Finite Group Databasebeta

← C2×#21447120 #29707890

Subgroups — C2×#21447120 #29707890

Order 15616.

1362 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519810C211yesmaximal, characteristic
2C2×#16839764C211yesmaximal, characteristic
3C22×#14519702C211yesmaximal, characteristic, complemented
4C22×#14519695C211yesmaximal, characteristic, complemented
5C2×#16839728C211yesmaximal, characteristic
6#21447120C218yesmaximal, direct product factor
7C2×#16839530C211yesmaximal, characteristic, complemented
8C22×#108×C61C211yesmaximal, characteristic, complemented
9C22×#11758222C2211yescharacteristic
10C23×Dic122C2211yescharacteristic
11C2×#14519810—24no—
12C2×#14519810—22no—
13C2×#14519810—24no—
14C2×#14519810C2214yes—
15C22×Dic244—21no—
16C22×#11758190—21no—
17C22×#11758194C2211yescharacteristic
18C22×C4⋊Dic61C2211yescharacteristic
19#16839764—22no—
20#16839764C2214yes—
21C2×#14519702—22no—
22C2×#14519702—22no—
23C2×#14519702—21no—
24C2×#14519702C2214yescomplemented
25C2×#14519699—21no—
26C2×#14519695—24no—
27C2×#14519695C2214yescomplemented
28#16839728—22no—
29#16839728C2214yes—
30C2×#14519689—22no—
31#16839530C2214yescomplemented
32C22×M16×C61C2211yescharacteristic
33C22×M16×C61C2211yescharacteristic
34C23×C8×C61C2211yescharacteristic
35C2×#108×C61—24no—
36C2×#108×C61C2214yescomplemented
37C2×#11758222—21no—
38C2×#11758222—21no—
39C2×#11758222—22no—
40C2×#11758222—22no—
41C2×#11758222—22no—
42C2×#11758222—22no—
43C2×#11758222D412yes—
44C2×#11758222C2312yes—
45C22×Dic122—21no—
46C22×Dic122—21no—
47C22×Dic122—21no—
48C22×Dic122—21no—
49C22×Dic122—22no—
50C22×Dic122—22no—
51C22×Dic122—21no—
52C22×Dic122—22no—
53C22×Dic122D414yes—
54C22×Dic122D411yescharacteristic
55C22×Dic122C2312yes—
56C22×D244D411yescharacteristic
57C22×C22⋊D61—21no—
58C23×Dic61—21no—
59C23×Dic61—21no—
60C22×C4×D61—21no—
61#14519810—216no—
62#14519810—28no—
63#14519810—28no—
64C2×Dic244—28no—
65C2×Dic244—24no—
66C2×#11758190—28no—
67C2×#11758190—24no—
68C2×#11758194—21no—
69C2×#11758194—22no—
70C2×#11758194—22no—
71C2×#11758194C2312yes—
72C22×#92418—21no—
73C2×C4⋊Dic61—21no—
74C2×C4⋊Dic61—21no—
75C2×C4⋊Dic61—21no—
76C2×C4⋊Dic61—21no—
77C2×C4⋊Dic61—21no—
78C2×C4⋊Dic61C2312yes—
79#14519702—24no—
80#14519702—28no—
81#14519699—24no—
82#14519695—28no—
83#14519689—28no—
84C23×C4×C61C2311yescharacteristic
85C2×M16×C61—22no—
86C2×M16×C61—21no—
87C2×M16×C61—21no—
88C2×M16×C61—22no—
89C2×M16×C61—22no—
90C2×M16×C61D414yes—
91C2×M16×C61C2312yes—
92C2×M16×C61C2312yes—
93C22×C8×C61—22no—
94C22×C8×C61—21no—
95C22×C8×C61—22no—
96C22×C8×C61—21no—
97C22×C8×C61D412yes—
98C22×C8×C61D412yes—
99C22×C8×C61C2312yes—
100#108×C61—28no—
101C24×C61#4111yescharacteristic
102C23×D61—21no—
103C22×C4×C61C2×D412yes—
104C22×C4×C61C2×D412yes—
105C22×C4×C61C2×D411yescharacteristic
106C22×C4×C61C2×D411yescharacteristic
107C22×C4×C61C2×D411yescharacteristic
108C22×C4×C61C2×D411yescharacteristic
109C22×C4×C61#4112yes—
110C22×C4×C61#4111yescharacteristic
111C22×C4×C61#4112yes—
112C22×C4×C61C2411yescharacteristic
113C2×C22⋊D61—22no—
114C2×C22⋊D61—22no—
115C2×C22⋊D61—42no—
116C2×C22⋊D61—42no—
117C22×Dic61—21no—
118C22×Dic61—24no—
119C22×Dic61—22no—
120C22×Dic61—22no—
121C22×Dic61—41no—
122C22×Dic61—41no—
123C22×Dic61—42no—
124C22×Dic61—41no—
125C22×Dic61—41no—
126C22×Dic61—82no—
127#11758222—24no—
128#11758222—24no—
129#11758222—22no—
130#11758222—22no—
131#11758222—22no—
132#11758222—22no—
133#11758222—42no—
134#11758222—42no—
135#11758222—42no—
136#11758222—42no—
137C2×D244—22no—
138C2×D244—22no—
139C2×D244—21no—
140C2×D244C2×D412yes—
141C2×C4×D61—22no—
142C2×C4×D61—22no—
143C2×C4×D61—42no—
144C2×C4×D61—42no—
145C2×Dic122—24no—
146C2×Dic122—24no—
147C2×Dic122—22no—
148C2×Dic122—24no—
149C2×Dic122—24no—
150C2×Dic122—22no—
151C2×Dic122—22no—
152C2×Dic122—22no—
153C2×Dic122—22no—
154C2×Dic122—22no—
155C2×Dic122—21no—
156C2×Dic122—24no—
157C2×Dic122—22no—
158C2×Dic122—42no—
159C2×Dic122—42no—
160C2×Dic122—41no—
161C2×Dic122—41no—
162C2×Dic122—42no—
163C2×Dic122—42no—
164C2×Dic122—42no—
165C2×Dic122C2×D414yes—
166C2×Dic122C2×D412yes—
167M16×C61—24no—
168M16×C61—22no—
169M16×C61—22no—
170M16×C61—22no—
171M16×C61—42no—
172M16×C61C2×D414yes—
173C2×C8×C61—24no—
174C2×C8×C61—24no—
175C2×C8×C61—24no—
176C2×C8×C61—22no—
177C2×C8×C61—22no—
178C2×C8×C61—22no—
179C2×C8×C61—22no—
180C2×C8×C61—42no—
181C2×C8×C61C2×D414yes—
182C4⋊Dic61—22no—
183C4⋊Dic61—22no—
184C4⋊Dic61—41no—
185C4⋊Dic61—41no—
186#11758194—22no—
187#11758194—22no—
188#11758194—42no—
189C2×#92418—22no—
190C2×#92418—42no—
191Dic244—216no—
192#11758190—216no—
193C23×C61—22no—
194C23×C61—22no—
195C23×C61#12111yescharacteristic
196C23×C61#12111yescharacteristic
197C23×C61#12312yes—
198C23×C61#12412yes—
199C23×C61C2×#4111yescharacteristic
200C22×D61—22no—
201C22×D61—42no—
202C22×D61—42no—
203C22×D61—42no—
204C2×C4×C61#12012yes—
205C2×C4×C61#12012yes—
206C2×C4×C61#12112yes—
207C2×C4×C61#12112yes—
208C2×C4×C61#12112yes—
209C2×C4×C61#12112yes—
210C2×C4×C61#12111yescharacteristic
211C2×C4×C61#12111yescharacteristic
212C2×C4×C61#12312yes—
213C2×C4×C61#12312yes—
214C2×C4×C61#12312yes—
215C2×C4×C61#12412yes—
216C2×C4×C61C22×D411yescharacteristic
217C2×C4×C61C22×D411yescharacteristic
218C2×C4×C61C22×D411yescharacteristic
219C2×C4×C61C22×D411yescharacteristic
220C2×C4×C61C2×#4111yescharacteristic
221C2×C4×C61C2×#4111yescharacteristic
222C22⋊D61—42no—
223C22⋊D61—42no—
224C22⋊D61—44no—
225C2×Dic61—22no—
226C2×Dic61—24no—
227C2×Dic61—42no—
228C2×Dic61—42no—
229C2×Dic61—44no—
230C2×Dic61—44no—
231C2×Dic61—42no—
232C2×Dic61—42no—
233C2×Dic61—82no—
234C2×Dic61—82no—
235C2×Dic61—82no—
236D244—22no—
237D244—22no—
238D244—42no—
239C4×D61—42no—
240C4×D61—42no—
241C4×D61—44no—
242Dic122—24no—
243Dic122—22no—
244Dic122—24no—
245Dic122—22no—
246Dic122—42no—
247Dic122—42no—
248Dic122—44no—
249Dic122—44no—
250Dic122—42no—
251C8×C61—24no—
252C8×C61—24no—
253C8×C61—42no—
254#92418—42no—
255C2×#2052—611nomaximal, Sylow
256C22×C61—24no—
257C22×C61—24no—
258C22×C61—21no—
259C22×C61—21no—
260C22×C61—21no—
261C22×C61—21no—
262C22×C61#39412yes—
263C22×C61#39412yes—
264C22×C61#47112yes—
265C22×C61#47312yes—
266C22×C61C2×#12111yescharacteristic
267C22×C61C2×#12311yescharacteristic
268C22×C61C2×#12411yescharacteristic
269C2×D61—42no—
270C2×D61—42no—
271C2×D61—42no—
272C2×D61—84no—
273C4×C61#39412yes—
274C4×C61#39412yes—
275C4×C61C2×#12011yescharacteristic
276C4×C61C2×#12111yescharacteristic
277C4×C61C2×#12111yescharacteristic
278C4×C61C2×#12311yescharacteristic
279Dic61—44no—
280Dic61—42no—
281Dic61—82no—
282C22×#137—611no—
283C22×#108D6111yescharacteristic, complemented
284C2×#417—611no—
285C22×#103—611no—
286C22×#101—611no—
287C2×#408—611no—
288#2052—618no—
289C2×#343—611no—
290C2×C61—21no—
291C2×C61—21no—
292C2×C61—22no—
293C2×C61#205214yescomplemented
294C2×C61C2×#39411yescharacteristic
295C2×C61C2×#47111yescharacteristic
296C2×C61C2×#47311yescharacteristic
297D61—82no—
298C22×#41—611no—
299C23×Q8—611no—
300C2×#137—614no—
301C2×#137—1224no—
302C2×#137—1222no—
303C2×#137—1224no—
304C22×Q16—1221no—
305C22×SD16—1221no—
306C22×M16—611no—
307C22×M16C2×D6111yescharacteristic
308C22×M16C2×D6111yescharacteristic
309C23×C8C2×D6111yescharacteristic
310C22×C4⋊C4—611no—
311C2×#108—24no—
312C2×#108C2×D6114yescomplemented
313#417—614no—
314#417—1222no—
315C2×#103—614no—
316C2×#103—1221no—
317C2×#103—1222no—
318C2×#103—1222no—
319C2×#102—1221no—
320C2×#101—614no—
321C2×#101—1224no—
322#408—614no—
323#408—1222no—
324C2×C22⋊C8—1222no—
325#343—614no—
326C61C2×#205211yescharacteristic, complemented, Sylow
327C2×#41—612no—
328C2×#41—612no—
329C2×#41—1221no—
330C2×#41—1221no—
331C2×#41—1222no—
332C2×#41—1222no—
333C2×#41—1222no—
334C2×#41—1222no—
335C22×Q8—611no—
336C22×Q8—614no—
337C22×Q8—612no—
338C22×Q8—1222no—
339C22×Q8—1221no—
340C22×Q8—1221no—
341C22×Q8—1221no—
342C22×Q8—1221no—
343C22×Q8—1221no—
344C22×Q8—1222no—
345C22×Q8—1222no—
346C22×D4—611no—
347C22×D4—1221no—
348C23×C4—1221no—
349C23×C4—1221no—
350C23×C4—1221no—
351C23×C4C22×D6111yescharacteristic
352#137—1228no—
353#137—12216no—
354#137—1228no—
355C2×Q16—1224no—
356C2×Q16—1228no—
357C2×SD16—1224no—
358C2×SD16—1228no—
359C2×M16—21no—
360C2×M16—22no—
361C2×M16—21no—
362C2×M16—22no—
363C2×M16—22no—
364C2×M16—612no—
365C2×M16—1221no—
366C2×M16—1222no—
367C2×M16—1222no—
368C2×M16C22⋊D6114yes—
369C2×M16C22×D6112yes—
370C2×M16C22×D6112yes—
371C22×C8—22no—
372C22×C8—21no—
373C22×C8—22no—
374C22×C8—21no—
375C22×C8—1221no—
376C22×C8D24412yes—
377C22×C8D24412yes—
378C22×C8C22×D6112yes—
379C2×C4⋊C4—612no—
380C2×C4⋊C4—1221no—
381C2×C4⋊C4—1221no—
382C2×C4⋊C4—1221no—
383C2×C4⋊C4—1221no—
384C2×C4⋊C4—1221no—
385#108—28no—
386#103—1224no—
387#103—1228no—
388#102—1224no—
389#101—1228no—
390C22⋊C8—1228no—
391C24—1221no—
392C24#1175822611yescharacteristic
393#41—1222no—
394#41—1222no—
395#41—1222no—
396#41—1222no—
397#41—1224no—
398#41—1224no—
399#41—2442no—
400#41—2442no—
401#41—2442no—
402#41—2442no—
403C2×Q8—614no—
404C2×Q8—612no—
405C2×Q8—1222no—
406C2×Q8—1221no—
407C2×Q8—1224no—
408C2×Q8—1222no—
409C2×Q8—1222no—
410C2×Q8—1222no—
411C2×Q8—1222no—
412C2×Q8—1224no—
413C2×Q8—1222no—
414C2×Q8—1224no—
415C2×Q8—1224no—
416C2×Q8—1224no—
417C2×Q8—1222no—
418C2×Q8—2442no—
419C2×Q8—2442no—
420C2×Q8—2441no—
421C2×Q8—2441no—
422C2×Q8—2442no—
423C2×Q8—2442no—
424C2×Q8—2442no—
425C2×D4—612no—
426C2×D4—1222no—
427C2×D4—1222no—
428C2×D4—1222no—
429C2×D4—1221no—
430C2×D4—1222no—
431C2×D4—2442no—
432C2×D4—2442no—
433C22×C4—1222no—
434C22×C4—1221no—
435C22×C4—1224no—
436C22×C4—1222no—
437C22×C4—1222no—
438C22×C4—1222no—
439C22×C4—4882no—
440C22×C4—2441no—
441C22×C4—2441no—
442C22×C4—2441no—
443C22×C4—2441no—
444C22×C4—2442no—
445C22×C4—2442no—
446C22×C4—2442no—
447C22×C4C2×D24411yescharacteristic
448C22×C4C2×D24411yescharacteristic
449C22×C4#1175822212yes—
450C22×C4D4×D6112yes—
451C22×C4D4×D6111yescharacteristic
452C22×C4D4×D6111yescharacteristic
453C22×C4#1175822612yes—
454C22×C4#1175822611yescharacteristic
455C22×C4C2×C22⋊D6112yes—
456C22×C4C23×D6111yescharacteristic
457Q16—12216no—
458SD16—12216no—
459M16—22no—
460M16—24no—
461M16—22no—
462M16—22no—
463M16—42no—
464M16—1222no—
465M16—1222no—
466M16—2442no—
467M16C2×C22⋊D6114yes—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—24no—
472C2×C8—24no—
473C2×C8—24no—
474C2×C8—22no—
475C2×C8—42no—
476C2×C8—1222no—
477C2×C8—2442no—
478C2×C8C2×D24414yes—
479C4⋊C4—1222no—
480C4⋊C4—1222no—
481C4⋊C4—2441no—
482C4⋊C4—2441no—
483C23—22no—
484C23—22no—
485C23—1222no—
486C23—2442no—
487C23—2442no—
488C23—2442no—
489C23#1451975211yescharacteristic
490C23#1451975211yescharacteristic
491C23#1451976212yes—
492C23#1451976612yes—
493C23C2×#1175822611yescharacteristic
494Q8—1224no—
495Q8—1222no—
496Q8—1224no—
497Q8—1222no—
498Q8—2442no—
499Q8—2442no—
500Q8—2444no—
501Q8—2444no—
502Q8—2442no—
503D4—1222no—
504D4—1222no—
505D4—2442no—
506D4—2442no—
507D4—2444no—
508D4—2442no—
509C2×C4—1222no—
510C2×C4—1224no—
511C2×C4—4882no—
512C2×C4—4882no—
513C2×C4—4882no—
514C2×C4—2442no—
515C2×C4—2442no—
516C2×C4—2442no—
517C2×C4—2442no—
518C2×C4—2444no—
519C2×C4—2444no—
520C2×C4—2442no—
521C2×C4—2442no—
522C2×C4—2444no—
523C2×C4#1451974512yes—
524C2×C4#1451974512yes—
525C2×C4#1451975112yes—
526C2×C4#1451975112yes—
527C2×C4#1451975212yes—
528C2×C4#1451975212yes—
529C2×C4#1451975211yescharacteristic
530C2×C4#1451975211yescharacteristic
531C2×C4#1451976212yes—
532C2×C4#1451976212yes—
533C2×C4#1451976212yes—
534C2×C4#1451976612yes—
535C2×C4C2×D4×D6111yescharacteristic
536C2×C4C2×D4×D6111yescharacteristic
537C2×C4C22×C22⋊D6111yescharacteristic
538C2×C4C22×D24411yescharacteristic
539C2×C4C2×#1175822211yescharacteristic
540C2×C4C2×#1175822611yescharacteristic
541C8—24no—
542C8—24no—
543C8—42no—
544C8—2442no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—21no—
549C22—24no—
550C22—24no—
551C22—4884no—
552C22—2442no—
553C22—2442no—
554C22—2442no—
555C22#1683967912yes—
556C22#1683967912yes—
557C22#1684002612yes—
558C22#1684003812yes—
559C22C2×#1451975211yescharacteristic
560C22C2×#1451976211yescharacteristic
561C22C2×#1451976611yescharacteristic
562C4—4882no—
563C4—2442no—
564C4—2444no—
565C4#1683967912yes—
566C4#1683967912yes—
567C4C2×#1451974511yescharacteristic
568C4C2×#1451975111yescharacteristic
569C4C2×#1451975211yescharacteristic
570C4C2×#1451976211yescharacteristic
571C2—21no—
572C2—21no—
573C2—22no—
574C2—4882no—
575C2#2144712014yesdirect product factor
576C2C2×#1683967911yescharacteristic
577C2C2×#1684002611yescharacteristic
578C2C2×#1684003811yescharacteristic
subgroupG/H
centerC23#14519752
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC22×#108×C61C2
socleC23×C61#121
prime radicalC22×#11758222C22
hypercenterC22×#108D61
hypocenterC61C2×#2052
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#108

Complements

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

NH ≅ G/Ntype
3. C22×#14519702C2semidirect
4. C22×#14519695C2semidirect
6. #21447120C2direct (N × H)
7. C2×#16839530C2semidirect
8. C22×#108×C61C2semidirect
24. C2×#14519702C22semidirect
27. C2×#14519695C22semidirect
31. #16839530C22semidirect
36. C2×#108×C61C22semidirect
283. C22×#108D61semidirect
293. C2×C61#2052semidirect
312. C2×#108C2×D61semidirect
326. C61C2×#2052semidirect
575. C2#21447120direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198102
C2×#168397642
C22×#145197022
C22×#145196952
C2×#168397282
#214471202
C2×#168395302
C22×#108×C612
C2×#205261