Finite Group Databasebeta

← C2×#21447119 #29707889

Subgroups — C2×#21447119 #29707889

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×#14519808C211yesmaximal, characteristic
2C22×#14519713C211yesmaximal, characteristic, complemented
3C2×#16839761C211yesmaximal, characteristic
4C22×#14519696C211yesmaximal, characteristic, complemented
5C2×#16839728C211yesmaximal, characteristic
6#21447119C218yesmaximal, direct product factor
7C2×#16839531C211yesmaximal, characteristic, complemented
8C22×#103×C61C211yesmaximal, characteristic, complemented
9C22×#11758222C2211yescharacteristic
10C2×#14519808—24no—
11C2×#14519808—24no—
12C2×#14519808—22no—
13C2×#14519808C2214yes—
14C22×#11758202—21no—
15C22×#11758201—21no—
16C22×#11758194C2211yescharacteristic
17C22×#11758194C2211yescharacteristic
18C22×#11758194C2211yescharacteristic
19C2×#14519713—24no—
20C2×#14519713C2214yescomplemented
21#16839761—22no—
22#16839761C2214yes—
23C2×#14519700—21no—
24C2×#14519697—21no—
25C2×#14519696—24no—
26C2×#14519696C2214yescomplemented
27#16839728—22no—
28#16839728C2214yes—
29C2×#14519689—22no—
30#16839531C2214yescomplemented
31C23×Q8×C61C2211yescharacteristic
32C23×C8×C61C2211yescharacteristic
33C22×C4⋊C4×C61C2211yescharacteristic
34C2×#103×C61—22no—
35C2×#103×C61—22no—
36C2×#103×C61C2214yescomplemented
37C2×#11758222—21no—
38C2×#11758222—21no—
39C2×#11758222—22no—
40C2×#11758222—22no—
41C2×#11758222—22no—
42C2×#11758222—22no—
43C2×#11758222D412yes—
44C2×#11758222C2312yes—
45C22×Dic122D411yescharacteristic
46C22×D244D411yescharacteristic
47C22×C22⋊D61—21no—
48C22×C4×D61—21no—
49#14519808—216no—
50#14519808—28no—
51#14519808—28no—
52C2×#11758202—28no—
53C2×#11758202—24no—
54C2×#11758201—28no—
55C2×#11758201—24no—
56C2×#11758194—22no—
57C2×#11758194—21no—
58C2×#11758194—21no—
59C2×#11758194—21no—
60C2×#11758194—22no—
61C2×#11758194—22no—
62C2×#11758194—22no—
63C2×#11758194—22no—
64C2×#11758194D414yes—
65C2×#11758194C2312yes—
66C2×#11758194C2312yes—
67C2×#11758194C2312yes—
68C22×#92418—21no—
69C22×#92418—21no—
70C22×#92418—21no—
71#14519713—28no—
72#14519700—24no—
73#14519697—24no—
74#14519696—28no—
75#14519689—28no—
76C22×Q8×C61—22no—
77C22×Q8×C61—21no—
78C22×Q8×C61—21no—
79C22×Q8×C61—21no—
80C22×Q8×C61—22no—
81C22×Q8×C61—21no—
82C22×Q8×C61—21no—
83C22×Q8×C61—22no—
84C22×Q8×C61D414yes—
85C22×Q8×C61C2312yes—
86C23×C4×C61—21no—
87C23×C4×C61—21no—
88C23×C4×C61C2311yescharacteristic
89C22×C8×C61—22no—
90C22×C8×C61—22no—
91C22×C8×C61D412yes—
92C22×C8×C61D412yes—
93C22×C8×C61C2312yes—
94C2×C4⋊C4×C61—21no—
95C2×C4⋊C4×C61—21no—
96C2×C4⋊C4×C61—21no—
97C2×C4⋊C4×C61—21no—
98C2×C4⋊C4×C61—21no—
99C2×C4⋊C4×C61C2312yes—
100#103×C61—28no—
101C24×C61#4111yescharacteristic
102C23×D61—21no—
103C2×Q8×C61—24no—
104C2×Q8×C61—22no—
105C2×Q8×C61—24no—
106C2×Q8×C61—24no—
107C2×Q8×C61—24no—
108C2×Q8×C61—24no—
109C2×Q8×C61—22no—
110C2×Q8×C61—22no—
111C2×Q8×C61—22no—
112C2×Q8×C61—22no—
113C2×Q8×C61—41no—
114C2×Q8×C61—41no—
115C2×Q8×C61—42no—
116C2×Q8×C61—42no—
117C2×Q8×C61—42no—
118C2×Q8×C61—42no—
119C2×Q8×C61—42no—
120C2×Q8×C61C2×D414yes—
121C22×C4×C61—24no—
122C22×C4×C61—22no—
123C22×C4×C61—22no—
124C22×C4×C61—41no—
125C22×C4×C61—41no—
126C22×C4×C61—42no—
127C22×C4×C61—41no—
128C22×C4×C61—41no—
129C22×C4×C61—82no—
130C22×C4×C61C2×D412yes—
131C22×C4×C61C2×D412yes—
132C22×C4×C61C2×D411yescharacteristic
133C22×C4×C61C2×D411yescharacteristic
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61#4112yes—
137C22×C4×C61#4111yescharacteristic
138C22×C4×C61#4112yes—
139C22×C4×C61C2411yescharacteristic
140C2×C22⋊D61—22no—
141C2×C22⋊D61—22no—
142C2×C22⋊D61—42no—
143C2×C22⋊D61—42no—
144C22×Dic61—21no—
145#11758222—24no—
146#11758222—24no—
147#11758222—22no—
148#11758222—22no—
149#11758222—22no—
150#11758222—22no—
151#11758222—42no—
152#11758222—42no—
153#11758222—42no—
154#11758222—42no—
155C2×D244—22no—
156C2×D244—22no—
157C2×D244—21no—
158C2×D244C2×D412yes—
159C2×C4×D61—22no—
160C2×C4×D61—22no—
161C2×C4×D61—42no—
162C2×C4×D61—42no—
163C2×Dic122—22no—
164C2×Dic122—22no—
165C2×Dic122—21no—
166C2×Dic122C2×D412yes—
167C2×C8×C61—24no—
168C2×C8×C61—24no—
169C2×C8×C61—22no—
170C2×C8×C61—22no—
171C2×C8×C61C2×D414yes—
172C4⋊C4×C61—22no—
173C4⋊C4×C61—22no—
174C4⋊C4×C61—41no—
175C4⋊C4×C61—41no—
176#11758202—216no—
177#11758201—216no—
178#11758194—24no—
179#11758194—22no—
180#11758194—22no—
181#11758194—22no—
182#11758194—22no—
183#11758194—22no—
184#11758194—42no—
185#11758194—42no—
186#11758194C2×D414yes—
187C2×#92418—24no—
188C2×#92418—22no—
189C2×#92418—22no—
190C2×#92418—22no—
191C2×#92418—42no—
192C2×#92418—42no—
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—
204Q8×C61—24no—
205Q8×C61—24no—
206Q8×C61—42no—
207Q8×C61—42no—
208Q8×C61—44no—
209Q8×C61—44no—
210C2×C4×C61—24no—
211C2×C4×C61—42no—
212C2×C4×C61—42no—
213C2×C4×C61—44no—
214C2×C4×C61—44no—
215C2×C4×C61—42no—
216C2×C4×C61—82no—
217C2×C4×C61—82no—
218C2×C4×C61—82no—
219C2×C4×C61#12012yes—
220C2×C4×C61#12012yes—
221C2×C4×C61#12112yes—
222C2×C4×C61#12112yes—
223C2×C4×C61#12112yes—
224C2×C4×C61#12112yes—
225C2×C4×C61#12111yescharacteristic
226C2×C4×C61#12111yescharacteristic
227C2×C4×C61#12312yes—
228C2×C4×C61#12312yes—
229C2×C4×C61#12312yes—
230C2×C4×C61#12412yes—
231C2×C4×C61C22×D411yescharacteristic
232C2×C4×C61C22×D411yescharacteristic
233C2×C4×C61C22×D411yescharacteristic
234C2×C4×C61C22×D411yescharacteristic
235C2×C4×C61C2×#4111yescharacteristic
236C2×C4×C61C2×#4111yescharacteristic
237C22⋊D61—42no—
238C22⋊D61—42no—
239C22⋊D61—44no—
240C2×Dic61—22no—
241C2×Dic61—42no—
242D244—22no—
243D244—22no—
244D244—42no—
245C4×D61—42no—
246C4×D61—42no—
247C4×D61—44no—
248Dic122—22no—
249Dic122—22no—
250Dic122—42no—
251C8×C61—24no—
252#92418—24no—
253#92418—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—44no—
274C4×C61—82no—
275C4×C61#39412yes—
276C4×C61#39412yes—
277C4×C61C2×#12011yescharacteristic
278C4×C61C2×#12111yescharacteristic
279C4×C61C2×#12111yescharacteristic
280C4×C61C2×#12311yescharacteristic
281Dic61—42no—
282C22×#137—611no—
283C22×#108—611no—
284C2×#417—611no—
285C22×#103D6111yescharacteristic, complemented
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×Q8C2×D6111yescharacteristic
300C2×#137—614no—
301C2×#137—1224no—
302C2×#137—1222no—
303C2×#137—1224no—
304C22×Q16—1221no—
305C22×SD16—1221no—
306C22×M16—611no—
307C22×M16—611no—
308C22×M16—611no—
309C23×C8C2×D6111yescharacteristic
310C22×C4⋊C4C2×D6111yescharacteristic
311C2×#108—614no—
312C2×#108—1224no—
313#417—614no—
314#417—1222no—
315C2×#103—22no—
316C2×#103—22no—
317C2×#103—1221no—
318C2×#103C2×D6114yescomplemented
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—21no—
336C22×Q8—22no—
337C22×Q8—22no—
338C22×Q8—21no—
339C22×Q8—21no—
340C22×Q8—22no—
341C22×Q8—21no—
342C22×Q8—21no—
343C22×Q8—611no—
344C22×Q8D24414yes—
345C22×Q8C22×D6112yes—
346C22×D4—611no—
347C22×D4—1221no—
348C23×C4—21no—
349C23×C4—21no—
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—614no—
360C2×M16—612no—
361C2×M16—612no—
362C2×M16—612no—
363C2×M16—1222no—
364C2×M16—1221no—
365C2×M16—1221no—
366C2×M16—1221no—
367C2×M16—1222no—
368C2×M16—1222no—
369C2×M16—1222no—
370C2×M16—1222no—
371C22×C8—22no—
372C22×C8—22no—
373C22×C8—1221no—
374C22×C8—1221no—
375C22×C8—1221no—
376C22×C8C22⋊D6112yes—
377C22×C8C22⋊D6112yes—
378C22×C8C22×D6112yes—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4C22×D6112yes—
385#108—1228no—
386#103—28no—
387#103—1224no—
388#102—1224no—
389#101—1228no—
390C22⋊C8—1228no—
391C24—1221no—
392C24#1175822411yescharacteristic
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—22no—
404C2×Q8—24no—
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8—22no—
408C2×Q8—22no—
409C2×Q8—24no—
410C2×Q8—24no—
411C2×Q8—24no—
412C2×Q8—24no—
413C2×Q8—41no—
414C2×Q8—41no—
415C2×Q8—42no—
416C2×Q8—42no—
417C2×Q8—42no—
418C2×Q8—42no—
419C2×Q8—42no—
420C2×Q8—612no—
421C2×Q8—1221no—
422C2×Q8—1222no—
423C2×Q8—1222no—
424C2×Q8C2×D24414yes—
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—22no—
434C22×C4—24no—
435C22×C4—22no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—42no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—82no—
442C22×C4—1221no—
443C22×C4—1222no—
444C22×C4—1222no—
445C22×C4—2442no—
446C22×C4—2442no—
447C22×C4C2×D24412yes—
448C22×C4#1175822212yes—
449C22×C4D4×D6111yescharacteristic
450C22×C4D4×D6111yescharacteristic
451C22×C4D4×D6112yes—
452C22×C4#1175822412yes—
453C22×C4#1175822411yescharacteristic
454C22×C4C2×C22⋊D6111yescharacteristic
455C22×C4C2×C22⋊D6111yescharacteristic
456C22×C4C23×D6111yescharacteristic
457Q16—12216no—
458SD16—12216no—
459M16—614no—
460M16—1222no—
461M16—1224no—
462M16—1222no—
463M16—1222no—
464M16—1222no—
465M16—1222no—
466M16—2442no—
467M16—2442no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—24no—
471C2×C8—24no—
472C2×C8—1222no—
473C2×C8—1224no—
474C2×C8—1222no—
475C2×C8—1222no—
476C2×C8—2442no—
477C2×C8—2442no—
478C2×C8C2×C22⋊D6114yes—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—41no—
482C4⋊C4—41no—
483C23—22no—
484C23—22no—
485C23—1222no—
486C23—2442no—
487C23—2442no—
488C23—2442no—
489C23#1451974811yescharacteristic
490C23#1451974811yescharacteristic
491C23#1451976112yes—
492C23#1451976312yes—
493C23C2×#1175822411yescharacteristic
494Q8—24no—
495Q8—24no—
496Q8—42no—
497Q8—42no—
498Q8—44no—
499Q8—44no—
500Q8—1222no—
501Q8—1222no—
502Q8—2442no—
503D4—1222no—
504D4—1222no—
505D4—2442no—
506D4—2442no—
507D4—2444no—
508D4—2442no—
509C2×C4—24no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—44no—
513C2×C4—44no—
514C2×C4—42no—
515C2×C4—82no—
516C2×C4—82no—
517C2×C4—82no—
518C2×C4—1222no—
519C2×C4—2442no—
520C2×C4—2442no—
521C2×C4—2442no—
522C2×C4—2444no—
523C2×C4#1451974712yes—
524C2×C4#1451974712yes—
525C2×C4#1451974811yescharacteristic
526C2×C4#1451974811yescharacteristic
527C2×C4#1451974912yes—
528C2×C4#1451974912yes—
529C2×C4#1451975112yes—
530C2×C4#1451975112yes—
531C2×C4#1451975912yes—
532C2×C4#1451975912yes—
533C2×C4#1451976112yes—
534C2×C4#1451976312yes—
535C2×C4C2×D4×D6111yescharacteristic
536C2×C4C2×D4×D6111yescharacteristic
537C2×C4C22×C22⋊D6111yescharacteristic
538C2×C4C22×D24411yescharacteristic
539C2×C4C2×#1175822411yescharacteristic
540C2×C4C2×#1175822211yescharacteristic
541C8—24no—
542C8—1224no—
543C8—2442no—
544C8—2442no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—21no—
549C22—24no—
550C22—24no—
551C22—4884no—
552C22—2442no—
553C22—2442no—
554C22—2442no—
555C22#1683967812yes—
556C22#1683967812yes—
557C22#1684002212yes—
558C22#1684003412yes—
559C22C2×#1451974811yescharacteristic
560C22C2×#1451976111yescharacteristic
561C22C2×#1451976311yescharacteristic
562C4—44no—
563C4—82no—
564C4—2442no—
565C4#1683967812yes—
566C4#1683967812yes—
567C4C2×#1451974711yescharacteristic
568C4C2×#1451974911yescharacteristic
569C4C2×#1451975111yescharacteristic
570C4C2×#1451975911yescharacteristic
571C2—21no—
572C2—21no—
573C2—22no—
574C2—4882no—
575C2#2144711914yesdirect product factor
576C2C2×#1683967811yescharacteristic
577C2C2×#1684002211yescharacteristic
578C2C2×#1684003411yescharacteristic
subgroupG/H
centerC23#14519748
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC22×#103×C61C2
socleC23×C61#121
prime radicalC22×#11758222C22
hypercenterC22×#103D61
hypocenterC61C2×#2052
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
2. C22×#14519713C2semidirect
4. C22×#14519696C2semidirect
6. #21447119C2direct (N × H)
7. C2×#16839531C2semidirect
8. C22×#103×C61C2semidirect
20. C2×#14519713C22semidirect
26. C2×#14519696C22semidirect
30. #16839531C22semidirect
36. C2×#103×C61C22semidirect
285. C22×#103D61semidirect
293. C2×C61#2052semidirect
318. C2×#103C2×D61semidirect
326. C61C2×#2052semidirect
575. C2#21447119direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198082
C22×#145197132
C2×#168397612
C22×#145196962
C2×#168397282
#214471192
C2×#168395312
C22×#103×C612
C2×#205261