Finite Group Databasebeta

← C2×#21445015 #29655922

Subgroups — C2×#21445015 #29655922

Order 15616.

1290 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840433C211yesmaximal, characteristic
2C2×#16840109C211yesmaximal, characteristic, complemented
3C2×#16840042C211yesmaximal, characteristic, complemented
4C2×#16839973C211yesmaximal, characteristic, complemented
5#21445015C218yesmaximal, direct product factor
6C2×#16839505C211yesmaximal, characteristic, complemented
7C2×#16839494C211yesmaximal, characteristic, complemented
8C2×C61×D4⋊C8C211yesmaximal, characteristic, complemented
9C22×#11758222—21no—
10C22×Dic244—21no—
11#16840433—22no—
12#16840433—22no—
13#16840433—22no—
14#16840433C2214yes—
15C2×#14519777C2211yescharacteristic
16C2×#14519774C2211yescharacteristic
17C2×#14519773—21no—
18C2×#14519751—21no—
19C2×#14519750—22no—
20C2×C4×Dic122C2211yescharacteristic
21C2×#14519739—21no—
22#16840109—22no—
23#16840109C2214yescomplemented
24#16840042—22no—
25#16840042C2214yescomplemented
26#16839973—22no—
27#16839973C2214yescomplemented
28C2×#14519710—21no—
29C2×C4⋊#92418C2211yescharacteristic
30C2×#14519702—21no—
31C2×#14519699—22no—
32C2×#14519698—21no—
33#16839505C2214yescomplemented
34#16839494C2214yescomplemented
35C2×C4×D4×C61C2211yescharacteristic
36C2×C4⋊C8×C61C2211yescharacteristic
37C2×C4×C8×C61C2211yescharacteristic
38C61×D4⋊C8C2214yescomplemented
39C2×#11758222—24no—
40C2×#11758222—24no—
41C2×#11758222—44no—
42C2×#11758222—44no—
43C22×Dic122—21no—
44C22×Dic122D411yescharacteristic
45C22×D244—21no—
46C22×D244—21no—
47C22×D244D412yes—
48C22×C22⋊D61—22no—
49C22×C22⋊D61—22no—
50C22×C4×D61—22no—
51C2×Dic244—24no—
52C2×Dic244—44no—
53C22×#92418—21no—
54#14519777—21no—
55#14519777—21no—
56#14519777—21no—
57#14519777C2312yes—
58#14519774—21no—
59#14519774—21no—
60#14519774D412yes—
61#14519774C2312yes—
62#14519773—24no—
63#14519773—24no—
64#14519751—24no—
65#14519751—24no—
66#14519750—28no—
67#14519750—28no—
68C4×Dic122—21no—
69C4×Dic122—21no—
70C4×Dic122D412yes—
71C4×Dic122C2312yes—
72#14519739—24no—
73#14519739—24no—
74C2×C4⋊Dic61—21no—
75C2×C4⋊Dic61—21no—
76C2×C4⋊Dic61D411yescharacteristic
77C2×#11758196—21no—
78C2×#11758198—22no—
79C2×C4×Dic61—21no—
80#14519710—24no—
81C4⋊#92418—21no—
82C4⋊#92418C2312yes—
83#14519702—24no—
84#14519699—28no—
85#14519698—24no—
86C22×D4×C61D411yescharacteristic
87C23×C4×C61—21no—
88C22×C8×C61—21no—
89C22×C8×C61—21no—
90C4×D4×C61—21no—
91C4×D4×C61—21no—
92C4×D4×C61D412yes—
93C4×D4×C61C2312yes—
94C2×C4⋊C4×C61D411yescharacteristic
95C2×C22⋊C4×C61—21no—
96C2×C42×C61C2311yescharacteristic
97C4⋊C8×C61—21no—
98C4⋊C8×C61C2312yes—
99C4×C8×C61—21no—
100C4×C8×C61C2312yes—
101C24×C61—21no—
102C23×D61—22no—
103C2×D4×C61—21no—
104C2×D4×C61—22no—
105C2×D4×C61—22no—
106C2×D4×C61C2×D412yes—
107C22×C4×C61—21no—
108C22×C4×C61—22no—
109C22×C4×C61—22no—
110C22×C4×C61—42no—
111C22×C4×C61—42no—
112C22×C4×C61C2×D411yescharacteristic
113C22×C4×C61C2×D411yescharacteristic
114C22×C4×C61C2×D411yescharacteristic
115C2×C22⋊D61—28no—
116C2×C22⋊D61—28no—
117C2×C22⋊D61—48no—
118C2×C22⋊D61—84no—
119C22×Dic61—21no—
120C22×Dic61—21no—
121C22×Dic61—41no—
122#11758222—48no—
123#11758222—416no—
124#11758222—48no—
125C2×D244—22no—
126C2×D244—22no—
127C2×D244—22no—
128C2×D244—22no—
129C2×D244—22no—
130C2×D244—42no—
131C2×D244—42no—
132C2×D244—42no—
133C2×D244—42no—
134C2×D244—44no—
135C2×D244C2×D414yes—
136C2×C4×D61—28no—
137C2×C4×D61—48no—
138C2×Dic122—21no—
139C2×Dic122—22no—
140C2×Dic122—22no—
141C2×Dic122—42no—
142C2×Dic122—42no—
143C2×Dic122—41no—
144C2×Dic122D814yes—
145C2×Dic122C2×D412yes—
146C2×C8×C61—22no—
147C2×C8×C61—22no—
148C2×C8×C61—42no—
149C2×C8×C61—42no—
150C4⋊C4×C61—21no—
151C4⋊C4×C61C2×D412yes—
152C22⋊C4×C61—22no—
153C22⋊C4×C61—22no—
154C42×C61C2×D411yescharacteristic
155C42×C61C2×D411yescharacteristic
156C42×C61C2×D411yescharacteristic
157C42×C61C2411yescharacteristic
158#11758198—28no—
159C4⋊Dic61—21no—
160C4⋊Dic61—22no—
161C4⋊Dic61—22no—
162C4⋊Dic61—41no—
163C4⋊Dic61—41no—
164C4⋊Dic61C2×D412yes—
165#11758196—22no—
166#11758196—22no—
167C4×Dic61—22no—
168C4×Dic61—22no—
169C2×#92418—22no—
170C2×#92418—42no—
171Dic244—48no—
172C23×C61—22no—
173C23×C61—42no—
174C23×C61—42no—
175C23×C61—42no—
176C23×C61#12011yescharacteristic
177C22×D61—24no—
178C22×D61—44no—
179C22×D61—44no—
180C22×D61—44no—
181D4×C61—22no—
182D4×C61—22no—
183D4×C61—42no—
184C2×C4×C61—22no—
185C2×C4×C61—22no—
186C2×C4×C61—42no—
187C2×C4×C61—42no—
188C2×C4×C61—42no—
189C2×C4×C61—44no—
190C2×C4×C61#12011yescharacteristic
191C2×C4×C61#12011yescharacteristic
192C2×C4×C61#12011yescharacteristic
193C2×C4×C61C2×D812yes—
194C2×C4×C61#13512yes—
195C2×C4×C61AGL(1,ℤ/8)12yes—
196C2×C4×C61#13712yes—
197C2×C4×C61C22×D411yescharacteristic
198C2×C4×C61C22×D411yescharacteristic
199C2×C4×C61C22×D411yescharacteristic
200C22⋊D61—416no—
201C22⋊D61—88no—
202C2×Dic61—22no—
203C2×Dic61—24no—
204C2×Dic61—22no—
205C2×Dic61—42no—
206C2×Dic61—42no—
207C2×Dic61—82no—
208D244—44no—
209D244—42no—
210D244—42no—
211D244—42no—
212D244—42no—
213D244—44no—
214D244—44no—
215D244—82no—
216C4×D61—416no—
217Dic122—22no—
218Dic122—24no—
219Dic122—42no—
220Dic122—42no—
221Dic122—82no—
222Dic122C2×D814yes—
223C8×C61—42no—
224C8×C61—42no—
225#92418—42no—
226C2×#1641—611nomaximal, Sylow
227C22×C61—42no—
228C22×C61—42no—
229C22×C61—42no—
230C22×C61—84no—
231C22×C61#44712yes—
232C22×C61#45212yes—
233C22×C61#45512yes—
234C22×C61C2×#12011yescharacteristic
235C2×D61—44no—
236C2×D61—44no—
237C2×D61—44no—
238C2×D61—88no—
239C4×C61—21no—
240C4×C61—21no—
241C4×C61—42no—
242C4×C61#44712yes—
243C4×C61#45212yes—
244C4×C61C22×D811yescharacteristic
245C4×C61C2×#13511yescharacteristic
246C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
247C4×C61C2×#13711yescharacteristic
248Dic61—24no—
249Dic61—42no—
250Dic61—82no—
251C2×#550—611no—
252C2×#486—611no—
253C2×#474—611no—
254C2×#462—611no—
255#1641—618no—
256C2×#331—611no—
257C2×Q8⋊C8—611no—
258C2×D4⋊C8D6111yescharacteristic, complemented
259C2×C61—82no—
260C2×C61#164114yescomplemented
261C2×C61C2×#44711yescharacteristic
262C2×C61C2×#45211yescharacteristic
263C2×C61C2×#45511yescharacteristic
264D61—84no—
265C22×#41—1221no—
266C22×Q16—1221no—
267#550—614no—
268#550—1222no—
269#550—1222no—
270#550—1222no—
271C2×C4⋊Q8—611no—
272C2×#127—611no—
273C2×#127—1221no—
274C2×#121—1222no—
275C2×#121—1221no—
276C2×C4×Q8—611no—
277C2×C4×D4—1221no—
278C2×C4×D4C2×D6111yescharacteristic
279#486—614no—
280#486—1222no—
281#474—614no—
282#474—1222no—
283#462—614no—
284#462—1222no—
285C2×#107—1221no—
286C2×C4⋊C8—611no—
287C2×C4⋊C8C2×D6111yescharacteristic
288C2×#103—1221no—
289C2×#102—1222no—
290C2×#102—1221no—
291C2×C4×C8C2×D6111yescharacteristic
292#331—614no—
293Q8⋊C8—614no—
294D4⋊C8C2×D6114yescomplemented
295C61C2×#164111yescharacteristic, complemented, Sylow
296C2×#41—1224no—
297C2×#41—1224no—
298C2×#41—2444no—
299C2×#41—2444no—
300C22×Q8—611no—
301C22×Q8—1221no—
302C22×D4—612no—
303C22×D4—1222no—
304C22×D4—1222no—
305C22×D4—1221no—
306C22×D4—1221no—
307C22×D4D24411yescharacteristic
308C23×C4—21no—
309C23×C4—1222no—
310C2×Q16—1224no—
311C2×Q16—2444no—
312C22×C8—21no—
313C22×C8—21no—
314C22×C8—1221no—
315C4⋊Q8—612no—
316C4⋊Q8—1221no—
317C4⋊Q8—1221no—
318C4⋊Q8—1221no—
319#127—612no—
320#127—612no—
321#127—1224no—
322#127—1224no—
323#127—1221no—
324#127—1221no—
325#121—1228no—
326#121—1228no—
327#121—1224no—
328#121—1224no—
329C4×Q8—612no—
330C4×Q8—612no—
331C4×Q8—1221no—
332C4×Q8—1221no—
333C4×D4—21no—
334C4×D4—21no—
335C4×D4—1224no—
336C4×D4—1224no—
337C4×D4D24412yes—
338C4×D4C22×D6112yes—
339C2×C4⋊C4—611no—
340C2×C4⋊C4—1221no—
341C2×C4⋊C4—1221no—
342C2×C4⋊C4—1221no—
343C2×C4⋊C4D24411yescharacteristic
344C2×C22⋊C4—21no—
345C2×C22⋊C4—1222no—
346C2×C42—1221no—
347C2×C42C22×D6111yescharacteristic
348#107—1224no—
349C4⋊C8—21no—
350C4⋊C8—612no—
351C4⋊C8—1221no—
352C4⋊C8C22×D6112yes—
353#103—1224no—
354#102—1228no—
355#102—1224no—
356C4×C8—21no—
357C4×C8C22×D6112yes—
358C24—21no—
359C24—1222no—
360#41—2448no—
361#41—2448no—
362#41—24416no—
363C2×Q8—612no—
364C2×Q8—614no—
365C2×Q8—1221no—
366C2×Q8—1222no—
367C2×Q8—1222no—
368C2×Q8—2442no—
369C2×Q8—2442no—
370C2×Q8—2441no—
371C2×D4—22no—
372C2×D4—21no—
373C2×D4—22no—
374C2×D4—614no—
375C2×D4—1228no—
376C2×D4—1228no—
377C2×D4—1222no—
378C2×D4—1222no—
379C2×D4—1222no—
380C2×D4—1222no—
381C2×D4—1222no—
382C2×D4—4884no—
383C2×D4—2444no—
384C2×D4—2448no—
385C2×D4—2442no—
386C2×D4—2442no—
387C2×D4—2442no—
388C2×D4—2442no—
389C2×D4C2×D24412yes—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—42no—
394C22×C4—42no—
395C22×C4—1228no—
396C22×C4—1221no—
397C22×C4—1221no—
398C22×C4—2448no—
399C22×C4—2441no—
400C22×C4C2×D24411yescharacteristic
401C22×C4D4×D6111yescharacteristic
402C22×C4D4×D6111yescharacteristic
403Q16—2448no—
404C2×C8—22no—
405C2×C8—22no—
406C2×C8—42no—
407C2×C8—42no—
408C2×C8—1222no—
409C2×C8—2442no—
410C4⋊C4—21no—
411C4⋊C4—612no—
412C4⋊C4—1222no—
413C4⋊C4—1221no—
414C4⋊C4—1222no—
415C4⋊C4—1222no—
416C4⋊C4—1222no—
417C4⋊C4—2441no—
418C4⋊C4—2441no—
419C4⋊C4C2×D24412yes—
420C22⋊C4—22no—
421C22⋊C4—22no—
422C22⋊C4—1228no—
423C42—1222no—
424C42—1222no—
425C42C2×D24411yescharacteristic
426C42D4×D6111yescharacteristic
427C42D4×D6111yescharacteristic
428C42C23×D6111yescharacteristic
429C23—22no—
430C23—42no—
431C23—42no—
432C23—42no—
433C23—1224no—
434C23—2444no—
435C23—2444no—
436C23—2444no—
437C23#1451974711yescharacteristic
438Q8—614no—
439Q8—1222no—
440Q8—1224no—
441Q8—4882no—
442Q8—2442no—
443Q8—2442no—
444D4—22no—
445D4—22no—
446D4—42no—
447D4—4882no—
448D4—4888no—
449D4—2444no—
450D4—24416no—
451D4—2442no—
452D4—2442no—
453D4—2442no—
454D4—2442no—
455D4—2444no—
456D4—2444no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—44no—
463C2×C4—1222no—
464C2×C4—1224no—
465C2×C4—1222no—
466C2×C4—4882no—
467C2×C4—24416no—
468C2×C4—2442no—
469C2×C4—2442no—
470C2×C4#1451974711yescharacteristic
471C2×C4#1451974711yescharacteristic
472C2×C4#1451974711yescharacteristic
473C2×C4D8×D6112yes—
474C2×C4#1451979912yes—
475C2×C4#1451980412yes—
476C2×C4#1451981012yes—
477C2×C4C2×D4×D6111yescharacteristic
478C2×C4C2×D4×D6111yescharacteristic
479C2×C4C22×D24411yescharacteristic
480C8—42no—
481C8—42no—
482C8—2442no—
483C22—42no—
484C22—42no—
485C22—42no—
486C22—84no—
487C22—4888no—
488C22—2444no—
489C22—2444no—
490C22—2444no—
491C22#1683989712yes—
492C22#1683992612yes—
493C22#1683994112yes—
494C22C2×#1451974711yescharacteristic
495C4—21no—
496C4—21no—
497C4—42no—
498C4—1224no—
499C4—4882no—
500C4—2442no—
501C4#1683989712yes—
502C4#1683992612yes—
503C4C2×D8×D6111yescharacteristic
504C4C2×#1451979911yescharacteristic
505C4C2×#1451980411yescharacteristic
506C4C2×#1451981011yescharacteristic
507C2—82no—
508C2—4884no—
509C2#2144501514yesdirect product factor
510C2C2×#1683989711yescharacteristic
511C2C2×#1683992611yescharacteristic
512C2C2×#1683994111yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×D4⋊C8C2
socleC23×C61#120
prime radicalC2×#16840433C2
hypercenterC2×D4⋊C8D61
hypocenterC61C2×#1641
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#16840109C2semidirect
3. C2×#16840042C2semidirect
4. C2×#16839973C2semidirect
5. #21445015C2direct (N × H)
6. C2×#16839505C2semidirect
7. C2×#16839494C2semidirect
8. C2×C61×D4⋊C8C2semidirect
23. #16840109C22semidirect
25. #16840042C22semidirect
27. #16839973C22semidirect
33. #16839505C22semidirect
34. #16839494C22semidirect
38. C61×D4⋊C8C22semidirect
258. C2×D4⋊C8D61semidirect
260. C2×C61#1641semidirect
294. D4⋊C8C2×D61semidirect
295. C61C2×#1641semidirect
509. C2#21445015direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404332
C2×#168401092
C2×#168400422
C2×#168399732
#214450152
C2×#168395052
C2×#168394942
C2×C61×D4⋊C82
C2×#164161