Finite Group Databasebeta

← #14790043

Subgroups — #14790043

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#13082426C211yesmaximal, characteristic, complemented
2#13078413C212yesmaximal
3#13069961C212yesmaximal, complemented
4#13069772C212yesmaximal
5#13069597C212yesmaximal, complemented
6#13069020C212yesmaximal
7#13068830C212yesmaximal, complemented
8#13068612C211yesmaximal, characteristic, complemented
9C11×#2326C211yesmaximal, characteristic
10C2×C11×#124C2211yescharacteristic
11C2×C4×Q8×C11C2211yescharacteristic
12C2×C4×D4×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×#390C2211yescharacteristic
23C11×#388—22no—
24C11×#385—22no—
25C11×#384C2211yescharacteristic
26C11×#376C2211yescharacteristic
27C2×#66900C2212yes—
28#10622828C2214yes—
29#10622622—24no—
30#10622621—22no—
31#10622620—22no—
32#10622577C2214yes—
33#10622537C2212yes—
34#10622168C2212yes—
35#10622161C2214yes—
36#10622161C2214yes—
37C22×Q8×C11C2311yescharacteristic
38C22×D4×C11C2311yescharacteristic
39C23×C4×C11—21no—
40C11×#124—22no—
41C11×#124Q814yescomplemented
42C4×Q8×C11—22no—
43C4×Q8×C11—22no—
44C4×D4×C11—22no—
45C4×D4×C11—22no—
46C2×C11×C4⋊C4—22no—
47C2×C11×C4⋊C4D412yes—
48C2×C11×C4⋊C4C2311yescharacteristic
49C2×C11×C4⋊C4C2311yescharacteristic
50C2×C11×C22⋊C4—22no—
51C2×C11×C22⋊C4—21no—
52C2×C11×C22⋊C4—22no—
53C2×C42×C11D412yes—
54C2×C42×C11C2311yescharacteristic
55C2×C42×C11C2311yescharacteristic
56C2×C42×C11C2311yescharacteristic
57Q8×Dic11—24no—
58Q8×Dic11—24no—
59#66979—24no—
60#66979C2314yes—
61#66977—22no—
62#66977—24no—
63#66977—22no—
64C2×#4318C2314yes—
65#66943—28no—
66#66943—24no—
67#66941—28no—
68#66941—24no—
69#66923—24no—
70#66923D414yes—
71#66922—22no—
72#66922—22no—
73#66922D412yes—
74#66922D412yes—
75C4×Dic22—24no—
76C4×Dic22—24no—
77C4×Dic22—22no—
78C4×Dic22—22no—
79C11×#95—21no—
80C11×#95—21no—
81C11×#95—22no—
82#66900—24no—
83#66896—24no—
84#66896—24no—
85#66872—24no—
86#66871—24no—
87C4⋊(C11⋊C8)—22no—
88C4⋊(C11⋊C8)—22no—
89#24317—111nomaximal, Sylow
90C24×C11—21no—
91C2×Q8×C11—22no—
92C2×Q8×C11—22no—
93C2×Q8×C11C2×Q812yes—
94C2×Q8×C11#4112yes—
95C2×D4×C11—22no—
96C2×D4×C11—21no—
97C2×D4×C11—22no—
98C2×D4×C11C2×Q812yes—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—42no—
103C22×C4×C11—82no—
104C22×C4×C11C2×D412yes—
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2411yescharacteristic
109C2×Dic22—24no—
110C2×Dic22—22no—
111C2×Dic22—22no—
112C11×C4⋊C4—24no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4—82no—
116C11×C22⋊C4—28no—
117C11×C22⋊C4—41no—
118C11×C22⋊C4—41no—
119C11×C22⋊C4—82no—
120C42×C11—22no—
121C42×C11—22no—
122C42×C11—21no—
123C42×C11—22no—
124C42×C11C2×D412yes—
125C42×C11C2×D412yes—
126C42×C11C2×Q812yes—
127C22⋊Dic11—24no—
128C4⋊Dic11—24no—
129C4⋊Dic11—24no—
130C4⋊Dic11—24no—
131C4⋊Dic11—22no—
132C4⋊Dic11—22no—
133C4⋊Dic11C2×D414yes—
134C4⋊Dic11C2×D414yes—
135Dic11⋊C4—28no—
136Dic11⋊C4—24no—
137Dic11⋊C4—24no—
138C4×Dic11—28no—
139C4×Dic11—24no—
140#4318—24no—
141#4318—24no—
142C2×C11⋊C8—24no—
143#3502—111no—
144#3077—112no—
145#2326D1111yescharacteristic
146#2060—112no—
147#2027—112no—
148#1995—112no—
149#1888—112no—
150#1857—112no—
151#1801—111no—
152C23×C11—22no—
153C23×C11—42no—
154C23×C11—42no—
155C23×C11—41no—
156C23×C11—41no—
157C23×C11C22×D411yescharacteristic
158Q8×C11—24no—
159Q8×C11—24no—
160D4×C11—24no—
161D4×C11—42no—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—42no—
171C2×C4×C11—41no—
172C2×C4×C11—42no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—84no—
177C2×C4×C11#12011yescharacteristic
178C2×C4×C11#12012yes—
179C2×C4×C11#12011yescharacteristic
180C2×C4×C11C22⋊Q814yes—
181C2×C4×C11C22×D412yes—
182C2×C4×C11C22×Q811yescharacteristic
183C2×C4×C11C2×#4111yescharacteristic
184C2×C4×C112−1+412yes—
185C2×Dic11—24no—
186C2×Dic11—24no—
187Dic22—44no—
188Dic22—82no—
189Dic22—84no—
190C11⋊C8—44no—
191Q82—222no—
192#557—224no—
193#557—222no—
194#544—112no—
195#544—222no—
196#533—112no—
197#533—222no—
198C2×#124C2×D1111yescharacteristic
199#519—112no—
200C2×C4×Q8C2×D1111yescharacteristic
201C2×C4×D4C2×D1111yescharacteristic
202#478—224no—
203#476—222no—
204#474—222no—
205#428—114no—
206#423—112no—
207#418—114no—
208C2×#101—112no—
209#391C2×D1111yescharacteristic
210#390C2×D1111yescharacteristic
211#388—22no—
212#385—22no—
213#384C2×D1111yescharacteristic
214#376C2×D1111yescharacteristic
215#343—112no—
216#339—114no—
217#339—114no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—44no—
221C22×C11—42no—
222C22×C11—82no—
223C22×C11—81no—
224C22×C11—81no—
225C22×C11C2×#12011yescharacteristic
226C22×C11C2×C22⋊Q811yescharacteristic
227C22×C11#53611yescharacteristic
228C4×C11—24no—
229C4×C11—21no—
230C4×C11—21no—
231C4×C11—22no—
232C4×C11—42no—
233C4×C11—42no—
234C4×C11—81no—
235C4×C11—81no—
236C4×C11#54812yes—
237C4×C11D4×Q812yes—
238Dic11—44no—
239Dic11—44no—
240C22×Q8C22×D1111yescharacteristic
241C22×D4C22×D1111yescharacteristic
242C23×C4—21no—
243C2×M16—114no—
244C4⋊Q8—112no—
245C4⋊Q8—112no—
246C4⋊Q8—222no—
247C4⋊Q8—222no—
248C4⋊Q8—224no—
249C4⋊Q8—228no—
250#125—114no—
251#125—224no—
252#125—224no—
253#125—228no—
254#124—22no—
255#124Dic2214yescomplemented
256C22⋊Q8—222no—
257C22⋊Q8—222no—
258C22⋊Q8—224no—
259C4×Q8—22no—
260C4×Q8—22no—
261C4×Q8—224no—
262C4×Q8—224no—
263C4×Q8—224no—
264C4×Q8—224no—
265C4×Q8—222no—
266C4×Q8—222no—
267C4×D4—22no—
268C4×D4—22no—
269#117—114no—
270#117—224no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4C22⋊D1112yes—
273C2×C4⋊C4C22×D1111yescharacteristic
274C2×C4⋊C4C22×D1111yescharacteristic
275C2×C22⋊C4—22no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—22no—
278C2×C42C22⋊D1112yes—
279C2×C42C22×D1111yescharacteristic
280C2×C42C22×D1111yescharacteristic
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—21no—
290#95—21no—
291#95—22no—
292C2×C11—21no—
293C2×C11—21no—
294C2×C11—82no—
295C2×C11#240911yescharacteristic
296C2×C11#302011yescharacteristic
297C2×C11#302111yescharacteristic
298C24—21no—
299C2×Q8—22no—
300C2×Q8—22no—
301C2×Q8—224no—
302C2×Q8—222no—
303C2×Q8—222no—
304C2×Q8C2×Dic2212yes—
305C2×Q8#433912yes—
306C2×D4—21no—
307C2×D4—22no—
308C2×D4—22no—
309C2×D4C2×Dic2212yes—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—42no—
314C22×C4—82no—
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—22no—
325C4⋊C4—22no—
326C4⋊C4—82no—
327C4⋊C4—114no—
328C4⋊C4—114no—
329C4⋊C4—224no—
330C4⋊C4—224no—
331C4⋊C4—224no—
332C4⋊C4—228no—
333C4⋊C4—224no—
334C4⋊C4—222no—
335C4⋊C4—224no—
336C4⋊C4—222no—
337C22⋊C4—28no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—82no—
341C22⋊C4—224no—
342C42—22no—
343C42—22no—
344C42—21no—
345C42—22no—
346C42—228no—
347C42—224no—
348C42C2×Dic2212yes—
349C42D4×D1112yes—
350C42D4×D1112yes—
351C11#2431711yescharacteristic, complemented, Sylow
352C23—22no—
353C23—42no—
354C23—42no—
355C23—41no—
356C23—41no—
357C23C22×C22⋊D1111yescharacteristic
358Q8—24no—
359Q8—24no—
360Q8—444no—
361Q8—882no—
362Q8—884no—
363D4—24no—
364D4—42no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—41no—
375C2×C4—42no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—84no—
380C2×C4—224no—
381C2×C4—224no—
382C2×C4#6697714yes—
383C2×C4#6699011yescharacteristic
384C2×C4#6699011yescharacteristic
385C2×C4#6699012yes—
386C2×C4C22×Dic2211yescharacteristic
387C2×C4C2×#433911yescharacteristic
388C2×C4C2×D4×D1112yes—
389C2×C4#6704312yes—
390C8—444no—
391C22—21no—
392C22—21no—
393C22—44no—
394C22—42no—
395C22—82no—
396C22—81no—
397C22—81no—
398C22C2×#6697711yescharacteristic
399C22C2×#6699011yescharacteristic
400C22#1062335611yescharacteristic
401C4—24no—
402C4—21no—
403C4—21no—
404C4—22no—
405C4—42no—
406C4—42no—
407C4—81no—
408C4—81no—
409C4—444no—
410C4—444no—
411C4D4×Dic2212yes—
412C4#1062308312yes—
413C2—21no—
414C2—21no—
415C2—82no—
416C2#1307198111yescharacteristic
417C2#1307797911yescharacteristic
418C2#1307798711yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2326C2
socleC22×C11C2×#120
prime radicalC22×D4×C11C23
hypercenter#2326D11
hypocenterC11#24317
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2326

Complements

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

NH ≅ G/Ntype
1. #13082426C2semidirect
3. #13069961C2semidirect
5. #13069597C2semidirect
7. #13068830C2semidirect
8. #13068612C2semidirect
41. C11×#124Q8semidirect
255. #124Dic22semidirect
351. C11#24317semidirect

Maximal subgroups

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

subgroupindex
#130824262
#130784132
#130699612
#130697722
#130695972
#130690202
#130688302
#130686122
C11×#23262
#2431711