Finite Group Databasebeta

← C2×#21444181 #29645982

Subgroups — C2×#21444181 #29645982

Order 15616.

1426 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519755C211yesmaximal, characteristic
2C2×#16839724C211yesmaximal, characteristic
3C2×C22⋊C8×D61C211yesmaximal, characteristic
4#21444181C218yesmaximal, direct product factor
5C2×#16839488C211yesmaximal, characteristic, complemented
6C2×#16839487C211yesmaximal, characteristic, complemented
7C2×#16839487C211yesmaximal, characteristic, complemented
8C2×C61×#324C211yesmaximal, characteristic, complemented
9C23×Dic122C411yescharacteristic
10C23×C4×D61C2211yescharacteristic
11C22×#11758189—21no—
12C22×C8×D61—21no—
13C2×#14519755—21no—
14C2×#14519755—21no—
15C2×#14519755—22no—
16C2×#14519755—21no—
17C2×#14519755—21no—
18C2×#14519755—22no—
19C2×#14519755C414yes—
20C2×#14519755C2214yes—
21C22×#11758196C411yescharacteristic
22C22×#11758196C2211yescharacteristic
23C22×#11758198C411yescharacteristic
24C22×#11758198C411yescharacteristic
25#16839724—22no—
26#16839724C2214yes—
27C2×C22⋊#92418C2211yescharacteristic
28C2×C22⋊#92418C2211yescharacteristic
29C2×#14519689—21no—
30C2×#14519689—21no—
31C22⋊C8×D61—22no—
32C22⋊C8×D61C2214yes—
33#16839488C2214yescomplemented
34#16839487C2214yescomplemented
35#16839487C2214yescomplemented
36C22×C4⋊C4×C61C2211yescharacteristic
37C2×C22⋊C8×C61C2211yescharacteristic
38C2×C22⋊C8×C61C2211yescharacteristic
39C61×#324C2214yescomplemented
40C24×D61C2×C411yescharacteristic
41C22×Dic122—21no—
42C22×Dic122—22no—
43C22×Dic122—21no—
44C22×Dic122—44no—
45C22×Dic122C2×C414yes—
46C23×Dic61C2×C411yescharacteristic
47C23×Dic61C2×C411yescharacteristic
48C23×Dic61C2×C411yescharacteristic
49C22×C4×D61—44no—
50C22×C4×D61C2×C412yes—
51C22×C4×D61D411yescharacteristic
52C22×C4×D61D411yescharacteristic
53C22×C4×D61D412yes—
54C22×C4×D61D411yescharacteristic
55C22×C4×D61D411yescharacteristic
56C22×C4×D61D412yes—
57C22×C4×D61C2312yes—
58C2×#11758189—24no—
59C2×#11758189—44no—
60C22×#92418—21no—
61C22×#92418—21no—
62C2×C8×D61—24no—
63C2×C8×D61—44no—
64#14519755—24no—
65#14519755—24no—
66#14519755—24no—
67#14519755—24no—
68#14519755—24no—
69#14519755—24no—
70#14519755—24no—
71#14519755—24no—
72C2×#11758196—21no—
73C2×#11758196—21no—
74C2×#11758196—21no—
75C2×#11758196—21no—
76C2×#11758196—22no—
77C2×#11758196—21no—
78C2×#11758196—21no—
79C2×#11758196C2×C414yes—
80C2×#11758196C2×C412yes—
81C2×#11758196C2312yes—
82C2×#11758198—21no—
83C2×#11758198—22no—
84C2×#11758198—21no—
85C2×#11758198—21no—
86C2×#11758198—22no—
87C2×#11758198—21no—
88C2×#11758198C2×C414yes—
89C2×#11758198C2×C414yes—
90C22⋊#92418—21no—
91C22⋊#92418—21no—
92C22⋊#92418C2312yes—
93C22⋊#92418C2312yes—
94#14519689—24no—
95#14519689—24no—
96C23×C4×C61C2×C411yescharacteristic
97C23×C4×C61C2×C411yescharacteristic
98C23×C4×C61C2311yescharacteristic
99C22×C8×C61—21no—
100C22×C8×C61—21no—
101C2×C4⋊C4×C61—21no—
102C2×C4⋊C4×C61—21no—
103C2×C4⋊C4×C61—21no—
104C2×C4⋊C4×C61—21no—
105C2×C4⋊C4×C61C2×C412yes—
106C2×C4⋊C4×C61C2312yes—
107C22⋊C8×C61—21no—
108C22⋊C8×C61—21no—
109C22⋊C8×C61C2312yes—
110C22⋊C8×C61C2312yes—
111C24×C61C22×C411yescharacteristic
112C23×D61—22no—
113C23×D61—22no—
114C23×D61—24no—
115C23×D61—42no—
116C23×D61C22⋊C411yescharacteristic
117C23×D61C22⋊C412yes—
118C23×D61C22⋊C411yescharacteristic
119C23×D61C22×C412yes—
120C22×C4×C61—21no—
121C22×C4×C61—21no—
122C22×C4×C61—21no—
123C22×C4×C61—21no—
124C22×C4×C61—22no—
125C22×C4×C61—22no—
126C22×C4×C61—42no—
127C22×C4×C61—42no—
128C22×C4×C61C22×C412yes—
129C22×C4×C61C22×C412yes—
130C22×C4×C61C22×C411yescharacteristic
131C22×C4×C61C2×D411yescharacteristic
132C22×C4×C61C2×D411yescharacteristic
133C22×C4×C61C2×D411yescharacteristic
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2411yescharacteristic
136C22×Dic61—24no—
137C22×Dic61—21no—
138C22×Dic61—21no—
139C22×Dic61—21no—
140C22×Dic61—21no—
141C22×Dic61—22no—
142C22×Dic61—22no—
143C22×Dic61—42no—
144C22×Dic61C22⋊C411yescharacteristic
145C22×Dic61C22⋊C412yes—
146C22×Dic61C22⋊C411yescharacteristic
147C22×Dic61C22×C412yes—
148C22×Dic61C22×C412yes—
149C22×Dic61C22×C412yes—
150C2×C4×D61—24no—
151C2×C4×D61—24no—
152C2×C4×D61—44no—
153C2×C4×D61—44no—
154C2×C4×D61—44no—
155C2×C4×D61—44no—
156C2×C4×D61—42no—
157C2×C4×D61—42no—
158C2×C4×D61C22⋊C412yes—
159C2×C4×D61C22⋊C412yes—
160C2×C4×D61C22⋊C412yes—
161C2×C4×D61C22⋊C412yes—
162C2×C4×D61C2×D412yes—
163C2×C4×D61C2×D412yes—
164C2×C4×D61C2×D412yes—
165C2×C4×D61C2×D412yes—
166C2×Dic122—24no—
167C2×Dic122—24no—
168C2×Dic122—44no—
169C2×Dic122—48no—
170C2×Dic122—44no—
171C2×Dic122—48no—
172C2×C8×C61—22no—
173C2×C8×C61—22no—
174C2×C8×C61—42no—
175C2×C8×C61—42no—
176C4⋊C4×C61—22no—
177C4⋊C4×C61—22no—
178C4⋊C4×C61—22no—
179C4⋊C4×C61—22no—
180#11758198—24no—
181#11758198—24no—
182#11758198—24no—
183#11758198—24no—
184#11758196—22no—
185#11758196—22no—
186#11758196—22no—
187#11758196—22no—
188#11758196—24no—
189#11758196—24no—
190C2×#92418—22no—
191C2×#92418—22no—
192C2×#92418—42no—
193C2×#92418—42no—
194#11758189—48no—
195C8×D61—48no—
196C23×C61—22no—
197C23×C61—22no—
198C23×C61C2×C22⋊C411yescharacteristic
199C23×C61C2×C22⋊C411yescharacteristic
200C23×C61#13112yes—
201C23×C61#13112yes—
202C23×C61C23×C411yescharacteristic
203C22×D61—22no—
204C22×D61—22no—
205C22×D61—22no—
206C22×D61—22no—
207C22×D61—24no—
208C22×D61—22no—
209C22×D61—22no—
210C22×D61—22no—
211C22×D61—24no—
212C22×D61—24no—
213C22×D61—42no—
214C22×D61—42no—
215C22×D61—48no—
216C22×D61—48no—
217C22×D61#10114yes—
218C22×D61C2×C22⋊C412yes—
219C22×D61C2×C22⋊C412yes—
220C2×C4×C61—22no—
221C2×C4×C61—22no—
222C2×C4×C61—22no—
223C2×C4×C61—22no—
224C2×C4×C61—22no—
225C2×C4×C61—22no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61—42no—
231C2×C4×C61—42no—
232C2×C4×C61—42no—
233C2×C4×C61—42no—
234C2×C4×C61—42no—
235C2×C4×C61C2×C22⋊C411yescharacteristic
236C2×C4×C61C2×C22⋊C411yescharacteristic
237C2×C4×C61C22×D411yescharacteristic
238C2×C4×C61C22×D411yescharacteristic
239C2×Dic61—22no—
240C2×Dic61—24no—
241C2×Dic61—24no—
242C2×Dic61—22no—
243C2×Dic61—22no—
244C2×Dic61—22no—
245C2×Dic61—22no—
246C2×Dic61—42no—
247C2×Dic61—42no—
248C2×Dic61—42no—
249C2×Dic61—42no—
250C2×Dic61—42no—
251C2×Dic61#9914yes—
252C2×Dic61C2×C22⋊C412yes—
253C2×Dic61C2×C22⋊C412yes—
254C4×D61—24no—
255C4×D61—24no—
256C4×D61—24no—
257C4×D61—24no—
258C4×D61—42no—
259C4×D61—42no—
260C4×D61—42no—
261C4×D61—42no—
262Dic122—48no—
263Dic122—48no—
264C8×C61—42no—
265C8×C61—42no—
266#92418—42no—
267#92418—42no—
268C2×#1472—611nomaximal, Sylow
269C22×C61—21no—
270C22×C61—21no—
271C22×C61—21no—
272C22×C61—21no—
273C22×C61—24no—
274C22×C61—24no—
275C22×C61#40812yes—
276C22×C61#40812yes—
277C22×C61C2×#9912yes—
278C22×C61C2×#10112yes—
279C22×C61C22×C22⋊C411yescharacteristic
280C22×C61C2×#13111yescharacteristic
281C22×C61C2×#13111yescharacteristic
282C2×D61—22no—
283C2×D61—22no—
284C2×D61—28no—
285C2×D61—22no—
286C2×D61—22no—
287C2×D61—22no—
288C2×D61—44no—
289C2×D61—44no—
290C2×D61—48no—
291C2×D61—44no—
292C2×D61C2×#10114yes—
293C4×C61—21no—
294C4×C61—21no—
295C4×C61—21no—
296C4×C61—21no—
297C4×C61—42no—
298C4×C61—42no—
299Dic61—22no—
300Dic61—42no—
301Dic61—42no—
302Dic61C2×#9914yes—
303C22×C22⋊Q8—611no—
304C2×#407—611no—
305C22×C22⋊C8—611no—
306#1472—618no—
307C2×#324—611no—
308C2×#324—611no—
309C2×#324—611no—
310C2×#324D6111yescharacteristic, complemented
311C2×C61—21no—
312C2×C61—21no—
313C2×C61—22no—
314C2×C61#147214yescomplemented
315C2×C61C2×#40811yescharacteristic
316C2×C61C22×#9911yescharacteristic
317C2×C61C22×#10111yescharacteristic
318D61—24no—
319D61—42no—
320C23×Q8—611no—
321C24×C4—611no—
322C22×M16—1221no—
323C23×C8—1221no—
324C2×C22⋊Q8—614no—
325C2×C22⋊Q8—614no—
326C2×C22⋊Q8—1221no—
327C2×C22⋊Q8—1221no—
328C2×C22⋊Q8—1222no—
329C2×C22⋊Q8—1221no—
330C2×C22⋊Q8—1221no—
331C2×C22⋊Q8—1222no—
332C22×C4⋊C4—611no—
333C22×C4⋊C4—611no—
334C22×C4⋊C4C2×D6111yescharacteristic
335C22×C22⋊C4—611no—
336C22×C22⋊C4—611no—
337#407—614no—
338#407—1222no—
339C2×C22⋊C8—611no—
340C2×C22⋊C8—611no—
341C2×C22⋊C8—614no—
342C2×C22⋊C8—1222no—
343C2×C22⋊C8—1221no—
344C2×C22⋊C8—1221no—
345C2×C22⋊C8C2×D6111yescharacteristic
346C2×C22⋊C8C2×D6111yescharacteristic
347#324—614no—
348#324—614no—
349#324—614no—
350#324C2×D6114yescomplemented
351C61C2×#147211yescharacteristic, complemented, Sylow
352C25—611no—
353C22×Q8—614no—
354C22×Q8—1222no—
355C22×Q8—1221no—
356C22×Q8—1221no—
357C22×Q8—2444no—
358C23×C4—611no—
359C23×C4—611no—
360C23×C4—611no—
361C23×C4—612no—
362C23×C4—612no—
363C23×C4—611no—
364C23×C4—611no—
365C23×C4—612no—
366C23×C4—612no—
367C23×C4—611no—
368C23×C4—611no—
369C23×C4—2444no—
370C23×C4C4×D6111yescharacteristic
371C23×C4C4×D6111yescharacteristic
372C23×C4C22×D6111yescharacteristic
373C2×M16—1224no—
374C2×M16—2444no—
375C22×C8—21no—
376C22×C8—21no—
377C22×C8—1224no—
378C22×C8—1221no—
379C22×C8—1221no—
380C22×C8—2444no—
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—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—614no—
394C2×C4⋊C4—612no—
395C2×C4⋊C4—612no—
396C2×C4⋊C4—1222no—
397C2×C4⋊C4—1221no—
398C2×C4⋊C4—1221no—
399C2×C4⋊C4—1221no—
400C2×C4⋊C4—1221no—
401C2×C4⋊C4—1221no—
402C2×C4⋊C4—1221no—
403C2×C4⋊C4C4×D6112yes—
404C2×C4⋊C4C22×D6112yes—
405C2×C22⋊C4—614no—
406C2×C22⋊C4—614no—
407C2×C22⋊C4—1222no—
408C2×C22⋊C4—1222no—
409C2×C22⋊C4—1221no—
410C2×C22⋊C4—1221no—
411C2×C22⋊C4—1221no—
412C2×C22⋊C4—1221no—
413C22⋊C8—21no—
414C22⋊C8—21no—
415C22⋊C8—612no—
416C22⋊C8—612no—
417C22⋊C8—1224no—
418C22⋊C8—1224no—
419C22⋊C8—1221no—
420C22⋊C8—1221no—
421C22⋊C8C22×D6112yes—
422C22⋊C8C22×D6112yes—
423C24—611no—
424C24—611no—
425C24—612no—
426C24—612no—
427C24—1224no—
428C24—1222no—
429C24—1222no—
430C24—2442no—
431C24C2×C4×D6111yescharacteristic
432C2×Q8—1224no—
433C2×Q8—1224no—
434C2×Q8—2444no—
435C2×Q8—2448no—
436C2×Q8—2448no—
437C2×Q8—2444no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—611no—
447C22×C4—612no—
448C22×C4—612no—
449C22×C4—611no—
450C22×C4—612no—
451C22×C4—612no—
452C22×C4—612no—
453C22×C4—612no—
454C22×C4—612no—
455C22×C4—612no—
456C22×C4—612no—
457C22×C4—612no—
458C22×C4—612no—
459C22×C4—612no—
460C22×C4—1224no—
461C22×C4—1224no—
462C22×C4—1224no—
463C22×C4—1221no—
464C22×C4—1221no—
465C22×C4—1221no—
466C22×C4—1221no—
467C22×C4—1222no—
468C22×C4—1222no—
469C22×C4—2442no—
470C22×C4—2442no—
471C22×C4—2444no—
472C22×C4—2444no—
473C22×C4—2444no—
474C22×C4—2444no—
475C22×C4—2442no—
476C22×C4C2×C4×D6112yes—
477C22×C4C2×C4×D6112yes—
478C22×C4C2×C4×D6111yescharacteristic
479C22×C4D4×D6111yescharacteristic
480C22×C4D4×D6111yescharacteristic
481C22×C4D4×D6111yescharacteristic
482C22×C4D4×D6111yescharacteristic
483C22×C4C23×D6111yescharacteristic
484M16—2448no—
485C2×C8—22no—
486C2×C8—22no—
487C2×C8—42no—
488C2×C8—42no—
489C2×C8—1222no—
490C2×C8—1222no—
491C2×C8—2448no—
492C2×C8—2442no—
493C2×C8—2442no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—1224no—
499C4⋊C4—1224no—
500C4⋊C4—1222no—
501C4⋊C4—1222no—
502C4⋊C4—1222no—
503C4⋊C4—1222no—
504C22⋊C4—1224no—
505C22⋊C4—1224no—
506C22⋊C4—1224no—
507C22⋊C4—1224no—
508C23—22no—
509C23—22no—
510C23—612no—
511C23—614no—
512C23—612no—
513C23—1224no—
514C23—1224no—
515C23—1222no—
516C23—1222no—
517C23—1224no—
518C23—1222no—
519C23—1222no—
520C23—1222no—
521C23—1222no—
522C23—1222no—
523C23—2442no—
524C23—2442no—
525C23—2448no—
526C23—2448no—
527C23C22⋊C4×D6111yescharacteristic
528C23C22⋊C4×D6111yescharacteristic
529C23#1451978312yes—
530C23#1451978512yes—
531C23C22×C4×D6111yescharacteristic
532Q8—2448no—
533Q8—2448no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—612no—
550C2×C4—614no—
551C2×C4—612no—
552C2×C4—1224no—
553C2×C4—1224no—
554C2×C4—1224no—
555C2×C4—1224no—
556C2×C4—1224no—
557C2×C4—1224no—
558C2×C4—1222no—
559C2×C4—1222no—
560C2×C4—1222no—
561C2×C4—1222no—
562C2×C4—1222no—
563C2×C4—2442no—
564C2×C4—2442no—
565C2×C4—2442no—
566C2×C4—2442no—
567C2×C4—2442no—
568C2×C4—2442no—
569C2×C4—2442no—
570C2×C4—2442no—
571C2×C4—2442no—
572C2×C4C22⋊C4×D6111yescharacteristic
573C2×C4C22⋊C4×D6111yescharacteristic
574C2×C4C2×D4×D6111yescharacteristic
575C2×C4C2×D4×D6111yescharacteristic
576C8—42no—
577C8—42no—
578C8—2442no—
579C8—2442no—
580C22—24no—
581C22—24no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—21no—
586C22—614no—
587C22—1228no—
588C22—1222no—
589C22—1222no—
590C22—1222no—
591C22—1222no—
592C22—1222no—
593C22—2448no—
594C22—2444no—
595C22—2444no—
596C22—2444no—
597C22#1683972712yes—
598C22#1683972712yes—
599C22#99×D6112yes—
600C22#101×D6112yes—
601C22C2×C22⋊C4×D6111yescharacteristic
602C22C2×#1451978311yescharacteristic
603C22C2×#1451978511yescharacteristic
604C4—21no—
605C4—21no—
606C4—21no—
607C4—21no—
608C4—42no—
609C4—42no—
610C4—614no—
611C4—1222no—
612C4—2442no—
613C4—2442no—
614C2—22no—
615C2—21no—
616C2—21no—
617C2—1224no—
618C2—2442no—
619C2#2144418114yesdirect product factor
620C2C2×#1683972711yescharacteristic
621C2C2×#99×D6111yescharacteristic
622C2C2×#101×D6111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#324C2
socleC23×C61C2×C22⋊C4
prime radicalC24×D61C2×C4
cosocleC22×C4×C61C24
hypercenterC2×#324D61
hypocenterC61C2×#1472
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
4. #21444181C2direct (N × H)
5. C2×#16839488C2semidirect
6. C2×#16839487C2semidirect
7. C2×#16839487C2semidirect
8. C2×C61×#324C2semidirect
33. #16839488C22semidirect
34. #16839487C22semidirect
35. #16839487C22semidirect
39. C61×#324C22semidirect
310. C2×#324D61semidirect
314. C2×C61#1472semidirect
350. #324C2×D61semidirect
351. C61C2×#1472semidirect
619. C2#21444181direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197552
C2×#168397242
C2×C22⋊C8×D612
#214441812
C2×#168394882
C2×#168394872
C2×C61×#3242
C2×#147261