Finite Group Databasebeta

← #14664668

Subgroups — #14664668

Order 2816.

432 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 69 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#13074177C211yesmaximal, characteristic
2#13068698C211yesmaximal, characteristic, complemented
3#13066929C211yesmaximal, characteristic, complemented
4#13066644C211yesmaximal, characteristic, complemented
5#13066642C211yesmaximal, characteristic, complemented
6#13066619C211yesmaximal, characteristic, complemented
7C11×#1345C211yesmaximal, characteristic, complemented
8C2×D4×Dic11C411yescharacteristic
9C2×#66945C2211yescharacteristic
10C11×#394C2211yescharacteristic
11#10622836C411yescharacteristic
12#10622739—21no—
13#10622599C2211yescharacteristic
14#10622571—21no—
15#10622569—21no—
16#10622564—21no—
17#10622563—21no—
18#10622331—21no—
19#10622290C411yescharacteristic
20#10622264C411yescharacteristic
21C11×#343C2211yescharacteristic
22C11×#324C2211yescharacteristic
23#10622192—21no—
24#10622168C2211yescharacteristic
25#10622166C2211yescharacteristic
26#10622106—21no—
27C22×D4×C11C2×C411yescharacteristic
28C22×C22⋊D11—21no—
29C23×Dic11—21no—
30C22×C4×D11D411yescharacteristic
31C2×C11×M16—21no—
32C2×C11×C4⋊C4C2311yescharacteristic
33C2×C11×C22⋊C4—21no—
34C2×C11×C22⋊C4—21no—
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—21no—
37D4×Dic11—41no—
38D4×Dic11—41no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4C2×C411yescharacteristic
41C2×(C2×D11)⋊C4D411yescharacteristic
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11C2×C411yescharacteristic
44C2×C4⋊Dic11D411yescharacteristic
45C2×C4×Dic11C2×C411yescharacteristic
46C2×C4×Dic11D411yescharacteristic
47C2×#4318—21no—
48#66945—41no—
49#66945—41no—
50C11×C22⋊C8—21no—
51C11×#95C2×C411yescharacteristic
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95C2×C411yescharacteristic
57C22⋊(C11⋊C8)—21no—
58(C2×D11)⋊C8—41no—
59(C2×D11)⋊C8—41no—
60Dic11⋊C8—41no—
61C8×Dic11—41no—
62#11847—111nomaximal, Sylow
63C24×C11—21no—
64C23×D11C22⋊C411yescharacteristic
65C2×D4×C11—41no—
66C2×D4×C11—42no—
67C22×C4×C11—21no—
68C22×C4×C11C22×C411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C2×C22⋊D11—42no—
72C2×C22⋊D11—42no—
73C2×C22⋊D11—81no—
74C22×Dic11—21no—
75C22×Dic11—21no—
76C22×Dic11—42no—
77C22×Dic11—81no—
78C22×Dic11—81no—
79C22×Dic11C22⋊C411yescharacteristic
80C22×Dic11C22⋊C411yescharacteristic
81C22×Dic11C22⋊C411yescharacteristic
82C2×C4×D11—21no—
83C2×C4×D11—21no—
84C2×C4×D11—21no—
85C2×C4×D11—21no—
86C2×C4×D11—41no—
87C11×M16—41no—
88C11×M16—41no—
89C2×C8×C11—41no—
90C2×C8×C11—41no—
91C11×C4⋊C4—41no—
92C11×C22⋊C4—42no—
93C11×C22⋊C4—41no—
94C11×C22⋊C4—41no—
95C22⋊Dic11—41no—
96C22⋊Dic11—41no—
97C22⋊Dic11—81no—
98(C2×D11)⋊C4—41no—
99(C2×D11)⋊C4—41no—
100(C2×D11)⋊C4—81no—
101C4⋊Dic11—41no—
102C4⋊Dic11—41no—
103C4⋊Dic11—81no—
104C4×Dic11—21no—
105C4×Dic11—21no—
106C4×Dic11—21no—
107C4×Dic11—21no—
108#4318—41no—
109#4318—41no—
110C2×C11⋊C8—41no—
111C2×C11⋊C8—41no—
112#2598—111no—
113#1822—111no—
114#1458—111no—
115#1353—111no—
116#1353—111no—
117#1345—111no—
118#1345D1111yescharacteristic, complemented
119C23×C11—22no—
120C23×C11—41no—
121C23×C11—41no—
122C23×C11—41no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11C2×C22⋊C411yescharacteristic
127C22×D11—21no—
128C22×D11—21no—
129C22×D11—21no—
130C22×D11—41no—
131C22×D11—41no—
132D4×C11—42no—
133D4×C11—42no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11#13511yescharacteristic
144C2×C4×C11#13511yescharacteristic
145C22⋊D11—84no—
146C2×Dic11—21no—
147C2×Dic11—21no—
148C2×Dic11—21no—
149C2×Dic11—21no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—84no—
159C2×Dic11#9911yescharacteristic
160C2×Dic11#9911yescharacteristic
161C4×D11—41no—
162C4×D11—41no—
163C4×D11—41no—
164C4×D11—41no—
165C8×C11—81no—
166C8×C11—81no—
167C11⋊C8—81no—
168C11⋊C8—81no—
169C2×C4×D4—111no—
170C2×#117—111no—
171#431—221no—
172#407—221no—
173#400—111no—
174#399—111no—
175#394C2×D1111yescharacteristic
176#392—111no—
177#388—221no—
178#386—221no—
179#386—221no—
180#385—221no—
181#383—111no—
182#343—111no—
183#343—221no—
184#343C2×D1111yescharacteristic
185#324—111no—
186#324C2×D1111yescharacteristic
187#323—221no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11—42no—
191C22×C11—42no—
192C22×C11—42no—
193C22×C11—81no—
194C22×C11—81no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11C2×#9911yescharacteristic
198C22×C11#41611yescharacteristic
199C22×C11#42111yescharacteristic
200C2×D11—42no—
201C2×D11—41no—
202C2×D11—41no—
203C2×D11—41no—
204C2×D11—81no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—41no—
208C4×C11—41no—
209C4×C11—81no—
210Dic11—21no—
211Dic11—21no—
212Dic11—41no—
213Dic11—41no—
214Dic11—81no—
215Dic11—81no—
216C22×D4—221no—
217C22×D4C4×D1111yescharacteristic
218C23×C4—111no—
219C23×C4—221no—
220C2×M16—21no—
221C2×M16—221no—
222C4×D4—441no—
223C4×D4—441no—
224#117—441no—
225#117—441no—
226C2×C4⋊C4—111no—
227C2×C4⋊C4—111no—
228C2×C4⋊C4—221no—
229C2×C4⋊C4C22×D1111yescharacteristic
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—111no—
233C2×C22⋊C4—111no—
234C2×C22⋊C4—221no—
235C2×C22⋊C4—221no—
236C2×C22⋊C4—221no—
237C2×C42—111no—
238C2×C42—111no—
239C4⋊C8—441no—
240C22⋊C8—21no—
241C22⋊C8—221no—
242C22⋊C8—441no—
243C22⋊C8—441no—
244C4×C8—441no—
245#95—111no—
246#95—221no—
247#95—221no—
248#95—221no—
249#95—221no—
250#95C4×D1111yescharacteristic
251C2×C11—21no—
252C2×C11—21no—
253C2×C11—82no—
254C2×C11#151611yescharacteristic
255C2×C11#212011yescharacteristic
256C2×C11#213411yescharacteristic
257D11—81no—
258C24—21no—
259C24—111no—
260C2×D4—41no—
261C2×D4—42no—
262C2×D4—442no—
263C2×D4—442no—
264C2×D4—881no—
265C22×C4—21no—
266C22×C4—111no—
267C22×C4—111no—
268C22×C4—111no—
269C22×C4—221no—
270C22×C4—221no—
271C22×C4—221no—
272C22×C4—221no—
273C22×C4—221no—
274C22×C4—221no—
275C22×C4—441no—
276C22×C4—442no—
277C22×C4—881no—
278C22×C4—881no—
279C22×C4C2×C4×D1111yescharacteristic
280C22×C4D4×D1111yescharacteristic
281C22×C4D4×D1111yescharacteristic
282M16—41no—
283M16—41no—
284M16—441no—
285M16—441no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—441no—
289C2×C8—441no—
290C4⋊C4—41no—
291C4⋊C4—441no—
292C4⋊C4—441no—
293C4⋊C4—881no—
294C22⋊C4—42no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—441no—
298C22⋊C4—441no—
299C22⋊C4—441no—
300C22⋊C4—441no—
301C22⋊C4—881no—
302C22⋊C4—881no—
303C42—221no—
304C42—221no—
305C42—221no—
306C42—221no—
307C11#1184711yescharacteristic, complemented, Sylow
308C23—22no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—221no—
316C23—221no—
317C23—221no—
318C23—441no—
319C23—441no—
320C23C22⋊C4×D1111yescharacteristic
321D4—42no—
322D4—42no—
323D4—884no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—111no—
334C2×C4—111no—
335C2×C4—221no—
336C2×C4—221no—
337C2×C4—221no—
338C2×C4—221no—
339C2×C4—441no—
340C2×C4—441no—
341C2×C4—441no—
342C2×C4—441no—
343C2×C4—441no—
344C2×C4—441no—
345C2×C4—441no—
346C2×C4—441no—
347C2×C4—441no—
348C2×C4—441no—
349C2×C4—441no—
350C2×C4—441no—
351C2×C4—884no—
352C2×C4#6696511yescharacteristic
353C2×C4#6696911yescharacteristic
354C8—81no—
355C8—81no—
356C8—881no—
357C8—881no—
358C22—21no—
359C22—21no—
360C22—42no—
361C22—42no—
362C22—42no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22—442no—
368C22—441no—
369C22—441no—
370C22—441no—
371C22—881no—
372C22D11×#9911yescharacteristic
373C22#1062238511yescharacteristic
374C22#1062243411yescharacteristic
375C4—21no—
376C4—21no—
377C4—41no—
378C4—41no—
379C4—81no—
380C4—221no—
381C4—221no—
382C4—441no—
383C4—441no—
384C4—881no—
385C4—881no—
386C2—21no—
387C2—21no—
388C2—82no—
389C2—881no—
390C2#1306716911yescharacteristic
391C2#1307025411yescharacteristic
392C2#1307030611yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1345C2
socleC22×C11C2×#99
prime radical#10622836C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1345D11
hypocenterC11#11847
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1345

Complements

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

NH ≅ G/Ntype
2. #13068698C2semidirect
3. #13066929C2semidirect
4. #13066644C2semidirect
5. #13066642C2semidirect
6. #13066619C2semidirect
7. C11×#1345C2semidirect
118. #1345D11semidirect
307. C11#11847semidirect

Maximal subgroups

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

subgroupindex
#130741772
#130686982
#130669292
#130666442
#130666422
#130666192
C11×#13452
#1184711