Finite Group Databasebeta

← C2×#13070734 #14908328

Subgroups — C2×#13070734 #14908328

Order 2816.

678 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66890C211yesmaximal, characteristic, complemented
2C2×#10622753C211yesmaximal, characteristic, complemented
3C2×#10622755C211yesmaximal, characteristic, complemented
4#13070734C218yesmaximal, direct product factor
5C2×#10622131C211yesmaximal, characteristic, complemented
6C2×#10622201C211yesmaximal, characteristic, complemented
7C2×#10622133C211yesmaximal, characteristic, complemented
8C2×C11×#472C211yesmaximal, characteristic, complemented
9C2×C11×AGL(1,ℤ/8)—21no—
10C22×C11×D8C2211yescharacteristic
11C2×C11×#131C2211yescharacteristic
12C2×#67002—21no—
13C22×D88C2211yescharacteristic
14C11×#472—22no—
15C11×#472C2214yescomplemented
16C2×C11×#108C2211yescharacteristic
17C2×C11×#100—21no—
18C2×#66890—22no—
19C2×#66890—21no—
20C2×#66890—21no—
21C2×#66890C2214yescomplemented
22#10622755—22no—
23#10622755C2214yescomplemented
24#10622753—22no—
25#10622753C2214yescomplemented
26C2×#66887—21no—
27C2×#66883C2211yescharacteristic
28C2×#66876—21no—
29C2×#66876C2211yescharacteristic
30C22×C11⋊C16—21no—
31C22×C11⋊C16C2211yescharacteristic
32#10622201C2214yescomplemented
33#10622133C2214yescomplemented
34#10622131C2214yescomplemented
35C2×C11×#41D411yescharacteristic
36C22×D4×C11—21no—
37C22×D44—21no—
38C11×AGL(1,ℤ/8)—24no—
39C11×AGL(1,ℤ/8)—42no—
40C2×C11×SD16—41no—
41C2×C11×D8—21no—
42C2×C11×D8—21no—
43C2×C11×D8—21no—
44C2×C11×D8—21no—
45C2×C11×D8—21no—
46C2×C11×D8—41no—
47C2×C11×D8C2312yes—
48C11×#131—21no—
49C11×#131—21no—
50C11×#131D412yes—
51C11×#131C2312yes—
52C2×C11×M16—21no—
53C2×C11×M16—21no—
54C2×C11×M16D411yescharacteristic
55C22×C8×C11—21no—
56C22×C8×C11C2311yescharacteristic
57#67002—24no—
58#67002—42no—
59C2×#4325—41no—
60C2×#4323—41no—
61C2×#4318—21no—
62C2×D88—21no—
63C2×D88—21no—
64C2×D88—21no—
65C2×D88—21no—
66C2×D88—21no—
67C2×D88C2312yes—
68C11×#108—21no—
69C11×#108C2312yes—
70C11×#100—24no—
71#66890—24no—
72#66890—24no—
73#66887—24no—
74#66883—21no—
75#66883C2312yes—
76#66876—21no—
77#66876—24no—
78#66876C2312yes—
79C2×C11⋊C16—21no—
80C2×C11⋊C16—24no—
81C2×C11⋊C16D412yes—
82C2×C11⋊C16D411yescharacteristic
83C2×C11⋊C16D411yescharacteristic
84C2×C11⋊C16C2312yes—
85C2×#2221—111nomaximal, Sylow
86C24×C11—41no—
87C23×D11—41no—
88C11×#41—21no—
89C11×#41—21no—
90C11×#41D812yes—
91C11×#41C2×D412yes—
92C2×Q8×C11D811yescharacteristic
93C2×D4×C11—21no—
94C2×D4×C11—22no—
95C2×D4×C11—41no—
96C2×D4×C11—41no—
97C2×D4×C11—41no—
98C2×D4×C11—41no—
99C2×D4×C11—41no—
100C2×D4×C11D811yescharacteristic
101C22×C4×C11—21no—
102C22×C4×C11C2×D411yescharacteristic
103C2×D44—22no—
104C2×D44—41no—
105C2×D44—41no—
106C2×D44—41no—
107C2×D44—41no—
108C2×D44—41no—
109C11×SD16—44no—
110C11×D8—22no—
111C11×D8—22no—
112C11×D8—41no—
113C11×D8—41no—
114C11×D8—44no—
115C11×M16—22no—
116C11×M16—22no—
117C11×M16—21no—
118C11×M16—22no—
119C11×M16—41no—
120C11×M16C2×D412yes—
121C2×C8×C11—22no—
122C2×C8×C11—22no—
123C2×C8×C11—21no—
124C2×C8×C11—41no—
125C2×C8×C11C2×D411yescharacteristic
126C2×C8×C11C2×D411yescharacteristic
127C2×C8×C11C2×D411yescharacteristic
128C2×C8×C11#4111yescharacteristic
129C2×C8×C11#4111yescharacteristic
130C2×C8×C11C2411yescharacteristic
131#4325—44no—
132#4323—44no—
133#4318—22no—
134#4318—41no—
135C2×C11⋊C8—41no—
136D88—22no—
137D88—22no—
138D88—41no—
139D88—41no—
140C11⋊C16—22no—
141C11⋊C16C2×D412yes—
142C11⋊C16C2×D412yes—
143C22×D16—111no—
144C2×#504—111no—
145C2×#472—111no—
146C2×#472D1111yescharacteristic, complemented
147#2221—118no—
148C2×#368—111no—
149C2×#361—111no—
150C2×#361—111no—
151C23×C11—21no—
152C23×C11—42no—
153C23×C11—81no—
154C23×C11—81no—
155C23×C11—162no—
156C23×C11#13511yescharacteristic
157C22×D11—42no—
158C22×D11—81no—
159C22×D11—81no—
160C22×D11—162no—
161Q8×C11—21no—
162Q8×C11C2×D812yes—
163D4×C11—22no—
164D4×C11—22no—
165D4×C11—21no—
166D4×C11—42no—
167D4×C11—42no—
168D4×C11—81no—
169D4×C11—81no—
170D4×C11C2×D812yes—
171C2×C4×C11—21no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11#12111yescharacteristic
175C2×C4×C11#12111yescharacteristic
176C2×C4×C11C2×D811yescharacteristic
177C2×C4×C11C2×D811yescharacteristic
178C2×C4×C11#13511yescharacteristic
179C2×C4×C11C22×D411yescharacteristic
180D44—42no—
181D44—42no—
182D44—81no—
183D44—81no—
184C8×C11—22no—
185C8×C11—42no—
186C8×C11#12111yescharacteristic
187C8×C11#12111yescharacteristic
188C8×C11C22×D411yescharacteristic
189C8×C11C2×#4111yescharacteristic
190C11⋊C8—42no—
191C2×AGL(1,ℤ/8)—21no—
192C2×AGL(1,ℤ/8)—221no—
193C22×D8—111no—
194C22×D8C2×D1111yescharacteristic
195C2×#131C2×D1111yescharacteristic
196C2×D16—114no—
197C2×D16—221no—
198C2×D16—221no—
199C2×D16—222no—
200#504—114no—
201#504—222no—
202C2×M32—111no—
203C2×M32—221no—
204C22×C16—111no—
205C22×C16—221no—
206#472—22no—
207#472—114no—
208#472—222no—
209#472C2×D1114yescomplemented
210C2×#108—111no—
211C2×#108C2×D1111yescharacteristic
212C2×#100—21no—
213C2×#100—221no—
214#368—114no—
215#361—114no—
216#361—114no—
217C22×C11—22no—
218C22×C11—22no—
219C22×C11—42no—
220C22×C11—82no—
221C22×C11—162no—
222C22×C11—162no—
223C22×C11—162no—
224C22×C11#46611yescharacteristic
225C22×C11#46611yescharacteristic
226C22×C11C2×#13511yescharacteristic
227C2×D11—82no—
228C2×D11—162no—
229C2×D11—162no—
230C2×D11—162no—
231C4×C11—22no—
232C4×C11#46611yescharacteristic
233C4×C11#46611yescharacteristic
234C4×C11C2×#12111yescharacteristic
235C4×C11C22×D811yescharacteristic
236C2×#41C22⋊D1111yescharacteristic
237C22×D4—21no—
238C22×D4—221no—
239AGL(1,ℤ/8)—24no—
240AGL(1,ℤ/8)—42no—
241AGL(1,ℤ/8)—224no—
242AGL(1,ℤ/8)—442no—
243C2×SD16—41no—
244C2×SD16—441no—
245C2×D8—21no—
246C2×D8—21no—
247C2×D8—21no—
248C2×D8—21no—
249C2×D8—21no—
250C2×D8—41no—
251C2×D8—112no—
252C2×D8—221no—
253C2×D8—221no—
254C2×D8—221no—
255C2×D8—221no—
256C2×D8—221no—
257C2×D8—441no—
258C2×D8C22×D1112yes—
259#131—21no—
260#131—21no—
261#131C22⋊D1112yes—
262#131C22×D1112yes—
263C2×M16—21no—
264C2×M16—21no—
265C2×M16—221no—
266C2×M16C22⋊D1111yescharacteristic
267C22×C8—21no—
268C22×C8C22×D1111yescharacteristic
269D16—224no—
270D16—224no—
271M32—112no—
272M32—224no—
273M32—221no—
274C2×C16—111no—
275C2×C16—111no—
276C2×C16—112no—
277C2×C16—112no—
278C2×C16—224no—
279C2×C16—221no—
280#108—21no—
281#108—112no—
282#108—221no—
283#108C22×D1112yes—
284#100—24no—
285#100—224no—
286C2×C11—21no—
287C2×C11—21no—
288C2×C11—42no—
289C2×C11—162no—
290C2×C11#222112yescomplemented
291C2×C11C2×#46611yescharacteristic
292D11—162no—
293C24—41no—
294C24—441no—
295#41—21no—
296#41—21no—
297#41#432312yes—
298#41C2×C22⋊D1112yes—
299C2×Q8#432311yescharacteristic
300C2×D4—21no—
301C2×D4—22no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—222no—
308C2×D4—441no—
309C2×D4—441no—
310C2×D4—441no—
311C2×D4—441no—
312C2×D4—441no—
313C2×D4#432311yescharacteristic
314C22×C4—21no—
315C22×C4C2×C22⋊D1111yescharacteristic
316SD16—44no—
317SD16—444no—
318D8—22no—
319D8—22no—
320D8—44no—
321D8—41no—
322D8—41no—
323D8—222no—
324D8—222no—
325D8—444no—
326D8—441no—
327D8—441no—
328M16—21no—
329M16—22no—
330M16—22no—
331M16—22no—
332M16—41no—
333M16—222no—
334M16—441no—
335M16C2×C22⋊D1112yes—
336C2×C8—21no—
337C2×C8—22no—
338C2×C8—22no—
339C2×C8—41no—
340C2×C8—441no—
341C2×C8D4×D1111yescharacteristic
342C2×C8D4×D1111yescharacteristic
343C2×C8#434111yescharacteristic
344C2×C8#434111yescharacteristic
345C2×C8C2×C22⋊D1111yescharacteristic
346C2×C8C23×D1111yescharacteristic
347C16—112no—
348C16—112no—
349C16—222no—
350C11C2×#222111yescharacteristic, complemented, Sylow
351C23—21no—
352C23—42no—
353C23—81no—
354C23—81no—
355C23—162no—
356C23—442no—
357C23—881no—
358C23—881no—
359C23—1762no—
360C23#6700311yescharacteristic
361Q8—21no—
362Q8C2×#432312yes—
363D4—22no—
364D4—22no—
365D4—21no—
366D4—42no—
367D4—42no—
368D4—81no—
369D4—81no—
370D4—442no—
371D4—442no—
372D4—881no—
373D4—881no—
374D4C2×#432312yes—
375C2×C4—21no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4C2×#432311yescharacteristic
379C2×C4C2×#432311yescharacteristic
380C2×C4#6699211yescharacteristic
381C2×C4#6699211yescharacteristic
382C2×C4#6700311yescharacteristic
383C2×C4C22×C22⋊D1111yescharacteristic
384C8—22no—
385C8—42no—
386C8—442no—
387C8#6699211yescharacteristic
388C8#6699211yescharacteristic
389C8C2×D4×D1111yescharacteristic
390C8C2×#434111yescharacteristic
391C22—22no—
392C22—22no—
393C22—42no—
394C22—82no—
395C22—162no—
396C22—162no—
397C22—162no—
398C22—882no—
399C22—1762no—
400C22—1762no—
401C22—1762no—
402C22#1062265111yescharacteristic
403C22#1062265111yescharacteristic
404C22C2×#6700311yescharacteristic
405C4—22no—
406C4#1062265111yescharacteristic
407C4#1062265111yescharacteristic
408C4C22×#432311yescharacteristic
409C4C2×#6699211yescharacteristic
410C2—21no—
411C2—21no—
412C2—42no—
413C2—162no—
414C2—1762no—
415C2#1307073412yesdirect product factor
416C2C2×#1062265111yescharacteristic
subgroupG/H
centerC22#10622651
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#472C2
socleC22×C11#466
hypercenterC2×#472D11
hypocenterC11C2×#2221
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131 ◁ C2×#472

Complements

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

NH ≅ G/Ntype
1. C22×#66890C2semidirect
2. C2×#10622753C2semidirect
3. C2×#10622755C2semidirect
4. #13070734C2direct (N × H)
5. C2×#10622131C2semidirect
6. C2×#10622201C2semidirect
7. C2×#10622133C2semidirect
8. C2×C11×#472C2semidirect
15. C11×#472C22semidirect
21. C2×#66890C22semidirect
23. #10622755C22semidirect
25. #10622753C22semidirect
32. #10622201C22semidirect
33. #10622133C22semidirect
34. #10622131C22semidirect
146. C2×#472D11semidirect
209. #472C2×D11semidirect
290. C2×C11#2221semidirect
350. C11C2×#2221semidirect
415. C2#13070734direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#668902
C2×#106227532
C2×#106227552
#130707342
C2×#106221312
C2×#106222012
C2×#106221332
C2×C11×#4722
C2×#222111