Finite Group Databasebeta

← C2×#21447893 #29834391

Subgroups — C2×#21447893 #29834391

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×#16840197C211yesmaximal, characteristic, complemented
2C2×#16840137C211yesmaximal, characteristic, complemented
3C2×#16839879C211yesmaximal, characteristic, complemented
4#21447893C218yesmaximal, direct product factor
5C2×#16839582C211yesmaximal, characteristic, complemented
6C2×#16839576C211yesmaximal, characteristic, complemented
7C2×#16839575C211yesmaximal, characteristic, complemented
8C2×C61×#509C211yesmaximal, characteristic, complemented
9C22×D488C2211yescharacteristic
10C22×#11758199—21no—
11C2×#14519784—21no—
12C2×#14519773—21no—
13#16840197—22no—
14#16840197C2214yescomplemented
15C2×#14519720—21no—
16C2×#14519718—21no—
17C2×#14519717C2211yescharacteristic
18#16840137—22no—
19#16840137C2214yescomplemented
20#16839879—22no—
21#16839879C2214yescomplemented
22C2×#14519713C2211yescharacteristic
23C2×#14519704—21no—
24C2×C8×Dic61C2211yescharacteristic
25#16839582C2214yescomplemented
26#16839576C2214yescomplemented
27#16839575C2214yescomplemented
28C2×#135×C61C2211yescharacteristic
29C22×D8×C61C2211yescharacteristic
30C61×#509—22no—
31C61×#509C2214yescomplemented
32C2×SD32×C61—21no—
33C2×D16×C61—21no—
34C2×M32×C61C2211yescharacteristic
35C22×D244—21no—
36C22×C22⋊D61—42no—
37C2×D488—21no—
38C2×D488—21no—
39C2×D488—21no—
40C2×D488—21no—
41C2×D488—21no—
42C2×D488C2312yes—
43C2×#11758199—24no—
44C2×#11758199—41no—
45C2×#11758199—41no—
46C2×#11758199—42no—
47#14519784—24no—
48#14519784—42no—
49C2×#11758194—21no—
50C2×#11758194—41no—
51C22×#92418—41no—
52C22×#92418D411yescharacteristic
53#14519773—24no—
54#14519773—42no—
55C2×C4×Dic61D411yescharacteristic
56#14519720—24no—
57#14519718—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×C61D412yescomplemented
71#135×C61C2312yes—
72C2×Q16×C61D411yescharacteristic, complemented
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, complemented
80C2×D8×C61C2312yes—
81C22×C8×C61C2311yescharacteristic
82SD32×C61—24no—
83D16×C61—24no—
84M32×C61—21no—
85M32×C61C2312yes—
86C2×C16×C61—21no—
87C24×C61—41no—
88C23×D61—41no—
89#41×C61—22no—
90#41×C61—22no—
91#41×C61—41no—
92#41×C61—41no—
93C2×Q8×C61—21no—
94C2×D4×C61—21no—
95C2×D4×C61—22no—
96C2×D4×C61—41no—
97C2×D4×C61—41no—
98C2×D4×C61—41no—
99C2×D4×C61—41no—
100C2×D4×C61—41no—
101C2×D4×C61—41no—
102C22×C4×C61—41no—
103C22×C4×C61C2×D411yescharacteristic
104C2×C22⋊D61—48no—
105C2×C22⋊D61—88no—
106C22×Dic61—21no—
107C2×D244—22no—
108C2×D244—41no—
109C2×D244—41no—
110C2×D244—41no—
111C2×D244—41no—
112C2×D244—41no—
113Q16×C61—21no—
114Q16×C61C2×D412yescomplemented
115SD16×C61—22no—
116SD16×C61—22no—
117D8×C61—21no—
118D8×C61—22no—
119D8×C61—22no—
120D8×C61—41no—
121D8×C61—41no—
122D8×C61C2×D412yescomplemented
123C2×C8×C61C2×D411yescharacteristic
124C2×C8×C61C2×D411yescharacteristic
125C2×C8×C61C2×D411yescharacteristic
126C2×C8×C61#4111yescharacteristic
127C2×C8×C61#4111yescharacteristic
128C2×C8×C61C2411yescharacteristic
129#11758199—44no—
130#11758199—44no—
131C4×Dic61—21no—
132C4×Dic61C2×D412yes—
133#11758194—22no—
134#11758194—41no—
135#11758194—44no—
136C2×#92418—41no—
137C2×#92418—44no—
138C2×#92418D811yescharacteristic
139C2×#92418D811yescharacteristic
140C2×#92418D812yes—
141C2×#92418C2×D412yes—
142D488—22no—
143D488—22no—
144D488—41no—
145D488—41no—
146C16×C61—22no—
147#11758185—22no—
148C23×C61—41no—
149C23×C61—42no—
150C23×C61—84no—
151C23×C61—81no—
152C23×C61—81no—
153C23×C61AGL(1,ℤ/8)11yescharacteristic
154C22×D61—42no—
155C22×D61—84no—
156C22×D61—81no—
157C22×D61—81no—
158Q8×C61—22no—
159Q8×C61—41no—
160D4×C61—22no—
161D4×C61—42no—
162D4×C61—42no—
163D4×C61—42no—
164D4×C61—42no—
165D4×C61—41no—
166D4×C61—81no—
167D4×C61—81no—
168C2×C4×C61—41no—
169C2×C4×C61—42no—
170C2×C4×C61—42no—
171C2×C4×C61#12111yescharacteristic
172C2×C4×C61#12111yescharacteristic
173C2×C4×C61C2×D811yescharacteristic
174C2×C4×C61C2×D811yescharacteristic
175C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
176C2×C4×C61C22×D411yescharacteristic
177C22⋊D61—816no—
178C2×Dic61—24no—
179C2×Dic61—22no—
180D244—42no—
181D244—42no—
182D244—81no—
183D244—81no—
184C8×C61#12111yescharacteristic
185C8×C61#12111yescharacteristic
186C8×C61C22×D411yescharacteristic
187C8×C61C2×#4111yescharacteristic
188#92418—42no—
189#92418C2×D812yes—
190#92418C2×D812yes—
191C2×#2213—611nomaximal, Sylow
192C22×C61—22no—
193C22×C61—42no—
194C22×C61—84no—
195C22×C61—82no—
196C22×C61—82no—
197C22×C61—162no—
198C22×C61—162no—
199C22×C61#45911yescharacteristic
200C22×C61#45911yescharacteristic
201C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
202C2×D61—84no—
203C2×D61—82no—
204C2×D61—162no—
205C2×D61—162no—
206C4×C61—42no—
207C4×C61#45911yescharacteristic
208C4×C61#45911yescharacteristic
209C4×C61C2×#12111yescharacteristic
210C4×C61C22×D811yescharacteristic
211Dic61—24no—
212C2×#509—611no—
213C2×#509D6111yescharacteristic, complemented
214C2×#493—611no—
215C2×#443—611no—
216#2213—618no—
217C2×#364—611no—
218C2×#361—611no—
219C2×#361—611no—
220C2×C61—21no—
221C2×C61—21no—
222C2×C61—82no—
223C2×C61—162no—
224C2×C61#221312yescomplemented
225C2×C61C2×#45911yescharacteristic
226D61—162no—
227C2×#135C2×D6111yescharacteristic
228C22×D8—611no—
229C22×D8—1221no—
230C22×D8C2×D6111yescharacteristic
231C2×#131—1221no—
232C2×#127—1221no—
233#509—22no—
234#509—614no—
235#509—1222no—
236#509C2×D6114yescomplemented
237C2×SD32—21no—
238C2×SD32—1221no—
239C2×D16—21no—
240C2×D16—1221no—
241C2×M32—611no—
242C2×M32C2×D6111yescharacteristic
243#493—614no—
244#493—1222no—
245#443—614no—
246#443—1222no—
247C2×#108—611no—
248C2×#104—1221no—
249C2×C4×C8—611no—
250#364—614no—
251#361—614no—
252#361—614no—
253C61C2×#221311yescharacteristic, complemented, Sylow
254C2×#41—21no—
255C22×D4—21no—
256C22×D4—1221no—
257C22×D4—2442no—
258#135—21no—
259#135—21no—
260#135C22⋊D6112yescomplemented
261#135C22×D6112yes—
262C2×Q16C22⋊D6111yescharacteristic, complemented
263C2×SD16—21no—
264C2×D8—21no—
265C2×D8—21no—
266C2×D8—21no—
267C2×D8—21no—
268C2×D8—21no—
269C2×D8—612no—
270C2×D8—1224no—
271C2×D8—1221no—
272C2×D8—1221no—
273C2×D8—1221no—
274C2×D8—1221no—
275C2×D8—1221no—
276C2×D8—2441no—
277C2×D8—2441no—
278C2×D8—2442no—
279C2×D8C22⋊D6111yescharacteristic, complemented
280C2×D8C22×D6112yes—
281#131—1224no—
282#131—2442no—
283C2×M16—1221no—
284C2×M16—2441no—
285C22×C8—611no—
286C22×C8—2441no—
287C22×C8C22×D6111yescharacteristic
288#127—1224no—
289#127—2442no—
290C2×C42—611no—
291SD32—24no—
292SD32—1224no—
293D16—24no—
294D16—1224no—
295M32—21no—
296M32—612no—
297M32—1221no—
298M32C22×D6112yes—
299C2×C16—21no—
300C2×C16—1221no—
301#108—612no—
302#108—1221no—
303#104—1224no—
304C4×C8—612no—
305C4×C8—612no—
306C24—41no—
307C24—2441no—
308#41—22no—
309#41—22no—
310#41—41no—
311#41—41no—
312C2×Q8—21no—
313C2×D4—22no—
314C2×D4—21no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—1222no—
322C2×D4—4888no—
323C2×D4—2448no—
324C2×D4—2441no—
325C2×D4—2441no—
326C2×D4—2441no—
327C2×D4—2441no—
328C2×D4—2441no—
329C22×C4—41no—
330C22×C4—1221no—
331C22×C4D4×D6111yescharacteristic
332Q16—21no—
333Q16C2×C22⋊D6112yescomplemented
334SD16—22no—
335SD16—22no—
336D8—22no—
337D8—22no—
338D8—21no—
339D8—41no—
340D8—41no—
341D8—1222no—
342D8—1222no—
343D8—2444no—
344D8—2444no—
345D8—2441no—
346D8—2441no—
347D8C2×C22⋊D6112yescomplemented
348M16—1222no—
349M16—2444no—
350M16—2441no—
351C2×C8—612no—
352C2×C8—611no—
353C2×C8—611no—
354C2×C8—612no—
355C2×C8—2444no—
356C2×C8—2441no—
357C2×C8D4×D6111yescharacteristic
358C2×C8#1175822411yescharacteristic
359C2×C8#1175822411yescharacteristic
360C2×C8C2×C22⋊D6111yescharacteristic
361C2×C8C2×C22⋊D6111yescharacteristic
362C2×C8C23×D6111yescharacteristic
363C42—612no—
364C42—1221no—
365C16—22no—
366C16—1222no—
367C23—41no—
368C23—42no—
369C23—84no—
370C23—81no—
371C23—81no—
372C23—4884no—
373C23—4881no—
374C23—4881no—
375C23—2442no—
376C23#1451980111yescharacteristic
377Q8—22no—
378Q8—41no—
379D4—22no—
380D4—42no—
381D4—42no—
382D4—41no—
383D4—42no—
384D4—42no—
385D4—81no—
386D4—81no—
387D4—48816no—
388D4—4881no—
389D4—4881no—
390D4—2442no—
391D4—2442no—
392C2×C4—41no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—1224no—
396C2×C4—1222no—
397C2×C4#1451974911yescharacteristic
398C2×C4#1451974911yescharacteristic
399C2×C4D8×D6111yescharacteristic
400C2×C4D8×D6111yescharacteristic
401C2×C4#1451980111yescharacteristic
402C2×C4C2×D4×D6111yescharacteristic
403C8—612no—
404C8—612no—
405C8—2442no—
406C8#1451974911yescharacteristic
407C8#1451974911yescharacteristic
408C8C22×C22⋊D6111yescharacteristic
409C8C2×#1175822411yescharacteristic
410C22—22no—
411C22—42no—
412C22—84no—
413C22—82no—
414C22—82no—
415C22—162no—
416C22—162no—
417C22—9762no—
418C22—9762no—
419C22—4884no—
420C22—4882no—
421C22#1683995511yescharacteristic
422C22#1683995511yescharacteristic
423C22C2×#1451980111yescharacteristic
424C4—42no—
425C4—1224no—
426C4#1683995511yescharacteristic
427C4#1683995511yescharacteristic
428C4C2×#1451974911yescharacteristic
429C4C2×D8×D6111yescharacteristic
430C2—21no—
431C2—21no—
432C2—82no—
433C2—162no—
434C2—9762no—
435C2#2144789312yesdirect product factor
436C2C2×#1683995511yescharacteristic
subgroupG/H
centerC22#16839955
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC2×C61×#509C2
socleC22×C61#459
hypercenterC2×#509D61
hypocenterC61C2×#2213
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×#16840197C2semidirect
2. C2×#16840137C2semidirect
3. C2×#16839879C2semidirect
4. #21447893C2direct (N × H)
5. C2×#16839582C2semidirect
6. C2×#16839576C2semidirect
7. C2×#16839575C2semidirect
8. C2×C61×#509C2semidirect
14. #16840197C22semidirect
19. #16840137C22semidirect
21. #16839879C22semidirect
25. #16839582C22semidirect
26. #16839576C22semidirect
27. #16839575C22semidirect
31. C61×#509C22semidirect
70. #135×C61D4semidirect
72. C2×Q16×C61D4semidirect
79. C2×D8×C61D4semidirect
114. Q16×C61C2×D4semidirect
122. D8×C61C2×D4semidirect
213. C2×#509D61semidirect
224. C2×C61#2213semidirect
236. #509C2×D61semidirect
253. C61C2×#2213semidirect
260. #135C22⋊D61semidirect
262. C2×Q16C22⋊D61semidirect
279. C2×D8C22⋊D61semidirect
333. Q16C2×C22⋊D61semidirect
347. D8C2×C22⋊D61semidirect
435. C2#21447893direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168401972
C2×#168401372
C2×#168398792
#214478932
C2×#168395822
C2×#168395762
C2×#168395752
C2×C61×#5092
C2×#221361