Finite Group Databasebeta

← #14649532

Subgroups — #14649532

Order 2816.

630 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#13076956C211yesmaximal, characteristic
2C2×#10622263C211yesmaximal, characteristic
3#13068682C211yesmaximal, characteristic
4C2×#10622105C211yesmaximal, characteristic
5C2×#10622090C211yesmaximal, characteristic
6#13066494C211yesmaximal, characteristic
7C11×#1294C211yesmaximal, characteristic
8C2×#66977C2211yescharacteristic
9C22×Dic11⋊C4—21no—
10C22×C4×Dic11C2211yescharacteristic
11C2×C11×C22⋊C8C2211yescharacteristic
12C11×#380C2211yescharacteristic
13C2×C11×#95C2211yescharacteristic
14C2×C11⋊#95—21no—
15C2×C11⋊#95C2211yescharacteristic
16C2×C22⋊(C11⋊C8)C2211yescharacteristic
17#10622598C412yescomplemented
18#10622587C412yescomplemented
19#10622563—21no—
20#10622556—21no—
21#10622266—22no—
22#10622263—22no—
23#10622263—22no—
24#10622188—22no—
25#10622105—22no—
26#10622090—22no—
27C23×C4×C11—21no—
28C23×C4×C11C2311yescharacteristic
29C23×Dic11—21no—
30C23×Dic11D411yescharacteristic
31C23×Dic11D411yescharacteristic
32C22×Dic22C2×C411yescharacteristic
33C22×C8×C11—21no—
34C2×C11×C4⋊C4C2×C412yes—
35C2×C11×C22⋊C4—21no—
36C2×C22⋊Dic11—21no—
37C2×C4⋊Dic11—22no—
38C2×C4⋊Dic11C2×C411yescharacteristic
39#66977—21no—
40#66977—21no—
41#66977—21no—
42#66977—21no—
43C2×Dic11⋊C4—24no—
44C2×Dic11⋊C4—21no—
45C2×Dic11⋊C4—42no—
46C2×Dic11⋊C4—42no—
47C2×C4×Dic11—21no—
48C2×C4×Dic11—21no—
49C2×C4×Dic11—21no—
50C2×C4×Dic11—21no—
51C2×C4×Dic11C2×C412yes—
52C2×C4×Dic11D412yes—
53C22×C11⋊C8—21no—
54C11×C22⋊C8—21no—
55C11×C22⋊C8—21no—
56C11×#95—21no—
57C11×#95—21no—
58C11×#95D412yes—
59C11⋊#95—24no—
60C11⋊#95—21no—
61C11⋊#95—22no—
62C11⋊#95—22no—
63C11⋊#95—22no—
64C11⋊#95D412yes—
65C22⋊(C11⋊C8)—21no—
66C22⋊(C11⋊C8)—21no—
67#9152—111nomaximal, Sylow
68C24×C11C2×D411yescharacteristic
69C22×C4×C11—22no—
70C22×C4×C11—22no—
71C22×C4×C11—42no—
72C22×C4×C11—42no—
73C22×C4×C11—42no—
74C22×C4×C11—41no—
75C22×C4×C11—41no—
76C22×C4×C11C22×C411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11#4111yescharacteristic
81C22×C4×C11#4111yescharacteristic
82C22×Dic11—21no—
83C22×Dic11—21no—
84C22×Dic11—21no—
85C22×Dic11—21no—
86C22×Dic11—22no—
87C22×Dic11—21no—
88C22×Dic11—21no—
89C22×Dic11—21no—
90C22×Dic11—21no—
91C22×Dic11—42no—
92C22×Dic11—42no—
93C22×Dic11—42no—
94C22×Dic11—41no—
95C22×Dic11—41no—
96C22×Dic11C22⋊C412yes—
97C22×Dic11C22⋊C412yes—
98C22×Dic11SD1612yes—
99C22×Dic11Q1612yes—
100C2×Dic22—21no—
101C2×Dic22—21no—
102C2×Dic22—42no—
103C2×C8×C11—42no—
104C2×C8×C11—41no—
105C11×C4⋊C4—42no—
106C11×C22⋊C4—41no—
107C11×C22⋊C4—41no—
108C22⋊Dic11—41no—
109C22⋊Dic11—41no—
110C4⋊Dic11—21no—
111C4⋊Dic11—21no—
112C4⋊Dic11—44no—
113Dic11⋊C4—48no—
114Dic11⋊C4—41no—
115Dic11⋊C4—41no—
116C4×Dic11—22no—
117C4×Dic11—22no—
118C4×Dic11—22no—
119C4×Dic11—22no—
120C2×C11⋊C8—42no—
121C2×C11⋊C8—41no—
122#2855—111no—
123C2×#382—111no—
124#1817—111no—
125C2×#328—111no—
126C2×#328—111no—
127#1294—111no—
128#1294D1111yescharacteristic
129C23×C11—22no—
130C23×C11—22no—
131C23×C11C2×C22⋊C411yescharacteristic
132C23×C11#12011yescharacteristic
133C23×C11#12311yescharacteristic
134C23×C11C2×SD1611yescharacteristic
135C23×C11C2×Q1611yescharacteristic
136C23×C11AGL(1,ℤ/8)11yescharacteristic
137C23×C11#13711yescharacteristic
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—42no—
145C2×C4×C11—42no—
146C2×C4×C11—42no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11—82no—
151C2×C4×C11—82no—
152C2×C4×C11C4×D411yescharacteristic
153C2×C4×C11C4×D411yescharacteristic
154C2×C4×C11#12111yescharacteristic
155C2×C4×C11#12111yescharacteristic
156C2×Dic11—22no—
157C2×Dic11—22no—
158C2×Dic11—22no—
159C2×Dic11—22no—
160C2×Dic11—22no—
161C2×Dic11—22no—
162C2×Dic11—22no—
163C2×Dic11—22no—
164C2×Dic11—22no—
165C2×Dic11—42no—
166C2×Dic11—42no—
167C2×Dic11—42no—
168C2×Dic11—42no—
169C2×Dic11—41no—
170C2×Dic11—41no—
171C2×Dic11—42no—
172C2×Dic11—42no—
173C2×Dic11—42no—
174C2×Dic11—82no—
175C2×Dic11—82no—
176C2×Dic11#10314yes—
177Dic22—81no—
178Dic22—81no—
179C8×C11—81no—
180C11⋊C8—81no—
181C2×C22⋊Q8—111no—
182C22×C4⋊C4—221no—
183C22×C42—111no—
184C2×C22⋊C8—111no—
185C2×C22⋊C8C2×D1111yescharacteristic
186#391—112no—
187#389—112no—
188#387—222no—
189#385—221no—
190#382—222no—
191#382—222no—
192#381—221no—
193#380C2×D1111yescharacteristic
194C2×#95—111no—
195C2×#95—221no—
196C2×#95C2×D1111yescharacteristic
197#336—222no—
198#328—222no—
199#328—222no—
200C22×C11—21no—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11—21no—
204C22×C11—22no—
205C22×C11—22no—
206C22×C11—22no—
207C22×C11—22no—
208C22×C11#38611yescharacteristic
209C22×C11#41012yes—
210C22×C11C2×#10311yescharacteristic
211C22×C11#41711yescharacteristic
212C22×C11#42112yes—
213C22×C11#45011yescharacteristic
214C22×C11#45111yescharacteristic
215C22×C11#48311yescharacteristic
216C22×C11#48411yescharacteristic
217C4×C11—21no—
218C4×C11—21no—
219C4×C11—21no—
220C4×C11—21no—
221C4×C11—82no—
222C4×C11—82no—
223Dic11—24no—
224Dic11—42no—
225Dic11—82no—
226Dic11—81no—
227Dic11—81no—
228C22×Q8—111no—
229C23×C4—21no—
230C23×C4—111no—
231C23×C4—111no—
232C23×C4—221no—
233C23×C4C22×D1111yescharacteristic
234C22×C8—21no—
235C22×C8—221no—
236C22⋊Q8—221no—
237C22⋊Q8—221no—
238C22⋊Q8—221no—
239C22⋊Q8—221no—
240C2×C4⋊C4—111no—
241C2×C4⋊C4—222no—
242C2×C4⋊C4—224no—
243C2×C4⋊C4—221no—
244C2×C4⋊C4—442no—
245C2×C4⋊C4—442no—
246C2×C4⋊C4C4×D1112yes—
247C2×C22⋊C4—21no—
248C2×C22⋊C4—221no—
249C2×C42—112no—
250C2×C42—112no—
251C2×C42—221no—
252C2×C42—221no—
253C2×C42—221no—
254C2×C42—221no—
255C22⋊C8—21no—
256C22⋊C8—21no—
257C22⋊C8—221no—
258C22⋊C8—221no—
259#95—21no—
260#95—21no—
261#95—112no—
262#95—222no—
263#95—222no—
264#95—222no—
265#95—224no—
266#95—221no—
267#95D4412yes—
268C2×C11—21no—
269C2×C11—21no—
270C2×C11—21no—
271C2×C11—21no—
272C2×C11#151212yes—
273C2×C11#151812yes—
274C2×C11#187211yescharacteristic
275C2×C11#189711yescharacteristic
276C2×C11#189911yescharacteristic
277C24D4×D1111yescharacteristic
278C2×Q8—221no—
279C2×Q8—221no—
280C2×Q8—442no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—112no—
289C22×C4—112no—
290C22×C4—112no—
291C22×C4—112no—
292C22×C4—221no—
293C22×C4—221no—
294C22×C4—221no—
295C22×C4—221no—
296C22×C4—221no—
297C22×C4—221no—
298C22×C4—221no—
299C22×C4—221no—
300C22×C4—222no—
301C22×C4—442no—
302C22×C4—442no—
303C22×C4—442no—
304C22×C4—441no—
305C22×C4—441no—
306C22×C4C2×C4×D1111yescharacteristic
307C22×C4C2×D4411yescharacteristic
308C22×C4#433911yescharacteristic
309C22×C4D4×D1111yescharacteristic
310C22×C4D4×D1111yescharacteristic
311C22×C4#434311yescharacteristic
312C2×C8—42no—
313C2×C8—41no—
314C2×C8—442no—
315C2×C8—441no—
316C4⋊C4—42no—
317C4⋊C4—221no—
318C4⋊C4—221no—
319C4⋊C4—448no—
320C4⋊C4—444no—
321C4⋊C4—441no—
322C4⋊C4—441no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—441no—
326C22⋊C4—441no—
327C42—222no—
328C42—222no—
329C42—222no—
330C42—222no—
331C11#915211yescharacteristic, complemented, Sylow
332C23—22no—
333C23—22no—
334C23C22⋊C4×D1111yescharacteristic
335C23#6693511yescharacteristic
336C23#6694711yescharacteristic
337C23#6696411yescharacteristic
338C23SD16×D1111yescharacteristic
339C23#6696811yescharacteristic
340C23Q16×D1111yescharacteristic
341Q8—881no—
342Q8—881no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—82no—
356C2×C4—82no—
357C2×C4—114no—
358C2×C4—222no—
359C2×C4—222no—
360C2×C4—222no—
361C2×C4—222no—
362C2×C4—222no—
363C2×C4—222no—
364C2×C4—222no—
365C2×C4—222no—
366C2×C4—222no—
367C2×C4—442no—
368C2×C4—442no—
369C2×C4—442no—
370C2×C4—442no—
371C2×C4—441no—
372C2×C4—441no—
373C2×C4—442no—
374C2×C4—442no—
375C2×C4—442no—
376C2×C4—882no—
377C2×C4—882no—
378C2×C4C4×D4411yescharacteristic
379C2×C4#6693711yescharacteristic
380C2×C4#6694611yescharacteristic
381C2×C4#6694811yescharacteristic
382C8—81no—
383C8—881no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—22no—
389C22—22no—
390C22—22no—
391C22—22no—
392C22#1062227811yescharacteristic
393C22#1062235312yes—
394C22#1062238411yescharacteristic
395C22#1062238911yescharacteristic
396C22D11×#10311yescharacteristic
397C22#1062242111yescharacteristic
398C22#1062243412yes—
399C22#1062247511yescharacteristic
400C22#1062249711yescharacteristic
401C4—21no—
402C4—21no—
403C4—21no—
404C4—21no—
405C4—82no—
406C4—82no—
407C4—224no—
408C4—442no—
409C4—882no—
410C4—881no—
411C4—881no—
412C2—21no—
413C2—21no—
414C2—21no—
415C2—21no—
416C2#1306715112yes—
417C2#1306717812yes—
418C2#1306892211yescharacteristic
419C2#1306906311yescharacteristic
420C2#1306907311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1294C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#1294D11
hypocenterC11#9152
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
17. #10622598C4semidirect
18. #10622587C4semidirect
331. C11#9152semidirect

Maximal subgroups

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

subgroupindex
#130769562
C2×#106222632
#130686822
C2×#106221052
C2×#106220902
#130664942
C11×#12942
#915211