Finite Group Databasebeta

← #14641971

Subgroups — #14641971

Order 2816.

590 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068684C211yesmaximal, characteristic, complemented
2#13068378C211yesmaximal, characteristic, complemented
3#13066439C212yesmaximal, complemented
4#13066437C212yesmaximal, complemented
5C4×C11×#121C211yesmaximal, characteristic
6C2×C11×#121C411yescharacteristic
7C2×C4×D4×C11—21no—
8C2×C4×D4×C11C411yescharacteristic
9C22×C42×C11C2211yescharacteristic
10C11×#390C2211yescharacteristic
11C11×#389C2211yescharacteristic
12C11×#388—21no—
13C11×#386—21no—
14C11×#380C411yescharacteristic
15C4×C11×C4⋊C4C411yescharacteristic
16C4×C11×C22⋊C4—21no—
17C2×C22⋊(C11⋊C8)—21no—
18C2×C22⋊(C11⋊C8)—21no—
19C2×#66867—21no—
20#10622162—21no—
21#10622162C2212yes—
22#10622162C2212yes—
23C22×D4×C11—21no—
24C22×D4×C11C2×C411yescharacteristic
25C23×C4×C11—21no—
26C23×C4×C11C2×C411yescharacteristic
27C23×C4×C11D411yescharacteristic
28C23×C4×C11D411yescharacteristic
29C11×#121—22no—
30C11×#121—22no—
31C4×D4×C11—42no—
32C4×D4×C11—44no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4C2×C411yescharacteristic
35C2×C11×C4⋊C4C2×C411yescharacteristic
36C2×C11×C4⋊C4C2×C411yescharacteristic
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C42×C11—21no—
43C2×C42×C11—42no—
44C2×C42×C11C2×C411yescharacteristic
45C2×C42×C11D411yescharacteristic
46C2×C42×C11D411yescharacteristic
47C2×C42×C11C2311yescharacteristic
48C22×C11⋊C8—22no—
49C22×C11⋊C8—22no—
50C11×#95—21no—
51C11×#95—21no—
52C11×#95—21no—
53C22⋊(C11⋊C8)—24no—
54C22⋊(C11⋊C8)—42no—
55#66867—42no—
56#7620—111nomaximal, Sylow
57C24×C11—21no—
58C24×C11C22⋊C411yescharacteristic
59C2×D4×C11—24no—
60C2×D4×C11—21no—
61C2×D4×C11—41no—
62C2×D4×C11—41no—
63C2×D4×C11—42no—
64C2×D4×C11—42no—
65C2×D4×C11M1612yes—
66C22×C4×C11—22no—
67C22×C4×C11—21no—
68C22×C4×C11—22no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—22no—
72C22×C4×C11—22no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—41no—
76C22×C4×C11—41no—
77C22×C4×C11—41no—
78C22×C4×C11—41no—
79C22×C4×C11—42no—
80C22×C4×C11—42no—
81C22×C4×C11—42no—
82C22×C4×C11C22⋊C411yescharacteristic
83C22×C4×C11C22⋊C411yescharacteristic
84C22×C4×C11C22⋊C411yescharacteristic
85C22×C4×C11C22×C411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C11×C4⋊C4—21no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—42no—
92C11×C4⋊C4M1612yes—
93C11×C22⋊C4—24no—
94C11×C22⋊C4—42no—
95C11×C22⋊C4—42no—
96C11×C22⋊C4—42no—
97C11×C22⋊C4—42no—
98C42×C11—22no—
99C42×C11—22no—
100C42×C11—41no—
101C42×C11—41no—
102C42×C11—42no—
103C2×C11⋊C8—24no—
104C2×C11⋊C8—42no—
105C2×C11⋊C8—42no—
106C2×C11⋊C8—42no—
107C2×C11⋊C8—42no—
108C2×C11⋊C8—42no—
109C4×#121D1111yescharacteristic
110#1817—111no—
111#1749—111no—
112#1271—112no—
113#1270—112no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—21no—
117C23×C11—21no—
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—22no—
121C23×C11—41no—
122C23×C11—41no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11#10412yes—
128C23×C11C2×C22⋊C411yescharacteristic
129D4×C11—42no—
130D4×C11—42no—
131D4×C11—48no—
132C2×C4×C11—21no—
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—21no—
140C2×C4×C11—21no—
141C2×C4×C11—22no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—44no—
148C2×C4×C11—44no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—84no—
160C2×C4×C11#9912yes—
161C2×C4×C11C2×M1611yescharacteristic
162C2×C4×C11C2×M1611yescharacteristic
163C2×C4×C11#13512yes—
164C2×C4×C11AGL(1,ℤ/8)12yes—
165C11⋊C8—44no—
166C11⋊C8—82no—
167C2×#121Dic1111yescharacteristic
168C2×C4×D4—21no—
169C2×C4×D4Dic1111yescharacteristic
170C22×C42C2×D1111yescharacteristic
171C2×C22⋊C8—221no—
172C2×C22⋊C8—221no—
173C2×#97—221no—
174#390C2×D1111yescharacteristic
175#389C2×D1111yescharacteristic
176#388—21no—
177#386—21no—
178#380Dic1111yescharacteristic
179C4×C4⋊C4Dic1111yescharacteristic
180C4×C22⋊C4—21no—
181#336—112no—
182#336—112no—
183#336—221no—
184C22×C11—22no—
185C22×C11—22no—
186C22×C11—22no—
187C22×C11—41no—
188C22×C11—41no—
189C22×C11—41no—
190C22×C11—41no—
191C22×C11—42no—
192C22×C11—42no—
193C22×C11—42no—
194C22×C11—81no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11—81no—
198C22×C11#40711yescharacteristic
199C22×C11C2×#9911yescharacteristic
200C22×C11#41311yescharacteristic
201C22×C11#41611yescharacteristic
202C22×C11#41811yescharacteristic
203C22×C11C2×#10411yescharacteristic
204C22×C11#42111yescharacteristic
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—22no—
208C4×C11—22no—
209C4×C11—22no—
210C4×C11—41no—
211C4×C11—42no—
212C4×C11—41no—
213C4×C11—81no—
214C4×C11—81no—
215C22×D4—21no—
216C22×D4C2×Dic1111yescharacteristic
217C23×C4—21no—
218C23×C4C2×Dic1111yescharacteristic
219C23×C4C22⋊D1111yescharacteristic
220C23×C4C22⋊D1111yescharacteristic
221C22×C8—222no—
222C22×C8—222no—
223#121—22no—
224#121—22no—
225C4×D4—42no—
226C4×D4—44no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4C2×Dic1111yescharacteristic
229C2×C4⋊C4C2×Dic1111yescharacteristic
230C2×C4⋊C4C2×Dic1111yescharacteristic
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C42—21no—
237C2×C42—42no—
238C2×C42C2×Dic1111yescharacteristic
239C2×C42C22⋊D1111yescharacteristic
240C2×C42C22⋊D1111yescharacteristic
241C2×C42C22×D1111yescharacteristic
242C22⋊C8—224no—
243C22⋊C8—442no—
244#97—442no—
245#95—21no—
246#95—21no—
247#95—21no—
248C2×C11—42no—
249C2×C11—82no—
250C2×C11#146511yescharacteristic
251C2×C11#148811yescharacteristic
252C2×C11#149011yescharacteristic
253C2×C11#150111yescharacteristic
254C2×C11#151011yescharacteristic
255C2×C11#153211yescharacteristic
256C2×C11#155311yescharacteristic
257C24—21no—
258C24C22⋊Dic1111yescharacteristic
259C2×D4—24no—
260C2×D4—21no—
261C2×D4—41no—
262C2×D4—41no—
263C2×D4—42no—
264C2×D4—42no—
265C2×D4#431812yes—
266C22×C4—22no—
267C22×C4—21no—
268C22×C4—22no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4C22⋊Dic1111yescharacteristic
283C22×C4C22⋊Dic1111yescharacteristic
284C22×C4C22⋊Dic1111yescharacteristic
285C22×C4C22×Dic1111yescharacteristic
286C22×C4C2×C22⋊D1111yescharacteristic
287C22×C4C2×C22⋊D1111yescharacteristic
288C2×C8—224no—
289C2×C8—442no—
290C2×C8—442no—
291C2×C8—442no—
292C2×C8—442no—
293C2×C8—442no—
294C4⋊C4—21no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—42no—
298C4⋊C4#431812yes—
299C22⋊C4—24no—
300C22⋊C4—42no—
301C22⋊C4—42no—
302C22⋊C4—42no—
303C22⋊C4—42no—
304C42—22no—
305C42—22no—
306C42—41no—
307C42—41no—
308C42—42no—
309C11#762011yescharacteristic, complemented, Sylow
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—22no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23#6690112yes—
324C23C2×C22⋊Dic1111yescharacteristic
325D4—42no—
326D4—42no—
327D4—48no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—22no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—44no—
344C2×C4—44no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—84no—
356C2×C4#6689812yes—
357C2×C4C2×#431811yescharacteristic
358C2×C4C2×#431811yescharacteristic
359C2×C4#6698512yes—
360C2×C4#6700312yes—
361C8—444no—
362C8—882no—
363C22—22no—
364C22—22no—
365C22—22no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—42no—
371C22—42no—
372C22—42no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22#1062282011yescharacteristic
378C22#1062282811yescharacteristic
379C22C2×#6689811yescharacteristic
380C22#1062284611yescharacteristic
381C22C2×#6690111yescharacteristic
382C22#1062284911yescharacteristic
383C22#1062285011yescharacteristic
384C4—22no—
385C4—22no—
386C4—22no—
387C4—21no—
388C4—21no—
389C4—42no—
390C4—41no—
391C4—41no—
392C4—81no—
393C4—81no—
394C2—42no—
395C2—82no—
396C2#1306695411yescharacteristic
397C2#1306705011yescharacteristic
398C2#1306705911yescharacteristic
399C2#1306710711yescharacteristic
400C2#1306714511yescharacteristic
401C2#1306723611yescharacteristic
402C2#1306732111yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC4×C11×#121C2
socleC23×C11C2×C22⋊C4
prime radicalC2×C11×#121C4
cosocleC2×C42×C11C23
hypercenterC4×#121D11
hypocenterC11#7620
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
1. #13068684C2semidirect
2. #13068378C2semidirect
3. #13066439C2semidirect
4. #13066437C2semidirect
309. C11#7620semidirect

Maximal subgroups

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

subgroupindex
#130686842
#130683782
#130664392
#130664372
C4×C11×#1212
#762011