Finite Group Databasebeta

← #14666324

Subgroups — #14666324

Order 2816.

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

normal subgroups only

This group has 432 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#13067567C211yesmaximal, characteristic
3#13067567C211yesmaximal, characteristic
4#13066637C211yesmaximal, characteristic, complemented
5#13066637C211yesmaximal, characteristic, complemented
6#13066564C211yesmaximal, characteristic, complemented
7C11×#2763C211yesmaximal, characteristic, complemented
8#10623024C2211yescharacteristic
9C11×#400—21no—
10C11×#395—21no—
11C11×#393C2211yescharacteristic
12C11×#393C2211yescharacteristic
13C11×#391—21no—
14C11×#388—21no—
15C11×#385—21no—
16C11×#385C2211yescharacteristic
17C11×#382—21no—
18#10622840—21no—
19#10622840—21no—
20#10622826—21no—
21C2×#66870—21no—
22#10622164C2211yescharacteristic
23#10622163C2211yescharacteristic
24#10622163C2211yescharacteristic
25#10622089—21no—
26#10622089—21no—
27C22×Q8×C11D411yescharacteristic
28C22×Q8×C11D411yescharacteristic
29C23×C4×C11D411yescharacteristic
30C22×C22⋊D11—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4D411yescharacteristic
38C2×C11×C22⋊C4C2311yescharacteristic
39C2×C42×C11—21no—
40C2×C22⋊Dic11—21no—
41C2×#4325—41no—
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×#95—21no—
55C11×#95D411yescharacteristic
56C11×#95D411yescharacteristic
57#66899—41no—
58#66899—41no—
59C11⋊#95—41no—
60C22⋊(C11⋊C8)—21no—
61C22⋊(C11⋊C8)—21no—
62#66870—42no—
63#12177—111nomaximal, Sylow
64C24×C11C2×D411yescharacteristic
65C23×D11—21no—
66C2×Q8×C11—42no—
67C2×Q8×C11—41no—
68C2×Q8×C11—41no—
69C2×Q8×C11—81no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—41no—
77C22×C4×C11—81no—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C2×C22⋊D11—41no—
81C2×C22⋊D11—41no—
82C2×C22⋊D11—41no—
83C2×C22⋊D11—41no—
84C2×C22⋊D11—41no—
85C2×C22⋊D11—41no—
86C22×Dic11—21no—
87C22×Dic11—41no—
88C2×D44—21no—
89C2×D44—21no—
90C11×C4⋊C4—81no—
91C11×C4⋊C4—81no—
92C11×C4⋊C4—81no—
93C11×C4⋊C4—81no—
94C11×C22⋊C4—21no—
95C11×C22⋊C4—41no—
96C11×C22⋊C4—42no—
97C11×C22⋊C4—81no—
98C11×C22⋊C4SD1612yescomplemented
99C42×C11—42no—
100C22⋊Dic11—41no—
101C22⋊Dic11—41no—
102#4325—82no—
103#4325—82no—
104(C2×D11)⋊C4—41no—
105(C2×D11)⋊C4—41no—
106(C2×D11)⋊C4—82no—
107C4⋊Dic11—21no—
108C4⋊Dic11—21no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8—41no—
111#2763D1111yescharacteristic, complemented
112#2044—111no—
113#1601—111no—
114#1601—111no—
115#1351—111no—
116#1351—111no—
117#1326—111no—
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—41no—
121C23×C11—41no—
122C23×C11#12011yescharacteristic
123C23×C11C2×SD1611yescharacteristic
124C23×C11#13711yescharacteristic
125C22×D11—41no—
126C22×D11—41no—
127C22×D11—41no—
128C22×D11—81no—
129C22×D11—81no—
130Q8×C11—42no—
131Q8×C11—42no—
132Q8×C11—81no—
133Q8×C11—81no—
134C2×C4×C11—22no—
135C2×C4×C11—22no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
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—42no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—81no—
158C22⋊D11—81no—
159C22⋊D11—81no—
160C22⋊D11—81no—
161C22⋊D11—81no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—81no—
166C2×Dic11—81no—
167C2×Dic11—81no—
168D44—81no—
169D44—81no—
170C11⋊C8—81no—
171C11⋊C8—81no—
172#534—111no—
173#448—221no—
174#448—221no—
175C2×#99—221no—
176#400—21no—
177#395—21no—
178#393C2×D1111yescharacteristic
179#393C2×D1111yescharacteristic
180#391—21no—
181#388—21no—
182#386—221no—
183#385—21no—
184#385C2×D1111yescharacteristic
185#382—21no—
186#342—111no—
187#327—221no—
188#327—221no—
189#323—111no—
190#323—111no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—41no—
196C22×C11—41no—
197C22×C11—41no—
198C22×C11—41no—
199C22×C11—81no—
200C22×C11#44811yescharacteristic
201C22×C11#45411yescharacteristic
202C22×C11B(4,𝔽2)11yescharacteristic
203C2×D11—82no—
204C2×D11—81no—
205C2×D11—81no—
206C2×D11—81no—
207C2×D11—161no—
208C4×C11—42no—
209C4×C11—42no—
210C4×C11—41no—
211C4×C11—41no—
212C4×C11—81no—
213C4×C11—81no—
214C4×C11—81no—
215C4×C11—81no—
216Dic11—81no—
217Dic11—161no—
218C22×Q8C22⋊D1111yescharacteristic
219C22×Q8C22⋊D1111yescharacteristic
220C22×D4—221no—
221C23×C4C22⋊D1111yescharacteristic
222C2×SD16—441no—
223C2×SD16—441no—
224#123—441no—
225#121—221no—
226#121—221no—
227#120—441no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—221no—
235C2×C22⋊C4—441no—
236C2×C22⋊C4C22⋊D1111yescharacteristic
237C2×C22⋊C4C22×D1111yescharacteristic
238C2×C42—21no—
239#103—441no—
240#103—441no—
241#99—442no—
242C22⋊C8—221no—
243C22⋊C8—221no—
244#95—21no—
245#95—21no—
246#95—21no—
247#95—21no—
248#95—21no—
249#95—21no—
250#95—21no—
251#95—441no—
252#95C22⋊D1111yescharacteristic
253#95C22⋊D1111yescharacteristic
254C2×C11—21no—
255C2×C11—21no—
256C2×C11—41no—
257C2×C11—41no—
258C2×C11#159911yescharacteristic
259C2×C11#219711yescharacteristic
260C2×C11#219911yescharacteristic
261D11—161no—
262C24—221no—
263C24C2×C22⋊D1111yescharacteristic
264C2×Q8—42no—
265C2×Q8—41no—
266C2×Q8—41no—
267C2×Q8—81no—
268C2×D4—221no—
269C2×D4—221no—
270C2×D4—441no—
271C2×D4—441no—
272C2×D4—441no—
273C2×D4—441no—
274C2×D4—441no—
275C2×D4—441no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—41no—
283C22×C4—81no—
284C22×C4—221no—
285C22×C4—441no—
286C22×C4C2×C22⋊D1111yescharacteristic
287C22×C4C2×C22⋊D1111yescharacteristic
288SD16—882no—
289SD16—882no—
290C2×C8—441no—
291C2×C8—441no—
292C4⋊C4—81no—
293C4⋊C4—81no—
294C4⋊C4—81no—
295C4⋊C4—81no—
296C4⋊C4—221no—
297C4⋊C4—221no—
298C22⋊C4—21no—
299C22⋊C4—41no—
300C22⋊C4—42no—
301C22⋊C4—81no—
302C22⋊C4—441no—
303C22⋊C4—441no—
304C22⋊C4—441no—
305C22⋊C4—441no—
306C22⋊C4—882no—
307C22⋊C4#432512yescomplemented
308C42—42no—
309C11#1217711yescharacteristic, complemented, Sylow
310C23—21no—
311C23—21no—
312C23—41no—
313C23—41no—
314C23—441no—
315C23—441no—
316C23—441no—
317C23—881no—
318C23—881no—
319C23C2×#432511yescharacteristic
320C23#6699511yescharacteristic
321C23#6700611yescharacteristic
322Q8—42no—
323Q8—42no—
324Q8—81no—
325Q8—81no—
326D4—881no—
327D4—881no—
328D4—881no—
329D4—881no—
330D4—881no—
331D4—881no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—41no—
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—41no—
350C2×C4—42no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—81no—
356C2×C4—441no—
357C2×C4—441no—
358C2×C4—441no—
359C2×C4—881no—
360C2×C4—881no—
361C2×C4—881no—
362C8—881no—
363C8—881no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—81no—
373C22—882no—
374C22—881no—
375C22—881no—
376C22—881no—
377C22—1761no—
378C22#1062284011yescharacteristic
379C22#1062285711yescharacteristic
380C22#1062285811yescharacteristic
381C4—42no—
382C4—41no—
383C4—42no—
384C4—41no—
385C4—81no—
386C4—81no—
387C4—81no—
388C4—81no—
389C4—881no—
390C4—1761no—
391C2—21no—
392C2—21no—
393C2—41no—
394C2—41no—
395C2—1761no—
396C2#1306755611yescharacteristic
397C2#1307060611yescharacteristic
398C2#1307061711yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC2×C11×C22⋊C4C23
FrattiniC2×C22⋊C4C22×D11
FittingC11×#2763C2
socleC22×C11B(4,𝔽2)
prime radical#10623024C22
hypercenter#2763D11
hypocenterC11#12177
LCSG ▷ C2×C11×C22⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2763

Complements

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

NH ≅ G/Ntype
4. #13066637C2semidirect
5. #13066637C2semidirect
6. #13066564C2semidirect
7. C11×#2763C2semidirect
98. C11×C22⋊C4SD16semidirect
111. #2763D11semidirect
307. C22⋊C4#4325semidirect
309. C11#12177semidirect

Maximal subgroups

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

subgroupindex
#130698672
#130675672
#130666372
#130665642
C11×#27632
#1217711