Finite Group Databasebeta

← #14907222

Subgroups — #14907222

Order 2816.

652 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081752C211yesmaximal, characteristic
2C2×#10622507C211yesmaximal, characteristic, complemented
3#13077416C211yesmaximal, characteristic, complemented
4#13070513C214yesmaximal, complemented
5#13070506C214yesmaximal, complemented
6#13070363C211yesmaximal, characteristic, complemented
7#13070351C211yesmaximal, characteristic, complemented
8C2×#10622150C211yesmaximal, characteristic, complemented
9C11×#2155C211yesmaximal, characteristic, complemented
10C2×#66960—21no—
11C2×#66957C2211yescharacteristic
12C2×#66957C2211yescharacteristic
13#10623053—21no—
14C2×C11×M32C2211yescharacteristic
15C2×C11×#108C2211yescharacteristic
16C11×#427C2211yescharacteristic
17C2×#66889—21no—
18C2×#66879C2211yescharacteristic
19C2×#66876C2211yescharacteristic
20#10622615—21no—
21#10622522C412yescomplemented
22#10622522C2212yes—
23#10622521C412yescomplemented
24#10622521C2212yes—
25#10622517C414yescomplemented
26#10622507—22no—
27#10622507C2214yes—
28#10622502—22no—
29#10622482C2212yescomplemented
30#10622466C2212yescomplemented
31C11×#365C2214yescomplemented
32#10622150C2214yescomplemented
33#10622134C2212yescomplemented
34#10622133C2212yescomplemented
35#10622126C2214yes—
36C2×#4339—21no—
37C2×#4339—21no—
38C2×C11×M16—21no—
39C22×C8×C11C2311yescharacteristic
40C11×#117—21no—
41C2×C4×Dic11D411yescharacteristic
42C22×C11⋊C8D411yescharacteristic
43#66960—24no—
44#66960—42no—
45C2×Dic44C2×C411yescharacteristic, complemented
46C2×Dic44C2311yescharacteristic
47#66957—21no—
48#66957—21no—
49#66957—21no—
50#66957—21no—
51#66957C2×C412yes—
52#66957C2×C412yes—
53#66957C2×C412yescomplemented
54#66957C2312yes—
55C2×D88C2×C411yescharacteristic, complemented
56C2×D88C2311yescharacteristic
57C2×#4314—21no—
58C2×#4314—21no—
59C2×#4313—41no—
60C2×C8×D11—41no—
61#66946—22no—
62#66940—22no—
63(C22⋊D11)⋊C4—42no—
64#66925—41no—
65C42×D11—41no—
66C11×M32C2×C412yescomplemented
67C11×M32C2312yes—
68C2×C11×C16C2×C412yescomplemented
69C11×#108—21no—
70C11×#108C2312yes—
71C11×#107—21no—
72C11×#106C2312yes—
73#66889—24no—
74#66879D412yes—
75#66879C2312yes—
76#66876—21no—
77#66876C2312yes—
78C2×C11⋊C16—21no—
79#66874—22no—
80#66873—22no—
81Dic88C2×C414yescomplemented
82#66864C2×C414yescomplemented
83#66864C2×C414yescomplemented
84D176C2×C414yescomplemented
85#33468—111nomaximal, Sylow
86C22×C4×C11C2×D411yescharacteristic
87C2×C22⋊D11—41no—
88C2×C22⋊D11—41no—
89C22×Dic11—21no—
90#4339—22no—
91#4339—22no—
92#4339—22no—
93#4339—22no—
94#4339—41no—
95#4339—41no—
96#4339—41no—
97#4339—41no—
98C2×D44—21no—
99C2×D44—21no—
100C2×C4×D11—42no—
101C2×C4×D11—41no—
102C2×C4×D11—41no—
103C2×Dic22—21no—
104C2×Dic22—21no—
105C11×M16—22no—
106C11×M16—41no—
107C2×C8×C11—41no—
108C2×C8×C11C22×C411yescharacteristic
109C2×C8×C11C22×C411yescharacteristic
110C2×C8×C11C2×D411yescharacteristic
111C2×C8×C11#4111yescharacteristic
112C2×C8×C11#4111yescharacteristic
113C2×C8×C11C2411yescharacteristic
114C11×C4⋊C4—22no—
115C11×C22⋊C4—41no—
116C42×C11—41no—
117(C2×D11)⋊C4—42no—
118Dic11⋊C4—42no—
119C4×Dic11—21no—
120C4×Dic11—42no—
121C4×Dic11C2×D412yes—
122C2×C11⋊C8—21no—
123C2×C11⋊C8—21no—
124C2×C11⋊C8C2×D412yes—
125Dic44—21no—
126Dic44—21no—
127Dic44C22×C412yes—
128Dic44C22×C412yes—
129D88—21no—
130D88—21no—
131D88C22×C412yes—
132D88C22×C412yes—
133#4314—22no—
134#4314—22no—
135#4314—22no—
136#4314—22no—
137#4313—44no—
138C8×D11—44no—
139C11×C16C22×C414yes—
140C11⋊C16—22no—
141#3414—111no—
142C2×#444—111no—
143#2943—111no—
144AGL(1,ℤ/16)—114no—
145#2180—114no—
146#2155D1111yescharacteristic, complemented
147#2148—111no—
148#2145—111no—
149C2×#347—111no—
150C23×C11AGL(1,ℤ/8)11yescharacteristic
151C22×D11—41no—
152C22×D11—41no—
153C2×C4×C11—42no—
154C2×C4×C11C4×D411yescharacteristic
155C2×C4×C11C4×D411yescharacteristic
156C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C11C22×D411yescharacteristic
160C22⋊D11—42no—
161C22⋊D11—42no—
162C22⋊D11—42no—
163C22⋊D11—42no—
164C2×Dic11—22no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—81no—
168D44—22no—
169D44—22no—
170D44—41no—
171D44—41no—
172C4×D11—42no—
173C4×D11—42no—
174C4×D11—42no—
175C4×D11—42no—
176C4×D11—84no—
177Dic22—22no—
178Dic22—22no—
179Dic22—41no—
180Dic22—41no—
181C8×C11—42no—
182C8×C11C4×D411yescharacteristic
183C8×C11C4×D411yescharacteristic
184C8×C11C23×C411yescharacteristic
185C8×C11C2×#4111yescharacteristic
186C11⋊C8—22no—
187C2×#135—111no—
188C2×#135—111no—
189C2×#131—221no—
190C4×#41—221no—
191#510—112no—
192#510—112no—
193#509—112no—
194#509—112no—
195#508—114no—
196C2×M32—111no—
197C2×M32C2×D1111yescharacteristic
198#444—114no—
199#444—222no—
200#442—112no—
201#441—112no—
202#440—222no—
203C2×#108C2×D1111yescharacteristic
204#427C2×D1111yescharacteristic
205C2×#104—221no—
206#416—221no—
207C2×#97—111no—
208#365C2×D1114yescomplemented
209#362—112no—
210#361—112no—
211#360—114no—
212#347—114no—
213C22×C11—41no—
214C22×C11#44211yescharacteristic
215C22×C11#44211yescharacteristic
216C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
217C2×D11—42no—
218C2×D11—42no—
219C2×D11—82no—
220C2×D11—82no—
221C4×C11—82no—
222C4×C11#44211yescharacteristic
223C4×C11#44211yescharacteristic
224C4×C11C2×C4×D411yescharacteristic
225C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
226Dic11—42no—
227Dic11—42no—
228Dic11—42no—
229C2×#41—221no—
230C2×#41—221no—
231#135—112no—
232#135—112no—
233#135—112no—
234#135—112no—
235#135—221no—
236#135—221no—
237#135—221no—
238#135—221no—
239C2×Q16—111no—
240C2×Q16—111no—
241C2×SD16—221no—
242C2×SD16—221no—
243C2×D8—111no—
244C2×D8—111no—
245#131—224no—
246#131—442no—
247C2×M16—21no—
248C2×M16—441no—
249C22×C8—111no—
250C22×C8—441no—
251C22×C8C22×D1111yescharacteristic
252C4×Q8—222no—
253C4×D4—222no—
254C4×D4—442no—
255#117—21no—
256#117—441no—
257C2×C42—111no—
258C2×C42—441no—
259Q32—114no—
260SD32—114no—
261SD32—114no—
262D16—114no—
263M32—112no—
264M32—221no—
265M32C4×D1112yescomplemented
266M32C22×D1112yes—
267C2×C16—221no—
268C2×C16C4×D1112yescomplemented
269#108—21no—
270#108C22×D1112yes—
271#107—21no—
272#106C22×D1112yes—
273#104—224no—
274#103—222no—
275#102—222no—
276#97—112no—
277#97—112no—
278C2×C11—21no—
279C2×C11—21no—
280C2×C11—21no—
281C2×C11C2×#44211yescharacteristic
282D11—82no—
283D11—82no—
284#41—222no—
285#41—222no—
286#41—222no—
287#41—222no—
288#41—441no—
289#41—441no—
290#41—441no—
291#41—441no—
292C2×Q8—221no—
293C2×Q8—221no—
294C2×D4—221no—
295C2×D4—221no—
296C2×D4—441no—
297C2×D4—441no—
298C22×C4—221no—
299C22×C4—442no—
300C22×C4—441no—
301C22×C4—441no—
302C22×C4D4×D1111yescharacteristic
303Q16—112no—
304Q16—112no—
305Q16—221no—
306Q16—221no—
307SD16—222no—
308SD16—222no—
309SD16—222no—
310SD16—222no—
311D8—112no—
312D8—112no—
313D8—221no—
314D8—221no—
315M16—22no—
316M16—41no—
317M16—444no—
318C2×C8—41no—
319C2×C8—112no—
320C2×C8—221no—
321C2×C8—221no—
322C2×C8—444no—
323C2×C8C2×C4×D1111yescharacteristic
324C2×C8C2×C4×D1111yescharacteristic
325C2×C8D4×D1111yescharacteristic
326C2×C8#434311yescharacteristic
327C2×C8#434311yescharacteristic
328C2×C8C23×D1111yescharacteristic
329C4⋊C4—22no—
330C4⋊C4—442no—
331C22⋊C4—41no—
332C22⋊C4—442no—
333C42—41no—
334C42—112no—
335C42—221no—
336C42—442no—
337C16—222no—
338C16C2×C4×D1114yes—
339C11#3346811yescharacteristic, complemented, Sylow
340C23—441no—
341C23—441no—
342C23#6696711yescharacteristic
343Q8—222no—
344Q8—222no—
345Q8—441no—
346Q8—441no—
347D4—222no—
348D4—222no—
349D4—442no—
350D4—442no—
351D4—442no—
352D4—442no—
353D4—441no—
354D4—441no—
355C2×C4—42no—
356C2×C4—222no—
357C2×C4—441no—
358C2×C4—441no—
359C2×C4—442no—
360C2×C4—442no—
361C2×C4—442no—
362C2×C4—442no—
363C2×C4—884no—
364C2×C4—881no—
365C2×C4#6694611yescharacteristic
366C2×C4#6694611yescharacteristic
367C2×C4#6696711yescharacteristic
368C2×C4#6696711yescharacteristic
369C2×C4#6696711yescharacteristic
370C2×C4C2×D4×D1111yescharacteristic
371C8—42no—
372C8—222no—
373C8#6694611yescharacteristic
374C8#6694611yescharacteristic
375C8C22×C4×D1111yescharacteristic
376C8C2×#434311yescharacteristic
377C22—41no—
378C22—442no—
379C22—442no—
380C22—882no—
381C22—882no—
382C22#1062248211yescharacteristic
383C22#1062248211yescharacteristic
384C22C2×#6696711yescharacteristic
385C4—82no—
386C4—442no—
387C4—442no—
388C4—442no—
389C4#1062248211yescharacteristic
390C4#1062248211yescharacteristic
391C4C2×#6694611yescharacteristic
392C4C2×#6696711yescharacteristic
393C2—21no—
394C2—21no—
395C2—21no—
396C2—882no—
397C2—882no—
398C2C2×#1062248211yescharacteristic
subgroupG/H
centerC4#10622482
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
FittingC11×#2155C2
socleC2×C11C2×#442
prime radical#13081752C2
cosocleC2×C8×C11C24
hypercenter#2155D11
hypocenterC11#33468
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ #2155

Complements

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

NH ≅ G/Ntype
2. C2×#10622507C2semidirect
3. #13077416C2semidirect
4. #13070513C2semidirect
5. #13070506C2semidirect
6. #13070363C2semidirect
7. #13070351C2semidirect
8. C2×#10622150C2semidirect
9. C11×#2155C2semidirect
21. #10622522C4semidirect
23. #10622521C4semidirect
25. #10622517C4semidirect
29. #10622482C22semidirect
30. #10622466C22semidirect
31. C11×#365C22semidirect
32. #10622150C22semidirect
33. #10622134C22semidirect
34. #10622133C22semidirect
45. C2×Dic44C2×C4semidirect
53. #66957C2×C4semidirect
55. C2×D88C2×C4semidirect
66. C11×M32C2×C4semidirect
68. C2×C11×C16C2×C4semidirect
81. Dic88C2×C4semidirect
82. #66864C2×C4semidirect
83. #66864C2×C4semidirect
84. D176C2×C4semidirect
146. #2155D11semidirect
208. #365C2×D11semidirect
265. M32C4×D11semidirect
268. C2×C16C4×D11semidirect
339. C11#33468semidirect

Maximal subgroups

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

subgroupindex
#130817522
C2×#106225072
#130774162
#130705132
#130705062
#130703632
#130703512
C2×#106221502
C11×#21552
#3346811