Finite Group Databasebeta

← C2×#21444825 #29652240

Subgroups — C2×#21444825 #29652240

Order 15616.

1028 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840391C211yesmaximal, characteristic
2C2×#16840092C211yesmaximal, characteristic
3C2×#16839693C211yesmaximal, characteristic
4#21444825C218yesmaximal, direct product factor
5C2×#16839500C211yesmaximal, characteristic
6C2×#16839499C211yesmaximal, characteristic
7C2×#16839487C211yesmaximal, characteristic
8C2×C61×#483C211yesmaximal, characteristic
9#16840391—22no—
10#16840391—22no—
11#16840391—22no—
12#16840391C2214yes—
13C2×#14519776—21no—
14C2×#14519775—21no—
15C2×#14519767—21no—
16C2×#14519767—21no—
17C2×#14519756C2211yescharacteristic
18C2×#14519754—21no—
19C2×#14519733—21no—
20C22×#11758196—21no—
21C22×#11758196C2211yescharacteristic
22#16840092—22no—
23#16840092C2214yes—
24C2×#14519708—21no—
25C2×#14519700—21no—
26C2×C22⋊#92418C2211yescharacteristic
27#16839693—22no—
28#16839693C2214yes—
29C2×#14519684—21no—
30C2×#14519684C2211yescharacteristic
31#16839500C2214yes—
32#16839499C2214yes—
33#16839487C2214yes—
34C2×C22⋊Q8×C61C2211yescharacteristic
35C22×C4⋊C4×C61C2211yescharacteristic
36C61×#483—22no—
37C61×#483C2214yes—
38C2×#106×C61—21no—
39C2×#103×C61—21no—
40C2×C22⋊C8×C61C2211yescharacteristic
41C22×Dic122—21no—
42C22×Dic122D411yescharacteristic
43C23×Dic61—21no—
44C23×Dic61D411yescharacteristic
45C23×Dic61D411yescharacteristic
46C22×#92418—21no—
47#14519776—24no—
48#14519776—24no—
49#14519775—24no—
50#14519775—24no—
51#14519767—24no—
52#14519767—24no—
53#14519767—24no—
54#14519767—24no—
55#14519756—21no—
56#14519756—21no—
57#14519756D412yes—
58#14519756C2312yes—
59#14519754—24no—
60#14519754—24no—
61#14519733—24no—
62#14519733—24no—
63C2×C4⋊Dic61—21no—
64C2×C4⋊Dic61D411yescharacteristic
65C2×#11758196—21no—
66C2×#11758196—21no—
67C2×#11758196—21no—
68C2×#11758196—21no—
69C2×#11758196—21no—
70C2×#11758196—21no—
71C2×#11758196—21no—
72C2×#11758196—21no—
73C2×#11758196—21no—
74C2×#11758196—24no—
75C2×#11758196—44no—
76C2×#11758196D412yes—
77C2×#11758196C2312yes—
78C2×C22⋊Dic61—21no—
79C2×C4×Dic61—21no—
80C2×C4×Dic61—21no—
81#14519708—24no—
82#14519700—24no—
83C22⋊#92418—21no—
84C22⋊#92418C2312yes—
85#14519684—21no—
86#14519684—24no—
87#14519684C2312yes—
88C22×Q8×C61D411yescharacteristic
89C23×C4×C61—21no—
90C23×C4×C61C2311yescharacteristic
91C22×C8×C61—21no—
92C22⋊Q8×C61—21no—
93C22⋊Q8×C61—21no—
94C22⋊Q8×C61D412yes—
95C22⋊Q8×C61C2312yes—
96C2×C4⋊C4×C61—21no—
97C2×C4⋊C4×C61—21no—
98C2×C4⋊C4×C61—21no—
99C2×C4⋊C4×C61—21no—
100C2×C4⋊C4×C61—21no—
101C2×C4⋊C4×C61—21no—
102C2×C4⋊C4×C61D411yescharacteristic
103C2×C4⋊C4×C61C2312yes—
104C2×C22⋊C4×C61—21no—
105#106×C61—24no—
106#103×C61—24no—
107C22⋊C8×C61—21no—
108C22⋊C8×C61C2312yes—
109C24×C61C2×D411yescharacteristic
110C2×Q8×C61—21no—
111C2×Q8×C61—42no—
112C2×Q8×C61C2×D412yes—
113C22×C4×C61—21no—
114C22×C4×C61—21no—
115C22×C4×C61—22no—
116C22×C4×C61—42no—
117C22×C4×C61—41no—
118C22×C4×C61—41no—
119C22×C4×C61—42no—
120C22×C4×C61—42no—
121C22×C4×C61C2×D411yescharacteristic
122C22×C4×C61C2×D411yescharacteristic
123C22×C4×C61C2×D411yescharacteristic
124C22×C4×C61C2×D411yescharacteristic
125C22×C4×C61C2×D411yescharacteristic
126C22×C4×C61C2411yescharacteristic
127C22×Dic61—21no—
128C22×Dic61—21no—
129C22×Dic61—22no—
130C22×Dic61—24no—
131C22×Dic61—21no—
132C22×Dic61—21no—
133C22×Dic61—21no—
134C22×Dic61—22no—
135C22×Dic61—21no—
136C22×Dic61—42no—
137C22×Dic61—42no—
138C22×Dic61—42no—
139C22×Dic61SD1614yes—
140C22×Dic61C2×D412yes—
141C22×Dic61C2×D412yes—
142C2×Dic122—24no—
143C2×Dic122—21no—
144C2×Dic122—42no—
145C2×Dic122—82no—
146C2×Dic122C2×D412yes—
147C2×C8×C61—22no—
148C2×C8×C61—42no—
149C4⋊C4×C61—22no—
150C4⋊C4×C61—21no—
151C4⋊C4×C61—22no—
152C4⋊C4×C61—22no—
153C4⋊C4×C61—22no—
154C4⋊C4×C61—41no—
155C4⋊C4×C61—41no—
156C4⋊C4×C61C2×D412yes—
157C22⋊C4×C61—22no—
158C22⋊C4×C61—22no—
159C22⋊Dic61—22no—
160C22⋊Dic61—22no—
161C4⋊Dic61—24no—
162C4⋊Dic61—21no—
163C4⋊Dic61C2×D412yes—
164#11758196—24no—
165#11758196—24no—
166#11758196—24no—
167#11758196—24no—
168#11758196—22no—
169#11758196—22no—
170#11758196—22no—
171#11758196—22no—
172#11758196—22no—
173#11758196—22no—
174#11758196—48no—
175C4×Dic61—24no—
176C4×Dic61—24no—
177C2×#92418—22no—
178C2×#92418—42no—
179C23×C61—22no—
180C23×C61—22no—
181C23×C61#12011yescharacteristic
182C23×C61#12011yescharacteristic
183C23×C61C2×SD1612yes—
184C23×C61#13712yes—
185C23×C61C22×D411yescharacteristic
186Q8×C61—42no—
187Q8×C61—81no—
188C2×C4×C61—22no—
189C2×C4×C61—22no—
190C2×C4×C61—22no—
191C2×C4×C61—22no—
192C2×C4×C61—41no—
193C2×C4×C61—41no—
194C2×C4×C61—41no—
195C2×C4×C61—41no—
196C2×C4×C61—42no—
197C2×C4×C61—42no—
198C2×C4×C61—42no—
199C2×C4×C61—42no—
200C2×C4×C61—42no—
201C2×C4×C61—82no—
202C2×C4×C61—82no—
203C2×C4×C61#12011yescharacteristic
204C2×C4×C61#12011yescharacteristic
205C2×C4×C61C22×D411yescharacteristic
206C2×C4×C61C22×D411yescharacteristic
207C2×Dic61—22no—
208C2×Dic61—22no—
209C2×Dic61—24no—
210C2×Dic61—24no—
211C2×Dic61—24no—
212C2×Dic61—22no—
213C2×Dic61—22no—
214C2×Dic61—22no—
215C2×Dic61—48no—
216C2×Dic61—42no—
217C2×Dic61—42no—
218C2×Dic61—42no—
219C2×Dic61—42no—
220C2×Dic61—42no—
221C2×Dic61—42no—
222C2×Dic61—81no—
223C2×Dic61C2×SD1614yes—
224Dic122—42no—
225Dic122—81no—
226Dic122—84no—
227C8×C61—42no—
228#92418—42no—
229C2×#1611—611nomaximal, Sylow
230C22×C61—24no—
231C22×C61—24no—
232C22×C61—21no—
233C22×C61—21no—
234C22×C61—21no—
235C22×C61—21no—
236C22×C61#44812yes—
237C22×C61#44812yes—
238C22×C61#45612yes—
239C22×C61#45812yes—
240C22×C61C2×#12011yescharacteristic
241C22×C61C22×SD1611yescharacteristic
242C22×C61C2×#13711yescharacteristic
243C4×C61—21no—
244C4×C61—21no—
245C4×C61—21no—
246C4×C61—21no—
247C4×C61—42no—
248C4×C61—42no—
249C4×C61—82no—
250Dic61—24no—
251Dic61—44no—
252Dic61—42no—
253Dic61—42no—
254Dic61—42no—
255C2×#544—611no—
256C2×#483—611no—
257C2×#483D6111yescharacteristic
258C2×#398—611no—
259#1611—618no—
260C2×#328—611no—
261C2×#328—611no—
262C2×#324—611no—
263C2×C61—21no—
264C2×C61—21no—
265C2×C61—22no—
266C2×C61#161114yescomplemented
267C2×C61C2×#44811yescharacteristic
268C2×C61C2×#45611yescharacteristic
269C2×C61C2×#45811yescharacteristic
270#544—614no—
271#544—1222no—
272#544—1222no—
273#544—1222no—
274C2×C4⋊Q8—1221no—
275C2×C4⋊Q8—1221no—
276C2×#125—1221no—
277C2×#125—1221no—
278C2×C22⋊Q8—611no—
279C2×C22⋊Q8—1221no—
280C2×C22⋊Q8C2×D6111yescharacteristic
281C2×#117—1221no—
282C22×C4⋊C4—611no—
283C22×C4⋊C4—1221no—
284C22×C4⋊C4C2×D6111yescharacteristic
285#483—22no—
286#483—614no—
287#483—1222no—
288#483C2×D6114yes—
289C2×#106—21no—
290C2×#106—1221no—
291C2×#103—21no—
292C2×#103—1221no—
293C2×C22⋊C8—611no—
294C2×C22⋊C8C2×D6111yescharacteristic
295#398—614no—
296#398—1222no—
297C2×#95—611no—
298C2×#95—1221no—
299#328—614no—
300#328—614no—
301#324—614no—
302C61C2×#161111yescharacteristic, complemented, Sylow
303C22×Q8—611no—
304C22×Q8—1221no—
305C22×Q8C22⋊D6111yescharacteristic
306C23×C4—21no—
307C23×C4—611no—
308C23×C4—611no—
309C23×C4—1221no—
310C23×C4C22×D6111yescharacteristic
311C22×C8—21no—
312C22×C8—1221no—
313C4⋊Q8—1224no—
314C4⋊Q8—1224no—
315C4⋊Q8—1224no—
316C4⋊Q8—1224no—
317#125—1224no—
318#125—1224no—
319#125—1224no—
320#125—1224no—
321C22⋊Q8—21no—
322C22⋊Q8—21no—
323C22⋊Q8—612no—
324C22⋊Q8—612no—
325C22⋊Q8—1224no—
326C22⋊Q8—1224no—
327C22⋊Q8—1221no—
328C22⋊Q8—1221no—
329C22⋊Q8C22⋊D6112yes—
330C22⋊Q8C22×D6112yes—
331#117—1224no—
332#117—1224no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—611no—
340C2×C4⋊C4—612no—
341C2×C4⋊C4—612no—
342C2×C4⋊C4—1221no—
343C2×C4⋊C4—1221no—
344C2×C4⋊C4—1221no—
345C2×C4⋊C4—1221no—
346C2×C4⋊C4—1221no—
347C2×C4⋊C4—1221no—
348C2×C4⋊C4—1221no—
349C2×C4⋊C4—1221no—
350C2×C4⋊C4—1221no—
351C2×C4⋊C4—1221no—
352C2×C4⋊C4—1224no—
353C2×C4⋊C4—2444no—
354C2×C4⋊C4C22⋊D6111yescharacteristic
355C2×C4⋊C4C22×D6112yes—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—1221no—
358C2×C42—1221no—
359C2×C42—1221no—
360#106—24no—
361#106—1224no—
362#103—24no—
363#103—1224no—
364C22⋊C8—21no—
365C22⋊C8—612no—
366C22⋊C8—1221no—
367C22⋊C8C22×D6112yes—
368#95—612no—
369#95—1224no—
370#95—1221no—
371C24D4×D6111yescharacteristic
372C2×Q8—21no—
373C2×Q8—42no—
374C2×Q8—612no—
375C2×Q8—1224no—
376C2×Q8—1221no—
377C2×Q8—4882no—
378C2×Q8—2442no—
379C2×Q8C2×C22⋊D6112yes—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—22no—
383C22×C4—42no—
384C22×C4—41no—
385C22×C4—41no—
386C22×C4—42no—
387C22×C4—42no—
388C22×C4—612no—
389C22×C4—614no—
390C22×C4—612no—
391C22×C4—1221no—
392C22×C4—1221no—
393C22×C4—1222no—
394C22×C4—1221no—
395C22×C4—1224no—
396C22×C4—1222no—
397C22×C4—1221no—
398C22×C4—1221no—
399C22×C4—1221no—
400C22×C4—2442no—
401C22×C4—2442no—
402C22×C4—2442no—
403C22×C4D4×D6111yescharacteristic
404C22×C4D4×D6111yescharacteristic
405C22×C4D4×D6111yescharacteristic
406C22×C4C2×C22⋊D6111yescharacteristic
407C22×C4C2×C22⋊D6111yescharacteristic
408C22×C4C23×D6111yescharacteristic
409C2×C8—22no—
410C2×C8—42no—
411C2×C8—1222no—
412C2×C8—2442no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—21no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—41no—
419C4⋊C4—41no—
420C4⋊C4—612no—
421C4⋊C4—1224no—
422C4⋊C4—1224no—
423C4⋊C4—1224no—
424C4⋊C4—1224no—
425C4⋊C4—1224no—
426C4⋊C4—1222no—
427C4⋊C4—1222no—
428C4⋊C4—1222no—
429C4⋊C4—1222no—
430C4⋊C4—1222no—
431C4⋊C4—1221no—
432C4⋊C4—1222no—
433C4⋊C4—2448no—
434C4⋊C4C2×C22⋊D6112yes—
435C22⋊C4—22no—
436C22⋊C4—22no—
437C22⋊C4—1222no—
438C22⋊C4—1222no—
439C42—1224no—
440C42—1224no—
441C23—22no—
442C23—22no—
443C23#1451974511yescharacteristic
444C23#1451974511yescharacteristic
445C23SD16×D6112yes—
446C23#1451980612yes—
447C23C2×D4×D6111yescharacteristic
448Q8—42no—
449Q8—81no—
450Q8—4881no—
451Q8—4884no—
452Q8—2442no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—82no—
467C2×C4—82no—
468C2×C4—614no—
469C2×C4—1222no—
470C2×C4—1222no—
471C2×C4—1224no—
472C2×C4—1224no—
473C2×C4—1224no—
474C2×C4—1222no—
475C2×C4—1222no—
476C2×C4—1222no—
477C2×C4—4881no—
478C2×C4—2442no—
479C2×C4—2448no—
480C2×C4—2442no—
481C2×C4—2442no—
482C2×C4—2442no—
483C2×C4—2442no—
484C2×C4—2442no—
485C2×C4#1451974511yescharacteristic
486C2×C4#1451974511yescharacteristic
487C2×C4C2×D4×D6111yescharacteristic
488C2×C4C22×C22⋊D6111yescharacteristic
489C8—42no—
490C8—2442no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—21no—
495C22—24no—
496C22—24no—
497C22#1683989912yes—
498C22#1683989912yes—
499C22#1683994312yes—
500C22#1683995112yes—
501C22C2×#1451974511yescharacteristic
502C22C2×SD16×D6111yescharacteristic
503C22C2×#1451980611yescharacteristic
504C4—21no—
505C4—21no—
506C4—21no—
507C4—21no—
508C4—42no—
509C4—42no—
510C4—82no—
511C4—1224no—
512C4—2444no—
513C4—2442no—
514C4—2442no—
515C4—2442no—
516C2—21no—
517C2—21no—
518C2—22no—
519C2#2144482514yesdirect product factor
520C2C2×#1683989911yescharacteristic
521C2C2×#1683994311yescharacteristic
522C2C2×#1683995111yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#483C2
socleC23×C61#120
prime radicalC24×C61C2×D4
hypercenterC2×#483D61
hypocenterC61C2×#1611
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
4. #21444825C2direct (N × H)
266. C2×C61#1611semidirect
302. C61C2×#1611semidirect
519. C2#21444825direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403912
C2×#168400922
C2×#168396932
#214448252
C2×#168395002
C2×#168394992
C2×#168394872
C2×C61×#4832
C2×#161161