Finite Group Databasebeta

← #14645235

Subgroups — #14645235

Order 2816.

876 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623001C211yesmaximal, characteristic
2#13068684C211yesmaximal, characteristic
3C2×#10622090C214yesmaximal
4C11×#1434C211yesmaximal, characteristic
5C22×C42×C11C2211yescharacteristic
6C2×#66979—21no—
7C2×#66977—21no—
8C2×#66977C2212yes—
9#10623001—28no—
10C2×#66923—21no—
11C2×#66922C411yescharacteristic, complemented
12C2×#66922C411yescharacteristic, complemented
13C2×C4×Dic22—21no—
14C2×C4×Dic22C412yescomplemented
15C2×C11×#95—21no—
16C2×C11×#95—21no—
17C2×C11×#95C2212yes—
18C2×C22⋊(C11⋊C8)C2212yes—
19#10622162—21no—
20#10622162—21no—
21#10622090—28no—
22C23×C4×C11—22no—
23C23×C4×C11D411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11C2311yescharacteristic
26C22×Dic22—21no—
27C22×Dic22C2×C412yes—
28C2×C42×C11—24no—
29C2×C42×C11C2×C411yescharacteristic
30C2×C42×C11C2×C411yescharacteristic
31C2×C42×C11D411yescharacteristic
32C2×C42×C11D411yescharacteristic
33C2×C22⋊Dic11—22no—
34#66979—28no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11C2×C412yes—
39#66977—28no—
40#66977—24no—
41#66977D418yes—
42C2×Dic11⋊C4—22no—
43C2×Dic11⋊C4—22no—
44C2×C4×Dic11—22no—
45C22×C11⋊C8—22no—
46#66923—28no—
47#66922—24no—
48#66922—24no—
49C4×Dic22—28no—
50C4×Dic22—24no—
51C4×Dic22—24no—
52C11×#95—24no—
53C11×#95—24no—
54C11×#95—42no—
55C22⋊(C11⋊C8)—24no—
56#8333—111nomaximal, Sylow
57C24×C11C2×D411yescharacteristic
58C22×C4×C11—22no—
59C22×C4×C11—22no—
60C22×C4×C11—22no—
61C22×C4×C11—22no—
62C22×C4×C11—24no—
63C22×C4×C11—41no—
64C22×C4×C11—41no—
65C22×C4×C11—41no—
66C22×C4×C11—42no—
67C22×C4×C11—42no—
68C22×C4×C11—42no—
69C22×C4×C11—42no—
70C22×C4×C11—42no—
71C22×C4×C11—42no—
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22⋊C411yescharacteristic
74C22×C4×C11C22⋊C411yescharacteristic
75C22×C4×C11C22⋊C411yescharacteristic
76C22×C4×C11SD1612yes—
77C22×C4×C11Q1612yes—
78C22×C4×C11C22×C411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D414yes—
81C22×Dic11—22no—
82C22×Dic11—22no—
83C2×Dic22—24no—
84C2×Dic22—22no—
85C2×Dic22—42no—
86C2×Dic22—42no—
87C2×Dic22—42no—
88C2×Dic22—42no—
89C2×Dic22C22⋊C414yes—
90C42×C11—22no—
91C42×C11—22no—
92C42×C11—22no—
93C42×C11—22no—
94C22⋊Dic11—28no—
95C4⋊Dic11—24no—
96C4⋊Dic11—24no—
97C4⋊Dic11—24no—
98C4⋊Dic11—22no—
99C4⋊Dic11C22⋊C414yes—
100Dic11⋊C4—28no—
101Dic11⋊C4—28no—
102C4×Dic11—28no—
103C2×C11⋊C8—42no—
104C2×C11⋊C8—42no—
105C2×C11⋊C8—42no—
106C2×#533—111no—
107#1817—111no—
108C2×#328—114no—
109#1434D1111yescharacteristic
110C23×C11—21no—
111C23×C11—21no—
112C23×C11—21no—
113C23×C11—21no—
114C23×C11C2×C22⋊C411yescharacteristic
115C23×C11#12012yes—
116C23×C11C2×SD1611yescharacteristic
117C23×C11C2×Q1611yescharacteristic
118C23×C11#13712yes—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—24no—
130C2×C4×C11—24no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—44no—
135C2×C4×C11—44no—
136C2×C4×C11—44no—
137C2×C4×C11—44no—
138C2×C4×C11—44no—
139C2×C4×C11—82no—
140C2×C4×C11—82no—
141C2×C4×C11—82no—
142C2×C4×C11—82no—
143C2×C4×C11#10312yes—
144C2×C4×C11#10312yes—
145C2×C4×C11#10412yes—
146C2×C4×C11C2×C22⋊C412yes—
147C2×C4×C11#12012yes—
148C2×Dic11—24no—
149C2×Dic11—24no—
150C2×Dic11—42no—
151C2×Dic11—42no—
152C2×Dic11—42no—
153C2×Dic11—42no—
154Dic22—44no—
155Dic22—48no—
156Dic22—44no—
157C11⋊C8—82no—
158#533—228no—
159C2×C4⋊Q8—111no—
160C2×C4⋊Q8—111no—
161C2×#125—221no—
162C2×C22⋊Q8—112no—
163C2×C22⋊Q8—221no—
164C2×C4×Q8—112no—
165C2×C4×Q8—221no—
166C2×#117—221no—
167C22×C42C2×D1111yescharacteristic
168C2×C22⋊C8—112no—
169C2×#95—21no—
170C2×#95—21no—
171C2×#95C2×D1112yes—
172#336—221no—
173#336—221no—
174#328—228no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11—22no—
178C22×C11—22no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11—22no—
182C22×C11—22no—
183C22×C11#37911yescharacteristic
184C22×C11#41011yescharacteristic
185C22×C11#41011yescharacteristic
186C22×C11C2×#10311yescharacteristic
187C22×C11#41911yescharacteristic
188C22×C11C2×#10411yescharacteristic
189C22×C11#42111yescharacteristic
190C22×C11#44812yes—
191C22×C11#45112yes—
192C4×C11—22no—
193C4×C11—22no—
194C4×C11—22no—
195C4×C11—22no—
196C4×C11—22no—
197C4×C11—41no—
198C4×C11—84no—
199Dic11—44no—
200Dic11—44no—
201C22×Q8—112no—
202C22×Q8—221no—
203C23×C4—22no—
204C23×C4C22⋊D1111yescharacteristic
205C23×C4C22⋊D1111yescharacteristic
206C23×C4C22×D1111yescharacteristic
207C22×C8—222no—
208C4⋊Q8—224no—
209C4⋊Q8—224no—
210#125—228no—
211C22⋊Q8—118no—
212C22⋊Q8—228no—
213C22⋊Q8—224no—
214C4×Q8—224no—
215C4×Q8—224no—
216C4×Q8—228no—
217#117—228no—
218C2×C4⋊C4—112no—
219C2×C4⋊C4—221no—
220C2×C4⋊C4—221no—
221C2×C4⋊C4—222no—
222C2×C4⋊C4—221no—
223C2×C4⋊C4—222no—
224C2×C22⋊C4—222no—
225C2×C42—24no—
226C2×C42—222no—
227C2×C42C4×D1111yescharacteristic
228C2×C42C4×D1111yescharacteristic
229C2×C42D4411yescharacteristic
230C2×C42D4411yescharacteristic
231C22⋊C8—224no—
232#95—24no—
233#95—24no—
234#95—42no—
235C2×C11—22no—
236C2×C11—22no—
237C2×C11#150311yescharacteristic
238C2×C11#150611yescharacteristic
239C2×C11#151511yescharacteristic
240C2×C11#151811yescharacteristic
241C2×C11#178211yescharacteristic
242C2×C11#178711yescharacteristic
243C2×C11#178911yescharacteristic
244C24C2×C22⋊D1111yescharacteristic
245C2×Q8—114no—
246C2×Q8—224no—
247C2×Q8—222no—
248C2×Q8—442no—
249C2×Q8—442no—
250C2×Q8—442no—
251C2×Q8—442no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—24no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4—42no—
263C22×C4—42no—
264C22×C4—42no—
265C22×C4—42no—
266C22×C4—222no—
267C22×C4—222no—
268C22×C4(C2×D11)⋊C411yescharacteristic
269C22×C4(C2×D11)⋊C411yescharacteristic
270C22×C4(C2×D11)⋊C411yescharacteristic
271C22×C4(C2×D11)⋊C411yescharacteristic
272C22×C4#432412yes—
273C22×C4#432612yes—
274C22×C4C2×C4×D1111yescharacteristic
275C22×C4C2×D4411yescharacteristic
276C22×C4D4×D1114yes—
277C2×C8—442no—
278C2×C8—442no—
279C2×C8—442no—
280C4⋊C4—114no—
281C4⋊C4—224no—
282C4⋊C4—224no—
283C4⋊C4—228no—
284C4⋊C4—224no—
285C4⋊C4—222no—
286C4⋊C4—228no—
287C22⋊C4—228no—
288C42—22no—
289C42—22no—
290C42—22no—
291C42—22no—
292C42—228no—
293C11#833311yescharacteristic, complemented, Sylow
294C23—21no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23C2×(C2×D11)⋊C411yescharacteristic
299C23C2×#432411yescharacteristic
300C23#6699012yes—
301C23C2×#432611yescharacteristic
302C23#6700412yes—
303Q8—444no—
304Q8—448no—
305Q8—444no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—24no—
317C2×C4—24no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—44no—
322C2×C4—44no—
323C2×C4—44no—
324C2×C4—44no—
325C2×C4—44no—
326C2×C4—82no—
327C2×C4—82no—
328C2×C4—82no—
329C2×C4—82no—
330C2×C4—224no—
331C2×C4—224no—
332C2×C4—442no—
333C2×C4—442no—
334C2×C4—442no—
335C2×C4—442no—
336C2×C4#6686912yes—
337C2×C4#6687412yes—
338C2×C4#6687412yes—
339C2×C4C22⋊C4×D1112yes—
340C2×C4#6693512yes—
341C8—882no—
342C22—22no—
343C22—21no—
344C22—21no—
345C22—22no—
346C22—22no—
347C22—21no—
348C22—21no—
349C22—22no—
350C22C2×#6686911yescharacteristic
351C22#1062256811yescharacteristic
352C22C2×#6687411yescharacteristic
353C22#1062261711yescharacteristic
354C22#1062261811yescharacteristic
355C22#1062261911yescharacteristic
356C22#1062261911yescharacteristic
357C22#1062265312yes—
358C22#1062266312yes—
359C4—22no—
360C4—22no—
361C4—22no—
362C4—22no—
363C4—22no—
364C4—41no—
365C4—84no—
366C4—444no—
367C4—444no—
368C2—22no—
369C2—22no—
370C2#1306711411yescharacteristic
371C2#1306712711yescharacteristic
372C2#1306716611yescharacteristic
373C2#1306717911yescharacteristic
374C2#1306853311yescharacteristic
375C2#1306855011yescharacteristic
376C2#1306856111yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1434C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#1434D11
hypocenterC11#8333
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1434

Complements

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

NH ≅ G/Ntype
11. C2×#66922C4semidirect
12. C2×#66922C4semidirect
14. C2×C4×Dic22C4semidirect
293. C11#8333semidirect

Maximal subgroups

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

subgroupindex
C2×#106230012
#130686842
C2×#106220902
C11×#14342
#833311