Finite Group Databasebeta

← #14669259

Subgroups — #14669259

Order 2816.

1766 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 1766 conjugacy classes of subgroups — too many to draw. Only its 147 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
1C2×#10622183C214yesmaximal, complemented
2#13068531C212yesmaximal, complemented
3C22×C11×#127C211yesmaximal, characteristic
4C23×D4×C11—22no—
5C23×D4×C11C411yescharacteristic, complemented
6C23×D4×C11C2211yescharacteristic
7C2×C11×#127—22no—
8C2×C11×#127—28no—
9C2×C11×#127C412yescomplemented
10C2×C11×#127C2212yes—
11C22×C42×C11C411yescharacteristic, complemented
12#10622860—22no—
13C2×#66898—22no—
14C2×#66898C2214yescomplemented
15#10622183—28no—
16C25×C11—21no—
17C25×C11D412yes—
18C22×D4×C11—216no—
19C22×D4×C11—24no—
20C22×D4×C11—24no—
21C22×D4×C11—24no—
22C22×D4×C11—24no—
23C22×D4×C11—21no—
24C22×D4×C11—42no—
25C22×D4×C11—42no—
26C22×D4×C11—42no—
27C22×D4×C11—416no—
28C22×D4×C11—42no—
29C22×D4×C11C2×C411yescharacteristic
30C22×D4×C11C2×C412yes—
31C22×D4×C11D412yes—
32C22×D4×C11C2311yescharacteristic
33C23×C4×C11—21no—
34C23×C4×C11C2×C411yescharacteristic
35C11×#127—216no—
36C11×#127—24no—
37C11×#127—24no—
38C11×#127—24no—
39C11×#127D418yes—
40C2×C42×C11—21no—
41C2×C42×C11—24no—
42C2×C42×C11C2×C412yes—
43C2×C22⋊Dic11—24no—
44C2×C22⋊Dic11—44no—
45#66898—28no—
46#66898—44no—
47#12693—111nomaximal, Sylow
48C24×C11—24no—
49C24×C11—22no—
50C24×C11—24no—
51C24×C11—24no—
52C24×C11—42no—
53C24×C11—48no—
54C24×C11—48no—
55C24×C11—42no—
56C24×C11—42no—
57C24×C11C22⋊C411yescharacteristic
58C24×C11C22⋊C412yes—
59C24×C11C2×D412yes—
60C2×D4×C11—24no—
61C2×D4×C11—216no—
62C2×D4×C11—24no—
63C2×D4×C11—216no—
64C2×D4×C11—24no—
65C2×D4×C11—22no—
66C2×D4×C11—22no—
67C2×D4×C11—41no—
68C2×D4×C11—41no—
69C2×D4×C11—42no—
70C2×D4×C11—41no—
71C2×D4×C11—41no—
72C2×D4×C11—416no—
73C2×D4×C11—416no—
74C2×D4×C11—416no—
75C2×D4×C11—416no—
76C2×D4×C11—464no—
77C2×D4×C11—42no—
78C2×D4×C11—42no—
79C2×D4×C11—42no—
80C2×D4×C11—42no—
81C2×D4×C11C22⋊C414yescomplemented
82C2×D4×C11C2×D414yes—
83C22×C4×C11—24no—
84C22×C4×C11—28no—
85C22×C4×C11—22no—
86C22×C4×C11—22no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11C22⋊C411yescharacteristic
90C22×C4×C11C22×C411yescharacteristic
91C22×Dic11—44no—
92C42×C11—24no—
93C42×C11—22no—
94C42×C11C22⋊C414yescomplemented
95C22⋊Dic11—44no—
96C22⋊Dic11—44no—
97C22⋊Dic11—88no—
98C22×#127D1111yescharacteristic
99C2×#353—114no—
100#1781—112no—
101C23×C11—24no—
102C23×C11—21no—
103C23×C11—21no—
104C23×C11—22no—
105C23×C11—22no—
106C23×C11—22no—
107C23×C11—24no—
108C23×C11—22no—
109C23×C11—22no—
110C23×C11—48no—
111C23×C11—44no—
112C23×C11—44no—
113C23×C11—416no—
114C23×C11—416no—
115C23×C11—48no—
116C23×C11—48no—
117C23×C11—48no—
118C23×C11—42no—
119C23×C11—42no—
120C23×C11—84no—
121C23×C11—88no—
122C23×C11—88no—
123C23×C11—84no—
124C23×C11—84no—
125C23×C11#9912yes—
126C23×C11C2×C22⋊C411yescharacteristic
127C23×C11#12014yes—
128D4×C11—44no—
129D4×C11—48no—
130D4×C11—44no—
131D4×C11—432no—
132D4×C11—432no—
133D4×C11—48no—
134D4×C11—44no—
135D4×C11—44no—
136C2×C4×C11—216no—
137C2×C4×C11—28no—
138C2×C4×C11—28no—
139C2×C4×C11—21no—
140C2×C4×C11—24no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11#9912yes—
145C2×C4×C11C2×C22⋊C412yes—
146C2×Dic11—84no—
147C2×Dic11—88no—
148C23×D4—22no—
149C23×D4Dic1111yescharacteristic, complemented
150C23×D4C2×D1111yescharacteristic
151C2×#127—22no—
152C2×#127—28no—
153C2×#127Dic1112yescomplemented
154C2×#127C2×D1112yes—
155C22×C42Dic1111yescharacteristic, complemented
156C2×#99—114no—
157C2×#99—222no—
158#379—222no—
159#353—228no—
160C22×C11—24no—
161C22×C11—24no—
162C22×C11—22no—
163C22×C11—22no—
164C22×C11—22no—
165C22×C11—24no—
166C22×C11—44no—
167C22×C11—44no—
168C22×C11—48no—
169C22×C11—44no—
170C22×C11—44no—
171C22×C11—42no—
172C22×C11—44no—
173C22×C11—82no—
174C22×C11—816no—
175C22×C11—82no—
176C22×C11—816no—
177C22×C11—84no—
178C22×C11—84no—
179C22×C11#35314yescomplemented
180C22×C11#37911yescharacteristic
181C22×C11C2×#9911yescharacteristic
182C22×C11C2×#9911yescharacteristic
183C4×C11—28no—
184C4×C11—22no—
185C4×C11—22no—
186Dic11—164no—
187C25—21no—
188C25C22⋊D1112yes—
189C22×D4—216no—
190C22×D4—24no—
191C22×D4—24no—
192C22×D4—24no—
193C22×D4—24no—
194C22×D4—21no—
195C22×D4—42no—
196C22×D4—42no—
197C22×D4—42no—
198C22×D4—416no—
199C22×D4—42no—
200C22×D4C2×Dic1111yescharacteristic
201C22×D4C2×Dic1112yes—
202C22×D4C22⋊D1112yes—
203C22×D4C22×D1111yescharacteristic
204C23×C4—21no—
205C23×C4C2×Dic1111yescharacteristic
206#127—216no—
207#127—24no—
208#127—24no—
209#127—24no—
210#127C22⋊D1118yes—
211C2×C22⋊C4—224no—
212C2×C22⋊C4—444no—
213C2×C42—21no—
214C2×C42—24no—
215C2×C42C2×Dic1112yes—
216#99—228no—
217#99—444no—
218C2×C11—21no—
219C2×C11—24no—
220C2×C11—21no—
221C2×C11—44no—
222C2×C11—82no—
223C2×C11—84no—
224C2×C11#178111yescharacteristic
225C2×C11C2×#35312yes—
226C24—24no—
227C24—22no—
228C24—24no—
229C24—24no—
230C24—42no—
231C24—48no—
232C24—42no—
233C24—48no—
234C24—42no—
235C24C22⋊Dic1112yes—
236C24C22⋊Dic1111yescharacteristic
237C24C2×C22⋊D1112yes—
238C2×D4—24no—
239C2×D4—216no—
240C2×D4—24no—
241C2×D4—216no—
242C2×D4—24no—
243C2×D4—22no—
244C2×D4—22no—
245C2×D4—41no—
246C2×D4—41no—
247C2×D4—41no—
248C2×D4—41no—
249C2×D4—42no—
250C2×D4—42no—
251C2×D4—42no—
252C2×D4—416no—
253C2×D4—416no—
254C2×D4—416no—
255C2×D4—416no—
256C2×D4—464no—
257C2×D4—42no—
258C2×D4—42no—
259C2×D4C22⋊Dic1114yescomplemented
260C2×D4C2×C22⋊D1114yes—
261C22×C4—24no—
262C22×C4—28no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—444no—
268C22×C4C22⋊Dic1111yescharacteristic
269C22×C4C22×Dic1111yescharacteristic
270C22⋊C4—444no—
271C22⋊C4—444no—
272C22⋊C4—888no—
273C42—24no—
274C42—22no—
275C42C22⋊Dic1114yescomplemented
276C11#1269311yescharacteristic, complemented, Sylow
277C23—21no—
278C23—21no—
279C23—24no—
280C23—22no—
281C23—22no—
282C23—22no—
283C23—22no—
284C23—24no—
285C23—22no—
286C23—48no—
287C23—44no—
288C23—44no—
289C23—416no—
290C23—416no—
291C23—48no—
292C23—48no—
293C23—42no—
294C23—42no—
295C23—48no—
296C23—84no—
297C23—88no—
298C23—88no—
299C23—84no—
300C23—84no—
301C23#6689812yes—
302C23C2×C22⋊Dic1111yescharacteristic
303C23#6700614yes—
304D4—44no—
305D4—48no—
306D4—44no—
307D4—432no—
308D4—432no—
309D4—48no—
310D4—44no—
311D4—44no—
312C2×C4—216no—
313C2×C4—28no—
314C2×C4—28no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—24no—
320C2×C4—884no—
321C2×C4—888no—
322C2×C4#6689812yes—
323C2×C4C2×C22⋊Dic1112yes—
324C22—24no—
325C22—24no—
326C22—22no—
327C22—22no—
328C22—22no—
329C22—24no—
330C22—44no—
331C22—44no—
332C22—48no—
333C22—44no—
334C22—44no—
335C22—42no—
336C22—44no—
337C22—82no—
338C22—816no—
339C22—82no—
340C22—84no—
341C22—816no—
342C22—84no—
343C22#1062218314yescomplemented
344C22C2×#6689811yescharacteristic
345C22C2×#6689811yescharacteristic
346C22#1062286011yescharacteristic
347C4—28no—
348C4—22no—
349C4—22no—
350C4—1764no—
351C2—21no—
352C2—21no—
353C2—24no—
354C2—44no—
355C2—82no—
356C2—84no—
357C2#1306853111yescharacteristic
358C2C2×#1062218312yes—
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC22×D4C22×D11
Fitting, prime radicalC22×C11×#127C2
socleC22×C11C2×#99
cosocleC22×D4×C11C23
hypercenterC22×#127D11
hypocenterC11#12693
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ C23×D4 ◁ C22×#127

Complements

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

NH ≅ G/Ntype
1. C2×#10622183C2semidirect
2. #13068531C2semidirect
5. C23×D4×C11C4semidirect
9. C2×C11×#127C4semidirect
11. C22×C42×C11C4semidirect
14. C2×#66898C22semidirect
81. C2×D4×C11C22⋊C4semidirect
94. C42×C11C22⋊C4semidirect
149. C23×D4Dic11semidirect
153. C2×#127Dic11semidirect
155. C22×C42Dic11semidirect
179. C22×C11#353semidirect
259. C2×D4C22⋊Dic11semidirect
275. C42C22⋊Dic11semidirect
276. C11#12693semidirect
343. C22#10622183semidirect

Maximal subgroups

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

subgroupindex
C2×#106221832
#130685312
C22×C11×#1272
#1269311