Finite Group Databasebeta

← #14810378

Subgroups — #14810378

Order 2816.

1306 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×#10622706C212yesmaximal, complemented
2#13076968C211yesmaximal, characteristic
3#13069754C214yesmaximal, complemented
4#13069578C212yesmaximal, complemented
5#13068923C214yesmaximal
6C4×C22⋊(C11⋊C8)C211yesmaximal, characteristic
7C22×C11×C4⋊Q8C211yesmaximal, characteristic
8C23×Q8×C11—21no—
9C2×C11×C4⋊Q8—28no—
10C2×C11×C4⋊Q8—21no—
11C2×C11×C4⋊Q8—21no—
12C2×C11×C4⋊Q8C2212yes—
13C2×C11×C4⋊Q8C2212yes—
14C22×C11×C4⋊C4—21no—
15C22×C11×C4⋊C4C2212yes—
16C22×C42×C11C2211yescharacteristic
17C2×#66977C2212yes—
18C2×#66922C2211yescharacteristic
19#10622825—21no—
20#10622825—21no—
21C2×C22⋊(C11⋊C8)C2212yes—
22#10622706—28no—
23C2×#66874C2218yes—
24#10622548C2211yescharacteristic
25#10622542C2212yes—
26#10622541—21no—
27#10622541—21no—
28C2×C4×C11⋊C8C2212yes—
29#10622167C2218yes—
30#10622162C2212yes—
31C22×Q8×C11—28no—
32C22×Q8×C11—22no—
33C22×Q8×C11—22no—
34C22×Q8×C11—44no—
35C22×Q8×C11—44no—
36C23×C4×C11—22no—
37C23×C4×C11D411yescharacteristic
38C23×C4×C11D411yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C22×Dic22C2312yes—
41C11×C4⋊Q8—28no—
42C11×C4⋊Q8—28no—
43C11×C4⋊Q8—28no—
44C11×C4⋊Q8—24no—
45C11×C4⋊Q8D418yes—
46C2×C11×C4⋊C4—28no—
47C2×C11×C4⋊C4—22no—
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4—28no—
51C2×C11×C4⋊C4C2314yes—
52C2×C42×C11—24no—
53C2×C42×C11D411yescharacteristic
54C2×C42×C11D411yescharacteristic
55C2×C42×C11C2311yescharacteristic
56C2×C42×C11C2311yescharacteristic
57C2×C22⋊Dic11—22no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11C2312yes—
63#66977—28no—
64C2×Dic11⋊C4—22no—
65C22×C11⋊C8C2314yes—
66#66922—24no—
67C11⋊#95—22no—
68C11⋊#95—22no—
69C22⋊(C11⋊C8)—24no—
70#66874—216no—
71C4×C11⋊C8—24no—
72#25902—111nomaximal, Sylow
73C24×C11C2×D411yescharacteristic
74C2×Q8×C11—28no—
75C2×Q8×C11—28no—
76C2×Q8×C11—44no—
77C2×Q8×C11—432no—
78C2×Q8×C11—44no—
79C2×Q8×C11—44no—
80C2×Q8×C11—44no—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11—22no—
86C22×C4×C11—22no—
87C22×C4×C11—28no—
88C22×C4×C11—24no—
89C22×C4×C11—44no—
90C22×C4×C11—44no—
91C22×C4×C11SD1614yes—
92C22×C4×C11Q1614yes—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11#4114yes—
99C22×C4×C11C2411yescharacteristic
100C22×Dic11—22no—
101C22×Dic11—22no—
102C2×Dic22—24no—
103C2×Dic22—24no—
104C2×Dic22—24no—
105C11×C4⋊C4—28no—
106C11×C4⋊C4—28no—
107C11×C4⋊C4—28no—
108C11×C4⋊C4—24no—
109C11×C4⋊C4C2×D418yes—
110C42×C11—22no—
111C42×C11—22no—
112C42×C11—22no—
113C42×C11C2×D414yes—
114C22⋊Dic11—44no—
115C4⋊Dic11—24no—
116C4⋊Dic11—42no—
117C4⋊Dic11—42no—
118C4⋊Dic11—42no—
119C4⋊Dic11—42no—
120Dic11⋊C4—44no—
121C2×C11⋊C8—24no—
122C2×C11⋊C8—24no—
123C2×C11⋊C8—24no—
124C22×C4⋊Q8D1111yescharacteristic
125C2×#487—112no—
126#2857—111no—
127#2024—114no—
128#1990—112no—
129#1872—114no—
130C4×C22⋊C8—111no—
131C23×C11—21no—
132C23×C11—21no—
133C23×C11—21no—
134C23×C11—21no—
135C23×C11#12412yes—
136C23×C11C2×SD1612yes—
137C23×C11C2×Q1612yes—
138C23×C11C22×D411yescharacteristic
139Q8×C11—416no—
140Q8×C11—416no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—28no—
148C2×C4×C11—28no—
149C2×C4×C11—28no—
150C2×C4×C11—28no—
151C2×C4×C11—416no—
152C2×C4×C11—44no—
153C2×C4×C11—44no—
154C2×C4×C11#12012yes—
155C2×C4×C11#12012yes—
156C2×C4×C11#12412yes—
157C2×C4×C11C2×SD1612yes—
158C2×C4×C11C2×SD1612yes—
159C2×C4×C11C2×Q1612yes—
160C2×C4×C11C2×Q1612yes—
161C2×C4×C11AGL(1,ℤ/8)12yes—
162C2×C4×C11#13712yes—
163C2×C4×C11C22×D412yes—
164C2×C4×C11C2×#4112yes—
165C2×C4×C112−1+412yes—
166C2×Dic11—42no—
167C2×Dic11—42no—
168C2×Dic11—42no—
169C2×Dic11—42no—
170C2×Dic11—42no—
171C2×Dic11—42no—
172Dic22—48no—
173C11⋊C8—44no—
174C23×Q8—21no—
175C2×C4⋊Q8—28no—
176C2×C4⋊Q8—21no—
177C2×C4⋊Q8—21no—
178C2×C4⋊Q8—111no—
179C2×C4⋊Q8C2×D1112yes—
180C2×C4⋊Q8C2×D1112yes—
181C2×C22⋊Q8—112no—
182C22×C4⋊C4—21no—
183C22×C4⋊C4C2×D1112yes—
184C22×C42C2×D1111yescharacteristic
185#487—228no—
186C2×#103—118no—
187C2×C22⋊C8—112no—
188C2×C4×C8—112no—
189#391—112no—
190#389—221no—
191#389—221no—
192#384—111no—
193#380—221no—
194#380—221no—
195#340—118no—
196#336—112no—
197C22×C11—22no—
198C22×C11—22no—
199C22×C11—22no—
200C22×C11—22no—
201C22×C11—22no—
202C22×C11—22no—
203C22×C11#48714yescomplemented
204C22×C11C2×#12011yescharacteristic
205C22×C11C2×#12411yescharacteristic
206C22×C11#53611yescharacteristic
207C22×C11C22×SD1611yescharacteristic
208C22×C11C22×Q1611yescharacteristic
209C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
210C22×C11C2×#13711yescharacteristic
211C4×C11—22no—
212C4×C11—22no—
213C4×C11—22no—
214C4×C11—48no—
215C4×C11#45014yes—
216C4×C11#45114yes—
217C4×C11#54814yes—
218Dic11—82no—
219Dic11—82no—
220C22×Q8—28no—
221C22×Q8—22no—
222C22×Q8—22no—
223C22×Q8—44no—
224C22×Q8—44no—
225C22×Q8—112no—
226C23×C4—22no—
227C23×C4C22⋊D1111yescharacteristic
228C23×C4C22⋊D1111yescharacteristic
229C23×C4C22×D1111yescharacteristic
230C22×C8—114no—
231C4⋊Q8—28no—
232C4⋊Q8—28no—
233C4⋊Q8—28no—
234C4⋊Q8—24no—
235C4⋊Q8—224no—
236C4⋊Q8C22⋊D1118yes—
237C22⋊Q8—228no—
238C2×C4⋊C4—28no—
239C2×C4⋊C4—22no—
240C2×C4⋊C4—22no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—28no—
243C2×C4⋊C4—112no—
244C2×C4⋊C4—222no—
245C2×C4⋊C4—221no—
246C2×C4⋊C4—221no—
247C2×C4⋊C4—221no—
248C2×C4⋊C4—221no—
249C2×C4⋊C4C22×D1114yes—
250C2×C22⋊C4—222no—
251C2×C42—24no—
252C2×C42C22⋊D1111yescharacteristic
253C2×C42C22⋊D1111yescharacteristic
254C2×C42C22×D1111yescharacteristic
255C2×C42C22×D1111yescharacteristic
256#103—2216no—
257C22⋊C8—224no—
258C4×C8—224no—
259#95—222no—
260#95—222no—
261C2×C11—24no—
262C2×C11#243611yescharacteristic
263C2×C11C2×#45011yescharacteristic
264C2×C11C2×#45111yescharacteristic
265C2×C11C2×#48711yescharacteristic
266C2×C11#314111yescharacteristic
267C2×C11#322911yescharacteristic
268C2×C11#323011yescharacteristic
269C24C2×C22⋊D1111yescharacteristic
270C2×Q8—28no—
271C2×Q8—28no—
272C2×Q8—44no—
273C2×Q8—432no—
274C2×Q8—44no—
275C2×Q8—44no—
276C2×Q8—44no—
277C2×Q8—224no—
278C2×Q8—224no—
279C2×Q8—224no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—28no—
287C22×C4—24no—
288C22×C4—44no—
289C22×C4—44no—
290C22×C4—222no—
291C22×C4—222no—
292C22×C4#432414yes—
293C22×C4#432614yes—
294C22×C4#434314yes—
295C22×C4C2×C22⋊D1111yescharacteristic
296C22×C4C2×C22⋊D1111yescharacteristic
297C22×C4C2×C22⋊D1111yescharacteristic
298C22×C4C2×C22⋊D1111yescharacteristic
299C22×C4C2×C22⋊D1111yescharacteristic
300C22×C4C23×D1111yescharacteristic
301C2×C8—224no—
302C2×C8—224no—
303C2×C8—224no—
304C4⋊C4—28no—
305C4⋊C4—28no—
306C4⋊C4—28no—
307C4⋊C4—24no—
308C4⋊C4—224no—
309C4⋊C4—442no—
310C4⋊C4—442no—
311C4⋊C4—444no—
312C4⋊C4—442no—
313C4⋊C4—442no—
314C4⋊C4C2×C22⋊D1118yes—
315C22⋊C4—444no—
316C42—22no—
317C42—22no—
318C42—22no—
319C42C2×C22⋊D1114yes—
320C11#2590211yescharacteristic, complemented, Sylow
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23C2×#432412yes—
326C23C2×#432612yes—
327C23#6700012yes—
328C23C22×C22⋊D1111yescharacteristic
329Q8—416no—
330Q8—416no—
331Q8—448no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—28no—
339C2×C4—28no—
340C2×C4—28no—
341C2×C4—28no—
342C2×C4—416no—
343C2×C4—44no—
344C2×C4—44no—
345C2×C4—442no—
346C2×C4—442no—
347C2×C4—442no—
348C2×C4—442no—
349C2×C4—442no—
350C2×C4—442no—
351C2×C4#6698512yes—
352C2×C4C2×#432412yes—
353C2×C4C2×#432412yes—
354C2×C4#6699512yes—
355C2×C4C2×#432612yes—
356C2×C4C2×#432612yes—
357C2×C4#6700012yes—
358C2×C4#6700612yes—
359C2×C4#6700612yes—
360C2×C4C2×#434312yes—
361C2×C4#6704012yes—
362C2×C4C22×C22⋊D1112yes—
363C8—444no—
364C22—22no—
365C22—22no—
366C22—22no—
367C22—22no—
368C22—22no—
369C22—22no—
370C22#1062270614yescomplemented
371C22C2×#6698511yescharacteristic
372C22C22×#432411yescharacteristic
373C22C2×#6699511yescharacteristic
374C22C22×#432611yescharacteristic
375C22C2×#6700011yescharacteristic
376C22#1062334711yescharacteristic
377C22C2×#6700611yescharacteristic
378C4—22no—
379C4—22no—
380C4—22no—
381C4—48no—
382C4—882no—
383C4—882no—
384C4#1062283114yes—
385C4#1062284114yes—
386C4#1062334814yes—
387C2—24no—
388C2#1307227011yescharacteristic
389C2C2×#1062283111yescharacteristic
390C2C2×#1062284111yescharacteristic
391C2C2×#1062270611yescharacteristic
392C2#1307901211yescharacteristic
393C2#1307976011yescharacteristic
394C2#1307976711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×C4⋊Q8C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenterC22×C4⋊Q8D11
hypocenterC11#25902
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#10622706C2semidirect
3. #13069754C2semidirect
4. #13069578C2semidirect
203. C22×C11#487semidirect
320. C11#25902semidirect
370. C22#10622706semidirect

Maximal subgroups

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

subgroupindex
C2×#106227062
#130769682
#130697542
#130695782
#130689232
C4×C22⋊(C11⋊C8)2
C22×C11×C4⋊Q82
#2590211