Finite Group Databasebeta

← #29606984

Subgroups — #29606984

Order 15616.

1254 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839701C211yesmaximal, characteristic
2C2×#16839660C211yesmaximal, characteristic
3#21444088C211yesmaximal, characteristic
4#21444083C211yesmaximal, characteristic
5#21444082C212yesmaximal
6#21444077C212yesmaximal
7#21444072C211yesmaximal, characteristic
8#21444052C212yesmaximal
9#21444046C212yesmaximal
10#21444046C211yesmaximal, characteristic
11C2×C4×C4⋊C4×C61C211yesmaximal, characteristic
12C22×C4⋊Dic61C2211yescharacteristic
13C22×C4⋊Dic61C2211yescharacteristic
14C22×#11758196C2212yes—
15C22×#11758196C2212yes—
16#16839701C418yescomplemented
17#16839660—24no—
18C2×#14519684C2212yes—
19C2×#14519684C2212yes—
20C2×#14519684C2212yes—
21C2×#14519684C2211yescharacteristic
22C2×#14519684C2212yes—
23C2×#14519684C2212yes—
24C2×#14519684C2212yes—
25C2×#14519684C2212yes—
26C2×#14519684C2212yes—
27C2×#14519684C2212yes—
28C2×#14519684C2211yescharacteristic
29C2×#14519684C2212yes—
30C22×C4⋊C4×C61C2211yescharacteristic
31C22×C4⋊C4×C61C2211yescharacteristic
32C22×C42×C61C2211yescharacteristic
33C22×C42×C61C2211yescharacteristic
34C22×C42×C61C2211yescharacteristic
35C4×C4⋊C4×C61—24no—
36C2×#95×C61C2211yescharacteristic
37C2×#95×C61C2211yescharacteristic
38C23×Dic61C2312yes—
39C23×Dic61C2312yes—
40C23×Dic61C2312yes—
41C23×Dic61C2312yes—
42C2×C4⋊Dic61—22no—
43C2×C4⋊Dic61—22no—
44C2×C4⋊Dic61—22no—
45C2×C4⋊Dic61—42no—
46C2×C4⋊Dic61C2×C414yes—
47C2×#11758196—24no—
48C2×#11758196—24no—
49C2×#11758196—42no—
50C2×#11758196—42no—
51C2×#11758196—42no—
52C2×#11758196—42no—
53#14519684—24no—
54#14519684—24no—
55#14519684—22no—
56#14519684—24no—
57#14519684—42no—
58#14519684—42no—
59#14519684—42no—
60#14519684—42no—
61#14519684—42no—
62#14519684C2×C414yes—
63#14519684C2×C418yes—
64#14519684C2×C418yes—
65C23×C4×C61C2311yescharacteristic
66C23×C4×C61C2311yescharacteristic
67C23×C4×C61C2311yescharacteristic
68C23×C4×C61C2311yescharacteristic
69C23×C4×C61C2311yescharacteristic
70C23×C4×C61C2311yescharacteristic
71C23×C4×C61C2311yescharacteristic
72C2×C4⋊C4×C61—22no—
73C2×C4⋊C4×C61—22no—
74C2×C4⋊C4×C61—22no—
75C2×C4⋊C4×C61—22no—
76C2×C4⋊C4×C61—22no—
77C2×C4⋊C4×C61C2×C414yes—
78C2×C42×C61—22no—
79C2×C42×C61—22no—
80C2×C42×C61—22no—
81C2×C42×C61—42no—
82C2×C42×C61—42no—
83C2×C42×C61D414yes—
84C2×C42×C61Q814yes—
85#95×C61—22no—
86#95×C61—22no—
87C24×C61C2411yescharacteristic
88C22×C4×C61—21no—
89C22×C4×C61—21no—
90C22×C4×C61—21no—
91C22×C4×C61—21no—
92C22×C4×C61—22no—
93C22×C4×C61—22no—
94C22×C4×C61—22no—
95C22×C4×C61—22no—
96C22×C4×C61—21no—
97C22×C4×C61—21no—
98C22×C4×C61—21no—
99C22×C4×C61—21no—
100C22×C4×C61—21no—
101C22×C4×C61—21no—
102C22×C4×C61—21no—
103C22×C4×C61—21no—
104C22×C4×C61—22no—
105C22×C4×C61—22no—
106C22×C4×C61—22no—
107C22×C4×C61—22no—
108C22×C4×C61—22no—
109C22×C4×C61—22no—
110C22×C4×C61—22no—
111C22×C4×C61—22no—
112C22×C4×C61C22×C412yes—
113C22×C4×C61C22×C412yes—
114C22×C4×C61C22×C412yes—
115C22×C4×C61C2×D412yes—
116C22×C4×C61C2×D412yes—
117C22×C4×C61C2×D412yes—
118C22×C4×C61C2×Q812yes—
119C22×C4×C61C2×Q812yes—
120C22×C4×C61C2×Q812yes—
121C22×C4×C61#4112yes—
122C22×C4×C61#4112yes—
123C22×C4×C61#4112yes—
124C22×C4×C61#4112yes—
125C22×Dic61—22no—
126C22×Dic61—22no—
127C22×Dic61—22no—
128C22×Dic61—22no—
129C22×Dic61—22no—
130C22×Dic61—22no—
131C22×Dic61—22no—
132C22×Dic61—22no—
133C22×Dic61—22no—
134C22×Dic61—22no—
135C22×Dic61—22no—
136C22×Dic61—22no—
137C22×Dic61—22no—
138C22×Dic61—22no—
139C22×Dic61—22no—
140C22×Dic61—22no—
141C22×Dic61—22no—
142C22×Dic61—22no—
143C22×Dic61—22no—
144C22×Dic61—22no—
145C22×Dic61—22no—
146C22×Dic61—22no—
147C22×Dic61—22no—
148C22×Dic61—22no—
149C22×Dic61—22no—
150C22×Dic61—22no—
151C22×Dic61C22×C414yes—
152C22×Dic61C22×C414yes—
153C4⋊C4×C61—28no—
154C4⋊C4×C61—28no—
155C42×C61—28no—
156C42×C61—44no—
157C42×C61—44no—
158C4⋊Dic61—28no—
159C4⋊Dic61—44no—
160#11758196—48no—
161#11758196—48no—
162C23×C61C23×C411yescharacteristic
163C23×C61C22×D411yescharacteristic
164C23×C61C22×Q811yescharacteristic
165C23×C61C2×#4111yescharacteristic
166C23×C61C2×#4111yescharacteristic
167C23×C61C2×#4111yescharacteristic
168C23×C61C2×#4111yescharacteristic
169C23×C61H(5,𝔽2)12yes—
170C23×C61H(5,𝔽2)12yes—
171C23×C612−1+412yes—
172C23×C612−1+412yes—
173C2×C4×C61—22no—
174C2×C4×C61—22no—
175C2×C4×C61—24no—
176C2×C4×C61—22no—
177C2×C4×C61—22no—
178C2×C4×C61—22no—
179C2×C4×C61—22no—
180C2×C4×C61—22no—
181C2×C4×C61—22no—
182C2×C4×C61—22no—
183C2×C4×C61—22no—
184C2×C4×C61—24no—
185C2×C4×C61—24no—
186C2×C4×C61—24no—
187C2×C4×C61—22no—
188C2×C4×C61—24no—
189C2×C4×C61—22no—
190C2×C4×C61—22no—
191C2×C4×C61—22no—
192C2×C4×C61—22no—
193C2×C4×C61—22no—
194C2×C4×C61—24no—
195C2×C4×C61—24no—
196C2×C4×C61—41no—
197C2×C4×C61—41no—
198C2×C4×C61—41no—
199C2×C4×C61—41no—
200C2×C4×C61—41no—
201C2×C4×C61—41no—
202C2×C4×C61—42no—
203C2×C4×C61—42no—
204C2×C4×C61—42no—
205C2×C4×C61—42no—
206C2×C4×C61—42no—
207C2×C4×C61C4×D414yes—
208C2×C4×C61C4×Q814yes—
209C2×C4×C61C22⋊Q814yes—
210C2×Dic61—24no—
211C2×Dic61—24no—
212C2×Dic61—24no—
213C2×Dic61—24no—
214C2×Dic61—24no—
215C2×Dic61—24no—
216C2×Dic61—42no—
217C2×Dic61—42no—
218C2×Dic61—42no—
219C2×Dic61—42no—
220C2×Dic61—42no—
221C2×Dic61—42no—
222C2×Dic61—42no—
223C2×Dic61—42no—
224C2×Dic61—42no—
225C2×Dic61—42no—
226C2×Dic61—42no—
227C2×Dic61—42no—
228C2×Dic61—42no—
229C2×Dic61—42no—
230C2×Dic61—42no—
231C2×Dic61—42no—
232C2×Dic61—42no—
233C2×Dic61—42no—
234C2×Dic61—42no—
235C2×Dic61—42no—
236C2×Dic61—42no—
237C2×Dic61—42no—
238#14318—611nomaximal, Sylow
239C22×C61C2×C4×D411yescharacteristic
240C22×C61C2×C4×Q811yescharacteristic
241C22×C61C4×#4111yescharacteristic
242C22×C61#52012yes—
243C22×C61#52012yes—
244C22×C61C2×C22⋊Q811yescharacteristic
245C22×C61#52511yescharacteristic
246C22×C61#52911yescharacteristic
247C22×C61#53311yescharacteristic
248C22×C61#53411yescharacteristic
249C22×C61#53511yescharacteristic
250C22×C61#53611yescharacteristic
251C22×C61#53611yescharacteristic
252C22×C61#53812yes—
253C22×C61#53912yes—
254C22×C61#53912yes—
255C22×C61#54012yes—
256C22×C61#54112yes—
257C22×C61#54112yes—
258C22×C61#54212yes—
259C22×C61#54212yes—
260C22×C61#54412yes—
261C22×C61#54412yes—
262C4×C61—24no—
263C4×C61—24no—
264C4×C61—24no—
265C4×C61—42no—
266C4×C61—42no—
267C4×C61—42no—
268C4×C61—42no—
269Dic61—44no—
270Dic61—44no—
271Dic61—82no—
272Dic61—82no—
273C2×#400—611no—
274C2×#389—611no—
275C2×C4×C4⋊C4D6111yescharacteristic
276#1445—611no—
277#1444—611no—
278#1444—612no—
279#1442—612no—
280#1441—611no—
281#1436—612no—
282#1434—611no—
283#1434—612no—
284C2×C61C4×C22⋊Q811yescharacteristic
285C2×C61#232211yescharacteristic
286C2×C61#232611yescharacteristic
287C2×C61#233012yes—
288C2×C61#233412yes—
289C2×C61#262711yescharacteristic
290C2×C61#262811yescharacteristic
291C2×C61#263411yescharacteristic
292C2×C61#263511yescharacteristic
293C2×C61#265412yes—
294C2×C61#266612yes—
295C22×C4⋊C4—611no—
296C22×C4⋊C4—612no—
297C22×C4⋊C4—612no—
298C22×C4⋊C4—611no—
299C22×C4⋊C4C2×D6111yescharacteristic
300C22×C4⋊C4C2×D6111yescharacteristic
301C22×C42C2×D6111yescharacteristic
302C22×C42C2×D6111yescharacteristic
303C22×C42C2×D6111yescharacteristic
304#400—618no—
305#389—1224no—
306C4×C4⋊C4—24no—
307C2×#95—612no—
308C2×#95—611no—
309C2×#95—612no—
310C2×#95—612no—
311C2×#95—612no—
312C2×#95—612no—
313C2×#95—611no—
314C2×#95—612no—
315C2×#95—612no—
316C2×#95—612no—
317C2×#95—612no—
318C2×#95—612no—
319C2×#95C2×D6111yescharacteristic
320C2×#95C2×D6111yescharacteristic
321C61#1431811yescharacteristic, complemented, Sylow
322C23×C4—612no—
323C23×C4—612no—
324C23×C4—612no—
325C23×C4—612no—
326C23×C4C22×D6111yescharacteristic
327C23×C4C22×D6111yescharacteristic
328C23×C4C22×D6111yescharacteristic
329C23×C4C22×D6111yescharacteristic
330C23×C4C22×D6111yescharacteristic
331C23×C4C22×D6111yescharacteristic
332C23×C4C22×D6111yescharacteristic
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—614no—
339C2×C4⋊C4—1222no—
340C2×C4⋊C4—1222no—
341C2×C4⋊C4—1224no—
342C2×C4⋊C4—1224no—
343C2×C4⋊C4—1222no—
344C2×C4⋊C4—2442no—
345C2×C4⋊C4—2442no—
346C2×C4⋊C4—2442no—
347C2×C4⋊C4—2442no—
348C2×C4⋊C4—2442no—
349C2×C4⋊C4C4×D6114yes—
350C2×C42—22no—
351C2×C42—22no—
352C2×C42—22no—
353C2×C42—42no—
354C2×C42—42no—
355C2×C42Dic12214yes—
356C2×C42C22⋊D6114yes—
357#95—22no—
358#95—22no—
359#95—614no—
360#95—618no—
361#95—618no—
362#95—1224no—
363#95—1222no—
364#95—1224no—
365#95—1224no—
366#95—2442no—
367#95—2442no—
368#95—2442no—
369#95—2442no—
370#95—2442no—
371C24C23×D6111yescharacteristic
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—614no—
397C22×C4—614no—
398C22×C4—1222no—
399C22×C4—1222no—
400C22×C4—1222no—
401C22×C4—1222no—
402C22×C4—1222no—
403C22×C4—1222no—
404C22×C4—1222no—
405C22×C4—1222no—
406C22×C4—1222no—
407C22×C4—1222no—
408C22×C4—1222no—
409C22×C4—1222no—
410C22×C4—1222no—
411C22×C4—1222no—
412C22×C4—1222no—
413C22×C4—1222no—
414C22×C4—1222no—
415C22×C4—1222no—
416C22×C4—1222no—
417C22×C4—1222no—
418C22×C4—1222no—
419C22×C4—1222no—
420C22×C4—1222no—
421C22×C4—1222no—
422C22×C4—1222no—
423C22×C4—1222no—
424C22×C4C2×Dic12212yes—
425C22×C4C2×Dic12212yes—
426C22×C4C2×Dic12212yes—
427C22×C4C2×C4×D6112yes—
428C22×C4C2×C4×D6112yes—
429C22×C4C2×C4×D6112yes—
430C22×C4#1175822212yes—
431C22×C4#1175822212yes—
432C22×C4#1175822212yes—
433C22×C4#1175822212yes—
434C22×C4C2×C22⋊D6112yes—
435C22×C4C2×C22⋊D6112yes—
436C22×C4C2×C22⋊D6112yes—
437C4⋊C4—28no—
438C4⋊C4—28no—
439C4⋊C4—1228no—
440C4⋊C4—2448no—
441C4⋊C4—2448no—
442C4⋊C4—2444no—
443C42—28no—
444C42—44no—
445C42—44no—
446C23C22×C4×D6111yescharacteristic
447C23C22×C22⋊D6111yescharacteristic
448C23C22×Dic12211yescharacteristic
449C23C2×#1175822211yescharacteristic
450C23C2×#1175822211yescharacteristic
451C23C2×#1175822211yescharacteristic
452C23C2×#1175822211yescharacteristic
453C23#1451982212yes—
454C23#1451982312yes—
455C23#1451982412yes—
456C23#1451982512yes—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—24no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—22no—
472C2×C4—24no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—1224no—
492C2×C4—1224no—
493C2×C4—1224no—
494C2×C4—1224no—
495C2×C4—1224no—
496C2×C4—1224no—
497C2×C4—2442no—
498C2×C4—2442no—
499C2×C4—2442no—
500C2×C4—2442no—
501C2×C4—2442no—
502C2×C4—2442no—
503C2×C4—2442no—
504C2×C4—2442no—
505C2×C4—2442no—
506C2×C4—2442no—
507C2×C4—2442no—
508C2×C4—2442no—
509C2×C4—2442no—
510C2×C4—2442no—
511C2×C4—2442no—
512C2×C4—2442no—
513C2×C4—2442no—
514C2×C4—2442no—
515C2×C4—2442no—
516C2×C4—2442no—
517C2×C4—2442no—
518C2×C4—2442no—
519C2×C4C4×C22⋊D6114yes—
520C2×C4C4×Dic12214yes—
521C2×C4#1451975614yes—
522C22C2×C4×C22⋊D6111yescharacteristic
523C22C2×C4×Dic12211yescharacteristic
524C22C4×#1175822211yescharacteristic
525C22#1684024112yes—
526C22#1684024412yes—
527C22C2×#1451975611yescharacteristic
528C22#1684027311yescharacteristic
529C22#1684029611yescharacteristic
530C22#1684031911yescharacteristic
531C22#1684032111yescharacteristic
532C22#1684032611yescharacteristic
533C22#1684033311yescharacteristic
534C22#1684033611yescharacteristic
535C22#1684034512yes—
536C22#1684035412yes—
537C22#1684035912yes—
538C22#1684036312yes—
539C22#1684037012yes—
540C22#1684037012yes—
541C22#1684038312yes—
542C22#1684038412yes—
543C22#1684039012yes—
544C22#1684039312yes—
545C4—24no—
546C4—24no—
547C4—24no—
548C4—42no—
549C4—42no—
550C4—42no—
551C4—42no—
552C4—4882no—
553C4—4882no—
554C4—2444no—
555C4—2444no—
556C2C4×#1451975611yescharacteristic
557C2#2144848411yescharacteristic
558C2#2144852611yescharacteristic
559C2#2144855612yes—
560C2#2144858812yes—
561C2#2145163211yescharacteristic
562C2#2145164011yescharacteristic
563C2#2145169511yescharacteristic
564C2#2145170311yescharacteristic
565C2#2145189112yes—
566C2#2145199812yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C4×C4⋊C4×C61C2
socle, prime radical, cosocleC24×C61C24
hypercenterC2×C4×C4⋊C4D61
hypocenterC61#14318
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
16. #16839701C4semidirect
321. C61#14318semidirect

Maximal subgroups

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

subgroupindex
C2×#168397012
C2×#168396602
#214440882
#214440832
#214440822
#214440772
#214440722
#214440522
#214440462
C2×C4×C4⋊C4×C612
#1431861