D4—48no—
264C2×D4—44no—
265C22×C4—28no—
266C22×C4—24no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—28no—
276C22×C4—42no—
277C22×C4—42no—
278C22×C4—44no—
279C22×C4—48no—
280C22×C4—48no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4C22⋊Dic1112yes—
284C22×C4C22⋊Dic1112yes—
285C22×C4C22⋊Dic1112yes—
286C22×C4C22⋊Dic1112yes—
287C22×C4C2×C22⋊D1112yes—
288C22×C4C2×C22⋊D1112yes—
289C22×C4C2×C22⋊D1112yes—
290C2×C8—448no—
291C2×C8—444no—
292C4⋊C4—28no—
293C4⋊C4—28no—
294C22⋊C4—28no—
295C22⋊C4—28no—
296C22⋊C4—28no—
297C11#830411yescharacteristic, complemented, Sylow
298C23—22no—
299C23—22no—
300C23—24no—
301C23—24no—
302C23—22no—
303C23—24no—
304C23—24no—
305C23—22no—
306C23—22no—
307C23—24no—
308C23—416no—
309C23—42no—
310C23—42no—
311C23—42no—
312C23—42no—
313C23—42no—
314C23—42no—
315C23—42no—
316C23—42no—
317C23—42no—
318C23—42no—
319C23—42no—
320C23—42no—
321C23—88no—
322C23#6689814yes—
323C23#6700114yes—
324C23C2×C22⋊Dic1111yescharacteristic
325C23C2×C22⋊Dic1111yescharacteristic
326C23C2×C22⋊Dic1111yescharacteristic
327D4—416no—
328C2×C4—24no—
329C2×C4—24no—
330C2×C4—24no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—416no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4#6700614yes—
349C8—884no—
350C22—21no—
351C22—21no—
352C22—28no—
353C22—21no—
354C22—21no—
355C22—28no—
356C22—24no—
357C22—48no—
358C22—48no—
359C22—42no—
360C22—44no—
361C22—42no—
362C22—42no—
363C22—42no—
364C22—42no—
365C22—84no—
366C22—84no—
367C22—84no—
368C22C2×#6689812yes—
369C22#1062284712yes—
370C22#1062284712yes—
371C22#1062284712yes—
372C22#1062285012yes—
373C22#1062286011yescharacteristic
374C4—24no—
375C4—42no—
376C4—42no—
377C4—42no—
378C4—42no—
379C2—22no—
380C2—22no—
381C2—44no—
382C2—82no—
383C2#1306696414yes—
384C2#1306852811yescharacteristic
385C2#1306853111yescharacteristic
386C2#1306854411yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC24×C11C22×C4
FrattiniC23×C4C22×D11
FittingC22×C11×#123C2
socleC23×C11C2×C22⋊C4
prime radicalC23×D4×C11C4
cosocleC23×C4×C11C23
hypercenterC22×#123D11
hypocenterC11#8304
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. #13068526C2semidirect
2. C2×#10622166C2semidirect
3. C2×#10622163C2semidirect
297. C11#8304semidirect

Maximal subgroups

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

subgroupindex
#130685262
C2×#106221662
C2×#106221632
C22×C11×#1232
#830411