Finite Group Databasebeta

← #14853483

Subgroups — #14853483

Order 2816.

706 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077003C211yesmaximal, characteristic, complemented
2C4×#66928C211yesmaximal, characteristic
3#13070185C212yesmaximal, complemented
4#13069858C212yesmaximal
5#13069313C212yesmaximal
6#13069306C212yesmaximal, complemented
7#13068632C211yesmaximal, characteristic, complemented
8#13068632C211yesmaximal, characteristic, complemented
9#13068627C211yesmaximal, characteristic
10#13068627C211yesmaximal, characteristic
11C11×#1767C211yesmaximal, characteristic, complemented
12C2×#66928C2211yescharacteristic
13C2×C4×D44C2211yescharacteristic
14C2×C4×Dic22C2211yescharacteristic
15C2×C11×C4⋊C8C2211yescharacteristic
16C2×C11×C4⋊C8C2211yescharacteristic
17C2×C11×#97C2212yes—
18C43×C11C2211yescharacteristic
19C2×#66885C2212yes—
20C2×#66885C2212yes—
21C2×#66880C2212yes—
22C2×#66880C2212yes—
23#10622553—22no—
24#10622552C2211yescharacteristic
25C4×(C2×D11)⋊C4—22no—
26#10622549C2211yescharacteristic
27#10622549C2211yescharacteristic
28#10622549C2211yescharacteristic
29#10622546—22no—
30#10622546—22no—
31#10622542C2211yescharacteristic
32#10622541C2212yes—
33#10622541C2212yes—
34C11×#336C2212yes—
35#10622189C2212yes—
36#10622189C2212yes—
37#10622189C2212yes—
38#10622189C2212yes—
39C22×D44C2311yescharacteristic
40C22×C4×D11—21no—
41C22×Dic22C2311yescharacteristic
42C22×C8×C11C2312yes—
43C22×C8×C11C2312yes—
44C2×C42×C11D412yes—
45C2×C42×C11D412yes—
46C2×C42×C11C2311yescharacteristic
47C2×C42×C11C2311yescharacteristic
48C2×C42×C11C2311yescharacteristic
49C2×(C2×D11)⋊C4—22no—
50C2×(C2×D11)⋊C4—21no—
51C2×(C2×D11)⋊C4—22no—
52C2×C4⋊Dic11C2312yes—
53C2×C4⋊Dic11C2312yes—
54C2×C4⋊Dic11C2311yescharacteristic
55C2×C4⋊Dic11C2311yescharacteristic
56C2×Dic11⋊C4—21no—
57C2×Dic11⋊C4—22no—
58C2×Dic11⋊C4—22no—
59C2×C4×Dic11—21no—
60#66928—22no—
61#66928—22no—
62C4×D44—22no—
63C4×D44—22no—
64C4×Dic22—22no—
65C4×Dic22—22no—
66C11×C4⋊C8—22no—
67C11×C4⋊C8—22no—
68C11×#97—42no—
69C11⋊#95—22no—
70C11⋊#95—22no—
71C11⋊#95—22no—
72C11⋊#95—21no—
73C11⋊#95—21no—
74C11⋊#95—21no—
75C11⋊#95—21no—
76C11⋊#95—22no—
77#66885—24no—
78#66885—42no—
79#66880—24no—
80#66880—42no—
81#29128—111nomaximal, Sylow
82C23×D11—21no—
83C22×C4×C11C2×D412yes—
84C22×C4×C11C2×D412yes—
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2411yescharacteristic
88C22×Dic11—21no—
89C22×Dic11—22no—
90C22×Dic11—22no—
91C22×Dic11—21no—
92C22×Dic11—21no—
93C2×D44—21no—
94C2×D44—21no—
95C2×D44—21no—
96C2×D44—21no—
97C2×D44—21no—
98C2×D44#4112yes—
99C2×C4×D11—44no—
100C2×C4×D11—42no—
101C2×Dic22—21no—
102C2×Dic22—21no—
103C2×Dic22—21no—
104C2×Dic22—21no—
105C2×Dic22—21no—
106C2×Dic22#4112yes—
107C2×C8×C11—22no—
108C2×C8×C11—22no—
109C2×C8×C11—22no—
110C2×C8×C11—22no—
111C2×C8×C11—22no—
112C2×C8×C11—22no—
113C42×C11—21no—
114C42×C11—21no—
115C42×C11—21no—
116C42×C11—21no—
117C42×C11—42no—
118C42×C11—42no—
119C42×C11#4112yes—
120C42×C11#4112yes—
121(C2×D11)⋊C4—28no—
122(C2×D11)⋊C4—44no—
123(C2×D11)⋊C4—42no—
124C4⋊Dic11—22no—
125C4⋊Dic11—22no—
126C4⋊Dic11—21no—
127C4⋊Dic11—21no—
128C4⋊Dic11—21no—
129C4⋊Dic11—21no—
130C4⋊Dic11—22no—
131C4⋊Dic11—22no—
132Dic11⋊C4—44no—
133Dic11⋊C4—44no—
134Dic11⋊C4—42no—
135C4×Dic11—42no—
136#2864—111no—
137C4×#124—111no—
138#2101—112no—
139#2042—112no—
140#1936—112no—
141#1935—112no—
142#1805—111no—
143#1805—111no—
144#1804—111no—
145#1804—111no—
146#1767D1111yescharacteristic, complemented
147C23×C11C22×D411yescharacteristic
148C22×D11—22no—
149C22×D11—41no—
150C22×D11—41no—
151C22×D11—42no—
152C22×D11—42no—
153C2×C4×C11—22no—
154C2×C4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11#12412yes—
162C2×C4×C11#12412yes—
163C2×C4×C11C2×#4111yescharacteristic
164C2×C4×C11C2×#4111yescharacteristic
165C2×C4×C11C2×#4111yescharacteristic
166C2×C4×C11C2×#4111yescharacteristic
167C2×C4×C11H(5,𝔽2)11yescharacteristic
168C2×C4×C112−1+411yescharacteristic
169C2×Dic11—22no—
170C2×Dic11—41no—
171C2×Dic11—41no—
172C2×Dic11—42no—
173C2×Dic11—41no—
174C2×Dic11—41no—
175C2×Dic11—42no—
176C2×Dic11—42no—
177C2×Dic11—42no—
178C2×Dic11—42no—
179C2×Dic11—42no—
180C2×Dic11—42no—
181C2×Dic11—42no—
182D44—22no—
183D44—22no—
184D44—41no—
185D44—41no—
186C4×D11—84no—
187Dic22—22no—
188Dic22—22no—
189Dic22—41no—
190Dic22—41no—
191C8×C11—42no—
192C8×C11—42no—
193C2×#124—111no—
194C2×C4×Q8—111no—
195C2×C4×D4—111no—
196C2×C4⋊C8C2×D1111yescharacteristic
197C2×C4⋊C8C2×D1111yescharacteristic
198C2×#103—112no—
199C2×#103—112no—
200C2×#102—112no—
201C2×#102—112no—
202C2×#97C2×D1112yes—
203#391—111no—
204#390—111no—
205#389—112no—
206#389—112no—
207#388—222no—
208#387—222no—
209#387—222no—
210#382—111no—
211#382—111no—
212#382—111no—
213C4×C22⋊C4—222no—
214C43C2×D1111yescharacteristic
215#340—112no—
216#340—112no—
217#340—112no—
218#340—112no—
219#336C2×D1112yes—
220C22×C11#52511yescharacteristic
221C22×C11C2×#12411yescharacteristic
222C22×C11#53711yescharacteristic
223C22×C11#57512yes—
224C22×C11#57512yes—
225C2×D11—42no—
226C2×D11—44no—
227C2×D11—81no—
228C2×D11—81no—
229C2×D11—82no—
230C4×C11—22no—
231C4×C11—22no—
232C4×C11—42no—
233C4×C11—42no—
234C4×C11#55211yescharacteristic
235C4×C11#55211yescharacteristic
236C4×C11#55311yescharacteristic
237C4×C11#55311yescharacteristic
238Dic11—42no—
239Dic11—82no—
240Dic11—81no—
241Dic11—81no—
242Dic11—82no—
243C22×Q8—111no—
244C22×D4—111no—
245C23×C4—221no—
246C22×C8C22×D1112yes—
247C22×C8C22×D1112yes—
248#124—222no—
249#124—222no—
250C4×Q8—222no—
251C4×Q8—222no—
252C4×D4—222no—
253C4×D4—222no—
254C2×C4⋊C4—111no—
255C2×C4⋊C4—111no—
256C2×C4⋊C4—112no—
257C2×C4⋊C4—112no—
258C2×C4⋊C4—221no—
259C2×C4⋊C4—222no—
260C2×C4⋊C4—222no—
261C2×C22⋊C4—222no—
262C2×C22⋊C4—221no—
263C2×C22⋊C4—222no—
264C2×C42—221no—
265C2×C42D4412yes—
266C2×C42D4412yes—
267C2×C42C22×D1111yescharacteristic
268C2×C42C22×D1111yescharacteristic
269C2×C42C22×D1111yescharacteristic
270C4⋊C8—22no—
271C4⋊C8—22no—
272#103—224no—
273#103—442no—
274#102—224no—
275#102—442no—
276#97—42no—
277#95—222no—
278#95—222no—
279#95—221no—
280#95—221no—
281#95—221no—
282#95—221no—
283#95—222no—
284#95—222no—
285C2×C11#256211yescharacteristic
286C2×C11#311112yes—
287C2×C11#313511yescharacteristic
288C2×C11#314011yescharacteristic
289C2×C11#325612yes—
290D11—82no—
291C24—221no—
292C2×Q8—112no—
293C2×Q8—221no—
294C2×Q8—221no—
295C2×Q8—221no—
296C2×Q8—221no—
297C2×Q8—221no—
298C2×D4—112no—
299C2×D4—221no—
300C2×D4—221no—
301C2×D4—221no—
302C2×D4—221no—
303C2×D4—221no—
304C22×C4—221no—
305C22×C4—221no—
306C22×C4—222no—
307C22×C4—222no—
308C22×C4—221no—
309C22×C4—444no—
310C22×C4—442no—
311C22×C4C2×D4412yes—
312C22×C4C2×D4412yes—
313C22×C4C2×D4411yescharacteristic
314C22×C4C2×D4411yescharacteristic
315C22×C4C23×D1111yescharacteristic
316C2×C8—22no—
317C2×C8—22no—
318C2×C8—22no—
319C2×C8—22no—
320C2×C8—22no—
321C2×C8—22no—
322C4⋊C4—221no—
323C4⋊C4—221no—
324C4⋊C4—221no—
325C4⋊C4—221no—
326C4⋊C4—222no—
327C4⋊C4—222no—
328C4⋊C4—222no—
329C4⋊C4—222no—
330C4⋊C4—444no—
331C4⋊C4—444no—
332C4⋊C4—442no—
333C22⋊C4—228no—
334C22⋊C4—444no—
335C22⋊C4—442no—
336C42—21no—
337C42—21no—
338C42—21no—
339C42—21no—
340C42—42no—
341C42—42no—
342C42—442no—
343C42#433912yes—
344C42#433912yes—
345C11#2912811yescharacteristic, complemented, Sylow
346C23—222no—
347C23—441no—
348C23—442no—
349C23—442no—
350C23—441no—
351C23C22×D4411yescharacteristic
352Q8—222no—
353Q8—222no—
354Q8—441no—
355Q8—441no—
356D4—222no—
357D4—222no—
358D4—441no—
359D4—441no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—222no—
369C2×C4—441no—
370C2×C4—441no—
371C2×C4—441no—
372C2×C4—441no—
373C2×C4—442no—
374C2×C4—442no—
375C2×C4—442no—
376C2×C4—442no—
377C2×C4—442no—
378C2×C4—442no—
379C2×C4—442no—
380C2×C4—442no—
381C2×C4—884no—
382C2×C4#6692812yes—
383C2×C4#6692812yes—
384C2×C4C2×#433911yescharacteristic
385C2×C4C2×#433911yescharacteristic
386C2×C4#6703711yescharacteristic
387C2×C4#6704011yescharacteristic
388C2×C4#41×D1111yescharacteristic
389C2×C4#41×D1111yescharacteristic
390C8—42no—
391C8—42no—
392C22—442no—
393C22—444no—
394C22—881no—
395C22—882no—
396C22—881no—
397C22C2×#6692811yescharacteristic
398C22#1062304111yescharacteristic
399C22#1062305511yescharacteristic
400C22#1062327912yes—
401C22#1062327912yes—
402C4—22no—
403C4—22no—
404C4—42no—
405C4—42no—
406C4—442no—
407C4—881no—
408C4—882no—
409C4—882no—
410C4—881no—
411C4#1062308911yescharacteristic
412C4#1062308911yescharacteristic
413C4#1062311211yescharacteristic
414C4#1062311211yescharacteristic
415C2—882no—
416C2#1307377711yescharacteristic
417C2#1307872712yes—
418C2#1307896211yescharacteristic
419C2#1307900311yescharacteristic
420C2#1308001712yes—
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1767C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1767D11
hypocenterC11#29128
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ #1767

Complements

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

NH ≅ G/Ntype
1. #13077003C2semidirect
3. #13070185C2semidirect
6. #13069306C2semidirect
7. #13068632C2semidirect
8. #13068632C2semidirect
11. C11×#1767C2semidirect
146. #1767D11semidirect
345. C11#29128semidirect

Maximal subgroups

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

subgroupindex
#130770032
C4×#669282
#130701852
#130698582
#130693132
#130693062
#130686322
#130686272
C11×#17672
#2912811