Finite Group Databasebeta

← C2×#21445877 #29679686

Subgroups — C2×#21445877 #29679686

Order 15616.

1374 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519785C211yesmaximal, characteristic
2C22×#14519712C211yesmaximal, characteristic, complemented
3C22×#14519708C211yesmaximal, characteristic, complemented
4C2×#16839764C211yesmaximal, characteristic
5C2×#16839761C211yesmaximal, characteristic
6#21445877C218yesmaximal, direct product factor
7C2×#16839530C211yesmaximal, characteristic, complemented
8C2×C61×#343C211yesmaximal, characteristic, complemented
9C22×#11758222C2211yescharacteristic
10C2×#14519785—24no—
11C2×#14519785—22no—
12C2×#14519785C418yescomplemented
13C2×#14519785C2214yes—
14C22×#11758194C2211yescharacteristic
15C22×#11758189—21no—
16C23×#92418C2211yescharacteristic
17C22×C8×D61—21no—
18C22×C4⋊Dic61C2211yescharacteristic
19C2×#14519712—24no—
20C2×#14519712C2214yescomplemented
21C2×#14519708—21no—
22C2×#14519708—21no—
23C2×#14519708—22no—
24C2×#14519708C2214yescomplemented
25#16839764—22no—
26#16839764C2214yes—
27#16839761—22no—
28#16839761C2214yes—
29C2×#14519702—21no—
30C2×#14519700—21no—
31C2×#14519699—21no—
32C2×#14519697—21no—
33#16839530C2214yescomplemented
34C22×M16×C61C2211yescharacteristic
35C22×M16×C61C2211yescharacteristic
36C22×C4⋊C4×C61C2211yescharacteristic
37C61×#343C2214yescomplemented
38C2×#11758222—22no—
39C2×#11758222—21no—
40C2×#11758222—21no—
41C2×#11758222—22no—
42C2×#11758222C2×C414yes—
43C2×#11758222D412yes—
44C2×#11758222Q814yes—
45C2×#11758222C2312yes—
46C22×Dic122D411yescharacteristic
47C22×D244D411yescharacteristic
48C22×C22⋊D61—21no—
49C23×Dic61—21no—
50C22×C4×D61—21no—
51#14519785—216no—
52#14519785—28no—
53#14519785C2×C4116yescomplemented
54C2×#11758194—21no—
55C2×#11758194—22no—
56C2×#11758194—22no—
57C2×#11758194C2312yes—
58C2×#11758189—28no—
59C2×#11758189—24no—
60C22×#92418—21no—
61C22×#92418C2×C414yes—
62C22×#92418D411yescharacteristic
63C22×#92418D411yescharacteristic
64C22×#92418D412yes—
65C22×#92418D414yes—
66C22×#92418C2312yes—
67C2×C8×D61—28no—
68C2×C8×D61—24no—
69C2×C4⋊Dic61—21no—
70C2×C4⋊Dic61—21no—
71C2×C4⋊Dic61—21no—
72C2×C4⋊Dic61—21no—
73C2×C4⋊Dic61—21no—
74C2×C4⋊Dic61C2312yes—
75#14519712—28no—
76#14519708—24no—
77#14519708—24no—
78#14519702—24no—
79#14519700—24no—
80#14519699—24no—
81#14519697—24no—
82C23×C4×C61—21no—
83C23×C4×C61C2311yescharacteristic
84C2×M16×C61—22no—
85C2×M16×C61—21no—
86C2×M16×C61—21no—
87C2×M16×C61—22no—
88C2×M16×C61—22no—
89C2×M16×C61C2×C414yes—
90C2×M16×C61C2312yes—
91C2×M16×C61C2312yes—
92C22×C8×C61—21no—
93C22×C8×C61—21no—
94C2×C4⋊C4×C61—21no—
95C2×C4⋊C4×C61—21no—
96C2×C4⋊C4×C61—21no—
97C2×C4⋊C4×C61—21no—
98C2×C4⋊C4×C61—21no—
99C2×C4⋊C4×C61C2312yes—
100C24×C61#4111yescharacteristic
101C23×D61—21no—
102C22×C4×C61—22no—
103C22×C4×C61—41no—
104C22×C4×C61—41no—
105C22×C4×C61—82no—
106C22×C4×C61C22×C412yes—
107C22×C4×C61C2×D412yes—
108C22×C4×C61C2×D411yescharacteristic
109C22×C4×C61C2×D411yescharacteristic
110C22×C4×C61C2×D411yescharacteristic
111C22×C4×C61C2×D411yescharacteristic
112C22×C4×C61C2×Q812yes—
113C22×C4×C61#4111yescharacteristic
114C22×C4×C61#4112yes—
115C22×C4×C61C2411yescharacteristic
116C2×C22⋊D61—24no—
117C2×C22⋊D61—22no—
118C2×C22⋊D61—24no—
119C2×C22⋊D61—22no—
120C22×Dic61—21no—
121C22×Dic61—22no—
122C22×Dic61—41no—
123C22×Dic61—41no—
124C22×Dic61—82no—
125#11758222—24no—
126#11758222—24no—
127#11758222—24no—
128#11758222—24no—
129#11758222—24no—
130#11758222—22no—
131#11758222—22no—
132#11758222C4⋊C418yes—
133#11758222C22×C414yes—
134#11758222C2×Q814yes—
135C2×D244—22no—
136C2×D244—21no—
137C2×D244C4⋊C414yes—
138C2×D244C2×D412yes—
139C2×C4×D61—24no—
140C2×C4×D61—22no—
141C2×C4×D61—24no—
142C2×C4×D61—22no—
143C2×Dic122—22no—
144C2×Dic122—21no—
145C2×Dic122C4⋊C414yes—
146C2×Dic122C2×D412yes—
147M16×C61—24no—
148M16×C61—22no—
149M16×C61—22no—
150M16×C61—22no—
151M16×C61—42no—
152M16×C61C22×C414yes—
153C2×C8×C61—24no—
154C2×C8×C61—22no—
155C2×C8×C61—22no—
156C2×C8×C61—42no—
157C4⋊C4×C61—22no—
158C4⋊C4×C61—22no—
159C4⋊C4×C61—41no—
160C4⋊C4×C61—41no—
161C4⋊Dic61—22no—
162C4⋊Dic61—22no—
163C4⋊Dic61—41no—
164C4⋊Dic61—41no—
165#11758194—22no—
166#11758194—22no—
167#11758194—42no—
168C2×#92418—22no—
169C2×#92418—42no—
170C2×#92418C22⋊C414yes—
171C2×#92418C22⋊C414yes—
172C2×#92418C22⋊C418yes—
173C2×#92418C22×C414yes—
174C2×#92418C2×D412yes—
175C2×#92418C2×D412yes—
176C2×#92418C2×D414yes—
177#11758189—216no—
178C8×D61—216no—
179C23×C61—22no—
180C23×C61—22no—
181C23×C61#11712yes—
182C23×C61#12111yescharacteristic
183C23×C61#12111yescharacteristic
184C23×C61C22⋊Q812yes—
185C23×C61C2×#4111yescharacteristic
186C22×D61—22no—
187C22×D61—24no—
188C22×D61—42no—
189C22×D61—42no—
190C2×C4×C61—42no—
191C2×C4×C61—82no—
192C2×C4×C61—82no—
193C2×C4×C61—82no—
194C2×C4×C61C2×C22⋊C412yes—
195C2×C4×C61C2×C22⋊C412yes—
196C2×C4×C61C2×C4⋊C412yes—
197C2×C4×C61C2×C4⋊C412yes—
198C2×C4×C61#11712yes—
199C2×C4×C61#12112yes—
200C2×C4×C61#12112yes—
201C2×C4×C61#12111yescharacteristic
202C2×C4×C61#12111yescharacteristic
203C2×C4×C61C22⋊Q812yes—
204C2×C4×C61C22⋊Q812yes—
205C2×C4×C61C22⋊Q812yes—
206C2×C4×C61C23×C411yescharacteristic
207C2×C4×C61C22×D411yescharacteristic
208C2×C4×C61C22×D411yescharacteristic
209C2×C4×C61C22×D411yescharacteristic
210C2×C4×C61C22×Q811yescharacteristic
211C2×C4×C61C2×#4111yescharacteristic
212C22⋊D61—24no—
213C22⋊D61—24no—
214C22⋊D61—28no—
215C2×Dic61—22no—
216C2×Dic61—24no—
217C2×Dic61—42no—
218C2×Dic61—82no—
219C2×Dic61—82no—
220C2×Dic61—82no—
221D244—22no—
222D244—24no—
223D244C2×C4⋊C414yes—
224C4×D61—24no—
225C4×D61—24no—
226C4×D61—28no—
227Dic122—22no—
228Dic122—24no—
229Dic122C2×C4⋊C414yes—
230C8×C61—24no—
231C8×C61—42no—
232#92418—42no—
233#92418C2×C22⋊C414yes—
234#92418C2×C22⋊C414yes—
235C2×#1815—611nomaximal, Sylow
236C22×C61—24no—
237C22×C61—24no—
238C22×C61—21no—
239C22×C61—21no—
240C22×C61—21no—
241C22×C61—21no—
242C22×C61#38012yes—
243C22×C61#38012yes—
244C22×C61#47112yes—
245C22×C61#47112yes—
246C22×C61C2×#11711yescharacteristic
247C22×C61C2×#12111yescharacteristic
248C22×C61C2×C22⋊Q811yescharacteristic
249C2×D61—24no—
250C2×D61—48no—
251C2×D61—42no—
252C2×D61—42no—
253C4×C61—82no—
254C4×C61#38012yes—
255C4×C61#38012yes—
256C4×C61C22×C22⋊C411yescharacteristic
257C4×C61C22×C4⋊C411yescharacteristic
258C4×C61C2×#12111yescharacteristic
259C4×C61C2×C22⋊Q811yescharacteristic
260Dic61—24no—
261Dic61—82no—
262C22×#131—611no—
263C22×#108—611no—
264C22×#106—611no—
265C2×#417—611no—
266C2×#417—611no—
267#1815—618no—
268C2×#343—611no—
269C2×#343D6111yescharacteristic, complemented
270C2×C61—21no—
271C2×C61—21no—
272C2×C61—22no—
273C2×C61#181514yescomplemented
274C2×C61C2×#38011yescharacteristic
275C2×C61C2×#47111yescharacteristic
276C2×C61C2×#47111yescharacteristic
277D61—44no—
278C22×#41—611no—
279C2×#131—618no—
280C2×#131—614no—
281C2×#131—1222no—
282C2×#131—1224no—
283C22×M16—611no—
284C22×M16—1221no—
285C22×M16C2×D6111yescharacteristic
286C22×M16C2×D6111yescharacteristic
287C23×C8—611no—
288C23×C8—1221no—
289C22×C4⋊C4—611no—
290C22×C4⋊C4C2×D6111yescharacteristic
291C2×#108—614no—
292C2×#108—1224no—
293C2×#106—614no—
294C2×#106—1221no—
295C2×#106—1221no—
296C2×#106—1222no—
297#417—614no—
298#417—614no—
299#417—1222no—
300#417—1222no—
301C2×#103—1221no—
302C2×#103—1221no—
303C2×#102—1221no—
304C2×#102—1221no—
305#343—614no—
306#343C2×D6114yescomplemented
307C61C2×#181511yescharacteristic, complemented, Sylow
308C2×#41—614no—
309C2×#41—612no—
310C2×#41—614no—
311C2×#41—612no—
312C2×#41—1221no—
313C2×#41—1222no—
314C2×#41—1221no—
315C2×#41—1222no—
316C22×Q8—611no—
317C22×D4—611no—
318C22×D4—1221no—
319C23×C4—21no—
320C23×C4—1221no—
321C23×C4—1221no—
322C23×C4C22×D6111yescharacteristic
323#131—6116no—
324#131—1228no—
325#131—12216no—
326C2×M16—21no—
327C2×M16—22no—
328C2×M16—21no—
329C2×M16—22no—
330C2×M16—22no—
331C2×M16—612no—
332C2×M16—1224no—
333C2×M16—1228no—
334C2×M16—1221no—
335C2×M16—1222no—
336C2×M16—1222no—
337C2×M16C4×D6114yes—
338C2×M16C22×D6112yes—
339C2×M16C22×D6112yes—
340C22×C8—21no—
341C22×C8—21no—
342C22×C8—614no—
343C22×C8—611no—
344C22×C8—611no—
345C22×C8—612no—
346C22×C8—614no—
347C22×C8—612no—
348C22×C8—1224no—
349C22×C8—1228no—
350C22×C8—1221no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—612no—
357C2×C4⋊C4—1221no—
358C2×C4⋊C4—1221no—
359C2×C4⋊C4—1221no—
360C2×C4⋊C4—1221no—
361C2×C4⋊C4—1221no—
362C2×C4⋊C4C22×D6112yes—
363#108—1228no—
364#106—1224no—
365#106—1224no—
366#103—1224no—
367#103—1224no—
368#102—1224no—
369#102—1224no—
370C24—1221no—
371C24#1175822211yescharacteristic
372#41—614no—
373#41—614no—
374#41—618no—
375#41—1222no—
376#41—1222no—
377#41—1224no—
378#41—1224no—
379#41—1224no—
380#41—1224no—
381#41—1224no—
382C2×Q8—612no—
383C2×Q8—614no—
384C2×Q8—1221no—
385C2×Q8—1222no—
386C2×D4—612no—
387C2×D4—614no—
388C2×D4—1222no—
389C2×D4—1224no—
390C2×D4—1222no—
391C2×D4—1224no—
392C2×D4—1222no—
393C2×D4—1221no—
394C22×C4—22no—
395C22×C4—41no—
396C22×C4—41no—
397C22×C4—82no—
398C22×C4—1221no—
399C22×C4—1222no—
400C22×C4—1224no—
401C22×C4—1222no—
402C22×C4—1224no—
403C22×C4—1222no—
404C22×C4—4882no—
405C22×C4—2441no—
406C22×C4—2441no—
407C22×C4C2×C4×D6112yes—
408C22×C4#1175822212yes—
409C22×C4#1175822211yescharacteristic
410C22×C4D4×D6112yes—
411C22×C4D4×D6111yescharacteristic
412C22×C4D4×D6111yescharacteristic
413C22×C4D4×D6111yescharacteristic
414C22×C4D4×D6111yescharacteristic
415C22×C4Q8×D6112yes—
416C22×C4C23×D6111yescharacteristic
417M16—22no—
418M16—24no—
419M16—22no—
420M16—22no—
421M16—42no—
422M16—12216no—
423M16—1222no—
424M16—1222no—
425M16—2442no—
426M16C2×C4×D6114yes—
427C2×C8—22no—
428C2×C8—24no—
429C2×C8—22no—
430C2×C8—42no—
431C2×C8—614no—
432C2×C8—612no—
433C2×C8—612no—
434C2×C8—614no—
435C2×C8—614no—
436C2×C8—614no—
437C2×C8—618no—
438C2×C8—12216no—
439C2×C8—1222no—
440C2×C8—2442no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—41no—
444C4⋊C4—41no—
445C4⋊C4—1222no—
446C4⋊C4—1222no—
447C4⋊C4—2441no—
448C4⋊C4—2441no—
449C23—22no—
450C23—22no—
451C23—1222no—
452C23—1224no—
453C23—2442no—
454C23—2442no—
455C23#1451973412yes—
456C23#1451975011yescharacteristic
457C23#1451975011yescharacteristic
458C23#1451975512yes—
459C23C2×#1175822211yescharacteristic
460Q8—614no—
461Q8—1222no—
462Q8—1224no—
463D4—614no—
464D4—1224no—
465D4—1224no—
466D4—1228no—
467D4—1222no—
468D4—1224no—
469C2×C4—42no—
470C2×C4—82no—
471C2×C4—82no—
472C2×C4—82no—
473C2×C4—1222no—
474C2×C4—1224no—
475C2×C4—1224no—
476C2×C4—1224no—
477C2×C4—1228no—
478C2×C4—4882no—
479C2×C4—4882no—
480C2×C4—4882no—
481C2×C4—2442no—
482C2×C4C22⋊C4×D6112yes—
483C2×C4C22⋊C4×D6112yes—
484C2×C4C4⋊C4×D6112yes—
485C2×C4C4⋊C4×D6112yes—
486C2×C4#1451973412yes—
487C2×C4#1451975012yes—
488C2×C4#1451975012yes—
489C2×C4#1451975011yescharacteristic
490C2×C4#1451975011yescharacteristic
491C2×C4#1451975512yes—
492C2×C4#1451975512yes—
493C2×C4#1451975512yes—
494C2×C4C22×C4×D6111yescharacteristic
495C2×C4C2×D4×D6111yescharacteristic
496C2×C4C2×D4×D6111yescharacteristic
497C2×C4C2×D4×D6111yescharacteristic
498C2×C4C2×Q8×D6111yescharacteristic
499C2×C4C2×#1175822211yescharacteristic
500C8—24no—
501C8—42no—
502C8—614no—
503C8—614no—
504C8—2442no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—24no—
510C22—24no—
511C22—1224no—
512C22—2442no—
513C22—2442no—
514C22—2448no—
515C22#1683962112yes—
516C22#1683962112yes—
517C22#1684002412yes—
518C22#1684002812yes—
519C22C2×#1451973411yescharacteristic
520C22C2×#1451975011yescharacteristic
521C22C2×#1451975511yescharacteristic
522C4—82no—
523C4—1224no—
524C4—4882no—
525C4#1683962112yes—
526C4#1683962112yes—
527C4C2×C22⋊C4×D6111yescharacteristic
528C4C2×C4⋊C4×D6111yescharacteristic
529C4C2×#1451975011yescharacteristic
530C4C2×#1451975511yescharacteristic
531C2—21no—
532C2—21no—
533C2—22no—
534C2—2444no—
535C2#2144587714yesdirect product factor
536C2C2×#1683962111yescharacteristic
537C2C2×#1684002411yescharacteristic
538C2C2×#1684002811yescharacteristic
subgroupG/H
centerC23#14519750
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#343C2
socleC23×C61#121
prime radicalC22×#11758222C22
cosocleC22×C4×C61C24
hypercenterC2×#343D61
hypocenterC61C2×#1815
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#343

Complements

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

NH ≅ G/Ntype
2. C22×#14519712C2semidirect
3. C22×#14519708C2semidirect
6. #21445877C2direct (N × H)
7. C2×#16839530C2semidirect
8. C2×C61×#343C2semidirect
12. C2×#14519785C4semidirect
20. C2×#14519712C22semidirect
24. C2×#14519708C22semidirect
33. #16839530C22semidirect
37. C61×#343C22semidirect
53. #14519785C2×C4semidirect
269. C2×#343D61semidirect
273. C2×C61#1815semidirect
306. #343C2×D61semidirect
307. C61C2×#1815semidirect
535. C2#21445877direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197852
C22×#145197122
C22×#145197082
C2×#168397642
C2×#168397612
#214458772
C2×#168395302
C2×C61×#3432
C2×#181561