Finite Group Databasebeta

← #14666188

Subgroups — #14666188

Order 2816.

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

normal subgroups only

This group has 458 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#13074287C211yesmaximal, characteristic, complemented
2#13069842C211yesmaximal, characteristic, complemented
3#13067619C211yesmaximal, characteristic, complemented
4#13066623C211yesmaximal, characteristic, complemented
5#13066619C211yesmaximal, characteristic, complemented
6#13066559C211yesmaximal, characteristic, complemented
7C11×#1598C211yesmaximal, characteristic
8C11×#537C2211yescharacteristic
9C2×#66930—21no—
10C11×#447—21no—
11C11×#394C2211yescharacteristic
12C2×#66901—21no—
13#10622845—21no—
14#10622833—21no—
15#10622646—21no—
16#10622596C2211yescharacteristic
17#10622590C2211yescharacteristic
18#10622564—21no—
19#10622561—21no—
20#10622559—21no—
21#10622265—21no—
22C11×#327—21no—
23C11×#324C2211yescharacteristic
24#10622175—21no—
25#10622168C2211yescharacteristic
26#10622166C2211yescharacteristic
27C2×C11×#41—21no—
28C22×D4×C11D411yescharacteristic
29C23×Dic11—21no—
30C2×C11×D8—41no—
31C11×C22⋊Q8—41no—
32C11×#121—21no—
33C11×#121—21no—
34C11×#121—41no—
35C2×C11×C4⋊C4C2311yescharacteristic
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C22⋊Dic11—21no—
39C2×C22⋊Dic11—21no—
40C2×C22⋊Dic11—21no—
41C2×C4⋊Dic11D411yescharacteristic
42C2×C4⋊Dic11D411yescharacteristic
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×Dic11⋊C4—21no—
46C2×C4×Dic11—21no—
47C2×C4×Dic11D411yescharacteristic
48C2×#4318—21no—
49#66930—42no—
50#66930—42no—
51C11×#102—41no—
52C11×C22⋊C8—21no—
53C11×#95D411yescharacteristic
54#66901—42no—
55#66899—41no—
56#66896—41no—
57#66896—41no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95—21no—
62C11⋊#95D411yescharacteristic
63C22⋊(C11⋊C8)—21no—
64#66871—41no—
65#12154—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—42no—
77C2×D4×C11—41no—
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—
87C22×Dic11—42no—
88C22×Dic11—42no—
89C22×Dic11—42no—
90C11×D8—82no—
91C2×C8×C11—41no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—41no—
95C11×C22⋊C4—41no—
96C11×C22⋊C4—41no—
97C11×C22⋊C4—42no—
98C11×C22⋊C4—41no—
99C11×C22⋊C4—41no—
100C22⋊Dic11—42no—
101C22⋊Dic11—42no—
102C22⋊Dic11—81no—
103C4⋊Dic11—41no—
104C4⋊Dic11—41no—
105Dic11⋊C4—42no—
106Dic11⋊C4—42no—
107Dic11⋊C4—41no—
108Dic11⋊C4—41no—
109C4×Dic11—21no—
110C4×Dic11—42no—
111C4×Dic11D812yescomplemented
112#4318—41no—
113#4318—41no—
114C2×C11⋊C8—41no—
115C2×C11⋊C8—41no—
116#2609—111no—
117#2040—111no—
118#1610—111no—
119#1598D1111yescharacteristic
120#1346—111no—
121#1345—111no—
122#1324—111no—
123C23×C11—22no—
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—22no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—48no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C8×C11—81no—
170C11⋊C8—81no—
171C11⋊C8—81no—
172#537C2×D1111yescharacteristic
173C2×#117—221no—
174#480—221no—
175#447—21no—
176C2×#104—221no—
177#417—221no—
178#398—111no—
179#396—221no—
180#394C2×D1111yescharacteristic
181#388—221no—
182#387—221no—
183#386—221no—
184#385—221no—
185#382—111no—
186#343—111no—
187#327—21no—
188#327—221no—
189#324—111no—
190#324C2×D1111yescharacteristic
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—42no—
194C22×C11—42no—
195C22×C11—42no—
196C22×C11—81no—
197C22×C11—81no—
198C22×C11—81no—
199C22×C11—81no—
200C22×C11—81no—
201C22×C11—81no—
202C22×C11—81no—
203C22×C11#44711yescharacteristic
204C22×C11#45411yescharacteristic
205C22×C11B(4,𝔽2)11yescharacteristic
206C4×C11—21no—
207C4×C11—21no—
208C4×C11—41no—
209C4×C11—41no—
210C4×C11—81no—
211C4×C11—81no—
212Dic11—42no—
213Dic11—42no—
214Dic11—81no—
215Dic11—81no—
216C2×#41—21no—
217C22×D4C22⋊D1111yescharacteristic
218C23×C4—221no—
219C2×D8—41no—
220C2×M16—221no—
221C22⋊Q8—41no—
222#121—21no—
223#121—21no—
224#121—41no—
225#117—442no—
226#117—442no—
227C2×C4⋊C4—111no—
228C2×C4⋊C4—111no—
229C2×C4⋊C4—221no—
230C2×C4⋊C4—221no—
231C2×C4⋊C4—221no—
232C2×C4⋊C4C22×D1111yescharacteristic
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—221no—
236C2×C22⋊C4—221no—
237C2×C22⋊C4—221no—
238C2×C42—111no—
239C2×C42—221no—
240#107—441no—
241#104—442no—
242#103—441no—
243#102—41no—
244#102—441no—
245#102—441no—
246C22⋊C8—21no—
247C22⋊C8—221no—
248#95—111no—
249#95—221no—
250#95—221no—
251#95—221no—
252#95—221no—
253#95C22⋊D1111yescharacteristic
254C2×C11—21no—
255C2×C11—21no—
256C2×C11—82no—
257C2×C11—161no—
258C2×C11#159811yescharacteristic
259C2×C11#219711yescharacteristic
260C2×C11#220411yescharacteristic
261C24—21no—
262#41—41no—
263#41—41no—
264#41—41no—
265#41—41no—
266C2×Q8—21no—
267C2×D4—21no—
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—41no—
271C2×D4—42no—
272C2×D4—41no—
273C22×C4—21no—
274C22×C4—41no—
275C22×C4—221no—
276C22×C4—221no—
277C22×C4—221no—
278C22×C4—221no—
279C22×C4—442no—
280C22×C4—442no—
281C22×C4—442no—
282C22×C4D4×D1111yescharacteristic
283C22×C4D4×D1111yescharacteristic
284C22×C4C2×C22⋊D1111yescharacteristic
285D8—82no—
286M16—441no—
287M16—441no—
288C2×C8—41no—
289C2×C8—441no—
290C2×C8—441no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—41no—
294C4⋊C4—441no—
295C4⋊C4—441no—
296C4⋊C4—442no—
297C4⋊C4—442no—
298C4⋊C4—441no—
299C4⋊C4—441no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C22⋊C4—42no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—442no—
306C22⋊C4—442no—
307C22⋊C4—881no—
308C42—112no—
309C42—221no—
310C42—442no—
311C11#1215411yescharacteristic, complemented, Sylow
312C23—22no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23#6699011yescharacteristic
321Q8—41no—
322Q8—41no—
323D4—41no—
324D4—41no—
325D4—42no—
326D4—81no—
327D4—81no—
328D4—81no—
329D4—81no—
330D4—81no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—222no—
344C2×C4—222no—
345C2×C4—441no—
346C2×C4—441no—
347C2×C4—441no—
348C2×C4—448no—
349C2×C4—441no—
350C2×C4—441no—
351C2×C4—441no—
352C2×C4—441no—
353C2×C4—441no—
354C2×C4—441no—
355C2×C4—441no—
356C2×C4D8×D1111yescharacteristic
357C2×C4#6696411yescharacteristic
358C8—81no—
359C8—881no—
360C8—881no—
361C22—21no—
362C22—21no—
363C22—42no—
364C22—42no—
365C22—42no—
366C22—81no—
367C22—81no—
368C22—81no—
369C22—81no—
370C22—81no—
371C22—81no—
372C22—81no—
373C22#1062264511yescharacteristic
374C22#1062276911yescharacteristic
375C22#1062281411yescharacteristic
376C4—21no—
377C4—21no—
378C4—41no—
379C4—41no—
380C4—81no—
381C4—81no—
382C4—442no—
383C4—442no—
384C4—881no—
385C4—881no—
386C2—21no—
387C2—21no—
388C2—82no—
389C2—161no—
390C2#1306754911yescharacteristic
391C2#1307060411yescharacteristic
392C2#1307064011yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
Fitting, prime radicalC11×#1598C2
socleC22×C11B(4,𝔽2)
hypercenter#1598D11
hypocenterC11#12154
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. #13074287C2semidirect
2. #13069842C2semidirect
3. #13067619C2semidirect
4. #13066623C2semidirect
5. #13066619C2semidirect
6. #13066559C2semidirect
111. C4×Dic11D8semidirect
311. C11#12154semidirect

Maximal subgroups

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

subgroupindex
#130742872
#130698422
#130676192
#130666232
#130666192
#130665592
C11×#15982
#1215411