Finite Group Databasebeta

← C2×#21446974 #29707372

Subgroups — C2×#21446974 #29707372

Order 15616.

1454 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840390C211yesmaximal, characteristic, complemented
2C2×#16839768C211yesmaximal, characteristic
3C2×#16839766C211yesmaximal, characteristic
4C2×#16839664C211yesmaximal, characteristic
5#21446974C218yesmaximal, direct product factor
6C2×#16839530C211yesmaximal, characteristic, complemented
7C2×#16839522C211yesmaximal, characteristic, complemented
8C2×C61×#339C211yesmaximal, characteristic, complemented
9C23×D244C2211yescharacteristic
10C22×#11758194C2211yescharacteristic
11#16840390—22no—
12#16840390—22no—
13#16840390—22no—
14#16840390C2214yescomplemented
15C2×#14519777—21no—
16C2×#14519776—21no—
17C2×#14519769—21no—
18C2×#14519768—21no—
19C2×#14519754—22no—
20C2×#14519736C2211yescharacteristic
21C22×C4⋊Dic61C2211yescharacteristic
22C22×#11758198—22no—
23#16839768—22no—
24#16839768C2214yes—
25#16839766—22no—
26#16839766C2214yes—
27C2×#14519699—21no—
28C2×#14519699—21no—
29C2×#14519697—21no—
30C2×#14519697—21no—
31#16839664—22no—
32#16839664C2214yes—
33#16839530C2214yescomplemented
34#16839522C2214yescomplemented
35C22×M16×C61C2211yescharacteristic
36C2×#117×C61C2211yescharacteristic
37C22×C42×C61C2211yescharacteristic
38C61×#339C2214yescomplemented
39C24×D61—21no—
40C22×Dic122—22no—
41C22×D244—21no—
42C22×D244—21no—
43C22×D244—21no—
44C22×D244—21no—
45C22×D244—22no—
46C22×D244—22no—
47C22×D244—21no—
48C22×D244—22no—
49C22×D244Q814yescomplemented
50C22×D244C2312yes—
51C23×Dic61D412yes—
52C2×#11758194—21no—
53C2×#11758194—22no—
54C2×#11758194—22no—
55C2×#11758194C2312yes—
56C22×#92418—21no—
57#14519777—24no—
58#14519777—24no—
59#14519776—24no—
60#14519776—24no—
61#14519769—24no—
62#14519769—24no—
63#14519768—24no—
64#14519768—24no—
65#14519754—28no—
66#14519754—28no—
67#14519736—21no—
68#14519736—21no—
69#14519736D412yes—
70#14519736C2312yes—
71C2×C4⋊Dic61—22no—
72C2×C4⋊Dic61—21no—
73C2×C4⋊Dic61—21no—
74C2×C4⋊Dic61—21no—
75C2×C4⋊Dic61—21no—
76C2×C4⋊Dic61D412yes—
77C2×C4⋊Dic61D411yescharacteristic
78C2×C4⋊Dic61D411yescharacteristic
79C2×C4⋊Dic61C2312yes—
80C2×#11758196—22no—
81C2×#11758196—22no—
82C2×C22⋊Dic61—21no—
83C2×#11758198—28no—
84C2×#11758198—48no—
85C2×C4×Dic61—21no—
86#14519699—24no—
87#14519699—24no—
88#14519697—24no—
89#14519697—24no—
90C23×C4×C61—21no—
91C23×C4×C61C2311yescharacteristic
92C2×M16×C61—21no—
93C2×M16×C61—22no—
94C2×M16×C61—22no—
95C2×M16×C61C2312yes—
96C22×C8×C61—21no—
97#117×C61—21no—
98#117×C61—21no—
99#117×C61D412yes—
100#117×C61C2312yes—
101C2×C4⋊C4×C61D411yescharacteristic
102C2×C4⋊C4×C61D411yescharacteristic
103C2×C22⋊C4×C61—21no—
104C2×C42×C61—21no—
105C2×C42×C61—22no—
106C2×C42×C61—22no—
107C2×C42×C61—21no—
108C2×C42×C61C2312yes—
109C24×C61C2×D411yescharacteristic
110C23×D61—24no—
111C23×D61—22no—
112C23×D61—44no—
113C23×D61—44no—
114C23×D61—41no—
115C23×D61—41no—
116C23×D61—42no—
117C22×C4×C61—24no—
118C22×C4×C61—21no—
119C22×C4×C61—21no—
120C22×C4×C61—22no—
121C22×C4×C61—42no—
122C22×C4×C61—42no—
123C22×C4×C61C2×D411yescharacteristic
124C22×C4×C61C2×D411yescharacteristic
125C22×C4×C61C2×D411yescharacteristic
126C22×C4×C61C2×D411yescharacteristic
127C22×C4×C61C2×D411yescharacteristic
128C22×C4×C61C2×Q812yes—
129C22×C4×C61#4112yes—
130C22×C4×C61#4112yes—
131C22×C4×C61#4112yes—
132C22×C4×C61C2411yescharacteristic
133C22×Dic61—22no—
134C22×Dic61—21no—
135C22×Dic61—21no—
136C22×Dic61—22no—
137C22×Dic61—44no—
138C22×Dic61C2×D414yes—
139C2×D244—24no—
140C2×D244—24no—
141C2×D244—24no—
142C2×D244—24no—
143C2×D244—22no—
144C2×D244—22no—
145C2×D244—22no—
146C2×D244—22no—
147C2×D244—24no—
148C2×D244—22no—
149C2×D244—41no—
150C2×D244—41no—
151C2×D244—42no—
152C2×D244—42no—
153C2×D244—42no—
154C2×D244—42no—
155C2×D244—42no—
156C2×D244C2×Q814yescomplemented
157C2×Dic122—28no—
158C2×Dic122—84no—
159M16×C61—22no—
160M16×C61—22no—
161M16×C61—42no—
162C2×C8×C61—22no—
163C2×C8×C61—42no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61C2×D412yes—
167C4⋊C4×C61C2×D412yes—
168C22⋊C4×C61—22no—
169C22⋊C4×C61—22no—
170C42×C61—22no—
171C42×C61—22no—
172C42×C61—22no—
173C42×C61—22no—
174C42×C61—42no—
175C22⋊Dic61—22no—
176C22⋊Dic61—22no—
177#11758198—416no—
178C4⋊Dic61—28no—
179C4⋊Dic61—22no—
180C4⋊Dic61—22no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—22no—
184C4⋊Dic61—22no—
185C4⋊Dic61C2×D412yes—
186C4⋊Dic61C2×D412yes—
187#11758196—28no—
188#11758196—28no—
189C4×Dic61—22no—
190C4×Dic61—22no—
191#11758194—22no—
192#11758194—22no—
193#11758194—42no—
194C2×#92418—22no—
195C2×#92418—42no—
196C23×C61—22no—
197C23×C61—22no—
198C23×C61#12011yescharacteristic
199C23×C61#12011yescharacteristic
200C23×C61C22⋊Q812yes—
201C23×C61#12412yes—
202C23×C61C22×D411yescharacteristic
203C22×D61—24no—
204C22×D61—44no—
205C22×D61—44no—
206C22×D61—416no—
207C22×D61—42no—
208C22×D61—42no—
209C22×D61—44no—
210C22×D61—44no—
211C22×D61—82no—
212C22×D61—82no—
213C22×D61—88no—
214C22×D61—82no—
215C22×D61—82no—
216C2×C4×C61—24no—
217C2×C4×C61—22no—
218C2×C4×C61—22no—
219C2×C4×C61—42no—
220C2×C4×C61—48no—
221C2×C4×C61—42no—
222C2×C4×C61—42no—
223C2×C4×C61—42no—
224C2×C4×C61#12011yescharacteristic
225C2×C4×C61#12011yescharacteristic
226C2×C4×C61C22⋊Q812yes—
227C2×C4×C61C22⋊Q812yes—
228C2×C4×C61C22⋊Q812yes—
229C2×C4×C61C22⋊Q812yes—
230C2×C4×C61C22⋊Q812yes—
231C2×C4×C61#12412yes—
232C2×C4×C61#12412yes—
233C2×C4×C61#12412yes—
234C2×C4×C61#12412yes—
235C2×C4×C61#12412yes—
236C2×C4×C61C22×D411yescharacteristic
237C2×C4×C61C22×D411yescharacteristic
238C2×C4×C61C22×Q811yescharacteristic
239C2×C4×C61C2×#4111yescharacteristic
240C2×C4×C61C2×#4111yescharacteristic
241C2×C4×C61C2×#4111yescharacteristic
242C2×Dic61—22no—
243C2×Dic61—22no—
244C2×Dic61—24no—
245C2×Dic61—42no—
246C2×Dic61—44no—
247C2×Dic61—42no—
248C2×Dic61—44no—
249C2×Dic61—82no—
250D244—24no—
251D244—24no—
252D244—42no—
253D244—42no—
254D244—44no—
255D244—44no—
256Dic122—88no—
257C8×C61—42no—
258#92418—42no—
259C2×#2027—611nomaximal, Sylow
260C22×C61—21no—
261C22×C61—21no—
262C22×C61—21no—
263C22×C61—21no—
264C22×C61—24no—
265C22×C61—24no—
266C22×C61#39312yes—
267C22×C61#39312yes—
268C22×C61#45312yes—
269C22×C61#45412yes—
270C22×C61C2×#12011yescharacteristic
271C22×C61C2×C22⋊Q811yescharacteristic
272C22×C61C2×#12411yescharacteristic
273C2×D61—48no—
274C2×D61—44no—
275C2×D61—84no—
276C2×D61—88no—
277C2×D61—82no—
278C2×D61—82no—
279C2×D61—88no—
280C4×C61—44no—
281C4×C61—42no—
282C4×C61—42no—
283C4×C61#39312yes—
284C4×C61#39312yes—
285C4×C61C2×C22⋊Q811yescharacteristic
286C4×C61C2×C22⋊Q811yescharacteristic
287C4×C61C2×#12411yescharacteristic
288C4×C61C2×#12411yescharacteristic
289Dic61—42no—
290Dic61—44no—
291Dic61—42no—
292C2×#544—611no—
293C2×#418—611no—
294C2×#418—611no—
295C2×#390—611no—
296#2027—618no—
297C2×#343—611no—
298C2×#339—611no—
299C2×#339D6111yescharacteristic, complemented
300C2×C61—21no—
301C2×C61—21no—
302C2×C61—22no—
303C2×C61#202714yescomplemented
304C2×C61C2×#39311yescharacteristic
305C2×C61C2×#45311yescharacteristic
306C2×C61C2×#45411yescharacteristic
307D61—84no—
308C23×D4—611no—
309C22×M16—611no—
310C22×M16C2×D6111yescharacteristic
311#544—614no—
312#544—1222no—
313#544—1222no—
314#544—1222no—
315C2×C4⋊Q8—1221no—
316C2×C4⋊Q8—1221no—
317C2×#125—1221no—
318C2×#125—1221no—
319C2×C22⋊Q8—1222no—
320C2×#117—611no—
321C2×#117C2×D6111yescharacteristic
322C22×C4⋊C4—611no—
323C22×C22⋊C4—1222no—
324C22×C42C2×D6111yescharacteristic
325#418—614no—
326#418—614no—
327#418—1222no—
328#418—1222no—
329C2×#102—1221no—
330C2×#102—1221no—
331C2×#102—1221no—
332C2×#102—1221no—
333#390—614no—
334#390—1222no—
335#343—614no—
336#339—614no—
337#339C2×D6114yescomplemented
338C61C2×#202711yescharacteristic, complemented, Sylow
339C25—1221no—
340C22×Q8—1222no—
341C22×D4—614no—
342C22×D4—612no—
343C22×D4—1221no—
344C22×D4—1221no—
345C22×D4—1222no—
346C22×D4—1222no—
347C22×D4—1221no—
348C22×D4—1221no—
349C22×D4—1221no—
350C22×D4—1222no—
351C23×C4—21no—
352C23×C4—612no—
353C23×C4C22×D6111yescharacteristic
354C2×M16—21no—
355C2×M16—22no—
356C2×M16—22no—
357C2×M16—612no—
358C2×M16—1221no—
359C2×M16—1222no—
360C2×M16—1222no—
361C2×M16C22×D6112yes—
362C22×C8—21no—
363C22×C8—1221no—
364C4⋊Q8—1224no—
365C4⋊Q8—1224no—
366C4⋊Q8—1224no—
367C4⋊Q8—1224no—
368#125—1224no—
369#125—1224no—
370#125—1224no—
371#125—1224no—
372C22⋊Q8—1228no—
373C22⋊Q8—1228no—
374#117—21no—
375#117—21no—
376#117—612no—
377#117—612no—
378#117—1221no—
379#117—1221no—
380#117D24412yes—
381#117C22×D6112yes—
382C2×C4⋊C4—611no—
383C2×C4⋊C4—611no—
384C2×C4⋊C4—612no—
385C2×C4⋊C4—612no—
386C2×C4⋊C4—1222no—
387C2×C4⋊C4—1222no—
388C2×C4⋊C4—1222no—
389C2×C4⋊C4—1221no—
390C2×C4⋊C4—1221no—
391C2×C4⋊C4—1221no—
392C2×C4⋊C4—1221no—
393C2×C4⋊C4D24411yescharacteristic
394C2×C4⋊C4D24411yescharacteristic
395C2×C22⋊C4—21no—
396C2×C22⋊C4—1221no—
397C2×C22⋊C4—1228no—
398C2×C22⋊C4—2448no—
399C2×C42—21no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—21no—
403C2×C42—1221no—
404C2×C42C22×D6112yes—
405#102—1224no—
406#102—1224no—
407#102—1224no—
408#102—1224no—
409C24—1222no—
410C24—1224no—
411C24—2444no—
412C24—2444no—
413C24—2441no—
414C24—2441no—
415C24—2442no—
416C24D4×D6111yescharacteristic
417C2×Q8—1228no—
418C2×Q8—4884no—
419C2×D4—614no—
420C2×D4—1222no—
421C2×D4—1222no—
422C2×D4—1222no—
423C2×D4—1222no—
424C2×D4—1222no—
425C2×D4—1224no—
426C2×D4—1224no—
427C2×D4—1224no—
428C2×D4—1224no—
429C2×D4—1224no—
430C2×D4—2441no—
431C2×D4—2441no—
432C2×D4—2442no—
433C2×D4—2442no—
434C2×D4—2442no—
435C2×D4—2442no—
436C2×D4—2442no—
437C22×C4—24no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—614no—
444C22×C4—1222no—
445C22×C4—1221no—
446C22×C4—1221no—
447C22×C4—1222no—
448C22×C4—2444no—
449C22×C4C2×D24411yescharacteristic
450C22×C4C2×D24411yescharacteristic
451C22×C4#1175822212yes—
452C22×C4#1175822212yes—
453C22×C4D4×D6111yescharacteristic
454C22×C4D4×D6111yescharacteristic
455C22×C4D4×D6111yescharacteristic
456C22×C4#1175822412yes—
457C22×C4Q8×D6112yes—
458C22×C4C23×D6111yescharacteristic
459M16—22no—
460M16—22no—
461M16—42no—
462M16—1222no—
463M16—1222no—
464M16—2442no—
465C2×C8—22no—
466C2×C8—42no—
467C2×C8—1222no—
468C2×C8—2442no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—612no—
472C4⋊C4—612no—
473C4⋊C4—1228no—
474C4⋊C4—1228no—
475C4⋊C4—1228no—
476C4⋊C4—1222no—
477C4⋊C4—1222no—
478C4⋊C4—1222no—
479C4⋊C4—1222no—
480C4⋊C4—1221no—
481C4⋊C4—1221no—
482C4⋊C4C2×D24412yes—
483C4⋊C4C2×D24412yes—
484C22⋊C4—22no—
485C22⋊C4—22no—
486C22⋊C4—1222no—
487C22⋊C4—1222no—
488C22⋊C4—24416no—
489C42—22no—
490C42—22no—
491C42—22no—
492C42—22no—
493C42—42no—
494C42—1222no—
495C42—1222no—
496C23—22no—
497C23—22no—
498C23—1224no—
499C23—4882no—
500C23—4882no—
501C23—4888no—
502C23—4882no—
503C23—4882no—
504C23—2444no—
505C23—2444no—
506C23—24416no—
507C23—2442no—
508C23—2442no—
509C23—2444no—
510C23—2444no—
511C23#1451974711yescharacteristic
512C23#1451974711yescharacteristic
513C23#1451975512yes—
514C23#1451976312yes—
515C23C2×D4×D6111yescharacteristic
516Q8—4888no—
517D4—1224no—
518D4—1224no—
519D4—2442no—
520D4—2442no—
521D4—2444no—
522D4—2444no—
523C2×C4—24no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—42no—
527C2×C4—48no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—1222no—
532C2×C4—1222no—
533C2×C4—1224no—
534C2×C4—4882no—
535C2×C4—2442no—
536C2×C4—2444no—
537C2×C4—2442no—
538C2×C4—2444no—
539C2×C4#1451974711yescharacteristic
540C2×C4#1451974711yescharacteristic
541C2×C4#1451975512yes—
542C2×C4#1451975512yes—
543C2×C4#1451975512yes—
544C2×C4#1451975712yes—
545C2×C4#1451975712yes—
546C2×C4#1451976312yes—
547C2×C4#1451976312yes—
548C2×C4#1451976312yes—
549C2×C4#1451976512yes—
550C2×C4#1451976512yes—
551C2×C4C2×D4×D6111yescharacteristic
552C2×C4C22×D24411yescharacteristic
553C2×C4C2×Q8×D6111yescharacteristic
554C2×C4C2×#1175822411yescharacteristic
555C2×C4C2×#1175822211yescharacteristic
556C2×C4C2×#1175822211yescharacteristic
557C8—42no—
558C8—2442no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—24no—
564C22—24no—
565C22—4884no—
566C22—4888no—
567C22—4882no—
568C22—4882no—
569C22—4888no—
570C22—2448no—
571C22—2444no—
572C22#1683967512yes—
573C22#1683967512yes—
574C22#1683993112yes—
575C22#1683993612yes—
576C22C2×#1451974711yescharacteristic
577C22C2×#1451975511yescharacteristic
578C22C2×#1451976311yescharacteristic
579C4—44no—
580C4—42no—
581C4—42no—
582C4—2444no—
583C4—2442no—
584C4—2442no—
585C4#1683967512yes—
586C4#1683967512yes—
587C4C2×#1451975511yescharacteristic
588C4C2×#1451975711yescharacteristic
589C4C2×#1451976311yescharacteristic
590C4C2×#1451976511yescharacteristic
591C2—21no—
592C2—22no—
593C2—21no—
594C2—4884no—
595C2#2144697414yesdirect product factor
596C2C2×#1683967511yescharacteristic
597C2C2×#1683993111yescharacteristic
598C2C2×#1683993611yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#339C2
socleC23×C61#120
prime radicalC23×D244C22
hypercenterC2×#339D61
hypocenterC61C2×#2027
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
1. C2×#16840390C2semidirect
5. #21446974C2direct (N × H)
6. C2×#16839530C2semidirect
7. C2×#16839522C2semidirect
8. C2×C61×#339C2semidirect
14. #16840390C22semidirect
33. #16839530C22semidirect
34. #16839522C22semidirect
38. C61×#339C22semidirect
49. C22×D244Q8semidirect
156. C2×D244C2×Q8semidirect
299. C2×#339D61semidirect
303. C2×C61#2027semidirect
337. #339C2×D61semidirect
338. C61C2×#2027semidirect
595. C2#21446974direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403902
C2×#168397682
C2×#168397662
C2×#168396642
#214469742
C2×#168395302
C2×#168395222
C2×C61×#3392
C2×#202761