Finite Group Databasebeta

← #14642178

Subgroups — #14642178

Order 2816.

538 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 538 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076917C211yesmaximal, characteristic
2C4×C22⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
3#13066441C212yesmaximal, complemented
4#13066436C212yesmaximal, complemented
5C11×#1817C211yesmaximal, characteristic, complemented
6C22×C42×C11C2211yescharacteristic
7C2×#66983C411yescharacteristic
8C2×#66977C411yescharacteristic
9C2×#66928C411yescharacteristic
10C2×C11×C22⋊C8—21no—
11#10622826—21no—
12#10622826—21no—
13C2×C22⋊(C11⋊C8)—21no—
14#10622553—21no—
15#10622553—21no—
16#10622552C2211yescharacteristic
17#10622549C411yescharacteristic
18#10622542C2211yescharacteristic
19C2×C4×C11⋊C8—21no—
20C11×#336—21no—
21C11×#336C2212yes—
22#10622162C2212yes—
23C23×C4×C11C2×C411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C22×C22⋊D11—21no—
27C22×D44C2×C411yescharacteristic
28C22×Dic22C2×C411yescharacteristic
29C22×C8×C11—22no—
30C2×C42×C11—42no—
31C2×C42×C11C2×C411yescharacteristic
32C2×C42×C11D411yescharacteristic
33C2×C42×C11D411yescharacteristic
34C2×C42×C11C2311yescharacteristic
35C2×C22⋊Dic11—21no—
36#66983—42no—
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×C4⋊Dic11C2×C411yescharacteristic
43C2×C4⋊Dic11C2×C411yescharacteristic
44#66977—42no—
45C2×Dic11⋊C4—21no—
46C22×C11⋊C8—22no—
47#66928—42no—
48C11×C22⋊C8—42no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C22⋊(C11⋊C8)—24no—
54C4×C11⋊C8—42no—
55#7670—111nomaximal, Sylow
56C24×C11C22⋊C411yescharacteristic
57C23×D11—21no—
58C22×C4×C11—22no—
59C22×C4×C11—22no—
60C22×C4×C11—22no—
61C22×C4×C11—22no—
62C22×C4×C11—22no—
63C22×C4×C11—22no—
64C22×C4×C11—41no—
65C22×C4×C11—41no—
66C22×C4×C11—41no—
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22×C411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C2×C22⋊D11—42no—
74C2×C22⋊D11—42no—
75C2×C22⋊D11—42no—
76C22×Dic11—21no—
77C22×Dic11—21no—
78C22×Dic11—21no—
79C2×D44—22no—
80C2×D44—41no—
81C2×D44—41no—
82C2×Dic22—22no—
83C2×Dic22—41no—
84C2×Dic22—41no—
85C2×C8×C11—42no—
86C2×C8×C11—42no—
87C2×C8×C11—42no—
88C42×C11—22no—
89C42×C11—22no—
90C42×C11—41no—
91C42×C11—41no—
92C22⋊Dic11—42no—
93(C2×D11)⋊C4—42no—
94(C2×D11)⋊C4—42no—
95(C2×D11)⋊C4—42no—
96(C2×D11)⋊C4—42no—
97(C2×D11)⋊C4—42no—
98C4⋊Dic11—41no—
99C4⋊Dic11—41no—
100Dic11⋊C4—42no—
101C2×C11⋊C8—24no—
102C2×C11⋊C8—42no—
103C2×C11⋊C8—42no—
104#2850—111no—
105#1817D1111yescharacteristic, complemented
106C4×C22⋊C8—111no—
107#1272—112no—
108#1270—112no—
109C23×C11—21no—
110C23×C11—21no—
111C23×C11—21no—
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11#10412yes—
116C23×C11C2×C22⋊C411yescharacteristic
117C22×D11—41no—
118C22×D11—41no—
119C22×D11—41no—
120C22×D11—41no—
121C22×D11—41no—
122C22×D11—41no—
123C22×D11—41no—
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—44no—
138C2×C4×C11—44no—
139C2×C4×C11—44no—
140C2×C4×C11#9912yes—
141C2×C4×C11#10012yes—
142C2×C4×C11#13112yes—
143C2×C4×C11#13512yes—
144C2×C4×C11#13512yes—
145C22⋊D11—84no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155D44—82no—
156Dic22—82no—
157C8×C11—82no—
158C11⋊C8—44no—
159C2×#124—111no—
160C2×C22⋊Q8—111no—
161C2×#121—111no—
162C22×C42C2×D1111yescharacteristic
163C2×C22⋊C8—21no—
164C2×C22⋊C8—221no—
165C2×C4×C8—221no—
166#391—111no—
167#390—111no—
168#388—221no—
169#388—221no—
170#386—221no—
171#386—221no—
172#382—111no—
173#336—21no—
174#336—112no—
175#336C2×D1112yes—
176C22×C11—22no—
177C22×C11—22no—
178C22×C11—22no—
179C22×C11—41no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11—41no—
183C22×C11#40811yescharacteristic
184C22×C11C2×#9911yescharacteristic
185C22×C11C2×#10011yescharacteristic
186C22×C11#41611yescharacteristic
187C22×C11#41611yescharacteristic
188C22×C11C2×#10411yescharacteristic
189C22×C11#42111yescharacteristic
190C2×D11—81no—
191C2×D11—81no—
192C2×D11—81no—
193C2×D11—81no—
194C2×D11—81no—
195C2×D11—81no—
196C2×D11—81no—
197C4×C11—22no—
198C4×C11—22no—
199C4×C11—22no—
200C4×C11—22no—
201C4×C11—22no—
202C4×C11—41no—
203Dic11—81no—
204Dic11—81no—
205Dic11—81no—
206C22×Q8—111no—
207C22×D4—111no—
208C22×D4—221no—
209C23×C4C4×D1111yescharacteristic
210C23×C4D4411yescharacteristic
211C23×C4C22⋊D1111yescharacteristic
212C22×C8—22no—
213C22×C8—222no—
214#124—442no—
215C22⋊Q8—442no—
216#121—442no—
217C2×C4⋊C4—111no—
218C2×C4⋊C4—111no—
219C2×C4⋊C4—221no—
220C2×C22⋊C4—221no—
221C2×C22⋊C4—221no—
222C2×C22⋊C4—221no—
223C2×C22⋊C4—221no—
224C2×C22⋊C4—221no—
225C2×C22⋊C4—221no—
226C2×C42—42no—
227C2×C42C4×D1111yescharacteristic
228C2×C42D4411yescharacteristic
229C2×C42C22⋊D1111yescharacteristic
230C2×C42C22×D1111yescharacteristic
231C22⋊C8—42no—
232C22⋊C8—224no—
233C4×C8—442no—
234#95—221no—
235#95—221no—
236#95—221no—
237#95—221no—
238C2×C11—42no—
239C2×C11#147111yescharacteristic
240C2×C11#148211yescharacteristic
241C2×C11#149411yescharacteristic
242C2×C11#150111yescharacteristic
243C2×C11#151611yescharacteristic
244C2×C11#152711yescharacteristic
245C2×C11#154311yescharacteristic
246D11—161no—
247C24—221no—
248C24(C2×D11)⋊C411yescharacteristic
249C2×Q8—222no—
250C2×Q8—441no—
251C2×Q8—441no—
252C2×D4—222no—
253C2×D4—441no—
254C2×D4—441no—
255C2×D4—442no—
256C2×D4—442no—
257C2×D4—442no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—221no—
268C22×C4—221no—
269C22×C4—221no—
270C22×C4(C2×D11)⋊C411yescharacteristic
271C22×C4(C2×D11)⋊C411yescharacteristic
272C22×C4(C2×D11)⋊C411yescharacteristic
273C22×C4C2×C4×D1111yescharacteristic
274C22×C4C2×D4411yescharacteristic
275C22×C4C2×C22⋊D1111yescharacteristic
276C2×C8—42no—
277C2×C8—42no—
278C2×C8—42no—
279C2×C8—224no—
280C2×C8—442no—
281C2×C8—442no—
282C4⋊C4—441no—
283C4⋊C4—441no—
284C4⋊C4—442no—
285C22⋊C4—442no—
286C22⋊C4—442no—
287C22⋊C4—442no—
288C22⋊C4—442no—
289C22⋊C4—442no—
290C22⋊C4—442no—
291C42—22no—
292C42—22no—
293C42—41no—
294C42—41no—
295C11#767011yescharacteristic, complemented, Sylow
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—441no—
303C23—441no—
304C23—441no—
305C23—441no—
306C23—441no—
307C23—441no—
308C23—441no—
309C23#6688912yes—
310C23C2×(C2×D11)⋊C411yescharacteristic
311Q8—882no—
312D4—882no—
313D4—884no—
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—44no—
328C2×C4—44no—
329C2×C4—44no—
330C2×C4—441no—
331C2×C4—441no—
332C2×C4—441no—
333C2×C4—441no—
334C2×C4—441no—
335C2×C4—441no—
336C2×C4—441no—
337C2×C4—441no—
338C2×C4—441no—
339C2×C4#6687012yes—
340C2×C4#6688712yes—
341C2×C4#6695712yes—
342C2×C4#6696012yes—
343C2×C4#6700312yes—
344C8—82no—
345C8—444no—
346C22—22no—
347C22—22no—
348C22—22no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—881no—
354C22—881no—
355C22—881no—
356C22—881no—
357C22—881no—
358C22—881no—
359C22—881no—
360C22C2×#6687011yescharacteristic
361C22#1062261511yescharacteristic
362C22#1062261811yescharacteristic
363C22#1062272611yescharacteristic
364C22#1062274211yescharacteristic
365C22C2×#6688711yescharacteristic
366C22C2×#6688911yescharacteristic
367C4—22no—
368C4—22no—
369C4—22no—
370C4—22no—
371C4—22no—
372C4—41no—
373C4—881no—
374C4—881no—
375C4—881no—
376C2—42no—
377C2—1761no—
378C2#1306697711yescharacteristic
379C2#1306702511yescharacteristic
380C2#1306707411yescharacteristic
381C2#1306710811yescharacteristic
382C2#1306717011yescharacteristic
383C2#1306721511yescharacteristic
384C2#1306727611yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1817C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#66983C4
cosocleC2×C42×C11C23
hypercenter#1817D11
hypocenterC11#7670
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1817

Complements

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

NH ≅ G/Ntype
2. C4×C22⋊(C11⋊C8)C2semidirect
3. #13066441C2semidirect
4. #13066436C2semidirect
5. C11×#1817C2semidirect
105. #1817D11semidirect
295. C11#7670semidirect

Maximal subgroups

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

subgroupindex
#130769172
C4×C22⋊(C11⋊C8)2
#130664412
#130664362
C11×#18172
#767011