Finite Group Databasebeta

← #14664332

Subgroups — #14664332

Order 2816.

544 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 83 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#13073513C211yesmaximal, characteristic
2#13066954C211yesmaximal, characteristic, complemented
3#13066615C212yesmaximal, complemented
4#13066612C212yesmaximal, complemented
5C4×C11×#99C211yesmaximal, characteristic, complemented
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66991—21no—
8C2×C4×D44C411yescharacteristic, complemented
9C2×C11×#99—21no—
10C4×C11×C22⋊C4—21no—
11#10622826—21no—
12#10622826—21no—
13#10622820—21no—
14#10622600—21no—
15#10622573C411yescharacteristic, complemented
16#10622573C2211yescharacteristic
17#10622566C411yescharacteristic, complemented
18#10622566C2211yescharacteristic
19#10622549C411yescharacteristic, complemented
20C11×#342C2212yes—
21#10622166—21no—
22#10622163C2212yes—
23C22×D4×C11D411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C22×C22⋊D11—21no—
27C22×C22⋊D11—21no—
28C22×D44C2×C411yescharacteristic
29C22×C4×D11—21no—
30C4×D4×C11—41no—
31C4×D4×C11—41no—
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C22⋊C4—22no—
34C2×C11×C22⋊C4C2×C411yescharacteristic
35C2×C11×C22⋊C4C2311yescharacteristic
36C2×C42×C11—41no—
37C2×C42×C11C2×C411yescharacteristic
38C2×C22⋊Dic11—21no—
39C2×C22⋊Dic11—21no—
40#66991—44no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11C2×C411yescharacteristic
46C2×#4318—41no—
47C4×D44—41no—
48C4×D44—41no—
49C11×#99—24no—
50C11×#95—41no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95C2×C411yescharacteristic
55C11⋊#95C2×C411yescharacteristic
56C22⋊(C11⋊C8)—22no—
57C22⋊(C11⋊C8)—41no—
58#11774—111nomaximal, Sylow
59C24×C11C22⋊C411yescharacteristic
60C24×C11C2×D411yescharacteristic
61C23×D11—21no—
62C2×D4×C11—22no—
63C2×D4×C11—22no—
64C2×D4×C11—41no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—42no—
70C22×C4×C11—81no—
71C22×C4×C11—81no—
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22⋊C411yescharacteristic
74C22×C4×C11C22⋊C411yescharacteristic
75C22×C4×C11C22×C411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C2×C22⋊D11—42no—
78C2×C22⋊D11—42no—
79C2×C22⋊D11—42no—
80C2×C22⋊D11—42no—
81C2×C22⋊D11—81no—
82C2×C22⋊D11—81no—
83C22×Dic11—21no—
84C22×Dic11—21no—
85C22×Dic11—21no—
86C2×D44—41no—
87C2×D44—42no—
88C2×C4×D11—42no—
89C2×C4×D11—42no—
90C2×C4×D11—42no—
91C11×C4⋊C4—41no—
92C11×C22⋊C4—24no—
93C11×C22⋊C4—41no—
94C11×C22⋊C4—41no—
95C11×C22⋊C4—42no—
96C42×C11—21no—
97C42×C11—21no—
98C42×C11—82no—
99C22⋊Dic11—42no—
100C22⋊Dic11—42no—
101(C2×D11)⋊C4—41no—
102(C2×D11)⋊C4—41no—
103(C2×D11)⋊C4—81no—
104(C2×D11)⋊C4—81no—
105C4⋊Dic11—41no—
106C4⋊Dic11—42no—
107#4318—82no—
108C2×C11⋊C8—42no—
109#2535—111no—
110C4×#99D1111yescharacteristic, complemented
111#1465—111no—
112#1344—112no—
113#1343—112no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—21no—
117C23×C11—21no—
118C23×C11—21no—
119C23×C11—41no—
120C23×C11—41no—
121C23×C11—41no—
122C23×C11—41no—
123C23×C11C2×C22⋊C411yescharacteristic
124C23×C11AGL(1,ℤ/8)12yes—
125C22×D11—22no—
126C22×D11—41no—
127C22×D11—41no—
128C22×D11—41no—
129C22×D11—41no—
130C22×D11—41no—
131C22×D11—41no—
132D4×C11—44no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—41no—
139C2×C4×C11—42no—
140C2×C4×C11—42no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—44no—
145C2×C4×C11—81no—
146C2×C4×C11—81no—
147C2×C4×C11—82no—
148C2×C4×C11—82no—
149C2×C4×C11#9911yescharacteristic
150C2×C4×C11#9911yescharacteristic
151C2×C4×C11#10412yes—
152C22⋊D11—84no—
153C22⋊D11—84no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163D44—42no—
164D44—42no—
165C4×D11—84no—
166C11⋊C8—82no—
167C2×#121—221no—
168C2×C4×D4—111no—
169C2×C4×D4C2×D1111yescharacteristic
170C2×#99—21no—
171#407—221no—
172#397—111no—
173#397—111no—
174#392—111no—
175#392—111no—
176#386—221no—
177#386—221no—
178#382—111no—
179#380—221no—
180C4×C22⋊C4—21no—
181#342C2×D1112yes—
182#324—221no—
183#323—112no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11—22no—
187C22×C11—42no—
188C22×C11—42no—
189C22×C11—41no—
190C22×C11—41no—
191C22×C11—41no—
192C22×C11—41no—
193C22×C11—41no—
194C22×C11—81no—
195C22×C11—81no—
196C22×C11C2×#9911yescharacteristic
197C22×C11#41811yescharacteristic
198C22×C11C2×#10411yescharacteristic
199C2×D11—42no—
200C2×D11—42no—
201C2×D11—42no—
202C2×D11—81no—
203C2×D11—81no—
204C2×D11—81no—
205C2×D11—81no—
206C4×C11—21no—
207C4×C11—21no—
208C4×C11—22no—
209C4×C11—41no—
210C4×C11—41no—
211C4×C11—41no—
212C4×C11—84no—
213Dic11—81no—
214Dic11—81no—
215Dic11—81no—
216C22×D4—111no—
217C22×D4—221no—
218C22×D4—221no—
219C22×D4C22⋊D1111yescharacteristic
220C23×C4—221no—
221C23×C4D4411yescharacteristic
222C23×C4C22⋊D1111yescharacteristic
223C2×M16—441no—
224#121—444no—
225C4×D4—41no—
226C4×D4—41no—
227C4×D4—441no—
228C4×D4—441no—
229C2×C4⋊C4—111no—
230C2×C4⋊C4—221no—
231C2×C4⋊C4D4411yescharacteristic
232C2×C22⋊C4—22no—
233C2×C22⋊C4—221no—
234C2×C22⋊C4—221no—
235C2×C22⋊C4—221no—
236C2×C22⋊C4—221no—
237C2×C22⋊C4—221no—
238C2×C22⋊C4C4×D1111yescharacteristic
239C2×C22⋊C4C22×D1111yescharacteristic
240C2×C42—41no—
241C2×C42C4×D1111yescharacteristic
242#99—24no—
243C22⋊C8—222no—
244C22⋊C8—441no—
245#95—41no—
246#95—111no—
247#95—111no—
248#95—221no—
249#95—221no—
250#95—221no—
251C2×C11—21no—
252C2×C11—21no—
253C2×C11—42no—
254C2×C11—81no—
255C2×C11#150711yescharacteristic
256C2×C11#212011yescharacteristic
257C2×C11#212711yescharacteristic
258D11—82no—
259C24—221no—
260C24(C2×D11)⋊C411yescharacteristic
261C24C2×C22⋊D1111yescharacteristic
262C2×D4—22no—
263C2×D4—22no—
264C2×D4—41no—
265C2×D4—441no—
266C2×D4—442no—
267C2×D4—442no—
268C2×D4—442no—
269C2×D4—442no—
270C2×D4—442no—
271C2×D4—881no—
272C2×D4—881no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—42no—
278C22×C4—81no—
279C22×C4—81no—
280C22×C4—221no—
281C22×C4—221no—
282C22×C4—221no—
283C22×C4—442no—
284C22×C4—442no—
285C22×C4—442no—
286C22×C4(C2×D11)⋊C411yescharacteristic
287C22×C4(C2×D11)⋊C411yescharacteristic
288C22×C4(C2×D11)⋊C411yescharacteristic
289C22×C4C2×C4×D1111yescharacteristic
290C22×C4C2×D4411yescharacteristic
291M16—882no—
292C2×C8—442no—
293C4⋊C4—41no—
294C4⋊C4—441no—
295C4⋊C4—442no—
296C22⋊C4—24no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—42no—
300C22⋊C4—442no—
301C22⋊C4—442no—
302C22⋊C4—441no—
303C22⋊C4—441no—
304C22⋊C4—881no—
305C22⋊C4—881no—
306C42—21no—
307C42—21no—
308C42—82no—
309C11#1177411yescharacteristic, complemented, Sylow
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—222no—
320C23—441no—
321C23—441no—
322C23—441no—
323C23—441no—
324C23—441no—
325C23—441no—
326C23C2×(C2×D11)⋊C411yescharacteristic
327C23#6700212yes—
328D4—44no—
329D4—442no—
330D4—442no—
331D4—884no—
332D4—884no—
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—44no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—82no—
348C2×C4—82no—
349C2×C4—441no—
350C2×C4—441no—
351C2×C4—441no—
352C2×C4—441no—
353C2×C4—441no—
354C2×C4—441no—
355C2×C4—441no—
356C2×C4—441no—
357C2×C4—441no—
358C2×C4—884no—
359C2×C4#6686912yes—
360C2×C4#6687011yescharacteristic
361C2×C4#6687011yescharacteristic
362C8—882no—
363C22—21no—
364C22—21no—
365C22—22no—
366C22—42no—
367C22—42no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—81no—
374C22—81no—
375C22—442no—
376C22—442no—
377C22—442no—
378C22—881no—
379C22—881no—
380C22—881no—
381C22—881no—
382C22C2×#6686911yescharacteristic
383C22C2×#6687011yescharacteristic
384C22#1062261411yescharacteristic
385C4—22no—
386C4—21no—
387C4—21no—
388C4—41no—
389C4—41no—
390C4—41no—
391C4—84no—
392C4—881no—
393C4—881no—
394C4—881no—
395C2—21no—
396C2—21no—
397C2—42no—
398C2—81no—
399C2—882no—
400C2#1306713111yescharacteristic
401C2#1307025511yescharacteristic
402C2#1307028311yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC4×C11×#99C2
socleC22×C11C2×#99
prime radical#13073513C2
cosocleC2×C11×C22⋊C4C23
hypercenterC4×#99D11
hypocenterC11#11774
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
2. #13066954C2semidirect
3. #13066615C2semidirect
4. #13066612C2semidirect
5. C4×C11×#99C2semidirect
8. C2×C4×D44C4semidirect
15. #10622573C4semidirect
17. #10622566C4semidirect
19. #10622549C4semidirect
110. C4×#99D11semidirect
309. C11#11774semidirect

Maximal subgroups

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

subgroupindex
#130735132
#130669542
#130666152
#130666122
C4×C11×#992
#1177411