Finite Group Databasebeta

← C2×#21447947 #29834580

Subgroups — C2×#21447947 #29834580

Order 15616.

658 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519721C211yesmaximal, characteristic, complemented
2C2×#16840179C211yesmaximal, characteristic, complemented
3C2×#16840037C211yesmaximal, characteristic, complemented
4#21447947C218yesmaximal, direct product factor
5C2×#16839591C211yesmaximal, characteristic, complemented
6C2×#16839577C211yesmaximal, characteristic, complemented
7C2×#16839575C211yesmaximal, characteristic, complemented
8C2×C61×#472C211yesmaximal, characteristic
9C2×#14519807—21no—
10C22×Dic244C2211yescharacteristic
11C2×#14519721—21no—
12C2×#14519721—21no—
13C2×#14519721—22no—
14C2×#14519721C2214yescomplemented
15#16840179—22no—
16#16840179C2214yescomplemented
17C2×#14519717—21no—
18C2×#14519717C2211yescharacteristic
19C22×#11758185—21no—
20C22×#11758185C2211yescharacteristic
21#16840037—22no—
22#16840037C2214yescomplemented
23C2×#14519713C2211yescharacteristic
24C2×#14519695—21no—
25#16839591C2214yescomplemented
26#16839577C2214yescomplemented
27#16839575C2214yescomplemented
28C2×AGL(1,ℤ/8)×C61—21no—
29C22×D8×C61C2211yescharacteristic
30C2×#131×C61C2211yescharacteristic
31C61×#472—22no—
32C61×#472C2214yes—
33C2×#108×C61C2211yescharacteristic
34C2×#100×C61—21no—
35C22×Dic122—21no—
36#14519807—24no—
37#14519807—42no—
38C2×Dic244—21no—
39C2×Dic244—21no—
40C2×Dic244—21no—
41C2×Dic244—21no—
42C2×Dic244—21no—
43C2×Dic244C2312yes—
44C2×#11758202—41no—
45C2×#11758200—41no—
46C2×#11758194—21no—
47#14519721—24no—
48#14519721—24no—
49#14519717—21no—
50#14519717—24no—
51#14519717C2312yes—
52C2×#11758185—21no—
53C2×#11758185—24no—
54C2×#11758185D411yescharacteristic
55C2×#11758185D411yescharacteristic
56C2×#11758185D412yes—
57C2×#11758185C2312yes—
58#14519713—21no—
59#14519713C2312yes—
60#14519695—24no—
61C2×#41×C61D411yescharacteristic
62C22×D4×C61—21no—
63AGL(1,ℤ/8)×C61—24no—
64AGL(1,ℤ/8)×C61—42no—
65C2×SD16×C61—41no—
66C2×D8×C61—21no—
67C2×D8×C61—21no—
68C2×D8×C61—21no—
69C2×D8×C61—21no—
70C2×D8×C61—21no—
71C2×D8×C61—41no—
72C2×D8×C61C2312yes—
73#131×C61—21no—
74#131×C61—21no—
75#131×C61D412yes—
76#131×C61C2312yes—
77C2×M16×C61—21no—
78C2×M16×C61—21no—
79C2×M16×C61D411yescharacteristic
80C22×C8×C61—21no—
81C22×C8×C61C2311yescharacteristic
82#108×C61—21no—
83#108×C61C2312yes—
84#100×C61—24no—
85C24×C61—41no—
86#41×C61—21no—
87#41×C61—21no—
88#41×C61D812yes—
89#41×C61C2×D412yes—
90C2×Q8×C61D811yescharacteristic
91C2×D4×C61—21no—
92C2×D4×C61—22no—
93C2×D4×C61—41no—
94C2×D4×C61—41no—
95C2×D4×C61—41no—
96C2×D4×C61—41no—
97C2×D4×C61—41no—
98C2×D4×C61D811yescharacteristic
99C22×C4×C61—21no—
100C22×C4×C61C2×D411yescharacteristic
101C22×Dic61—41no—
102C2×Dic122—22no—
103C2×Dic122—41no—
104C2×Dic122—41no—
105C2×Dic122—41no—
106C2×Dic122—41no—
107C2×Dic122—41no—
108SD16×C61—44no—
109D8×C61—22no—
110D8×C61—22no—
111D8×C61—44no—
112D8×C61—41no—
113D8×C61—41no—
114M16×C61—21no—
115M16×C61—22no—
116M16×C61—22no—
117M16×C61—22no—
118M16×C61—41no—
119M16×C61C2×D412yes—
120C2×C8×C61—21no—
121C2×C8×C61—22no—
122C2×C8×C61—22no—
123C2×C8×C61—41no—
124C2×C8×C61C2×D411yescharacteristic
125C2×C8×C61C2×D411yescharacteristic
126C2×C8×C61C2×D411yescharacteristic
127C2×C8×C61#4111yescharacteristic
128C2×C8×C61#4111yescharacteristic
129C2×C8×C61C2411yescharacteristic
130#11758202—44no—
131#11758200—44no—
132#11758194—22no—
133#11758194—41no—
134C2×#92418—41no—
135Dic244—22no—
136Dic244—22no—
137Dic244—41no—
138Dic244—41no—
139#11758185—22no—
140#11758185C2×D412yes—
141#11758185C2×D412yes—
142C23×C61—21no—
143C23×C61—42no—
144C23×C61—81no—
145C23×C61—81no—
146C23×C61—162no—
147C23×C61#13511yescharacteristic
148Q8×C61—21no—
149Q8×C61C2×D812yes—
150D4×C61—22no—
151D4×C61—22no—
152D4×C61—21no—
153D4×C61—42no—
154D4×C61—42no—
155D4×C61—81no—
156D4×C61—81no—
157D4×C61C2×D812yes—
158C2×C4×C61—21no—
159C2×C4×C61—22no—
160C2×C4×C61—22no—
161C2×C4×C61#12111yescharacteristic
162C2×C4×C61#12111yescharacteristic
163C2×C4×C61C2×D811yescharacteristic
164C2×C4×C61C2×D811yescharacteristic
165C2×C4×C61#13511yescharacteristic
166C2×C4×C61C22×D411yescharacteristic
167C2×Dic61—42no—
168C2×Dic61—81no—
169C2×Dic61—81no—
170Dic122—42no—
171Dic122—42no—
172Dic122—81no—
173Dic122—81no—
174C8×C61—22no—
175C8×C61—42no—
176C8×C61#12111yescharacteristic
177C8×C61#12111yescharacteristic
178C8×C61C22×D411yescharacteristic
179C8×C61C2×#4111yescharacteristic
180#92418—42no—
181C2×#2223—611nomaximal, Sylow
182C22×C61—22no—
183C22×C61—22no—
184C22×C61—42no—
185C22×C61—82no—
186C22×C61—162no—
187C22×C61—162no—
188C22×C61—162no—
189C22×C61#46611yescharacteristic
190C22×C61#46611yescharacteristic
191C22×C61C2×#13511yescharacteristic
192C4×C61—22no—
193C4×C61#46611yescharacteristic
194C4×C61#46611yescharacteristic
195C4×C61C2×#12111yescharacteristic
196C4×C61C22×D811yescharacteristic
197Dic61—82no—
198C22×SD32—611no—
199C2×#504—611no—
200C2×#473—611no—
201C2×#472D6111yescharacteristic
202#2223—618no—
203C2×#368—611no—
204C2×#362—611no—
205C2×#361—611no—
206C2×C61—21no—
207C2×C61—21no—
208C2×C61—42no—
209C2×C61—162no—
210C2×C61#222312yescomplemented
211C2×C61C2×#46611yescharacteristic
212C2×#137—1221no—
213C2×AGL(1,ℤ/8)—21no—
214C22×Q16—611no—
215C22×D8C2×D6111yescharacteristic
216C2×#131C2×D6111yescharacteristic
217C2×SD32—614no—
218C2×SD32—1221no—
219C2×SD32—1221no—
220C2×SD32—1222no—
221#504—614no—
222#504—1222no—
223C2×M32—611no—
224C2×M32—1221no—
225C22×C16—611no—
226C22×C16—1221no—
227#473—614no—
228#473—1222no—
229#472—22no—
230#472C2×D6114yes—
231C2×#108—611no—
232C2×#108C2×D6111yescharacteristic
233C2×#101—1221no—
234C2×#100—21no—
235#368—614no—
236#362—614no—
237#361—614no—
238C61C2×#222311yescharacteristic, complemented, Sylow
239C2×#41C22⋊D6111yescharacteristic
240C22×Q8—1221no—
241C22×D4—21no—
242#137—1224no—
243#137—2442no—
244AGL(1,ℤ/8)—24no—
245AGL(1,ℤ/8)—42no—
246C2×Q16—612no—
247C2×Q16—1221no—
248C2×Q16—1221no—
249C2×Q16—1221no—
250C2×Q16—1221no—
251C2×Q16—1221no—
252C2×Q16—2441no—
253C2×SD16—41no—
254C2×SD16—2441no—
255C2×D8—21no—
256C2×D8—21no—
257C2×D8—21no—
258C2×D8—21no—
259C2×D8—21no—
260C2×D8—41no—
261C2×D8C22×D6112yes—
262#131—21no—
263#131—21no—
264#131C22⋊D6112yes—
265#131C22×D6112yes—
266C2×M16—21no—
267C2×M16—21no—
268C2×M16—1221no—
269C2×M16C22⋊D6111yescharacteristic
270C22×C8—21no—
271C22×C8C22×D6111yescharacteristic
272SD32—1224no—
273SD32—1224no—
274M32—612no—
275M32—1224no—
276M32—1221no—
277C2×C16—611no—
278C2×C16—611no—
279C2×C16—612no—
280C2×C16—612no—
281C2×C16—1224no—
282C2×C16—1221no—
283#108—21no—
284#108—612no—
285#108—1221no—
286#108C22×D6112yes—
287#101—1224no—
288#100—24no—
289C24—41no—
290#41—21no—
291#41—21no—
292#41#1175819912yes—
293#41C2×C22⋊D6112yes—
294C2×Q8—1222no—
295C2×Q8—2441no—
296C2×Q8—2441no—
297C2×Q8—2441no—
298C2×Q8—2441no—
299C2×Q8—2441no—
300C2×Q8#1175819911yescharacteristic
301C2×D4—21no—
302C2×D4—22no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4#1175819911yescharacteristic
309C22×C4—21no—
310C22×C4—2441no—
311C22×C4C2×C22⋊D6111yescharacteristic
312Q16—1222no—
313Q16—1222no—
314Q16—2444no—
315Q16—2441no—
316Q16—2441no—
317SD16—44no—
318SD16—2444no—
319D8—22no—
320D8—22no—
321D8—44no—
322D8—41no—
323D8—41no—
324M16—21no—
325M16—22no—
326M16—22no—
327M16—22no—
328M16—41no—
329M16—1222no—
330M16—2441no—
331M16C2×C22⋊D6112yes—
332C2×C8—21no—
333C2×C8—22no—
334C2×C8—22no—
335C2×C8—41no—
336C2×C8—2441no—
337C2×C8D4×D6111yescharacteristic
338C2×C8D4×D6111yescharacteristic
339C2×C8#1175822411yescharacteristic
340C2×C8#1175822411yescharacteristic
341C2×C8C2×C22⋊D6111yescharacteristic
342C2×C8C23×D6111yescharacteristic
343C16—612no—
344C16—612no—
345C16—1222no—
346C23—21no—
347C23—42no—
348C23—81no—
349C23—81no—
350C23—162no—
351C23#1451979711yescharacteristic
352Q8—21no—
353Q8—4881no—
354Q8—4881no—
355Q8—2442no—
356Q8—2442no—
357Q8C2×#1175819912yes—
358D4—22no—
359D4—22no—
360D4—21no—
361D4—42no—
362D4—42no—
363D4—81no—
364D4—81no—
365D4C2×#1175819912yes—
366C2×C4—21no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—4881no—
370C2×C4—4881no—
371C2×C4—2442no—
372C2×C4#1451974911yescharacteristic
373C2×C4#1451974911yescharacteristic
374C2×C4C2×#1175819911yescharacteristic
375C2×C4C2×#1175819911yescharacteristic
376C2×C4#1451979711yescharacteristic
377C2×C4C22×C22⋊D6111yescharacteristic
378C8—22no—
379C8—42no—
380C8—2442no—
381C8#1451974911yescharacteristic
382C8#1451974911yescharacteristic
383C8C2×D4×D6111yescharacteristic
384C8C2×#1175822411yescharacteristic
385C22—22no—
386C22—22no—
387C22—42no—
388C22—82no—
389C22—162no—
390C22—162no—
391C22—162no—
392C22#1683999611yescharacteristic
393C22#1683999611yescharacteristic
394C22C2×#1451979711yescharacteristic
395C4—22no—
396C4—4882no—
397C4#1683999611yescharacteristic
398C4#1683999611yescharacteristic
399C4C2×#1451974911yescharacteristic
400C4C22×#1175819911yescharacteristic
401C2—21no—
402C2—21no—
403C2—42no—
404C2—162no—
405C2#2144794712yesdirect product factor
406C2C2×#1683999611yescharacteristic
subgroupG/H
centerC22#16839996
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
Fitting, prime radicalC2×C61×#472C2
socleC22×C61#466
hypercenterC2×#472D61
hypocenterC61C2×#2223
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131 ◁ C2×#472

Complements

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

NH ≅ G/Ntype
1. C22×#14519721C2semidirect
2. C2×#16840179C2semidirect
3. C2×#16840037C2semidirect
4. #21447947C2direct (N × H)
5. C2×#16839591C2semidirect
6. C2×#16839577C2semidirect
7. C2×#16839575C2semidirect
14. C2×#14519721C22semidirect
16. #16840179C22semidirect
22. #16840037C22semidirect
25. #16839591C22semidirect
26. #16839577C22semidirect
27. #16839575C22semidirect
210. C2×C61#2223semidirect
238. C61C2×#2223semidirect
405. C2#21447947direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197212
C2×#168401792
C2×#168400372
#214479472
C2×#168395912
C2×#168395772
C2×#168395752
C2×C61×#4722
C2×#222361