Finite Group Databasebeta

← #14670686

Subgroups — #14670686

Order 2816.

456 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622520C211yesmaximal, characteristic, complemented
2#13077517C211yesmaximal, characteristic
3#13070243C211yesmaximal, characteristic, complemented
4C2×#10622199C211yesmaximal, characteristic, complemented
5#13066706C211yesmaximal, characteristic, complemented
6#13066703C211yesmaximal, characteristic, complemented
7C11×#2115C211yesmaximal, characteristic, complemented
8C2×C11×#131C2211yescharacteristic
9#10623353C411yescharacteristic
10C2×#66954C2211yescharacteristic
11C2×C11×M32C2211yescharacteristic
12C2×C11×M32C2211yescharacteristic
13#10622849C411yescharacteristic
14#10622758—22no—
15#10622757—22no—
16#10622752C411yescharacteristic
17#10622737C411yescharacteristic
18#10622714C2211yescharacteristic
19C2×#66876C2211yescharacteristic
20C22×C11⋊C16C2211yescharacteristic
21#10622520—22no—
22#10622520—22no—
23C2×#66862—21no—
24C2×C16×D11—21no—
25C11×#349—22no—
26#10622199—21no—
27#10622199—21no—
28#10622146—22no—
29C2×C11×#41C2×C411yescharacteristic
30C2×#4339C2×C411yescharacteristic
31C11×#131—21no—
32C11×#131—21no—
33C11×#131—21no—
34C11×#131—21no—
35C2×C11×M16—21no—
36C2×C11×M16C2×C411yescharacteristic
37C22×C8×C11—21no—
38C22×C8×C11C2311yescharacteristic
39#67004—21no—
40#67003—22no—
41#67002—21no—
42#66995C812yes—
43#66985C812yes—
44#66979C2×C411yescharacteristic
45C2×#4318C2×C411yescharacteristic
46C2×#4318C2×C411yescharacteristic
47#66954—21no—
48#66954—21no—
49#66954D412yes—
50#66954D412yes—
51C2×#4313—21no—
52C2×C8×D11—21no—
53C11×M32—21no—
54C11×M32—21no—
55C11×M32—21no—
56C11×M32D412yes—
57C2×C11×C16—21no—
58C2×C11×C16—21no—
59#66901—22no—
60#66889—22no—
61#66886—22no—
62#66879—21no—
63C8×Dic11—21no—
64#66876—21no—
65#66876—21no—
66C2×C11⋊C16—21no—
67C2×C11⋊C16—21no—
68C2×C11⋊C16—21no—
69C2×C11⋊C16D411yescharacteristic
70C2×C11⋊C16D411yescharacteristic
71#66862—24no—
72C16×D11—24no—
73#12987—111nomaximal, Sylow
74C11×#41—21no—
75C11×#41—21no—
76C11×#41—21no—
77C11×#41—21no—
78C2×Q8×C11C2×C811yescharacteristic
79C2×D4×C11—21no—
80C2×D4×C11C2×C811yescharacteristic
81C22×C4×C11—21no—
82C22×C4×C11C22×C411yescharacteristic
83C2×C22⋊D11—21no—
84#4339—21no—
85#4339—21no—
86#4339C22⋊C412yes—
87#4339C2×C812yes—
88C2×D44M1611yescharacteristic
89C2×C4×D11—21no—
90C2×Dic22M1611yescharacteristic
91C11×M16—21no—
92C11×M16—21no—
93C11×M16—41no—
94C11×M16—41no—
95C2×C8×C11—21no—
96C2×C8×C11—41no—
97C2×C8×C11—41no—
98C2×C8×C11C2×D411yescharacteristic
99C2×C8×C11C2×D411yescharacteristic
100C2×C8×C11C2×D411yescharacteristic
101C2×C8×C11C2×D411yescharacteristic
102C2×C8×C11#4111yescharacteristic
103C2×C8×C11#4111yescharacteristic
104C22⋊Dic11—21no—
105#4326—22no—
106#4325—22no—
107#4324—22no—
108#4323—22no—
109C4⋊Dic11—21no—
110C4×Dic11—21no—
111#4318—21no—
112#4318—21no—
113#4318C22⋊C412yes—
114#4318C2×C812yes—
115C2×C11⋊C8—21no—
116C2×C11⋊C8—21no—
117#4313—22no—
118#4313—22no—
119C8×D11—22no—
120C8×D11—22no—
121C11×C16—22no—
122C11×C16—41no—
123C11⋊C16—21no—
124C11⋊C16—21no—
125C11⋊C16—41no—
126C2×#504—111no—
127#2955—111no—
128#2117—111no—
129C2×#350—111no—
130#2115D1111yescharacteristic, complemented
131#1379—111no—
132#1378—111no—
133C23×C11—21no—
134C23×C11#13111yescharacteristic
135C22×D11—21no—
136Q8×C11—21no—
137Q8×C11—21no—
138D4×C11—21no—
139D4×C11—21no—
140D4×C11—41no—
141D4×C11—41no—
142C2×C4×C11—21no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11C2×C22⋊C411yescharacteristic
146C2×C4×C11C4×D411yescharacteristic
147C2×C4×C11C4×D411yescharacteristic
148C2×C4×C11C22×C811yescharacteristic
149C2×C4×C11C2×M1611yescharacteristic
150C2×C4×C11#13111yescharacteristic
151C22⋊D11—22no—
152C22⋊D11—22no—
153C2×Dic11—21no—
154C2×Dic11—41no—
155D44—21no—
156D44C22⋊C812yes—
157C4×D11—22no—
158C4×D11—22no—
159Dic22—21no—
160Dic22C22⋊C812yes—
161C8×C11—41no—
162C8×C11#12011yescharacteristic
163C8×C11#12111yescharacteristic
164C8×C11#12111yescharacteristic
165C8×C11#12311yescharacteristic
166C11⋊C8—22no—
167C11⋊C8—22no—
168#575—111no—
169C2×#131—111no—
170C2×#131C2×D1111yescharacteristic
171#504—222no—
172#504—222no—
173C2×M32—111no—
174C2×M32—221no—
175C2×M32C2×D1111yescharacteristic
176C2×M32C2×D1111yescharacteristic
177C22×C16—111no—
178C22×C16—221no—
179#444—222no—
180#443—222no—
181#430—111no—
182#421—111no—
183#421—111no—
184#405—111no—
185#350—222no—
186#350—221no—
187#350—221no—
188#349—22no—
189C22×C11—41no—
190C22×C11—41no—
191C22×C11—81no—
192C22×C11#40811yescharacteristic
193C22×C11C8×D411yescharacteristic
194C22×C11#43511yescharacteristic
195C2×D11—22no—
196C2×D11—42no—
197C4×C11—41no—
198C4×C11#38611yescharacteristic
199C4×C11C2×C22⋊C811yescharacteristic
200C4×C11C8×D411yescharacteristic
201C4×C11#43511yescharacteristic
202Dic11—22no—
203Dic11—81no—
204C2×#41—111no—
205C2×#41C4×D1111yescharacteristic
206#137—112no—
207#137—221no—
208AGL(1,ℤ/8)—112no—
209AGL(1,ℤ/8)—221no—
210#135—222no—
211#131—21no—
212#131—21no—
213#131—21no—
214#131—21no—
215#131—112no—
216#131—112no—
217#131—221no—
218#131—221no—
219C2×M16—21no—
220C2×M16—111no—
221C2×M16—111no—
222C2×M16—221no—
223C2×M16C4×D1111yescharacteristic
224C22×C8—21no—
225C22×C8—221no—
226C22×C8C22×D1111yescharacteristic
227#117—111no—
228M32—21no—
229M32—21no—
230M32—21no—
231M32—224no—
232M32—221no—
233M32—221no—
234M32C22⋊D1112yes—
235C2×C16—21no—
236C2×C16—21no—
237C2×C16—111no—
238C2×C16—111no—
239C2×C16—224no—
240C2×C16—221no—
241C2×C16—221no—
242C2×C16—221no—
243#108—222no—
244#104—222no—
245#104—222no—
246#97—221no—
247C4×C8—221no—
248C2×C11—21no—
249C2×C11—21no—
250C2×C11—21no—
251C2×C11—81no—
252C2×C11#186911yescharacteristic
253D11—42no—
254#41—21no—
255#41—21no—
256#41—21no—
257#41—21no—
258#41—112no—
259#41—112no—
260#41—221no—
261#41—221no—
262C2×Q8—111no—
263C2×Q8C8×D1111yescharacteristic
264C2×D4—21no—
265C2×D4—111no—
266C2×D4—221no—
267C2×D4C8×D1111yescharacteristic
268C22×C4—21no—
269C22×C4—221no—
270C22×C4C2×C4×D1111yescharacteristic
271Q16—222no—
272SD16—222no—
273SD16—222no—
274D8—222no—
275M16—21no—
276M16—21no—
277M16—41no—
278M16—41no—
279M16—112no—
280M16—112no—
281M16—221no—
282M16—221no—
283M16—222no—
284M16—222no—
285C2×C8—21no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—221no—
289C2×C8—221no—
290C2×C8—222no—
291C2×C8—222no—
292C2×C8#433911yescharacteristic
293C2×C8D4×D1111yescharacteristic
294C2×C8D4×D1111yescharacteristic
295C2×C8D4×D1111yescharacteristic
296C2×C8#434111yescharacteristic
297C2×C8C2×C22⋊D1111yescharacteristic
298C4⋊C4—221no—
299C22⋊C4—221no—
300C42—221no—
301C16—22no—
302C16—41no—
303C16—221no—
304C16—221no—
305C16—441no—
306C11#1298711yescharacteristic, complemented, Sylow
307C23—21no—
308C23—221no—
309C23#6695411yescharacteristic
310Q8—21no—
311Q8—21no—
312Q8—112no—
313Q8—221no—
314D4—21no—
315D4—21no—
316D4—41no—
317D4—41no—
318D4—112no—
319D4—222no—
320D4—222no—
321D4—221no—
322C2×C4—21no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—221no—
326C2×C4—222no—
327C2×C4—222no—
328C2×C4—441no—
329C2×C4C22⋊C4×D1111yescharacteristic
330C2×C4(C22⋊D11)⋊C411yescharacteristic
331C2×C4C2×C8×D1111yescharacteristic
332C2×C4M16×D1111yescharacteristic
333C2×C4#6696011yescharacteristic
334C2×C4C4×C22⋊D1111yescharacteristic
335C8—41no—
336C8—222no—
337C8—222no—
338C8#6693611yescharacteristic
339C8#6693711yescharacteristic
340C8#6699011yescharacteristic
341C8#6699111yescharacteristic
342C22—41no—
343C22—41no—
344C22—81no—
345C22—222no—
346C22—442no—
347C22#1062234011yescharacteristic
348C22#1062234111yescharacteristic
349C22C8×C22⋊D1111yescharacteristic
350C4—41no—
351C4—222no—
352C4—881no—
353C4D11×C22⋊C811yescharacteristic
354C4(C22⋊D11)⋊C811yescharacteristic
355C4#1062256911yescharacteristic
356C4#1062274011yescharacteristic
357C2—21no—
358C2—21no—
359C2—21no—
360C2—81no—
361C2—442no—
362C2#1306890511yescharacteristic
subgroupG/H
centerC8#66937
commutatorC2×C4×C11C22×C8
FrattiniC22×C8C22×D11
FittingC11×#2115C2
socleC2×C11#1869
prime radical#10623353C4
cosocleC22×C8×C11C23
hypercenter#2115D11
hypocenterC11#12987
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C8 ◁ C22×C8 ◁ #2115

Complements

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

NH ≅ G/Ntype
1. C2×#10622520C2semidirect
3. #13070243C2semidirect
4. C2×#10622199C2semidirect
5. #13066706C2semidirect
6. #13066703C2semidirect
7. C11×#2115C2semidirect
130. #2115D11semidirect
306. C11#12987semidirect

Maximal subgroups

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

subgroupindex
C2×#106225202
#130775172
#130702432
C2×#106221992
#130667062
#130667032
C11×#21152
#1298711