Finite Group Databasebeta

← C2×#13070735 #14908329

Subgroups — C2×#13070735 #14908329

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×#10622520C211yesmaximal, characteristic, complemented
3C2×#10622510C211yesmaximal, characteristic, complemented
4C2×#10622773C211yesmaximal, characteristic, complemented
5#13070735C218yesmaximal, direct product factor
6C2×#10622131C211yesmaximal, characteristic, complemented
7C2×#10622154C211yesmaximal, characteristic, complemented
8C2×C11×#361C211yesmaximal, characteristic, complemented
9C22×C11×D8C2211yescharacteristic
10C2×#66985—21no—
11C2×#66961—21no—
12C22×D88C2211yescharacteristic
13C2×#66954C2211yescharacteristic
14C2×C11×M32C2211yescharacteristic
15C2×C11×#108C2211yescharacteristic
16C2×#66897—21no—
17#10622773—22no—
18#10622773C2214yescomplemented
19C2×#66890—21no—
20C2×#66890—21no—
21C2×#66890—22no—
22C2×#66890C2214yescomplemented
23C2×#66887—21no—
24C2×#66883C2211yescharacteristic
25C22×C11⋊C16C2211yescharacteristic
26#10622520—22no—
27#10622520C2214yescomplemented
28C2×#66862—21no—
29C2×C16×D11—21no—
30#10622510—22no—
31#10622510C2214yescomplemented
32C11×#361C2214yescomplemented
33#10622154C2214yescomplemented
34#10622131C2214yescomplemented
35C22×D4×C11—21no—
36C2×#4339D411yescharacteristic
37C22×D44—21no—
38C2×C11×D8—21no—
39C2×C11×D8—21no—
40C2×C11×D8—21no—
41C2×C11×D8—21no—
42C2×C11×D8—21no—
43C2×C11×D8C2312yes—
44C2×C11×M16—21no—
45C22×C8×C11C2311yescharacteristic
46C2×#4324—41no—
47#66985—24no—
48#66985—42no—
49C2×#4323—41no—
50C2×#4318—21no—
51C2×#4318D411yescharacteristic
52#66961—24no—
53#66961—42no—
54C2×D88—21no—
55C2×D88—21no—
56C2×D88—21no—
57C2×D88—21no—
58C2×D88—21no—
59C2×D88—41no—
60C2×D88C2312yes—
61C2×#4314—41no—
62#66954—21no—
63#66954—21no—
64#66954D412yes—
65#66954C2312yes—
66C2×#4313—21no—
67C2×C8×D11—21no—
68C11×M32—21no—
69C11×M32C2312yes—
70C2×C11×C16—21no—
71C11×#108—21no—
72C11×#108C2312yes—
73#66897—24no—
74#66890—24no—
75#66890—24no—
76#66887—24no—
77#66883—21no—
78#66883C2312yes—
79C2×C11⋊C16D411yescharacteristic
80C2×C11⋊C16D411yescharacteristic
81C2×C11⋊C16D412yes—
82C2×C11⋊C16C2312yes—
83#66862—24no—
84C16×D11—24no—
85C2×#2221—111nomaximal, Sylow
86C24×C11—41no—
87C23×D11—41no—
88C2×D4×C11—22no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C2×D4×C11—41no—
94C22×C4×C11C2×D411yescharacteristic
95C2×C22⋊D11—21no—
96#4339—21no—
97#4339—21no—
98#4339D812yes—
99#4339C2×D412yes—
100C2×D44—22no—
101C2×D44—41no—
102C2×D44—41no—
103C2×D44—41no—
104C2×D44—41no—
105C2×D44—41no—
106C2×D44D811yescharacteristic
107C2×C4×D11—21no—
108C2×Dic22D811yescharacteristic
109C11×D8—22no—
110C11×D8—22no—
111C11×D8—41no—
112C11×D8—41no—
113C11×M16—22no—
114C11×M16—41no—
115C2×C8×C11—41no—
116C2×C8×C11C2×D411yescharacteristic
117C2×C8×C11C2×D411yescharacteristic
118C2×C8×C11C2×D411yescharacteristic
119C2×C8×C11#4111yescharacteristic
120C2×C8×C11#4111yescharacteristic
121C2×C8×C11C2411yescharacteristic
122#4324—44no—
123#4323—44no—
124#4318—21no—
125#4318—22no—
126#4318—41no—
127#4318C2×D412yes—
128C2×C11⋊C8—21no—
129C2×C11⋊C8—41no—
130D88—22no—
131D88—22no—
132D88—44no—
133D88—41no—
134D88—41no—
135#4314—44no—
136#4313—22no—
137#4313—22no—
138C8×D11—22no—
139C8×D11—22no—
140C11×C16—22no—
141C11⋊C16C2×D412yes—
142C11⋊C16C2×D412yes—
143C22×D16—111no—
144C2×#504—111no—
145C2×#472—111no—
146C2×#472—111no—
147#2221—118no—
148C2×#368—111no—
149C2×#361—111no—
150C2×#361D1111yescharacteristic, complemented
151C23×C11—42no—
152C23×C11—81no—
153C23×C11—81no—
154C23×C11—162no—
155C23×C11#13511yescharacteristic
156C22×D11—21no—
157C22×D11—42no—
158C22×D11—81no—
159C22×D11—81no—
160C22×D11—162no—
161D4×C11—42no—
162D4×C11—42no—
163D4×C11—81no—
164D4×C11—81no—
165C2×C4×C11#12111yescharacteristic
166C2×C4×C11#12111yescharacteristic
167C2×C4×C11C2×D811yescharacteristic
168C2×C4×C11C2×D811yescharacteristic
169C2×C4×C11#13511yescharacteristic
170C2×C4×C11C22×D411yescharacteristic
171C22⋊D11—22no—
172C22⋊D11—22no—
173C2×Dic11—21no—
174D44—21no—
175D44—42no—
176D44—42no—
177D44—81no—
178D44—81no—
179D44C2×D812yes—
180C4×D11—22no—
181C4×D11—22no—
182Dic22—21no—
183Dic22C2×D812yes—
184C8×C11—42no—
185C8×C11#12111yescharacteristic
186C8×C11#12111yescharacteristic
187C8×C11C22×D411yescharacteristic
188C8×C11C2×#4111yescharacteristic
189C11⋊C8—22no—
190C11⋊C8—42no—
191C2×AGL(1,ℤ/8)—221no—
192C2×AGL(1,ℤ/8)—221no—
193C22×D8—111no—
194C22×D8C2×D1111yescharacteristic
195C2×#131—111no—
196C2×D16—114no—
197C2×D16—221no—
198C2×D16—221no—
199C2×D16—222no—
200#504—114no—
201#504—222no—
202C2×M32—221no—
203C2×M32C2×D1111yescharacteristic
204C22×C16—111no—
205C22×C16—221no—
206#472—114no—
207#472—114no—
208#472—222no—
209#472—222no—
210C2×#108—111no—
211C2×#108C2×D1111yescharacteristic
212C2×#100—221no—
213C2×#100—221no—
214#368—114no—
215#361—114no—
216#361C2×D1114yescomplemented
217C22×C11—22no—
218C22×C11—82no—
219C22×C11—162no—
220C22×C11—162no—
221C22×C11—162no—
222C22×C11#46611yescharacteristic
223C22×C11#46611yescharacteristic
224C22×C11C2×#13511yescharacteristic
225C2×D11—22no—
226C2×D11—42no—
227C2×D11—82no—
228C2×D11—162no—
229C2×D11—162no—
230C2×D11—162no—
231C4×C11#46611yescharacteristic
232C4×C11#46611yescharacteristic
233C4×C11C2×#12111yescharacteristic
234C4×C11C22×D811yescharacteristic
235Dic11—22no—
236C2×#41—111no—
237C22×D4—21no—
238C22×D4—221no—
239AGL(1,ℤ/8)—224no—
240AGL(1,ℤ/8)—224no—
241AGL(1,ℤ/8)—442no—
242AGL(1,ℤ/8)—442no—
243C2×SD16—441no—
244C2×SD16—441no—
245C2×D8—21no—
246C2×D8—21no—
247C2×D8—21no—
248C2×D8—21no—
249C2×D8—21no—
250C2×D8—112no—
251C2×D8—221no—
252C2×D8—221no—
253C2×D8—221no—
254C2×D8—221no—
255C2×D8—221no—
256C2×D8—441no—
257C2×D8—441no—
258C2×D8C22×D1112yes—
259#131—112no—
260#131—112no—
261#131—221no—
262#131—221no—
263C2×M16—21no—
264C2×M16—111no—
265C2×M16—221no—
266C2×M16—221no—
267C22×C8—221no—
268C22×C8C22×D1111yescharacteristic
269D16—224no—
270D16—224no—
271M32—21no—
272M32—224no—
273M32C22×D1112yes—
274C2×C16—21no—
275C2×C16—111no—
276C2×C16—111no—
277C2×C16—112no—
278C2×C16—112no—
279C2×C16—224no—
280#108—21no—
281#108—112no—
282#108—221no—
283#108C22×D1112yes—
284#100—224no—
285#100—224no—
286C2×C11—21no—
287C2×C11—21no—
288C2×C11—162no—
289C2×C11#222112yescomplemented
290C2×C11C2×#46611yescharacteristic
291D11—42no—
292D11—162no—
293C24—41no—
294C24—441no—
295#41—112no—
296#41—112no—
297#41—221no—
298#41—221no—
299C2×Q8—111no—
300C2×D4—22no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—111no—
307C2×D4—221no—
308C2×D4—222no—
309C2×D4—441no—
310C2×D4—441no—
311C2×D4—441no—
312C2×D4—441no—
313C2×D4—441no—
314C22×C4—221no—
315C22×C4D4×D1111yescharacteristic
316SD16—444no—
317SD16—444no—
318D8—22no—
319D8—22no—
320D8—41no—
321D8—41no—
322D8—222no—
323D8—222no—
324D8—444no—
325D8—444no—
326D8—441no—
327D8—441no—
328M16—22no—
329M16—41no—
330M16—112no—
331M16—221no—
332M16—222no—
333M16—222no—
334M16—222no—
335M16—441no—
336C2×C8—41no—
337C2×C8—221no—
338C2×C8—222no—
339C2×C8—222no—
340C2×C8—441no—
341C2×C8#433911yescharacteristic
342C2×C8#433911yescharacteristic
343C2×C8D4×D1111yescharacteristic
344C2×C8D4×D1111yescharacteristic
345C2×C8D4×D1111yescharacteristic
346C2×C8C23×D1111yescharacteristic
347C16—22no—
348C16—112no—
349C16—112no—
350C11C2×#222111yescharacteristic, complemented, Sylow
351C23—42no—
352C23—81no—
353C23—81no—
354C23—162no—
355C23—221no—
356C23—442no—
357C23—881no—
358C23—881no—
359C23—1762no—
360C23#6696911yescharacteristic
361Q8—112no—
362Q8—221no—
363D4—42no—
364D4—42no—
365D4—81no—
366D4—81no—
367D4—112no—
368D4—222no—
369D4—222no—
370D4—221no—
371D4—442no—
372D4—442no—
373D4—881no—
374D4—881no—
375C2×C4—221no—
376C2×C4—222no—
377C2×C4—222no—
378C2×C4#6693711yescharacteristic
379C2×C4#6693711yescharacteristic
380C2×C4D8×D1111yescharacteristic
381C2×C4D8×D1111yescharacteristic
382C2×C4#6696911yescharacteristic
383C2×C4C2×D4×D1111yescharacteristic
384C8—42no—
385C8—222no—
386C8—442no—
387C8#6693711yescharacteristic
388C8#6693711yescharacteristic
389C8C2×#433911yescharacteristic
390C8C2×D4×D1111yescharacteristic
391C22—22no—
392C22—82no—
393C22—162no—
394C22—162no—
395C22—162no—
396C22—222no—
397C22—442no—
398C22—882no—
399C22—1762no—
400C22—1762no—
401C22—1762no—
402C22#1062238811yescharacteristic
403C22#1062238811yescharacteristic
404C22C2×#6696911yescharacteristic
405C4—222no—
406C4#1062238811yescharacteristic
407C4#1062238811yescharacteristic
408C4C2×#6693711yescharacteristic
409C4C2×D8×D1111yescharacteristic
410C2—21no—
411C2—21no—
412C2—162no—
413C2—442no—
414C2—1762no—
415C2#1307073512yesdirect product factor
416C2C2×#1062238811yescharacteristic
subgroupG/H
centerC22#10622388
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#361C2
socleC22×C11#466
hypercenterC2×#361D11
hypocenterC11C2×#2221
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#361

Complements

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

NH ≅ G/Ntype
1. C22×#66890C2semidirect
2. C2×#10622520C2semidirect
3. C2×#10622510C2semidirect
4. C2×#10622773C2semidirect
5. #13070735C2direct (N × H)
6. C2×#10622131C2semidirect
7. C2×#10622154C2semidirect
8. C2×C11×#361C2semidirect
18. #10622773C22semidirect
22. C2×#66890C22semidirect
27. #10622520C22semidirect
31. #10622510C22semidirect
32. C11×#361C22semidirect
33. #10622154C22semidirect
34. #10622131C22semidirect
150. C2×#361D11semidirect
216. #361C2×D11semidirect
289. C2×C11#2221semidirect
350. C11C2×#2221semidirect
415. C2#13070735direct (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×#106225202
C2×#106225102
C2×#106227732
#130707352
C2×#106221312
C2×#106221542
C2×C11×#3612
C2×#222111