Finite Group Databasebeta

← C2×#21447712 #29833448

Subgroups — C2×#21447712 #29833448

Order 15616.

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×#16840205C211yesmaximal, characteristic
2C2×#16839885C211yesmaximal, characteristic
3C2×#16839870C211yesmaximal, characteristic, complemented
4#21447712C218yesmaximal, direct product factor
5C2×#16839585C211yesmaximal, characteristic, complemented
6C2×#16839579C211yesmaximal, characteristic, complemented
7C2×#16839573C211yesmaximal, characteristic
8C2×C61×#347C211yesmaximal, characteristic, complemented
9C2×#14519799C2211yescharacteristic
10C22×Dic244C2211yescharacteristic
11C2×#14519783—21no—
12C2×C4×Dic122—21no—
13#16840205C414yescomplemented
14#16840205C2214yes—
15C2×Dic488C412yescomplemented
16C2×#14519722C412yescomplemented
17#16839885—22no—
18#16839885C2214yes—
19#16839870—22no—
20#16839870C2214yescomplemented
21C2×#14519713C2211yescharacteristic
22C2×#14519709C2211yescharacteristic
23C2×#14519705—21no—
24C2×#14519702—21no—
25#16839585C2214yescomplemented
26#16839579C2214yescomplemented
27#16839573C2214yes—
28C2×M32×C61C2211yescharacteristic
29C2×M32×C61C2211yescharacteristic
30C2×#97×C61C2211yescharacteristic
31C61×#347C2214yescomplemented
32C2×#11758222—21no—
33C22×Dic122—21no—
34#14519799—21no—
35#14519799—21no—
36#14519799C2×C412yes—
37#14519799C2312yes—
38C2×Dic244—21no—
39C2×Dic244—21no—
40C2×Dic244—21no—
41C2×Dic244C2×C412yes—
42C2×Dic244C2×C412yes—
43C2×Dic244C2×C411yescharacteristic
44C2×Dic244C2312yes—
45C2×#11758190—21no—
46C2×D488C2×C411yescharacteristic
47#14519783—24no—
48#14519783—42no—
49C2×#11758194—21no—
50C2×#11758189—41no—
51C2×C8×D61—41no—
52C4×Dic122—24no—
53C4×Dic122—42no—
54C2×C4⋊Dic61—21no—
55C2×#11758196—41no—
56C2×C4×Dic61—41no—
57Dic488C2×C418yescomplemented
58#14519722C2×C418yescomplemented
59#14519713—21no—
60#14519713C2312yes—
61#14519709—21no—
62#14519709C2312yes—
63#14519705—24no—
64#14519702—24no—
65C22×C8×C61D411yescharacteristic
66C22×C8×C61C2311yescharacteristic
67C2×C42×C61D411yescharacteristic
68M32×C61—21no—
69M32×C61C2×C412yes—
70M32×C61C2312yes—
71M32×C61C2312yes—
72C2×C16×C61—21no—
73C2×C16×C61C2×C412yes—
74#97×C61D412yes—
75#97×C61C2312yes—
76C22×C4×C61—21no—
77C22×C4×C61C2×D411yescharacteristic
78C2×C22⋊D61—41no—
79C22×Dic61—41no—
80C22×Dic61—41no—
81#11758222—22no—
82#11758222—22no—
83#11758222—41no—
84#11758222—41no—
85C2×D244—21no—
86C2×C4×D61—41no—
87C2×Dic122—22no—
88C2×Dic122—22no—
89C2×Dic122—21no—
90C2×Dic122—22no—
91C2×Dic122—41no—
92C2×Dic122—41no—
93C2×Dic122—41no—
94C2×C8×C61—21no—
95C2×C8×C61—21no—
96C2×C8×C61C22×C411yescharacteristic
97C2×C8×C61C22×C411yescharacteristic
98C2×C8×C61C2×D412yes—
99C2×C8×C61C2×D411yescharacteristic
100C2×C8×C61#4111yescharacteristic
101C2×C8×C61#4111yescharacteristic
102C2×C8×C61C2411yescharacteristic
103C42×C61—21no—
104C42×C61C2×D412yes—
105C4⋊Dic61—22no—
106C4⋊Dic61—41no—
107#11758196—44no—
108C4×Dic61—44no—
109#11758194—22no—
110#11758194—41no—
111C2×#92418—41no—
112Dic244—22no—
113Dic244—22no—
114Dic244—21no—
115Dic244—22no—
116Dic244C22×C414yes—
117Dic244C22×C412yes—
118D488—21no—
119D488C22×C412yes—
120#11758190—22no—
121#11758190—22no—
122#11758189—44no—
123C8×D61—44no—
124C16×C61—22no—
125C16×C61C22×C414yes—
126C23×C61AGL(1,ℤ/8)11yescharacteristic
127C22×D61—41no—
128C2×C4×C61—22no—
129C2×C4×C61—42no—
130C2×C4×C61C4×D411yescharacteristic
131C2×C4×C61C4×D411yescharacteristic
132C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C61C22×D411yescharacteristic
136C22⋊D61—42no—
137C22⋊D61—42no—
138C2×Dic61—42no—
139C2×Dic61—42no—
140C2×Dic61—42no—
141C2×Dic61—41no—
142C2×Dic61—42no—
143C2×Dic61—82no—
144D244—22no—
145D244—41no—
146C4×D61—42no—
147C4×D61—42no—
148Dic122—22no—
149Dic122—24no—
150Dic122—42no—
151Dic122—42no—
152Dic122—42no—
153Dic122—41no—
154C8×C61—22no—
155C8×C61C4×D411yescharacteristic
156C8×C61C4×D411yescharacteristic
157C8×C61C23×C411yescharacteristic
158C8×C61C2×#4111yescharacteristic
159#92418—42no—
160C2×#2180—611nomaximal, Sylow
161C22×C61—22no—
162C22×C61#44211yescharacteristic
163C22×C61#44211yescharacteristic
164C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
165C2×D61—42no—
166C2×D61—82no—
167C4×C61—42no—
168C4×C61#44211yescharacteristic
169C4×C61#44211yescharacteristic
170C4×C61C2×C4×D411yescharacteristic
171C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
172Dic61—44no—
173Dic61—42no—
174Dic61—82no—
175C2×#510—611no—
176C2×#444—611no—
177C2×#441—611no—
178#2180—618no—
179C2×#365—611no—
180C2×#362—611no—
181C2×#360—611no—
182C2×#347D6111yescharacteristic, complemented
183C2×C61—21no—
184C2×C61—21no—
185C2×C61#218012yescomplemented
186C2×C61C2×#44211yescharacteristic
187D61—82no—
188C2×#135—611no—
189C22×Q16—611no—
190C2×#131—1221no—
191C2×C4×Q8—1221no—
192#510—614no—
193#510—614no—
194C2×Q32—612no—
195C2×SD32—612no—
196C2×M32C2×D6111yescharacteristic
197C2×M32C2×D6111yescharacteristic
198#444—614no—
199#444—1222no—
200#441—614no—
201#441—1222no—
202C2×#108—611no—
203C2×#106—611no—
204C2×#104—1221no—
205C2×#103—1221no—
206C2×#97C2×D6111yescharacteristic
207#365—614no—
208#362—614no—
209#360—614no—
210#347C2×D6114yescomplemented
211C61C2×#218011yescharacteristic, complemented, Sylow
212C2×#41—1221no—
213C22×Q8—1221no—
214#135—612no—
215#135—612no—
216#135—1221no—
217#135—1221no—
218C2×Q16—612no—
219C2×Q16—612no—
220C2×Q16—611no—
221C2×Q16—612no—
222C2×Q16—1221no—
223C2×Q16—1221no—
224C2×Q16—1221no—
225C2×SD16—1221no—
226C2×D8—611no—
227#131—1224no—
228#131—2442no—
229C2×M16—1221no—
230C2×M16—2441no—
231C22×C8—2441no—
232C22×C8D24411yescharacteristic
233C22×C8C22×D6111yescharacteristic
234C4×Q8—1224no—
235C4×Q8—2442no—
236C2×C4⋊C4—1221no—
237C2×C4⋊C4—2441no—
238C2×C42—2441no—
239C2×C42D24411yescharacteristic
240Q32—618no—
241SD32—618no—
242M32—21no—
243M32C4×D6112yes—
244M32C22×D6112yes—
245M32C22×D6112yes—
246C2×C16—21no—
247C2×C16C4×D6112yes—
248#108—612no—
249#108—1221no—
250#106—612no—
251#106—1221no—
252#104—1224no—
253#103—1224no—
254#97D24412yes—
255#97C22×D6112yes—
256#41—1222no—
257#41—1222no—
258#41—2441no—
259#41—2441no—
260C2×Q8—1222no—
261C2×Q8—1221no—
262C2×Q8—1222no—
263C2×Q8—1222no—
264C2×Q8—2441no—
265C2×Q8—2441no—
266C2×Q8—2441no—
267C2×D4—1221no—
268C2×D4—2441no—
269C22×C4—21no—
270C22×C4—2441no—
271C22×C4—2441no—
272C22×C4—2441no—
273C22×C4C2×D24411yescharacteristic
274Q16—614no—
275Q16—612no—
276Q16—1222no—
277Q16—1222no—
278Q16—1222no—
279Q16—1221no—
280SD16—1222no—
281SD16—1222no—
282D8—612no—
283D8—1221no—
284M16—1222no—
285M16—2444no—
286M16—2441no—
287C2×C8—21no—
288C2×C8—21no—
289C2×C8—2444no—
290C2×C8—2441no—
291C2×C8C2×C4×D6111yescharacteristic
292C2×C8C2×C4×D6111yescharacteristic
293C2×C8C2×D24412yes—
294C2×C8C2×D24411yescharacteristic
295C2×C8#1175822211yescharacteristic
296C2×C8#1175822211yescharacteristic
297C2×C8C23×D6111yescharacteristic
298C4⋊C4—1222no—
299C4⋊C4—2444no—
300C4⋊C4—2441no—
301C42—21no—
302C42—2444no—
303C42C2×D24412yes—
304C16—22no—
305C16C2×C4×D6114yes—
306C23—2441no—
307C23#1451980511yescharacteristic
308Q8—1222no—
309Q8—1224no—
310Q8—2442no—
311Q8—2442no—
312Q8—2442no—
313Q8—2441no—
314D4—1222no—
315D4—2442no—
316D4—2442no—
317D4—2441no—
318C2×C4—22no—
319C2×C4—42no—
320C2×C4—4882no—
321C2×C4—2442no—
322C2×C4—2442no—
323C2×C4—2442no—
324C2×C4—2441no—
325C2×C4—2442no—
326C2×C4—2442no—
327C2×C4—2442no—
328C2×C4C4×D24411yescharacteristic
329C2×C4C4×D24411yescharacteristic
330C2×C4#1451980511yescharacteristic
331C2×C4#1451980511yescharacteristic
332C2×C4#1451980511yescharacteristic
333C2×C4C22×D24411yescharacteristic
334C8—22no—
335C8—2442no—
336C8C4×D24411yescharacteristic
337C8C4×D24411yescharacteristic
338C8C22×C4×D6111yescharacteristic
339C8C2×#1175822211yescharacteristic
340C22—22no—
341C22—4882no—
342C22—2442no—
343C22#1683987511yescharacteristic
344C22#1683987511yescharacteristic
345C22C2×#1451980511yescharacteristic
346C4—42no—
347C4—4882no—
348C4—2442no—
349C4—2444no—
350C4#1683987511yescharacteristic
351C4#1683987511yescharacteristic
352C4C2×C4×D24411yescharacteristic
353C4C2×#1451980511yescharacteristic
354C2—21no—
355C2—21no—
356C2—4882no—
357C2#2144771212yesdirect product factor
358C2C2×#1683987511yescharacteristic
subgroupG/H
centerC22#16839875
commutatorC8×C61C23×C4
FrattiniC2×C8C23×D61
FittingC2×C61×#347C2
socleC22×C61#442
prime radicalC2×#14519799C22
cosocleC2×C8×C61C24
hypercenterC2×#347D61
hypocenterC61C2×#2180
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#97 ◁ C2×#347

Complements

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

NH ≅ G/Ntype
3. C2×#16839870C2semidirect
4. #21447712C2direct (N × H)
5. C2×#16839585C2semidirect
6. C2×#16839579C2semidirect
8. C2×C61×#347C2semidirect
13. #16840205C4semidirect
15. C2×Dic488C4semidirect
16. C2×#14519722C4semidirect
20. #16839870C22semidirect
25. #16839585C22semidirect
26. #16839579C22semidirect
31. C61×#347C22semidirect
57. Dic488C2×C4semidirect
58. #14519722C2×C4semidirect
182. C2×#347D61semidirect
185. C2×C61#2180semidirect
210. #347C2×D61semidirect
211. C61C2×#2180semidirect
357. C2#21447712direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402052
C2×#168398852
C2×#168398702
#214477122
C2×#168395852
C2×#168395792
C2×#168395732
C2×C61×#3472
C2×#218061