Finite Group Databasebeta

← C2×#21447483 #29832792

Subgroups — C2×#21447483 #29832792

Order 15616.

1338 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840311C211yesmaximal, characteristic
2C2×#16839734C212yesmaximal, complemented
3#21447483C218yesmaximal, direct product factor
4C2×#16839557C211yesmaximal, characteristic, complemented
5C2×#16839554C212yesmaximal, complemented
6C2×C61×#354C211yesmaximal, characteristic, complemented
7C22×#11758226C411yescharacteristic, complemented
8C22×#11758224C2211yescharacteristic
9#16840311—24no—
10#16840311C414yescomplemented
11#16840311C2214yes—
12C2×#14519775C411yescharacteristic, complemented
13C2×#14519773C2211yescharacteristic
14C2×#14519765C411yescharacteristic, complemented
15C2×#14519750—22no—
16C2×#14519737—22no—
17C2×#14519733—22no—
18C2×C42×D61C411yescharacteristic, complemented
19#16839734—24no—
20#16839734C2218yescomplemented
21C2×#14519692C2212yes—
22C2×#14519691—22no—
23#16839557C2214yescomplemented
24#16839554C2218yescomplemented
25C2×#124×C61C2211yescharacteristic
26C2×#99×C61C2212yes—
27C61×#354C2214yescomplemented
28C2×#11758226—22no—
29C2×#11758226—42no—
30C2×#11758226—41no—
31C2×#11758226—41no—
32C2×#11758226C2×C414yescomplemented
33C2×#11758224—41no—
34C2×#11758224—41no—
35C2×#11758224—42no—
36C2×#11758224C2×C412yes—
37C2×#11758224D414yes—
38C2×#11758224C2312yes—
39C22×Dic122C2×C411yescharacteristic
40C22×D244—21no—
41C22×D244C2×C411yescharacteristic
42C22×C22⋊D61—22no—
43C22×C22⋊D61D412yes—
44C23×Dic61D412yes—
45C22×C4×D61—21no—
46C22×C4×D61—21no—
47C22×C4×D61C2×C411yescharacteristic
48#14519775—22no—
49#14519775C2×C414yescomplemented
50#14519773—22no—
51#14519773C2×C412yes—
52#14519773C2312yes—
53#14519765—22no—
54#14519765C2×C414yescomplemented
55#14519750—28no—
56#14519750—28no—
57#14519737—28no—
58#14519737—28no—
59#14519733—28no—
60#14519733—44no—
61C2×#11758196—22no—
62C2×#11758196—42no—
63C2×C22⋊Dic61—22no—
64C2×#11758198—22no—
65C2×C4×Dic61—21no—
66C2×C4×Dic61—42no—
67C2×C4×Dic61C2×C411yescharacteristic
68C42×D61—22no—
69C42×D61C2×C414yescomplemented
70#14519692—22no—
71#14519692C2314yes—
72#14519691—28no—
73C22×Q8×C61C2×C411yescharacteristic
74C22×D4×C61C2311yescharacteristic
75#124×C61—22no—
76#124×C61C2×C412yes—
77#124×C61C2312yes—
78C2×C22⋊C4×C61—22no—
79C2×C22⋊C4×C61—22no—
80C2×C42×C61C2×C411yescharacteristic
81#99×C61—22no—
82#99×C61C2314yes—
83C24×C61C2×D412yes—
84C23×D61—21no—
85C23×D61C22⋊C411yescharacteristic
86C2×Q8×C61—21no—
87C2×Q8×C61—41no—
88C2×Q8×C61—41no—
89C2×Q8×C61C22×C412yes—
90C2×D4×C61—41no—
91C2×D4×C61—41no—
92C2×D4×C61C22×C411yescharacteristic
93C2×D4×C61C2×D412yes—
94C2×D4×C61C2411yescharacteristic
95C22×C4×C61—21no—
96C22×C4×C61—21no—
97C22×C4×C61—42no—
98C22×C4×C61C22×C411yescharacteristic
99C2×C22⋊D61—24no—
100C2×C22⋊D61—24no—
101C2×C22⋊D61—42no—
102C2×C22⋊D61—42no—
103C2×C22⋊D61—48no—
104C2×C22⋊D61C22⋊C414yes—
105C2×C22⋊D61C2×D414yes—
106C22×Dic61—21no—
107C22×Dic61—22no—
108C22×Dic61—22no—
109C22×Dic61—24no—
110C22×Dic61—42no—
111C22×Dic61C22⋊C412yes—
112C22×Dic61C22⋊C414yes—
113C22×Dic61C22⋊C411yescharacteristic
114C22×Dic61C2×D414yes—
115#11758226—44no—
116#11758226—44no—
117#11758226—44no—
118#11758226—44no—
119#11758224—42no—
120#11758224—42no—
121#11758224—44no—
122#11758224—44no—
123#11758224—42no—
124#11758224—42no—
125C2×D244—24no—
126C2×D244—21no—
127C2×D244—41no—
128C2×D244—41no—
129C2×D244—42no—
130C2×D244—42no—
131C2×D244C22×C412yes—
132C2×C4×D61—22no—
133C2×C4×D61—21no—
134C2×C4×D61—21no—
135C2×C4×D61—24no—
136C2×C4×D61—24no—
137C2×C4×D61—44no—
138C2×C4×D61—42no—
139C2×C4×D61—41no—
140C2×C4×D61—41no—
141C2×C4×D61C22⋊C412yes—
142C2×C4×D61C22×C412yes—
143C2×Dic122—41no—
144C2×Dic122—41no—
145C2×Dic122C22⋊C412yes—
146C2×Dic122C22×C412yes—
147C22⋊C4×C61—24no—
148C22⋊C4×C61—24no—
149C22⋊C4×C61—24no—
150C22⋊C4×C61—42no—
151C42×C61—21no—
152C42×C61C22×C412yes—
153C22⋊Dic61—24no—
154C22⋊Dic61—42no—
155#11758198—28no—
156#11758196—28no—
157#11758196—48no—
158C4×Dic61—21no—
159C4×Dic61—24no—
160C4×Dic61—48no—
161C4×Dic61C22×C412yes—
162C23×C61—22no—
163C23×C61—22no—
164C23×C61—44no—
165C23×C61C2×C22⋊C411yescharacteristic
166C23×C61C2×C22⋊C412yes—
167C23×C61C22×D412yes—
168C22×D61—21no—
169C22×D61—21no—
170C22×D61—22no—
171C22×D61—42no—
172C22×D61—44no—
173C22×D61—41no—
174C22×D61—41no—
175C22×D61C2×C22⋊C412yes—
176Q8×C61—42no—
177Q8×C61—42no—
178D4×C61—41no—
179D4×C61—42no—
180D4×C61—41no—
181C2×C4×C61—21no—
182C2×C4×C61—21no—
183C2×C4×C61—22no—
184C2×C4×C61—22no—
185C2×C4×C61—42no—
186C2×C4×C61—41no—
187C2×C4×C61—41no—
188C2×C4×C61—44no—
189C2×C4×C61—84no—
190C2×C4×C61C2×C22⋊C411yescharacteristic
191C2×C4×C61C23×C411yescharacteristic
192C22⋊D61—44no—
193C22⋊D61—44no—
194C22⋊D61—48no—
195C22⋊D61—48no—
196C2×Dic61—24no—
197C2×Dic61—22no—
198C2×Dic61—22no—
199C2×Dic61—22no—
200C2×Dic61—24no—
201C2×Dic61—24no—
202C2×Dic61—24no—
203C2×Dic61—24no—
204C2×Dic61—44no—
205C2×Dic61—84no—
206C2×Dic61#9912yes—
207C2×Dic61#9911yescharacteristic
208C2×Dic61#9911yescharacteristic
209C2×Dic61C2×C22⋊C414yes—
210C2×Dic61C2×C22⋊C412yes—
211D244—42no—
212D244—42no—
213D244—48no—
214C4×D61—22no—
215C4×D61—22no—
216C4×D61—22no—
217C4×D61—22no—
218C4×D61—48no—
219C4×D61—44no—
220C4×D61—44no—
221Dic122—42no—
222Dic122—42no—
223C2×#2126—611nomaximal, Sylow
224C22×C61—22no—
225C22×C61—22no—
226C22×C61—22no—
227C22×C61—42no—
228C22×C61—42no—
229C22×C61—44no—
230C22×C61—82no—
231C22×C61C2×#9911yescharacteristic
232C22×C61C2×#9911yescharacteristic
233C22×C61C22×C22⋊C411yescharacteristic
234C2×D61—22no—
235C2×D61—42no—
236C2×D61—42no—
237C2×D61—42no—
238C2×D61—44no—
239C2×D61—42no—
240C2×D61—82no—
241C2×D61—82no—
242C4×C61—21no—
243C4×C61—21no—
244C4×C61—42no—
245C4×C61—42no—
246C4×C61—84no—
247Dic61—24no—
248Dic61—24no—
249Dic61—84no—
250Dic61C2×#9912yes—
251Dic61C2×#9912yes—
252C2×#532—611no—
253C2×#410—612no—
254#2126—618no—
255C2×#354—611no—
256C2×#354D6111yescharacteristic, complemented
257C2×#353—612no—
258C2×C61—21no—
259C2×C61—21no—
260C2×C61—42no—
261C2×C61—42no—
262C2×C61#212612yescomplemented
263C2×C61C22×#9911yescharacteristic
264D61—42no—
265D61—82no—
266C22×#41—611no—
267C22×#41—611no—
268#532—614no—
269#532—614no—
270#532—1224no—
271C2×C4⋊Q8—611no—
272C2×#127—611no—
273C2×#124—611no—
274C2×#124C2×D6111yescharacteristic
275C2×#121—1222no—
276C2×C4×D4—1222no—
277C2×#117—1222no—
278C22×C42—611no—
279#410—618no—
280#410—1224no—
281C2×#99—612no—
282C2×#99—1222no—
283C2×#99C2×D6112yes—
284#354—614no—
285#354C2×D6114yescomplemented
286#353—618no—
287C61C2×#212611yescharacteristic, complemented, Sylow
288C2×#41—612no—
289C2×#41—614no—
290C2×#41—612no—
291C2×#41—614no—
292C2×#41—1222no—
293C2×#41—2441no—
294C2×#41—2441no—
295C2×#41—2442no—
296C2×#41—2442no—
297C2×#41—2441no—
298C2×#41—2441no—
299C22×Q8—611no—
300C22×Q8C4×D6111yescharacteristic
301C22×D4—612no—
302C22×D4—611no—
303C22×D4—1221no—
304C22×D4—1222no—
305C22×D4C22×D6111yescharacteristic
306C23×C4—612no—
307C23×C4—611no—
308C23×C4—1221no—
309C23×C4—1221no—
310C4⋊Q8—614no—
311C4⋊Q8—1222no—
312#127—612no—
313#127—612no—
314#127—1222no—
315#124—22no—
316#124—614no—
317#124—1222no—
318#124C4×D6112yes—
319#124C22×D6112yes—
320#121—1228no—
321#121—1228no—
322C4×D4—1228no—
323C4×D4—1228no—
324#117—1228no—
325#117—2444no—
326C2×C4⋊C4—1222no—
327C2×C4⋊C4—2442no—
328C2×C22⋊C4—22no—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—1222no—
331C2×C22⋊C4—1222no—
332C2×C42—611no—
333C2×C42—614no—
334C2×C42—1222no—
335C2×C42—1221no—
336C2×C42—2442no—
337C2×C42C4×D6111yescharacteristic
338#99—22no—
339#99—614no—
340#99—1228no—
341#99—1222no—
342#99C22×D6114yes—
343C24—611no—
344C24—1221no—
345C24D4×D6112yes—
346#41—2442no—
347#41—2444no—
348#41—2442no—
349#41—2444no—
350#41—2442no—
351#41—2442no—
352#41—2444no—
353#41—2444no—
354#41—2444no—
355#41—2444no—
356C2×Q8—21no—
357C2×Q8—41no—
358C2×Q8—41no—
359C2×Q8—612no—
360C2×Q8—612no—
361C2×Q8—2441no—
362C2×Q8—2441no—
363C2×Q8C2×C4×D6112yes—
364C2×D4—41no—
365C2×D4—41no—
366C2×D4—614no—
367C2×D4—614no—
368C2×D4—612no—
369C2×D4—1224no—
370C2×D4—1224no—
371C2×D4—1224no—
372C2×D4—1221no—
373C2×D4—2441no—
374C2×D4—2441no—
375C2×D4—2442no—
376C2×D4—2442no—
377C2×D4—2442no—
378C2×D4—2442no—
379C2×D4—2448no—
380C2×D4C2×C4×D6111yescharacteristic
381C2×D4D4×D6112yes—
382C2×D4C23×D6111yescharacteristic
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—42no—
386C22×C4—611no—
387C22×C4—614no—
388C22×C4—614no—
389C22×C4—612no—
390C22×C4—612no—
391C22×C4—612no—
392C22×C4—1222no—
393C22×C4—1221no—
394C22×C4—1221no—
395C22×C4—1224no—
396C22×C4—1224no—
397C22×C4—1222no—
398C22×C4—1222no—
399C22×C4—1224no—
400C22×C4—1221no—
401C22×C4—2442no—
402C22×C4—2441no—
403C22×C4—2441no—
404C22×C4—2444no—
405C22×C4—2442no—
406C22×C4C2×C4×D6111yescharacteristic
407C4⋊C4—1228no—
408C4⋊C4—2448no—
409C22⋊C4—24no—
410C22⋊C4—24no—
411C22⋊C4—24no—
412C22⋊C4—42no—
413C22⋊C4—1228no—
414C22⋊C4—1224no—
415C22⋊C4—2442no—
416C42—21no—
417C42—612no—
418C42—1224no—
419C42—1221no—
420C42—2448no—
421C42C2×C4×D6112yes—
422C23—22no—
423C23—22no—
424C23—44no—
425C23—612no—
426C23—1221no—
427C23—1221no—
428C23—1222no—
429C23—2444no—
430C23—2442no—
431C23—2441no—
432C23—2441no—
433C23C22⋊C4×D6112yes—
434C23C22⋊C4×D6111yescharacteristic
435C23C2×D4×D6112yes—
436Q8—42no—
437Q8—42no—
438Q8—2442no—
439Q8—2442no—
440D4—41no—
441D4—42no—
442D4—41no—
443D4—2442no—
444D4—2442no—
445D4—2448no—
446D4—2444no—
447D4—2444no—
448D4—2448no—
449D4—2448no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—42no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—44no—
458C2×C4—84no—
459C2×C4—612no—
460C2×C4—612no—
461C2×C4—611no—
462C2×C4—611no—
463C2×C4—614no—
464C2×C4—1222no—
465C2×C4—1222no—
466C2×C4—1222no—
467C2×C4—1222no—
468C2×C4—1224no—
469C2×C4—1224no—
470C2×C4—1224no—
471C2×C4—1224no—
472C2×C4—1224no—
473C2×C4—1222no—
474C2×C4—1222no—
475C2×C4—1222no—
476C2×C4—4884no—
477C2×C4—2444no—
478C2×C4—2444no—
479C2×C4—2448no—
480C2×C4—2444no—
481C2×C4C22⋊C4×D6111yescharacteristic
482C2×C4C22×C4×D6111yescharacteristic
483C22—22no—
484C22—22no—
485C22—22no—
486C22—42no—
487C22—42no—
488C22—44no—
489C22—82no—
490C22—1222no—
491C22—4882no—
492C22—4882no—
493C22—2444no—
494C22—2442no—
495C22—2442no—
496C22—2442no—
497C22—2442no—
498C22#99×D6111yescharacteristic
499C22#99×D6111yescharacteristic
500C22C2×C22⋊C4×D6111yescharacteristic
501C4—21no—
502C4—21no—
503C4—42no—
504C4—42no—
505C4—84no—
506C4—612no—
507C4—612no—
508C4—1224no—
509C4—1224no—
510C4—4884no—
511C2—21no—
512C2—21no—
513C2—42no—
514C2—42no—
515C2—4882no—
516C2—2442no—
517C2#2144748312yesdirect product factor
518C2C2×#99×D6111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC2×C4×C61C23×C4
FrattiniC2×D4C23×D61
FittingC2×C61×#354C2
socleC22×C61C2×#99
prime radicalC2×#16840311C2
cosocleC2×D4×C61C24
hypercenterC2×#354D61
hypocenterC61C2×#2126
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#354

Complements

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

NH ≅ G/Ntype
2. C2×#16839734C2semidirect
3. #21447483C2direct (N × H)
4. C2×#16839557C2semidirect
5. C2×#16839554C2semidirect
6. C2×C61×#354C2semidirect
7. C22×#11758226C4semidirect
10. #16840311C4semidirect
12. C2×#14519775C4semidirect
14. C2×#14519765C4semidirect
18. C2×C42×D61C4semidirect
20. #16839734C22semidirect
23. #16839557C22semidirect
24. #16839554C22semidirect
27. C61×#354C22semidirect
32. C2×#11758226C2×C4semidirect
49. #14519775C2×C4semidirect
54. #14519765C2×C4semidirect
69. C42×D61C2×C4semidirect
256. C2×#354D61semidirect
262. C2×C61#2126semidirect
285. #354C2×D61semidirect
287. C61C2×#2126semidirect
517. C2#21447483direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403112
C2×#168397342
#214474832
C2×#168395572
C2×#168395542
C2×C61×#3542
C2×#212661