Finite Group Databasebeta

← C2×#21447886 #29834383

Subgroups — C2×#21447886 #29834383

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×#16840202C211yesmaximal, characteristic, complemented
2C2×#16840145C211yesmaximal, characteristic, complemented
3C2×#16839879C211yesmaximal, characteristic, complemented
4#21447886C218yesmaximal, direct product factor
5C2×#16839582C211yesmaximal, characteristic, complemented
6C2×#16839579C211yesmaximal, characteristic, complemented
7C2×#16839575C211yesmaximal, characteristic, complemented
8C2×C61×#509C211yesmaximal, characteristic
9C22×Dic244C2211yescharacteristic
10C22×#11758200—21no—
11C2×#14519784—21no—
12C2×#14519764—21no—
13#16840202—22no—
14#16840202C2214yescomplemented
15C2×#14519723—21no—
16C2×#14519721—21no—
17C2×#14519717C2211yescharacteristic
18#16840145—22no—
19#16840145C2214yescomplemented
20#16839879—22no—
21#16839879C2214yescomplemented
22C2×#14519713C2211yescharacteristic
23C2×#14519704—21no—
24C2×C8×Dic61C2211yescharacteristic
25#16839582C2214yescomplemented
26#16839579C2214yescomplemented
27#16839575C2214yescomplemented
28C2×#135×C61C2211yescharacteristic
29C22×D8×C61C2211yescharacteristic
30C61×#509—22no—
31C61×#509C2214yes—
32C2×SD32×C61—21no—
33C2×D16×C61—21no—
34C2×M32×C61C2211yescharacteristic
35C22×Dic122—21no—
36C2×Dic244—21no—
37C2×Dic244—21no—
38C2×Dic244—21no—
39C2×Dic244—21no—
40C2×Dic244—21no—
41C2×Dic244C2312yes—
42C2×#11758200—24no—
43C2×#11758200—41no—
44C2×#11758200—41no—
45C2×#11758200—42no—
46#14519784—24no—
47#14519784—42no—
48C2×#11758194—21no—
49C2×#11758194—41no—
50C22×#92418—41no—
51C22×#92418D411yescharacteristic
52#14519764—24no—
53#14519764—42no—
54C2×C22⋊Dic61—42no—
55C2×C4×Dic61D411yescharacteristic
56#14519723—24no—
57#14519721—24no—
58#14519717—21no—
59#14519717C2312yes—
60C2×#11758185—21no—
61#14519713—21no—
62#14519713C2312yes—
63#14519704—24no—
64C8×Dic61D412yes—
65C8×Dic61C2312yes—
66C2×#41×C61—21no—
67C22×D4×C61—21no—
68#135×C61—21no—
69#135×C61—21no—
70#135×C61D412yes—
71#135×C61C2312yes—
72C2×Q16×C61D411yescharacteristic
73C2×SD16×C61—21no—
74C2×D8×C61—21no—
75C2×D8×C61—21no—
76C2×D8×C61—21no—
77C2×D8×C61—21no—
78C2×D8×C61—21no—
79C2×D8×C61D411yescharacteristic
80C2×D8×C61C2312yes—
81C22×C8×C61C2311yescharacteristic
82SD32×C61—24no—
83D16×C61—24no—
84M32×C61—21no—
85M32×C61C2312yes—
86C2×C16×C61—21no—
87C24×C61—41no—
88#41×C61—22no—
89#41×C61—22no—
90#41×C61—41no—
91#41×C61—41no—
92C2×Q8×C61—21no—
93C2×D4×C61—21no—
94C2×D4×C61—22no—
95C2×D4×C61—41no—
96C2×D4×C61—41no—
97C2×D4×C61—41no—
98C2×D4×C61—41no—
99C2×D4×C61—41no—
100C2×D4×C61—41no—
101C22×C4×C61—41no—
102C22×C4×C61C2×D411yescharacteristic
103C22×Dic61—21no—
104C22×Dic61—41no—
105C2×Dic122—22no—
106C2×Dic122—41no—
107C2×Dic122—41no—
108C2×Dic122—41no—
109C2×Dic122—41no—
110C2×Dic122—41no—
111Q16×C61—21no—
112Q16×C61C2×D412yes—
113SD16×C61—22no—
114SD16×C61—22no—
115D8×C61—21no—
116D8×C61—22no—
117D8×C61—22no—
118D8×C61—41no—
119D8×C61—41no—
120D8×C61C2×D412yes—
121C2×C8×C61C2×D411yescharacteristic
122C2×C8×C61C2×D411yescharacteristic
123C2×C8×C61C2×D411yescharacteristic
124C2×C8×C61#4111yescharacteristic
125C2×C8×C61#4111yescharacteristic
126C2×C8×C61C2411yescharacteristic
127C22⋊Dic61—48no—
128#11758200—44no—
129#11758200—44no—
130C4×Dic61—21no—
131C4×Dic61C2×D412yes—
132#11758194—22no—
133#11758194—41no—
134#11758194—44no—
135C2×#92418—41no—
136C2×#92418—44no—
137C2×#92418D811yescharacteristic
138C2×#92418D811yescharacteristic
139C2×#92418D812yes—
140C2×#92418C2×D412yes—
141Dic244—22no—
142Dic244—22no—
143Dic244—41no—
144Dic244—41no—
145C16×C61—22no—
146#11758185—22no—
147C23×C61—41no—
148C23×C61—42no—
149C23×C61—84no—
150C23×C61—81no—
151C23×C61—81no—
152C23×C61AGL(1,ℤ/8)11yescharacteristic
153Q8×C61—22no—
154Q8×C61—41no—
155D4×C61—22no—
156D4×C61—42no—
157D4×C61—42no—
158D4×C61—42no—
159D4×C61—42no—
160D4×C61—41no—
161D4×C61—81no—
162D4×C61—81no—
163C2×C4×C61—41no—
164C2×C4×C61—42no—
165C2×C4×C61—42no—
166C2×C4×C61#12111yescharacteristic
167C2×C4×C61#12111yescharacteristic
168C2×C4×C61C2×D811yescharacteristic
169C2×C4×C61C2×D811yescharacteristic
170C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C61C22×D411yescharacteristic
172C2×Dic61—22no—
173C2×Dic61—42no—
174C2×Dic61—42no—
175C2×Dic61—81no—
176C2×Dic61—81no—
177Dic122—42no—
178Dic122—42no—
179Dic122—81no—
180Dic122—81no—
181C8×C61#12111yescharacteristic
182C8×C61#12111yescharacteristic
183C8×C61C22×D411yescharacteristic
184C8×C61C2×#4111yescharacteristic
185#92418—42no—
186#92418C2×D812yes—
187#92418C2×D812yes—
188C2×#2212—611nomaximal, Sylow
189C22×C61—22no—
190C22×C61—42no—
191C22×C61—84no—
192C22×C61—82no—
193C22×C61—82no—
194C22×C61—162no—
195C22×C61—162no—
196C22×C61#45911yescharacteristic
197C22×C61#45911yescharacteristic
198C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
199C4×C61—42no—
200C4×C61#45911yescharacteristic
201C4×C61#45911yescharacteristic
202C4×C61C2×#12111yescharacteristic
203C4×C61C22×D811yescharacteristic
204Dic61—42no—
205Dic61—82no—
206C2×#510—611no—
207C2×#509D6111yescharacteristic
208C2×#495—611no—
209C2×#443—611no—
210#2212—618no—
211C2×#364—611no—
212C2×#362—611no—
213C2×#361—611no—
214C2×C61—21no—
215C2×C61—21no—
216C2×C61—82no—
217C2×C61—162no—
218C2×C61#221212yescomplemented
219C2×C61C2×#45911yescharacteristic
220C2×#135C2×D6111yescharacteristic
221C22×Q16—611no—
222C22×SD16—1221no—
223C22×D8C2×D6111yescharacteristic
224C2×#131—1221no—
225C2×#124—1221no—
226#510—614no—
227#510—1222no—
228#509—22no—
229#509C2×D6114yes—
230C2×Q32—1221no—
231C2×SD32—21no—
232C2×SD32—1221no—
233C2×D16—21no—
234C2×M32—611no—
235C2×M32C2×D6111yescharacteristic
236#495—614no—
237#495—1222no—
238#443—614no—
239#443—1222no—
240C2×#108—611no—
241C2×#104—1221no—
242C2×C4×C8—611no—
243#364—614no—
244#362—614no—
245#361—614no—
246C61C2×#221211yescharacteristic, complemented, Sylow
247C2×#41—21no—
248C22×Q8—1221no—
249C22×D4—21no—
250#135—21no—
251#135—21no—
252#135C22⋊D6112yes—
253#135C22×D6112yes—
254C2×Q16—612no—
255C2×Q16—1221no—
256C2×Q16—1221no—
257C2×Q16—1221no—
258C2×Q16—1221no—
259C2×Q16—1221no—
260C2×Q16C22⋊D6111yescharacteristic
261C2×SD16—21no—
262C2×SD16—1224no—
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×D8C22⋊D6111yescharacteristic
272C2×D8C22×D6112yes—
273#131—1224no—
274#131—2442no—
275C2×M16—1221no—
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—24no—
286SD32—1224no—
287D16—24no—
288M32—21no—
289M32—612no—
290M32—1221no—
291M32C22×D6112yes—
292C2×C16—21no—
293C2×C16—1221no—
294#108—612no—
295#108—1221no—
296#104—1224no—
297C4×C8—612no—
298C4×C8—612no—
299C24—41no—
300#41—22no—
301#41—22no—
302#41—41no—
303#41—41no—
304C2×Q8—21no—
305C2×Q8—1222no—
306C2×Q8—2441no—
307C2×Q8—2441no—
308C2×Q8—2441no—
309C2×Q8—2441no—
310C2×Q8—2441no—
311C2×D4—22no—
312C2×D4—21no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C22×C4—41no—
320C22×C4—1221no—
321C22×C4—2441no—
322C22×C4D4×D6111yescharacteristic
323Q16—21no—
324Q16—1222no—
325Q16—1222no—
326Q16—2441no—
327Q16—2441no—
328Q16C2×C22⋊D6112yes—
329SD16—22no—
330SD16—22no—
331SD16—2444no—
332SD16—2444no—
333D8—22no—
334D8—22no—
335D8—21no—
336D8—41no—
337D8—41no—
338D8C2×C22⋊D6112yes—
339M16—1222no—
340M16—2444no—
341M16—2441no—
342C2×C8—612no—
343C2×C8—611no—
344C2×C8—611no—
345C2×C8—612no—
346C2×C8—2444no—
347C2×C8—2441no—
348C2×C8D4×D6111yescharacteristic
349C2×C8#1175822411yescharacteristic
350C2×C8#1175822411yescharacteristic
351C2×C8C2×C22⋊D6111yescharacteristic
352C2×C8C2×C22⋊D6111yescharacteristic
353C2×C8C23×D6111yescharacteristic
354C22⋊C4—2448no—
355C42—612no—
356C42—1221no—
357C16—22no—
358C16—1222no—
359C23—41no—
360C23—42no—
361C23—84no—
362C23—81no—
363C23—81no—
364C23#1451980111yescharacteristic
365Q8—22no—
366Q8—41no—
367Q8—4881no—
368Q8—4881no—
369Q8—2442no—
370Q8—2442no—
371D4—22no—
372D4—42no—
373D4—42no—
374D4—41no—
375D4—42no—
376D4—42no—
377D4—81no—
378D4—81no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—1222no—
383C2×C4—4881no—
384C2×C4—4881no—
385C2×C4—2442no—
386C2×C4—2442no—
387C2×C4#1451974911yescharacteristic
388C2×C4#1451974911yescharacteristic
389C2×C4D8×D6111yescharacteristic
390C2×C4D8×D6111yescharacteristic
391C2×C4#1451980111yescharacteristic
392C2×C4C2×D4×D6111yescharacteristic
393C8—612no—
394C8—612no—
395C8—2442no—
396C8#1451974911yescharacteristic
397C8#1451974911yescharacteristic
398C8C22×C22⋊D6111yescharacteristic
399C8C2×#1175822411yescharacteristic
400C22—22no—
401C22—42no—
402C22—84no—
403C22—82no—
404C22—82no—
405C22—162no—
406C22—162no—
407C22#1683995511yescharacteristic
408C22#1683995511yescharacteristic
409C22C2×#1451980111yescharacteristic
410C4—42no—
411C4—4882no—
412C4—2442no—
413C4#1683995511yescharacteristic
414C4#1683995511yescharacteristic
415C4C2×#1451974911yescharacteristic
416C4C2×D8×D6111yescharacteristic
417C2—21no—
418C2—21no—
419C2—82no—
420C2—162no—
421C2#2144788612yesdirect product factor
422C2C2×#1683995511yescharacteristic
subgroupG/H
centerC22#16839955
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
Fitting, prime radicalC2×C61×#509C2
socleC22×C61#459
hypercenterC2×#509D61
hypocenterC61C2×#2212
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#509

Complements

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

NH ≅ G/Ntype
1. C2×#16840202C2semidirect
2. C2×#16840145C2semidirect
3. C2×#16839879C2semidirect
4. #21447886C2direct (N × H)
5. C2×#16839582C2semidirect
6. C2×#16839579C2semidirect
7. C2×#16839575C2semidirect
14. #16840202C22semidirect
19. #16840145C22semidirect
21. #16839879C22semidirect
25. #16839582C22semidirect
26. #16839579C22semidirect
27. #16839575C22semidirect
218. C2×C61#2212semidirect
246. C61C2×#2212semidirect
421. C2#21447886direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402022
C2×#168401452
C2×#168398792
#214478862
C2×#168395822
C2×#168395792
C2×#168395752
C2×C61×#5092
C2×#221261