Finite Group Databasebeta

← #14647883

Subgroups — #14647883

Order 2816.

464 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 93 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#13077661C211yesmaximal, characteristic
2#13068918C211yesmaximal, characteristic
3#13068821C211yesmaximal, characteristic, complemented
4#13067105C211yesmaximal, characteristic
5#13066502C211yesmaximal, characteristic, complemented
6#13066463C211yesmaximal, characteristic, complemented
7C11×#1851C211yesmaximal, characteristic, complemented
8C22×C11×M16C2211yescharacteristic
9#10623322C2211yescharacteristic
10C2×C11×C4⋊C8—21no—
11C2×C11×C22⋊C8C2211yescharacteristic
12C4×C11×C22⋊C4C2211yescharacteristic
13C4×C22⋊Dic11C2211yescharacteristic
14#10622820C2211yescharacteristic
15C2×C22⋊(C11⋊C8)C2211yescharacteristic
16C2×#66889—21no—
17C2×#66886—21no—
18#10622724—21no—
19C8×C22⋊D11—21no—
20#10622342—21no—
21#10622341—21no—
22#10622340—21no—
23#10622333—21no—
24C11×#336—21no—
25#10622196—21no—
26#10622193—21no—
27#10622090C411yescharacteristic, complemented
28#10622090C411yescharacteristic, complemented
29#10622089C411yescharacteristic, complemented
30#10622089C411yescharacteristic, complemented
31C23×C4×C11C2311yescharacteristic
32C2×#4339D411yescharacteristic
33C2×C11×M16—21no—
34C2×C11×M16—21no—
35C2×C11×M16—42no—
36C22×C8×C11—21no—
37C22×C8×C11D411yescharacteristic
38C22×C8×C11D411yescharacteristic
39C2×C11×C22⋊C4—21no—
40C2×C42×C11—21no—
41#67006—21no—
42C2×C22⋊Dic11—21no—
43#66983C2×C411yescharacteristic
44#66983Q811yescharacteristic
45#66982—21no—
46C4×C22⋊D11—21no—
47C4×C22⋊D11—21no—
48#66979D411yescharacteristic
49#66977C2×C411yescharacteristic
50#66977Q811yescharacteristic
51C2×C4×Dic11—21no—
52C2×#4318D411yescharacteristic
53C2×#4318D411yescharacteristic
54C22×C11⋊C8—21no—
55C2×#4313—21no—
56C2×C8×D11—21no—
57C11×C4⋊C8—42no—
58C11×C22⋊C8—21no—
59C11×C22⋊C8—21no—
60C11×#95C2×C411yescharacteristic
61C11×#95C2×C411yescharacteristic
62C11⋊#95—21no—
63C22⋊(C11⋊C8)—21no—
64C22⋊(C11⋊C8)—21no—
65C22⋊(C11⋊C8)—21no—
66C22⋊(C11⋊C8)C2×C411yescharacteristic
67C22⋊(C11⋊C8)C2×C411yescharacteristic
68#66889—42no—
69#66886—42no—
70(C2×D11)⋊C8—21no—
71(C2×D11)⋊C8—21no—
72#66879—21no—
73Dic11⋊C8—21no—
74Dic11⋊C8—21no—
75C8×Dic11—21no—
76#8875—111nomaximal, Sylow
77C24×C11#4111yescharacteristic
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—41no—
81C22×C4×C11—41no—
82C22×C4×C11C22×C411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×Q811yescharacteristic
87C22×C4×C11#4111yescharacteristic
88C2×C22⋊D11—21no—
89C2×C22⋊D11—21no—
90C2×C22⋊D11—21no—
91C22×Dic11—41no—
92#4339—41no—
93#4339—41no—
94C2×D44C4⋊C411yescharacteristic
95C2×C4×D11—21no—
96C2×Dic22C4⋊C411yescharacteristic
97C11×M16—22no—
98C11×M16—22no—
99C11×M16—41no—
100C11×M16—41no—
101C2×C8×C11—22no—
102C2×C8×C11—21no—
103C2×C8×C11—21no—
104C2×C8×C11—41no—
105C2×C8×C11—41no—
106C2×C8×C11—41no—
107C2×C8×C11—41no—
108C11×C22⋊C4—42no—
109C42×C11—41no—
110C42×C11—41no—
111C22⋊Dic11—22no—
112C22⋊Dic11—21no—
113C22⋊Dic11—21no—
114C22⋊Dic11—21no—
115C22⋊Dic11—41no—
116(C2×D11)⋊C4—21no—
117(C2×D11)⋊C4—21no—
118C4⋊Dic11C4⋊C411yescharacteristic
119C4⋊Dic11C4⋊C411yescharacteristic
120Dic11⋊C4—21no—
121Dic11⋊C4—21no—
122C4×Dic11—21no—
123C4×Dic11—41no—
124C4×Dic11—41no—
125#4318—41no—
126#4318—41no—
127C2×C11⋊C8—21no—
128C2×C11⋊C8—21no—
129C2×C11⋊C8—21no—
130C2×C11⋊C8—21no—
131C2×C11⋊C8—41no—
132C2×C11⋊C8—41no—
133#4313—81no—
134C8×D11—81no—
135#2976—111no—
136#1871—111no—
137#1855—111no—
138#1851D1111yescharacteristic, complemented
139#1501—111no—
140#1297—111no—
141#1282—111no—
142C23×C11—21no—
143C23×C11—21no—
144C23×C11—41no—
145C23×C11—41no—
146C23×C11C4×D411yescharacteristic
147C23×C11C22⋊Q811yescharacteristic
148C23×C11#12311yescharacteristic
149C22×D11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—22no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11C2×C4⋊C411yescharacteristic
166C2×C4×C11C4×D411yescharacteristic
167C2×C4×C11#12011yescharacteristic
168C2×C4×C11C22⋊Q811yescharacteristic
169C22⋊D11—41no—
170C22⋊D11—41no—
171C22⋊D11—81no—
172C22⋊D11—81no—
173C2×Dic11—21no—
174C2×Dic11—21no—
175C2×Dic11—21no—
176C2×Dic11—42no—
177C2×Dic11—81no—
178C2×Dic11—81no—
179D44—41no—
180C4×D11—41no—
181C4×D11—41no—
182Dic22—41no—
183C8×C11—41no—
184C8×C11—42no—
185C8×C11—41no—
186C11⋊C8—41no—
187C11⋊C8—41no—
188C11⋊C8—41no—
189C11⋊C8—41no—
190C22×M16C2×D1111yescharacteristic
191#525—111no—
192#436—221no—
193#435—221no—
194#435—221no—
195C8×D4—221no—
196#433—221no—
197C2×#108—221no—
198C2×C4⋊C8—21no—
199C2×#104—221no—
200#408—221no—
201#407—111no—
202C2×C22⋊C8—111no—
203C2×C22⋊C8C2×D1111yescharacteristic
204C4×C22⋊C4—111no—
205C4×C22⋊C4C2×D1111yescharacteristic
206#341—221no—
207#339—221no—
208#336—21no—
209#328—111no—
210#328—111no—
211#327—111no—
212#327—111no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—21no—
221C22×C11—81no—
222C22×C11—81no—
223C22×C11#38511yescharacteristic
224C22×C11#44311yescharacteristic
225C22×C11#44411yescharacteristic
226C2×D11—41no—
227C2×D11—41no—
228C2×D11—41no—
229C4×C11—21no—
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—42no—
233C4×C11—81no—
234C4×C11B(4,𝔽2)11yescharacteristic
235C4×C11#45811yescharacteristic
236Dic11—41no—
237Dic11—41no—
238Dic11—41no—
239Dic11—82no—
240C2×#41—111no—
241C23×C4C22×D1111yescharacteristic
242C2×M16—21no—
243C2×M16—21no—
244C2×M16—42no—
245C2×M16—111no—
246C2×M16—111no—
247C2×M16—221no—
248C22×C8—21no—
249C22×C8—221no—
250C22×C8—221no—
251C22×C8C22⋊D1111yescharacteristic
252C22×C8C22⋊D1111yescharacteristic
253#123—221no—
254C22⋊Q8—111no—
255C22⋊Q8—111no—
256#121—111no—
257#121—111no—
258#120—221no—
259C4×D4—221no—
260C4×D4—221no—
261#117—111no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—221no—
264C2×C42—21no—
265C2×C42—221no—
266#108—442no—
267C4⋊C8—42no—
268C4⋊C8—221no—
269C4⋊C8—221no—
270#104—442no—
271C22⋊C8—21no—
272C22⋊C8—21no—
273C22⋊C8—111no—
274C22⋊C8—111no—
275C22⋊C8—221no—
276C22⋊C8—221no—
277C22⋊C8—221no—
278C22⋊C8—221no—
279C22⋊C8—221no—
280#97—221no—
281C4×C8—221no—
282#95—221no—
283#95C4×D1111yescharacteristic
284#95C4×D1111yescharacteristic
285C2×C11—21no—
286C2×C11—21no—
287C2×C11—41no—
288C2×C11—41no—
289C2×C11#186111yescharacteristic
290C2×C11#186611yescharacteristic
291C2×C11#186711yescharacteristic
292D11—81no—
293C24#433911yescharacteristic
294#41—441no—
295#41—441no—
296C2×Q8—111no—
297C2×D4—111no—
298C2×D4—221no—
299C2×D4—221no—
300C2×D4—221no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—221no—
306C22×C4—441no—
307C22×C4C2×C4×D1111yescharacteristic
308C22×C4D4×D1111yescharacteristic
309C22×C4D4×D1111yescharacteristic
310C22×C4Q8×D1111yescharacteristic
311C22×C4#434311yescharacteristic
312C22×C4C2×C22⋊D1111yescharacteristic
313M16—22no—
314M16—22no—
315M16—41no—
316M16—41no—
317M16—441no—
318M16—441no—
319M16—881no—
320C2×C8—22no—
321C2×C8—21no—
322C2×C8—21no—
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—41no—
327C2×C8—221no—
328C2×C8—221no—
329C2×C8—221no—
330C2×C8—221no—
331C2×C8—441no—
332C2×C8—441no—
333C2×C8—881no—
334C4⋊C4—111no—
335C4⋊C4—111no—
336C4⋊C4—221no—
337C4⋊C4—221no—
338C22⋊C4—42no—
339C22⋊C4—221no—
340C22⋊C4—221no—
341C22⋊C4—221no—
342C22⋊C4—221no—
343C22⋊C4—221no—
344C22⋊C4—222no—
345C22⋊C4—441no—
346C42—41no—
347C42—41no—
348C42—221no—
349C42—441no—
350C42—441no—
351C11#887511yescharacteristic, complemented, Sylow
352C23—21no—
353C23—21no—
354C23—41no—
355C23—41no—
356C23—221no—
357C23#6694711yescharacteristic
358C23#6694911yescharacteristic
359C23C4×C22⋊D1111yescharacteristic
360Q8—441no—
361D4—441no—
362D4—441no—
363D4—441no—
364D4—881no—
365D4—881no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—22no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—221no—
382C2×C4—221no—
383C2×C4—221no—
384C2×C4—441no—
385C2×C4—441no—
386C2×C4—442no—
387C2×C4—881no—
388C2×C4—881no—
389C2×C4C4⋊C4×D1111yescharacteristic
390C2×C4#6694611yescharacteristic
391C2×C4#6699011yescharacteristic
392C2×C4#6699911yescharacteristic
393C8—42no—
394C8—41no—
395C8—41no—
396C8—441no—
397C8—441no—
398C8—441no—
399C8—441no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—81no—
409C22—81no—
410C22—441no—
411C22—441no—
412C22—441no—
413C22#1062260211yescharacteristic
414C22#1062275711yescharacteristic
415C22#1062275811yescharacteristic
416C4—21no—
417C4—21no—
418C4—21no—
419C4—42no—
420C4—81no—
421C4—441no—
422C4—441no—
423C4—441no—
424C4—882no—
425C4#1062264511yescharacteristic
426C4#1062266611yescharacteristic
427C2—21no—
428C2—21no—
429C2—41no—
430C2—41no—
431C2—881no—
432C2#1306885511yescharacteristic
433C2#1306889011yescharacteristic
434C2#1306889511yescharacteristic
subgroupG/H
centerC2×C4#66990
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1851C2
socleC22×C11#385
prime radical#10623322C22
cosocleC23×C4×C11C23
hypercenter#1851D11
hypocenterC11#8875
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1851

Complements

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

NH ≅ G/Ntype
3. #13068821C2semidirect
5. #13066502C2semidirect
6. #13066463C2semidirect
7. C11×#1851C2semidirect
27. #10622090C4semidirect
28. #10622090C4semidirect
29. #10622089C4semidirect
30. #10622089C4semidirect
138. #1851D11semidirect
351. C11#8875semidirect

Maximal subgroups

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

subgroupindex
#130776612
#130689182
#130688212
#130671052
#130665022
#130664632
C11×#18512
#887511