Finite Group Databasebeta

← C2×#21460661 #30596304

Subgroups — C2×#21460661 #30596304

Order 15616.

1130 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D61⋊(C22⋊C8)C211yesmaximal, characteristic
2C2×C4×C22⋊#6923C211yesmaximal, characteristic
3#21460661C214yesmaximal, direct product factor
4C22×#14519689C211yesmaximal, characteristic
5C22×D61⋊C8—21no—
6C22×C22⋊#6923C412yes—
7C22×C4×#6923—21no—
8C2×#14519834—21no—
9D61⋊(C22⋊C8)—21no—
10D61⋊(C22⋊C8)—21no—
11D61⋊(C22⋊C8)C412yescomplemented
12D61⋊(C22⋊C8)C2212yes—
13C2×C22⋊#92420C412yescomplemented
14C4×C22⋊#6923—21no—
15C4×C22⋊#6923—21no—
16C4×C22⋊#6923C412yes—
17C4×C22⋊#6923C2212yes—
18C2×(C2×#6923)⋊C4—21no—
19C23×C4×D61C2211yescharacteristic
20C23×#92418C411yescharacteristic, complemented
21C2×#14519689—21no—
22C2×#14519689—21no—
23C2×#14519689—21no—
24C2×#14519689—21no—
25C2×#14519689C412yescomplemented
26C2×#14519689C2212yes—
27C23×C8×C61C411yescharacteristic, complemented
28C23×#6923—22no—
29C2×D61⋊C8—22no—
30C2×D61⋊C8—22no—
31C2×D61⋊C8—42no—
32C2×D61⋊C8—42no—
33C22×#92420—22no—
34C2×C22⋊#6923—22no—
35C2×C22⋊#6923—24no—
36C2×C22⋊#6923C818yescomplemented
37C2×C22⋊#6923C2×C414yes—
38C2×C4×#6923—22no—
39C2×C4×#6923—22no—
40C2×C4×#6923—42no—
41C2×C4×#6923—42no—
42#14519834—22no—
43#14519834—22no—
44C22⋊#92420—22no—
45C22⋊#92420C2×C414yescomplemented
46(C2×#6923)⋊C4—22no—
47(C2×#6923)⋊C4—22no—
48C24×D61C2×C411yescharacteristic
49C23×Dic61C2×C411yescharacteristic
50C22×C4×D61—42no—
51C22×C4×D61—42no—
52C22×C4×D61C2×C411yescharacteristic
53C22×C4×D61C2×C411yescharacteristic
54C22×C4×D61C2×C411yescharacteristic
55C22×C4×D61D411yescharacteristic
56C22×C4×D61D411yescharacteristic
57C22×C4×D61D411yescharacteristic
58C22×C4×D61D411yescharacteristic
59C22×C4×D61D411yescharacteristic
60C22×C4×D61D411yescharacteristic
61C22×C4×D61Q811yescharacteristic
62C22×C4×D61Q811yescharacteristic
63C22×C4×D61C2311yescharacteristic
64C22×#92418—21no—
65C22×#92418—21no—
66C22×#92418—42no—
67C22×#92418C2×C412yescomplemented
68#14519689—22no—
69#14519689—22no—
70#14519689—22no—
71#14519689—22no—
72C23×C4×C61C2×C411yescharacteristic
73C22×C8×C61—21no—
74C22×C8×C61—21no—
75C22×C8×C61—42no—
76C22×C8×C61C2×C412yescomplemented
77C24×C61C4211yescharacteristic
78C23×D61—42no—
79C23×D61—42no—
80C23×D61C4211yescharacteristic
81C23×D61C22⋊C411yescharacteristic
82C23×D61C22⋊C411yescharacteristic
83C23×D61C4⋊C411yescharacteristic
84C23×D61C4⋊C411yescharacteristic
85C23×D61C2×C814yes—
86C23×D61M1614yes—
87C23×D61C22×C411yescharacteristic
88C22×#6923—28no—
89C22×#6923—24no—
90C22×#6923—44no—
91C22×#6923—44no—
92C22×C4×C61—22no—
93C22×C4×C61—22no—
94C22×C4×C61C4211yescharacteristic
95C22×C4×C61C22⋊C411yescharacteristic
96C22×C4×C61C22⋊C411yescharacteristic
97C22×C4×C61C4⋊C411yescharacteristic
98C22×C4×C61C4⋊C411yescharacteristic
99C22×C4×C61C22×C411yescharacteristic
100C22×Dic61—42no—
101C22×Dic61C4211yescharacteristic
102C22×Dic61C22⋊C411yescharacteristic
103C22×Dic61C22⋊C411yescharacteristic
104C22×Dic61C4⋊C411yescharacteristic
105C22×Dic61C4⋊C411yescharacteristic
106C22×Dic61C22×C411yescharacteristic
107C2×C4×D61—22no—
108C2×C4×D61—22no—
109C2×C4×D61—22no—
110C2×C4×D61—22no—
111C2×C4×D61—42no—
112C2×C4×D61—42no—
113C2×C4×D61—41no—
114C2×C4×D61—41no—
115C2×C4×D61—42no—
116C2×C4×D61—41no—
117C2×C4×D61—41no—
118C2×C4×D61—41no—
119C2×C4×D61—41no—
120C2×C4×D61—42no—
121C2×C4×D61—41no—
122C2×C4×D61—41no—
123C2×C4×D61—42no—
124C2×C4×D61—42no—
125C2×C4×D61C22⋊C411yescharacteristic
126C2×C4×D61C22⋊C411yescharacteristic
127C2×C4×D61C22⋊C411yescharacteristic
128C2×C4×D61C22⋊C411yescharacteristic
129C2×C4×D61C22⋊C411yescharacteristic
130C2×C4×D61C22⋊C411yescharacteristic
131C2×C4×D61C4⋊C411yescharacteristic
132C2×C4×D61C4⋊C411yescharacteristic
133C2×C4×D61C4⋊C411yescharacteristic
134C2×C4×D61C4⋊C411yescharacteristic
135C2×C4×D61C4⋊C411yescharacteristic
136C2×C4×D61C4⋊C411yescharacteristic
137C2×C4×D61C2×D411yescharacteristic
138C2×C4×D61C2×D411yescharacteristic
139C2×C4×D61C2×D411yescharacteristic
140C2×C4×D61C2×Q811yescharacteristic
141C22⋊#6923—28no—
142C22⋊#6923—24no—
143C22⋊#6923C2×C818yescomplemented
144C2×#92420—24no—
145C2×#92420—44no—
146C4×#6923—44no—
147C4×#6923—42no—
148C4×#6923—42no—
149D61⋊C8—44no—
150D61⋊C8—42no—
151D61⋊C8—42no—
152C2×C8×C61—22no—
153C2×C8×C61—42no—
154C2×C8×C61—42no—
155C2×C8×C61—42no—
156C2×#92418—22no—
157C2×#92418—42no—
158C2×#92418—42no—
159C2×#92418—42no—
160C23×C61—22no—
161C23×C61—22no—
162C23×C61#9511yescharacteristic
163C23×C61#9511yescharacteristic
164C23×C61C4×C812yes—
165C23×C61#9712yes—
166C23×C61C2×C4211yescharacteristic
167C22×D61—22no—
168C22×D61—22no—
169C22×D61—22no—
170C22×D61—22no—
171C22×D61—41no—
172C22×D61—41no—
173C22×D61—41no—
174C22×D61—41no—
175C22×D61—41no—
176C22×D61—41no—
177C22×D61—41no—
178C22×D61—48no—
179C22×D61—48no—
180C22×D61—41no—
181C22×D61#9511yescharacteristic
182C22×D61#9511yescharacteristic
183C22×D61C4×C812yes—
184C22×D61#9712yes—
185C22×D61C22⋊C814yes—
186C22×D61C22⋊C814yes—
187C22×D61C4⋊C814yes—
188C22×D61C4⋊C814yes—
189C22×D61C2×C22⋊C411yescharacteristic
190C22×D61C2×C4⋊C411yescharacteristic
191C22×D61C22×C812yes—
192C22×D61C2×M1612yes—
193C2×#6923—28no—
194C2×#6923—44no—
195C2×#6923—416no—
196C2×#6923—44no—
197C2×C4×C61—22no—
198C2×C4×C61—22no—
199C2×C4×C61—22no—
200C2×C4×C61—21no—
201C2×C4×C61—21no—
202C2×C4×C61—21no—
203C2×C4×C61—21no—
204C2×C4×C61#9511yescharacteristic
205C2×C4×C61#9511yescharacteristic
206C2×C4×C61#9912yes—
207C2×C4×C61#9912yes—
208C2×C4×C61C2×C22⋊C411yescharacteristic
209C2×C4×C61C2×C4⋊C411yescharacteristic
210C2×Dic61—22no—
211C2×Dic61—22no—
212C2×Dic61—41no—
213C2×Dic61—41no—
214C2×Dic61—41no—
215C2×Dic61—41no—
216C2×Dic61#9511yescharacteristic
217C2×Dic61#9511yescharacteristic
218C2×Dic61C2×C22⋊C411yescharacteristic
219C2×Dic61C2×C4⋊C411yescharacteristic
220C4×D61—22no—
221C4×D61—22no—
222C4×D61—22no—
223C4×D61—22no—
224C4×D61—21no—
225C4×D61—21no—
226C4×D61—21no—
227C4×D61—21no—
228C4×D61—21no—
229C4×D61—21no—
230C4×D61—21no—
231C4×D61—21no—
232C4×D61—41no—
233C4×D61—41no—
234C4×D61—41no—
235C4×D61—41no—
236C4×D61—41no—
237C4×D61—41no—
238C4×D61—41no—
239C4×D61—41no—
240#92420—44no—
241C8×C61—42no—
242#92418—42no—
243C2×#1282—611nomaximal, Sylow
244C22×C61—24no—
245C22×C61—24no—
246C22×C61—21no—
247C22×C61—21no—
248C22×C61—21no—
249C22×C61—21no—
250C22×C61#33612yes—
251C22×C61#33612yes—
252C22×C61#34212yes—
253C22×C61#34412yes—
254C22×C61C2×#9511yescharacteristic
255C22×C61C2×C4×C811yescharacteristic
256C22×C61C2×#9711yescharacteristic
257C2×D61—28no—
258C2×D61—28no—
259C2×D61—21no—
260C2×D61—21no—
261C2×D61—21no—
262C2×D61—21no—
263C2×D61—21no—
264C2×D61—21no—
265C2×D61—21no—
266C2×D61—21no—
267C2×D61—42no—
268C2×D61—42no—
269C2×D61—44no—
270C2×D61—44no—
271C2×D61—42no—
272C2×D61—42no—
273C2×D61#33612yes—
274C2×D61#33612yes—
275C2×D61C2×C22⋊C812yes—
276C2×D61C2×C4⋊C812yes—
277#6923—48no—
278C4×C61—21no—
279C4×C61—21no—
280C4×C61#34212yes—
281C4×C61C2×#9911yescharacteristic
282C4×C61C2×#9911yescharacteristic
283Dic61—21no—
284Dic61—21no—
285Dic61—21no—
286Dic61—21no—
287C22×C22⋊C8—611no—
288C22×C22⋊C8—611no—
289C2×C4×C22⋊C4—611no—
290#1282—614no—
291C2×C61—22no—
292C2×C61—21no—
293C2×C61—21no—
294C2×C61#128214yescomplemented
295C2×C61C2×#33611yescharacteristic
296C2×C61C2×#34211yescharacteristic
297C2×C61C2×#34411yescharacteristic
298D61—22no—
299D61—22no—
300D61—22no—
301D61—22no—
302C24×C4—611no—
303C23×C8—611no—
304C23×C8—1221no—
305C23×C8#692311yescharacteristic, complemented
306C22×C22⋊C4—612no—
307C22×C42—1221no—
308C2×C22⋊C8—612no—
309C2×C22⋊C8—612no—
310C2×C22⋊C8—612no—
311C2×C22⋊C8—612no—
312C2×C22⋊C8—612no—
313C2×C22⋊C8—1221no—
314C2×C22⋊C8—1221no—
315C2×C22⋊C8—1221no—
316C2×C22⋊C8—1221no—
317C2×C22⋊C8—1221no—
318C2×C22⋊C8—1221no—
319C2×C22⋊C8—1221no—
320C4×C22⋊C4—612no—
321C4×C22⋊C4—612no—
322C4×C22⋊C4—1221no—
323C4×C22⋊C4—1221no—
324C2×#95—1221no—
325C61C2×#128211yescharacteristic, complemented, Sylow
326C25—611no—
327C23×C4—611no—
328C23×C4—611no—
329C23×C4—611no—
330C23×C4—611no—
331C23×C4—611no—
332C23×C4—611no—
333C23×C4—611no—
334C23×C4—611no—
335C23×C4—611no—
336C23×C4—611no—
337C23×C4—611no—
338C23×C4—611no—
339C23×C4—611no—
340C23×C4—1222no—
341C23×C4—2442no—
342C23×C4—2442no—
343C23×C4C2×#692311yescharacteristic
344C22×C8—21no—
345C22×C8—21no—
346C22×C8—42no—
347C22×C8—612no—
348C22×C8—1222no—
349C22×C8—1222no—
350C22×C8—1222no—
351C22×C8—1221no—
352C22×C8—1221no—
353C22×C8—2442no—
354C22×C8—2442no—
355C22×C8—2442no—
356C22×C8C2×#692312yescomplemented
357C2×C22⋊C4—618no—
358C2×C22⋊C4—614no—
359C2×C22⋊C4—1224no—
360C2×C22⋊C4—1222no—
361C2×C42—1222no—
362C2×C42—1222no—
363C2×C42—2442no—
364C2×C42—2442no—
365C22⋊C8—614no—
366C22⋊C8—1222no—
367C22⋊C8—1222no—
368C22⋊C8—1222no—
369C22⋊C8—1222no—
370C22⋊C8—1222no—
371C22⋊C8—1222no—
372C22⋊C8—1222no—
373#95—1222no—
374#95—1222no—
375C24—611no—
376C24—611no—
377C24—611no—
378C24—611no—
379C24—614no—
380C24—614no—
381C24—611no—
382C24—611no—
383C24—2442no—
384C24—2442no—
385C24C4×#692311yescharacteristic
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—611no—
389C22×C4—611no—
390C22×C4—611no—
391C22×C4—611no—
392C22×C4—611no—
393C22×C4—611no—
394C22×C4—611no—
395C22×C4—611no—
396C22×C4—611no—
397C22×C4—611no—
398C22×C4—611no—
399C22×C4—611no—
400C22×C4—611no—
401C22×C4—611no—
402C22×C4—611no—
403C22×C4—611no—
404C22×C4—611no—
405C22×C4—611no—
406C22×C4—611no—
407C22×C4—611no—
408C22×C4—611no—
409C22×C4—611no—
410C22×C4—1222no—
411C22×C4—1222no—
412C22×C4—1222no—
413C22×C4—1222no—
414C22×C4—1224no—
415C22×C4—1228no—
416C22×C4—2441no—
417C22×C4—2441no—
418C22×C4—2441no—
419C22×C4—2441no—
420C22×C4—2441no—
421C22×C4—2441no—
422C22×C4—2441no—
423C22×C4—2441no—
424C22×C4—2442no—
425C22×C4—2442no—
426C22×C4—2442no—
427C22×C4—2442no—
428C22×C4—2442no—
429C22×C4—2442no—
430C22×C4—2442no—
431C22×C4—2444no—
432C22×C4—2444no—
433C22×C4C4×#692311yescharacteristic
434C22×C4C4⋊#692311yescharacteristic
435C22×C4C4⋊#692311yescharacteristic
436C22×C4C22⋊#692311yescharacteristic
437C22×C4C22⋊#692311yescharacteristic
438C22×C4C22×#692311yescharacteristic
439C2×C8—22no—
440C2×C8—42no—
441C2×C8—42no—
442C2×C8—42no—
443C2×C8—1224no—
444C2×C8—1222no—
445C2×C8—2442no—
446C2×C8—2442no—
447C2×C8—2442no—
448C2×C8—2444no—
449C2×C8—2444no—
450C2×C8—2442no—
451C2×C8—2442no—
452C22⋊C4—618no—
453C22⋊C4—1224no—
454C22⋊C4—1228no—
455C42—2442no—
456C42—2442no—
457C42—2444no—
458C23—22no—
459C23—22no—
460C23—614no—
461C23—614no—
462C23—611no—
463C23—611no—
464C23—611no—
465C23—611no—
466C23—612no—
467C23—612no—
468C23—612no—
469C23—612no—
470C23—614no—
471C23—614no—
472C23—1222no—
473C23—1222no—
474C23—1222no—
475C23—1222no—
476C23—2441no—
477C23—2441no—
478C23—2441no—
479C23—2441no—
480C23—2441no—
481C23—2441no—
482C23—2441no—
483C23—2441no—
484C23—2448no—
485C23—2448no—
486C23(C2×#6923)⋊C411yescharacteristic
487C23(C2×#6923)⋊C411yescharacteristic
488C23C8×#692312yes—
489C23#1451983112yes—
490C23C2×C4×#692311yescharacteristic
491C2×C4—22no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—611no—
499C2×C4—611no—
500C2×C4—611no—
501C2×C4—611no—
502C2×C4—1222no—
503C2×C4—1222no—
504C2×C4—1221no—
505C2×C4—1221no—
506C2×C4—1221no—
507C2×C4—1221no—
508C2×C4—1221no—
509C2×C4—1221no—
510C2×C4—1221no—
511C2×C4—1221no—
512C2×C4—1222no—
513C2×C4—1222no—
514C2×C4—1222no—
515C2×C4—1222no—
516C2×C4—1228no—
517C2×C4—2441no—
518C2×C4—2441no—
519C2×C4—2441no—
520C2×C4—2441no—
521C2×C4—2441no—
522C2×C4—2441no—
523C2×C4—2441no—
524C2×C4—2441no—
525C2×C4—2441no—
526C2×C4—2441no—
527C2×C4—2441no—
528C2×C4—2441no—
529C2×C4—2444no—
530C2×C4—2444no—
531C2×C4—24416no—
532C2×C4(C2×#6923)⋊C411yescharacteristic
533C2×C4(C2×#6923)⋊C411yescharacteristic
534C2×C4#1451983512yes—
535C2×C4#1451983612yes—
536C2×C4C2×C22⋊#692311yescharacteristic
537C2×C4C2×C4⋊#692311yescharacteristic
538C8—42no—
539C8—2444no—
540C8—2442no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—21no—
545C22—24no—
546C22—24no—
547C22—612no—
548C22—612no—
549C22—612no—
550C22—612no—
551C22—1221no—
552C22—1221no—
553C22—1221no—
554C22—1221no—
555C22—1221no—
556C22—1221no—
557C22—1221no—
558C22—1221no—
559C22—1228no—
560C22—1228no—
561C22—2442no—
562C22—2442no—
563C22—2442no—
564C22—2442no—
565C22—2444no—
566C22—2444no—
567C22(C2×#6923)⋊C812yes—
568C22(C2×#6923)⋊C812yes—
569C22#1684064012yes—
570C22#1684064412yes—
571C22C2×(C2×#6923)⋊C411yescharacteristic
572C22C2×C8×#692311yescharacteristic
573C22C2×#1451983111yescharacteristic
574C4—21no—
575C4—21no—
576C4—1221no—
577C4—1221no—
578C4—1221no—
579C4—1221no—
580C4—2448no—
581C4#1684064012yes—
582C4C2×#1451983511yescharacteristic
583C4C2×#1451983611yescharacteristic
584C2—21no—
585C2—21no—
586C2—22no—
587C2—1222no—
588C2—1222no—
589C2—1222no—
590C2—1222no—
591C2#2146066114yesdirect product factor
592C2C2×(C2×#6923)⋊C811yescharacteristic
593C2C2×#1684064011yescharacteristic
594C2C2×#1684064411yescharacteristic
subgroupG/H
centerC22×C4C22⋊#6923
commutatorC22×C61C2×C4×C8
FrattiniC22×C4C22×#6923
FittingC23×C8×C61C4
socleC23×C61#95
prime radicalC24×D61C2×C4
cosocleC22×C4×D61C23
hypercenterC23×C8#6923
hypocenterC61C2×#1282
LCSG ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C23×C8

Complements

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

NH ≅ G/Ntype
3. #21460661C2direct (N × H)
11. D61⋊(C22⋊C8)C4semidirect
13. C2×C22⋊#92420C4semidirect
20. C23×#92418C4semidirect
25. C2×#14519689C4semidirect
27. C23×C8×C61C4semidirect
36. C2×C22⋊#6923C8semidirect
45. C22⋊#92420C2×C4semidirect
67. C22×#92418C2×C4semidirect
76. C22×C8×C61C2×C4semidirect
143. C22⋊#6923C2×C8semidirect
294. C2×C61#1282semidirect
305. C23×C8#6923semidirect
325. C61C2×#1282semidirect
356. C22×C8C2×#6923semidirect
591. C2#21460661direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D61⋊(C22⋊C8)2
C2×C4×C22⋊#69232
#214606612
C22×#145196892
C2×#128261