Finite Group Databasebeta

← #14655560

Subgroups — #14655560

Order 2816.

642 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 642 conjugacy classes of subgroups — too many to draw. Only its 105 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#13079534C211yesmaximal, characteristic
2#13079012C211yesmaximal, characteristic, complemented
3#13069457C211yesmaximal, characteristic, complemented
4#13067301C211yesmaximal, characteristic, complemented
5#13067068C211yesmaximal, characteristic, complemented
6#13066453C211yesmaximal, characteristic, complemented
7C2×C11×#492C211yesmaximal, characteristic, complemented
8C22×C11×SD16—22no—
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×#127C2211yescharacteristic
11#10623008C2211yescharacteristic
12C11×#492—22no—
13C11×#492—22no—
14C2×C4×C8×C11C2211yescharacteristic
15#10622830—22no—
16C2×#66897—22no—
17#10622706—21no—
18#10622702—22no—
19#10622701—21no—
20#10622686—21no—
21#10622685—22no—
22#10622683—21no—
23#10622579—22no—
24#10622538C2211yescharacteristic
25#10622537C2211yescharacteristic
26C4×#4318C2211yescharacteristic
27#10622185—22no—
28#10622097—22no—
29C22×Q8×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11D412yes—
33C2×#4339—21no—
34C2×C11×SD16—28no—
35C2×C11×SD16—48no—
36C22×C8×C11—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8D412yes—
41C11×#127—21no—
42C11×#127—21no—
43C11×#127—21no—
44C11×#127—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C42×C11C2311yescharacteristic
48C2×#4323—24no—
49#66983—21no—
50#66983—21no—
51C2×#4318—21no—
52C2×#4318D412yes—
53#66928—21no—
54#66927D411yescharacteristic
55C4×D44—21no—
56C4×D44—21no—
57#66922D411yescharacteristic
58C4×C8×C11—21no—
59C4×C8×C11D412yes—
60#66897—44no—
61#66896—24no—
62C22⋊(C11⋊C8)—21no—
63#66874—24no—
64#66873—24no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)D412yes—
68#66867—21no—
69C4×C11⋊C8—21no—
70C4×C11⋊C8—21no—
71#10152—111nomaximal, Sylow
72C24×C11—22no—
73C2×Q8×C11—22no—
74C2×Q8×C11—44no—
75C2×Q8×C11—41no—
76C2×D4×C11—22no—
77C2×D4×C11—22no—
78C2×D4×C11—44no—
79C2×D4×C11—41no—
80C2×D4×C11—41no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11—42no—
84C2×D4×C11—42no—
85C2×D4×C11—82no—
86C22×C4×C11—41no—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11#4111yescharacteristic
90C2×C22⋊D11—41no—
91#4339—42no—
92#4339—42no—
93C2×D44—21no—
94C2×D44—21no—
95C2×D44—21no—
96C2×C4×D11—41no—
97C2×Dic22—21no—
98C11×SD16—416no—
99C2×C8×C11—24no—
100C2×C8×C11—22no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C42×C11C2×D411yescharacteristic
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109#4323—84no—
110(C2×D11)⋊C4—41no—
111(C2×D11)⋊C4—41no—
112C4⋊Dic11—21no—
113C4⋊Dic11—21no—
114#4318—22no—
115#4318—22no—
116#4318—42no—
117C2×C11⋊C8—22no—
118C2×C11⋊C8—22no—
119C2×C11⋊C8—41no—
120#3205—111no—
121C2×#492D1111yescharacteristic, complemented
122#3141—111no—
123#1965—111no—
124#1549—111no—
125#1492—111no—
126#1278—111no—
127C23×C11—42no—
128C23×C11—44no—
129C23×C11—82no—
130C23×C11—82no—
131C23×C11#12111yescharacteristic
132C22×D11—41no—
133Q8×C11—44no—
134Q8×C11—82no—
135D4×C11—44no—
136D4×C11—44no—
137D4×C11—82no—
138D4×C11—82no—
139D4×C11—82no—
140D4×C11—81no—
141D4×C11—81no—
142C2×C4×C11—22no—
143C2×C4×C11—22no—
144C2×C4×C11—42no—
145C2×C4×C11—82no—
146C2×C4×C11#12011yescharacteristic
147C2×C4×C11#12011yescharacteristic
148C2×C4×C11#12011yescharacteristic
149C2×C4×C11#12111yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#12711yescharacteristic
152C2×C4×C11#13512yes—
153C2×C4×C11AGL(1,ℤ/8)12yes—
154C22⋊D11—82no—
155C2×Dic11—41no—
156D44—42no—
157D44—42no—
158D44—42no—
159C4×D11—81no—
160C4×D11—81no—
161Dic22—42no—
162C8×C11—24no—
163C11⋊C8—42no—
164C11⋊C8—42no—
165C11⋊C8—81no—
166C22×SD16—22no—
167#532—111no—
168C2×C4⋊Q8C2×D1111yescharacteristic
169C2×#127C2×D1111yescharacteristic
170#493—221no—
171#492—22no—
172#492—22no—
173#489—222no—
174#487—221no—
175#486—221no—
176#486—221no—
177#459—222no—
178#447—222no—
179#431—111no—
180#423—111no—
181#417—222no—
182C2×#100—222no—
183C4×M16—111no—
184C2×C4×C8C2×D1111yescharacteristic
185#332—222no—
186D4⋊C8—222no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—82no—
190C22×C11—82no—
191C22×C11—82no—
192C22×C11—164no—
193C22×C11#39211yescharacteristic
194C22×C11#46312yes—
195C2×D11—81no—
196C2×D11—81no—
197C2×D11—81no—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—82no—
201C4×C11#44912yes—
202C4×C11#45312yes—
203C4×C11#47112yes—
204C4×C11#49511yescharacteristic
205C4×C11#49611yescharacteristic
206Dic11—81no—
207C2×#41—221no—
208C22×Q8—21no—
209C22×D4—21no—
210C22×D4—21no—
211C22×D4C22⋊D1112yes—
212C2×SD16—28no—
213C2×SD16—48no—
214C2×D8—224no—
215C2×M16—112no—
216C2×M16—221no—
217C22×C8—21no—
218C4⋊Q8—21no—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221C4⋊Q8—111no—
222C4⋊Q8C22⋊D1112yes—
223#127—21no—
224#127—21no—
225#127—21no—
226#127—21no—
227#127—111no—
228#124—221no—
229#121—221no—
230#121—221no—
231C4×D4—221no—
232C4×D4—221no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C42C22×D1111yescharacteristic
236C4⋊C8—112no—
237C4⋊C8—221no—
238C4⋊C8—221no—
239#103—224no—
240#102—224no—
241#102—224no—
242#100—444no—
243C22⋊C8—221no—
244#97—221no—
245C4×C8—21no—
246C4×C8—221no—
247C4×C8—221no—
248C4×C8C22⋊D1112yes—
249C2×C11—22no—
250C2×C11—162no—
251C2×C11#200211yescharacteristic
252C2×C11#201211yescharacteristic
253C2×C11#201911yescharacteristic
254D11—161no—
255C24—22no—
256#41—442no—
257#41—442no—
258C2×Q8—22no—
259C2×Q8—44no—
260C2×Q8—41no—
261C2×Q8—221no—
262C2×D4—22no—
263C2×D4—22no—
264C2×D4—44no—
265C2×D4—42no—
266C2×D4—42no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—41no—
271C2×D4—82no—
272C2×D4—221no—
273C2×D4—221no—
274C2×D4—221no—
275C2×D4—441no—
276C22×C4—41no—
277C22×C4—441no—
278C22×C4D4×D1111yescharacteristic
279C22×C4#434111yescharacteristic
280C22×C4C2×C22⋊D1111yescharacteristic
281SD16—416no—
282D8—884no—
283M16—222no—
284M16—222no—
285M16—442no—
286C2×C8—24no—
287C2×C8—22no—
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—441no—
298C22⋊C4—441no—
299C42D4×D1111yescharacteristic
300C42D4×D1111yescharacteristic
301C42C2×C22⋊D1111yescharacteristic
302C42C2×C22⋊D1111yescharacteristic
303C11#1015211yescharacteristic, complemented, Sylow
304C23—42no—
305C23—44no—
306C23—82no—
307C23—82no—
308C23—441no—
309C23#6699211yescharacteristic
310Q8—44no—
311Q8—82no—
312Q8—442no—
313D4—44no—
314D4—44no—
315D4—82no—
316D4—81no—
317D4—82no—
318D4—81no—
319D4—82no—
320D4—442no—
321D4—442no—
322D4—442no—
323D4—882no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—42no—
327C2×C4—82no—
328C2×C4—441no—
329C2×C4—881no—
330C2×C4—881no—
331C2×C4#6696712yes—
332C2×C4#6696912yes—
333C2×C4#6699011yescharacteristic
334C2×C4#6699011yescharacteristic
335C2×C4#6699111yescharacteristic
336C2×C4#6699211yescharacteristic
337C2×C4#6699311yescharacteristic
338C2×C4#6700611yescharacteristic
339C8—24no—
340C8—442no—
341C8—442no—
342C8—881no—
343C22—21no—
344C22—21no—
345C22—82no—
346C22—82no—
347C22—82no—
348C22—164no—
349C22—881no—
350C22—881no—
351C22—881no—
352C22#1062277812yes—
353C22#1062283611yescharacteristic
354C4—21no—
355C4—21no—
356C4—82no—
357C4—881no—
358C4#1062269012yes—
359C4#1062278111yescharacteristic
360C4#1062278512yes—
361C4#1062278911yescharacteristic
362C4#1062279012yes—
363C2—22no—
364C2—162no—
365C2—1761no—
366C2#1306963111yescharacteristic
367C2#1306969011yescharacteristic
368C2#1306972811yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#492C2
socleC22×C11#392
prime radical#13079534C2
hypercenterC2×#492D11
hypocenterC11#10152
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#492

Complements

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

NH ≅ G/Ntype
2. #13079012C2semidirect
3. #13069457C2semidirect
4. #13067301C2semidirect
5. #13067068C2semidirect
6. #13066453C2semidirect
7. C2×C11×#492C2semidirect
121. C2×#492D11semidirect
303. C11#10152semidirect

Maximal subgroups

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

subgroupindex
#130795342
#130790122
#130694572
#130673012
#130670682
#130664532
C2×C11×#4922
#1015211