Finite Group Databasebeta

← #14649535

Subgroups — #14649535

Order 2816.

586 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076950C211yesmaximal, characteristic
2C2×#10622264C211yesmaximal, characteristic
3#13068682C211yesmaximal, characteristic
4C2×#10622176C211yesmaximal, characteristic
5#13066496C211yesmaximal, characteristic
6#13066495C211yesmaximal, characteristic
7C2×C11×#328C211yesmaximal, characteristic
8C2×C11×C22⋊Q8C2211yescharacteristic
9C22×C4×Dic11C2211yescharacteristic
10C2×C11×C22⋊C8C2211yescharacteristic
11C2×C11×#95C2211yescharacteristic
12#10622843C412yescomplemented
13#10622825C2211yescharacteristic
14C2×C11⋊#95—21no—
15C2×C11⋊#95—21no—
16C2×C11⋊#95C2211yescharacteristic
17C2×C22⋊(C11⋊C8)C2211yescharacteristic
18#10622591—22no—
19#10622586C412yescomplemented
20#10622559—21no—
21#10622556—21no—
22#10622264—22no—
23#10622264—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—21no—
45C2×C4×Dic11—21no—
46C2×C4×Dic11—21no—
47C2×C4×Dic11—21no—
48C2×C4×Dic11C2×C412yes—
49C2×C4×Dic11D412yes—
50C22×C11⋊C8—21no—
51C11×C22⋊C8—21no—
52C11×C22⋊C8—21no—
53C11×#95—21no—
54C11×#95D412yes—
55C11⋊#95—24no—
56C11⋊#95—24no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—22no—
60C11⋊#95—22no—
61C11⋊#95—22no—
62C11⋊#95D412yes—
63C22⋊(C11⋊C8)—21no—
64C22⋊(C11⋊C8)—21no—
65#9153—111nomaximal, Sylow
66C24×C11C2×D411yescharacteristic
67C2×Q8×C11—21no—
68C2×Q8×C11—21no—
69C2×Q8×C11—42no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—22no—
73C22×C4×C11—42no—
74C22×C4×C11—42no—
75C22×C4×C11—42no—
76C22×C4×C11—41no—
77C22×C4×C11—41no—
78C22×C4×C11C22×C411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11#4111yescharacteristic
83C22×C4×C11#4111yescharacteristic
84C22×Dic11—22no—
85C22×Dic11—21no—
86C22×Dic11—21no—
87C22×Dic11—22no—
88C22×Dic11—21no—
89C22×Dic11—21no—
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—
101C2×C8×C11—42no—
102C2×C8×C11—41no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C22⋊C4—41no—
108C11×C22⋊C4—41no—
109C22⋊Dic11—41no—
110C22⋊Dic11—41no—
111C4⋊Dic11—42no—
112Dic11⋊C4—44no—
113C4×Dic11—22no—
114C4×Dic11—22no—
115C4×Dic11—22no—
116C4×Dic11—22no—
117C2×C11⋊C8—42no—
118C2×C11⋊C8—41no—
119#2855—111no—
120C2×#383—111no—
121#1817—111no—
122C2×#328—111no—
123C2×#328D1111yescharacteristic
124#1294—111no—
125#1294—111no—
126C23×C11—22no—
127C23×C11—22no—
128C23×C11C2×C22⋊C411yescharacteristic
129C23×C11#12011yescharacteristic
130C23×C11#12311yescharacteristic
131C23×C11#13511yescharacteristic
132C23×C11#13511yescharacteristic
133C23×C11#13711yescharacteristic
134C23×C11#13711yescharacteristic
135Q8×C11—81no—
136Q8×C11—81no—
137C2×C4×C11—22no—
138C2×C4×C11—22no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
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—42no—
163C2×Dic11—42no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—42no—
169C2×Dic11—42no—
170C2×Dic11—42no—
171C2×Dic11—42no—
172C2×Dic11—42no—
173C2×Dic11—42no—
174C2×Dic11—82no—
175C2×Dic11—82no—
176C8×C11—81no—
177C11⋊C8—81no—
178C2×C22⋊Q8C2×D1111yescharacteristic
179C22×C42—111no—
180C2×C22⋊C8—111no—
181C2×C22⋊C8C2×D1111yescharacteristic
182#391—112no—
183#389—112no—
184#387—222no—
185#385—221no—
186#383—222no—
187#383—222no—
188#381—221no—
189#380—111no—
190C2×#95—111no—
191C2×#95—221no—
192C2×#95—221no—
193C2×#95C2×D1111yescharacteristic
194#336—222no—
195#328—22no—
196#328—222no—
197C22×C11—21no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11—22no—
202C22×C11—22no—
203C22×C11—22no—
204C22×C11—22no—
205C22×C11#38611yescharacteristic
206C22×C11#41012yes—
207C22×C11#41611yescharacteristic
208C22×C11#41911yescharacteristic
209C22×C11#42112yes—
210C22×C11#45211yescharacteristic
211C22×C11#45211yescharacteristic
212C22×C11#48511yescharacteristic
213C22×C11#48511yescharacteristic
214C4×C11—21no—
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—82no—
219C4×C11—81no—
220C4×C11—81no—
221Dic11—42no—
222Dic11—42no—
223Dic11—82no—
224Dic11—82no—
225C22×Q8C4×D1111yescharacteristic
226C23×C4—21no—
227C23×C4—111no—
228C23×C4—111no—
229C23×C4—221no—
230C23×C4C22×D1111yescharacteristic
231C22×C8—21no—
232C22×C8—221no—
233C22⋊Q8—21no—
234C22⋊Q8—21no—
235C22⋊Q8—21no—
236C22⋊Q8—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—112no—
239C2×C4⋊C4—222no—
240C2×C4⋊C4C4×D1111yescharacteristic
241C2×C22⋊C4—21no—
242C2×C22⋊C4—221no—
243C2×C42—112no—
244C2×C42—112no—
245C2×C42—221no—
246C2×C42—221no—
247C2×C42—221no—
248C2×C42—221no—
249C22⋊C8—21no—
250C22⋊C8—21no—
251C22⋊C8—221no—
252C22⋊C8—221no—
253#95—21no—
254#95—112no—
255#95—222no—
256#95—222no—
257#95—222no—
258#95—224no—
259#95—224no—
260#95—221no—
261#95—221no—
262#95C22⋊D1112yes—
263C2×C11—21no—
264C2×C11—21no—
265C2×C11—21no—
266C2×C11—21no—
267C2×C11#151512yes—
268C2×C11#152112yes—
269C2×C11#187311yescharacteristic
270C2×C11#189711yescharacteristic
271C2×C11#189911yescharacteristic
272C24D4×D1111yescharacteristic
273C2×Q8—21no—
274C2×Q8—21no—
275C2×Q8—42no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—22no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—112no—
285C22×C4—112no—
286C22×C4—221no—
287C22×C4—221no—
288C22×C4—221no—
289C22×C4—221no—
290C22×C4—221no—
291C22×C4—221no—
292C22×C4—221no—
293C22×C4—221no—
294C22×C4—222no—
295C22×C4—222no—
296C22×C4—442no—
297C22×C4—442no—
298C22×C4—442no—
299C22×C4—441no—
300C22×C4—441no—
301C22×C4C2×C4×D1111yescharacteristic
302C22×C4#433911yescharacteristic
303C22×C4D4×D1111yescharacteristic
304C22×C4D4×D1111yescharacteristic
305C22×C4#434111yescharacteristic
306C22×C4C2×C22⋊D1111yescharacteristic
307C2×C8—42no—
308C2×C8—41no—
309C2×C8—442no—
310C2×C8—441no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—442no—
316C4⋊C4—444no—
317C22⋊C4—41no—
318C22⋊C4—41no—
319C22⋊C4—441no—
320C22⋊C4—441no—
321C42—222no—
322C42—222no—
323C42—222no—
324C42—222no—
325C11#915311yescharacteristic, complemented, Sylow
326C23—22no—
327C23—22no—
328C23C22⋊C4×D1111yescharacteristic
329C23#6693611yescharacteristic
330C23#6696811yescharacteristic
331C23#6696911yescharacteristic
332C23#6697111yescharacteristic
333C23#6697211yescharacteristic
334C23#6699011yescharacteristic
335Q8—81no—
336Q8—81no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—82no—
351C2×C4—82no—
352C2×C4—222no—
353C2×C4—222no—
354C2×C4—222no—
355C2×C4—222no—
356C2×C4—222no—
357C2×C4—222no—
358C2×C4—442no—
359C2×C4—442no—
360C2×C4—441no—
361C2×C4—441no—
362C2×C4—441no—
363C2×C4—441no—
364C2×C4—442no—
365C2×C4—442no—
366C2×C4—442no—
367C2×C4—442no—
368C2×C4—442no—
369C2×C4—442no—
370C2×C4—882no—
371C2×C4—882no—
372C2×C4(C22⋊D11)⋊C411yescharacteristic
373C2×C4#6693711yescharacteristic
374C2×C4C4×C22⋊D1111yescharacteristic
375C2×C4#6699111yescharacteristic
376C8—81no—
377C8—881no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—22no—
383C22—22no—
384C22—22no—
385C22—22no—
386C22#1062235312yes—
387C22#1062241511yescharacteristic
388C22#1062241711yescharacteristic
389C22#1062242711yescharacteristic
390C22#1062242811yescharacteristic
391C22#1062243412yes—
392C22#1062256911yescharacteristic
393C22#1062278611yescharacteristic
394C22#1062280011yescharacteristic
395C4—21no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—82no—
400C4—81no—
401C4—81no—
402C4—442no—
403C4—442no—
404C4—882no—
405C4—882no—
406C2—21no—
407C2—21no—
408C2—21no—
409C2—21no—
410C2#1306716512yes—
411C2#1306719212yes—
412C2#1306892511yescharacteristic
413C2#1306906111yescharacteristic
414C2#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#9153
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
12. #10622843C4semidirect
19. #10622586C4semidirect
325. C11#9153semidirect

Maximal subgroups

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

subgroupindex
#130769502
C2×#106222642
#130686822
C2×#106221762
#130664962
#130664952
C2×C11×#3282
#915311