Finite Group Databasebeta

← C2×#21447889 #29834386

Subgroups — C2×#21447889 #29834386

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×#16840200C211yesmaximal, characteristic
3C2×#16840146C211yesmaximal, characteristic, complemented
4C2×#16839880C211yesmaximal, characteristic, complemented
5#21447889C218yesmaximal, direct product factor
6C2×#16839579C211yesmaximal, characteristic, complemented
7C2×#16839576C211yesmaximal, characteristic, complemented
8C2×C61×#364C211yesmaximal, characteristic, complemented
9C2×#14519799C2211yescharacteristic
10C22×Dic244C2211yescharacteristic
11C22×#11758190—21no—
12C22×D488C2211yescharacteristic
13C2×#14519783—21no—
14C2×#14519765—21no—
15#16840205—22no—
16#16840205C2214yescomplemented
17#16840200—22no—
18#16840200C2214yes—
19C2×Dic488—21no—
20C2×#14519722—21no—
21C2×#14519722—21no—
22C2×D976—21no—
23#16840146—22no—
24#16840146C2214yescomplemented
25#16839880—22no—
26#16839880C2214yescomplemented
27C2×#14519713C2211yescharacteristic
28C2×#14519705—21no—
29#16839579C2214yescomplemented
30#16839576C2214yescomplemented
31C2×M32×C61C2211yescharacteristic
32C2×M32×C61C2211yescharacteristic
33C2×C4×C8×C61C2211yescharacteristic
34C61×#364C2214yescomplemented
35C2×#11758222—21no—
36C22×Dic122—21no—
37C22×D244—21no—
38#14519799—21no—
39#14519799—21no—
40#14519799D412yes—
41#14519799C2312yes—
42C2×Dic244—21no—
43C2×Dic244—21no—
44C2×Dic244—21no—
45C2×Dic244—21no—
46C2×Dic244—21no—
47C2×Dic244D411yescharacteristic
48C2×Dic244C2312yes—
49C2×#11758190—21no—
50C2×#11758190—24no—
51C2×#11758190—41no—
52C2×#11758190—41no—
53C2×#11758190—42no—
54C2×D488—21no—
55C2×D488—21no—
56C2×D488—21no—
57C2×D488—21no—
58C2×D488—21no—
59C2×D488D411yescharacteristic
60C2×D488C2312yes—
61#14519783—24no—
62#14519783—42no—
63C2×#11758194—21no—
64C2×#11758189—41no—
65C2×C8×D61—41no—
66#14519765—24no—
67#14519765—42no—
68C2×#11758198—42no—
69Dic488—24no—
70#14519722—24no—
71#14519722—24no—
72D976—24no—
73#14519713—21no—
74#14519713C2312yes—
75#14519705—24no—
76C22×C8×C61D411yescharacteristic
77C22×C8×C61C2311yescharacteristic
78C2×C42×C61D411yescharacteristic
79M32×C61—21no—
80M32×C61—21no—
81M32×C61C2312yes—
82M32×C61C2312yes—
83C2×C16×C61—21no—
84C2×C16×C61—21no—
85C4×C8×C61D412yes—
86C4×C8×C61C2312yes—
87C23×D61—41no—
88C22×C4×C61—21no—
89C22×C4×C61C2×D411yescharacteristic
90C2×C22⋊D61—41no—
91C22×Dic61—41no—
92#11758222—22no—
93#11758222—22no—
94#11758222—41no—
95#11758222—41no—
96C2×D244—21no—
97C2×D244—22no—
98C2×D244—41no—
99C2×D244—41no—
100C2×D244—41no—
101C2×D244—41no—
102C2×D244—41no—
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—
111C2×C8×C61D811yescharacteristic
112C2×C8×C61D811yescharacteristic
113C2×C8×C61D812yes—
114C2×C8×C61C2×D411yescharacteristic
115C2×C8×C61C2×D411yescharacteristic
116C2×C8×C61C2×D411yescharacteristic
117C2×C8×C61C2×D412yes—
118C2×C8×C61#4111yescharacteristic
119C2×C8×C61#4111yescharacteristic
120C2×C8×C61C2411yescharacteristic
121C42×C61—21no—
122C42×C61C2×D412yes—
123#11758198—48no—
124#11758194—22no—
125#11758194—41no—
126C2×#92418—41no—
127Dic244—21no—
128Dic244—22no—
129Dic244—22no—
130Dic244—41no—
131Dic244—41no—
132Dic244C2×D412yes—
133D488—21no—
134D488—22no—
135D488—22no—
136D488—41no—
137D488—41no—
138D488C2×D412yes—
139#11758190—22no—
140#11758190—22no—
141#11758190—44no—
142#11758190—44no—
143#11758189—44no—
144C8×D61—44no—
145C16×C61—22no—
146C16×C61—22no—
147C23×C61AGL(1,ℤ/8)11yescharacteristic
148C22×D61—41no—
149C22×D61—42no—
150C22×D61—84no—
151C22×D61—81no—
152C22×D61—81no—
153C2×C4×C61—22no—
154C2×C4×C61—42no—
155C2×C4×C61#12111yescharacteristic
156C2×C4×C61#12111yescharacteristic
157C2×C4×C61C2×D811yescharacteristic
158C2×C4×C61C2×D811yescharacteristic
159C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C61C22×D411yescharacteristic
161C22⋊D61—42no—
162C22⋊D61—42no—
163C2×Dic61—41no—
164C2×Dic61—42no—
165C2×Dic61—81no—
166C2×Dic61—81no—
167D244—22no—
168D244—42no—
169D244—42no—
170D244—41no—
171D244—81no—
172D244—81no—
173C4×D61—42no—
174C4×D61—42no—
175Dic122—22no—
176Dic122—41no—
177Dic122—42no—
178Dic122—42no—
179Dic122—81no—
180Dic122—81no—
181C8×C61#12111yescharacteristic
182C8×C61#12111yescharacteristic
183C8×C61C2×D812yes—
184C8×C61C2×D812yes—
185C8×C61C22×D411yescharacteristic
186C8×C61C2×#4111yescharacteristic
187#92418—42no—
188C2×#2212—611nomaximal, Sylow
189C22×C61—22no—
190C22×C61#45911yescharacteristic
191C22×C61#45911yescharacteristic
192C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
193C2×D61—42no—
194C2×D61—82no—
195C2×D61—84no—
196C2×D61—82no—
197C2×D61—162no—
198C2×D61—162no—
199C4×C61—42no—
200C4×C61#45911yescharacteristic
201C4×C61#45911yescharacteristic
202C4×C61C2×#12111yescharacteristic
203C4×C61C22×D811yescharacteristic
204Dic61—42no—
205Dic61—82no—
206C2×#510—611no—
207C2×#509—611no—
208C2×#495—611no—
209C2×#443—611no—
210#2212—618no—
211C2×#364D6111yescharacteristic, complemented
212C2×#362—611no—
213C2×#361—611no—
214C2×C61—21no—
215C2×C61—21no—
216C2×C61#221212yescomplemented
217C2×C61C2×#45911yescharacteristic
218D61—82no—
219D61—162no—
220C2×#135—611no—
221C22×Q16—611no—
222C22×SD16—1221no—
223C22×D8—611no—
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×M32C2×D6111yescharacteristic
235C2×M32C2×D6111yescharacteristic
236#495—614no—
237#495—1222no—
238#443—614no—
239#443—1222no—
240C2×#108—611no—
241C2×#104—1221no—
242C2×C4×C8C2×D6111yescharacteristic
243#364C2×D6114yescomplemented
244#362—614no—
245#361—614no—
246C61C2×#221211yescharacteristic, complemented, Sylow
247C2×#41—1221no—
248C22×Q8—1221no—
249C22×D4—1221no—
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—611no—
267C2×D8—612no—
268C2×D8—1221no—
269C2×D8—1221no—
270C2×D8—1221no—
271C2×D8—1221no—
272C2×D8—1221no—
273#131—1224no—
274#131—2442no—
275C2×M16—1221no—
276C2×M16—2441no—
277C22×C8—2441no—
278C22×C8D24411yescharacteristic
279C22×C8C22×D6111yescharacteristic
280#124—1224no—
281#124—2442no—
282C2×C22⋊C4—2442no—
283C2×C42D24411yescharacteristic
284Q32—1224no—
285SD32—1224no—
286SD32—1224no—
287D16—1224no—
288M32—21no—
289M32—21no—
290M32C22×D6112yes—
291M32C22×D6112yes—
292C2×C16—21no—
293C2×C16—21no—
294#108—612no—
295#108—1221no—
296#104—1224no—
297C4×C8D24412yes—
298C4×C8C22×D6112yes—
299C24—2441no—
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—1222no—
312C2×D4—1221no—
313C2×D4—2441no—
314C2×D4—2441no—
315C2×D4—2441no—
316C2×D4—2441no—
317C2×D4—2441no—
318C2×D4—2441no—
319C22×C4—21no—
320C22×C4—2441no—
321C22×C4—2441no—
322C22×C4C2×D24411yescharacteristic
323Q16—612no—
324Q16—1222no—
325Q16—1222no—
326Q16—1221no—
327Q16—2441no—
328Q16—2441no—
329SD16—1222no—
330SD16—1222no—
331SD16—2444no—
332SD16—2444no—
333D8—612no—
334D8—1222no—
335D8—1222no—
336D8—1221no—
337D8—2441no—
338D8—2441no—
339M16—1222no—
340M16—2441no—
341M16—2444no—
342C2×C8—2441no—
343C2×C8—2444no—
344C2×C8D48811yescharacteristic
345C2×C8D48811yescharacteristic
346C2×C8D48812yes—
347C2×C8C2×D24411yescharacteristic
348C2×C8C2×D24412yes—
349C2×C8D4×D6111yescharacteristic
350C2×C8D4×D6111yescharacteristic
351C2×C8#1175822611yescharacteristic
352C2×C8#1175822611yescharacteristic
353C2×C8C23×D6111yescharacteristic
354C22⋊C4—2448no—
355C42—21no—
356C42C2×D24412yes—
357C16—22no—
358C16—22no—
359C23—4884no—
360C23—4881no—
361C23—4881no—
362C23—2442no—
363C23—2441no—
364C23#1451980511yescharacteristic
365Q8—1222no—
366Q8—4881no—
367Q8—4881no—
368Q8—2442no—
369Q8—2442no—
370Q8—2441no—
371D4—1222no—
372D4—4881no—
373D4—4881no—
374D4—2442no—
375D4—2442no—
376D4—2441no—
377D4—2442no—
378D4—2442no—
379C2×C4—22no—
380C2×C4—42no—
381C2×C4—4881no—
382C2×C4—4881no—
383C2×C4—2442no—
384C2×C4—2441no—
385C2×C4—2442no—
386C2×C4—2442no—
387C2×C4#1451975211yescharacteristic
388C2×C4#1451975211yescharacteristic
389C2×C4C2×D48811yescharacteristic
390C2×C4C2×D48811yescharacteristic
391C2×C4#1451980511yescharacteristic
392C2×C4C22×D24411yescharacteristic
393C8—2442no—
394C8#1451975211yescharacteristic
395C8#1451975211yescharacteristic
396C8C2×D48812yes—
397C8C2×D48812yes—
398C8C2×D4×D6111yescharacteristic
399C8C2×#1175822611yescharacteristic
400C22—22no—
401C22—9762no—
402C22—9762no—
403C22—4884no—
404C22—4882no—
405C22—4882no—
406C22—2442no—
407C22#1683995811yescharacteristic
408C22#1683995811yescharacteristic
409C22C2×#1451980511yescharacteristic
410C4—42no—
411C4—4882no—
412C4—2442no—
413C4#1683995811yescharacteristic
414C4#1683995811yescharacteristic
415C4C2×#1451975211yescharacteristic
416C4C22×D48811yescharacteristic
417C2—21no—
418C2—21no—
419C2—9762no—
420C2—4882no—
421C2#2144788912yesdirect product factor
422C2C2×#1683995811yescharacteristic
subgroupG/H
centerC22#16839958
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC2×C61×#364C2
socleC22×C61#459
prime radicalC2×#16840200C2
hypercenterC2×#364D61
hypocenterC61C2×#2212
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×#364

Complements

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

NH ≅ G/Ntype
1. C2×#16840205C2semidirect
3. C2×#16840146C2semidirect
4. C2×#16839880C2semidirect
5. #21447889C2direct (N × H)
6. C2×#16839579C2semidirect
7. C2×#16839576C2semidirect
8. C2×C61×#364C2semidirect
16. #16840205C22semidirect
24. #16840146C22semidirect
26. #16839880C22semidirect
29. #16839579C22semidirect
30. #16839576C22semidirect
34. C61×#364C22semidirect
211. C2×#364D61semidirect
216. C2×C61#2212semidirect
243. #364C2×D61semidirect
246. C61C2×#2212semidirect
421. C2#21447889direct (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×#168402002
C2×#168401462
C2×#168398802
#214478892
C2×#168395792
C2×#168395762
C2×C61×#3642
C2×#221261