Finite Group Databasebeta

← #14664760

Subgroups — #14664760

Order 2816.

376 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 73 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#13078276C211yesmaximal, characteristic
2#13070235C211yesmaximal, characteristic, complemented
3#13068661C211yesmaximal, characteristic, complemented
4#13066605C211yesmaximal, characteristic, complemented
5#13066603C211yesmaximal, characteristic, complemented
6#13066601C211yesmaximal, characteristic, complemented
7C11×#1339C211yesmaximal, characteristic, complemented
8C2×#66965C411yescharacteristic, complemented
9C2×#66960C2211yescharacteristic
10#10623139—21no—
11C11×#469C2211yescharacteristic
12#10622772C411yescharacteristic, complemented
13#10622750C2211yescharacteristic
14#10622654—21no—
15#10622619—21no—
16#10622611—21no—
17D11×M32—21no—
18#10622481C411yescharacteristic, complemented
19D11×#106C411yescharacteristic, complemented
20#10622391—21no—
21#10622384—21no—
22C11×#349C2211yescharacteristic
23C11×H(3,ℤ/4)C2211yescharacteristic
24#10622195C2211yescharacteristic
25#10622191C2211yescharacteristic
26#10622152—21no—
27C2×#4341—21no—
28C2×#4339D411yescharacteristic
29C2×C11×D8C2×C411yescharacteristic
30C2×C11×M16C2311yescharacteristic
31C11×#121—21no—
32C11×#117—21no—
33#66992—41no—
34#66991—21no—
35#66991—41no—
36C2×#4324—21no—
37#66979—21no—
38#66977—21no—
39C22×C11⋊C8D411yescharacteristic
40#66965—41no—
41#66965—41no—
42#66960—41no—
43#66960—41no—
44C2×Dic44C2×C411yescharacteristic
45C2×#4313C2×C411yescharacteristic
46C2×#4313D411yescharacteristic
47C2×C8×D11C2×C411yescharacteristic
48C2×C8×D11D411yescharacteristic
49#66950—21no—
50C4⋊C4×D11—21no—
51#66937—41no—
52#66931—41no—
53C11×M32—21no—
54C11×#106C2×C411yescharacteristic
55C11×#102—21no—
56#66896—21no—
57#66881C2×C411yescharacteristic
58#66880—21no—
59#66876—21no—
60#66874—21no—
61#66872—21no—
62#66872—41no—
63#66871—41no—
64#66870—41no—
65#66870—41no—
66#66862—41no—
67C16×D11—41no—
68#11867—111nomaximal, Sylow
69C2×D4×C11—21no—
70C2×D4×C11—41no—
71C22×C4×C11C2×D411yescharacteristic
72C2×C22⋊D11—41no—
73C2×C22⋊D11—41no—
74C2×C22⋊D11D811yescharacteristic
75C2×C22⋊D11D811yescharacteristic
76C22×Dic11—41no—
77#4341—42no—
78#4341—42no—
79#4339—41no—
80#4339—41no—
81C2×D44SD1611yescharacteristic
82C2×C4×D11—41no—
83C2×C4×D11C22⋊C411yescharacteristic
84C2×C4×D11C22⋊C411yescharacteristic
85C2×Dic22—21no—
86C2×Dic22SD1611yescharacteristic
87C11×D8—41no—
88C11×M16—41no—
89C2×C8×C11C22×C411yescharacteristic
90C2×C8×C11C2×D411yescharacteristic
91C11×C4⋊C4—21no—
92C11×C4⋊C4—41no—
93C11×C22⋊C4—41no—
94C11×C22⋊C4—41no—
95C42×C11—41no—
96C22⋊Dic11—41no—
97C22⋊Dic11—41no—
98C22⋊Dic11—41no—
99#4324—41no—
100#4324—41no—
101(C2×D11)⋊C4—41no—
102C4⋊Dic11—21no—
103C4⋊Dic11—41no—
104C4⋊Dic11—41no—
105Dic11⋊C4—41no—
106Dic11⋊C4—41no—
107C4×Dic11—41no—
108C2×C11⋊C8—21no—
109C2×C11⋊C8—21no—
110C2×C11⋊C8C22⋊C411yescharacteristic
111C2×C11⋊C8C22⋊C411yescharacteristic
112Dic44—41no—
113#4313—41no—
114#4313—41no—
115C8×D11—21no—
116C8×D11—21no—
117C8×D11—21no—
118C8×D11—21no—
119C11×C16—41no—
120C11⋊C16—41no—
121#3060—111no—
122#2115—111no—
123#1812—111no—
124#1340—111no—
125#1340—111no—
126#1339—111no—
127#1339D1111yescharacteristic, complemented
128C23×C11—41no—
129C23×C11C2×D811yescharacteristic
130C22×D11#10211yescharacteristic
131C22×D11#10211yescharacteristic
132D4×C11—41no—
133D4×C11—41no—
134D4×C11—161no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—41no—
138C2×C4×C11—81no—
139C2×C4×C11C2×C22⋊C411yescharacteristic
140C2×C4×C11C2×SD1611yescharacteristic
141C22⋊D11—41no—
142C22⋊D11—41no—
143C22⋊D11—82no—
144C22⋊D11—161no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—82no—
148C2×Dic11—81no—
149C2×Dic11#10211yescharacteristic
150C2×Dic11#10211yescharacteristic
151D44—41no—
152C4×D11—21no—
153C4×D11—21no—
154C4×D11—21no—
155C4×D11—21no—
156C4×D11—161no—
157Dic22—41no—
158Dic22—41no—
159Dic22—41no—
160C8×C11—21no—
161C8×C11—21no—
162C11⋊C8—21no—
163C11⋊C8#9911yescharacteristic
164C11⋊C8#9911yescharacteristic
165C2×#135—111no—
166C2×#131—111no—
167#537—221no—
168C2×M32—221no—
169#470—111no—
170#470—111no—
171#469—111no—
172#469C2×D1111yescharacteristic
173#465—221no—
174#465—221no—
175#427—221no—
176C2×#106—111no—
177#417—221no—
178#410—221no—
179#349—111no—
180#349—221no—
181#349C2×D1111yescharacteristic
182H(3,ℤ/4)—111no—
183H(3,ℤ/4)C2×D1111yescharacteristic
184C22×C11—21no—
185C22×C11—41no—
186C22×C11—81no—
187C22×C11—81no—
188C22×C11—81no—
189C22×C11C2×#10211yescharacteristic
190C2×D11—21no—
191C2×D11—21no—
192C2×D11—41no—
193C2×D11—41no—
194C4×C11—21no—
195C4×C11—81no—
196C4×C11—161no—
197C4×C11C2×#9911yescharacteristic
198C4×C11#42111yescharacteristic
199Dic11—21no—
200Dic11—21no—
201Dic11—81no—
202Dic11—81no—
203Dic11—161no—
204C2×#41—111no—
205C2×#41—221no—
206#135—441no—
207#135—441no—
208C2×Q16—111no—
209C2×SD16—221no—
210C2×D8C4×D1111yescharacteristic
211#131—441no—
212#131—441no—
213C2×M16—111no—
214C2×M16—111no—
215C2×M16C22×D1111yescharacteristic
216C22×C8—111no—
217C22×C8—111no—
218C22×C8—111no—
219C22⋊Q8—221no—
220C22⋊Q8—221no—
221C22⋊Q8—441no—
222#121—21no—
223#121—221no—
224#121—441no—
225#121—441no—
226#121—441no—
227#117—21no—
228#117—221no—
229C2×C4⋊C4—221no—
230M32—21no—
231M32—221no—
232M32—441no—
233C2×C16—441no—
234#107—441no—
235#106—111no—
236#106—221no—
237#106—441no—
238#106C4×D1111yescharacteristic
239#103—221no—
240#103—221no—
241#102—21no—
242#102—221no—
243#99—441no—
244#99—441no—
245C2×C11—21no—
246C2×C11—41no—
247C2×C11—161no—
248C2×C11#151911yescharacteristic
249D11—41no—
250D11—41no—
251#41—441no—
252#41—441no—
253#41—442no—
254#41—442no—
255C2×Q8—111no—
256C2×Q8—221no—
257C2×D4—21no—
258C2×D4—41no—
259C2×D4—111no—
260C2×D4—111no—
261C2×D4—111no—
262C2×D4—441no—
263C2×D4—441no—
264C22×C4—111no—
265C22×C4—111no—
266C22×C4—441no—
267C22×C4—441no—
268C22×C4D4×D1111yescharacteristic
269Q16—441no—
270SD16—441no—
271SD16—441no—
272D8—41no—
273M16—41no—
274M16—441no—
275M16—441no—
276C2×C8—111no—
277C2×C8—111no—
278C2×C8—221no—
279C2×C8—221no—
280C2×C8—221no—
281C2×C8—221no—
282C2×C8—221no—
283C2×C8—221no—
284C2×C8C2×C4×D1111yescharacteristic
285C2×C8D4×D1111yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—41no—
288C4⋊C4—221no—
289C4⋊C4—441no—
290C4⋊C4—441no—
291C4⋊C4—441no—
292C4⋊C4—441no—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C22⋊C4—441no—
296C22⋊C4—441no—
297C22⋊C4—441no—
298C22⋊C4—441no—
299C42—41no—
300C42—441no—
301C16—41no—
302C16—441no—
303C11#1186711yescharacteristic, complemented, Sylow
304C23—41no—
305C23—111no—
306C23—111no—
307C23D8×D1111yescharacteristic
308Q8—441no—
309Q8—441no—
310Q8—441no—
311D4—41no—
312D4—41no—
313D4—161no—
314D4—441no—
315D4—441no—
316D4—441no—
317D4—882no—
318D4—1761no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—41no—
322C2×C4—81no—
323C2×C4—111no—
324C2×C4—111no—
325C2×C4—221no—
326C2×C4—221no—
327C2×C4—221no—
328C2×C4—221no—
329C2×C4—441no—
330C2×C4—441no—
331C2×C4—882no—
332C2×C4—881no—
333C2×C4—1761no—
334C2×C4C22⋊C4×D1111yescharacteristic
335C2×C4SD16×D1111yescharacteristic
336C8—21no—
337C8—21no—
338C8—111no—
339C8—111no—
340C8—221no—
341C22—21no—
342C22—41no—
343C22—81no—
344C22—81no—
345C22—81no—
346C22—221no—
347C22—221no—
348C22—441no—
349C22—441no—
350C22D11×#10211yescharacteristic
351C4—21no—
352C4—81no—
353C4—161no—
354C4—221no—
355C4—221no—
356C4—881no—
357C4—881no—
358C4—1761no—
359C4D11×#9911yescharacteristic
360C4#1062243411yescharacteristic
361C2—21no—
362C2—41no—
363C2—161no—
364C2—441no—
365C2—441no—
366C2#1306718211yescharacteristic
subgroupG/H
centerC2#13067182
commutatorC2×C8×C11C22×C4
FrattiniC2×M16C22×D11
FittingC11×#1339C2
socleC2×C11#1519
prime radical#13078276C2
cosocleC2×C11×M16C23
hypercenter#1339D11
hypocenterC11#11867
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #1339

Complements

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

NH ≅ G/Ntype
2. #13070235C2semidirect
3. #13068661C2semidirect
4. #13066605C2semidirect
5. #13066603C2semidirect
6. #13066601C2semidirect
7. C11×#1339C2semidirect
8. C2×#66965C4semidirect
12. #10622772C4semidirect
18. #10622481C4semidirect
19. D11×#106C4semidirect
127. #1339D11semidirect
303. C11#11867semidirect

Maximal subgroups

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

subgroupindex
#130782762
#130702352
#130686612
#130666052
#130666032
#130666012
C11×#13392
#1186711