Finite Group Databasebeta

← #14790055

Subgroups — #14790055

Order 2816.

930 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078417C212yesmaximal
2#13071332C211yesmaximal, characteristic
3#13069963C212yesmaximal
4#13069774C212yesmaximal
5#13069598C212yesmaximal
6#13069009C212yesmaximal
7#13068831C212yesmaximal
8#13068612C211yesmaximal, characteristic
9C11×#3502C211yesmaximal, characteristic
10Q82×C11—22no—
11C11×#557—22no—
12C11×#557—24no—
13C11×#544—22no—
14C11×#544C2212yes—
15C11×#533—22no—
16C11×#533C2212yes—
17C11×#519C2212yes—
18C2×C4×Q8×C11C2211yescharacteristic
19C2×#66997C2211yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21#10622843C2211yescharacteristic
22C2×#66900C2212yes—
23#10622707—22no—
24#10622704—22no—
25#10622676—24no—
26#10622617C2214yes—
27#10622608C2214yes—
28#10622591—22no—
29#10622590C2211yescharacteristic
30#10622587C2211yescharacteristic
31#10622546—22no—
32#10622545C2211yescharacteristic
33#10622537C2212yes—
34#10622170C2214yes—
35#10622170C2214yes—
36#10622168C2212yes—
37C22×Q8×C11C2311yescharacteristic
38C22×Dic22C2311yescharacteristic
39C11×C4⋊Q8—22no—
40C11×C4⋊Q8—22no—
41C11×C4⋊Q8—28no—
42C11×C4⋊Q8—24no—
43C11×C4⋊Q8D412yes—
44C11×C4⋊Q8D412yes—
45C11×#125—24no—
46C11×#125—28no—
47C11×#125—24no—
48C11×#125D414yes—
49C11×C22⋊Q8—22no—
50C11×C22⋊Q8—24no—
51C11×C22⋊Q8—22no—
52C4×Q8×C11—24no—
53C4×Q8×C11—24no—
54C4×Q8×C11—24no—
55C4×Q8×C11—24no—
56C4×Q8×C11—22no—
57C4×Q8×C11—22no—
58C4×Q8×C11—22no—
59C4×Q8×C11—22no—
60C11×#117—24no—
61C11×#117C2314yes—
62C2×C11×C4⋊C4D412yes—
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C42×C11D412yes—
65C2×C42×C11C2311yescharacteristic
66#66997—22no—
67#66997Q814yescomplemented
68C2×C4⋊Dic11C2311yescharacteristic
69C2×Dic11⋊C4—22no—
70C2×Dic11⋊C4—21no—
71C2×C4×Dic11—21no—
72C2×C4×Dic11C2311yescharacteristic
73C2×C4×Dic11C2311yescharacteristic
74C2×#4318C2314yes—
75C4×Dic22—22no—
76C4×Dic22—22no—
77#66900—24no—
78C11⋊#95—21no—
79C11⋊#95—21no—
80C11⋊#95—22no—
81C11⋊#95—22no—
82C11⋊#95—22no—
83#66874—24no—
84#66874—24no—
85#66872—24no—
86#66871—24no—
87C4⋊(C11⋊C8)—22no—
88C4⋊(C11⋊C8)—22no—
89#24319—111nomaximal, Sylow
90C2×Q8×C11—24no—
91C2×Q8×C11—22no—
92C2×Q8×C11—22no—
93C2×Q8×C11—22no—
94C2×Q8×C11—22no—
95C2×Q8×C11C2×Q812yes—
96C2×Q8×C11#4112yes—
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2×D412yes—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2411yescharacteristic
102C22×Dic11—21no—
103C22×Dic11—21no—
104C22×Dic11—21no—
105C22×Dic11—21no—
106C2×Dic22—22no—
107C2×Dic22—21no—
108C2×Dic22—22no—
109C2×Dic22C2×Q812yes—
110C11×C4⋊C4—24no—
111C11×C4⋊C4—24no—
112C11×C4⋊C4—24no—
113C11×C4⋊C4—28no—
114C11×C4⋊C4—24no—
115C11×C4⋊C4—24no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—24no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4C2×D414yes—
121C11×C4⋊C4C2×D414yes—
122C11×C22⋊C4—24no—
123C42×C11—28no—
124C42×C11—22no—
125C42×C11—22no—
126C42×C11—24no—
127C42×C11C2×D412yes—
128C42×C11C2×D412yes—
129C4⋊Dic11—22no—
130Dic11⋊C4—28no—
131Dic11⋊C4—41no—
132Dic11⋊C4—41no—
133C4×Dic11—21no—
134C4×Dic11—22no—
135C4×Dic11—42no—
136C4×Dic11C2×Q812yes—
137#4318—24no—
138#4318—24no—
139C2×C11⋊C8—24no—
140#3502D1111yescharacteristic
141#3078—112no—
142#2327—111no—
143#2061—112no—
144#2028—112no—
145#1995—112no—
146#1886—112no—
147#1857—112no—
148#1801—111no—
149C23×C11C22×D411yescharacteristic
150Q8×C11—24no—
151Q8×C11—24no—
152Q8×C11—44no—
153Q8×C11—82no—
154Q8×C11—84no—
155C2×C4×C11—22no—
156C2×C4×C11—22no—
157C2×C4×C11—24no—
158C2×C4×C11—24no—
159C2×C4×C11—22no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—42no—
163C2×C4×C11#12012yes—
164C2×C4×C11#12011yescharacteristic
165C2×C4×C11#12011yescharacteristic
166C2×C4×C11C22⋊Q814yes—
167C2×C4×C11C22×D412yes—
168C2×C4×C11C22×Q811yescharacteristic
169C2×C4×C11C2×#4111yescharacteristic
170C2×C4×C112−1+412yes—
171C2×Dic11—22no—
172C2×Dic11—22no—
173C2×Dic11—41no—
174C2×Dic11—41no—
175C2×Dic11—41no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—42no—
180C2×Dic11—41no—
181C2×Dic11—41no—
182Dic22—24no—
183Dic22—42no—
184C11⋊C8—44no—
185Q82—22no—
186#557—22no—
187#557—24no—
188#544—22no—
189#544C2×D1112yes—
190#533—22no—
191#533C2×D1112yes—
192C2×C4⋊Q8—111no—
193#519C2×D1112yes—
194C2×C4×Q8—111no—
195C2×C4×Q8C2×D1111yescharacteristic
196#479—224no—
197#477—222no—
198#475—222no—
199#428—114no—
200#423—112no—
201#419—114no—
202C2×#101—112no—
203#391—111no—
204#391—111no—
205#387—222no—
206#387—222no—
207#382—111no—
208#376—111no—
209#343—112no—
210#339—114no—
211#339—114no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11C2×#12011yescharacteristic
215C22×C11C2×C22⋊Q811yescharacteristic
216C22×C11#53611yescharacteristic
217C4×C11—24no—
218C4×C11—21no—
219C4×C11—21no—
220C4×C11—22no—
221C4×C11—44no—
222C4×C11—42no—
223C4×C11—44no—
224C4×C11#54812yes—
225C4×C11D4×Q812yes—
226Dic11—42no—
227Dic11—42no—
228Dic11—81no—
229Dic11—81no—
230C22×Q8—111no—
231C22×Q8C22×D1111yescharacteristic
232C2×M16—114no—
233C4⋊Q8—22no—
234C4⋊Q8—22no—
235C4⋊Q8—28no—
236C4⋊Q8—24no—
237C4⋊Q8—114no—
238C4⋊Q8—222no—
239C4⋊Q8C22⋊D1112yes—
240C4⋊Q8C22⋊D1112yes—
241#125—24no—
242#125—28no—
243#125—24no—
244#125C22⋊D1114yes—
245C22⋊Q8—22no—
246C22⋊Q8—24no—
247C22⋊Q8—22no—
248C4×Q8—24no—
249C4×Q8—24no—
250C4×Q8—24no—
251C4×Q8—24no—
252C4×Q8—22no—
253C4×Q8—22no—
254C4×Q8—22no—
255C4×Q8—22no—
256C4×Q8—222no—
257C4×Q8—222no—
258#117—24no—
259#117C22×D1114yes—
260C2×C4⋊C4—111no—
261C2×C4⋊C4—222no—
262C2×C4⋊C4—221no—
263C2×C4⋊C4C22⋊D1112yes—
264C2×C4⋊C4C22×D1111yescharacteristic
265C2×C42—111no—
266C2×C42—111no—
267C2×C42—221no—
268C2×C42C22⋊D1112yes—
269C2×C42C22×D1111yescharacteristic
270#107—224no—
271#106—224no—
272C4⋊C8—222no—
273C4⋊C8—222no—
274#103—224no—
275#103—224no—
276#101—224no—
277#95—221no—
278#95—221no—
279#95—222no—
280#95—222no—
281#95—222no—
282C2×C11—21no—
283C2×C11—21no—
284C2×C11#240911yescharacteristic
285C2×C11#302011yescharacteristic
286C2×C11#302211yescharacteristic
287C2×Q8—24no—
288C2×Q8—22no—
289C2×Q8—22no—
290C2×Q8—22no—
291C2×Q8—22no—
292C2×Q8—112no—
293C2×Q8—221no—
294C2×Q8—222no—
295C2×Q8—222no—
296C2×Q8Q8×D1112yes—
297C2×Q8#434312yes—
298C22×C4—221no—
299C22×C4—221no—
300C22×C4—221no—
301C22×C4—221no—
302C22×C4C2×C22⋊D1112yes—
303C22×C4C2×C22⋊D1112yes—
304C22×C4C2×C22⋊D1111yescharacteristic
305C22×C4C2×C22⋊D1111yescharacteristic
306C22×C4C23×D1111yescharacteristic
307M16—224no—
308M16—224no—
309C2×C8—224no—
310C4⋊C4—24no—
311C4⋊C4—24no—
312C4⋊C4—24no—
313C4⋊C4—28no—
314C4⋊C4—24no—
315C4⋊C4—24no—
316C4⋊C4—22no—
317C4⋊C4—22no—
318C4⋊C4—24no—
319C4⋊C4—22no—
320C4⋊C4—228no—
321C4⋊C4—222no—
322C4⋊C4—441no—
323C4⋊C4—441no—
324C4⋊C4C2×C22⋊D1114yes—
325C4⋊C4C2×C22⋊D1114yes—
326C22⋊C4—24no—
327C42—28no—
328C42—22no—
329C42—22no—
330C42—24no—
331C42—112no—
332C42—221no—
333C42—222no—
334C42—442no—
335C42C2×C22⋊D1112yes—
336C42C2×C22⋊D1112yes—
337C11#2431911yescharacteristic, complemented, Sylow
338C23C22×C22⋊D1111yescharacteristic
339Q8—24no—
340Q8—24no—
341Q8—44no—
342Q8—82no—
343Q8—84no—
344Q8—224no—
345Q8—442no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—24no—
349C2×C4—24no—
350C2×C4—22no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—222no—
355C2×C4—222no—
356C2×C4—441no—
357C2×C4—441no—
358C2×C4—441no—
359C2×C4—441no—
360C2×C4—441no—
361C2×C4—441no—
362C2×C4—442no—
363C2×C4—441no—
364C2×C4—441no—
365C2×C4#6699914yes—
366C2×C4#6700611yescharacteristic
367C2×C4#6700611yescharacteristic
368C2×C4#6700612yes—
369C2×C4C2×Q8×D1111yescharacteristic
370C2×C4C2×#434311yescharacteristic
371C2×C4#6704012yes—
372C2×C4C22×C22⋊D1112yes—
373C8—444no—
374C22—21no—
375C22—21no—
376C22C2×#6699911yescharacteristic
377C22#1062334711yescharacteristic
378C22C2×#6700611yescharacteristic
379C4—24no—
380C4—21no—
381C4—21no—
382C4—22no—
383C4—44no—
384C4—42no—
385C4—44no—
386C4—442no—
387C4—442no—
388C4—881no—
389C4—881no—
390C4Q8×C22⋊D1112yes—
391C4#1062334812yes—
392C2—21no—
393C2—21no—
394C2#1307197511yescharacteristic
395C2#1307798011yescharacteristic
396C2#1307799511yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3502C2
socleC22×C11C2×#120
prime radicalC23×C11C22×D4
hypercenter#3502D11
hypocenterC11#24319
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3502

Complements

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

NH ≅ G/Ntype
67. #66997Q8semidirect
337. C11#24319semidirect

Maximal subgroups

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

subgroupindex
#130784172
#130713322
#130699632
#130697742
#130695982
#130690092
#130688312
#130686122
C11×#35022
#2431911