Finite Group Databasebeta

← C2×#21462517 #30625297

Subgroups — C2×#21462517 #30625297

Order 15616.

2178 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462517C2116yesmaximal, direct product factor
2C2×#16840787C212yesmaximal, complemented
3C2×#16840786C212yesmaximal, complemented
4C2×#16840785C211yesmaximal, characteristic, complemented
5C2×#16840782C211yesmaximal, characteristic, complemented
6C2×#16840780C211yesmaximal, characteristic, complemented
7C2×#16840779C211yesmaximal, characteristic, complemented
8C2×#16840765C211yesmaximal, characteristic, complemented
9C22×#14519844C211yesmaximal, characteristic, complemented
10C2×#16840735C212yesmaximal
11C2×#16840726C212yesmaximal, complemented
12C2×C4×#11758224C211yesmaximal, characteristic
13C22×#11758217C2212yes—
14C23×#92420C2212yes—
15#16840787C22116yescomplemented
16#16840786C22116yescomplemented
17#16840785C2218yescomplemented
18#16840782C2218yescomplemented
19#16840780C2218yescomplemented
20#16840779C2218yescomplemented
21#16840765C2218yescomplemented
22C2×#14519844C2211yescharacteristic
23C2×#14519844C2211yescharacteristic
24C2×#14519844C2212yes—
25C2×#14519844C2211yescharacteristic
26C2×#14519844C2211yescharacteristic
27C2×#14519844C2218yescomplemented
28C2×C4⋊#92420C2212yes—
29#16840735C22116yes—
30C2×#14519834C2212yes—
31C2×#14519834C2212yes—
32C2×C22⋊#92420C2212yes—
33C2×C22⋊#92420C2212yes—
34#16840726C22116yescomplemented
35C2×#14519832C2212yes—
36C2×#14519832C2212yes—
37C2×C4×#92420C2212yes—
38C2×C4×#92420C2212yes—
39C22×#11758224C2211yescharacteristic
40C4×#11758224C418yes—
41C4×#11758224C2218yes—
42C2×C4×Dic122C411yescharacteristic
43C2×#14519742C411yescharacteristic
44C2×D4×Dic61C411yescharacteristic
45C2×C4×C22⋊D61C411yescharacteristic
46C2×C4×C22⋊D61C411yescharacteristic
47C2×#14519737C411yescharacteristic
48C2×#14519737C411yescharacteristic
49C2×#14519735C2211yescharacteristic
50C2×#14519733C2211yescharacteristic
51C2×#14519733C2211yescharacteristic
52C22×C4×Dic61C2211yescharacteristic
53C22×C4×Dic61C2211yescharacteristic
54C2×C42×D61C2211yescharacteristic
55C2×C4×D4×C61C411yescharacteristic
56C2×#11758217—28no—
57C2×#11758217C2318yes—
58C22×#92420—28no—
59C22×#92420C2312yes—
60C22×#92420C2312yes—
61C22×#92420C2312yes—
62C22×#92420C2312yes—
63C22×#92420C2318yes—
64#14519844C2314yes—
65#14519844C2314yes—
66#14519844C2318yes—
67#14519844C2314yes—
68#14519844C2314yes—
69C4⋊#92420C2318yes—
70#14519834C2318yes—
71#14519834C2318yes—
72C22⋊#92420C2318yes—
73C22⋊#92420C2318yes—
74#14519832C2318yes—
75#14519832C2318yes—
76C4×#92420C2318yes—
77C4×#92420C2318yes—
78C2×#11758224—24no—
79C2×#11758224—24no—
80C2×#11758224C2×C414yes—
81C2×#11758224C2314yes—
82C22×Dic122C2×C411yescharacteristic
83C22×C22⋊D61C2×C411yescharacteristic
84C22×C22⋊D61C2×C411yescharacteristic
85C23×Dic61C2×C411yescharacteristic
86C23×Dic61C2×C411yescharacteristic
87C23×Dic61C2311yescharacteristic
88C23×Dic61C2311yescharacteristic
89C22×C4×D61C2×C411yescharacteristic
90C22×C4×D61C2×C411yescharacteristic
91C22×C4×D61C2311yescharacteristic
92C4×Dic122C2×C418yes—
93#14519742C2×C418yes—
94D4×Dic61C2×C418yes—
95C4×C22⋊D61C2×C418yes—
96C4×C22⋊D61C2×C418yes—
97#14519737C2×C418yes—
98#14519737C2×C418yes—
99#14519735C2×C414yes—
100#14519735C2314yes—
101#14519733C2×C414yes—
102#14519733C2×C414yes—
103#14519733C2314yes—
104#14519733C2314yes—
105C2×C4⋊Dic61C2×C411yescharacteristic
106C2×#11758196C2×C411yescharacteristic
107C2×#11758196C2×C411yescharacteristic
108C2×#11758196C2×C411yescharacteristic
109C2×#11758196C2×C411yescharacteristic
110C2×C22⋊Dic61C2×C411yescharacteristic
111C2×C22⋊Dic61C2×C411yescharacteristic
112C2×#11758198C2×C411yescharacteristic
113C2×#11758198C2×C411yescharacteristic
114C2×C4×Dic61C2×C411yescharacteristic
115C2×C4×Dic61C2×C411yescharacteristic
116C2×C4×Dic61C2×C411yescharacteristic
117C2×C4×Dic61C2×C411yescharacteristic
118C2×C4×Dic61C2×C411yescharacteristic
119C2×C4×Dic61C2×C414yes—
120C2×C4×Dic61C2×C414yes—
121C2×C4×Dic61C2311yescharacteristic
122C2×C4×Dic61C2311yescharacteristic
123C2×C4×Dic61C2311yescharacteristic
124C2×C4×Dic61C2311yescharacteristic
125C2×C4×Dic61C2314yes—
126C2×C4×Dic61C2314yes—
127C42×D61C2×C414yes—
128C42×D61C2314yes—
129C22×D4×C61C2×C411yescharacteristic
130C23×C4×C61C2×C411yescharacteristic
131C23×C4×C61C2×C411yescharacteristic
132C4×D4×C61C2×C418yes—
133C2×C4⋊C4×C61C2×C411yescharacteristic
134C2×C22⋊C4×C61C2×C411yescharacteristic
135C2×C22⋊C4×C61C2×C411yescharacteristic
136C2×C42×C61C2×C411yescharacteristic
137C24×C61C22×C411yescharacteristic
138C24×C61C22×C411yescharacteristic
139C23×D61C22×C411yescharacteristic
140C2×D4×C61—24no—
141C2×D4×C61C22×C414yes—
142C22×C4×C61—42no—
143C22×C4×C61—42no—
144C22×C4×C61C22×C411yescharacteristic
145C22×C4×C61C22×C411yescharacteristic
146C22×C4×C61C22×C411yescharacteristic
147C22×C4×C61C22×C411yescharacteristic
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C22×C414yes—
150C22×C4×C61C22×C414yes—
151C2×C22⋊D61—24no—
152C2×C22⋊D61—24no—
153C2×C22⋊D61C22×C414yes—
154C2×C22⋊D61C22×C414yes—
155C22×Dic61—24no—
156C22×Dic61—24no—
157C22×Dic61—22no—
158C22×Dic61—22no—
159C22×Dic61C22×C411yescharacteristic
160C22×Dic61C22×C411yescharacteristic
161C22×Dic61C22×C411yescharacteristic
162C22×Dic61C22×C414yes—
163C22×Dic61C22×C414yes—
164C22×Dic61C22×C411yescharacteristic
165C22×Dic61C22×C412yes—
166C22×Dic61C22×C411yescharacteristic
167C22×Dic61C22×C412yes—
168C22×Dic61C22×C411yescharacteristic
169C22×Dic61#4114yes—
170C22×Dic61#4114yes—
171C22×Dic61C2412yes—
172C22×Dic61C2411yescharacteristic
173C22×Dic61C2412yes—
174#11758224—216no—
175#11758224—28no—
176#11758224—28no—
177C2×C4×D61—24no—
178C2×C4×D61—22no—
179C2×C4×D61—22no—
180C2×C4×D61—42no—
181C2×C4×D61C22×C414yes—
182C2×C4×D61C22×C412yes—
183C2×C4×D61C22×C414yes—
184C2×C4×D61C2412yes—
185C2×Dic122—24no—
186C2×Dic122C22×C414yes—
187#11758217—216no—
188C2×#92420—24no—
189C2×#92420—24no—
190C2×#92420—216no—
191C2×#92420—24no—
192C2×#92420—24no—
193C2×#92420C2414yes—
194C2×#92420C2414yes—
195C2×#92420C2414yes—
196C2×#92420C2414yes—
197C4⋊C4×C61C22×C414yes—
198C22⋊C4×C61C22×C414yes—
199C22⋊C4×C61C22×C414yes—
200C42×C61C22×C414yes—
201C22⋊Dic61C22×C414yes—
202C22⋊Dic61C22×C414yes—
203#11758198C22×C414yes—
204#11758198C22×C414yes—
205C4⋊Dic61C22×C414yes—
206#11758196C22×C414yes—
207#11758196C22×C414yes—
208#11758196C22×C414yes—
209#11758196C22×C414yes—
210C4×Dic61C22×C412yes—
211C4×Dic61C22×C412yes—
212C4×Dic61C22×C414yes—
213C4×Dic61C22×C412yes—
214C4×Dic61C22×C412yes—
215C4×Dic61C22×C414yes—
216C4×Dic61C22×C414yes—
217C4×Dic61C22×C414yes—
218C4×Dic61C22×C414yes—
219C4×Dic61C2412yes—
220C4×Dic61C2412yes—
221C4×Dic61C2412yes—
222C4×Dic61C2412yes—
223C23×C61—22no—
224C23×C61—22no—
225C23×C61—22no—
226C23×C61—22no—
227C23×C61—22no—
228C23×C61#11714yes—
229C23×C61C23×C412yes—
230C23×C61C23×C412yes—
231C23×C61C23×C411yescharacteristic
232C22×D61—22no—
233C22×D61—22no—
234C22×D61—22no—
235C22×D61C23×C412yes—
236D4×C61—28no—
237C2×C4×C61—22no—
238C2×C4×C61—22no—
239C2×C4×C61—22no—
240C2×C4×C61—22no—
241C2×C4×C61—22no—
242C2×C4×C61—44no—
243C2×C4×C61—44no—
244C2×C4×C61C23×C412yes—
245C2×C4×C61C23×C412yes—
246C2×C4×C61C23×C412yes—
247C2×C4×C61C23×C412yes—
248C2×C4×C61C23×C412yes—
249C22⋊D61—28no—
250C22⋊D61—28no—
251C2×Dic61—22no—
252C2×Dic61—22no—
253C2×Dic61—22no—
254C2×Dic61—22no—
255C2×Dic61—24no—
256C2×Dic61—28no—
257C2×Dic61—28no—
258C2×Dic61—22no—
259C2×Dic61—22no—
260C2×Dic61#11714yes—
261C2×Dic61#11718yes—
262C2×Dic61#13114yes—
263C2×Dic61C23×C412yes—
264C2×Dic61C23×C412yes—
265C2×Dic61C23×C412yes—
266C2×Dic61C23×C412yes—
267C2×Dic61C23×C411yescharacteristic
268C2×Dic61C23×C412yes—
269C2×Dic61C23×C412yes—
270C2×Dic61C2×#4112yes—
271C2×Dic61C2×#4112yes—
272C2×Dic61C2×#4114yes—
273C2×Dic61C2×#4114yes—
274C2×Dic61C2511yescharacteristic
275C4×D61—24no—
276C4×D61—28no—
277C4×D61—22no—
278C4×D61—22no—
279C4×D61—44no—
280Dic122—28no—
281#92420—24no—
282#92420—24no—
283#92420—24no—
284#92420—24no—
285C2×#2925—611nomaximal, Sylow
286C22×C61—28no—
287C22×C61—22no—
288C22×C61—22no—
289C22×C61—22no—
290C22×C61—22no—
291C22×C61—22no—
292C22×C61—44no—
293C22×C61C2×#11714yes—
294C22×C61C2×#11712yes—
295C22×C61C2×#13112yes—
296C22×C61#56812yes—
297C22×C61C24×C411yescharacteristic
298C2×D61—22no—
299C2×D61—22no—
300C2×D61—22no—
301C2×D61—44no—
302C4×C61—22no—
303C4×C61—22no—
304C4×C61—22no—
305C4×C61—22no—
306C4×C61—22no—
307Dic61—22no—
308Dic61—22no—
309Dic61—22no—
310Dic61—22no—
311Dic61C2×#11714yes—
312Dic61C2×#11712yes—
313Dic61C2×#13114yes—
314Dic61C22×#4111yescharacteristic
315Dic61C22×#4111yescharacteristic
316C2×C4×#41—611no—
317#2925—6116no—
318C2×#433—612no—
319C2×#433—612no—
320C2×#432—611no—
321C2×#432—611no—
322C2×#431—611no—
323C2×#431—611no—
324C2×#423—611no—
325C22×C4⋊C8—611no—
326C2×#408—612no—
327C2×#405—612no—
328C2×C61—24no—
329C2×C61—42no—
330C2×C61#292514yescomplemented
331C2×C61C22×#11711yescharacteristic
332C2×C61C22×#13111yescharacteristic
333C2×C61C2×#56811yescharacteristic
334D61—42no—
335C22×#41—611no—
336C22×M16—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#692311yescharacteristic
348C2×#117—611no—
349C2×#117—611no—
350C2×#117—611no—
351C22×C42—611no—
352C22×C42—611no—
353C22×C42—611no—
354#433—6116no—
355#433—6116no—
356#432—618no—
357#432—618no—
358#431—618no—
359#431—618no—
360#423—618no—
361C2×C4⋊C8—612no—
362C2×C4⋊C8—611no—
363C2×C4⋊C8—611no—
364C2×C4⋊C8—612no—
365C2×C4⋊C8—611no—
366C2×C4⋊C8—611no—
367C2×C4⋊C8—618no—
368#408—6116no—
369C2×C22⋊C8—612no—
370C2×C22⋊C8—612no—
371C2×C22⋊C8—612no—
372C2×C22⋊C8—612no—
373#405—6116no—
374C2×#97—612no—
375C2×#97—612no—
376C2×C4×C8—612no—
377C2×C4×C8—612no—
378C61C2×#292511yescharacteristic, complemented, Sylow
379C2×#41—614no—
380C2×#41—614no—
381C2×#41—1224no—
382C2×#41—1224no—
383C22×Q8—611no—
384C22×D4—611no—
385C22×D4—611no—
386C22×D4C2×#692311yescharacteristic
387C23×C4—611no—
388C23×C4—611no—
389C23×C4—611no—
390C23×C4—611no—
391C23×C4—611no—
392C23×C4—611no—
393C23×C4—611no—
394C23×C4C2×#692311yescharacteristic
395C23×C4C2×#692311yescharacteristic
396C2×M16—618no—
397C2×M16—1228no—
398C22×C8—612no—
399C22×C8—612no—
400C22×C8—618no—
401C22×C8—612no—
402C22×C8—612no—
403C22×C8—1228no—
404C4×Q8—618no—
405C4×Q8—618no—
406C4×D4—618no—
407C4×D4—618no—
408C4×D4—618no—
409C4×D4—618no—
410C4×D4—618no—
411C4×D4C2×#692318yes—
412#117—614no—
413#117—614no—
414#117—614no—
415#117—614no—
416#117—614no—
417#117—614no—
418C2×C4⋊C4—611no—
419C2×C4⋊C4—611no—
420C2×C4⋊C4—611no—
421C2×C4⋊C4—611no—
422C2×C4⋊C4—611no—
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—611no—
438C2×C42—614no—
439C2×C42—614no—
440C2×C42—614no—
441C2×C42—614no—
442C2×C42—611no—
443C2×C42—614no—
444C2×C42—614no—
445C2×C42C2×#692311yescharacteristic
446C4⋊C8—618no—
447C4⋊C8—614no—
448C4⋊C8—614no—
449C4⋊C8—618no—
450C4⋊C8—614no—
451C4⋊C8—614no—
452C22⋊C8—618no—
453C22⋊C8—618no—
454C22⋊C8—618no—
455C22⋊C8—618no—
456#97—618no—
457#97—618no—
458C4×C8—618no—
459C4×C8—618no—
460C24—611no—
461C24C22×#692311yescharacteristic
462C24C22×#692311yescharacteristic
463#41—12216no—
464#41—1228no—
465#41—1228no—
466C2×Q8—614no—
467C2×Q8—1224no—
468C2×D4—24no—
469C2×D4—614no—
470C2×D4—614no—
471C2×D4—1224no—
472C2×D4—1224no—
473C2×D4C22×#692314yes—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—614no—
477C22×C4—614no—
478C22×C4—612no—
479C22×C4—612no—
480C22×C4—611no—
481C22×C4—611no—
482C22×C4—611no—
483C22×C4—612no—
484C22×C4—612no—
485C22×C4—614no—
486C22×C4—614no—
487C22×C4—611no—
488C22×C4—611no—
489C22×C4—611no—
490C22×C4—611no—
491C22×C4—612no—
492C22×C4—612no—
493C22×C4—614no—
494C22×C4—614no—
495C22×C4—1224no—
496C22×C4—1222no—
497C22×C4—1222no—
498C22×C4—1222no—
499C22×C4—1222no—
500C22×C4—1224no—
501C22×C4—1224no—
502C22×C4—2442no—
503C22×C4C22×#692311yescharacteristic
504C22×C4C22×#692311yescharacteristic
505C22×C4C22×#692311yescharacteristic
506C22×C4C22×#692311yescharacteristic
507C22×C4C22×#692311yescharacteristic
508C22×C4C22×#692314yes—
509C22×C4C22×#692314yes—
510M16—12216no—
511C2×C8—614no—
512C2×C8—614no—
513C2×C8—614no—
514C2×C8—614no—
515C2×C8—1224no—
516C2×C8—1224no—
517C2×C8—12216no—
518C2×C8—1224no—
519C2×C8—1224no—
520C4⋊C4—614no—
521C4⋊C4—614no—
522C4⋊C4—614no—
523C4⋊C4—614no—
524C4⋊C4—614no—
525C4⋊C4C22×#692314yes—
526C22⋊C4—614no—
527C22⋊C4—614no—
528C22⋊C4—614no—
529C22⋊C4—614no—
530C22⋊C4C22×#692314yes—
531C22⋊C4C22×#692314yes—
532C42—612no—
533C42—612no—
534C42—612no—
535C42—612no—
536C42—612no—
537C42—612no—
538C42—612no—
539C42—612no—
540C42—614no—
541C42—614no—
542C42—614no—
543C42—614no—
544C42—614no—
545C42C22×#692314yes—
546C23—22no—
547C23—22no—
548C23—22no—
549C23—22no—
550C23—22no—
551C23—612no—
552C23—1222no—
553C23—1222no—
554C23—1222no—
555C23#1451985614yes—
556C23C23×#692312yes—
557C23C23×#692312yes—
558C23C23×#692311yescharacteristic
559Q8—1228no—
560D4—28no—
561D4—1228no—
562D4—1228no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—44no—
569C2×C4—44no—
570C2×C4—614no—
571C2×C4—618no—
572C2×C4—612no—
573C2×C4—612no—
574C2×C4—614no—
575C2×C4—614no—
576C2×C4—614no—
577C2×C4—611no—
578C2×C4—612no—
579C2×C4—612no—
580C2×C4—611no—
581C2×C4—612no—
582C2×C4—612no—
583C2×C4—612no—
584C2×C4—612no—
585C2×C4—1228no—
586C2×C4—1224no—
587C2×C4—1222no—
588C2×C4—1222no—
589C2×C4—1228no—
590C2×C4—1228no—
591C2×C4—1224no—
592C2×C4—1222no—
593C2×C4—1222no—
594C2×C4—1222no—
595C2×C4—1222no—
596C2×C4—1222no—
597C2×C4—1222no—
598C2×C4—2444no—
599C2×C4C23×#692312yes—
600C2×C4C23×#692312yes—
601C2×C4C23×#692312yes—
602C2×C4C23×#692312yes—
603C2×C4C23×#692312yes—
604C8—1224no—
605C8—1224no—
606C8—1224no—
607C8—1224no—
608C22—22no—
609C22—22no—
610C22—28no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—44no—
615C22—1222no—
616C22—1222no—
617C22—1222no—
618C22—2444no—
619C22C2×#1451985614yes—
620C22C2×#1451985612yes—
621C22D61⋊#13112yes—
622C22#1684084012yes—
623C22C24×#692311yescharacteristic
624C4—22no—
625C4—22no—
626C4—22no—
627C4—22no—
628C4—22no—
629C4—612no—
630C4—614no—
631C4—611no—
632C4—611no—
633C4—614no—
634C4—1222no—
635C4—1222no—
636C4—1222no—
637C4—1222no—
638C2—24no—
639C2—42no—
640C2—2442no—
641C2#2146251714yesdirect product factor
642C2C22×#1451985611yescharacteristic
643C2C2×D61⋊#13111yescharacteristic
644C2C2×#1684084011yescharacteristic
subgroupG/H
centerC23C23×#6923
commutatorC22×C61C24×C4
FrattiniC22C24×#6923
FittingC2×C4×D4×C61C4
socleC23×C61C23×C4
prime radicalC22×#11758224C22
cosocleC2×Dic61C25
hypercenterC2×C4×D4#6923
hypocenterC61C2×#2925
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #21462517C2direct (N × H)
2. C2×#16840787C2semidirect
3. C2×#16840786C2semidirect
4. C2×#16840785C2semidirect
5. C2×#16840782C2semidirect
6. C2×#16840780C2semidirect
7. C2×#16840779C2semidirect
8. C2×#16840765C2semidirect
9. C22×#14519844C2semidirect
11. C2×#16840726C2semidirect
15. #16840787C22semidirect
16. #16840786C22semidirect
17. #16840785C22semidirect
18. #16840782C22semidirect
19. #16840780C22semidirect
20. #16840779C22semidirect
21. #16840765C22semidirect
27. C2×#14519844C22semidirect
34. #16840726C22semidirect
330. C2×C61#2925semidirect
378. C61C2×#2925semidirect
641. C2#21462517direct (N × H)

Maximal subgroups

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

subgroupindex
#214625172
C2×#168407872
C2×#168407862
C2×#168407852
C2×#168407822
C2×#168407802
C2×#168407792
C2×#168407652
C22×#145198442
C2×#168407352
C2×#168407262
C2×C4×#117582242
C2×#292561