Finite Group Databasebeta

← C2×#21447713 #29833449

Subgroups — C2×#21447713 #29833449

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×#16840203C211yesmaximal, characteristic
2C2×#16839883C211yesmaximal, characteristic
3C2×#16839869C211yesmaximal, characteristic, complemented
4#21447713C218yesmaximal, direct product factor
5C2×#16839586C211yesmaximal, characteristic, complemented
6C2×#16839573C211yesmaximal, characteristic
7C2×#16839539C211yesmaximal, characteristic, complemented
8C2×C61×#362C211yesmaximal, characteristic, complemented
9C2×#14519799C2211yescharacteristic
10C2×#14519785—21no—
11C2×Q8×Dic61—21no—
12#16840203C414yescomplemented
13#16840203C2214yes—
14C2×#14519723C412yescomplemented
15C2×#14519720C412yescomplemented
16C2×#14519717C2211yescharacteristic
17#16839883—22no—
18#16839883C2214yes—
19#16839869—22no—
20#16839869C2214yescomplemented
21C2×#14519709C2211yescharacteristic
22C2×#14519703—21no—
23C2×#14519701—21no—
24C2×#14519687C2211yescharacteristic
25#16839586C2214yescomplemented
26#16839573C2214yes—
27#16839539C2214yescomplemented
28C22×Q16×C61C2211yescharacteristic
29C2×M32×C61C2211yescharacteristic
30C2×#108×C61C2211yescharacteristic
31C61×#362C2214yescomplemented
32C2×#11758222—21no—
33#14519799—21no—
34#14519799—21no—
35#14519799C2×C412yes—
36#14519799C2312yes—
37C2×Dic244C2×C411yescharacteristic
38C2×#11758190—21no—
39C2×D488C2×C411yescharacteristic
40#14519785—24no—
41#14519785—42no—
42C2×#11758189—41no—
43C22×#92418D411yescharacteristic
44C2×C8×D61—41no—
45Q8×Dic61—24no—
46Q8×Dic61—42no—
47C2×C4⋊Dic61—21no—
48C2×C4⋊Dic61—41no—
49C2×C4×Dic61—41no—
50C2×C4×Dic61D411yescharacteristic
51#14519723C2×C418yescomplemented
52#14519720C2×C418yescomplemented
53#14519717C2×C412yes—
54#14519717C2312yes—
55C2×#11758185C2×C412yes—
56#14519709—21no—
57#14519709C2312yes—
58#14519703—24no—
59#14519701—24no—
60#14519687D412yes—
61#14519687C2312yes—
62C22×Q8×C61—21no—
63C2×Q16×C61—21no—
64C2×Q16×C61—21no—
65C2×Q16×C61—21no—
66C2×Q16×C61C2×C412yes—
67C2×Q16×C61C2×C412yes—
68C2×Q16×C61C2312yes—
69C2×M16×C61—21no—
70C22×C8×C61C2311yescharacteristic
71M32×C61—21no—
72M32×C61C2312yes—
73C2×C16×C61—21no—
74#108×C61—21no—
75#108×C61C2312yes—
76C2×Q8×C61—22no—
77C2×Q8×C61—22no—
78C2×Q8×C61—22no—
79C2×Q8×C61—41no—
80C2×Q8×C61—41no—
81C2×Q8×C61—41no—
82C22×C4×C61—41no—
83C22×C4×C61C2×D411yescharacteristic
84C2×C22⋊D61—41no—
85C22×Dic61—21no—
86C22×Dic61—41no—
87#11758222—22no—
88#11758222—22no—
89#11758222—41no—
90#11758222—41no—
91C2×D244—21no—
92C2×C4×D61—41no—
93C2×Dic122—21no—
94Q16×C61—22no—
95Q16×C61—22no—
96Q16×C61—22no—
97Q16×C61C22×C414yes—
98M16×C61—22no—
99M16×C61—41no—
100C2×C8×C61—41no—
101C2×C8×C61C22×C411yescharacteristic
102C2×C8×C61C22×C411yescharacteristic
103C2×C8×C61C2×D411yescharacteristic
104C2×C8×C61#4111yescharacteristic
105C2×C8×C61#4111yescharacteristic
106C2×C8×C61C2411yescharacteristic
107C4⋊Dic61—22no—
108C4⋊Dic61—44no—
109C4⋊Dic61—41no—
110C4×Dic61—21no—
111C4×Dic61—44no—
112C4×Dic61C2×D412yes—
113C2×#92418—21no—
114C2×#92418—21no—
115C2×#92418C2×D412yes—
116Dic244—21no—
117Dic244C22×C412yes—
118D488—21no—
119D488C22×C412yes—
120#11758190—22no—
121#11758190—22no—
122#11758189—44no—
123C8×D61—44no—
124C16×C61—22no—
125#11758185C22×C414yes—
126C23×C61AGL(1,ℤ/8)11yescharacteristic
127C22×D61—41no—
128Q8×C61—24no—
129Q8×C61—42no—
130Q8×C61—42no—
131Q8×C61—42no—
132C2×C4×C61—42no—
133C2×C4×C61—42no—
134C2×C4×C61—42no—
135C2×C4×C61C4×D411yescharacteristic
136C2×C4×C61C4×D411yescharacteristic
137C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C61C22×D411yescharacteristic
141C22⋊D61—42no—
142C22⋊D61—42no—
143C2×Dic61—22no—
144C2×Dic61—42no—
145C2×Dic61—41no—
146C2×Dic61—42no—
147C2×Dic61—82no—
148D244—22no—
149D244—41no—
150C4×D61—42no—
151C4×D61—42no—
152Dic122—22no—
153Dic122—41no—
154C8×C61—42no—
155C8×C61C4×D411yescharacteristic
156C8×C61C4×D411yescharacteristic
157C8×C61C23×C411yescharacteristic
158C8×C61C2×#4111yescharacteristic
159#92418—22no—
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—44no—
168C4×C61#44211yescharacteristic
169C4×C61#44211yescharacteristic
170C4×C61C2×C4×D411yescharacteristic
171C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
172Dic61—42no—
173Dic61—42no—
174Dic61—82no—
175C2×#510—611no—
176C2×#444—611no—
177C2×#441—611no—
178#2180—618no—
179C2×#365—611no—
180C2×#362D6111yescharacteristic, complemented
181C2×#360—611no—
182C2×#347—611no—
183C2×C61—21no—
184C2×C61—21no—
185C2×C61#218012yescomplemented
186C2×C61C2×#44211yescharacteristic
187D61—82no—
188C2×#135—611no—
189C22×Q16C2×D6111yescharacteristic
190C2×#131—1221no—
191C2×C4×Q8—1221no—
192#510—614no—
193#510—614no—
194C2×Q32—612no—
195C2×SD32—612no—
196C2×M32—611no—
197C2×M32C2×D6111yescharacteristic
198#444—614no—
199#444—1222no—
200#441—614no—
201#441—1222no—
202C2×#108C2×D6111yescharacteristic
203C2×#106—611no—
204C2×#104—1221no—
205C2×#103—1221no—
206C2×#97—611no—
207#365—614no—
208#362C2×D6114yescomplemented
209#360—614no—
210#347—614no—
211C61C2×#218011yescharacteristic, complemented, Sylow
212C2×#41—1221no—
213C22×Q8—21no—
214#135—612no—
215#135—612no—
216#135—1221no—
217#135—1221no—
218C2×Q16—21no—
219C2×Q16—21no—
220C2×Q16—21no—
221C2×Q16—611no—
222C2×Q16C4×D6112yes—
223C2×Q16C4×D6112yes—
224C2×Q16C22×D6112yes—
225C2×SD16—1221no—
226C2×D8—611no—
227#131—1224no—
228#131—2442no—
229C2×M16—21no—
230C2×M16—2441no—
231C22×C8—611no—
232C22×C8—2441no—
233C22×C8C22×D6111yescharacteristic
234C4×Q8—1224no—
235C4×Q8—2442no—
236C2×C4⋊C4—1221no—
237C2×C4⋊C4—2441no—
238C2×C42—611no—
239C2×C42—2441no—
240Q32—618no—
241SD32—618no—
242M32—21no—
243M32—612no—
244M32—612no—
245M32C22×D6112yes—
246C2×C16—21no—
247C2×C16—612no—
248#108—21no—
249#108C22×D6112yes—
250#106—612no—
251#106—1221no—
252#104—1224no—
253#103—1224no—
254#97—612no—
255#97—612no—
256#41—1222no—
257#41—1222no—
258#41—2441no—
259#41—2441no—
260C2×Q8—22no—
261C2×Q8—22no—
262C2×Q8—22no—
263C2×Q8—41no—
264C2×Q8—41no—
265C2×Q8—41no—
266C2×Q8—1221no—
267C2×D4—1221no—
268C2×D4—2441no—
269C22×C4—41no—
270C22×C4—1221no—
271C22×C4—2441no—
272C22×C4—2441no—
273C22×C4D4×D6111yescharacteristic
274Q16—22no—
275Q16—22no—
276Q16—22no—
277Q16—612no—
278Q16—1221no—
279Q16C2×C4×D6114yes—
280SD16—1222no—
281SD16—1222no—
282D8—612no—
283D8—1221no—
284M16—22no—
285M16—41no—
286M16—2444no—
287C2×C8—41no—
288C2×C8—612no—
289C2×C8—1221no—
290C2×C8—1221no—
291C2×C8—2444no—
292C2×C8C2×C4×D6111yescharacteristic
293C2×C8C2×C4×D6111yescharacteristic
294C2×C8D4×D6111yescharacteristic
295C2×C8#1175822411yescharacteristic
296C2×C8#1175822411yescharacteristic
297C2×C8C23×D6111yescharacteristic
298C4⋊C4—1222no—
299C4⋊C4—2444no—
300C4⋊C4—2441no—
301C42—612no—
302C42—1221no—
303C42—2444no—
304C16—22no—
305C16—614no—
306C23—2441no—
307C23#1451980411yescharacteristic
308Q8—24no—
309Q8—42no—
310Q8—42no—
311Q8—42no—
312Q8—1222no—
313Q8—2441no—
314D4—1222no—
315D4—2442no—
316D4—2442no—
317D4—2441no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—1222no—
322C2×C4—4882no—
323C2×C4—2442no—
324C2×C4—2442no—
325C2×C4—2441no—
326C2×C4—2442no—
327C2×C4—2442no—
328C2×C4#1451973711yescharacteristic
329C2×C4#1451973711yescharacteristic
330C2×C4#1451980111yescharacteristic
331C2×C4#1451980111yescharacteristic
332C2×C4#1451980411yescharacteristic
333C2×C4C2×D4×D6111yescharacteristic
334C8—42no—
335C8—1222no—
336C8#1451973711yescharacteristic
337C8#1451973711yescharacteristic
338C8C22×C4×D6111yescharacteristic
339C8C2×#1175822411yescharacteristic
340C22—22no—
341C22—4882no—
342C22—2442no—
343C22#1683987111yescharacteristic
344C22#1683987111yescharacteristic
345C22C2×#1451980411yescharacteristic
346C4—44no—
347C4—4882no—
348C4—2442no—
349C4—2442no—
350C4#1683987111yescharacteristic
351C4#1683987111yescharacteristic
352C4C2×#1451973711yescharacteristic
353C4C2×#1451980111yescharacteristic
354C2—21no—
355C2—21no—
356C2—4882no—
357C2#2144771312yesdirect product factor
358C2C2×#1683987111yescharacteristic
subgroupG/H
centerC22#16839871
commutatorC8×C61C23×C4
FrattiniC2×C8C23×D61
FittingC2×C61×#362C2
socleC22×C61#442
prime radicalC2×#14519799C22
cosocleC2×C8×C61C24
hypercenterC2×#362D61
hypocenterC61C2×#2180
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#362

Complements

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

NH ≅ G/Ntype
3. C2×#16839869C2semidirect
4. #21447713C2direct (N × H)
5. C2×#16839586C2semidirect
7. C2×#16839539C2semidirect
8. C2×C61×#362C2semidirect
12. #16840203C4semidirect
14. C2×#14519723C4semidirect
15. C2×#14519720C4semidirect
20. #16839869C22semidirect
25. #16839586C22semidirect
27. #16839539C22semidirect
31. C61×#362C22semidirect
51. #14519723C2×C4semidirect
52. #14519720C2×C4semidirect
180. C2×#362D61semidirect
185. C2×C61#2180semidirect
208. #362C2×D61semidirect
211. C61C2×#2180semidirect
357. C2#21447713direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402032
C2×#168398832
C2×#168398692
#214477132
C2×#168395862
C2×#168395732
C2×#168395392
C2×C61×#3622
C2×#218061