Finite Group Databasebeta

← #14651729

Subgroups — #14651729

Order 2816.

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

normal subgroups only

This group has 544 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#13072918C211yesmaximal, 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×#66982C412yes—
10C2×C4×C22⋊D11C2211yescharacteristic
11C11×#407C2211yescharacteristic
12C11×#407C2211yescharacteristic
13#10622825C2211yescharacteristic
14#10622824C412yes—
15#10622820C2211yescharacteristic
16#10622820C2211yescharacteristic
17#10622740—22no—
18#10622606—21no—
19#10622600—21no—
20#10622593—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—
43#66982—44no—
44C4×C22⋊D11—21no—
45C4×C22⋊D11—21no—
46C4×C22⋊D11—21no—
47C4×C22⋊D11—21no—
48C2×(C2×D11)⋊C4—22no—
49C2×(C2×D11)⋊C4D411yescharacteristic
50C2×C4⋊Dic11—21no—
51C2×Dic11⋊C4—22no—
52C2×Dic11⋊C4D411yescharacteristic
53C2×C4×Dic11D411yescharacteristic
54C2×#4318—21no—
55C2×#4318D412yes—
56C2×C8×D11—22no—
57C11×C22⋊C8—21no—
58C11×C22⋊C8—21no—
59C11×C22⋊C8—21no—
60C11×C22⋊C8—21no—
61C11⋊#95—21no—
62C11⋊#95—22no—
63C11⋊#95—22no—
64C22⋊(C11⋊C8)—21no—
65C22⋊(C11⋊C8)—21no—
66C22⋊(C11⋊C8)—21no—
67C22⋊(C11⋊C8)—21no—
68(C2×D11)⋊C8—22no—
69#66879—22no—
70Dic11⋊C8—22no—
71#9507—111nomaximal, Sylow
72C24×C11C22×C411yescharacteristic
73C23×D11C22⋊C411yescharacteristic
74C22×C4×C11—22no—
75C22×C4×C11—22no—
76C22×C4×C11—22no—
77C22×C4×C11—42no—
78C22×C4×C11—42no—
79C22×C4×C11—42no—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11#4111yescharacteristic
85C22×C4×C11#4111yescharacteristic
86C2×C22⋊D11—21no—
87C2×C22⋊D11—21no—
88C2×C22⋊D11—22no—
89C2×C22⋊D11—41no—
90C22×Dic11—22no—
91C22×Dic11C22⋊C411yescharacteristic
92C22×Dic11C22⋊C411yescharacteristic
93C22×Dic11C22⋊C411yescharacteristic
94C2×C4×D11—21no—
95C2×C4×D11—21no—
96C2×C4×D11—42no—
97C11×M16—42no—
98C11×M16—42no—
99C2×C8×C11—22no—
100C2×C8×C11—41no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C22⋊Dic11—21no—
106C22⋊Dic11—21no—
107C22⋊Dic11—42no—
108(C2×D11)⋊C4—21no—
109(C2×D11)⋊C4—21no—
110(C2×D11)⋊C4—44no—
111C4⋊Dic11—42no—
112Dic11⋊C4—21no—
113Dic11⋊C4—21no—
114Dic11⋊C4—44no—
115C4×Dic11—21no—
116C4×Dic11—21no—
117#4318—42no—
118#4318—42no—
119C2×C11⋊C8—22no—
120C2×C11⋊C8—41no—
121C8×D11—82no—
122#2973—111no—
123#2486—111no—
124#1821—111no—
125#1821D1111yescharacteristic, complemented
126#1465—111no—
127#1305—111no—
128#1305—111no—
129C23×C11—21no—
130C23×C11—21no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11C2×C22⋊C411yescharacteristic
134C23×C11C4×D411yescharacteristic
135C23×C11C4×D411yescharacteristic
136C22×D11—21no—
137C22×D11—21no—
138C22×D11—41no—
139C22×D11—41no—
140C22×D11#10012yes—
141C2×C4×C11—22no—
142C2×C4×C11—22no—
143C2×C4×C11—22no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11—82no—
151C2×C4×C11—82no—
152C2×C4×C11#12011yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11#12111yescharacteristic
155C2×C4×C11#12311yescharacteristic
156C22⋊D11—42no—
157C22⋊D11—42no—
158C2×Dic11—21no—
159C2×Dic11—21no—
160C2×Dic11—21no—
161C2×Dic11—21no—
162C2×Dic11—21no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—42no—
166C2×Dic11—42no—
167C2×Dic11—42no—
168C4×D11—42no—
169C4×D11—81no—
170C8×C11—42no—
171C8×C11—81no—
172C11⋊C8—42no—
173C11⋊C8—81no—
174C2×#123—112no—
175C2×C4×D4—111no—
176C22×C4⋊C4C2×D1111yescharacteristic
177#435—222no—
178#435—222no—
179#432—221no—
180#407—111no—
181#407—111no—
182#407C2×D1111yescharacteristic
183#407C2×D1111yescharacteristic
184C2×C22⋊C8—221no—
185#398—221no—
186#397—221no—
187#389—221no—
188#381—112no—
189#380—111no—
190#380—221no—
191#343—22no—
192#343—222no—
193#324—221no—
194#323—221no—
195C22×C11—21no—
196C22×C11—21no—
197C22×C11—21no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11—42no—
204C22×C11—42no—
205C22×C11#38611yescharacteristic
206C22×C11C2×#10011yescharacteristic
207C22×C11#41311yescharacteristic
208C2×D11—22no—
209C2×D11—41no—
210C2×D11—41no—
211C2×D11—42no—
212C2×D11—81no—
213C4×C11—21no—
214C4×C11—21no—
215C4×C11—21no—
216C4×C11—82no—
217C4×C11#45812yes—
218Dic11—41no—
219Dic11—41no—
220Dic11—41no—
221Dic11—82no—
222C22×D4—111no—
223C23×C4—111no—
224C23×C4C4×D1112yes—
225C23×C4C22×D1111yescharacteristic
226C2×M16—21no—
227C2×M16—112no—
228C2×M16—221no—
229C2×M16C22⋊D1112yes—
230C22×C8—222no—
231#123—444no—
232C4×D4—221no—
233C4×D4—221no—
234C4×D4—221no—
235C4×D4—221no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—111no—
243C2×C4⋊C4—222no—
244C2×C4⋊C4—221no—
245C2×C22⋊C4—111no—
246C2×C22⋊C4—111no—
247C2×C22⋊C4—112no—
248C2×C22⋊C4—222no—
249C2×C42—111no—
250C4⋊C8—222no—
251C22⋊C8—21no—
252C22⋊C8—21no—
253C22⋊C8—21no—
254C22⋊C8—21no—
255C22⋊C8—222no—
256C22⋊C8—221no—
257C22⋊C8—221no—
258C22⋊C8—221no—
259C22⋊C8—221no—
260#97—222no—
261#95—222no—
262#95—222no—
263#95—221no—
264C2×C11—21no—
265C2×C11—21no—
266C2×C11—41no—
267C2×C11—41no—
268C2×C11#189011yescharacteristic
269C2×C11#190011yescharacteristic
270C2×C11#191511yescharacteristic
271D11—42no—
272C24—111no—
273C24C2×C4×D1111yescharacteristic
274C2×D4—222no—
275C2×D4—221no—
276C2×D4—221no—
277C2×D4—441no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—111no—
285C22×C4—111no—
286C22×C4—111no—
287C22×C4—221no—
288C22×C4—221no—
289C22×C4—222no—
290C22×C4—442no—
291C22×C4#433911yescharacteristic
292C22×C4D4×D1111yescharacteristic
293C22×C4D4×D1111yescharacteristic
294C22×C4D4×D1111yescharacteristic
295C22×C4#434111yescharacteristic
296C22×C4C2×C22⋊D1111yescharacteristic
297M16—42no—
298M16—42no—
299M16—442no—
300M16—442no—
301C2×C8—22no—
302C2×C8—41no—
303C2×C8—222no—
304C2×C8—441no—
305C2×C8—882no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—221no—
311C4⋊C4—221no—
312C4⋊C4—442no—
313C4⋊C4—444no—
314C22⋊C4—221no—
315C22⋊C4—221no—
316C22⋊C4—221no—
317C22⋊C4—221no—
318C22⋊C4—444no—
319C22⋊C4—442no—
320C42—221no—
321C42—221no—
322C11#950711yescharacteristic, complemented, Sylow
323C23—21no—
324C23—21no—
325C23—41no—
326C23—41no—
327C23—112no—
328C23—221no—
329C23—221no—
330C23—441no—
331C23—441no—
332C23C22⋊C4×D1111yescharacteristic
333C23(C22⋊D11)⋊C411yescharacteristic
334C23C4×C22⋊D1111yescharacteristic
335D4—442no—
336D4—442no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—82no—
347C2×C4—82no—
348C2×C4—221no—
349C2×C4—221no—
350C2×C4—221no—
351C2×C4—221no—
352C2×C4—221no—
353C2×C4—442no—
354C2×C4—441no—
355C2×C4—441no—
356C2×C4—442no—
357C2×C4—442no—
358C2×C4—442no—
359C2×C4—881no—
360C2×C4#6693611yescharacteristic
361C2×C4#6693711yescharacteristic
362C2×C4#6699011yescharacteristic
363C2×C4#6699111yescharacteristic
364C8—42no—
365C8—81no—
366C8—442no—
367C8—881no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—42no—
377C22—42no—
378C22—222no—
379C22—442no—
380C22—441no—
381C22—441no—
382C22—881no—
383C22D11×#10011yescharacteristic
384C22#1062235811yescharacteristic
385C22#1062256911yescharacteristic
386C4—21no—
387C4—21no—
388C4—21no—
389C4—82no—
390C4—441no—
391C4—441no—
392C4—441no—
393C4—882no—
394C4#1062266612yes—
395C2—21no—
396C2—21no—
397C2—41no—
398C2—41no—
399C2—442no—
400C2#1306902611yescharacteristic
401C2#1306907611yescharacteristic
402C2#1306916511yescharacteristic
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#9507
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
125. #1821D11semidirect
322. C11#9507semidirect

Maximal subgroups

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

subgroupindex
#130776432
#130729182
#130686962
#130669522
#130665232
#130665212
C11×#18212
#950711