Finite Group Databasebeta

← #14653824

Subgroups — #14653824

Order 2816.

556 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622546C211yesmaximal, characteristic
2#13068378C211yesmaximal, characteristic
3#13066458C212yesmaximal
4#13066458C212yesmaximal
5C11×#1797C211yesmaximal, characteristic
6C22×C42×C11C2211yescharacteristic
7C22×Dic11⋊C4C411yescharacteristic
8C22×Dic11⋊C4C411yescharacteristic
9C2×C11×C4⋊C8—21no—
10C2×C11×C22⋊C8C2212yes—
11C2×C11⋊#95C411yescharacteristic
12C2×C11⋊#95C411yescharacteristic
13C2×C11⋊#95C2211yescharacteristic
14C2×C11⋊#95C2211yescharacteristic
15C2×C22⋊(C11⋊C8)C2212yes—
16#10622546—21no—
17#10622546—21no—
18#10622546—21no—
19#10622546—21no—
20C2×#66867—21no—
21C11×#336—21no—
22#10622162—21no—
23C23×C4×C11C2×C411yescharacteristic
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11C2311yescharacteristic
26C23×Dic11C2×C411yescharacteristic
27C23×Dic11C2×C411yescharacteristic
28C23×Dic11C2×C411yescharacteristic
29C23×Dic11C2×C411yescharacteristic
30C22×C8×C11—22no—
31C2×C42×C11—42no—
32C2×C42×C11D411yescharacteristic
33C2×C42×C11D411yescharacteristic
34C2×C42×C11D411yescharacteristic
35C2×C42×C11D411yescharacteristic
36C2×Dic11⋊C4—21no—
37C2×Dic11⋊C4—21no—
38C2×Dic11⋊C4—22no—
39C2×Dic11⋊C4—22no—
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—42no—
43C22×C11⋊C8—22no—
44C11×C4⋊C8—42no—
45C11×C22⋊C8—24no—
46C11⋊#95—21no—
47C11⋊#95—21no—
48C11⋊#95—21no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C22⋊(C11⋊C8)—22no—
55C22⋊(C11⋊C8)Q814yes—
56#66867—42no—
57#9881—111nomaximal, Sylow
58C24×C11C22×C411yescharacteristic
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—22no—
62C22×C4×C11—22no—
63C22×C4×C11—41no—
64C22×C4×C11—41no—
65C22×C4×C11—41no—
66C22×C4×C11—41no—
67C22×C4×C11—41no—
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×Q812yes—
75C22×C4×C11#4112yes—
76C22×Dic11—21no—
77C22×Dic11—21no—
78C22×Dic11—21no—
79C22×Dic11—21no—
80C22×Dic11—21no—
81C22×Dic11—21no—
82C22×Dic11—22no—
83C22×Dic11—22no—
84C22×Dic11—41no—
85C22×Dic11—41no—
86C22×Dic11—41no—
87C22×Dic11—41no—
88C22×Dic11—41no—
89C22×Dic11—41no—
90C22×Dic11—41no—
91C22×Dic11—41no—
92C22×Dic11M1612yes—
93C22×Dic11M1612yes—
94C2×C8×C11—42no—
95C2×C8×C11—42no—
96C2×C8×C11—42no—
97C42×C11—22no—
98C42×C11—22no—
99C42×C11—41no—
100C42×C11—41no—
101Dic11⋊C4—24no—
102Dic11⋊C4—24no—
103Dic11⋊C4—42no—
104Dic11⋊C4—42no—
105C2×C11⋊C8—24no—
106C2×C11⋊C8—42no—
107C2×C11⋊C8—42no—
108C2×#387—111no—
109#1797D1111yescharacteristic
110#1749—111no—
111#1280—112no—
112#1280—112no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—21no—
117C23×C11C2×C22⋊C411yescharacteristic
118C23×C11C4×Q812yes—
119C23×C11C2×M1611yescharacteristic
120C23×C11C2×M1611yescharacteristic
121C23×C11#13112yes—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11—44no—
140C2×C4×C11—42no—
141C2×C4×C11—42no—
142C2×C4×C11#9912yes—
143C2×C4×C11C22⋊Q812yes—
144C2×C4×C11#12411yescharacteristic
145C2×C4×C11C4⋊Q811yescharacteristic
146C2×Dic11—22no—
147C2×Dic11—22no—
148C2×Dic11—42no—
149C2×Dic11—42no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—42no—
155C2×Dic11—42no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—82no—
163C2×Dic11—82no—
164C8×C11—82no—
165C11⋊C8—44no—
166C22×C4⋊C4—111no—
167C22×C4⋊C4—111no—
168C22×C42C2×D1111yescharacteristic
169C2×C4⋊C8—21no—
170C2×C22⋊C8—112no—
171C2×C22⋊C8C2×D1112yes—
172C2×#97—221no—
173#387—221no—
174#387—221no—
175#387—221no—
176#387—221no—
177C2×#95—111no—
178C2×#95—111no—
179C2×#95—111no—
180C2×#95—111no—
181#336—21no—
182#336—221no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11—22no—
188C22×C11—22no—
189C22×C11—22no—
190C22×C11—22no—
191C22×C11#39111yescharacteristic
192C22×C11#40711yescharacteristic
193C22×C11#40811yescharacteristic
194C22×C11C2×#9911yescharacteristic
195C22×C11#41011yescharacteristic
196C22×C11#41311yescharacteristic
197C22×C11#41311yescharacteristic
198C22×C11#44612yes—
199C22×C11#44612yes—
200C4×C11—22no—
201C4×C11—22no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—41no—
205C4×C11—41no—
206C4×C11—41no—
207Dic11—42no—
208Dic11—42no—
209Dic11—81no—
210Dic11—81no—
211C23×C4—111no—
212C23×C4—111no—
213C23×C4—111no—
214C23×C4—111no—
215C23×C4C4×D1111yescharacteristic
216C23×C4C4×D1111yescharacteristic
217C23×C4C22×D1111yescharacteristic
218C22×C8—22no—
219C22×C8—222no—
220C2×C4⋊C4—222no—
221C2×C4⋊C4—222no—
222C2×C4⋊C4—221no—
223C2×C4⋊C4—221no—
224C2×C4⋊C4—221no—
225C2×C4⋊C4—221no—
226C2×C4⋊C4—442no—
227C2×C42—42no—
228C2×C42D4411yescharacteristic
229C2×C42D4411yescharacteristic
230C2×C42C22⋊D1111yescharacteristic
231C2×C42C22⋊D1111yescharacteristic
232C4⋊C8—42no—
233C22⋊C8—24no—
234C22⋊C8—114no—
235C22⋊C8—222no—
236#97—442no—
237#95—221no—
238#95—221no—
239#95—221no—
240#95—221no—
241#95—221no—
242#95—221no—
243#95—221no—
244#95—221no—
245C2×C11—22no—
246C2×C11—22no—
247C2×C11#146411yescharacteristic
248C2×C11#146511yescharacteristic
249C2×C11#146811yescharacteristic
250C2×C11#147311yescharacteristic
251C2×C11#198511yescharacteristic
252C2×C11#199611yescharacteristic
253C2×C11#199811yescharacteristic
254C24C2×C4×D1111yescharacteristic
255C22×C4—22no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—22no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—112no—
265C22×C4—112no—
266C22×C4—221no—
267C22×C4—221no—
268C22×C4—221no—
269C22×C4—221no—
270C22×C4—221no—
271C22×C4—221no—
272C22×C4—222no—
273C22×C4—222no—
274C22×C4—441no—
275C22×C4—441no—
276C22×C4—441no—
277C22×C4—441no—
278C22×C4—441no—
279C22×C4—441no—
280C22×C4—441no—
281C22×C4—441no—
282C22×C4(C2×D11)⋊C411yescharacteristic
283C22×C4(C2×D11)⋊C411yescharacteristic
284C22×C4(C2×D11)⋊C411yescharacteristic
285C22×C4(C2×D11)⋊C411yescharacteristic
286C22×C4C2×D4411yescharacteristic
287C22×C4#434112yes—
288C22×C4Q8×D1112yes—
289C22×C4C2×C22⋊D1111yescharacteristic
290C2×C8—42no—
291C2×C8—42no—
292C2×C8—42no—
293C2×C8—224no—
294C2×C8—442no—
295C2×C8—442no—
296C4⋊C4—224no—
297C4⋊C4—224no—
298C4⋊C4—442no—
299C4⋊C4—442no—
300C42—22no—
301C42—22no—
302C42—41no—
303C42—41no—
304C11#988111yescharacteristic, complemented, Sylow
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23#6694012yes—
310C23#6695412yes—
311C23M16×D1111yescharacteristic
312C23M16×D1111yescharacteristic
313C23C2×(C2×D11)⋊C411yescharacteristic
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—44no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—222no—
335C2×C4—222no—
336C2×C4—442no—
337C2×C4—442no—
338C2×C4—441no—
339C2×C4—441no—
340C2×C4—441no—
341C2×C4—441no—
342C2×C4—442no—
343C2×C4—442no—
344C2×C4—441no—
345C2×C4—441no—
346C2×C4—441no—
347C2×C4—441no—
348C2×C4—441no—
349C2×C4—441no—
350C2×C4—882no—
351C2×C4—882no—
352C2×C4#6687012yes—
353C2×C4#6695012yes—
354C2×C4#6698911yescharacteristic
355C2×C4#6699711yescharacteristic
356C8—82no—
357C8—444no—
358C22—22no—
359C22—22no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—22no—
365C22—22no—
366C22#1062244112yes—
367C22#1062244112yes—
368C22C2×#6687011yescharacteristic
369C22#1062258711yescharacteristic
370C22#1062261911yescharacteristic
371C22#1062272311yescharacteristic
372C22#1062273911yescharacteristic
373C22#1062274511yescharacteristic
374C22#1062274511yescharacteristic
375C4—21no—
376C4—22no—
377C4—21no—
378C4—22no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—442no—
383C4—442no—
384C4—881no—
385C4—881no—
386C2—22no—
387C2—22no—
388C2#1306694811yescharacteristic
389C2#1306695211yescharacteristic
390C2#1306696211yescharacteristic
391C2#1306698311yescharacteristic
392C2#1306955511yescharacteristic
393C2#1306960011yescharacteristic
394C2#1306960811yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutator, prime radicalC24×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1797C2
socleC23×C11C2×C22⋊C4
cosocleC23×C4×C11C23
hypercenter#1797D11
hypocenterC11#9881
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
304. C11#9881semidirect

Maximal subgroups

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

subgroupindex
C2×#106225462
#130683782
#130664582
C11×#17972
#988111