Finite Group Databasebeta

← #14763596

Subgroups — #14763596

Order 2816.

1098 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623046C211yesmaximal, characteristic
2#13071234C211yesmaximal, characteristic, complemented
3#13069601C212yesmaximal, complemented
4#13069452C212yesmaximal
5#13069072C214yesmaximal, complemented
6#13068601C214yesmaximal, complemented
7C11×#2313C211yesmaximal, characteristic, complemented
8C22×C11×C4⋊C4C2211yescharacteristic
9C2×#66983C2211yescharacteristic
10C2×#66982C2212yes—
11C2×C4×C22⋊D11C2212yes—
12C2×#66979C2212yes—
13C2×#66977C2211yescharacteristic
14#10623046—24no—
15#10623046—24no—
16C2×#66951C412yescomplemented
17C2×#66949C412yescomplemented
18C2×#66947C412yescomplemented
19C2×#66942C412yescomplemented
20C11×#387—24no—
21C11×#381C2212yes—
22C11×#380C2212yes—
23C4×C11×C22⋊C4C2212yes—
24#10622825C2212yes—
25#10622825C2212yes—
26#10622598—24no—
27C2×#66870C2218yes—
28#10622165C2218yes—
29C23×C4×C11C2311yescharacteristic
30C23×C4×C11C2311yescharacteristic
31C23×C4×C11C2311yescharacteristic
32C22×C22⋊D11C2312yes—
33C22×D44C2×C411yescharacteristic
34C22×C4×D11C2×C412yes—
35C22×Dic22C2×C411yescharacteristic
36C2×C11×C4⋊C4—22no—
37C2×C11×C4⋊C4C2×C412yes—
38C2×C11×C4⋊C4C2×C412yes—
39C2×C11×C4⋊C4D414yes—
40C2×C11×C4⋊C4D414yes—
41C2×C11×C22⋊C4C2314yes—
42C2×C42×C11—22no—
43C2×C22⋊Dic11C2314yes—
44C2×C22⋊Dic11C2312yes—
45#66983—22no—
46#66983—22no—
47#66982—24no—
48#66982—24no—
49C4×C22⋊D11—24no—
50C4×C22⋊D11—24no—
51C2×(C2×D11)⋊C4C2×C412yes—
52C2×(C2×D11)⋊C4C2×C412yes—
53C2×(C2×D11)⋊C4C2×C412yes—
54C2×(C2×D11)⋊C4C2×C412yes—
55#66979—44no—
56C2×C4⋊Dic11—22no—
57C2×C4⋊Dic11—22no—
58C2×C4⋊Dic11—22no—
59C2×C4⋊Dic11C2×C411yescharacteristic
60C2×C4⋊Dic11C2×C411yescharacteristic
61#66977—22no—
62#66977—22no—
63C2×Dic11⋊C4C2×C412yes—
64C2×Dic11⋊C4C2×C412yes—
65C2×Dic11⋊C4C2×C412yes—
66C2×Dic11⋊C4C2×C412yes—
67C2×C4×Dic11—22no—
68C2×C4×Dic11C2×C412yes—
69#66951—28no—
70#66949—28no—
71#66947—28no—
72#66942—28no—
73C11×#95—22no—
74C11×#95—22no—
75C11×#95—24no—
76C11⋊#95—22no—
77C11⋊#95—22no—
78#66870—48no—
79#21877—111nomaximal, Sylow
80C24×C11C2411yescharacteristic
81C23×D11C22×C412yes—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—24no—
85C22×C4×C11—81no—
86C22×C4×C11—81no—
87C22×C4×C11C22×C412yes—
88C22×C4×C11C22×C412yes—
89C22×C4×C11C22×C411yescharacteristic
90C22×C4×C11C22×C411yescharacteristic
91C22×C4×C11C2×D412yes—
92C22×C4×C11C2×D412yes—
93C22×C4×C11C2×D412yes—
94C22×C4×C11C2×D412yes—
95C22×C4×C11C2×D412yes—
96C22×C4×C11C2×D412yes—
97C2×C22⋊D11—22no—
98C2×C22⋊D11—22no—
99C2×C22⋊D11—24no—
100C2×C22⋊D11—24no—
101C22×Dic11—24no—
102C22×Dic11C22×C412yes—
103C22×Dic11C22×C412yes—
104C22×Dic11C22×C412yes—
105C2×D44—22no—
106C2×D44—81no—
107C2×C4×D11—24no—
108C2×C4×D11—82no—
109C2×Dic22—22no—
110C2×Dic22—81no—
111C11×C4⋊C4—82no—
112C11×C4⋊C4C22⋊C418yes—
113C11×C4⋊C4C22⋊C418yes—
114C11×C22⋊C4—24no—
115C11×C22⋊C4—24no—
116C42×C11—82no—
117C22⋊Dic11—22no—
118C22⋊Dic11—22no—
119C22⋊Dic11—28no—
120(C2×D11)⋊C4—24no—
121(C2×D11)⋊C4—24no—
122(C2×D11)⋊C4—24no—
123(C2×D11)⋊C4—24no—
124C4⋊Dic11—22no—
125C4⋊Dic11—22no—
126C4⋊Dic11—44no—
127C4⋊Dic11—82no—
128C4⋊Dic11—82no—
129Dic11⋊C4—24no—
130Dic11⋊C4—24no—
131Dic11⋊C4—24no—
132Dic11⋊C4—24no—
133C4×Dic11—24no—
134C4×Dic11—44no—
135C2×#539—111no—
136#2316—111no—
137#2313D1111yescharacteristic, complemented
138#1996—112no—
139#1964—112no—
140#1899—114no—
141#1799—114no—
142C23×C11—41no—
143C23×C11—41no—
144C23×C11C23×C411yescharacteristic
145C23×C11C22×D411yescharacteristic
146C23×C11C22×D411yescharacteristic
147C23×C11H(5,𝔽2)12yes—
148C23×C112−1+412yes—
149C22×D11—22no—
150C22×D11—24no—
151C22×D11—42no—
152C22×D11—42no—
153C2×C4×C11—24no—
154C2×C4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11—24no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11—42no—
160C2×C4×C11—42no—
161C2×C4×C11—41no—
162C2×C4×C11—42no—
163C2×C4×C11—41no—
164C2×C4×C11—44no—
165C2×C4×C11—44no—
166C2×C4×C11—44no—
167C2×C4×C11C2×C22⋊C414yes—
168C2×C4×C11C2×C22⋊C412yes—
169C2×C4×C11C2×C22⋊C414yes—
170C2×C4×C11C2×C22⋊C412yes—
171C22⋊D11—42no—
172C22⋊D11—42no—
173C22⋊D11—44no—
174C2×Dic11—22no—
175C2×Dic11—22no—
176C2×Dic11—22no—
177C2×Dic11—24no—
178C2×Dic11—42no—
179C2×Dic11—42no—
180C2×Dic11—44no—
181C2×Dic11—44no—
182C2×Dic11—44no—
183D44—82no—
184C4×D11—84no—
185Dic22—82no—
186#539—224no—
187#539—224no—
188C2×#126—112no—
189C2×#125—112no—
190C2×#123—112no—
191C2×#123—112no—
192C2×C22⋊Q8—111no—
193C2×C22⋊Q8—112no—
194C2×#121—111no—
195C2×C4×D4—112no—
196C2×#117—112no—
197C22×C4⋊C4C2×D1111yescharacteristic
198C2×#99—118no—
199#389—224no—
200#387—24no—
201#381C2×D1112yes—
202#380—112no—
203#380—112no—
204#380C2×D1112yes—
205C4×C22⋊C4C2×D1112yes—
206#342—118no—
207C22×C11—21no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—42no—
214C22×C11—42no—
215C22×C11C22×C22⋊C411yescharacteristic
216C22×C11#52012yes—
217C22×C11#53511yescharacteristic
218C22×C11#53611yescharacteristic
219C22×C11#53712yes—
220C2×D11—42no—
221C2×D11—42no—
222C2×D11—42no—
223C2×D11—84no—
224C4×C11—24no—
225C4×C11—22no—
226C4×C11—24no—
227C4×C11—22no—
228C4×C11—84no—
229Dic11—42no—
230Dic11—42no—
231Dic11—42no—
232Dic11—84no—
233C22×Q8—111no—
234C22×D4—112no—
235C22×D4—111no—
236C23×C4—112no—
237C23×C4C22×D1111yescharacteristic
238C23×C4C22×D1111yescharacteristic
239C23×C4C22×D1111yescharacteristic
240#126—228no—
241#125—228no—
242#123—224no—
243#123—224no—
244#123—228no—
245C22⋊Q8—222no—
246C22⋊Q8—222no—
247C22⋊Q8—228no—
248#121—222no—
249#121—222no—
250C4×D4—224no—
251C4×D4—224no—
252#117—444no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—112no—
255C2×C4⋊C4—111no—
256C2×C4⋊C4—112no—
257C2×C4⋊C4—112no—
258C2×C4⋊C4—111no—
259C2×C4⋊C4—112no—
260C2×C4⋊C4—222no—
261C2×C4⋊C4—222no—
262C2×C4⋊C4—222no—
263C2×C4⋊C4C4×D1112yes—
264C2×C4⋊C4C4×D1112yes—
265C2×C4⋊C4D4414yes—
266C2×C4⋊C4C22⋊D1114yes—
267C2×C22⋊C4—112no—
268C2×C22⋊C4—112no—
269C2×C22⋊C4—112no—
270C2×C22⋊C4—112no—
271C2×C22⋊C4—112no—
272C2×C22⋊C4—114no—
273C2×C22⋊C4C22×D1114yes—
274C2×C42—22no—
275C2×C42—112no—
276C2×C42—222no—
277#99—448no—
278#95—22no—
279#95—22no—
280#95—24no—
281#95—222no—
282#95—222no—
283C2×C11—21no—
284C2×C11—22no—
285C2×C11—22no—
286C2×C11—21no—
287C2×C11#231111yescharacteristic
288C2×C11#288311yescharacteristic
289C2×C11#288411yescharacteristic
290D11—82no—
291C24—112no—
292C24C23×D1111yescharacteristic
293C2×Q8—222no—
294C2×Q8—881no—
295C2×D4—222no—
296C2×D4—224no—
297C2×D4—224no—
298C2×D4—222no—
299C2×D4—222no—
300C2×D4—881no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—24no—
304C22×C4—81no—
305C22×C4—81no—
306C22×C4—112no—
307C22×C4—112no—
308C22×C4—112no—
309C22×C4—224no—
310C22×C4—224no—
311C22×C4—882no—
312C22×C4C2×C4×D1112yes—
313C22×C4C2×C4×D1112yes—
314C22×C4C2×C4×D1111yescharacteristic
315C22×C4C2×C4×D1111yescharacteristic
316C22×C4C2×D4412yes—
317C22×C4C2×D4412yes—
318C22×C4C2×D4412yes—
319C22×C4C2×C22⋊D1112yes—
320C22×C4C2×C22⋊D1112yes—
321C22×C4C2×C22⋊D1112yes—
322C4⋊C4—82no—
323C4⋊C4—224no—
324C4⋊C4—222no—
325C4⋊C4—224no—
326C4⋊C4—224no—
327C4⋊C4—222no—
328C4⋊C4—224no—
329C4⋊C4—444no—
330C4⋊C4—882no—
331C4⋊C4—882no—
332C4⋊C4(C2×D11)⋊C418yes—
333C4⋊C4(C2×D11)⋊C418yes—
334C22⋊C4—24no—
335C22⋊C4—24no—
336C22⋊C4—222no—
337C22⋊C4—222no—
338C22⋊C4—224no—
339C22⋊C4—224no—
340C22⋊C4—224no—
341C22⋊C4—224no—
342C22⋊C4—228no—
343C42—82no—
344C42—224no—
345C42—444no—
346C11#2187711yescharacteristic, complemented, Sylow
347C23—41no—
348C23—41no—
349C23—222no—
350C23—224no—
351C23—442no—
352C23—442no—
353C23C22×C4×D1111yescharacteristic
354C23C22×D4411yescharacteristic
355C23#6704212yes—
356C23#6704312yes—
357C23C22×C22⋊D1111yescharacteristic
358Q8—882no—
359D4—442no—
360D4—442no—
361D4—444no—
362D4—882no—
363C2×C4—24no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—24no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—44no—
375C2×C4—44no—
376C2×C4—44no—
377C2×C4—224no—
378C2×C4—222no—
379C2×C4—222no—
380C2×C4—222no—
381C2×C4—442no—
382C2×C4—442no—
383C2×C4—444no—
384C2×C4—444no—
385C2×C4—444no—
386C2×C4—884no—
387C2×C4C2×(C2×D11)⋊C414yes—
388C2×C4C2×(C2×D11)⋊C414yes—
389C2×C4C2×(C2×D11)⋊C412yes—
390C2×C4C2×(C2×D11)⋊C412yes—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—42no—
398C22—42no—
399C22—442no—
400C22—442no—
401C22—442no—
402C22—884no—
403C22#1062305412yes—
404C22#1062305611yescharacteristic
405C22#1062305711yescharacteristic
406C22C22×(C2×D11)⋊C411yescharacteristic
407C22#1062336412yes—
408C4—24no—
409C4—22no—
410C4—22no—
411C4—24no—
412C4—84no—
413C4—442no—
414C4—442no—
415C4—442no—
416C4—884no—
417C2—22no—
418C2—21no—
419C2—22no—
420C2—21no—
421C2—882no—
422C2#1307120411yescharacteristic
423C2#1307707611yescharacteristic
424C2#1307707911yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC11×#2313C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#66983C22
cosocleC24×C11C24
hypercenter#2313D11
hypocenterC11#21877
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4⋊C4 ◁ #2313

Complements

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

NH ≅ G/Ntype
2. #13071234C2semidirect
3. #13069601C2semidirect
5. #13069072C2semidirect
6. #13068601C2semidirect
7. C11×#2313C2semidirect
16. C2×#66951C4semidirect
17. C2×#66949C4semidirect
18. C2×#66947C4semidirect
19. C2×#66942C4semidirect
137. #2313D11semidirect
346. C11#21877semidirect

Maximal subgroups

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

subgroupindex
C2×#106230462
#130712342
#130696012
#130694522
#130690722
#130686012
C11×#23132
#2187711