Finite Group Databasebeta

← C2×#21444797 #29652210

Subgroups — C2×#21444797 #29652210

Order 15616.

1328 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840350C211yesmaximal, characteristic
2C2×#16839918C211yesmaximal, characteristic, complemented
3C2×#16839901C211yesmaximal, characteristic, complemented
4#21444797C218yesmaximal, direct product factor
5C2×#16839498C211yesmaximal, characteristic, complemented
6C2×#16839495C211yesmaximal, characteristic, complemented
7C2×#16839486C211yesmaximal, characteristic, complemented
8C2×C61×#393C211yesmaximal, characteristic, complemented
9C22×#11758202—21no—
10C22×#11758201—21no—
11#16840350—22no—
12#16840350—22no—
13#16840350—22no—
14#16840350C2214yes—
15C2×#14519770—21no—
16C2×#14519763—21no—
17C2×#14519759—21no—
18C2×#14519756C2211yescharacteristic
19C2×#14519751C2211yescharacteristic
20C2×#14519750—21no—
21C2×#14519746—21no—
22C2×C4×C22⋊D61—21no—
23#16839918—22no—
24#16839918C2214yescomplemented
25#16839901—22no—
26#16839901C2214yescomplemented
27C2×#14519701—21no—
28C2×#14519701—21no—
29C2×C22⋊#92418C2211yescharacteristic
30C2×C22⋊#92418C2211yescharacteristic
31#16839498C2214yescomplemented
32#16839495C2214yescomplemented
33#16839486C2214yescomplemented
34C23×Q8×C61C2211yescharacteristic
35C22×C22⋊C4×C61—21no—
36C22×C22⋊C4×C61C2211yescharacteristic
37C61×#393—22no—
38C61×#393C2214yescomplemented
39C2×#95×C61—21no—
40C2×#95×C61C2211yescharacteristic
41C22×Dic122D411yescharacteristic
42C22×D244D411yescharacteristic
43C22×C22⋊D61—21no—
44C22×C22⋊D61—21no—
45C22×C22⋊D61—21no—
46C22×C4×D61—21no—
47C2×#11758202—24no—
48C2×#11758202—44no—
49C2×#11758201—24no—
50C2×#11758201—44no—
51C22×#92418—21no—
52C22×#92418—21no—
53#14519770—24no—
54#14519770—24no—
55#14519763—24no—
56#14519763—24no—
57#14519759—24no—
58#14519759—24no—
59#14519756—21no—
60#14519756—21no—
61#14519756D412yes—
62#14519756C2312yes—
63#14519751—21no—
64#14519751—21no—
65#14519751D412yes—
66#14519751C2312yes—
67#14519750—24no—
68#14519750—24no—
69#14519746—24no—
70#14519746—24no—
71C4×C22⋊D61—24no—
72C4×C22⋊D61—24no—
73C2×C4⋊Dic61D411yescharacteristic
74C2×C4⋊Dic61D411yescharacteristic
75C2×#11758196—21no—
76C2×#11758196—21no—
77C2×C22⋊Dic61—21no—
78C2×C22⋊Dic61—21no—
79C2×C22⋊Dic61—21no—
80C2×#11758198—21no—
81C2×#11758198—21no—
82C2×C4×Dic61—21no—
83#14519701—24no—
84#14519701—24no—
85C22⋊#92418—21no—
86C22⋊#92418—21no—
87C22⋊#92418C2312yes—
88C22⋊#92418C2312yes—
89C25×C61D411yescharacteristic
90C22×Q8×C61—21no—
91C22×Q8×C61—21no—
92C22×Q8×C61—21no—
93C22×Q8×C61—21no—
94C22×Q8×C61—21no—
95C22×Q8×C61—44no—
96C22×Q8×C61C2312yes—
97C23×C4×C61—21no—
98C23×C4×C61—21no—
99C23×C4×C61D411yescharacteristic
100C23×C4×C61C2311yescharacteristic
101C2×C22⋊C4×C61—21no—
102C2×C22⋊C4×C61—21no—
103C2×C22⋊C4×C61—21no—
104C2×C22⋊C4×C61—21no—
105C2×C22⋊C4×C61—24no—
106C2×C22⋊C4×C61—44no—
107C2×C22⋊C4×C61D412yes—
108C2×C22⋊C4×C61C2312yes—
109#95×C61—24no—
110#95×C61—21no—
111#95×C61C2312yes—
112C24×C61—21no—
113C24×C61—22no—
114C24×C61—21no—
115C24×C61—22no—
116C24×C61—42no—
117C24×C61—42no—
118C24×C61C2×D411yescharacteristic
119C24×C61C2×D412yes—
120C23×D61—21no—
121C2×Q8×C61—24no—
122C2×Q8×C61—24no—
123C2×Q8×C61—22no—
124C2×Q8×C61—22no—
125C2×Q8×C61—44no—
126C2×Q8×C61—42no—
127C2×Q8×C61—42no—
128C2×Q8×C61—44no—
129C2×Q8×C61—44no—
130C2×Q8×C61—44no—
131C2×Q8×C61—41no—
132C2×Q8×C61—41no—
133C22×C4×C61—24no—
134C22×C4×C61—21no—
135C22×C4×C61—22no—
136C22×C4×C61—21no—
137C22×C4×C61—22no—
138C22×C4×C61—42no—
139C22×C4×C61—42no—
140C22×C4×C61—41no—
141C22×C4×C61—41no—
142C22×C4×C61—42no—
143C22×C4×C61—42no—
144C22×C4×C61—42no—
145C22×C4×C61—42no—
146C22×C4×C61C2×D411yescharacteristic
147C22×C4×C61C2×D411yescharacteristic
148C22×C4×C61C2×D412yes—
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2411yescharacteristic
153C2×C22⋊D61—22no—
154C2×C22⋊D61—22no—
155C2×C22⋊D61—24no—
156C2×C22⋊D61—24no—
157C2×C22⋊D61—42no—
158C2×C22⋊D61—42no—
159C2×C22⋊D61—82no—
160C2×C22⋊D61—82no—
161C22×Dic61—21no—
162C22×Dic61—21no—
163C22×Dic61—21no—
164C2×D244—21no—
165C2×D244—42no—
166C2×D244C2×D412yes—
167C2×C4×D61—24no—
168C2×C4×D61—82no—
169C2×Dic122—21no—
170C2×Dic122—42no—
171C2×Dic122C2×D412yes—
172C22⋊C4×C61—22no—
173C22⋊C4×C61—22no—
174C22⋊C4×C61—22no—
175C22⋊C4×C61—22no—
176C22⋊C4×C61—48no—
177C22⋊Dic61—24no—
178C22⋊Dic61—24no—
179C22⋊Dic61—22no—
180C22⋊Dic61—22no—
181#11758202—48no—
182#11758201—48no—
183#11758198—24no—
184#11758198—22no—
185#11758198—22no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61C2×D412yes—
189C4⋊Dic61C2×D412yes—
190#11758196—24no—
191#11758196—22no—
192#11758196—22no—
193C4×Dic61—24no—
194C2×#92418—22no—
195C2×#92418—22no—
196C2×#92418—42no—
197C2×#92418—42no—
198C23×C61—22no—
199C23×C61—22no—
200C23×C61—22no—
201C23×C61—22no—
202C23×C61—22no—
203C23×C61—42no—
204C23×C61—42no—
205C23×C61—48no—
206C23×C61—42no—
207C23×C61—42no—
208C23×C61—42no—
209C23×C61—42no—
210C23×C61—81no—
211C23×C61—81no—
212C23×C61—84no—
213C23×C61#12011yescharacteristic
214C23×C61#12011yescharacteristic
215C23×C61#13512yes—
216C23×C61#13712yes—
217C23×C61C22×D411yescharacteristic
218C22×D61—22no—
219C22×D61—42no—
220C22×D61—42no—
221C22×D61—42no—
222Q8×C61—24no—
223Q8×C61—24no—
224Q8×C61—42no—
225Q8×C61—42no—
226Q8×C61—44no—
227Q8×C61—44no—
228C2×C4×C61—22no—
229C2×C4×C61—22no—
230C2×C4×C61—24no—
231C2×C4×C61—22no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—42no—
237C2×C4×C61—44no—
238C2×C4×C61—42no—
239C2×C4×C61—42no—
240C2×C4×C61—44no—
241C2×C4×C61—42no—
242C2×C4×C61—42no—
243C2×C4×C61—42no—
244C2×C4×C61—42no—
245C2×C4×C61—81no—
246C2×C4×C61—84no—
247C2×C4×C61#12011yescharacteristic
248C2×C4×C61#12011yescharacteristic
249C2×C4×C61C22×D411yescharacteristic
250C2×C4×C61C22×D411yescharacteristic
251C22⋊D61—42no—
252C22⋊D61—42no—
253C22⋊D61—44no—
254C22⋊D61—84no—
255C22⋊D61—84no—
256C2×Dic61—22no—
257C2×Dic61—22no—
258C2×Dic61—22no—
259C2×Dic61—42no—
260C2×Dic61—42no—
261C2×Dic61—42no—
262D244—42no—
263D244—81no—
264C4×D61—84no—
265Dic122—42no—
266Dic122—81no—
267#92418—42no—
268#92418—42no—
269C2×#1606—611nomaximal, Sylow
270C22×C61—24no—
271C22×C61—24no—
272C22×C61—21no—
273C22×C61—21no—
274C22×C61—21no—
275C22×C61—21no—
276C22×C61—44no—
277C22×C61—42no—
278C22×C61—42no—
279C22×C61—42no—
280C22×C61—82no—
281C22×C61—84no—
282C22×C61—84no—
283C22×C61#45212yes—
284C22×C61#45212yes—
285C22×C61#45512yes—
286C22×C61B(4,𝔽2)12yes—
287C22×C61C2×#12011yescharacteristic
288C22×C61C2×#13511yescharacteristic
289C22×C61C2×#13711yescharacteristic
290C2×D61—42no—
291C2×D61—42no—
292C2×D61—42no—
293C2×D61—84no—
294C4×C61—21no—
295C4×C61—21no—
296C4×C61—21no—
297C4×C61—21no—
298C4×C61—42no—
299C4×C61—44no—
300C4×C61—82no—
301Dic61—42no—
302Dic61—42no—
303Dic61—42no—
304C2×#538—611no—
305C2×#451—611no—
306C2×#448—611no—
307C2×#393D6111yescharacteristic, complemented
308#1606—618no—
309C2×#328—611no—
310C2×#327—611no—
311C2×#323—611no—
312C2×C61—21no—
313C2×C61—21no—
314C2×C61—22no—
315C2×C61—82no—
316C2×C61#160614yescomplemented
317C2×C61C2×#45211yescharacteristic
318C2×C61C2×#45511yescharacteristic
319C2×C61C2×B(4,𝔽2)11yescharacteristic
320D61—82no—
321C23×Q8C2×D6111yescharacteristic
322C22×Q16—1221no—
323C22×SD16—1221no—
324#538—614no—
325#538—1222no—
326#538—1222no—
327#538—1222no—
328C2×#126—1221no—
329C2×#124—1221no—
330C2×#123—1221no—
331C2×C22⋊Q8—611no—
332C2×#121—611no—
333C2×#121—1221no—
334C2×#120—1221no—
335C2×C4×D4—1221no—
336C22×C22⋊C4—21no—
337C22×C22⋊C4C2×D6111yescharacteristic
338#451—614no—
339#451—1222no—
340#448—614no—
341#448—1222no—
342C2×#103—1221no—
343C2×#103—1221no—
344C2×C22⋊C8—611no—
345C2×C22⋊C8—611no—
346#393—22no—
347#393C2×D6114yescomplemented
348C2×#95—21no—
349C2×#95C2×D6111yescharacteristic
350#328—614no—
351#327—614no—
352#323—614no—
353C61C2×#160611yescharacteristic, complemented, Sylow
354C25C22⋊D6111yescharacteristic
355C22×Q8—21no—
356C22×Q8—21no—
357C22×Q8—21no—
358C22×Q8—21no—
359C22×Q8—21no—
360C22×Q8—44no—
361C22×Q8—611no—
362C22×Q8C22×D6112yes—
363C22×D4—611no—
364C22×D4—1221no—
365C22×D4—1221no—
366C22×D4—1221no—
367C23×C4—21no—
368C23×C4—21no—
369C23×C4—1221no—
370C23×C4C22⋊D6111yescharacteristic
371C23×C4C22×D6111yescharacteristic
372C2×Q16—1224no—
373C2×Q16—2444no—
374C2×SD16—1224no—
375C2×SD16—2444no—
376C22×C8—1221no—
377C22×C8—1221no—
378#126—1224no—
379#126—1224no—
380#124—1224no—
381#124—1224no—
382#123—1224no—
383#123—1224no—
384C22⋊Q8—612no—
385C22⋊Q8—612no—
386C22⋊Q8—1221no—
387C22⋊Q8—1221no—
388#121—612no—
389#121—612no—
390#121—1224no—
391#121—1224no—
392#121—1221no—
393#121—1221no—
394#120—1224no—
395#120—1224no—
396C4×D4—1224no—
397C4×D4—1224no—
398C2×C4⋊C4—611no—
399C2×C4⋊C4—611no—
400C2×C4⋊C4—1221no—
401C2×C4⋊C4—1221no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—24no—
407C2×C22⋊C4—44no—
408C2×C22⋊C4—1221no—
409C2×C22⋊C4—1221no—
410C2×C22⋊C4—1221no—
411C2×C22⋊C4—1221no—
412C2×C22⋊C4—1221no—
413C2×C22⋊C4C22⋊D6112yes—
414C2×C22⋊C4C22×D6112yes—
415C2×C42—1221no—
416#103—1224no—
417#103—1224no—
418C22⋊C8—612no—
419C22⋊C8—612no—
420C22⋊C8—1221no—
421C22⋊C8—1221no—
422#95—24no—
423#95—21no—
424#95C22×D6112yes—
425C24—22no—
426C24—21no—
427C24—21no—
428C24—22no—
429C24—42no—
430C24—42no—
431C24—1221no—
432C24C2×C22⋊D6111yescharacteristic
433C24C2×C22⋊D6112yes—
434C2×Q8—24no—
435C2×Q8—24no—
436C2×Q8—22no—
437C2×Q8—22no—
438C2×Q8—44no—
439C2×Q8—42no—
440C2×Q8—42no—
441C2×Q8—44no—
442C2×Q8—44no—
443C2×Q8—44no—
444C2×Q8—41no—
445C2×Q8—41no—
446C2×Q8—612no—
447C2×Q8—1221no—
448C2×Q8—2442no—
449C2×D4—612no—
450C2×D4—1224no—
451C2×D4—1224no—
452C2×D4—1222no—
453C2×D4—1222no—
454C2×D4—1221no—
455C2×D4—4882no—
456C2×D4—4882no—
457C2×D4—2442no—
458C2×D4—2442no—
459C2×D4—2442no—
460C22×C4—24no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—1224no—
474C22×C4—1221no—
475C22×C4—1221no—
476C22×C4—1221no—
477C22×C4—4882no—
478C22×C4D4×D6111yescharacteristic
479C22×C4D4×D6111yescharacteristic
480C22×C4D4×D6111yescharacteristic
481C22×C4D4×D6111yescharacteristic
482C22×C4C2×C22⋊D6112yes—
483C22×C4C2×C22⋊D6111yescharacteristic
484C22×C4C23×D6111yescharacteristic
485Q16—2448no—
486SD16—2448no—
487C2×C8—1222no—
488C2×C8—1222no—
489C2×C8—2442no—
490C2×C8—2442no—
491C4⋊C4—612no—
492C4⋊C4—612no—
493C4⋊C4—1224no—
494C4⋊C4—1222no—
495C4⋊C4—1221no—
496C4⋊C4—1221no—
497C4⋊C4—1222no—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—22no—
501C22⋊C4—22no—
502C22⋊C4—48no—
503C22⋊C4—1224no—
504C22⋊C4—1224no—
505C22⋊C4—1224no—
506C22⋊C4—1222no—
507C22⋊C4—1222no—
508C22⋊C4—1222no—
509C22⋊C4—1222no—
510C42—1224no—
511C23—22no—
512C23—22no—
513C23—22no—
514C23—22no—
515C23—22no—
516C23—42no—
517C23—42no—
518C23—48no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—81no—
524C23—81no—
525C23—84no—
526C23—1222no—
527C23—2442no—
528C23—2442no—
529C23—2442no—
530C23#1451974511yescharacteristic
531C23#1451974511yescharacteristic
532C23#1451979712yes—
533C23#1451980812yes—
534C23C22×C22⋊D6111yescharacteristic
535Q8—24no—
536Q8—24no—
537Q8—42no—
538Q8—42no—
539Q8—44no—
540Q8—44no—
541Q8—4881no—
542Q8—2442no—
543D4—4881no—
544D4—4884no—
545D4—4884no—
546D4—2442no—
547D4—2442no—
548D4—2442no—
549D4—2444no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—22no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—42no—
559C2×C4—44no—
560C2×C4—42no—
561C2×C4—44no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—81no—
568C2×C4—84no—
569C2×C4—1222no—
570C2×C4—1222no—
571C2×C4—1222no—
572C2×C4—4884no—
573C2×C4—2442no—
574C2×C4—2442no—
575C2×C4—2442no—
576C2×C4#1451974511yescharacteristic
577C2×C4#1451974511yescharacteristic
578C2×C4C2×D4×D6111yescharacteristic
579C2×C4C2×D4×D6111yescharacteristic
580C8—2442no—
581C8—2442no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—21no—
586C22—24no—
587C22—24no—
588C22—44no—
589C22—42no—
590C22—42no—
591C22—42no—
592C22—82no—
593C22—84no—
594C22—84no—
595C22—4884no—
596C22—2442no—
597C22—2442no—
598C22—2442no—
599C22#1683992212yes—
600C22#1683992212yes—
601C22#1683993912yes—
602C22#1683994812yes—
603C22C2×#1451974511yescharacteristic
604C22C2×#1451979711yescharacteristic
605C22C2×#1451980811yescharacteristic
606C4—21no—
607C4—21no—
608C4—21no—
609C4—21no—
610C4—42no—
611C4—44no—
612C4—82no—
613C4—2442no—
614C4—2442no—
615C4—2442no—
616C2—21no—
617C2—21no—
618C2—22no—
619C2—82no—
620C2—4882no—
621C2#2144479714yesdirect product factor
622C2C2×#1683992211yescharacteristic
623C2C2×#1683993911yescharacteristic
624C2C2×#1683994811yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#393C2
socleC23×C61#120
prime radicalC2×#16840350C2
hypercenterC2×#393D61
hypocenterC61C2×#1606
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#393

Complements

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

NH ≅ G/Ntype
2. C2×#16839918C2semidirect
3. C2×#16839901C2semidirect
4. #21444797C2direct (N × H)
5. C2×#16839498C2semidirect
6. C2×#16839495C2semidirect
7. C2×#16839486C2semidirect
8. C2×C61×#393C2semidirect
24. #16839918C22semidirect
26. #16839901C22semidirect
31. #16839498C22semidirect
32. #16839495C22semidirect
33. #16839486C22semidirect
38. C61×#393C22semidirect
307. C2×#393D61semidirect
316. C2×C61#1606semidirect
347. #393C2×D61semidirect
353. C61C2×#1606semidirect
621. C2#21444797direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403502
C2×#168399182
C2×#168399012
#214447972
C2×#168394982
C2×#168394952
C2×#168394862
C2×C61×#3932
C2×#160661