Finite Group Databasebeta

← C2×#13070504 #14907203

Subgroups — C2×#13070504 #14907203

Order 2816.

646 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622808C211yesmaximal, characteristic
2C2×#10622810C211yesmaximal, characteristic
3C2×#10622466C211yesmaximal, characteristic, complemented
4#13070504C218yesmaximal, direct product factor
5C2×#10622125C211yesmaximal, characteristic, complemented
6C2×#10622155C211yesmaximal, characteristic, complemented
7C2×#10622150C211yesmaximal, characteristic, complemented
8C2×C11×#360C211yesmaximal, characteristic
9C2×C11×#135C2211yescharacteristic
10C2×#67001—21no—
11C22×Dic44C2211yescharacteristic
12C2×#66940—21no—
13C2×C11×M32C2211yescharacteristic
14C2×C11×#106C2211yescharacteristic
15C2×#66901—21no—
16#10622810—22no—
17#10622810C2214yes—
18#10622808C414yescomplemented
19#10622808C2214yes—
20C2×#66893C412yescomplemented
21C2×#66891C412yescomplemented
22C2×#66883C2211yescharacteristic
23C2×#66879C2211yescharacteristic
24C2×#66876C2211yescharacteristic
25C2×#66874—21no—
26#10622466—22no—
27#10622466C2214yescomplemented
28C11×#360C2214yes—
29#10622155C2214yescomplemented
30#10622150C2214yescomplemented
31#10622125C2214yescomplemented
32C2×C11×#41—21no—
33C22×Dic22—21no—
34C11×#135—21no—
35C11×#135—21no—
36C11×#135C2×C412yes—
37C11×#135C2312yes—
38C2×C11×Q16C2×C411yescharacteristic
39C2×C11×SD16—21no—
40C2×C11×D8C2×C411yescharacteristic
41C22×C8×C11C2311yescharacteristic
42C2×C11×C4⋊C4—21no—
43#67001—24no—
44#67001—42no—
45C2×Dic11⋊C4—41no—
46C2×C4×Dic11—41no—
47C2×C4×Dic11D411yescharacteristic
48C2×#4318—21no—
49C2×#4318—41no—
50C22×C11⋊C8—41no—
51C22×C11⋊C8D411yescharacteristic
52C2×Dic44—21no—
53C2×Dic44—21no—
54C2×Dic44—21no—
55C2×Dic44C2×C412yes—
56C2×Dic44C2×C412yes—
57C2×Dic44C2312yes—
58#66940—24no—
59#66940—42no—
60C11×M32—21no—
61C11×M32C2312yes—
62C2×C11×C16—21no—
63C11×#106—21no—
64C11×#106C2312yes—
65#66901—24no—
66#66893C2×C418yescomplemented
67#66891C2×C418yescomplemented
68#66883—21no—
69#66883C2312yes—
70#66879D412yes—
71#66879C2312yes—
72#66876C2×C412yes—
73#66876C2312yes—
74C2×C11⋊C16C2×C412yes—
75#66874—24no—
76C2×#2180—111nomaximal, Sylow
77C11×#41—22no—
78C11×#41—22no—
79C11×#41—41no—
80C11×#41—41no—
81C2×Q8×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11—41no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11C2×D411yescharacteristic
87C22×Dic11—21no—
88C22×Dic11—41no—
89C2×Dic22—22no—
90C2×Dic22—22no—
91C2×Dic22—22no—
92C2×Dic22—41no—
93C2×Dic22—41no—
94C2×Dic22—41no—
95C11×Q16—21no—
96C11×Q16C22×C412yes—
97C11×SD16—22no—
98C11×SD16—22no—
99C11×D8—21no—
100C11×D8C22×C412yes—
101C2×C8×C11C22×C411yescharacteristic
102C2×C8×C11C22×C411yescharacteristic
103C2×C8×C11C2×D411yescharacteristic
104C2×C8×C11#4111yescharacteristic
105C2×C8×C11#4111yescharacteristic
106C2×C8×C11C2411yescharacteristic
107C11×C4⋊C4—22no—
108C11×C4⋊C4—41no—
109Dic11⋊C4—44no—
110C4×Dic11—21no—
111C4×Dic11—44no—
112C4×Dic11C2×D412yes—
113#4318—22no—
114#4318—44no—
115#4318—41no—
116C2×C11⋊C8—21no—
117C2×C11⋊C8—21no—
118C2×C11⋊C8—44no—
119C2×C11⋊C8—41no—
120C2×C11⋊C8C2×D412yes—
121Dic44—22no—
122Dic44—22no—
123Dic44—22no—
124Dic44C22×C414yes—
125C11×C16—22no—
126C11⋊C16C22×C414yes—
127C2×#510—111no—
128C2×#444—111no—
129C2×#441—111no—
130#2180—118no—
131C2×#365—111no—
132C2×#362—111no—
133C2×#360D1111yescharacteristic
134C2×#347—111no—
135C23×C11—41no—
136C23×C11AGL(1,ℤ/8)11yescharacteristic
137Q8×C11—22no—
138Q8×C11—41no—
139D4×C11—22no—
140D4×C11—42no—
141D4×C11—42no—
142D4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—42no—
145C2×C4×C11—42no—
146C2×C4×C11—42no—
147C2×C4×C11—82no—
148C2×C4×C11C4×D411yescharacteristic
149C2×C4×C11C4×D411yescharacteristic
150C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C11C22×D411yescharacteristic
154C2×Dic11—22no—
155C2×Dic11—42no—
156C2×Dic11—42no—
157C2×Dic11—42no—
158C2×Dic11—42no—
159Dic22—24no—
160Dic22—42no—
161Dic22—42no—
162Dic22—42no—
163C8×C11C4×D411yescharacteristic
164C8×C11C4×D411yescharacteristic
165C8×C11C23×C411yescharacteristic
166C8×C11C2×#4111yescharacteristic
167C11⋊C8—22no—
168C11⋊C8—42no—
169C2×#135C2×D1111yescharacteristic
170C22×Q16—111no—
171C2×#131—221no—
172C2×C4×Q8—221no—
173#510—114no—
174#510—114no—
175C2×Q32—112no—
176C2×SD32—112no—
177C2×M32—111no—
178C2×M32C2×D1111yescharacteristic
179#444—114no—
180#444—222no—
181#441—114no—
182#441—222no—
183C2×#108—111no—
184C2×#106C2×D1111yescharacteristic
185C2×#104—221no—
186C2×#103—221no—
187C2×#97—111no—
188#365—114no—
189#362—114no—
190#360C2×D1114yes—
191#347—114no—
192C22×C11—22no—
193C22×C11—42no—
194C22×C11—82no—
195C22×C11#44211yescharacteristic
196C22×C11#44211yescharacteristic
197C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
198C4×C11—42no—
199C4×C11—82no—
200C4×C11#44211yescharacteristic
201C4×C11#44211yescharacteristic
202C4×C11C2×C4×D411yescharacteristic
203C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
204Dic11—42no—
205Dic11—44no—
206C2×#41—21no—
207C22×Q8—221no—
208#135—21no—
209#135—21no—
210#135C4×D1112yes—
211#135C22×D1112yes—
212C2×Q16—112no—
213C2×Q16—112no—
214C2×Q16—112no—
215C2×Q16—221no—
216C2×Q16—221no—
217C2×Q16—221no—
218C2×Q16C4×D1111yescharacteristic
219C2×SD16—21no—
220C2×D8C4×D1111yescharacteristic
221#131—224no—
222#131—442no—
223C2×M16—221no—
224C2×M16—441no—
225C22×C8—111no—
226C22×C8—441no—
227C22×C8C22×D1111yescharacteristic
228C4×Q8—224no—
229C4×Q8—442no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—441no—
232C2×C42—111no—
233C2×C42—441no—
234Q32—118no—
235SD32—118no—
236M32—21no—
237M32—112no—
238M32—112no—
239M32C22×D1112yes—
240C2×C16—21no—
241C2×C16—112no—
242#108—112no—
243#108—221no—
244#106—21no—
245#106C22×D1112yes—
246#104—224no—
247#103—224no—
248#97—112no—
249#97—112no—
250C2×C11—21no—
251C2×C11—21no—
252C2×C11—82no—
253C2×C11#218012yescomplemented
254C2×C11C2×#44211yescharacteristic
255#41—22no—
256#41—22no—
257#41—41no—
258#41—41no—
259C2×Q8—21no—
260C2×Q8—222no—
261C2×Q8—222no—
262C2×Q8—222no—
263C2×Q8—441no—
264C2×Q8—441no—
265C2×Q8—441no—
266C2×D4—21no—
267C2×D4—41no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—221no—
271C22×C4—441no—
272C22×C4D4×D1111yescharacteristic
273Q16—21no—
274Q16—114no—
275Q16—222no—
276Q16—222no—
277Q16—222no—
278Q16C2×C4×D1112yes—
279SD16—22no—
280SD16—22no—
281D8—21no—
282D8C2×C4×D1112yes—
283M16—222no—
284M16—444no—
285M16—441no—
286C2×C8—112no—
287C2×C8—221no—
288C2×C8—221no—
289C2×C8—444no—
290C2×C8—441no—
291C2×C8C2×C4×D1111yescharacteristic
292C2×C8C2×C4×D1111yescharacteristic
293C2×C8D4×D1111yescharacteristic
294C2×C8#434111yescharacteristic
295C2×C8#434111yescharacteristic
296C2×C8C23×D1111yescharacteristic
297C4⋊C4—22no—
298C4⋊C4—41no—
299C4⋊C4—444no—
300C42—112no—
301C42—221no—
302C42—444no—
303C16—22no—
304C16—114no—
305C11C2×#218011yescharacteristic, complemented, Sylow
306C23—41no—
307C23#6696411yescharacteristic
308Q8—22no—
309Q8—41no—
310Q8—224no—
311Q8—442no—
312Q8—442no—
313Q8—442no—
314D4—22no—
315D4—42no—
316D4—42no—
317D4—41no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—82no—
323C2×C4—222no—
324C2×C4—442no—
325C2×C4—442no—
326C2×C4—442no—
327C2×C4—442no—
328C2×C4(C22⋊D11)⋊C411yescharacteristic
329C2×C4(C22⋊D11)⋊C411yescharacteristic
330C2×C4#6696411yescharacteristic
331C2×C4#6696711yescharacteristic
332C2×C4#6696711yescharacteristic
333C2×C4C2×D4×D1111yescharacteristic
334C8—222no—
335C8—442no—
336C8(C22⋊D11)⋊C411yescharacteristic
337C8(C22⋊D11)⋊C411yescharacteristic
338C8C22×C4×D1111yescharacteristic
339C8C2×#434111yescharacteristic
340C22—22no—
341C22—42no—
342C22—82no—
343C22#1062239811yescharacteristic
344C22#1062239811yescharacteristic
345C22C2×#6696411yescharacteristic
346C4—42no—
347C4—82no—
348C4—442no—
349C4—444no—
350C4#1062239811yescharacteristic
351C4#1062239811yescharacteristic
352C4C2×(C22⋊D11)⋊C411yescharacteristic
353C4C2×#6696711yescharacteristic
354C2—21no—
355C2—21no—
356C2—82no—
357C2#1307050412yesdirect product factor
358C2C2×#1062239811yescharacteristic
subgroupG/H
centerC22#10622398
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
FittingC2×C11×#360C2
socleC22×C11#442
prime radicalC2×C11×#135C22
cosocleC2×C8×C11C24
hypercenterC2×#360D11
hypocenterC11C2×#2180
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#360

Complements

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

NH ≅ G/Ntype
3. C2×#10622466C2semidirect
4. #13070504C2direct (N × H)
5. C2×#10622125C2semidirect
6. C2×#10622155C2semidirect
7. C2×#10622150C2semidirect
18. #10622808C4semidirect
20. C2×#66893C4semidirect
21. C2×#66891C4semidirect
27. #10622466C22semidirect
29. #10622155C22semidirect
30. #10622150C22semidirect
31. #10622125C22semidirect
66. #66893C2×C4semidirect
67. #66891C2×C4semidirect
253. C2×C11#2180semidirect
305. C11C2×#2180semidirect
357. C2#13070504direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106228082
C2×#106228102
C2×#106224662
#130705042
C2×#106221252
C2×#106221552
C2×#106221502
C2×C11×#3602
C2×#218011