Finite Group Databasebeta

← #14648452

Subgroups — #14648452

Order 2816.

542 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077699C211yesmaximal, characteristic, complemented
2C4×#66928C211yesmaximal, characteristic
3#13067008C211yesmaximal, characteristic
4#13067006C211yesmaximal, characteristic
5#13066939C211yesmaximal, characteristic, complemented
6#13066449C211yesmaximal, characteristic, complemented
7C11×#1276C211yesmaximal, characteristic, complemented
8C2×#66928C411yescharacteristic
9C2×C4×D44C2211yescharacteristic
10C2×C4×Dic22C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#431C2211yescharacteristic
13C43×C11C2211yescharacteristic
14#10622553—22no—
15#10622552C411yescharacteristic
16C4×(C2×D11)⋊C4—22no—
17#10622549C411yescharacteristic
18#10622542C411yescharacteristic
19#10622538C2211yescharacteristic
20#10622538C2211yescharacteristic
21#10622444—22no—
22#10622332—22no—
23#10622292—22no—
24#10622121—22no—
25#10622107—22no—
26#10622097—22no—
27C22×D44C2×C411yescharacteristic
28C22×C4×D11—21no—
29C22×Dic22C2×C411yescharacteristic
30C2×C42×C11—21no—
31C2×C42×C11—21no—
32C2×C42×C11C2×C411yescharacteristic
33C2×C42×C11C2×C411yescharacteristic
34C2×C42×C11C2311yescharacteristic
35C2×(C2×D11)⋊C4—22no—
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4—22no—
38C2×C4⋊Dic11C2×C411yescharacteristic
39C2×C4⋊Dic11C2×C411yescharacteristic
40C2×Dic11⋊C4D412yes—
41C2×C4×Dic11D412yes—
42#66928—22no—
43#66928—22no—
44C4×D44—21no—
45C4×D44—21no—
46C4×D44—21no—
47C4×D44—21no—
48C4×Dic22—21no—
49C4×Dic22—21no—
50C4×Dic22—21no—
51C4×Dic22—21no—
52C11×C4⋊C8—21no—
53C11×C4⋊C8D412yes—
54C11×C22⋊C8—21no—
55C11×C22⋊C8—21no—
56C4×C8×C11—21no—
57C4×C8×C11—21no—
58C11⋊#95—22no—
59C11⋊#95—22no—
60C22⋊(C11⋊C8)—21no—
61C22⋊(C11⋊C8)—21no—
62#66879—24no—
63Dic11⋊C8—24no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)D412yes—
66C4×C11⋊C8—21no—
67C4×C11⋊C8—21no—
68#8964—111nomaximal, Sylow
69C23×D11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11C22×C411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×Dic11—21no—
76C22×Dic11C22⋊C412yes—
77C22×Dic11C22⋊C412yes—
78C2×D44—21no—
79C2×D44—21no—
80C2×D44—21no—
81C2×D44—21no—
82C2×D44—21no—
83C2×D44M1612yes—
84C2×C4×D11—44no—
85C2×C4×D11—41no—
86C2×C4×D11—41no—
87C2×Dic22—21no—
88C2×Dic22—21no—
89C2×Dic22—21no—
90C2×Dic22—21no—
91C2×Dic22—21no—
92C2×Dic22—21no—
93C2×C8×C11—22no—
94C2×C8×C11—41no—
95C42×C11—21no—
96C42×C11—21no—
97C42×C11—21no—
98C42×C11—42no—
99C42×C11—42no—
100C42×C11M1612yes—
101C42×C11C2×D411yescharacteristic
102C42×C11C2×D411yescharacteristic
103C42×C11#4111yescharacteristic
104C42×C11#4111yescharacteristic
105(C2×D11)⋊C4—28no—
106(C2×D11)⋊C4—44no—
107(C2×D11)⋊C4—41no—
108(C2×D11)⋊C4—41no—
109C4⋊Dic11—21no—
110C4⋊Dic11—21no—
111C4⋊Dic11—21no—
112C4⋊Dic11—21no—
113Dic11⋊C4—22no—
114Dic11⋊C4—22no—
115C4×Dic11—22no—
116C4×Dic11—22no—
117C2×C11⋊C8—22no—
118C2×C11⋊C8—41no—
119#2983—111no—
120C4×#124—111no—
121#1478—111no—
122#1478—111no—
123#1461—111no—
124#1276—111no—
125#1276D1111yescharacteristic, complemented
126C23×C11C2×C22⋊C411yescharacteristic
127C22×D11—22no—
128C22×D11—42no—
129C22×D11—42no—
130C22×D11—41no—
131C22×D11—41no—
132C2×C4×C11—22no—
133C2×C4×C11—22no—
134C2×C4×C11—22no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11C4×D411yescharacteristic
141C2×C4×C11C4×D411yescharacteristic
142C2×C4×C11#12011yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#12111yescharacteristic
145C2×C4×C11#12311yescharacteristic
146C2×C4×C11C2×M1611yescharacteristic
147C2×C4×C11C2×M1611yescharacteristic
148C2×C4×C11#13111yescharacteristic
149C2×C4×C11#13111yescharacteristic
150C2×Dic11—22no—
151C2×Dic11—22no—
152C2×Dic11—22no—
153C2×Dic11—22no—
154C2×Dic11—42no—
155C2×Dic11—42no—
156C2×Dic11—41no—
157D44—22no—
158D44—22no—
159D44—41no—
160D44—41no—
161C4×D11—82no—
162C4×D11—82no—
163Dic22—41no—
164Dic22—41no—
165Dic22—41no—
166Dic22—41no—
167C8×C11—42no—
168C8×C11—81no—
169C11⋊C8—42no—
170C11⋊C8—81no—
171C2×#124—111no—
172C2×C4×Q8—111no—
173C2×C4×D4—111no—
174#446—222no—
175#446—222no—
176#432—222no—
177#431—111no—
178#431—111no—
179#431C2×D1111yescharacteristic
180#431C2×D1111yescharacteristic
181#391—111no—
182#390—111no—
183#388—222no—
184#382—111no—
185C4×C22⋊C4—222no—
186C43C2×D1111yescharacteristic
187D4⋊C8—222no—
188D4⋊C8—222no—
189#324—222no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11#38611yescharacteristic
193C22×C11#40711yescharacteristic
194C22×C11#40811yescharacteristic
195C2×D11—44no—
196C2×D11—42no—
197C2×D11—82no—
198C2×D11—81no—
199C2×D11—81no—
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—42no—
204C4×C11—42no—
205C4×C11#43511yescharacteristic
206C4×C11#43511yescharacteristic
207C4×C11#43611yescharacteristic
208C4×C11#43611yescharacteristic
209C4×C11#45412yes—
210Dic11—42no—
211Dic11—42no—
212Dic11—81no—
213C22×Q8—111no—
214C22×D4—111no—
215C23×C4—221no—
216#124—222no—
217#124—222no—
218C4×Q8—221no—
219C4×Q8—221no—
220C4×Q8—221no—
221C4×Q8—221no—
222C4×D4—221no—
223C4×D4—221no—
224C4×D4—221no—
225C4×D4—221no—
226C2×C4⋊C4—111no—
227C2×C4⋊C4—112no—
228C2×C4⋊C4—111no—
229C2×C22⋊C4—222no—
230C2×C22⋊C4—222no—
231C2×C22⋊C4—221no—
232C2×C42—21no—
233C2×C42—21no—
234C2×C42—112no—
235C2×C42C4×D1111yescharacteristic
236C2×C42C4×D1111yescharacteristic
237C2×C42C22×D1111yescharacteristic
238C4⋊C8—21no—
239C4⋊C8—112no—
240C4⋊C8—224no—
241C4⋊C8—221no—
242C4⋊C8D4412yes—
243C22⋊C8—21no—
244C22⋊C8—21no—
245C22⋊C8—221no—
246C22⋊C8—221no—
247#97—224no—
248C4×C8—21no—
249C4×C8—21no—
250C4×C8—221no—
251C4×C8—221no—
252#95—222no—
253#95—222no—
254C2×C11—21no—
255C2×C11—21no—
256C2×C11#187011yescharacteristic
257C2×C11#188411yescharacteristic
258C2×C11#188811yescharacteristic
259D11—82no—
260C24—221no—
261C2×Q8—221no—
262C2×Q8—221no—
263C2×Q8—221no—
264C2×Q8—221no—
265C2×Q8—221no—
266C2×Q8—221no—
267C2×D4—112no—
268C2×D4—221no—
269C2×D4—221no—
270C2×D4—221no—
271C2×D4—221no—
272C2×D4—221no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—112no—
276C22×C4—112no—
277C22×C4—221no—
278C22×C4—444no—
279C22×C4—441no—
280C22×C4—441no—
281C22×C4C2×C4×D1111yescharacteristic
282C22×C4D4×D1111yescharacteristic
283C22×C4D4×D1111yescharacteristic
284C2×C8—22no—
285C2×C8—41no—
286C2×C8—222no—
287C2×C8—441no—
288C4⋊C4—221no—
289C4⋊C4—222no—
290C4⋊C4—221no—
291C4⋊C4—222no—
292C4⋊C4—221no—
293C4⋊C4—221no—
294C22⋊C4—228no—
295C22⋊C4—444no—
296C22⋊C4—441no—
297C22⋊C4—441no—
298C42—21no—
299C42—21no—
300C42—21no—
301C42—42no—
302C42—42no—
303C42—222no—
304C42—222no—
305C42#431312yes—
306C42C2×D4411yescharacteristic
307C42#433911yescharacteristic
308C42D4×D1111yescharacteristic
309C42#434311yescharacteristic
310C11#896411yescharacteristic, complemented, Sylow
311C23—222no—
312C23—442no—
313C23—442no—
314C23—441no—
315C23—441no—
316C23C22⋊C4×D1111yescharacteristic
317Q8—441no—
318Q8—441no—
319Q8—441no—
320Q8—441no—
321D4—222no—
322D4—222no—
323D4—441no—
324D4—441no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—222no—
334C2×C4—222no—
335C2×C4—222no—
336C2×C4—222no—
337C2×C4—442no—
338C2×C4—442no—
339C2×C4—441no—
340C2×C4—882no—
341C2×C4—882no—
342C2×C4C4×D4411yescharacteristic
343C2×C4#6693511yescharacteristic
344C2×C4#6693711yescharacteristic
345C2×C4#6694611yescharacteristic
346C2×C4#6694711yescharacteristic
347C2×C4#6694811yescharacteristic
348C2×C4C2×#431311yescharacteristic
349C2×C4#6695411yescharacteristic
350C2×C4M16×D1111yescharacteristic
351C2×C4#6696011yescharacteristic
352C8—42no—
353C8—81no—
354C8—442no—
355C8—881no—
356C22—21no—
357C22—21no—
358C22—444no—
359C22—442no—
360C22—882no—
361C22—881no—
362C22—881no—
363C22#1062227811yescharacteristic
364C22#1062233911yescharacteristic
365C22#1062234011yescharacteristic
366C4—21no—
367C4—21no—
368C4—21no—
369C4—42no—
370C4—42no—
371C4—442no—
372C4—442no—
373C4—881no—
374C4#1062230111yescharacteristic
375C4#1062231911yescharacteristic
376C4#1062244012yes—
377C4#1062244911yescharacteristic
378C4#1062245111yescharacteristic
379C2—21no—
380C2—21no—
381C2—882no—
382C2#1306891211yescharacteristic
383C2#1306899811yescharacteristic
384C2#1306901811yescharacteristic
subgroupG/H
centerC2×C4#66935
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1276C2
socleC22×C11#386
prime radicalC22×D44C2×C4
cosocleC2×C42×C11C23
hypercenter#1276D11
hypocenterC11#8964
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1276

Complements

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

NH ≅ G/Ntype
1. #13077699C2semidirect
5. #13066939C2semidirect
6. #13066449C2semidirect
7. C11×#1276C2semidirect
125. #1276D11semidirect
310. C11#8964semidirect

Maximal subgroups

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

subgroupindex
#130776992
C4×#669282
#130670082
#130670062
#130669392
#130664492
C11×#12762
#896411