Finite Group Databasebeta

← C2×#21455948 #30548215

Subgroups — C2×#21455948 #30548215

Order 15616.

2118 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840317C211yesmaximal, characteristic
2C2×C4×Q8×D61C211yesmaximal, characteristic
3#21455948C2116yesmaximal, direct product factor
4C2×#16840091C212yesmaximal
5C2×#16840048C211yesmaximal, characteristic, complemented
6C2×#16840047C211yesmaximal, characteristic, complemented
7C2×#16839969C211yesmaximal, characteristic, complemented
8C2×#16839916C212yesmaximal
9C2×#16839869C212yesmaximal, complemented
10C2×#16839866C212yesmaximal, complemented
11C2×#16839818C211yesmaximal, characteristic
12C2×C61×#462C211yesmaximal, characteristic, complemented
13C22×Q8×D61C2211yescharacteristic
14C22×#11758202C2212yes—
15#16840317—24no—
16#16840317C2218yes—
17C2×#14519777C2211yescharacteristic
18C2×#14519768—21no—
19C2×#14519757—21no—
20C2×#14519753C2212yes—
21C2×Q8×Dic61C2212yes—
22C2×Q8×Dic61C2211yescharacteristic
23C2×C4×Dic122—21no—
24C2×C4×Dic122C2211yescharacteristic
25C2×#14519742—21no—
26C2×#14519742—21no—
27C2×#14519742C2211yescharacteristic
28C4×Q8×D61—24no—
29C4×Q8×D61C2218yes—
30C2×#14519735—21no—
31C2×C4⋊C4×D61—21no—
32C2×C4⋊C4×D61C2211yescharacteristic
33C2×C42×D61—21no—
34C2×C42×D61C2211yescharacteristic
35#16840091C22116yes—
36#16840048C2218yescomplemented
37#16840047C2218yescomplemented
38#16839969C2218yescomplemented
39#16839916C22116yes—
40#16839869C22116yescomplemented
41#16839866C22116yescomplemented
42#16839818C2218yes—
43C2×#14519709C2212yes—
44C2×#14519708C2212yes—
45C2×C4⋊#92418C2211yescharacteristic
46C2×#14519702C2212yes—
47C2×#14519701C2212yes—
48C2×#14519701C2212yes—
49C2×#14519689C2212yes—
50C2×#14519687C2212yes—
51C22×Q16×C61C2212yes—
52C2×C4⋊Q8×C61C2211yescharacteristic
53C2×C4×Q8×C61C2211yescharacteristic
54C61×#462C2218yescomplemented
55C2×C4⋊C8×C61C2211yescharacteristic
56C2×#103×C61C2212yes—
57C22×Dic122—21no—
58C22×Dic122—21no—
59C22×Dic122C2311yescharacteristic
60C2×Q8×D61—24no—
61C2×Q8×D61—22no—
62C2×Q8×D61—24no—
63C2×Q8×D61C2314yes—
64C22×C4×D61—21no—
65C22×C4×D61—21no—
66C22×C4×D61D411yescharacteristic
67C22×C4×D61D411yescharacteristic
68C22×C4×D61C2311yescharacteristic
69C2×#11758202—28no—
70C2×#11758202C2318yes—
71C22×#92418C2312yes—
72#14519777—22no—
73#14519777C2314yes—
74#14519768—28no—
75#14519757—28no—
76#14519753—24no—
77#14519753C2318yes—
78Q8×Dic61—22no—
79Q8×Dic61—24no—
80Q8×Dic61C2314yes—
81Q8×Dic61C2318yes—
82C4×Dic122—22no—
83C4×Dic122—28no—
84C4×Dic122C2314yes—
85#14519742—22no—
86#14519742—28no—
87#14519742—28no—
88#14519742C2314yes—
89#14519735—28no—
90C2×C4⋊Dic61—21no—
91C2×C4⋊Dic61—21no—
92C2×C4⋊Dic61—22no—
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2312yes—
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×#11758196—22no—
99C4⋊C4×D61—28no—
100C4⋊C4×D61—22no—
101C4⋊C4×D61C2314yes—
102C2×#11758198—22no—
103C2×C4×Dic61—21no—
104C2×C4×Dic61—21no—
105C2×C4×Dic61—21no—
106C2×C4×Dic61—22no—
107C2×C4×Dic61D411yescharacteristic
108C2×C4×Dic61D411yescharacteristic
109C2×C4×Dic61C2311yescharacteristic
110C42×D61—28no—
111C42×D61D414yes—
112C42×D61C2314yes—
113#14519709C2318yes—
114#14519708C2318yes—
115C4⋊#92418C2314yes—
116#14519702C2318yes—
117#14519701C2318yes—
118#14519701C2318yes—
119#14519689C2318yes—
120#14519687C2318yes—
121C22×Q8×C61C2312yes—
122C22×Q8×C61C2311yescharacteristic
123C2×Q16×C61—28no—
124C2×Q16×C61C2318yes—
125C22×C8×C61C2312yes—
126C4⋊Q8×C61—22no—
127C4⋊Q8×C61C2314yes—
128C4×Q8×C61—22no—
129C4×Q8×C61C2314yes—
130C2×C4⋊C4×C61—21no—
131C2×C4⋊C4×C61—21no—
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C42×C61—21no—
135C2×C42×C61C2311yescharacteristic
136C4⋊C8×C61C2314yes—
137#103×C61C2318yes—
138C23×D61C2×D411yescharacteristic
139C2×Q8×C61—21no—
140C2×Q8×C61—22no—
141C2×Q8×C61—22no—
142C2×Q8×C61—24no—
143C2×Q8×C61—24no—
144C2×Q8×C61#4114yes—
145C2×Q8×C61C2414yes—
146C2×Q8×C61C2412yes—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—22no—
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2411yescharacteristic
153C22×Dic61—21no—
154C22×Dic61—21no—
155C22×Dic61—22no—
156C22×Dic61C2×D411yescharacteristic
157C22×Dic61C2×D411yescharacteristic
158C22×Dic61C2×D411yescharacteristic
159Q8×D61—216no—
160Q8×D61—28no—
161Q8×D61—28no—
162C2×C4×D61—28no—
163C2×C4×D61—24no—
164C2×C4×D61—24no—
165C2×C4×D61—24no—
166C2×C4×D61—22no—
167C2×C4×D61—22no—
168C2×C4×D61—24no—
169C2×C4×D61—44no—
170C2×C4×D61C2×D414yes—
171C2×C4×D61C2×D414yes—
172C2×C4×D61C2×D412yes—
173C2×C4×D61C2412yes—
174C2×Dic122—28no—
175C2×Dic122—21no—
176C2×Dic122—22no—
177C2×Dic122—24no—
178C2×Dic122—24no—
179C2×Dic122—44no—
180C2×Dic122#4114yes—
181C2×Dic122C2412yes—
182Q16×C61—216no—
183C2×C8×C61—24no—
184C2×C8×C61C2414yes—
185C4⋊C4×C61—24no—
186C4⋊C4×C61—24no—
187C4⋊C4×C61—24no—
188C4⋊C4×C61—21no—
189C4⋊C4×C61C2412yes—
190C42×C61—24no—
191C42×C61C2×D412yes—
192C42×C61C2412yes—
193#11758202—216no—
194#11758198—28no—
195C4⋊Dic61—21no—
196C4⋊Dic61—24no—
197C4⋊Dic61—22no—
198C4⋊Dic61—24no—
199C4⋊Dic61—28no—
200C4⋊Dic61C2412yes—
201C4⋊Dic61C2414yes—
202#11758196—24no—
203#11758196—24no—
204#11758196—24no—
205#11758196—28no—
206C4×Dic61—24no—
207C4×Dic61—24no—
208C4×Dic61—24no—
209C4×Dic61—28no—
210C4×Dic61C2×D412yes—
211C4×Dic61C2×D414yes—
212C4×Dic61C2×D414yes—
213C4×Dic61C2412yes—
214C2×#92418—24no—
215C2×#92418C2414yes—
216C23×C61C22×D411yescharacteristic
217C22×D61—22no—
218C22×D61—22no—
219C22×D61#13714yes—
220C22×D61C22×D412yes—
221Q8×C61—24no—
222Q8×C61—22no—
223Q8×C61—24no—
224Q8×C61—24no—
225Q8×C61—44no—
226Q8×C61C2×#4114yes—
227C2×C4×C61—24no—
228C2×C4×C61—22no—
229C2×C4×C61—22no—
230C2×C4×C61—22no—
231C2×C4×C61—24no—
232C2×C4×C61—44no—
233C2×C4×C61—42no—
234C2×C4×C61#13714yes—
235C2×C4×C61C22×D412yes—
236C2×C4×C61C22×D411yescharacteristic
237C2×C4×C61C22×D412yes—
238C2×C4×C61C2×#4112yes—
239C2×C4×C61C2×#4112yes—
240C2×C4×C61C2511yescharacteristic
241C2×Dic61—22no—
242C2×Dic61—24no—
243C2×Dic61—22no—
244C2×Dic61—22no—
245C2×Dic61—22no—
246C2×Dic61—22no—
247C2×Dic61—24no—
248C2×Dic61—44no—
249C2×Dic61—42no—
250C2×Dic61C22×D412yes—
251C2×Dic61C22×D412yes—
252C2×Dic61C22×D412yes—
253C4×D61—216no—
254C4×D61—28no—
255C4×D61—24no—
256C4×D61—28no—
257C4×D61—22no—
258C4×D61—22no—
259C4×D61—48no—
260Dic122—216no—
261Dic122—24no—
262Dic122—22no—
263Dic122—48no—
264Dic122C2×#4114yes—
265C8×C61—24no—
266#92418—24no—
267C2×#3113—611nomaximal, Sylow
268C22×C61#52512yes—
269C22×C61C2×#13712yes—
270C22×C61C2×#13712yes—
271C22×C61C23×D411yescharacteristic
272C2×D61—28no—
273C2×D61—22no—
274C2×D61—22no—
275C2×D61C2×#13714yes—
276C4×C61—24no—
277C4×C61—22no—
278C4×C61—44no—
279C4×C61—42no—
280C4×C61#52512yes—
281C4×C61C2×#13714yes—
282C4×C61C22×#4111yescharacteristic
283C4×C61C22×#4111yescharacteristic
284Dic61—22no—
285Dic61—24no—
286Dic61—22no—
287Dic61—22no—
288Dic61—44no—
289Dic61—42no—
290C2×#533—611no—
291C22×C4×Q8—611no—
292#3113—6116no—
293C2×#483—612no—
294C2×#475—611no—
295C2×#475—611no—
296C2×#462—611no—
297C2×#462D6111yescharacteristic, complemented
298C2×#451—612no—
299C2×#441—612no—
300C2×#441—612no—
301C2×#432—611no—
302C2×C61#311314yescomplemented
303C2×C61C2×#52511yescharacteristic
304C2×C61C22×#13711yescharacteristic
305C2×C61C22×#13711yescharacteristic
306D61—24no—
307C23×Q8—611no—
308C22×Q16—612no—
309C22×Q16C2×D6112yes—
310#533—618no—
311#533—1224no—
312C2×C4⋊Q8—611no—
313C2×C4⋊Q8C2×D6111yescharacteristic
314C2×#125—1221no—
315C2×C22⋊Q8—612no—
316C2×C22⋊Q8—1221no—
317C2×C4×Q8—611no—
318C2×C4×Q8—612no—
319C2×C4×Q8—618no—
320C2×C4×Q8—611no—
321C2×C4×Q8—611no—
322C2×C4×Q8—1221no—
323C2×C4×Q8—1221no—
324C2×C4×Q8—1221no—
325C2×C4×Q8—1224no—
326C2×C4×Q8C2×D6111yescharacteristic
327C2×#117—1221no—
328C22×C4⋊C4—611no—
329C22×C4⋊C4—1221no—
330C22×C42—611no—
331C22×C42—1221no—
332#483—6116no—
333#475—618no—
334#475—618no—
335#462—618no—
336#462C2×D6118yescomplemented
337#451—6116no—
338#441—6116no—
339#441—6116no—
340#432—618no—
341C2×#106—612no—
342C2×#106—612no—
343C2×C4⋊C8—611no—
344C2×C4⋊C8C2×D6111yescharacteristic
345C2×#103—612no—
346C2×#103—612no—
347C2×#103—612no—
348C2×#103C2×D6112yes—
349C2×C22⋊C8—612no—
350C2×#97—612no—
351C61C2×#311311yescharacteristic, complemented, Sylow
352C22×Q8—614no—
353C22×Q8—611no—
354C22×Q8—1221no—
355C22×Q8—1222no—
356C22×Q8—1224no—
357C22×Q8—1224no—
358C22×Q8—1221no—
359C22×Q8C22×D6112yes—
360C22×Q8C22×D6111yescharacteristic
361C23×C4—611no—
362C23×C4—611no—
363C23×C4—611no—
364C23×C4—1221no—
365C23×C4—1221no—
366C2×Q16—28no—
367C2×Q16—618no—
368C2×Q16—1228no—
369C2×Q16C22×D6118yes—
370C22×C8—612no—
371C22×C8C22×D6112yes—
372C4⋊Q8—22no—
373C4⋊Q8—614no—
374C4⋊Q8—1222no—
375C4⋊Q8C22×D6114yes—
376#125—1228no—
377C22⋊Q8—618no—
378C22⋊Q8—1228no—
379C22⋊Q8—1224no—
380C4×Q8—22no—
381C4×Q8—614no—
382C4×Q8—618no—
383C4×Q8—614no—
384C4×Q8—614no—
385C4×Q8—1228no—
386C4×Q8—1222no—
387C4×Q8—1228no—
388C4×Q8—1228no—
389C4×Q8—1222no—
390C4×Q8—1224no—
391C4×Q8—1222no—
392C4×Q8C22×D6114yes—
393#117—1228no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—611no—
398C2×C4⋊C4—612no—
399C2×C4⋊C4—614no—
400C2×C4⋊C4—1222no—
401C2×C4⋊C4—1228no—
402C2×C4⋊C4—1221no—
403C2×C4⋊C4—1221no—
404C2×C4⋊C4—1221no—
405C2×C4⋊C4—1222no—
406C2×C4⋊C4—1222no—
407C2×C4⋊C4—1221no—
408C2×C4⋊C4—1221no—
409C2×C4⋊C4C22×D6111yescharacteristic
410C2×C22⋊C4—1222no—
411C2×C42—21no—
412C2×C42—611no—
413C2×C42—611no—
414C2×C42—611no—
415C2×C42—614no—
416C2×C42—614no—
417C2×C42—1228no—
418C2×C42—1222no—
419C2×C42—1221no—
420C2×C42—1221no—
421C2×C42—1221no—
422C2×C42C22×D6111yescharacteristic
423#106—618no—
424#106—618no—
425C4⋊C8—614no—
426C4⋊C8C22×D6114yes—
427#103—618no—
428#103—618no—
429#103—618no—
430#103C22×D6118yes—
431C22⋊C8—618no—
432#97—618no—
433C24—611no—
434C2×Q8—21no—
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8—24no—
438C2×Q8—24no—
439C2×Q8—614no—
440C2×Q8—612no—
441C2×Q8—1224no—
442C2×Q8—1228no—
443C2×Q8—1228no—
444C2×Q8—12216no—
445C2×Q8—1228no—
446C2×Q8—1221no—
447C2×Q8—1224no—
448C2×Q8—1222no—
449C2×Q8—2444no—
450C2×Q8#1175822414yes—
451C2×Q8C23×D6114yes—
452C2×Q8C23×D6112yes—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—611no—
457C22×C4—611no—
458C22×C4—611no—
459C22×C4—614no—
460C22×C4—614no—
461C22×C4—612no—
462C22×C4—612no—
463C22×C4—1224no—
464C22×C4—1224no—
465C22×C4—1228no—
466C22×C4—1224no—
467C22×C4—1221no—
468C22×C4—1224no—
469C22×C4—1222no—
470C22×C4—1222no—
471C22×C4—1221no—
472C22×C4—1222no—
473C22×C4—2444no—
474C22×C4D4×D6111yescharacteristic
475C22×C4D4×D6111yescharacteristic
476C22×C4C23×D6111yescharacteristic
477Q16—216no—
478Q16—12216no—
479C2×C8—24no—
480C2×C8—614no—
481C2×C8—1224no—
482C2×C8C23×D6114yes—
483C4⋊C4—24no—
484C4⋊C4—24no—
485C4⋊C4—24no—
486C4⋊C4—21no—
487C4⋊C4—612no—
488C4⋊C4—614no—
489C4⋊C4—1224no—
490C4⋊C4—1224no—
491C4⋊C4—1224no—
492C4⋊C4—1228no—
493C4⋊C4—1228no—
494C4⋊C4—1221no—
495C4⋊C4—1222no—
496C4⋊C4—1224no—
497C4⋊C4—1224no—
498C4⋊C4C23×D6112yes—
499C22⋊C4—1228no—
500C42—24no—
501C42—612no—
502C42—614no—
503C42—614no—
504C42—612no—
505C42—1224no—
506C42—1224no—
507C42—1228no—
508C42—1224no—
509C42D4×D6112yes—
510C42C23×D6112yes—
511C23—614no—
512C23—612no—
513C23—1222no—
514C23—1222no—
515C23C2×D4×D6111yescharacteristic
516Q8—24no—
517Q8—22no—
518Q8—24no—
519Q8—24no—
520Q8—44no—
521Q8—614no—
522Q8—12216no—
523Q8—1224no—
524Q8—1222no—
525Q8—2448no—
526Q8C2×#1175822414yes—
527C2×C4—24no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—24no—
532C2×C4—44no—
533C2×C4—42no—
534C2×C4—612no—
535C2×C4—612no—
536C2×C4—612no—
537C2×C4—1228no—
538C2×C4—12216no—
539C2×C4—1222no—
540C2×C4—1224no—
541C2×C4—1222no—
542C2×C4—1222no—
543C2×C4—1222no—
544C2×C4—1224no—
545C2×C4—1228no—
546C2×C4—1222no—
547C2×C4—1222no—
548C2×C4—1222no—
549C2×C4—1224no—
550C2×C4—2448no—
551C2×C4—2442no—
552C2×C4—2444no—
553C2×C4#1451980914yes—
554C2×C4C2×D4×D6112yes—
555C2×C4C2×D4×D6111yescharacteristic
556C2×C4C2×D4×D6112yes—
557C2×C4#41×D6112yes—
558C2×C4C2×#1175822412yes—
559C2×C4C24×D6111yescharacteristic
560C8—24no—
561C8—1224no—
562C22—614no—
563C22—1228no—
564C22—1222no—
565C22—1222no—
566C22#1684027212yes—
567C22#137×D6112yes—
568C22C2×#1451980912yes—
569C22C22×D4×D6111yescharacteristic
570C4—22no—
571C4—24no—
572C4—42no—
573C4—44no—
574C4—1222no—
575C4—1222no—
576C4—1222no—
577C4—1224no—
578C4—2442no—
579C4—2444no—
580C4#1684027212yes—
581C4C2×#1451980914yes—
582C4C2×#41×D6111yescharacteristic
583C4C22×#1175822411yescharacteristic
584C2—1224no—
585C2#2145594814yesdirect product factor
586C2C2×#1684027211yescharacteristic
587C2C2×#137×D6111yescharacteristic
588C2C22×#1451980911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#462C2
socleC23×C61C22×D4
prime radicalC23×D61C2×D4
hypercenterC2×#462D61
hypocenterC61C2×#3113
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
3. #21455948C2direct (N × H)
5. C2×#16840048C2semidirect
6. C2×#16840047C2semidirect
7. C2×#16839969C2semidirect
9. C2×#16839869C2semidirect
10. C2×#16839866C2semidirect
12. C2×C61×#462C2semidirect
36. #16840048C22semidirect
37. #16840047C22semidirect
38. #16839969C22semidirect
40. #16839869C22semidirect
41. #16839866C22semidirect
54. C61×#462C22semidirect
297. C2×#462D61semidirect
302. C2×C61#3113semidirect
336. #462C2×D61semidirect
351. C61C2×#3113semidirect
585. C2#21455948direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403172
C2×C4×Q8×D612
#214559482
C2×#168400912
C2×#168400482
C2×#168400472
C2×#168399692
C2×#168399162
C2×#168398692
C2×#168398662
C2×#168398182
C2×C61×#4622
C2×#311361