Finite Group Databasebeta

← #14651739

Subgroups — #14651739

Order 2816.

524 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 95 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#13077643C211yesmaximal, characteristic
2#13072927C211yesmaximal, characteristic
3#13068696C211yesmaximal, characteristic, complemented
4#13066952C211yesmaximal, characteristic
5#13066523C211yesmaximal, characteristic, complemented
6#13066521C211yesmaximal, characteristic, complemented
7C11×#1821C211yesmaximal, characteristic, complemented
8C22×C11×C4⋊C4C2211yescharacteristic
9C2×C4×C22⋊D11C2211yescharacteristic
10C11×#407C2211yescharacteristic
11C11×#407C2211yescharacteristic
12#10622826C412yes—
13#10622825C2211yescharacteristic
14#10622823C412yes—
15#10622820C2211yescharacteristic
16#10622820C2211yescharacteristic
17#10622740—22no—
18#10622605—21no—
19#10622600—21no—
20#10622595—21no—
21#10622586—21no—
22#10622341—22no—
23D11×C22⋊C8—21no—
24#10622332—21no—
25C11×#343—22no—
26#10622168—22no—
27#10622107—21no—
28#10622106—21no—
29C23×C4×C11C2×C412yes—
30C23×C4×C11C2311yescharacteristic
31C22×C22⋊D11C2×C411yescharacteristic
32C22×C4×D11D411yescharacteristic
33C2×C11×M16—21no—
34C2×C11×M16D412yes—
35C2×C11×C4⋊C4—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×C22⋊Dic11C2×C411yescharacteristic
42C2×C22⋊Dic11C2×C412yes—
43C4×C22⋊D11—21no—
44C4×C22⋊D11—21no—
45C4×C22⋊D11—21no—
46C4×C22⋊D11—21no—
47C2×(C2×D11)⋊C4—22no—
48C2×(C2×D11)⋊C4D411yescharacteristic
49C2×C4⋊Dic11—21no—
50C2×Dic11⋊C4—22no—
51C2×Dic11⋊C4D411yescharacteristic
52C2×C4×Dic11D411yescharacteristic
53C2×#4318—21no—
54C2×#4318D412yes—
55C2×C8×D11—22no—
56C11×C22⋊C8—21no—
57C11×C22⋊C8—21no—
58C11×C22⋊C8—21no—
59C11×C22⋊C8—21no—
60C11⋊#95—21no—
61C11⋊#95—22no—
62C11⋊#95—22no—
63C22⋊(C11⋊C8)—21no—
64C22⋊(C11⋊C8)—21no—
65C22⋊(C11⋊C8)—21no—
66C22⋊(C11⋊C8)—21no—
67(C2×D11)⋊C8—22no—
68#66879—22no—
69Dic11⋊C8—22no—
70#9509—111nomaximal, Sylow
71C24×C11C22×C411yescharacteristic
72C23×D11C22⋊C411yescharacteristic
73C22×C4×C11—22no—
74C22×C4×C11—22no—
75C22×C4×C11—22no—
76C22×C4×C11—42no—
77C22×C4×C11—82no—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11#4111yescharacteristic
83C22×C4×C11#4111yescharacteristic
84C2×C22⋊D11—21no—
85C2×C22⋊D11—21no—
86C2×C22⋊D11—22no—
87C2×C22⋊D11—41no—
88C22×Dic11—22no—
89C22×Dic11C22⋊C411yescharacteristic
90C22×Dic11C22⋊C411yescharacteristic
91C22×Dic11C22⋊C411yescharacteristic
92C2×C4×D11—21no—
93C2×C4×D11—21no—
94C2×C4×D11—42no—
95C11×M16—42no—
96C11×M16—42no—
97C2×C8×C11—22no—
98C2×C8×C11—41no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C22⋊Dic11—21no—
104C22⋊Dic11—21no—
105C22⋊Dic11—42no—
106(C2×D11)⋊C4—21no—
107(C2×D11)⋊C4—21no—
108(C2×D11)⋊C4—82no—
109C4⋊Dic11—42no—
110Dic11⋊C4—21no—
111Dic11⋊C4—21no—
112Dic11⋊C4—82no—
113C4×Dic11—21no—
114C4×Dic11—21no—
115#4318—42no—
116#4318—42no—
117C2×C11⋊C8—22no—
118C2×C11⋊C8—41no—
119C8×D11—82no—
120#2973—111no—
121#2487—111no—
122#1821—111no—
123#1821D1111yescharacteristic, complemented
124#1465—111no—
125#1305—111no—
126#1305—111no—
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—41no—
130C23×C11—41no—
131C23×C11C2×C22⋊C411yescharacteristic
132C23×C11C4×D411yescharacteristic
133C23×C11C4×D411yescharacteristic
134C22×D11—21no—
135C22×D11—21no—
136C22×D11—41no—
137C22×D11—41no—
138C22×D11#10112yes—
139C2×C4×C11—22no—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—42no—
146C2×C4×C11—42no—
147C2×C4×C11—42no—
148C2×C4×C11—82no—
149C2×C4×C11—82no—
150C2×C4×C11#12011yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12311yescharacteristic
154C22⋊D11—42no—
155C22⋊D11—42no—
156C2×Dic11—21no—
157C2×Dic11—21no—
158C2×Dic11—21no—
159C2×Dic11—21no—
160C2×Dic11—21no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—42no—
164C2×Dic11—42no—
165C2×Dic11—42no—
166C4×D11—42no—
167C4×D11—81no—
168C8×C11—42no—
169C8×C11—81no—
170C11⋊C8—42no—
171C11⋊C8—81no—
172C2×C4×D4—111no—
173C22×C4⋊C4C2×D1111yescharacteristic
174#435—222no—
175#435—222no—
176#432—221no—
177#407—111no—
178#407—111no—
179#407C2×D1111yescharacteristic
180#407C2×D1111yescharacteristic
181C2×C22⋊C8—221no—
182#400—221no—
183#399—221no—
184#389—221no—
185#386—112no—
186#385—112no—
187#380—111no—
188#380—221no—
189#343—22no—
190#343—222no—
191#324—221no—
192#323—221no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11—21no—
197C22×C11—21no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11—42no—
202C22×C11—42no—
203C22×C11#38611yescharacteristic
204C22×C11C2×#10111yescharacteristic
205C22×C11#41311yescharacteristic
206C2×D11—22no—
207C2×D11—41no—
208C2×D11—41no—
209C2×D11—42no—
210C2×D11—81no—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—82no—
215C4×C11#45812yes—
216Dic11—41no—
217Dic11—41no—
218Dic11—41no—
219Dic11—82no—
220C22×D4—111no—
221C23×C4—111no—
222C23×C4C4×D1112yes—
223C23×C4C22×D1111yescharacteristic
224C2×M16—21no—
225C2×M16—112no—
226C2×M16—221no—
227C2×M16C22⋊D1112yes—
228C22×C8—222no—
229C4×D4—221no—
230C4×D4—221no—
231C4×D4—221no—
232C4×D4—221no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—111no—
240C2×C4⋊C4—221no—
241C2×C4⋊C4—222no—
242C2×C22⋊C4—111no—
243C2×C22⋊C4—111no—
244C2×C22⋊C4—112no—
245C2×C22⋊C4—222no—
246C2×C42—111no—
247C4⋊C8—222no—
248C22⋊C8—21no—
249C22⋊C8—21no—
250C22⋊C8—21no—
251C22⋊C8—21no—
252C22⋊C8—222no—
253C22⋊C8—221no—
254C22⋊C8—221no—
255C22⋊C8—221no—
256C22⋊C8—221no—
257#97—222no—
258#95—222no—
259#95—222no—
260#95—221no—
261C2×C11—21no—
262C2×C11—21no—
263C2×C11—41no—
264C2×C11—41no—
265C2×C11#189011yescharacteristic
266C2×C11#190111yescharacteristic
267C2×C11#191411yescharacteristic
268D11—42no—
269C24—111no—
270C24C2×C4×D1111yescharacteristic
271C2×D4—222no—
272C2×D4—221no—
273C2×D4—221no—
274C2×D4—441no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—42no—
279C22×C4—82no—
280C22×C4—111no—
281C22×C4—111no—
282C22×C4—111no—
283C22×C4—221no—
284C22×C4—221no—
285C22×C4—222no—
286C22×C4—442no—
287C22×C4#433911yescharacteristic
288C22×C4D4×D1111yescharacteristic
289C22×C4D4×D1111yescharacteristic
290C22×C4D4×D1111yescharacteristic
291C22×C4#434111yescharacteristic
292C22×C4C2×C22⋊D1111yescharacteristic
293M16—42no—
294M16—42no—
295M16—442no—
296M16—442no—
297C2×C8—22no—
298C2×C8—41no—
299C2×C8—222no—
300C2×C8—441no—
301C2×C8—882no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—221no—
307C4⋊C4—221no—
308C4⋊C4—442no—
309C4⋊C4—882no—
310C22⋊C4—221no—
311C22⋊C4—221no—
312C22⋊C4—221no—
313C22⋊C4—221no—
314C22⋊C4—442no—
315C22⋊C4—882no—
316C42—221no—
317C42—221no—
318C11#950911yescharacteristic, complemented, Sylow
319C23—21no—
320C23—21no—
321C23—41no—
322C23—41no—
323C23—112no—
324C23—221no—
325C23—221no—
326C23—441no—
327C23—441no—
328C23C22⋊C4×D1111yescharacteristic
329C23(C22⋊D11)⋊C411yescharacteristic
330C23C4×C22⋊D1111yescharacteristic
331D4—442no—
332D4—442no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—82no—
343C2×C4—82no—
344C2×C4—221no—
345C2×C4—221no—
346C2×C4—221no—
347C2×C4—221no—
348C2×C4—221no—
349C2×C4—442no—
350C2×C4—441no—
351C2×C4—441no—
352C2×C4—442no—
353C2×C4—442no—
354C2×C4—442no—
355C2×C4—881no—
356C2×C4#6693611yescharacteristic
357C2×C4#6693711yescharacteristic
358C2×C4#6699011yescharacteristic
359C2×C4#6699111yescharacteristic
360C8—42no—
361C8—81no—
362C8—442no—
363C8—881no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—42no—
373C22—42no—
374C22—222no—
375C22—442no—
376C22—441no—
377C22—441no—
378C22—881no—
379C22D11×#10111yescharacteristic
380C22#1062236411yescharacteristic
381C22#1062256911yescharacteristic
382C4—21no—
383C4—21no—
384C4—21no—
385C4—82no—
386C4—441no—
387C4—441no—
388C4—441no—
389C4—882no—
390C4#1062266612yes—
391C2—21no—
392C2—21no—
393C2—41no—
394C2—41no—
395C2—442no—
396C2#1306902611yescharacteristic
397C2#1306908111yescharacteristic
398C2#1306916011yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC24×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1821C2
socleC22×C11#386
prime radicalC22×C22⋊D11C2×C4
cosocleC23×C4×C11C23
hypercenter#1821D11
hypocenterC11#9509
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1821

Complements

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

NH ≅ G/Ntype
3. #13068696C2semidirect
5. #13066523C2semidirect
6. #13066521C2semidirect
7. C11×#1821C2semidirect
123. #1821D11semidirect
318. C11#9509semidirect

Maximal subgroups

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

subgroupindex
#130776432
#130729272
#130686962
#130669522
#130665232
#130665212
C11×#18212
#950911