Finite Group Databasebeta

← #14649443

Subgroups — #14649443

Order 2816.

728 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076961C211yesmaximal, characteristic
2#13068596C211yesmaximal, characteristic, complemented
3C2×#10622123C212yesmaximal, complemented
4#13066500C212yesmaximal, complemented
5C2×C11×#431C211yesmaximal, characteristic, complemented
6C22×C42×C11C2211yescharacteristic
7C2×#66983—21no—
8C2×#66983—21no—
9C2×#66983C412yes—
10C2×#66927C2211yescharacteristic
11C11×#431—24no—
12C2×C11×C4⋊C8C2212yes—
13C2×C11×C22⋊C8—21no—
14C2×C4×C8×C11—21no—
15C2×C22⋊(C11⋊C8)—21no—
16#10622552—21no—
17#10622552—21no—
18#10622552C412yes—
19#10622548C2211yescharacteristic
20C2×C4⋊(C11⋊C8)C2212yes—
21#10622162—21no—
22#10622123—24no—
23C23×C4×C11C2×C411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C22×C22⋊D11—22no—
27C22×D44—21no—
28C22×D44—21no—
29C22×D44C2×C412yes—
30C22×C8×C11—22no—
31C2×C42×C11—22no—
32C2×C42×C11—22no—
33C2×C42×C11C2×C411yescharacteristic
34C2×C42×C11D411yescharacteristic
35C2×C42×C11D411yescharacteristic
36C2×C42×C11C2311yescharacteristic
37#66983—44no—
38#66983—42no—
39#66983—42no—
40#66983—44no—
41C2×(C2×D11)⋊C4—22no—
42C2×(C2×D11)⋊C4—22no—
43C2×(C2×D11)⋊C4—22no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11—21no—
46C2×C4⋊Dic11C2×C412yes—
47C22×C11⋊C8—22no—
48#66927—22no—
49#66927—22no—
50C11×C4⋊C8—22no—
51C11×C4⋊C8D414yescomplemented
52C11×C22⋊C8—24no—
53C4×C8×C11—24no—
54C22⋊(C11⋊C8)—42no—
55C4⋊(C11⋊C8)—22no—
56C4⋊(C11⋊C8)—22no—
57#9134—111nomaximal, Sylow
58C24×C11C22⋊C411yescharacteristic
59C23×D11—22no—
60C22×C4×C11—22no—
61C22×C4×C11—22no—
62C22×C4×C11—22no—
63C22×C4×C11—22no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—22no—
67C22×C4×C11—22no—
68C22×C4×C11—41no—
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11D812yes—
73C22×C4×C11SD1612yes—
74C22×C4×C11C22×C411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C2×C22⋊D11—44no—
78C2×C22⋊D11—44no—
79C2×C22⋊D11—44no—
80C22×Dic11—22no—
81C2×D44—24no—
82C2×D44—42no—
83C2×D44—42no—
84C2×D44—41no—
85C2×D44—42no—
86C2×D44—41no—
87C2×D44—41no—
88C2×D44—41no—
89C2×D44—42no—
90C2×D44—42no—
91C2×D44—42no—
92C2×C8×C11—24no—
93C2×C8×C11—42no—
94C2×C8×C11—42no—
95C42×C11—22no—
96C42×C11—21no—
97C42×C11—22no—
98C42×C11—21no—
99C42×C11C2×D412yes—
100C42×C11#4112yes—
101(C2×D11)⋊C4—44no—
102(C2×D11)⋊C4—44no—
103(C2×D11)⋊C4—44no—
104C4⋊Dic11—42no—
105C4⋊Dic11—41no—
106C4⋊Dic11—41no—
107C4⋊Dic11—42no—
108C2×C11⋊C8—42no—
109C2×C11⋊C8—42no—
110C2×C11⋊C8—42no—
111C2×#431D1111yescharacteristic, complemented
112#2856—111no—
113#1797—111no—
114C2×#331—112no—
115#1296—112no—
116C23×C11—21no—
117C23×C11—21no—
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11#10212yes—
123C23×C11C2×C22⋊C411yescharacteristic
124C22×D11—42no—
125C22×D11—42no—
126C22×D11—42no—
127C22×D11—42no—
128C22×D11—42no—
129C22×D11—42no—
130C22×D11—42no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—24no—
138C2×C4×C11—24no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—44no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11#10012yes—
146C2×C4×C11#10212yes—
147C2×C4×C11C4×D412yes—
148C2×C4×C11#12011yescharacteristic
149C2×C4×C11#12112yes—
150C2×C4×C11#12311yescharacteristic
151C2×C4×C11C2×D811yescharacteristic
152C2×C4×C11C2×SD1611yescharacteristic
153C2×C4×C11#13512yes—
154C2×C4×C11#13512yes—
155C2×C4×C11AGL(1,ℤ/8)12yes—
156C22⋊D11—88no—
157C2×Dic11—42no—
158C2×Dic11—42no—
159C2×Dic11—42no—
160D44—84no—
161D44—82no—
162D44—82no—
163D44—82no—
164D44—82no—
165C8×C11—44no—
166C11⋊C8—82no—
167C2×#127—111no—
168C2×#121—112no—
169C2×#121—221no—
170C2×#121—221no—
171C22×C42C2×D1111yescharacteristic
172#431—24no—
173C2×C4⋊C8—112no—
174C2×C4⋊C8C2×D1112yes—
175C2×C22⋊C8—21no—
176C2×C22⋊C8—221no—
177C2×C4×C8—21no—
178#390—112no—
179#390—221no—
180#390—221no—
181#384—111no—
182#336—221no—
183#331—224no—
184C22×C11—22no—
185C22×C11—22no—
186C22×C11—22no—
187C22×C11—41no—
188C22×C11—41no—
189C22×C11—41no—
190C22×C11—41no—
191C22×C11#38611yescharacteristic
192C22×C11C2×#10011yescharacteristic
193C22×C11#41311yescharacteristic
194C22×C11C2×#10211yescharacteristic
195C22×C11#41611yescharacteristic
196C22×C11#41611yescharacteristic
197C22×C11#41811yescharacteristic
198C2×D11—82no—
199C2×D11—82no—
200C2×D11—82no—
201C2×D11—82no—
202C2×D11—82no—
203C2×D11—82no—
204C2×D11—82no—
205C4×C11—22no—
206C4×C11—22no—
207C4×C11—22no—
208C4×C11—41no—
209C4×C11#44912yes—
210C4×C11#46512yes—
211C4×C11#46612yes—
212C4×C11#48212yes—
213Dic11—82no—
214C22×D4—112no—
215C22×D4—222no—
216C22×D4—221no—
217C22×D4—221no—
218C23×C4C4×D1111yescharacteristic
219C23×C4D4411yescharacteristic
220C23×C4C22⋊D1111yescharacteristic
221C22×C8—22no—
222C22×C8—222no—
223#127—222no—
224#127—222no—
225#121—444no—
226#121—442no—
227#121—442no—
228#121—444no—
229C2×C4⋊C4—112no—
230C2×C4⋊C4—221no—
231C2×C4⋊C4—221no—
232C2×C22⋊C4—222no—
233C2×C22⋊C4—222no—
234C2×C22⋊C4—222no—
235C2×C42—22no—
236C2×C42—22no—
237C2×C42C4×D1111yescharacteristic
238C2×C42D4411yescharacteristic
239C2×C42C22⋊D1111yescharacteristic
240C2×C42C22×D1111yescharacteristic
241C4⋊C8—22no—
242C4⋊C8—222no—
243C4⋊C8—222no—
244C4⋊C8C22⋊D1114yescomplemented
245C22⋊C8—24no—
246C22⋊C8—442no—
247C4×C8—24no—
248C2×C11—42no—
249C2×C11#154011yescharacteristic
250C2×C11#154311yescharacteristic
251C2×C11#154511yescharacteristic
252C2×C11#155311yescharacteristic
253C2×C11#187511yescharacteristic
254C2×C11#189311yescharacteristic
255C2×C11#190011yescharacteristic
256D11—162no—
257C24—222no—
258C24(C2×D11)⋊C411yescharacteristic
259C2×D4—224no—
260C2×D4—442no—
261C2×D4—442no—
262C2×D4—444no—
263C2×D4—444no—
264C2×D4—444no—
265C2×D4—441no—
266C2×D4—441no—
267C2×D4—442no—
268C2×D4—441no—
269C2×D4—442no—
270C2×D4—442no—
271C2×D4—442no—
272C2×D4—441no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—21no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—21no—
281C22×C4—41no—
282C22×C4—222no—
283C22×C4#431412yes—
284C22×C4D8812yes—
285C22×C4(C2×D11)⋊C411yescharacteristic
286C22×C4(C2×D11)⋊C411yescharacteristic
287C22×C4(C2×D11)⋊C411yescharacteristic
288C22×C4C2×C4×D1111yescharacteristic
289C22×C4C2×D4411yescharacteristic
290C22×C4C2×C22⋊D1111yescharacteristic
291C2×C8—24no—
292C2×C8—42no—
293C2×C8—42no—
294C2×C8—442no—
295C2×C8—442no—
296C2×C8—442no—
297C4⋊C4—442no—
298C4⋊C4—441no—
299C4⋊C4—441no—
300C4⋊C4—442no—
301C22⋊C4—444no—
302C22⋊C4—444no—
303C22⋊C4—444no—
304C42—22no—
305C42—21no—
306C42—22no—
307C42—21no—
308C42#433912yes—
309C42C2×C22⋊D1112yes—
310C11#913411yescharacteristic, complemented, Sylow
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—442no—
318C23—442no—
319C23—442no—
320C23—442no—
321C23—442no—
322C23—442no—
323C23—442no—
324C23#6688512yes—
325C23C2×(C2×D11)⋊C411yescharacteristic
326D4—884no—
327D4—888no—
328D4—882no—
329D4—882no—
330D4—882no—
331D4—882no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—24no—
339C2×C4—24no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—44no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—442no—
347C2×C4—442no—
348C2×C4—442no—
349C2×C4#6688512yes—
350C2×C4#6688712yes—
351C2×C4C2×#431411yescharacteristic
352C2×C4C2×D8811yescharacteristic
353C2×C4#6695712yes—
354C2×C4C4×C22⋊D1112yes—
355C2×C4#6698211yescharacteristic
356C2×C4#6698312yes—
357C2×C4#6700212yes—
358C2×C4#6700312yes—
359C2×C4#6700611yescharacteristic
360C8—44no—
361C8—882no—
362C22—22no—
363C22—22no—
364C22—22no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—882no—
370C22—882no—
371C22—882no—
372C22—882no—
373C22—882no—
374C22—882no—
375C22—882no—
376C22#1062261411yescharacteristic
377C22#1062261511yescharacteristic
378C22C2×#6688511yescharacteristic
379C22#1062272611yescharacteristic
380C22C2×#6688711yescharacteristic
381C22#1062274511yescharacteristic
382C22#1062282611yescharacteristic
383C4—22no—
384C4—22no—
385C4—22no—
386C4—41no—
387C4—882no—
388C4#1062261612yes—
389C4#1062272712yes—
390C4#1062272812yes—
391C4#1062285112yes—
392C2—42no—
393C2—1762no—
394C2#1306726311yescharacteristic
395C2#1306727611yescharacteristic
396C2#1306728311yescharacteristic
397C2#1306731911yescharacteristic
398C2#1306893811yescharacteristic
399C2#1306904411yescharacteristic
400C2#1306907911yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#431C2
socleC23×C11C2×C22⋊C4
prime radical#13076961C2
cosocleC2×C42×C11C23
hypercenterC2×#431D11
hypocenterC11#9134
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#431

Complements

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

NH ≅ G/Ntype
2. #13068596C2semidirect
3. C2×#10622123C2semidirect
4. #13066500C2semidirect
5. C2×C11×#431C2semidirect
51. C11×C4⋊C8D4semidirect
111. C2×#431D11semidirect
244. C4⋊C8C22⋊D11semidirect
310. C11#9134semidirect

Maximal subgroups

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

subgroupindex
#130769612
#130685962
C2×#106221232
#130665002
C2×C11×#4312
#913411