Finite Group Databasebeta

← #14719942

Subgroups — #14719942

Order 2816.

912 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623065C211yesmaximal, characteristic
2#13077700C212yesmaximal, complemented
3#13066984C214yesmaximal, complemented
4#13066966C214yesmaximal, complemented
5#13066956C212yesmaximal, complemented
6#13066950C211yesmaximal, characteristic, complemented
7C11×#1464C211yesmaximal, characteristic, complemented
8C2×C11×#117C2211yescharacteristic
9C2×#66983C411yescharacteristic
10C2×#66977C411yescharacteristic
11#10623065—24no—
12#10623065—24no—
13C2×#66951C2212yes—
14C2×#66949C412yes—
15C2×#66938C2212yes—
16C2×#66936C412yes—
17C2×#66928C411yescharacteristic
18C2×C4×D44C2211yescharacteristic
19C2×#66922C411yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21C11×#432C2212yes—
22#10622539C2212yes—
23#10622441—24no—
24#10622332C2214yes—
25#10622331C2214yes—
26#10622314—24no—
27C11×#324C2212yes—
28C11×#323C2212yes—
29#10622166C2212yes—
30#10622163C2212yes—
31#10622106C2218yes—
32C23×C4×C11C2×C411yescharacteristic
33C22×C22⋊D11C2×C412yes—
34C22×D44C2×C411yescharacteristic
35C22×C4×D11C2×C412yes—
36C22×Dic22C2×C412yes—
37C22×Dic22C2×C411yescharacteristic
38C11×#117—22no—
39C11×#117—22no—
40C2×C11×C4⋊C4C2×C411yescharacteristic
41C2×C11×C4⋊C4C2311yescharacteristic
42C2×C11×C22⋊C4C2×C411yescharacteristic
43C2×C11×C22⋊C4C2311yescharacteristic
44C2×C42×C11C2×C411yescharacteristic
45C2×C42×C11C2311yescharacteristic
46C2×C22⋊Dic11C2×C412yes—
47#66983—22no—
48#66983—22no—
49C2×(C2×D11)⋊C4C2×C412yes—
50C2×(C2×D11)⋊C4C2×C412yes—
51C2×(C2×D11)⋊C4C2×C412yes—
52C2×(C2×D11)⋊C4C2312yes—
53C2×C4⋊Dic11C2×C411yescharacteristic
54C2×C4⋊Dic11C2×C412yes—
55C2×C4⋊Dic11C2×C411yescharacteristic
56#66977—22no—
57#66977—22no—
58C2×Dic11⋊C4C2×C412yes—
59C2×Dic11⋊C4C2×C412yes—
60C2×C4×Dic11C2312yes—
61#66951—24no—
62#66951—24no—
63#66949—28no—
64#66938—24no—
65#66938—24no—
66#66936—28no—
67#66928—22no—
68#66928—22no—
69C4×D44—22no—
70C4×D44—22no—
71#66922—22no—
72#66922—22no—
73C4×Dic22D414yes—
74C4×Dic22D414yes—
75C11×C4⋊C8—22no—
76C11×C22⋊C8C2314yes—
77C11×#97—22no—
78C22⋊(C11⋊C8)C2314yes—
79#66879—24no—
80Dic11⋊C8—24no—
81Dic11⋊C8—24no—
82C8×Dic11—24no—
83C4⋊(C11⋊C8)—22no—
84#66867—22no—
85#17409—111nomaximal, Sylow
86C24×C11C22×C411yescharacteristic
87C23×D11C22×C412yes—
88C22×C4×C11—21no—
89C22×C4×C11—21no—
90C22×C4×C11—42no—
91C22×C4×C11C22×C411yescharacteristic
92C22×C4×C11C22×C411yescharacteristic
93C22×C4×C11C22×C411yescharacteristic
94C22×C4×C11C22×C411yescharacteristic
95C22×C4×C11C22×C411yescharacteristic
96C22×C4×C11C2411yescharacteristic
97C2×C22⋊D11—24no—
98C2×C22⋊D11—82no—
99C22×Dic11C22×C412yes—
100C22×Dic11C22×C412yes—
101C22×Dic11C22×C412yes—
102C2×D44—21no—
103C2×D44—21no—
104C2×D44—42no—
105C2×C4×D11—24no—
106C2×C4×D11—82no—
107C2×Dic22—24no—
108C2×Dic22—42no—
109C2×Dic22—82no—
110C2×Dic22C22⋊C412yes—
111C2×Dic22C22⋊C412yes—
112C2×C8×C11—24no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—22no—
115C11×C22⋊C4—22no—
116C11×C22⋊C4—22no—
117C42×C11—21no—
118C42×C11—21no—
119C42×C11C2×D412yes—
120C42×C11C2×D412yes—
121C22⋊Dic11—24no—
122(C2×D11)⋊C4—24no—
123(C2×D11)⋊C4—24no—
124(C2×D11)⋊C4—24no—
125(C2×D11)⋊C4—22no—
126(C2×D11)⋊C4—22no—
127C4⋊Dic11—24no—
128C4⋊Dic11—21no—
129C4⋊Dic11—21no—
130C4⋊Dic11C22⋊C412yes—
131C4⋊Dic11C22⋊C412yes—
132Dic11⋊C4—24no—
133Dic11⋊C4C22⋊C418yes—
134C4×Dic11C2×D414yes—
135C4×Dic11C2×D414yes—
136C2×C11⋊C8—24no—
137C2×#542—111no—
138#2983—112no—
139#1473—114no—
140#1469—114no—
141#1466—112no—
142#1464—111no—
143#1464D1111yescharacteristic, complemented
144C23×C11—21no—
145C23×C11—22no—
146C23×C11—41no—
147C23×C11—41no—
148C23×C11C23×C411yescharacteristic
149C22×D11—22no—
150C22×D11—24no—
151C22×D11—42no—
152C22×D11—42no—
153C2×C4×C11—22no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—22no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11C2×C22⋊C412yes—
165C2×C4×C11C2×C22⋊C411yescharacteristic
166C2×C4×C11C2×C22⋊C411yescharacteristic
167C2×C4×C11C22×D412yes—
168C22⋊D11—84no—
169C2×Dic11—24no—
170C2×Dic11—22no—
171C2×Dic11—42no—
172C2×Dic11—42no—
173C2×Dic11C2×C22⋊C414yes—
174C2×Dic11C2×C22⋊C414yes—
175D44—42no—
176D44—42no—
177C4×D11—84no—
178Dic22—42no—
179Dic22—42no—
180Dic22—84no—
181C8×C11—44no—
182C11⋊C8—44no—
183#542—224no—
184#542—224no—
185C2×C4⋊Q8—111no—
186C2×#126—112no—
187C2×#124—112no—
188C2×#124—111no—
189C2×#123—112no—
190C2×C22⋊Q8—111no—
191C2×C22⋊Q8—112no—
192C2×#121—111no—
193C2×C4×Q8—111no—
194C2×C4×D4—111no—
195C2×#117C2×D1111yescharacteristic
196#446—224no—
197#446—224no—
198#432—112no—
199#432—114no—
200#432C2×D1112yes—
201#431—114no—
202#324—112no—
203#324C2×D1112yes—
204#323—112no—
205#323—118no—
206#323C2×D1112yes—
207C22×C11—21no—
208C22×C11—21no—
209C22×C11—41no—
210C22×C11—41no—
211C22×C11—41no—
212C22×C11—82no—
213C22×C11C22×C22⋊C411yescharacteristic
214C22×C11#56812yes—
215C2×D11—42no—
216C2×D11—42no—
217C2×D11—42no—
218C2×D11—84no—
219C4×C11—21no—
220C4×C11—21no—
221C4×C11—22no—
222C4×C11—22no—
223C4×C11—41no—
224C4×C11—41no—
225C4×C11—41no—
226Dic11—24no—
227Dic11—24no—
228Dic11—42no—
229C22×Q8—111no—
230C22×Q8—112no—
231C22×D4—112no—
232C22×D4—111no—
233C23×C4—112no—
234C23×C4C4×D1111yescharacteristic
235C4⋊Q8—222no—
236C4⋊Q8—222no—
237#126—224no—
238#126—224no—
239#124—222no—
240#124—222no—
241#124—224no—
242#124—224no—
243#123—228no—
244C22⋊Q8—228no—
245C22⋊Q8—222no—
246C22⋊Q8—222no—
247#121—222no—
248#121—222no—
249C4×Q8—114no—
250C4×Q8—114no—
251C4×D4—222no—
252C4×D4—222no—
253#117—22no—
254#117—22no—
255C2×C4⋊C4—111no—
256C2×C4⋊C4—112no—
257C2×C4⋊C4—111no—
258C2×C4⋊C4—112no—
259C2×C4⋊C4—112no—
260C2×C4⋊C4C4×D1111yescharacteristic
261C2×C4⋊C4C22×D1111yescharacteristic
262C2×C22⋊C4—112no—
263C2×C22⋊C4—112no—
264C2×C22⋊C4—112no—
265C2×C22⋊C4—112no—
266C2×C22⋊C4—112no—
267C2×C22⋊C4C4×D1111yescharacteristic
268C2×C22⋊C4C22×D1111yescharacteristic
269C2×C42—112no—
270C2×C42C4×D1111yescharacteristic
271C2×C42C22×D1111yescharacteristic
272C4⋊C8—22no—
273C4⋊C8—224no—
274C4⋊C8—224no—
275C4⋊C8—222no—
276C22⋊C8—114no—
277C22⋊C8C22×D1114yes—
278#97—22no—
279#97—224no—
280#97—222no—
281C4×C8—224no—
282C2×C11—22no—
283C2×C11—81no—
284C2×C11#287911yescharacteristic
285C2×C11#288411yescharacteristic
286C2×C11#288811yescharacteristic
287D11—82no—
288C24—112no—
289C24C2×C4×D1111yescharacteristic
290C2×Q8—112no—
291C2×Q8—112no—
292C2×Q8—224no—
293C2×Q8—442no—
294C2×Q8—882no—
295C2×D4—224no—
296C2×D4—221no—
297C2×D4—221no—
298C2×D4—442no—
299C2×D4—882no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—42no—
303C22×C4—112no—
304C22×C4—112no—
305C22×C4—112no—
306C22×C4—224no—
307C22×C4—882no—
308C22×C4C2×C4×D1111yescharacteristic
309C22×C4C2×C4×D1111yescharacteristic
310C22×C4C2×C4×D1111yescharacteristic
311C22×C4C2×C4×D1111yescharacteristic
312C22×C4C2×C4×D1111yescharacteristic
313C22×C4C23×D1111yescharacteristic
314C2×C8—24no—
315C2×C8—224no—
316C4⋊C4—22no—
317C4⋊C4—22no—
318C4⋊C4—112no—
319C4⋊C4—112no—
320C4⋊C4—118no—
321C4⋊C4—224no—
322C4⋊C4—224no—
323C4⋊C4—221no—
324C4⋊C4—221no—
325C22⋊C4—22no—
326C22⋊C4—22no—
327C22⋊C4—224no—
328C22⋊C4—224no—
329C22⋊C4—224no—
330C22⋊C4—224no—
331C22⋊C4—222no—
332C22⋊C4—222no—
333C42—21no—
334C42—21no—
335C42—114no—
336C42—114no—
337C42D4×D1112yes—
338C42D4×D1112yes—
339C11#1740911yescharacteristic, complemented, Sylow
340C23—21no—
341C23—22no—
342C23—41no—
343C23—41no—
344C23—222no—
345C23—224no—
346C23—442no—
347C23—442no—
348C23C22×C4×D1111yescharacteristic
349Q8—442no—
350Q8—442no—
351Q8—884no—
352D4—442no—
353D4—442no—
354D4—884no—
355C2×C4—22no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—22no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—114no—
367C2×C4—114no—
368C2×C4—224no—
369C2×C4—222no—
370C2×C4—442no—
371C2×C4—442no—
372C2×C4—884no—
373C2×C4C22⋊C4×D1111yescharacteristic
374C2×C4C22⋊C4×D1111yescharacteristic
375C2×C4C22⋊C4×D1112yes—
376C2×C4C2×D4×D1112yes—
377C8—44no—
378C8—444no—
379C22—21no—
380C22—21no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—82no—
385C22—442no—
386C22—442no—
387C22—442no—
388C22—884no—
389C22C2×C22⋊C4×D1111yescharacteristic
390C22#1062327612yes—
391C4—21no—
392C4—21no—
393C4—22no—
394C4—22no—
395C4—41no—
396C4—41no—
397C4—41no—
398C4—224no—
399C4—224no—
400C4—442no—
401C2—22no—
402C2—81no—
403C2—882no—
404C2#1307705911yescharacteristic
405C2#1307707811yescharacteristic
406C2#1307709311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1464C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#66983C4
cosocleC22×C4×C11C24
hypercenter#1464D11
hypocenterC11#17409
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1464

Complements

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

NH ≅ G/Ntype
2. #13077700C2semidirect
3. #13066984C2semidirect
4. #13066966C2semidirect
5. #13066956C2semidirect
6. #13066950C2semidirect
7. C11×#1464C2semidirect
143. #1464D11semidirect
339. C11#17409semidirect

Maximal subgroups

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

subgroupindex
C2×#106230652
#130777002
#130669842
#130669662
#130669562
#130669502
C11×#14642
#1740911