Finite Group Databasebeta

← #29602243

Subgroups — #29602243

Order 15616.

2278 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D61C211yesmaximal, characteristic
2C2×#16839624C214yesmaximal
3C2×#16839619C211yesmaximal, characteristic
4C2×C4×#11758198C211yesmaximal, characteristic
5#21444085C214yesmaximal, complemented
6#21444049C211yesmaximal, characteristic, complemented
7#21444048C211yesmaximal, characteristic, complemented
8#21444048C211yesmaximal, characteristic, complemented
9C61×C4⋊#95C211yesmaximal, characteristic, complemented
10C23×C4×D61C2212yes—
11C23×C4×D61C2211yescharacteristic
12C22×C4⋊Dic61C2211yescharacteristic
13C22×C4⋊Dic61C2211yescharacteristic
14C22×#11758196C2212yes—
15C2×C4⋊C4×D61—24no—
16C2×C4⋊C4×D61—24no—
17C2×C4⋊C4×D61C418yescomplemented
18C22×#11758198C2212yes—
19C22×#11758198C2212yes—
20C22×C4×Dic61C2211yescharacteristic
21#16839624—216no—
22#16839619—24no—
23C4×#11758198—24no—
24C2×#14519684C2214yes—
25C2×#14519684C2214yes—
26C2×#14519684C2214yes—
27C2×#14519684C2212yes—
28C2×#14519684C2212yes—
29C22×C4⋊C4×C61C2211yescharacteristic
30C22×C4⋊C4×C61C2211yescharacteristic
31C22×C42×C61C2211yescharacteristic
32C2×#95×C61C2214yes—
33C24×D61C2311yescharacteristic
34C23×Dic61C2312yes—
35C23×Dic61C2312yes—
36C23×Dic61C2312yes—
37C23×Dic61C2311yescharacteristic
38C22×C4×D61—22no—
39C22×C4×D61—22no—
40C22×C4×D61—22no—
41C22×C4×D61—22no—
42C22×C4×D61—24no—
43C22×C4×D61—24no—
44C22×C4×D61—28no—
45C22×C4×D61—28no—
46C22×C4×D61C2×C418yes—
47C22×C4×D61C2×C414yes—
48C22×C4×D61D414yes—
49C22×C4×D61D414yes—
50C2×C4⋊Dic61—22no—
51C2×C4⋊Dic61—22no—
52C2×C4⋊Dic61—22no—
53C2×C4⋊Dic61—22no—
54C2×C4⋊Dic61—22no—
55C2×C4⋊Dic61C2×C414yes—
56C2×#11758196—24no—
57C2×#11758196—24no—
58C2×#11758196C2×C418yes—
59C4⋊C4×D61—232no—
60C2×#11758198—24no—
61C2×#11758198—24no—
62C2×#11758198—24no—
63C2×#11758198—28no—
64C2×#11758198D418yes—
65C2×C4×Dic61—22no—
66C2×C4×Dic61—22no—
67C2×C4×Dic61—22no—
68#14519684—28no—
69#14519684—24no—
70#14519684—24no—
71#14519684—28no—
72#14519684—28no—
73C23×C4×C61C2312yes—
74C23×C4×C61C2312yes—
75C23×C4×C61C2312yes—
76C23×C4×C61C2311yescharacteristic
77C2×C4⋊C4×C61—22no—
78C2×C4⋊C4×C61—22no—
79C2×C4⋊C4×C61—22no—
80C2×C4⋊C4×C61—22no—
81C2×C4⋊C4×C61—22no—
82C2×C4⋊C4×C61C2×C414yes—
83C2×C42×C61—22no—
84C2×C42×C61—22no—
85C2×C42×C61—22no—
86#95×C61—28no—
87C24×C61C2411yescharacteristic
88C23×D61—21no—
89C23×D61—21no—
90C23×D61—21no—
91C23×D61—21no—
92C23×D61—22no—
93C23×D61—22no—
94C23×D61C22×C412yes—
95C23×D61C2×D412yes—
96C23×D61C2×D412yes—
97C23×D61C2×D414yes—
98C23×D61#4114yes—
99C22×C4×C61—24no—
100C22×C4×C61—22no—
101C22×C4×C61—22no—
102C22×C4×C61—22no—
103C22×C4×C61—24no—
104C22×C4×C61—22no—
105C22×C4×C61—22no—
106C22×C4×C61—22no—
107C22×C4×C61—22no—
108C22×C4×C61—22no—
109C22×C4×C61—24no—
110C22×C4×C61—22no—
111C22×C4×C61—22no—
112C22×C4×C61—22no—
113C22×C4×C61—24no—
114C22×C4×C61C22×C414yes—
115C22×C4×C61C22×C412yes—
116C22×C4×C61C2×D414yes—
117C22×C4×C61C2×D412yes—
118C22×C4×C61C2×D412yes—
119C22×C4×C61#4112yes—
120C22×C4×C61#4112yes—
121C22×C4×C61#4112yes—
122C22×C4×C61#4112yes—
123C22×Dic61—21no—
124C22×Dic61—21no—
125C22×Dic61—21no—
126C22×Dic61—21no—
127C22×Dic61—24no—
128C22×Dic61—22no—
129C22×Dic61—22no—
130C22×Dic61—22no—
131C22×Dic61—24no—
132C22×Dic61—22no—
133C22×Dic61—22no—
134C22×Dic61—22no—
135C22×Dic61—22no—
136C22×Dic61—22no—
137C22×Dic61—24no—
138C22×Dic61—22no—
139C22×Dic61—22no—
140C22×Dic61—22no—
141C22×Dic61—24no—
142C22×Dic61C22×C414yes—
143C22×Dic61C22×C412yes—
144C22×Dic61C2×D414yes—
145C22×Dic61C2×D412yes—
146C22×Dic61C2×D412yes—
147C2×C4×D61—28no—
148C2×C4×D61—28no—
149C2×C4×D61—28no—
150C2×C4×D61—28no—
151C2×C4×D61—28no—
152C2×C4×D61—28no—
153C2×C4×D61—216no—
154C2×C4×D61—232no—
155C2×C4×D61—416no—
156C2×C4×D61—48no—
157C2×C4×D61—48no—
158C2×C4×D61C22⋊C4116yes—
159C4⋊C4×C61—28no—
160C4⋊C4×C61—44no—
161C42×C61—44no—
162#11758198—216no—
163#11758198—48no—
164C4⋊Dic61—28no—
165C4⋊Dic61—44no—
166#11758196—216no—
167C4×Dic61—44no—
168C23×C61C23×C411yescharacteristic
169C23×C61C22×D411yescharacteristic
170C23×C61C22×D411yescharacteristic
171C23×C61C22×D412yes—
172C23×C61C2×#4111yescharacteristic
173C23×C61C2×#4111yescharacteristic
174C23×C61C2×#4111yescharacteristic
175C23×C61C2×#4111yescharacteristic
176C23×C61C2×#4112yes—
177C23×C612−1+412yes—
178C23×C612−1+412yes—
179C22×D61—22no—
180C22×D61—22no—
181C22×D61—24no—
182C22×D61—22no—
183C22×D61—22no—
184C22×D61—22no—
185C22×D61—22no—
186C22×D61—24no—
187C22×D61—22no—
188C22×D61—22no—
189C22×D61—24no—
190C22×D61—24no—
191C22×D61—24no—
192C22×D61—24no—
193C22×D61—24no—
194C22×D61—24no—
195C22×D61—24no—
196C22×D61—24no—
197C22×D61C2×C22⋊C414yes—
198C22×D61C4×D418yes—
199C22×D61#12118yes—
200C22×D61#12414yes—
201C22×D61#12714yes—
202C2×C4×C61—24no—
203C2×C4×C61—28no—
204C2×C4×C61—24no—
205C2×C4×C61—24no—
206C2×C4×C61—24no—
207C2×C4×C61—44no—
208C2×C4×C61—42no—
209C2×C4×C61—42no—
210C2×C4×C61—42no—
211C2×C4×C61—42no—
212C2×C4×C61—42no—
213C2×C4×C61—42no—
214C2×C4×C61—42no—
215C2×C4×C61—42no—
216C2×C4×C61—42no—
217C2×C4×C61—44no—
218C2×C4×C61—44no—
219C2×C4×C61C2×C22⋊C414yes—
220C2×C4×C61#11714yes—
221C2×C4×C61#11714yes—
222C2×C4×C61#12314yes—
223C2×C4×C61#12314yes—
224C2×C4×C61#12314yes—
225C2×C4×C61#12314yes—
226C2×Dic61—22no—
227C2×Dic61—22no—
228C2×Dic61—22no—
229C2×Dic61—22no—
230C2×Dic61—22no—
231C2×Dic61—22no—
232C2×Dic61—24no—
233C2×Dic61—28no—
234C2×Dic61—24no—
235C2×Dic61—24no—
236C2×Dic61—24no—
237C2×Dic61—44no—
238C2×Dic61—42no—
239C2×Dic61—42no—
240C2×Dic61—42no—
241C2×Dic61—42no—
242C2×Dic61—42no—
243C2×Dic61—42no—
244C2×Dic61—42no—
245C2×Dic61—42no—
246C2×Dic61—42no—
247C2×Dic61—44no—
248C2×Dic61—44no—
249C2×Dic61C2×C22⋊C414yes—
250C4×D61—232no—
251C4×D61—432no—
252#13904—611nomaximal, Sylow
253C22×C61C22×C22⋊C411yescharacteristic
254C22×C61C2×#11711yescharacteristic
255C22×C61C2×#11711yescharacteristic
256C22×C61C2×C4×D412yes—
257C22×C61#51912yes—
258C22×C61C2×#12112yes—
259C22×C61C2×#12311yescharacteristic
260C22×C61C2×#12311yescharacteristic
261C22×C61C2×#12311yescharacteristic
262C22×C61C2×#12311yescharacteristic
263C22×C61C2×#12411yescharacteristic
264C22×C61C2×#12711yescharacteristic
265C22×C61#53611yescharacteristic
266C22×C61#53612yes—
267C22×C61#53611yescharacteristic
268C22×C61#54712yes—
269C22×C61#54712yes—
270C22×C61#54712yes—
271C22×C61#54712yes—
272C22×C61#55212yes—
273C22×C61#55212yes—
274C22×C61#55212yes—
275C22×C61#55212yes—
276C2×D61—24no—
277C2×D61—28no—
278C2×D61—28no—
279C2×D61—28no—
280C2×D61—28no—
281C2×D61—24no—
282C2×D61—24no—
283C2×D61—24no—
284C2×D61—24no—
285C2×D61—24no—
286C2×D61#39018yes—
287C4×C61—44no—
288C4×C61—44no—
289C4×C61—82no—
290C4×C61#38118yescomplemented
291Dic61—24no—
292Dic61—44no—
293Dic61—44no—
294Dic61—82no—
295C23×C4⋊C4—611no—
296C2×#381—614no—
297C2×#380—611no—
298C2×C4×C22⋊C4—611no—
299#1445—614no—
300C4⋊#95—611no—
301C4⋊#95—611no—
302C4⋊#95—611no—
303C4⋊#95D6111yescharacteristic, complemented
304C2×C61C2×#38111yescharacteristic
305C2×C61C2×#39011yescharacteristic
306C2×C61#231011yescharacteristic
307C2×C61#234412yes—
308C2×C61#234412yes—
309C2×C61#248612yes—
310C2×C61#248612yes—
311C2×C61#250111yescharacteristic
312C2×C61#250111yescharacteristic
313C2×C61#250311yescharacteristic
314C2×C61#250311yescharacteristic
315D61—28no—
316C24×C4—611no—
317C24×C4—612no—
318C22×C4⋊C4—612no—
319C22×C4⋊C4—611no—
320C22×C4⋊C4—618no—
321C22×C4⋊C4—611no—
322C22×C4⋊C4—1224no—
323C22×C4⋊C4—1224no—
324C22×C4⋊C4C2×D6111yescharacteristic
325C22×C4⋊C4C2×D6111yescharacteristic
326C22×C22⋊C4—612no—
327C22×C22⋊C4—612no—
328C22×C42—611no—
329C22×C42C2×D6111yescharacteristic
330#381—12216no—
331#380—1224no—
332C4×C22⋊C4—1224no—
333C2×#95—614no—
334C2×#95—614no—
335C2×#95—614no—
336C2×#95—612no—
337C2×#95—612no—
338C2×#95C2×D6114yes—
339C61#1390411yescharacteristic, complemented, Sylow
340C25—611no—
341C23×C4—611no—
342C23×C4—614no—
343C23×C4—614no—
344C23×C4—614no—
345C23×C4—612no—
346C23×C4—612no—
347C23×C4—618no—
348C23×C4—612no—
349C23×C4—1224no—
350C23×C4—1224no—
351C23×C4—1228no—
352C23×C4—1228no—
353C23×C4—1222no—
354C23×C4—1222no—
355C23×C4—1222no—
356C23×C4—1222no—
357C23×C4C22×D6112yes—
358C23×C4C22×D6112yes—
359C23×C4C22×D6112yes—
360C23×C4C22×D6111yescharacteristic
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—618no—
367C2×C4⋊C4—614no—
368C2×C4⋊C4—12232no—
369C2×C4⋊C4—1224no—
370C2×C4⋊C4—1224no—
371C2×C4⋊C4—1222no—
372C2×C4⋊C4—1222no—
373C2×C4⋊C4—1222no—
374C2×C4⋊C4—1222no—
375C2×C4⋊C4—1222no—
376C2×C4⋊C4C4×D6114yes—
377C2×C22⋊C4—618no—
378C2×C22⋊C4—1224no—
379C2×C22⋊C4—1224no—
380C2×C22⋊C4—1224no—
381C2×C22⋊C4—1228no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—1222no—
386C2×C42—1222no—
387C2×C42—1222no—
388#95—28no—
389#95—1224no—
390#95—1224no—
391#95—1228no—
392#95—1228no—
393#95—1228no—
394C24—612no—
395C24—614no—
396C24—612no—
397C24—612no—
398C24—614no—
399C24—1221no—
400C24—1221no—
401C24—1221no—
402C24—1221no—
403C24—1222no—
404C24—1222no—
405C24C23×D6111yescharacteristic
406C22×C4—24no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—24no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—24no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—24no—
421C22×C4—612no—
422C22×C4—612no—
423C22×C4—612no—
424C22×C4—6116no—
425C22×C4—614no—
426C22×C4—614no—
427C22×C4—12216no—
428C22×C4—12232no—
429C22×C4—1221no—
430C22×C4—1221no—
431C22×C4—1221no—
432C22×C4—1221no—
433C22×C4—1228no—
434C22×C4—1228no—
435C22×C4—1228no—
436C22×C4—1228no—
437C22×C4—1228no—
438C22×C4—1228no—
439C22×C4—1224no—
440C22×C4—1222no—
441C22×C4—1222no—
442C22×C4—1222no—
443C22×C4—1222no—
444C22×C4—1224no—
445C22×C4—1222no—
446C22×C4—1222no—
447C22×C4—1222no—
448C22×C4—1222no—
449C22×C4—1224no—
450C22×C4—1222no—
451C22×C4—1222no—
452C22×C4—1222no—
453C22×C4—1224no—
454C22×C4—24416no—
455C22×C4—2448no—
456C22×C4—2448no—
457C22×C4C2×C4×D6114yes—
458C22×C4C2×C4×D6112yes—
459C22×C4#1175822212yes—
460C22×C4#1175822212yes—
461C22×C4D4×D6114yes—
462C22×C4D4×D6112yes—
463C22×C4D4×D6112yes—
464C22×C4#1175822412yes—
465C22×C4#1175822612yes—
466C4⋊C4—28no—
467C4⋊C4—44no—
468C4⋊C4—12216no—
469C4⋊C4—1228no—
470C4⋊C4—2444no—
471C22⋊C4—12216no—
472C22⋊C4—2448no—
473C42—44no—
474C42—2444no—
475C23—614no—
476C23—618no—
477C23—618no—
478C23—614no—
479C23—614no—
480C23—1224no—
481C23—1224no—
482C23—1224no—
483C23—1222no—
484C23—1222no—
485C23—1224no—
486C23—1222no—
487C23—1222no—
488C23—1222no—
489C23—1222no—
490C23—1222no—
491C23—1224no—
492C23—1222no—
493C23—1224no—
494C23—1224no—
495C23—1224no—
496C23—1224no—
497C23—1224no—
498C23C22×C4×D6111yescharacteristic
499C23C2×D4×D6111yescharacteristic
500C23C2×D4×D6111yescharacteristic
501C23C2×D4×D6112yes—
502C23#41×D6112yes—
503C23C2×#1175822411yescharacteristic
504C23C2×#1175822211yescharacteristic
505C23C2×#1175822211yescharacteristic
506C23C2×#1175822611yescharacteristic
507C23#1451982412yes—
508C23#1451982512yes—
509C2×C4—24no—
510C2×C4—28no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—42no—
515C2×C4—44no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—44no—
525C2×C4—44no—
526C2×C4—614no—
527C2×C4—1222no—
528C2×C4—1222no—
529C2×C4—1222no—
530C2×C4—1222no—
531C2×C4—1222no—
532C2×C4—1222no—
533C2×C4—12232no—
534C2×C4—1224no—
535C2×C4—1228no—
536C2×C4—1224no—
537C2×C4—1224no—
538C2×C4—1224no—
539C2×C4—24432no—
540C2×C4—2442no—
541C2×C4—2442no—
542C2×C4—2442no—
543C2×C4—2444no—
544C2×C4—2444no—
545C2×C4—2442no—
546C2×C4—2442no—
547C2×C4—2444no—
548C2×C4—2442no—
549C2×C4—2442no—
550C2×C4—2442no—
551C2×C4—2442no—
552C2×C4C22⋊C4×D6114yes—
553C2×C4#1451973414yes—
554C2×C4#1451973514yes—
555C2×C4#1451975914yes—
556C2×C4#1451975914yes—
557C2×C4#1451976214yes—
558C2×C4#1451976214yes—
559C22—618no—
560C22—1224no—
561C22—1224no—
562C22—1224no—
563C22—1224no—
564C22—1224no—
565C22—1228no—
566C22—1228no—
567C22—1224no—
568C22—1228no—
569C22—1228no—
570C22C2×C22⋊C4×D6111yescharacteristic
571C22C2×#1451973411yescharacteristic
572C22C2×#1451973511yescharacteristic
573C22C4×D4×D6112yes—
574C22#1684023812yes—
575C22#121×D6112yes—
576C22C2×#1451975911yescharacteristic
577C22C2×#1451975911yescharacteristic
578C22C2×#1451976211yescharacteristic
579C22C2×#1451976211yescharacteristic
580C22#124×D6111yescharacteristic
581C22#127×D6111yescharacteristic
582C22#1684033211yescharacteristic
583C22#1684033512yes—
584C22#1684033711yescharacteristic
585C22#1684041212yes—
586C22#1684041312yes—
587C22#1684041512yes—
588C22#1684041712yes—
589C22#1684044612yes—
590C22#1684045012yes—
591C22#1684045112yes—
592C22#1684045312yes—
593C4—44no—
594C4—44no—
595C4—82no—
596C4—1224no—
597C4—4882no—
598C4—2444no—
599C4—2444no—
600C4#1683962418yescomplemented
601C2—1228no—
602C2C2×#1683962411yescharacteristic
603C2#390×D6111yescharacteristic
604C2#2144840211yescharacteristic
605C2#2144868412yes—
606C2#2144868712yes—
607C2#2145012312yes—
608C2#2145012512yes—
609C2#2145028711yescharacteristic
610C2#2145028911yescharacteristic
611C2#2145030111yescharacteristic
612C2#2145030311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×C4⋊#95C2
socle, cosocleC24×C61C24
prime radicalC24×D61C23
hypercenterC4⋊#95D61
hypocenterC61#13904
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
5. #21444085C2semidirect
6. #21444049C2semidirect
7. #21444048C2semidirect
8. #21444048C2semidirect
9. C61×C4⋊#95C2semidirect
17. C2×C4⋊C4×D61C4semidirect
290. C4×C61#381semidirect
303. C4⋊#95D61semidirect
339. C61#13904semidirect
600. C4#16839624semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D612
C2×#168396242
C2×#168396192
C2×C4×#117581982
#214440852
#214440492
#214440482
C61×C4⋊#952
#1390461