Finite Group Databasebeta

← #30602780

Subgroups — #30602780

Order 15616.

1338 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840704C211yesmaximal, characteristic
2C2×C4×C22⋊#6923C211yesmaximal, characteristic
3C2×#16840639C214yesmaximal
4#380×D61C211yesmaximal, characteristic
5C22×C4⋊#6923C412yescomplemented
6C22×C22⋊#6923C2212yes—
7C22×C22⋊#6923C2212yes—
8C22×C4×#6923—21no—
9#16840704—21no—
10#16840704—21no—
11#16840704—21no—
12#16840704—21no—
13C4×C22⋊#6923—21no—
14C4×C22⋊#6923—21no—
15C4×C22⋊#6923C412yescomplemented
16C4×C22⋊#6923C412yescomplemented
17C2×(C2×#6923)⋊C4—21no—
18C2×(C2×#6923)⋊C4C412yescomplemented
19#16840639—28no—
20C23×C4×D61C2211yescharacteristic
21C2×C4⋊C4×D61—21no—
22C2×C22⋊C4×D61C2212yes—
23#16839622C411yescharacteristic, complemented
24#16839621—21no—
25#16839620C412yescomplemented
26#16839619—21no—
27#95×D61—21no—
28C61×#380C411yescharacteristic, complemented
29C23×#6923—22no—
30C23×#6923C2×C414yes—
31C2×C4⋊#6923—22no—
32C2×C4⋊#6923—22no—
33C2×C4⋊#6923—44no—
34C2×C22⋊#6923—22no—
35C2×C22⋊#6923—22no—
36C2×C22⋊#6923—22no—
37C2×C22⋊#6923—22no—
38C2×C22⋊#6923—22no—
39C2×C22⋊#6923—24no—
40C2×C22⋊#6923—24no—
41C2×C22⋊#6923C2×C414yes—
42C2×C22⋊#6923D414yes—
43C2×C22⋊#6923Q814yes—
44C2×C4×#6923—22no—
45C2×C4×#6923—22no—
46C2×C4×#6923—44no—
47(C2×#6923)⋊C4—22no—
48(C2×#6923)⋊C4—22no—
49(C2×#6923)⋊C4—22no—
50(C2×#6923)⋊C4—22no—
51C24×D61C2311yescharacteristic
52C23×Dic61C2×C411yescharacteristic
53C22×C4×D61—22no—
54C22×C4×D61—44no—
55C22×C4×D61C2×C411yescharacteristic
56C22×C4×D61C2×C411yescharacteristic
57C22×C4×D61C2×C411yescharacteristic
58C22×C4×D61C2×C411yescharacteristic
59C22×C4×D61D411yescharacteristic
60C22×C4×D61D411yescharacteristic
61C22×C4×D61D411yescharacteristic
62C22×C4×D61D411yescharacteristic
63C22×C4×D61D411yescharacteristic
64C22×C4×D61D411yescharacteristic
65C22×C4×D61Q811yescharacteristic
66C22×C4×D61Q811yescharacteristic
67C2×C4⋊Dic61—21no—
68C2×#11758196—22no—
69C4⋊C4×D61—44no—
70C2×C22⋊Dic61C2×C412yes—
71C2×#11758198—22no—
72C22⋊C4×D61—24no—
73C22⋊C4×D61—24no—
74#14519684—21no—
75#14519684—22no—
76C23×C4×C61C2×C411yescharacteristic
77C2×C4⋊C4×C61—21no—
78C2×C22⋊C4×C61C2×C412yes—
79#95×C61—21no—
80C24×C61C22×C411yescharacteristic
81C23×D61—42no—
82C23×D61—42no—
83C23×D61C22×C411yescharacteristic
84C23×D61C22×C411yescharacteristic
85C23×D61C2×D411yescharacteristic
86C23×D61C2×D411yescharacteristic
87C23×D61C2×D411yescharacteristic
88C23×D61C2×D412yes—
89C23×D61C2×Q811yescharacteristic
90C23×D61C2×Q812yes—
91C23×D61#4112yes—
92C23×D61#4112yes—
93C22×#6923—24no—
94C22×#6923—24no—
95C22×#6923—24no—
96C22×#6923—24no—
97C22×#6923—28no—
98C22×#6923—44no—
99C22×#6923—44no—
100C22×#6923—44no—
101C22×#6923—44no—
102C22×C4×C61—22no—
103C22×C4×C61—42no—
104C22×C4×C61C4211yescharacteristic
105C22×C4×C61C4211yescharacteristic
106C22×C4×C61C22⋊C411yescharacteristic
107C22×C4×C61C22⋊C411yescharacteristic
108C22×C4×C61C4⋊C411yescharacteristic
109C22×C4×C61C4⋊C411yescharacteristic
110C22×Dic61—22no—
111C22×Dic61—42no—
112C22×Dic61C4211yescharacteristic
113C22×Dic61C4211yescharacteristic
114C22×Dic61C22⋊C411yescharacteristic
115C22×Dic61C22⋊C411yescharacteristic
116C22×Dic61C4⋊C411yescharacteristic
117C22×Dic61C4⋊C411yescharacteristic
118C2×C4×D61—24no—
119C2×C4×D61—24no—
120C2×C4×D61—24no—
121C2×C4×D61—42no—
122C2×C4×D61—42no—
123C2×C4×D61—42no—
124C2×C4×D61—42no—
125C2×C4×D61—42no—
126C2×C4×D61—42no—
127C2×C4×D61—42no—
128C2×C4×D61—42no—
129C2×C4×D61—42no—
130C2×C4×D61—44no—
131C2×C4×D61—44no—
132C2×C4×D61—42no—
133C2×C4×D61—42no—
134C2×C4×D61C22⋊C411yescharacteristic
135C2×C4×D61C22⋊C411yescharacteristic
136C2×C4×D61C22⋊C411yescharacteristic
137C2×C4×D61C22⋊C411yescharacteristic
138C2×C4×D61C22⋊C411yescharacteristic
139C2×C4×D61C22⋊C411yescharacteristic
140C2×C4×D61C22⋊C411yescharacteristic
141C2×C4×D61C22⋊C411yescharacteristic
142C2×C4×D61C4⋊C411yescharacteristic
143C2×C4×D61C4⋊C411yescharacteristic
144C2×C4×D61C4⋊C411yescharacteristic
145C2×C4×D61C4⋊C411yescharacteristic
146C2×C4×D61C4⋊C411yescharacteristic
147C2×C4×D61C4⋊C411yescharacteristic
148C2×C4×D61C4⋊C411yescharacteristic
149C2×C4×D61C4⋊C411yescharacteristic
150C22⋊#6923—24no—
151C22⋊#6923—24no—
152C22⋊#6923—24no—
153C22⋊#6923—44no—
154C22⋊#6923—42no—
155C22⋊#6923—42no—
156C22⋊#6923C4⋊C418yescomplemented
157C4⋊#6923—44no—
158C4⋊#6923—44no—
159C4×#6923—44no—
160C4×#6923—44no—
161C4⋊C4×C61—42no—
162C22⋊C4×C61—24no—
163C22⋊Dic61—24no—
164#11758198—44no—
165C4⋊Dic61—42no—
166#11758196—44no—
167C23×C61—41no—
168C23×C61—41no—
169C23×C61C2×C4211yescharacteristic
170C23×C61C2×C22⋊C411yescharacteristic
171C23×C61C2×C4⋊C411yescharacteristic
172C23×C61C4×D412yes—
173C23×C61C4×Q812yes—
174C22×D61—22no—
175C22×D61—22no—
176C22×D61—22no—
177C22×D61—22no—
178C22×D61—22no—
179C22×D61—22no—
180C22×D61—44no—
181C22×D61—44no—
182C22×D61—44no—
183C22×D61—44no—
184C22×D61—41no—
185C22×D61—41no—
186C22×D61—41no—
187C22×D61—41no—
188C22×D61—41no—
189C22×D61—41no—
190C22×D61C2×C22⋊C411yescharacteristic
191C22×D61C2×C22⋊C411yescharacteristic
192C22×D61C2×C4⋊C411yescharacteristic
193C22×D61C2×C4⋊C411yescharacteristic
194C22×D61C2×C4⋊C412yes—
195C22×D61#11712yes—
196C22×D61C4×D412yes—
197C22×D61C4×Q812yes—
198C22×D61#12112yes—
199C22×D61#12112yes—
200C22×D61C22⋊Q812yes—
201C22×D61C22⋊Q812yes—
202C22×D61#12411yescharacteristic
203C22×D61#12411yescharacteristic
204C22×D61#12512yes—
205C22×D61#12711yescharacteristic
206C22×D61C4⋊Q811yescharacteristic
207C22×D61C4⋊Q812yes—
208C2×#6923—28no—
209C2×#6923—44no—
210C2×#6923—44no—
211C2×#6923—48no—
212C2×#6923—48no—
213C2×#6923—44no—
214C2×#6923—44no—
215C2×#6923—44no—
216C2×#6923—88no—
217C2×C4×C61—22no—
218C2×C4×C61—22no—
219C2×C4×C61—22no—
220C2×C4×C61—41no—
221C2×C4×C61—41no—
222C2×C4×C61—41no—
223C2×C4×C61—42no—
224C2×C4×C61—42no—
225C2×C4×C61—42no—
226C2×C4×C61#9511yescharacteristic
227C2×C4×C61#9511yescharacteristic
228C2×C4×C61#9511yescharacteristic
229C2×C4×C61#9511yescharacteristic
230C2×Dic61—22no—
231C2×Dic61—22no—
232C2×Dic61—22no—
233C2×Dic61—41no—
234C2×Dic61—41no—
235C2×Dic61—41no—
236C2×Dic61—42no—
237C2×Dic61—42no—
238C2×Dic61—42no—
239C2×Dic61#9511yescharacteristic
240C2×Dic61#9511yescharacteristic
241C2×Dic61#9511yescharacteristic
242C2×Dic61#9511yescharacteristic
243C4×D61—22no—
244C4×D61—22no—
245C4×D61—22no—
246C4×D61—22no—
247C4×D61—22no—
248C4×D61—22no—
249C4×D61—22no—
250C4×D61—22no—
251C4×D61—22no—
252C4×D61—41no—
253C4×D61—41no—
254C4×D61—41no—
255C4×D61—41no—
256C4×D61—41no—
257C4×D61—41no—
258C4×D61—84no—
259C4×D61—84no—
260C4×D61#9914yes—
261#10854—611nomaximal, Sylow
262C22×C61—21no—
263C22×C61—21no—
264C22×C61—21no—
265C22×C61—21no—
266C22×C61—21no—
267C22×C61—21no—
268C22×C61—42no—
269C22×C61—42no—
270C22×C61C2×#9511yescharacteristic
271C22×C61C4×C4⋊C412yes—
272C22×C61#38912yes—
273C22×C61#39011yescharacteristic
274C22×C61#39111yescharacteristic
275C2×D61—21no—
276C2×D61—21no—
277C2×D61—21no—
278C2×D61—21no—
279C2×D61—21no—
280C2×D61—21no—
281C2×D61—22no—
282C2×D61—24no—
283C2×D61—24no—
284C2×D61—22no—
285C2×D61—22no—
286C2×D61—24no—
287C2×D61—24no—
288C2×D61—22no—
289C2×D61—42no—
290C2×D61—42no—
291C2×D61—42no—
292C2×D61—42no—
293C2×D61—42no—
294C2×D61—42no—
295C2×D61#38012yes—
296C2×D61#38211yescharacteristic
297C2×D61#38411yescharacteristic
298C2×D61#38912yes—
299C2×D61#39011yescharacteristic
300C2×D61#39111yescharacteristic
301C2×D61C2×#9912yes—
302C2×D61#41012yes—
303#6923—48no—
304#6923—84no—
305C4×C61—21no—
306C4×C61—21no—
307C4×C61—21no—
308C4×C61—82no—
309C4×C61#34212yescomplemented
310Dic61—21no—
311Dic61—21no—
312Dic61—21no—
313Dic61—82no—
314Dic61#34212yescomplemented
315C2×#380—611no—
316C2×#380—611no—
317C2×C4×C22⋊C4—611no—
318C2×#342—614no—
319C2×C61—21no—
320C2×C61—22no—
321C2×C61—22no—
322C2×C61—21no—
323C2×C61C4⋊#9511yescharacteristic
324C2×C61C2×#34211yescharacteristic
325C2×C61#174011yescharacteristic
326D61—22no—
327D61—21no—
328D61—21no—
329D61—22no—
330D61#196412yes—
331D61#199612yes—
332C24×C4—611no—
333C22×C4⋊C4—612no—
334C22×C4⋊C4—1221no—
335C22×C22⋊C4—612no—
336C22×C22⋊C4—612no—
337C22×C22⋊C4—612no—
338C22×C42—1221no—
339#380—611no—
340#380—612no—
341#380—1221no—
342#380—1221no—
343#380—1221no—
344#380—1221no—
345#380—1221no—
346#380—1221no—
347#380#692311yescharacteristic, complemented
348C4×C22⋊C4—612no—
349C4×C22⋊C4—612no—
350C4×C22⋊C4—1221no—
351C4×C22⋊C4—1221no—
352C2×#95—612no—
353C2×#95—1221no—
354C2×#95—1221no—
355#342—1228no—
356C61#1085411yescharacteristic, complemented, Sylow
357C25—611no—
358C23×C4—611no—
359C23×C4—611no—
360C23×C4—611no—
361C23×C4—611no—
362C23×C4—611no—
363C23×C4—611no—
364C23×C4—611no—
365C23×C4—611no—
366C23×C4—611no—
367C23×C4—611no—
368C23×C4—611no—
369C23×C4—611no—
370C23×C4—611no—
371C23×C4—614no—
372C23×C4—1222no—
373C23×C4—1222no—
374C23×C4—2444no—
375C23×C4C2×#692311yescharacteristic
376C2×C4⋊C4—21no—
377C2×C4⋊C4—1222no—
378C2×C4⋊C4—1222no—
379C2×C4⋊C4—1222no—
380C2×C4⋊C4—1221no—
381C2×C4⋊C4—2444no—
382C2×C4⋊C4—2444no—
383C2×C22⋊C4—614no—
384C2×C22⋊C4—614no—
385C2×C22⋊C4—614no—
386C2×C22⋊C4—612no—
387C2×C22⋊C4—1224no—
388C2×C22⋊C4—1224no—
389C2×C22⋊C4—1222no—
390C2×C22⋊C4—1222no—
391C2×C22⋊C4—1222no—
392C2×C22⋊C4—1222no—
393C2×C22⋊C4—1224no—
394C2×C22⋊C4—1224no—
395C2×C22⋊C4—1222no—
396C2×C22⋊C4—1222no—
397C2×C22⋊C4C2×#692312yes—
398C2×C42—1222no—
399C2×C42—1222no—
400C2×C42—2444no—
401#95—21no—
402#95—1222no—
403#95—1222no—
404#95—1222no—
405#95—1222no—
406#95—1222no—
407#95—1221no—
408C24—611no—
409C24—611no—
410C24—611no—
411C24—611no—
412C24—611no—
413C24—611no—
414C24—612no—
415C24—612no—
416C24—612no—
417C24—612no—
418C24—2442no—
419C24—2442no—
420C24C22×#692311yescharacteristic
421C22×C4—22no—
422C22×C4—42no—
423C22×C4—611no—
424C22×C4—611no—
425C22×C4—611no—
426C22×C4—611no—
427C22×C4—611no—
428C22×C4—611no—
429C22×C4—611no—
430C22×C4—611no—
431C22×C4—611no—
432C22×C4—611no—
433C22×C4—611no—
434C22×C4—611no—
435C22×C4—611no—
436C22×C4—611no—
437C22×C4—611no—
438C22×C4—611no—
439C22×C4—611no—
440C22×C4—611no—
441C22×C4—611no—
442C22×C4—611no—
443C22×C4—611no—
444C22×C4—611no—
445C22×C4—1224no—
446C22×C4—1224no—
447C22×C4—1224no—
448C22×C4—1224no—
449C22×C4—1224no—
450C22×C4—1224no—
451C22×C4—1228no—
452C22×C4—1224no—
453C22×C4—1222no—
454C22×C4—2442no—
455C22×C4—2442no—
456C22×C4—2442no—
457C22×C4—2442no—
458C22×C4—2442no—
459C22×C4—2442no—
460C22×C4—2442no—
461C22×C4—2442no—
462C22×C4—2442no—
463C22×C4—2442no—
464C22×C4—2442no—
465C22×C4—2444no—
466C22×C4—2444no—
467C22×C4—2442no—
468C22×C4—2444no—
469C22×C4—2444no—
470C22×C4—2444no—
471C22×C4—2444no—
472C22×C4C4×#692311yescharacteristic
473C22×C4C4×#692311yescharacteristic
474C22×C4C4⋊#692311yescharacteristic
475C22×C4C4⋊#692311yescharacteristic
476C22×C4C22⋊#692311yescharacteristic
477C22×C4C22⋊#692311yescharacteristic
478C4⋊C4—42no—
479C4⋊C4—2442no—
480C4⋊C4—2444no—
481C4⋊C4—2444no—
482C4⋊C4—2444no—
483C22⋊C4—24no—
484C22⋊C4—618no—
485C22⋊C4—1224no—
486C22⋊C4—1224no—
487C22⋊C4—1224no—
488C22⋊C4—1224no—
489C22⋊C4—2444no—
490C22⋊C4—2444no—
491C22⋊C4—2442no—
492C22⋊C4—2442no—
493C42—2444no—
494C42—2444no—
495C23—41no—
496C23—41no—
497C23—611no—
498C23—612no—
499C23—612no—
500C23—611no—
501C23—611no—
502C23—611no—
503C23—611no—
504C23—611no—
505C23—611no—
506C23—611no—
507C23—612no—
508C23—612no—
509C23—612no—
510C23—612no—
511C23—612no—
512C23—612no—
513C23—612no—
514C23—612no—
515C23—1222no—
516C23—1222no—
517C23—1222no—
518C23—1222no—
519C23—1222no—
520C23—1222no—
521C23—2441no—
522C23—2441no—
523C23—2441no—
524C23—2441no—
525C23—2441no—
526C23—2441no—
527C23—2444no—
528C23—2444no—
529C23—2444no—
530C23—2444no—
531C23C2×C4×#692311yescharacteristic
532C23C2×C22⋊#692311yescharacteristic
533C23C2×C4⋊#692311yescharacteristic
534C23D4×#692312yes—
535C23Q8×#692312yes—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—611no—
546C2×C4—614no—
547C2×C4—611no—
548C2×C4—611no—
549C2×C4—611no—
550C2×C4—1222no—
551C2×C4—1222no—
552C2×C4—1222no—
553C2×C4—1222no—
554C2×C4—1222no—
555C2×C4—1222no—
556C2×C4—1222no—
557C2×C4—1222no—
558C2×C4—1222no—
559C2×C4—1222no—
560C2×C4—1222no—
561C2×C4—1222no—
562C2×C4—1228no—
563C2×C4—4884no—
564C2×C4—4884no—
565C2×C4—4888no—
566C2×C4—2441no—
567C2×C4—2441no—
568C2×C4—2441no—
569C2×C4—2441no—
570C2×C4—2441no—
571C2×C4—2441no—
572C2×C4—2441no—
573C2×C4—2441no—
574C2×C4—2441no—
575C2×C4—2442no—
576C2×C4—2442no—
577C2×C4—2444no—
578C2×C4—2444no—
579C2×C4—2444no—
580C2×C4—2442no—
581C2×C4—2444no—
582C2×C4—2448no—
583C2×C4—2448no—
584C2×C4—2444no—
585C2×C4(C2×#6923)⋊C411yescharacteristic
586C2×C4(C2×#6923)⋊C411yescharacteristic
587C2×C4(C2×#6923)⋊C411yescharacteristic
588C2×C4(C2×#6923)⋊C411yescharacteristic
589C22—21no—
590C22—21no—
591C22—21no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—42no—
596C22—42no—
597C22—611no—
598C22—611no—
599C22—612no—
600C22—612no—
601C22—612no—
602C22—611no—
603C22—611no—
604C22—612no—
605C22—1222no—
606C22—1222no—
607C22—1224no—
608C22—1224no—
609C22—1224no—
610C22—1222no—
611C22—1222no—
612C22—1224no—
613C22—1221no—
614C22—1221no—
615C22—1221no—
616C22—1221no—
617C22—1221no—
618C22—1221no—
619C22—2442no—
620C22—2442no—
621C22—2442no—
622C22—2442no—
623C22—2442no—
624C22—2442no—
625C22C2×(C2×#6923)⋊C411yescharacteristic
626C22C4⋊C4×#692312yes—
627C22#1684071312yes—
628C22#1684071411yescharacteristic
629C22(C2×#6923)⋊Q811yescharacteristic
630C4—21no—
631C4—21no—
632C4—21no—
633C4—82no—
634C4—612no—
635C4—1221no—
636C4—1221no—
637C4—1221no—
638C4—4882no—
639C4—4884no—
640C4—2448no—
641C4#1684063912yescomplemented
642C2—21no—
643C2—22no—
644C2—21no—
645C2—22no—
646C2—612no—
647C2—612no—
648C2—1222no—
649C2—1221no—
650C2—1221no—
651C2—1222no—
652C2#2146099611yescharacteristic
653C2C2×#1684063911yescharacteristic
654C2#2146151711yescharacteristic
subgroupG/H
centerC22C2×(C2×#6923)⋊C4
commutatorC23×C61C2×C42
FrattiniC24C22×#6923
FittingC61×#380C4
socleC22×C61C2×#95
prime radical, cosocleC24×D61C23
hypercenter#380#6923
hypocenterC61#10854
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
5. C22×C4⋊#6923C4semidirect
15. C4×C22⋊#6923C4semidirect
16. C4×C22⋊#6923C4semidirect
18. C2×(C2×#6923)⋊C4C4semidirect
23. #16839622C4semidirect
25. #16839620C4semidirect
28. C61×#380C4semidirect
156. C22⋊#6923C4⋊C4semidirect
309. C4×C61#342semidirect
314. Dic61#342semidirect
347. #380#6923semidirect
356. C61#10854semidirect
641. C4#16840639semidirect

Maximal subgroups

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

subgroupindex
C2×#168407042
C2×C4×C22⋊#69232
C2×#168406392
#380×D612
#1085461