Finite Group Databasebeta

← C2×#21447894 #29834392

Subgroups — C2×#21447894 #29834392

Order 15616.

790 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840200C211yesmaximal, characteristic, complemented
2C2×#16840198C211yesmaximal, characteristic, complemented
3C2×#16840137C211yesmaximal, characteristic, complemented
4C2×#16839878C211yesmaximal, characteristic, complemented
5#21447894C218yesmaximal, direct product factor
6C2×#16839582C211yesmaximal, characteristic, complemented
7C2×#16839574C211yesmaximal, characteristic, complemented
8C2×C61×#361C211yesmaximal, characteristic, complemented
9C2×#14519799C2211yescharacteristic
10C22×D488C2211yescharacteristic
11C22×#11758199—21no—
12C2×#14519785—21no—
13C2×#14519773—21no—
14#16840200—22no—
15#16840200C2214yescomplemented
16#16840198—22no—
17#16840198C2214yescomplemented
18C2×#14519722—21no—
19C2×#14519721—21no—
20C2×D976—21no—
21C2×#14519718—21no—
22C2×#14519717C2211yescharacteristic
23#16840137—22no—
24#16840137C2214yescomplemented
25#16839878—22no—
26#16839878C2214yescomplemented
27C2×#14519703—21no—
28C2×C8×Dic61C2211yescharacteristic
29#16839582C2214yescomplemented
30#16839574C2214yescomplemented
31C22×D8×C61C2211yescharacteristic
32C2×M32×C61C2211yescharacteristic
33C2×#108×C61C2211yescharacteristic
34C61×#361C2214yescomplemented
35C2×#11758222—21no—
36C22×D244—21no—
37C22×C22⋊D61—42no—
38#14519799—21no—
39#14519799—21no—
40#14519799D412yescomplemented
41#14519799C2312yes—
42C2×Dic244D411yescharacteristic, complemented
43C2×#11758190—21no—
44C2×D488—21no—
45C2×D488—21no—
46C2×D488—21no—
47C2×D488—21no—
48C2×D488—21no—
49C2×D488D411yescharacteristic, complemented
50C2×D488C2312yes—
51C2×#11758199—24no—
52C2×#11758199—41no—
53C2×#11758199—41no—
54C2×#11758199—42no—
55#14519785—24no—
56#14519785—42no—
57C2×#11758189—41no—
58C22×#92418D411yescharacteristic
59C2×C8×D61—41no—
60#14519773—24no—
61#14519773—42no—
62C2×C4×Dic61D411yescharacteristic
63#14519722—24no—
64#14519721—24no—
65D976—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—
88C23×D61—41no—
89C2×D4×C61—22no—
90C2×D4×C61—41no—
91C2×D4×C61—41no—
92C2×D4×C61—41no—
93C2×D4×C61—41no—
94C2×D4×C61—41no—
95C22×C4×C61C2×D411yescharacteristic
96C2×C22⋊D61—48no—
97C2×C22⋊D61—41no—
98C2×C22⋊D61—88no—
99C22×Dic61—21no—
100#11758222—22no—
101#11758222—22no—
102#11758222—41no—
103#11758222—41no—
104C2×D244—21no—
105C2×D244—22no—
106C2×D244—41no—
107C2×D244—41no—
108C2×D244—41no—
109C2×D244—41no—
110C2×D244—41no—
111C2×C4×D61—41no—
112C2×Dic122—21no—
113D8×C61—22no—
114D8×C61—22no—
115D8×C61—41no—
116D8×C61—41no—
117M16×C61—22no—
118M16×C61—41no—
119C2×C8×C61—41no—
120C2×C8×C61C2×D411yescharacteristic
121C2×C8×C61C2×D411yescharacteristic
122C2×C8×C61C2×D411yescharacteristic
123C2×C8×C61#4111yescharacteristic
124C2×C8×C61#4111yescharacteristic
125C2×C8×C61C2411yescharacteristic
126#11758199—44no—
127#11758199—44no—
128C4×Dic61—21no—
129C4×Dic61C2×D412yes—
130C2×#92418D811yescharacteristic
131C2×#92418D811yescharacteristic
132C2×#92418D812yes—
133C2×#92418C2×D412yes—
134Dic244—21no—
135Dic244C2×D412yescomplemented
136D488—21no—
137D488—22no—
138D488—22no—
139D488—41no—
140D488—41no—
141D488C2×D412yescomplemented
142#11758190—22no—
143#11758190—22no—
144#11758189—44no—
145C8×D61—44no—
146C16×C61—22no—
147#11758185—22no—
148C23×C61—42no—
149C23×C61—84no—
150C23×C61—81no—
151C23×C61—81no—
152C23×C61AGL(1,ℤ/8)11yescharacteristic
153C22×D61—41no—
154C22×D61—42no—
155C22×D61—84no—
156C22×D61—81no—
157C22×D61—81no—
158D4×C61—42no—
159D4×C61—42no—
160D4×C61—81no—
161D4×C61—81no—
162C2×C4×C61#12111yescharacteristic
163C2×C4×C61#12111yescharacteristic
164C2×C4×C61C2×D811yescharacteristic
165C2×C4×C61C2×D811yescharacteristic
166C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C61C22×D411yescharacteristic
168C22⋊D61—42no—
169C22⋊D61—42no—
170C22⋊D61—816no—
171C2×Dic61—24no—
172C2×Dic61—22no—
173C2×Dic61—41no—
174D244—22no—
175D244—42no—
176D244—42no—
177D244—41no—
178D244—81no—
179D244—81no—
180C4×D61—42no—
181C4×D61—42no—
182Dic122—22no—
183Dic122—41no—
184C8×C61—42no—
185C8×C61#12111yescharacteristic
186C8×C61#12111yescharacteristic
187C8×C61C22×D411yescharacteristic
188C8×C61C2×#4111yescharacteristic
189#92418C2×D812yes—
190#92418C2×D812yes—
191C2×#2213—611nomaximal, Sylow
192C22×C61—22no—
193C22×C61—84no—
194C22×C61—82no—
195C22×C61—162no—
196C22×C61—162no—
197C22×C61#45911yescharacteristic
198C22×C61#45911yescharacteristic
199C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
200C2×D61—42no—
201C2×D61—82no—
202C2×D61—84no—
203C2×D61—82no—
204C2×D61—162no—
205C2×D61—162no—
206C4×C61#45911yescharacteristic
207C4×C61#45911yescharacteristic
208C4×C61C2×#12111yescharacteristic
209C4×C61C22×D811yescharacteristic
210Dic61—24no—
211Dic61—42no—
212C2×#509—611no—
213C2×#509—611no—
214C2×#493—611no—
215C2×#443—611no—
216#2213—618no—
217C2×#364—611no—
218C2×#361—611no—
219C2×#361D6111yescharacteristic, complemented
220C2×C61—21no—
221C2×C61—21no—
222C2×C61—162no—
223C2×C61#221312yescomplemented
224C2×C61C2×#45911yescharacteristic
225D61—82no—
226D61—162no—
227C2×#135—611no—
228C22×D8—611no—
229C22×D8—1221no—
230C22×D8C2×D6111yescharacteristic
231C2×#131—1221no—
232C2×#127—1221no—
233#509—614no—
234#509—614no—
235#509—1222no—
236#509—1222no—
237C2×SD32—1221no—
238C2×SD32—1221no—
239C2×D16—1221no—
240C2×D16—1221no—
241C2×M32—611no—
242C2×M32C2×D6111yescharacteristic
243#493—614no—
244#493—1222no—
245#443—614no—
246#443—1222no—
247C2×#108C2×D6111yescharacteristic
248C2×#104—1221no—
249C2×C4×C8—611no—
250#364—614no—
251#361—614no—
252#361C2×D6114yescomplemented
253C61C2×#221311yescharacteristic, complemented, Sylow
254C2×#41—1221no—
255C22×D4—21no—
256C22×D4—1221no—
257C22×D4—2442no—
258#135—612no—
259#135—612no—
260#135—1221no—
261#135—1221no—
262C2×Q16—611no—
263C2×SD16—1221no—
264C2×D8—21no—
265C2×D8—21no—
266C2×D8—21no—
267C2×D8—21no—
268C2×D8—21no—
269C2×D8—611no—
270C2×D8—612no—
271C2×D8—1224no—
272C2×D8—1221no—
273C2×D8—1221no—
274C2×D8—1221no—
275C2×D8—1221no—
276C2×D8—1221no—
277C2×D8—2441no—
278C2×D8—2441no—
279C2×D8—2442no—
280C2×D8C22×D6112yes—
281#131—1224no—
282#131—2442no—
283C2×M16—21no—
284C2×M16—2441no—
285C22×C8—611no—
286C22×C8—2441no—
287C22×C8C22×D6111yescharacteristic
288#127—1224no—
289#127—2442no—
290C2×C42—611no—
291SD32—1224no—
292SD32—1224no—
293D16—1224no—
294D16—1224no—
295M32—21no—
296M32—612no—
297M32—1221no—
298M32C22×D6112yes—
299C2×C16—21no—
300C2×C16—1221no—
301#108—21no—
302#108C22×D6112yes—
303#104—1224no—
304C4×C8—612no—
305C4×C8—612no—
306C24—41no—
307C24—2441no—
308#41—1222no—
309#41—1222no—
310#41—2441no—
311#41—2441no—
312C2×Q8—1221no—
313C2×D4—22no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—1222no—
320C2×D4—1221no—
321C2×D4—4888no—
322C2×D4—2448no—
323C2×D4—2441no—
324C2×D4—2441no—
325C2×D4—2441no—
326C2×D4—2441no—
327C2×D4—2441no—
328C2×D4—2441no—
329C22×C4—1221no—
330C22×C4—2441no—
331C22×C4D4×D6111yescharacteristic
332Q16—612no—
333Q16—1221no—
334SD16—1222no—
335SD16—1222no—
336D8—22no—
337D8—22no—
338D8—41no—
339D8—41no—
340D8—612no—
341D8—1222no—
342D8—1222no—
343D8—1221no—
344D8—2444no—
345D8—2444no—
346D8—2441no—
347D8—2441no—
348M16—22no—
349M16—41no—
350M16—2444no—
351C2×C8—41no—
352C2×C8—612no—
353C2×C8—611no—
354C2×C8—611no—
355C2×C8—612no—
356C2×C8—2444no—
357C2×C8#1175822211yescharacteristic
358C2×C8#1175822211yescharacteristic
359C2×C8D4×D6111yescharacteristic
360C2×C8D4×D6111yescharacteristic
361C2×C8D4×D6111yescharacteristic
362C2×C8C23×D6111yescharacteristic
363C42—612no—
364C42—1221no—
365C16—22no—
366C16—1222no—
367C23—42no—
368C23—84no—
369C23—81no—
370C23—81no—
371C23—4884no—
372C23—4881no—
373C23—4881no—
374C23—2442no—
375C23—2441no—
376C23#1451980411yescharacteristic
377Q8—1222no—
378Q8—2441no—
379D4—42no—
380D4—42no—
381D4—81no—
382D4—81no—
383D4—1222no—
384D4—48816no—
385D4—4881no—
386D4—4881no—
387D4—2442no—
388D4—2442no—
389D4—2441no—
390D4—2442no—
391D4—2442no—
392C2×C4—1224no—
393C2×C4—1222no—
394C2×C4—2441no—
395C2×C4—2442no—
396C2×C4—2442no—
397C2×C4#1451975011yescharacteristic
398C2×C4#1451975011yescharacteristic
399C2×C4D8×D6111yescharacteristic
400C2×C4D8×D6111yescharacteristic
401C2×C4#1451980411yescharacteristic
402C2×C4C2×D4×D6111yescharacteristic
403C8—42no—
404C8—612no—
405C8—612no—
406C8#1451975011yescharacteristic
407C8#1451975011yescharacteristic
408C8C2×D4×D6111yescharacteristic
409C8C2×#1175822211yescharacteristic
410C22—22no—
411C22—84no—
412C22—82no—
413C22—162no—
414C22—162no—
415C22—9762no—
416C22—9762no—
417C22—4884no—
418C22—4882no—
419C22—4882no—
420C22—2442no—
421C22#1683995611yescharacteristic
422C22#1683995611yescharacteristic
423C22C2×#1451980411yescharacteristic
424C4—1224no—
425C4—2442no—
426C4#1683995611yescharacteristic
427C4#1683995611yescharacteristic
428C4C2×#1451975011yescharacteristic
429C4C2×D8×D6111yescharacteristic
430C2—21no—
431C2—21no—
432C2—162no—
433C2—9762no—
434C2—4882no—
435C2#2144789412yesdirect product factor
436C2C2×#1683995611yescharacteristic
subgroupG/H
centerC22#16839956
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC2×C61×#361C2
socleC22×C61#459
hypercenterC2×#361D61
hypocenterC61C2×#2213
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×#16840200C2semidirect
2. C2×#16840198C2semidirect
3. C2×#16840137C2semidirect
4. C2×#16839878C2semidirect
5. #21447894C2direct (N × H)
6. C2×#16839582C2semidirect
7. C2×#16839574C2semidirect
8. C2×C61×#361C2semidirect
15. #16840200C22semidirect
17. #16840198C22semidirect
24. #16840137C22semidirect
26. #16839878C22semidirect
29. #16839582C22semidirect
30. #16839574C22semidirect
34. C61×#361C22semidirect
40. #14519799D4semidirect
42. C2×Dic244D4semidirect
49. C2×D488D4semidirect
135. Dic244C2×D4semidirect
141. D488C2×D4semidirect
219. C2×#361D61semidirect
223. C2×C61#2213semidirect
252. #361C2×D61semidirect
253. C61C2×#2213semidirect
435. C2#21447894direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402002
C2×#168401982
C2×#168401372
C2×#168398782
#214478942
C2×#168395822
C2×#168395742
C2×C61×#3612
C2×#221361