Finite Group Databasebeta

← C2×#21447950 #29834583

Subgroups — C2×#21447950 #29834583

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×#14519722C211yesmaximal, characteristic, complemented
2C2×#16840178C211yesmaximal, characteristic, complemented
3C2×#16840038C211yesmaximal, characteristic, complemented
4C2×#16840033C211yesmaximal, characteristic
5#21447950C218yesmaximal, direct product factor
6C2×#16839577C211yesmaximal, characteristic, complemented
7C2×#16839574C211yesmaximal, characteristic, complemented
8C2×C61×#368C211yesmaximal, characteristic, complemented
9C2×#14519810—21no—
10C2×#14519805—21no—
11C22×Dic244C2211yescharacteristic
12C22×D488C2211yescharacteristic
13C2×#14519783C2211yescharacteristic
14C2×#14519722—21no—
15C2×#14519722—21no—
16C2×#14519722—22no—
17C2×#14519722C2214yescomplemented
18#16840178—22no—
19#16840178C2214yescomplemented
20C2×#14519717C2211yescharacteristic
21C2×#14519716—21no—
22C2×C16×D61—21no—
23#16840038—22no—
24#16840038C2214yescomplemented
25#16840033—22no—
26#16840033C2214yes—
27C2×#14519695—21no—
28C2×#14519693—21no—
29#16839577C2214yescomplemented
30#16839574C2214yescomplemented
31C22×C16×C61C2211yescharacteristic
32C2×#108×C61C2211yescharacteristic
33C2×#108×C61C2211yescharacteristic
34C61×#368C2214yescomplemented
35C2×#11758222D411yescharacteristic
36C22×Dic122—21no—
37C22×D244—21no—
38#14519810—24no—
39#14519810—42no—
40#14519805—24no—
41#14519805—42no—
42C2×Dic244—21no—
43C2×Dic244—21no—
44C2×Dic244—21no—
45C2×Dic244—21no—
46C2×Dic244—21no—
47C2×Dic244—41no—
48C2×Dic244C2312yes—
49C2×#11758190—41no—
50C2×#11758190—41no—
51C2×D488—21no—
52C2×D488—21no—
53C2×D488—21no—
54C2×D488—21no—
55C2×D488—21no—
56C2×D488—41no—
57C2×D488C2312yes—
58#14519783—21no—
59#14519783—21no—
60#14519783D412yes—
61#14519783C2312yes—
62C2×#11758194D411yescharacteristic
63C2×#11758189—21no—
64C2×C8×D61—21no—
65#14519722—24no—
66#14519722—24no—
67#14519717—21no—
68#14519717C2312yes—
69#14519716—24no—
70C2×#11758185—21no—
71C16×D61—24no—
72#14519695—24no—
73#14519693—24no—
74C2×M16×C61—21no—
75C2×M16×C61—21no—
76C22×C8×C61C2311yescharacteristic
77C2×C16×C61D411yescharacteristic
78C2×C16×C61D411yescharacteristic
79C2×C16×C61D412yes—
80C2×C16×C61C2312yes—
81#108×C61—21no—
82#108×C61—21no—
83#108×C61C2312yes—
84#108×C61C2312yes—
85C23×D61—41no—
86C22×C4×C61C2×D411yescharacteristic
87C2×C22⋊D61—21no—
88C22×Dic61—41no—
89#11758222—21no—
90#11758222—21no—
91#11758222D812yes—
92#11758222C2×D412yes—
93C2×D244—22no—
94C2×D244—41no—
95C2×D244—41no—
96C2×D244—41no—
97C2×D244—41no—
98C2×D244—41no—
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
108M16×C61—22no—
109M16×C61—22no—
110M16×C61—41no—
111M16×C61—41no—
112C2×C8×C61—41no—
113C2×C8×C61—41no—
114C2×C8×C61C2×D411yescharacteristic
115C2×C8×C61C2×D411yescharacteristic
116C2×C8×C61C2×D411yescharacteristic
117C2×C8×C61#4111yescharacteristic
118C2×C8×C61#4111yescharacteristic
119C2×C8×C61C2411yescharacteristic
120#11758194—21no—
121#11758194C2×D412yes—
122C2×#92418—21no—
123Dic244—22no—
124Dic244—22no—
125Dic244—44no—
126Dic244—41no—
127Dic244—41no—
128D488—22no—
129D488—22no—
130D488—44no—
131D488—41no—
132D488—41no—
133#11758190—44no—
134#11758190—44no—
135#11758189—22no—
136#11758189—22no—
137C8×D61—22no—
138C8×D61—22no—
139C16×C61C2×D412yes—
140C16×C61C2×D412yes—
141#11758185—22no—
142C23×C61#13511yescharacteristic
143C22×D61—21no—
144C22×D61—42no—
145C22×D61—81no—
146C22×D61—81no—
147C22×D61—162no—
148C2×C4×C61#12111yescharacteristic
149C2×C4×C61#12111yescharacteristic
150C2×C4×C61C2×D811yescharacteristic
151C2×C4×C61C2×D811yescharacteristic
152C2×C4×C61#13511yescharacteristic
153C2×C4×C61C22×D411yescharacteristic
154C22⋊D61—22no—
155C22⋊D61—22no—
156C2×Dic61—21no—
157C2×Dic61—42no—
158C2×Dic61—81no—
159C2×Dic61—81no—
160D244—21no—
161D244—42no—
162D244—42no—
163D244—81no—
164D244—81no—
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—42no—
176C8×C61#12111yescharacteristic
177C8×C61#12111yescharacteristic
178C8×C61C22×D411yescharacteristic
179C8×C61C2×#4111yescharacteristic
180#92418—22no—
181C2×#2223—611nomaximal, Sylow
182C22×C61—22no—
183C22×C61#46611yescharacteristic
184C22×C61#46611yescharacteristic
185C22×C61C2×#13511yescharacteristic
186C2×D61—22no—
187C2×D61—42no—
188C2×D61—82no—
189C2×D61—162no—
190C2×D61—162no—
191C2×D61—162no—
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×#368D6111yescharacteristic, complemented
204C2×#362—611no—
205C2×#361—611no—
206C2×C61—21no—
207C2×C61—21no—
208C2×C61#222312yescomplemented
209C2×C61C2×#46611yescharacteristic
210D61—42no—
211D61—162no—
212C2×#137—1221no—
213C2×AGL(1,ℤ/8)—1221no—
214C22×Q16—611no—
215C22×D8—611no—
216C2×#131—611no—
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—1221no—
226C22×C16C2×D6111yescharacteristic
227#473—614no—
228#473—1222no—
229#472—614no—
230#472—1222no—
231C2×#108C2×D6111yescharacteristic
232C2×#108C2×D6111yescharacteristic
233C2×#101—1221no—
234C2×#100—1221no—
235#368C2×D6114yescomplemented
236#362—614no—
237#361—614no—
238C61C2×#222311yescharacteristic, complemented, Sylow
239C2×#41—611no—
240C22×Q8—1221no—
241C22×D4—1221no—
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—612no—
256C2×D8—1221no—
257C2×D8—1221no—
258C2×D8—1221no—
259C2×D8—1221no—
260C2×D8—1221no—
261C2×D8—2441no—
262#131—612no—
263#131—612no—
264#131—1221no—
265#131—1221no—
266C2×M16—21no—
267C2×M16—21no—
268C2×M16—611no—
269C2×M16—1221no—
270C22×C8—1221no—
271C22×C8C22×D6111yescharacteristic
272SD32—1224no—
273SD32—1224no—
274M32—612no—
275M32—1221no—
276M32—1224no—
277C2×C16—1221no—
278C2×C16—1224no—
279C2×C16D24411yescharacteristic
280C2×C16D24411yescharacteristic
281C2×C16D24412yes—
282C2×C16C22×D6112yes—
283#108—21no—
284#108—21no—
285#108C22×D6112yes—
286#108C22×D6112yes—
287#101—1224no—
288#100—1224no—
289C24—2441no—
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—611no—
302C2×D4—1221no—
303C2×D4—1222no—
304C2×D4—2441no—
305C2×D4—2441no—
306C2×D4—2441no—
307C2×D4—2441no—
308C2×D4—2441no—
309C22×C4—1221no—
310C22×C4—2441no—
311C22×C4D4×D6111yescharacteristic
312Q16—1222no—
313Q16—1222no—
314Q16—2444no—
315Q16—2441no—
316Q16—2441no—
317SD16—2444no—
318SD16—2444no—
319D8—1222no—
320D8—1222no—
321D8—2444no—
322D8—2441no—
323D8—2441no—
324M16—22no—
325M16—22no—
326M16—41no—
327M16—41no—
328M16—612no—
329M16—1221no—
330M16—1222no—
331M16—1222no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—1221no—
335C2×C8—1222no—
336C2×C8—1222no—
337C2×C8C2×D24411yescharacteristic
338C2×C8C2×D24411yescharacteristic
339C2×C8D4×D6111yescharacteristic
340C2×C8#1175822611yescharacteristic
341C2×C8#1175822611yescharacteristic
342C2×C8C23×D6111yescharacteristic
343C16—1222no—
344C16C2×D24412yes—
345C16C2×D24412yes—
346C23—1221no—
347C23—9762no—
348C23—4881no—
349C23—4881no—
350C23—2442no—
351C23#1451980011yescharacteristic
352Q8—612no—
353Q8—1221no—
354Q8—4881no—
355Q8—4881no—
356Q8—2442no—
357Q8—2442no—
358D4—612no—
359D4—1222no—
360D4—1222no—
361D4—1221no—
362D4—4881no—
363D4—4881no—
364D4—2442no—
365D4—2442no—
366C2×C4—1221no—
367C2×C4—1222no—
368C2×C4—1222no—
369C2×C4—4881no—
370C2×C4—4881no—
371C2×C4—2442no—
372C2×C4#1451975211yescharacteristic
373C2×C4#1451975211yescharacteristic
374C2×C4D8×D6111yescharacteristic
375C2×C4D8×D6111yescharacteristic
376C2×C4#1451980011yescharacteristic
377C2×C4C2×D4×D6111yescharacteristic
378C8—42no—
379C8—42no—
380C8—1222no—
381C8#1451975211yescharacteristic
382C8#1451975211yescharacteristic
383C8C22×D24411yescharacteristic
384C8C2×#1175822611yescharacteristic
385C22—22no—
386C22—1222no—
387C22—9762no—
388C22—9762no—
389C22—9762no—
390C22—4882no—
391C22—2442no—
392C22#1683999911yescharacteristic
393C22#1683999911yescharacteristic
394C22C2×#1451980011yescharacteristic
395C4—1222no—
396C4—4882no—
397C4#1683999911yescharacteristic
398C4#1683999911yescharacteristic
399C4C2×#1451975211yescharacteristic
400C4C2×D8×D6111yescharacteristic
401C2—21no—
402C2—21no—
403C2—9762no—
404C2—2442no—
405C2#2144795012yesdirect product factor
406C2C2×#1683999911yescharacteristic
subgroupG/H
centerC22#16839999
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC2×C61×#368C2
socleC22×C61#466
prime radicalC2×#16840033C2
hypercenterC2×#368D61
hypocenterC61C2×#2223
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#368

Complements

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

NH ≅ G/Ntype
1. C22×#14519722C2semidirect
2. C2×#16840178C2semidirect
3. C2×#16840038C2semidirect
5. #21447950C2direct (N × H)
6. C2×#16839577C2semidirect
7. C2×#16839574C2semidirect
8. C2×C61×#368C2semidirect
17. C2×#14519722C22semidirect
19. #16840178C22semidirect
24. #16840038C22semidirect
29. #16839577C22semidirect
30. #16839574C22semidirect
34. C61×#368C22semidirect
203. C2×#368D61semidirect
208. C2×C61#2223semidirect
235. #368C2×D61semidirect
238. C61C2×#2223semidirect
405. C2#21447950direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197222
C2×#168401782
C2×#168400382
C2×#168400332
#214479502
C2×#168395772
C2×#168395742
C2×C61×#3682
C2×#222361