Finite Group Databasebeta

← #30609379

Subgroups — #30609379

Order 15616.

1346 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840713C212yesmaximal
2C2×#16840711C212yesmaximal
3#21461005C212yesmaximal
4#21461004C212yesmaximal
5#21461004C212yesmaximal
6#21460999C212yesmaximal
7#21460997C211yesmaximal, characteristic
8#21460995C211yesmaximal, characteristic
9#389×D61C211yesmaximal, characteristic
10C22×C4⋊#6923C2212yes—
11C22×C4⋊#6923C2212yes—
12C22×C4⋊#6923C2212yes—
13C22×C4×#6923C2212yes—
14#16840713—28no—
15#16840711—28no—
16C2×(C2×#6923)⋊C4C2212yes—
17C2×(C2×#6923)⋊C4C2211yescharacteristic
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)⋊C4C2211yescharacteristic
25C2×(C2×#6923)⋊C4C2211yescharacteristic
26C2×(C2×#6923)⋊C4C2212yes—
27C2×(C2×#6923)⋊C4C2211yescharacteristic
28C2×C4⋊C4×D61C2212yes—
29C2×C4⋊C4×D61C2211yescharacteristic
30C2×C4⋊C4×D61C2211yescharacteristic
31C2×C42×D61C2211yescharacteristic
32#16839661C411yescharacteristic, complemented
33#16839660C411yescharacteristic, complemented
34#16839659C412yescomplemented
35#16839658C411yescharacteristic, complemented
36#16839657C412yescomplemented
37#95×D61C2212yes—
38C61×#389C411yescharacteristic, complemented
39C23×#6923C2312yes—
40C23×#6923C2312yes—
41C23×#6923C2312yes—
42C23×#6923C2312yes—
43C2×C4⋊#6923—24no—
44C2×C4⋊#6923—24no—
45C2×C4⋊#6923—24no—
46C2×C4⋊#6923—24no—
47C2×C4⋊#6923—24no—
48C2×C4⋊#6923—24no—
49C2×C4⋊#6923—42no—
50C2×C4⋊#6923—42no—
51C2×C4⋊#6923—42no—
52C2×C4×#6923—24no—
53C2×C4×#6923—24no—
54C2×C4×#6923—42no—
55(C2×#6923)⋊C4—24no—
56(C2×#6923)⋊C4—24no—
57(C2×#6923)⋊C4—24no—
58(C2×#6923)⋊C4—24no—
59(C2×#6923)⋊C4—24no—
60(C2×#6923)⋊C4—24no—
61(C2×#6923)⋊C4—22no—
62(C2×#6923)⋊C4—41no—
63(C2×#6923)⋊C4—41no—
64(C2×#6923)⋊C4—42no—
65(C2×#6923)⋊C4—42no—
66(C2×#6923)⋊C4D414yes—
67C22×C4×D61C2311yescharacteristic
68C22×C4×D61C2312yes—
69C22×C4×D61C2311yescharacteristic
70C22×C4×D61C2312yes—
71C22×C4×D61C2311yescharacteristic
72C2×C4⋊Dic61C2×C412yes—
73C2×C4⋊Dic61C2×C411yescharacteristic
74C2×C4⋊Dic61C2×C411yescharacteristic
75C2×#11758196C2×C412yes—
76C2×#11758196C2×C412yes—
77C2×#11758196C2×C412yes—
78C2×#11758196C2×C412yes—
79C4⋊C4×D61—24no—
80C4⋊C4×D61—24no—
81C4⋊C4×D61—42no—
82C4⋊C4×D61D414yes—
83C4⋊C4×D61Q814yes—
84C2×C4×Dic61C2×C411yescharacteristic
85C2×C4×Dic61C2×C411yescharacteristic
86C2×C4×Dic61C2×C411yescharacteristic
87C42×D61—42no—
88#14519684C2×C412yes—
89#14519684C2×C412yes—
90#14519684C2×C412yes—
91C2×C4⋊C4×C61C2×C412yes—
92C2×C4⋊C4×C61C2×C411yescharacteristic
93C2×C4⋊C4×C61C2×C411yescharacteristic
94C2×C42×C61C2×C411yescharacteristic
95#95×C61C2×C412yes—
96C23×D61C2411yescharacteristic
97C22×#6923—22no—
98C22×#6923—22no—
99C22×#6923—22no—
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×#6923C2×D414yes—
124C22×#6923#4114yes—
125C22×C4×C61C22×C411yescharacteristic
126C22×C4×C61C22×C412yes—
127C22×C4×C61C22×C412yes—
128C22×C4×C61C22×C411yescharacteristic
129C22×C4×C61C22×C411yescharacteristic
130C22×Dic61C22×C411yescharacteristic
131C22×Dic61C22×C412yes—
132C22×Dic61C22×C412yes—
133C22×Dic61C22×C411yescharacteristic
134C22×Dic61C22×C411yescharacteristic
135C2×C4×D61—22no—
136C2×C4×D61—22no—
137C2×C4×D61—22no—
138C2×C4×D61—22no—
139C2×C4×D61—22no—
140C2×C4×D61—22no—
141C2×C4×D61—22no—
142C2×C4×D61—22no—
143C2×C4×D61—22no—
144C2×C4×D61—22no—
145C2×C4×D61—22no—
146C2×C4×D61—22no—
147C2×C4×D61—21no—
148C2×C4×D61—22no—
149C2×C4×D61—22no—
150C2×C4×D61—22no—
151C2×C4×D61—22no—
152C2×C4×D61—21no—
153C2×C4×D61C2×D412yes—
154C2×C4×D61C2×D414yes—
155C2×C4×D61C2×D412yes—
156C2×C4×D61C2×Q812yes—
157C2×C4×D61C2×Q814yes—
158C2×C4×D61#4112yes—
159C4⋊#6923—48no—
160C4⋊#6923—48no—
161C4⋊#6923—48no—
162C4×#6923—48no—
163C4⋊C4×C61—24no—
164C4⋊C4×C61—41no—
165C4⋊C4×C61C4⋊C414yescomplemented
166C42×C61—41no—
167C4⋊Dic61—24no—
168C4⋊Dic61—41no—
169C4⋊Dic61C4⋊C414yescomplemented
170#11758196—24no—
171#11758196—24no—
172#11758196—42no—
173#11758196C4⋊C418yescomplemented
174C4×Dic61—41no—
175C4×Dic61—41no—
176C4×Dic61—41no—
177C23×C61C23×C411yescharacteristic
178C22×D61C22×D411yescharacteristic
179C22×D61C22×D411yescharacteristic
180C22×D61C22×Q811yescharacteristic
181C22×D61C2×#4112yes—
182C22×D61C2×#4111yescharacteristic
183C22×D61H(5,𝔽2)12yes—
184C22×D61H(5,𝔽2)11yescharacteristic
185C22×D612−1+412yes—
186C22×D612−1+412yes—
187C22×D612−1+411yescharacteristic
188C2×#6923—24no—
189C2×#6923—24no—
190C2×#6923—24no—
191C2×#6923—24no—
192C2×#6923—24no—
193C2×#6923—24no—
194C2×#6923—42no—
195C2×#6923—42no—
196C2×#6923—42no—
197C2×#6923—42no—
198C2×#6923—42no—
199C2×#6923—42no—
200C2×#6923—42no—
201C2×#6923—42no—
202C2×#6923—42no—
203C2×#6923—42no—
204C2×#6923—42no—
205C2×#6923—42no—
206C2×#6923—42no—
207C2×#6923—42no—
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×C4×C61—22no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—22no—
222C2×C4×C61—22no—
223C2×C4×C61—22no—
224C2×C4×C61—21no—
225C2×C4×C61—22no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61C2×C4⋊C414yes—
229C2×C4×C61C2×C4⋊C412yes—
230C2×C4×C61C4×D412yes—
231C2×Dic61—22no—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—22no—
237C2×Dic61—22no—
238C2×Dic61—22no—
239C2×Dic61—21no—
240C2×Dic61—22no—
241C2×Dic61—21no—
242C2×Dic61—21no—
243C2×Dic61C2×C4⋊C412yes—
244C2×Dic61C2×C4⋊C414yes—
245C2×Dic61C4×D412yes—
246C4×D61—24no—
247C4×D61—24no—
248C4×D61—24no—
249C4×D61—24no—
250C4×D61—24no—
251C4×D61—24no—
252C4×D61—24no—
253C4×D61—24no—
254C4×D61—42no—
255C4×D61—42no—
256C4×D61—42no—
257C4×D61—42no—
258C4×D61—42no—
259C4×D61—42no—
260#14439—611nomaximal, Sylow
261C22×C61C22×C4⋊C411yescharacteristic
262C22×C61C2×C4×D411yescharacteristic
263C22×C61C4×#4111yescharacteristic
264C22×C61#51811yescharacteristic
265C22×C61#51911yescharacteristic
266C22×C61#51911yescharacteristic
267C22×C61#52011yescharacteristic
268C2×D61#53612yes—
269C2×D61#53712yes—
270C2×D61#53912yes—
271C2×D61#54112yes—
272C2×D61#54112yes—
273C2×D61#54412yes—
274C2×D61D4211yescharacteristic
275C2×D61#54612yes—
276C2×D61#54711yescharacteristic
277C2×D61#54812yes—
278C2×D61D4×Q811yescharacteristic
279C2×D61#55312yes—
280C2×D61#55411yescharacteristic
281C2×D61#55712yes—
282C2×D61#56212yes—
283C2×D61#56312yes—
284#6923—44no—
285#6923—44no—
286#6923—82no—
287#6923—82no—
288C4×C61—22no—
289C4×C61—24no—
290C4×C61—22no—
291C4×C61—42no—
292C4×C61—41no—
293Dic61—22no—
294Dic61—24no—
295Dic61—22no—
296Dic61—42no—
297Dic61—41no—
298C2×#389—611no—
299C2×#389—612no—
300C2×#387—612no—
301#1442—612no—
302#1441—612no—
303#1441—612no—
304#1436—612no—
305C4⋊#95—611no—
306#1434—611no—
307C2×C61#231611yescharacteristic
308C2×C61#232711yescharacteristic
309C2×C61#233611yescharacteristic
310C2×C61D4×C4⋊C411yescharacteristic
311C2×C61#235111yescharacteristic
312C2×C61#236411yescharacteristic
313C2×C61#237811yescharacteristic
314D61#268112yes—
315D61#271312yes—
316D61#272512yes—
317D61#280212yes—
318C22×C4⋊C4—611no—
319C22×C4⋊C4—612no—
320C22×C4⋊C4—611no—
321C22×C4⋊C4—612no—
322C22×C4⋊C4—612no—
323C22×C4⋊C4—612no—
324C22×C42—611no—
325C22×C42—612no—
326#389—612no—
327#389—611no—
328#389—611no—
329#389—611no—
330#389—612no—
331#389—1228no—
332#389#692311yescharacteristic, complemented
333#387—1228no—
334C2×#95—611no—
335C2×#95—612no—
336C2×#95—611no—
337C2×#95—612no—
338C2×#95—612no—
339C2×#95—612no—
340C2×#95—612no—
341C2×#95—612no—
342C2×#95—612no—
343C2×#95—612no—
344C2×#95—611no—
345C2×#95—611no—
346C2×#95—612no—
347C61#1443911yescharacteristic, complemented, Sylow
348C23×C4—611no—
349C23×C4—612no—
350C23×C4—611no—
351C23×C4—612no—
352C23×C4—612no—
353C23×C4—612no—
354C23×C4—611no—
355C23×C4—612no—
356C23×C4—612no—
357C2×C4⋊C4—612no—
358C2×C4⋊C4—611no—
359C2×C4⋊C4—614no—
360C2×C4⋊C4—614no—
361C2×C4⋊C4—612no—
362C2×C4⋊C4—612no—
363C2×C4⋊C4—612no—
364C2×C4⋊C4—612no—
365C2×C4⋊C4—611no—
366C2×C4⋊C4—1224no—
367C2×C4⋊C4—1224no—
368C2×C4⋊C4—1224no—
369C2×C4⋊C4—1224no—
370C2×C4⋊C4—1224no—
371C2×C4⋊C4—1224no—
372C2×C4⋊C4—1224no—
373C2×C4⋊C4—1224no—
374C2×C4⋊C4—2442no—
375C2×C4⋊C4—2442no—
376C2×C4⋊C4—2442no—
377C2×C4⋊C4—2442no—
378C2×C4⋊C4C2×#692312yes—
379C2×C4⋊C4C2×#692311yescharacteristic
380C2×C4⋊C4C2×#692311yescharacteristic
381C2×C42—611no—
382C2×C42—611no—
383C2×C42—611no—
384C2×C42—1224no—
385C2×C42—1224no—
386C2×C42—2442no—
387C2×C42—2442no—
388C2×C42C2×#692311yescharacteristic
389#95—614no—
390#95—612no—
391#95—612no—
392#95—612no—
393#95—1222no—
394#95—1224no—
395#95—1224no—
396#95—1224no—
397#95—1224no—
398#95—1224no—
399#95—1224no—
400#95—2441no—
401#95—2441no—
402#95—2442no—
403#95—2442no—
404#95C2×#692312yes—
405C24—611no—
406C22×C4—612no—
407C22×C4—611no—
408C22×C4—611no—
409C22×C4—612no—
410C22×C4—614no—
411C22×C4—614no—
412C22×C4—612no—
413C22×C4—612no—
414C22×C4—612no—
415C22×C4—614no—
416C22×C4—614no—
417C22×C4—611no—
418C22×C4—612no—
419C22×C4—1222no—
420C22×C4—1222no—
421C22×C4—1222no—
422C22×C4—1222no—
423C22×C4—1222no—
424C22×C4—1222no—
425C22×C4—1222no—
426C22×C4—1222no—
427C22×C4—1222no—
428C22×C4—1222no—
429C22×C4—1221no—
430C22×C4—1222no—
431C22×C4—1222no—
432C22×C4—1222no—
433C22×C4—1222no—
434C22×C4—1222no—
435C22×C4—1222no—
436C22×C4—1221no—
437C22×C4—1222no—
438C22×C4—1222no—
439C22×C4—1222no—
440C22×C4—1222no—
441C22×C4—1222no—
442C22×C4—1222no—
443C22×C4—1222no—
444C22×C4—1222no—
445C22×C4—1222no—
446C22×C4—1222no—
447C22×C4—1222no—
448C22×C4—1222no—
449C22×C4—1222no—
450C22×C4—1222no—
451C22×C4—1222no—
452C22×C4—1222no—
453C22×C4—1222no—
454C22×C4—1222no—
455C22×C4—1222no—
456C22×C4—1222no—
457C22×C4—1222no—
458C22×C4—1222no—
459C22×C4—1222no—
460C22×C4—1222no—
461C22×C4—1222no—
462C22×C4—1222no—
463C22×C4C22×#692311yescharacteristic
464C22×C4C22×#692312yes—
465C22×C4C22×#692312yes—
466C22×C4C22×#692311yescharacteristic
467C22×C4C22×#692311yescharacteristic
468C4⋊C4—24no—
469C4⋊C4—41no—
470C4⋊C4—618no—
471C4⋊C4—614no—
472C4⋊C4—1224no—
473C4⋊C4—1224no—
474C4⋊C4—1224no—
475C4⋊C4—2442no—
476C4⋊C4—2441no—
477C4⋊C4—2448no—
478C4⋊C4—2448no—
479C4⋊C4—2448no—
480C4⋊C4C4⋊#692314yescomplemented
481C42—41no—
482C42—2441no—
483C42—2441no—
484C42—2441no—
485C42—2448no—
486C23—611no—
487C23—611no—
488C23—611no—
489C23—611no—
490C23—612no—
491C23—612no—
492C23—612no—
493C23—612no—
494C23—611no—
495C23—611no—
496C23C23×#692311yescharacteristic
497C2×C4—22no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—21no—
506C2×C4—22no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—612no—
510C2×C4—614no—
511C2×C4—612no—
512C2×C4—1224no—
513C2×C4—1224no—
514C2×C4—1224no—
515C2×C4—1224no—
516C2×C4—1224no—
517C2×C4—1224no—
518C2×C4—1224no—
519C2×C4—1224no—
520C2×C4—1222no—
521C2×C4—1221no—
522C2×C4—1221no—
523C2×C4—1221no—
524C2×C4—1221no—
525C2×C4—1222no—
526C2×C4—1224no—
527C2×C4—1224no—
528C2×C4—1224no—
529C2×C4—1224no—
530C2×C4—1224no—
531C2×C4—1224no—
532C2×C4—1222no—
533C2×C4—1222no—
534C2×C4—1221no—
535C2×C4—1222no—
536C2×C4—1221no—
537C2×C4—1221no—
538C2×C4—2442no—
539C2×C4—2442no—
540C2×C4—2442no—
541C2×C4—2442no—
542C2×C4—2442no—
543C2×C4—2442no—
544C2×C4—2442no—
545C2×C4—2442no—
546C2×C4—2442no—
547C2×C4—2442no—
548C2×C4—2442no—
549C2×C4—2442no—
550C2×C4—2442no—
551C2×C4—2442no—
552C2×C4—2442no—
553C2×C4—2442no—
554C2×C4—2442no—
555C2×C4—2442no—
556C2×C4—2442no—
557C2×C4—2442no—
558C2×C4—2442no—
559C2×C4—2442no—
560C2×C4—2442no—
561C2×C4—2442no—
562C2×C4—2442no—
563C2×C4—2442no—
564C2×C4—2442no—
565C2×C4—2442no—
566C2×C4C2×C4⋊#692312yes—
567C2×C4C2×C4⋊#692314yes—
568C2×C4D4×#692312yes—
569C22—612no—
570C22—612no—
571C22—612no—
572C22—612no—
573C22—612no—
574C22—612no—
575C22—611no—
576C22—611no—
577C22—611no—
578C22—611no—
579C22—612no—
580C22—612no—
581C22—612no—
582C22—612no—
583C22—612no—
584C22—612no—
585C22C22×C4⋊#692311yescharacteristic
586C22C2×D4×#692311yescharacteristic
587C22#41×#692311yescharacteristic
588C22#1684082911yescharacteristic
589C22#1684083011yescharacteristic
590C22#1684083011yescharacteristic
591C22#1684083111yescharacteristic
592C4—22no—
593C4—24no—
594C4—22no—
595C4—42no—
596C4—41no—
597C4—1222no—
598C4—1224no—
599C4—1222no—
600C4—4882no—
601C4—4882no—
602C4—2444no—
603C4—2444no—
604C4—2442no—
605C4—2441no—
606C2—612no—
607C2—612no—
608C2—612no—
609C2—612no—
610C2#2146229911yescharacteristic
611C2#2146231011yescharacteristic
612C2#2146231911yescharacteristic
613C2D4×C4⋊#692311yescharacteristic
614C2#2146233411yescharacteristic
615C2#2146234711yescharacteristic
616C2#2146236111yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#389C4
prime radical, cosocleC23×D61C24
hypercenter#389#6923
hypocenterC61#14439
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
32. #16839661C4semidirect
33. #16839660C4semidirect
34. #16839659C4semidirect
35. #16839658C4semidirect
36. #16839657C4semidirect
38. C61×#389C4semidirect
165. C4⋊C4×C61C4⋊C4semidirect
169. C4⋊Dic61C4⋊C4semidirect
173. #11758196C4⋊C4semidirect
332. #389#6923semidirect
347. C61#14439semidirect
480. C4⋊C4C4⋊#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168407132
C2×#168407112
#214610052
#214610042
#214609992
#214609972
#214609952
#389×D612
#1443961