Finite Group Databasebeta

← #14664334

Subgroups — #14664334

Order 2816.

544 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 91 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
1C4×#66898C211yesmaximal, characteristic, complemented
2#13066954C211yesmaximal, characteristic, complemented
3#13066616C212yesmaximal, complemented
4#13066613C212yesmaximal, complemented
5C11×#2535C211yesmaximal, characteristic
6C2×C11×#121—21no—
7C2×C4×D4×C11C411yescharacteristic, complemented
8C2×C4×D4×C11C2211yescharacteristic
9C11×#397C411yescharacteristic, complemented
10C11×#397C2211yescharacteristic
11C11×#392C411yescharacteristic, complemented
12C11×#392C2211yescharacteristic
13C11×#386—21no—
14C11×#386—21no—
15C11×#382C411yescharacteristic, complemented
16C11×#380—21no—
17C2×#66898—21no—
18C4×C22⋊Dic11—21no—
19#10622820—21no—
20#10622166—21no—
21#10622164C2212yes—
22#10622163C2212yes—
23C22×D4×C11—21no—
24C22×D4×C11—21no—
25C22×D4×C11C2×C411yescharacteristic
26C22×D4×C11D411yescharacteristic
27C23×C4×C11—21no—
28C23×C4×C11D411yescharacteristic
29C23×C4×C11D411yescharacteristic
30C11×#121—44no—
31C4×D4×C11—41no—
32C4×D4×C11—41no—
33C4×D4×C11—41no—
34C4×D4×C11—41no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4C2×C411yescharacteristic
37C2×C11×C4⋊C4D411yescharacteristic
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4C2×C411yescharacteristic
44C2×C11×C22⋊C4C2311yescharacteristic
45C2×C42×C11C2×C411yescharacteristic
46C2×C22⋊Dic11—22no—
47C2×C4×Dic11—41no—
48C2×#4318—41no—
49C11×#95—21no—
50C11×#95—21no—
51C11×#95—21no—
52C11×#95C2×C411yescharacteristic
53C11×#95C2×C411yescharacteristic
54#66898—24no—
55C11⋊#95—41no—
56C22⋊(C11⋊C8)—22no—
57C22⋊(C11⋊C8)—41no—
58#11774—111nomaximal, Sylow
59C24×C11—21no—
60C24×C11C22⋊C411yescharacteristic
61C24×C11C2×D411yescharacteristic
62C2×D4×C11—22no—
63C2×D4×C11—22no—
64C2×D4×C11—41no—
65C2×D4×C11—41no—
66C2×D4×C11—42no—
67C2×D4×C11—42no—
68C2×D4×C11—42no—
69C2×D4×C11—42no—
70C2×D4×C11—42no—
71C2×D4×C11—81no—
72C2×D4×C11—81no—
73C22×C4×C11—21no—
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—42no—
81C22×C4×C11—42no—
82C22×C4×C11—42no—
83C22×C4×C11—81no—
84C22×C4×C11—81no—
85C22×C4×C11C22⋊C411yescharacteristic
86C22×C4×C11C22⋊C411yescharacteristic
87C22×C4×C11C22⋊C411yescharacteristic
88C22×C4×C11C22×C411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×Dic11—42no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—42no—
93C11×C4⋊C4—41no—
94C11×C22⋊C4—41no—
95C11×C22⋊C4—41no—
96C11×C22⋊C4—42no—
97C11×C22⋊C4—42no—
98C11×C22⋊C4—41no—
99C11×C22⋊C4—41no—
100C11×C22⋊C4—81no—
101C11×C22⋊C4—81no—
102C42×C11—21no—
103C42×C11—21no—
104C22⋊Dic11—24no—
105C22⋊Dic11—42no—
106C4×Dic11—82no—
107#4318—82no—
108C2×C11⋊C8—42no—
109#2535D1111yescharacteristic
110C4×#99—111no—
111#1465—111no—
112#1344—112no—
113#1343—112no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—22no—
117C23×C11—21no—
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—41no—
121C23×C11—41no—
122C23×C11—41no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11—41no—
129C23×C11—41no—
130C23×C11C2×C22⋊C411yescharacteristic
131C23×C11AGL(1,ℤ/8)12yes—
132D4×C11—44no—
133D4×C11—42no—
134D4×C11—42no—
135D4×C11—84no—
136D4×C11—84no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—41no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—81no—
158C2×C4×C11—81no—
159C2×C4×C11—84no—
160C2×C4×C11#9911yescharacteristic
161C2×C4×C11#9911yescharacteristic
162C2×C4×C11#10412yes—
163C2×Dic11—44no—
164C2×Dic11—82no—
165C2×Dic11—82no—
166C11⋊C8—82no—
167C2×#121—21no—
168C2×C4×D4Dic1111yescharacteristic, complemented
169C2×C4×D4C2×D1111yescharacteristic
170C2×#99—221no—
171#407—221no—
172#397Dic1111yescharacteristic, complemented
173#397C2×D1111yescharacteristic
174#392Dic1111yescharacteristic, complemented
175#392C2×D1111yescharacteristic
176#386—21no—
177#386—21no—
178#382Dic1111yescharacteristic, complemented
179#380—21no—
180C4×C22⋊C4—221no—
181#342—112no—
182#324—221no—
183#323—112no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11—22no—
187C22×C11—42no—
188C22×C11—42no—
189C22×C11—42no—
190C22×C11—42no—
191C22×C11—41no—
192C22×C11—41no—
193C22×C11—42no—
194C22×C11—41no—
195C22×C11—41no—
196C22×C11—41no—
197C22×C11—81no—
198C22×C11—81no—
199C22×C11—81no—
200C22×C11—81no—
201C22×C11—81no—
202C22×C11—81no—
203C22×C11C2×#9911yescharacteristic
204C22×C11#41811yescharacteristic
205C22×C11C2×#10411yescharacteristic
206C4×C11—21no—
207C4×C11—21no—
208C4×C11—22no—
209C4×C11—41no—
210C4×C11—41no—
211C4×C11—41no—
212C4×C11—81no—
213C4×C11—81no—
214C4×C11—81no—
215Dic11—84no—
216C22×D4—21no—
217C22×D4—21no—
218C22×D4C2×Dic1111yescharacteristic
219C22×D4C22⋊D1111yescharacteristic
220C23×C4—21no—
221C23×C4C22⋊D1111yescharacteristic
222C23×C4C22⋊D1111yescharacteristic
223C2×M16—441no—
224#121—44no—
225C4×D4—41no—
226C4×D4—41no—
227C4×D4—41no—
228C4×D4—41no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4C2×Dic1111yescharacteristic
231C2×C4⋊C4C22⋊D1111yescharacteristic
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4—222no—
238C2×C22⋊C4C2×Dic1111yescharacteristic
239C2×C22⋊C4C22×D1111yescharacteristic
240C2×C42—441no—
241C2×C42C2×Dic1111yescharacteristic
242#99—224no—
243C22⋊C8—222no—
244C22⋊C8—441no—
245#95—21no—
246#95—21no—
247#95—21no—
248#95—441no—
249#95C2×Dic1111yescharacteristic
250#95C2×Dic1111yescharacteristic
251C2×C11—21no—
252C2×C11—21no—
253C2×C11—42no—
254C2×C11—81no—
255C2×C11—82no—
256C2×C11#150711yescharacteristic
257C2×C11#212011yescharacteristic
258C2×C11#212711yescharacteristic
259C24—21no—
260C24C22⋊Dic1111yescharacteristic
261C24C2×C22⋊D1111yescharacteristic
262C2×D4—22no—
263C2×D4—22no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—42no—
267C2×D4—42no—
268C2×D4—42no—
269C2×D4—42no—
270C2×D4—42no—
271C2×D4—81no—
272C2×D4—81no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—81no—
284C22×C4—81no—
285C22×C4—442no—
286C22×C4C22⋊Dic1111yescharacteristic
287C22×C4C22⋊Dic1111yescharacteristic
288C22×C4C22⋊Dic1111yescharacteristic
289C22×C4C22×Dic1111yescharacteristic
290C22×C4C2×C22⋊D1111yescharacteristic
291M16—882no—
292C2×C8—442no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—42no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—42no—
299C22⋊C4—42no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C22⋊C4—81no—
303C22⋊C4—81no—
304C22⋊C4—224no—
305C22⋊C4—442no—
306C42—21no—
307C42—21no—
308C42—882no—
309C11#1177411yescharacteristic, complemented, Sylow
310C23—21no—
311C23—21no—
312C23—22no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23#6698512yes—
327C23C2×C22⋊Dic1111yescharacteristic
328D4—44no—
329D4—42no—
330D4—42no—
331D4—84no—
332D4—84no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—84no—
356C2×C4—444no—
357C2×C4—882no—
358C2×C4—882no—
359C2×C4#6689811yescharacteristic
360C2×C4#6689811yescharacteristic
361C2×C4#6690112yes—
362C8—882no—
363C22—21no—
364C22—21no—
365C22—22no—
366C22—42no—
367C22—42no—
368C22—42no—
369C22—42no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—42no—
374C22—41no—
375C22—41no—
376C22—81no—
377C22—81no—
378C22—81no—
379C22—81no—
380C22—81no—
381C22—81no—
382C22#1062282811yescharacteristic
383C22C2×#6689811yescharacteristic
384C22C2×#6690111yescharacteristic
385C4—22no—
386C4—21no—
387C4—21no—
388C4—41no—
389C4—41no—
390C4—41no—
391C4—81no—
392C4—81no—
393C4—81no—
394C4—884no—
395C2—21no—
396C2—21no—
397C2—42no—
398C2—81no—
399C2—82no—
400C2#1306713211yescharacteristic
401C2#1307025711yescharacteristic
402C2#1307028511yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
Fitting, prime radicalC11×#2535C2
socleC22×C11C2×#99
cosocleC2×C11×C22⋊C4C23
hypercenter#2535D11
hypocenterC11#11774
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2535

Complements

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

NH ≅ G/Ntype
1. C4×#66898C2semidirect
2. #13066954C2semidirect
3. #13066616C2semidirect
4. #13066613C2semidirect
7. C2×C4×D4×C11C4semidirect
9. C11×#397C4semidirect
11. C11×#392C4semidirect
15. C11×#382C4semidirect
168. C2×C4×D4Dic11semidirect
172. #397Dic11semidirect
174. #392Dic11semidirect
178. #382Dic11semidirect
309. C11#11774semidirect

Maximal subgroups

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

subgroupindex
C4×#668982
#130669542
#130666162
#130666132
C11×#25352
#1177411