Finite Group Databasebeta

← C2×#21462658 #30625587

Subgroups — C2×#21462658 #30625587

Order 15616.

2254 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462658C2116yesmaximal, direct product factor
2C2×#16840814C212yesmaximal, complemented
3C2×#16840792C212yesmaximal, complemented
4C2×#16840791C212yesmaximal, complemented
5C2×#16840789C212yesmaximal, complemented
6C2×#16840785C211yesmaximal, characteristic, complemented
7C2×#16840784C211yesmaximal, characteristic, complemented
8C2×#16840782C211yesmaximal, characteristic, complemented
9C2×C4×#11758213C211yesmaximal, characteristic, complemented
10C2×#16840721C211yesmaximal, characteristic, complemented
11C22×#14519832C211yesmaximal, characteristic, complemented
12C2×#16840230C211yesmaximal, characteristic
13C22×#11758213C2212yes—
14C22×D61⋊C8C2212yes—
15C23×#92420C2212yes—
16#16840814C22116yescomplemented
17#16840792C22116yescomplemented
18#16840791C22116yescomplemented
19#16840789C22116yescomplemented
20#16840785C2218yescomplemented
21#16840784C2218yescomplemented
22#16840782C2218yescomplemented
23C2×#14519844C2212yes—
24C2×#14519844C2212yes—
25C2×C4⋊#92420C2212yes—
26C2×#14519834C2212yes—
27C2×#14519834C2212yes—
28C2×C22⋊#92420C2212yes—
29C4×#11758213C2218yescomplemented
30#16840721C2218yescomplemented
31C2×#14519832C2212yes—
32C2×#14519832C2212yes—
33C2×#14519832C2211yescharacteristic
34C2×#14519832C2211yescharacteristic
35C2×#14519832C2211yescharacteristic
36C2×#14519832C2211yescharacteristic
37C2×#14519832C2218yescomplemented
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—28no—
57C2×#11758213C2318yes—
58C2×D61⋊C8—28no—
59C2×D61⋊C8C2318yes—
60C22×#92420—28no—
61C22×#92420C2312yes—
62C22×#92420C2312yes—
63C22×#92420C2312yes—
64C22×#92420C2318yes—
65C22×#92420C2312yes—
66#14519844C2318yes—
67#14519844C2318yes—
68C4⋊#92420C2318yes—
69#14519834C2318yes—
70#14519834C2318yes—
71C22⋊#92420C2318yes—
72#14519832C2314yes—
73#14519832C2314yes—
74#14519832C2318yes—
75#14519832C2314yes—
76#14519832C2318yes—
77#14519832C2314yes—
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—42no—
154C22×Dic61C22×C411yescharacteristic
155C22×Dic61C22×C411yescharacteristic
156C22×Dic61C22×C411yescharacteristic
157C22×Dic61C22×C411yescharacteristic
158C22×Dic61C22×C412yes—
159C22×Dic61C22×C414yes—
160C22×Dic61C22×C411yescharacteristic
161C22×Dic61C2412yes—
162C22×Dic61C2411yescharacteristic
163#11758222—232no—
164C2×D244—24no—
165C2×D244C22×C414yes—
166C2×C4×D61—24no—
167C2×C4×D61—24no—
168C2×C4×D61—24no—
169C2×C4×D61—24no—
170C2×C4×D61—42no—
171C2×C4×D61—42no—
172C2×C4×D61C22×C414yes—
173C2×C4×D61C22×C414yes—
174C2×C4×D61C22×C412yes—
175C2×C4×D61C22×C412yes—
176C2×C4×D61C22×C414yes—
177C2×C4×D61C22×C414yes—
178C2×C4×D61C2412yes—
179C2×C4×D61C2412yes—
180C2×Dic122—24no—
181C2×Dic122C22×C414yes—
182C2×#92420—24no—
183C2×#92420—24no—
184C2×#92420—24no—
185C2×#92420—216no—
186C2×#92420#4118yescomplemented
187C2×#92420C2414yes—
188C2×#92420C2414yes—
189C2×#92420C2414yes—
190C2×#92420C2414yes—
191#11758213—216no—
192D61⋊C8—216no—
193C4⋊C4×C61C22×C414yes—
194C4⋊C4×C61C22×C414yes—
195C22⋊C4×C61C22×C414yes—
196C22⋊C4×C61C22×C414yes—
197C42×C61C22×C414yes—
198C42×C61C22×C414yes—
199#11758198C22×C414yes—
200#11758198C22×C414yes—
201#11758198C22×C414yes—
202#11758198C22×C414yes—
203#11758196C22×C414yes—
204#11758196C22×C414yes—
205#11758196C22×C414yes—
206#11758196C22×C414yes—
207C4×Dic61C22×C412yes—
208C4×Dic61C22×C412yes—
209C4×Dic61C22×C412yes—
210C4×Dic61C22×C414yes—
211C4×Dic61C22×C414yes—
212C4×Dic61C22×C414yes—
213C4×Dic61C22×C414yes—
214C4×Dic61C22×C412yes—
215C4×Dic61C2412yes—
216C4×Dic61C2412yes—
217C4×Dic61C2412yes—
218C4×Dic61C2412yes—
219C23×C61—22no—
220C23×C61—22no—
221C23×C61C2×M1614yes—
222C23×C61C23×C412yes—
223C23×C61C23×C411yescharacteristic
224C22×D61—22no—
225C22×D61—22no—
226C22×D61—22no—
227C22×D61—22no—
228C22×D61—22no—
229C22×D61C2×M1614yes—
230C22×D61C23×C412yes—
231C22×D61C23×C412yes—
232C2×C4×C61—22no—
233C2×C4×C61—22no—
234C2×C4×C61—22no—
235C2×C4×C61—22no—
236C2×C4×C61—28no—
237C2×C4×C61—22no—
238C2×C4×C61—22no—
239C2×C4×C61C23×C412yes—
240C2×C4×C61C23×C412yes—
241C2×C4×C61C23×C412yes—
242C2×C4×C61C23×C412yes—
243C2×C4×C61C23×C412yes—
244C2×C4×C61C23×C412yes—
245C22⋊D61—28no—
246C22⋊D61C2×M16116yescomplemented
247C2×Dic61—22no—
248C2×Dic61—22no—
249C2×Dic61—22no—
250C2×Dic61—22no—
251C2×Dic61—24no—
252C2×Dic61—24no—
253C2×Dic61—44no—
254C2×Dic61C2×M1614yes—
255C2×Dic61C23×C412yes—
256C2×Dic61C23×C412yes—
257C2×Dic61C23×C412yes—
258C2×Dic61C23×C412yes—
259C2×Dic61C23×C411yescharacteristic
260C2×Dic61C23×C412yes—
261C2×Dic61C2×#4114yes—
262C2×Dic61C2511yescharacteristic
263D244—28no—
264C4×D61—28no—
265C4×D61—24no—
266C4×D61—24no—
267C4×D61—28no—
268C4×D61—24no—
269C4×D61—24no—
270C4×D61—44no—
271C4×D61—44no—
272Dic122—28no—
273#92420—24no—
274#92420—24no—
275#92420—24no—
276#92420C2×#4118yescomplemented
277C2×#2970—611nomaximal, Sylow
278C22×C61—22no—
279C22×C61—28no—
280C22×C61—22no—
281C22×C61C4×#4112yes—
282C22×C61C22×M1614yes—
283C22×C61C22×M1612yes—
284C22×C61#56812yes—
285C22×C61C24×C411yescharacteristic
286C2×D61—22no—
287C2×D61—28no—
288C2×D61—22no—
289C2×D61—22no—
290C2×D61—22no—
291C2×D61—22no—
292C2×D61—44no—
293C2×D61C22×M1614yes—
294C4×C61—22no—
295C4×C61—22no—
296C4×C61—22no—
297C4×C61—22no—
298C4×C61—22no—
299C4×C61—22no—
300Dic61—22no—
301Dic61—22no—
302Dic61—22no—
303Dic61—22no—
304Dic61C4×#4112yes—
305Dic61C22×M1614yes—
306Dic61C22×#4112yes—
307C2×C4×#41—611no—
308#2970—6116no—
309C2×#446—612no—
310C2×#435—612no—
311C2×#435—612no—
312C2×C8×D4—612no—
313C2×#432—611no—
314C2×#432—611no—
315C2×#432—611no—
316C2×C4×M16—611no—
317C22×#97—611no—
318C22×#97—611no—
319C2×C61—24no—
320C2×C61#297014yescomplemented
321C2×C61C2×C4×#4111yescharacteristic
322C2×C61C23×M1611yescharacteristic
323C2×C61C2×#56811yescharacteristic
324D61—24no—
325D61—42no—
326C22×#41—611no—
327C22×M16—612no—
328C23×C8—612no—
329C23×C8—612no—
330C4×#41—618no—
331C4×#41—618no—
332C2×C4×Q8—611no—
333C2×C4×Q8—611no—
334C2×C4×D4—611no—
335C2×C4×D4—611no—
336C2×C4×D4—611no—
337C2×C4×D4—611no—
338C2×C4×D4—611no—
339C2×C4×D4—611no—
340C2×#117—611no—
341C2×#117—611no—
342C2×#117#692311yescharacteristic
343C22×C42—611no—
344C22×C42—611no—
345C22×C42—611no—
346#446—6116no—
347#435—6116no—
348#435—6116no—
349C8×D4—6116no—
350#432—618no—
351#432—618no—
352#432—618no—
353C2×C4⋊C8—612no—
354C2×C4⋊C8—612no—
355C2×C4⋊C8—612no—
356C2×C22⋊C8—612no—
357C2×C22⋊C8—612no—
358C2×C22⋊C8—612no—
359C4×M16—618no—
360C2×#97—611no—
361C2×#97—611no—
362C2×#97—611no—
363C2×#97—612no—
364C2×#97—612no—
365C2×#97—611no—
366C2×#97—618no—
367C2×#97—618no—
368C2×C4×C8—612no—
369C61C2×#297011yescharacteristic, complemented, Sylow
370C2×#41—618no—
371C2×#41—1228no—
372C22×Q8—611no—
373C22×D4—611no—
374C22×D4—611no—
375C22×D4—611no—
376C23×C4—611no—
377C23×C4—611no—
378C23×C4—611no—
379C23×C4—611no—
380C23×C4—611no—
381C23×C4—611no—
382C23×C4—611no—
383C23×C4—611no—
384C23×C4C2×#692311yescharacteristic
385C2×M16—618no—
386C2×M16—1228no—
387C22×C8—612no—
388C22×C8—612no—
389C22×C8—612no—
390C22×C8—618no—
391C22×C8—612no—
392C22×C8—618no—
393C22×C8—1228no—
394C22×C8—1228no—
395C4×Q8—614no—
396C4×Q8—618no—
397C4×Q8—614no—
398C4×D4—614no—
399C4×D4—614no—
400C4×D4—618no—
401C4×D4—614no—
402C4×D4—614no—
403C4×D4—614no—
404C4×D4—614no—
405C4×D4—618no—
406C4×D4—618no—
407#117—618no—
408#117—618no—
409#117C2×#692318yes—
410C2×C4⋊C4—611no—
411C2×C4⋊C4—611no—
412C2×C4⋊C4—611no—
413C2×C4⋊C4—611no—
414C2×C4⋊C4C2×#692311yescharacteristic
415C2×C4⋊C4C2×#692311yescharacteristic
416C2×C22⋊C4—611no—
417C2×C22⋊C4—611no—
418C2×C22⋊C4—611no—
419C2×C22⋊C4—611no—
420C2×C22⋊C4C2×#692311yescharacteristic
421C2×C22⋊C4C2×#692311yescharacteristic
422C2×C42—611no—
423C2×C42—611no—
424C2×C42—611no—
425C2×C42—611no—
426C2×C42—611no—
427C2×C42—611no—
428C2×C42—611no—
429C2×C42—614no—
430C2×C42—614no—
431C2×C42—611no—
432C2×C42—614no—
433C2×C42—614no—
434C2×C42—614no—
435C2×C42—614no—
436C2×C42C2×#692311yescharacteristic
437C2×C42C2×#692311yescharacteristic
438C4⋊C8—618no—
439C4⋊C8—618no—
440C4⋊C8—618no—
441C22⋊C8—618no—
442C22⋊C8—618no—
443C22⋊C8—618no—
444#97—614no—
445#97—614no—
446#97—614no—
447#97—618no—
448#97—618no—
449#97—614no—
450C4×C8—618no—
451C24—611no—
452C24—611no—
453C24C22×#692311yescharacteristic
454#41—12232no—
455C2×Q8—614no—
456C2×Q8—1224no—
457C2×D4—618no—
458C2×D4—614no—
459C2×D4—614no—
460C2×D4—614no—
461C2×D4—1224no—
462C2×D4—1224no—
463C22×C4—24no—
464C22×C4—611no—
465C22×C4—611no—
466C22×C4—612no—
467C22×C4—612no—
468C22×C4—611no—
469C22×C4—611no—
470C22×C4—611no—
471C22×C4—611no—
472C22×C4—614no—
473C22×C4—612no—
474C22×C4—612no—
475C22×C4—614no—
476C22×C4—614no—
477C22×C4—612no—
478C22×C4—612no—
479C22×C4—614no—
480C22×C4—614no—
481C22×C4—1224no—
482C22×C4—1224no—
483C22×C4—1224no—
484C22×C4—1224no—
485C22×C4—1224no—
486C22×C4—2442no—
487C22×C4—2442no—
488C22×C4—2442no—
489C22×C4C22×#692314yes—
490C22×C4C22×#692311yescharacteristic
491C22×C4C22×#692311yescharacteristic
492C22×C4C22×#692311yescharacteristic
493C22×C4C22×#692311yescharacteristic
494C22×C4C22×#692311yescharacteristic
495C22×C4C22×#692311yescharacteristic
496M16—12216no—
497C2×C8—614no—
498C2×C8—618no—
499C2×C8—614no—
500C2×C8—614no—
501C2×C8—614no—
502C2×C8—12216no—
503C2×C8—12216no—
504C2×C8—1224no—
505C2×C8—1224no—
506C2×C8—1224no—
507C4⋊C4—614no—
508C4⋊C4—614no—
509C4⋊C4—614no—
510C4⋊C4—614no—
511C4⋊C4C22×#692314yes—
512C4⋊C4C22×#692314yes—
513C22⋊C4—614no—
514C22⋊C4—614no—
515C22⋊C4—614no—
516C22⋊C4—614no—
517C22⋊C4C22×#692314yes—
518C22⋊C4C22×#692314yes—
519C42—612no—
520C42—612no—
521C42—612no—
522C42—612no—
523C42—612no—
524C42—614no—
525C42—612no—
526C42—612no—
527C42—612no—
528C42—614no—
529C42—614no—
530C42—614no—
531C42C22×#692314yes—
532C42C22×#692314yes—
533C23—22no—
534C23—22no—
535C23—614no—
536C23—612no—
537C23—612no—
538C23—1222no—
539C23—1222no—
540C23—1222no—
541C23—1222no—
542C23—1222no—
543C23D61⋊M1614yes—
544C23C23×#692312yes—
545C23C23×#692311yescharacteristic
546Q8—1228no—
547D4—6116no—
548D4—1228no—
549D4—1228no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—28no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—614no—
558C2×C4—614no—
559C2×C4—611no—
560C2×C4—612no—
561C2×C4—611no—
562C2×C4—612no—
563C2×C4—612no—
564C2×C4—612no—
565C2×C4—612no—
566C2×C4—1224no—
567C2×C4—1224no—
568C2×C4—1224no—
569C2×C4—1224no—
570C2×C4—1228no—
571C2×C4—1228no—
572C2×C4—1224no—
573C2×C4—1224no—
574C2×C4—1222no—
575C2×C4—1222no—
576C2×C4—1222no—
577C2×C4—1222no—
578C2×C4—2444no—
579C2×C4—2444no—
580C2×C4—2444no—
581C2×C4C23×#692312yes—
582C2×C4C23×#692312yes—
583C2×C4C23×#692312yes—
584C2×C4C23×#692312yes—
585C2×C4C23×#692312yes—
586C2×C4C23×#692312yes—
587C8—618no—
588C8—1224no—
589C8—1224no—
590C8—1224no—
591C22—22no—
592C22—22no—
593C22—28no—
594C22—614no—
595C22—1222no—
596C22—1222no—
597C22—1228no—
598C22—1222no—
599C22—1222no—
600C22—1222no—
601C22—2444no—
602C22#41×#692312yes—
603C22C2×D61⋊M1614yes—
604C22C2×D61⋊M1612yes—
605C22#1684084112yes—
606C22C24×#692311yescharacteristic
607C4—22no—
608C4—22no—
609C4—22no—
610C4—22no—
611C4—22no—
612C4—22no—
613C4—612no—
614C4—612no—
615C4—614no—
616C4—1222no—
617C4—1222no—
618C4—1222no—
619C4—1222no—
620C2—24no—
621C2—1224no—
622C2—2442no—
623C2#2146265814yesdirect product factor
624C2C2×#41×#692311yescharacteristic
625C2C22×D61⋊M1611yescharacteristic
626C2C2×#1684084111yescharacteristic
subgroupG/H
centerC23C23×#6923
commutatorC22×C61C24×C4
FrattiniC22C24×#6923
FittingC2×#117×C61C4
socleC23×C61C23×C4
prime radicalC22×#11758222C4
cosocleC2×Dic61C25
hypercenterC2×#117#6923
hypocenterC61C2×#2970
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. #21462658C2direct (N × H)
2. C2×#16840814C2semidirect
3. C2×#16840792C2semidirect
4. C2×#16840791C2semidirect
5. C2×#16840789C2semidirect
6. C2×#16840785C2semidirect
7. C2×#16840784C2semidirect
8. C2×#16840782C2semidirect
9. C2×C4×#11758213C2semidirect
10. C2×#16840721C2semidirect
11. C22×#14519832C2semidirect
16. #16840814C22semidirect
17. #16840792C22semidirect
18. #16840791C22semidirect
19. #16840789C22semidirect
20. #16840785C22semidirect
21. #16840784C22semidirect
22. #16840782C22semidirect
29. C4×#11758213C22semidirect
30. #16840721C22semidirect
37. C2×#14519832C22semidirect
149. C2×C22⋊D61M16semidirect
186. C2×#92420#41semidirect
246. C22⋊D61C2×M16semidirect
276. #92420C2×#41semidirect
320. C2×C61#2970semidirect
369. C61C2×#2970semidirect
623. C2#21462658direct (N × H)

Maximal subgroups

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

subgroupindex
#214626582
C2×#168408142
C2×#168407922
C2×#168407912
C2×#168407892
C2×#168407852
C2×#168407842
C2×#168407822
C2×C4×#117582132
C2×#168407212
C22×#145198322
C2×#168402302
C2×#297061