Finite Group Databasebeta

← #14908356

Subgroups — #14908356

Order 2816.

656 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622760C211yesmaximal, characteristic, complemented
2#13081719C211yesmaximal, characteristic, complemented
3#13078336C211yesmaximal, characteristic, complemented
4#13070744C214yesmaximal, complemented
5#13070734C214yesmaximal, complemented
6#13070410C211yesmaximal, characteristic, complemented
7#13070363C211yesmaximal, characteristic, complemented
8C2×#10622201C211yesmaximal, characteristic, complemented
9C2×C11×#472C211yesmaximal, characteristic, complemented
10C2×C11×AGL(1,ℤ/8)—21no—
11C22×C11×D8C2211yescharacteristic
12C2×C11×#131C2211yescharacteristic
13#10623353—21no—
14C2×#66957C2211yescharacteristic
15C11×#472—22no—
16C11×#472C2214yes—
17C2×C11×#108C2211yescharacteristic
18C2×C11×#100—21no—
19C2×#66891C2212yescomplemented
20#10622760—22no—
21#10622760—22no—
22C2×#66890C2212yescomplemented
23#10622756C2212yescomplemented
24#10622755C2212yescomplemented
25#10622754—22no—
26#10622753—22no—
27#10622753C2214yescomplemented
28#10622745—21no—
29C2×#66883C2211yescharacteristic
30C2×#66876—22no—
31C2×#66876C2211yescharacteristic
32C2×#66876C2211yescharacteristic
33#10622201C2214yescomplemented
34#10622134C2212yescomplemented
35#10622133C2212yescomplemented
36#10622131C2214yescomplemented
37C2×C11×#41D411yescharacteristic
38C22×D4×C11—21no—
39C2×#4339—21no—
40C11×AGL(1,ℤ/8)—24no—
41C11×AGL(1,ℤ/8)—42no—
42C2×C11×SD16—41no—
43C2×C11×D8—21no—
44C2×C11×D8—21no—
45C2×C11×D8—21no—
46C2×C11×D8—21no—
47C2×C11×D8—21no—
48C2×C11×D8—41no—
49C2×C11×D8C2312yes—
50C11×#131—21no—
51C11×#131—21no—
52C11×#131D412yes—
53C11×#131C2312yes—
54C2×C11×M16—21no—
55C2×C11×M16—21no—
56C2×C11×M16D411yescharacteristic
57C22×C8×C11—21no—
58C22×C8×C11C2311yescharacteristic
59#67004—22no—
60#67003—42no—
61#67002—22no—
62#66995—41no—
63#66985—41no—
64C2×#4318—21no—
65C2×Dic44C2311yescharacteristic
66#66957—21no—
67#66957—21no—
68#66957—21no—
69#66957—21no—
70C2×D88C2311yescharacteristic
71C2×#4314—21no—
72C11×#108—21no—
73C11×#108C2312yes—
74C11×#100—24no—
75#66891—24no—
76#66890—24no—
77#66888—22no—
78#66887—22no—
79#66883—21no—
80#66883C2312yes—
81#66876—21no—
82#66876—24no—
83#66876D412yes—
84#66876D412yes—
85#66876C2312yes—
86C2×C11⋊C16—21no—
87C2×C11⋊C16—24no—
88C2×C11⋊C16C2312yes—
89#33618—111nomaximal, Sylow
90C24×C11—41no—
91C11×#41—21no—
92C11×#41—21no—
93C11×#41D812yes—
94C11×#41C2×D412yes—
95C2×Q8×C11D811yescharacteristic
96C2×D4×C11—21no—
97C2×D4×C11—22no—
98C2×D4×C11—41no—
99C2×D4×C11—41no—
100C2×D4×C11—41no—
101C2×D4×C11—41no—
102C2×D4×C11—41no—
103C2×D4×C11D811yescharacteristic
104C22×C4×C11—21no—
105C22×C4×C11C2×D411yescharacteristic
106C2×C22⋊D11—41no—
107#4339—41no—
108#4339—41no—
109#4339—41no—
110#4339—41no—
111C2×D44—21no—
112C2×C4×D11—41no—
113C2×Dic22—21no—
114C11×SD16—44no—
115C11×D8—22no—
116C11×D8—22no—
117C11×D8—41no—
118C11×D8—41no—
119C11×D8—44no—
120C11×M16—22no—
121C11×M16—22no—
122C11×M16—21no—
123C11×M16—22no—
124C11×M16—41no—
125C11×M16C2×D412yes—
126C2×C8×C11—22no—
127C2×C8×C11—22no—
128C2×C8×C11—21no—
129C2×C8×C11—41no—
130C2×C8×C11C2×D411yescharacteristic
131C2×C8×C11C2×D411yescharacteristic
132C2×C8×C11C2×D411yescharacteristic
133C2×C8×C11#4111yescharacteristic
134C2×C8×C11#4111yescharacteristic
135C2×C8×C11C2411yescharacteristic
136#4326—42no—
137#4325—42no—
138#4324—42no—
139#4323—42no—
140#4318—22no—
141#4318—41no—
142C2×C11⋊C8—41no—
143Dic44—21no—
144Dic44—21no—
145D88—21no—
146D88—21no—
147#4314—41no—
148#4314—41no—
149C11⋊C16—22no—
150C11⋊C16C2×D414yes—
151C2×#509—111no—
152#3407—111no—
153#3067—111no—
154C2×#472D1111yescharacteristic, complemented
155#2223—114no—
156#2221—114no—
157#2161—111no—
158#2148—111no—
159C2×#361—111no—
160C23×C11—21no—
161C23×C11—42no—
162C23×C11—81no—
163C23×C11—81no—
164C23×C11—162no—
165C23×C11#13511yescharacteristic
166C22×D11—41no—
167Q8×C11—21no—
168Q8×C11C2×D812yes—
169D4×C11—22no—
170D4×C11—22no—
171D4×C11—21no—
172D4×C11—42no—
173D4×C11—42no—
174D4×C11—81no—
175D4×C11—81no—
176D4×C11C2×D812yes—
177C2×C4×C11—21no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11#12111yescharacteristic
182C2×C4×C11C2×D811yescharacteristic
183C2×C4×C11C2×D811yescharacteristic
184C2×C4×C11#13511yescharacteristic
185C2×C4×C11C22×D411yescharacteristic
186C22⋊D11—81no—
187C22⋊D11—81no—
188C2×Dic11—41no—
189D44—41no—
190D44—41no—
191C4×D11—81no—
192C4×D11—81no—
193Dic22—41no—
194Dic22—41no—
195C8×C11—22no—
196C8×C11—42no—
197C8×C11#12111yescharacteristic
198C8×C11#12111yescharacteristic
199C8×C11C22×D411yescharacteristic
200C8×C11C2×#4111yescharacteristic
201C11⋊C8—42no—
202#575—221no—
203C2×AGL(1,ℤ/8)—21no—
204C2×#135—111no—
205C22×D8C2×D1111yescharacteristic
206C2×#131C2×D1111yescharacteristic
207#509—222no—
208#509—222no—
209C2×SD32—112no—
210C2×D16—112no—
211#504—114no—
212#504—222no—
213C2×M32—111no—
214C2×M32—111no—
215C2×M32—222no—
216#473—112no—
217#472—22no—
218#472—112no—
219#472C2×D1114yes—
220#471—222no—
221C2×#108—111no—
222C2×#108C2×D1111yescharacteristic
223#413—221no—
224C2×#100—21no—
225#368—114no—
226#362—112no—
227#361—114no—
228#361—112no—
229C22×C11—22no—
230C22×C11—41no—
231C22×C11—81no—
232C22×C11—82no—
233C22×C11—162no—
234C22×C11—162no—
235C22×C11—162no—
236C22×C11#46611yescharacteristic
237C22×C11#46611yescharacteristic
238C22×C11C2×#13511yescharacteristic
239C2×D11—81no—
240C2×D11—161no—
241C4×C11—22no—
242C4×C11#46611yescharacteristic
243C4×C11#46611yescharacteristic
244C4×C11C2×#12111yescharacteristic
245C4×C11C22×D811yescharacteristic
246Dic11—81no—
247C2×#41—221no—
248C2×#41C22⋊D1111yescharacteristic
249C22×D4—21no—
250#137—222no—
251#137—441no—
252AGL(1,ℤ/8)—24no—
253AGL(1,ℤ/8)—42no—
254AGL(1,ℤ/8)—222no—
255AGL(1,ℤ/8)—441no—
256#135—221no—
257#135—221no—
258#135—221no—
259#135—221no—
260#135—442no—
261C2×Q16—111no—
262C2×SD16—41no—
263C2×SD16—221no—
264C2×D8—21no—
265C2×D8—21no—
266C2×D8—21no—
267C2×D8—21no—
268C2×D8—21no—
269C2×D8—41no—
270C2×D8—111no—
271C2×D8C22×D1112yes—
272#131—21no—
273#131—21no—
274#131C22⋊D1112yes—
275#131C22×D1112yes—
276C2×M16—21no—
277C2×M16—21no—
278C2×M16—221no—
279C2×M16C22⋊D1111yescharacteristic
280C22×C8—21no—
281C22×C8C22×D1111yescharacteristic
282SD32—224no—
283D16—224no—
284M32—112no—
285M32—112no—
286M32—112no—
287M32—224no—
288M32—221no—
289C2×C16—112no—
290C2×C16—224no—
291C2×C16—221no—
292#108—21no—
293#108—112no—
294#108—221no—
295#108C22×D1112yes—
296#101—222no—
297#100—24no—
298#100—222no—
299C2×C11—21no—
300C2×C11—21no—
301C2×C11—21no—
302C2×C11—42no—
303C2×C11—162no—
304C2×C11C2×#46611yescharacteristic
305D11—161no—
306C24—41no—
307#41—21no—
308#41—21no—
309#41—441no—
310#41—441no—
311#41—441no—
312#41—441no—
313#41#432312yes—
314#41C2×C22⋊D1112yes—
315C2×Q8—221no—
316C2×Q8#432311yescharacteristic
317C2×D4—21no—
318C2×D4—22no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—221no—
325C2×D4—441no—
326C2×D4#432311yescharacteristic
327C22×C4—21no—
328C22×C4—441no—
329C22×C4C2×C22⋊D1111yescharacteristic
330Q16—221no—
331Q16—221no—
332Q16—442no—
333SD16—44no—
334SD16—442no—
335SD16—442no—
336SD16—441no—
337SD16—441no—
338D8—22no—
339D8—22no—
340D8—44no—
341D8—41no—
342D8—41no—
343D8—221no—
344D8—221no—
345D8—442no—
346M16—21no—
347M16—22no—
348M16—22no—
349M16—22no—
350M16—41no—
351M16—222no—
352M16—441no—
353M16C2×C22⋊D1112yes—
354C2×C8—21no—
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—41no—
358C2×C8—441no—
359C2×C8D4×D1111yescharacteristic
360C2×C8D4×D1111yescharacteristic
361C2×C8#434111yescharacteristic
362C2×C8#434111yescharacteristic
363C2×C8C2×C22⋊D1111yescharacteristic
364C2×C8C23×D1111yescharacteristic
365C16—114no—
366C16—222no—
367C11#3361811yescharacteristic, complemented, Sylow
368C23—21no—
369C23—42no—
370C23—81no—
371C23—81no—
372C23—162no—
373C23—441no—
374C23#6700311yescharacteristic
375Q8—21no—
376Q8—441no—
377Q8—441no—
378Q8C2×#432312yes—
379D4—22no—
380D4—22no—
381D4—21no—
382D4—42no—
383D4—42no—
384D4—81no—
385D4—81no—
386D4—441no—
387D4—441no—
388D4—881no—
389D4—881no—
390D4C2×#432312yes—
391C2×C4—21no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—441no—
395C2×C4—881no—
396C2×C4—881no—
397C2×C4C2×#432311yescharacteristic
398C2×C4C2×#432311yescharacteristic
399C2×C4#6699211yescharacteristic
400C2×C4#6699211yescharacteristic
401C2×C4#6700311yescharacteristic
402C2×C4C22×C22⋊D1111yescharacteristic
403C8—22no—
404C8—42no—
405C8—442no—
406C8#6699211yescharacteristic
407C8#6699211yescharacteristic
408C8C2×D4×D1111yescharacteristic
409C8C2×#434111yescharacteristic
410C22—22no—
411C22—41no—
412C22—81no—
413C22—82no—
414C22—162no—
415C22—162no—
416C22—162no—
417C22—881no—
418C22—1761no—
419C22#1062265111yescharacteristic
420C22#1062265111yescharacteristic
421C22C2×#6700311yescharacteristic
422C4—22no—
423C4—881no—
424C4#1062265111yescharacteristic
425C4#1062265111yescharacteristic
426C4C22×#432311yescharacteristic
427C4C2×#6699211yescharacteristic
428C2—21no—
429C2—21no—
430C2—21no—
431C2—42no—
432C2—162no—
433C2—1761no—
434C2C2×#1062265111yescharacteristic
subgroupG/H
centerC2C2×#10622651
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#472C2
socleC2×C11C2×#466
hypercenterC2×#472D11
hypocenterC11#33618
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#131 ◁ C2×#472

Complements

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

NH ≅ G/Ntype
1. C2×#10622760C2semidirect
2. #13081719C2semidirect
3. #13078336C2semidirect
4. #13070744C2semidirect
5. #13070734C2semidirect
6. #13070410C2semidirect
7. #13070363C2semidirect
8. C2×#10622201C2semidirect
9. C2×C11×#472C2semidirect
19. C2×#66891C22semidirect
22. C2×#66890C22semidirect
23. #10622756C22semidirect
24. #10622755C22semidirect
27. #10622753C22semidirect
33. #10622201C22semidirect
34. #10622134C22semidirect
35. #10622133C22semidirect
36. #10622131C22semidirect
154. C2×#472D11semidirect
367. C11#33618semidirect

Maximal subgroups

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

subgroupindex
C2×#106227602
#130817192
#130783362
#130707442
#130707342
#130704102
#130703632
C2×#106222012
C2×C11×#4722
#3361811