Finite Group Databasebeta

← C2×#21444308 #29647105

Subgroups — C2×#21444308 #29647105

Order 15616.

1606 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840273C211yesmaximal, characteristic
2C22×C22⋊#92418C211yesmaximal, characteristic, complemented
3#21444308C218yesmaximal, direct product factor
4C2×#16839498C212yesmaximal, complemented
5C2×#16839495C212yesmaximal, complemented
6C2×C4×C22⋊C4×C61C211yesmaximal, characteristic, complemented
7C22×#11758222C411yescharacteristic, complemented
8C23×#92418—21no—
9#16840273—22no—
10#16840273—22no—
11#16840273C414yescomplemented
12#16840273C2214yes—
13C2×#14519760—21no—
14C2×#14519756C411yescharacteristic, complemented
15C2×#14519756C2211yescharacteristic
16C2×#14519751C411yescharacteristic, complemented
17C2×#14519751C2211yescharacteristic
18C2×#14519746—21no—
19C2×C4×C22⋊D61—21no—
20C2×C4×C22⋊D61—21no—
21C2×#14519736C411yescharacteristic, complemented
22C2×C22⋊#92418—21no—
23C2×C22⋊#92418—22no—
24C2×C22⋊#92418C2212yes—
25C2×C22⋊#92418C2214yescomplemented
26#16839498C2218yescomplemented
27#16839495C2218yescomplemented
28C24×C4×C61C2211yescharacteristic
29C22×C22⋊C4×C61—21no—
30C22×C42×C61—21no—
31C4×C22⋊C4×C61—22no—
32C4×C22⋊C4×C61C2214yescomplemented
33C2×#95×C61C2212yes—
34C2×#11758222—22no—
35C2×#11758222—44no—
36C2×#11758222C2×C414yescomplemented
37C22×Dic122C2×C411yescharacteristic
38C22×D244C2×C411yescharacteristic
39C22×C22⋊D61—21no—
40C22×C22⋊D61—21no—
41C22×C22⋊D61—21no—
42C22×C4×D61—21no—
43C22×#92418—22no—
44C22×#92418—24no—
45C22×#92418—44no—
46#14519760—24no—
47#14519760—24no—
48#14519756—22no—
49#14519756—21no—
50#14519756—21no—
51#14519756C2×C412yes—
52#14519756C2×C414yescomplemented
53#14519756C2312yes—
54#14519751—22no—
55#14519751—21no—
56#14519751—21no—
57#14519751C2×C412yes—
58#14519751C2×C414yescomplemented
59#14519751C2312yes—
60#14519746—24no—
61#14519746—24no—
62C4×C22⋊D61—24no—
63C4×C22⋊D61—24no—
64C4×C22⋊D61—24no—
65C4×C22⋊D61—24no—
66#14519736—22no—
67#14519736C2×C414yescomplemented
68C2×C4⋊Dic61C2×C411yescharacteristic
69C2×C4⋊Dic61C2×C411yescharacteristic
70C2×#11758196—21no—
71C2×#11758196—21no—
72C2×C22⋊Dic61—21no—
73C2×C22⋊Dic61—21no—
74C2×C22⋊Dic61—21no—
75C2×#11758198—21no—
76C2×#11758198—21no—
77C2×C4×Dic61—21no—
78C22⋊#92418—22no—
79C22⋊#92418—24no—
80C22⋊#92418C2314yes—
81C25×C61D411yescharacteristic
82C23×C4×C61—22no—
83C23×C4×C61—44no—
84C23×C4×C61C2×C411yescharacteristic
85C23×C4×C61C2×C411yescharacteristic
86C23×C4×C61C2×C412yes—
87C23×C4×C61D411yescharacteristic
88C23×C4×C61D411yescharacteristic
89C23×C4×C61D412yes—
90C23×C4×C61D411yescharacteristic
91C23×C4×C61D412yes—
92C23×C4×C61C2311yescharacteristic
93C23×C4×C61C2312yes—
94C2×C22⋊C4×C61—28no—
95C2×C22⋊C4×C61—24no—
96C2×C42×C61—24no—
97C2×C42×C61—44no—
98#95×C61—22no—
99#95×C61C2314yes—
100C24×C61—24no—
101C24×C61—24no—
102C24×C61—42no—
103C24×C61C22⋊C411yescharacteristic
104C24×C61C22⋊C412yes—
105C24×C61C22⋊C411yescharacteristic
106C24×C61C2×D412yes—
107C24×C61C2×D411yescharacteristic
108C23×D61—21no—
109C22×C4×C61—24no—
110C22×C4×C61—24no—
111C22×C4×C61—24no—
112C22×C4×C61—28no—
113C22×C4×C61—24no—
114C22×C4×C61—44no—
115C22×C4×C61—44no—
116C22×C4×C61—44no—
117C22×C4×C61—44no—
118C22×C4×C61—42no—
119C22×C4×C61—42no—
120C22×C4×C61—42no—
121C22×C4×C61—44no—
122C22×C4×C61—44no—
123C22×C4×C61C22⋊C412yes—
124C22×C4×C61C22⋊C411yescharacteristic
125C22×C4×C61C22⋊C412yes—
126C22×C4×C61C22⋊C412yes—
127C22×C4×C61C22⋊C412yes—
128C22×C4×C61C22⋊C412yes—
129C22×C4×C61C22⋊C411yescharacteristic
130C22×C4×C61C22×C411yescharacteristic
131C22×C4×C61C22×C412yes—
132C22×C4×C61C22×C411yescharacteristic
133C22×C4×C61C22×C412yes—
134C22×C4×C61C2×D412yes—
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2×D412yes—
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2×D411yescharacteristic
139C22×C4×C61C2×D412yes—
140C22×C4×C61C2411yescharacteristic
141C2×C22⋊D61—24no—
142C2×C22⋊D61—22no—
143C2×C22⋊D61—24no—
144C2×C22⋊D61—22no—
145C2×C22⋊D61—44no—
146C2×C22⋊D61—44no—
147C2×C22⋊D61—44no—
148C22×Dic61—21no—
149C22×Dic61—21no—
150C22×Dic61—21no—
151#11758222—48no—
152#11758222—48no—
153C2×D244—21no—
154C2×D244—42no—
155C2×D244C22×C412yes—
156C2×C4×D61—24no—
157C2×C4×D61—44no—
158C2×Dic122—21no—
159C2×Dic122—42no—
160C2×Dic122C22×C412yes—
161C22⋊C4×C61—216no—
162C42×C61—48no—
163C22⋊Dic61—24no—
164C22⋊Dic61—22no—
165C22⋊Dic61—24no—
166C22⋊Dic61—22no—
167#11758198—22no—
168#11758198—24no—
169#11758198—22no—
170C4⋊Dic61—21no—
171C4⋊Dic61—21no—
172C4⋊Dic61C22×C412yes—
173C4⋊Dic61C22×C412yes—
174#11758196—22no—
175#11758196—24no—
176#11758196—22no—
177C4×Dic61—24no—
178C2×#92418—24no—
179C2×#92418—44no—
180C2×#92418—48no—
181C23×C61—22no—
182C23×C61—22no—
183C23×C61—22no—
184C23×C61—22no—
185C23×C61—24no—
186C23×C61—22no—
187C23×C61—24no—
188C23×C61—22no—
189C23×C61—24no—
190C23×C61—24no—
191C23×C61—22no—
192C23×C61—42no—
193C23×C61—42no—
194C23×C61—416no—
195C23×C61#10414yes—
196C23×C61C2×C22⋊C412yes—
197C23×C61C2×C22⋊C411yescharacteristic
198C23×C61C2×C22⋊C412yes—
199C23×C61C2×C22⋊C411yescharacteristic
200C23×C61#13514yes—
201C23×C61C22×D411yescharacteristic
202C22×D61—22no—
203C22×D61—42no—
204C22×D61—42no—
205C22×D61—42no—
206C2×C4×C61—22no—
207C2×C4×C61—22no—
208C2×C4×C61—22no—
209C2×C4×C61—24no—
210C2×C4×C61—24no—
211C2×C4×C61—24no—
212C2×C4×C61—24no—
213C2×C4×C61—24no—
214C2×C4×C61—24no—
215C2×C4×C61—28no—
216C2×C4×C61—42no—
217C2×C4×C61—42no—
218C2×C4×C61—41no—
219C2×C4×C61—42no—
220C2×C4×C61—41no—
221C2×C4×C61—42no—
222C2×C4×C61—41no—
223C2×C4×C61—41no—
224C2×C4×C61—44no—
225C2×C4×C61—416no—
226C2×C4×C61—44no—
227C2×C4×C61#9914yes—
228C2×C4×C61C2×C22⋊C411yescharacteristic
229C2×C4×C61C2×C22⋊C412yes—
230C2×C4×C61C2×C22⋊C411yescharacteristic
231C2×C4×C61C2×C22⋊C412yes—
232C2×C4×C61C23×C411yescharacteristic
233C2×C4×C61C22×D411yescharacteristic
234C22⋊D61—48no—
235C22⋊D61—44no—
236C22⋊D61—44no—
237C22⋊D61—48no—
238C2×Dic61—22no—
239C2×Dic61—22no—
240C2×Dic61—22no—
241C2×Dic61—42no—
242C2×Dic61—42no—
243C2×Dic61—42no—
244D244—42no—
245D244—42no—
246C4×D61—48no—
247Dic122—42no—
248Dic122—42no—
249#92418—44no—
250C2×#1501—611nomaximal, Sylow
251C22×C61—21no—
252C22×C61—21no—
253C22×C61—22no—
254C22×C61—22no—
255C22×C61—21no—
256C22×C61—21no—
257C22×C61—28no—
258C22×C61—28no—
259C22×C61—22no—
260C22×C61—22no—
261C22×C61—22no—
262C22×C61—48no—
263C22×C61—48no—
264C22×C61—44no—
265C22×C61C2×#9912yes—
266C22×C61#41612yes—
267C22×C61#41612yes—
268C22×C61C2×#10414yes—
269C22×C61C2×#10412yes—
270C22×C61C22×C22⋊C411yescharacteristic
271C22×C61C2×#13512yes—
272C2×D61—42no—
273C2×D61—42no—
274C2×D61—42no—
275C2×D61—84no—
276C4×C61—21no—
277C4×C61—21no—
278C4×C61—21no—
279C4×C61—21no—
280C4×C61—22no—
281C4×C61—48no—
282C4×C61C2×#9914yes—
283Dic61—42no—
284Dic61—42no—
285Dic61—42no—
286C2×#525—611no—
287C22×C22⋊C8—611no—
288C2×C4×C22⋊C4D6111yescharacteristic, complemented
289#1501—618no—
290C2×#328—612no—
291C2×#327—612no—
292C2×C61—22no—
293C2×C61—22no—
294C2×C61—24no—
295C2×C61—42no—
296C2×C61#150114yescomplemented
297C2×C61C22×#9911yescharacteristic
298C2×C61C2×#41611yescharacteristic
299C2×C61C22×#10411yescharacteristic
300D61—82no—
301C22×#41—611no—
302C24×C4C2×D6111yescharacteristic
303C23×C8—1221no—
304#525—614no—
305#525—614no—
306#525—1222no—
307#525—1222no—
308C2×#123—1221no—
309C2×C22⋊Q8—611no—
310C2×C22⋊Q8—611no—
311C2×#121—611no—
312C2×#121—611no—
313C2×#120—1221no—
314C2×C4×D4—1221no—
315C2×C4×D4—1221no—
316C2×#117—611no—
317C22×C22⋊C4—21no—
318C22×C42—21no—
319C2×C22⋊C8—612no—
320C2×C22⋊C8—614no—
321C2×C22⋊C8—1221no—
322C2×C22⋊C8—1222no—
323C4×C22⋊C4—22no—
324C4×C22⋊C4C2×D6114yescomplemented
325C2×#95C2×D6112yes—
326#328—618no—
327#327—618no—
328C61C2×#150111yescharacteristic, complemented, Sylow
329C25C22⋊D6111yescharacteristic
330C2×#41—614no—
331C2×#41—1222no—
332C2×#41—2444no—
333C22×Q8—611no—
334C22×D4—611no—
335C22×D4—1221no—
336C22×D4—1221no—
337C22×D4—1221no—
338C23×C4—22no—
339C23×C4—44no—
340C23×C4—1221no—
341C23×C4C4×D6111yescharacteristic
342C23×C4C4×D6111yescharacteristic
343C23×C4C4×D6112yes—
344C23×C4D24411yescharacteristic
345C23×C4D24411yescharacteristic
346C23×C4D24412yes—
347C23×C4C22⋊D6111yescharacteristic
348C23×C4C22⋊D6112yes—
349C23×C4C22×D6111yescharacteristic
350C23×C4C22×D6112yes—
351C22×C8—1222no—
352C22×C8—1224no—
353C22×C8—2444no—
354#123—1224no—
355#123—1224no—
356C22⋊Q8—612no—
357C22⋊Q8—614no—
358C22⋊Q8—612no—
359C22⋊Q8—1222no—
360C22⋊Q8—1221no—
361C22⋊Q8—1221no—
362#121—612no—
363#121—614no—
364#121—612no—
365#121—1222no—
366#121—1221no—
367#121—1221no—
368#120—1224no—
369#120—1224no—
370C4×D4—1224no—
371C4×D4—1224no—
372C4×D4—1224no—
373C4×D4—1224no—
374#117—614no—
375#117—1222no—
376C2×C4⋊C4—611no—
377C2×C4⋊C4—611no—
378C2×C4⋊C4—1221no—
379C2×C4⋊C4—1221no—
380C2×C22⋊C4—28no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—1221no—
383C2×C22⋊C4—1221no—
384C2×C22⋊C4—1221no—
385C2×C22⋊C4—1221no—
386C2×C22⋊C4—1221no—
387C2×C42—24no—
388C2×C42—44no—
389C2×C42—1221no—
390C22⋊C8—614no—
391C22⋊C8—1222no—
392C22⋊C8—1224no—
393#95—22no—
394#95C22×D6114yes—
395C24—24no—
396C24—24no—
397C24—42no—
398C24—1221no—
399C24#1175819811yescharacteristic
400C24#1175819812yes—
401C24#1175819811yescharacteristic
402C24C2×C22⋊D6112yes—
403C24C2×C22⋊D6111yescharacteristic
404#41—2448no—
405#41—2448no—
406C2×Q8—612no—
407C2×Q8—1221no—
408C2×Q8—2442no—
409C2×D4—612no—
410C2×D4—1222no—
411C2×D4—1222no—
412C2×D4—1224no—
413C2×D4—1224no—
414C2×D4—1221no—
415C2×D4—2442no—
416C2×D4—2444no—
417C2×D4—2444no—
418C2×D4—2444no—
419C22×C4—24no—
420C22×C4—24no—
421C22×C4—24no—
422C22×C4—28no—
423C22×C4—24no—
424C22×C4—44no—
425C22×C4—44no—
426C22×C4—44no—
427C22×C4—44no—
428C22×C4—42no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—44no—
432C22×C4—44no—
433C22×C4—1221no—
434C22×C4—1221no—
435C22×C4—1221no—
436C22×C4—1224no—
437C22×C4—2444no—
438C22×C4#1175819811yescharacteristic
439C22×C4#1175819812yes—
440C22×C4#1175819812yes—
441C22×C4#1175819812yes—
442C22×C4#1175819812yes—
443C22×C4#1175819812yes—
444C22×C4#1175819811yescharacteristic
445C22×C4C2×C4×D6111yescharacteristic
446C22×C4C2×C4×D6112yes—
447C22×C4C2×C4×D6111yescharacteristic
448C22×C4C2×C4×D6112yes—
449C22×C4C2×D24411yescharacteristic
450C22×C4C2×D24412yes—
451C22×C4C2×D24411yescharacteristic
452C22×C4C2×D24412yes—
453C22×C4C2×C22⋊D6112yes—
454C22×C4C2×C22⋊D6111yescharacteristic
455C22×C4C23×D6111yescharacteristic
456C2×C8—1224no—
457C2×C8—2444no—
458C2×C8—2448no—
459C4⋊C4—612no—
460C4⋊C4—612no—
461C4⋊C4—1222no—
462C4⋊C4—1221no—
463C4⋊C4—1221no—
464C4⋊C4—1224no—
465C4⋊C4—1222no—
466C22⋊C4—216no—
467C22⋊C4—1222no—
468C22⋊C4—1224no—
469C22⋊C4—1222no—
470C22⋊C4—1224no—
471C22⋊C4—1222no—
472C22⋊C4—1224no—
473C22⋊C4—1222no—
474C42—48no—
475C42—1224no—
476C23—22no—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—24no—
482C23—22no—
483C23—24no—
484C23—24no—
485C23—24no—
486C23—22no—
487C23—42no—
488C23—42no—
489C23—416no—
490C23—1222no—
491C23—2442no—
492C23—2442no—
493C23—2442no—
494C23#1451970514yes—
495C23C2×#1175819812yes—
496C23C2×#1175819811yescharacteristic
497C23C2×#1175819812yes—
498C23C2×#1175819811yescharacteristic
499C23#1451979714yes—
500C23C22×C22⋊D6111yescharacteristic
501Q8—2442no—
502Q8—2442no—
503D4—2442no—
504D4—2442no—
505D4—2448no—
506D4—2444no—
507D4—2444no—
508D4—2448no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—28no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—44no—
528C2×C4—416no—
529C2×C4—44no—
530C2×C4—1222no—
531C2×C4—1222no—
532C2×C4—1222no—
533C2×C4—2442no—
534C2×C4—2442no—
535C2×C4—2442no—
536C2×C4—2448no—
537C2×C4#1451969114yes—
538C2×C4C2×#1175819812yes—
539C2×C4C2×#1175819811yescharacteristic
540C2×C4C2×#1175819811yescharacteristic
541C2×C4C2×#1175819812yes—
542C2×C4C22×C4×D6111yescharacteristic
543C2×C4C22×D24411yescharacteristic
544C8—2444no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—21no—
549C22—22no—
550C22—28no—
551C22—28no—
552C22—22no—
553C22—22no—
554C22—22no—
555C22—22no—
556C22—48no—
557C22—48no—
558C22—44no—
559C22—4884no—
560C22—2442no—
561C22—2442no—
562C22—2442no—
563C22C2×#1451969112yes—
564C22#1683975612yes—
565C22#1683975612yes—
566C22C2×#1451970514yes—
567C22C2×#1451970512yes—
568C22C22×#1175819811yescharacteristic
569C22C2×#1451979712yes—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—22no—
574C4—21no—
575C4—48no—
576C4—2442no—
577C4—2442no—
578C4—2442no—
579C4C2×#1451969114yes—
580C2—22no—
581C2—22no—
582C2—24no—
583C2—42no—
584C2—4882no—
585C2#2144430814yesdirect product factor
586C2C22×#1451969111yescharacteristic
587C2C2×#1683975611yescharacteristic
588C2C22×#1451970511yescharacteristic
subgroupG/H
centerC22×C4#11758198
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C4×C22⋊C4×C61C2
socleC23×C61C2×C22⋊C4
prime radicalC2×#16840273C2
cosocleC22×C4×C61C24
hypercenterC2×C4×C22⋊C4D61
hypocenterC61C2×#1501
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C22⋊#92418C2semidirect
3. #21444308C2direct (N × H)
4. C2×#16839498C2semidirect
5. C2×#16839495C2semidirect
6. C2×C4×C22⋊C4×C61C2semidirect
7. C22×#11758222C4semidirect
11. #16840273C4semidirect
14. C2×#14519756C4semidirect
16. C2×#14519751C4semidirect
21. C2×#14519736C4semidirect
25. C2×C22⋊#92418C22semidirect
26. #16839498C22semidirect
27. #16839495C22semidirect
32. C4×C22⋊C4×C61C22semidirect
36. C2×#11758222C2×C4semidirect
52. #14519756C2×C4semidirect
58. #14519751C2×C4semidirect
67. #14519736C2×C4semidirect
288. C2×C4×C22⋊C4D61semidirect
296. C2×C61#1501semidirect
324. C4×C22⋊C4C2×D61semidirect
328. C61C2×#1501semidirect
585. C2#21444308direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402732
C22×C22⋊#924182
#214443082
C2×#168394982
C2×#168394952
C2×C4×C22⋊C4×C612
C2×#150161