Finite Group Databasebeta

← C2×#21446232 #29681632

Subgroups — C2×#21446232 #29681632

Order 15616.

2102 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519758C211yesmaximal, characteristic
2C22×#14519692C211yesmaximal, characteristic
3C2×#16839623C212yesmaximal, complemented
4#21446232C218yesmaximal, direct product factor
5C2×#16839529C212yesmaximal, complemented
6C2×C61×#518C211yesmaximal, characteristic
7C24×Dic61C2211yescharacteristic
8C2×#14519758—24no—
9C2×#14519758—22no—
10C2×#14519758C418yescomplemented
11C2×#14519758C2214yes—
12C22×#11758196—21no—
13C22×C22⋊Dic61—21no—
14C22×C22⋊Dic61C2212yes—
15C22×C22⋊Dic61C2211yescharacteristic
16C2×#14519692—24no—
17C2×#14519692C2214yes—
18#16839623—24no—
19#16839623C2218yescomplemented
20C2×#14519684—24no—
21#16839529C2218yescomplemented
22C23×D4×C61C2211yescharacteristic
23C61×#518—22no—
24C61×#518—24no—
25C61×#518C2214yes—
26C2×C4×D4×C61—24no—
27C2×#117×C61—21no—
28C22×C22⋊C4×C61—21no—
29C22×C22⋊C4×C61C2212yes—
30C23×Dic61—21no—
31C23×Dic61—21no—
32C23×Dic61—22no—
33C23×Dic61—21no—
34C23×Dic61—22no—
35C23×Dic61—22no—
36C23×Dic61—24no—
37C23×Dic61—22no—
38C23×Dic61C2×C414yescomplemented
39C23×Dic61C2312yes—
40#14519758—216no—
41#14519758—28no—
42#14519758C2×C4116yescomplemented
43C2×#11758196—28no—
44C2×#11758196—24no—
45C2×C22⋊Dic61—28no—
46C2×C22⋊Dic61—24no—
47C2×C22⋊Dic61—22no—
48C2×C22⋊Dic61—21no—
49C2×C22⋊Dic61—24no—
50C2×C22⋊Dic61—24no—
51C2×C22⋊Dic61—22no—
52C2×C22⋊Dic61C2×C414yescomplemented
53C2×C22⋊Dic61C2314yes—
54C2×C22⋊Dic61C2312yes—
55#14519692—28no—
56#14519684—216no—
57C25×C61D411yescharacteristic
58C25×C61C2311yescharacteristic
59C22×D4×C61—22no—
60C22×D4×C61—22no—
61C22×D4×C61—24no—
62C22×D4×C61C2×C414yes—
63C22×D4×C61D414yes—
64C22×D4×C61D412yes—
65C22×D4×C61C2312yes—
66C23×C4×C61—22no—
67C23×C4×C61D411yescharacteristic
68C23×C4×C61D414yes—
69C4×D4×C61—216no—
70C4×D4×C61—216no—
71#117×C61—24no—
72#117×C61—24no—
73C2×C4⋊C4×C61—22no—
74C2×C22⋊C4×C61—22no—
75C2×C22⋊C4×C61—24no—
76C2×C22⋊C4×C61—22no—
77C2×C22⋊C4×C61—24no—
78C2×C22⋊C4×C61—22no—
79C2×C22⋊C4×C61—22no—
80C2×C22⋊C4×C61—22no—
81C2×C22⋊C4×C61D414yes—
82C2×C22⋊C4×C61C2314yes—
83C2×C42×C61—22no—
84C24×C61—21no—
85C24×C61—21no—
86C24×C61—22no—
87C24×C61—44no—
88C24×C61—44no—
89C24×C61C22⋊C414yes—
90C24×C61C22×C412yes—
91C24×C61C2×D411yescharacteristic
92C24×C61C2×D412yes—
93C24×C61C2×D412yes—
94C24×C61C2×D411yescharacteristic
95C24×C61C2×D412yes—
96C24×C61C2×D412yes—
97C24×C61#4114yes—
98C24×C61C2411yescharacteristic
99C2×D4×C61—28no—
100C2×D4×C61—28no—
101C2×D4×C61—24no—
102C2×D4×C61—28no—
103C2×D4×C61—28no—
104C2×D4×C61—24no—
105C2×D4×C61—24no—
106C2×D4×C61—24no—
107C2×D4×C61C22⋊C418yes—
108C2×D4×C61C22×C414yes—
109C2×D4×C61C2×D414yes—
110C22×C4×C61—21no—
111C22×C4×C61—21no—
112C22×C4×C61—22no—
113C22×C4×C61—24no—
114C22×C4×C61—28no—
115C22×C4×C61—24no—
116C22×C4×C61—48no—
117C22×C4×C61—84no—
118C22×C4×C61C22⋊C414yes—
119C22×C4×C61C2×D412yes—
120C22×C4×C61C2×D418yes—
121C22×Dic61—24no—
122C22×Dic61—24no—
123C22×Dic61—24no—
124C22×Dic61—28no—
125C22×Dic61—28no—
126C22×Dic61—24no—
127C22×Dic61—22no—
128C22×Dic61—22no—
129C22×Dic61—22no—
130C22×Dic61—24no—
131C22×Dic61—24no—
132C22×Dic61—44no—
133C22×Dic61—41no—
134C22×Dic61—42no—
135C22×Dic61—41no—
136C22×Dic61—44no—
137C22×Dic61—44no—
138C22×Dic61—42no—
139C22×Dic61—42no—
140C22×Dic61—48no—
141C22×Dic61—44no—
142C22×Dic61C22×C414yescomplemented
143C4⋊C4×C61—28no—
144C22⋊C4×C61—28no—
145C22⋊C4×C61—24no—
146C22⋊C4×C61—24no—
147C22⋊C4×C61—24no—
148C22⋊C4×C61—24no—
149C42×C61—28no—
150C22⋊Dic61—216no—
151C22⋊Dic61—24no—
152C22⋊Dic61—22no—
153C22⋊Dic61—24no—
154C22⋊Dic61—24no—
155C22⋊Dic61—44no—
156C22⋊Dic61C22×C414yescomplemented
157#11758196—216no—
158C23×C61—28no—
159C23×C61—24no—
160C23×C61—22no—
161C23×C61—24no—
162C23×C61—22no—
163C23×C61—24no—
164C23×C61—44no—
165C23×C61—44no—
166C23×C61—44no—
167C23×C61—42no—
168C23×C61—48no—
169C23×C61—42no—
170C23×C61—48no—
171C23×C61—44no—
172C23×C61—44no—
173C23×C61—84no—
174C23×C61—82no—
175C23×C61C2×C22⋊C412yes—
176C23×C61C2×C22⋊C414yes—
177C23×C61C2×C22⋊C412yes—
178C23×C61C4×D414yes—
179C23×C61C4×D414yes—
180C23×C61#12011yescharacteristic
181C23×C61#12012yes—
182C23×C61#12011yescharacteristic
183C23×C61#12114yes—
184C23×C61#12114yes—
185C23×C61#12312yes—
186C23×C61#12312yes—
187C23×C61C23×C411yescharacteristic
188C23×C61C22×D411yescharacteristic
189C23×C61C22×D412yes—
190C23×C61C22×D411yescharacteristic
191C23×C61C2×#4112yes—
192D4×C61—28no—
193D4×C61—28no—
194D4×C61—216no—
195C2×C4×C61—22no—
196C2×C4×C61—22no—
197C2×C4×C61—24no—
198C2×C4×C61—24no—
199C2×C4×C61—28no—
200C2×C4×C61—48no—
201C2×C4×C61—48no—
202C2×C4×C61—84no—
203C2×C4×C61—88no—
204C2×C4×C61C2×C22⋊C414yes—
205C2×Dic61—24no—
206C2×Dic61—24no—
207C2×Dic61—28no—
208C2×Dic61—48no—
209C2×Dic61—44no—
210C2×Dic61—42no—
211C2×Dic61—44no—
212C2×Dic61—42no—
213C2×Dic61—44no—
214C2×Dic61—48no—
215C2×Dic61—44no—
216C2×Dic61—48no—
217C2×Dic61—44no—
218C2×Dic61—88no—
219C2×#1890—611nomaximal, Sylow
220C22×C61—24no—
221C22×C61—28no—
222C22×C61—24no—
223C22×C61—28no—
224C22×C61—24no—
225C22×C61—22no—
226C22×C61—24no—
227C22×C61—22no—
228C22×C61—24no—
229C22×C61—42no—
230C22×C61—44no—
231C22×C61—44no—
232C22×C61—42no—
233C22×C61—41no—
234C22×C61—41no—
235C22×C61—42no—
236C22×C61—44no—
237C22×C61—48no—
238C22×C61—44no—
239C22×C61—82no—
240C22×C61—84no—
241C22×C61#38612yes—
242C22×C61#38614yes—
243C22×C61#38612yes—
244C22×C61#45814yes—
245C22×C61C22×C22⋊C411yescharacteristic
246C22×C61C2×C4×D412yes—
247C22×C61C2×#12011yescharacteristic
248C22×C61C2×#12112yes—
249C22×C61C2×#12311yescharacteristic
250C4×C61—24no—
251C4×C61—48no—
252Dic61—44no—
253Dic61—44no—
254Dic61—84no—
255C22×#123—611no—
256C2×#518D6111yescharacteristic
257C22×#99—611no—
258C2×#381—612no—
259#1890—618no—
260C2×#342—612no—
261C2×C61—21no—
262C2×C61—22no—
263C2×C61—21no—
264C2×C61—22no—
265C2×C61—22no—
266C2×C61—24no—
267C2×C61—44no—
268C2×C61#189014yescomplemented
269C2×C61C2×#38611yescharacteristic
270C2×C61C2×#45812yes—
271C23×D4C2×D6111yescharacteristic
272C24×C4—611no—
273C2×#123—618no—
274C2×#123—614no—
275C2×#123—1224no—
276C2×#123—1222no—
277#518—22no—
278#518—24no—
279#518C2×D6114yes—
280C2×C4×D4—24no—
281C2×#117—21no—
282C22×C4⋊C4—1221no—
283C22×C22⋊C4—21no—
284C22×C22⋊C4—611no—
285C22×C22⋊C4—612no—
286C22×C22⋊C4—1221no—
287C22×C22⋊C4C2×D6112yes—
288C2×#99—614no—
289C2×#99—1224no—
290#381—618no—
291#381—1224no—
292C2×#95—1224no—
293#342—618no—
294C61C2×#189011yescharacteristic, complemented, Sylow
295C25C22⋊D6111yescharacteristic
296C25C22×D6111yescharacteristic
297C22×D4—24no—
298C22×D4—22no—
299C22×D4—22no—
300C22×D4C4×D6114yes—
301C22×D4D24414yes—
302C22×D4C22⋊D6112yes—
303C22×D4C22×D6112yes—
304C23×C4—22no—
305C23×C4—614no—
306C23×C4—612no—
307C23×C4—1222no—
308C23×C4—1224no—
309C23×C4—1221no—
310C23×C4—1221no—
311C23×C4—1221no—
312C23×C4—1222no—
313C23×C4—1222no—
314C23×C4—1222no—
315C23×C4C22⋊D6111yescharacteristic
316C23×C4C22⋊D6114yes—
317#123—6116no—
318#123—12216no—
319#123—1228no—
320C4×D4—216no—
321C4×D4—216no—
322#117—24no—
323#117—24no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—1228no—
326C2×C4⋊C4—1224no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—614no—
335C2×C22⋊C4—612no—
336C2×C22⋊C4—614no—
337C2×C22⋊C4—1228no—
338C2×C22⋊C4—1222no—
339C2×C22⋊C4—1221no—
340C2×C22⋊C4—1224no—
341C2×C22⋊C4—1224no—
342C2×C22⋊C4—1224no—
343C2×C22⋊C4—1222no—
344C2×C22⋊C4C22⋊D6114yes—
345C2×C22⋊C4C22×D6114yes—
346C2×C42—22no—
347#99—1228no—
348#95—12216no—
349C24—21no—
350C24—21no—
351C24—22no—
352C24—44no—
353C24—44no—
354C24#1175819814yes—
355C24C2×C4×D6112yes—
356C24C2×D24412yes—
357C24#1175822214yes—
358C24C2×C22⋊D6111yescharacteristic
359C24C2×C22⋊D6112yes—
360C24C2×C22⋊D6112yes—
361C24C2×C22⋊D6111yescharacteristic
362C24C2×C22⋊D6112yes—
363C24C23×D6111yescharacteristic
364C2×D4—24no—
365C2×D4—24no—
366C2×D4—28no—
367C2×D4—28no—
368C2×D4—24no—
369C2×D4—28no—
370C2×D4—28no—
371C2×D4—24no—
372C2×D4#1175819818yes—
373C2×D4C2×C4×D6114yes—
374C2×D4C2×D24414yes—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—22no—
378C22×C4—24no—
379C22×C4—28no—
380C22×C4—24no—
381C22×C4—48no—
382C22×C4—84no—
383C22×C4—614no—
384C22×C4—1224no—
385C22×C4—1222no—
386C22×C4—1222no—
387C22×C4—1222no—
388C22×C4—1224no—
389C22×C4—1224no—
390C22×C4—1224no—
391C22×C4—1224no—
392C22×C4—1228no—
393C22×C4—1228no—
394C22×C4—1224no—
395C22×C4—2448no—
396C22×C4—2444no—
397C22×C4—2444no—
398C22×C4—2441no—
399C22×C4—2442no—
400C22×C4—2441no—
401C22×C4—2444no—
402C22×C4—2444no—
403C22×C4—2442no—
404C22×C4—2442no—
405C22×C4#1175819814yes—
406C22×C4C2×C22⋊D6112yes—
407C22×C4C2×C22⋊D6118yes—
408C4⋊C4—28no—
409C4⋊C4—12216no—
410C22⋊C4—28no—
411C22⋊C4—24no—
412C22⋊C4—24no—
413C22⋊C4—24no—
414C22⋊C4—24no—
415C22⋊C4—614no—
416C22⋊C4—1222no—
417C22⋊C4—1224no—
418C22⋊C4—12216no—
419C22⋊C4—1224no—
420C22⋊C4—1224no—
421C22⋊C4—2444no—
422C42—28no—
423C23—28no—
424C23—24no—
425C23—22no—
426C23—24no—
427C23—22no—
428C23—24no—
429C23—44no—
430C23—44no—
431C23—48no—
432C23—44no—
433C23—42no—
434C23—42no—
435C23—48no—
436C23—44no—
437C23—44no—
438C23—84no—
439C23—82no—
440C23C2×#1175819812yes—
441C23C2×#1175819814yes—
442C23C2×#1175819812yes—
443C23C4×C22⋊D6114yes—
444C23C4×C22⋊D6114yes—
445C23#1451974611yescharacteristic
446C23#1451974612yes—
447C23#1451974611yescharacteristic
448C23#1451975114yes—
449C23#1451975114yes—
450C23#1451976012yes—
451C23#1451976012yes—
452C23C22×C4×D6111yescharacteristic
453C23C22×C22⋊D6111yescharacteristic
454C23C22×C22⋊D6112yes—
455C23C22×D24411yescharacteristic
456C23C2×#1175822212yes—
457D4—28no—
458D4—28no—
459D4—216no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—28no—
465C2×C4—48no—
466C2×C4—48no—
467C2×C4—84no—
468C2×C4—88no—
469C2×C4—1224no—
470C2×C4—1224no—
471C2×C4—1228no—
472C2×C4—4888no—
473C2×C4—2448no—
474C2×C4—2444no—
475C2×C4—2448no—
476C2×C4—2444no—
477C2×C4—2442no—
478C2×C4—2444no—
479C2×C4—2442no—
480C2×C4—2444no—
481C2×C4—2448no—
482C2×C4—2444no—
483C2×C4C2×#1175819814yes—
484C22—28no—
485C22—24no—
486C22—24no—
487C22—28no—
488C22—24no—
489C22—24no—
490C22—22no—
491C22—22no—
492C22—24no—
493C22—41no—
494C22—41no—
495C22—42no—
496C22—42no—
497C22—44no—
498C22—44no—
499C22—42no—
500C22—44no—
501C22—48no—
502C22—44no—
503C22—82no—
504C22—84no—
505C22#1683964112yes—
506C22#1683964114yes—
507C22#1683964112yes—
508C22#1683995214yes—
509C22C22×#1175819811yescharacteristic
510C22C2×C4×C22⋊D6112yes—
511C22C2×#1451974611yescharacteristic
512C22C2×#1451975112yes—
513C22C2×#1451976011yescharacteristic
514C4—24no—
515C4—48no—
516C4—4884no—
517C4—2444no—
518C4—2444no—
519C2—22no—
520C2—21no—
521C2—21no—
522C2—22no—
523C2—22no—
524C2—24no—
525C2—44no—
526C2#2144623214yesdirect product factor
527C2C2×#1683964111yescharacteristic
528C2C2×#1683995212yes—
subgroupG/H
centerC23#14519746
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC2×C61×#518C2
socleC23×C61#120
prime radicalC23×D4×C61C22
cosocleC24×C61C24
hypercenterC2×#518D61
hypocenterC61C2×#1890
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C25 ◁ C2×#518

Complements

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

NH ≅ G/Ntype
3. C2×#16839623C2semidirect
4. #21446232C2direct (N × H)
5. C2×#16839529C2semidirect
10. C2×#14519758C4semidirect
19. #16839623C22semidirect
21. #16839529C22semidirect
38. C23×Dic61C2×C4semidirect
42. #14519758C2×C4semidirect
52. C2×C22⋊Dic61C2×C4semidirect
142. C22×Dic61C22×C4semidirect
156. C22⋊Dic61C22×C4semidirect
268. C2×C61#1890semidirect
294. C61C2×#1890semidirect
526. C2#21446232direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197582
C22×#145196922
C2×#168396232
#214462322
C2×#168395292
C2×C61×#5182
C2×#189061