Finite Group Databasebeta

← #14908365

Subgroups — #14908365

Order 2816.

636 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622792C211yesmaximal, characteristic, complemented
2#13081719C211yesmaximal, characteristic, complemented
3#13078336C211yesmaximal, characteristic
4#13070748C214yesmaximal, complemented
5#13070739C214yesmaximal, complemented
6#13070410C211yesmaximal, characteristic, complemented
7#13070363C211yesmaximal, characteristic, complemented
8C2×#10622203C211yesmaximal, characteristic, complemented
9C2×C11×#473C211yesmaximal, characteristic, complemented
10C2×C11×#137—21no—
11C22×C11×Q16C2211yescharacteristic
12C2×C11×#131C2211yescharacteristic
13#10623353—21no—
14C2×#66957C2211yescharacteristic
15C11×#473—22no—
16C11×#473C2214yes—
17C2×C11×#108C2211yescharacteristic
18C2×C11×#101—21no—
19C2×#66893C2212yescomplemented
20#10622792—22no—
21#10622792—22no—
22C2×#66892C2212yescomplemented
23#10622756C2212yes—
24#10622755C2212yes—
25#10622754—22no—
26#10622753—22no—
27#10622753C2214yes—
28#10622745—21no—
29C2×#66883C2211yescharacteristic
30C2×#66876—22no—
31C2×#66876C2211yescharacteristic
32C2×#66876C2211yescharacteristic
33#10622203C2214yescomplemented
34#10622134C2212yescomplemented
35#10622133C2212yescomplemented
36#10622131C2214yescomplemented
37C2×C11×#41D411yescharacteristic
38C22×Q8×C11—21no—
39C2×#4339—21no—
40C11×#137—24no—
41C11×#137—42no—
42C2×C11×Q16—21no—
43C2×C11×Q16—21no—
44C2×C11×Q16—21no—
45C2×C11×Q16—21no—
46C2×C11×Q16—21no—
47C2×C11×Q16—41no—
48C2×C11×Q16C2312yes—
49C2×C11×SD16—41no—
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×#101—24no—
75#66893—24no—
76#66892—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#33619—111nomaximal, Sylow
90C11×#41—21no—
91C11×#41—21no—
92C11×#41D812yes—
93C11×#41C2×D412yes—
94C2×Q8×C11—22no—
95C2×Q8×C11—41no—
96C2×Q8×C11—41no—
97C2×Q8×C11—41no—
98C2×Q8×C11—41no—
99C2×Q8×C11—41no—
100C2×Q8×C11D811yescharacteristic
101C2×D4×C11—21no—
102C2×D4×C11D811yescharacteristic
103C22×C4×C11—21no—
104C22×C4×C11—41no—
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×Q16—22no—
115C11×Q16—22no—
116C11×Q16—41no—
117C11×Q16—41no—
118C11×Q16—44no—
119C11×SD16—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×#510—111no—
152#3407—111no—
153#3067—111no—
154C2×#473D1111yescharacteristic, complemented
155#2223—114no—
156#2222—114no—
157#2161—111no—
158#2148—111no—
159C2×#362—111no—
160C23×C11—21no—
161C23×C11#13511yescharacteristic
162C22×D11—41no—
163Q8×C11—21no—
164Q8×C11—42no—
165Q8×C11—42no—
166Q8×C11—81no—
167Q8×C11—81no—
168Q8×C11C2×D812yes—
169D4×C11—22no—
170D4×C11—22no—
171D4×C11—21no—
172D4×C11C2×D812yes—
173C2×C4×C11—21no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—42no—
177C2×C4×C11—81no—
178C2×C4×C11—81no—
179C2×C4×C11#12111yescharacteristic
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11C2×D811yescharacteristic
182C2×C4×C11C2×D811yescharacteristic
183C2×C4×C11#13511yescharacteristic
184C2×C4×C11C22×D411yescharacteristic
185C22⋊D11—81no—
186C22⋊D11—81no—
187C2×Dic11—41no—
188D44—41no—
189D44—41no—
190C4×D11—81no—
191C4×D11—81no—
192Dic22—41no—
193Dic22—41no—
194C8×C11—22no—
195C8×C11—42no—
196C8×C11#12111yescharacteristic
197C8×C11#12111yescharacteristic
198C8×C11C22×D411yescharacteristic
199C8×C11C2×#4111yescharacteristic
200C11⋊C8—42no—
201#575—221no—
202C2×#137—21no—
203C2×#135—111no—
204C22×Q16C2×D1111yescharacteristic
205C2×#131C2×D1111yescharacteristic
206#510—222no—
207#510—222no—
208C2×Q32—112no—
209C2×SD32—112no—
210#504—114no—
211#504—222no—
212C2×M32—111no—
213C2×M32—111no—
214C2×M32—222no—
215#473—22no—
216#473—112no—
217#473C2×D1114yes—
218#472—112no—
219#471—222no—
220C2×#108—111no—
221C2×#108C2×D1111yescharacteristic
222#413—221no—
223C2×#101—21no—
224#368—114no—
225#362—114no—
226#362—112no—
227#361—112no—
228C22×C11—22no—
229C22×C11—41no—
230C22×C11—81no—
231C22×C11#46611yescharacteristic
232C22×C11#46611yescharacteristic
233C22×C11C2×#13511yescharacteristic
234C2×D11—81no—
235C2×D11—161no—
236C4×C11—22no—
237C4×C11—82no—
238C4×C11#46611yescharacteristic
239C4×C11#46611yescharacteristic
240C4×C11C2×#12111yescharacteristic
241C4×C11C22×D811yescharacteristic
242Dic11—81no—
243C2×#41—221no—
244C2×#41C22⋊D1111yescharacteristic
245C22×Q8—21no—
246#137—24no—
247#137—42no—
248#137—222no—
249#137—441no—
250AGL(1,ℤ/8)—222no—
251AGL(1,ℤ/8)—441no—
252#135—221no—
253#135—221no—
254#135—221no—
255#135—221no—
256#135—442no—
257C2×Q16—21no—
258C2×Q16—21no—
259C2×Q16—21no—
260C2×Q16—21no—
261C2×Q16—21no—
262C2×Q16—41no—
263C2×Q16—111no—
264C2×Q16C22×D1112yes—
265C2×SD16—41no—
266C2×SD16—221no—
267C2×D8—111no—
268#131—21no—
269#131—21no—
270#131C22⋊D1112yes—
271#131C22×D1112yes—
272C2×M16—21no—
273C2×M16—21no—
274C2×M16—221no—
275C2×M16C22⋊D1111yescharacteristic
276C22×C8—21no—
277C22×C8C22×D1111yescharacteristic
278Q32—224no—
279SD32—224no—
280M32—112no—
281M32—112no—
282M32—112no—
283M32—224no—
284M32—221no—
285C2×C16—112no—
286C2×C16—224no—
287C2×C16—221no—
288#108—21no—
289#108—112no—
290#108—221no—
291#108C22×D1112yes—
292#101—24no—
293#101—222no—
294#100—222no—
295C2×C11—21no—
296C2×C11—21no—
297C2×C11—21no—
298C2×C11—42no—
299C2×C11C2×#46611yescharacteristic
300D11—161no—
301#41—21no—
302#41—21no—
303#41—441no—
304#41—441no—
305#41—441no—
306#41—441no—
307#41#432312yes—
308#41C2×C22⋊D1112yes—
309C2×Q8—22no—
310C2×Q8—41no—
311C2×Q8—41no—
312C2×Q8—41no—
313C2×Q8—41no—
314C2×Q8—41no—
315C2×Q8—221no—
316C2×Q8#432311yescharacteristic
317C2×D4—21no—
318C2×D4—221no—
319C2×D4—441no—
320C2×D4#432311yescharacteristic
321C22×C4—21no—
322C22×C4—41no—
323C22×C4—441no—
324C22×C4C2×C22⋊D1111yescharacteristic
325Q16—22no—
326Q16—22no—
327Q16—44no—
328Q16—41no—
329Q16—41no—
330Q16—221no—
331Q16—221no—
332Q16—442no—
333SD16—44no—
334SD16—442no—
335SD16—442no—
336SD16—441no—
337SD16—441no—
338D8—221no—
339D8—221no—
340D8—442no—
341M16—21no—
342M16—22no—
343M16—22no—
344M16—22no—
345M16—41no—
346M16—222no—
347M16—441no—
348M16C2×C22⋊D1112yes—
349C2×C8—21no—
350C2×C8—22no—
351C2×C8—22no—
352C2×C8—41no—
353C2×C8—441no—
354C2×C8D4×D1111yescharacteristic
355C2×C8D4×D1111yescharacteristic
356C2×C8#434111yescharacteristic
357C2×C8#434111yescharacteristic
358C2×C8C2×C22⋊D1111yescharacteristic
359C2×C8C23×D1111yescharacteristic
360C16—114no—
361C16—222no—
362C11#3361911yescharacteristic, complemented, Sylow
363C23—21no—
364C23—441no—
365C23#6700311yescharacteristic
366Q8—21no—
367Q8—42no—
368Q8—42no—
369Q8—81no—
370Q8—81no—
371Q8—441no—
372Q8—441no—
373Q8C2×#432312yes—
374D4—22no—
375D4—22no—
376D4—21no—
377D4—441no—
378D4—441no—
379D4—881no—
380D4—881no—
381D4C2×#432312yes—
382C2×C4—21no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—42no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—441no—
389C2×C4—881no—
390C2×C4—881no—
391C2×C4C2×#432311yescharacteristic
392C2×C4C2×#432311yescharacteristic
393C2×C4#6699211yescharacteristic
394C2×C4#6699211yescharacteristic
395C2×C4#6700311yescharacteristic
396C2×C4C22×C22⋊D1111yescharacteristic
397C8—22no—
398C8—42no—
399C8—442no—
400C8#6699211yescharacteristic
401C8#6699211yescharacteristic
402C8C2×D4×D1111yescharacteristic
403C8C2×#434111yescharacteristic
404C22—22no—
405C22—41no—
406C22—81no—
407C22—881no—
408C22—1761no—
409C22#1062265111yescharacteristic
410C22#1062265111yescharacteristic
411C22C2×#6700311yescharacteristic
412C4—22no—
413C4—82no—
414C4—881no—
415C4#1062265111yescharacteristic
416C4#1062265111yescharacteristic
417C4C22×#432311yescharacteristic
418C4C2×#6699211yescharacteristic
419C2—21no—
420C2—21no—
421C2—21no—
422C2—42no—
423C2—1761no—
424C2C2×#1062265111yescharacteristic
subgroupG/H
centerC2C2×#10622651
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#473C2
socleC2×C11C2×#466
prime radical#13078336C2
hypercenterC2×#473D11
hypocenterC11#33619
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#131 ◁ C2×#473

Complements

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

NH ≅ G/Ntype
1. C2×#10622792C2semidirect
2. #13081719C2semidirect
4. #13070748C2semidirect
5. #13070739C2semidirect
6. #13070410C2semidirect
7. #13070363C2semidirect
8. C2×#10622203C2semidirect
9. C2×C11×#473C2semidirect
19. C2×#66893C22semidirect
22. C2×#66892C22semidirect
33. #10622203C22semidirect
34. #10622134C22semidirect
35. #10622133C22semidirect
36. #10622131C22semidirect
154. C2×#473D11semidirect
362. C11#33619semidirect

Maximal subgroups

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

subgroupindex
C2×#106227922
#130817192
#130783362
#130707482
#130707392
#130704102
#130703632
C2×#106222032
C2×C11×#4732
#3361911