Finite Group Databasebeta

← #14651764

Subgroups — #14651764

Order 2816.

478 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 89 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#13077251C211yesmaximal, characteristic
2#13072903C211yesmaximal, characteristic
3#13068697C211yesmaximal, characteristic
4#13066946C211yesmaximal, characteristic
5#13066525C211yesmaximal, characteristic
6#13066525C211yesmaximal, characteristic
7C11×#1463C211yesmaximal, characteristic
8C22×C11×C4⋊C4C2211yescharacteristic
9C2×#66979C2211yescharacteristic
10C11×#407C2211yescharacteristic
11C11×#407C2211yescharacteristic
12#10622824C411yescharacteristic
13#10622824C411yescharacteristic
14#10622824C2211yescharacteristic
15#10622823C411yescharacteristic
16#10622823C411yescharacteristic
17#10622820C2211yescharacteristic
18#10622820C2211yescharacteristic
19#10622731—21no—
20M16×Dic11—21no—
21#10622599—21no—
22#10622596—21no—
23#10622591—21no—
24#10622591—21no—
25#10622333—22no—
26#10622333—22no—
27C11×#324—22no—
28#10622192—21no—
29#10622192—21no—
30#10622166—22no—
31C23×C4×C11C2×C411yescharacteristic
32C23×C4×C11C2×C411yescharacteristic
33C23×C4×C11C2311yescharacteristic
34C2×C11×M16—21no—
35C2×C11×M16—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—21no—
42C2×C22⋊Dic11C2×C411yescharacteristic
43C2×C22⋊Dic11C2×C411yescharacteristic
44C2×C22⋊Dic11C2×C411yescharacteristic
45C2×C22⋊Dic11C2×C411yescharacteristic
46#66979—21no—
47#66979—21no—
48#66979—21no—
49#66979—21no—
50C2×C4⋊Dic11D411yescharacteristic
51C2×C4⋊Dic11D411yescharacteristic
52C2×Dic11⋊C4—21no—
53C2×Dic11⋊C4—21no—
54C2×C4×Dic11D411yescharacteristic
55C2×C4×Dic11D411yescharacteristic
56C2×#4318—21no—
57C2×#4318—21no—
58C11×C22⋊C8—21no—
59C11×C22⋊C8—21no—
60C11×C22⋊C8—21no—
61C11×C22⋊C8D412yes—
62C11⋊#95—21no—
63C11⋊#95—21no—
64C11⋊#95—21no—
65C11⋊#95—21no—
66C11⋊#95—21no—
67C11⋊#95—21no—
68C11⋊#95—21no—
69C11⋊#95—21no—
70C22⋊(C11⋊C8)—21no—
71C22⋊(C11⋊C8)—21no—
72C22⋊(C11⋊C8)—21no—
73C22⋊(C11⋊C8)D412yes—
74#66879—22no—
75Dic11⋊C8—24no—
76C8×Dic11—22no—
77#9514—111nomaximal, Sylow
78C24×C11C22×C411yescharacteristic
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—42no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11#4111yescharacteristic
95C22×C4×C11#4111yescharacteristic
96C22×Dic11—21no—
97C22×Dic11—21no—
98C22×Dic11C22⋊C411yescharacteristic
99C22×Dic11C22⋊C411yescharacteristic
100C22×Dic11C22⋊C411yescharacteristic
101C22×Dic11C22⋊C411yescharacteristic
102C11×M16—41no—
103C11×M16—41no—
104C11×M16—41no—
105C11×M16—41no—
106C2×C8×C11—22no—
107C2×C8×C11—41no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C22⋊Dic11—21no—
113C22⋊Dic11—21no—
114C22⋊Dic11—21no—
115C22⋊Dic11—21no—
116C22⋊Dic11—41no—
117C22⋊Dic11—41no—
118C4⋊Dic11—21no—
119C4⋊Dic11—21no—
120C4⋊Dic11—21no—
121C4⋊Dic11—21no—
122Dic11⋊C4—42no—
123Dic11⋊C4—42no—
124C4×Dic11—21no—
125C4×Dic11—21no—
126C4×Dic11—21no—
127C4×Dic11—21no—
128#4318—41no—
129#4318—41no—
130#4318—41no—
131#4318—41no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—41no—
134#2921—111no—
135#2484—111no—
136#1822—111no—
137#1463—111no—
138#1463D1111yescharacteristic
139#1306—111no—
140#1306—111no—
141C23×C11—21no—
142C23×C11—21no—
143C23×C11—41no—
144C23×C11—41no—
145C23×C11C2×C22⋊C411yescharacteristic
146C23×C11C4×D411yescharacteristic
147C23×C11C4×D411yescharacteristic
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—22no—
153C2×C4×C11—22no—
154C2×C4×C11—22no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
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×C11—41no—
166C2×C4×C11—81no—
167C2×C4×C11—81no—
168C2×C4×C11#12011yescharacteristic
169C2×C4×C11#12111yescharacteristic
170C2×C4×C11#12111yescharacteristic
171C2×C4×C11#12311yescharacteristic
172C2×Dic11—21no—
173C2×Dic11—21no—
174C2×Dic11—21no—
175C2×Dic11—21no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11—41no—
186C8×C11—42no—
187C8×C11—81no—
188C11⋊C8—42no—
189C11⋊C8—81no—
190C2×#117—111no—
191C22×C4⋊C4C2×D1111yescharacteristic
192#433—222no—
193#433—222no—
194#423—221no—
195#407—111no—
196#407—111no—
197#407C2×D1111yescharacteristic
198#407C2×D1111yescharacteristic
199C4×M16—221no—
200#400—221no—
201#398—221no—
202#387—221no—
203#387—221no—
204#385—111no—
205#385—111no—
206#381—111no—
207#381—111no—
208#381—111no—
209#343—221no—
210#343—221no—
211#324—22no—
212#324—222no—
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—42no—
222C22×C11—42no—
223C22×C11#38611yescharacteristic
224C22×C11#41011yescharacteristic
225C22×C11#41011yescharacteristic
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—21no—
229C4×C11—21no—
230C4×C11—42no—
231C4×C11—81no—
232Dic11—41no—
233Dic11—41no—
234Dic11—41no—
235Dic11—41no—
236Dic11—81no—
237Dic11—81no—
238C23×C4C4×D1111yescharacteristic
239C23×C4C4×D1111yescharacteristic
240C23×C4C22×D1111yescharacteristic
241C2×M16—21no—
242C2×M16—21no—
243C2×M16—221no—
244C2×M16—221no—
245#117—221no—
246#117—221no—
247#117—221no—
248#117—221no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—111no—
256C2×C4⋊C4—111no—
257C2×C4⋊C4—221no—
258C2×C4⋊C4—221no—
259C2×C22⋊C4—111no—
260C2×C22⋊C4—111no—
261C2×C22⋊C4—111no—
262C2×C22⋊C4—111no—
263C2×C42—111no—
264C2×C42—111no—
265C4⋊C8—224no—
266C22⋊C8—21no—
267C22⋊C8—21no—
268C22⋊C8—21no—
269C22⋊C8—112no—
270C22⋊C8—221no—
271C22⋊C8—221no—
272C22⋊C8—221no—
273C22⋊C8C22⋊D1112yes—
274#97—222no—
275C4×C8—222no—
276#95—221no—
277#95—221no—
278#95—221no—
279#95—221no—
280#95—221no—
281#95—221no—
282#95—221no—
283#95—221no—
284C2×C11—21no—
285C2×C11—21no—
286C2×C11—41no—
287C2×C11—41no—
288C2×C11#189111yescharacteristic
289C2×C11#189911yescharacteristic
290C2×C11#191511yescharacteristic
291C24C2×C4×D1111yescharacteristic
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—42no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—111no—
304C22×C4—111no—
305C22×C4—111no—
306C22×C4—111no—
307C22×C4—221no—
308C22×C4—221no—
309C22×C4#433911yescharacteristic
310C22×C4D4×D1111yescharacteristic
311C22×C4D4×D1111yescharacteristic
312C22×C4D4×D1111yescharacteristic
313C22×C4#434111yescharacteristic
314C22×C4C2×C22⋊D1111yescharacteristic
315M16—41no—
316M16—41no—
317M16—41no—
318M16—41no—
319M16—441no—
320M16—441no—
321M16—441no—
322M16—441no—
323C2×C8—22no—
324C2×C8—41no—
325C2×C8—222no—
326C2×C8—441no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—221no—
332C4⋊C4—221no—
333C4⋊C4—221no—
334C4⋊C4—221no—
335C4⋊C4—442no—
336C4⋊C4—442no—
337C22⋊C4—221no—
338C22⋊C4—221no—
339C22⋊C4—221no—
340C22⋊C4—221no—
341C22⋊C4—441no—
342C22⋊C4—441no—
343C42—221no—
344C42—221no—
345C42—221no—
346C42—221no—
347C11#951411yescharacteristic, complemented, Sylow
348C23—21no—
349C23—21no—
350C23—41no—
351C23—41no—
352C23C22⋊C4×D1111yescharacteristic
353C23(C22⋊D11)⋊C411yescharacteristic
354C23C4×C22⋊D1111yescharacteristic
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4—221no—
376C2×C4—221no—
377C2×C4—221no—
378C2×C4—221no—
379C2×C4—441no—
380C2×C4—441no—
381C2×C4—441no—
382C2×C4—441no—
383C2×C4—441no—
384C2×C4—441no—
385C2×C4—441no—
386C2×C4—441no—
387C2×C4—441no—
388C2×C4—441no—
389C2×C4#6693611yescharacteristic
390C2×C4#6693711yescharacteristic
391C2×C4#6699011yescharacteristic
392C2×C4#6699111yescharacteristic
393C8—42no—
394C8—81no—
395C8—442no—
396C8—881no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—42no—
406C22—42no—
407C22#1062235311yescharacteristic
408C22#1062235311yescharacteristic
409C22#1062256911yescharacteristic
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—42no—
415C4—81no—
416C4—441no—
417C4—441no—
418C4—441no—
419C4—441no—
420C4—881no—
421C4—881no—
422C2—21no—
423C2—21no—
424C2—41no—
425C2—41no—
426C2#1306903111yescharacteristic
427C2#1306907111yescharacteristic
428C2#1306916511yescharacteristic
subgroupG/H
centerC22#10622569
commutator, prime radicalC24×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1463C2
socleC22×C11#386
cosocleC23×C4×C11C23
hypercenter#1463D11
hypocenterC11#9514
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
347. C11#9514semidirect

Maximal subgroups

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

subgroupindex
#130772512
#130729032
#130686972
#130669462
#130665252
C11×#14632
#951411