Finite Group Databasebeta

← C2×#21447948 #29834581

Subgroups — C2×#21447948 #29834581

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×#16840180C211yesmaximal, characteristic, complemented
3C2×#16840038C211yesmaximal, characteristic, complemented
4C2×#16840029C211yesmaximal, characteristic
5#21447948C218yesmaximal, direct product factor
6C2×#16839591C211yesmaximal, characteristic, complemented
7C2×#16839579C211yesmaximal, characteristic, complemented
8C2×C61×#361C211yesmaximal, characteristic, complemented
9C2×#14519810—21no—
10C2×#14519803—21no—
11C22×Dic244C2211yescharacteristic
12C2×#14519783C2211yescharacteristic
13C2×#14519721—21no—
14C2×#14519721—21no—
15C2×#14519721—22no—
16C2×#14519721C2214yescomplemented
17#16840180—22no—
18#16840180C2214yescomplemented
19C2×#14519716—21no—
20C22×#11758185C2211yescharacteristic
21C2×C16×D61—21no—
22#16840038—22no—
23#16840038C2214yescomplemented
24#16840029—22no—
25#16840029C2214yes—
26C2×#14519713C2211yescharacteristic
27C2×#14519695—21no—
28C2×#14519694—21no—
29#16839591C2214yescomplemented
30#16839579C2214yescomplemented
31C22×D8×C61C2211yescharacteristic
32C2×M32×C61C2211yescharacteristic
33C2×#108×C61C2211yescharacteristic
34C61×#361C2214yescomplemented
35C2×#11758222D411yescharacteristic
36C22×Dic122—21no—
37#14519810—24no—
38#14519810—42no—
39#14519803—24no—
40#14519803—42no—
41C2×Dic244—21no—
42C2×Dic244—21no—
43C2×Dic244—21no—
44C2×Dic244—21no—
45C2×Dic244—21no—
46C2×Dic244—41no—
47C2×Dic244C2312yes—
48C2×#11758190—41no—
49C2×#11758200—41no—
50C2×#11758199—41no—
51#14519783—21no—
52#14519783—21no—
53#14519783D412yes—
54#14519783C2312yes—
55C2×#11758194—21no—
56C2×#11758194D411yescharacteristic
57C2×#11758189—21no—
58C2×C8×D61—21no—
59#14519721—24no—
60#14519721—24no—
61#14519716—24no—
62C2×#11758185D411yescharacteristic
63C2×#11758185D411yescharacteristic
64C2×#11758185D412yes—
65C2×#11758185C2312yes—
66C16×D61—24no—
67#14519713—21no—
68#14519713C2312yes—
69#14519695—24no—
70#14519694—24no—
71C22×D4×C61—21no—
72C2×D8×C61—21no—
73C2×D8×C61—21no—
74C2×D8×C61—21no—
75C2×D8×C61—21no—
76C2×D8×C61—21no—
77C2×D8×C61C2312yes—
78C2×M16×C61—21no—
79C22×C8×C61C2311yescharacteristic
80M32×C61—21no—
81M32×C61C2312yes—
82C2×C16×C61—21no—
83#108×C61—21no—
84#108×C61C2312yes—
85C24×C61—41no—
86C2×D4×C61—22no—
87C2×D4×C61—41no—
88C2×D4×C61—41no—
89C2×D4×C61—41no—
90C2×D4×C61—41no—
91C2×D4×C61—41no—
92C22×C4×C61C2×D411yescharacteristic
93C2×C22⋊D61—21no—
94C22×Dic61—41no—
95#11758222—21no—
96#11758222—21no—
97#11758222D812yes—
98#11758222C2×D412yes—
99C2×D244D811yescharacteristic
100C2×C4×D61—21no—
101C2×Dic122—22no—
102C2×Dic122—41no—
103C2×Dic122—41no—
104C2×Dic122—41no—
105C2×Dic122—41no—
106C2×Dic122—41no—
107C2×Dic122D811yescharacteristic
108D8×C61—22no—
109D8×C61—22no—
110D8×C61—41no—
111D8×C61—41no—
112M16×C61—22no—
113M16×C61—41no—
114C2×C8×C61—41no—
115C2×C8×C61C2×D411yescharacteristic
116C2×C8×C61C2×D411yescharacteristic
117C2×C8×C61C2×D411yescharacteristic
118C2×C8×C61#4111yescharacteristic
119C2×C8×C61#4111yescharacteristic
120C2×C8×C61C2411yescharacteristic
121#11758200—44no—
122#11758199—44no—
123#11758194—21no—
124#11758194—22no—
125#11758194—41no—
126#11758194C2×D412yes—
127C2×#92418—21no—
128C2×#92418—41no—
129Dic244—22no—
130Dic244—22no—
131Dic244—44no—
132Dic244—41no—
133Dic244—41no—
134#11758190—44no—
135#11758189—22no—
136#11758189—22no—
137C8×D61—22no—
138C8×D61—22no—
139C16×C61—22no—
140#11758185C2×D412yes—
141#11758185C2×D412yes—
142C23×C61—42no—
143C23×C61—81no—
144C23×C61—81no—
145C23×C61—162no—
146C23×C61#13511yescharacteristic
147C22×D61—21no—
148D4×C61—42no—
149D4×C61—42no—
150D4×C61—81no—
151D4×C61—81no—
152C2×C4×C61#12111yescharacteristic
153C2×C4×C61#12111yescharacteristic
154C2×C4×C61C2×D811yescharacteristic
155C2×C4×C61C2×D811yescharacteristic
156C2×C4×C61#13511yescharacteristic
157C2×C4×C61C22×D411yescharacteristic
158C22⋊D61—22no—
159C22⋊D61—22no—
160C2×Dic61—21no—
161C2×Dic61—42no—
162C2×Dic61—81no—
163C2×Dic61—81no—
164D244—21no—
165D244C2×D812yes—
166C4×D61—22no—
167C4×D61—22no—
168Dic122—21no—
169Dic122—42no—
170Dic122—42no—
171Dic122—81no—
172Dic122—81no—
173Dic122C2×D812yes—
174C8×C61—42no—
175C8×C61#12111yescharacteristic
176C8×C61#12111yescharacteristic
177C8×C61C22×D411yescharacteristic
178C8×C61C2×#4111yescharacteristic
179#92418—22no—
180#92418—42no—
181C2×#2223—611nomaximal, Sylow
182C22×C61—22no—
183C22×C61—82no—
184C22×C61—162no—
185C22×C61—162no—
186C22×C61—162no—
187C22×C61#46611yescharacteristic
188C22×C61#46611yescharacteristic
189C22×C61C2×#13511yescharacteristic
190C2×D61—22no—
191C2×D61—42no—
192C4×C61#46611yescharacteristic
193C4×C61#46611yescharacteristic
194C4×C61C2×#12111yescharacteristic
195C4×C61C22×D811yescharacteristic
196Dic61—22no—
197Dic61—82no—
198C22×SD32—611no—
199C2×#504—611no—
200C2×#473—611no—
201C2×#472—611no—
202#2223—618no—
203C2×#368—611no—
204C2×#362—611no—
205C2×#361D6111yescharacteristic, complemented
206C2×C61—21no—
207C2×C61—21no—
208C2×C61—162no—
209C2×C61#222312yescomplemented
210C2×C61C2×#46611yescharacteristic
211D61—42no—
212C2×#137—1221no—
213C2×AGL(1,ℤ/8)—1221no—
214C22×Q16—611no—
215C22×D8C2×D6111yescharacteristic
216C2×#131—611no—
217C2×SD32—614no—
218C2×SD32—1221no—
219C2×SD32—1221no—
220C2×SD32—1222no—
221#504—614no—
222#504—1222no—
223C2×M32—1221no—
224C2×M32C2×D6111yescharacteristic
225C22×C16—611no—
226C22×C16—1221no—
227#473—614no—
228#473—1222no—
229#472—614no—
230#472—1222no—
231C2×#108—611no—
232C2×#108C2×D6111yescharacteristic
233C2×#101—1221no—
234C2×#100—1221no—
235#368—614no—
236#362—614no—
237#361C2×D6114yescomplemented
238C61C2×#222311yescharacteristic, complemented, Sylow
239C2×#41—611no—
240C22×Q8—1221no—
241C22×D4—21no—
242#137—1224no—
243#137—2442no—
244AGL(1,ℤ/8)—1224no—
245AGL(1,ℤ/8)—2442no—
246C2×Q16—612no—
247C2×Q16—1221no—
248C2×Q16—1221no—
249C2×Q16—1221no—
250C2×Q16—1221no—
251C2×Q16—1221no—
252C2×Q16—2441no—
253C2×SD16—2441no—
254C2×SD16—2441no—
255C2×D8—21no—
256C2×D8—21no—
257C2×D8—21no—
258C2×D8—21no—
259C2×D8—21no—
260C2×D8—2441no—
261C2×D8C22×D6112yes—
262#131—612no—
263#131—612no—
264#131—1221no—
265#131—1221no—
266C2×M16—21no—
267C2×M16—611no—
268C2×M16—1221no—
269C2×M16—1221no—
270C22×C8—1221no—
271C22×C8C22×D6111yescharacteristic
272SD32—1224no—
273SD32—1224no—
274M32—21no—
275M32—1224no—
276M32C22×D6112yes—
277C2×C16—21no—
278C2×C16—611no—
279C2×C16—611no—
280C2×C16—612no—
281C2×C16—612no—
282C2×C16—1224no—
283#108—21no—
284#108—612no—
285#108—1221no—
286#108C22×D6112yes—
287#101—1224no—
288#100—1224no—
289C24—41no—
290#41—612no—
291#41—612no—
292#41—1221no—
293#41—1221no—
294C2×Q8—611no—
295C2×Q8—1222no—
296C2×Q8—2441no—
297C2×Q8—2441no—
298C2×Q8—2441no—
299C2×Q8—2441no—
300C2×Q8—2441no—
301C2×D4—22no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—611no—
308C2×D4—1221no—
309C22×C4—1221no—
310C22×C4—2441no—
311C22×C4D4×D6111yescharacteristic
312Q16—1222no—
313Q16—1222no—
314Q16—2444no—
315Q16—2441no—
316Q16—2441no—
317SD16—2444no—
318SD16—2444no—
319D8—22no—
320D8—22no—
321D8—41no—
322D8—41no—
323D8—2444no—
324M16—22no—
325M16—41no—
326M16—612no—
327M16—1221no—
328M16—1222no—
329M16—1222no—
330M16—1222no—
331M16—2441no—
332C2×C8—41no—
333C2×C8—1221no—
334C2×C8—1222no—
335C2×C8—1222no—
336C2×C8—2441no—
337C2×C8#1175822211yescharacteristic
338C2×C8#1175822211yescharacteristic
339C2×C8D4×D6111yescharacteristic
340C2×C8D4×D6111yescharacteristic
341C2×C8D4×D6111yescharacteristic
342C2×C8C23×D6111yescharacteristic
343C16—22no—
344C16—612no—
345C16—612no—
346C23—42no—
347C23—81no—
348C23—81no—
349C23—162no—
350C23—1221no—
351C23#1451979811yescharacteristic
352Q8—612no—
353Q8—1221no—
354Q8—4881no—
355Q8—4881no—
356Q8—2442no—
357Q8—2442no—
358D4—42no—
359D4—42no—
360D4—81no—
361D4—81no—
362D4—612no—
363D4—1222no—
364D4—1222no—
365D4—1221no—
366C2×C4—1221no—
367C2×C4—1222no—
368C2×C4—1222no—
369C2×C4—4881no—
370C2×C4—4881no—
371C2×C4—2442no—
372C2×C4#1451975011yescharacteristic
373C2×C4#1451975011yescharacteristic
374C2×C4D8×D6111yescharacteristic
375C2×C4D8×D6111yescharacteristic
376C2×C4#1451979811yescharacteristic
377C2×C4C2×D4×D6111yescharacteristic
378C8—42no—
379C8—1222no—
380C8—2442no—
381C8#1451975011yescharacteristic
382C8#1451975011yescharacteristic
383C8C2×D4×D6111yescharacteristic
384C8C2×#1175822211yescharacteristic
385C22—22no—
386C22—82no—
387C22—162no—
388C22—162no—
389C22—162no—
390C22—1222no—
391C22—2442no—
392C22#1683999711yescharacteristic
393C22#1683999711yescharacteristic
394C22C2×#1451979811yescharacteristic
395C4—1222no—
396C4—4882no—
397C4#1683999711yescharacteristic
398C4#1683999711yescharacteristic
399C4C2×#1451975011yescharacteristic
400C4C2×D8×D6111yescharacteristic
401C2—21no—
402C2—21no—
403C2—162no—
404C2—2442no—
405C2#2144794812yesdirect product factor
406C2C2×#1683999711yescharacteristic
subgroupG/H
centerC22#16839997
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC2×C61×#361C2
socleC22×C61#466
prime radicalC2×#16840029C2
hypercenterC2×#361D61
hypocenterC61C2×#2223
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#361

Complements

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

NH ≅ G/Ntype
1. C22×#14519721C2semidirect
2. C2×#16840180C2semidirect
3. C2×#16840038C2semidirect
5. #21447948C2direct (N × H)
6. C2×#16839591C2semidirect
7. C2×#16839579C2semidirect
8. C2×C61×#361C2semidirect
16. C2×#14519721C22semidirect
18. #16840180C22semidirect
23. #16840038C22semidirect
29. #16839591C22semidirect
30. #16839579C22semidirect
34. C61×#361C22semidirect
205. C2×#361D61semidirect
209. C2×C61#2223semidirect
237. #361C2×D61semidirect
238. C61C2×#2223semidirect
405. C2#21447948direct (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×#168401802
C2×#168400382
C2×#168400292
#214479482
C2×#168395912
C2×#168395792
C2×C61×#3612
C2×#222361