Finite Group Databasebeta

← C2×#21444325 #29647156

Subgroups — C2×#21444325 #29647156

Order 15616.

1410 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840307C211yesmaximal, characteristic
2C2×#16839816C211yesmaximal, characteristic, complemented
3C2×#16839607C211yesmaximal, characteristic, complemented
4#21444325C218yesmaximal, direct product factor
5C2×#16839497C211yesmaximal, characteristic, complemented
6C2×#16839496C211yesmaximal, characteristic, complemented
7C2×#16839495C211yesmaximal, characteristic, complemented
8C2×C61×#327C211yesmaximal, characteristic, complemented
9C22×#11758224—21no—
10#16840307—22no—
11#16840307—22no—
12#16840307C414yescomplemented
13#16840307C2214yes—
14C2×#14519776C411yescharacteristic, complemented
15C2×#14519773C411yescharacteristic, complemented
16C2×#14519763—21no—
17C2×#14519751C2211yescharacteristic
18C2×#14519749—21no—
19C2×D4×Dic61C411yescharacteristic, complemented
20C2×#14519739C411yescharacteristic, complemented
21C2×#14519737—21no—
22C22×C4×Dic61—21no—
23C22×C4×Dic61C2211yescharacteristic
24#16839816—22no—
25#16839816C2214yescomplemented
26C2×#14519706—21no—
27C2×C22⋊#92418C2211yescharacteristic
28C2×#14519687—21no—
29#16839607—22no—
30#16839607C2214yescomplemented
31C2×#14519684—21no—
32C2×#14519684C2211yescharacteristic
33#16839497C2214yescomplemented
34#16839496C2214yescomplemented
35#16839495C2214yescomplemented
36C2×#121×C61C2211yescharacteristic
37C2×C22⋊C8×C61C2211yescharacteristic
38C2×#95×C61C2211yescharacteristic
39C61×#327C2214yescomplemented
40C2×#11758224—24no—
41C2×#11758224—24no—
42C2×#11758224—44no—
43C2×#11758224—44no—
44C22×Dic122—21no—
45C22×D244C2×C411yescharacteristic
46C22×C22⋊D61—21no—
47C22×C22⋊D61—21no—
48C22×C22⋊D61—21no—
49C23×Dic61—21no—
50C23×Dic61—21no—
51C23×Dic61D411yescharacteristic
52C23×Dic61D411yescharacteristic
53C22×C4×D61—21no—
54C22×#92418—21no—
55#14519776—22no—
56#14519776C2×C414yescomplemented
57#14519773—22no—
58#14519773C2×C414yescomplemented
59#14519763—24no—
60#14519763—24no—
61#14519751—21no—
62#14519751—21no—
63#14519751C2×C412yes—
64#14519751C2312yes—
65#14519749—24no—
66#14519749—24no—
67D4×Dic61—22no—
68D4×Dic61C2×C414yescomplemented
69#14519739—22no—
70#14519739C2×C414yescomplemented
71#14519737—24no—
72#14519737—24no—
73C2×C4⋊Dic61C2×C411yescharacteristic
74C2×#11758196—21no—
75C2×C22⋊Dic61—21no—
76C2×#11758198—21no—
77C2×#11758198—21no—
78C2×C4×Dic61—28no—
79C2×C4×Dic61—24no—
80C2×C4×Dic61C2×C411yescharacteristic
81C2×C4×Dic61C2×C411yescharacteristic
82C2×C4×Dic61C2×C412yes—
83C2×C4×Dic61D412yes—
84C2×C4×Dic61D411yescharacteristic
85C2×C4×Dic61D411yescharacteristic
86C2×C4×Dic61D412yes—
87C2×C4×Dic61C2312yes—
88#14519706—24no—
89C22⋊#92418—21no—
90C22⋊#92418C2312yes—
91#14519687—24no—
92#14519684—21no—
93#14519684—24no—
94#14519684C2312yes—
95C22×D4×C61—21no—
96C22×D4×C61C2×C411yescharacteristic
97C23×C4×C61—21no—
98C23×C4×C61C2311yescharacteristic
99C22×C8×C61—21no—
100#121×C61—21no—
101#121×C61—21no—
102#121×C61C2×C412yes—
103#121×C61C2312yes—
104C2×C4⋊C4×C61C2×C411yescharacteristic
105C2×C22⋊C4×C61—21no—
106C22⋊C8×C61—21no—
107C22⋊C8×C61C2312yes—
108#95×C61—21no—
109#95×C61C2312yes—
110C24×C61—21no—
111C24×C61C2×D411yescharacteristic
112C23×D61—21no—
113C2×D4×C61—22no—
114C2×D4×C61—22no—
115C2×D4×C61—21no—
116C2×D4×C61—42no—
117C2×D4×C61—42no—
118C2×D4×C61—42no—
119C2×D4×C61C22×C412yes—
120C22×C4×C61—24no—
121C22×C4×C61—21no—
122C22×C4×C61—22no—
123C22×C4×C61—42no—
124C22×C4×C61—42no—
125C22×C4×C61—42no—
126C22×C4×C61C22×C411yescharacteristic
127C22×C4×C61C22×C411yescharacteristic
128C22×C4×C61C2×D411yescharacteristic
129C22×C4×C61C2×D411yescharacteristic
130C22×C4×C61C2×D411yescharacteristic
131C22×C4×C61C2411yescharacteristic
132C2×C22⋊D61—22no—
133C2×C22⋊D61—22no—
134C2×C22⋊D61—24no—
135C2×C22⋊D61—24no—
136C2×C22⋊D61—44no—
137C2×C22⋊D61—42no—
138C2×C22⋊D61—42no—
139C2×C22⋊D61—44no—
140C22×Dic61—22no—
141C22×Dic61—22no—
142C22×Dic61—24no—
143C22×Dic61—24no—
144C22×Dic61—21no—
145C22×Dic61—22no—
146C22×Dic61—24no—
147C22×Dic61—44no—
148C22×Dic61—42no—
149C22×Dic61—42no—
150C22×Dic61C22⋊C411yescharacteristic
151C22×Dic61C22⋊C411yescharacteristic
152C22×Dic61C22⋊C412yes—
153C22×Dic61C22⋊C411yescharacteristic
154C22×Dic61C22⋊C412yes—
155C22×Dic61C22⋊C411yescharacteristic
156C22×Dic61C2×D412yes—
157C22×Dic61C2×D412yes—
158#11758224—48no—
159#11758224—48no—
160#11758224—416no—
161C2×D244—21no—
162C2×D244—42no—
163C2×D244C22×C412yes—
164C2×C4×D61—24no—
165C2×C4×D61—44no—
166C2×Dic122—24no—
167C2×Dic122—44no—
168C2×C8×C61—22no—
169C2×C8×C61—42no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61C22×C412yes—
172C22⋊C4×C61—22no—
173C22⋊C4×C61—22no—
174C22⋊Dic61—24no—
175#11758198—22no—
176#11758198—22no—
177#11758198—24no—
178C4⋊Dic61—21no—
179C4⋊Dic61C22×C412yes—
180#11758196—24no—
181C4×Dic61—216no—
182C4×Dic61C22⋊C412yes—
183C4×Dic61C22⋊C412yes—
184C4×Dic61C22⋊C412yes—
185C4×Dic61C22⋊C412yes—
186C4×Dic61C22×C412yes—
187C4×Dic61C22×C412yes—
188C4×Dic61C2×D412yes—
189C4×Dic61C2×D412yes—
190C2×#92418—22no—
191C2×#92418—42no—
192C23×C61—22no—
193C23×C61—22no—
194C23×C61—22no—
195C23×C61—42no—
196C23×C61—42no—
197C23×C61—42no—
198C23×C61C2×C22⋊C411yescharacteristic
199C23×C61C2×C22⋊C411yescharacteristic
200C23×C61AGL(1,ℤ/8)12yes—
201C23×C61AGL(1,ℤ/8)12yes—
202C23×C61C22×D411yescharacteristic
203C22×D61—22no—
204C22×D61—42no—
205C22×D61—42no—
206C22×D61—42no—
207D4×C61—42no—
208D4×C61—42no—
209D4×C61—42no—
210D4×C61—42no—
211D4×C61—44no—
212C2×C4×C61—22no—
213C2×C4×C61—22no—
214C2×C4×C61—24no—
215C2×C4×C61—22no—
216C2×C4×C61—41no—
217C2×C4×C61—41no—
218C2×C4×C61—41no—
219C2×C4×C61—41no—
220C2×C4×C61—42no—
221C2×C4×C61—48no—
222C2×C4×C61—42no—
223C2×C4×C61—42no—
224C2×C4×C61C2×C22⋊C411yescharacteristic
225C2×C4×C61C2×C22⋊C411yescharacteristic
226C2×C4×C61C23×C411yescharacteristic
227C2×C4×C61C22×D411yescharacteristic
228C22⋊D61—48no—
229C22⋊D61—42no—
230C22⋊D61—42no—
231C22⋊D61—44no—
232C22⋊D61—48no—
233C2×Dic61—22no—
234C2×Dic61—22no—
235C2×Dic61—22no—
236C2×Dic61—22no—
237C2×Dic61—24no—
238C2×Dic61—22no—
239C2×Dic61—24no—
240C2×Dic61—24no—
241C2×Dic61—24no—
242C2×Dic61—22no—
243C2×Dic61—48no—
244C2×Dic61—42no—
245C2×Dic61—48no—
246C2×Dic61—42no—
247C2×Dic61—42no—
248C2×Dic61#10414yes—
249C2×Dic61C2×C22⋊C412yes—
250C2×Dic61C2×C22⋊C412yes—
251C2×Dic61C2×C22⋊C412yes—
252C2×Dic61C2×C22⋊C412yes—
253D244—42no—
254D244—42no—
255C4×D61—48no—
256Dic122—48no—
257C8×C61—42no—
258#92418—42no—
259C2×#1505—611nomaximal, Sylow
260C22×C61—21no—
261C22×C61—21no—
262C22×C61—21no—
263C22×C61—21no—
264C22×C61—24no—
265C22×C61—24no—
266C22×C61—42no—
267C22×C61—42no—
268C22×C61—42no—
269C22×C61—84no—
270C22×C61#41012yes—
271C22×C61#41812yes—
272C22×C61#41812yes—
273C22×C61C2×#10412yes—
274C22×C61C22×C22⋊C411yescharacteristic
275C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
276C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
277C2×D61—42no—
278C2×D61—42no—
279C2×D61—42no—
280C2×D61—84no—
281C4×C61—21no—
282C4×C61—21no—
283C4×C61—21no—
284C4×C61—21no—
285C4×C61—44no—
286C4×C61—42no—
287Dic61—22no—
288Dic61—22no—
289Dic61—22no—
290Dic61—44no—
291Dic61—42no—
292Dic61C2×#10414yes—
293C2×#532—611no—
294C2×#432—611no—
295C2×#376—611no—
296#1505—618no—
297C2×#327—611no—
298C2×#327—611no—
299C2×#327—611no—
300C2×#327D6111yescharacteristic, complemented
301C2×C61—21no—
302C2×C61—21no—
303C2×C61—22no—
304C2×C61—82no—
305C2×C61#150514yescomplemented
306C2×C61C2×#41011yescharacteristic
307C2×C61C2×#41811yescharacteristic
308C2×C61C22×#10411yescharacteristic
309D61—82no—
310C22×#41—1221no—
311#532—614no—
312#532—614no—
313#532—1222no—
314#532—1222no—
315C2×C4⋊Q8—611no—
316C2×#127—611no—
317C2×#124—1221no—
318C2×#121—611no—
319C2×#121—1221no—
320C2×#121C2×D6111yescharacteristic
321C2×C4×D4—611no—
322C2×C4×D4—611no—
323C2×C4×D4—1221no—
324C22×C42—611no—
325C22×C42—1221no—
326#432—614no—
327#432—1222no—
328C2×C4⋊C8—1221no—
329C2×C22⋊C8—611no—
330C2×C22⋊C8C2×D6111yescharacteristic
331C2×#97—1221no—
332#376—614no—
333#376—1222no—
334C2×#95—611no—
335C2×#95—1221no—
336C2×#95C2×D6111yescharacteristic
337#327—614no—
338#327—614no—
339#327—614no—
340#327C2×D6114yescomplemented
341C61C2×#150511yescharacteristic, complemented, Sylow
342C2×#41—1224no—
343C2×#41—1224no—
344C2×#41—2444no—
345C2×#41—2444no—
346C22×Q8—1221no—
347C22×D4—21no—
348C22×D4—611no—
349C22×D4—1221no—
350C22×D4—1221no—
351C22×D4—1221no—
352C22×D4C4×D6111yescharacteristic
353C23×C4—21no—
354C23×C4—611no—
355C23×C4—611no—
356C23×C4—1221no—
357C23×C4—1221no—
358C23×C4—1221no—
359C23×C4C22×D6111yescharacteristic
360C22×C8—21no—
361C22×C8—1221no—
362C4⋊Q8—614no—
363C4⋊Q8—1222no—
364#127—614no—
365#127—1222no—
366#124—1224no—
367#124—1224no—
368#121—21no—
369#121—21no—
370#121—612no—
371#121—612no—
372#121—1224no—
373#121—1224no—
374#121—1221no—
375#121—1221no—
376#121C4×D6112yes—
377#121C22×D6112yes—
378C4×D4—614no—
379C4×D4—614no—
380C4×D4—1224no—
381C4×D4—1224no—
382C4×D4—1222no—
383C4×D4—1222no—
384C2×C4⋊C4—611no—
385C2×C4⋊C4—1221no—
386C2×C4⋊C4C4×D6111yescharacteristic
387C2×C22⋊C4—21no—
388C2×C22⋊C4—1221no—
389C2×C22⋊C4—1221no—
390C2×C22⋊C4—1221no—
391C2×C42—611no—
392C2×C42—611no—
393C2×C42—612no—
394C2×C42—611no—
395C2×C42—611no—
396C2×C42—612no—
397C2×C42—612no—
398C2×C42—612no—
399C2×C42—1224no—
400C2×C42—1228no—
401C4⋊C8—1224no—
402C22⋊C8—21no—
403C22⋊C8—612no—
404C22⋊C8—1221no—
405C22⋊C8C22×D6112yes—
406#97—1224no—
407#95—21no—
408#95—612no—
409#95—1224no—
410#95—1221no—
411#95C22×D6112yes—
412C24—21no—
413C24—1221no—
414C24D4×D6111yescharacteristic
415#41—24416no—
416#41—2448no—
417#41—2448no—
418C2×Q8—1224no—
419C2×Q8—2444no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—21no—
423C2×D4—42no—
424C2×D4—42no—
425C2×D4—42no—
426C2×D4—612no—
427C2×D4—1224no—
428C2×D4—1224no—
429C2×D4—1222no—
430C2×D4—1222no—
431C2×D4—1221no—
432C2×D4—2442no—
433C2×D4—2444no—
434C2×D4—2444no—
435C2×D4—2442no—
436C2×D4—2442no—
437C2×D4C2×C4×D6112yes—
438C22×C4—24no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—611no—
445C22×C4—612no—
446C22×C4—612no—
447C22×C4—612no—
448C22×C4—612no—
449C22×C4—611no—
450C22×C4—611no—
451C22×C4—611no—
452C22×C4—1224no—
453C22×C4—1224no—
454C22×C4—1224no—
455C22×C4—1222no—
456C22×C4—1222no—
457C22×C4—1224no—
458C22×C4—1222no—
459C22×C4—1221no—
460C22×C4—2444no—
461C22×C4—2444no—
462C22×C4—2442no—
463C22×C4—2442no—
464C22×C4C2×C4×D6111yescharacteristic
465C22×C4C2×C4×D6111yescharacteristic
466C22×C4D4×D6111yescharacteristic
467C22×C4D4×D6111yescharacteristic
468C22×C4D4×D6111yescharacteristic
469C22×C4C23×D6111yescharacteristic
470C2×C8—22no—
471C2×C8—42no—
472C2×C8—1222no—
473C2×C8—2442no—
474C4⋊C4—21no—
475C4⋊C4—612no—
476C4⋊C4—1224no—
477C4⋊C4—1221no—
478C4⋊C4C2×C4×D6112yes—
479C22⋊C4—22no—
480C22⋊C4—22no—
481C22⋊C4—1224no—
482C22⋊C4—1224no—
483C22⋊C4—1222no—
484C22⋊C4—1222no—
485C42—612no—
486C42—612no—
487C42—612no—
488C42—612no—
489C42—612no—
490C42—612no—
491C42—612no—
492C42—612no—
493C42—12216no—
494C23—22no—
495C23—22no—
496C23—22no—
497C23—42no—
498C23—42no—
499C23—42no—
500C23—1222no—
501C23—2442no—
502C23—2442no—
503C23—2442no—
504C23C22⋊C4×D6111yescharacteristic
505C23C22⋊C4×D6111yescharacteristic
506C23#1451980112yes—
507C23#1451980412yes—
508C23C2×D4×D6111yescharacteristic
509Q8—2448no—
510D4—42no—
511D4—42no—
512D4—44no—
513D4—42no—
514D4—42no—
515D4—2442no—
516D4—2442no—
517D4—2448no—
518D4—2448no—
519D4—2444no—
520D4—2442no—
521D4—2442no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—24no—
525C2×C4—22no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—42no—
531C2×C4—48no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—612no—
535C2×C4—614no—
536C2×C4—612no—
537C2×C4—612no—
538C2×C4—612no—
539C2×C4—1224no—
540C2×C4—1224no—
541C2×C4—1222no—
542C2×C4—1222no—
543C2×C4—1224no—
544C2×C4—1222no—
545C2×C4—1222no—
546C2×C4—1222no—
547C2×C4—1224no—
548C2×C4—1222no—
549C2×C4—2448no—
550C2×C4—2448no—
551C2×C4—2442no—
552C2×C4—2448no—
553C2×C4—2442no—
554C2×C4—2442no—
555C2×C4C22⋊C4×D6111yescharacteristic
556C2×C4C22⋊C4×D6111yescharacteristic
557C2×C4C22×C4×D6111yescharacteristic
558C2×C4C2×D4×D6111yescharacteristic
559C8—42no—
560C8—2442no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—21no—
565C22—24no—
566C22—24no—
567C22—42no—
568C22—42no—
569C22—42no—
570C22—84no—
571C22—4884no—
572C22—2442no—
573C22—2442no—
574C22—2442no—
575C22#1683973412yes—
576C22#1683976512yes—
577C22#1683976512yes—
578C22#104×D6112yes—
579C22C2×C22⋊C4×D6111yescharacteristic
580C22C2×#1451980111yescharacteristic
581C22C2×#1451980411yescharacteristic
582C4—21no—
583C4—21no—
584C4—21no—
585C4—21no—
586C4—44no—
587C4—42no—
588C4—614no—
589C4—1222no—
590C4—1222no—
591C4—1222no—
592C4—2444no—
593C4—2442no—
594C2—21no—
595C2—21no—
596C2—22no—
597C2—82no—
598C2—4882no—
599C2#2144432514yesdirect product factor
600C2C2×#1683973411yescharacteristic
601C2C2×#1683976511yescharacteristic
602C2C2×#104×D6111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#327C2
socleC23×C61C2×C22⋊C4
prime radicalC2×#16840307C2
cosocleC22×C4×C61C24
hypercenterC2×#327D61
hypocenterC61C2×#1505
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. C2×#16839816C2semidirect
3. C2×#16839607C2semidirect
4. #21444325C2direct (N × H)
5. C2×#16839497C2semidirect
6. C2×#16839496C2semidirect
7. C2×#16839495C2semidirect
8. C2×C61×#327C2semidirect
12. #16840307C4semidirect
14. C2×#14519776C4semidirect
15. C2×#14519773C4semidirect
19. C2×D4×Dic61C4semidirect
20. C2×#14519739C4semidirect
25. #16839816C22semidirect
30. #16839607C22semidirect
33. #16839497C22semidirect
34. #16839496C22semidirect
35. #16839495C22semidirect
39. C61×#327C22semidirect
56. #14519776C2×C4semidirect
58. #14519773C2×C4semidirect
68. D4×Dic61C2×C4semidirect
70. #14519739C2×C4semidirect
300. C2×#327D61semidirect
305. C2×C61#1505semidirect
340. #327C2×D61semidirect
341. C61C2×#1505semidirect
599. C2#21444325direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403072
C2×#168398162
C2×#168396072
#214443252
C2×#168394972
C2×#168394962
C2×#168394952
C2×C61×#3272
C2×#150561