Finite Group Databasebeta

← #14664405

Subgroups — #14664405

Order 2816.

572 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 73 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#13071976C211yesmaximal, characteristic
2#13068407C211yesmaximal, characteristic
3#13066953C211yesmaximal, characteristic
4#13066647C211yesmaximal, characteristic, complemented
5#13066646C211yesmaximal, characteristic, complemented
6#13066645C211yesmaximal, characteristic, complemented
7C11×#1354C211yesmaximal, characteristic, complemented
8C22×Q8×D11C411yescharacteristic
9C2×#66949—21no—
10C2×#66946C2211yescharacteristic
11C11×#395C2211yescharacteristic
12#10622844C411yescharacteristic
13C2×#66887—21no—
14M16×Dic11—21no—
15#10622602—21no—
16#10622592C2211yescharacteristic
17#10622339—21no—
18#10622286C411yescharacteristic
19#10622280C411yescharacteristic
20#10622278—21no—
21#10622259—21no—
22C11×#343C2211yescharacteristic
23C11×#324C2211yescharacteristic
24#10622168C2211yescharacteristic
25#10622166C2211yescharacteristic
26#10622106—21no—
27C22×Q8×C11C2×C411yescharacteristic
28C2×Q8×D11—44no—
29C2×Q8×D11—41no—
30C2×Q8×D11—41no—
31C22×D44D411yescharacteristic
32C22×C4×D11—21no—
33C22×C4×D11C2×C411yescharacteristic
34C22×C4×D11D411yescharacteristic
35C22×Dic22—21no—
36C22×Dic22C2×C411yescharacteristic
37C2×C11×M16—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4C2311yescharacteristic
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4C2×C411yescharacteristic
44C2×(C2×D11)⋊C4D411yescharacteristic
45C2×Dic11⋊C4—21no—
46C2×Dic11⋊C4—21no—
47C2×C4×Dic11D411yescharacteristic
48C2×#4318—21no—
49C2×#4313—41no—
50#66949—44no—
51#66946—41no—
52#66946—41no—
53C11×C22⋊C8—21no—
54C11×#95—21no—
55C11×#95C2×C411yescharacteristic
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95C2×C411yescharacteristic
60C22⋊(C11⋊C8)—21no—
61#66887—24no—
62(C2×D11)⋊C8—41no—
63#66879—41no—
64C8×Dic11—41no—
65#11791—111nomaximal, Sylow
66C23×D11C22⋊C411yescharacteristic
67C23×D11C22⋊C411yescharacteristic
68C2×Q8×C11—42no—
69C2×Q8×C11—41no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11C22×C411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×Dic11—21no—
76C22×Dic11—21no—
77C22×Dic11C22⋊C411yescharacteristic
78C22×Dic11C22⋊C411yescharacteristic
79Q8×D11—44no—
80Q8×D11—44no—
81Q8×D11—44no—
82Q8×D11—44no—
83C2×D44—22no—
84C2×D44—21no—
85C2×D44—21no—
86C2×D44—41no—
87C2×C4×D11—21no—
88C2×C4×D11—21no—
89C2×C4×D11—21no—
90C2×C4×D11—21no—
91C2×C4×D11—42no—
92C2×C4×D11—42no—
93C2×C4×D11—42no—
94C2×C4×D11—42no—
95C2×C4×D11—42no—
96C2×Dic22—24no—
97C2×Dic22—41no—
98C2×Dic22—42no—
99C2×Dic22—41no—
100C2×Dic22—41no—
101C2×Dic22—42no—
102C11×M16—22no—
103C11×M16—41no—
104C2×C8×C11—41no—
105C2×C8×C11—41no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—42no—
108(C2×D11)⋊C4—41no—
109(C2×D11)⋊C4—41no—
110(C2×D11)⋊C4—42no—
111(C2×D11)⋊C4—42no—
112(C2×D11)⋊C4—42no—
113Dic11⋊C4—42no—
114Dic11⋊C4—42no—
115C4×Dic11—21no—
116C4×Dic11—21no—
117#4318—22no—
118#4318—41no—
119C2×C11⋊C8—41no—
120C2×C11⋊C8—41no—
121#4313—82no—
122#2409—111no—
123C4×#100—111no—
124#1465—111no—
125#1354—111no—
126#1354—111no—
127#1354—111no—
128#1354D1111yescharacteristic, complemented
129C23×C11C2×C22⋊C411yescharacteristic
130C22×D11—21no—
131C22×D11—21no—
132C22×D11—21no—
133C22×D11—21no—
134C22×D11—21no—
135C22×D11—41no—
136C22×D11—41no—
137C22×D11—41no—
138C22×D11—41no—
139C22×D11#10412yes—
140Q8×C11—42no—
141Q8×C11—42no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—22no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11#13711yescharacteristic
155C2×C4×C11#13711yescharacteristic
156C2×Dic11—22no—
157C2×Dic11—22no—
158C2×Dic11—21no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11#9911yescharacteristic
166C2×Dic11#9911yescharacteristic
167D44—42no—
168D44—42no—
169C4×D11—42no—
170C4×D11—48no—
171C4×D11—42no—
172C4×D11—42no—
173C4×D11—81no—
174Dic22—44no—
175Dic22—42no—
176Dic22—44no—
177Dic22—42no—
178C8×C11—42no—
179C8×C11—81no—
180C11⋊C8—42no—
181C11⋊C8—81no—
182C23×Q8—111no—
183C2×C22⋊Q8—221no—
184C2×C4×D4—111no—
185C2×#100—221no—
186#407—221no—
187C4×M16—221no—
188#395—111no—
189#395C2×D1111yescharacteristic
190#393—111no—
191#393—111no—
192#391—221no—
193#386—221no—
194#385—221no—
195#380—111no—
196#343—111no—
197#343C2×D1111yescharacteristic
198#324—111no—
199#324C2×D1111yescharacteristic
200#323—221no—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11C2×#9911yescharacteristic
204C22×C11#41911yescharacteristic
205C22×C11C2×#10411yescharacteristic
206C2×D11—22no—
207C2×D11—42no—
208C2×D11—41no—
209C2×D11—41no—
210C2×D11—42no—
211C2×D11—42no—
212C2×D11—41no—
213C2×D11—41no—
214C2×D11—41no—
215C2×D11—81no—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—42no—
219C4×C11—41no—
220C4×C11—41no—
221C4×C11—81no—
222Dic11—21no—
223Dic11—42no—
224Dic11—41no—
225Dic11—81no—
226Dic11AΣL(1,𝔽16)12yes—
227C22×Q8—111no—
228C22×Q8—221no—
229C22×Q8—441no—
230C22×Q8—441no—
231C22×Q8—444no—
232C22×Q8C4×D1111yescharacteristic
233C22×D4—111no—
234C23×C4—111no—
235C23×C4—111no—
236C23×C4—221no—
237C2×M16—21no—
238C2×M16—221no—
239C2×M16—441no—
240C22⋊Q8—444no—
241C4×D4—441no—
242C4×D4—441no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—221no—
245C2×C4⋊C4—221no—
246C2×C4⋊C4C22×D1111yescharacteristic
247C2×C22⋊C4—111no—
248C2×C22⋊C4—111no—
249C2×C22⋊C4—221no—
250C2×C22⋊C4—221no—
251C2×C22⋊C4—221no—
252C2×C42—111no—
253#100—224no—
254C22⋊C8—21no—
255C22⋊C8—221no—
256C22⋊C8—441no—
257#97—441no—
258C4×C8—441no—
259#95—21no—
260#95—111no—
261#95—221no—
262#95—221no—
263#95—221no—
264#95C4×D1111yescharacteristic
265C2×C11—21no—
266C2×C11—21no—
267C2×C11#150811yescharacteristic
268C2×C11C2×AΣL(1,𝔽16)11yescharacteristic
269C2×C11#213511yescharacteristic
270D11—42no—
271D11—81no—
272C24—111no—
273C24—111no—
274C2×Q8—42no—
275C2×Q8—41no—
276C2×Q8—224no—
277C2×Q8—441no—
278C2×Q8—441no—
279C2×Q8—441no—
280C2×Q8—442no—
281C2×Q8—442no—
282C2×Q8—444no—
283C2×Q8—444no—
284C2×Q8—444no—
285C2×Q8—444no—
286C2×D4—222no—
287C2×D4—221no—
288C2×D4—221no—
289C2×D4—441no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—111no—
293C22×C4—111no—
294C22×C4—221no—
295C22×C4—221no—
296C22×C4—221no—
297C22×C4—221no—
298C22×C4—221no—
299C22×C4—221no—
300C22×C4—442no—
301C22×C4—442no—
302C22×C4—442no—
303C22×C4—442no—
304C22×C4—442no—
305C22×C4C2×C4×D1111yescharacteristic
306C22×C4D4×D1111yescharacteristic
307C22×C4D4×D1111yescharacteristic
308M16—22no—
309M16—41no—
310M16—222no—
311M16—441no—
312M16—882no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—441no—
316C2×C8—441no—
317C4⋊C4—41no—
318C4⋊C4—42no—
319C4⋊C4—442no—
320C4⋊C4—442no—
321C22⋊C4—441no—
322C22⋊C4—441no—
323C22⋊C4—442no—
324C22⋊C4—442no—
325C22⋊C4—442no—
326C42—221no—
327C42—221no—
328C11#1179111yescharacteristic, complemented, Sylow
329C23—112no—
330C23—221no—
331C23—221no—
332C23—221no—
333C23—221no—
334C23—221no—
335C23—441no—
336C23—441no—
337C23—441no—
338C23—441no—
339C23C22⋊C4×D1111yescharacteristic
340Q8—42no—
341Q8—42no—
342Q8—444no—
343Q8—444no—
344Q8—442no—
345Q8—442no—
346D4—442no—
347D4—442no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—22no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—111no—
361C2×C4—111no—
362C2×C4—222no—
363C2×C4—222no—
364C2×C4—221no—
365C2×C4—442no—
366C2×C4—442no—
367C2×C4—442no—
368C2×C4—448no—
369C2×C4—441no—
370C2×C4—441no—
371C2×C4—441no—
372C2×C4—441no—
373C2×C4—441no—
374C2×C4—441no—
375C2×C4—881no—
376C2×C4#6696811yescharacteristic
377C2×C4#6697111yescharacteristic
378C8—42no—
379C8—81no—
380C8—442no—
381C8—881no—
382C22—21no—
383C22—21no—
384C22—222no—
385C22—442no—
386C22—442no—
387C22—442no—
388C22—441no—
389C22—441no—
390C22—441no—
391C22—441no—
392C22—441no—
393C22—881no—
394C22D11×#9911yescharacteristic
395C22#1062241511yescharacteristic
396C22D11×#10411yescharacteristic
397C4—21no—
398C4—21no—
399C4—41no—
400C4—42no—
401C4—41no—
402C4—81no—
403C4—112no—
404C4—221no—
405C4—442no—
406C4—441no—
407C4—881no—
408C2—21no—
409C2—21no—
410C2—442no—
411C2—881no—
412C2#1306713411yescharacteristic
413C2D11×AΣL(1,𝔽16)11yescharacteristic
414C2#1307030911yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1354C2
socleC22×C11C2×#99
prime radicalC22×D44D4
cosocleC2×C11×C4⋊C4C23
hypercenter#1354D11
hypocenterC11#11791
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1354

Complements

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

NH ≅ G/Ntype
4. #13066647C2semidirect
5. #13066646C2semidirect
6. #13066645C2semidirect
7. C11×#1354C2semidirect
128. #1354D11semidirect
328. C11#11791semidirect

Maximal subgroups

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

subgroupindex
#130719762
#130684072
#130669532
#130666472
#130666462
#130666452
C11×#13542
#1179111