Finite Group Databasebeta

← #14790037

Subgroups — #14790037

Order 2816.

978 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078409C212yesmaximal
2#13071323C211yesmaximal, characteristic
3#13069958C212yesmaximal, complemented
4#13069769C212yesmaximal
5#13069598C212yesmaximal, complemented
6#13069019C212yesmaximal
7#13068831C212yesmaximal, complemented
8#13068612C211yesmaximal, characteristic, complemented
9C11×#3502C211yesmaximal, characteristic, complemented
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×#67000C2211yescharacteristic
20C2×C4×D44C2211yescharacteristic
21#10622843C2211yescharacteristic
22C2×#66900C2212yes—
23#10622700—22no—
24#10622697—22no—
25#10622679—24no—
26#10622614C2214yes—
27#10622608C2214yes—
28#10622602—22no—
29#10622601C2211yescharacteristic
30#10622589C2211yescharacteristic
31#10622553—22no—
32#10622545C2211yescharacteristic
33#10622537C2212yes—
34#10622170C2214yes—
35#10622170C2214yes—
36#10622168C2212yes—
37C22×Q8×C11C2311yescharacteristic
38C22×D44C2311yescharacteristic
39C22×C4×D11—21no—
40C11×C4⋊Q8—22no—
41C11×C4⋊Q8—22no—
42C11×C4⋊Q8—28no—
43C11×C4⋊Q8—24no—
44C11×C4⋊Q8D412yes—
45C11×C4⋊Q8D412yes—
46C11×#125—24no—
47C11×#125—28no—
48C11×#125—24no—
49C11×#125D414yes—
50C11×C22⋊Q8—22no—
51C11×C22⋊Q8—24no—
52C11×C22⋊Q8—22no—
53C4×Q8×C11—24no—
54C4×Q8×C11—24no—
55C4×Q8×C11—24no—
56C4×Q8×C11—24no—
57C4×Q8×C11—22no—
58C4×Q8×C11—22no—
59C4×Q8×C11—22no—
60C4×Q8×C11—22no—
61C11×#117—24no—
62C11×#117C2314yes—
63C2×C11×C4⋊C4D412yes—
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C42×C11D412yes—
66C2×C42×C11C2311yescharacteristic
67#67000—22no—
68#67000Q814yescomplemented
69C2×(C2×D11)⋊C4—22no—
70C2×(C2×D11)⋊C4—21no—
71C2×(C2×D11)⋊C4—22no—
72C2×C4⋊Dic11C2311yescharacteristic
73C2×Dic11⋊C4—22no—
74C2×C4×Dic11C2311yescharacteristic
75C2×C4×Dic11C2311yescharacteristic
76C2×#4318C2314yes—
77C4×D44—22no—
78C4×D44—22no—
79#66900—24no—
80C11⋊#95—21no—
81C11⋊#95—21no—
82C11⋊#95—22no—
83#66873—24no—
84#66873—24no—
85#66872—24no—
86#66871—24no—
87C4⋊(C11⋊C8)—22no—
88C4⋊(C11⋊C8)—22no—
89#24317—111nomaximal, Sylow
90C23×D11—21no—
91C2×Q8×C11—24no—
92C2×Q8×C11—22no—
93C2×Q8×C11—22no—
94C2×Q8×C11—22no—
95C2×Q8×C11—22no—
96C2×Q8×C11C2×Q812yes—
97C2×Q8×C11#4112yes—
98C22×C4×C11C2×D412yes—
99C22×C4×C11C2×D412yes—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2411yescharacteristic
103C22×Dic11—21no—
104C22×Dic11—21no—
105C22×Dic11—21no—
106C2×D44—22no—
107C2×D44—21no—
108C2×D44—22no—
109C2×D44C2×Q812yes—
110C2×C4×D11—42no—
111C2×C4×D11—82no—
112C11×C4⋊C4—24no—
113C11×C4⋊C4—24no—
114C11×C4⋊C4—24no—
115C11×C4⋊C4—28no—
116C11×C4⋊C4—24no—
117C11×C4⋊C4—24no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—24no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4C2×D414yes—
123C11×C4⋊C4C2×D414yes—
124C11×C22⋊C4—24no—
125C42×C11—28no—
126C42×C11—22no—
127C42×C11—22no—
128C42×C11—24no—
129C42×C11C2×D412yes—
130C42×C11C2×D412yes—
131(C2×D11)⋊C4—28no—
132(C2×D11)⋊C4—41no—
133(C2×D11)⋊C4—41no—
134(C2×D11)⋊C4—82no—
135C4⋊Dic11—22no—
136Dic11⋊C4—82no—
137C4×Dic11—21no—
138C4×Dic11—22no—
139C4×Dic11C2×Q812yes—
140#4318—24no—
141#4318—24no—
142C2×C11⋊C8—24no—
143#3502D1111yescharacteristic, complemented
144#3077—112no—
145#2326—111no—
146#2060—112no—
147#2027—112no—
148#1995—112no—
149#1888—112no—
150#1857—112no—
151#1801—111no—
152C23×C11C22×D411yescharacteristic
153C22×D11—22no—
154C22×D11—42no—
155C22×D11—42no—
156C22×D11—41no—
157C22×D11—41no—
158Q8×C11—24no—
159Q8×C11—24no—
160Q8×C11—44no—
161Q8×C11—82no—
162Q8×C11—84no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—24no—
166C2×C4×C11—24no—
167C2×C4×C11—22no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—42no—
171C2×C4×C11#12011yescharacteristic
172C2×C4×C11#12011yescharacteristic
173C2×C4×C11#12012yes—
174C2×C4×C11C22⋊Q814yes—
175C2×C4×C11C22×D412yes—
176C2×C4×C11C22×Q811yescharacteristic
177C2×C4×C11C2×#4111yescharacteristic
178C2×C4×C112−1+412yes—
179C2×Dic11—22no—
180C2×Dic11—41no—
181C2×Dic11—41no—
182C2×Dic11—42no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11—41no—
186C2×Dic11—41no—
187D44—24no—
188D44—42no—
189C4×D11—84no—
190C11⋊C8—44no—
191Q82—22no—
192#557—22no—
193#557—24no—
194#544—22no—
195#544C2×D1112yes—
196#533—22no—
197#533C2×D1112yes—
198C2×#124—111no—
199#519C2×D1112yes—
200C2×C4×Q8C2×D1111yescharacteristic
201C2×C4×D4—111no—
202#478—224no—
203#476—222no—
204#474—222no—
205#428—114no—
206#423—112no—
207#418—114no—
208C2×#101—112no—
209#391—111no—
210#390—111no—
211#388—222no—
212#385—222no—
213#384—111no—
214#376—111no—
215#343—112no—
216#339—114no—
217#339—114no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11C2×#12011yescharacteristic
221C22×C11C2×C22⋊Q811yescharacteristic
222C22×C11#53611yescharacteristic
223C2×D11—44no—
224C2×D11—42no—
225C2×D11—82no—
226C2×D11—81no—
227C2×D11—81no—
228C4×C11—24no—
229C4×C11—21no—
230C4×C11—21no—
231C4×C11—22no—
232C4×C11—44no—
233C4×C11—42no—
234C4×C11—44no—
235C4×C11#54812yes—
236C4×C11D4×Q812yes—
237Dic11—42no—
238Dic11—81no—
239Dic11—81no—
240C22×Q8C22×D1111yescharacteristic
241C22×D4—111no—
242C23×C4—221no—
243C2×M16—114no—
244C4⋊Q8—22no—
245C4⋊Q8—22no—
246C4⋊Q8—28no—
247C4⋊Q8—24no—
248C4⋊Q8C22⋊D1112yes—
249C4⋊Q8C22⋊D1112yes—
250#125—24no—
251#125—28no—
252#125—24no—
253#125C22⋊D1114yes—
254#124—114no—
255#124—222no—
256C22⋊Q8—22no—
257C22⋊Q8—24no—
258C22⋊Q8—22no—
259C4×Q8—24no—
260C4×Q8—24no—
261C4×Q8—24no—
262C4×Q8—24no—
263C4×Q8—22no—
264C4×Q8—22no—
265C4×Q8—22no—
266C4×Q8—22no—
267C4×D4—222no—
268C4×D4—222no—
269#117—24no—
270#117C22×D1114yes—
271C2×C4⋊C4—111no—
272C2×C4⋊C4—222no—
273C2×C4⋊C4C22⋊D1112yes—
274C2×C4⋊C4C22×D1111yescharacteristic
275C2×C22⋊C4—222no—
276C2×C22⋊C4—221no—
277C2×C22⋊C4—222no—
278C2×C42—111no—
279C2×C42—111no—
280C2×C42C22⋊D1112yes—
281C2×C42C22×D1111yescharacteristic
282#107—224no—
283#106—224no—
284C4⋊C8—222no—
285C4⋊C8—222no—
286#102—224no—
287#102—224no—
288#101—224no—
289#95—221no—
290#95—221no—
291#95—222no—
292C2×C11—21no—
293C2×C11—21no—
294C2×C11#240911yescharacteristic
295C2×C11#302011yescharacteristic
296C2×C11#302111yescharacteristic
297D11—82no—
298C24—221no—
299C2×Q8—24no—
300C2×Q8—22no—
301C2×Q8—22no—
302C2×Q8—22no—
303C2×Q8—22no—
304C2×Q8Q8×D1112yes—
305C2×Q8#434312yes—
306C2×D4—112no—
307C2×D4—221no—
308C2×D4—222no—
309C2×D4—222no—
310C22×C4—221no—
311C22×C4—221no—
312C22×C4—221no—
313C22×C4—442no—
314C22×C4—882no—
315C22×C4C2×C22⋊D1112yes—
316C22×C4C2×C22⋊D1112yes—
317C22×C4C2×C22⋊D1111yescharacteristic
318C22×C4C2×C22⋊D1111yescharacteristic
319C22×C4C23×D1111yescharacteristic
320M16—224no—
321M16—224no—
322C2×C8—224no—
323C4⋊C4—24no—
324C4⋊C4—24no—
325C4⋊C4—24no—
326C4⋊C4—28no—
327C4⋊C4—24no—
328C4⋊C4—24no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—24no—
332C4⋊C4—22no—
333C4⋊C4—222no—
334C4⋊C4—882no—
335C4⋊C4C2×C22⋊D1114yes—
336C4⋊C4C2×C22⋊D1114yes—
337C22⋊C4—24no—
338C22⋊C4—228no—
339C22⋊C4—441no—
340C22⋊C4—441no—
341C22⋊C4—882no—
342C42—28no—
343C42—22no—
344C42—22no—
345C42—24no—
346C42—112no—
347C42—221no—
348C42—222no—
349C42C2×C22⋊D1112yes—
350C42C2×C22⋊D1112yes—
351C11#2431711yescharacteristic, complemented, Sylow
352C23—222no—
353C23—442no—
354C23—442no—
355C23—441no—
356C23—441no—
357C23C22×C22⋊D1111yescharacteristic
358Q8—24no—
359Q8—24no—
360Q8—44no—
361Q8—82no—
362Q8—84no—
363D4—224no—
364D4—442no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—24no—
368C2×C4—24no—
369C2×C4—22no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—42no—
373C2×C4—222no—
374C2×C4—441no—
375C2×C4—441no—
376C2×C4—441no—
377C2×C4—442no—
378C2×C4—441no—
379C2×C4—441no—
380C2×C4—441no—
381C2×C4—884no—
382C2×C4#6699914yes—
383C2×C4#6700611yescharacteristic
384C2×C4#6700611yescharacteristic
385C2×C4#6700612yes—
386C2×C4C2×Q8×D1111yescharacteristic
387C2×C4C2×#434311yescharacteristic
388C2×C4#6704012yes—
389C2×C4C22×C22⋊D1112yes—
390C8—444no—
391C22—21no—
392C22—21no—
393C22—444no—
394C22—442no—
395C22—882no—
396C22—881no—
397C22—881no—
398C22C2×#6699911yescharacteristic
399C22#1062334711yescharacteristic
400C22C2×#6700611yescharacteristic
401C4—24no—
402C4—21no—
403C4—21no—
404C4—22no—
405C4—44no—
406C4—42no—
407C4—44no—
408C4—442no—
409C4—881no—
410C4—881no—
411C4Q8×C22⋊D1112yes—
412C4#1062334812yes—
413C2—21no—
414C2—21no—
415C2—882no—
416C2#1307197511yescharacteristic
417C2#1307798011yescharacteristic
418C2#1307798811yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3502C2
socleC22×C11C2×#120
prime radicalC22×D44C23
hypercenter#3502D11
hypocenterC11#24317
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
3. #13069958C2semidirect
5. #13069598C2semidirect
7. #13068831C2semidirect
8. #13068612C2semidirect
9. C11×#3502C2semidirect
68. #67000Q8semidirect
143. #3502D11semidirect
351. C11#24317semidirect

Maximal subgroups

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

subgroupindex
#130784092
#130713232
#130699582
#130697692
#130695982
#130690192
#130688312
#130686122
C11×#35022
#2431711