Finite Group Databasebeta

← #14645202

Subgroups — #14645202

Order 2816.

748 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 748 conjugacy classes of subgroups — too many to draw. Only its 123 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
1C2×#10623065C211yesmaximal, characteristic
2#13067012C212yesmaximal, complemented
3#13067006C212yesmaximal, complemented
4#13066930C211yesmaximal, characteristic, complemented
5C11×#1458C211yesmaximal, characteristic, complemented
6C2×C11×#117C2211yescharacteristic
7C2×#66983C411yescharacteristic
8C2×#66977C411yescharacteristic
9#10623065—24no—
10#10623065—24no—
11C2×#66951—21no—
12C2×#66949—21no—
13C2×#66938—21no—
14C2×#66936—21no—
15C2×#66928C411yescharacteristic
16C2×C4×D44C2211yescharacteristic
17C2×#66922C411yescharacteristic
18C2×C4×Dic22C2211yescharacteristic
19C11×#431C2212yes—
20#10622538C2212yes—
21C11×#324—21no—
22C11×#323—21no—
23#10622166—21no—
24#10622163—21no—
25#10622121—24no—
26#10622094—24no—
27C23×C4×C11C2×C411yescharacteristic
28C22×C22⋊D11—21no—
29C22×D44C2×C411yescharacteristic
30C22×C4×D11—21no—
31C22×Dic22—21no—
32C22×Dic22C2×C411yescharacteristic
33C11×#117—22no—
34C11×#117—22no—
35C2×C11×C4⋊C4D411yescharacteristic
36C2×C11×C4⋊C4D411yescharacteristic
37C2×C11×C22⋊C4D411yescharacteristic
38C2×C11×C22⋊C4D411yescharacteristic
39C2×C42×C11C2×C411yescharacteristic
40C2×C42×C11C2311yescharacteristic
41C2×C22⋊Dic11—21no—
42#66983—22no—
43#66983—22no—
44C2×(C2×D11)⋊C4—21no—
45C2×(C2×D11)⋊C4—21no—
46C2×(C2×D11)⋊C4—21no—
47C2×(C2×D11)⋊C4—21no—
48C2×C4⋊Dic11—21no—
49C2×C4⋊Dic11C2×C411yescharacteristic
50C2×C4⋊Dic11C2×C411yescharacteristic
51#66977—22no—
52#66977—22no—
53C2×Dic11⋊C4—21no—
54C2×Dic11⋊C4—21no—
55C2×C4×Dic11—21no—
56#66951—28no—
57#66949—28no—
58#66938—28no—
59#66936—28no—
60#66928—22no—
61#66928—22no—
62C4×D44—22no—
63C4×D44D414yes—
64#66922—22no—
65#66922—22no—
66C4×Dic22—22no—
67C4×Dic22D414yes—
68C11×C4⋊C8—22no—
69C11×C22⋊C8—22no—
70C4×C8×C11—22no—
71C22⋊(C11⋊C8)—22no—
72C4⋊(C11⋊C8)—22no—
73C4×C11⋊C8—22no—
74#8325—111nomaximal, Sylow
75C24×C11C22⋊C411yescharacteristic
76C23×D11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—22no—
80C22×C4×C11—22no—
81C22×C4×C11C22⋊C411yescharacteristic
82C22×C4×C11C22⋊C411yescharacteristic
83C22×C4×C11C22⋊C411yescharacteristic
84C22×C4×C11C22×C411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C2×C22⋊D11—24no—
88C2×C22⋊D11—82no—
89C22×Dic11—21no—
90C22×Dic11—21no—
91C22×Dic11—21no—
92C2×D44—21no—
93C2×D44—22no—
94C2×D44—22no—
95C2×D44C22⋊C412yes—
96C2×C4×D11—24no—
97C2×C4×D11—82no—
98C2×Dic22—24no—
99C2×Dic22—21no—
100C2×Dic22—22no—
101C2×Dic22—22no—
102C2×Dic22—82no—
103C2×Dic22C22⋊C412yes—
104C2×C8×C11—42no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—22no—
107C11×C22⋊C4—22no—
108C11×C22⋊C4—22no—
109C42×C11—21no—
110C42×C11—21no—
111C42×C11C2×D412yes—
112C42×C11C2×D412yes—
113C22⋊Dic11—24no—
114(C2×D11)⋊C4—24no—
115(C2×D11)⋊C4—24no—
116(C2×D11)⋊C4—24no—
117(C2×D11)⋊C4—24no—
118C4⋊Dic11—24no—
119C4⋊Dic11—21no—
120C4⋊Dic11—21no—
121C4⋊Dic11C22⋊C412yes—
122C4⋊Dic11C22⋊C412yes—
123Dic11⋊C4—24no—
124Dic11⋊C4—24no—
125C4×Dic11—24no—
126C2×C11⋊C8—42no—
127C2×#542—111no—
128#1479—112no—
129#1478—112no—
130#1458—111no—
131#1458D1111yescharacteristic, complemented
132C23×C11—21no—
133C23×C11—21no—
134C23×C11—21no—
135C23×C11—41no—
136C23×C11—41no—
137C23×C11C2×C22⋊C411yescharacteristic
138C22×D11—22no—
139C22×D11—42no—
140C22×D11—42no—
141C22×D11—41no—
142C22×D11—41no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11C2×C22⋊C411yescharacteristic
155C2×C4×C11C2×C22⋊C411yescharacteristic
156C2×C4×C11#12012yes—
157C2×C4×C11#12012yes—
158C2×C4×C11#13112yes—
159C2×C4×C11#13112yes—
160C22⋊D11—84no—
161C2×Dic11—22no—
162C2×Dic11—22no—
163C2×Dic11—22no—
164C2×Dic11—42no—
165C2×Dic11—42no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168D44—24no—
169D44—42no—
170C4×D11—84no—
171Dic22—24no—
172Dic22—42no—
173Dic22—84no—
174C8×C11—82no—
175C11⋊C8—82no—
176#542—224no—
177#542—224no—
178C2×C4⋊Q8—111no—
179C2×#126—221no—
180C2×#124—111no—
181C2×#124—221no—
182C2×#123—221no—
183C2×C22⋊Q8—111no—
184C2×C22⋊Q8—221no—
185C2×#121—111no—
186C2×C4×Q8—111no—
187C2×C4×D4—111no—
188C2×#117C2×D1111yescharacteristic
189#431—112no—
190#431C2×D1112yes—
191Q8⋊C8—224no—
192D4⋊C8—224no—
193#324—21no—
194#324—221no—
195#323—21no—
196#323—221no—
197C22×C11—21no—
198C22×C11—21no—
199C22×C11—41no—
200C22×C11—41no—
201C22×C11—41no—
202C22×C11—81no—
203C22×C11—81no—
204C22×C11#37911yescharacteristic
205C22×C11#40811yescharacteristic
206C22×C11#40811yescharacteristic
207C2×D11—42no—
208C2×D11—42no—
209C2×D11—42no—
210C2×D11—82no—
211C2×D11—82no—
212C4×C11—22no—
213C4×C11—22no—
214C4×C11—41no—
215C4×C11—41no—
216C4×C11—41no—
217C4×C11#40812yes—
218C4×C11#40812yes—
219Dic11—42no—
220Dic11—42no—
221Dic11—42no—
222C22×Q8—111no—
223C22×Q8—221no—
224C22×D4—111no—
225C22×D4—221no—
226C23×C4—221no—
227C23×C4C4×D1111yescharacteristic
228C4⋊Q8—222no—
229C4⋊Q8—222no—
230#126—228no—
231#124—222no—
232#124—222no—
233#124—228no—
234#123—228no—
235C22⋊Q8—228no—
236C22⋊Q8—222no—
237C22⋊Q8—222no—
238#121—222no—
239#121—222no—
240C4×Q8—114no—
241C4×Q8—222no—
242C4×D4—114no—
243C4×D4—222no—
244#117—22no—
245#117—22no—
246C2×C4⋊C4—111no—
247C2×C4⋊C4—111no—
248C2×C4⋊C4—221no—
249C2×C4⋊C4—221no—
250C2×C4⋊C4—221no—
251C2×C4⋊C4D4411yescharacteristic
252C2×C4⋊C4C22⋊D1111yescharacteristic
253C2×C22⋊C4—221no—
254C2×C22⋊C4—221no—
255C2×C22⋊C4—221no—
256C2×C22⋊C4—221no—
257C2×C22⋊C4—221no—
258C2×C22⋊C4D4411yescharacteristic
259C2×C22⋊C4C22⋊D1111yescharacteristic
260C2×C42—221no—
261C2×C42C4×D1111yescharacteristic
262C2×C42C22×D1111yescharacteristic
263C4⋊C8—22no—
264C4⋊C8—222no—
265C22⋊C8—22no—
266C22⋊C8—222no—
267C4×C8—22no—
268C4×C8—222no—
269C2×C11—21no—
270C2×C11—21no—
271C2×C11—81no—
272C2×C11#178011yescharacteristic
273C2×C11#179511yescharacteristic
274C2×C11#179611yescharacteristic
275D11—82no—
276C24—221no—
277C24(C2×D11)⋊C411yescharacteristic
278C2×Q8—112no—
279C2×Q8—224no—
280C2×Q8—221no—
281C2×Q8—222no—
282C2×Q8—222no—
283C2×Q8—882no—
284C2×D4—112no—
285C2×D4—224no—
286C2×D4—221no—
287C2×D4—222no—
288C2×D4—222no—
289C2×D4—882no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—22no—
293C22×C4—22no—
294C22×C4—221no—
295C22×C4—221no—
296C22×C4—221no—
297C22×C4—224no—
298C22×C4—882no—
299C22×C4(C2×D11)⋊C411yescharacteristic
300C22×C4(C2×D11)⋊C411yescharacteristic
301C22×C4(C2×D11)⋊C411yescharacteristic
302C22×C4C2×C4×D1111yescharacteristic
303C22×C4C2×D4411yescharacteristic
304C22×C4C2×C22⋊D1111yescharacteristic
305C2×C8—42no—
306C2×C8—442no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—112no—
310C4⋊C4—112no—
311C4⋊C4—224no—
312C4⋊C4—224no—
313C4⋊C4—221no—
314C4⋊C4—221no—
315C4⋊C4—224no—
316C22⋊C4—22no—
317C22⋊C4—22no—
318C22⋊C4—224no—
319C22⋊C4—224no—
320C22⋊C4—224no—
321C22⋊C4—224no—
322C22⋊C4—224no—
323C42—21no—
324C42—21no—
325C42—224no—
326C42D4×D1112yes—
327C42D4×D1112yes—
328C11#832511yescharacteristic, complemented, Sylow
329C23—21no—
330C23—21no—
331C23—21no—
332C23—41no—
333C23—41no—
334C23—222no—
335C23—442no—
336C23—442no—
337C23—441no—
338C23—441no—
339C23C2×(C2×D11)⋊C411yescharacteristic
340Q8—224no—
341Q8—442no—
342Q8—884no—
343D4—224no—
344D4—442no—
345D4—884no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—222no—
358C2×C4—222no—
359C2×C4—222no—
360C2×C4—442no—
361C2×C4—442no—
362C2×C4—441no—
363C2×C4—441no—
364C2×C4—884no—
365C2×C4C22⋊C4×D1111yescharacteristic
366C2×C4C22⋊C4×D1111yescharacteristic
367C2×C4#6693512yes—
368C2×C4#6695412yes—
369C2×C4#6696012yes—
370C2×C4#6699012yes—
371C8—82no—
372C8—882no—
373C22—21no—
374C22—21no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—81no—
379C22—81no—
380C22—442no—
381C22—442no—
382C22—442no—
383C22—882no—
384C22—882no—
385C22#1062256811yescharacteristic
386C22#1062272311yescharacteristic
387C22#1062274211yescharacteristic
388C4—22no—
389C4—22no—
390C4—41no—
391C4—41no—
392C4—41no—
393C4—442no—
394C4—442no—
395C4—442no—
396C4#1062234012yes—
397C4#1062234012yes—
398C2—21no—
399C2—21no—
400C2—81no—
401C2—882no—
402C2#1306852711yescharacteristic
403C2#1306858411yescharacteristic
404C2#1306859211yescharacteristic
subgroupG/H
centerC22#10622568
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1458C2
socleC22×C11#379
prime radicalC2×#66983C4
cosocleC2×C42×C11C23
hypercenter#1458D11
hypocenterC11#8325
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1458

Complements

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

NH ≅ G/Ntype
2. #13067012C2semidirect
3. #13067006C2semidirect
4. #13066930C2semidirect
5. C11×#1458C2semidirect
131. #1458D11semidirect
328. C11#8325semidirect

Maximal subgroups

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

subgroupindex
C2×#106230652
#130670122
#130670062
#130669302
C11×#14582
#832511