Finite Group Databasebeta

← C2×#21445141 #29661174

Subgroups — C2×#21445141 #29661174

Order 15616.

958 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840506C211yesmaximal, characteristic
2C2×#16840130C211yesmaximal, characteristic, complemented
3C2×#16840124C211yesmaximal, characteristic, complemented
4#21445141C218yesmaximal, direct product factor
5C2×#16839503C211yesmaximal, characteristic, complemented
6C2×#16839502C211yesmaximal, characteristic, complemented
7C2×#16839501C211yesmaximal, characteristic, complemented
8C2×C61×#489C211yesmaximal, characteristic, complemented
9#16840506—22no—
10#16840506—22no—
11#16840506—22no—
12#16840506C2214yes—
13C2×#14519769C2211yescharacteristic
14C2×#14519765C2211yescharacteristic
15C2×#14519761—21no—
16C2×#14519759—21no—
17C2×#14519754—21no—
18C2×#14519753—21no—
19C2×#14519750—21no—
20C2×#14519749—21no—
21#16840130—22no—
22#16840130C2214yescomplemented
23#16840124—22no—
24#16840124C2214yescomplemented
25C2×#14519701—21no—
26C2×#14519701—21no—
27C2×#14519700—21no—
28C2×#14519697—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—
47C22×#92418—21no—
48C22×#92418—21no—
49#14519769—21no—
50#14519769—21no—
51#14519769D412yes—
52#14519769C2312yes—
53#14519765—21no—
54#14519765—21no—
55#14519765D412yes—
56#14519765C2312yes—
57#14519761—24no—
58#14519761—24no—
59#14519759—24no—
60#14519759—24no—
61#14519754—24no—
62#14519754—24no—
63#14519753—24no—
64#14519753—24no—
65#14519750—24no—
66#14519750—24no—
67#14519749—24no—
68#14519749—24no—
69C2×C4⋊Dic61—21no—
70C2×C4⋊Dic61D411yescharacteristic
71C2×C4⋊Dic61D411yescharacteristic
72C2×#11758196—21no—
73C2×#11758196—21no—
74C2×#11758196—21no—
75C2×C22⋊Dic61—21no—
76C2×#11758198—21no—
77C2×#11758198—21no—
78C2×#11758198—21no—
79#14519701—24no—
80#14519701—24no—
81#14519700—24no—
82#14519697—24no—
83#14519688—21no—
84#14519688—21no—
85#14519688C2312yes—
86#14519688C2312yes—
87C22×Q8×C61—21no—
88C22×Q8×C61D411yescharacteristic
89C22×D4×C61D411yescharacteristic
90C22×C8×C61—21no—
91C4⋊Q8×C61—21no—
92C4⋊Q8×C61—21no—
93C4⋊Q8×C61—21no—
94C4⋊Q8×C61C2312yes—
95#124×C61—21no—
96#124×C61—21no—
97#124×C61D412yes—
98#124×C61C2312yes—
99C2×C4⋊C4×C61—21no—
100C2×C4⋊C4×C61—21no—
101C2×C22⋊C4×C61—21no—
102C2×C22⋊C4×C61—21no—
103C2×C42×C61C2311yescharacteristic
104#103×C61—24no—
105#102×C61—24no—
106#97×C61—21no—
107#97×C61C2312yes—
108C24×C61—21no—
109C23×D61—21no—
110C2×Q8×C61—21no—
111C2×Q8×C61—22no—
112C2×Q8×C61—42no—
113C2×Q8×C61—44no—
114C2×Q8×C61—41no—
115C2×Q8×C61C2×D412yes—
116C2×D4×C61—21no—
117C2×D4×C61—42no—
118C2×D4×C61C2×D412yes—
119C22×C4×C61—21no—
120C22×C4×C61—41no—
121C22×C4×C61C2×D411yescharacteristic
122C22×C4×C61C2×D411yescharacteristic
123C22×C4×C61C2×D411yescharacteristic
124C2×C22⋊D61—24no—
125C2×C22⋊D61—24no—
126C2×C22⋊D61—82no—
127C2×C22⋊D61—82no—
128C22×Dic61—21no—
129C22×Dic61—21no—
130C22×Dic61—21no—
131C22×Dic61—24no—
132C22×Dic61—82no—
133C2×D244—21no—
134C2×D244—42no—
135C2×D244C2×D412yes—
136C2×C4×D61—24no—
137C2×C4×D61—82no—
138C2×Dic122—21no—
139C2×Dic122—42no—
140C2×Dic122C2×D412yes—
141C2×C8×C61—22no—
142C2×C8×C61—42no—
143C4⋊C4×C61—22no—
144C4⋊C4×C61—22no—
145C4⋊C4×C61—41no—
146C4⋊C4×C61—41no—
147C22⋊C4×C61—22no—
148C22⋊C4×C61—22no—
149C22⋊C4×C61—22no—
150C22⋊C4×C61—22no—
151C42×C61C2×D411yescharacteristic
152C42×C61C2×D411yescharacteristic
153C42×C61C2×D411yescharacteristic
154C42×C61C2411yescharacteristic
155C22⋊Dic61—24no—
156#11758198—24no—
157#11758198—22no—
158#11758198—22no—
159#11758198—22no—
160#11758198—22no—
161C4⋊Dic61—24no—
162C4⋊Dic61—21no—
163C4⋊Dic61—21no—
164C4⋊Dic61C2×D412yes—
165C4⋊Dic61C2×D412yes—
166#11758196—24no—
167#11758196—22no—
168#11758196—22no—
169#11758196—22no—
170#11758196—22no—
171C2×#92418—22no—
172C2×#92418—22no—
173C2×#92418—42no—
174C2×#92418—42no—
175C23×C61—22no—
176C23×C61—42no—
177C23×C61—42no—
178C23×C61—42no—
179C23×C61#12011yescharacteristic
180C22×D61—22no—
181C22×D61—42no—
182C22×D61—42no—
183C22×D61—42no—
184Q8×C61—42no—
185Q8×C61—44no—
186Q8×C61—81no—
187Q8×C61—82no—
188D4×C61—42no—
189D4×C61—81no—
190C2×C4×C61—22no—
191C2×C4×C61—22no—
192C2×C4×C61—22no—
193C2×C4×C61—22no—
194C2×C4×C61—42no—
195C2×C4×C61—42no—
196C2×C4×C61—82no—
197C2×C4×C61#12011yescharacteristic
198C2×C4×C61#12011yescharacteristic
199C2×C4×C61#12011yescharacteristic
200C2×C4×C61C22×D411yescharacteristic
201C2×C4×C61C22×D411yescharacteristic
202C2×C4×C61C22×D411yescharacteristic
203C22⋊D61—84no—
204C22⋊D61—84no—
205C2×Dic61—22no—
206C2×Dic61—22no—
207C2×Dic61—22no—
208C2×Dic61—42no—
209C2×Dic61—42no—
210C2×Dic61—42no—
211C2×Dic61—84no—
212D244—42no—
213D244—81no—
214C4×D61—84no—
215Dic122—42no—
216Dic122—81no—
217C8×C61—42no—
218#92418—42no—
219#92418—42no—
220C2×#1662—611nomaximal, Sylow
221C22×C61—42no—
222C22×C61—42no—
223C22×C61—42no—
224C22×C61—84no—
225C22×C61#45412yes—
226C22×C61#45512yes—
227C22×C61#45512yes—
228C22×C61C2×#12011yescharacteristic
229C2×D61—42no—
230C2×D61—42no—
231C2×D61—42no—
232C2×D61—84no—
233C4×C61—21no—
234C4×C61—21no—
235C4×C61—21no—
236C4×C61—21no—
237C4×C61—21no—
238C4×C61—21no—
239C4×C61—42no—
240C4×C61—82no—
241Dic61—42no—
242Dic61—42no—
243Dic61—42no—
244C2×#562—611no—
245C2×#491—611no—
246C2×#489—611no—
247C2×#489D6111yescharacteristic, complemented
248#1662—618no—
249C2×#330—611no—
250C2×#329—611no—
251C2×#329—611no—
252C2×C61—82no—
253C2×C61#166214yescomplemented
254C2×C61C2×#45511yescharacteristic
255C2×C61C2×#45511yescharacteristic
256C2×C61C2×#45411yescharacteristic
257D61—82no—
258#562—614no—
259#562—1222no—
260#562—1222no—
261#562—1222no—
262C2×C4⋊Q8C2×D6111yescharacteristic
263C2×#125—611no—
264C2×#124—611no—
265C2×#124C2×D6111yescharacteristic
266C2×#123—1221no—
267C2×#123—1221no—
268C2×C22⋊Q8—1221no—
269C2×C22⋊Q8—1221no—
270C2×#121—1221no—
271C2×#121—1221no—
272#491—614no—
273#491—1222no—
274#489—22no—
275#489—614no—
276#489—1222no—
277#489C2×D6114yescomplemented
278C2×#103—21no—
279C2×#103—1221no—
280C2×#103—1221no—
281C2×#103—1221no—
282C2×#102—21no—
283C2×#102—1221no—
284C2×#97—611no—
285C2×#97—611no—
286C2×#97C2×D6111yescharacteristic
287#330—614no—
288#329—614no—
289#329—614no—
290C61C2×#166211yescharacteristic, complemented, Sylow
291C22×Q8—21no—
292C22×Q8—611no—
293C22×Q8C22⋊D6111yescharacteristic
294C22×D4—611no—
295C22×D4—1221no—
296C22×D4—1221no—
297C22×D4C22⋊D6111yescharacteristic
298C23×C4—1221no—
299C23×C4—1221no—
300C22×C8—21no—
301C22×C8—1221no—
302C22×C8—1221no—
303C4⋊Q8—21no—
304C4⋊Q8—21no—
305C4⋊Q8—21no—
306C4⋊Q8C22×D6112yes—
307#125—612no—
308#125—612no—
309#125—1221no—
310#125—1221no—
311#124—21no—
312#124—21no—
313#124—612no—
314#124—612no—
315#124—1221no—
316#124—1221no—
317#124C22⋊D6112yes—
318#124C22×D6112yes—
319#123—1224no—
320#123—1224no—
321#123—1224no—
322#123—1224no—
323C22⋊Q8—1224no—
324C22⋊Q8—1224no—
325C22⋊Q8—1224no—
326C22⋊Q8—1224no—
327#121—1224no—
328#121—1224no—
329#121—1224no—
330#121—1224no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—611no—
334C2×C4⋊C4—611no—
335C2×C4⋊C4—1221no—
336C2×C4⋊C4—1221no—
337C2×C4⋊C4—1221no—
338C2×C4⋊C4—1221no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—1221no—
342C2×C22⋊C4—1221no—
343C2×C22⋊C4—1221no—
344C2×C22⋊C4—1221no—
345C2×C42C22×D6111yescharacteristic
346#103—24no—
347#103—1224no—
348#103—1224no—
349#103—1224no—
350#102—24no—
351#102—1224no—
352#97—21no—
353#97—612no—
354#97—612no—
355#97—1221no—
356#97—1221no—
357#97C22×D6112yes—
358C24—21no—
359C24—1221no—
360C2×Q8—21no—
361C2×Q8—22no—
362C2×Q8—42no—
363C2×Q8—44no—
364C2×Q8—41no—
365C2×Q8—612no—
366C2×Q8—1221no—
367C2×Q8—2442no—
368C2×Q8C2×C22⋊D6112yes—
369C2×D4—21no—
370C2×D4—42no—
371C2×D4—612no—
372C2×D4—1224no—
373C2×D4—1224no—
374C2×D4—1221no—
375C2×D4—4882no—
376C2×D4—4882no—
377C2×D4—2442no—
378C2×D4C2×C22⋊D6112yes—
379C22×C4—21no—
380C22×C4—41no—
381C22×C4—1224no—
382C22×C4—1224no—
383C22×C4—1221no—
384C22×C4—1221no—
385C22×C4—1221no—
386C22×C4—4882no—
387C22×C4—4882no—
388C22×C4D4×D6111yescharacteristic
389C22×C4D4×D6111yescharacteristic
390C22×C4C2×C22⋊D6111yescharacteristic
391C2×C8—22no—
392C2×C8—42no—
393C2×C8—1222no—
394C2×C8—1222no—
395C2×C8—2442no—
396C2×C8—2442no—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—41no—
400C4⋊C4—41no—
401C4⋊C4—612no—
402C4⋊C4—612no—
403C4⋊C4—1224no—
404C4⋊C4—1224no—
405C4⋊C4—1222no—
406C4⋊C4—1222no—
407C4⋊C4—1221no—
408C4⋊C4—1221no—
409C4⋊C4—1222no—
410C4⋊C4—1222no—
411C22⋊C4—22no—
412C22⋊C4—22no—
413C22⋊C4—22no—
414C22⋊C4—22no—
415C22⋊C4—1224no—
416C22⋊C4—1224no—
417C22⋊C4—1222no—
418C22⋊C4—1222no—
419C22⋊C4—1222no—
420C22⋊C4—1222no—
421C42D4×D6111yescharacteristic
422C42D4×D6111yescharacteristic
423C42C2×C22⋊D6111yescharacteristic
424C42C23×D6111yescharacteristic
425C23—22no—
426C23—42no—
427C23—42no—
428C23—42no—
429C23—1222no—
430C23—2442no—
431C23—2442no—
432C23—2442no—
433C23#1451974511yescharacteristic
434Q8—42no—
435Q8—44no—
436Q8—81no—
437Q8—82no—
438Q8—4881no—
439Q8—2442no—
440D4—42no—
441D4—81no—
442D4—4881no—
443D4—4884no—
444D4—4884no—
445D4—2442no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—82no—
453C2×C4—1222no—
454C2×C4—1222no—
455C2×C4—1222no—
456C2×C4—4884no—
457C2×C4—4884no—
458C2×C4—2442no—
459C2×C4—2442no—
460C2×C4—2442no—
461C2×C4#1451974511yescharacteristic
462C2×C4#1451974511yescharacteristic
463C2×C4#1451974511yescharacteristic
464C2×C4C2×D4×D6111yescharacteristic
465C2×C4C2×D4×D6111yescharacteristic
466C2×C4C22×C22⋊D6111yescharacteristic
467C8—42no—
468C8—2442no—
469C8—2442no—
470C22—42no—
471C22—42no—
472C22—42no—
473C22—84no—
474C22—4884no—
475C22—2442no—
476C22—2442no—
477C22—2442no—
478C22#1683993312yes—
479C22#1683993812yes—
480C22#1683993912yes—
481C22C2×#1451974511yescharacteristic
482C4—21no—
483C4—21no—
484C4—21no—
485C4—21no—
486C4—21no—
487C4—21no—
488C4—42no—
489C4—82no—
490C4—2442no—
491C4—2442no—
492C4—2442no—
493C2—82no—
494C2—4882no—
495C2#2144514114yesdirect product factor
496C2C2×#1683993811yescharacteristic
497C2C2×#1683993911yescharacteristic
498C2C2×#1683993311yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#489C2
socleC23×C61#120
prime radicalC2×#16840506C2
hypercenterC2×#489D61
hypocenterC61C2×#1662
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×#16840130C2semidirect
3. C2×#16840124C2semidirect
4. #21445141C2direct (N × H)
5. C2×#16839503C2semidirect
6. C2×#16839502C2semidirect
7. C2×#16839501C2semidirect
8. C2×C61×#489C2semidirect
22. #16840130C22semidirect
24. #16840124C22semidirect
31. #16839503C22semidirect
32. #16839502C22semidirect
33. #16839501C22semidirect
37. C61×#489C22semidirect
247. C2×#489D61semidirect
253. C2×C61#1662semidirect
277. #489C2×D61semidirect
290. C61C2×#1662semidirect
495. C2#21445141direct (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×#168401302
C2×#168401242
#214451412
C2×#168395032
C2×#168395022
C2×#168395012
C2×C61×#4892
C2×#166261