Finite Group Databasebeta

← #14664263

Subgroups — #14664263

Order 2816.

436 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 71 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#13074307C211yesmaximal, characteristic
2#13068347C211yesmaximal, characteristic
3#13066947C211yesmaximal, characteristic
4#13066640C211yesmaximal, characteristic
5#13066617C211yesmaximal, characteristic
6#13066615C211yesmaximal, characteristic
7C11×#1352C211yesmaximal, characteristic
8C2×#66943C411yescharacteristic, complemented
9C2×#66930—21no—
10C2×#66930C2211yescharacteristic
11C11×#399C2211yescharacteristic
12#10622595C411yescharacteristic, complemented
13#10622594—21no—
14#10622586—21no—
15#10622566C2211yescharacteristic
16#10622563—21no—
17#10622557—21no—
18#10622332—21no—
19#10622274C411yescharacteristic, complemented
20#10622261C411yescharacteristic, complemented
21C11×#342C2211yescharacteristic
22C11×#323C2211yescharacteristic
23#10622165—21no—
24#10622164C2211yescharacteristic
25#10622163C2211yescharacteristic
26#10622107—21no—
27C23×Dic11D411yescharacteristic
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4C2×C411yescharacteristic
30C2×C11×C22⋊C4—21no—
31C2×C11×C22⋊C4—21no—
32C2×C11×C22⋊C4C2311yescharacteristic
33C2×C22⋊Dic11—21no—
34C2×C22⋊Dic11—21no—
35C2×C22⋊Dic11D411yescharacteristic
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11C2×C411yescharacteristic
39C2×Dic11⋊C4—21no—
40C2×Dic11⋊C4—41no—
41C2×Dic11⋊C4C2×C411yescharacteristic
42C2×Dic11⋊C4D411yescharacteristic
43C2×C4×Dic11—21no—
44C2×C4×Dic11—41no—
45C2×C4×Dic11C2×C411yescharacteristic
46C2×C4×Dic11D411yescharacteristic
47#66943—41no—
48#66943—41no—
49#66930—24no—
50#66930—41no—
51#66930—41no—
52#66930—42no—
53C11×C22⋊C8—21no—
54C11×#95C2×C411yescharacteristic
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95C2×C411yescharacteristic
61C22⋊(C11⋊C8)—21no—
62#66879—41no—
63Dic11⋊C8—41no—
64#11760—111nomaximal, Sylow
65C24×C11C2×D411yescharacteristic
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—41no—
69C22×C4×C11C22×C411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×Dic11—21no—
72C22×Dic11—21no—
73C22×Dic11—22no—
74C22×Dic11—21no—
75C22×Dic11—21no—
76C22×Dic11—21no—
77C22×Dic11—21no—
78C22×Dic11—41no—
79C22×Dic11C22⋊C411yescharacteristic
80C22×Dic11C22⋊C411yescharacteristic
81C22×Dic11C22⋊C411yescharacteristic
82C22×Dic11C22⋊C411yescharacteristic
83C2×C8×C11—41no—
84C11×C4⋊C4—42no—
85C11×C4⋊C4—41no—
86C11×C22⋊C4—22no—
87C11×C22⋊C4—41no—
88C11×C22⋊C4—42no—
89C11×C22⋊C4—41no—
90C22⋊Dic11—22no—
91C22⋊Dic11—41no—
92C22⋊Dic11—41no—
93C22⋊Dic11—41no—
94C22⋊Dic11—41no—
95C4⋊Dic11—41no—
96C4⋊Dic11—41no—
97C4⋊Dic11—41no—
98C4⋊Dic11—42no—
99Dic11⋊C4—41no—
100Dic11⋊C4—41no—
101Dic11⋊C4—44no—
102Dic11⋊C4—42no—
103C4×Dic11—21no—
104C4×Dic11—21no—
105C4×Dic11—21no—
106C4×Dic11—21no—
107C4×Dic11—42no—
108C4×Dic11—44no—
109C2×C11⋊C8—41no—
110#2611—111no—
111#1740—111no—
112#1464—111no—
113#1352—111no—
114#1352D1111yescharacteristic
115#1344—111no—
116#1344—111no—
117C23×C11—21no—
118C23×C11—21no—
119C23×C11—41no—
120C23×C11—41no—
121C23×C11C2×C22⋊C411yescharacteristic
122C23×C11AGL(1,ℤ/8)11yescharacteristic
123C23×C11#13711yescharacteristic
124C2×C4×C11—22no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—42no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—81no—
136C2×C4×C11—81no—
137C2×Dic11—22no—
138C2×Dic11—22no—
139C2×Dic11—22no—
140C2×Dic11—22no—
141C2×Dic11—21no—
142C2×Dic11—21no—
143C2×Dic11—21no—
144C2×Dic11—21no—
145C2×Dic11—21no—
146C2×Dic11—21no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—42no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—81no—
157C2×Dic11—81no—
158C2×Dic11#9911yescharacteristic
159C2×Dic11#9911yescharacteristic
160C2×Dic11#10412yes—
161C8×C11—81no—
162C11⋊C8—81no—
163C2×#125—111no—
164C2×#117—111no—
165C2×#117—221no—
166#432—221no—
167#400—111no—
168#399C2×D1111yescharacteristic
169#398—111no—
170#397—111no—
171#389—221no—
172#388—221no—
173#387—221no—
174#385—221no—
175#376—111no—
176#342—111no—
177#342—221no—
178#342C2×D1111yescharacteristic
179#324—221no—
180#323—111no—
181#323C2×D1111yescharacteristic
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11—41no—
187C22×C11—41no—
188C22×C11—41no—
189C22×C11—41no—
190C22×C11—81no—
191C22×C11C2×#9911yescharacteristic
192C22×C11#41711yescharacteristic
193C22×C11C2×#10411yescharacteristic
194C4×C11—42no—
195C4×C11—41no—
196C4×C11—41no—
197C4×C11—82no—
198C4×C11—81no—
199Dic11—21no—
200Dic11—21no—
201Dic11—22no—
202Dic11—41no—
203Dic11—41no—
204Dic11—81no—
205Dic11—82no—
206Dic11—81no—
207C23×C4—111no—
208#125—441no—
209#125—441no—
210#117—224no—
211#117—441no—
212#117—441no—
213#117—442no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—111no—
216C2×C4⋊C4—111no—
217C2×C4⋊C4—111no—
218C2×C4⋊C4—221no—
219C2×C4⋊C4—221no—
220C2×C4⋊C4—221no—
221C2×C4⋊C4—441no—
222C2×C4⋊C4C4×D1111yescharacteristic
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—111no—
226C2×C22⋊C4—221no—
227C2×C22⋊C4—221no—
228C2×C22⋊C4C22×D1111yescharacteristic
229C2×C42—111no—
230C2×C42—111no—
231C2×C42—221no—
232C2×C42—441no—
233C4⋊C8—441no—
234C22⋊C8—21no—
235C22⋊C8—221no—
236#97—441no—
237#95—111no—
238#95—221no—
239#95—221no—
240#95—221no—
241#95—221no—
242#95—221no—
243#95C4×D1111yescharacteristic
244C2×C11—21no—
245C2×C11—21no—
246C2×C11—41no—
247C2×C11—41no—
248C2×C11#150411yescharacteristic
249C2×C11#212311yescharacteristic
250C2×C11#212611yescharacteristic
251C24D4×D1111yescharacteristic
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—41no—
255C22×C4—111no—
256C22×C4—111no—
257C22×C4—111no—
258C22×C4—111no—
259C22×C4—221no—
260C22×C4—221no—
261C22×C4—222no—
262C22×C4—221no—
263C22×C4—221no—
264C22×C4—221no—
265C22×C4—221no—
266C22×C4—441no—
267C22×C4C2×C4×D1111yescharacteristic
268C22×C4D4×D1111yescharacteristic
269C2×C8—41no—
270C2×C8—441no—
271C4⋊C4—41no—
272C4⋊C4—42no—
273C4⋊C4—441no—
274C4⋊C4—441no—
275C4⋊C4—441no—
276C4⋊C4—441no—
277C4⋊C4—441no—
278C4⋊C4—442no—
279C4⋊C4—442no—
280C4⋊C4—444no—
281C22⋊C4—22no—
282C22⋊C4—41no—
283C22⋊C4—42no—
284C22⋊C4—41no—
285C22⋊C4—222no—
286C22⋊C4—441no—
287C22⋊C4—441no—
288C22⋊C4—441no—
289C22⋊C4—441no—
290C42—221no—
291C42—221no—
292C42—221no—
293C42—221no—
294C42—442no—
295C42—444no—
296C11#1176011yescharacteristic, complemented, Sylow
297C23—21no—
298C23—21no—
299C23—41no—
300C23—41no—
301C23C22⋊C4×D1111yescharacteristic
302C23#6696711yescharacteristic
303C23#6697111yescharacteristic
304C2×C4—22no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—111no—
318C2×C4—111no—
319C2×C4—112no—
320C2×C4—222no—
321C2×C4—222no—
322C2×C4—222no—
323C2×C4—222no—
324C2×C4—221no—
325C2×C4—221no—
326C2×C4—221no—
327C2×C4—221no—
328C2×C4—221no—
329C2×C4—221no—
330C2×C4—441no—
331C2×C4—441no—
332C2×C4—442no—
333C2×C4—441no—
334C2×C4—441no—
335C2×C4—441no—
336C2×C4—441no—
337C2×C4—441no—
338C2×C4—441no—
339C2×C4—881no—
340C2×C4—881no—
341C8—81no—
342C8—881no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—81no—
352C22D11×#9911yescharacteristic
353C22#1062241611yescharacteristic
354C22D11×#10411yescharacteristic
355C4—42no—
356C4—41no—
357C4—41no—
358C4—82no—
359C4—81no—
360C4—221no—
361C4—221no—
362C4—222no—
363C4—441no—
364C4—441no—
365C4—881no—
366C4—882no—
367C4—881no—
368C2—21no—
369C2—21no—
370C2—41no—
371C2—41no—
372C2#1306711911yescharacteristic
373C2#1307026811yescharacteristic
374C2#1307027811yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1352C2
socleC22×C11C2×#99
prime radicalC24×C11C2×D4
cosocleC2×C11×C22⋊C4C23
hypercenter#1352D11
hypocenterC11#11760
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1352

Complements

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

NH ≅ G/Ntype
8. C2×#66943C4semidirect
12. #10622595C4semidirect
19. #10622274C4semidirect
20. #10622261C4semidirect
296. C11#11760semidirect

Maximal subgroups

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

subgroupindex
#130743072
#130683472
#130669472
#130666402
#130666172
#130666152
C11×#13522
#1176011