Finite Group Databasebeta

← C2×#21462328 #30624662

Subgroups — C2×#21462328 #30624662

Order 15616.

3094 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462328C2116yesmaximal, direct product factor
2C2×#16840713C212yesmaximal, complemented
3C2×#16840711C214yesmaximal, complemented
4C2×#16840704C211yesmaximal, characteristic
5C2×#16840704C212yesmaximal
6C2×C4⋊C4×#6923C212yesmaximal, complemented
7C2×C4×C22⋊#6923C211yesmaximal, characteristic
8C2×C4×C22⋊#6923C212yesmaximal
9C22×C4⋊C4×D61C211yesmaximal, characteristic
10C22×C4⋊#6923C2212yes—
11C22×C4⋊#6923C2214yes—
12C22×C22⋊#6923C2211yescharacteristic
13C22×C22⋊#6923C2212yes—
14C22×C22⋊#6923C2211yescharacteristic
15C22×C4×#6923C2212yes—
16C22×C4×#6923C2214yes—
17#16840713C22116yescomplemented
18#16840711C22132yescomplemented
19#16840704C2218yes—
20#16840704C22116yes—
21C4⋊C4×#6923C22116yescomplemented
22C4×C22⋊#6923C2218yes—
23C4×C22⋊#6923C22116yes—
24C2×(C2×#6923)⋊C4C2214yes—
25C2×(C2×#6923)⋊C4C2212yes—
26C2×(C2×#6923)⋊C4C2214yes—
27C2×(C2×#6923)⋊C4C2212yes—
28C23×C4×D61C2211yescharacteristic
29C23×C4×D61C2212yes—
30C22×C4⋊Dic61C411yescharacteristic, complemented
31C22×#11758196C412yescomplemented
32C2×C4⋊C4×D61C411yescharacteristic, complemented
33C2×C4⋊C4×D61C411yescharacteristic, complemented
34C2×C4⋊C4×D61C412yescomplemented
35C2×C4⋊C4×D61C418yescomplemented
36C2×C4⋊C4×D61C2211yescharacteristic
37C2×C4⋊C4×D61C2211yescharacteristic
38C2×C4⋊C4×D61C2212yes—
39C2×C4⋊C4×D61C2218yes—
40C22×C4⋊C4×C61C411yescharacteristic, complemented
41C23×#6923C2312yes—
42C23×#6923C2314yes—
43C23×#6923C2312yes—
44C2×C4⋊#6923—28no—
45C2×C4⋊#6923—48no—
46C2×C4⋊#6923C2318yes—
47C2×C4⋊#6923C23116yes—
48C2×C22⋊#6923—24no—
49C2×C22⋊#6923—28no—
50C2×C22⋊#6923Q818yes—
51C2×C22⋊#6923C2314yes—
52C2×C22⋊#6923C2318yes—
53C2×C22⋊#6923C2314yes—
54C2×C4×#6923—28no—
55C2×C4×#6923—48no—
56C2×C4×#6923C2318yes—
57C2×C4×#6923C23116yes—
58(C2×#6923)⋊C4C2318yes—
59(C2×#6923)⋊C4C23116yes—
60(C2×#6923)⋊C4C2318yes—
61(C2×#6923)⋊C4C23116yes—
62C24×D61C2311yescharacteristic
63C23×Dic61C2×C411yescharacteristic
64C23×Dic61C2×C412yes—
65C22×C4×D61—28no—
66C22×C4×D61—48no—
67C22×C4×D61C2×C411yescharacteristic
68C22×C4×D61C2×C411yescharacteristic
69C22×C4×D61C2×C414yes—
70C22×C4×D61C2×C418yes—
71C22×C4×D61C2×C412yes—
72C22×C4×D61C2×C412yes—
73C22×C4×D61C2314yes—
74C22×C4×D61C2312yes—
75C22×C4×D61C2312yes—
76C22×C4×D61C2311yescharacteristic
77C22×C4×D61C2318yes—
78C22×C4×D61C2311yescharacteristic
79C2×C4⋊Dic61C2×C412yes—
80C2×C4⋊Dic61C2×C411yescharacteristic
81C2×C4⋊Dic61C2×C411yescharacteristic
82C2×C4⋊Dic61C2×C418yescomplemented
83C2×#11758196C2×C412yes—
84C2×#11758196C2×C412yes—
85C2×#11758196C2×C412yes—
86C2×#11758196C2×C412yes—
87C2×#11758196C2×C4116yescomplemented
88C4⋊C4×D61C2×C418yes—
89C4⋊C4×D61C2×C414yes—
90C4⋊C4×D61C2×C414yes—
91C4⋊C4×D61C2×C418yescomplemented
92C4⋊C4×D61C2×C418yescomplemented
93C4⋊C4×D61C2×C4116yescomplemented
94C4⋊C4×D61C2318yes—
95C4⋊C4×D61C2314yes—
96C4⋊C4×D61C2314yes—
97C23×C4×C61C2×C411yescharacteristic
98C23×C4×C61C2×C412yes—
99C2×C4⋊C4×C61C2×C412yes—
100C2×C4⋊C4×C61C2×C411yescharacteristic
101C2×C4⋊C4×C61C2×C411yescharacteristic
102C2×C4⋊C4×C61C2×C418yescomplemented
103C24×C61C22×C411yescharacteristic
104C23×D61—24no—
105C23×D61—24no—
106C23×D61C22×C411yescharacteristic
107C23×D61C22×C412yes—
108C23×D61C2×Q814yes—
109C23×D61#4114yes—
110C23×D61C2412yes—
111C23×D61C2411yescharacteristic
112C22×#6923—24no—
113C22×#6923—24no—
114C22×#6923—24no—
115C22×#6923—24no—
116C22×#6923—28no—
117C22×#6923—28no—
118C22×#6923—28no—
119C22×#6923—24no—
120C22×#6923C2×Q818yes—
121C22×#6923C2414yes—
122C22×#6923C2418yes—
123C22×#6923C2414yes—
124C22×C4×C61—24no—
125C22×C4×C61—44no—
126C22×C4×C61C22×C412yes—
127C22×C4×C61C22×C412yes—
128C22×C4×C61C22×C411yescharacteristic
129C22×C4×C61C22×C414yes—
130C22×C4×C61C22×C418yes—
131C22×C4×C61C22×C411yescharacteristic
132C22×Dic61—24no—
133C22×Dic61—44no—
134C22×Dic61C22×C411yescharacteristic
135C22×Dic61C22×C412yes—
136C22×Dic61C22×C412yes—
137C22×Dic61C22×C414yes—
138C22×Dic61C22×C418yes—
139C22×Dic61C22×C411yescharacteristic
140C2×C4×D61—24no—
141C2×C4×D61—28no—
142C2×C4×D61—28no—
143C2×C4×D61—24no—
144C2×C4×D61—24no—
145C2×C4×D61—216no—
146C2×C4×D61—216no—
147C2×C4×D61—416no—
148C2×C4×D61—416no—
149C2×C4×D61—44no—
150C2×C4×D61—44no—
151C2×C4×D61C22×C412yes—
152C2×C4×D61C22×C414yes—
153C2×C4×D61C22×C414yes—
154C2×C4×D61C22×C414yes—
155C2×C4×D61C22×C414yes—
156C2×C4×D61C22×C418yes—
157C2×C4×D61C22×C418yes—
158C2×C4×D61C22×C412yes—
159C2×C4×D61#4118yes—
160C2×C4×D61C2412yes—
161C2×C4×D61C2414yes—
162C2×C4×D61C2414yes—
163C2×C4×D61C2412yes—
164C22⋊#6923—28no—
165C22⋊#6923—216no—
166C22⋊#6923C2×Q8116yes—
167C4⋊#6923—216no—
168C4⋊#6923—416no—
169C4×#6923—216no—
170C4×#6923—416no—
171C4⋊C4×C61C22×C418yes—
172C4⋊C4×C61C22×C414yes—
173C4⋊C4×C61C22×C414yes—
174C4⋊Dic61C22×C418yes—
175C4⋊Dic61C22×C414yes—
176C4⋊Dic61C22×C414yes—
177#11758196C22×C418yes—
178#11758196C22×C418yes—
179#11758196C22×C418yes—
180#11758196C22×C418yes—
181C23×C61—22no—
182C23×C61—22no—
183C23×C61C4×Q814yes—
184C23×C61C23×C412yes—
185C23×C61C23×C411yescharacteristic
186C22×D61—22no—
187C22×D61—22no—
188C22×D61—24no—
189C22×D61—24no—
190C22×D61—216no—
191C22×D61—216no—
192C22×D61—24no—
193C22×D61—24no—
194C22×D61C4×Q814yes—
195C22×D61C4×Q818yes—
196C22×D61C23×C412yes—
197C22×D61C23×C411yescharacteristic
198C22×D61C22×Q814yes—
199C22×D61C22×Q812yes—
200C22×D61C2×#4114yes—
201C22×D61C2×#4114yes—
202C22×D61C2×#4112yes—
203C22×D61H(5,𝔽2)14yes—
204C22×D61C2511yescharacteristic
205C2×#6923—216no—
206C2×#6923—24no—
207C2×#6923—24no—
208C2×#6923—24no—
209C2×#6923—28no—
210C2×#6923—24no—
211C2×#6923—28no—
212C2×#6923—28no—
213C2×#6923—24no—
214C2×#6923—48no—
215C2×#6923—416no—
216C2×#6923C22×Q818yes—
217C2×C4×C61—22no—
218C2×C4×C61—24no—
219C2×C4×C61—24no—
220C2×C4×C61—28no—
221C2×C4×C61—48no—
222C2×C4×C61#11714yes—
223C2×C4×C61C23×C414yes—
224C2×C4×C61C23×C414yes—
225C2×C4×C61C23×C412yes—
226C2×C4×C61C23×C412yes—
227C2×Dic61—22no—
228C2×Dic61—24no—
229C2×Dic61—24no—
230C2×Dic61—28no—
231C2×Dic61—48no—
232C2×Dic61#11714yes—
233C2×Dic61C23×C412yes—
234C2×Dic61C23×C414yes—
235C2×Dic61C23×C414yes—
236C2×Dic61C23×C412yes—
237C4×D61—24no—
238C4×D61—28no—
239C4×D61—28no—
240C4×D61—24no—
241C4×D61—28no—
242C4×D61—28no—
243C4×D61—28no—
244C4×D61—28no—
245C4×D61—48no—
246C4×D61—48no—
247C4×D61#11718yes—
248C4×D61C2×#4118yes—
249C2×#2345—611nomaximal, Sylow
250C22×C61—28no—
251C22×C61—22no—
252C22×C61—22no—
253C22×C61C2×#11712yes—
254C22×C61C2×C4×Q814yes—
255C22×C61C2×C4×Q812yes—
256C22×C61#51812yes—
257C22×C61C24×C411yescharacteristic
258C2×D61—28no—
259C2×D61—22no—
260C2×D61—22no—
261C2×D61—216no—
262C2×D61—28no—
263C2×D61—28no—
264C2×D61C2×#11712yes—
265C2×D61C2×C4×Q814yes—
266C2×D61C2×C4×Q812yes—
267C2×D61#51812yes—
268C2×D61#55318yes—
269C2×D61#55418yes—
270C2×D61C23×Q811yescharacteristic
271C2×D61C22×#4111yescharacteristic
272C2×D61C22×#4112yes—
273C2×D61C2×H(5,𝔽2)12yes—
274#6923—28no—
275#6923—44no—
276#6923—48no—
277C4×C61—22no—
278C4×C61—24no—
279C4×C61—24no—
280C4×C61C2×#11714yes—
281Dic61—22no—
282Dic61—24no—
283Dic61—24no—
284Dic61C2×#11714yes—
285C23×C4⋊C4—611no—
286#2345—6116no—
287C2×#389—612no—
288C2×#387—614no—
289C2×#380—611no—
290C2×#380—612no—
291C2×C4×C4⋊C4—612no—
292C2×C4×C22⋊C4—611no—
293C2×C4×C22⋊C4—612no—
294C2×C61—24no—
295C2×C61#234514yescomplemented
296C2×C61C22×#11711yescharacteristic
297C2×C61C22×C4×Q811yescharacteristic
298C2×C61C2×#51811yescharacteristic
299D61—24no—
300D61#234514yescomplemented
301D61C2×#55312yes—
302D61C2×#55412yes—
303C24×C4—611no—
304C24×C4—612no—
305C22×C4⋊C4—612no—
306C22×C4⋊C4—611no—
307C22×C4⋊C4—612no—
308C22×C4⋊C4—611no—
309C22×C4⋊C4—611no—
310C22×C4⋊C4—611no—
311C22×C4⋊C4—612no—
312C22×C4⋊C4—611no—
313C22×C4⋊C4—618no—
314C22×C4⋊C4—618no—
315C22×C4⋊C4—612no—
316C22×C4⋊C4—614no—
317C22×C4⋊C4#692311yescharacteristic, complemented
318C22×C22⋊C4—611no—
319C22×C22⋊C4—611no—
320C22×C22⋊C4—612no—
321C22×C42—612no—
322C22×C42—614no—
323#389—6116no—
324#387—6132no—
325#380—6116no—
326#380—618no—
327C4×C4⋊C4—6116no—
328C4×C22⋊C4—618no—
329C4×C22⋊C4—6116no—
330C2×#95—612no—
331C2×#95—614no—
332C2×#95—614no—
333C2×#95—612no—
334C61C2×#234511yescharacteristic, complemented, Sylow
335C25—611no—
336C23×C4—611no—
337C23×C4—612no—
338C23×C4—611no—
339C23×C4—612no—
340C23×C4—612no—
341C23×C4—611no—
342C23×C4—614no—
343C23×C4—611no—
344C23×C4—611no—
345C23×C4—612no—
346C23×C4—614no—
347C23×C4—612no—
348C23×C4—612no—
349C23×C4—618no—
350C23×C4—618no—
351C23×C4—612no—
352C23×C4—614no—
353C23×C4—1228no—
354C23×C4—2448no—
355C23×C4C2×#692311yescharacteristic
356C23×C4C2×#692312yes—
357C2×C4⋊C4—612no—
358C2×C4⋊C4—612no—
359C2×C4⋊C4—612no—
360C2×C4⋊C4—612no—
361C2×C4⋊C4—6116no—
362C2×C4⋊C4—612no—
363C2×C4⋊C4—611no—
364C2×C4⋊C4—611no—
365C2×C4⋊C4—618no—
366C2×C4⋊C4—614no—
367C2×C4⋊C4—618no—
368C2×C4⋊C4—614no—
369C2×C4⋊C4—614no—
370C2×C4⋊C4—614no—
371C2×C4⋊C4—618no—
372C2×C4⋊C4—6116no—
373C2×C4⋊C4—618no—
374C2×C4⋊C4—618no—
375C2×C4⋊C4—618no—
376C2×C4⋊C4—6116no—
377C2×C4⋊C4—1228no—
378C2×C4⋊C4—2448no—
379C2×C4⋊C4C2×#692312yes—
380C2×C4⋊C4C2×#692311yescharacteristic
381C2×C4⋊C4C2×#692311yescharacteristic
382C2×C4⋊C4C2×#692318yescomplemented
383C2×C22⋊C4—618no—
384C2×C22⋊C4—614no—
385C2×C22⋊C4—614no—
386C2×C22⋊C4—618no—
387C2×C22⋊C4—1224no—
388C2×C22⋊C4—1228no—
389C2×C42—618no—
390C2×C42—6116no—
391C2×C42—1228no—
392C2×C42—2448no—
393#95—618no—
394#95—6116no—
395#95—6116no—
396#95—618no—
397C24—611no—
398C24—614no—
399C24—614no—
400C24—612no—
401C24—612no—
402C24—611no—
403C24—1224no—
404C24—1224no—
405C24C22×#692311yescharacteristic
406C22×C4—24no—
407C22×C4—44no—
408C22×C4—611no—
409C22×C4—618no—
410C22×C4—612no—
411C22×C4—612no—
412C22×C4—614no—
413C22×C4—618no—
414C22×C4—614no—
415C22×C4—611no—
416C22×C4—612no—
417C22×C4—612no—
418C22×C4—618no—
419C22×C4—612no—
420C22×C4—614no—
421C22×C4—614no—
422C22×C4—614no—
423C22×C4—612no—
424C22×C4—614no—
425C22×C4—614no—
426C22×C4—614no—
427C22×C4—618no—
428C22×C4—618no—
429C22×C4—614no—
430C22×C4—618no—
431C22×C4—1224no—
432C22×C4—12216no—
433C22×C4—12216no—
434C22×C4—1228no—
435C22×C4—1228no—
436C22×C4—1224no—
437C22×C4—1224no—
438C22×C4—1224no—
439C22×C4—1224no—
440C22×C4—1224no—
441C22×C4—1224no—
442C22×C4—1228no—
443C22×C4—1224no—
444C22×C4—1228no—
445C22×C4—1228no—
446C22×C4—1224no—
447C22×C4—2444no—
448C22×C4—2444no—
449C22×C4—24416no—
450C22×C4—24416no—
451C22×C4—2444no—
452C22×C4C22×#692314yes—
453C22×C4C22×#692311yescharacteristic
454C22×C4C22×#692312yes—
455C22×C4C22×#692312yes—
456C22×C4C22×#692318yes—
457C22×C4C22×#692311yescharacteristic
458C4⋊C4—618no—
459C4⋊C4—618no—
460C4⋊C4—618no—
461C4⋊C4—618no—
462C4⋊C4—618no—
463C4⋊C4—614no—
464C4⋊C4—614no—
465C4⋊C4—12216no—
466C4⋊C4—24416no—
467C4⋊C4C22×#692318yes—
468C4⋊C4C22×#692314yes—
469C4⋊C4C22×#692314yes—
470C22⋊C4—6116no—
471C22⋊C4—1228no—
472C22⋊C4—12216no—
473C42—12216no—
474C42—24416no—
475C23—22no—
476C23—22no—
477C23—614no—
478C23—612no—
479C23—612no—
480C23—614no—
481C23—611no—
482C23—611no—
483C23—618no—
484C23—614no—
485C23—614no—
486C23—614no—
487C23—612no—
488C23—1224no—
489C23—1224no—
490C23—1224no—
491C23—1224no—
492C23—12216no—
493C23—12216no—
494C23—1222no—
495C23—1222no—
496C23Q8×#692314yes—
497C23C23×#692312yes—
498C23C23×#692311yescharacteristic
499C2×C4—22no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—28no—
503C2×C4—48no—
504C2×C4—614no—
505C2×C4—612no—
506C2×C4—618no—
507C2×C4—618no—
508C2×C4—618no—
509C2×C4—612no—
510C2×C4—614no—
511C2×C4—614no—
512C2×C4—1228no—
513C2×C4—1228no—
514C2×C4—1228no—
515C2×C4—1224no—
516C2×C4—1224no—
517C2×C4—1228no—
518C2×C4—1228no—
519C2×C4—1228no—
520C2×C4—1224no—
521C2×C4—1224no—
522C2×C4—12216no—
523C2×C4—1222no—
524C2×C4—1224no—
525C2×C4—1224no—
526C2×C4—1228no—
527C2×C4—1224no—
528C2×C4—1228no—
529C2×C4—1224no—
530C2×C4—1228no—
531C2×C4—1228no—
532C2×C4—1224no—
533C2×C4—2448no—
534C2×C4—2448no—
535C2×C4—2448no—
536C2×C4—2448no—
537C2×C4—24416no—
538C2×C4#1451985614yes—
539C2×C4C23×#692312yes—
540C2×C4C23×#692314yes—
541C2×C4C23×#692314yes—
542C2×C4C23×#692312yes—
543C22—22no—
544C22—22no—
545C22—28no—
546C22—612no—
547C22—612no—
548C22—611no—
549C22—611no—
550C22—612no—
551C22—612no—
552C22—612no—
553C22—618no—
554C22—618no—
555C22—614no—
556C22—1228no—
557C22—1228no—
558C22—12216no—
559C22—1222no—
560C22—1222no—
561C22—1228no—
562C22C2×#1451985612yes—
563C22C2×Q8×#692314yes—
564C22C2×Q8×#692312yes—
565C22#1684082912yes—
566C22C24×#692311yescharacteristic
567C4—22no—
568C4—24no—
569C4—24no—
570C4—614no—
571C4—1228no—
572C4—1222no—
573C4—1224no—
574C4—1224no—
575C4—2444no—
576C4—2448no—
577C4C2×#1451985614yes—
578C2—24no—
579C2—612no—
580C2—612no—
581C2—614no—
582C2—1224no—
583C2#2146232814yesdirect product factor
584C2C22×#1451985611yescharacteristic
585C2C22×Q8×#692311yescharacteristic
586C2C2×#1684082911yescharacteristic
subgroupG/H
centerC23C23×#6923
commutatorC22×C61C24×C4
FrattiniC22C24×#6923
FittingC22×C4⋊C4×C61C4
socleC23×C61C23×C4
prime radicalC24×D61C23
cosocleC22×D61C25
hypercenterC22×C4⋊C4#6923
hypocenterC61C2×#2345
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #21462328C2direct (N × H)
2. C2×#16840713C2semidirect
3. C2×#16840711C2semidirect
6. C2×C4⋊C4×#6923C2semidirect
17. #16840713C22semidirect
18. #16840711C22semidirect
21. C4⋊C4×#6923C22semidirect
30. C22×C4⋊Dic61C4semidirect
31. C22×#11758196C4semidirect
32. C2×C4⋊C4×D61C4semidirect
33. C2×C4⋊C4×D61C4semidirect
34. C2×C4⋊C4×D61C4semidirect
35. C2×C4⋊C4×D61C4semidirect
40. C22×C4⋊C4×C61C4semidirect
82. C2×C4⋊Dic61C2×C4semidirect
87. C2×#11758196C2×C4semidirect
91. C4⋊C4×D61C2×C4semidirect
92. C4⋊C4×D61C2×C4semidirect
93. C4⋊C4×D61C2×C4semidirect
102. C2×C4⋊C4×C61C2×C4semidirect
295. C2×C61#2345semidirect
300. D61#2345semidirect
317. C22×C4⋊C4#6923semidirect
334. C61C2×#2345semidirect
382. C2×C4⋊C4C2×#6923semidirect
583. C2#21462328direct (N × H)

Maximal subgroups

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

subgroupindex
#214623282
C2×#168407132
C2×#168407112
C2×#168407042
C2×C4⋊C4×#69232
C2×C4×C22⋊#69232
C22×C4⋊C4×D612
C2×#234561