Finite Group Databasebeta

← #14664552

Subgroups — #14664552

Order 2816.

464 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 79 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#13074500C211yesmaximal, characteristic
2#13066957C211yesmaximal, characteristic, complemented
3#13066639C212yesmaximal, complemented
4#13066612C212yesmaximal, complemented
5C11×#1799C211yesmaximal, characteristic, complemented
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66983C411yescharacteristic, complemented
8C2×C11×#99—21no—
9C11×#380—21no—
10#10622836—21no—
11#10622826—21no—
12#10622824C411yescharacteristic, complemented
13#10622604C411yescharacteristic, complemented
14#10622599C411yescharacteristic, complemented
15#10622573C2211yescharacteristic
16#10622572—21no—
17#10622562C2211yescharacteristic
18#10622553—21no—
19#10622539—21no—
20C11×#342C2212yes—
21#10622163—21no—
22#10622163C2212yes—
23C22×D4×C11D411yescharacteristic
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C22×C22⋊D11—21no—
27C22×C22⋊D11—21no—
28C22×D44C2×C411yescharacteristic
29C4×D4×C11—41no—
30C4×D4×C11—41no—
31C2×C11×C4⋊C4—41no—
32C2×C11×C4⋊C4C2×C411yescharacteristic
33C2×C11×C22⋊C4—22no—
34C2×C11×C22⋊C4D411yescharacteristic
35C2×C11×C22⋊C4C2311yescharacteristic
36C2×C42×C11D411yescharacteristic
37C2×C22⋊Dic11—21no—
38C2×C22⋊Dic11—21no—
39#66983—41no—
40#66983—41no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×C4⋊Dic11C2×C411yescharacteristic
46C2×Dic11⋊C4—21no—
47C11×#99—42no—
48C11×#95—41no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95C2×C411yescharacteristic
53C11⋊#95C2×C411yescharacteristic
54C22⋊(C11⋊C8)—22no—
55C4⋊(C11⋊C8)—41no—
56#66867—41no—
57#11824—111nomaximal, Sylow
58C24×C11C22⋊C411yescharacteristic
59C24×C11C2×D411yescharacteristic
60C23×D11—21no—
61C2×D4×C11—21no—
62C2×D4×C11—21no—
63C2×D4×C11—41no—
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—41no—
79C2×C22⋊D11—41no—
80C2×C22⋊D11—81no—
81C2×C22⋊D11—81no—
82C2×C22⋊D11—81no—
83C2×C22⋊D11—81no—
84C22×Dic11—21no—
85C22×Dic11—21no—
86C22×Dic11—21no—
87C2×D44—41no—
88C2×D44—81no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—82no—
91C11×C22⋊C4—41no—
92C11×C22⋊C4—41no—
93C11×C22⋊C4—42no—
94C11×C22⋊C4—42no—
95C42×C11—21no—
96C42×C11—21no—
97C22⋊Dic11—81no—
98C22⋊Dic11—81no—
99(C2×D11)⋊C4—42no—
100(C2×D11)⋊C4—41no—
101(C2×D11)⋊C4—41no—
102(C2×D11)⋊C4—81no—
103(C2×D11)⋊C4—81no—
104C4⋊Dic11—41no—
105Dic11⋊C4—81no—
106C2×C11⋊C8—42no—
107#2635—111no—
108#1799D1111yescharacteristic, complemented
109#1466—111no—
110#1352—112no—
111#1343—112no—
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—21no—
117C23×C11—41no—
118C23×C11—41no—
119C23×C11—41no—
120C23×C11—41no—
121C23×C11C2×C22⋊C411yescharacteristic
122C23×C11AGL(1,ℤ/8)11yescharacteristic
123C23×C11#13711yescharacteristic
124C22×D11—41no—
125C22×D11—41no—
126C22×D11—41no—
127C22×D11—41no—
128C22×D11—41no—
129C22×D11—41no—
130C22×D11—41no—
131D4×C11—42no—
132D4×C11—42no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—41no—
140C2×C4×C11—42no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—81no—
145C2×C4×C11—81no—
146C2×C4×C11—81no—
147C2×C4×C11—82no—
148C2×C4×C11—82no—
149C2×C4×C11—82no—
150C2×C4×C11#9911yescharacteristic
151C2×C4×C11#9911yescharacteristic
152C22⋊D11—82no—
153C22⋊D11—82no—
154C22⋊D11—84no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164D44—82no—
165C11⋊C8—82no—
166C2×#121—111no—
167C2×C4×D4C2×D1111yescharacteristic
168#432—221no—
169C2×#99—21no—
170#400—111no—
171#399—111no—
172#394—111no—
173#394—221no—
174#392—111no—
175#392—221no—
176#388—221no—
177#386—221no—
178#381—111no—
179#380—21no—
180#342C2×D1112yes—
181#323—112no—
182#323—221no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11—41no—
188C22×C11—41no—
189C22×C11—41no—
190C22×C11—41no—
191C22×C11—41no—
192C22×C11—41no—
193C22×C11—41no—
194C22×C11—81no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11C2×#9911yescharacteristic
198C22×C11#41711yescharacteristic
199C22×C11#42111yescharacteristic
200C2×D11—81no—
201C2×D11—81no—
202C2×D11—81no—
203C2×D11—81no—
204C2×D11—81no—
205C2×D11—81no—
206C2×D11—81no—
207C4×C11—21no—
208C4×C11—21no—
209C4×C11—41no—
210C4×C11—41no—
211C4×C11—41no—
212C4×C11—41no—
213C4×C11—162no—
214Dic11—81no—
215Dic11—81no—
216Dic11—81no—
217C22×D4—111no—
218C22×D4—221no—
219C22×D4—221no—
220C22×D4C22⋊D1111yescharacteristic
221C23×C4C4×D1111yescharacteristic
222C23×C4C22⋊D1111yescharacteristic
223#121—441no—
224#121—441no—
225C4×D4—41no—
226C4×D4—41no—
227C2×C4⋊C4—41no—
228C2×C4⋊C4—111no—
229C2×C4⋊C4—221no—
230C2×C4⋊C4C4×D1111yescharacteristic
231C2×C22⋊C4—22no—
232C2×C22⋊C4—221no—
233C2×C22⋊C4—221no—
234C2×C22⋊C4—221no—
235C2×C22⋊C4—221no—
236C2×C22⋊C4—221no—
237C2×C22⋊C4—221no—
238C2×C22⋊C4D4411yescharacteristic
239C2×C22⋊C4C22×D1111yescharacteristic
240C2×C42D4411yescharacteristic
241C4⋊C8—441no—
242#99—42no—
243C22⋊C8—222no—
244#97—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—41no—
254C2×C11—41no—
255C2×C11—81no—
256C2×C11#151311yescharacteristic
257C2×C11#212111yescharacteristic
258C2×C11#212811yescharacteristic
259D11—161no—
260C24—221no—
261C24(C2×D11)⋊C411yescharacteristic
262C24C2×C22⋊D1111yescharacteristic
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—441no—
268C2×D4—442no—
269C2×D4—441no—
270C2×D4—441no—
271C2×D4—881no—
272C2×D4—881no—
273C2×D4—881no—
274C2×D4—881no—
275C2×D4—881no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—42no—
281C22×C4—81no—
282C22×C4—81no—
283C22×C4—221no—
284C22×C4—221no—
285C22×C4—221no—
286C22×C4(C2×D11)⋊C411yescharacteristic
287C22×C4(C2×D11)⋊C411yescharacteristic
288C22×C4(C2×D11)⋊C411yescharacteristic
289C22×C4C2×C4×D1111yescharacteristic
290C22×C4C2×D4411yescharacteristic
291C2×C8—442no—
292C4⋊C4—41no—
293C4⋊C4—82no—
294C4⋊C4—441no—
295C4⋊C4—881no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—42no—
299C22⋊C4—42no—
300C22⋊C4—442no—
301C22⋊C4—441no—
302C22⋊C4—441no—
303C22⋊C4—881no—
304C22⋊C4—881no—
305C22⋊C4—881no—
306C22⋊C4—881no—
307C42—21no—
308C42—21no—
309C11#1182411yescharacteristic, complemented, Sylow
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—441no—
320C23—441no—
321C23—441no—
322C23—441no—
323C23—441no—
324C23—441no—
325C23—441no—
326C23C2×(C2×D11)⋊C411yescharacteristic
327C23#6698511yescharacteristic
328C23#6699511yescharacteristic
329D4—42no—
330D4—42no—
331D4—882no—
332D4—882no—
333D4—882no—
334D4—884no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4—82no—
350C2×C4—82no—
351C2×C4—82no—
352C2×C4—441no—
353C2×C4—441no—
354C2×C4—441no—
355C2×C4—441no—
356C2×C4—441no—
357C2×C4—441no—
358C2×C4—441no—
359C2×C4—441no—
360C2×C4—441no—
361C2×C4#6687011yescharacteristic
362C2×C4#6687011yescharacteristic
363C8—882no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22—881no—
379C22—881no—
380C22—881no—
381C22—881no—
382C22—881no—
383C22—881no—
384C22—881no—
385C22C2×#6687011yescharacteristic
386C22#1062257911yescharacteristic
387C22#1062261811yescharacteristic
388C4—21no—
389C4—21no—
390C4—41no—
391C4—41no—
392C4—41no—
393C4—41no—
394C4—162no—
395C4—881no—
396C4—881no—
397C4—881no—
398C2—21no—
399C2—21no—
400C2—41no—
401C2—41no—
402C2—81no—
403C2—1761no—
404C2#1306715711yescharacteristic
405C2#1307026011yescharacteristic
406C2#1307028711yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1799C2
socleC22×C11C2×#99
prime radical#13074500C2
cosocleC2×C11×C22⋊C4C23
hypercenter#1799D11
hypocenterC11#11824
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1799

Complements

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

NH ≅ G/Ntype
2. #13066957C2semidirect
3. #13066639C2semidirect
4. #13066612C2semidirect
5. C11×#1799C2semidirect
7. C2×#66983C4semidirect
12. #10622824C4semidirect
13. #10622604C4semidirect
14. #10622599C4semidirect
108. #1799D11semidirect
309. C11#11824semidirect

Maximal subgroups

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

subgroupindex
#130745002
#130669572
#130666392
#130666122
C11×#17992
#1182411