Finite Group Databasebeta

← #14642230

Subgroups — #14642230

Order 2816.

568 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068310C211yesmaximal, characteristic
2C2×#10622162C211yesmaximal, characteristic
3#13066442C212yesmaximal, complemented
4#13066439C212yesmaximal, complemented
5C11×#2855C211yesmaximal, characteristic
6C2×C11×C22⋊Q8C411yescharacteristic
7C22×C42×C11C2211yescharacteristic
8C22×#4318—21no—
9C23×C11⋊C8—21no—
10C11×#391C411yescharacteristic
11C11×#391C2211yescharacteristic
12C11×#389C411yescharacteristic
13C11×#389C2211yescharacteristic
14C11×#387—21no—
15C11×#387—21no—
16C11×#385—21no—
17C11×#381—21no—
18C11×#380C411yescharacteristic
19#10622162—21no—
20#10622162—21no—
21#10622162C2212yes—
22#10622162C2212yes—
23C22×Q8×C11C2×C411yescharacteristic
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C11×C22⋊Q8—42no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C11×C4⋊C4C2×C411yescharacteristic
33C2×C11×C4⋊C4C2×C411yescharacteristic
34C2×C11×C22⋊C4—21no—
35C2×C11×C22⋊C4—21no—
36C2×C42×C11—42no—
37C2×C42×C11C2×C411yescharacteristic
38C2×C42×C11D411yescharacteristic
39C2×C42×C11D411yescharacteristic
40C2×C42×C11C2311yescharacteristic
41C2×#4318—24no—
42C2×#4318—42no—
43C2×#4318—42no—
44C22×C11⋊C8—24no—
45C22×C11⋊C8—22no—
46C22×C11⋊C8—22no—
47C22×C11⋊C8—42no—
48C22×C11⋊C8—42no—
49C11×#95—21no—
50C11×#95—21no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95—21no—
56#7681—111nomaximal, Sylow
57C24×C11C22⋊C411yescharacteristic
58C2×Q8×C11—22no—
59C2×Q8×C11—41no—
60C2×Q8×C11—41no—
61C22×C4×C11—22no—
62C22×C4×C11—22no—
63C22×C4×C11—22no—
64C22×C4×C11—22no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—22no—
68C22×C4×C11—22no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—41no—
74C22×C4×C11C22⋊C411yescharacteristic
75C22×C4×C11C22⋊C411yescharacteristic
76C22×C4×C11C22⋊C411yescharacteristic
77C22×C4×C11SD1612yes—
78C22×C4×C11Q1612yes—
79C22×C4×C11C22×C411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C11×C4⋊C4—22no—
83C11×C4⋊C4—42no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—42no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C11×C22⋊C4—42no—
90C11×C22⋊C4—42no—
91C42×C11—41no—
92C42×C11—41no—
93C42×C11—41no—
94C42×C11—41no—
95#4318—48no—
96C2×C11⋊C8—24no—
97C2×C11⋊C8—24no—
98C2×C11⋊C8—48no—
99C2×C11⋊C8—42no—
100C2×C11⋊C8—42no—
101C2×C11⋊C8—42no—
102C2×C11⋊C8—42no—
103#2855D1111yescharacteristic
104#1728—111no—
105C2×#336—111no—
106#1272—112no—
107#1271—112no—
108C23×C11—21no—
109C23×C11—21no—
110C23×C11—21no—
111C23×C11—21no—
112C23×C11#9912yes—
113C23×C11#10312yes—
114C23×C11#10412yes—
115C23×C11C2×C22⋊C411yescharacteristic
116Q8×C11—82no—
117C2×C4×C11—24no—
118C2×C4×C11—24no—
119C2×C4×C11—24no—
120C2×C4×C11—24no—
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—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—44no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11#10312yes—
148C2×C4×C11#10412yes—
149C2×C4×C11#13112yes—
150C2×C4×C11C2×SD1611yescharacteristic
151C2×C4×C11C2×Q1611yescharacteristic
152C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C11#13711yescharacteristic
154C11⋊C8—44no—
155C11⋊C8—44no—
156C22×M16—221no—
157C23×C8—221no—
158C2×C22⋊Q8Dic1111yescharacteristic
159C22×C42C2×D1111yescharacteristic
160#391Dic1111yescharacteristic
161#391C2×D1111yescharacteristic
162#389Dic1111yescharacteristic
163#389C2×D1111yescharacteristic
164#387—21no—
165#387—21no—
166#385—21no—
167#381—21no—
168#380Dic1111yescharacteristic
169#336—112no—
170#336—112no—
171#336—221no—
172#336—221no—
173C22×C11—22no—
174C22×C11—22no—
175C22×C11—22no—
176C22×C11—22no—
177C22×C11—22no—
178C22×C11—22no—
179C22×C11#32814yes—
180C22×C11#40811yescharacteristic
181C22×C11C2×#9911yescharacteristic
182C22×C11#41311yescharacteristic
183C22×C11C2×#10311yescharacteristic
184C22×C11#41711yescharacteristic
185C22×C11C2×#10411yescharacteristic
186C22×C11C2×#10411yescharacteristic
187C4×C11—22no—
188C4×C11—22no—
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—22no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—41no—
195C4×C11—81no—
196C4×C11—81no—
197C4×C11—81no—
198C4×C11—81no—
199C22×Q8C2×Dic1111yescharacteristic
200C23×C4C2×Dic1111yescharacteristic
201C23×C4C22⋊D1111yescharacteristic
202C23×C4C22⋊D1111yescharacteristic
203C2×M16—224no—
204C2×M16—442no—
205C2×M16—442no—
206C22×C8—224no—
207C22×C8—222no—
208C22×C8—222no—
209C22×C8—442no—
210C22×C8—442no—
211C22⋊Q8—42no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4C2×Dic1111yescharacteristic
216C2×C4⋊C4C2×Dic1111yescharacteristic
217C2×C4⋊C4C2×Dic1111yescharacteristic
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C42—42no—
221C2×C42C2×Dic1111yescharacteristic
222C2×C42C22⋊D1111yescharacteristic
223C2×C42C22⋊D1111yescharacteristic
224C2×C42C22×D1111yescharacteristic
225#95—21no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95—21no—
232C2×C11—24no—
233C2×C11#146811yescharacteristic
234C2×C11#148311yescharacteristic
235C2×C11#149311yescharacteristic
236C2×C11C2×#32811yescharacteristic
237C2×C11#150411yescharacteristic
238C2×C11#152411yescharacteristic
239C2×C11#155011yescharacteristic
240C24C22⋊Dic1111yescharacteristic
241C2×Q8—22no—
242C2×Q8—41no—
243C2×Q8—41no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—41no—
257C22×C4#432512yes—
258C22×C4#432612yes—
259C22×C4C22⋊Dic1111yescharacteristic
260C22×C4C22⋊Dic1111yescharacteristic
261C22×C4C22⋊Dic1111yescharacteristic
262C22×C4C22×Dic1111yescharacteristic
263C22×C4C2×C22⋊D1111yescharacteristic
264C22×C4C2×C22⋊D1111yescharacteristic
265M16—448no—
266C2×C8—224no—
267C2×C8—224no—
268C2×C8—448no—
269C2×C8—442no—
270C2×C8—442no—
271C2×C8—442no—
272C2×C8—442no—
273C4⋊C4—22no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—42no—
277C4⋊C4—42no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C22⋊C4—42no—
281C22⋊C4—42no—
282C42—41no—
283C42—41no—
284C42—41no—
285C42—41no—
286C11#768111yescharacteristic, complemented, Sylow
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23#6689812yes—
292C23#6689912yes—
293C23#6690112yes—
294C23C2×C22⋊Dic1111yescharacteristic
295Q8—82no—
296C2×C4—24no—
297C2×C4—24no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—24no—
309C2×C4—24no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—44no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4#6689912yes—
327C2×C4#6690112yes—
328C2×C4C2×#432511yescharacteristic
329C2×C4C2×#432611yescharacteristic
330C2×C4#6700112yes—
331C2×C4#6700211yescharacteristic
332C2×C4#6700411yescharacteristic
333C8—444no—
334C8—444no—
335C22—22no—
336C22—22no—
337C22—22no—
338C22—22no—
339C22—22no—
340C22—22no—
341C22#1062217614yes—
342C22C2×#6689811yescharacteristic
343C22C2×#6689911yescharacteristic
344C22#1062284511yescharacteristic
345C22#1062284711yescharacteristic
346C22C2×#6690111yescharacteristic
347C22C2×#6690111yescharacteristic
348C22#1062285011yescharacteristic
349C4—21no—
350C4—22no—
351C4—21no—
352C4—21no—
353C4—22no—
354C4—21no—
355C4—22no—
356C4—41no—
357C4—81no—
358C4—81no—
359C4—81no—
360C4—81no—
361C2—24no—
362C2#1306696411yescharacteristic
363C2#1306702911yescharacteristic
364C2#1306707111yescharacteristic
365C2C2×#1062217611yescharacteristic
366C2#1306712011yescharacteristic
367C2#1306720411yescharacteristic
368C2#1306730611yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2855C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#2855D11
hypocenterC11#7681
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2855

Complements

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

NH ≅ G/Ntype
3. #13066442C2semidirect
4. #13066439C2semidirect
286. C11#7681semidirect

Maximal subgroups

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

subgroupindex
#130683102
C2×#106221622
#130664422
#130664392
C11×#28552
#768111