Finite Group Databasebeta

← #30609386

Subgroups — #30609386

Order 15616.

1246 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840711C212yesmaximal
2#21461008C212yesmaximal
3#21461005C212yesmaximal
4#21461004C212yesmaximal
5#21460999C212yesmaximal
6#21460998C212yesmaximal
7#21460997C211yesmaximal, characteristic
8#21460997C211yesmaximal, characteristic
9#389×D61C211yesmaximal, characteristic
10C22×C4⋊#6923C2211yescharacteristic
11C22×C4⋊#6923C2211yescharacteristic
12C22×C4⋊#6923C2211yescharacteristic
13C22×C4⋊#6923C2211yescharacteristic
14C22×C4×#6923C2212yes—
15#16840711—28no—
16C2×(C2×#6923)⋊C4C2212yes—
17C2×(C2×#6923)⋊C4C2212yes—
18C2×(C2×#6923)⋊C4C2212yes—
19C2×(C2×#6923)⋊C4C2212yes—
20C2×(C2×#6923)⋊C4C2212yes—
21C2×(C2×#6923)⋊C4C2212yes—
22C2×(C2×#6923)⋊C4C2212yes—
23C2×(C2×#6923)⋊C4C2212yes—
24C2×(C2×#6923)⋊C4C2212yes—
25C2×(C2×#6923)⋊C4C2212yes—
26C2×(C2×#6923)⋊C4C2212yes—
27C2×C4⋊C4×D61C2212yes—
28C2×C4⋊C4×D61C2211yescharacteristic
29C2×C4⋊C4×D61C2211yescharacteristic
30C2×C42×D61C2211yescharacteristic
31#16839661C411yescharacteristic, complemented
32#16839660C411yescharacteristic, complemented
33#16839659C412yescomplemented
34#16839658C411yescharacteristic, complemented
35#16839657C412yescomplemented
36#95×D61C2212yes—
37C61×#389C411yescharacteristic, complemented
38C23×#6923C2312yes—
39C23×#6923C2312yes—
40C23×#6923C2312yes—
41C23×#6923C2312yes—
42C2×C4⋊#6923—22no—
43C2×C4⋊#6923—22no—
44C2×C4⋊#6923—41no—
45C2×C4⋊#6923—41no—
46C2×C4⋊#6923—41no—
47C2×C4⋊#6923—41no—
48C2×C4⋊#6923—41no—
49C2×C4⋊#6923—41no—
50C2×C4⋊#6923—41no—
51C2×C4⋊#6923—41no—
52C2×C4⋊#6923D414yes—
53C2×C4⋊#6923Q814yes—
54C2×C4×#6923—24no—
55C2×C4×#6923—42no—
56C2×C4×#6923—42no—
57(C2×#6923)⋊C4—24no—
58(C2×#6923)⋊C4—24no—
59(C2×#6923)⋊C4—24no—
60(C2×#6923)⋊C4—24no—
61(C2×#6923)⋊C4—24no—
62(C2×#6923)⋊C4—24no—
63(C2×#6923)⋊C4—24no—
64(C2×#6923)⋊C4—42no—
65(C2×#6923)⋊C4—42no—
66(C2×#6923)⋊C4—42no—
67(C2×#6923)⋊C4—42no—
68C22×C4×D61C2312yes—
69C22×C4×D61C2312yes—
70C22×C4×D61C2311yescharacteristic
71C22×C4×D61C2311yescharacteristic
72C22×C4×D61C2311yescharacteristic
73C2×C4⋊Dic61C2×C411yescharacteristic
74C2×C4⋊Dic61C2×C412yes—
75C2×C4⋊Dic61C2×C411yescharacteristic
76C2×#11758196C2×C412yes—
77C2×#11758196C2×C412yes—
78C2×#11758196C2×C412yes—
79C2×#11758196C2×C412yes—
80C4⋊C4×D61—24no—
81C4⋊C4×D61—24no—
82C4⋊C4×D61—22no—
83C4⋊C4×D61—22no—
84C4⋊C4×D61—41no—
85C4⋊C4×D61—41no—
86C2×C4×Dic61C2×C411yescharacteristic
87C2×C4×Dic61C2×C411yescharacteristic
88C2×C4×Dic61C2×C411yescharacteristic
89C42×D61—41no—
90C42×D61—41no—
91#14519684C2×C412yes—
92#14519684C2×C412yes—
93#14519684C2×C412yes—
94C2×C4⋊C4×C61C2×C412yes—
95C2×C4⋊C4×C61C2×C411yescharacteristic
96C2×C4⋊C4×C61C2×C411yescharacteristic
97C2×C42×C61C2×C411yescharacteristic
98#95×C61C2×C412yes—
99C23×D61C2411yescharacteristic
100C22×#6923—22no—
101C22×#6923—22no—
102C22×#6923—22no—
103C22×#6923—22no—
104C22×#6923—22no—
105C22×#6923—22no—
106C22×#6923—22no—
107C22×#6923—22no—
108C22×#6923—22no—
109C22×#6923—22no—
110C22×#6923—22no—
111C22×#6923—22no—
112C22×#6923—22no—
113C22×#6923—22no—
114C22×#6923—22no—
115C22×#6923—22no—
116C22×#6923—22no—
117C22×#6923—22no—
118C22×#6923—22no—
119C22×#6923—22no—
120C22×#6923—22no—
121C22×#6923—22no—
122C22×#6923—22no—
123C22×#6923—22no—
124C22×#6923—22no—
125C22×#6923—22no—
126C22×#6923C2×D414yes—
127C22×#6923C2×Q814yes—
128C22×C4×C61C22×C412yes—
129C22×C4×C61C22×C412yes—
130C22×C4×C61C22×C411yescharacteristic
131C22×C4×C61C22×C411yescharacteristic
132C22×C4×C61C22×C411yescharacteristic
133C22×Dic61C22×C412yes—
134C22×Dic61C22×C412yes—
135C22×Dic61C22×C411yescharacteristic
136C22×Dic61C22×C411yescharacteristic
137C22×Dic61C22×C411yescharacteristic
138C2×C4×D61—21no—
139C2×C4×D61—21no—
140C2×C4×D61—21no—
141C2×C4×D61—21no—
142C2×C4×D61—21no—
143C2×C4×D61—21no—
144C2×C4×D61—21no—
145C2×C4×D61—21no—
146C2×C4×D61—21no—
147C2×C4×D61—21no—
148C2×C4×D61—21no—
149C2×C4×D61—21no—
150C2×C4×D61—22no—
151C2×C4×D61—22no—
152C2×C4×D61—22no—
153C2×C4×D61—22no—
154C2×C4×D61—22no—
155C2×C4×D61—22no—
156C2×C4×D61—22no—
157C2×C4×D61—22no—
158C2×C4×D61—22no—
159C2×C4×D61—22no—
160C2×C4×D61—22no—
161C2×C4×D61—22no—
162C2×C4×D61C2×D412yes—
163C2×C4×D61C2×Q812yes—
164C2×C4×D61#4112yes—
165C2×C4×D61#4112yes—
166C2×C4×D61#4112yes—
167C2×C4×D61#4112yes—
168C4⋊#6923—44no—
169C4⋊#6923—44no—
170C4⋊#6923—44no—
171C4⋊#6923—44no—
172C4×#6923—48no—
173C4⋊C4×C61—22no—
174C4⋊C4×C61—24no—
175C4⋊C4×C61—41no—
176C42×C61—41no—
177C4⋊Dic61—22no—
178C4⋊Dic61—24no—
179C4⋊Dic61—41no—
180#11758196—24no—
181#11758196—24no—
182#11758196—24no—
183#11758196—42no—
184C4×Dic61—41no—
185C4×Dic61—41no—
186C4×Dic61—41no—
187C23×C61C23×C411yescharacteristic
188C22×D61C22×D411yescharacteristic
189C22×D61C22×Q811yescharacteristic
190C22×D61C2×#4111yescharacteristic
191C22×D61C2×#4111yescharacteristic
192C22×D61C2×#4111yescharacteristic
193C22×D61C2×#4111yescharacteristic
194C22×D61H(5,𝔽2)11yescharacteristic
195C22×D61H(5,𝔽2)11yescharacteristic
196C22×D61H(5,𝔽2)11yescharacteristic
197C22×D61H(5,𝔽2)11yescharacteristic
198C22×D612−1+411yescharacteristic
199C22×D612−1+411yescharacteristic
200C22×D612−1+411yescharacteristic
201C22×D612−1+411yescharacteristic
202C2×#6923—24no—
203C2×#6923—24no—
204C2×#6923—24no—
205C2×#6923—24no—
206C2×#6923—24no—
207C2×#6923—24no—
208C2×#6923—42no—
209C2×#6923—42no—
210C2×#6923—42no—
211C2×#6923—42no—
212C2×#6923—42no—
213C2×#6923—42no—
214C2×#6923—42no—
215C2×#6923—42no—
216C2×#6923—42no—
217C2×#6923—42no—
218C2×#6923—42no—
219C2×#6923—42no—
220C2×#6923—42no—
221C2×#6923—42no—
222C2×#6923—42no—
223C2×#6923—42no—
224C2×#6923—42no—
225C2×#6923—42no—
226C2×#6923—42no—
227C2×#6923—42no—
228C2×#6923—42no—
229C2×#6923—42no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
236C2×C4×C61—22no—
237C2×C4×C61—22no—
238C2×C4×C61—22no—
239C2×C4×C61—22no—
240C2×C4×C61—22no—
241C2×C4×C61—22no—
242C2×C4×C61#11712yes—
243C2×C4×C61C4×D412yes—
244C2×C4×C61C4×Q812yes—
245C2×Dic61—21no—
246C2×Dic61—21no—
247C2×Dic61—21no—
248C2×Dic61—21no—
249C2×Dic61—21no—
250C2×Dic61—21no—
251C2×Dic61—22no—
252C2×Dic61—22no—
253C2×Dic61—22no—
254C2×Dic61—22no—
255C2×Dic61—22no—
256C2×Dic61—22no—
257C2×Dic61#11712yes—
258C2×Dic61C4×D412yes—
259C2×Dic61C4×Q812yes—
260C4×D61—22no—
261C4×D61—22no—
262C4×D61—22no—
263C4×D61—22no—
264C4×D61—22no—
265C4×D61—22no—
266C4×D61—22no—
267C4×D61—22no—
268C4×D61—22no—
269C4×D61—22no—
270C4×D61—22no—
271C4×D61—22no—
272C4×D61—42no—
273C4×D61—42no—
274C4×D61—42no—
275C4×D61—42no—
276C4×D61—42no—
277C4×D61—42no—
278C4×D61—42no—
279C4×D61—42no—
280#14446—611nomaximal, Sylow
281C22×C61C2×#11711yescharacteristic
282C22×C61C2×C4×D411yescharacteristic
283C22×C61C2×C4×Q811yescharacteristic
284C22×C61#51811yescharacteristic
285C22×C61#51911yescharacteristic
286C22×C61#52011yescharacteristic
287C22×C61#52011yescharacteristic
288C2×D61#53411yescharacteristic
289C2×D61#53711yescharacteristic
290C2×D61#53811yescharacteristic
291C2×D61#53811yescharacteristic
292C2×D61#53911yescharacteristic
293C2×D61#53911yescharacteristic
294C2×D61#53911yescharacteristic
295C2×D61#53911yescharacteristic
296C2×D61#53911yescharacteristic
297C2×D61#53911yescharacteristic
298C2×D61#54311yescharacteristic
299C2×D61#54411yescharacteristic
300C2×D61#54711yescharacteristic
301C2×D61#54711yescharacteristic
302C2×D61D4×Q811yescharacteristic
303C2×D61#55011yescharacteristic
304C2×D61#55411yescharacteristic
305C2×D61#55511yescharacteristic
306C2×D61#55611yescharacteristic
307C2×D61#55611yescharacteristic
308C2×D61#55611yescharacteristic
309C2×D61#55711yescharacteristic
310C2×D61#55711yescharacteristic
311C2×D61#55911yescharacteristic
312C2×D61#56211yescharacteristic
313C2×D61#56311yescharacteristic
314C2×D61#56311yescharacteristic
315C2×D61#56411yescharacteristic
316#6923—44no—
317#6923—44no—
318#6923—82no—
319#6923—82no—
320C4×C61—22no—
321C4×C61—22no—
322C4×C61—22no—
323C4×C61—42no—
324C4×C61—42no—
325Dic61—22no—
326Dic61—22no—
327Dic61—22no—
328Dic61—42no—
329Dic61—42no—
330C2×#389—611no—
331C2×#387—612no—
332#1445—612no—
333#1442—612no—
334#1441—612no—
335#1436—612no—
336#1436—612no—
337C4⋊#95—611no—
338C4⋊#95—611no—
339C2×C61#231311yescharacteristic
340C2×C61#232511yescharacteristic
341C2×C61#232911yescharacteristic
342C2×C61#235411yescharacteristic
343C2×C61#235511yescharacteristic
344C2×C61#236511yescharacteristic
345C2×C61#238211yescharacteristic
346D61#272411yescharacteristic
347D61#272611yescharacteristic
348D61#272711yescharacteristic
349D61#273211yescharacteristic
350D61#280511yescharacteristic
351D61#280811yescharacteristic
352D61#280911yescharacteristic
353D61#281011yescharacteristic
354C22×C4⋊C4—611no—
355C22×C4⋊C4—611no—
356C22×C4⋊C4—612no—
357C22×C4⋊C4—611no—
358C22×C4⋊C4—611no—
359C22×C4⋊C4—611no—
360C22×C4⋊C4—611no—
361C22×C42—611no—
362C22×C42—612no—
363#389—612no—
364#389—611no—
365#389—611no—
366#389—611no—
367#389—612no—
368#389#692311yescharacteristic, complemented
369#387—1228no—
370C2×#95—612no—
371C2×#95—612no—
372C2×#95—612no—
373C2×#95—612no—
374C2×#95—612no—
375C2×#95—612no—
376C2×#95—612no—
377C2×#95—612no—
378C2×#95—612no—
379C2×#95—612no—
380C2×#95—612no—
381C2×#95—612no—
382C61#1444611yescharacteristic, complemented, Sylow
383C23×C4—611no—
384C23×C4—611no—
385C23×C4—611no—
386C23×C4—612no—
387C23×C4—612no—
388C23×C4—612no—
389C23×C4—612no—
390C23×C4—612no—
391C23×C4—612no—
392C2×C4⋊C4—612no—
393C2×C4⋊C4—612no—
394C2×C4⋊C4—612no—
395C2×C4⋊C4—612no—
396C2×C4⋊C4—611no—
397C2×C4⋊C4—614no—
398C2×C4⋊C4—614no—
399C2×C4⋊C4—612no—
400C2×C4⋊C4—611no—
401C2×C4⋊C4—1224no—
402C2×C4⋊C4—1222no—
403C2×C4⋊C4—1222no—
404C2×C4⋊C4—1224no—
405C2×C4⋊C4—1222no—
406C2×C4⋊C4—1222no—
407C2×C4⋊C4—2441no—
408C2×C4⋊C4—2441no—
409C2×C4⋊C4—2441no—
410C2×C4⋊C4—2441no—
411C2×C4⋊C4—2441no—
412C2×C4⋊C4—2441no—
413C2×C4⋊C4—2441no—
414C2×C4⋊C4—2441no—
415C2×C4⋊C4—2441no—
416C2×C4⋊C4—2441no—
417C2×C4⋊C4C2×#692311yescharacteristic
418C2×C4⋊C4C2×#692312yes—
419C2×C4⋊C4C2×#692311yescharacteristic
420C2×C42—611no—
421C2×C42—611no—
422C2×C42—611no—
423C2×C42—1224no—
424C2×C42—2441no—
425C2×C42—2441no—
426C2×C42—2442no—
427C2×C42—2442no—
428C2×C42C2×#692311yescharacteristic
429#95—612no—
430#95—612no—
431#95—612no—
432#95—1224no—
433#95—1224no—
434#95—1224no—
435#95—1224no—
436#95—1224no—
437#95—1224no—
438#95—1224no—
439#95—2442no—
440#95—2442no—
441#95—2442no—
442#95—2442no—
443#95C2×#692312yes—
444C24—611no—
445C22×C4—611no—
446C22×C4—611no—
447C22×C4—611no—
448C22×C4—612no—
449C22×C4—612no—
450C22×C4—612no—
451C22×C4—612no—
452C22×C4—612no—
453C22×C4—612no—
454C22×C4—614no—
455C22×C4—614no—
456C22×C4—612no—
457C22×C4—612no—
458C22×C4—1221no—
459C22×C4—1221no—
460C22×C4—1221no—
461C22×C4—1221no—
462C22×C4—1221no—
463C22×C4—1221no—
464C22×C4—1221no—
465C22×C4—1221no—
466C22×C4—1221no—
467C22×C4—1221no—
468C22×C4—1221no—
469C22×C4—1221no—
470C22×C4—1222no—
471C22×C4—1222no—
472C22×C4—1222no—
473C22×C4—1222no—
474C22×C4—1222no—
475C22×C4—1222no—
476C22×C4—1222no—
477C22×C4—1222no—
478C22×C4—1222no—
479C22×C4—1222no—
480C22×C4—1222no—
481C22×C4—1222no—
482C22×C4—1222no—
483C22×C4—1222no—
484C22×C4—1222no—
485C22×C4—1222no—
486C22×C4—1222no—
487C22×C4—1222no—
488C22×C4—1222no—
489C22×C4—1222no—
490C22×C4—1222no—
491C22×C4—1222no—
492C22×C4—1222no—
493C22×C4—1222no—
494C22×C4—1222no—
495C22×C4—1222no—
496C22×C4—1222no—
497C22×C4—1222no—
498C22×C4—1222no—
499C22×C4—1222no—
500C22×C4—1222no—
501C22×C4—1222no—
502C22×C4—1222no—
503C22×C4—1222no—
504C22×C4—1222no—
505C22×C4—1222no—
506C22×C4—1222no—
507C22×C4—1222no—
508C22×C4C22×#692312yes—
509C22×C4C22×#692312yes—
510C22×C4C22×#692311yescharacteristic
511C22×C4C22×#692311yescharacteristic
512C22×C4C22×#692311yescharacteristic
513C4⋊C4—22no—
514C4⋊C4—24no—
515C4⋊C4—41no—
516C4⋊C4—1224no—
517C4⋊C4—1224no—
518C4⋊C4—1224no—
519C4⋊C4—1222no—
520C4⋊C4—1224no—
521C4⋊C4—2442no—
522C4⋊C4—2441no—
523C4⋊C4—2444no—
524C4⋊C4—2444no—
525C4⋊C4—2444no—
526C4⋊C4—2444no—
527C42—41no—
528C42—2441no—
529C42—2441no—
530C42—2441no—
531C42—2448no—
532C23—611no—
533C23—611no—
534C23—611no—
535C23—611no—
536C23—611no—
537C23—611no—
538C23—611no—
539C23—611no—
540C23—611no—
541C23—611no—
542C23—611no—
543C23—611no—
544C23—611no—
545C23—611no—
546C23C23×#692311yescharacteristic
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—612no—
560C2×C4—612no—
561C2×C4—612no—
562C2×C4—1222no—
563C2×C4—1222no—
564C2×C4—1222no—
565C2×C4—1222no—
566C2×C4—1222no—
567C2×C4—1222no—
568C2×C4—1222no—
569C2×C4—1222no—
570C2×C4—1222no—
571C2×C4—1222no—
572C2×C4—1222no—
573C2×C4—1222no—
574C2×C4—1221no—
575C2×C4—1221no—
576C2×C4—1221no—
577C2×C4—1221no—
578C2×C4—1221no—
579C2×C4—1221no—
580C2×C4—1224no—
581C2×C4—1224no—
582C2×C4—1224no—
583C2×C4—1224no—
584C2×C4—1224no—
585C2×C4—1224no—
586C2×C4—1222no—
587C2×C4—1222no—
588C2×C4—1222no—
589C2×C4—1222no—
590C2×C4—1222no—
591C2×C4—1222no—
592C2×C4—2442no—
593C2×C4—2442no—
594C2×C4—2442no—
595C2×C4—2442no—
596C2×C4—2442no—
597C2×C4—2442no—
598C2×C4—2442no—
599C2×C4—2442no—
600C2×C4—2442no—
601C2×C4—2442no—
602C2×C4—2442no—
603C2×C4—2442no—
604C2×C4—2442no—
605C2×C4—2442no—
606C2×C4—2442no—
607C2×C4—2442no—
608C2×C4—2442no—
609C2×C4—2442no—
610C2×C4—2442no—
611C2×C4—2442no—
612C2×C4—2442no—
613C2×C4—2442no—
614C2×C4—2442no—
615C2×C4—2442no—
616C2×C4—2442no—
617C2×C4—2442no—
618C2×C4—2442no—
619C2×C4—2442no—
620C2×C4—2442no—
621C2×C4—2442no—
622C2×C4#1451985612yes—
623C2×C4D4×#692312yes—
624C2×C4Q8×#692312yes—
625C22—611no—
626C22—611no—
627C22—611no—
628C22—611no—
629C22—611no—
630C22—611no—
631C22—611no—
632C22—611no—
633C22—611no—
634C22—611no—
635C22—611no—
636C22—611no—
637C22—611no—
638C22—611no—
639C22—611no—
640C22—611no—
641C22—611no—
642C22—611no—
643C22—611no—
644C22—611no—
645C22—611no—
646C22—611no—
647C22—611no—
648C22—611no—
649C22—611no—
650C22—611no—
651C22—611no—
652C22—611no—
653C22C2×#1451985611yescharacteristic
654C22C2×D4×#692311yescharacteristic
655C22C2×Q8×#692311yescharacteristic
656C22#1684082911yescharacteristic
657C22#1684083011yescharacteristic
658C22#1684083111yescharacteristic
659C22#1684083111yescharacteristic
660C4—22no—
661C4—22no—
662C4—22no—
663C4—42no—
664C4—42no—
665C4—1222no—
666C4—1222no—
667C4—1222no—
668C4—4882no—
669C4—4882no—
670C4—2444no—
671C4—2444no—
672C4—2442no—
673C4—2442no—
674C2—611no—
675C2—611no—
676C2—611no—
677C2—611no—
678C2—611no—
679C2—611no—
680C2—611no—
681C2—611no—
682C2#2146229611yescharacteristic
683C2#2146230811yescharacteristic
684C2#2146231211yescharacteristic
685C2#2146233711yescharacteristic
686C2#2146233811yescharacteristic
687C2#2146234811yescharacteristic
688C2#2146236511yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#389C4
prime radical, cosocleC23×D61C24
hypercenter#389#6923
hypocenterC61#14446
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
31. #16839661C4semidirect
32. #16839660C4semidirect
33. #16839659C4semidirect
34. #16839658C4semidirect
35. #16839657C4semidirect
37. C61×#389C4semidirect
368. #389#6923semidirect
382. C61#14446semidirect

Maximal subgroups

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

subgroupindex
C2×#168407112
#214610082
#214610052
#214610042
#214609992
#214609982
#214609972
#389×D612
#1444661