Finite Group Databasebeta

← C2×#13070829 #14908656

Subgroups — C2×#13070829 #14908656

Order 2816.

604 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622772C211yesmaximal, characteristic
2C2×#10622506C211yesmaximal, characteristic, complemented
3#13070829C218yesmaximal, direct product factor
4C2×#10622132C211yesmaximal, characteristic, complemented
5C2×#10622151C211yesmaximal, characteristic, complemented
6C2×#10622201C211yesmaximal, characteristic, complemented
7C2×#10622152C211yesmaximal, characteristic, complemented
8C2×C11×#361C211yesmaximal, characteristic, complemented
9C22×C11×D8C2211yescharacteristic
10C2×#66991—21no—
11C2×M16×D11—21no—
12C22×#4313C2211yescharacteristic
13C2×C11×M32C2211yescharacteristic
14C2×C11×#108C2211yescharacteristic
15C2×#66896—21no—
16#10622772—22no—
17#10622772C2214yes—
18C2×#66886—21no—
19C2×#66883C2211yescharacteristic
20C2×#66881C2211yescharacteristic
21C2×#66876C2211yescharacteristic
22#10622506—22no—
23#10622506C2214yescomplemented
24C11×#361C2214yescomplemented
25#10622201C2214yescomplemented
26#10622152C2214yescomplemented
27#10622151C2214yescomplemented
28#10622132C2214yescomplemented
29C22×D4×C11—21no—
30C22×C22⋊D11—41no—
31C22×C4×D11D411yescharacteristic
32C2×C11×D8—21no—
33C2×C11×D8—21no—
34C2×C11×D8—21no—
35C2×C11×D8—21no—
36C2×C11×D8—21no—
37C2×C11×D8C2312yes—
38C2×C11×M16—21no—
39C22×C8×C11C2311yescharacteristic
40C2×C22⋊Dic11—41no—
41#66991—24no—
42#66991—42no—
43C2×C4⋊Dic11—21no—
44C2×#4318—21no—
45C22×C11⋊C8D411yescharacteristic
46M16×D11—24no—
47M16×D11—42no—
48C2×#4313—21no—
49C2×#4313—21no—
50C2×#4313—21no—
51C2×#4313—21no—
52C2×#4313—41no—
53C2×#4313D412yes—
54C2×#4313C2312yes—
55C2×C8×D11—41no—
56C11×M32—21no—
57C11×M32C2312yes—
58C2×C11×C16—21no—
59C11×#108—21no—
60C11×#108C2312yes—
61#66896—24no—
62#66886—24no—
63#66883—21no—
64#66883C2312yes—
65#66881—21no—
66#66881C2312yes—
67#66876—21no—
68#66876C2312yes—
69C2×C11⋊C16—21no—
70C2×#2238—111nomaximal, Sylow
71C24×C11—41no—
72C23×D11SD1611yescharacteristic
73C2×D4×C11—22no—
74C2×D4×C11—41no—
75C2×D4×C11—41no—
76C2×D4×C11—41no—
77C2×D4×C11—41no—
78C2×D4×C11—41no—
79C22×C4×C11C2×D411yescharacteristic
80C2×C22⋊D11—44no—
81C2×C22⋊D11—84no—
82C22×Dic11—41no—
83C22×Dic11SD1611yescharacteristic
84C2×C4×D11—21no—
85C2×C4×D11—21no—
86C2×C4×D11—21no—
87C2×C4×D11—21no—
88C2×C4×D11SD1612yes—
89C2×C4×D11C2×D412yes—
90C11×D8—22no—
91C11×D8—22no—
92C11×D8—41no—
93C11×D8—41no—
94C11×M16—22no—
95C11×M16—41no—
96C2×C8×C11—41no—
97C2×C8×C11C2×D411yescharacteristic
98C2×C8×C11#4111yescharacteristic
99C2×C8×C11#4111yescharacteristic
100C2×C8×C11#4111yescharacteristic
101C2×C8×C11#4111yescharacteristic
102C2×C8×C11C2411yescharacteristic
103C22⋊Dic11—44no—
104C4⋊Dic11—22no—
105C4⋊Dic11—41no—
106#4318—22no—
107#4318—41no—
108C2×C11⋊C8—21no—
109C2×C11⋊C8—21no—
110C2×C11⋊C8—41no—
111C2×C11⋊C8C2×D412yes—
112#4313—22no—
113#4313—22no—
114#4313—22no—
115#4313—22no—
116#4313—44no—
117C8×D11—44no—
118C11×C16—22no—
119C11⋊C16—22no—
120C2×#469—111no—
121C2×#430—111no—
122#2238—118no—
123C2×#365—111no—
124C2×#365—111no—
125C2×#361—111no—
126C2×#361D1111yescharacteristic, complemented
127C2×#349—111no—
128C23×C11—42no—
129C23×C11—82no—
130C23×C11—82no—
131C23×C11—81no—
132C23×C11—81no—
133C23×C11C2×SD1611yescharacteristic
134C22×D11—21no—
135C22×D11—21no—
136C22×D11—42no—
137C22×D11C2×SD1612yes—
138D4×C11—42no—
139D4×C11—42no—
140D4×C11—81no—
141D4×C11—81no—
142C2×C4×C11#12311yescharacteristic
143C2×C4×C11#12311yescharacteristic
144C2×C4×C11C2×SD1611yescharacteristic
145C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C11C22×D411yescharacteristic
148C22⋊D11—88no—
149C2×Dic11—21no—
150C2×Dic11—21no—
151C2×Dic11—42no—
152C2×Dic11—82no—
153C2×Dic11C2×SD1612yes—
154C4×D11—22no—
155C4×D11—22no—
156C4×D11—22no—
157C4×D11—22no—
158C8×C11—42no—
159C8×C11#12311yescharacteristic
160C8×C11#12311yescharacteristic
161C8×C11C2×#4111yescharacteristic
162C8×C11C2×#4111yescharacteristic
163C11⋊C8—22no—
164C11⋊C8—42no—
165C22×D8C2×D1111yescharacteristic
166C22×M16—111no—
167C22×M16—221no—
168C2×#121—221no—
169C2×M32—111no—
170C2×M32C2×D1111yescharacteristic
171#469—114no—
172#469—222no—
173#430—114no—
174#430—222no—
175C2×#108—111no—
176C2×#108—221no—
177C2×#108C2×D1111yescharacteristic
178C2×#106—111no—
179C2×#102—221no—
180#365—114no—
181#365—114no—
182#361—114no—
183#361C2×D1114yescomplemented
184#349—114no—
185C22×C11—22no—
186C22×C11—82no—
187C22×C11—82no—
188C22×C11—82no—
189C22×C11—162no—
190C22×C11—162no—
191C22×C11#48111yescharacteristic
192C22×C11#48111yescharacteristic
193C22×C11C22×SD1611yescharacteristic
194C2×D11—22no—
195C2×D11—42no—
196C2×D11—42no—
197C2×D11—81no—
198C4×C11#48111yescharacteristic
199C4×C11#48111yescharacteristic
200C4×C11C2×#12311yescharacteristic
201C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
202Dic11—22no—
203Dic11—82no—
204C22×D4—21no—
205C22×D4—441no—
206C23×C4—111no—
207C2×D8—21no—
208C2×D8—21no—
209C2×D8—21no—
210C2×D8—21no—
211C2×D8—21no—
212C2×D8C22×D1112yes—
213C2×M16—21no—
214C2×M16—112no—
215C2×M16—112no—
216C2×M16—221no—
217C2×M16—221no—
218C2×M16—221no—
219C2×M16—221no—
220C2×M16—224no—
221C2×M16—221no—
222C2×M16—441no—
223C2×M16—442no—
224C22×C8—111no—
225C22×C8—441no—
226C22×C8C22×D1111yescharacteristic
227#121—224no—
228#121—442no—
229C2×C4⋊C4—221no—
230C2×C22⋊C4—441no—
231M32—21no—
232M32—112no—
233M32—221no—
234M32C22×D1112yes—
235C2×C16—21no—
236C2×C16—221no—
237#108—21no—
238#108—112no—
239#108—224no—
240#108—221no—
241#108C22×D1112yes—
242#106—112no—
243#106—221no—
244#102—224no—
245C2×C11—21no—
246C2×C11—21no—
247C2×C11—162no—
248C2×C11#223812yescomplemented
249C2×C11C2×#48111yescharacteristic
250D11—42no—
251C24—41no—
252C24—111no—
253C2×D4—22no—
254C2×D4—41no—
255C2×D4—41no—
256C2×D4—41no—
257C2×D4—41no—
258C2×D4—41no—
259C2×D4—444no—
260C2×D4—884no—
261C22×C4—111no—
262C22×C4—112no—
263C22×C4—112no—
264C22×C4—221no—
265C22×C4—221no—
266C22×C4—221no—
267C22×C4—221no—
268C22×C4—441no—
269C22×C4D4×D1111yescharacteristic
270D8—22no—
271D8—22no—
272D8—41no—
273D8—41no—
274M16—22no—
275M16—41no—
276M16—222no—
277M16—222no—
278M16—222no—
279M16—222no—
280M16—222no—
281M16—444no—
282M16—441no—
283C2×C8—41no—
284C2×C8—112no—
285C2×C8—221no—
286C2×C8—221no—
287C2×C8—444no—
288C2×C8—441no—
289C2×C8#433911yescharacteristic
290C2×C8#433911yescharacteristic
291C2×C8D4×D1111yescharacteristic
292C2×C8#434111yescharacteristic
293C2×C8#434111yescharacteristic
294C2×C8C23×D1111yescharacteristic
295C4⋊C4—222no—
296C4⋊C4—441no—
297C22⋊C4—444no—
298C16—22no—
299C16—222no—
300C11C2×#223811yescharacteristic, complemented, Sylow
301C23—42no—
302C23—82no—
303C23—82no—
304C23—81no—
305C23—81no—
306C23—112no—
307C23—221no—
308C23—221no—
309C23—442no—
310C23SD16×D1111yescharacteristic
311D4—42no—
312D4—42no—
313D4—81no—
314D4—81no—
315D4—888no—
316C2×C4—112no—
317C2×C4—221no—
318C2×C4—221no—
319C2×C4—222no—
320C2×C4—222no—
321C2×C4—222no—
322C2×C4—222no—
323C2×C4—442no—
324C2×C4—882no—
325C2×C4#6693611yescharacteristic
326C2×C4#6693611yescharacteristic
327C2×C4#6696411yescharacteristic
328C2×C4#6696411yescharacteristic
329C2×C4SD16×D1111yescharacteristic
330C2×C4C2×D4×D1111yescharacteristic
331C8—42no—
332C8—222no—
333C8—442no—
334C8#6693611yescharacteristic
335C8#6693611yescharacteristic
336C8C2×#433911yescharacteristic
337C8C2×#434111yescharacteristic
338C22—22no—
339C22—82no—
340C22—82no—
341C22—82no—
342C22—162no—
343C22—162no—
344C22—222no—
345C22—442no—
346C22—442no—
347C22—881no—
348C22#1062239011yescharacteristic
349C22#1062239011yescharacteristic
350C22C2×SD16×D1111yescharacteristic
351C4—222no—
352C4—882no—
353C4#1062239011yescharacteristic
354C4#1062239011yescharacteristic
355C4C2×#6693611yescharacteristic
356C4C2×#6696411yescharacteristic
357C2—21no—
358C2—21no—
359C2—162no—
360C2—442no—
361C2#1307082912yesdirect product factor
362C2C2×#1062239011yescharacteristic
subgroupG/H
centerC22#10622390
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#361C2
socleC22×C11#481
prime radicalC2×#10622772C2
hypercenterC2×#361D11
hypocenterC11C2×#2238
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
2. C2×#10622506C2semidirect
3. #13070829C2direct (N × H)
4. C2×#10622132C2semidirect
5. C2×#10622151C2semidirect
6. C2×#10622201C2semidirect
7. C2×#10622152C2semidirect
8. C2×C11×#361C2semidirect
23. #10622506C22semidirect
24. C11×#361C22semidirect
25. #10622201C22semidirect
26. #10622152C22semidirect
27. #10622151C22semidirect
28. #10622132C22semidirect
126. C2×#361D11semidirect
183. #361C2×D11semidirect
248. C2×C11#2238semidirect
300. C11C2×#2238semidirect
361. C2#13070829direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106227722
C2×#106225062
#130708292
C2×#106221322
C2×#106221512
C2×#106222012
C2×#106221522
C2×C11×#3612
C2×#223811