Finite Group Databasebeta

← #14655143

Subgroups — #14655143

Order 2816.

534 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 85 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#13079603C211yesmaximal, characteristic
2#13079012C211yesmaximal, characteristic, complemented
3#13067333C211yesmaximal, characteristic, complemented
4#13067214C211yesmaximal, characteristic, complemented
5#13067123C211yesmaximal, characteristic, complemented
6#13066509C211yesmaximal, characteristic, complemented
7C11×#2640C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×#124C2211yescharacteristic
10#10623008C2211yescharacteristic
11C11×#397—22no—
12C11×#393—22no—
13C11×#391—21no—
14C11×#390—21no—
15C11×#376C2211yescharacteristic
16#10622840—21no—
17#10622830—21no—
18#10622706—21no—
19#10622702—22no—
20#10622701—21no—
21#10622671—21no—
22#10622670—22no—
23#10622668—21no—
24#10622579—22no—
25#10622539C2211yescharacteristic
26#10622539C2211yescharacteristic
27C4×#4318C2211yescharacteristic
28#10622185—22no—
29#10622178—22no—
30#10622089—22no—
31C22×Q8×C11—21no—
32C22×Q8×C11D411yescharacteristic
33C22×D4×C11D411yescharacteristic
34C2×#4339—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×#124—21no—
40C11×#124—21no—
41C11×#124—21no—
42C11×#124—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4D412yes—
45C2×C11×C22⋊C4—21no—
46C2×C11×C22⋊C4—21no—
47C2×C11×C22⋊C4—24no—
48C2×C42×C11—21no—
49C2×C42×C11C2311yescharacteristic
50C2×#4325—22no—
51C2×#4323—22no—
52#66983—21no—
53#66983—21no—
54C2×#4318—21no—
55#66928—21no—
56#66927D411yescharacteristic
57C4×D44—21no—
58C4×D44—21no—
59#66922D411yescharacteristic
60C11×#95—24no—
61C11×#95—21no—
62C11×#95D412yes—
63#66899—22no—
64#66896—22no—
65C22⋊(C11⋊C8)—21no—
66C22⋊(C11⋊C8)—21no—
67#66874—24no—
68#66873—24no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)D412yes—
71#66867—21no—
72#66867—21no—
73#66867D412yes—
74C4×C11⋊C8—21no—
75#10092—111nomaximal, Sylow
76C24×C11—21no—
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C2×Q8×C11—42no—
80C2×Q8×C11—41no—
81C2×Q8×C11—41no—
82C2×Q8×C11—82no—
83C2×D4×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—42no—
86C22×C4×C11—21no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C2×C22⋊D11—41no—
93#4339—44no—
94C2×D44—21no—
95C2×D44—21no—
96C2×D44—21no—
97C2×C4×D11—41no—
98C2×Dic22—21no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C22⋊C4—41no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—41no—
106C11×C22⋊C4—41no—
107C11×C22⋊C4—84no—
108C42×C11—42no—
109C42×C11C2×D411yescharacteristic
110C42×C11C2×D411yescharacteristic
111C42×C11C2×D411yescharacteristic
112C42×C11#4111yescharacteristic
113#4325—82no—
114#4323—82no—
115(C2×D11)⋊C4—41no—
116(C2×D11)⋊C4—41no—
117C4⋊Dic11—21no—
118C4⋊Dic11—21no—
119#4318—42no—
120C2×C11⋊C8—22no—
121C2×C11⋊C8—22no—
122C2×C11⋊C8—41no—
123#3213—111no—
124#3141—111no—
125#2640D1111yescharacteristic, complemented
126#1556—111no—
127#1527—111no—
128#1505—111no—
129#1300—111no—
130C23×C11—42no—
131C23×C11—42no—
132C23×C11—41no—
133C23×C11—42no—
134C23×C11#12011yescharacteristic
135C22×D11—41no—
136Q8×C11—42no—
137Q8×C11—81no—
138Q8×C11—82no—
139Q8×C11—82no—
140D4×C11—42no—
141D4×C11—81no—
142C2×C4×C11—22no—
143C2×C4×C11—22no—
144C2×C4×C11—41no—
145C2×C4×C11—42no—
146C2×C4×C11—42no—
147C2×C4×C11—44no—
148C2×C4×C11—42no—
149C2×C4×C11—41no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11#12011yescharacteristic
153C2×C4×C11#12011yescharacteristic
154C2×C4×C11#12111yescharacteristic
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12711yescharacteristic
158C22⋊D11—82no—
159C2×Dic11—41no—
160D44—42no—
161D44—42no—
162D44—81no—
163C4×D11—82no—
164Dic22—42no—
165C11⋊C8—42no—
166C11⋊C8—42no—
167C11⋊C8—81no—
168#532—111no—
169C2×C4⋊Q8C2×D1111yescharacteristic
170C2×#124C2×D1111yescharacteristic
171#496—221no—
172#489—222no—
173#489—221no—
174#487—221no—
175#486—221no—
176#463—222no—
177#448—221no—
178#447—221no—
179#432—111no—
180#432—111no—
181#417—222no—
182C4×M16—111no—
183#397—22no—
184#393—22no—
185#391—21no—
186#390—21no—
187#376C2×D1111yescharacteristic
188#332—222no—
189#329—222no—
190#327—222no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—84no—
194C22×C11—81no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11#39211yescharacteristic
198C22×C11#45412yes—
199C2×D11—81no—
200C2×D11—81no—
201C2×D11—81no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—82no—
208C4×C11—81no—
209C4×C11—82no—
210C4×C11#45512yes—
211Dic11—81no—
212C2×#41—221no—
213C22×Q8—21no—
214C22×Q8C22⋊D1111yescharacteristic
215C22×D4C22⋊D1111yescharacteristic
216C2×SD16—222no—
217C2×D8—222no—
218C2×M16—221no—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221C4⋊Q8—21no—
222C4⋊Q8—21no—
223C4⋊Q8—111no—
224#127—111no—
225#124—21no—
226#124—21no—
227#124—21no—
228#124—21no—
229#124—221no—
230#121—221no—
231#121—221no—
232C4×D4—221no—
233C4×D4—221no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4C22⋊D1112yes—
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—24no—
239C2×C42—21no—
240C2×C42C22×D1111yescharacteristic
241C4⋊C8—112no—
242C4⋊C8—221no—
243#103—224no—
244#103—222no—
245#102—224no—
246#102—222no—
247C22⋊C8—221no—
248C22⋊C8—221no—
249#97—112no—
250#97—221no—
251#97—221no—
252C4×C8—221no—
253#95—24no—
254#95—21no—
255#95C22⋊D1112yes—
256C2×C11—22no—
257C2×C11—161no—
258C2×C11#200311yescharacteristic
259C2×C11#200411yescharacteristic
260C2×C11#200811yescharacteristic
261D11—161no—
262C24—21no—
263#41—444no—
264C2×Q8—21no—
265C2×Q8—21no—
266C2×Q8—42no—
267C2×Q8—41no—
268C2×Q8—41no—
269C2×Q8—82no—
270C2×Q8—221no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—42no—
274C2×D4—221no—
275C2×D4—221no—
276C2×D4—221no—
277C2×D4—441no—
278C22×C4—21no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—441no—
282C22×C4C2×C22⋊D1111yescharacteristic
283C22×C4C2×C22⋊D1111yescharacteristic
284C22×C4C2×C22⋊D1111yescharacteristic
285SD16—882no—
286D8—882no—
287M16—442no—
288C2×C8—222no—
289C2×C8—222no—
290C2×C8—441no—
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—221no—
296C4⋊C4—221no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—84no—
302C22⋊C4—441no—
303C22⋊C4—441no—
304C42—42no—
305C42D4×D1111yescharacteristic
306C42D4×D1111yescharacteristic
307C42D4×D1111yescharacteristic
308C42#434111yescharacteristic
309C11#1009211yescharacteristic, complemented, Sylow
310C23—42no—
311C23—42no—
312C23—41no—
313C23—42no—
314C23—441no—
315C23#6700611yescharacteristic
316Q8—42no—
317Q8—81no—
318Q8—82no—
319Q8—82no—
320Q8—442no—
321D4—42no—
322D4—81no—
323D4—442no—
324D4—442no—
325D4—881no—
326D4—882no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—44no—
333C2×C4—42no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—441no—
338C2×C4—882no—
339C2×C4#6699011yescharacteristic
340C2×C4#6699011yescharacteristic
341C2×C4#6699111yescharacteristic
342C2×C4#6699211yescharacteristic
343C2×C4#6699211yescharacteristic
344C2×C4#6699311yescharacteristic
345C8—442no—
346C8—442no—
347C8—881no—
348C22—21no—
349C22—21no—
350C22—84no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22—881no—
355C22—881no—
356C22—881no—
357C22#1062283611yescharacteristic
358C22#1062285812yes—
359C4—21no—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—82no—
365C4—81no—
366C4—82no—
367C4—881no—
368C4#1062267412yes—
369C2—22no—
370C2—161no—
371C2—1761no—
372C2#1306963611yescharacteristic
373C2#1306964511yescharacteristic
374C2#1306966911yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2640C2
socleC22×C11#392
prime radical#13079603C2
hypercenter#2640D11
hypocenterC11#10092
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2640

Complements

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

NH ≅ G/Ntype
2. #13079012C2semidirect
3. #13067333C2semidirect
4. #13067214C2semidirect
5. #13067123C2semidirect
6. #13066509C2semidirect
7. C11×#2640C2semidirect
125. #2640D11semidirect
309. C11#10092semidirect

Maximal subgroups

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

subgroupindex
#130796032
#130790122
#130673332
#130672142
#130671232
#130665092
C11×#26402
#1009211