Finite Group Databasebeta

← #14666195

Subgroups — #14666195

Order 2816.

416 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 57 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#13076687C211yesmaximal, characteristic, complemented
2#13069837C211yesmaximal, characteristic, complemented
3#13067619C211yesmaximal, characteristic, complemented
4#13066623C211yesmaximal, characteristic, complemented
5#13066619C211yesmaximal, characteristic, complemented
6#13066561C211yesmaximal, characteristic, complemented
7C11×#1598C211yesmaximal, characteristic
8C11×#537C2211yescharacteristic
9C2×#66932—21no—
10C11×#447—21no—
11C11×#394C2211yescharacteristic
12C2×#66901—21no—
13#10622845—21no—
14#10622835—21no—
15#10622646—21no—
16#10622596C2211yescharacteristic
17#10622589C2211yescharacteristic
18#10622561—21no—
19#10622561—21no—
20#10622561—21no—
21#10622270—21no—
22C11×#327—21no—
23C11×#324C2211yescharacteristic
24#10622175—21no—
25#10622168C2211yescharacteristic
26#10622166C2211yescharacteristic
27C2×C11×#41—21no—
28C22×D4×C11D411yescharacteristic
29C2×C11×D8—41no—
30C11×C22⋊Q8—41no—
31C11×#121—21no—
32C11×#121—21no—
33C11×#121—41no—
34C2×C11×C4⋊C4C2311yescharacteristic
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—21no—
37C2×C22⋊Dic11—21no—
38C2×C22⋊Dic11—21no—
39C2×C22⋊Dic11—21no—
40C2×C22⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11D411yescharacteristic
43C2×C4⋊Dic11D411yescharacteristic
44C2×Dic11⋊C4—21no—
45C2×Dic11⋊C4—21no—
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—21no—
48C2×Dic11⋊C4—21no—
49C2×C4×Dic11D411yescharacteristic
50C2×#4318—21no—
51#66932—42no—
52#66932—42no—
53C11×#102—41no—
54C11×C22⋊C8—21no—
55C11×#95D411yescharacteristic
56#66901—42no—
57#66899—41no—
58#66896—41no—
59#66896—41no—
60C11⋊#95—21no—
61C11⋊#95—21no—
62C11⋊#95D411yescharacteristic
63C22⋊(C11⋊C8)—21no—
64#66871—41no—
65#12155—111nomaximal, Sylow
66C24×C11—21no—
67C11×#41—41no—
68C11×#41—41no—
69C11×#41—41no—
70C11×#41—41no—
71C2×Q8×C11—21no—
72C2×D4×C11—21no—
73C2×D4×C11—21no—
74C2×D4×C11—21no—
75C2×D4×C11—41no—
76C2×D4×C11—41no—
77C2×D4×C11—81no—
78C22×C4×C11—21no—
79C22×C4×C11—41no—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×Dic11—21no—
84C22×Dic11—21no—
85C22×Dic11—21no—
86C22×Dic11—21no—
87C11×D8—82no—
88C2×C8×C11—41no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4—41no—
92C11×C22⋊C4—41no—
93C11×C22⋊C4—41no—
94C11×C22⋊C4—41no—
95C11×C22⋊C4—41no—
96C11×C22⋊C4—81no—
97C22⋊Dic11—42no—
98C22⋊Dic11—42no—
99C22⋊Dic11—81no—
100C22⋊Dic11—81no—
101C4⋊Dic11—41no—
102C4⋊Dic11—41no—
103C4⋊Dic11—42no—
104Dic11⋊C4—42no—
105Dic11⋊C4—41no—
106Dic11⋊C4—41no—
107Dic11⋊C4—81no—
108Dic11⋊C4—81no—
109Dic11⋊C4—81no—
110C4×Dic11—21no—
111C4×Dic11D812yescomplemented
112#4318—41no—
113#4318—41no—
114C2×C11⋊C8—41no—
115C2×C11⋊C8—41no—
116#2823—111no—
117#2039—111no—
118#1610—111no—
119#1598D1111yescharacteristic
120#1346—111no—
121#1345—111no—
122#1325—111no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11—41no—
129C23×C11—41no—
130C23×C11—41no—
131C23×C11#12011yescharacteristic
132Q8×C11—41no—
133Q8×C11—41no—
134D4×C11—41no—
135D4×C11—41no—
136D4×C11—42no—
137D4×C11—81no—
138D4×C11—81no—
139D4×C11—81no—
140D4×C11—81no—
141D4×C11—81no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
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—81no—
153C2×C4×C11—81no—
154C2×C4×C11C2×D811yescharacteristic
155C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
156C2×Dic11—22no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C8×C11—81no—
169C11⋊C8—81no—
170C11⋊C8—81no—
171#537C2×D1111yescharacteristic
172C2×#126—221no—
173#480—221no—
174#447—21no—
175C2×#104—221no—
176#417—221no—
177#398—111no—
178#398—221no—
179#396—221no—
180#396—221no—
181#396—221no—
182#394—221no—
183#394C2×D1111yescharacteristic
184#384—111no—
185#343—111no—
186#327—21no—
187#327—221no—
188#324—111no—
189#324C2×D1111yescharacteristic
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—81no—
193C22×C11—81no—
194C22×C11—81no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11—81no—
198C22×C11—81no—
199C22×C11—81no—
200C22×C11—81no—
201C22×C11—81no—
202C22×C11#44711yescharacteristic
203C22×C11#45411yescharacteristic
204C22×C11B(4,𝔽2)11yescharacteristic
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—41no—
208C4×C11—41no—
209C4×C11—81no—
210C4×C11—81no—
211Dic11—42no—
212Dic11—81no—
213Dic11—81no—
214Dic11—81no—
215C2×#41—21no—
216C22×D4C22⋊D1111yescharacteristic
217C2×D8—41no—
218C2×M16—221no—
219#126—442no—
220#126—442no—
221C22⋊Q8—41no—
222#121—21no—
223#121—21no—
224#121—41no—
225C2×C4⋊C4—111no—
226C2×C4⋊C4—111no—
227C2×C4⋊C4—221no—
228C2×C4⋊C4—221no—
229C2×C4⋊C4—221no—
230C2×C4⋊C4—221no—
231C2×C4⋊C4—221no—
232C2×C4⋊C4—221no—
233C2×C4⋊C4C22×D1111yescharacteristic
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—221no—
237C2×C22⋊C4—221no—
238C2×C22⋊C4—221no—
239C2×C22⋊C4—221no—
240C2×C42—111no—
241#107—441no—
242#104—442no—
243#103—441no—
244#102—41no—
245#102—441no—
246#102—441no—
247C22⋊C8—21no—
248C22⋊C8—221no—
249#95—111no—
250#95—221no—
251#95—221no—
252#95C22⋊D1111yescharacteristic
253C2×C11—21no—
254C2×C11—21no—
255C2×C11—161no—
256C2×C11—161no—
257C2×C11#159811yescharacteristic
258C2×C11#220011yescharacteristic
259C2×C11#220311yescharacteristic
260C24—21no—
261#41—41no—
262#41—41no—
263#41—41no—
264#41—41no—
265C2×Q8—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—21no—
269C2×D4—41no—
270C2×D4—41no—
271C2×D4—81no—
272C22×C4—21no—
273C22×C4—41no—
274C22×C4—221no—
275C22×C4—221no—
276C22×C4—221no—
277C22×C4—221no—
278C22×C4D4×D1111yescharacteristic
279C22×C4D4×D1111yescharacteristic
280C22×C4C2×C22⋊D1111yescharacteristic
281D8—82no—
282M16—441no—
283M16—441no—
284C2×C8—41no—
285C2×C8—441no—
286C2×C8—441no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—41no—
290C4⋊C4—441no—
291C4⋊C4—441no—
292C4⋊C4—442no—
293C4⋊C4—442no—
294C4⋊C4—441no—
295C4⋊C4—441no—
296C4⋊C4—881no—
297C4⋊C4—881no—
298C4⋊C4—881no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C22⋊C4—41no—
303C22⋊C4—81no—
304C22⋊C4—442no—
305C22⋊C4—442no—
306C22⋊C4—881no—
307C22⋊C4—881no—
308C42—112no—
309C42—221no—
310C11#1215511yescharacteristic, complemented, Sylow
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23#6699011yescharacteristic
320Q8—41no—
321Q8—41no—
322D4—41no—
323D4—41no—
324D4—42no—
325D4—81no—
326D4—81no—
327D4—81no—
328D4—81no—
329D4—81no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—222no—
343C2×C4—441no—
344C2×C4—441no—
345C2×C4—441no—
346C2×C4—441no—
347C2×C4—441no—
348C2×C4—441no—
349C2×C4—441no—
350C2×C4—441no—
351C2×C4—441no—
352C2×C4—441no—
353C2×C4—441no—
354C2×C4D8×D1111yescharacteristic
355C2×C4#6696411yescharacteristic
356C8—81no—
357C8—881no—
358C8—881no—
359C22—21no—
360C22—21no—
361C22—81no—
362C22—81no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22—81no—
369C22—81no—
370C22—81no—
371C22#1062264511yescharacteristic
372C22#1062276911yescharacteristic
373C22#1062281411yescharacteristic
374C4—21no—
375C4—21no—
376C4—41no—
377C4—41no—
378C4—81no—
379C4—81no—
380C4—442no—
381C4—881no—
382C4—881no—
383C4—881no—
384C2—21no—
385C2—21no—
386C2—161no—
387C2—161no—
388C2#1306754911yescharacteristic
389C2#1307062111yescharacteristic
390C2#1307063611yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
Fitting, prime radicalC11×#1598C2
socleC22×C11B(4,𝔽2)
hypercenter#1598D11
hypocenterC11#12155
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1598

Complements

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

NH ≅ G/Ntype
1. #13076687C2semidirect
2. #13069837C2semidirect
3. #13067619C2semidirect
4. #13066623C2semidirect
5. #13066619C2semidirect
6. #13066561C2semidirect
111. C4×Dic11D8semidirect
310. C11#12155semidirect

Maximal subgroups

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

subgroupindex
#130766872
#130698372
#130676192
#130666232
#130666192
#130665612
C11×#15982
#1215511