Finite Group Databasebeta

← C2×#21445135 #29661144

Subgroups — C2×#21445135 #29661144

Order 15616.

1022 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840506C211yesmaximal, characteristic
2C2×#16840168C211yesmaximal, characteristic, complemented
3C2×#16840154C211yesmaximal, characteristic, complemented
4#21445135C218yesmaximal, direct product factor
5C2×#16839503C211yesmaximal, characteristic, complemented
6C2×#16839502C211yesmaximal, characteristic, complemented
7C2×#16839501C211yesmaximal, characteristic, complemented
8C2×C61×#489C211yesmaximal, characteristic, complemented
9C22×#11758202—21no—
10C22×#11758201—21no—
11#16840506—22no—
12#16840506—22no—
13#16840506—22no—
14#16840506C2214yes—
15C2×#14519769C2211yescharacteristic
16C2×#14519765C2211yescharacteristic
17C2×#14519761—21no—
18C2×#14519759—21no—
19C2×#14519754—21no—
20C2×#14519753—21no—
21C2×#14519750—21no—
22C2×#14519749—21no—
23#16840168—22no—
24#16840168C2214yescomplemented
25#16840154—22no—
26#16840154C2214yescomplemented
27C2×#14519710—21no—
28C2×#14519708—21no—
29C2×#14519688C2211yescharacteristic
30C2×#14519688C2211yescharacteristic
31#16839503C2214yescomplemented
32#16839502C2214yescomplemented
33#16839501C2214yescomplemented
34C2×C4⋊Q8×C61C2211yescharacteristic
35C2×#124×C61C2211yescharacteristic
36C61×#489—22no—
37C61×#489C2214yescomplemented
38C2×#103×C61—21no—
39C2×#102×C61—21no—
40C2×#97×C61C2211yescharacteristic
41C22×Dic122D411yescharacteristic
42C22×D244D411yescharacteristic
43C22×C22⋊D61—21no—
44C22×C22⋊D61—21no—
45C23×Dic61—21no—
46C22×C4×D61—21no—
47C2×#11758202—24no—
48C2×#11758202—44no—
49C2×#11758201—24no—
50C2×#11758201—44no—
51C22×#92418—21no—
52C22×#92418—21no—
53#14519769—21no—
54#14519769—21no—
55#14519769D412yes—
56#14519769C2312yes—
57#14519765—21no—
58#14519765—21no—
59#14519765D412yes—
60#14519765C2312yes—
61#14519761—24no—
62#14519761—24no—
63#14519759—24no—
64#14519759—24no—
65#14519754—24no—
66#14519754—24no—
67#14519753—24no—
68#14519753—24no—
69#14519750—24no—
70#14519750—24no—
71#14519749—24no—
72#14519749—24no—
73C2×C4⋊Dic61—21no—
74C2×C4⋊Dic61D411yescharacteristic
75C2×C4⋊Dic61D411yescharacteristic
76C2×#11758196—21no—
77C2×#11758196—21no—
78C2×#11758196—21no—
79C2×C22⋊Dic61—21no—
80C2×#11758198—21no—
81C2×#11758198—21no—
82C2×#11758198—21no—
83#14519710—24no—
84#14519708—24no—
85#14519688—21no—
86#14519688—21no—
87#14519688C2312yes—
88#14519688C2312yes—
89C22×Q8×C61—21no—
90C22×Q8×C61D411yescharacteristic
91C22×D4×C61D411yescharacteristic
92C22×C8×C61—21no—
93C4⋊Q8×C61—21no—
94C4⋊Q8×C61—21no—
95C4⋊Q8×C61—21no—
96C4⋊Q8×C61C2312yes—
97#124×C61—21no—
98#124×C61—21no—
99#124×C61D412yes—
100#124×C61C2312yes—
101C2×C4⋊C4×C61—21no—
102C2×C4⋊C4×C61—21no—
103C2×C22⋊C4×C61—21no—
104C2×C22⋊C4×C61—21no—
105C2×C42×C61C2311yescharacteristic
106#103×C61—24no—
107#102×C61—24no—
108#97×C61—21no—
109#97×C61C2312yes—
110C24×C61—21no—
111C23×D61—21no—
112C2×Q8×C61—21no—
113C2×Q8×C61—22no—
114C2×Q8×C61—42no—
115C2×Q8×C61—42no—
116C2×Q8×C61—42no—
117C2×Q8×C61—41no—
118C2×Q8×C61C2×D412yes—
119C2×D4×C61—21no—
120C2×D4×C61—42no—
121C2×D4×C61C2×D412yes—
122C22×C4×C61—21no—
123C22×C4×C61—41no—
124C22×C4×C61C2×D411yescharacteristic
125C22×C4×C61C2×D411yescharacteristic
126C22×C4×C61C2×D411yescharacteristic
127C2×C22⋊D61—24no—
128C2×C22⋊D61—24no—
129C2×C22⋊D61—82no—
130C2×C22⋊D61—82no—
131C22×Dic61—21no—
132C22×Dic61—21no—
133C22×Dic61—21no—
134C22×Dic61—24no—
135C22×Dic61—82no—
136C2×D244—21no—
137C2×D244—42no—
138C2×D244C2×D412yes—
139C2×C4×D61—24no—
140C2×C4×D61—82no—
141C2×Dic122—21no—
142C2×Dic122—42no—
143C2×Dic122C2×D412yes—
144C2×C8×C61—22no—
145C2×C8×C61—42no—
146C4⋊C4×C61—22no—
147C4⋊C4×C61—22no—
148C4⋊C4×C61—41no—
149C4⋊C4×C61—41no—
150C22⋊C4×C61—22no—
151C22⋊C4×C61—22no—
152C22⋊C4×C61—22no—
153C22⋊C4×C61—22no—
154C42×C61C2×D411yescharacteristic
155C42×C61C2×D411yescharacteristic
156C42×C61C2×D411yescharacteristic
157C42×C61C2411yescharacteristic
158C22⋊Dic61—24no—
159#11758202—48no—
160#11758201—48no—
161#11758198—24no—
162#11758198—22no—
163#11758198—22no—
164#11758198—22no—
165#11758198—22no—
166C4⋊Dic61—24no—
167C4⋊Dic61—21no—
168C4⋊Dic61—21no—
169C4⋊Dic61C2×D412yes—
170C4⋊Dic61C2×D412yes—
171#11758196—24no—
172#11758196—22no—
173#11758196—22no—
174#11758196—22no—
175#11758196—22no—
176C2×#92418—24no—
177C2×#92418—24no—
178C2×#92418—22no—
179C2×#92418—22no—
180C23×C61—22no—
181C23×C61—42no—
182C23×C61—42no—
183C23×C61—42no—
184C23×C61#12011yescharacteristic
185C22×D61—22no—
186C22×D61—42no—
187C22×D61—42no—
188C22×D61—42no—
189Q8×C61—42no—
190Q8×C61—42no—
191Q8×C61—42no—
192Q8×C61—81no—
193Q8×C61—82no—
194D4×C61—42no—
195D4×C61—81no—
196C2×C4×C61—22no—
197C2×C4×C61—22no—
198C2×C4×C61—22no—
199C2×C4×C61—22no—
200C2×C4×C61—42no—
201C2×C4×C61—42no—
202C2×C4×C61—82no—
203C2×C4×C61#12011yescharacteristic
204C2×C4×C61#12011yescharacteristic
205C2×C4×C61#12011yescharacteristic
206C2×C4×C61C22×D411yescharacteristic
207C2×C4×C61C22×D411yescharacteristic
208C2×C4×C61C22×D411yescharacteristic
209C22⋊D61—84no—
210C22⋊D61—84no—
211C2×Dic61—22no—
212C2×Dic61—22no—
213C2×Dic61—22no—
214C2×Dic61—42no—
215C2×Dic61—42no—
216C2×Dic61—42no—
217C2×Dic61—84no—
218D244—42no—
219D244—81no—
220C4×D61—84no—
221Dic122—42no—
222Dic122—81no—
223C8×C61—42no—
224#92418—24no—
225#92418—24no—
226C2×#1661—611nomaximal, Sylow
227C22×C61—42no—
228C22×C61—42no—
229C22×C61—42no—
230C22×C61—84no—
231C22×C61#45312yes—
232C22×C61#45512yes—
233C22×C61#45612yes—
234C22×C61C2×#12011yescharacteristic
235C2×D61—42no—
236C2×D61—42no—
237C2×D61—42no—
238C2×D61—84no—
239C4×C61—21no—
240C4×C61—21no—
241C4×C61—21no—
242C4×C61—21no—
243C4×C61—21no—
244C4×C61—21no—
245C4×C61—42no—
246C4×C61—82no—
247Dic61—42no—
248Dic61—42no—
249Dic61—42no—
250C2×#562—611no—
251C2×#501—611no—
252C2×#497—611no—
253C2×#489D6111yescharacteristic, complemented
254#1661—618no—
255C2×#330—611no—
256C2×#329—611no—
257C2×#329—611no—
258C2×C61—82no—
259C2×C61#166114yescomplemented
260C2×C61C2×#45311yescharacteristic
261C2×C61C2×#45511yescharacteristic
262C2×C61C2×#45611yescharacteristic
263D61—82no—
264C22×Q16—1221no—
265C22×SD16—1221no—
266#562—614no—
267#562—1222no—
268#562—1222no—
269#562—1222no—
270C2×C4⋊Q8C2×D6111yescharacteristic
271C2×#125—611no—
272C2×#124—611no—
273C2×#124C2×D6111yescharacteristic
274C2×#123—1221no—
275C2×#123—1221no—
276C2×C22⋊Q8—1221no—
277C2×C22⋊Q8—1221no—
278C2×#121—1221no—
279C2×#121—1221no—
280#501—614no—
281#501—1222no—
282#497—614no—
283#497—1222no—
284#489—22no—
285#489C2×D6114yescomplemented
286C2×#107—1221no—
287C2×#106—1221no—
288C2×#103—21no—
289C2×#102—21no—
290C2×#97—611no—
291C2×#97—611no—
292C2×#97C2×D6111yescharacteristic
293#330—614no—
294#329—614no—
295#329—614no—
296C61C2×#166111yescharacteristic, complemented, Sylow
297C22×Q8—21no—
298C22×Q8—611no—
299C22×Q8C22⋊D6111yescharacteristic
300C22×D4—611no—
301C22×D4—1221no—
302C22×D4—1221no—
303C22×D4C22⋊D6111yescharacteristic
304C23×C4—1221no—
305C23×C4—1221no—
306C2×Q16—1224no—
307C2×Q16—2444no—
308C2×SD16—1224no—
309C2×SD16—2444no—
310C22×C8—21no—
311C22×C8—1221no—
312C22×C8—1221no—
313C4⋊Q8—21no—
314C4⋊Q8—21no—
315C4⋊Q8—21no—
316C4⋊Q8C22×D6112yes—
317#125—612no—
318#125—612no—
319#125—1221no—
320#125—1221no—
321#124—21no—
322#124—21no—
323#124—612no—
324#124—612no—
325#124—1221no—
326#124—1221no—
327#124C22⋊D6112yes—
328#124C22×D6112yes—
329#123—1224no—
330#123—1224no—
331#123—1224no—
332#123—1224no—
333C22⋊Q8—1224no—
334C22⋊Q8—1224no—
335C22⋊Q8—1224no—
336C22⋊Q8—1224no—
337#121—1224no—
338#121—1224no—
339#121—1224no—
340#121—1224no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—611no—
344C2×C4⋊C4—611no—
345C2×C4⋊C4—1221no—
346C2×C4⋊C4—1221no—
347C2×C4⋊C4—1221no—
348C2×C4⋊C4—1221no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—1221no—
352C2×C22⋊C4—1221no—
353C2×C22⋊C4—1221no—
354C2×C22⋊C4—1221no—
355C2×C42C22×D6111yescharacteristic
356#107—1224no—
357#106—1224no—
358#103—24no—
359#102—24no—
360#97—21no—
361#97—612no—
362#97—612no—
363#97—1221no—
364#97—1221no—
365#97C22×D6112yes—
366C24—21no—
367C24—1221no—
368C2×Q8—21no—
369C2×Q8—22no—
370C2×Q8—42no—
371C2×Q8—42no—
372C2×Q8—42no—
373C2×Q8—41no—
374C2×Q8—612no—
375C2×Q8—1221no—
376C2×Q8—2442no—
377C2×Q8C2×C22⋊D6112yes—
378C2×D4—21no—
379C2×D4—42no—
380C2×D4—612no—
381C2×D4—1224no—
382C2×D4—1224no—
383C2×D4—1221no—
384C2×D4—4882no—
385C2×D4—4882no—
386C2×D4—2442no—
387C2×D4C2×C22⋊D6112yes—
388C22×C4—21no—
389C22×C4—41no—
390C22×C4—1224no—
391C22×C4—1224no—
392C22×C4—1221no—
393C22×C4—1221no—
394C22×C4—1221no—
395C22×C4—4882no—
396C22×C4—4882no—
397C22×C4D4×D6111yescharacteristic
398C22×C4D4×D6111yescharacteristic
399C22×C4C2×C22⋊D6111yescharacteristic
400Q16—2448no—
401SD16—2448no—
402C2×C8—22no—
403C2×C8—42no—
404C2×C8—1224no—
405C2×C8—1224no—
406C2×C8—1222no—
407C2×C8—1222no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—41no—
411C4⋊C4—41no—
412C4⋊C4—612no—
413C4⋊C4—612no—
414C4⋊C4—1224no—
415C4⋊C4—1224no—
416C4⋊C4—1222no—
417C4⋊C4—1222no—
418C4⋊C4—1221no—
419C4⋊C4—1221no—
420C4⋊C4—1222no—
421C4⋊C4—1222no—
422C22⋊C4—22no—
423C22⋊C4—22no—
424C22⋊C4—22no—
425C22⋊C4—22no—
426C22⋊C4—1224no—
427C22⋊C4—1224no—
428C22⋊C4—1222no—
429C22⋊C4—1222no—
430C22⋊C4—1222no—
431C22⋊C4—1222no—
432C42D4×D6111yescharacteristic
433C42D4×D6111yescharacteristic
434C42C2×C22⋊D6111yescharacteristic
435C42C23×D6111yescharacteristic
436C23—22no—
437C23—42no—
438C23—42no—
439C23—42no—
440C23—1222no—
441C23—2442no—
442C23—2442no—
443C23—2442no—
444C23#1451974511yescharacteristic
445Q8—42no—
446Q8—42no—
447Q8—42no—
448Q8—81no—
449Q8—82no—
450Q8—4881no—
451Q8—2442no—
452D4—42no—
453D4—81no—
454D4—4881no—
455D4—4884no—
456D4—4884no—
457D4—2442no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—82no—
465C2×C4—1222no—
466C2×C4—1222no—
467C2×C4—1222no—
468C2×C4—4884no—
469C2×C4—4884no—
470C2×C4—2442no—
471C2×C4—2442no—
472C2×C4—2442no—
473C2×C4#1451974511yescharacteristic
474C2×C4#1451974511yescharacteristic
475C2×C4#1451974511yescharacteristic
476C2×C4C2×D4×D6111yescharacteristic
477C2×C4C2×D4×D6111yescharacteristic
478C2×C4C22×C22⋊D6111yescharacteristic
479C8—42no—
480C8—1224no—
481C8—1224no—
482C22—42no—
483C22—42no—
484C22—42no—
485C22—84no—
486C22—4884no—
487C22—2442no—
488C22—2442no—
489C22—2442no—
490C22#1683992812yes—
491C22#1683993912yes—
492C22#1683994312yes—
493C22C2×#1451974511yescharacteristic
494C4—21no—
495C4—21no—
496C4—21no—
497C4—21no—
498C4—21no—
499C4—21no—
500C4—42no—
501C4—82no—
502C4—2442no—
503C4—2442no—
504C4—2442no—
505C2—82no—
506C2—4882no—
507C2#2144513514yesdirect product factor
508C2C2×#1683992811yescharacteristic
509C2C2×#1683993911yescharacteristic
510C2C2×#1683994311yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#489C2
socleC23×C61#120
prime radicalC2×#16840506C2
hypercenterC2×#489D61
hypocenterC61C2×#1661
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#489

Complements

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

NH ≅ G/Ntype
2. C2×#16840168C2semidirect
3. C2×#16840154C2semidirect
4. #21445135C2direct (N × H)
5. C2×#16839503C2semidirect
6. C2×#16839502C2semidirect
7. C2×#16839501C2semidirect
8. C2×C61×#489C2semidirect
24. #16840168C22semidirect
26. #16840154C22semidirect
31. #16839503C22semidirect
32. #16839502C22semidirect
33. #16839501C22semidirect
37. C61×#489C22semidirect
253. C2×#489D61semidirect
259. C2×C61#1661semidirect
285. #489C2×D61semidirect
296. C61C2×#1661semidirect
507. C2#21445135direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168405062
C2×#168401682
C2×#168401542
#214451352
C2×#168395032
C2×#168395022
C2×#168395012
C2×C61×#4892
C2×#166161