Finite Group Databasebeta

← C2×#21444376 #29647348

Subgroups — C2×#21444376 #29647348

Order 15616.

1498 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840273C211yesmaximal, characteristic
2C2×#16839625C211yesmaximal, characteristic, complemented
3#21444376C218yesmaximal, direct product factor
4C2×#16839500C212yesmaximal, complemented
5C2×#16839497C212yesmaximal, complemented
6C22×C22⋊C8×C61C211yesmaximal, characteristic, complemented
7C22×#11758222C411yescharacteristic, complemented
8#16840273—22no—
9#16840273—22no—
10#16840273C414yescomplemented
11#16840273C2214yes—
12C2×#14519760—21no—
13C2×#14519756C411yescharacteristic, complemented
14C2×#14519756C2211yescharacteristic
15C2×#14519751C411yescharacteristic, complemented
16C2×#14519751C2211yescharacteristic
17C2×#14519746—21no—
18C2×C4×C22⋊D61—21no—
19C2×C4×C22⋊D61—21no—
20C2×#14519736C411yescharacteristic, complemented
21C22×C22⋊Dic61—21no—
22#16839625—22no—
23#16839625C2214yescomplemented
24C2×#14519684—21no—
25C2×#14519684C2212yes—
26#16839500C2218yescomplemented
27#16839497C2218yescomplemented
28C24×C4×C61C2211yescharacteristic
29C23×C8×C61—21no—
30C2×C22⋊C8×C61—22no—
31C2×C22⋊C8×C61—21no—
32C2×C22⋊C8×C61C2212yes—
33C2×C22⋊C8×C61C2214yescomplemented
34C2×#11758222—22no—
35C2×#11758222—44no—
36C2×#11758222C2×C414yescomplemented
37C22×Dic122C2×C411yescharacteristic
38C22×D244C2×C411yescharacteristic
39C22×C22⋊D61—21no—
40C22×C22⋊D61—21no—
41C22×C22⋊D61—21no—
42C23×Dic61—22no—
43C22×C4×D61—21no—
44#14519760—24no—
45#14519760—24no—
46#14519756—22no—
47#14519756—21no—
48#14519756—21no—
49#14519756C2×C412yes—
50#14519756C2×C414yescomplemented
51#14519756C2312yes—
52#14519751—22no—
53#14519751—21no—
54#14519751—21no—
55#14519751C2×C412yes—
56#14519751C2×C414yescomplemented
57#14519751C2312yes—
58#14519746—24no—
59#14519746—24no—
60C4×C22⋊D61—24no—
61C4×C22⋊D61—24no—
62C4×C22⋊D61—24no—
63C4×C22⋊D61—24no—
64#14519736—22no—
65#14519736C2×C414yescomplemented
66C2×C4⋊Dic61C2×C411yescharacteristic
67C2×C4⋊Dic61C2×C411yescharacteristic
68C2×#11758196—21no—
69C2×#11758196—21no—
70C2×C22⋊Dic61—21no—
71C2×C22⋊Dic61—21no—
72C2×C22⋊Dic61—21no—
73C2×C22⋊Dic61—24no—
74C2×C22⋊Dic61—44no—
75C2×#11758198—21no—
76C2×#11758198—21no—
77C2×C4×Dic61—21no—
78#14519684—24no—
79#14519684—22no—
80#14519684C2314yes—
81C25×C61D411yescharacteristic
82C23×C4×C61—44no—
83C23×C4×C61C2×C411yescharacteristic
84C23×C4×C61C2×C411yescharacteristic
85C23×C4×C61C2×C412yes—
86C23×C4×C61D411yescharacteristic
87C23×C4×C61D412yes—
88C23×C4×C61D411yescharacteristic
89C23×C4×C61D411yescharacteristic
90C23×C4×C61D412yes—
91C23×C4×C61C2311yescharacteristic
92C23×C4×C61C2312yes—
93C22×C8×C61—22no—
94C22×C8×C61—24no—
95C22×C8×C61—44no—
96C22⋊C8×C61—22no—
97C22⋊C8×C61—24no—
98C22⋊C8×C61C2314yes—
99C24×C61—24no—
100C24×C61—24no—
101C24×C61—42no—
102C24×C61C22⋊C411yescharacteristic
103C24×C61C22⋊C412yes—
104C24×C61C22⋊C411yescharacteristic
105C24×C61C2×D412yes—
106C24×C61C2×D411yescharacteristic
107C23×D61—21no—
108C22×C4×C61—24no—
109C22×C4×C61—24no—
110C22×C4×C61—42no—
111C22×C4×C61—44no—
112C22×C4×C61—42no—
113C22×C4×C61—44no—
114C22×C4×C61—42no—
115C22×C4×C61—44no—
116C22×C4×C61—42no—
117C22×C4×C61—44no—
118C22×C4×C61C22⋊C411yescharacteristic
119C22×C4×C61C22⋊C412yes—
120C22×C4×C61C22⋊C411yescharacteristic
121C22×C4×C61C22⋊C412yes—
122C22×C4×C61C22⋊C412yes—
123C22×C4×C61C22⋊C412yes—
124C22×C4×C61C22⋊C412yes—
125C22×C4×C61C22×C411yescharacteristic
126C22×C4×C61C22×C412yes—
127C22×C4×C61C22×C411yescharacteristic
128C22×C4×C61C22×C412yes—
129C22×C4×C61C2×D411yescharacteristic
130C22×C4×C61C2×D412yes—
131C22×C4×C61C2×D412yes—
132C22×C4×C61C2×D411yescharacteristic
133C22×C4×C61C2×D412yes—
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2411yescharacteristic
136C2×C22⋊D61—24no—
137C2×C22⋊D61—22no—
138C2×C22⋊D61—24no—
139C2×C22⋊D61—22no—
140C2×C22⋊D61—44no—
141C2×C22⋊D61—44no—
142C2×C22⋊D61—44no—
143C22×Dic61—21no—
144C22×Dic61—21no—
145C22×Dic61—21no—
146C22×Dic61—24no—
147C22×Dic61—44no—
148C22×Dic61—44no—
149C22×Dic61—44no—
150#11758222—48no—
151#11758222—48no—
152C2×D244—21no—
153C2×D244—42no—
154C2×D244C22×C412yes—
155C2×C4×D61—24no—
156C2×C4×D61—44no—
157C2×Dic122—21no—
158C2×Dic122—42no—
159C2×Dic122C22×C412yes—
160C2×C8×C61—24no—
161C2×C8×C61—44no—
162C2×C8×C61—48no—
163C22⋊Dic61—24no—
164C22⋊Dic61—22no—
165C22⋊Dic61—24no—
166C22⋊Dic61—22no—
167C22⋊Dic61—48no—
168#11758198—22no—
169#11758198—24no—
170#11758198—22no—
171C4⋊Dic61—21no—
172C4⋊Dic61—21no—
173C4⋊Dic61C22×C412yes—
174C4⋊Dic61C22×C412yes—
175#11758196—22no—
176#11758196—24no—
177#11758196—22no—
178C4×Dic61—24no—
179C23×C61—22no—
180C23×C61—22no—
181C23×C61—22no—
182C23×C61—22no—
183C23×C61—24no—
184C23×C61—24no—
185C23×C61—24no—
186C23×C61—22no—
187C23×C61—24no—
188C23×C61—22no—
189C23×C61—22no—
190C23×C61—42no—
191C23×C61—42no—
192C23×C61—416no—
193C23×C61#9914yes—
194C23×C61C2×C22⋊C412yes—
195C23×C61C2×C22⋊C412yes—
196C23×C61C2×C22⋊C411yescharacteristic
197C23×C61C2×C22⋊C411yescharacteristic
198C23×C61#13514yes—
199C23×C61C22×D411yescharacteristic
200C22×D61—22no—
201C22×D61—42no—
202C22×D61—42no—
203C22×D61—42no—
204C2×C4×C61—24no—
205C2×C4×C61—22no—
206C2×C4×C61—22no—
207C2×C4×C61—22no—
208C2×C4×C61—24no—
209C2×C4×C61—24no—
210C2×C4×C61—24no—
211C2×C4×C61—22no—
212C2×C4×C61—42no—
213C2×C4×C61—42no—
214C2×C4×C61—42no—
215C2×C4×C61—41no—
216C2×C4×C61—42no—
217C2×C4×C61—41no—
218C2×C4×C61—42no—
219C2×C4×C61—41no—
220C2×C4×C61—42no—
221C2×C4×C61—41no—
222C2×C4×C61C2×C22⋊C412yes—
223C2×C4×C61C2×C22⋊C411yescharacteristic
224C2×C4×C61C2×C22⋊C412yes—
225C2×C4×C61C2×C22⋊C411yescharacteristic
226C2×C4×C61C23×C411yescharacteristic
227C2×C4×C61C22×D411yescharacteristic
228C22⋊D61—48no—
229C22⋊D61—44no—
230C22⋊D61—48no—
231C22⋊D61—44no—
232C2×Dic61—22no—
233C2×Dic61—22no—
234C2×Dic61—22no—
235C2×Dic61—42no—
236C2×Dic61—42no—
237C2×Dic61—42no—
238C2×Dic61—44no—
239C2×Dic61—44no—
240C2×Dic61—44no—
241C2×Dic61—88no—
242D244—42no—
243D244—42no—
244C4×D61—48no—
245Dic122—42no—
246Dic122—42no—
247C8×C61—44no—
248C2×#1516—611nomaximal, Sylow
249C22×C61—21no—
250C22×C61—21no—
251C22×C61—22no—
252C22×C61—21no—
253C22×C61—22no—
254C22×C61—21no—
255C22×C61—28no—
256C22×C61—28no—
257C22×C61—22no—
258C22×C61—22no—
259C22×C61—22no—
260C22×C61—48no—
261C22×C61—48no—
262C22×C61—44no—
263C22×C61C2×#9914yes—
264C22×C61C2×#9912yes—
265C22×C61#41612yes—
266C22×C61#41612yes—
267C22×C61#42112yes—
268C22×C61C22×C22⋊C411yescharacteristic
269C22×C61C2×#13512yes—
270C2×D61—42no—
271C2×D61—42no—
272C2×D61—42no—
273C2×D61—84no—
274C4×C61—21no—
275C4×C61—21no—
276C4×C61—21no—
277C4×C61—22no—
278C4×C61—22no—
279C4×C61—21no—
280Dic61—42no—
281Dic61—42no—
282Dic61—42no—
283Dic61—84no—
284C2×#525—611no—
285C22×C22⋊C8D6111yescharacteristic, complemented
286C2×#381—611no—
287#1516—618no—
288C2×#328—612no—
289C2×#327—612no—
290C2×C61—22no—
291C2×C61—24no—
292C2×C61—22no—
293C2×C61—42no—
294C2×C61#151614yescomplemented
295C2×C61C22×#9911yescharacteristic
296C2×C61C2×#41611yescharacteristic
297C2×C61C2×#42111yescharacteristic
298D61—82no—
299C22×#41—611no—
300C24×C4C2×D6111yescharacteristic
301C23×C8—21no—
302#525—614no—
303#525—614no—
304#525—1222no—
305#525—1222no—
306C2×#123—1221no—
307C2×C22⋊Q8—611no—
308C2×C22⋊Q8—611no—
309C2×#121—611no—
310C2×#121—611no—
311C2×#120—1221no—
312C2×C4×D4—1221no—
313C2×C4×D4—1221no—
314C2×#117—611no—
315C22×C22⋊C4—1221no—
316C2×C22⋊C8—22no—
317C2×C22⋊C8—21no—
318C2×C22⋊C8C2×D6112yes—
319C2×C22⋊C8C2×D6114yescomplemented
320#381—614no—
321#381—1222no—
322C2×#95—612no—
323C2×#95—1221no—
324#328—618no—
325#327—618no—
326C61C2×#151611yescharacteristic, complemented, Sylow
327C25D24411yescharacteristic
328C2×#41—614no—
329C2×#41—1222no—
330C2×#41—2444no—
331C22×Q8—611no—
332C22×D4—611no—
333C22×D4—1221no—
334C22×D4—1221no—
335C22×D4—1221no—
336C23×C4—44no—
337C23×C4—1221no—
338C23×C4—1222no—
339C23×C4C4×D6111yescharacteristic
340C23×C4C4×D6111yescharacteristic
341C23×C4C4×D6112yes—
342C23×C4D24411yescharacteristic
343C23×C4D24412yes—
344C23×C4C22⋊D6111yescharacteristic
345C23×C4C22⋊D6111yescharacteristic
346C23×C4C22⋊D6112yes—
347C23×C4C22×D6111yescharacteristic
348C23×C4C22×D6112yes—
349C22×C8—22no—
350C22×C8—24no—
351C22×C8—44no—
352#123—1224no—
353#123—1224no—
354C22⋊Q8—612no—
355C22⋊Q8—614no—
356C22⋊Q8—612no—
357C22⋊Q8—1222no—
358C22⋊Q8—1221no—
359C22⋊Q8—1221no—
360#121—612no—
361#121—614no—
362#121—612no—
363#121—1222no—
364#121—1221no—
365#121—1221no—
366#120—1224no—
367#120—1224no—
368C4×D4—1224no—
369C4×D4—1224no—
370C4×D4—1224no—
371C4×D4—1224no—
372#117—614no—
373#117—1222no—
374C2×C4⋊C4—611no—
375C2×C4⋊C4—611no—
376C2×C4⋊C4—1221no—
377C2×C4⋊C4—1221no—
378C2×C22⋊C4—1221no—
379C2×C22⋊C4—1221no—
380C2×C22⋊C4—1221no—
381C2×C22⋊C4—1221no—
382C2×C22⋊C4—1221no—
383C2×C22⋊C4—1224no—
384C2×C22⋊C4—2444no—
385C2×C42—1221no—
386C22⋊C8—22no—
387C22⋊C8—24no—
388C22⋊C8C22×D6114yes—
389#95—614no—
390#95—1222no—
391#95—1224no—
392C24—24no—
393C24—24no—
394C24—42no—
395C24—1221no—
396C24#1175819811yescharacteristic
397C24#1175819812yes—
398C24#1175819811yescharacteristic
399C24C2×D24412yes—
400C24C2×D24411yescharacteristic
401#41—2448no—
402#41—2448no—
403C2×Q8—612no—
404C2×Q8—1221no—
405C2×Q8—2442no—
406C2×D4—612no—
407C2×D4—1222no—
408C2×D4—1224no—
409C2×D4—1222no—
410C2×D4—1224no—
411C2×D4—1221no—
412C2×D4—2442no—
413C2×D4—2444no—
414C2×D4—2444no—
415C2×D4—2444no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—42no—
419C22×C4—44no—
420C22×C4—42no—
421C22×C4—44no—
422C22×C4—42no—
423C22×C4—44no—
424C22×C4—42no—
425C22×C4—44no—
426C22×C4—1221no—
427C22×C4—1221no—
428C22×C4—1221no—
429C22×C4—1224no—
430C22×C4—1224no—
431C22×C4—2444no—
432C22×C4—2444no—
433C22×C4—2444no—
434C22×C4—2444no—
435C22×C4#1175819812yes—
436C22×C4#1175819812yes—
437C22×C4#1175819811yescharacteristic
438C22×C4#1175819811yescharacteristic
439C22×C4#1175819812yes—
440C22×C4#1175819812yes—
441C22×C4#1175819812yes—
442C22×C4C2×C4×D6112yes—
443C22×C4C2×C4×D6111yescharacteristic
444C22×C4C2×C4×D6112yes—
445C22×C4C2×C4×D6111yescharacteristic
446C22×C4C2×D24412yes—
447C22×C4C2×D24411yescharacteristic
448C22×C4C2×C22⋊D6112yes—
449C22×C4C2×C22⋊D6111yescharacteristic
450C22×C4C2×C22⋊D6112yes—
451C22×C4C2×C22⋊D6111yescharacteristic
452C22×C4C23×D6111yescharacteristic
453C2×C8—24no—
454C2×C8—44no—
455C2×C8—48no—
456C4⋊C4—612no—
457C4⋊C4—612no—
458C4⋊C4—1222no—
459C4⋊C4—1221no—
460C4⋊C4—1221no—
461C4⋊C4—1224no—
462C4⋊C4—1222no—
463C22⋊C4—1222no—
464C22⋊C4—1224no—
465C22⋊C4—1224no—
466C22⋊C4—1222no—
467C22⋊C4—1222no—
468C22⋊C4—1224no—
469C22⋊C4—1222no—
470C22⋊C4—2448no—
471C42—1224no—
472C23—22no—
473C23—22no—
474C23—22no—
475C23—22no—
476C23—24no—
477C23—24no—
478C23—22no—
479C23—24no—
480C23—22no—
481C23—24no—
482C23—22no—
483C23—42no—
484C23—42no—
485C23—416no—
486C23—1222no—
487C23—2442no—
488C23—2442no—
489C23—2442no—
490C23#1451969114yes—
491C23C2×#1175819812yes—
492C23C2×#1175819812yes—
493C23C2×#1175819811yescharacteristic
494C23C2×#1175819811yescharacteristic
495C23#1451979914yes—
496C23C22×D24411yescharacteristic
497Q8—2442no—
498Q8—2442no—
499D4—2442no—
500D4—2442no—
501D4—2448no—
502D4—2448no—
503D4—2444no—
504D4—2444no—
505C2×C4—24no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—24no—
511C2×C4—22no—
512C2×C4—24no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—41no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—1222no—
524C2×C4—1222no—
525C2×C4—1222no—
526C2×C4—4888no—
527C2×C4—2448no—
528C2×C4—2444no—
529C2×C4—2444no—
530C2×C4—2444no—
531C2×C4—2442no—
532C2×C4—2442no—
533C2×C4—2442no—
534C2×C4C2×#1175819812yes—
535C2×C4C2×#1175819811yescharacteristic
536C2×C4C2×#1175819812yes—
537C2×C4C2×#1175819811yescharacteristic
538C2×C4C22×C4×D6111yescharacteristic
539C2×C4C22×C22⋊D6111yescharacteristic
540C8—44no—
541C22—28no—
542C22—28no—
543C22—21no—
544C22—22no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—22no—
549C22—22no—
550C22—22no—
551C22—22no—
552C22—48no—
553C22—48no—
554C22—44no—
555C22—4884no—
556C22—2442no—
557C22—2442no—
558C22—2442no—
559C22C2×#1451969114yes—
560C22C2×#1451969112yes—
561C22#1683975912yes—
562C22#1683975912yes—
563C22#1683977812yes—
564C22C22×#1175819811yescharacteristic
565C22C2×#1451979912yes—
566C4—21no—
567C4—22no—
568C4—21no—
569C4—22no—
570C4—21no—
571C4—21no—
572C4—4884no—
573C4—2442no—
574C4—2442no—
575C4—2442no—
576C2—22no—
577C2—24no—
578C2—22no—
579C2—42no—
580C2—4882no—
581C2#2144437614yesdirect product factor
582C2C22×#1451969111yescharacteristic
583C2C2×#1683975911yescharacteristic
584C2C2×#1683977811yescharacteristic
subgroupG/H
centerC23C2×#11758198
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC22×C22⋊C8×C61C2
socleC23×C61C2×C22⋊C4
prime radicalC2×#16840273C2
cosocleC22×C4×C61C24
hypercenterC22×C22⋊C8D61
hypocenterC61C2×#1516
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#16839625C2semidirect
3. #21444376C2direct (N × H)
4. C2×#16839500C2semidirect
5. C2×#16839497C2semidirect
6. C22×C22⋊C8×C61C2semidirect
7. C22×#11758222C4semidirect
10. #16840273C4semidirect
13. C2×#14519756C4semidirect
15. C2×#14519751C4semidirect
20. C2×#14519736C4semidirect
23. #16839625C22semidirect
26. #16839500C22semidirect
27. #16839497C22semidirect
33. C2×C22⋊C8×C61C22semidirect
36. C2×#11758222C2×C4semidirect
50. #14519756C2×C4semidirect
56. #14519751C2×C4semidirect
65. #14519736C2×C4semidirect
285. C22×C22⋊C8D61semidirect
294. C2×C61#1516semidirect
319. C2×C22⋊C8C2×D61semidirect
326. C61C2×#1516semidirect
581. C2#21444376direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402732
C2×#168396252
#214443762
C2×#168395002
C2×#168394972
C22×C22⋊C8×C612
C2×#151661