Finite Group Databasebeta

← C2×#21445537 #29677415

Subgroups — C2×#21445537 #29677415

Order 15616.

2574 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
1C23×#11758189C211yesmaximal, characteristic
2C22×#14519735C211yesmaximal, characteristic
3C22×C4⋊C4×D61C211yesmaximal, characteristic
4#21445537C218yesmaximal, direct product factor
5C2×#16839525C211yesmaximal, characteristic, complemented
6C2×#16839524C211yesmaximal, characteristic, complemented
7C2×#16839524C211yesmaximal, characteristic, complemented
8C2×C61×#340C211yesmaximal, characteristic, complemented
9C23×C4×D61—21no—
10C23×C4×D61C2211yescharacteristic
11C22×#11758189—24no—
12C22×#11758189—24no—
13C22×#11758189C418yescomplemented
14C22×#11758189C2214yes—
15C23×#92418C2211yescharacteristic
16C2×#14519735—22no—
17C2×#14519735—24no—
18C2×#14519735C418yescomplemented
19C2×#14519735C2214yes—
20C22×C4⋊Dic61C2211yescharacteristic
21C22×C4⋊Dic61C2211yescharacteristic
22C22×#11758196—21no—
23C2×C4⋊C4×D61—24no—
24C2×C4⋊C4×D61—22no—
25C2×C4⋊C4×D61C418yescomplemented
26C2×C4⋊C4×D61C2214yes—
27C22×#11758198—21no—
28C22×C4×Dic61—21no—
29#16839525C2214yescomplemented
30#16839524C2214yescomplemented
31#16839524C2214yescomplemented
32C23×C8×C61C2211yescharacteristic
33C22×C4⋊C4×C61C2211yescharacteristic
34C22×C4⋊C4×C61C2211yescharacteristic
35C61×#340C2214yescomplemented
36C24×D61D411yescharacteristic
37C23×Dic61—21no—
38C23×Dic61—21no—
39C23×Dic61D411yescharacteristic
40C22×C4×D61—28no—
41C22×C4×D61—24no—
42C22×C4×D61—44no—
43C22×C4×D61—44no—
44C22×C4×D61C2×C414yes—
45C22×C4×D61C2×C414yes—
46C22×C4×D61C2×C414yes—
47C22×C4×D61D412yes—
48C22×C4×D61D414yes—
49C22×C4×D61D414yes—
50C22×C4×D61Q814yes—
51C22×C4×D61C2312yes—
52C2×#11758189—232no—
53C2×#11758189—28no—
54C2×#11758189—28no—
55C2×#11758189C2×C4116yescomplemented
56C22×#92418—22no—
57C22×#92418—22no—
58C22×#92418C2×C414yescomplemented
59C22×#92418C2312yes—
60#14519735—216no—
61#14519735—28no—
62#14519735C2×C4116yescomplemented
63C2×C4⋊Dic61—21no—
64C2×C4⋊Dic61—22no—
65C2×C4⋊Dic61—21no—
66C2×C4⋊Dic61—22no—
67C2×C4⋊Dic61C2×C414yes—
68C2×C4⋊Dic61C2×C414yescomplemented
69C2×C4⋊Dic61C2312yes—
70C2×C4⋊Dic61C2312yes—
71C2×#11758196—28no—
72C2×#11758196—24no—
73C4⋊C4×D61—216no—
74C4⋊C4×D61—28no—
75C4⋊C4×D61C2×C4116yescomplemented
76C2×#11758198—28no—
77C2×#11758198—24no—
78C2×C4×Dic61—28no—
79C2×C4×Dic61—24no—
80C23×C4×C61—21no—
81C23×C4×C61—21no—
82C23×C4×C61C2311yescharacteristic
83C22×C8×C61—22no—
84C22×C8×C61—22no—
85C22×C8×C61C2×C414yescomplemented
86C22×C8×C61C2312yes—
87C2×C4⋊C4×C61—21no—
88C2×C4⋊C4×C61—22no—
89C2×C4⋊C4×C61—21no—
90C2×C4⋊C4×C61—22no—
91C2×C4⋊C4×C61C2×C414yes—
92C2×C4⋊C4×C61C2×C414yescomplemented
93C2×C4⋊C4×C61C2312yes—
94C2×C4⋊C4×C61C2312yes—
95C24×C61C2×D411yescharacteristic
96C23×D61—22no—
97C23×D61—22no—
98C23×D61—22no—
99C23×D61—22no—
100C23×D61C22⋊C414yes—
101C23×D61C22⋊C414yes—
102C23×D61C4⋊C414yes—
103C23×D61C2×D412yes—
104C22×C4×C61—24no—
105C22×C4×C61—24no—
106C22×C4×C61—22no—
107C22×C4×C61—22no—
108C22×C4×C61—42no—
109C22×C4×C61—42no—
110C22×C4×C61—42no—
111C22×C4×C61—42no—
112C22×C4×C61C22×C412yes—
113C22×C4×C61C22×C412yes—
114C22×C4×C61C22×C412yes—
115C22×C4×C61C2×D411yescharacteristic
116C22×C4×C61C2×D412yes—
117C22×C4×C61C2×D412yes—
118C22×C4×C61C2×Q812yes—
119C22×C4×C61C2411yescharacteristic
120C22×Dic61—24no—
121C22×Dic61—24no—
122C22×Dic61—22no—
123C22×Dic61—22no—
124C22×Dic61—42no—
125C22×Dic61—42no—
126C22×Dic61—42no—
127C22×Dic61—42no—
128C22×Dic61C22⋊C414yes—
129C22×Dic61C22⋊C414yes—
130C22×Dic61C4⋊C414yes—
131C22×Dic61C2×D412yes—
132C2×C4×D61—216no—
133C2×C4×D61—48no—
134C2×C4×D61—48no—
135C2×C4×D61—432no—
136C2×C4×D61C42116yes—
137C2×C4×D61C22⋊C418yes—
138C2×C4×D61C22⋊C418yes—
139C2×C4×D61C22⋊C4116yes—
140C2×C4×D61C4⋊C418yes—
141C2×C4×D61C4⋊C4116yes—
142C2×C4×D61C4⋊C4116yes—
143C2×C4×D61C22×C414yes—
144C2×C4×D61C22×C414yes—
145C2×C4×D61C22×C414yes—
146C2×C4×D61C2×D414yes—
147C2×C4×D61C2×D414yes—
148C2×C4×D61C2×Q814yes—
149C2×C8×C61—28no—
150C2×C8×C61—22no—
151C2×C8×C61—22no—
152C2×C8×C61C22×C414yescomplemented
153C4⋊C4×C61—24no—
154C4⋊C4×C61—24no—
155C4⋊C4×C61—22no—
156C4⋊C4×C61—22no—
157C4⋊C4×C61C22×C414yes—
158C4⋊C4×C61C22×C414yescomplemented
159#11758198—216no—
160C4⋊Dic61—24no—
161C4⋊Dic61—24no—
162C4⋊Dic61—22no—
163C4⋊Dic61—22no—
164C4⋊Dic61C22×C414yes—
165C4⋊Dic61C22×C414yescomplemented
166#11758196—216no—
167C4×Dic61—216no—
168C2×#92418—28no—
169C2×#92418—22no—
170C2×#92418—22no—
171C2×#92418C22×C414yescomplemented
172#11758189—232no—
173C23×C61C2×C22⋊C412yes—
174C23×C61C2×C22⋊C412yes—
175C23×C61C2×C4⋊C412yes—
176C23×C61AGL(1,ℤ/8)12yes—
177C23×C61AGL(1,ℤ/8)12yes—
178C23×C61#13712yes—
179C23×C61#13712yes—
180C23×C61C22×D411yescharacteristic
181C22×D61—22no—
182C22×D61—22no—
183C22×D61—22no—
184C22×D61—22no—
185C22×D61—28no—
186C22×D61—28no—
187C22×D61—28no—
188C22×D61—28no—
189C22×D61—28no—
190C22×D61—28no—
191C22×D61#95116yes—
192C22×D61C2×C22⋊C414yes—
193C22×D61C2×C22⋊C414yes—
194C22×D61C2×C4⋊C414yes—
195C2×C4×C61—24no—
196C2×C4×C61—24no—
197C2×C4×C61—42no—
198C2×C4×C61—42no—
199C2×C4×C61—42no—
200C2×C4×C61—42no—
201C2×C4×C61—48no—
202C2×C4×C61—48no—
203C2×C4×C61C2×C4214yes—
204C2×C4×C61C2×C22⋊C414yes—
205C2×C4×C61C2×C22⋊C412yes—
206C2×C4×C61C2×C22⋊C412yes—
207C2×C4×C61C2×C4⋊C414yes—
208C2×C4×C61C2×C4⋊C414yes—
209C2×C4×C61C2×C4⋊C412yes—
210C2×C4×C61C23×C411yescharacteristic
211C2×C4×C61C23×C411yescharacteristic
212C2×C4×C61C23×C411yescharacteristic
213C2×C4×C61C22×D411yescharacteristic
214C2×C4×C61C22×D411yescharacteristic
215C2×C4×C61C22×Q811yescharacteristic
216C2×Dic61—24no—
217C2×Dic61—24no—
218C2×Dic61—42no—
219C2×Dic61—42no—
220C2×Dic61—42no—
221C2×Dic61—42no—
222C2×Dic61—48no—
223C2×Dic61—48no—
224C2×Dic61#95116yes—
225C2×Dic61C2×C22⋊C414yes—
226C2×Dic61C2×C22⋊C414yes—
227C2×Dic61C2×C4⋊C414yes—
228C4×D61—432no—
229C4×D61#95132yes—
230C4×D61C2×C4218yes—
231C4×D61C2×C22⋊C418yes—
232C4×D61C2×C4⋊C418yes—
233C4×D61C2×C4⋊C418yes—
234C8×C61—24no—
235#92418—24no—
236C2×#1736—611nomaximal, Sylow
237C22×C61C2×#9514yes—
238C22×C61#41714yes—
239C22×C61#41714yes—
240C22×C61#41814yes—
241C22×C61#41914yes—
242C22×C61#42814yes—
243C22×C61#42814yes—
244C22×C61C22×C22⋊C411yescharacteristic
245C22×C61C22×C22⋊C411yescharacteristic
246C22×C61C22×C4⋊C411yescharacteristic
247C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
248C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
249C22×C61C2×#13711yescharacteristic
250C22×C61C2×#13711yescharacteristic
251C2×D61—24no—
252C2×D61—24no—
253C2×D61—24no—
254C2×D61—24no—
255C2×D61—24no—
256C2×D61—24no—
257C2×D61—232no—
258C2×D61C2×#9518yes—
259C4×C61—44no—
260C4×C61—44no—
261C4×C61C2×#9514yes—
262C4×C61C22×C4211yescharacteristic
263C4×C61C22×C22⋊C411yescharacteristic
264C4×C61C22×C4⋊C411yescharacteristic
265C4×C61C22×C4⋊C411yescharacteristic
266Dic61—44no—
267Dic61—44no—
268Dic61C2×#9518yes—
269C23×M16—611no—
270C22×#117—611no—
271C23×C4⋊C4—611no—
272#1736—618no—
273C2×#340—611no—
274C2×#340—611no—
275C2×#340—611no—
276C2×#340D6111yescharacteristic, complemented
277C2×C61#173618yescomplemented
278C2×C61C22×#9511yescharacteristic
279C2×C61C2×#41811yescharacteristic
280C2×C61C2×#41911yescharacteristic
281C2×C61C2×#41711yescharacteristic
282C2×C61C2×#41711yescharacteristic
283C2×C61C2×#42811yescharacteristic
284C2×C61C2×#42811yescharacteristic
285D61—28no—
286C24×C4—611no—
287C24×C4—1221no—
288C22×M16—618no—
289C22×M16—614no—
290C22×M16—1224no—
291C22×M16—1224no—
292C23×C8—611no—
293C23×C8C2×D6111yescharacteristic
294C2×#117—618no—
295C2×#117—614no—
296C2×#117—1222no—
297C2×#117—1224no—
298C22×C4⋊C4—611no—
299C22×C4⋊C4—611no—
300C22×C4⋊C4—618no—
301C22×C4⋊C4—614no—
302C22×C4⋊C4—1222no—
303C22×C4⋊C4—1224no—
304C22×C4⋊C4—1221no—
305C22×C4⋊C4C2×D6111yescharacteristic
306C22×C4⋊C4C2×D6111yescharacteristic
307C22×C22⋊C4—1221no—
308C22×C42—1221no—
309#340—614no—
310#340—614no—
311#340—614no—
312#340C2×D6114yescomplemented
313C61C2×#173611yescharacteristic, complemented, Sylow
314C25—611no—
315C23×C4—21no—
316C23×C4—21no—
317C23×C4—611no—
318C23×C4—614no—
319C23×C4—614no—
320C23×C4—614no—
321C23×C4—612no—
322C23×C4—614no—
323C23×C4—614no—
324C23×C4—614no—
325C23×C4—612no—
326C23×C4—1224no—
327C23×C4—1228no—
328C23×C4—1221no—
329C23×C4—1221no—
330C23×C4—2444no—
331C23×C4—2444no—
332C23×C4C22×D6111yescharacteristic
333C2×M16—6116no—
334C2×M16—1228no—
335C2×M16—1228no—
336C2×M16—12232no—
337C22×C8—22no—
338C22×C8—22no—
339C22×C8—614no—
340C22×C8—612no—
341C22×C8—1222no—
342C22×C8—1222no—
343C22×C8C4×D6114yescomplemented
344C22×C8C22×D6112yes—
345#117—6116no—
346#117—1228no—
347#117—12216no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—614no—
353C2×C4⋊C4—614no—
354C2×C4⋊C4—612no—
355C2×C4⋊C4—612no—
356C2×C4⋊C4—6116no—
357C2×C4⋊C4—1228no—
358C2×C4⋊C4—12216no—
359C2×C4⋊C4—1224no—
360C2×C4⋊C4—1228no—
361C2×C4⋊C4—1222no—
362C2×C4⋊C4—1221no—
363C2×C4⋊C4—1222no—
364C2×C4⋊C4—1221no—
365C2×C4⋊C4C4×D6114yes—
366C2×C4⋊C4C4×D6114yescomplemented
367C2×C4⋊C4C22×D6112yes—
368C2×C4⋊C4C22×D6112yes—
369C2×C22⋊C4—1224no—
370C2×C22⋊C4—1228no—
371C2×C42—1224no—
372C2×C42—1228no—
373C24—612no—
374C24—614no—
375C24—614no—
376C24—614no—
377C24—1222no—
378C24—1222no—
379C24—1222no—
380C24—1222no—
381C24D4×D6111yescharacteristic
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—24no—
385C22×C4—24no—
386C22×C4—42no—
387C22×C4—42no—
388C22×C4—42no—
389C22×C4—42no—
390C22×C4—612no—
391C22×C4—614no—
392C22×C4—614no—
393C22×C4—614no—
394C22×C4—614no—
395C22×C4—614no—
396C22×C4—614no—
397C22×C4—614no—
398C22×C4—614no—
399C22×C4—614no—
400C22×C4—6116no—
401C22×C4—618no—
402C22×C4—618no—
403C22×C4—6116no—
404C22×C4—618no—
405C22×C4—6116no—
406C22×C4—6116no—
407C22×C4—12216no—
408C22×C4—1222no—
409C22×C4—1222no—
410C22×C4—1224no—
411C22×C4—1224no—
412C22×C4—24432no—
413C22×C4—2448no—
414C22×C4—2448no—
415C22×C4—2442no—
416C22×C4—2442no—
417C22×C4—2442no—
418C22×C4—2442no—
419C22×C4C2×C4×D6112yes—
420C22×C4C2×C4×D6112yes—
421C22×C4C2×C4×D6112yes—
422C22×C4D4×D6112yes—
423C22×C4D4×D6112yes—
424C22×C4D4×D6111yescharacteristic
425C22×C4Q8×D6112yes—
426C22×C4C23×D6111yescharacteristic
427M16—12232no—
428C2×C8—22no—
429C2×C8—22no—
430C2×C8—28no—
431C2×C8—614no—
432C2×C8—1222no—
433C2×C8—1222no—
434C2×C8—1228no—
435C2×C8C2×C4×D6114yescomplemented
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—24no—
439C4⋊C4—24no—
440C4⋊C4—614no—
441C4⋊C4—614no—
442C4⋊C4—12216no—
443C4⋊C4—1222no—
444C4⋊C4—1222no—
445C4⋊C4—1224no—
446C4⋊C4—1224no—
447C4⋊C4C2×C4×D6114yes—
448C4⋊C4C2×C4×D6114yescomplemented
449C22⋊C4—12216no—
450C42—12216no—
451C23—614no—
452C23—614no—
453C23—614no—
454C23—6116no—
455C23—1228no—
456C23—1228no—
457C23—1228no—
458C23—1228no—
459C23—1222no—
460C23—1222no—
461C23—1222no—
462C23—1222no—
463C23—1228no—
464C23—1228no—
465C23C22⋊C4×D6112yes—
466C23C22⋊C4×D6112yes—
467C23C4⋊C4×D6112yes—
468C23#1451980112yes—
469C23#1451980412yes—
470C23#1451980612yes—
471C23#1451980912yes—
472C23C2×D4×D6111yescharacteristic
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—48no—
476C2×C4—48no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—614no—
482C2×C4—614no—
483C2×C4—614no—
484C2×C4—6116no—
485C2×C4—618no—
486C2×C4—618no—
487C2×C4—618no—
488C2×C4—618no—
489C2×C4—6132no—
490C2×C4—1224no—
491C2×C4—1224no—
492C2×C4—24432no—
493C2×C4—2448no—
494C2×C4—2448no—
495C2×C4—2442no—
496C2×C4—2442no—
497C2×C4—2442no—
498C2×C4—2442no—
499C2×C4C42×D6114yes—
500C2×C4C22⋊C4×D6114yes—
501C2×C4C22⋊C4×D6112yes—
502C2×C4C22⋊C4×D6112yes—
503C2×C4C4⋊C4×D6114yes—
504C2×C4C4⋊C4×D6114yes—
505C2×C4C4⋊C4×D6112yes—
506C2×C4C22×C4×D6111yescharacteristic
507C2×C4C22×C4×D6111yescharacteristic
508C2×C4C22×C4×D6111yescharacteristic
509C2×C4C2×D4×D6111yescharacteristic
510C2×C4C2×D4×D6111yescharacteristic
511C2×C4C2×Q8×D6111yescharacteristic
512C8—24no—
513C8—1224no—
514C22—618no—
515C22—1224no—
516C22—1224no—
517C22—12232no—
518C22—1224no—
519C22—1224no—
520C22—1224no—
521C22—1224no—
522C22#95×D6114yes—
523C22#1683976014yes—
524C22#1683976214yes—
525C22#1683976514yes—
526C22#1683976914yes—
527C22#1683980114yes—
528C22#1683980314yes—
529C22C2×C22⋊C4×D6111yescharacteristic
530C22C2×C22⋊C4×D6111yescharacteristic
531C22C2×C4⋊C4×D6111yescharacteristic
532C22C2×#1451980111yescharacteristic
533C22C2×#1451980411yescharacteristic
534C22C2×#1451980611yescharacteristic
535C22C2×#1451980911yescharacteristic
536C4—44no—
537C4—44no—
538C4—618no—
539C4—2444no—
540C4—2444no—
541C4#95×D6114yes—
542C4C2×C42×D6111yescharacteristic
543C4C2×C22⋊C4×D6111yescharacteristic
544C4C2×C4⋊C4×D6111yescharacteristic
545C4C2×C4⋊C4×D6111yescharacteristic
546C2—1228no—
547C2#2144553718yesdirect product factor
548C2C2×#95×D6111yescharacteristic
549C2C2×#1683976511yescharacteristic
550C2C2×#1683976911yescharacteristic
551C2C2×#1683976011yescharacteristic
552C2C2×#1683976211yescharacteristic
553C2C2×#1683980111yescharacteristic
554C2C2×#1683980311yescharacteristic
subgroupG/H
centerC24D4×D61
commutatorC4×C61C22×C42
FrattiniC22×C4C23×D61
FittingC2×C61×#340C2
socleC24×C61C2×D4
prime radicalC24×D61D4
cosocleC22×C4×C61C24
hypercenterC2×#340D61
hypocenterC61C2×#1736
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
4. #21445537C2direct (N × H)
5. C2×#16839525C2semidirect
6. C2×#16839524C2semidirect
7. C2×#16839524C2semidirect
8. C2×C61×#340C2semidirect
13. C22×#11758189C4semidirect
18. C2×#14519735C4semidirect
25. C2×C4⋊C4×D61C4semidirect
29. #16839525C22semidirect
30. #16839524C22semidirect
31. #16839524C22semidirect
35. C61×#340C22semidirect
55. C2×#11758189C2×C4semidirect
58. C22×#92418C2×C4semidirect
62. #14519735C2×C4semidirect
68. C2×C4⋊Dic61C2×C4semidirect
75. C4⋊C4×D61C2×C4semidirect
85. C22×C8×C61C2×C4semidirect
92. C2×C4⋊C4×C61C2×C4semidirect
152. C2×C8×C61C22×C4semidirect
158. C4⋊C4×C61C22×C4semidirect
165. C4⋊Dic61C22×C4semidirect
171. C2×#92418C22×C4semidirect
276. C2×#340D61semidirect
277. C2×C61#1736semidirect
312. #340C2×D61semidirect
313. C61C2×#1736semidirect
343. C22×C8C4×D61semidirect
366. C2×C4⋊C4C4×D61semidirect
435. C2×C8C2×C4×D61semidirect
448. C4⋊C4C2×C4×D61semidirect
547. C2#21445537direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#117581892
C22×#145197352
C22×C4⋊C4×D612
#214455372
C2×#168395252
C2×#168395242
C2×C61×#3402
C2×#173661