Finite Group Databasebeta

← C2×#16840369 #21459182

Subgroups — C2×#16840369 #21459182

Order 7808.

1004 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840369C2116yesmaximal, direct product factor
2C2×#14519776C211yesmaximal, characteristic, complemented
3C2×#14519770C211yesmaximal, characteristic
4C2×#14519770C211yesmaximal, characteristic
5C2×#14519770C211yesmaximal, characteristic
6C2×#14519769C211yesmaximal, characteristic, complemented
7C2×#14519768C211yesmaximal, characteristic, complemented
8C2×#14519767C211yesmaximal, characteristic, complemented
9C2×#14519767C211yesmaximal, characteristic, complemented
10C2×#14519767C211yesmaximal, characteristic, complemented
11C2×#14519754C211yesmaximal, characteristic
12C2×#14519754C211yesmaximal, characteristic
13C2×C4×Dic122C211yesmaximal, characteristic, complemented
14C2×#14519742C211yesmaximal, characteristic, complemented
15C2×#14519733C211yesmaximal, characteristic
16C2×#126×C61C211yesmaximal, characteristic
17C22×Dic122C2211yescharacteristic
18C22×Dic122C2211yescharacteristic
19C23×Dic61C2211yescharacteristic
20#14519776C2218yescomplemented
21#14519770C2218yes—
22#14519770C2218yes—
23#14519770C2218yes—
24#14519769C2218yescomplemented
25#14519768C2218yescomplemented
26#14519767C2218yescomplemented
27#14519767C2218yescomplemented
28#14519767C2218yescomplemented
29#14519754C2218yes—
30#14519754C2218yes—
31C4×Dic122C2218yescomplemented
32#14519742C2218yescomplemented
33#14519733C2218yes—
34C2×C4⋊Dic61C2211yescharacteristic
35C2×C4⋊Dic61C2211yescharacteristic
36C2×C4⋊Dic61C2211yescharacteristic
37C2×C4⋊Dic61C2211yescharacteristic
38C2×C4⋊Dic61C2211yescharacteristic
39C2×#11758196C2211yescharacteristic
40C2×#11758196C2211yescharacteristic
41C2×#11758196C2211yescharacteristic
42C2×#11758196C2211yescharacteristic
43C2×#11758196C2211yescharacteristic
44C2×#11758196C2211yescharacteristic
45C2×#11758196C2211yescharacteristic
46C2×#11758196C2211yescharacteristic
47C2×#11758196C2211yescharacteristic
48C2×#11758196C2211yescharacteristic
49C2×#11758196C2211yescharacteristic
50C2×#11758196C2211yescharacteristic
51C2×C22⋊Dic61C2211yescharacteristic
52C2×C22⋊Dic61C2211yescharacteristic
53C2×C22⋊Dic61C2211yescharacteristic
54C2×C4×Dic61C2211yescharacteristic
55C2×C4×Dic61C2211yescharacteristic
56C2×C4×Dic61C2211yescharacteristic
57C2×C4×Dic61C2211yescharacteristic
58C2×C4×Dic61C2211yescharacteristic
59#126×C61C2218yes—
60C2×C4⋊C4×C61C2211yescharacteristic
61C2×C4⋊C4×C61C2211yescharacteristic
62C2×C4⋊C4×C61C2211yescharacteristic
63C2×C22⋊C4×C61C2211yescharacteristic
64C2×C22⋊C4×C61C2211yescharacteristic
65C2×C22⋊C4×C61C2211yescharacteristic
66C2×C42×C61C2211yescharacteristic
67C24×C61C2311yescharacteristic
68C22×C4×C61C2311yescharacteristic
69C22×C4×C61C2311yescharacteristic
70C22×C4×C61C2311yescharacteristic
71C22×C4×C61C2311yescharacteristic
72C22×C4×C61C2311yescharacteristic
73C22×C4×C61C2311yescharacteristic
74C22×Dic61—24no—
75C22×Dic61C2311yescharacteristic
76C22×Dic61C2314yes—
77C22×Dic61C2311yescharacteristic
78C22×Dic61C2311yescharacteristic
79C22×Dic61C2311yescharacteristic
80C22×Dic61C2311yescharacteristic
81C22×Dic61C2311yescharacteristic
82C22×Dic61C2311yescharacteristic
83C22×Dic61C2311yescharacteristic
84C2×Dic122—24no—
85C2×Dic122—24no—
86C2×Dic122C2314yes—
87C2×Dic122C2314yes—
88C4⋊C4×C61C2314yes—
89C4⋊C4×C61C2314yes—
90C4⋊C4×C61C2314yes—
91C22⋊C4×C61C2314yes—
92C22⋊C4×C61C2314yes—
93C22⋊C4×C61C2314yes—
94C42×C61C2314yes—
95C22⋊Dic61C2314yes—
96C22⋊Dic61C2314yes—
97C22⋊Dic61C2314yes—
98C4⋊Dic61C2314yes—
99C4⋊Dic61C2314yes—
100C4⋊Dic61C2314yes—
101C4⋊Dic61C2314yes—
102C4⋊Dic61C2314yes—
103#11758196C2314yes—
104#11758196C2314yes—
105#11758196C2314yes—
106#11758196C2314yes—
107#11758196C2314yes—
108#11758196C2314yes—
109#11758196C2314yes—
110#11758196C2314yes—
111#11758196C2314yes—
112#11758196C2314yes—
113#11758196C2314yes—
114#11758196C2314yes—
115C4×Dic61C2314yes—
116C4×Dic61C2314yes—
117C4×Dic61C2314yes—
118C4×Dic61C2314yes—
119C4×Dic61C2314yes—
120C23×C61—22no—
121C23×C61—22no—
122C23×C61—22no—
123C23×C61C2412yes—
124C23×C61C2411yescharacteristic
125C2×C4×C61—22no—
126C2×C4×C61—22no—
127C2×C4×C61—22no—
128C2×C4×C61—22no—
129C2×C4×C61—22no—
130C2×C4×C61—22no—
131C2×C4×C61C2412yes—
132C2×C4×C61C2412yes—
133C2×C4×C61C2412yes—
134C2×C4×C61C2412yes—
135C2×C4×C61C2412yes—
136C2×C4×C61C2412yes—
137C2×Dic61—22no—
138C2×Dic61—22no—
139C2×Dic61—22no—
140C2×Dic61—22no—
141C2×Dic61—22no—
142C2×Dic61—22no—
143C2×Dic61—22no—
144C2×Dic61—28no—
145C2×Dic61#4114yes—
146C2×Dic61C2412yes—
147C2×Dic61C2412yes—
148C2×Dic61C2412yes—
149C2×Dic61C2412yes—
150C2×Dic61C2412yes—
151C2×Dic61C2412yes—
152C2×Dic61C2412yes—
153C2×Dic61C2412yes—
154Dic122—28no—
155Dic122—28no—
156C22×C61—22no—
157C22×C61—22no—
158C22×C61—22no—
159C22×C61—44no—
160C22×C61C2×#4112yes—
161C22×C612−1+412yes—
162C22×C612−1+412yes—
163C22×C61C2511yescharacteristic
164C4×C61—22no—
165C4×C61—22no—
166C4×C61—22no—
167C4×C61—22no—
168C4×C61—22no—
169C4×C61—22no—
170Dic61—22no—
171Dic61—22no—
172Dic61—22no—
173Dic61—22no—
174Dic61—22no—
175Dic61—22no—
176Dic61—22no—
177Dic61C2×#4114yes—
178C2×#541—611nomaximal, Sylow
179C2×C61—42no—
180C2×C61#54114yescomplemented
181C2×C61C22×#4111yescharacteristic
182C2×C61C2×2−1+411yescharacteristic
183C2×C61C2×2−1+411yescharacteristic
184#541—6116no—
185C2×C4⋊Q8—611no—
186C2×#126—611no—
187C2×#126—611no—
188C2×#126—611no—
189C2×#126D6111yescharacteristic
190C2×#125—611no—
191C2×#125—611no—
192C2×#125—611no—
193C2×#125—611no—
194C2×#125—611no—
195C2×C22⋊Q8—611no—
196C2×C22⋊Q8—611no—
197C2×C4×Q8—611no—
198C2×C4×Q8—611no—
199C2×#117—611no—
200C61C2×#54111yescharacteristic, complemented, Sylow
201C22×Q8—611no—
202C22×Q8—611no—
203C23×C4—611no—
204C4⋊Q8—618no—
205#126—618no—
206#126—618no—
207#126—618no—
208#126C2×D6118yes—
209#125—618no—
210#125—618no—
211#125—618no—
212#125—618no—
213#125—618no—
214C22⋊Q8—618no—
215C22⋊Q8—618no—
216C4×Q8—618no—
217C4×Q8—618no—
218#117—618no—
219C2×C4⋊C4—611no—
220C2×C4⋊C4—611no—
221C2×C4⋊C4—611no—
222C2×C4⋊C4—611no—
223C2×C4⋊C4—611no—
224C2×C4⋊C4—611no—
225C2×C4⋊C4—611no—
226C2×C4⋊C4—611no—
227C2×C4⋊C4—611no—
228C2×C4⋊C4—611no—
229C2×C4⋊C4—611no—
230C2×C4⋊C4—611no—
231C2×C4⋊C4—611no—
232C2×C4⋊C4—611no—
233C2×C4⋊C4—611no—
234C2×C4⋊C4—611no—
235C2×C4⋊C4—611no—
236C2×C4⋊C4C2×D6111yescharacteristic
237C2×C4⋊C4C2×D6111yescharacteristic
238C2×C4⋊C4C2×D6111yescharacteristic
239C2×C22⋊C4—611no—
240C2×C22⋊C4—611no—
241C2×C22⋊C4—611no—
242C2×C22⋊C4C2×D6111yescharacteristic
243C2×C22⋊C4C2×D6111yescharacteristic
244C2×C22⋊C4C2×D6111yescharacteristic
245C2×C42—611no—
246C2×C42—611no—
247C2×C42—611no—
248C2×C42—611no—
249C2×C42—611no—
250C2×C42C2×D6111yescharacteristic
251C24C22×D6111yescharacteristic
252C2×Q8—614no—
253C2×Q8—614no—
254C2×Q8—1224no—
255C2×Q8—1224no—
256C22×C4—611no—
257C22×C4—614no—
258C22×C4—611no—
259C22×C4—611no—
260C22×C4—611no—
261C22×C4—611no—
262C22×C4—611no—
263C22×C4—611no—
264C22×C4—611no—
265C22×C4—1224no—
266C22×C4C22×D6111yescharacteristic
267C22×C4C22×D6111yescharacteristic
268C22×C4C22×D6111yescharacteristic
269C22×C4C22×D6111yescharacteristic
270C22×C4C22×D6111yescharacteristic
271C22×C4C22×D6111yescharacteristic
272C4⋊C4—614no—
273C4⋊C4—614no—
274C4⋊C4—614no—
275C4⋊C4—614no—
276C4⋊C4—614no—
277C4⋊C4—614no—
278C4⋊C4—614no—
279C4⋊C4—614no—
280C4⋊C4—614no—
281C4⋊C4—614no—
282C4⋊C4—614no—
283C4⋊C4—614no—
284C4⋊C4—614no—
285C4⋊C4—614no—
286C4⋊C4—614no—
287C4⋊C4—614no—
288C4⋊C4—614no—
289C4⋊C4C22×D6114yes—
290C4⋊C4C22×D6114yes—
291C4⋊C4C22×D6114yes—
292C22⋊C4—614no—
293C22⋊C4—614no—
294C22⋊C4—614no—
295C22⋊C4C22×D6114yes—
296C22⋊C4C22×D6114yes—
297C22⋊C4C22×D6114yes—
298C42—614no—
299C42—614no—
300C42—614no—
301C42—614no—
302C42—614no—
303C42C22×D6114yes—
304C23—22no—
305C23—22no—
306C23—22no—
307C23C23×D6112yes—
308C23C23×D6111yescharacteristic
309Q8—1228no—
310Q8—1228no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—614no—
318C2×C4—612no—
319C2×C4—612no—
320C2×C4—612no—
321C2×C4—612no—
322C2×C4—612no—
323C2×C4—612no—
324C2×C4—612no—
325C2×C4—612no—
326C2×C4—1228no—
327C2×C4—1222no—
328C2×C4—1222no—
329C2×C4—1222no—
330C2×C4—1222no—
331C2×C4—1222no—
332C2×C4—1222no—
333C2×C4—1222no—
334C2×C4C23×D6112yes—
335C2×C4C23×D6112yes—
336C2×C4C23×D6112yes—
337C2×C4C23×D6112yes—
338C2×C4C23×D6112yes—
339C2×C4C23×D6112yes—
340C22—22no—
341C22—22no—
342C22—22no—
343C22—44no—
344C22#41×D6112yes—
345C22#1451982412yes—
346C22#1451982412yes—
347C22C24×D6111yescharacteristic
348C4—22no—
349C4—22no—
350C4—22no—
351C4—22no—
352C4—22no—
353C4—22no—
354C4—614no—
355C4—1222no—
356C4—1222no—
357C4—1222no—
358C4—1222no—
359C4—1222no—
360C4—1222no—
361C4—1222no—
362C2—42no—
363C2#1684036914yesdirect product factor
364C2C2×#41×D6111yescharacteristic
365C2C2×#1451982411yescharacteristic
366C2C2×#1451982411yescharacteristic
subgroupG/H
centerC23C23×D61
commutatorC22×C61C25
FrattiniC22C24×D61
FittingC2×#126×C61C2
socleC23×C61C24
hypercenterC2×#126D61
hypocenterC61C2×#541
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. #16840369C2direct (N × H)
2. C2×#14519776C2semidirect
6. C2×#14519769C2semidirect
7. C2×#14519768C2semidirect
8. C2×#14519767C2semidirect
9. C2×#14519767C2semidirect
10. C2×#14519767C2semidirect
13. C2×C4×Dic122C2semidirect
14. C2×#14519742C2semidirect
20. #14519776C22semidirect
24. #14519769C22semidirect
25. #14519768C22semidirect
26. #14519767C22semidirect
27. #14519767C22semidirect
28. #14519767C22semidirect
31. C4×Dic122C22semidirect
32. #14519742C22semidirect
180. C2×C61#541semidirect
200. C61C2×#541semidirect
363. C2#16840369direct (N × H)