Finite Group Databasebeta

← C2×#21447938 #29834569

Subgroups — C2×#21447938 #29834569

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×#16840180C211yesmaximal, characteristic, complemented
3C2×#16840033C211yesmaximal, characteristic, complemented
4C2×#16840029C211yesmaximal, characteristic, complemented
5#21447938C218yesmaximal, direct product factor
6C2×#16839591C211yesmaximal, characteristic, complemented
7C2×#16839576C211yesmaximal, characteristic, complemented
8C2×C61×#361C211yesmaximal, characteristic, complemented
9C2×#14519805—21no—
10C2×#14519803—21no—
11C22×D488C2211yescharacteristic
12C2×#14519783C2211yescharacteristic
13C2×#14519718—21no—
14C2×#14519718—21no—
15C2×#14519718—22no—
16C2×#14519718C2214yescomplemented
17#16840180—22no—
18#16840180C2214yescomplemented
19C2×#14519716—21no—
20C22×#11758185C2211yescharacteristic
21C2×C16×D61—21no—
22#16840033—22no—
23#16840033C2214yescomplemented
24#16840029—22no—
25#16840029C2214yescomplemented
26C2×#14519713C2211yescharacteristic
27C2×#14519694—21no—
28C2×#14519693—21no—
29#16839591C2214yescomplemented
30#16839576C2214yescomplemented
31C22×D8×C61C2211yescharacteristic
32C2×M32×C61C2211yescharacteristic
33C2×#108×C61C2211yescharacteristic
34C61×#361C2214yescomplemented
35C2×#11758222D411yescharacteristic
36C22×D244—21no—
37#14519805—24no—
38#14519805—42no—
39#14519803—24no—
40#14519803—42no—
41C2×#11758190—41no—
42C2×#11758200—41no—
43C2×D488—21no—
44C2×D488—21no—
45C2×D488—21no—
46C2×D488—21no—
47C2×D488—21no—
48C2×D488—41no—
49C2×D488C2312yes—
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#14519718—24no—
60#14519718—24no—
61#14519716—24no—
62C2×#11758185D411yescharacteristic
63C2×#11758185D411yescharacteristic
64C2×#11758185D412yes—
65C2×#11758185C2312yes—
66C16×D61—24no—
67#14519713—21no—
68#14519713C2312yes—
69#14519694—24no—
70#14519693—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—
86C23×D61—41no—
87C2×D4×C61—22no—
88C2×D4×C61—41no—
89C2×D4×C61—41no—
90C2×D4×C61—41no—
91C2×D4×C61—41no—
92C2×D4×C61—41no—
93C22×C4×C61C2×D411yescharacteristic
94C2×C22⋊D61—21no—
95#11758222—21no—
96#11758222—21no—
97#11758222D812yes—
98#11758222C2×D412yes—
99C2×D244—22no—
100C2×D244—41no—
101C2×D244—41no—
102C2×D244—41no—
103C2×D244—41no—
104C2×D244—41no—
105C2×D244D811yescharacteristic
106C2×C4×D61—21no—
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—
129D488—22no—
130D488—22no—
131D488—44no—
132D488—41no—
133D488—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—
148C22×D61—42no—
149C22×D61—81no—
150C22×D61—81no—
151C22×D61—162no—
152D4×C61—42no—
153D4×C61—42no—
154D4×C61—81no—
155D4×C61—81no—
156C2×C4×C61#12111yescharacteristic
157C2×C4×C61#12111yescharacteristic
158C2×C4×C61C2×D811yescharacteristic
159C2×C4×C61C2×D811yescharacteristic
160C2×C4×C61#13511yescharacteristic
161C2×C4×C61C22×D411yescharacteristic
162C22⋊D61—22no—
163C22⋊D61—22no—
164C2×Dic61—21no—
165D244—21no—
166D244—42no—
167D244—42no—
168D244—81no—
169D244—81no—
170D244C2×D812yes—
171C4×D61—22no—
172C4×D61—22no—
173Dic122—21no—
174Dic122C2×D812yes—
175C8×C61—42no—
176C8×C61#12111yescharacteristic
177C8×C61#12111yescharacteristic
178C8×C61C22×D411yescharacteristic
179C8×C61C2×#4111yescharacteristic
180#92418—22no—
181#92418—42no—
182C2×#2221—611nomaximal, Sylow
183C22×C61—22no—
184C22×C61—82no—
185C22×C61—162no—
186C22×C61—162no—
187C22×C61—162no—
188C22×C61#46611yescharacteristic
189C22×C61#46611yescharacteristic
190C22×C61C2×#13511yescharacteristic
191C2×D61—22no—
192C2×D61—42no—
193C2×D61—82no—
194C2×D61—162no—
195C2×D61—162no—
196C2×D61—162no—
197C4×C61#46611yescharacteristic
198C4×C61#46611yescharacteristic
199C4×C61C2×#12111yescharacteristic
200C4×C61C22×D811yescharacteristic
201Dic61—22no—
202C22×D16—611no—
203C2×#504—611no—
204C2×#472—611no—
205C2×#472—611no—
206#2221—618no—
207C2×#368—611no—
208C2×#361—611no—
209C2×#361D6111yescharacteristic, complemented
210C2×C61—21no—
211C2×C61—21no—
212C2×C61—162no—
213C2×C61#222112yescomplemented
214C2×C61C2×#46611yescharacteristic
215D61—42no—
216D61—162no—
217C2×AGL(1,ℤ/8)—1221no—
218C2×AGL(1,ℤ/8)—1221no—
219C22×D8—611no—
220C22×D8C2×D6111yescharacteristic
221C2×#131—611no—
222C2×D16—614no—
223C2×D16—1221no—
224C2×D16—1221no—
225C2×D16—1222no—
226#504—614no—
227#504—1222no—
228C2×M32—1221no—
229C2×M32C2×D6111yescharacteristic
230C22×C16—611no—
231C22×C16—1221no—
232#472—614no—
233#472—614no—
234#472—1222no—
235#472—1222no—
236C2×#108—611no—
237C2×#108C2×D6111yescharacteristic
238C2×#100—1221no—
239C2×#100—1221no—
240#368—614no—
241#361—614no—
242#361C2×D6114yescomplemented
243C61C2×#222111yescharacteristic, complemented, Sylow
244C2×#41—611no—
245C22×D4—21no—
246C22×D4—1221no—
247AGL(1,ℤ/8)—1224no—
248AGL(1,ℤ/8)—1224no—
249AGL(1,ℤ/8)—2442no—
250AGL(1,ℤ/8)—2442no—
251C2×SD16—2441no—
252C2×SD16—2441no—
253C2×D8—21no—
254C2×D8—21no—
255C2×D8—21no—
256C2×D8—21no—
257C2×D8—21no—
258C2×D8—612no—
259C2×D8—1221no—
260C2×D8—1221no—
261C2×D8—1221no—
262C2×D8—1221no—
263C2×D8—1221no—
264C2×D8—2441no—
265C2×D8—2441no—
266C2×D8C22×D6112yes—
267#131—612no—
268#131—612no—
269#131—1221no—
270#131—1221no—
271C2×M16—21no—
272C2×M16—611no—
273C2×M16—1221no—
274C2×M16—1221no—
275C22×C8—1221no—
276C22×C8C22×D6111yescharacteristic
277D16—1224no—
278D16—1224no—
279M32—21no—
280M32—1224no—
281M32C22×D6112yes—
282C2×C16—21no—
283C2×C16—611no—
284C2×C16—611no—
285C2×C16—612no—
286C2×C16—612no—
287C2×C16—1224no—
288#108—21no—
289#108—612no—
290#108—1221no—
291#108C22×D6112yes—
292#100—1224no—
293#100—1224no—
294C24—41no—
295C24—2441no—
296#41—612no—
297#41—612no—
298#41—1221no—
299#41—1221no—
300C2×Q8—611no—
301C2×D4—22no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—611no—
308C2×D4—1221no—
309C2×D4—1222no—
310C2×D4—2441no—
311C2×D4—2441no—
312C2×D4—2441no—
313C2×D4—2441no—
314C2×D4—2441no—
315C22×C4—1221no—
316C22×C4D4×D6111yescharacteristic
317SD16—2444no—
318SD16—2444no—
319D8—22no—
320D8—22no—
321D8—41no—
322D8—41no—
323D8—1222no—
324D8—1222no—
325D8—2444no—
326D8—2444no—
327D8—2441no—
328D8—2441no—
329M16—22no—
330M16—41no—
331M16—612no—
332M16—1221no—
333M16—1222no—
334M16—1222no—
335M16—1222no—
336M16—2441no—
337C2×C8—41no—
338C2×C8—1221no—
339C2×C8—1222no—
340C2×C8—1222no—
341C2×C8—2441no—
342C2×C8#1175822211yescharacteristic
343C2×C8#1175822211yescharacteristic
344C2×C8D4×D6111yescharacteristic
345C2×C8D4×D6111yescharacteristic
346C2×C8D4×D6111yescharacteristic
347C2×C8C23×D6111yescharacteristic
348C16—22no—
349C16—612no—
350C16—612no—
351C23—42no—
352C23—81no—
353C23—81no—
354C23—162no—
355C23—1221no—
356C23—9762no—
357C23—4881no—
358C23—4881no—
359C23—2442no—
360C23#1451979811yescharacteristic
361Q8—612no—
362Q8—1221no—
363D4—42no—
364D4—42no—
365D4—81no—
366D4—81no—
367D4—612no—
368D4—1222no—
369D4—1222no—
370D4—1221no—
371D4—4881no—
372D4—4881no—
373D4—2442no—
374D4—2442no—
375C2×C4—1221no—
376C2×C4—1222no—
377C2×C4—1222no—
378C2×C4#1451975011yescharacteristic
379C2×C4#1451975011yescharacteristic
380C2×C4D8×D6111yescharacteristic
381C2×C4D8×D6111yescharacteristic
382C2×C4#1451979811yescharacteristic
383C2×C4C2×D4×D6111yescharacteristic
384C8—42no—
385C8—1222no—
386C8—2442no—
387C8#1451975011yescharacteristic
388C8#1451975011yescharacteristic
389C8C2×D4×D6111yescharacteristic
390C8C2×#1175822211yescharacteristic
391C22—22no—
392C22—82no—
393C22—162no—
394C22—162no—
395C22—162no—
396C22—1222no—
397C22—9762no—
398C22—9762no—
399C22—9762no—
400C22—4882no—
401C22—2442no—
402C22#1683999711yescharacteristic
403C22#1683999711yescharacteristic
404C22C2×#1451979811yescharacteristic
405C4—1222no—
406C4#1683999711yescharacteristic
407C4#1683999711yescharacteristic
408C4C2×#1451975011yescharacteristic
409C4C2×D8×D6111yescharacteristic
410C2—21no—
411C2—21no—
412C2—162no—
413C2—9762no—
414C2—2442no—
415C2#2144793812yesdirect product factor
416C2C2×#1683999711yescharacteristic
subgroupG/H
centerC22#16839997
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC2×C61×#361C2
socleC22×C61#466
hypercenterC2×#361D61
hypocenterC61C2×#2221
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×#14519718C2semidirect
2. C2×#16840180C2semidirect
3. C2×#16840033C2semidirect
4. C2×#16840029C2semidirect
5. #21447938C2direct (N × H)
6. C2×#16839591C2semidirect
7. C2×#16839576C2semidirect
8. C2×C61×#361C2semidirect
16. C2×#14519718C22semidirect
18. #16840180C22semidirect
23. #16840033C22semidirect
25. #16840029C22semidirect
29. #16839591C22semidirect
30. #16839576C22semidirect
34. C61×#361C22semidirect
209. C2×#361D61semidirect
213. C2×C61#2221semidirect
242. #361C2×D61semidirect
243. C61C2×#2221semidirect
415. C2#21447938direct (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×#168401802
C2×#168400332
C2×#168400292
#214479382
C2×#168395912
C2×#168395762
C2×C61×#3612
C2×#222161