Finite Group Databasebeta

← #14649495

Subgroups — #14649495

Order 2816.

694 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076950C211yesmaximal, characteristic
2C2×#10622261C211yesmaximal, characteristic
3#13068682C211yesmaximal, characteristic
4C2×#10622176C211yesmaximal, characteristic
5#13066496C211yesmaximal, characteristic
6#13066495C211yesmaximal, characteristic
7C2×C11×#328C211yesmaximal, characteristic
8C2×C11×C22⋊Q8C2211yescharacteristic
9C22×C4×Dic11—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#10622261—22no—
23#10622261—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—22no—
44C2×C4×Dic11—24no—
45C2×C4×Dic11—28no—
46C2×C4×Dic11—21no—
47C2×C4×Dic11—21no—
48C2×C4×Dic11—21no—
49C2×C4×Dic11—21no—
50C2×C4×Dic11C2×C412yes—
51C2×C4×Dic11D412yes—
52C22×C11⋊C8—21no—
53C11×C22⋊C8—21no—
54C11×C22⋊C8—21no—
55C11×#95—21no—
56C11×#95D412yes—
57C11⋊#95—24no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—22no—
61C11⋊#95—22no—
62C11⋊#95—22no—
63C11⋊#95D412yes—
64C22⋊(C11⋊C8)—21no—
65C22⋊(C11⋊C8)—21no—
66#9145—111nomaximal, Sylow
67C24×C11C2×D411yescharacteristic
68C2×Q8×C11—21no—
69C2×Q8×C11—21no—
70C2×Q8×C11—42no—
71C22×C4×C11—24no—
72C22×C4×C11—22no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—42no—
76C22×C4×C11—42no—
77C22×C4×C11—41no—
78C22×C4×C11—41no—
79C22×C4×C11C22×C411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11#4111yescharacteristic
84C22×C4×C11#4111yescharacteristic
85C22×Dic11—24no—
86C22×Dic11—24no—
87C22×Dic11—22no—
88C22×Dic11—21no—
89C22×Dic11—21no—
90C22×Dic11—22no—
91C22×Dic11—21no—
92C22×Dic11—21no—
93C22×Dic11—21no—
94C22×Dic11—21no—
95C22×Dic11—21no—
96C22×Dic11—21no—
97C22×Dic11—42no—
98C22×Dic11—41no—
99C22×Dic11—41no—
100C22×Dic11C22⋊C412yes—
101C22×Dic11C22⋊C412yes—
102C2×C8×C11—42no—
103C2×C8×C11—41no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C22⋊C4—41no—
109C11×C22⋊C4—41no—
110C22⋊Dic11—41no—
111C22⋊Dic11—41no—
112C4⋊Dic11—42no—
113Dic11⋊C4—44no—
114C4×Dic11—216no—
115C4×Dic11—22no—
116C4×Dic11—22no—
117C4×Dic11—22no—
118C4×Dic11—22no—
119C2×C11⋊C8—42no—
120C2×C11⋊C8—41no—
121#2855—111no—
122C2×#376—111no—
123#1817—111no—
124C2×#328—111no—
125C2×#328D1111yescharacteristic
126#1294—111no—
127#1294—111no—
128C23×C11—22no—
129C23×C11—22no—
130C23×C11C2×C22⋊C411yescharacteristic
131C23×C11#12011yescharacteristic
132C23×C11#12311yescharacteristic
133C23×C11#13511yescharacteristic
134C23×C11#13511yescharacteristic
135C23×C11#13711yescharacteristic
136C23×C11#13711yescharacteristic
137Q8×C11—81no—
138Q8×C11—81no—
139C2×C4×C11—22no—
140C2×C4×C11—22no—
141C2×C4×C11—24no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—42no—
147C2×C4×C11—44no—
148C2×C4×C11—44no—
149C2×C4×C11—42no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11C4×D411yescharacteristic
155C2×C4×C11C4×D411yescharacteristic
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×Dic11—24no—
159C2×Dic11—24no—
160C2×Dic11—22no—
161C2×Dic11—22no—
162C2×Dic11—24no—
163C2×Dic11—22no—
164C2×Dic11—22no—
165C2×Dic11—22no—
166C2×Dic11—42no—
167C2×Dic11—44no—
168C2×Dic11—44no—
169C2×Dic11—41no—
170C2×Dic11—41no—
171C2×Dic11—42no—
172C2×Dic11—41no—
173C2×Dic11—41no—
174C2×Dic11—42no—
175C2×Dic11—42no—
176C2×Dic11—42no—
177C2×Dic11#10414yes—
178C8×C11—81no—
179C11⋊C8—81no—
180C2×C22⋊Q8C2×D1111yescharacteristic
181C22×C42—111no—
182C22×C42—221no—
183C2×C22⋊C8—111no—
184C2×C22⋊C8C2×D1111yescharacteristic
185#391—112no—
186#389—112no—
187#387—222no—
188#385—221no—
189#381—221no—
190#380—111no—
191#376—222no—
192#376—222no—
193C2×#95—111no—
194C2×#95—221no—
195C2×#95C2×D1111yescharacteristic
196#336—222no—
197#328—22no—
198#328—222no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11—22no—
204C22×C11—22no—
205C22×C11—22no—
206C22×C11—22no—
207C22×C11#38611yescharacteristic
208C22×C11#41012yes—
209C22×C11#41611yescharacteristic
210C22×C11#41911yescharacteristic
211C22×C11C2×#10412yes—
212C22×C11#45211yescharacteristic
213C22×C11#45211yescharacteristic
214C22×C11#48511yescharacteristic
215C22×C11#48511yescharacteristic
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—21no—
219C4×C11—21no—
220C4×C11—44no—
221C4×C11—81no—
222C4×C11—81no—
223Dic11—24no—
224Dic11—44no—
225Dic11—42no—
226Dic11—82no—
227C22×Q8C4×D1111yescharacteristic
228C23×C4—21no—
229C23×C4—111no—
230C23×C4—111no—
231C23×C4—221no—
232C23×C4C22×D1111yescharacteristic
233C22×C8—21no—
234C22×C8—221no—
235C22⋊Q8—21no—
236C22⋊Q8—21no—
237C22⋊Q8—21no—
238C22⋊Q8—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—112no—
241C2×C4⋊C4—222no—
242C2×C4⋊C4C4×D1111yescharacteristic
243C2×C22⋊C4—21no—
244C2×C22⋊C4—221no—
245C2×C42—112no—
246C2×C42—112no—
247C2×C42—224no—
248C2×C42—228no—
249C2×C42—221no—
250C2×C42—221no—
251C2×C42—221no—
252C2×C42—221no—
253C22⋊C8—21no—
254C22⋊C8—21no—
255C22⋊C8—221no—
256C22⋊C8—221no—
257#95—21no—
258#95—112no—
259#95—222no—
260#95—222no—
261#95—222no—
262#95—224no—
263#95—221no—
264#95—221no—
265#95C22⋊D1112yes—
266C2×C11—21no—
267C2×C11—21no—
268C2×C11—21no—
269C2×C11—21no—
270C2×C11#150012yes—
271C2×C11#150612yes—
272C2×C11#187311yescharacteristic
273C2×C11#189611yescharacteristic
274C2×C11#189911yescharacteristic
275C24D4×D1111yescharacteristic
276C2×Q8—21no—
277C2×Q8—21no—
278C2×Q8—42no—
279C22×C4—24no—
280C22×C4—22no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—112no—
288C22×C4—112no—
289C22×C4—224no—
290C22×C4—221no—
291C22×C4—221no—
292C22×C4—224no—
293C22×C4—221no—
294C22×C4—221no—
295C22×C4—221no—
296C22×C4—221no—
297C22×C4—221no—
298C22×C4—222no—
299C22×C4—221no—
300C22×C4—222no—
301C22×C4—442no—
302C22×C4—441no—
303C22×C4—441no—
304C22×C4C2×C4×D1111yescharacteristic
305C22×C4#433911yescharacteristic
306C22×C4D4×D1111yescharacteristic
307C22×C4D4×D1111yescharacteristic
308C22×C4#434111yescharacteristic
309C22×C4C2×C22⋊D1111yescharacteristic
310C2×C8—42no—
311C2×C8—41no—
312C2×C8—442no—
313C2×C8—441no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—442no—
319C4⋊C4—444no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—441no—
323C22⋊C4—441no—
324C42—2216no—
325C42—222no—
326C42—222no—
327C42—222no—
328C42—222no—
329C11#914511yescharacteristic, complemented, Sylow
330C23—22no—
331C23—22no—
332C23C22⋊C4×D1111yescharacteristic
333C23#6693611yescharacteristic
334C23#6696811yescharacteristic
335C23#6696911yescharacteristic
336C23#6697111yescharacteristic
337C23#6697211yescharacteristic
338C23#6699011yescharacteristic
339Q8—81no—
340Q8—81no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—24no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—44no—
350C2×C4—44no—
351C2×C4—42no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—114no—
357C2×C4—224no—
358C2×C4—224no—
359C2×C4—222no—
360C2×C4—222no—
361C2×C4—224no—
362C2×C4—222no—
363C2×C4—222no—
364C2×C4—222no—
365C2×C4—442no—
366C2×C4—444no—
367C2×C4—444no—
368C2×C4—441no—
369C2×C4—441no—
370C2×C4—442no—
371C2×C4—441no—
372C2×C4—441no—
373C2×C4—442no—
374C2×C4—442no—
375C2×C4—442no—
376C2×C4(C22⋊D11)⋊C411yescharacteristic
377C2×C4#6693711yescharacteristic
378C2×C4C4×C22⋊D1111yescharacteristic
379C2×C4#6699111yescharacteristic
380C8—81no—
381C8—881no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—22no—
387C22—22no—
388C22—22no—
389C22—22no—
390C22#1062235312yes—
391C22#1062241511yescharacteristic
392C22#1062241711yescharacteristic
393C22#1062242711yescharacteristic
394C22#1062242811yescharacteristic
395C22D11×#10412yes—
396C22#1062256911yescharacteristic
397C22#1062278611yescharacteristic
398C22#1062280011yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—44no—
404C4—81no—
405C4—81no—
406C4—224no—
407C4—444no—
408C4—442no—
409C4—882no—
410C2—21no—
411C2—21no—
412C2—21no—
413C2—21no—
414C2#1306710112yes—
415C2#1306712612yes—
416C2#1306892511yescharacteristic
417C2#1306905611yescharacteristic
418C2#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#9145
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
329. C11#9145semidirect

Maximal subgroups

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

subgroupindex
#130769502
C2×#106222612
#130686822
C2×#106221762
#130664962
#130664952
C2×C11×#3282
#914511