Finite Group Databasebeta

← C2×#21447545 #29832939

Subgroups — C2×#21447545 #29832939

Order 15616.

1154 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#135×D61C211yesmaximal, characteristic
2C22×#14519716C211yesmaximal, characteristic, complemented
3C2×#108×D61C211yesmaximal, characteristic, complemented
4#21447545C218yesmaximal, direct product factor
5C2×#16839570C211yesmaximal, characteristic, complemented
6C2×#16839569C211yesmaximal, characteristic, complemented
7C2×#16839568C211yesmaximal, characteristic, complemented
8C2×C61×#359C211yesmaximal, characteristic, complemented
9C2×#41×D61—21no—
10C2×#14519800C411yescharacteristic
11C2×#14519799C2211yescharacteristic
12C2×#14519798—21no—
13C2×#14519797—21no—
14C2×#14519796C411yescharacteristic
15#135×D61—22no—
16#135×D61—22no—
17#135×D61C414yes—
18#135×D61C2214yes—
19C2×Q16×D61C411yescharacteristic
20C2×SD16×D61—21no—
21C2×D8×D61C411yescharacteristic
22C2×M16×D61—21no—
23C22×C8×D61C2211yescharacteristic
24C2×#14519716—21no—
25C2×#14519716—22no—
26C2×#14519716—21no—
27C2×#14519716C2214yescomplemented
28C22×#11758185C2211yescharacteristic, complemented
29C2×#14519713C2211yescharacteristic, complemented
30C2×#14519712—21no—
31#108×D61—22no—
32#108×D61C2214yescomplemented
33#16839570C2214yescomplemented
34#16839569C2214yescomplemented
35#16839568C2214yescomplemented
36C2×#135×C61C2211yescharacteristic
37C22×C16×C61C2211yescharacteristic, complemented
38C2×#108×C61C2211yescharacteristic, complemented
39C61×#359C2214yescomplemented
40C2×#11758226—21no—
41C2×#11758222—21no—
42C2×#11758222—41no—
43C2×#11758224—21no—
44C2×#11758224—41no—
45#41×D61—24no—
46#41×D61—24no—
47#41×D61—42no—
48#41×D61—42no—
49C2×Q8×D61—21no—
50C2×D4×D61—21no—
51C2×D4×D61—41no—
52C22×C4×D61—41no—
53C22×C4×D61D411yescharacteristic
54#14519800—22no—
55#14519800C2×C414yes—
56#14519799—21no—
57#14519799—21no—
58#14519799C2×C412yes—
59#14519799C2312yes—
60#14519798—24no—
61#14519798—24no—
62#14519797—24no—
63#14519797—24no—
64#14519796—22no—
65#14519796C2×C414yes—
66C2×Dic244C2×C411yescharacteristic
67C2×#11758202—21no—
68Q16×D61—22no—
69Q16×D61C2×C414yes—
70C2×#11758190—21no—
71C2×#11758200—21no—
72C2×#11758201—21no—
73SD16×D61—24no—
74SD16×D61—24no—
75C2×D488C2×C411yescharacteristic
76C2×#11758199—21no—
77D8×D61—22no—
78D8×D61C2×C414yes—
79C2×#11758194—21no—
80C2×#11758189—41no—
81M16×D61—24no—
82M16×D61—42no—
83C22×#92418D411yescharacteristic
84C2×C8×D61—41no—
85C2×C8×D61C2×C411yescharacteristic
86C2×C8×D61C2×C412yes—
87C2×C8×D61C2×C411yescharacteristic
88C2×C8×D61D412yes—
89C2×C8×D61D411yescharacteristic
90C2×C8×D61D412yes—
91C2×C8×D61D411yescharacteristic
92C2×C8×D61C2312yes—
93#14519716—24no—
94#14519716—24no—
95C2×#11758185—21no—
96C2×#11758185—21no—
97C2×#11758185C2312yescomplemented
98#14519713—21no—
99#14519713C2312yescomplemented
100#14519712—24no—
101C2×#41×C61—21no—
102#135×C61—21no—
103#135×C61—21no—
104#135×C61C2×C412yes—
105#135×C61C2312yes—
106C2×Q16×C61C2×C411yescharacteristic
107C2×SD16×C61—21no—
108C2×D8×C61C2×C411yescharacteristic
109C2×M16×C61—21no—
110C22×C8×C61C2311yescharacteristic
111C2×C16×C61—21no—
112C2×C16×C61—21no—
113C2×C16×C61C2312yescomplemented
114#108×C61—21no—
115#108×C61C2312yescomplemented
116C23×D61—41no—
117C23×D61SD1611yescharacteristic
118#41×C61—22no—
119#41×C61—22no—
120#41×C61—41no—
121#41×C61—41no—
122C2×Q8×C61—21no—
123C2×D4×C61—21no—
124C2×D4×C61—41no—
125C22×C4×C61—41no—
126C22×C4×C61C2×D411yescharacteristic
127C2×C22⋊D61—41no—
128C2×C22⋊D61—41no—
129C2×C22⋊D61—41no—
130C22×Dic61—41no—
131C22×Dic61SD1611yescharacteristic
132#11758226—24no—
133#11758226—42no—
134Q8×D61—24no—
135Q8×D61—42no—
136#11758224—24no—
137#11758224—44no—
138#11758224—44no—
139#11758224—42no—
140D4×D61—24no—
141D4×D61—44no—
142D4×D61—44no—
143D4×D61—42no—
144#11758222—22no—
145#11758222—22no—
146#11758222—41no—
147#11758222—41no—
148#11758222—44no—
149#11758222—44no—
150C2×D244—21no—
151C2×D244—41no—
152C2×C4×D61—41no—
153C2×C4×D61—41no—
154C2×C4×D61—41no—
155C2×C4×D61—44no—
156C2×C4×D61—44no—
157C2×C4×D61C22⋊C411yescharacteristic
158C2×C4×D61C22⋊C412yes—
159C2×C4×D61C22⋊C411yescharacteristic
160C2×C4×D61D811yescharacteristic
161C2×C4×D61D812yes—
162C2×C4×D61D811yescharacteristic
163C2×C4×D61SD1612yes—
164C2×C4×D61C2×D412yes—
165C2×Dic122—21no—
166C2×Dic122—41no—
167Q16×C61—21no—
168Q16×C61C22×C412yes—
169SD16×C61—22no—
170SD16×C61—22no—
171D8×C61—21no—
172D8×C61C22×C412yes—
173M16×C61—22no—
174M16×C61—41no—
175C2×C8×C61—41no—
176C2×C8×C61C22×C411yescharacteristic
177C2×C8×C61C22×C411yescharacteristic
178C2×C8×C61C2×D411yescharacteristic
179C2×C8×C61C2×D411yescharacteristic
180C2×C8×C61C2×D411yescharacteristic
181C2×C8×C61C2411yescharacteristic
182#11758202—24no—
183#11758201—24no—
184#11758200—24no—
185#11758199—24no—
186#11758194—22no—
187#11758194—41no—
188C2×#92418—41no—
189C2×#92418C22⋊C411yescharacteristic
190C2×#92418C22⋊C411yescharacteristic
191C2×#92418C22⋊C412yes—
192C2×#92418C2×D412yes—
193Dic244—21no—
194Dic244C22×C412yes—
195D488—21no—
196D488C22×C412yes—
197#11758190—22no—
198#11758190—22no—
199#11758189—44no—
200C8×D61—44no—
201C8×D61C22⋊C412yes—
202C8×D61C22⋊C412yes—
203C8×D61C22⋊C412yes—
204C8×D61C22⋊C412yes—
205C8×D61C22×C412yes—
206C8×D61C22×C412yes—
207C8×D61C2×D412yes—
208C8×D61C2×D412yes—
209C16×C61—22no—
210#11758185—22no—
211C23×C61—41no—
212C23×C61C2×SD1611yescharacteristic
213C22×D61—42no—
214C22×D61—41no—
215C22×D61—44no—
216C22×D61—84no—
217C22×D61#10211yescharacteristic
218C22×D61#10211yescharacteristic
219C22×D61#10212yes—
220C22×D61C2×SD1612yes—
221Q8×C61—22no—
222Q8×C61—41no—
223D4×C61—22no—
224D4×C61—42no—
225D4×C61—42no—
226D4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61—42no—
229C2×C4×C61—42no—
230C2×C4×C61C2×C22⋊C411yescharacteristic
231C2×C4×C61C2×C22⋊C411yescharacteristic
232C2×C4×C61C2×D811yescharacteristic
233C2×C4×C61C2×D811yescharacteristic
234C2×C4×C61C2×SD1611yescharacteristic
235C2×C4×C61C22×D411yescharacteristic
236C22⋊D61—42no—
237C22⋊D61—42no—
238C22⋊D61—44no—
239C22⋊D61—44no—
240C2×Dic61—41no—
241C2×Dic61—44no—
242C2×Dic61#10211yescharacteristic
243C2×Dic61#10211yescharacteristic
244C2×Dic61#10212yes—
245C2×Dic61C2×SD1612yes—
246D244—22no—
247D244—44no—
248D244—41no—
249C4×D61—44no—
250C4×D61—42no—
251C4×D61—42no—
252C4×D61—44no—
253C4×D61#10212yes—
254C4×D61#10212yes—
255C4×D61#10212yes—
256C4×D61#10212yes—
257C4×D61C2×C22⋊C412yes—
258C4×D61C2×C22⋊C412yes—
259C4×D61C2×D812yes—
260C4×D61C2×D812yes—
261Dic122—22no—
262Dic122—41no—
263Dic122—44no—
264C8×C61—42no—
265C8×C61C2×C22⋊C411yescharacteristic
266C8×C61C2×C22⋊C411yescharacteristic
267C8×C61C23×C411yescharacteristic
268C8×C61C22×D411yescharacteristic
269#92418—42no—
270#92418C2×C22⋊C412yes—
271#92418C2×C22⋊C412yes—
272C2×#2143—611nomaximal, Sylow
273C22×C61—22no—
274C22×C61—42no—
275C22×C61—82no—
276C22×C61C2×#10211yescharacteristic
277C22×C61C2×#10211yescharacteristic
278C22×C61C22×SD1611yescharacteristic
279C2×D61—22no—
280C2×D61—22no—
281C2×D61—42no—
282C2×D61—42no—
283C2×D61—42no—
284C2×D61—88no—
285C2×D61—82no—
286C2×D61C2×#10212yes—
287C2×D61C2×#10212yes—
288C4×C61—42no—
289C4×C61C2×#10211yescharacteristic
290C4×C61C2×#10211yescharacteristic
291C4×C61C22×C22⋊C411yescharacteristic
292C4×C61C22×D811yescharacteristic
293Dic61—42no—
294Dic61C2×#10212yes—
295Dic61C2×#10212yes—
296C22×#135—611no—
297C22×M32—611no—
298C22×#108—611no—
299#2143—618no—
300C2×#359—611no—
301C2×#359—611no—
302C2×#359—611no—
303C2×#359D6111yescharacteristic, complemented
304C2×C61—21no—
305C2×C61—21no—
306C2×C61—82no—
307C2×C61#214312yescomplemented
308C2×C61C22×#10211yescharacteristic
309D61—22no—
310D61—22no—
311D61—82no—
312C22×#41—1221no—
313C2×#135—614no—
314C2×#135—614no—
315C2×#135—611no—
316C2×#135—611no—
317C2×#135—611no—
318C2×#135—1221no—
319C2×#135—1222no—
320C2×#135—1222no—
321C2×#135—1221no—
322C2×#135C2×D6111yescharacteristic
323C22×Q16—611no—
324C22×SD16—1221no—
325C22×D8—611no—
326C22×M16—1221no—
327C23×C8—611no—
328C2×M32—614no—
329C2×M32—1221no—
330C2×M32—1221no—
331C2×M32—1222no—
332C22×C16—611no—
333C22×C16C2×D6111yescharacteristic, complemented
334C2×#108—611no—
335C2×#108—614no—
336C2×#108—1222no—
337C2×#108—1221no—
338C2×#108C2×D6111yescharacteristic, complemented
339#359—614no—
340#359—614no—
341#359—614no—
342#359C2×D6114yescomplemented
343C61C2×#214311yescharacteristic, complemented, Sylow
344C2×#41—21no—
345C2×#41—1221no—
346C2×#41—1221no—
347C2×#41—1224no—
348C2×#41—1224no—
349C2×#41—1221no—
350C2×#41—2441no—
351C2×#41—2441no—
352C2×#41—2442no—
353C2×#41—2442no—
354C22×Q8—1221no—
355C22×D4—1221no—
356C22×D4—2441no—
357C23×C4—611no—
358C23×C4—2441no—
359#135—21no—
360#135—21no—
361#135—614no—
362#135—614no—
363#135—612no—
364#135—612no—
365#135—1222no—
366#135—1224no—
367#135—1224no—
368#135—1222no—
369#135—1224no—
370#135—1224no—
371#135—1221no—
372#135—1221no—
373#135C4×D6112yes—
374#135C22×D6112yes—
375C2×Q16—614no—
376C2×Q16—611no—
377C2×Q16—1222no—
378C2×Q16—1221no—
379C2×Q16C4×D6111yescharacteristic
380C2×SD16—21no—
381C2×SD16—1224no—
382C2×SD16—1224no—
383C2×SD16—1221no—
384C2×SD16—1221no—
385C2×SD16—1221no—
386C2×D8—614no—
387C2×D8—611no—
388C2×D8—1222no—
389C2×D8—1221no—
390C2×D8C4×D6111yescharacteristic
391C2×M16—21no—
392C2×M16—1224no—
393C2×M16—1221no—
394C2×M16—2441no—
395C2×M16—2442no—
396C22×C8—611no—
397C22×C8—611no—
398C22×C8—611no—
399C22×C8—612no—
400C22×C8—611no—
401C22×C8—612no—
402C22×C8—611no—
403C22×C8—612no—
404C22×C8—612no—
405C22×C8—2441no—
406C22×C8C22×D6111yescharacteristic
407M32—1224no—
408M32—1224no—
409C2×C16—21no—
410C2×C16—21no—
411C2×C16—612no—
412C2×C16—1221no—
413C2×C16—1221no—
414C2×C16C22×D6112yescomplemented
415#108—21no—
416#108—612no—
417#108—1224no—
418#108—1221no—
419#108C22×D6112yescomplemented
420C24—611no—
421C24—2441no—
422#41—22no—
423#41—22no—
424#41—41no—
425#41—41no—
426#41—1224no—
427#41—1224no—
428#41—1222no—
429#41—1222no—
430#41—2444no—
431#41—2444no—
432#41—2444no—
433#41—2444no—
434#41—2442no—
435#41—2442no—
436#41—2441no—
437#41—2441no—
438C2×Q8—21no—
439C2×Q8—1224no—
440C2×Q8—1221no—
441C2×Q8—2441no—
442C2×Q8—2442no—
443C2×D4—21no—
444C2×D4—41no—
445C2×D4—1224no—
446C2×D4—1221no—
447C2×D4—2441no—
448C2×D4—2442no—
449C2×D4—2441no—
450C2×D4—2444no—
451C2×D4—2444no—
452C2×D4—2441no—
453C2×D4—2441no—
454C22×C4—41no—
455C22×C4—611no—
456C22×C4—612no—
457C22×C4—611no—
458C22×C4—611no—
459C22×C4—612no—
460C22×C4—612no—
461C22×C4—611no—
462C22×C4—611no—
463C22×C4—612no—
464C22×C4—2441no—
465C22×C4—2444no—
466C22×C4—2444no—
467C22×C4—2441no—
468C22×C4—2441no—
469C22×C4—2441no—
470C22×C4D4×D6111yescharacteristic
471Q16—21no—
472Q16—612no—
473Q16—1224no—
474Q16—1221no—
475Q16C2×C4×D6112yes—
476SD16—22no—
477SD16—22no—
478SD16—1224no—
479SD16—1224no—
480SD16—1222no—
481SD16—1222no—
482D8—21no—
483D8—612no—
484D8—1224no—
485D8—1221no—
486D8C2×C4×D6112yes—
487M16—22no—
488M16—41no—
489M16—1222no—
490M16—2444no—
491M16—2441no—
492C2×C8—41no—
493C2×C8—612no—
494C2×C8—611no—
495C2×C8—611no—
496C2×C8—612no—
497C2×C8—612no—
498C2×C8—612no—
499C2×C8—612no—
500C2×C8—612no—
501C2×C8—612no—
502C2×C8—612no—
503C2×C8—612no—
504C2×C8—612no—
505C2×C8—2444no—
506C2×C8—2441no—
507C2×C8C2×C4×D6111yescharacteristic
508C2×C8C2×C4×D6111yescharacteristic
509C2×C8D4×D6111yescharacteristic
510C2×C8D4×D6111yescharacteristic
511C2×C8D4×D6111yescharacteristic
512C2×C8C23×D6111yescharacteristic
513C16—22no—
514C16—1222no—
515C23—41no—
516C23—611no—
517C23—611no—
518C23—612no—
519C23—612no—
520C23—4884no—
521C23—2442no—
522C23—2444no—
523C23—2441no—
524C23SD16×D6111yescharacteristic
525Q8—22no—
526Q8—41no—
527Q8—1222no—
528Q8—2444no—
529Q8—2441no—
530D4—22no—
531D4—42no—
532D4—42no—
533D4—41no—
534D4—1222no—
535D4—2444no—
536D4—2444no—
537D4—2444no—
538D4—2442no—
539D4—2442no—
540D4—2441no—
541C2×C4—41no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—611no—
545C2×C4—611no—
546C2×C4—612no—
547C2×C4—612no—
548C2×C4—612no—
549C2×C4—612no—
550C2×C4—612no—
551C2×C4—612no—
552C2×C4—612no—
553C2×C4—612no—
554C2×C4—612no—
555C2×C4—612no—
556C2×C4—2444no—
557C2×C4—2444no—
558C2×C4—2444no—
559C2×C4—2441no—
560C2×C4—2442no—
561C2×C4—2442no—
562C2×C4C22⋊C4×D6111yescharacteristic
563C2×C4C22⋊C4×D6111yescharacteristic
564C2×C4D8×D6111yescharacteristic
565C2×C4D8×D6111yescharacteristic
566C2×C4SD16×D6111yescharacteristic
567C2×C4C2×D4×D6111yescharacteristic
568C8—42no—
569C8—612no—
570C8—612no—
571C8—2442no—
572C8C22⋊C4×D6111yescharacteristic
573C8C22⋊C4×D6111yescharacteristic
574C8C22×C4×D6111yescharacteristic
575C8C2×D4×D6111yescharacteristic
576C22—22no—
577C22—42no—
578C22—82no—
579C22—612no—
580C22—612no—
581C22—1222no—
582C22—1222no—
583C22—4888no—
584C22—4882no—
585C22—2442no—
586C22—2442no—
587C22—2442no—
588C22#102×D6111yescharacteristic
589C22#102×D6111yescharacteristic
590C22C2×SD16×D6111yescharacteristic
591C4—42no—
592C4—612no—
593C4—612no—
594C4—2442no—
595C4#102×D6111yescharacteristic
596C4#102×D6111yescharacteristic
597C4C2×C22⋊C4×D6111yescharacteristic
598C4C2×D8×D6111yescharacteristic
599C2—21no—
600C2—21no—
601C2—82no—
602C2—1222no—
603C2—1222no—
604C2—4882no—
605C2#2144754512yesdirect product factor
606C2C2×#102×D6111yescharacteristic
subgroupG/H
centerC2×C4D8×D61
commutatorC8×C61C23×C4
FrattiniC2×C8C23×D61
FittingC2×C61×#359C2
socleC22×C61C2×#102
prime radicalC2×#135×D61C2
cosocleC2×C8×C61C24
hypercenterC2×#359D61
hypocenterC61C2×#2143
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C2×#359

Complements

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

NH ≅ G/Ntype
2. C22×#14519716C2semidirect
3. C2×#108×D61C2semidirect
4. #21447545C2direct (N × H)
5. C2×#16839570C2semidirect
6. C2×#16839569C2semidirect
7. C2×#16839568C2semidirect
8. C2×C61×#359C2semidirect
27. C2×#14519716C22semidirect
28. C22×#11758185C22semidirect
29. C2×#14519713C22semidirect
32. #108×D61C22semidirect
33. #16839570C22semidirect
34. #16839569C22semidirect
35. #16839568C22semidirect
37. C22×C16×C61C22semidirect
38. C2×#108×C61C22semidirect
39. C61×#359C22semidirect
97. C2×#11758185C23semidirect
99. #14519713C23semidirect
113. C2×C16×C61C23semidirect
115. #108×C61C23semidirect
303. C2×#359D61semidirect
307. C2×C61#2143semidirect
333. C22×C16C2×D61semidirect
338. C2×#108C2×D61semidirect
342. #359C2×D61semidirect
343. C61C2×#2143semidirect
414. C2×C16C22×D61semidirect
419. #108C22×D61semidirect
605. C2#21447545direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#135×D612
C22×#145197162
C2×#108×D612
#214475452
C2×#168395702
C2×#168395692
C2×#168395682
C2×C61×#3592
C2×#214361