Finite Group Databasebeta

← #14664327

Subgroups — #14664327

Order 2816.

482 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 73 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#13072917C211yesmaximal, characteristic
2#13068403C211yesmaximal, characteristic
3#13066955C211yesmaximal, characteristic
4#13066617C211yesmaximal, characteristic, complemented
5#13066616C211yesmaximal, characteristic, complemented
6#13066615C211yesmaximal, characteristic, complemented
7C11×#1344C211yesmaximal, characteristic, complemented
8C2×C4⋊C4×D11C411yescharacteristic, complemented
9C2×#66936—21no—
10C2×(C22⋊D11)⋊C4C2211yescharacteristic
11C11×#397C2211yescharacteristic
12#10622593C411yescharacteristic, complemented
13C2×#66870—21no—
14#10622566C2211yescharacteristic
15#10622555—21no—
16C22⋊C4×Dic11—21no—
17#10622332—21no—
18#10622280C411yescharacteristic, complemented
19#10622277—21no—
20#10622274C411yescharacteristic, complemented
21#10622260—21no—
22C11×#342C2211yescharacteristic
23C11×#323C2211yescharacteristic
24#10622164C2211yescharacteristic
25#10622163C2211yescharacteristic
26#10622106—21no—
27C22×C22⋊D11D411yescharacteristic
28C23×Dic11D411yescharacteristic
29C22×C4×D11—21no—
30C22×C4×D11C2×C411yescharacteristic
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C11×C22⋊C4—21no—
33C2×C11×C22⋊C4—21no—
34C2×C11×C22⋊C4C2311yescharacteristic
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—21no—
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4D411yescharacteristic
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11C2×C411yescharacteristic
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4C2×C411yescharacteristic
45C2×C4×Dic11—41no—
46C2×C4×Dic11D411yescharacteristic
47C4⋊C4×D11—41no—
48C4⋊C4×D11—41no—
49#66936—42no—
50#66936—42no—
51(C22⋊D11)⋊C4—41no—
52(C22⋊D11)⋊C4—41no—
53C11×C22⋊C8—21no—
54C11×#95—21no—
55C11×#95C2×C411yescharacteristic
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—41no—
60C11⋊#95C2×C411yescharacteristic
61C22⋊(C11⋊C8)—21no—
62#66879—41no—
63Dic11⋊C8—41no—
64#66870—24no—
65#11773—111nomaximal, Sylow
66C24×C11C2×D411yescharacteristic
67C23×D11C22⋊C411yescharacteristic
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—41no—
71C22×C4×C11C22×C411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C2×C22⋊D11—21no—
74C2×C22⋊D11—21no—
75C2×C22⋊D11—22no—
76C2×C22⋊D11—41no—
77C22×Dic11—21no—
78C22×Dic11—21no—
79C22×Dic11—21no—
80C22×Dic11—21no—
81C22×Dic11—41no—
82C22×Dic11—42no—
83C22×Dic11C22⋊C411yescharacteristic
84C22×Dic11C22⋊C411yescharacteristic
85C22×Dic11C22⋊C411yescharacteristic
86C2×C4×D11—21no—
87C2×C4×D11—21no—
88C2×C4×D11—42no—
89C2×C4×D11—42no—
90C2×C4×D11—42no—
91C2×C4×D11—42no—
92C2×C8×C11—41no—
93C11×C4⋊C4—41no—
94C11×C22⋊C4—22no—
95C11×C22⋊C4—41no—
96C11×C22⋊C4—41no—
97C11×C22⋊C4—41no—
98C11×C22⋊C4—41no—
99C22⋊Dic11—22no—
100C22⋊Dic11—41no—
101C22⋊Dic11—41no—
102C22⋊Dic11—41no—
103(C2×D11)⋊C4—41no—
104(C2×D11)⋊C4—42no—
105C4⋊Dic11—41no—
106C4⋊Dic11—42no—
107Dic11⋊C4—41no—
108Dic11⋊C4—42no—
109Dic11⋊C4—42no—
110Dic11⋊C4—41no—
111Dic11⋊C4—41no—
112C4×Dic11—21no—
113C4×Dic11—21no—
114C4×Dic11—82no—
115C2×C11⋊C8—41no—
116#2486—111no—
117C4×#99—111no—
118#1466—111no—
119#1344—111no—
120#1344—111no—
121#1344—111no—
122#1344D1111yescharacteristic, complemented
123C23×C11—21no—
124C23×C11—21no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11C2×C22⋊C411yescharacteristic
128C23×C11AGL(1,ℤ/8)11yescharacteristic
129C23×C11AGL(1,ℤ/8)11yescharacteristic
130C22×D11—21no—
131C22×D11—21no—
132C22×D11—41no—
133C22×D11—41no—
134C22×D11#10412yes—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—42no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—81no—
147C2×C4×C11—81no—
148C22⋊D11—42no—
149C22⋊D11—42no—
150C2×Dic11—22no—
151C2×Dic11—21no—
152C2×Dic11—21no—
153C2×Dic11—21no—
154C2×Dic11—21no—
155C2×Dic11—42no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—42no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—81no—
165C2×Dic11—81no—
166C2×Dic11—81no—
167C2×Dic11#9911yescharacteristic
168C2×Dic11#9911yescharacteristic
169C4×D11—42no—
170C4×D11—42no—
171C4×D11—84no—
172C8×C11—81no—
173C11⋊C8—81no—
174C2×#123—221no—
175C2×C4×D4—111no—
176C22×C4⋊C4—111no—
177#432—221no—
178C2×#99—221no—
179#398—111no—
180#398—111no—
181#397—111no—
182#397C2×D1111yescharacteristic
183#389—221no—
184#381—221no—
185#380—111no—
186#380—221no—
187C4×C22⋊C4—221no—
188#342—111no—
189#342C2×D1111yescharacteristic
190#323—111no—
191#323—221no—
192#323C2×D1111yescharacteristic
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11—21no—
197C22×C11—41no—
198C22×C11—41no—
199C22×C11—41no—
200C22×C11—41no—
201C22×C11—81no—
202C22×C11C2×#9911yescharacteristic
203C22×C11#41811yescharacteristic
204C22×C11C2×#10411yescharacteristic
205C2×D11—22no—
206C2×D11—42no—
207C2×D11—41no—
208C2×D11—41no—
209C2×D11—42no—
210C4×C11—41no—
211C4×C11—41no—
212C4×C11—81no—
213C4×C11—82no—
214C4×C11—81no—
215Dic11—21no—
216Dic11—41no—
217Dic11—41no—
218Dic11—81no—
219Dic11—82no—
220Dic11—81no—
221Dic11#35212yes—
222C22×D4—111no—
223C23×C4—111no—
224C23×C4—111no—
225C23×C4—221no—
226#123—442no—
227#123—442no—
228C4×D4—441no—
229C4×D4—441no—
230C2×C4⋊C4—111no—
231C2×C4⋊C4—111no—
232C2×C4⋊C4—221no—
233C2×C4⋊C4—221no—
234C2×C4⋊C4—221no—
235C2×C4⋊C4—221no—
236C2×C4⋊C4—441no—
237C2×C4⋊C4—441no—
238C2×C4⋊C4C4×D1111yescharacteristic
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—111no—
242C2×C22⋊C4—221no—
243C2×C22⋊C4—221no—
244C2×C22⋊C4—221no—
245C2×C22⋊C4C22×D1111yescharacteristic
246C2×C42—111no—
247C2×C42—441no—
248C4⋊C8—441no—
249#99—224no—
250C22⋊C8—21no—
251C22⋊C8—221no—
252#97—441no—
253#95—21no—
254#95—111no—
255#95—221no—
256#95—221no—
257#95—221no—
258#95—441no—
259#95C4×D1111yescharacteristic
260C2×C11—21no—
261C2×C11—21no—
262C2×C11—41no—
263C2×C11—41no—
264C2×C11#150711yescharacteristic
265C2×C11C2×#35211yescharacteristic
266C2×C11#212911yescharacteristic
267D11—42no—
268C24—111no—
269C24D4×D1111yescharacteristic
270C2×D4—222no—
271C2×D4—221no—
272C2×D4—221no—
273C2×D4—441no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—41no—
277C22×C4—111no—
278C22×C4—111no—
279C22×C4—111no—
280C22×C4—221no—
281C22×C4—221no—
282C22×C4—221no—
283C22×C4—221no—
284C22×C4—221no—
285C22×C4—221no—
286C22×C4—442no—
287C22×C4—442no—
288C22×C4—442no—
289C22×C4—442no—
290C22×C4—442no—
291C22×C4—441no—
292C22×C4C2×C4×D1111yescharacteristic
293C22×C4D4×D1111yescharacteristic
294C2×C8—41no—
295C2×C8—441no—
296C4⋊C4—41no—
297C4⋊C4—441no—
298C4⋊C4—441no—
299C4⋊C4—441no—
300C4⋊C4—441no—
301C4⋊C4—442no—
302C4⋊C4—442no—
303C4⋊C4—442no—
304C22⋊C4—22no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—222no—
310C22⋊C4—441no—
311C22⋊C4—442no—
312C22⋊C4—441no—
313C22⋊C4—441no—
314C22⋊C4—441no—
315C42—221no—
316C42—221no—
317C42—882no—
318C11#1177311yescharacteristic, complemented, Sylow
319C23—21no—
320C23—21no—
321C23—41no—
322C23—41no—
323C23—112no—
324C23—221no—
325C23—221no—
326C23—441no—
327C23—441no—
328C23C22⋊C4×D1111yescharacteristic
329C23#6696411yescharacteristic
330C23#6696711yescharacteristic
331D4—442no—
332D4—442no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—111no—
347C2×C4—111no—
348C2×C4—222no—
349C2×C4—221no—
350C2×C4—221no—
351C2×C4—221no—
352C2×C4—221no—
353C2×C4—442no—
354C2×C4—442no—
355C2×C4—442no—
356C2×C4—441no—
357C2×C4—442no—
358C2×C4—441no—
359C2×C4—441no—
360C2×C4—441no—
361C2×C4—441no—
362C2×C4—441no—
363C2×C4—441no—
364C2×C4—884no—
365C2×C4—881no—
366C2×C4—881no—
367C2×C4—881no—
368C8—81no—
369C8—881no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—81no—
379C22—222no—
380C22—442no—
381C22—442no—
382C22—441no—
383C22—441no—
384C22D11×#9911yescharacteristic
385C22#1062238311yescharacteristic
386C22D11×#10411yescharacteristic
387C4—41no—
388C4—41no—
389C4—81no—
390C4—82no—
391C4—81no—
392C4—112no—
393C4—221no—
394C4—441no—
395C4—441no—
396C4—881no—
397C4—882no—
398C4—881no—
399C2—21no—
400C2—21no—
401C2—41no—
402C2—41no—
403C2—442no—
404C2#1306713011yescharacteristic
405C2D11×#35211yescharacteristic
406C2#1307028911yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1344C2
socleC22×C11C2×#99
prime radicalC22×C22⋊D11D4
cosocleC2×C11×C22⋊C4C23
hypercenter#1344D11
hypocenterC11#11773
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1344

Complements

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

NH ≅ G/Ntype
4. #13066617C2semidirect
5. #13066616C2semidirect
6. #13066615C2semidirect
7. C11×#1344C2semidirect
8. C2×C4⋊C4×D11C4semidirect
12. #10622593C4semidirect
18. #10622280C4semidirect
20. #10622274C4semidirect
122. #1344D11semidirect
318. C11#11773semidirect

Maximal subgroups

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

subgroupindex
#130729172
#130684032
#130669552
#130666172
#130666162
#130666152
C11×#13442
#1177311