Finite Group Databasebeta

← #14649530

Subgroups — #14649530

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#13076950C211yesmaximal, characteristic
2C2×#10622263C211yesmaximal, characteristic
3#13068682C211yesmaximal, characteristic
4C2×#10622176C211yesmaximal, characteristic
5#13066496C211yesmaximal, characteristic
6#13066495C211yesmaximal, characteristic
7C2×C11×#328C211yesmaximal, characteristic
8C2×C11×C22⋊Q8C2211yescharacteristic
9C22×Dic11⋊C4—21no—
10C22×C4×Dic11C2211yescharacteristic
11C2×C11×C22⋊C8C2211yescharacteristic
12C2×C11×#95C2211yescharacteristic
13#10622843C412yescomplemented
14#10622825C2211yescharacteristic
15C2×C11⋊#95—21no—
16C2×C11⋊#95C2211yescharacteristic
17C2×C22⋊(C11⋊C8)C2211yescharacteristic
18#10622591—22no—
19#10622586C412yescomplemented
20#10622559—21no—
21#10622556—21no—
22#10622263—22no—
23#10622263—22no—
24C11×#328—22no—
25#10622188—22no—
26#10622176—22no—
27C22×Q8×C11C2×C411yescharacteristic
28C23×C4×C11—21no—
29C23×C4×C11C2311yescharacteristic
30C23×Dic11—21no—
31C23×Dic11D411yescharacteristic
32C23×Dic11D411yescharacteristic
33C22×C8×C11—21no—
34C11×C22⋊Q8—21no—
35C11×C22⋊Q8—21no—
36C11×C22⋊Q8—21no—
37C11×C22⋊Q8—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4C2×C411yescharacteristic
40C2×C11×C22⋊C4—21no—
41C2×C22⋊Dic11—21no—
42C2×C4⋊Dic11C2×C412yes—
43C2×Dic11⋊C4—24no—
44C2×Dic11⋊C4—22no—
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×#95D412yes—
58C11⋊#95—24no—
59C11⋊#95—21no—
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
69C2×Q8×C11—21no—
70C2×Q8×C11—21no—
71C2×Q8×C11—42no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—22no—
75C22×C4×C11—42no—
76C22×C4×C11—42no—
77C22×C4×C11—42no—
78C22×C4×C11—41no—
79C22×C4×C11—41no—
80C22×C4×C11C22×C411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11#4111yescharacteristic
85C22×C4×C11#4111yescharacteristic
86C22×Dic11—22no—
87C22×Dic11—21no—
88C22×Dic11—21no—
89C22×Dic11—22no—
90C22×Dic11—21no—
91C22×Dic11—21no—
92C22×Dic11—21no—
93C22×Dic11—21no—
94C22×Dic11—42no—
95C22×Dic11—42no—
96C22×Dic11—42no—
97C22×Dic11—41no—
98C22×Dic11—41no—
99C22×Dic11C22⋊C412yes—
100C22×Dic11C22⋊C412yes—
101C22×Dic11SD1612yes—
102C22×Dic11Q1612yes—
103C2×C8×C11—42no—
104C2×C8×C11—41no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C22⋊C4—41no—
110C11×C22⋊C4—41no—
111C22⋊Dic11—41no—
112C22⋊Dic11—41no—
113C4⋊Dic11—42no—
114Dic11⋊C4—44no—
115Dic11⋊C4—48no—
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×#328D1111yescharacteristic
127#1294—111no—
128#1294—111no—
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
138Q8×C11—81no—
139Q8×C11—81no—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—42no—
147C2×C4×C11—42no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—82no—
154C2×C4×C11—82no—
155C2×C4×C11C4×D411yescharacteristic
156C2×C4×C11C4×D411yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12111yescharacteristic
159C2×Dic11—22no—
160C2×Dic11—22no—
161C2×Dic11—22no—
162C2×Dic11—22no—
163C2×Dic11—22no—
164C2×Dic11—22no—
165C2×Dic11—22no—
166C2×Dic11—22no—
167C2×Dic11—22no—
168C2×Dic11—42no—
169C2×Dic11—42no—
170C2×Dic11—42no—
171C2×Dic11—42no—
172C2×Dic11—42no—
173C2×Dic11—42no—
174C2×Dic11—42no—
175C2×Dic11—42no—
176C2×Dic11—82no—
177C2×Dic11—82no—
178C2×Dic11#10314yes—
179C8×C11—81no—
180C11⋊C8—81no—
181C2×C22⋊Q8C2×D1111yescharacteristic
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#380—111no—
194C2×#95—111no—
195C2×#95—221no—
196C2×#95C2×D1111yescharacteristic
197#336—222no—
198#328—22no—
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—81no—
223C4×C11—81no—
224Dic11—24no—
225Dic11—42no—
226Dic11—82no—
227Dic11—82no—
228C22×Q8C4×D1111yescharacteristic
229C23×C4—21no—
230C23×C4—111no—
231C23×C4—111no—
232C23×C4—221no—
233C23×C4C22×D1111yescharacteristic
234C22×C8—21no—
235C22×C8—221no—
236C22⋊Q8—21no—
237C22⋊Q8—21no—
238C22⋊Q8—21no—
239C22⋊Q8—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—112no—
242C2×C4⋊C4—222no—
243C2×C4⋊C4—224no—
244C2×C4⋊C4—442no—
245C2×C4⋊C4—442no—
246C2×C4⋊C4C4×D1111yescharacteristic
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—112no—
261#95—222no—
262#95—222no—
263#95—222no—
264#95—224no—
265#95—221no—
266#95—221no—
267#95C22⋊D1112yes—
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—21no—
279C2×Q8—21no—
280C2×Q8—42no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—22no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—112no—
290C22×C4—112no—
291C22×C4—112no—
292C22×C4—112no—
293C22×C4—221no—
294C22×C4—221no—
295C22×C4—221no—
296C22×C4—221no—
297C22×C4—221no—
298C22×C4—221no—
299C22×C4—222no—
300C22×C4—222no—
301C22×C4—442no—
302C22×C4—442no—
303C22×C4—442no—
304C22×C4—441no—
305C22×C4—441no—
306C22×C4C2×C4×D1111yescharacteristic
307C22×C4#433911yescharacteristic
308C22×C4D4×D1111yescharacteristic
309C22×C4D4×D1111yescharacteristic
310C22×C4#434111yescharacteristic
311C22×C4C2×C22⋊D1111yescharacteristic
312C2×C8—42no—
313C2×C8—41no—
314C2×C8—442no—
315C2×C8—441no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—442no—
321C4⋊C4—448no—
322C4⋊C4—444no—
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#6693611yescharacteristic
336C23SD16×D1111yescharacteristic
337C23#6696711yescharacteristic
338C23Q16×D1111yescharacteristic
339C23#6697111yescharacteristic
340C23#6699011yescharacteristic
341Q8—81no—
342Q8—81no—
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—41no—
353C2×C4—41no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—82no—
357C2×C4—82no—
358C2×C4—114no—
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—222no—
368C2×C4—442no—
369C2×C4—442no—
370C2×C4—442no—
371C2×C4—442no—
372C2×C4—442no—
373C2×C4—442no—
374C2×C4—442no—
375C2×C4—442no—
376C2×C4—882no—
377C2×C4—882no—
378C2×C4(C22⋊D11)⋊C411yescharacteristic
379C2×C4#6693711yescharacteristic
380C2×C4C4×C22⋊D1111yescharacteristic
381C2×C4#6699111yescharacteristic
382C8—81no—
383C8—881no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—22no—
389C22—22no—
390C22—22no—
391C22—22no—
392C22#1062235312yes—
393C22D11×#10311yescharacteristic
394C22#1062241611yescharacteristic
395C22#1062241811yescharacteristic
396C22#1062242211yescharacteristic
397C22#1062243412yes—
398C22#1062256911yescharacteristic
399C22#1062278211yescharacteristic
400C22#1062279911yescharacteristic
401C4—21no—
402C4—21no—
403C4—21no—
404C4—21no—
405C4—82no—
406C4—81no—
407C4—81no—
408C4—224no—
409C4—442no—
410C4—882no—
411C4—882no—
412C2—21no—
413C2—21no—
414C2—21no—
415C2—21no—
416C2#1306715312yes—
417C2#1306717812yes—
418C2#1306892011yescharacteristic
419C2#1306906111yescharacteristic
420C2#1306907111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#328C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenterC2×#328D11
hypocenterC11#9152
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
13. #10622843C4semidirect
19. #10622586C4semidirect
331. C11#9152semidirect

Maximal subgroups

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

subgroupindex
#130769502
C2×#106222632
#130686822
C2×#106221762
#130664962
#130664952
C2×C11×#3282
#915211