Finite Group Databasebeta

← C2×#21447937 #29834568

Subgroups — C2×#21447937 #29834568

Order 15616.

678 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519718C211yesmaximal, characteristic, complemented
2C2×#16840179C211yesmaximal, characteristic, complemented
3C2×#16840032C211yesmaximal, characteristic, complemented
4#21447937C218yesmaximal, direct product factor
5C2×#16839591C211yesmaximal, characteristic, complemented
6C2×#16839575C211yesmaximal, characteristic, complemented
7C2×#16839574C211yesmaximal, characteristic, complemented
8C2×C61×#472C211yesmaximal, characteristic, complemented
9C2×#14519802—21no—
10C22×D488C2211yescharacteristic
11C2×#14519718—21no—
12C2×#14519718—21no—
13C2×#14519718—22no—
14C2×#14519718C2214yescomplemented
15#16840179—22no—
16#16840179C2214yescomplemented
17C2×#14519717—21no—
18C2×#14519717C2211yescharacteristic
19C22×#11758185—21no—
20C22×#11758185C2211yescharacteristic
21#16840032—22no—
22#16840032C2214yescomplemented
23C2×#14519713C2211yescharacteristic
24C2×#14519693—21no—
25#16839591C2214yescomplemented
26#16839575C2214yescomplemented
27#16839574C2214yescomplemented
28C2×AGL(1,ℤ/8)×C61—21no—
29C22×D8×C61C2211yescharacteristic
30C2×#131×C61C2211yescharacteristic
31C61×#472—22no—
32C61×#472C2214yescomplemented
33C2×#108×C61C2211yescharacteristic
34C2×#100×C61—21no—
35C22×D244—21no—
36#14519802—24no—
37#14519802—42no—
38C2×#11758201—41no—
39C2×D488—21no—
40C2×D488—21no—
41C2×D488—21no—
42C2×D488—21no—
43C2×D488—21no—
44C2×D488C2312yes—
45C2×#11758199—41no—
46C2×#11758194—21no—
47#14519718—24no—
48#14519718—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#14519693—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—
86C23×D61—41no—
87#41×C61—21no—
88#41×C61—21no—
89#41×C61D812yes—
90#41×C61C2×D412yes—
91C2×Q8×C61D811yescharacteristic
92C2×D4×C61—21no—
93C2×D4×C61—22no—
94C2×D4×C61—41no—
95C2×D4×C61—41no—
96C2×D4×C61—41no—
97C2×D4×C61—41no—
98C2×D4×C61—41no—
99C2×D4×C61D811yescharacteristic
100C22×C4×C61—21no—
101C22×C4×C61C2×D411yescharacteristic
102C2×D244—22no—
103C2×D244—41no—
104C2×D244—41no—
105C2×D244—41no—
106C2×D244—41no—
107C2×D244—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#11758201—44no—
131#11758199—44no—
132#11758194—22no—
133#11758194—41no—
134C2×#92418—41no—
135D488—22no—
136D488—22no—
137D488—41no—
138D488—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
148C22×D61—42no—
149C22×D61—81no—
150C22×D61—81no—
151C22×D61—162no—
152Q8×C61—21no—
153Q8×C61C2×D812yes—
154D4×C61—22no—
155D4×C61—22no—
156D4×C61—21no—
157D4×C61—42no—
158D4×C61—42no—
159D4×C61—81no—
160D4×C61—81no—
161D4×C61C2×D812yes—
162C2×C4×C61—21no—
163C2×C4×C61—22no—
164C2×C4×C61—22no—
165C2×C4×C61#12111yescharacteristic
166C2×C4×C61#12111yescharacteristic
167C2×C4×C61C2×D811yescharacteristic
168C2×C4×C61C2×D811yescharacteristic
169C2×C4×C61#13511yescharacteristic
170C2×C4×C61C22×D411yescharacteristic
171D244—42no—
172D244—42no—
173D244—81no—
174D244—81no—
175C8×C61—22no—
176C8×C61—42no—
177C8×C61#12111yescharacteristic
178C8×C61#12111yescharacteristic
179C8×C61C22×D411yescharacteristic
180C8×C61C2×#4111yescharacteristic
181#92418—42no—
182C2×#2221—611nomaximal, Sylow
183C22×C61—22no—
184C22×C61—22no—
185C22×C61—42no—
186C22×C61—82no—
187C22×C61—162no—
188C22×C61—162no—
189C22×C61—162no—
190C22×C61#46611yescharacteristic
191C22×C61#46611yescharacteristic
192C22×C61C2×#13511yescharacteristic
193C2×D61—82no—
194C2×D61—162no—
195C2×D61—162no—
196C2×D61—162no—
197C4×C61—22no—
198C4×C61#46611yescharacteristic
199C4×C61#46611yescharacteristic
200C4×C61C2×#12111yescharacteristic
201C4×C61C22×D811yescharacteristic
202C22×D16—611no—
203C2×#504—611no—
204C2×#472—611no—
205C2×#472D6111yescharacteristic, complemented
206#2221—618no—
207C2×#368—611no—
208C2×#361—611no—
209C2×#361—611no—
210C2×C61—21no—
211C2×C61—21no—
212C2×C61—42no—
213C2×C61—162no—
214C2×C61#222112yescomplemented
215C2×C61C2×#46611yescharacteristic
216D61—162no—
217C2×AGL(1,ℤ/8)—21no—
218C2×AGL(1,ℤ/8)—1221no—
219C22×D8—611no—
220C22×D8C2×D6111yescharacteristic
221C2×#131C2×D6111yescharacteristic
222C2×D16—614no—
223C2×D16—1221no—
224C2×D16—1221no—
225C2×D16—1222no—
226#504—614no—
227#504—1222no—
228C2×M32—611no—
229C2×M32—1221no—
230C22×C16—611no—
231C22×C16—1221no—
232#472—22no—
233#472—614no—
234#472—1222no—
235#472C2×D6114yescomplemented
236C2×#108—611no—
237C2×#108C2×D6111yescharacteristic
238C2×#100—21no—
239C2×#100—1221no—
240#368—614no—
241#361—614no—
242#361—614no—
243C61C2×#222111yescharacteristic, complemented, Sylow
244C2×#41C22⋊D6111yescharacteristic
245C22×D4—21no—
246C22×D4—1221no—
247AGL(1,ℤ/8)—24no—
248AGL(1,ℤ/8)—42no—
249AGL(1,ℤ/8)—1224no—
250AGL(1,ℤ/8)—2442no—
251C2×SD16—41no—
252C2×SD16—2441no—
253C2×D8—21no—
254C2×D8—21no—
255C2×D8—21no—
256C2×D8—21no—
257C2×D8—21no—
258C2×D8—41no—
259C2×D8—612no—
260C2×D8—1221no—
261C2×D8—1221no—
262C2×D8—1221no—
263C2×D8—1221no—
264C2×D8—1221no—
265C2×D8—2441no—
266C2×D8C22×D6112yes—
267#131—21no—
268#131—21no—
269#131C22⋊D6112yes—
270#131C22×D6112yes—
271C2×M16—21no—
272C2×M16—21no—
273C2×M16—1221no—
274C2×M16C22⋊D6111yescharacteristic
275C22×C8—21no—
276C22×C8C22×D6111yescharacteristic
277D16—1224no—
278D16—1224no—
279M32—612no—
280M32—1224no—
281M32—1221no—
282C2×C16—611no—
283C2×C16—611no—
284C2×C16—612no—
285C2×C16—612no—
286C2×C16—1224no—
287C2×C16—1221no—
288#108—21no—
289#108—612no—
290#108—1221no—
291#108C22×D6112yes—
292#100—24no—
293#100—1224no—
294C24—41no—
295C24—2441no—
296#41—21no—
297#41—21no—
298#41#1175819912yes—
299#41C2×C22⋊D6112yes—
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—1222no—
309C2×D4—2441no—
310C2×D4—2441no—
311C2×D4—2441no—
312C2×D4—2441no—
313C2×D4—2441no—
314C2×D4#1175819911yescharacteristic
315C22×C4—21no—
316C22×C4C2×C22⋊D6111yescharacteristic
317SD16—44no—
318SD16—2444no—
319D8—22no—
320D8—22no—
321D8—44no—
322D8—41no—
323D8—41no—
324D8—1222no—
325D8—1222no—
326D8—2444no—
327D8—2441no—
328D8—2441no—
329M16—21no—
330M16—22no—
331M16—22no—
332M16—22no—
333M16—41no—
334M16—1222no—
335M16—2441no—
336M16C2×C22⋊D6112yes—
337C2×C8—21no—
338C2×C8—22no—
339C2×C8—22no—
340C2×C8—41no—
341C2×C8—2441no—
342C2×C8D4×D6111yescharacteristic
343C2×C8D4×D6111yescharacteristic
344C2×C8#1175822411yescharacteristic
345C2×C8#1175822411yescharacteristic
346C2×C8C2×C22⋊D6111yescharacteristic
347C2×C8C23×D6111yescharacteristic
348C16—612no—
349C16—612no—
350C16—1222no—
351C23—21no—
352C23—42no—
353C23—81no—
354C23—81no—
355C23—162no—
356C23—9762no—
357C23—4881no—
358C23—4881no—
359C23—2442no—
360C23#1451979711yescharacteristic
361Q8—21no—
362Q8C2×#1175819912yes—
363D4—22no—
364D4—22no—
365D4—21no—
366D4—42no—
367D4—42no—
368D4—81no—
369D4—81no—
370D4—4881no—
371D4—4881no—
372D4—2442no—
373D4—2442no—
374D4C2×#1175819912yes—
375C2×C4—21no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4#1451974911yescharacteristic
379C2×C4#1451974911yescharacteristic
380C2×C4C2×#1175819911yescharacteristic
381C2×C4C2×#1175819911yescharacteristic
382C2×C4#1451979711yescharacteristic
383C2×C4C22×C22⋊D6111yescharacteristic
384C8—22no—
385C8—42no—
386C8—2442no—
387C8#1451974911yescharacteristic
388C8#1451974911yescharacteristic
389C8C2×D4×D6111yescharacteristic
390C8C2×#1175822411yescharacteristic
391C22—22no—
392C22—22no—
393C22—42no—
394C22—82no—
395C22—162no—
396C22—162no—
397C22—162no—
398C22—9762no—
399C22—9762no—
400C22—9762no—
401C22—4882no—
402C22#1683999611yescharacteristic
403C22#1683999611yescharacteristic
404C22C2×#1451979711yescharacteristic
405C4—22no—
406C4#1683999611yescharacteristic
407C4#1683999611yescharacteristic
408C4C2×#1451974911yescharacteristic
409C4C22×#1175819911yescharacteristic
410C2—21no—
411C2—21no—
412C2—42no—
413C2—162no—
414C2—9762no—
415C2#2144793712yesdirect product factor
416C2C2×#1683999611yescharacteristic
subgroupG/H
centerC22#16839996
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC2×C61×#472C2
socleC22×C61#466
hypercenterC2×#472D61
hypocenterC61C2×#2221
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×#14519718C2semidirect
2. C2×#16840179C2semidirect
3. C2×#16840032C2semidirect
4. #21447937C2direct (N × H)
5. C2×#16839591C2semidirect
6. C2×#16839575C2semidirect
7. C2×#16839574C2semidirect
8. C2×C61×#472C2semidirect
14. C2×#14519718C22semidirect
16. #16840179C22semidirect
22. #16840032C22semidirect
25. #16839591C22semidirect
26. #16839575C22semidirect
27. #16839574C22semidirect
32. C61×#472C22semidirect
205. C2×#472D61semidirect
214. C2×C61#2221semidirect
235. #472C2×D61semidirect
243. C61C2×#2221semidirect
415. C2#21447937direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197182
C2×#168401792
C2×#168400322
#214479372
C2×#168395912
C2×#168395752
C2×#168395742
C2×C61×#4722
C2×#222161