Finite Group Databasebeta

← #30602752

Subgroups — #30602752

Order 15616.

1338 conjugacy classes of subgroups.

The subgroup lattice has 654 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⋊#6923—21no—
6C22×C22⋊#6923C2212yes—
7C22×C22⋊#6923C2212yes—
8C22×C4×#6923C412yescomplemented
9#16840704—21no—
10#16840704—21no—
11#16840704C412yescomplemented
12#16840704C412yescomplemented
13C4×C22⋊#6923—21no—
14C4×C22⋊#6923—21no—
15C4×C22⋊#6923—21no—
16C4×C22⋊#6923—21no—
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—24no—
39C2×C22⋊#6923—24no—
40C2×C22⋊#6923—22no—
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—44no—
97C22×#6923—44no—
98C22×#6923—44no—
99C22×#6923—44no—
100C22×#6923—44no—
101C22×#6923C4⋊C418yescomplemented
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—44no—
133C2×C4×D61C22⋊C411yescharacteristic
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×D61C4⋊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
149C22⋊#6923—24no—
150C22⋊#6923—24no—
151C22⋊#6923—24no—
152C22⋊#6923—24no—
153C22⋊#6923—28no—
154C22⋊#6923—42no—
155C22⋊#6923—42no—
156C4⋊#6923—44no—
157C4⋊#6923—44no—
158C4×#6923—44no—
159C4×#6923—44no—
160C4⋊C4×C61—42no—
161C22⋊C4×C61—24no—
162C22⋊Dic61—24no—
163#11758198—42no—
164#11758198—42no—
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⋊C412yes—
193C22×D61C2×C4⋊C411yescharacteristic
194C22×D61C2×C4⋊C411yescharacteristic
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⋊Q812yes—
207C22×D61C4⋊Q811yescharacteristic
208C2×#6923—28no—
209C2×#6923—48no—
210C2×#6923—44no—
211C2×#6923—44no—
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—88no—
259C4×D61#9914yes—
260#10846—611nomaximal, Sylow
261C22×C61—21no—
262C22×C61—21no—
263C22×C61—21no—
264C22×C61—21no—
265C22×C61—21no—
266C22×C61—21no—
267C22×C61—42no—
268C22×C61—42no—
269C22×C61C2×#9511yescharacteristic
270C22×C61C4×C4⋊C412yes—
271C22×C61#38912yes—
272C22×C61#39011yescharacteristic
273C22×C61#39111yescharacteristic
274C2×D61—21no—
275C2×D61—21no—
276C2×D61—21no—
277C2×D61—21no—
278C2×D61—21no—
279C2×D61—21no—
280C2×D61—24no—
281C2×D61—24no—
282C2×D61—24no—
283C2×D61—24no—
284C2×D61—24no—
285C2×D61—24no—
286C2×D61—42no—
287C2×D61—42no—
288C2×D61—41no—
289C2×D61—41no—
290C2×D61—42no—
291C2×D61—41no—
292C2×D61—42no—
293C2×D61—41no—
294C2×D61#38012yes—
295C2×D61#38211yescharacteristic
296C2×D61#38411yescharacteristic
297C2×D61#38912yes—
298C2×D61#39011yescharacteristic
299C2×D61#39111yescharacteristic
300C2×D61C2×#9912yes—
301C2×D61#41012yes—
302#6923—48no—
303#6923—84no—
304C4×C61—21no—
305C4×C61—21no—
306C4×C61—21no—
307C4×C61—82no—
308C4×C61#34212yescomplemented
309Dic61—21no—
310Dic61—21no—
311Dic61—21no—
312Dic61—82no—
313Dic61#34212yescomplemented
314C2×#380—611no—
315C2×#380—611no—
316C2×C4×C22⋊C4—611no—
317C2×#342—614no—
318C2×C61—21no—
319C2×C61—22no—
320C2×C61—22no—
321C2×C61—21no—
322C2×C61C4⋊#9511yescharacteristic
323C2×C61C2×#34211yescharacteristic
324C2×C61#174011yescharacteristic
325D61—21no—
326D61—21no—
327D61—21no—
328D61—22no—
329D61—21no—
330D61#179914yes—
331C24×C4—611no—
332C22×C4⋊C4—1221no—
333C22×C4⋊C4—1221no—
334C22×C22⋊C4—612no—
335C22×C22⋊C4—612no—
336C22×C22⋊C4—612no—
337C22×C42—612no—
338#380—612no—
339#380—612no—
340#380—611no—
341#380—612no—
342#380—1221no—
343#380—1221no—
344#380—1221no—
345#380—1221no—
346#380#692311yescharacteristic, complemented
347C4×C22⋊C4—1221no—
348C4×C22⋊C4—1221no—
349C4×C22⋊C4—1221no—
350C4×C22⋊C4—1221no—
351C2×#95—612no—
352C2×#95—1221no—
353C2×#95—1221no—
354#342—1228no—
355C61#1084611yescharacteristic, complemented, Sylow
356C25—611no—
357C23×C4—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—614no—
371C23×C4—1222no—
372C23×C4—1222no—
373C23×C4—2444no—
374C23×C4C2×#692311yescharacteristic
375C2×C4⋊C4—21no—
376C2×C4⋊C4—1222no—
377C2×C4⋊C4—1222no—
378C2×C4⋊C4—1222no—
379C2×C4⋊C4—1221no—
380C2×C4⋊C4—2444no—
381C2×C4⋊C4—2444no—
382C2×C22⋊C4—614no—
383C2×C22⋊C4—614no—
384C2×C22⋊C4—614no—
385C2×C22⋊C4—612no—
386C2×C22⋊C4—1224no—
387C2×C22⋊C4—1224no—
388C2×C22⋊C4—1222no—
389C2×C22⋊C4—1222no—
390C2×C22⋊C4—1222no—
391C2×C22⋊C4—1222no—
392C2×C22⋊C4—1224no—
393C2×C22⋊C4—1224no—
394C2×C22⋊C4—1222no—
395C2×C22⋊C4—1222no—
396C2×C22⋊C4C2×#692312yes—
397C2×C42—1222no—
398C2×C42—1222no—
399C2×C42—2444no—
400#95—21no—
401#95—1222no—
402#95—1222no—
403#95—1222no—
404#95—1222no—
405#95—1222no—
406#95—1221no—
407C24—611no—
408C24—611no—
409C24—611no—
410C24—611no—
411C24—611no—
412C24—611no—
413C24—612no—
414C24—612no—
415C24—612no—
416C24—612no—
417C24—2442no—
418C24—2442no—
419C24C22×#692311yescharacteristic
420C22×C4—22no—
421C22×C4—42no—
422C22×C4—611no—
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—618no—
445C22×C4—1224no—
446C22×C4—1224no—
447C22×C4—1224no—
448C22×C4—1224no—
449C22×C4—1224no—
450C22×C4—1224no—
451C22×C4—1222no—
452C22×C4—2442no—
453C22×C4—2442no—
454C22×C4—2442no—
455C22×C4—2442no—
456C22×C4—2442no—
457C22×C4—2442no—
458C22×C4—2442no—
459C22×C4—2442no—
460C22×C4—2442no—
461C22×C4—2444no—
462C22×C4—2444no—
463C22×C4—2444no—
464C22×C4—2442no—
465C22×C4—2444no—
466C22×C4—2444no—
467C22×C4—2444no—
468C22×C4—2444no—
469C22×C4—2444no—
470C22×C4C4×#692311yescharacteristic
471C22×C4C4×#692311yescharacteristic
472C22×C4C4⋊#692311yescharacteristic
473C22×C4C4⋊#692311yescharacteristic
474C22×C4C22⋊#692311yescharacteristic
475C22×C4C22⋊#692311yescharacteristic
476C4⋊C4—42no—
477C4⋊C4—2442no—
478C4⋊C4—2444no—
479C4⋊C4—2444no—
480C4⋊C4—2444no—
481C22⋊C4—24no—
482C22⋊C4—1224no—
483C22⋊C4—1224no—
484C22⋊C4—1224no—
485C22⋊C4—1224no—
486C22⋊C4—1228no—
487C22⋊C4—1224no—
488C22⋊C4—2442no—
489C22⋊C4—2442no—
490C22⋊C4—2442no—
491C22⋊C4—2442no—
492C42—2444no—
493C42—2444no—
494C23—41no—
495C23—41no—
496C23—611no—
497C23—612no—
498C23—612no—
499C23—612no—
500C23—612no—
501C23—611no—
502C23—611no—
503C23—611no—
504C23—612no—
505C23—612no—
506C23—612no—
507C23—612no—
508C23—611no—
509C23—611no—
510C23—611no—
511C23—611no—
512C23—612no—
513C23—612no—
514C23—1222no—
515C23—1222no—
516C23—1222no—
517C23—1222no—
518C23—1222no—
519C23—1222no—
520C23—2441no—
521C23—2441no—
522C23—2441no—
523C23—2441no—
524C23—2441no—
525C23—2441no—
526C23—2444no—
527C23—2444no—
528C23—2444no—
529C23—2444no—
530C23C2×C4×#692311yescharacteristic
531C23C2×C22⋊#692311yescharacteristic
532C23C2×C4⋊#692311yescharacteristic
533C23D4×#692312yes—
534C23Q8×#692312yes—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—611no—
545C2×C4—614no—
546C2×C4—611no—
547C2×C4—611no—
548C2×C4—611no—
549C2×C4—1222no—
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—1228no—
562C2×C4—4888no—
563C2×C4—4888no—
564C2×C4—2441no—
565C2×C4—2441no—
566C2×C4—2441no—
567C2×C4—2441no—
568C2×C4—2441no—
569C2×C4—2441no—
570C2×C4—2441no—
571C2×C4—2441no—
572C2×C4—2441no—
573C2×C4—2442no—
574C2×C4—2442no—
575C2×C4—2444no—
576C2×C4—2444no—
577C2×C4—2444no—
578C2×C4—2442no—
579C2×C4—2444no—
580C2×C4—2444no—
581C2×C4—2448no—
582C2×C4—2448no—
583C2×C4(C2×#6923)⋊C411yescharacteristic
584C2×C4(C2×#6923)⋊C411yescharacteristic
585C2×C4(C2×#6923)⋊C411yescharacteristic
586C2×C4(C2×#6923)⋊C411yescharacteristic
587C22—21no—
588C22—21no—
589C22—21no—
590C22—21no—
591C22—21no—
592C22—21no—
593C22—42no—
594C22—42no—
595C22—612no—
596C22—612no—
597C22—612no—
598C22—611no—
599C22—611no—
600C22—611no—
601C22—612no—
602C22—611no—
603C22—1224no—
604C22—1224no—
605C22—1224no—
606C22—1224no—
607C22—1224no—
608C22—1224no—
609C22—1221no—
610C22—1221no—
611C22—1221no—
612C22—1221no—
613C22—1221no—
614C22—1221no—
615C22—2441no—
616C22—2441no—
617C22—2442no—
618C22—2442no—
619C22—2441no—
620C22—2441no—
621C22—2442no—
622C22—2442no—
623C22C2×(C2×#6923)⋊C411yescharacteristic
624C22C4⋊C4×#692312yes—
625C22#1684071312yes—
626C22#1684071411yescharacteristic
627C22(C2×#6923)⋊Q811yescharacteristic
628C4—21no—
629C4—21no—
630C4—21no—
631C4—82no—
632C4—612no—
633C4—1221no—
634C4—1221no—
635C4—1221no—
636C4—4882no—
637C4—4884no—
638C4—2448no—
639C4#1684063912yescomplemented
640C2—21no—
641C2—22no—
642C2—21no—
643C2—22no—
644C2—614no—
645C2—1221no—
646C2—1221no—
647C2—1221no—
648C2—1222no—
649C2—1221no—
650C2#2146099611yescharacteristic
651C2C2×#1684063911yescharacteristic
652C2#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#10846
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
8. C22×C4×#6923C4semidirect
11. #16840704C4semidirect
12. #16840704C4semidirect
18. C2×(C2×#6923)⋊C4C4semidirect
23. #16839622C4semidirect
25. #16839620C4semidirect
28. C61×#380C4semidirect
101. C22×#6923C4⋊C4semidirect
308. C4×C61#342semidirect
313. Dic61#342semidirect
346. #380#6923semidirect
355. C61#10846semidirect
639. 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
#1084661