Finite Group Databasebeta

← #14790061

Subgroups — #14790061

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#13082426C211yesmaximal, characteristic
2#13078421C212yesmaximal
3#13069966C212yesmaximal
4#13069777C212yesmaximal
5#13069597C212yesmaximal
6#13069010C212yesmaximal
7#13068830C212yesmaximal
8#13068612C211yesmaximal, characteristic
9C11×#2327C211yesmaximal, characteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C4×Q8×C11C2211yescharacteristic
12C2×C4×Q8×C11C2211yescharacteristic
13#10623343C2212yes—
14#10623101—22no—
15#10623100—24no—
16Q8×Dic22—22no—
17#10623031—22no—
18#10623031C2212yes—
19#10623001—22no—
20#10623001C2212yes—
21C11×#391C2211yescharacteristic
22C11×#391C2211yescharacteristic
23C11×#387—22no—
24C11×#387—22no—
25C11×#382C2211yescharacteristic
26C11×#376C2211yescharacteristic
27C2×#66900C2212yes—
28#10622838C2214yes—
29#10622635—24no—
30#10622634—22no—
31#10622633—22no—
32#10622577C2214yes—
33#10622537C2212yes—
34#10622168C2212yes—
35#10622161C2214yes—
36#10622161C2214yes—
37C22×Q8×C11C2311yescharacteristic
38C22×Q8×C11C2311yescharacteristic
39C11×C4⋊Q8—22no—
40C11×C4⋊Q8Q814yescomplemented
41C4×Q8×C11—22no—
42C4×Q8×C11—22no—
43C4×Q8×C11—22no—
44C4×Q8×C11—22no—
45C2×C11×C4⋊C4—22no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4D412yes—
48C2×C11×C4⋊C4C2311yescharacteristic
49C2×C11×C4⋊C4C2311yescharacteristic
50C2×C42×C11—21no—
51C2×C42×C11D412yes—
52C2×C42×C11C2311yescharacteristic
53C2×C42×C11C2311yescharacteristic
54C2×C42×C11C2311yescharacteristic
55Q8×Dic11—24no—
56Q8×Dic11—24no—
57#66979—24no—
58#66979C2314yes—
59#66977—22no—
60#66977—24no—
61#66977—22no—
62C2×#4318C2314yes—
63#66943—28no—
64#66943—24no—
65#66941—28no—
66#66941—24no—
67#66923—24no—
68#66923D414yes—
69#66922—22no—
70#66922—22no—
71#66922D412yes—
72#66922D412yes—
73C4×Dic22—24no—
74C4×Dic22—24no—
75C4×Dic22—22no—
76C4×Dic22—22no—
77C11×#95—21no—
78C11×#95—21no—
79C11×#95—22no—
80C11×#95—22no—
81C11×#95—22no—
82#66900—24no—
83#66899—24no—
84#66899—24no—
85#66872—24no—
86#66871—24no—
87C4⋊(C11⋊C8)—22no—
88C4⋊(C11⋊C8)—22no—
89#24319—111nomaximal, Sylow
90C2×Q8×C11—22no—
91C2×Q8×C11—21no—
92C2×Q8×C11—22no—
93C2×Q8×C11—22no—
94C2×Q8×C11—22no—
95C2×Q8×C11C2×Q812yes—
96C2×Q8×C11C2×Q812yes—
97C2×Q8×C11#4112yes—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11C2×D412yes—
103C22×C4×C11C2×D412yes—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2411yescharacteristic
107C2×Dic22—24no—
108C2×Dic22—22no—
109C2×Dic22—22no—
110C11×C4⋊C4—24no—
111C11×C4⋊C4—28no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C42×C11—22no—
117C42×C11—22no—
118C42×C11—21no—
119C42×C11—22no—
120C42×C11—42no—
121C42×C11C2×D412yes—
122C42×C11C2×D412yes—
123C42×C11C2×Q812yes—
124C22⋊Dic11—24no—
125C4⋊Dic11—24no—
126C4⋊Dic11—24no—
127C4⋊Dic11—24no—
128C4⋊Dic11—22no—
129C4⋊Dic11—22no—
130C4⋊Dic11C2×D414yes—
131C4⋊Dic11C2×D414yes—
132Dic11⋊C4—28no—
133Dic11⋊C4—24no—
134Dic11⋊C4—24no—
135C4×Dic11—28no—
136C4×Dic11—24no—
137#4318—24no—
138#4318—24no—
139C2×C11⋊C8—24no—
140#3502—111no—
141#3078—112no—
142#2327D1111yescharacteristic
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—24no—
153Q8×C11—42no—
154C2×C4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—42no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—42no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11#12011yescharacteristic
172C2×C4×C11#12012yes—
173C2×C4×C11#12011yescharacteristic
174C2×C4×C11C22⋊Q814yes—
175C2×C4×C11C22×D412yes—
176C2×C4×C11C22×Q811yescharacteristic
177C2×C4×C11C2×#4111yescharacteristic
178C2×C4×C112−1+412yes—
179C2×Dic11—24no—
180C2×Dic11—24no—
181Dic22—44no—
182Dic22—82no—
183Dic22—84no—
184C11⋊C8—44no—
185Q82—222no—
186#557—224no—
187#557—222no—
188#544—112no—
189#544—222no—
190#533—112no—
191#533—222no—
192C2×C4⋊Q8C2×D1111yescharacteristic
193#519—112no—
194C2×C4×Q8C2×D1111yescharacteristic
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#391C2×D1111yescharacteristic
204#391C2×D1111yescharacteristic
205#387—22no—
206#387—22no—
207#382C2×D1111yescharacteristic
208#376C2×D1111yescharacteristic
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—42no—
222C4×C11—42no—
223C4×C11—42no—
224C4×C11—81no—
225C4×C11—81no—
226C4×C11#54812yes—
227C4×C11D4×Q812yes—
228Dic11—44no—
229Dic11—44no—
230C22×Q8C22×D1111yescharacteristic
231C22×Q8C22×D1111yescharacteristic
232C2×M16—114no—
233C4⋊Q8—22no—
234C4⋊Q8—112no—
235C4⋊Q8—112no—
236C4⋊Q8—222no—
237C4⋊Q8—222no—
238C4⋊Q8—224no—
239C4⋊Q8—228no—
240C4⋊Q8Dic2214yescomplemented
241#125—114no—
242#125—224no—
243#125—224no—
244#125—228no—
245C22⋊Q8—222no—
246C22⋊Q8—222no—
247C22⋊Q8—224no—
248C4×Q8—22no—
249C4×Q8—22no—
250C4×Q8—22no—
251C4×Q8—22no—
252C4×Q8—224no—
253C4×Q8—224no—
254C4×Q8—224no—
255C4×Q8—224no—
256C4×Q8—222no—
257C4×Q8—222no—
258#117—114no—
259#117—224no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4C22⋊D1112yes—
263C2×C4⋊C4C22×D1111yescharacteristic
264C2×C4⋊C4C22×D1111yescharacteristic
265C2×C42—21no—
266C2×C42C22⋊D1112yes—
267C2×C42C22×D1111yescharacteristic
268C2×C42C22×D1111yescharacteristic
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—21no—
278#95—21no—
279#95—22no—
280#95—22no—
281#95—22no—
282C2×C11—21no—
283C2×C11—21no—
284C2×C11#240911yescharacteristic
285C2×C11#302011yescharacteristic
286C2×C11#302211yescharacteristic
287C2×Q8—21no—
288C2×Q8—22no—
289C2×Q8—22no—
290C2×Q8—22no—
291C2×Q8—22no—
292C2×Q8—224no—
293C2×Q8—222no—
294C2×Q8—222no—
295C2×Q8C2×Dic2212yes—
296C2×Q8C2×Dic2212yes—
297C2×Q8#433912yes—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
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—28no—
311C4⋊C4—24no—
312C4⋊C4—22no—
313C4⋊C4—22no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—114no—
317C4⋊C4—114no—
318C4⋊C4—224no—
319C4⋊C4—224no—
320C4⋊C4—224no—
321C4⋊C4—228no—
322C4⋊C4—224no—
323C4⋊C4—222no—
324C4⋊C4—224no—
325C4⋊C4—222no—
326C22⋊C4—224no—
327C42—22no—
328C42—22no—
329C42—21no—
330C42—22no—
331C42—42no—
332C42—228no—
333C42—224no—
334C42C2×Dic2212yes—
335C42D4×D1112yes—
336C42D4×D1112yes—
337C11#2431911yescharacteristic, complemented, Sylow
338C23C22×C22⋊D1111yescharacteristic
339Q8—24no—
340Q8—24no—
341Q8—24no—
342Q8—42no—
343Q8—444no—
344Q8—882no—
345Q8—884no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—42no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—224no—
364C2×C4—224no—
365C2×C4#6697714yes—
366C2×C4#6699011yescharacteristic
367C2×C4#6699011yescharacteristic
368C2×C4#6699012yes—
369C2×C4C22×Dic2211yescharacteristic
370C2×C4C2×#433911yescharacteristic
371C2×C4C2×D4×D1112yes—
372C2×C4#6704312yes—
373C8—444no—
374C22—21no—
375C22—21no—
376C22C2×#6697711yescharacteristic
377C22C2×#6699011yescharacteristic
378C22#1062335611yescharacteristic
379C4—24no—
380C4—21no—
381C4—21no—
382C4—22no—
383C4—42no—
384C4—42no—
385C4—42no—
386C4—81no—
387C4—81no—
388C4—444no—
389C4—444no—
390C4D4×Dic2212yes—
391C4#1062308312yes—
392C2—21no—
393C2—21no—
394C2#1307198111yescharacteristic
395C2#1307797911yescharacteristic
396C2#1307799411yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2327C2
socleC22×C11C2×#120
prime radicalC23×C11C22×D4
hypercenter#2327D11
hypocenterC11#24319
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2327

Complements

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

NH ≅ G/Ntype
40. C11×C4⋊Q8Q8semidirect
240. C4⋊Q8Dic22semidirect
337. C11#24319semidirect

Maximal subgroups

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

subgroupindex
#130824262
#130784212
#130699662
#130697772
#130695972
#130690102
#130688302
#130686122
C11×#23272
#2431911