Finite Group Databasebeta

← #14780942

Subgroups — #14780942

Order 2816.

2018 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67004C212yesmaximal
2C22×#66922C211yesmaximal, characteristic, complemented
3C2×#10622617C212yesmaximal, complemented
4#13069715C214yesmaximal, complemented
5#13069698C214yesmaximal, complemented
6#13068310C211yesmaximal, characteristic, complemented
7C11×#2297C211yesmaximal, characteristic
8C22×C11×#41C2211yescharacteristic
9C23×Dic22C2212yes—
10C2×C11×#117C2211yescharacteristic
11C22×C42×C11C2211yescharacteristic
12C2×#67004—28no—
13C2×#67004—28no—
14C2×#67004—28no—
15C22×#4326C2214yes—
16C22×#4324C2214yes—
17C22×C4⋊Dic11—22no—
18C22×#4318C2212yes—
19C2×#66922—28no—
20C2×#66922—22no—
21C2×#66922C2214yes—
22C11×#391C2212yes—
23C11×#390C2212yes—
24C11×#386—22no—
25C4×C11×C22⋊C4—22no—
26#10622617—28no—
27C2×#66874C2218yes—
28#10622162C2214yes—
29C2×C11×#41—22no—
30C2×C11×#41—24no—
31C2×C11×#41—24no—
32C2×C11×#41D414yes—
33C22×Q8×C11C2311yescharacteristic
34C22×D4×C11—21no—
35C22×D4×C11C2311yescharacteristic
36C23×C4×C11—21no—
37C23×C4×C11D412yes—
38C23×C4×C11C2311yescharacteristic
39C23×Dic11—22no—
40C22×Dic22—24no—
41C22×Dic22—24no—
42C22×Dic22—24no—
43C22×Dic22—24no—
44C22×Dic22—24no—
45C22×Dic22—22no—
46C22×Dic22D418yes—
47C22×Dic22C2314yes—
48C11×#117—24no—
49C2×C11×C4⋊C4C2312yes—
50C2×C11×C22⋊C4—21no—
51C2×C11×C22⋊C4—24no—
52C2×C42×C11—24no—
53C2×C42×C11—21no—
54C2×C42×C11D412yes—
55C2×C42×C11C2312yes—
56#67004—264no—
57C2×#4326—28no—
58C2×#4326—28no—
59C2×#4326—28no—
60C2×#4324—28no—
61C2×#4324—28no—
62C2×#4324—28no—
63C2×C4⋊Dic11—216no—
64C2×C4⋊Dic11—28no—
65C2×#4318—24no—
66C2×#4318—24no—
67C2×#4318D418yes—
68C22×C11⋊C8C2314yes—
69#66922—216no—
70#66922—216no—
71C11×#95—24no—
72#66874—216no—
73#23432—111nomaximal, Sylow
74C24×C11—21no—
75C24×C11C2×D411yescharacteristic
76C11×#41—216no—
77C11×#41—48no—
78C2×Q8×C11—21no—
79C2×Q8×C11—22no—
80C2×Q8×C11—22no—
81C2×Q8×C11C2×D412yes—
82C2×D4×C11—24no—
83C2×D4×C11—22no—
84C2×D4×C11—22no—
85C2×D4×C11—21no—
86C2×D4×C11—42no—
87C2×D4×C11—42no—
88C2×D4×C11C2×D412yes—
89C22×C4×C11—24no—
90C22×C4×C11—28no—
91C22×C4×C11—21no—
92C22×C4×C11—24no—
93C22×C4×C11—22no—
94C22×C4×C11—42no—
95C22×C4×C11—42no—
96C22×C4×C11C2×D414yes—
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2×D414yes—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D414yes—
101C22×C4×C11#4112yes—
102C22×C4×C11C2411yescharacteristic
103C22×Dic11—28no—
104C22×Dic11—24no—
105C22×Dic11—44no—
106C22×Dic11—44no—
107C2×Dic22—216no—
108C2×Dic22—28no—
109C2×Dic22—216no—
110C2×Dic22—24no—
111C2×Dic22—24no—
112C2×Dic22—24no—
113C2×Dic22—24no—
114C2×Dic22—24no—
115C2×Dic22—48no—
116C2×Dic22—48no—
117C2×Dic22—44no—
118C2×Dic22—44no—
119C2×Dic22C2×D418yes—
120C11×C4⋊C4—24no—
121C11×C22⋊C4—42no—
122C11×C22⋊C4—48no—
123C42×C11—24no—
124C42×C11—24no—
125C42×C11—42no—
126#4326—232no—
127#4324—232no—
128C4⋊Dic11—232no—
129#4318—216no—
130C2×C11⋊C8—24no—
131C2×C11⋊C8—24no—
132C2×C11⋊C8C2×D418yes—
133C22×#137—112no—
134C22×C4⋊Q8—111no—
135C2×#419—112no—
136#2297D1111yescharacteristic
137#2016—114no—
138#2013—114no—
139#1728—111no—
140C23×C11—24no—
141C23×C11—22no—
142C23×C11—41no—
143C23×C11—41no—
144C23×C11—44no—
145C23×C11#12012yes—
146C23×C11#12112yes—
147C23×C11#12712yes—
148C23×C11C22×D411yescharacteristic
149Q8×C11—24no—
150Q8×C11—42no—
151D4×C11—24no—
152D4×C11—48no—
153D4×C11—42no—
154C2×C4×C11—216no—
155C2×C4×C11—24no—
156C2×C4×C11—24no—
157C2×C4×C11—22no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—48no—
161C2×C4×C11—42no—
162C2×C4×C11—44no—
163C2×C4×C11#12018yes—
164C2×C4×C11#12012yes—
165C2×C4×C11#12118yes—
166C2×C4×C11#12112yes—
167C2×C4×C11#12712yes—
168C2×C4×C11#13718yescomplemented
169C2×C4×C11C22×D411yescharacteristic
170C2×C4×C11C22×D412yes—
171C2×C4×C11C22×D412yes—
172C2×C4×C11C2×#4111yescharacteristic
173C2×Dic11—28no—
174C2×Dic11—44no—
175C2×Dic11—44no—
176C2×Dic11—416no—
177Dic22—28no—
178Dic22—28no—
179Dic22—44no—
180Dic22—44no—
181Dic22—416no—
182C11⋊C8—28no—
183C22×#41C2×D1111yescharacteristic
184C23×Q8—112no—
185C2×#137—228no—
186C2×#137—228no—
187C2×#137—228no—
188C22×Q16—114no—
189C22×SD16—114no—
190C22×M16—112no—
191C2×C4⋊Q8—114no—
192C2×C4⋊Q8—228no—
193C2×C4⋊Q8—222no—
194C2×#117C2×D1111yescharacteristic
195C22×C4⋊C4—222no—
196C22×C42C2×D1111yescharacteristic
197#419—228no—
198C2×#103—118no—
199#391C2×D1112yes—
200#390C2×D1112yes—
201#386—22no—
202C4×C22⋊C4—22no—
203#336—114no—
204C22×C11—24no—
205C22×C11—24no—
206C22×C11—24no—
207C22×C11—42no—
208C22×C11—44no—
209C22×C11—82no—
210C22×C11—82no—
211C22×C11#39214yes—
212C22×C11C2×#12011yescharacteristic
213C22×C11C2×#12111yescharacteristic
214C22×C11C2×#12711yescharacteristic
215C22×C11C2×#13714yes—
216C4×C11—28no—
217C4×C11—42no—
218C4×C11—82no—
219C4×C11#39214yes—
220C4×C11C2×#12012yes—
221C4×C11C2×#12112yes—
222Dic11—48no—
223C2×#41—22no—
224C2×#41—24no—
225C2×#41—24no—
226C2×#41D4414yes—
227C22×Q8—118no—
228C22×Q8—114no—
229C22×Q8—224no—
230C22×Q8—222no—
231C22×Q8—224no—
232C22×Q8—224no—
233C22×Q8—224no—
234C22×Q8—224no—
235C22×Q8C22×D1111yescharacteristic
236C22×D4—21no—
237C22×D4C22×D1111yescharacteristic
238C23×C4—21no—
239C23×C4—222no—
240C23×C4C22⋊D1112yes—
241C23×C4C22×D1111yescharacteristic
242#137—2264no—
243C2×Q16—228no—
244C2×Q16—228no—
245C2×Q16—228no—
246C2×SD16—228no—
247C2×SD16—228no—
248C2×SD16—228no—
249C2×M16—118no—
250C2×M16—224no—
251C2×M16—224no—
252C22×C8—114no—
253C4⋊Q8—2216no—
254C4⋊Q8—2216no—
255#117—24no—
256C2×C4⋊C4—2216no—
257C2×C4⋊C4—228no—
258C2×C4⋊C4C22×D1112yes—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—24no—
261C2×C42—24no—
262C2×C42—21no—
263C2×C42C22⋊D1112yes—
264C2×C42C22×D1112yes—
265#103—2216no—
266#95—24no—
267C2×C11—24no—
268C2×C11—82no—
269C2×C11C2×#39211yescharacteristic
270C2×C11#300412yes—
271C2×C11#303912yes—
272C2×C11#315212yes—
273C24—21no—
274C24C2×C22⋊D1111yescharacteristic
275#41—216no—
276#41—48no—
277C2×Q8—21no—
278C2×Q8—22no—
279C2×Q8—22no—
280C2×Q8—118no—
281C2×Q8—228no—
282C2×Q8—224no—
283C2×Q8—2216no—
284C2×Q8—2216no—
285C2×Q8—224no—
286C2×Q8—224no—
287C2×Q8—224no—
288C2×Q8—224no—
289C2×Q8—448no—
290C2×Q8—448no—
291C2×Q8—444no—
292C2×Q8—444no—
293C2×Q8C2×D4412yes—
294C2×D4—24no—
295C2×D4—21no—
296C2×D4—22no—
297C2×D4—22no—
298C2×D4—42no—
299C2×D4—42no—
300C2×D4C2×D4412yes—
301C22×C4—24no—
302C22×C4—28no—
303C22×C4—21no—
304C22×C4—24no—
305C22×C4—22no—
306C22×C4—42no—
307C22×C4—42no—
308C22×C4—228no—
309C22×C4—224no—
310C22×C4—444no—
311C22×C4—444no—
312C22×C4C2×D4412yes—
313C22×C4#433912yes—
314C22×C4D4×D1114yes—
315C22×C4D4×D1114yes—
316C22×C4C2×C22⋊D1114yes—
317C22×C4C2×C22⋊D1111yescharacteristic
318C22×C4C23×D1111yescharacteristic
319Q16—2232no—
320SD16—2232no—
321M16—2216no—
322C2×C8—118no—
323C2×C8—224no—
324C2×C8—224no—
325C4⋊C4—24no—
326C4⋊C4—2232no—
327C22⋊C4—42no—
328C22⋊C4—48no—
329C42—24no—
330C42—24no—
331C42—42no—
332C11#2343211yescharacteristic, complemented, Sylow
333C23—24no—
334C23—22no—
335C23—41no—
336C23—41no—
337C23—44no—
338C23#6698312yes—
339C23#6699012yes—
340C23#6699312yes—
341C23C22×C22⋊D1111yescharacteristic
342Q8—24no—
343Q8—42no—
344Q8—228no—
345Q8—228no—
346Q8—444no—
347Q8—444no—
348Q8—4416no—
349D4—24no—
350D4—48no—
351D4—42no—
352C2×C4—216no—
353C2×C4—24no—
354C2×C4—24no—
355C2×C4—22no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—48no—
359C2×C4—42no—
360C2×C4—44no—
361C2×C4—228no—
362C2×C4—444no—
363C2×C4—444no—
364C2×C4—4416no—
365C2×C4#6693518yes—
366C2×C4#6693718yes—
367C2×C4#6698312yes—
368C2×C4#6699012yes—
369C2×C4#6699312yes—
370C2×C4#6700418yescomplemented
371C2×C4C22×D4411yescharacteristic
372C2×C4C2×#433911yescharacteristic
373C2×C4C2×D4×D1112yes—
374C2×C4C2×D4×D1112yes—
375C8—228no—
376C22—24no—
377C22—24no—
378C22—24no—
379C22—44no—
380C22—42no—
381C22—82no—
382C22—82no—
383C22#1062257314yes—
384C22C2×#6698311yescharacteristic
385C22C2×#6699011yescharacteristic
386C22C2×#6699311yescharacteristic
387C22C2×#6700414yes—
388C4—28no—
389C4—42no—
390C4—82no—
391C4—448no—
392C4#1062257314yes—
393C4C2×#6693512yes—
394C4C2×#6693712yes—
395C2—24no—
396C2—82no—
397C2C2×#1062257311yescharacteristic
398C2#1307784912yes—
399C2#1307810312yes—
400C2#1307907612yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2297C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
hypercenter#2297D11
hypocenterC11#23432
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2297

Complements

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

NH ≅ G/Ntype
2. C22×#66922C2semidirect
3. C2×#10622617C2semidirect
4. #13069715C2semidirect
5. #13069698C2semidirect
6. #13068310C2semidirect
168. C2×C4×C11#137semidirect
332. C11#23432semidirect
370. C2×C4#67004semidirect

Maximal subgroups

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

subgroupindex
C22×#670042
C22×#669222
C2×#106226172
#130697152
#130696982
#130683102
C11×#22972
#2343211