Finite Group Databasebeta

← #14649526

Subgroups — #14649526

Order 2816.

946 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076903C211yesmaximal, characteristic
2C2×#10622825C211yesmaximal, characteristic
3C2×#10622105C212yesmaximal, complemented
4#13066496C212yesmaximal, complemented
5C11×#1779C211yesmaximal, characteristic
6C24×C4×C11C2211yescharacteristic
7C22×C22⋊Dic11—21no—
8C22×C4⋊Dic11—21no—
9C2×#66977C412yescomplemented
10C2×#66977C2211yescharacteristic
11C2×C11×C22⋊C8—22no—
12C2×C11×C22⋊C8C2212yes—
13#10622860—21no—
14#10622825—24no—
15#10622825C412yescomplemented
16#10622825C2211yescharacteristic
17#10622823—21no—
18#10622823—22no—
19C2×C11⋊#95C2212yes—
20#10622105—24no—
21C25×C11D411yescharacteristic
22C23×C4×C11—22no—
23C23×C4×C11—22no—
24C23×C4×C11—44no—
25C23×C4×C11C2×C412yes—
26C23×C4×C11D411yescharacteristic
27C23×C4×C11D412yes—
28C23×C4×C11C2311yescharacteristic
29C23×Dic11—22no—
30C22×Dic22C2×C411yescharacteristic
31C22×C8×C11—22no—
32C2×C22⋊Dic11—24no—
33C2×C22⋊Dic11—22no—
34C2×C22⋊Dic11—22no—
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11—42no—
38C2×C22⋊Dic11—42no—
39C2×C4⋊Dic11—24no—
40C2×C4⋊Dic11—44no—
41C2×C4⋊Dic11C2×C411yescharacteristic
42C2×C4⋊Dic11C2×C412yes—
43#66977—22no—
44#66977—22no—
45#66977—44no—
46C2×Dic11⋊C4—22no—
47C2×Dic11⋊C4—21no—
48C11×C22⋊C8—22no—
49C11×C22⋊C8—22no—
50C11×C22⋊C8—44no—
51C11⋊#95—22no—
52C11⋊#95—22no—
53C11⋊#95—21no—
54C11⋊#95D414yes—
55#9151—111nomaximal, Sylow
56C24×C11—21no—
57C24×C11—21no—
58C24×C11—21no—
59C24×C11—21no—
60C24×C11—42no—
61C24×C11—42no—
62C24×C11C22⋊C412yes—
63C24×C11SD1612yes—
64C24×C11Q1612yes—
65C24×C11C2×D411yescharacteristic
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—24no—
69C22×C4×C11—24no—
70C22×C4×C11—24no—
71C22×C4×C11—24no—
72C22×C4×C11—24no—
73C22×C4×C11—42no—
74C22×C4×C11—42no—
75C22×C4×C11—42no—
76C22×C4×C11—48no—
77C22×C4×C11—48no—
78C22×C4×C11C22⋊C412yes—
79C22×C4×C11C22×C411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D412yes—
82C22×C4×C11#4112yes—
83C22×Dic11—21no—
84C22×Dic11—22no—
85C22×Dic11—21no—
86C22×Dic11—24no—
87C22×Dic11—44no—
88C22×Dic11—44no—
89C22×Dic11—42no—
90C22×Dic11—42no—
91C2×Dic22—22no—
92C2×Dic22—42no—
93C2×C8×C11—44no—
94C2×C8×C11—42no—
95C22⋊Dic11—44no—
96C22⋊Dic11—44no—
97C22⋊Dic11—48no—
98C22⋊Dic11—41no—
99C22⋊Dic11—41no—
100C22⋊Dic11—41no—
101C22⋊Dic11—41no—
102C4⋊Dic11—22no—
103C4⋊Dic11—42no—
104C4⋊Dic11—48no—
105Dic11⋊C4—44no—
106Dic11⋊C4—42no—
107#2848—111no—
108C2×#380—111no—
109#1779D1111yescharacteristic
110C2×#328—112no—
111#1294—112no—
112C23×C11—22no—
113C23×C11—22no—
114C23×C11—22no—
115C23×C11—22no—
116C23×C11—22no—
117C23×C11—22no—
118C23×C11—22no—
119C23×C11—22no—
120C23×C11—22no—
121C23×C11—22no—
122C23×C11—22no—
123C23×C11—22no—
124C23×C11—44no—
125C23×C11—44no—
126C23×C11—42no—
127C23×C11—42no—
128C23×C11—42no—
129C23×C11—42no—
130C23×C11—44no—
131C23×C11—44no—
132C23×C11#10314yes—
133C23×C11C2×C22⋊C411yescharacteristic
134C23×C11#12011yescharacteristic
135C23×C11#12311yescharacteristic
136C23×C11C2×SD1611yescharacteristic
137C23×C11C2×Q1611yescharacteristic
138C23×C11AGL(1,ℤ/8)11yescharacteristic
139C23×C11#13711yescharacteristic
140C2×C4×C11—24no—
141C2×C4×C11—24no—
142C2×C4×C11—22no—
143C2×C4×C11—22no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—42no—
147C2×C4×C11—42no—
148C2×C4×C11—48no—
149C2×C4×C11—48no—
150C2×C4×C11#9914yes—
151C2×C4×C11C4×D412yes—
152C2×C4×C11#12112yes—
153C2×Dic11—44no—
154C2×Dic11—44no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—42no—
158C2×Dic11—42no—
159C2×Dic11—42no—
160C2×Dic11—42no—
161C2×Dic11—42no—
162C2×Dic11—44no—
163C2×Dic11—84no—
164C2×Dic11—84no—
165Dic22—82no—
166C8×C11—82no—
167C24×C4C2×D1111yescharacteristic
168C2×C22⋊Q8—111no—
169C2×C22⋊Q8—112no—
170C22×C4⋊C4—221no—
171C22×C22⋊C4—221no—
172C2×C22⋊C8—22no—
173C2×C22⋊C8C2×D1112yes—
174#385—221no—
175#385—222no—
176#380—111no—
177#380—112no—
178#380—224no—
179#379—221no—
180C2×#95—112no—
181#328—224no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11—22no—
187C22×C11—22no—
188C22×C11—22no—
189C22×C11—22no—
190C22×C11—24no—
191C22×C11—24no—
192C22×C11—24no—
193C22×C11—44no—
194C22×C11—44no—
195C22×C11—44no—
196C22×C11—44no—
197C22×C11—42no—
198C22×C11—42no—
199C22×C11—42no—
200C22×C11—42no—
201C22×C11#38611yescharacteristic
202C22×C11C2×#9912yes—
203C22×C11C2×#10311yescharacteristic
204C22×C11#41711yescharacteristic
205C22×C11#42112yes—
206C22×C11#45011yescharacteristic
207C22×C11#45111yescharacteristic
208C22×C11#48311yescharacteristic
209C22×C11#48411yescharacteristic
210C4×C11—24no—
211C4×C11—22no—
212C4×C11—22no—
213Dic11—84no—
214Dic11—81no—
215Dic11—81no—
216Dic11—82no—
217C25D4411yescharacteristic
218C22×Q8—111no—
219C23×C4—22no—
220C23×C4—22no—
221C23×C4—44no—
222C23×C4—222no—
223C23×C4C4×D1112yes—
224C23×C4D4411yescharacteristic
225C23×C4C22⋊D1112yes—
226C23×C4C22×D1111yescharacteristic
227C22×C8—22no—
228C22⋊Q8—222no—
229C22⋊Q8—222no—
230C22⋊Q8—444no—
231C2×C4⋊C4—111no—
232C2×C4⋊C4—112no—
233C2×C4⋊C4—224no—
234C2×C4⋊C4—222no—
235C2×C4⋊C4—221no—
236C2×C4⋊C4—444no—
237C2×C22⋊C4—224no—
238C2×C22⋊C4—222no—
239C2×C22⋊C4—222no—
240C2×C22⋊C4—221no—
241C2×C22⋊C4—221no—
242C2×C22⋊C4—442no—
243C2×C22⋊C4—442no—
244C22⋊C8—22no—
245C22⋊C8—22no—
246C22⋊C8—44no—
247#95—114no—
248#95—222no—
249#95—222no—
250#95—221no—
251C2×C11—21no—
252C2×C11—21no—
253C2×C11—21no—
254C2×C11—21no—
255C2×C11—44no—
256C2×C11#151312yes—
257C2×C11#152012yes—
258C2×C11#187211yescharacteristic
259C2×C11#189711yescharacteristic
260C2×C11#189811yescharacteristic
261C24—21no—
262C24—21no—
263C24—21no—
264C24—21no—
265C24—42no—
266C24—42no—
267C24#431412yes—
268C24Dic4412yes—
269C24(C2×D11)⋊C412yes—
270C24C2×D4411yescharacteristic
271C2×Q8—222no—
272C2×Q8—442no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—24no—
276C22×C4—24no—
277C22×C4—24no—
278C22×C4—24no—
279C22×C4—24no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—48no—
284C22×C4—48no—
285C22×C4—224no—
286C22×C4—222no—
287C22×C4—221no—
288C22×C4—221no—
289C22×C4—444no—
290C22×C4—444no—
291C22×C4—442no—
292C22×C4—442no—
293C22×C4(C2×D11)⋊C412yes—
294C22×C4C2×C4×D1111yescharacteristic
295C22×C4D4×D1112yes—
296C22×C4#434112yes—
297C22×C4C2×C22⋊D1111yescharacteristic
298C2×C8—44no—
299C2×C8—42no—
300C4⋊C4—222no—
301C4⋊C4—442no—
302C4⋊C4—448no—
303C4⋊C4—444no—
304C4⋊C4—442no—
305C22⋊C4—448no—
306C22⋊C4—444no—
307C22⋊C4—444no—
308C22⋊C4—441no—
309C22⋊C4—441no—
310C22⋊C4—441no—
311C22⋊C4—441no—
312C11#915111yescharacteristic, complemented, Sylow
313C23—22no—
314C23—22no—
315C23—22no—
316C23—22no—
317C23—22no—
318C23—22no—
319C23—22no—
320C23—22no—
321C23—22no—
322C23—22no—
323C23—22no—
324C23—22no—
325C23—44no—
326C23—44no—
327C23—42no—
328C23—42no—
329C23—42no—
330C23—42no—
331C23—44no—
332C23—44no—
333C23#6688014yes—
334C23#6693511yescharacteristic
335C23#6693911yescharacteristic
336C23C2×#431411yescharacteristic
337C23C2×Dic4411yescharacteristic
338C23#6696111yescharacteristic
339C23#6696211yescharacteristic
340C23C2×(C2×D11)⋊C411yescharacteristic
341Q8—882no—
342C2×C4—24no—
343C2×C4—24no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—48no—
351C2×C4—48no—
352C2×C4—444no—
353C2×C4—444no—
354C2×C4—442no—
355C2×C4—442no—
356C2×C4—442no—
357C2×C4—442no—
358C2×C4—442no—
359C2×C4—441no—
360C2×C4—441no—
361C2×C4—444no—
362C2×C4—884no—
363C2×C4—884no—
364C2×C4#6687014yes—
365C2×C4(C22⋊D11)⋊C412yes—
366C2×C4#6699212yes—
367C8—82no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—22no—
376C22—24no—
377C22—24no—
378C22—24no—
379C22—44no—
380C22—44no—
381C22—44no—
382C22—44no—
383C22—42no—
384C22—42no—
385C22—42no—
386C22—42no—
387C22#1062233411yescharacteristic
388C22#1062233511yescharacteristic
389C22#1062234411yescharacteristic
390C22#1062235211yescharacteristic
391C22C2×#6687012yes—
392C22#1062257111yescharacteristic
393C22C2×#6688011yescharacteristic
394C22#1062274611yescharacteristic
395C22#1062275212yes—
396C4—22no—
397C4—24no—
398C4—22no—
399C4—884no—
400C4—881no—
401C4—881no—
402C4—882no—
403C2—21no—
404C2—21no—
405C2—21no—
406C2—21no—
407C2—44no—
408C2#1306716012yes—
409C2#1306718912yes—
410C2#1306892111yescharacteristic
411C2#1306906211yescharacteristic
412C2#1306906711yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1779C2
socleC23×C11C2×C22⋊C4
prime radicalC25×C11D4
cosocleC23×C4×C11C23
hypercenter#1779D11
hypocenterC11#9151
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ #1779

Complements

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

NH ≅ G/Ntype
3. C2×#10622105C2semidirect
4. #13066496C2semidirect
9. C2×#66977C4semidirect
15. #10622825C4semidirect
312. C11#9151semidirect

Maximal subgroups

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

subgroupindex
#130769032
C2×#106228252
C2×#106221052
#130664962
C11×#17792
#915111