Finite Group Databasebeta

← #14666331

Subgroups — #14666331

Order 2816.

422 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 63 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#13069867C211yesmaximal, characteristic
2#13067635C211yesmaximal, characteristic
3#13067567C211yesmaximal, characteristic
4#13066640C211yesmaximal, characteristic, complemented
5#13066637C211yesmaximal, characteristic, complemented
6#13066564C211yesmaximal, characteristic, complemented
7C11×#2742C211yesmaximal, characteristic, complemented
8#10623024C2211yescharacteristic
9C11×#400—21no—
10C11×#399C2211yescharacteristic
11C11×#395—21no—
12C11×#393C2211yescharacteristic
13C11×#389—21no—
14C11×#388—21no—
15C11×#387—21no—
16C11×#385C2211yescharacteristic
17C11×#380—21no—
18#10622840—21no—
19#10622826—21no—
20#10622581—21no—
21C2×#66870—21no—
22#10622164C2211yescharacteristic
23#10622163C2211yescharacteristic
24#10622163C2211yescharacteristic
25#10622089—21no—
26#10622089—21no—
27C22×Q8×C11D411yescharacteristic
28C23×C4×C11D411yescharacteristic
29C22×C22⋊D11—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4D411yescharacteristic
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4D411yescharacteristic
39C2×C11×C22⋊C4C2311yescharacteristic
40C2×C42×C11—21no—
41C2×C22⋊Dic11—21no—
42C2×#4325—41no—
43#66983—21no—
44#66983—21no—
45C2×(C2×D11)⋊C4—41no—
46#66939—41no—
47#66935—41no—
48C11×#95—21no—
49C11×#95—21no—
50C11×#95—21no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95D411yescharacteristic
55C11×#95D411yescharacteristic
56#66899—41no—
57C11⋊#95—41no—
58C22⋊(C11⋊C8)—21no—
59C22⋊(C11⋊C8)—21no—
60#66873—41no—
61#66872—41no—
62#66870—42no—
63#12178—111nomaximal, Sylow
64C24×C11C2×D411yescharacteristic
65C23×D11—21no—
66C2×Q8×C11—41no—
67C2×Q8×C11—81no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—42no—
75C22×C4×C11—41no—
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C2×C22⋊D11—41no—
79C2×C22⋊D11—41no—
80C2×C22⋊D11—41no—
81C2×C22⋊D11—41no—
82C2×C22⋊D11—41no—
83C2×C22⋊D11—41no—
84C22×Dic11—21no—
85C22×Dic11—41no—
86C2×D44—21no—
87C2×D44—21no—
88C11×C4⋊C4—42no—
89C11×C4⋊C4—42no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—81no—
92C11×C4⋊C4—81no—
93C11×C4⋊C4—81no—
94C11×C22⋊C4—21no—
95C11×C22⋊C4—41no—
96C11×C22⋊C4—81no—
97C11×C22⋊C4—81no—
98C11×C22⋊C4SD1612yescomplemented
99C42×C11—81no—
100C22⋊Dic11—41no—
101C22⋊Dic11—41no—
102#4325—82no—
103(C2×D11)⋊C4—41no—
104(C2×D11)⋊C4—41no—
105(C2×D11)⋊C4—82no—
106C4⋊Dic11—21no—
107C4⋊Dic11—21no—
108C2×C11⋊C8—41no—
109C2×C11⋊C8—41no—
110#2742D1111yescharacteristic, complemented
111#2044—111no—
112#1613—111no—
113#1601—111no—
114#1352—111no—
115#1351—111no—
116#1326—111no—
117C23×C11—21no—
118C23×C11—21no—
119C23×C11—41no—
120C23×C11—41no—
121C23×C11#12011yescharacteristic
122C23×C11C2×SD1611yescharacteristic
123C23×C11#13711yescharacteristic
124C22×D11—41no—
125C22×D11—41no—
126C22×D11—41no—
127C22×D11—81no—
128C22×D11—81no—
129Q8×C11—42no—
130Q8×C11—81no—
131C2×C4×C11—22no—
132C2×C4×C11—22no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—42no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—81no—
155C22⋊D11—81no—
156C22⋊D11—81no—
157C22⋊D11—81no—
158C22⋊D11—81no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—81no—
163C2×Dic11—81no—
164C2×Dic11—81no—
165D44—81no—
166D44—81no—
167C11⋊C8—81no—
168C11⋊C8—81no—
169#534—111no—
170#481—221no—
171#448—221no—
172C2×#99—221no—
173#400—21no—
174#399C2×D1111yescharacteristic
175#395—21no—
176#393C2×D1111yescharacteristic
177#389—21no—
178#388—21no—
179#387—21no—
180#386—221no—
181#385C2×D1111yescharacteristic
182#380—21no—
183#342—111no—
184#327—221no—
185#327—221no—
186#323—111no—
187#323—111no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—41no—
193C22×C11—41no—
194C22×C11—41no—
195C22×C11—41no—
196C22×C11—81no—
197C22×C11#44811yescharacteristic
198C22×C11#45411yescharacteristic
199C22×C11B(4,𝔽2)11yescharacteristic
200C2×D11—82no—
201C2×D11—81no—
202C2×D11—81no—
203C2×D11—81no—
204C2×D11—161no—
205C4×C11—42no—
206C4×C11—42no—
207C4×C11—41no—
208C4×C11—41no—
209C4×C11—81no—
210C4×C11—81no—
211C4×C11—81no—
212C4×C11—81no—
213Dic11—81no—
214Dic11—161no—
215C22×Q8C22⋊D1111yescharacteristic
216C22×D4—221no—
217C23×C4C22⋊D1111yescharacteristic
218C2×SD16—441no—
219#123—441no—
220#121—221no—
221#121—221no—
222#120—441no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4C22⋊D1111yescharacteristic
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—221no—
232C2×C22⋊C4—441no—
233C2×C22⋊C4C22⋊D1111yescharacteristic
234C2×C22⋊C4C22×D1111yescharacteristic
235C2×C42—21no—
236#106—441no—
237#103—441no—
238#102—441no—
239#99—442no—
240C22⋊C8—221no—
241C22⋊C8—221no—
242#95—21no—
243#95—21no—
244#95—21no—
245#95—21no—
246#95—21no—
247#95—21no—
248#95—441no—
249#95C22⋊D1111yescharacteristic
250#95C22⋊D1111yescharacteristic
251C2×C11—21no—
252C2×C11—21no—
253C2×C11—41no—
254C2×C11—41no—
255C2×C11#159911yescharacteristic
256C2×C11#219711yescharacteristic
257C2×C11#220011yescharacteristic
258D11—161no—
259C24—221no—
260C24C2×C22⋊D1111yescharacteristic
261C2×Q8—41no—
262C2×Q8—81no—
263C2×D4—221no—
264C2×D4—221no—
265C2×D4—441no—
266C2×D4—441no—
267C2×D4—441no—
268C2×D4—441no—
269C2×D4—441no—
270C2×D4—441no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—42no—
278C22×C4—41no—
279C22×C4—221no—
280C22×C4—441no—
281C22×C4C2×C22⋊D1111yescharacteristic
282C22×C4C2×C22⋊D1111yescharacteristic
283SD16—882no—
284C2×C8—441no—
285C2×C8—441no—
286C4⋊C4—41no—
287C4⋊C4—42no—
288C4⋊C4—42no—
289C4⋊C4—81no—
290C4⋊C4—81no—
291C4⋊C4—81no—
292C4⋊C4—221no—
293C4⋊C4—221no—
294C22⋊C4—21no—
295C22⋊C4—41no—
296C22⋊C4—81no—
297C22⋊C4—81no—
298C22⋊C4—441no—
299C22⋊C4—441no—
300C22⋊C4—441no—
301C22⋊C4—441no—
302C22⋊C4—882no—
303C22⋊C4#432512yescomplemented
304C42—81no—
305C11#1217811yescharacteristic, complemented, Sylow
306C23—21no—
307C23—21no—
308C23—41no—
309C23—41no—
310C23—441no—
311C23—441no—
312C23—441no—
313C23—881no—
314C23—881no—
315C23C2×#432511yescharacteristic
316C23#6699511yescharacteristic
317C23#6700611yescharacteristic
318Q8—42no—
319Q8—81no—
320D4—881no—
321D4—881no—
322D4—881no—
323D4—881no—
324D4—881no—
325D4—881no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—81no—
350C2×C4—441no—
351C2×C4—441no—
352C2×C4—441no—
353C2×C4—881no—
354C2×C4—881no—
355C2×C4—881no—
356C8—881no—
357C8—881no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—81no—
367C22—882no—
368C22—881no—
369C22—881no—
370C22—881no—
371C22—1761no—
372C22#1062284011yescharacteristic
373C22#1062285711yescharacteristic
374C22#1062285811yescharacteristic
375C4—42no—
376C4—41no—
377C4—42no—
378C4—41no—
379C4—81no—
380C4—81no—
381C4—81no—
382C4—81no—
383C4—881no—
384C4—1761no—
385C2—21no—
386C2—21no—
387C2—41no—
388C2—41no—
389C2—1761no—
390C2#1306755611yescharacteristic
391C2#1307060611yescharacteristic
392C2#1307062311yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC2×C11×C22⋊C4C23
FrattiniC2×C22⋊C4C22×D11
FittingC11×#2742C2
socleC22×C11B(4,𝔽2)
prime radical#10623024C22
hypercenter#2742D11
hypocenterC11#12178
LCSG ▷ C2×C11×C22⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2742

Complements

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

NH ≅ G/Ntype
4. #13066640C2semidirect
5. #13066637C2semidirect
6. #13066564C2semidirect
7. C11×#2742C2semidirect
98. C11×C22⋊C4SD16semidirect
110. #2742D11semidirect
303. C22⋊C4#4325semidirect
305. C11#12178semidirect

Maximal subgroups

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

subgroupindex
#130698672
#130676352
#130675672
#130666402
#130666372
#130665642
C11×#27422
#1217811