Finite Group Databasebeta

← C2×#21462748 #30625970

Subgroups — C2×#21462748 #30625970

Order 15616.

2210 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462748C2116yesmaximal, direct product factor
2C2×#16840814C212yesmaximal, complemented
3C2×#16840792C212yesmaximal, complemented
4C2×#16840791C212yesmaximal, complemented
5C2×#16840789C212yesmaximal, complemented
6C2×#16840785C211yesmaximal, characteristic, complemented
7C2×#16840782C211yesmaximal, characteristic, complemented
8C2×#16840780C211yesmaximal, characteristic, complemented
9C2×#16840767C211yesmaximal, characteristic, complemented
10C22×#14519844C211yesmaximal, characteristic, complemented
11C2×D61⋊(C4⋊C8)C211yesmaximal, characteristic, complemented
12C2×#16840230C211yesmaximal, characteristic
13C22×#11758213C2212yes—
14C22×D61⋊C8C2212yes—
15C23×#92420C2212yes—
16#16840814C22116yescomplemented
17#16840792C22116yescomplemented
18#16840791C22116yescomplemented
19#16840789C22116yescomplemented
20#16840785C2218yescomplemented
21#16840782C2218yescomplemented
22#16840780C2218yescomplemented
23#16840767C2218yescomplemented
24C2×#14519844C2212yes—
25C2×#14519844C2212yes—
26C2×#14519844C2211yescharacteristic
27C2×#14519844C2211yescharacteristic
28C2×#14519844C2211yescharacteristic
29C2×#14519844C2211yescharacteristic
30C2×#14519844C2218yescomplemented
31D61⋊(C4⋊C8)C2218yescomplemented
32C2×C4⋊#92420C2212yes—
33C2×#14519834C2212yes—
34C2×#14519834C2212yes—
35C2×C22⋊#92420C2212yes—
36C2×#14519832C2212yes—
37C2×#14519832C2212yes—
38C2×C4×#92420C2212yes—
39C22×#11758222C411yescharacteristic
40#16840230C418yes—
41#16840230C2218yes—
42C2×#14519742C411yescharacteristic
43C2×#14519742C2211yescharacteristic
44C2×#14519739C411yescharacteristic
45C2×#14519739C2211yescharacteristic
46C2×#14519737C411yescharacteristic
47C2×#14519737C411yescharacteristic
48C2×#14519737C2211yescharacteristic
49C2×#14519737C2211yescharacteristic
50C2×#14519734C411yescharacteristic
51C2×#14519734C411yescharacteristic
52C22×C4×Dic61C2211yescharacteristic
53C2×C42×D61C2211yescharacteristic
54C2×C42×D61C2211yescharacteristic
55C2×#117×C61C411yescharacteristic
56C2×#11758213—44no—
57C2×#11758213C2318yes—
58C2×D61⋊C8—44no—
59C2×D61⋊C8C2318yes—
60C22×#92420—44no—
61C22×#92420C2312yes—
62C22×#92420C2312yes—
63C22×#92420C2312yes—
64C22×#92420C2312yes—
65C22×#92420C2318yes—
66#14519844C2314yes—
67#14519844C2314yes—
68#14519844C2314yes—
69#14519844C2318yes—
70#14519844C2318yes—
71#14519844C2314yes—
72C4⋊#92420C2318yes—
73#14519834C2318yes—
74#14519834C2318yes—
75C22⋊#92420C2318yes—
76#14519832C2318yes—
77#14519832C2318yes—
78C4×#92420C2318yes—
79C2×#11758222—28no—
80C2×#11758222C2×C418yes—
81C22×Dic122C2×C411yescharacteristic
82C22×D244C2×C411yescharacteristic
83C22×C22⋊D61C2×C411yescharacteristic
84C22×C22⋊D61C2×C411yescharacteristic
85C23×Dic61C2×C411yescharacteristic
86C23×Dic61C2311yescharacteristic
87C22×C4×D61C2×C411yescharacteristic
88C22×C4×D61C2×C411yescharacteristic
89C22×C4×D61C2×C411yescharacteristic
90C22×C4×D61C2×C411yescharacteristic
91C22×C4×D61C2311yescharacteristic
92C22×C4×D61C2311yescharacteristic
93#14519742C2×C418yes—
94#14519742C2×C414yes—
95#14519742C2314yes—
96#14519739C2×C418yes—
97#14519739C2×C414yes—
98#14519739C2314yes—
99#14519737C2×C418yes—
100#14519737C2×C418yes—
101#14519737C2×C414yes—
102#14519737C2×C414yes—
103#14519737C2314yes—
104#14519737C2314yes—
105#14519734C2×C418yes—
106#14519734C2×C418yes—
107C2×#11758196C2×C411yescharacteristic
108C2×#11758196C2×C411yescharacteristic
109C2×#11758196C2×C411yescharacteristic
110C2×#11758196C2×C411yescharacteristic
111C2×#11758198C2×C411yescharacteristic
112C2×#11758198C2×C411yescharacteristic
113C2×#11758198C2×C411yescharacteristic
114C2×#11758198C2×C411yescharacteristic
115C2×C4×Dic61C2×C411yescharacteristic
116C2×C4×Dic61C2×C411yescharacteristic
117C2×C4×Dic61C2×C411yescharacteristic
118C2×C4×Dic61C2×C411yescharacteristic
119C2×C4×Dic61C2×C414yes—
120C2×C4×Dic61C2311yescharacteristic
121C2×C4×Dic61C2311yescharacteristic
122C2×C4×Dic61C2311yescharacteristic
123C2×C4×Dic61C2311yescharacteristic
124C2×C4×Dic61C2314yes—
125C42×D61C2×C414yes—
126C42×D61C2×C414yes—
127C42×D61C2314yes—
128C42×D61C2314yes—
129C23×C4×C61C2×C411yescharacteristic
130#117×C61C2×C418yes—
131C2×C4⋊C4×C61C2×C411yescharacteristic
132C2×C4⋊C4×C61C2×C411yescharacteristic
133C2×C22⋊C4×C61C2×C411yescharacteristic
134C2×C22⋊C4×C61C2×C411yescharacteristic
135C2×C42×C61C2×C411yescharacteristic
136C2×C42×C61C2×C411yescharacteristic
137C24×C61C22×C411yescharacteristic
138C23×D61C22×C411yescharacteristic
139C23×D61C22×C411yescharacteristic
140C22×C4×C61—24no—
141C22×C4×C61C22×C411yescharacteristic
142C22×C4×C61C22×C411yescharacteristic
143C22×C4×C61C22×C411yescharacteristic
144C22×C4×C61C22×C411yescharacteristic
145C22×C4×C61C22×C411yescharacteristic
146C22×C4×C61C22×C411yescharacteristic
147C22×C4×C61C22×C414yes—
148C2×C22⋊D61—24no—
149C2×C22⋊D61M1618yescomplemented
150C2×C22⋊D61C22×C414yes—
151C2×C22⋊D61C22×C414yes—
152C22×Dic61—24no—
153C22×Dic61—22no—
154C22×Dic61—22no—
155C22×Dic61C22×C411yescharacteristic
156C22×Dic61C22×C411yescharacteristic
157C22×Dic61C22×C414yes—
158C22×Dic61C22×C411yescharacteristic
159C22×Dic61C22×C412yes—
160C22×Dic61C22×C411yescharacteristic
161C22×Dic61C22×C411yescharacteristic
162C22×Dic61C2412yes—
163C22×Dic61C2411yescharacteristic
164#11758222—232no—
165C2×D244—24no—
166C2×D244C22×C414yes—
167C2×C4×D61—24no—
168C2×C4×D61—24no—
169C2×C4×D61—24no—
170C2×C4×D61—24no—
171C2×C4×D61—22no—
172C2×C4×D61—22no—
173C2×C4×D61—22no—
174C2×C4×D61—22no—
175C2×C4×D61C22×C414yes—
176C2×C4×D61C22×C414yes—
177C2×C4×D61C22×C414yes—
178C2×C4×D61C22×C414yes—
179C2×C4×D61C22×C412yes—
180C2×C4×D61C22×C412yes—
181C2×C4×D61C2412yes—
182C2×C4×D61C2412yes—
183C2×Dic122—24no—
184C2×Dic122C22×C414yes—
185C2×#92420—24no—
186C2×#92420—24no—
187C2×#92420—24no—
188C2×#92420—24no—
189C2×#92420—48no—
190C2×#92420C2414yes—
191C2×#92420C2414yes—
192C2×#92420C2414yes—
193C2×#92420C2414yes—
194#11758213—48no—
195D61⋊C8—48no—
196C4⋊C4×C61C22×C414yes—
197C4⋊C4×C61C22×C414yes—
198C22⋊C4×C61C22×C414yes—
199C22⋊C4×C61C22×C414yes—
200C42×C61C22×C414yes—
201C42×C61C22×C414yes—
202#11758198C22×C414yes—
203#11758198C22×C414yes—
204#11758198C22×C414yes—
205#11758198C22×C414yes—
206#11758196C22×C414yes—
207#11758196C22×C414yes—
208#11758196C22×C414yes—
209#11758196C22×C414yes—
210C4×Dic61C22×C412yes—
211C4×Dic61C22×C412yes—
212C4×Dic61C22×C412yes—
213C4×Dic61C22×C414yes—
214C4×Dic61C22×C414yes—
215C4×Dic61C22×C414yes—
216C4×Dic61C22×C414yes—
217C4×Dic61C22×C412yes—
218C4×Dic61C2412yes—
219C4×Dic61C2412yes—
220C4×Dic61C2412yes—
221C4×Dic61C2412yes—
222C23×C61—22no—
223C23×C61—22no—
224C23×C61C2×M1614yes—
225C23×C61C23×C412yes—
226C23×C61C23×C411yescharacteristic
227C22×D61—22no—
228C22×D61—22no—
229C22×D61—22no—
230C22×D61—22no—
231C22×D61—22no—
232C22×D61C2×M1614yes—
233C22×D61C23×C412yes—
234C22×D61C23×C412yes—
235C2×C4×C61—22no—
236C2×C4×C61—22no—
237C2×C4×C61—22no—
238C2×C4×C61—22no—
239C2×C4×C61—28no—
240C2×C4×C61—22no—
241C2×C4×C61—22no—
242C2×C4×C61C23×C412yes—
243C2×C4×C61C23×C412yes—
244C2×C4×C61C23×C412yes—
245C2×C4×C61C23×C412yes—
246C2×C4×C61C23×C412yes—
247C2×C4×C61C23×C412yes—
248C22⋊D61—28no—
249C22⋊D61C2×M16116yescomplemented
250C2×Dic61—22no—
251C2×Dic61—22no—
252C2×Dic61—22no—
253C2×Dic61—24no—
254C2×Dic61—28no—
255C2×Dic61—22no—
256C2×Dic61—22no—
257C2×Dic61C2×M1614yes—
258C2×Dic61#13114yes—
259C2×Dic61C23×C412yes—
260C2×Dic61C23×C412yes—
261C2×Dic61C23×C412yes—
262C2×Dic61C23×C411yescharacteristic
263C2×Dic61C23×C412yes—
264C2×Dic61C23×C412yes—
265C2×Dic61H(5,𝔽2)12yes—
266C2×Dic612−1+412yes—
267C2×Dic61C2511yescharacteristic
268D244—28no—
269C4×D61—28no—
270C4×D61—24no—
271C4×D61—24no—
272C4×D61—28no—
273C4×D61—28no—
274C4×D61—28no—
275C4×D61—22no—
276C4×D61—22no—
277C4×D61—22no—
278C4×D61—22no—
279Dic122—28no—
280#92420—24no—
281#92420—24no—
282#92420—24no—
283#92420—24no—
284C2×#2990—611nomaximal, Sylow
285C22×C61—22no—
286C22×C61—28no—
287C22×C61—22no—
288C22×C61#52012yes—
289C22×C61C22×M1614yes—
290C22×C61C22×M1612yes—
291C22×C61C2×#13112yes—
292C22×C61C24×C411yescharacteristic
293C2×D61—22no—
294C2×D61—28no—
295C2×D61—22no—
296C2×D61—22no—
297C2×D61—22no—
298C2×D61—22no—
299C2×D61—44no—
300C2×D61C22×M1614yes—
301C4×C61—22no—
302C4×C61—22no—
303C4×C61—22no—
304C4×C61—22no—
305C4×C61—22no—
306C4×C61—22no—
307Dic61—22no—
308Dic61—22no—
309Dic61—22no—
310Dic61#52012yes—
311Dic61C22×M1614yes—
312Dic61C2×#13114yes—
313Dic61C2×H(5,𝔽2)11yescharacteristic
314Dic61C2×2−1+411yescharacteristic
315C2×C4×#41—611no—
316#2990—6116no—
317C2×#446—612no—
318C2×#435—612no—
319C2×#435—612no—
320C2×C8×D4—612no—
321C2×#432—611no—
322C2×#432—611no—
323C2×#431—611no—
324C2×#423—611no—
325C22×C4⋊C8—611no—
326C22×C4⋊C8—611no—
327C2×C61—24no—
328C2×C61#299014yescomplemented
329C2×C61C2×#52011yescharacteristic
330C2×C61C23×M1611yescharacteristic
331C2×C61C22×#13111yescharacteristic
332D61—24no—
333D61—42no—
334C22×#41—611no—
335C22×M16—612no—
336C23×C8—612no—
337C23×C8—612no—
338C4×#41—618no—
339C4×#41—618no—
340C2×C4×Q8—611no—
341C2×C4×Q8—611no—
342C2×C4×D4—611no—
343C2×C4×D4—611no—
344C2×C4×D4—611no—
345C2×C4×D4—611no—
346C2×C4×D4—611no—
347C2×C4×D4—611no—
348C2×#117—611no—
349C2×#117—611no—
350C2×#117#692311yescharacteristic
351C22×C42—611no—
352C22×C42—611no—
353C22×C42—611no—
354#446—6116no—
355#435—6116no—
356#435—6116no—
357C8×D4—6116no—
358#432—618no—
359#432—618no—
360#431—618no—
361#423—618no—
362C2×C4⋊C8—612no—
363C2×C4⋊C8—618no—
364C2×C4⋊C8—611no—
365C2×C4⋊C8—611no—
366C2×C4⋊C8—611no—
367C2×C4⋊C8—612no—
368C2×C4⋊C8—612no—
369C2×C4⋊C8—611no—
370C2×C4⋊C8—618no—
371C2×C22⋊C8—612no—
372C2×C22⋊C8—612no—
373C2×C22⋊C8—612no—
374C2×#97—612no—
375C2×#97—612no—
376C2×C4×C8—612no—
377C61C2×#299011yescharacteristic, complemented, Sylow
378C2×#41—618no—
379C2×#41—1228no—
380C22×Q8—611no—
381C22×D4—611no—
382C22×D4—611no—
383C22×D4—611no—
384C23×C4—611no—
385C23×C4—611no—
386C23×C4—611no—
387C23×C4—611no—
388C23×C4—611no—
389C23×C4—611no—
390C23×C4—611no—
391C23×C4—611no—
392C23×C4C2×#692311yescharacteristic
393C2×M16—618no—
394C2×M16—2444no—
395C22×C8—612no—
396C22×C8—612no—
397C22×C8—612no—
398C22×C8—612no—
399C22×C8—618no—
400C22×C8—618no—
401C22×C8—2444no—
402C22×C8—2444no—
403C4×Q8—614no—
404C4×Q8—618no—
405C4×Q8—614no—
406C4×D4—614no—
407C4×D4—618no—
408C4×D4—614no—
409C4×D4—614no—
410C4×D4—614no—
411C4×D4—618no—
412C4×D4—614no—
413C4×D4—618no—
414C4×D4—614no—
415#117—618no—
416#117—618no—
417#117C2×#692318yes—
418C2×C4⋊C4—611no—
419C2×C4⋊C4—611no—
420C2×C4⋊C4—611no—
421C2×C4⋊C4—611no—
422C2×C4⋊C4C2×#692311yescharacteristic
423C2×C4⋊C4C2×#692311yescharacteristic
424C2×C22⋊C4—611no—
425C2×C22⋊C4—611no—
426C2×C22⋊C4—611no—
427C2×C22⋊C4—611no—
428C2×C22⋊C4C2×#692311yescharacteristic
429C2×C22⋊C4C2×#692311yescharacteristic
430C2×C42—611no—
431C2×C42—611no—
432C2×C42—611no—
433C2×C42—611no—
434C2×C42—611no—
435C2×C42—611no—
436C2×C42—611no—
437C2×C42—614no—
438C2×C42—614no—
439C2×C42—611no—
440C2×C42—614no—
441C2×C42—614no—
442C2×C42—614no—
443C2×C42—614no—
444C2×C42C2×#692311yescharacteristic
445C2×C42C2×#692311yescharacteristic
446C4⋊C8—618no—
447C4⋊C8—614no—
448C4⋊C8—614no—
449C4⋊C8—614no—
450C4⋊C8—618no—
451C4⋊C8—618no—
452C4⋊C8—614no—
453C22⋊C8—618no—
454C22⋊C8—618no—
455C22⋊C8—618no—
456#97—618no—
457#97—618no—
458C4×C8—618no—
459C24—611no—
460C24—611no—
461C24C22×#692311yescharacteristic
462#41—12232no—
463C2×Q8—614no—
464C2×Q8—1224no—
465C2×D4—618no—
466C2×D4—614no—
467C2×D4—614no—
468C2×D4—614no—
469C2×D4—1224no—
470C2×D4—1224no—
471C22×C4—24no—
472C22×C4—611no—
473C22×C4—611no—
474C22×C4—611no—
475C22×C4—612no—
476C22×C4—614no—
477C22×C4—612no—
478C22×C4—611no—
479C22×C4—611no—
480C22×C4—611no—
481C22×C4—612no—
482C22×C4—612no—
483C22×C4—614no—
484C22×C4—614no—
485C22×C4—614no—
486C22×C4—612no—
487C22×C4—614no—
488C22×C4—612no—
489C22×C4—1222no—
490C22×C4—1222no—
491C22×C4—1222no—
492C22×C4—1222no—
493C22×C4—1224no—
494C22×C4—1224no—
495C22×C4—1224no—
496C22×C4—1224no—
497C22×C4—1222no—
498C22×C4—1222no—
499C22×C4—1224no—
500C22×C4C22×#692314yes—
501C22×C4C22×#692311yescharacteristic
502C22×C4C22×#692311yescharacteristic
503C22×C4C22×#692311yescharacteristic
504C22×C4C22×#692311yescharacteristic
505C22×C4C22×#692311yescharacteristic
506C22×C4C22×#692311yescharacteristic
507M16—2448no—
508C2×C8—614no—
509C2×C8—614no—
510C2×C8—614no—
511C2×C8—614no—
512C2×C8—1224no—
513C2×C8—1224no—
514C2×C8—1224no—
515C2×C8—1224no—
516C2×C8—2448no—
517C2×C8—2448no—
518C4⋊C4—614no—
519C4⋊C4—614no—
520C4⋊C4—614no—
521C4⋊C4—614no—
522C4⋊C4C22×#692314yes—
523C4⋊C4C22×#692314yes—
524C22⋊C4—614no—
525C22⋊C4—614no—
526C22⋊C4—614no—
527C22⋊C4—614no—
528C22⋊C4C22×#692314yes—
529C22⋊C4C22×#692314yes—
530C42—612no—
531C42—612no—
532C42—612no—
533C42—612no—
534C42—612no—
535C42—614no—
536C42—612no—
537C42—614no—
538C42—612no—
539C42—614no—
540C42—612no—
541C42—614no—
542C42C22×#692314yes—
543C42C22×#692314yes—
544C23—22no—
545C23—22no—
546C23—614no—
547C23—612no—
548C23—612no—
549C23—1222no—
550C23—1222no—
551C23—1222no—
552C23—1222no—
553C23—1222no—
554C23D61⋊M1614yes—
555C23C23×#692312yes—
556C23C23×#692311yescharacteristic
557Q8—1228no—
558D4—6116no—
559D4—1228no—
560D4—1228no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—28no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—612no—
569C2×C4—612no—
570C2×C4—614no—
571C2×C4—614no—
572C2×C4—611no—
573C2×C4—612no—
574C2×C4—612no—
575C2×C4—611no—
576C2×C4—612no—
577C2×C4—612no—
578C2×C4—612no—
579C2×C4—1222no—
580C2×C4—1222no—
581C2×C4—1224no—
582C2×C4—1224no—
583C2×C4—1222no—
584C2×C4—1222no—
585C2×C4—1228no—
586C2×C4—1228no—
587C2×C4—1228no—
588C2×C4—1228no—
589C2×C4—1222no—
590C2×C4—1224no—
591C2×C4—1222no—
592C2×C4—1228no—
593C2×C4—1222no—
594C2×C4—1222no—
595C2×C4—1222no—
596C2×C4C23×#692312yes—
597C2×C4C23×#692312yes—
598C2×C4C23×#692312yes—
599C2×C4C23×#692312yes—
600C2×C4C23×#692312yes—
601C2×C4C23×#692312yes—
602C8—1224no—
603C8—1224no—
604C8—1224no—
605C8—1224no—
606C22—22no—
607C22—22no—
608C22—28no—
609C22—614no—
610C22—1222no—
611C22—1222no—
612C22—1228no—
613C22—1222no—
614C22—1222no—
615C22—1222no—
616C22—2444no—
617C22#1684083112yes—
618C22C2×D61⋊M1614yes—
619C22C2×D61⋊M1612yes—
620C22D61⋊#13112yes—
621C22C24×#692311yescharacteristic
622C4—22no—
623C4—22no—
624C4—22no—
625C4—22no—
626C4—22no—
627C4—22no—
628C4—612no—
629C4—611no—
630C4—611no—
631C4—614no—
632C4—614no—
633C4—1222no—
634C4—1222no—
635C4—1222no—
636C2—24no—
637C2—1224no—
638C2—2442no—
639C2#2146274814yesdirect product factor
640C2C2×#1684083111yescharacteristic
641C2C22×D61⋊M1611yescharacteristic
642C2C2×D61⋊#13111yescharacteristic
subgroupG/H
centerC23C23×#6923
commutatorC22×C61C24×C4
FrattiniC22C24×#6923
FittingC2×#117×C61C4
socleC23×C61C23×C4
prime radicalC22×#11758222C4
cosocleC2×Dic61C25
hypercenterC2×#117#6923
hypocenterC61C2×#2990
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. #21462748C2direct (N × H)
2. C2×#16840814C2semidirect
3. C2×#16840792C2semidirect
4. C2×#16840791C2semidirect
5. C2×#16840789C2semidirect
6. C2×#16840785C2semidirect
7. C2×#16840782C2semidirect
8. C2×#16840780C2semidirect
9. C2×#16840767C2semidirect
10. C22×#14519844C2semidirect
11. C2×D61⋊(C4⋊C8)C2semidirect
16. #16840814C22semidirect
17. #16840792C22semidirect
18. #16840791C22semidirect
19. #16840789C22semidirect
20. #16840785C22semidirect
21. #16840782C22semidirect
22. #16840780C22semidirect
23. #16840767C22semidirect
30. C2×#14519844C22semidirect
31. D61⋊(C4⋊C8)C22semidirect
149. C2×C22⋊D61M16semidirect
249. C22⋊D61C2×M16semidirect
328. C2×C61#2990semidirect
377. C61C2×#2990semidirect
639. C2#21462748direct (N × H)

Maximal subgroups

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

subgroupindex
#214627482
C2×#168408142
C2×#168407922
C2×#168407912
C2×#168407892
C2×#168407852
C2×#168407822
C2×#168407802
C2×#168407672
C22×#145198442
C2×D61⋊(C4⋊C8)2
C2×#168402302
C2×#299061