Finite Group Databasebeta

← #14672083

Subgroups — #14672083

Order 2816.

724 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 724 conjugacy classes of subgroups — too many to draw. Only its 111 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#13068604C211yesmaximal, characteristic, complemented
3C4×#66898C211yesmaximal, characteristic, complemented
4C11×#2541C211yesmaximal, characteristic
5C2×C11×#127C411yescharacteristic, complemented
6C2×C11×#127C2212yes—
7C2×C11×#121—21no—
8C2×C11×#121—21no—
9C2×C4×D4×C11C2211yescharacteristic
10C11×#392—21no—
11C11×#392—21no—
12C11×#390C412yescomplemented
13C4×C11×C4⋊C4C411yescharacteristic, complemented
14C2×#66898C2212yes—
15C2×#66898C2212yes—
16#10622825—21no—
17C4×C22⋊Dic11—21no—
18#10622183—28no—
19#10622164—21no—
20#10622164—21no—
21C22×D4×C11—22no—
22C22×D4×C11—22no—
23C22×D4×C11—21no—
24C22×D4×C11—21no—
25C22×D4×C11C2×C412yes—
26C22×D4×C11C2311yescharacteristic
27C23×C4×C11D411yescharacteristic
28C23×C4×C11D411yescharacteristic
29C11×#127—24no—
30C11×#127—24no—
31C11×#127—41no—
32C11×#127—41no—
33C11×#121—44no—
34C11×#121—44no—
35C4×D4×C11—41no—
36C4×D4×C11—41no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4C2×C411yescharacteristic
39C2×C11×C22⋊C4—22no—
40C2×C11×C22⋊C4—22no—
41C2×C11×C22⋊C4D411yescharacteristic
42C2×C11×C22⋊C4D411yescharacteristic
43C2×C42×C11C2×C412yes—
44C2×C42×C11C2×C411yescharacteristic
45C2×C22⋊Dic11—22no—
46C2×C22⋊Dic11—22no—
47C2×C4⋊Dic11—41no—
48C2×C4×Dic11—41no—
49C11×#95—21no—
50#66898—22no—
51#66898—24no—
52#66898D414yescomplemented
53C11⋊#95—41no—
54C11⋊#95—41no—
55#13223—111nomaximal, Sylow
56C24×C11—22no—
57C24×C11C2×D411yescharacteristic
58C24×C11C2×D411yescharacteristic
59C2×D4×C11—24no—
60C2×D4×C11—41no—
61C2×D4×C11—41no—
62C2×D4×C11—42no—
63C2×D4×C11—42no—
64C2×D4×C11—44no—
65C2×D4×C11—44no—
66C2×D4×C11—42no—
67C2×D4×C11—42no—
68C2×D4×C11—42no—
69C2×D4×C11—44no—
70C2×D4×C11—42no—
71C2×D4×C11—42no—
72C2×D4×C11—41no—
73C2×D4×C11—41no—
74C2×D4×C11—82no—
75C2×D4×C11—82no—
76C2×D4×C11—82no—
77C2×D4×C11C2×D412yes—
78C2×D4×C11#4112yes—
79C22×C4×C11—22no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—42no—
85C22×C4×C11—42no—
86C22×C4×C11C22⋊C411yescharacteristic
87C22×C4×C11C22⋊C411yescharacteristic
88C22×C4×C11C22⋊C411yescharacteristic
89C22×C4×C11C22⋊C411yescharacteristic
90C22×C4×C11C22×C411yescharacteristic
91C22×Dic11—42no—
92C22×Dic11—42no—
93C11×C4⋊C4—24no—
94C11×C4⋊C4—41no—
95C11×C22⋊C4—41no—
96C11×C22⋊C4—41no—
97C11×C22⋊C4—44no—
98C11×C22⋊C4—44no—
99C42×C11—21no—
100C42×C11—21no—
101C42×C11—24no—
102C22⋊Dic11—24no—
103C22⋊Dic11—42no—
104C22⋊Dic11—42no—
105C22⋊Dic11—42no—
106C4⋊Dic11—82no—
107C4×Dic11—82no—
108#2541D1111yescharacteristic
109C2×#353—114no—
110#1799—111no—
111C4×#99—111no—
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—41no—
117C23×C11—41no—
118C23×C11—41no—
119C23×C11—41no—
120C23×C11—42no—
121C23×C11—42no—
122C23×C11—42no—
123C23×C11—42no—
124C23×C11—42no—
125C23×C11—42no—
126C23×C11—42no—
127C23×C11C2×C22⋊C411yescharacteristic
128C23×C11#12112yes—
129C23×C11#12411yescharacteristic
130C23×C11#12711yescharacteristic
131D4×C11—42no—
132D4×C11—42no—
133D4×C11—84no—
134D4×C11—82no—
135D4×C11—88no—
136D4×C11—84no—
137D4×C11—84no—
138D4×C11—84no—
139D4×C11—82no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—22no—
143C2×C4×C11—24no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—81no—
155C2×C4×C11—81no—
156C2×C4×C11#9911yescharacteristic
157C2×C4×C11#9911yescharacteristic
158C2×C4×C11C4×D412yes—
159C2×Dic11—44no—
160C2×Dic11—82no—
161C2×Dic11—82no—
162C2×Dic11—82no—
163C2×Dic11—82no—
164C2×Dic11—82no—
165C2×#127Dic1111yescharacteristic, complemented
166C2×#127C2×D1112yes—
167C2×#121—21no—
168C2×#121—21no—
169C2×C4×D4C2×D1111yescharacteristic
170C2×#99—112no—
171C2×#99—112no—
172#392—21no—
173#392—21no—
174#390Dic1112yescomplemented
175#380—221no—
176C4×C4⋊C4Dic1111yescharacteristic, complemented
177C4×C22⋊C4—221no—
178#353—228no—
179#342—221no—
180#342—221no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11—22no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11—42no—
187C22×C11—41no—
188C22×C11—41no—
189C22×C11—41no—
190C22×C11—41no—
191C22×C11—41no—
192C22×C11—41no—
193C22×C11—81no—
194C22×C11—81no—
195C22×C11—82no—
196C22×C11—82no—
197C22×C11—82no—
198C22×C11—82no—
199C22×C11—82no—
200C22×C11—82no—
201C22×C11—82no—
202C22×C11#39011yescharacteristic
203C22×C11C2×#9911yescharacteristic
204C22×C11#41011yescharacteristic
205C4×C11—21no—
206C4×C11—22no—
207C4×C11—44no—
208C4×C11—41no—
209C4×C11—41no—
210C4×C11—41no—
211C4×C11#35312yescomplemented
212Dic11—84no—
213Dic11—162no—
214C22×D4—22no—
215C22×D4—22no—
216C22×D4—21no—
217C22×D4—21no—
218C22×D4C2×Dic1112yes—
219C22×D4C22×D1111yescharacteristic
220C23×C4C22⋊D1111yescharacteristic
221C23×C4C22⋊D1111yescharacteristic
222#127—24no—
223#127—24no—
224#127—41no—
225#127—41no—
226#121—44no—
227#121—44no—
228C4×D4—41no—
229C4×D4—41no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—441no—
232C2×C4⋊C4C2×Dic1111yescharacteristic
233C2×C22⋊C4—22no—
234C2×C22⋊C4—22no—
235C2×C22⋊C4—222no—
236C2×C22⋊C4—222no—
237C2×C22⋊C4C22⋊D1111yescharacteristic
238C2×C22⋊C4C22⋊D1111yescharacteristic
239C2×C42—441no—
240C2×C42C2×Dic1112yes—
241C2×C42C2×Dic1111yescharacteristic
242#99—114no—
243#99—222no—
244#99—224no—
245#95—21no—
246#95—441no—
247#95—441no—
248C2×C11—21no—
249C2×C11—21no—
250C2×C11—42no—
251C2×C11—41no—
252C2×C11—41no—
253C2×C11—162no—
254C2×C11#196411yescharacteristic
255C2×C11C2×#35311yescharacteristic
256C2×C11#212811yescharacteristic
257C24—22no—
258C24C2×C22⋊D1111yescharacteristic
259C24C2×C22⋊D1111yescharacteristic
260C2×D4—24no—
261C2×D4—41no—
262C2×D4—41no—
263C2×D4—42no—
264C2×D4—42no—
265C2×D4—42no—
266C2×D4—42no—
267C2×D4—44no—
268C2×D4—44no—
269C2×D4—42no—
270C2×D4—42no—
271C2×D4—44no—
272C2×D4—42no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—82no—
276C2×D4—82no—
277C2×D4—82no—
278C2×D4D4×D1112yes—
279C2×D4#434112yes—
280C22×C4—22no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—442no—
288C22×C4—442no—
289C22×C4C22⋊Dic1111yescharacteristic
290C22×C4C22⋊Dic1111yescharacteristic
291C22×C4C22⋊Dic1111yescharacteristic
292C22×C4C22⋊Dic1111yescharacteristic
293C22×C4C22×Dic1111yescharacteristic
294C4⋊C4—24no—
295C4⋊C4—41no—
296C4⋊C4—882no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—44no—
300C22⋊C4—44no—
301C22⋊C4—224no—
302C22⋊C4—442no—
303C22⋊C4—442no—
304C22⋊C4—442no—
305C42—21no—
306C42—21no—
307C42—24no—
308C42—882no—
309C11#1322311yescharacteristic, complemented, Sylow
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—42no—
319C23—42no—
320C23—42no—
321C23—42no—
322C23—42no—
323C23—42no—
324C23—42no—
325C23#6698911yescharacteristic
326C23#6699112yes—
327C23#6699311yescharacteristic
328C23C2×C22⋊Dic1111yescharacteristic
329D4—42no—
330D4—42no—
331D4—84no—
332D4—82no—
333D4—84no—
334D4—88no—
335D4—84no—
336D4—84no—
337D4—82no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—24no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—81no—
353C2×C4—81no—
354C2×C4—444no—
355C2×C4—882no—
356C2×C4—882no—
357C2×C4—882no—
358C2×C4—882no—
359C2×C4—882no—
360C2×C4#6689811yescharacteristic
361C2×C4#6689811yescharacteristic
362C2×C4D4×Dic1112yes—
363C22—21no—
364C22—21no—
365C22—22no—
366C22—21no—
367C22—21no—
368C22—41no—
369C22—42no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—81no—
376C22—81no—
377C22—82no—
378C22—82no—
379C22—82no—
380C22—82no—
381C22—82no—
382C22—82no—
383C22—82no—
384C22C2×#6689811yescharacteristic
385C22#1062283411yescharacteristic
386C22#1062285311yescharacteristic
387C4—22no—
388C4—21no—
389C4—44no—
390C4—41no—
391C4—41no—
392C4—41no—
393C4—884no—
394C4—1762no—
395C4#1062218312yescomplemented
396C2—21no—
397C2—21no—
398C2—42no—
399C2—41no—
400C2—41no—
401C2—162no—
402C2#1306945311yescharacteristic
403C2C2×#1062218311yescharacteristic
404C2#1307028811yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC22×D4C22×D11
Fitting, prime radicalC11×#2541C2
socleC22×C11C2×#99
cosocleC22×D4×C11C23
hypercenter#2541D11
hypocenterC11#13223
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2541

Complements

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

NH ≅ G/Ntype
1. C2×#10622183C2semidirect
2. #13068604C2semidirect
3. C4×#66898C2semidirect
5. C2×C11×#127C4semidirect
12. C11×#390C4semidirect
13. C4×C11×C4⋊C4C4semidirect
52. #66898D4semidirect
165. C2×#127Dic11semidirect
174. #390Dic11semidirect
176. C4×C4⋊C4Dic11semidirect
211. C4×C11#353semidirect
309. C11#13223semidirect
395. C4#10622183semidirect

Maximal subgroups

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

subgroupindex
C2×#106221832
#130686042
C4×#668982
C11×#25412
#1322311