Finite Group Databasebeta

← C2×#21462010 #30616490

Subgroups — C2×#21462010 #30616490

Order 15616.

1698 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840704C211yesmaximal, characteristic
2C2×C4×C22⋊#6923C211yesmaximal, characteristic
3#21462010C218yesmaximal, direct product factor
4C2×#16840640C212yesmaximal
5C2×#16840640C212yesmaximal
6C22×#14519755C211yesmaximal, characteristic
7C22×C4⋊#6923—21no—
8C22×C22⋊#6923C2212yes—
9C22×C22⋊#6923C2212yes—
10C22×C4×#6923—21no—
11#16840704—22no—
12#16840704C2214yes—
13C4×C22⋊#6923—22no—
14C4×C22⋊#6923C2214yes—
15C2×(C2×#6923)⋊C4—21no—
16C2×(C2×#6923)⋊C4—21no—
17#16840640C2218yes—
18#16840640C2218yes—
19C23×Dic122C411yescharacteristic, complemented
20C23×C4×D61C2211yescharacteristic
21C2×#14519755—21no—
22C2×#14519755—21no—
23C2×#14519755—22no—
24C2×#14519755—21no—
25C2×#14519755—21no—
26C2×#14519755—22no—
27C2×#14519755C414yescomplemented
28C2×#14519755C2214yes—
29C22×#11758196C411yescharacteristic, complemented
30C22×#11758196C411yescharacteristic, complemented
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×C4⋊C4×C61C411yescharacteristic, complemented
34C23×#6923—22no—
35C23×#6923—22no—
36C2×C4⋊#6923—24no—
37C2×C4⋊#6923—44no—
38C2×C22⋊#6923—22no—
39C2×C22⋊#6923—24no—
40C2×C22⋊#6923—28no—
41C2×C22⋊#6923—22no—
42C2×C22⋊#6923Q818yescomplemented
43C2×C22⋊#6923C2314yes—
44C2×C22⋊#6923C2314yes—
45C2×C4×#6923—24no—
46C2×C4×#6923—44no—
47(C2×#6923)⋊C4—24no—
48(C2×#6923)⋊C4—24no—
49C24×D61C2311yescharacteristic
50C22×Dic122—21no—
51C22×Dic122—22no—
52C22×Dic122—21no—
53C22×Dic122—44no—
54C22×Dic122C2×C414yescomplemented
55C23×Dic61C2×C411yescharacteristic
56C23×Dic61C2×C411yescharacteristic
57C23×Dic61C2×C411yescharacteristic
58C22×C4×D61—44no—
59C22×C4×D61C2×C412yes—
60C22×C4×D61D411yescharacteristic
61C22×C4×D61D411yescharacteristic
62C22×C4×D61D412yes—
63C22×C4×D61D411yescharacteristic
64C22×C4×D61D411yescharacteristic
65C22×C4×D61D412yes—
66C22×C4×D61C2312yes—
67#14519755—24no—
68#14519755—24no—
69#14519755—24no—
70#14519755—24no—
71#14519755—24no—
72#14519755—24no—
73#14519755—24no—
74#14519755—24no—
75C2×#11758196—21no—
76C2×#11758196—21no—
77C2×#11758196—22no—
78C2×#11758196—22no—
79C2×#11758196—21no—
80C2×#11758196—21no—
81C2×#11758196C2×C414yescomplemented
82C2×#11758196C2×C414yescomplemented
83C2×#11758198—21no—
84C2×#11758198—21no—
85C2×#11758198—21no—
86C2×#11758198—21no—
87C2×#11758198—21no—
88C2×#11758198—21no—
89C2×#11758198—21no—
90C2×#11758198—21no—
91C2×#11758198C2×C412yes—
92C2×#11758198C2×C412yes—
93C2×#11758198C2312yes—
94C2×#11758198C2312yes—
95C23×C4×C61C2×C411yescharacteristic
96C23×C4×C61C2×C411yescharacteristic
97C23×C4×C61C2×C411yescharacteristic
98C2×C4⋊C4×C61—21no—
99C2×C4⋊C4×C61—21no—
100C2×C4⋊C4×C61—22no—
101C2×C4⋊C4×C61C2×C414yescomplemented
102C24×C61C22×C411yescharacteristic
103C23×D61—42no—
104C23×D61—42no—
105C23×D61C22×C411yescharacteristic
106C23×D61C2×D411yescharacteristic
107C23×D61C2×D411yescharacteristic
108C23×D61C2×D411yescharacteristic
109C23×D61C2×D411yescharacteristic
110C23×D61C2×Q814yes—
111C23×D61#4114yes—
112C23×D61C2411yescharacteristic
113C22×#6923—28no—
114C22×#6923—24no—
115C22×#6923—24no—
116C22×#6923—44no—
117C22×#6923—44no—
118C22×#6923—44no—
119C22×#6923—44no—
120C22×#6923—44no—
121C22×C4×C61—21no—
122C22×C4×C61—21no—
123C22×C4×C61—21no—
124C22×C4×C61—21no—
125C22×C4×C61—42no—
126C22×C4×C61—42no—
127C22×C4×C61—42no—
128C22×C4×C61C22⋊C411yescharacteristic
129C22×C4×C61C22⋊C411yescharacteristic
130C22×C4×C61C22⋊C412yes—
131C22×C4×C61C22×C412yes—
132C22×C4×C61C22×C412yes—
133C22×C4×C61C22×C412yes—
134C22×Dic61—24no—
135C22×Dic61—21no—
136C22×Dic61—21no—
137C22×Dic61—21no—
138C22×Dic61—21no—
139C22×Dic61—42no—
140C22×Dic61—42no—
141C22×Dic61C22⋊C411yescharacteristic
142C22×Dic61C22⋊C412yes—
143C22×Dic61C22⋊C411yescharacteristic
144C22×Dic61C22×C412yes—
145C22×Dic61C22×C412yes—
146C22×Dic61C22×C412yes—
147C2×C4×D61—24no—
148C2×C4×D61—24no—
149C2×C4×D61—44no—
150C2×C4×D61—44no—
151C2×C4×D61—44no—
152C2×C4×D61—44no—
153C2×C4×D61—42no—
154C2×C4×D61—42no—
155C2×C4×D61C22⋊C412yes—
156C2×C4×D61C22⋊C412yes—
157C2×C4×D61C22⋊C412yes—
158C2×C4×D61C22⋊C412yes—
159C2×C4×D61C2×D412yes—
160C2×C4×D61C2×D412yes—
161C2×C4×D61C2×D412yes—
162C2×C4×D61C2×D412yes—
163C2×Dic122—24no—
164C2×Dic122—24no—
165C2×Dic122—44no—
166C2×Dic122—48no—
167C2×Dic122—44no—
168C2×Dic122—48no—
169C22⋊#6923—28no—
170C22⋊#6923—24no—
171C22⋊#6923—28no—
172C22⋊#6923—44no—
173C22⋊#6923C2×Q818yescomplemented
174C4⋊#6923—48no—
175C4×#6923—48no—
176C4⋊C4×C61—24no—
177C4⋊C4×C61—24no—
178#11758198—22no—
179#11758198—22no—
180#11758198—22no—
181#11758198—22no—
182#11758198—22no—
183#11758198—22no—
184#11758198—22no—
185#11758198—22no—
186#11758196—24no—
187#11758196—24no—
188#11758196—24no—
189#11758196—24no—
190C23×C61—22no—
191C23×C61—22no—
192C23×C61C2×C22⋊C411yescharacteristic
193C23×C61C2×C22⋊C411yescharacteristic
194C23×C61C4×Q814yes—
195C23×C61C23×C411yescharacteristic
196C22×D61—22no—
197C22×D61—22no—
198C22×D61—22no—
199C22×D61—22no—
200C22×D61—41no—
201C22×D61—41no—
202C22×D61—41no—
203C22×D61—41no—
204C22×D61—41no—
205C22×D61—41no—
206C22×D61—41no—
207C22×D61—48no—
208C22×D61—48no—
209C22×D61—41no—
210C22×D61C2×C22⋊C411yescharacteristic
211C22×D61C2×C22⋊C411yescharacteristic
212C22×D61C4×Q814yes—
213C22×D61C22⋊Q814yes—
214C22×D61C22⋊Q814yes—
215C22×D61#12412yes—
216C22×D61#12412yes—
217C22×D61C4⋊Q812yes—
218C22×D61C4⋊Q812yes—
219C22×D61C22×D411yescharacteristic
220C22×D61C22×D411yescharacteristic
221C22×D61C22×Q812yes—
222C22×D61C2×#4112yes—
223C2×#6923—28no—
224C2×#6923—44no—
225C2×#6923—44no—
226C2×#6923—416no—
227C2×#6923—44no—
228C2×#6923—44no—
229C2×#6923—44no—
230C2×#6923—88no—
231C2×C4×C61—22no—
232C2×C4×C61—22no—
233C2×C4×C61—22no—
234C2×C4×C61—22no—
235C2×C4×C61—42no—
236C2×C4×C61—42no—
237C2×C4×C61—42no—
238C2×C4×C61—42no—
239C2×C4×C61—42no—
240C2×C4×C61—42no—
241C2×C4×C61—42no—
242C2×C4×C61—42no—
243C2×C4×C61C2×C22⋊C412yes—
244C2×C4×C61C2×C22⋊C412yes—
245C2×Dic61—22no—
246C2×Dic61—24no—
247C2×Dic61—24no—
248C2×Dic61—22no—
249C2×Dic61—22no—
250C2×Dic61—42no—
251C2×Dic61—42no—
252C2×Dic61—42no—
253C2×Dic61—42no—
254C2×Dic61—42no—
255C2×Dic61—42no—
256C2×Dic61#9914yes—
257C2×Dic61C2×C22⋊C412yes—
258C2×Dic61C2×C22⋊C412yes—
259C4×D61—24no—
260C4×D61—24no—
261C4×D61—24no—
262C4×D61—24no—
263C4×D61—42no—
264C4×D61—42no—
265C4×D61—42no—
266C4×D61—42no—
267Dic122—48no—
268Dic122—48no—
269C2×#1996—611nomaximal, Sylow
270C22×C61—21no—
271C22×C61—21no—
272C22×C61—21no—
273C22×C61—21no—
274C22×C61—28no—
275C22×C61#39112yes—
276C22×C61#39112yes—
277C22×C61C2×#9912yes—
278C22×C61#41012yes—
279C22×C61C22×C22⋊C411yescharacteristic
280C22×C61C2×C4×Q812yes—
281C2×D61—21no—
282C2×D61—21no—
283C2×D61—21no—
284C2×D61—21no—
285C2×D61—21no—
286C2×D61—21no—
287C2×D61—21no—
288C2×D61—21no—
289C2×D61—28no—
290C2×D61—24no—
291C2×D61—24no—
292C2×D61—44no—
293C2×D61—44no—
294C2×D61—42no—
295C2×D61—42no—
296C2×D61—42no—
297C2×D61—42no—
298C2×D61#39112yes—
299C2×D61#39112yes—
300C2×D61C2×C22⋊Q812yes—
301C2×D61C2×#12411yescharacteristic
302C2×D61C2×C4⋊Q811yescharacteristic
303#6923—48no—
304#6923—84no—
305C4×C61—22no—
306C4×C61—22no—
307C4×C61—42no—
308C4×C61—42no—
309Dic61—22no—
310Dic61—42no—
311Dic61—42no—
312Dic61C2×#9914yes—
313C22×C22⋊Q8—611no—
314C2×#380—611no—
315C2×C4×C22⋊C4—611no—
316#1996—618no—
317C2×#342—612no—
318C2×#342—612no—
319C2×C61—22no—
320C2×C61—22no—
321C2×C61#199614yescomplemented
322C2×C61C2×#39111yescharacteristic
323C2×C61C22×#9911yescharacteristic
324C2×C61C2×#41011yescharacteristic
325D61—22no—
326D61—21no—
327D61—21no—
328D61—22no—
329D61—22no—
330C23×Q8—611no—
331C24×C4—611no—
332C2×C22⋊Q8—614no—
333C2×C22⋊Q8—614no—
334C2×C22⋊Q8—1221no—
335C2×C22⋊Q8—1221no—
336C2×C22⋊Q8—1221no—
337C2×C22⋊Q8—1221no—
338C2×C22⋊Q8—1222no—
339C2×C22⋊Q8—1222no—
340C22×C4⋊C4—611no—
341C22×C4⋊C4—611no—
342C22×C4⋊C4—1221no—
343C22×C4⋊C4#692311yescharacteristic, complemented
344C22×C22⋊C4—612no—
345C22×C22⋊C4—611no—
346C22×C22⋊C4—611no—
347C22×C22⋊C4—612no—
348C22×C42—1221no—
349#380—614no—
350#380—1222no—
351C4×C22⋊C4—614no—
352C4×C22⋊C4—1222no—
353C2×#95—1221no—
354C2×#95—1221no—
355#342—618no—
356#342—618no—
357C61C2×#199611yescharacteristic, complemented, Sylow
358C25—611no—
359C22×Q8—614no—
360C22×Q8—1222no—
361C22×Q8—1221no—
362C22×Q8—1221no—
363C22×Q8—2444no—
364C23×C4—611no—
365C23×C4—611no—
366C23×C4—611no—
367C23×C4—611no—
368C23×C4—611no—
369C23×C4—612no—
370C23×C4—612no—
371C23×C4—612no—
372C23×C4—612no—
373C23×C4—611no—
374C23×C4—611no—
375C23×C4—1222no—
376C23×C4—1222no—
377C23×C4—2444no—
378C23×C4C2×#692311yescharacteristic
379C23×C4C2×#692311yescharacteristic
380C23×C4C2×#692311yescharacteristic
381C22⋊Q8—1224no—
382C22⋊Q8—1224no—
383C22⋊Q8—1224no—
384C22⋊Q8—1224no—
385C22⋊Q8—1224no—
386C22⋊Q8—1224no—
387C22⋊Q8—1224no—
388C22⋊Q8—1224no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—614no—
393C2×C4⋊C4—614no—
394C2×C4⋊C4—1222no—
395C2×C4⋊C4—1221no—
396C2×C4⋊C4—1221no—
397C2×C4⋊C4—1222no—
398C2×C4⋊C4—1221no—
399C2×C4⋊C4—1221no—
400C2×C4⋊C4—1224no—
401C2×C4⋊C4—2444no—
402C2×C4⋊C4C2×#692314yescomplemented
403C2×C22⋊C4—618no—
404C2×C22⋊C4—614no—
405C2×C22⋊C4—612no—
406C2×C22⋊C4—612no—
407C2×C22⋊C4—612no—
408C2×C22⋊C4—612no—
409C2×C22⋊C4—614no—
410C2×C22⋊C4—1221no—
411C2×C22⋊C4—1221no—
412C2×C22⋊C4—1221no—
413C2×C22⋊C4—1221no—
414C2×C22⋊C4—1221no—
415C2×C22⋊C4—1221no—
416C2×C22⋊C4—1221no—
417C2×C22⋊C4—1221no—
418C2×C22⋊C4—1224no—
419C2×C22⋊C4—1222no—
420C2×C22⋊C4—1228no—
421C2×C22⋊C4—1222no—
422C2×C42—1224no—
423C2×C42—2444no—
424#95—1224no—
425#95—1224no—
426C24—611no—
427C24—611no—
428C24—611no—
429C24—611no—
430C24—614no—
431C24—614no—
432C24—611no—
433C24—611no—
434C24—2442no—
435C24—2442no—
436C24C22×#692311yescharacteristic
437C2×Q8—1224no—
438C2×Q8—1224no—
439C2×Q8—2444no—
440C2×Q8—2448no—
441C2×Q8—2448no—
442C2×Q8—2444no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—611no—
451C22×C4—612no—
452C22×C4—611no—
453C22×C4—612no—
454C22×C4—612no—
455C22×C4—612no—
456C22×C4—612no—
457C22×C4—612no—
458C22×C4—612no—
459C22×C4—612no—
460C22×C4—612no—
461C22×C4—612no—
462C22×C4—612no—
463C22×C4—612no—
464C22×C4—1224no—
465C22×C4—1224no—
466C22×C4—1224no—
467C22×C4—1224no—
468C22×C4—1228no—
469C22×C4—1221no—
470C22×C4—1221no—
471C22×C4—1221no—
472C22×C4—1221no—
473C22×C4—1224no—
474C22×C4—2442no—
475C22×C4—2442no—
476C22×C4—2444no—
477C22×C4—2444no—
478C22×C4—2444no—
479C22×C4—2444no—
480C22×C4—2444no—
481C22×C4—2444no—
482C22×C4—2444no—
483C22×C4—2444no—
484C22×C4—2444no—
485C22×C4—2442no—
486C22×C4—2442no—
487C22×C4C22⋊#692311yescharacteristic
488C22×C4C22⋊#692311yescharacteristic
489C22×C4C22⋊#692312yes—
490C22×C4C22×#692312yes—
491C22×C4C22×#692312yes—
492C22×C4C22×#692312yes—
493C4⋊C4—24no—
494C4⋊C4—24no—
495C4⋊C4—1224no—
496C4⋊C4—1224no—
497C4⋊C4—1224no—
498C4⋊C4—1224no—
499C4⋊C4—2448no—
500C22⋊C4—618no—
501C22⋊C4—1222no—
502C22⋊C4—1222no—
503C22⋊C4—1222no—
504C22⋊C4—1222no—
505C22⋊C4—1222no—
506C22⋊C4—1222no—
507C22⋊C4—1222no—
508C22⋊C4—1222no—
509C22⋊C4—1228no—
510C22⋊C4—1224no—
511C22⋊C4—1228no—
512C22⋊C4—2444no—
513C42—2448no—
514C23—22no—
515C23—22no—
516C23—614no—
517C23—612no—
518C23—612no—
519C23—611no—
520C23—611no—
521C23—611no—
522C23—611no—
523C23—614no—
524C23—612no—
525C23—612no—
526C23—614no—
527C23—612no—
528C23—612no—
529C23—1222no—
530C23—1222no—
531C23—1222no—
532C23—1222no—
533C23—2441no—
534C23—2441no—
535C23—2441no—
536C23—2441no—
537C23—2441no—
538C23—2441no—
539C23—2441no—
540C23—2441no—
541C23—2448no—
542C23—2448no—
543C23C2×C22⋊#692311yescharacteristic
544C23C2×C22⋊#692311yescharacteristic
545C23Q8×#692314yes—
546C23C23×#692311yescharacteristic
547Q8—2448no—
548Q8—2448no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—614no—
562C2×C4—612no—
563C2×C4—612no—
564C2×C4—1224no—
565C2×C4—1224no—
566C2×C4—1224no—
567C2×C4—1224no—
568C2×C4—1224no—
569C2×C4—1224no—
570C2×C4—1222no—
571C2×C4—1228no—
572C2×C4—1222no—
573C2×C4—1222no—
574C2×C4—4888no—
575C2×C4—2442no—
576C2×C4—2442no—
577C2×C4—2442no—
578C2×C4—2442no—
579C2×C4—2444no—
580C2×C4—2444no—
581C2×C4—2444no—
582C2×C4—2442no—
583C2×C4—2442no—
584C2×C4—2444no—
585C2×C4—2444no—
586C2×C4—24416no—
587C2×C4—2442no—
588C2×C4—2442no—
589C2×C4—2442no—
590C2×C4—2442no—
591C2×C4C2×C22⋊#692312yes—
592C2×C4C2×C22⋊#692312yes—
593C22—21no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—28no—
598C22—612no—
599C22—611no—
600C22—611no—
601C22—612no—
602C22—612no—
603C22—1221no—
604C22—1221no—
605C22—1221no—
606C22—1221no—
607C22—1221no—
608C22—1221no—
609C22—1221no—
610C22—1221no—
611C22—1224no—
612C22—1228no—
613C22—1224no—
614C22—2442no—
615C22—2444no—
616C22—2442no—
617C22—2442no—
618C22—2442no—
619C22—2444no—
620C22(C2×#6923)⋊Q812yes—
621C22(C2×#6923)⋊Q812yes—
622C22D61⋊#9912yes—
623C22#1684074112yes—
624C22C22×C22⋊#692311yescharacteristic
625C22C2×Q8×#692312yes—
626C4—22no—
627C4—22no—
628C4—42no—
629C4—42no—
630C4—614no—
631C4—1222no—
632C4—4884no—
633C4—2448no—
634C4—2442no—
635C4—2442no—
636C2—22no—
637C2—22no—
638C2—1221no—
639C2—1222no—
640C2—1221no—
641C2—1222no—
642C2—1222no—
643C2#2146201014yesdirect product factor
644C2C2×(C2×#6923)⋊Q811yescharacteristic
645C2C2×D61⋊#9911yescharacteristic
646C2C2×#1684074111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC22×C4⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC24×D61C23
cosocleC23×D61C24
hypercenterC22×C4⋊C4#6923
hypocenterC61C2×#1996
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #21462010C2direct (N × H)
19. C23×Dic122C4semidirect
27. C2×#14519755C4semidirect
29. C22×#11758196C4semidirect
30. C22×#11758196C4semidirect
33. C22×C4⋊C4×C61C4semidirect
42. C2×C22⋊#6923Q8semidirect
54. C22×Dic122C2×C4semidirect
81. C2×#11758196C2×C4semidirect
82. C2×#11758196C2×C4semidirect
101. C2×C4⋊C4×C61C2×C4semidirect
173. C22⋊#6923C2×Q8semidirect
321. C2×C61#1996semidirect
343. C22×C4⋊C4#6923semidirect
357. C61C2×#1996semidirect
402. C2×C4⋊C4C2×#6923semidirect
643. C2#21462010direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407042
C2×C4×C22⋊#69232
#214620102
C2×#168406402
C22×#145197552
C2×#199661