Finite Group Databasebeta

← C2×#21447471 #29832748

Subgroups — C2×#21447471 #29832748

Order 15616.

1214 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840334C211yesmaximal, characteristic
2C2×#16839743C211yesmaximal, characteristic
3C2×#16839734C211yesmaximal, characteristic
4#21447471C218yesmaximal, direct product factor
5C2×#16839553C211yesmaximal, characteristic, complemented
6C2×#16839552C211yesmaximal, characteristic, complemented
7C2×#16839551C211yesmaximal, characteristic, complemented
8C2×C61×#352C211yesmaximal, characteristic, complemented
9C22×#11758224C2211yescharacteristic
10C23×Dic122C411yescharacteristic, complemented
11C2×M16×D61—21no—
12#16840334—22no—
13#16840334—22no—
14#16840334C414yescomplemented
15#16840334C2214yes—
16C2×#14519776—21no—
17C2×#14519763—21no—
18C2×#14519761C411yescharacteristic, complemented
19C2×#14519760C411yescharacteristic, complemented
20C2×#14519758C2211yescharacteristic
21C2×#14519755—21no—
22C2×#14519754—21no—
23C2×#14519733—21no—
24C2×#14519733C411yescharacteristic, complemented
25#16839743—22no—
26#16839743C2214yes—
27C2×#14519695—21no—
28C2×#14519694C2211yescharacteristic
29#16839734—22no—
30#16839734C2214yes—
31C2×#14519692C2211yescharacteristic
32C2×#14519691—21no—
33#16839553C2214yescomplemented
34#16839552C2214yescomplemented
35#16839551C2214yescomplemented
36C2×#123×C61C2211yescharacteristic
37C2×#100×C61C2211yescharacteristic
38C2×#99×C61C2211yescharacteristic
39C61×#352C2214yescomplemented
40C2×#11758224—41no—
41C2×#11758224—42no—
42C2×#11758224—41no—
43C2×#11758224C2×C412yes—
44C2×#11758224D412yes—
45C2×#11758224D412yes—
46C2×#11758224C2312yes—
47C22×Dic122—21no—
48C22×Dic122—21no—
49C22×Dic122—22no—
50C22×Dic122—42no—
51C22×Dic122—41no—
52C22×Dic122—41no—
53C22×Dic122C2×C414yescomplemented
54C22×Dic122D411yescharacteristic
55C22×C22⋊D61C2×C411yescharacteristic
56C22×C22⋊D61D411yescharacteristic
57C23×Dic61C2×C411yescharacteristic
58C23×Dic61C2×C411yescharacteristic
59C23×Dic61D411yescharacteristic
60C22×C4×D61D411yescharacteristic
61C2×#11758194—21no—
62C2×#11758189—41no—
63M16×D61—24no—
64M16×D61—42no—
65C2×C8×D61—41no—
66#14519776—24no—
67#14519776—24no—
68#14519763—24no—
69#14519763—24no—
70#14519761—22no—
71#14519761C2×C414yescomplemented
72#14519760—22no—
73#14519760C2×C414yescomplemented
74#14519758—21no—
75#14519758—21no—
76#14519758C2×C412yes—
77#14519758C2312yes—
78#14519755—24no—
79#14519755—24no—
80#14519754—24no—
81#14519754—24no—
82#14519733—22no—
83#14519733—24no—
84#14519733—42no—
85#14519733C2×C414yescomplemented
86C2×C4⋊Dic61—21no—
87C2×#11758196—21no—
88C2×#11758196—21no—
89C2×#11758196—21no—
90C2×#11758196—41no—
91C2×C22⋊Dic61—21no—
92C2×C22⋊Dic61—21no—
93C2×C22⋊Dic61C2×C411yescharacteristic
94C2×#11758198—21no—
95C2×#11758198—21no—
96C2×C4×Dic61—21no—
97C2×C4×Dic61—41no—
98#14519695—24no—
99#14519694—21no—
100#14519694C2312yes—
101#14519692—21no—
102#14519692C2312yes—
103#14519691—24no—
104C22×D4×C61C2311yescharacteristic
105C23×C4×C61C2×C411yescharacteristic
106C2×M16×C61—21no—
107#123×C61—21no—
108#123×C61—21no—
109#123×C61C2×C412yes—
110#123×C61C2312yes—
111C2×C4⋊C4×C61—21no—
112C2×C22⋊C4×C61—21no—
113C2×C22⋊C4×C61—21no—
114C2×C22⋊C4×C61C2×C411yescharacteristic
115#100×C61—21no—
116#100×C61C2312yes—
117#99×C61—21no—
118#99×C61C2312yes—
119C24×C61C22×C411yescharacteristic
120C24×C61C2×D411yescharacteristic
121C23×D61C22⋊C411yescharacteristic
122C2×D4×C61—41no—
123C2×D4×C61—41no—
124C2×D4×C61C22×C411yescharacteristic
125C2×D4×C61C2×D411yescharacteristic
126C2×D4×C61C2×D411yescharacteristic
127C2×D4×C61C2411yescharacteristic
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61—41no—
132C22×C4×C61—41no—
133C22×C4×C61—41no—
134C22×C4×C61C22×C412yes—
135C22×C4×C61C2×D411yescharacteristic
136C2×C22⋊D61—41no—
137C2×C22⋊D61—41no—
138C2×C22⋊D61—41no—
139C2×C22⋊D61—41no—
140C2×C22⋊D61C22⋊C412yes—
141C2×C22⋊D61C22⋊C412yes—
142C2×C22⋊D61C22×C412yes—
143C2×C22⋊D61C2×D412yes—
144C22×Dic61—22no—
145C22×Dic61—21no—
146C22×Dic61—21no—
147C22×Dic61—21no—
148C22×Dic61—21no—
149C22×Dic61—22no—
150C22×Dic61—21no—
151C22×Dic61—21no—
152C22×Dic61—21no—
153C22×Dic61—41no—
154C22×Dic61—41no—
155C22×Dic61—41no—
156C22×Dic61C22⋊C411yescharacteristic
157C22×Dic61C22⋊C412yes—
158C22×Dic61C22⋊C411yescharacteristic
159C22×Dic61C22⋊C412yes—
160C22×Dic61C22⋊C411yescharacteristic
161C22×Dic61C22×C412yes—
162C22×Dic61C22×C412yes—
163C22×Dic61C2×D412yes—
164#11758224—42no—
165#11758224—42no—
166#11758224—42no—
167#11758224—42no—
168#11758224—42no—
169#11758224—42no—
170#11758224—42no—
171#11758224—42no—
172C2×C4×D61—21no—
173C2×C4×D61—22no—
174C2×C4×D61—21no—
175C2×C4×D61C22⋊C412yes—
176C2×C4×D61C2×D412yes—
177C2×Dic122—24no—
178C2×Dic122—24no—
179C2×Dic122—41no—
180C2×Dic122—41no—
181C2×Dic122—42no—
182C2×Dic122—42no—
183C2×Dic122—44no—
184C2×Dic122—44no—
185C2×Dic122—42no—
186C2×Dic122—41no—
187C2×Dic122—41no—
188C2×Dic122—44no—
189C2×Dic122—44no—
190C2×Dic122C22⋊C412yes—
191C2×Dic122C2×D412yes—
192M16×C61—22no—
193M16×C61—41no—
194C2×C8×C61—41no—
195C4⋊C4×C61—22no—
196C4⋊C4×C61—22no—
197C22⋊C4×C61—22no—
198C22⋊C4×C61—21no—
199C22⋊C4×C61—22no—
200C22⋊C4×C61—22no—
201C22⋊C4×C61—41no—
202C22⋊C4×C61C22×C412yes—
203C22⋊Dic61—22no—
204C22⋊Dic61—21no—
205C22⋊Dic61—22no—
206C22⋊Dic61—22no—
207C22⋊Dic61—41no—
208C22⋊Dic61C22×C412yes—
209#11758198—24no—
210#11758198—24no—
211C4⋊Dic61—24no—
212#11758196—22no—
213#11758196—22no—
214#11758196—24no—
215#11758196—24no—
216#11758196—44no—
217C4×Dic61—24no—
218C4×Dic61—44no—
219#11758194—22no—
220#11758194—41no—
221C2×#92418—41no—
222#11758189—44no—
223C8×D61—44no—
224C23×C61—21no—
225C23×C61—21no—
226C23×C61—21no—
227C23×C61—21no—
228C23×C61—42no—
229C23×C61—42no—
230C23×C61C2×C22⋊C411yescharacteristic
231C23×C61C2×C22⋊C411yescharacteristic
232C23×C61C2×C22⋊C411yescharacteristic
233C23×C61C23×C411yescharacteristic
234C23×C61C22×D411yescharacteristic
235C22×D61—21no—
236C22×D61—21no—
237C22×D61—42no—
238C22×D61C2×C22⋊C412yes—
239D4×C61—41no—
240D4×C61—41no—
241D4×C61—41no—
242D4×C61—41no—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61—22no—
246C2×C4×C61—22no—
247C2×C4×C61—42no—
248C2×C4×C61—42no—
249C2×C4×C61—41no—
250C2×C4×C61—41no—
251C2×C4×C61—42no—
252C2×C4×C61—42no—
253C2×C4×C61—82no—
254C2×C4×C61C2×C22⋊C411yescharacteristic
255C2×C4×C61C22×D411yescharacteristic
256C22⋊D61—42no—
257C22⋊D61—42no—
258C22⋊D61—42no—
259C22⋊D61—42no—
260C2×Dic61—21no—
261C2×Dic61—21no—
262C2×Dic61—21no—
263C2×Dic61—21no—
264C2×Dic61—22no—
265C2×Dic61—22no—
266C2×Dic61—22no—
267C2×Dic61—22no—
268C2×Dic61—22no—
269C2×Dic61—22no—
270C2×Dic61—22no—
271C2×Dic61—22no—
272C2×Dic61—22no—
273C2×Dic61—22no—
274C2×Dic61—42no—
275C2×Dic61—42no—
276C2×Dic61—41no—
277C2×Dic61—41no—
278C2×Dic61—42no—
279C2×Dic61—42no—
280C2×Dic61—82no—
281C2×Dic61#9912yes—
282C2×Dic61#9911yescharacteristic
283C2×Dic61#9911yescharacteristic
284C2×Dic61C2×C22⋊C412yes—
285C2×Dic61C2×C22⋊C412yes—
286C2×Dic61C2×C22⋊C412yes—
287C4×D61—22no—
288C4×D61—22no—
289C4×D61—22no—
290C4×D61—22no—
291Dic122—42no—
292Dic122—42no—
293Dic122—48no—
294Dic122—44no—
295Dic122—44no—
296C8×C61—42no—
297#92418—42no—
298C2×#2123—611nomaximal, Sylow
299C22×C61—22no—
300C22×C61—21no—
301C22×C61—21no—
302C22×C61—21no—
303C22×C61—21no—
304C22×C61—41no—
305C22×C61—41no—
306C22×C61—41no—
307C22×C61—41no—
308C22×C61—42no—
309C22×C61—42no—
310C22×C61—42no—
311C22×C61—81no—
312C22×C61C2×#9911yescharacteristic
313C22×C61C2×#9911yescharacteristic
314C22×C61C22×C22⋊C411yescharacteristic
315C2×D61—22no—
316C2×D61—42no—
317C2×D61—42no—
318C2×D61—81no—
319C4×C61—21no—
320C4×C61—21no—
321C4×C61—42no—
322C4×C61—42no—
323C4×C61—82no—
324Dic61—22no—
325Dic61—22no—
326Dic61—42no—
327Dic61—42no—
328Dic61—82no—
329Dic61C2×#9912yes—
330Dic61C2×#9912yes—
331C2×#536—611no—
332C2×#413—611no—
333C2×#410—611no—
334#2123—618no—
335C2×#352—611no—
336C2×#352—611no—
337C2×#352—611no—
338C2×#352D6111yescharacteristic, complemented
339C2×C61—21no—
340C2×C61—21no—
341C2×C61—41no—
342C2×C61—41no—
343C2×C61—41no—
344C2×C61—41no—
345C2×C61#212312yescomplemented
346C2×C61C22×#9911yescharacteristic
347D61—42no—
348C22×#41—611no—
349C23×Q8—611no—
350C22×M16—1221no—
351#536—614no—
352#536—614no—
353#536—1222no—
354#536—1222no—
355C2×C4⋊Q8—1221no—
356C2×#124—1221no—
357C2×#123—611no—
358C2×#123—611no—
359C2×#123—611no—
360C2×#123C2×D6111yescharacteristic
361C2×C22⋊Q8—1221no—
362C2×C22⋊Q8—1221no—
363C2×#117—611no—
364C2×#117—1221no—
365#413—614no—
366#413—1222no—
367C2×#101—1221no—
368C2×#100—611no—
369C2×#100C2×D6111yescharacteristic
370#410—614no—
371#410—1222no—
372C2×#99—611no—
373C2×#99—1221no—
374C2×#99C2×D6111yescharacteristic
375#352—614no—
376#352—614no—
377#352—614no—
378#352C2×D6114yescomplemented
379C61C2×#212311yescharacteristic, complemented, Sylow
380C2×#41—612no—
381C2×#41—612no—
382C2×#41—612no—
383C2×#41—612no—
384C2×#41—2441no—
385C2×#41—2441no—
386C2×#41—2442no—
387C22×Q8—614no—
388C22×Q8—611no—
389C22×Q8—1221no—
390C22×Q8—1221no—
391C22×Q8—1222no—
392C22×Q8—2442no—
393C22×Q8—2441no—
394C22×Q8—2441no—
395C22×D4—611no—
396C22×D4—611no—
397C22×D4C22×D6111yescharacteristic
398C23×C4—611no—
399C23×C4—611no—
400C23×C4—611no—
401C23×C4—611no—
402C23×C4C4×D6111yescharacteristic
403C2×M16—21no—
404C2×M16—1224no—
405C2×M16—1221no—
406C2×M16—2441no—
407C2×M16—2442no—
408C22×C8—2441no—
409C4⋊Q8—1224no—
410C4⋊Q8—1224no—
411#124—1224no—
412#124—1224no—
413#123—21no—
414#123—21no—
415#123—612no—
416#123—612no—
417#123—614no—
418#123—614no—
419#123—1222no—
420#123—1222no—
421#123—1221no—
422#123—1221no—
423#123C4×D6112yes—
424#123C22×D6112yes—
425C22⋊Q8—1224no—
426C22⋊Q8—1224no—
427C22⋊Q8—1224no—
428C22⋊Q8—1224no—
429#117—614no—
430#117—1222no—
431#117—1224no—
432#117—2442no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—1221no—
435C2×C4⋊C4—1221no—
436C2×C4⋊C4—1221no—
437C2×C4⋊C4—1221no—
438C2×C4⋊C4—2441no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—611no—
442C2×C22⋊C4—1221no—
443C2×C22⋊C4—1221no—
444C2×C22⋊C4—1221no—
445C2×C22⋊C4—1221no—
446C2×C22⋊C4C4×D6111yescharacteristic
447C2×C42—1221no—
448C2×C42—2441no—
449#101—1224no—
450#100—21no—
451#100—612no—
452#100—1221no—
453#100C22×D6112yes—
454#99—21no—
455#99—612no—
456#99—1224no—
457#99—1221no—
458#99C22×D6112yes—
459C24—611no—
460C24C2×C4×D6111yescharacteristic
461C24D4×D6111yescharacteristic
462#41—2442no—
463#41—2442no—
464#41—2442no—
465#41—2442no—
466#41—2442no—
467#41—2442no—
468#41—2442no—
469#41—2442no—
470C2×Q8—612no—
471C2×Q8—612no—
472C2×Q8—1224no—
473C2×Q8—1224no—
474C2×Q8—2441no—
475C2×Q8—2441no—
476C2×Q8—2442no—
477C2×Q8—2441no—
478C2×Q8—2441no—
479C2×Q8—2444no—
480C2×Q8—2444no—
481C2×Q8—2444no—
482C2×Q8—2444no—
483C2×Q8—2442no—
484C2×Q8—2442no—
485C2×D4—41no—
486C2×D4—41no—
487C2×D4—612no—
488C2×D4—612no—
489C2×D4—612no—
490C2×D4—612no—
491C2×D4—2441no—
492C2×D4—2441no—
493C2×D4—2441no—
494C2×D4—2441no—
495C2×D4C2×C4×D6111yescharacteristic
496C2×D4D4×D6111yescharacteristic
497C2×D4D4×D6111yescharacteristic
498C2×D4C23×D6111yescharacteristic
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—611no—
506C22×C4—612no—
507C22×C4—612no—
508C22×C4—612no—
509C22×C4—612no—
510C22×C4—611no—
511C22×C4—611no—
512C22×C4—612no—
513C22×C4—612no—
514C22×C4—612no—
515C22×C4—1221no—
516C22×C4—1222no—
517C22×C4—1221no—
518C22×C4—1221no—
519C22×C4—1221no—
520C22×C4—1222no—
521C22×C4—1222no—
522C22×C4—1221no—
523C22×C4—1221no—
524C22×C4—1221no—
525C22×C4—1221no—
526C22×C4—1221no—
527C22×C4—2441no—
528C22×C4—2441no—
529C22×C4—2441no—
530C22×C4C2×C4×D6112yes—
531C22×C4D4×D6111yescharacteristic
532M16—22no—
533M16—41no—
534M16—1222no—
535M16—2444no—
536M16—2441no—
537C2×C8—41no—
538C2×C8—2444no—
539C2×C8—2441no—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—1224no—
543C4⋊C4—1224no—
544C4⋊C4—1224no—
545C4⋊C4—1222no—
546C4⋊C4—1222no—
547C4⋊C4—2444no—
548C22⋊C4—22no—
549C22⋊C4—22no—
550C22⋊C4—21no—
551C22⋊C4—22no—
552C22⋊C4—41no—
553C22⋊C4—612no—
554C22⋊C4—1224no—
555C22⋊C4—1224no—
556C22⋊C4—1222no—
557C22⋊C4—1221no—
558C22⋊C4—1222no—
559C22⋊C4—1222no—
560C22⋊C4—2441no—
561C22⋊C4C2×C4×D6112yes—
562C42—1224no—
563C42—2444no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—42no—
569C23—42no—
570C23—612no—
571C23—1221no—
572C23—1221no—
573C23—2442no—
574C23C22⋊C4×D6111yescharacteristic
575C23C22⋊C4×D6111yescharacteristic
576C23C22⋊C4×D6111yescharacteristic
577C23C22×C4×D6111yescharacteristic
578C23C2×D4×D6111yescharacteristic
579Q8—2442no—
580Q8—2442no—
581Q8—2444no—
582Q8—2444no—
583Q8—2448no—
584D4—41no—
585D4—41no—
586D4—41no—
587D4—41no—
588D4—2442no—
589D4—2442no—
590D4—2442no—
591D4—2442no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—82no—
603C2×C4—612no—
604C2×C4—612no—
605C2×C4—611no—
606C2×C4—611no—
607C2×C4—612no—
608C2×C4—612no—
609C2×C4—1222no—
610C2×C4—1222no—
611C2×C4—1222no—
612C2×C4—1222no—
613C2×C4—1222no—
614C2×C4—1222no—
615C2×C4—1222no—
616C2×C4—1222no—
617C2×C4—1222no—
618C2×C4—1222no—
619C2×C4—1222no—
620C2×C4—1222no—
621C2×C4—1221no—
622C2×C4—1221no—
623C2×C4—1221no—
624C2×C4—1221no—
625C2×C4—1222no—
626C2×C4—1222no—
627C2×C4—4882no—
628C2×C4—2442no—
629C2×C4—2442no—
630C2×C4—2442no—
631C2×C4—2441no—
632C2×C4—2441no—
633C2×C4—2442no—
634C2×C4C22⋊C4×D6111yescharacteristic
635C2×C4C2×D4×D6111yescharacteristic
636C8—42no—
637C8—2442no—
638C22—22no—
639C22—21no—
640C22—21no—
641C22—21no—
642C22—21no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22—42no—
648C22—42no—
649C22—42no—
650C22—81no—
651C22—1222no—
652C22—4881no—
653C22—2442no—
654C22—2442no—
655C22#99×D6111yescharacteristic
656C22#99×D6111yescharacteristic
657C22C2×C22⋊C4×D6111yescharacteristic
658C4—21no—
659C4—21no—
660C4—42no—
661C4—42no—
662C4—82no—
663C4—612no—
664C4—612no—
665C4—1222no—
666C4—1222no—
667C4—4882no—
668C4—2442no—
669C4—2442no—
670C2—21no—
671C2—21no—
672C2—41no—
673C2—41no—
674C2—41no—
675C2—41no—
676C2—2442no—
677C2#2144747112yesdirect product factor
678C2C2×#99×D6111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC23×C61C23×C4
FrattiniC2×D4C23×D61
FittingC2×C61×#352C2
socleC22×C61C2×#99
prime radicalC22×#11758224C22
cosocleC2×D4×C61C24
hypercenterC2×#352D61
hypocenterC61C2×#2123
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#352

Complements

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

NH ≅ G/Ntype
4. #21447471C2direct (N × H)
5. C2×#16839553C2semidirect
6. C2×#16839552C2semidirect
7. C2×#16839551C2semidirect
8. C2×C61×#352C2semidirect
10. C23×Dic122C4semidirect
14. #16840334C4semidirect
18. C2×#14519761C4semidirect
19. C2×#14519760C4semidirect
24. C2×#14519733C4semidirect
33. #16839553C22semidirect
34. #16839552C22semidirect
35. #16839551C22semidirect
39. C61×#352C22semidirect
53. C22×Dic122C2×C4semidirect
71. #14519761C2×C4semidirect
73. #14519760C2×C4semidirect
85. #14519733C2×C4semidirect
338. C2×#352D61semidirect
345. C2×C61#2123semidirect
378. #352C2×D61semidirect
379. C61C2×#2123semidirect
677. C2#21447471direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403342
C2×#168397432
C2×#168397342
#214474712
C2×#168395532
C2×#168395522
C2×#168395512
C2×C61×#3522
C2×#212361