Finite Group Databasebeta

← C2×#21447278 #29708949

Subgroups — C2×#21447278 #29708949

Order 15616.

1006 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839811C211yesmaximal, characteristic, complemented
2C2×#16839768C211yesmaximal, characteristic
3C2×#16839766C211yesmaximal, characteristic
4C22×#14519693C211yesmaximal, characteristic
5#21447278C218yesmaximal, direct product factor
6C2×#16839533C211yesmaximal, characteristic, complemented
7C2×#16839518C211yesmaximal, characteristic, complemented
8C2×C61×#344C211yesmaximal, characteristic, complemented
9C23×D244C2211yescharacteristic
10C22×#11758194C2211yescharacteristic
11C22×#11758194C2211yescharacteristic
12C2×#14519736C2211yescharacteristic
13#16839811—22no—
14#16839811C2214yescomplemented
15C2×#14519713—22no—
16#16839768—22no—
17#16839768C2214yes—
18#16839766—22no—
19#16839766C2214yes—
20C2×#14519699—22no—
21C2×#14519697—22no—
22C2×#14519693—22no—
23C2×#14519693—22no—
24C2×#14519693C2214yes—
25#16839533C2214yescomplemented
26#16839518C2214yescomplemented
27C22×M16×C61C2211yescharacteristic
28C22×M16×C61C2211yescharacteristic
29C2×#117×C61C2211yescharacteristic
30C61×#344C2214yescomplemented
31C24×D61—21no—
32C22×D244—21no—
33C22×D244—21no—
34C22×D244—21no—
35C22×D244—21no—
36C22×D244—21no—
37C22×D244—21no—
38C22×D244—21no—
39C22×D244—21no—
40C22×D244—21no—
41C22×D244—21no—
42C22×D244—21no—
43C22×D244D412yes—
44C22×D244D412yes—
45C22×D244C2312yes—
46C2×#11758194—21no—
47C2×#11758194—21no—
48C2×#11758194—21no—
49C2×#11758194—21no—
50C2×#11758194—21no—
51C2×#11758194—21no—
52C2×#11758194—21no—
53C2×#11758194—21no—
54C2×#11758194—21no—
55C2×#11758194—21no—
56C2×#11758194C2312yes—
57C2×#11758194C2312yes—
58C22×#92418—21no—
59C22×#92418—21no—
60#14519736—21no—
61#14519736—21no—
62#14519736—21no—
63#14519736C2312yes—
64C2×C4⋊Dic61—21no—
65C2×C22⋊Dic61—21no—
66C2×C4×Dic61—21no—
67#14519713—28no—
68#14519699—28no—
69#14519697—28no—
70#14519693—28no—
71C23×C4×C61C2311yescharacteristic
72C2×M16×C61—21no—
73C2×M16×C61—21no—
74C2×M16×C61—21no—
75C2×M16×C61—21no—
76C2×M16×C61—21no—
77C2×M16×C61—21no—
78C2×M16×C61—21no—
79C2×M16×C61—21no—
80C2×M16×C61—21no—
81C2×M16×C61D412yes—
82C2×M16×C61C2312yes—
83C2×M16×C61C2312yes—
84C22×C8×C61—21no—
85C22×C8×C61D412yes—
86#117×C61—21no—
87#117×C61—21no—
88#117×C61—21no—
89#117×C61C2312yes—
90C2×C4⋊C4×C61—21no—
91C2×C22⋊C4×C61—21no—
92C2×C42×C61—21no—
93C24×C61#4111yescharacteristic
94C23×D61—22no—
95C23×D61—22no—
96C23×D61—22no—
97C23×D61—41no—
98C23×D61—41no—
99C23×D61—41no—
100C23×D61—41no—
101C23×D61—84no—
102C22×C4×C61—41no—
103C22×C4×C61C2×D411yescharacteristic
104C22×C4×C61C2×D411yescharacteristic
105C22×C4×C61C2×D411yescharacteristic
106C22×C4×C61C2×D411yescharacteristic
107C22×C4×C61#4111yescharacteristic
108C22×C4×C61#4111yescharacteristic
109C22×C4×C61#4111yescharacteristic
110C22×C4×C61#4111yescharacteristic
111C22×C4×C61#4111yescharacteristic
112C22×C4×C61#4111yescharacteristic
113C22×C4×C61#4111yescharacteristic
114C22×C4×C61#4111yescharacteristic
115C22×C4×C61#4111yescharacteristic
116C22×C4×C61C2411yescharacteristic
117C22×Dic61—41no—
118C2×D244—22no—
119C2×D244—22no—
120C2×D244—22no—
121C2×D244—22no—
122C2×D244—22no—
123C2×D244—22no—
124C2×D244—22no—
125C2×D244—22no—
126C2×D244—22no—
127C2×D244—22no—
128C2×D244—22no—
129C2×D244—22no—
130C2×D244—22no—
131C2×D244—22no—
132C2×D244—22no—
133C2×D244—41no—
134C2×D244—41no—
135C2×D244—41no—
136C2×D244—41no—
137C2×D244—41no—
138C2×D244—41no—
139C2×D244—41no—
140C2×D244—41no—
141C2×D244—41no—
142C2×D244—41no—
143C2×D244—41no—
144C2×D244—41no—
145C2×D244C2×D414yes—
146M16×C61—22no—
147M16×C61—22no—
148M16×C61—22no—
149M16×C61—22no—
150M16×C61—22no—
151M16×C61—22no—
152M16×C61—41no—
153M16×C61—41no—
154C2×C8×C61—22no—
155C2×C8×C61—22no—
156C2×C8×C61—22no—
157C2×C8×C61—41no—
158C2×C8×C61—41no—
159C2×C8×C61C2×D414yes—
160C4⋊C4×C61—22no—
161C4⋊C4×C61—41no—
162C22⋊C4×C61—22no—
163C22⋊C4×C61—41no—
164C42×C61—22no—
165C42×C61—41no—
166C22⋊Dic61—22no—
167C22⋊Dic61—41no—
168C4⋊Dic61—22no—
169C4⋊Dic61—41no—
170C4×Dic61—22no—
171C4×Dic61—41no—
172#11758194—22no—
173#11758194—22no—
174#11758194—22no—
175#11758194—22no—
176#11758194—41no—
177#11758194—41no—
178#11758194—41no—
179#11758194—41no—
180C2×#92418—22no—
181C2×#92418—22no—
182C2×#92418—41no—
183C2×#92418—41no—
184C2×#92418—41no—
185C2×#92418—41no—
186C23×C61—42no—
187C23×C61#12311yescharacteristic
188C23×C61#12311yescharacteristic
189C23×C61#12411yescharacteristic
190C23×C61#12411yescharacteristic
191C23×C61#12611yescharacteristic
192C23×C61#12611yescharacteristic
193C23×C61C2×#4111yescharacteristic
194C22×D61—24no—
195C22×D61—42no—
196C22×D61—42no—
197C22×D61—42no—
198C22×D61—42no—
199C22×D61—42no—
200C22×D61—42no—
201C22×D61—84no—
202C22×D61—84no—
203C22×D61—84no—
204C22×D61—84no—
205C22×D61—84no—
206C22×D61—84no—
207C22×D61—84no—
208C2×C4×C61—42no—
209C2×C4×C61—82no—
210C2×C4×C61#12111yescharacteristic
211C2×C4×C61#12111yescharacteristic
212C2×C4×C61#12111yescharacteristic
213C2×C4×C61#12111yescharacteristic
214C2×C4×C61#12311yescharacteristic
215C2×C4×C61#12311yescharacteristic
216C2×C4×C61#12311yescharacteristic
217C2×C4×C61#12311yescharacteristic
218C2×C4×C61#12311yescharacteristic
219C2×C4×C61#12311yescharacteristic
220C2×C4×C61#12311yescharacteristic
221C2×C4×C61#12311yescharacteristic
222C2×C4×C61#12311yescharacteristic
223C2×C4×C61#12311yescharacteristic
224C2×C4×C61#12411yescharacteristic
225C2×C4×C61#12411yescharacteristic
226C2×C4×C61#12611yescharacteristic
227C2×C4×C61#12611yescharacteristic
228C2×C4×C61#12611yescharacteristic
229C2×C4×C61#12611yescharacteristic
230C2×C4×C61#12611yescharacteristic
231C2×C4×C61#12611yescharacteristic
232C2×C4×C61C22×D411yescharacteristic
233C2×C4×C61C22×D411yescharacteristic
234C2×C4×C61C2×#4111yescharacteristic
235C2×C4×C61C2×#4111yescharacteristic
236C2×C4×C61C2×#4111yescharacteristic
237C2×C4×C61C2×#4111yescharacteristic
238C2×Dic61—42no—
239C2×Dic61—82no—
240D244—24no—
241D244—24no—
242D244—42no—
243D244—42no—
244D244—42no—
245D244—42no—
246D244—42no—
247D244—42no—
248C8×C61—24no—
249C8×C61—42no—
250#92418—42no—
251#92418—42no—
252C2×#2081—611nomaximal, Sylow
253C22×C61—22no—
254C22×C61—22no—
255C22×C61—22no—
256C22×C61—41no—
257C22×C61—41no—
258C22×C61—41no—
259C22×C61—41no—
260C22×C61#39711yescharacteristic
261C22×C61#39711yescharacteristic
262C22×C61#39711yescharacteristic
263C22×C61#39711yescharacteristic
264C22×C61C2×#12311yescharacteristic
265C22×C61C2×#12411yescharacteristic
266C22×C61C2×#12611yescharacteristic
267C2×D61—44no—
268C2×D61—84no—
269C2×D61—84no—
270C2×D61—84no—
271C2×D61—84no—
272C2×D61—84no—
273C2×D61—84no—
274C2×D61—84no—
275C4×C61—82no—
276C4×C61#39711yescharacteristic
277C4×C61#39711yescharacteristic
278C4×C61#39711yescharacteristic
279C4×C61#39711yescharacteristic
280C4×C61C2×#12111yescharacteristic
281C4×C61C2×#12311yescharacteristic
282C4×C61C2×#12311yescharacteristic
283C4×C61C2×#12611yescharacteristic
284Dic61—82no—
285C2×#430—611no—
286C2×#418—611no—
287C2×#418—611no—
288C22×#100—611no—
289#2081—618no—
290C2×#344—611no—
291C2×#344D6111yescharacteristic, complemented
292C2×H(3,ℤ/4)—611no—
293C2×C61—21no—
294C2×C61—21no—
295C2×C61—21no—
296C2×C61—21no—
297C2×C61—21no—
298C2×C61—21no—
299C2×C61#208112yescomplemented
300C2×C61C2×#39711yescharacteristic
301D61—84no—
302C23×D4—611no—
303C22×M16—611no—
304C22×M16—611no—
305C22×M16C2×D6111yescharacteristic
306C22×M16C2×D6111yescharacteristic
307C2×#117—611no—
308C2×#117C2×D6111yescharacteristic
309#430—614no—
310#430—1222no—
311C2×#108—1222no—
312#418—614no—
313#418—614no—
314#418—1222no—
315#418—1222no—
316C2×#102—1222no—
317C2×#102—1222no—
318C2×#100—614no—
319C2×#100—1222no—
320C2×#100—1222no—
321#344—614no—
322#344C2×D6114yescomplemented
323H(3,ℤ/4)—614no—
324C61C2×#208111yescharacteristic, complemented, Sylow
325C25—1221no—
326C22×D4—612no—
327C22×D4—612no—
328C22×D4—612no—
329C22×D4—1221no—
330C22×D4—1221no—
331C22×D4—1221no—
332C22×D4—1221no—
333C22×D4—1221no—
334C22×D4—1221no—
335C22×D4—1221no—
336C22×D4—1221no—
337C22×D4—1221no—
338C22×D4—1221no—
339C22×D4—1221no—
340C23×C4C22×D6111yescharacteristic
341C2×M16—21no—
342C2×M16—21no—
343C2×M16—21no—
344C2×M16—21no—
345C2×M16—21no—
346C2×M16—21no—
347C2×M16—21no—
348C2×M16—21no—
349C2×M16—21no—
350C2×M16—612no—
351C2×M16—612no—
352C2×M16—1221no—
353C2×M16—1221no—
354C2×M16—1221no—
355C2×M16—1221no—
356C2×M16—1221no—
357C2×M16—1221no—
358C2×M16—1221no—
359C2×M16—1221no—
360C2×M16—1221no—
361C2×M16—1221no—
362C2×M16D24412yes—
363C2×M16C22×D6112yes—
364C2×M16C22×D6112yes—
365C22×C8—21no—
366C22×C8—1221no—
367C22×C8—1221no—
368C22×C8D24412yes—
369#117—21no—
370#117—21no—
371#117—21no—
372#117—612no—
373#117—1221no—
374#117—1221no—
375#117—1221no—
376#117C22×D6112yes—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—1221no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—1221no—
381C2×C42—21no—
382C2×C42—1221no—
383#108—1228no—
384#102—1228no—
385#102—1228no—
386#100—1228no—
387C24—1222no—
388C24—1222no—
389C24—1222no—
390C24—4884no—
391C24—2441no—
392C24—2441no—
393C24—2441no—
394C24—2441no—
395C24#1175822211yescharacteristic
396C2×D4—614no—
397C2×D4—1222no—
398C2×D4—1222no—
399C2×D4—1222no—
400C2×D4—1222no—
401C2×D4—1222no—
402C2×D4—1222no—
403C2×D4—1222no—
404C2×D4—1222no—
405C2×D4—1222no—
406C2×D4—1222no—
407C2×D4—1222no—
408C2×D4—1222no—
409C2×D4—1222no—
410C2×D4—1222no—
411C2×D4—1222no—
412C2×D4—2441no—
413C2×D4—2441no—
414C2×D4—2441no—
415C2×D4—2441no—
416C2×D4—2441no—
417C2×D4—2441no—
418C2×D4—2441no—
419C2×D4—2441no—
420C2×D4—2441no—
421C2×D4—2441no—
422C2×D4—2441no—
423C2×D4—2441no—
424C22×C4—41no—
425C22×C4—2441no—
426C22×C4C2×D24411yescharacteristic
427C22×C4C2×D24411yescharacteristic
428C22×C4#1175822211yescharacteristic
429C22×C4#1175822211yescharacteristic
430C22×C4#1175822211yescharacteristic
431C22×C4D4×D6111yescharacteristic
432C22×C4D4×D6111yescharacteristic
433C22×C4#1175822411yescharacteristic
434C22×C4#1175822411yescharacteristic
435C22×C4#1175822411yescharacteristic
436C22×C4#1175822411yescharacteristic
437C22×C4#1175822611yescharacteristic
438C22×C4#1175822611yescharacteristic
439C22×C4C23×D6111yescharacteristic
440M16—22no—
441M16—22no—
442M16—22no—
443M16—22no—
444M16—22no—
445M16—22no—
446M16—41no—
447M16—41no—
448M16—1222no—
449M16—1222no—
450M16—1222no—
451M16—1222no—
452M16—2441no—
453M16—2441no—
454M16—2441no—
455M16—2441no—
456C2×C8—22no—
457C2×C8—22no—
458C2×C8—22no—
459C2×C8—41no—
460C2×C8—41no—
461C2×C8—1222no—
462C2×C8—1222no—
463C2×C8—2441no—
464C2×C8—2441no—
465C2×C8—2441no—
466C2×C8—2441no—
467C2×C8C2×D24414yes—
468C4⋊C4—22no—
469C4⋊C4—41no—
470C4⋊C4—1222no—
471C4⋊C4—2441no—
472C22⋊C4—22no—
473C22⋊C4—41no—
474C22⋊C4—1222no—
475C22⋊C4—2441no—
476C42—22no—
477C42—41no—
478C42—1222no—
479C42—2441no—
480C23—42no—
481C23—1224no—
482C23—4884no—
483C23—4884no—
484C23—4884no—
485C23—4884no—
486C23—4884no—
487C23—4884no—
488C23—4884no—
489C23—2442no—
490C23—2442no—
491C23—2442no—
492C23—2442no—
493C23—2442no—
494C23—2442no—
495C23#1451975911yescharacteristic
496C23#1451975911yescharacteristic
497C23#1451976511yescharacteristic
498C23#1451976511yescharacteristic
499C23#1451977211yescharacteristic
500C23#1451977211yescharacteristic
501C23C2×#1175822211yescharacteristic
502D4—1224no—
503D4—1224no—
504D4—2442no—
505D4—2442no—
506D4—2442no—
507D4—2442no—
508D4—2442no—
509D4—2442no—
510C2×C4—42no—
511C2×C4—82no—
512C2×C4—4882no—
513C2×C4—2442no—
514C2×C4#1451975211yescharacteristic
515C2×C4#1451975211yescharacteristic
516C2×C4#1451975211yescharacteristic
517C2×C4#1451975211yescharacteristic
518C2×C4#1451975911yescharacteristic
519C2×C4#1451975911yescharacteristic
520C2×C4#1451975911yescharacteristic
521C2×C4#1451975911yescharacteristic
522C2×C4#1451975911yescharacteristic
523C2×C4#1451975911yescharacteristic
524C2×C4#1451976111yescharacteristic
525C2×C4#1451976111yescharacteristic
526C2×C4#1451976111yescharacteristic
527C2×C4#1451976111yescharacteristic
528C2×C4#1451976511yescharacteristic
529C2×C4#1451976511yescharacteristic
530C2×C4#1451977211yescharacteristic
531C2×C4#1451977211yescharacteristic
532C2×C4#1451977211yescharacteristic
533C2×C4#1451977211yescharacteristic
534C2×C4#1451977211yescharacteristic
535C2×C4#1451977211yescharacteristic
536C2×C4C2×D4×D6111yescharacteristic
537C2×C4C22×D24411yescharacteristic
538C2×C4C2×#1175822411yescharacteristic
539C2×C4C2×#1175822411yescharacteristic
540C2×C4C2×#1175822211yescharacteristic
541C2×C4C2×#1175822611yescharacteristic
542C8—24no—
543C8—42no—
544C8—2442no—
545C8—2442no—
546C22—22no—
547C22—22no—
548C22—22no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—4884no—
554C22—4884no—
555C22—4884no—
556C22—4884no—
557C22—4884no—
558C22—4884no—
559C22—4884no—
560C22—2444no—
561C22#1683968911yescharacteristic
562C22#1683968911yescharacteristic
563C22#1683968911yescharacteristic
564C22#1683968911yescharacteristic
565C22C2×#1451975911yescharacteristic
566C22C2×#1451976511yescharacteristic
567C22C2×#1451977211yescharacteristic
568C4—82no—
569C4—4882no—
570C4#1683968911yescharacteristic
571C4#1683968911yescharacteristic
572C4#1683968911yescharacteristic
573C4#1683968911yescharacteristic
574C4C2×#1451975211yescharacteristic
575C4C2×#1451975911yescharacteristic
576C4C2×#1451976111yescharacteristic
577C4C2×#1451977211yescharacteristic
578C2—21no—
579C2—21no—
580C2—21no—
581C2—21no—
582C2—21no—
583C2—21no—
584C2—4884no—
585C2#2144727812yesdirect product factor
586C2C2×#1683968911yescharacteristic
subgroupG/H
centerC22#16839689
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#344C2
socleC22×C61#397
prime radicalC23×D244C22
hypercenterC2×#344D61
hypocenterC61C2×#2081
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
1. C2×#16839811C2semidirect
5. #21447278C2direct (N × H)
6. C2×#16839533C2semidirect
7. C2×#16839518C2semidirect
8. C2×C61×#344C2semidirect
14. #16839811C22semidirect
25. #16839533C22semidirect
26. #16839518C22semidirect
30. C61×#344C22semidirect
291. C2×#344D61semidirect
299. C2×C61#2081semidirect
322. #344C2×D61semidirect
324. C61C2×#2081semidirect
585. C2#21447278direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168398112
C2×#168397682
C2×#168397662
C22×#145196932
#214472782
C2×#168395332
C2×#168395182
C2×C61×#3442
C2×#208161