Finite Group Databasebeta

← C2×#21447887 #29834384

Subgroups — C2×#21447887 #29834384

Order 15616.

706 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840205C211yesmaximal, characteristic, complemented
2C2×#16840198C211yesmaximal, characteristic
3C2×#16840145C211yesmaximal, characteristic, complemented
4C2×#16839878C211yesmaximal, characteristic, complemented
5#21447887C218yesmaximal, direct product factor
6C2×#16839582C211yesmaximal, characteristic, complemented
7C2×#16839577C211yesmaximal, characteristic, complemented
8C2×C61×#361C211yesmaximal, characteristic, complemented
9C2×#14519799C2211yescharacteristic
10C22×Dic244C2211yescharacteristic
11C22×#11758200—21no—
12C2×#14519785—21no—
13C2×#14519764—21no—
14#16840205—22no—
15#16840205C2214yescomplemented
16#16840198—22no—
17#16840198C2214yes—
18C2×Dic488—21no—
19C2×#14519722—21no—
20C2×#14519721—21no—
21C2×#14519718—21no—
22C2×#14519717C2211yescharacteristic
23#16840145—22no—
24#16840145C2214yescomplemented
25#16839878—22no—
26#16839878C2214yescomplemented
27C2×#14519703—21no—
28C2×C8×Dic61C2211yescharacteristic
29#16839582C2214yescomplemented
30#16839577C2214yescomplemented
31C22×D8×C61C2211yescharacteristic
32C2×M32×C61C2211yescharacteristic
33C2×#108×C61C2211yescharacteristic
34C61×#361C2214yescomplemented
35C2×#11758222—21no—
36C22×Dic122—21no—
37#14519799—21no—
38#14519799—21no—
39#14519799D412yes—
40#14519799C2312yes—
41C2×Dic244—21no—
42C2×Dic244—21no—
43C2×Dic244—21no—
44C2×Dic244—21no—
45C2×Dic244—21no—
46C2×Dic244D411yescharacteristic
47C2×Dic244C2312yes—
48C2×#11758190—21no—
49C2×#11758200—24no—
50C2×#11758200—41no—
51C2×#11758200—41no—
52C2×#11758200—42no—
53C2×D488D411yescharacteristic
54#14519785—24no—
55#14519785—42no—
56C2×#11758189—41no—
57C22×#92418D411yescharacteristic
58C2×C8×D61—41no—
59#14519764—24no—
60#14519764—42no—
61C2×C22⋊Dic61—42no—
62C2×C4×Dic61D411yescharacteristic
63Dic488—24no—
64#14519722—24no—
65#14519721—24no—
66#14519718—24no—
67#14519717—21no—
68#14519717C2312yes—
69C2×#11758185—21no—
70#14519703—24no—
71C8×Dic61D412yes—
72C8×Dic61C2312yes—
73C22×D4×C61—21no—
74C2×D8×C61—21no—
75C2×D8×C61—21no—
76C2×D8×C61—21no—
77C2×D8×C61—21no—
78C2×D8×C61—21no—
79C2×D8×C61C2312yes—
80C2×M16×C61—21no—
81C22×C8×C61C2311yescharacteristic
82M32×C61—21no—
83M32×C61C2312yes—
84C2×C16×C61—21no—
85#108×C61—21no—
86#108×C61C2312yes—
87C24×C61—41no—
88C2×D4×C61—22no—
89C2×D4×C61—41no—
90C2×D4×C61—41no—
91C2×D4×C61—41no—
92C2×D4×C61—41no—
93C2×D4×C61—41no—
94C22×C4×C61C2×D411yescharacteristic
95C2×C22⋊D61—41no—
96C22×Dic61—21no—
97C22×Dic61—41no—
98#11758222—22no—
99#11758222—22no—
100#11758222—41no—
101#11758222—41no—
102C2×D244—21no—
103C2×C4×D61—41no—
104C2×Dic122—21no—
105C2×Dic122—22no—
106C2×Dic122—41no—
107C2×Dic122—41no—
108C2×Dic122—41no—
109C2×Dic122—41no—
110C2×Dic122—41no—
111D8×C61—22no—
112D8×C61—22no—
113D8×C61—41no—
114D8×C61—41no—
115M16×C61—22no—
116M16×C61—41no—
117C2×C8×C61—41no—
118C2×C8×C61C2×D411yescharacteristic
119C2×C8×C61C2×D411yescharacteristic
120C2×C8×C61C2×D411yescharacteristic
121C2×C8×C61#4111yescharacteristic
122C2×C8×C61#4111yescharacteristic
123C2×C8×C61C2411yescharacteristic
124C22⋊Dic61—48no—
125#11758200—44no—
126#11758200—44no—
127C4×Dic61—21no—
128C4×Dic61C2×D412yes—
129C2×#92418D811yescharacteristic
130C2×#92418D811yescharacteristic
131C2×#92418D812yes—
132C2×#92418C2×D412yes—
133Dic244—21no—
134Dic244—22no—
135Dic244—22no—
136Dic244—41no—
137Dic244—41no—
138Dic244C2×D412yes—
139D488—21no—
140D488C2×D412yes—
141#11758190—22no—
142#11758190—22no—
143#11758189—44no—
144C8×D61—44no—
145C16×C61—22no—
146#11758185—22no—
147C23×C61—42no—
148C23×C61—84no—
149C23×C61—81no—
150C23×C61—81no—
151C23×C61AGL(1,ℤ/8)11yescharacteristic
152C22×D61—41no—
153D4×C61—42no—
154D4×C61—42no—
155D4×C61—81no—
156D4×C61—81no—
157C2×C4×C61#12111yescharacteristic
158C2×C4×C61#12111yescharacteristic
159C2×C4×C61C2×D811yescharacteristic
160C2×C4×C61C2×D811yescharacteristic
161C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C61C22×D411yescharacteristic
163C22⋊D61—42no—
164C22⋊D61—42no—
165C2×Dic61—22no—
166C2×Dic61—42no—
167C2×Dic61—41no—
168C2×Dic61—42no—
169C2×Dic61—81no—
170C2×Dic61—81no—
171D244—22no—
172D244—41no—
173C4×D61—42no—
174C4×D61—42no—
175Dic122—22no—
176Dic122—41no—
177Dic122—42no—
178Dic122—42no—
179Dic122—81no—
180Dic122—81no—
181C8×C61—42no—
182C8×C61#12111yescharacteristic
183C8×C61#12111yescharacteristic
184C8×C61C22×D411yescharacteristic
185C8×C61C2×#4111yescharacteristic
186#92418C2×D812yes—
187#92418C2×D812yes—
188C2×#2212—611nomaximal, Sylow
189C22×C61—22no—
190C22×C61—84no—
191C22×C61—82no—
192C22×C61—162no—
193C22×C61—162no—
194C22×C61#45911yescharacteristic
195C22×C61#45911yescharacteristic
196C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
197C2×D61—42no—
198C2×D61—82no—
199C4×C61#45911yescharacteristic
200C4×C61#45911yescharacteristic
201C4×C61C2×#12111yescharacteristic
202C4×C61C22×D811yescharacteristic
203Dic61—42no—
204Dic61—42no—
205Dic61—82no—
206C2×#510—611no—
207C2×#509—611no—
208C2×#495—611no—
209C2×#443—611no—
210#2212—618no—
211C2×#364—611no—
212C2×#362—611no—
213C2×#361D6111yescharacteristic, complemented
214C2×C61—21no—
215C2×C61—21no—
216C2×C61—162no—
217C2×C61#221212yescomplemented
218C2×C61C2×#45911yescharacteristic
219D61—82no—
220C2×#135—611no—
221C22×Q16—611no—
222C22×SD16—1221no—
223C22×D8C2×D6111yescharacteristic
224C2×#131—1221no—
225C2×#124—1221no—
226#510—614no—
227#510—1222no—
228#509—614no—
229#509—1222no—
230C2×Q32—1221no—
231C2×SD32—1221no—
232C2×SD32—1221no—
233C2×D16—1221no—
234C2×M32—611no—
235C2×M32C2×D6111yescharacteristic
236#495—614no—
237#495—1222no—
238#443—614no—
239#443—1222no—
240C2×#108C2×D6111yescharacteristic
241C2×#104—1221no—
242C2×C4×C8—611no—
243#364—614no—
244#362—614no—
245#361C2×D6114yescomplemented
246C61C2×#221211yescharacteristic, complemented, Sylow
247C2×#41—1221no—
248C22×Q8—1221no—
249C22×D4—21no—
250#135—612no—
251#135—612no—
252#135—1221no—
253#135—1221no—
254C2×Q16—611no—
255C2×Q16—612no—
256C2×Q16—1221no—
257C2×Q16—1221no—
258C2×Q16—1221no—
259C2×Q16—1221no—
260C2×Q16—1221no—
261C2×SD16—1224no—
262C2×SD16—1221no—
263C2×SD16—2441no—
264C2×SD16—2441no—
265C2×SD16—2442no—
266C2×D8—21no—
267C2×D8—21no—
268C2×D8—21no—
269C2×D8—21no—
270C2×D8—21no—
271C2×D8—611no—
272C2×D8C22×D6112yes—
273#131—1224no—
274#131—2442no—
275C2×M16—21no—
276C2×M16—2441no—
277C22×C8—611no—
278C22×C8—2441no—
279C22×C8C22×D6111yescharacteristic
280#124—1224no—
281#124—2442no—
282C2×C22⋊C4—2442no—
283C2×C42—611no—
284Q32—1224no—
285SD32—1224no—
286SD32—1224no—
287D16—1224no—
288M32—21no—
289M32—612no—
290M32—1221no—
291M32C22×D6112yes—
292C2×C16—21no—
293C2×C16—1221no—
294#108—21no—
295#108C22×D6112yes—
296#104—1224no—
297C4×C8—612no—
298C4×C8—612no—
299C24—41no—
300#41—1222no—
301#41—1222no—
302#41—2441no—
303#41—2441no—
304C2×Q8—1222no—
305C2×Q8—1221no—
306C2×Q8—2441no—
307C2×Q8—2441no—
308C2×Q8—2441no—
309C2×Q8—2441no—
310C2×Q8—2441no—
311C2×D4—22no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—1221no—
318C2×D4—2441no—
319C22×C4—1221no—
320C22×C4—2441no—
321C22×C4—2441no—
322C22×C4D4×D6111yescharacteristic
323Q16—612no—
324Q16—1222no—
325Q16—1222no—
326Q16—1221no—
327Q16—2441no—
328Q16—2441no—
329SD16—1222no—
330SD16—1222no—
331SD16—2444no—
332SD16—2444no—
333D8—22no—
334D8—22no—
335D8—41no—
336D8—41no—
337D8—612no—
338D8—1221no—
339M16—22no—
340M16—41no—
341M16—2444no—
342C2×C8—41no—
343C2×C8—612no—
344C2×C8—611no—
345C2×C8—611no—
346C2×C8—612no—
347C2×C8—2444no—
348C2×C8#1175822211yescharacteristic
349C2×C8#1175822211yescharacteristic
350C2×C8D4×D6111yescharacteristic
351C2×C8D4×D6111yescharacteristic
352C2×C8D4×D6111yescharacteristic
353C2×C8C23×D6111yescharacteristic
354C22⋊C4—2448no—
355C42—612no—
356C42—1221no—
357C16—22no—
358C16—1222no—
359C23—42no—
360C23—84no—
361C23—81no—
362C23—81no—
363C23—2441no—
364C23#1451980411yescharacteristic
365Q8—1222no—
366Q8—4881no—
367Q8—4881no—
368Q8—2442no—
369Q8—2442no—
370Q8—2441no—
371D4—42no—
372D4—42no—
373D4—81no—
374D4—81no—
375D4—1222no—
376D4—2442no—
377D4—2442no—
378D4—2441no—
379C2×C4—1222no—
380C2×C4—4881no—
381C2×C4—4881no—
382C2×C4—2442no—
383C2×C4—2442no—
384C2×C4—2441no—
385C2×C4—2442no—
386C2×C4—2442no—
387C2×C4#1451975011yescharacteristic
388C2×C4#1451975011yescharacteristic
389C2×C4D8×D6111yescharacteristic
390C2×C4D8×D6111yescharacteristic
391C2×C4#1451980411yescharacteristic
392C2×C4C2×D4×D6111yescharacteristic
393C8—42no—
394C8—612no—
395C8—612no—
396C8#1451975011yescharacteristic
397C8#1451975011yescharacteristic
398C8C2×D4×D6111yescharacteristic
399C8C2×#1175822211yescharacteristic
400C22—22no—
401C22—84no—
402C22—82no—
403C22—162no—
404C22—162no—
405C22—4882no—
406C22—2442no—
407C22#1683995611yescharacteristic
408C22#1683995611yescharacteristic
409C22C2×#1451980411yescharacteristic
410C4—4882no—
411C4—2442no—
412C4—2442no—
413C4#1683995611yescharacteristic
414C4#1683995611yescharacteristic
415C4C2×#1451975011yescharacteristic
416C4C2×D8×D6111yescharacteristic
417C2—21no—
418C2—21no—
419C2—162no—
420C2—4882no—
421C2#2144788712yesdirect product factor
422C2C2×#1683995611yescharacteristic
subgroupG/H
centerC22#16839956
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC2×C61×#361C2
socleC22×C61#459
prime radicalC2×#16840198C2
hypercenterC2×#361D61
hypocenterC61C2×#2212
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. C2×#16840205C2semidirect
3. C2×#16840145C2semidirect
4. C2×#16839878C2semidirect
5. #21447887C2direct (N × H)
6. C2×#16839582C2semidirect
7. C2×#16839577C2semidirect
8. C2×C61×#361C2semidirect
15. #16840205C22semidirect
24. #16840145C22semidirect
26. #16839878C22semidirect
29. #16839582C22semidirect
30. #16839577C22semidirect
34. C61×#361C22semidirect
213. C2×#361D61semidirect
217. C2×C61#2212semidirect
245. #361C2×D61semidirect
246. C61C2×#2212semidirect
421. C2#21447887direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402052
C2×#168401982
C2×#168401452
C2×#168398782
#214478872
C2×#168395822
C2×#168395772
C2×C61×#3612
C2×#221261