Finite Group Databasebeta

← #14782570

Subgroups — #14782570

Order 2816.

1122 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622614C211yesmaximal, characteristic
2C22×#66885C211yesmaximal, characteristic
3#13071236C211yesmaximal, characteristic, complemented
4#13071196C211yesmaximal, characteristic
5#13070033C214yesmaximal, complemented
6#13070023C214yesmaximal, complemented
7#13068337C211yesmaximal, characteristic, complemented
8#13068312C211yesmaximal, characteristic, complemented
9C11×#1735C211yesmaximal, characteristic, complemented
10C23×D44C2211yescharacteristic
11C23×C8×C11C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C2×#66979C2211yescharacteristic
15C22×C4⋊Dic11C2211yescharacteristic
16C22×#4318C2211yescharacteristic
17C2×#66885—24no—
18C2×#66885C2214yes—
19#10622614—24no—
20#10622601C2214yes—
21#10622590C2212yescomplemented
22#10622589C2212yescomplemented
23C2×#66873C2212yes—
24C2×#66873C2212yes—
25#10622568—22no—
26#10622559—22no—
27#10622552—22no—
28#10622541—22no—
29C11×#340C2212yescomplemented
30C11×#340C2212yescomplemented
31#10622188C2214yescomplemented
32#10622167C2214yescomplemented
33C24×D11—21no—
34C23×C4×C11C2311yescharacteristic
35C23×Dic11—21no—
36C22×D44—22no—
37C22×D44—22no—
38C22×D44—22no—
39C22×D44—22no—
40C22×D44—21no—
41C22×D44—22no—
42C22×D44D414yes—
43C22×D44C2312yes—
44C22×C8×C11—22no—
45C22×C8×C11—22no—
46C22×C8×C11—22no—
47C22×C8×C11C2312yes—
48C11×#117—22no—
49C11×#117—22no—
50C11×#117—22no—
51C11×#117—22no—
52C2×C11×C4⋊C4C2311yescharacteristic
53C2×C11×C4⋊C4C2311yescharacteristic
54C2×C11×C4⋊C4C2312yes—
55C2×C11×C22⋊C4—21no—
56C2×C11×C22⋊C4—21no—
57C2×C42×C11—21no—
58C2×C42×C11—21no—
59C2×C22⋊Dic11D412yes—
60C2×(C2×D11)⋊C4—24no—
61C2×(C2×D11)⋊C4—24no—
62#66979—22no—
63#66979—22no—
64C2×C4⋊Dic11—22no—
65C2×C4⋊Dic11—22no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11D412yes—
68C2×C4⋊Dic11C2312yes—
69C2×Dic11⋊C4—24no—
70C2×C4×Dic11C2312yes—
71C2×#4318—22no—
72C2×#4318—22no—
73C2×#4318—22no—
74C22×C11⋊C8C2312yes—
75C11⋊#95—24no—
76#66885—28no—
77#66873—24no—
78#66873—24no—
79#23632—111nomaximal, Sylow
80C24×C11C2×D411yescharacteristic
81C23×D11—22no—
82C23×D11—24no—
83C23×D11—42no—
84C23×D11—42no—
85C23×D11—82no—
86C23×D11—82no—
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11—22no—
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D412yes—
92C22×C4×C11#4112yes—
93C22×C4×C11#4112yes—
94C22×C4×C11#4112yes—
95C22×C4×C11#4112yes—
96C22×C4×C11#4112yes—
97C22×C4×C11C2411yescharacteristic
98C22×Dic11—22no—
99C22×Dic11—42no—
100C22×Dic11—82no—
101C22×Dic11C2×D414yes—
102C2×D44—24no—
103C2×D44—28no—
104C2×D44—28no—
105C2×D44—22no—
106C2×D44—22no—
107C2×D44—22no—
108C2×D44—22no—
109C2×D44—22no—
110C2×D44—42no—
111C2×D44—42no—
112C2×D44—44no—
113C2×D44—44no—
114C2×D44C2×D414yes—
115C2×C8×C11—22no—
116C2×C8×C11—22no—
117C2×C8×C11—22no—
118C2×C8×C11—44no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—22no—
125C11×C22⋊C4—42no—
126C11×C22⋊C4—42no—
127C42×C11—42no—
128C42×C11—42no—
129C22⋊Dic11—24no—
130(C2×D11)⋊C4—84no—
131(C2×D11)⋊C4—84no—
132C4⋊Dic11—24no—
133C4⋊Dic11—22no—
134C4⋊Dic11—22no—
135C4⋊Dic11—42no—
136Dic11⋊C4—84no—
137C4×Dic11—22no—
138C4×Dic11—22no—
139#4318—44no—
140C2×C11⋊C8—22no—
141C2×C11⋊C8—22no—
142C2×C11⋊C8—22no—
143C2×#418—111no—
144C22×#102—111no—
145#2317—111no—
146#2309—111no—
147#2073—114no—
148#2071—114no—
149#1736—111no—
150#1735D1111yescharacteristic, complemented
151#1729—111no—
152C23×C11—22no—
153C23×C11—22no—
154C23×C11#12112yes—
155C23×C11#12312yes—
156C23×C11#12412yes—
157C23×C11C22×D411yescharacteristic
158C22×D11—24no—
159C22×D11—42no—
160C22×D11—42no—
161C22×D11—44no—
162C22×D11—44no—
163C22×D11—48no—
164C22×D11—84no—
165C22×D11—84no—
166C22×D11—88no—
167C22×D11—88no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11#12112yes—
176C2×C4×C11#12314yes—
177C2×C4×C11#12314yes—
178C2×C4×C11#12312yes—
179C2×C4×C11#12412yes—
180C2×C4×C11#12614yes—
181C2×C4×C11#12614yes—
182C2×C4×C11C22×D411yescharacteristic
183C2×C4×C11C2×#4111yescharacteristic
184C2×C4×C11C2×#4111yescharacteristic
185C2×C4×C11C2×#4111yescharacteristic
186C2×C4×C11C2×#4111yescharacteristic
187C2×C4×C11C2×#4111yescharacteristic
188C2×Dic11—24no—
189C2×Dic11—24no—
190C2×Dic11—24no—
191C2×Dic11—42no—
192C2×Dic11—44no—
193C2×Dic11—84no—
194D44—24no—
195D44—24no—
196D44—42no—
197D44—42no—
198D44—48no—
199C8×C11—42no—
200C11⋊C8—42no—
201C23×D4—111no—
202C22×M16—111no—
203C23×C8C2×D1111yescharacteristic
204C2×#117—111no—
205C2×#117C2×D1111yescharacteristic
206C2×#117C2×D1111yescharacteristic
207C22×C4⋊C4—111no—
208#418—224no—
209C2×#102—114no—
210C2×#102—112no—
211C2×#102—112no—
212C2×#102—224no—
213#390—114no—
214#390—222no—
215#389—222no—
216#385—222no—
217#384—112no—
218#382—112no—
219#379—222no—
220#340—114no—
221#340C2×D1112yescomplemented
222#340C2×D1112yescomplemented
223#336—114no—
224C22×C11—24no—
225C22×C11—24no—
226C22×C11—22no—
227C22×C11—22no—
228C22×C11#39714yes—
229C22×C11C2×#12111yescharacteristic
230C22×C11C2×#12311yescharacteristic
231C22×C11C2×#12411yescharacteristic
232C22×C11#57612yes—
233C22×C11#57712yes—
234C2×D11—44no—
235C2×D11—44no—
236C2×D11—44no—
237C2×D11—816no—
238C2×D11—84no—
239C2×D11—84no—
240C4×C11—82no—
241C4×C11—81no—
242C4×C11—81no—
243C4×C11#39714yes—
244C4×C11C2×#12311yescharacteristic
245C4×C11C2×#12311yescharacteristic
246C4×C11C2×#12611yescharacteristic
247C4×C11C2×#12611yescharacteristic
248Dic11—44no—
249Dic11—82no—
250C25—221no—
251C22×D4—114no—
252C22×D4—112no—
253C22×D4—222no—
254C22×D4—222no—
255C22×D4—222no—
256C22×D4—221no—
257C22×D4—222no—
258C22×D4—222no—
259C23×C4—221no—
260C23×C4C22×D1111yescharacteristic
261C2×M16—222no—
262C2×M16—222no—
263C2×M16—222no—
264C22×C8—22no—
265C22×C8—22no—
266C22×C8—22no—
267C22×C8—112no—
268C22×C8C22×D1112yes—
269#117—22no—
270#117—22no—
271#117—22no—
272#117—22no—
273#117—222no—
274#117—222no—
275C2×C4⋊C4—112no—
276C2×C4⋊C4—112no—
277C2×C4⋊C4—222no—
278C2×C4⋊C4—222no—
279C2×C4⋊C4—221no—
280C2×C4⋊C4—224no—
281C2×C4⋊C4C22×D1112yes—
282C2×C4⋊C4C22×D1111yescharacteristic
283C2×C4⋊C4C22×D1111yescharacteristic
284C2×C22⋊C4—21no—
285C2×C22⋊C4—21no—
286C2×C22⋊C4—112no—
287C2×C22⋊C4—224no—
288C2×C22⋊C4—224no—
289C2×C42—21no—
290C2×C42—21no—
291C2×C42—112no—
292#102—224no—
293#102—224no—
294#102—228no—
295#95—224no—
296C2×C11—24no—
297C2×C11C2×#39711yescharacteristic
298C2×C11#304111yescharacteristic
299C2×C11#304211yescharacteristic
300C2×C11#309612yes—
301C2×C11#313612yes—
302D11—84no—
303C24—222no—
304C24—224no—
305C24—442no—
306C24—442no—
307C24—882no—
308C24—882no—
309C24D4×D1111yescharacteristic
310C2×D4—114no—
311C2×D4—228no—
312C2×D4—224no—
313C2×D4—228no—
314C2×D4—222no—
315C2×D4—222no—
316C2×D4—222no—
317C2×D4—222no—
318C2×D4—222no—
319C2×D4—444no—
320C2×D4—442no—
321C2×D4—442no—
322C2×D4—444no—
323C22×C4—21no—
324C22×C4—22no—
325C22×C4—21no—
326C22×C4—114no—
327C22×C4—222no—
328C22×C4—442no—
329C22×C4—882no—
330C22×C4#433912yes—
331C22×C4#433912yes—
332C22×C4#433912yes—
333C22×C4D4×D1112yes—
334C22×C4D4×D1111yescharacteristic
335C22×C4#434112yes—
336C22×C4#434312yes—
337C22×C4C23×D1111yescharacteristic
338M16—444no—
339C2×C8—22no—
340C2×C8—22no—
341C2×C8—22no—
342C2×C8—44no—
343C2×C8—222no—
344C2×C8—222no—
345C2×C8—222no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—22no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—22no—
352C4⋊C4—224no—
353C4⋊C4—222no—
354C4⋊C4—222no—
355C4⋊C4—442no—
356C4⋊C4—884no—
357C22⋊C4—42no—
358C22⋊C4—42no—
359C22⋊C4—224no—
360C22⋊C4—884no—
361C22⋊C4—884no—
362C42—42no—
363C42—42no—
364C42—222no—
365C42—222no—
366C11#2363211yescharacteristic, complemented, Sylow
367C23—22no—
368C23—22no—
369C23—224no—
370C23—442no—
371C23—442no—
372C23—444no—
373C23—444no—
374C23—448no—
375C23—884no—
376C23—884no—
377C23—888no—
378C23—888no—
379C23#6693712yes—
380C23#6693812yes—
381C23#6694712yes—
382C23C2×D4×D1111yescharacteristic
383D4—224no—
384D4—224no—
385D4—442no—
386D4—442no—
387D4—448no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—224no—
396C2×C4—224no—
397C2×C4—224no—
398C2×C4—442no—
399C2×C4—444no—
400C2×C4—884no—
401C2×C4#6692914yes—
402C2×C4#6693614yes—
403C2×C4#6693712yes—
404C2×C4#6693812yes—
405C2×C4#6694714yes—
406C2×C4#6694712yes—
407C2×C4#6695114yes—
408C2×C4C2×#433911yescharacteristic
409C2×C4C2×#433911yescharacteristic
410C2×C4C2×#433911yescharacteristic
411C2×C4C2×D4×D1111yescharacteristic
412C2×C4C2×#434111yescharacteristic
413C2×C4C2×#434311yescharacteristic
414C8—42no—
415C8—442no—
416C22—24no—
417C22—22no—
418C22—22no—
419C22—24no—
420C22—444no—
421C22—444no—
422C22—444no—
423C22—8816no—
424C22—884no—
425C22—884no—
426C22#1062228814yes—
427C22C2×#6693711yescharacteristic
428C22C2×#6693811yescharacteristic
429C22C2×#6694711yescharacteristic
430C22#1062330012yes—
431C22#1062330112yes—
432C4—81no—
433C4—81no—
434C4—82no—
435C4—444no—
436C4—882no—
437C4#1062228814yes—
438C4C2×#6692911yescharacteristic
439C4C2×#6693611yescharacteristic
440C4C2×#6694711yescharacteristic
441C4C2×#6695111yescharacteristic
442C2—24no—
443C2—884no—
444C2C2×#1062228811yescharacteristic
445C2#1307812211yescharacteristic
446C2#1307813111yescharacteristic
447C2#1307857712yes—
448C2#1307897412yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1735C2
socleC23×C11C22×D4
prime radicalC23×D44C22
hypercenter#1735D11
hypocenterC11#23632
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1735

Complements

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

NH ≅ G/Ntype
3. #13071236C2semidirect
5. #13070033C2semidirect
6. #13070023C2semidirect
7. #13068337C2semidirect
8. #13068312C2semidirect
9. C11×#1735C2semidirect
21. #10622590C22semidirect
22. #10622589C22semidirect
29. C11×#340C22semidirect
30. C11×#340C22semidirect
31. #10622188C22semidirect
32. #10622167C22semidirect
150. #1735D11semidirect
221. #340C2×D11semidirect
222. #340C2×D11semidirect
366. C11#23632semidirect

Maximal subgroups

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

subgroupindex
C2×#106226142
C22×#668852
#130712362
#130711962
#130700332
#130700232
#130683372
#130683122
C11×#17352
#2363211