Finite Group Databasebeta

← #14719945

Subgroups — #14719945

Order 2816.

912 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623092C211yesmaximal, characteristic
2#13077700C212yesmaximal, complemented
3#13066982C214yesmaximal, complemented
4#13066966C214yesmaximal, complemented
5#13066957C211yesmaximal, characteristic, complemented
6#13066948C212yesmaximal, complemented
7C11×#1466C211yesmaximal, characteristic, complemented
8C2×C4×D4×C11C2211yescharacteristic
9C2×#66991C411yescharacteristic
10C2×#66989C411yescharacteristic
11C2×#66982C412yes—
12C2×#66977C412yes—
13#10623092—24no—
14#10623092—24no—
15C2×#66950C411yescharacteristic
16C2×#66941C411yescharacteristic
17C2×#66938C2212yes—
18C2×#66932C2212yes—
19C2×#66925C2211yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21C11×#432C2212yes—
22#10622539C2212yes—
23#10622441—24no—
24#10622332C2214yes—
25#10622331C2214yes—
26#10622314—24no—
27C11×#323C2214yes—
28#10622163C2214yes—
29#10622107C2214yes—
30#10622106C2214yes—
31C22×D4×C11C2×C411yescharacteristic
32C23×C4×C11C2×C412yes—
33C22×C22⋊D11C2×C412yes—
34C22×C4×D11C2×C411yescharacteristic
35C22×Dic22C2×C412yes—
36C22×Dic22C2×C411yescharacteristic
37C4×D4×C11—22no—
38C4×D4×C11—22no—
39C2×C11×C4⋊C4C2×C411yescharacteristic
40C2×C11×C22⋊C4C2312yes—
41C2×C42×C11C2311yescharacteristic
42C2×C22⋊Dic11C2×C412yes—
43C2×C22⋊Dic11C2×C412yes—
44C2×C22⋊Dic11C2×C412yes—
45#66991—24no—
46#66989—24no—
47#66982—24no—
48#66982—24no—
49C2×(C2×D11)⋊C4C2×C411yescharacteristic
50C2×(C2×D11)⋊C4C2×C412yes—
51C2×(C2×D11)⋊C4C2311yescharacteristic
52C2×C4⋊Dic11C2×C412yes—
53C2×C4⋊Dic11C2×C411yescharacteristic
54#66977—24no—
55#66977—24no—
56C2×Dic11⋊C4C2×C411yescharacteristic
57C2×Dic11⋊C4C2×C412yes—
58C2×Dic11⋊C4C2×C412yes—
59C2×Dic11⋊C4C2311yescharacteristic
60C2×C4×Dic11C2×C411yescharacteristic
61C2×C4×Dic11C2312yes—
62#66950—24no—
63#66941—24no—
64#66938—24no—
65#66938—24no—
66#66932—24no—
67#66932—24no—
68#66925—22no—
69#66925—22no—
70C4×Dic22D414yes—
71C4×Dic22D414yes—
72C11×C4⋊C8—22no—
73C11×C22⋊C8C2314yes—
74C11×#97—22no—
75C22⋊(C11⋊C8)C2314yes—
76#66879—24no—
77Dic11⋊C8—24no—
78Dic11⋊C8—24no—
79C8×Dic11—24no—
80C4⋊(C11⋊C8)—22no—
81#66867—22no—
82#17409—111nomaximal, Sylow
83C24×C11C22×C412yes—
84C23×D11C22×C411yescharacteristic
85C2×D4×C11—22no—
86C2×D4×C11—42no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—82no—
90C22×C4×C11C22×C411yescharacteristic
91C22×C4×C11C22×C412yes—
92C22×C4×C11C22×C411yescharacteristic
93C22×C4×C11C2411yescharacteristic
94C2×C22⋊D11—24no—
95C2×C22⋊D11—82no—
96C22×Dic11C22×C411yescharacteristic
97C22×Dic11C22×C412yes—
98C22×Dic11C22×C411yescharacteristic
99C22×Dic11C22×C411yescharacteristic
100C22×Dic11C22×C412yes—
101C2×C4×D11—22no—
102C2×C4×D11—42no—
103C2×Dic22—24no—
104C2×Dic22—42no—
105C2×Dic22—82no—
106C2×Dic22C22⋊C414yes—
107C2×C8×C11—24no—
108C11×C4⋊C4—22no—
109C11×C22⋊C4—22no—
110C11×C22⋊C4—22no—
111C42×C11C2×D412yes—
112C42×C11C2×D412yes—
113C22⋊Dic11—24no—
114C22⋊Dic11—24no—
115C22⋊Dic11—24no—
116(C2×D11)⋊C4—24no—
117(C2×D11)⋊C4—21no—
118(C2×D11)⋊C4—21no—
119(C2×D11)⋊C4—22no—
120C4⋊Dic11—24no—
121C4⋊Dic11C22⋊C414yes—
122Dic11⋊C4—24no—
123Dic11⋊C4—21no—
124Dic11⋊C4—21no—
125Dic11⋊C4—22no—
126Dic11⋊C4C22⋊C414yes—
127Dic11⋊C4C22⋊C414yes—
128C4×Dic11—22no—
129C4×Dic11C2×D414yes—
130C4×Dic11C2×D414yes—
131C2×C11⋊C8—24no—
132C2×#542—111no—
133#2983—112no—
134#1473—114no—
135#1469—114no—
136#1466—111no—
137#1466D1111yescharacteristic, complemented
138#1464—112no—
139C23×C11—22no—
140C23×C11—24no—
141C23×C11—42no—
142C23×C11—42no—
143C23×C11C23×C411yescharacteristic
144C22×D11—21no—
145C22×D11—22no—
146C22×D11—41no—
147C22×D11—41no—
148D4×C11—44no—
149C2×C4×C11—22no—
150C2×C4×C11—22no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—42no—
154C2×C4×C11—82no—
155C2×C4×C11—82no—
156C2×C4×C11C2×C22⋊C412yes—
157C2×C4×C11C2×C22⋊C411yescharacteristic
158C2×C4×C11C2×C22⋊C411yescharacteristic
159C2×C4×C11C22×D412yes—
160C22⋊D11—84no—
161C2×Dic11—24no—
162C2×Dic11—21no—
163C2×Dic11—21no—
164C2×Dic11—21no—
165C2×Dic11—22no—
166C2×Dic11—42no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11C2×C22⋊C414yes—
170C2×Dic11C2×C22⋊C414yes—
171C4×D11—44no—
172Dic22—44no—
173Dic22—84no—
174C8×C11—44no—
175C11⋊C8—44no—
176#542—224no—
177#542—224no—
178C2×C4⋊Q8—111no—
179C2×#126—112no—
180C2×#124—111no—
181C2×#124—112no—
182C2×#123—112no—
183C2×C22⋊Q8—112no—
184C2×C22⋊Q8—111no—
185C2×#121—111no—
186C2×C4×Q8—111no—
187C2×C4×D4C2×D1111yescharacteristic
188C2×#117—111no—
189#446—224no—
190#446—224no—
191#432—112no—
192#432—114no—
193#432C2×D1112yes—
194#431—114no—
195#324—114no—
196#323—114no—
197#323—114no—
198#323C2×D1114yes—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11—42no—
202C22×C11—42no—
203C22×C11—42no—
204C22×C11—84no—
205C22×C11C22×C22⋊C411yescharacteristic
206C22×C11#56812yes—
207C2×D11—41no—
208C2×D11—41no—
209C2×D11—41no—
210C2×D11—82no—
211C4×C11—22no—
212C4×C11—22no—
213C4×C11—21no—
214C4×C11—21no—
215C4×C11—42no—
216Dic11—24no—
217Dic11—24no—
218Dic11—41no—
219Dic11—41no—
220Dic11—41no—
221C22×Q8—111no—
222C22×Q8—112no—
223C22×D4—112no—
224C22×D4C4×D1111yescharacteristic
225C23×C4—111no—
226C23×C4C4×D1112yes—
227C4⋊Q8—224no—
228#126—224no—
229#126—224no—
230#124—224no—
231#124—224no—
232#124—224no—
233#123—224no—
234#123—224no—
235C22⋊Q8—224no—
236C22⋊Q8—224no—
237C22⋊Q8—224no—
238#121—224no—
239C4×Q8—114no—
240C4×Q8—114no—
241C4×D4—22no—
242C4×D4—22no—
243#117—222no—
244#117—222no—
245C2×C4⋊C4—111no—
246C2×C4⋊C4—112no—
247C2×C4⋊C4—111no—
248C2×C4⋊C4—112no—
249C2×C4⋊C4—112no—
250C2×C4⋊C4—111no—
251C2×C4⋊C4C4×D1111yescharacteristic
252C2×C22⋊C4—112no—
253C2×C22⋊C4—112no—
254C2×C22⋊C4—112no—
255C2×C22⋊C4—111no—
256C2×C22⋊C4—112no—
257C2×C22⋊C4—111no—
258C2×C22⋊C4C22×D1112yes—
259C2×C42—112no—
260C2×C42—111no—
261C2×C42C22×D1111yescharacteristic
262C4⋊C8—22no—
263C4⋊C8—224no—
264C4⋊C8—224no—
265C4⋊C8—222no—
266C22⋊C8—114no—
267C22⋊C8C22×D1114yes—
268#97—22no—
269#97—224no—
270#97—222no—
271C4×C8—224no—
272C2×C11—22no—
273C2×C11—82no—
274C2×C11#287911yescharacteristic
275C2×C11#288411yescharacteristic
276C2×C11#288811yescharacteristic
277D11—81no—
278C24—111no—
279C24C2×C4×D1112yes—
280C2×Q8—114no—
281C2×Q8—224no—
282C2×Q8—442no—
283C2×Q8—882no—
284C2×D4—22no—
285C2×D4—42no—
286C2×D4—224no—
287C2×D4—882no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—82no—
291C22×C4—112no—
292C22×C4—112no—
293C22×C4—111no—
294C22×C4—111no—
295C22×C4—111no—
296C22×C4—222no—
297C22×C4—442no—
298C22×C4C2×C4×D1111yescharacteristic
299C22×C4C2×C4×D1112yes—
300C22×C4C2×C4×D1111yescharacteristic
301C22×C4C23×D1111yescharacteristic
302C2×C8—24no—
303C2×C8—224no—
304C4⋊C4—22no—
305C4⋊C4—114no—
306C4⋊C4—114no—
307C4⋊C4—114no—
308C4⋊C4—224no—
309C4⋊C4—224no—
310C4⋊C4—221no—
311C4⋊C4—221no—
312C4⋊C4—222no—
313C22⋊C4—22no—
314C22⋊C4—22no—
315C22⋊C4—224no—
316C22⋊C4—224no—
317C22⋊C4—224no—
318C22⋊C4—224no—
319C22⋊C4—221no—
320C22⋊C4—221no—
321C22⋊C4—222no—
322C42—114no—
323C42—114no—
324C42—222no—
325C42D4×D1112yes—
326C42D4×D1112yes—
327C11#1740911yescharacteristic, complemented, Sylow
328C23—22no—
329C23—24no—
330C23—42no—
331C23—42no—
332C23—221no—
333C23—222no—
334C23—441no—
335C23—441no—
336C23C22×C4×D1111yescharacteristic
337Q8—444no—
338Q8—884no—
339D4—44no—
340D4—884no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—82no—
347C2×C4—82no—
348C2×C4—114no—
349C2×C4—114no—
350C2×C4—224no—
351C2×C4—221no—
352C2×C4—221no—
353C2×C4—221no—
354C2×C4—222no—
355C2×C4—444no—
356C2×C4—442no—
357C2×C4—441no—
358C2×C4—441no—
359C2×C4C22⋊C4×D1112yes—
360C2×C4C22⋊C4×D1111yescharacteristic
361C2×C4C22⋊C4×D1111yescharacteristic
362C2×C4C2×D4×D1112yes—
363C8—44no—
364C8—444no—
365C22—21no—
366C22—21no—
367C22—42no—
368C22—42no—
369C22—42no—
370C22—84no—
371C22—441no—
372C22—441no—
373C22—441no—
374C22—882no—
375C22C2×C22⋊C4×D1111yescharacteristic
376C22#1062327612yes—
377C4—22no—
378C4—22no—
379C4—21no—
380C4—21no—
381C4—42no—
382C4—224no—
383C4—224no—
384C4—441no—
385C4—441no—
386C4—441no—
387C2—22no—
388C2—82no—
389C2—881no—
390C2#1307705911yescharacteristic
391C2#1307707811yescharacteristic
392C2#1307709211yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1466C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#66991C4
cosocleC22×C4×C11C24
hypercenter#1466D11
hypocenterC11#17409
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1466

Complements

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

NH ≅ G/Ntype
2. #13077700C2semidirect
3. #13066982C2semidirect
4. #13066966C2semidirect
5. #13066957C2semidirect
6. #13066948C2semidirect
7. C11×#1466C2semidirect
137. #1466D11semidirect
327. C11#17409semidirect

Maximal subgroups

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

subgroupindex
C2×#106230922
#130777002
#130669822
#130669662
#130669572
#130669482
C11×#14662
#1740911