Finite Group Databasebeta

← C2×#21447899 #29834398

Subgroups — C2×#21447899 #29834398

Order 15616.

686 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840205C211yesmaximal, characteristic
2C2×#16840203C211yesmaximal, characteristic
3C2×#16840140C211yesmaximal, characteristic, complemented
4C2×#16839878C211yesmaximal, characteristic
5#21447899C218yesmaximal, direct product factor
6C2×#16839582C211yesmaximal, characteristic, complemented
7C2×#16839577C211yesmaximal, characteristic, complemented
8C2×C61×#362C211yesmaximal, characteristic, complemented
9C2×#14519799C2211yescharacteristic
10C22×Dic244C2211yescharacteristic
11C22×#11758202—21no—
12C2×#14519785—21no—
13C2×#14519775—21no—
14#16840205—22no—
15#16840205C2214yes—
16#16840203—22no—
17#16840203C2214yes—
18C2×Dic488—21no—
19C2×#14519723—21no—
20C2×#14519722—21no—
21C2×#14519720—21no—
22C2×#14519717C2211yescharacteristic
23#16840140—22no—
24#16840140C2214yescomplemented
25#16839878—22no—
26#16839878C2214yes—
27C2×#14519703—21no—
28C2×C8×Dic61C2211yescharacteristic
29#16839582C2214yescomplemented
30#16839577C2214yescomplemented
31C22×Q16×C61C2211yescharacteristic
32C2×M32×C61C2211yescharacteristic
33C2×#108×C61C2211yescharacteristic
34C61×#362C2214yescomplemented
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×#11758202—24no—
49C2×#11758202—41no—
50C2×#11758202—41no—
51C2×#11758202—42no—
52C2×#11758190—21no—
53C2×D488D411yescharacteristic
54#14519785—24no—
55#14519785—42no—
56C2×#11758189—41no—
57C22×#92418D411yescharacteristic
58C2×C8×D61—41no—
59#14519775—24no—
60#14519775—42no—
61C2×#11758196—42no—
62C2×C4×Dic61D411yescharacteristic
63Dic488—24no—
64#14519723—24no—
65#14519722—24no—
66#14519720—24no—
67#14519717—21no—
68#14519717C2312yes—
69C2×#11758185—21no—
70#14519703—24no—
71C8×Dic61D412yes—
72C8×Dic61C2312yes—
73C22×Q8×C61—21no—
74C2×Q16×C61—21no—
75C2×Q16×C61—21no—
76C2×Q16×C61—21no—
77C2×Q16×C61—21no—
78C2×Q16×C61—21no—
79C2×Q16×C61C2312yes—
80C2×M16×C61—21no—
81C22×C8×C61C2311yescharacteristic
82M32×C61—21no—
83M32×C61C2312yes—
84C2×C16×C61—21no—
85#108×C61—21no—
86#108×C61C2312yes—
87C2×Q8×C61—22no—
88C2×Q8×C61—41no—
89C2×Q8×C61—41no—
90C2×Q8×C61—41no—
91C2×Q8×C61—41no—
92C2×Q8×C61—41no—
93C22×C4×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—
111Q16×C61—22no—
112Q16×C61—22no—
113Q16×C61—41no—
114Q16×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
124#11758202—44no—
125#11758202—44no—
126#11758196—48no—
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×C61AGL(1,ℤ/8)11yescharacteristic
148C22×D61—41no—
149Q8×C61—42no—
150Q8×C61—42no—
151Q8×C61—81no—
152Q8×C61—81no—
153C2×C4×C61—42no—
154C2×C4×C61—81no—
155C2×C4×C61—81no—
156C2×C4×C61#12111yescharacteristic
157C2×C4×C61#12111yescharacteristic
158C2×C4×C61C2×D811yescharacteristic
159C2×C4×C61C2×D811yescharacteristic
160C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C61C22×D411yescharacteristic
162C22⋊D61—42no—
163C22⋊D61—42no—
164C2×Dic61—24no—
165C2×Dic61—22no—
166C2×Dic61—41no—
167C2×Dic61—42no—
168C2×Dic61—81no—
169C2×Dic61—81no—
170D244—22no—
171D244—41no—
172C4×D61—42no—
173C4×D61—42no—
174Dic122—22no—
175Dic122—41no—
176Dic122—42no—
177Dic122—42no—
178Dic122—81no—
179Dic122—81no—
180C8×C61—42no—
181C8×C61#12111yescharacteristic
182C8×C61#12111yescharacteristic
183C8×C61C22×D411yescharacteristic
184C8×C61C2×#4111yescharacteristic
185#92418C2×D812yes—
186#92418C2×D812yes—
187C2×#2214—611nomaximal, Sylow
188C22×C61—22no—
189C22×C61#45911yescharacteristic
190C22×C61#45911yescharacteristic
191C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
192C2×D61—42no—
193C2×D61—82no—
194C4×C61—82no—
195C4×C61#45911yescharacteristic
196C4×C61#45911yescharacteristic
197C4×C61C2×#12111yescharacteristic
198C4×C61C22×D811yescharacteristic
199Dic61—24no—
200Dic61—42no—
201Dic61—82no—
202C2×#510—611no—
203C2×#510—611no—
204C2×#494—611no—
205C2×#443—611no—
206#2214—618no—
207C2×#364—611no—
208C2×#362—611no—
209C2×#362D6111yescharacteristic, complemented
210C2×C61—21no—
211C2×C61—21no—
212C2×C61#221412yescomplemented
213C2×C61C2×#45911yescharacteristic
214D61—82no—
215C2×#135—611no—
216C22×Q16—611no—
217C22×Q16—1221no—
218C22×Q16C2×D6111yescharacteristic
219C2×#131—1221no—
220C2×C4⋊Q8—1221no—
221#510—614no—
222#510—614no—
223#510—1222no—
224#510—1222no—
225C2×Q32—1221no—
226C2×Q32—1221no—
227C2×SD32—1221no—
228C2×SD32—1221no—
229C2×M32—611no—
230C2×M32C2×D6111yescharacteristic
231#494—614no—
232#494—1222no—
233#443—614no—
234#443—1222no—
235C2×#108C2×D6111yescharacteristic
236C2×#104—1221no—
237C2×C4×C8—611no—
238#364—614no—
239#362—614no—
240#362C2×D6114yescomplemented
241C61C2×#221411yescharacteristic, complemented, Sylow
242C2×#41—1221no—
243C22×Q8—21no—
244C22×Q8—1221no—
245#135—612no—
246#135—612no—
247#135—1221no—
248#135—1221no—
249C2×Q16—21no—
250C2×Q16—21no—
251C2×Q16—21no—
252C2×Q16—21no—
253C2×Q16—21no—
254C2×Q16—611no—
255C2×Q16—612no—
256C2×Q16—1224no—
257C2×Q16—1221no—
258C2×Q16—1221no—
259C2×Q16—1221no—
260C2×Q16—1221no—
261C2×Q16—1221no—
262C2×Q16—2441no—
263C2×Q16—2441no—
264C2×Q16—2442no—
265C2×Q16C22×D6112yes—
266C2×SD16—1221no—
267C2×D8—611no—
268#131—1224no—
269#131—2442no—
270C2×M16—21no—
271C2×M16—2441no—
272C22×C8—611no—
273C22×C8—2441no—
274C22×C8C22×D6111yescharacteristic
275C4⋊Q8—1224no—
276C4⋊Q8—2442no—
277C2×C4⋊C4—2442no—
278C2×C42—611no—
279Q32—1224no—
280Q32—1224no—
281SD32—1224no—
282SD32—1224no—
283M32—21no—
284M32—612no—
285M32—1221no—
286M32C22×D6112yes—
287C2×C16—21no—
288C2×C16—1221no—
289#108—21no—
290#108C22×D6112yes—
291#104—1224no—
292C4×C8—612no—
293C4×C8—612no—
294#41—1222no—
295#41—1222no—
296#41—2441no—
297#41—2441no—
298C2×Q8—22no—
299C2×Q8—41no—
300C2×Q8—41no—
301C2×Q8—41no—
302C2×Q8—41no—
303C2×Q8—41no—
304C2×Q8—1222no—
305C2×Q8—1221no—
306C2×Q8—2441no—
307C2×Q8—2441no—
308C2×Q8—2441no—
309C2×Q8—2441no—
310C2×Q8—2441no—
311C2×D4—1221no—
312C2×D4—2441no—
313C22×C4—41no—
314C22×C4—1221no—
315C22×C4—2441no—
316C22×C4—2441no—
317C22×C4D4×D6111yescharacteristic
318Q16—22no—
319Q16—22no—
320Q16—41no—
321Q16—41no—
322Q16—612no—
323Q16—1222no—
324Q16—1222no—
325Q16—1221no—
326Q16—2444no—
327Q16—2444no—
328Q16—2441no—
329Q16—2441no—
330SD16—1222no—
331SD16—1222no—
332D8—612no—
333D8—1221no—
334M16—22no—
335M16—41no—
336M16—2444no—
337C2×C8—41no—
338C2×C8—612no—
339C2×C8—611no—
340C2×C8—611no—
341C2×C8—612no—
342C2×C8—2444no—
343C2×C8#1175822211yescharacteristic
344C2×C8#1175822211yescharacteristic
345C2×C8D4×D6111yescharacteristic
346C2×C8D4×D6111yescharacteristic
347C2×C8D4×D6111yescharacteristic
348C2×C8C23×D6111yescharacteristic
349C4⋊C4—2448no—
350C42—612no—
351C42—1221no—
352C16—22no—
353C16—1222no—
354C23—2441no—
355C23#1451980411yescharacteristic
356Q8—42no—
357Q8—42no—
358Q8—81no—
359Q8—81no—
360Q8—1222no—
361Q8—4881no—
362Q8—4881no—
363Q8—2442no—
364Q8—2442no—
365Q8—2441no—
366D4—1222no—
367D4—2442no—
368D4—2442no—
369D4—2441no—
370C2×C4—42no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4—1224no—
374C2×C4—1222no—
375C2×C4—4881no—
376C2×C4—4881no—
377C2×C4—2442no—
378C2×C4—2441no—
379C2×C4—2442no—
380C2×C4—2442no—
381C2×C4#1451975011yescharacteristic
382C2×C4#1451975011yescharacteristic
383C2×C4D8×D6111yescharacteristic
384C2×C4D8×D6111yescharacteristic
385C2×C4#1451980411yescharacteristic
386C2×C4C2×D4×D6111yescharacteristic
387C8—42no—
388C8—612no—
389C8—612no—
390C8#1451975011yescharacteristic
391C8#1451975011yescharacteristic
392C8C2×D4×D6111yescharacteristic
393C8C2×#1175822211yescharacteristic
394C22—22no—
395C22—4882no—
396C22—2442no—
397C22#1683995611yescharacteristic
398C22#1683995611yescharacteristic
399C22C2×#1451980411yescharacteristic
400C4—82no—
401C4—1224no—
402C4—4882no—
403C4—2442no—
404C4#1683995611yescharacteristic
405C4#1683995611yescharacteristic
406C4C2×#1451975011yescharacteristic
407C4C2×D8×D6111yescharacteristic
408C2—21no—
409C2—21no—
410C2—4882no—
411C2#2144789912yesdirect product factor
412C2C2×#1683995611yescharacteristic
subgroupG/H
centerC22#16839956
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC2×C61×#362C2
socleC22×C61#459
prime radicalC2×#14519799C22
hypercenterC2×#362D61
hypocenterC61C2×#2214
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#362

Complements

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

NH ≅ G/Ntype
3. C2×#16840140C2semidirect
5. #21447899C2direct (N × H)
6. C2×#16839582C2semidirect
7. C2×#16839577C2semidirect
8. C2×C61×#362C2semidirect
24. #16840140C22semidirect
29. #16839582C22semidirect
30. #16839577C22semidirect
34. C61×#362C22semidirect
209. C2×#362D61semidirect
212. C2×C61#2214semidirect
240. #362C2×D61semidirect
241. C61C2×#2214semidirect
411. C2#21447899direct (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×#168402032
C2×#168401402
C2×#168398782
#214478992
C2×#168395822
C2×#168395772
C2×C61×#3622
C2×#221461