Finite Group Databasebeta

← C2×#21444187 #29645989

Subgroups — C2×#21444187 #29645989

Order 15616.

1066 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519772C211yesmaximal, characteristic
2C2×#16839816C211yesmaximal, characteristic, complemented
3C2×#16839812C211yesmaximal, characteristic, complemented
4#21444187C218yesmaximal, direct product factor
5C2×#16839488C211yesmaximal, characteristic, complemented
6C2×#16839485C211yesmaximal, characteristic
7C2×#16839485C211yesmaximal, characteristic
8C2×C61×#324C211yesmaximal, characteristic, complemented
9C2×#14519772—21no—
10C2×#14519772—21no—
11C2×#14519772—21no—
12C2×#14519772—21no—
13C2×#14519772—22no—
14C2×#14519772—22no—
15C2×#14519772C414yes—
16C2×#14519772C2214yes—
17C22×C4⋊Dic61C411yescharacteristic
18C22×#11758196C411yescharacteristic
19C22×#11758198C411yescharacteristic
20C22×#11758198C411yescharacteristic
21C22×#11758198C2211yescharacteristic
22C22×C4×Dic61C2211yescharacteristic
23#16839816—22no—
24#16839816C2214yescomplemented
25#16839812—22no—
26#16839812C2214yescomplemented
27C2×#14519706—21no—
28C2×#14519706—21no—
29C2×C22⋊#92418C2211yescharacteristic
30C2×C22⋊#92418C2211yescharacteristic
31C2×#14519687—21no—
32C2×C8×Dic61—21no—
33#16839488C2214yescomplemented
34#16839485C2214yes—
35#16839485C2214yes—
36C22×C4⋊C4×C61C2211yescharacteristic
37C2×C22⋊C8×C61C2211yescharacteristic
38C2×C22⋊C8×C61C2211yescharacteristic
39C61×#324C2214yescomplemented
40C24×D61C2×C411yescharacteristic
41C23×Dic61C2×C411yescharacteristic
42C23×Dic61C2×C411yescharacteristic
43C23×Dic61C2×C411yescharacteristic
44C22×#92418—21no—
45C22×#92418—21no—
46#14519772—24no—
47#14519772—24no—
48#14519772—24no—
49#14519772—24no—
50#14519772—24no—
51#14519772—24no—
52#14519772—24no—
53#14519772—24no—
54C2×C4⋊Dic61—21no—
55C2×C4⋊Dic61—21no—
56C2×C4⋊Dic61—22no—
57C2×C4⋊Dic61C2×C414yes—
58C2×#11758196—22no—
59C2×#11758196—21no—
60C2×#11758196—21no—
61C2×#11758196C2×C414yes—
62C2×#11758198—21no—
63C2×#11758198—21no—
64C2×#11758198—21no—
65C2×#11758198—21no—
66C2×#11758198—22no—
67C2×#11758198—21no—
68C2×#11758198—21no—
69C2×#11758198—21no—
70C2×#11758198—21no—
71C2×#11758198—22no—
72C2×#11758198C2×C414yes—
73C2×#11758198C2×C414yes—
74C2×#11758198C2×C412yes—
75C2×#11758198C2312yes—
76C2×C4×Dic61C2×C412yes—
77C2×C4×Dic61D411yescharacteristic
78C2×C4×Dic61D411yescharacteristic
79C2×C4×Dic61D411yescharacteristic
80C2×C4×Dic61D411yescharacteristic
81C2×C4×Dic61D412yes—
82C2×C4×Dic61D412yes—
83C2×C4×Dic61C2312yes—
84#14519706—24no—
85#14519706—24no—
86C22⋊#92418—21no—
87C22⋊#92418—21no—
88C22⋊#92418C2312yes—
89C22⋊#92418C2312yes—
90#14519687—24no—
91C8×Dic61—24no—
92C23×C4×C61C2×C411yescharacteristic
93C23×C4×C61C2×C411yescharacteristic
94C23×C4×C61C2311yescharacteristic
95C22×C8×C61—21no—
96C22×C8×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×C61C2×C412yes—
102C2×C4⋊C4×C61C2312yes—
103C22⋊C8×C61—21no—
104C22⋊C8×C61—21no—
105C22⋊C8×C61C2312yes—
106C22⋊C8×C61C2312yes—
107C24×C61C22×C411yescharacteristic
108C23×D61—21no—
109C23×D61—21no—
110C23×D61—22no—
111C23×D61—22no—
112C23×D61—42no—
113C23×D61—42no—
114C23×D61C22×C412yes—
115C22×C4×C61—21no—
116C22×C4×C61—21no—
117C22×C4×C61—21no—
118C22×C4×C61—21no—
119C22×C4×C61—22no—
120C22×C4×C61—22no—
121C22×C4×C61—42no—
122C22×C4×C61—42no—
123C22×C4×C61C22×C412yes—
124C22×C4×C61C22×C412yes—
125C22×C4×C61C22×C411yescharacteristic
126C22×C4×C61C2×D411yescharacteristic
127C22×C4×C61C2×D411yescharacteristic
128C22×C4×C61C2×D411yescharacteristic
129C22×C4×C61C2×D411yescharacteristic
130C22×C4×C61C2411yescharacteristic
131C22×Dic61—22no—
132C22×Dic61—22no—
133C22×Dic61—21no—
134C22×Dic61—21no—
135C22×Dic61—42no—
136C22×Dic61—42no—
137C22×Dic61C22⋊C412yes—
138C22×Dic61C22⋊C411yescharacteristic
139C22×Dic61C22⋊C411yescharacteristic
140C22×Dic61C22⋊C411yescharacteristic
141C22×Dic61C22⋊C411yescharacteristic
142C22×Dic61C22⋊C412yes—
143C22×Dic61C22×C412yes—
144C22×Dic61C22×C412yes—
145C22×Dic61C22×C412yes—
146C2×C8×C61—22no—
147C2×C8×C61—22no—
148C2×C8×C61—42no—
149C2×C8×C61—42no—
150C4⋊C4×C61—22no—
151C4⋊C4×C61—22no—
152C4⋊C4×C61—22no—
153C4⋊C4×C61—22no—
154#11758198—22no—
155#11758198—22no—
156#11758198—22no—
157#11758198—22no—
158#11758198—24no—
159#11758198—24no—
160#11758198—24no—
161#11758198—24no—
162C4⋊Dic61—24no—
163C4⋊Dic61—24no—
164#11758196—24no—
165#11758196—24no—
166C4×Dic61C22⋊C412yes—
167C4×Dic61C22⋊C412yes—
168C4×Dic61C22⋊C412yes—
169C4×Dic61C22⋊C412yes—
170C4×Dic61C2×D412yes—
171C4×Dic61C2×D412yes—
172C4×Dic61C2×D412yes—
173C4×Dic61C2×D412yes—
174C2×#92418—22no—
175C2×#92418—22no—
176C2×#92418—42no—
177C2×#92418—42no—
178C23×C61—22no—
179C23×C61—22no—
180C23×C61C2×C22⋊C411yescharacteristic
181C23×C61C2×C22⋊C411yescharacteristic
182C23×C61#13112yes—
183C23×C61#13112yes—
184C23×C61C23×C411yescharacteristic
185C22×D61—22no—
186C22×D61—22no—
187C22×D61—22no—
188C22×D61—42no—
189C22×D61—42no—
190C22×D61—42no—
191C22×D61—42no—
192C22×D61—42no—
193C22×D61—42no—
194C22×D61—42no—
195C22×D61—42no—
196C22×D61—84no—
197C22×D61—84no—
198C2×C4×C61—22no—
199C2×C4×C61—22no—
200C2×C4×C61—22no—
201C2×C4×C61—22no—
202C2×C4×C61—22no—
203C2×C4×C61—22no—
204C2×C4×C61—41no—
205C2×C4×C61—41no—
206C2×C4×C61—41no—
207C2×C4×C61—41no—
208C2×C4×C61—42no—
209C2×C4×C61—42no—
210C2×C4×C61—42no—
211C2×C4×C61—42no—
212C2×C4×C61—42no—
213C2×C4×C61C2×C22⋊C411yescharacteristic
214C2×C4×C61C2×C22⋊C411yescharacteristic
215C2×C4×C61C22×D411yescharacteristic
216C2×C4×C61C22×D411yescharacteristic
217C2×Dic61—22no—
218C2×Dic61—22no—
219C2×Dic61—24no—
220C2×Dic61—22no—
221C2×Dic61—22no—
222C2×Dic61—22no—
223C2×Dic61—22no—
224C2×Dic61—22no—
225C2×Dic61—42no—
226C2×Dic61—42no—
227C2×Dic61—42no—
228C2×Dic61—42no—
229C2×Dic61—42no—
230C2×Dic61C2×C22⋊C412yes—
231C2×Dic61C2×C22⋊C412yes—
232C2×Dic61C2×C22⋊C412yes—
233C2×Dic61C2×C22⋊C412yes—
234C8×C61—42no—
235C8×C61—42no—
236#92418—42no—
237#92418—42no—
238C2×#1473—611nomaximal, Sylow
239C22×C61—21no—
240C22×C61—21no—
241C22×C61—21no—
242C22×C61—21no—
243C22×C61—24no—
244C22×C61—24no—
245C22×C61#40812yes—
246C22×C61#40812yes—
247C22×C61#41012yes—
248C22×C61#41312yes—
249C22×C61C22×C22⋊C411yescharacteristic
250C22×C61C2×#13111yescharacteristic
251C22×C61C2×#13111yescharacteristic
252C2×D61—42no—
253C2×D61—42no—
254C2×D61—42no—
255C2×D61—84no—
256C2×D61—84no—
257C2×D61—82no—
258C2×D61—82no—
259C4×C61—21no—
260C4×C61—21no—
261C4×C61—21no—
262C4×C61—21no—
263C4×C61—42no—
264C4×C61—42no—
265Dic61—22no—
266Dic61—22no—
267Dic61—22no—
268Dic61—22no—
269Dic61—42no—
270C22×#126—611no—
271C2×#432—611no—
272C2×#431—611no—
273#1473—618no—
274C2×#324—611no—
275C2×#324D6111yescharacteristic, complemented
276C2×#323—611no—
277C2×#323—611no—
278C2×C61—21no—
279C2×C61—21no—
280C2×C61—22no—
281C2×C61#147314yescomplemented
282C2×C61C2×#40811yescharacteristic
283C2×C61C2×#41011yescharacteristic
284C2×C61C2×#41311yescharacteristic
285D61—82no—
286C2×#126—614no—
287C2×#126—614no—
288C2×#126—1221no—
289C2×#126—1221no—
290C2×#126—1221no—
291C2×#126—1221no—
292C2×#126—1222no—
293C2×#126—1222no—
294C22×C4⋊C4—611no—
295C22×C4⋊C4—611no—
296C22×C4⋊C4C2×D6111yescharacteristic
297C22×C22⋊C4—611no—
298C22×C22⋊C4—611no—
299C22×C22⋊C4—611no—
300C22×C42—611no—
301#432—614no—
302#432—1222no—
303#431—614no—
304#431—1222no—
305C2×C4⋊C8—1221no—
306C2×C4⋊C8—1221no—
307C2×C22⋊C8—611no—
308C2×C22⋊C8—611no—
309C2×C22⋊C8C2×D6111yescharacteristic
310C2×C22⋊C8C2×D6111yescharacteristic
311C2×#97—1221no—
312C2×C4×C8—1221no—
313#324—614no—
314#324C2×D6114yescomplemented
315#323—614no—
316#323—614no—
317C61C2×#147311yescharacteristic, complemented, Sylow
318C25—611no—
319C23×C4—611no—
320C23×C4—611no—
321C23×C4—611no—
322C23×C4C4×D6111yescharacteristic
323C23×C4C4×D6111yescharacteristic
324C23×C4C22×D6111yescharacteristic
325C22×C8—21no—
326C22×C8—21no—
327C22×C8—1221no—
328C22×C8—1221no—
329#126—1224no—
330#126—1224no—
331#126—1224no—
332#126—1224no—
333#126—1224no—
334#126—1224no—
335#126—1224no—
336#126—1224no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—614no—
342C2×C4⋊C4—614no—
343C2×C4⋊C4—1222no—
344C2×C4⋊C4—1221no—
345C2×C4⋊C4—1221no—
346C2×C4⋊C4—1222no—
347C2×C4⋊C4—1221no—
348C2×C4⋊C4—1221no—
349C2×C4⋊C4C4×D6112yes—
350C2×C4⋊C4C22×D6112yes—
351C2×C22⋊C4—614no—
352C2×C22⋊C4—614no—
353C2×C22⋊C4—612no—
354C2×C22⋊C4—612no—
355C2×C22⋊C4—1222no—
356C2×C22⋊C4—1222no—
357C2×C22⋊C4—1221no—
358C2×C22⋊C4—1221no—
359C2×C22⋊C4—1221no—
360C2×C22⋊C4—1221no—
361C2×C22⋊C4—1221no—
362C2×C22⋊C4—1221no—
363C2×C22⋊C4—1221no—
364C2×C22⋊C4—1221no—
365C2×C42—612no—
366C2×C42—611no—
367C2×C42—611no—
368C2×C42—611no—
369C2×C42—611no—
370C2×C42—612no—
371C2×C42—612no—
372C2×C42—612no—
373C4⋊C8—1224no—
374C4⋊C8—1224no—
375C22⋊C8—21no—
376C22⋊C8—21no—
377C22⋊C8—612no—
378C22⋊C8—612no—
379C22⋊C8—1221no—
380C22⋊C8—1221no—
381C22⋊C8C22×D6112yes—
382C22⋊C8C22×D6112yes—
383#97—1224no—
384C4×C8—1224no—
385C24—612no—
386C24—1222no—
387C24—1222no—
388C24—1221no—
389C24—1221no—
390C24—2442no—
391C24—2442no—
392C24C2×C4×D6111yescharacteristic
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—42no—
400C22×C4—42no—
401C22×C4—612no—
402C22×C4—612no—
403C22×C4—611no—
404C22×C4—611no—
405C22×C4—611no—
406C22×C4—611no—
407C22×C4—612no—
408C22×C4—612no—
409C22×C4—612no—
410C22×C4—1222no—
411C22×C4—1222no—
412C22×C4—1221no—
413C22×C4—1221no—
414C22×C4—2442no—
415C22×C4—2442no—
416C22×C4C2×C4×D6112yes—
417C22×C4C2×C4×D6112yes—
418C22×C4C2×C4×D6111yescharacteristic
419C22×C4D4×D6111yescharacteristic
420C22×C4D4×D6111yescharacteristic
421C22×C4D4×D6111yescharacteristic
422C22×C4D4×D6111yescharacteristic
423C22×C4C23×D6111yescharacteristic
424C2×C8—22no—
425C2×C8—22no—
426C2×C8—42no—
427C2×C8—42no—
428C2×C8—1222no—
429C2×C8—1222no—
430C2×C8—2442no—
431C2×C8—2442no—
432C4⋊C4—22no—
433C4⋊C4—22no—
434C4⋊C4—22no—
435C4⋊C4—22no—
436C4⋊C4—1224no—
437C4⋊C4—1224no—
438C4⋊C4—1224no—
439C4⋊C4—1224no—
440C22⋊C4—1224no—
441C22⋊C4—1224no—
442C22⋊C4—1224no—
443C22⋊C4—1224no—
444C22⋊C4—1222no—
445C22⋊C4—1222no—
446C22⋊C4—1222no—
447C22⋊C4—1222no—
448C42—612no—
449C42—612no—
450C42—612no—
451C42—612no—
452C42—612no—
453C42—612no—
454C42—612no—
455C42—612no—
456C23—22no—
457C23—22no—
458C23—1222no—
459C23—1222no—
460C23—1222no—
461C23—4884no—
462C23—4884no—
463C23—2442no—
464C23—2442no—
465C23—2442no—
466C23—2442no—
467C23—2442no—
468C23—2442no—
469C23—2442no—
470C23—2442no—
471C23C22⋊C4×D6111yescharacteristic
472C23C22⋊C4×D6111yescharacteristic
473C23#1451978312yes—
474C23#1451978512yes—
475C23C22×C4×D6111yescharacteristic
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—612no—
492C2×C4—612no—
493C2×C4—612no—
494C2×C4—612no—
495C2×C4—1224no—
496C2×C4—1222no—
497C2×C4—1222no—
498C2×C4—1222no—
499C2×C4—1222no—
500C2×C4—1222no—
501C2×C4—1222no—
502C2×C4—1222no—
503C2×C4—2442no—
504C2×C4—2442no—
505C2×C4—2442no—
506C2×C4—2442no—
507C2×C4—2442no—
508C2×C4C22⋊C4×D6111yescharacteristic
509C2×C4C22⋊C4×D6111yescharacteristic
510C2×C4C2×D4×D6111yescharacteristic
511C2×C4C2×D4×D6111yescharacteristic
512C8—42no—
513C8—42no—
514C8—2442no—
515C8—2442no—
516C22—24no—
517C22—24no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—21no—
522C22—4882no—
523C22—4882no—
524C22—4884no—
525C22—4884no—
526C22—2442no—
527C22—2442no—
528C22—2442no—
529C22#1683972712yes—
530C22#1683972712yes—
531C22#1683973412yes—
532C22#1683974512yes—
533C22C2×C22⋊C4×D6111yescharacteristic
534C22C2×#1451978311yescharacteristic
535C22C2×#1451978511yescharacteristic
536C4—21no—
537C4—21no—
538C4—21no—
539C4—21no—
540C4—42no—
541C4—42no—
542C4—1222no—
543C4—1222no—
544C4—1222no—
545C4—1222no—
546C4—2442no—
547C2—22no—
548C2—21no—
549C2—21no—
550C2—4882no—
551C2#2144418714yesdirect product factor
552C2C2×#1683972711yescharacteristic
553C2C2×#1683973411yescharacteristic
554C2C2×#1683974511yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#324C2
socleC23×C61C2×C22⋊C4
prime radicalC24×D61C2×C4
cosocleC22×C4×C61C24
hypercenterC2×#324D61
hypocenterC61C2×#1473
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
2. C2×#16839816C2semidirect
3. C2×#16839812C2semidirect
4. #21444187C2direct (N × H)
5. C2×#16839488C2semidirect
8. C2×C61×#324C2semidirect
24. #16839816C22semidirect
26. #16839812C22semidirect
33. #16839488C22semidirect
39. C61×#324C22semidirect
275. C2×#324D61semidirect
281. C2×C61#1473semidirect
314. #324C2×D61semidirect
317. C61C2×#1473semidirect
551. C2#21444187direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197722
C2×#168398162
C2×#168398122
#214441872
C2×#168394882
C2×#168394852
C2×C61×#3242
C2×#147361