Finite Group Databasebeta

← #29606672

Subgroups — #29606672

Order 15616.

1414 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519767C211yesmaximal, characteristic
2C2×#16839629C211yesmaximal, characteristic
3C2×C4×#11758196C211yesmaximal, characteristic
4#21444085C212yesmaximal
5#21444085C212yesmaximal
6#21444071C212yesmaximal
7#21444070C212yesmaximal
8#21444054C211yesmaximal, characteristic
9#21444052C211yesmaximal, characteristic
10#21444051C211yesmaximal, characteristic
11C61×#1436C211yesmaximal, characteristic
12C2×#14519767—24no—
13C2×#14519767—24no—
14C2×#14519767C418yescomplemented
15C22×C4⋊Dic61C2211yescharacteristic
16C22×#11758196C2212yes—
17C22×#11758196C2211yescharacteristic
18C22×#11758196C2211yescharacteristic
19C22×#11758196C2211yescharacteristic
20C22×#11758196C2211yescharacteristic
21C22×C4×Dic61C2211yescharacteristic
22C22×C4×Dic61C2211yescharacteristic
23#16839629—24no—
24C4×#11758196—24no—
25C2×#14519684C2211yescharacteristic
26C2×#14519684C2212yes—
27C2×#14519684C2212yes—
28C2×#14519684C2212yes—
29C2×#14519684C2212yes—
30C2×#14519684C2212yes—
31C2×#14519684C2212yes—
32C2×#14519684C2212yes—
33C2×#14519684C2212yes—
34C2×#14519684C2212yes—
35C22×C4⋊C4×C61C2211yescharacteristic
36C22×C42×C61C2211yescharacteristic
37C2×#95×C61C2211yescharacteristic
38C2×#95×C61C2212yes—
39C2×#95×C61C2212yes—
40C23×Dic61C2312yes—
41C23×Dic61C2311yescharacteristic
42C23×Dic61C2311yescharacteristic
43C23×Dic61C2312yes—
44C23×Dic61C2311yescharacteristic
45C23×Dic61C2311yescharacteristic
46#14519767—232no—
47C2×C4⋊Dic61—22no—
48C2×C4⋊Dic61—22no—
49C2×C4⋊Dic61C2×C414yes—
50C2×#11758196—22no—
51C2×#11758196—22no—
52C2×#11758196—24no—
53C2×#11758196—22no—
54C2×#11758196—22no—
55C2×#11758196—22no—
56C2×#11758196—22no—
57C2×#11758196—22no—
58C2×#11758196—22no—
59C2×#11758196—24no—
60C2×#11758196—24no—
61C2×#11758196C2×C414yes—
62C2×#11758196C2×C414yes—
63C2×#11758196C2×C414yes—
64C2×#11758196C2×C414yes—
65C2×C4×Dic61—22no—
66C2×C4×Dic61—42no—
67C2×C4×Dic61C2×C414yes—
68C2×C4×Dic61D414yes—
69C2×C4×Dic61D414yes—
70#14519684—22no—
71#14519684—24no—
72#14519684—24no—
73#14519684—24no—
74#14519684—24no—
75#14519684—24no—
76#14519684—24no—
77#14519684—42no—
78#14519684—42no—
79#14519684—42no—
80C23×C4×C61C2312yes—
81C23×C4×C61C2311yescharacteristic
82C23×C4×C61C2311yescharacteristic
83C23×C4×C61C2312yes—
84C23×C4×C61C2311yescharacteristic
85C2×C4⋊C4×C61—22no—
86C2×C4⋊C4×C61—22no—
87C2×C4⋊C4×C61C2×C414yes—
88C2×C42×C61—22no—
89C2×C42×C61—42no—
90#95×C61—22no—
91#95×C61—24no—
92#95×C61—42no—
93C24×C61C2411yescharacteristic
94C22×C4×C61—22no—
95C22×C4×C61—22no—
96C22×C4×C61—22no—
97C22×C4×C61—21no—
98C22×C4×C61—21no—
99C22×C4×C61—21no—
100C22×C4×C61—21no—
101C22×C4×C61—22no—
102C22×C4×C61—22no—
103C22×C4×C61—22no—
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×C61—22no—
113C22×C4×C61—22no—
114C22×C4×C61—22no—
115C22×C4×C61—22no—
116C22×C4×C61—22no—
117C22×C4×C61C22×C412yes—
118C22×C4×C61C22×C412yes—
119C22×C4×C61C22×C412yes—
120C22×C4×C61C2×D412yes—
121C22×C4×C61C2×D412yes—
122C22×C4×C61#4114yes—
123C22×Dic61—22no—
124C22×Dic61—22no—
125C22×Dic61—22no—
126C22×Dic61—22no—
127C22×Dic61—22no—
128C22×Dic61—21no—
129C22×Dic61—21no—
130C22×Dic61—21no—
131C22×Dic61—21no—
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×Dic61C22×C412yes—
149C22×Dic61C22×C412yes—
150C22×Dic61C22×C412yes—
151C22×Dic61C22×C412yes—
152C22×Dic61C2×D412yes—
153C22×Dic61C2×D412yes—
154C22×Dic61C2×D412yes—
155C22×Dic61C2×D412yes—
156C22×Dic61#4114yes—
157C4⋊C4×C61—28no—
158C42×C61—44no—
159C4⋊Dic61—28no—
160#11758196—216no—
161#11758196—28no—
162#11758196—28no—
163#11758196—28no—
164#11758196—28no—
165C4×Dic61—44no—
166C4×Dic61C22⋊C4116yes—
167C23×C61C23×C411yescharacteristic
168C23×C61C22×D411yescharacteristic
169C23×C61C22×D411yescharacteristic
170C23×C61C2×#4112yes—
171C23×C61C2×#4112yes—
172C23×C61H(5,𝔽2)12yes—
173C23×C612−1+412yes—
174C23×C612−1+412yes—
175C23×C612−1+412yes—
176C2×C4×C61—24no—
177C2×C4×C61—22no—
178C2×C4×C61—22no—
179C2×C4×C61—24no—
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—24no—
188C2×C4×C61—42no—
189C2×C4×C61—42no—
190C2×C4×C61—42no—
191C2×C4×C61—41no—
192C2×C4×C61—41no—
193C2×C4×C61—42no—
194C2×C4×C61—42no—
195C2×C4×C61—42no—
196C2×C4×C61—42no—
197C2×C4×C61—42no—
198C2×C4×C61—42no—
199C2×C4×C61—42no—
200C2×C4×C61—42no—
201C2×C4×C61—42no—
202C2×C4×C61—42no—
203C2×C4×C61—42no—
204C2×C4×C61C2×C22⋊C414yes—
205C2×Dic61—22no—
206C2×Dic61—22no—
207C2×Dic61—24no—
208C2×Dic61—24no—
209C2×Dic61—24no—
210C2×Dic61—22no—
211C2×Dic61—24no—
212C2×Dic61—22no—
213C2×Dic61—22no—
214C2×Dic61—22no—
215C2×Dic61—22no—
216C2×Dic61—22no—
217C2×Dic61—24no—
218C2×Dic61—24no—
219C2×Dic61—24no—
220C2×Dic61—24no—
221C2×Dic61—42no—
222C2×Dic61—42no—
223C2×Dic61—42no—
224C2×Dic61—41no—
225C2×Dic61—41no—
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×Dic61C2×C22⋊C414yes—
238C2×Dic61C2×C22⋊C414yes—
239#14289—611nomaximal, Sylow
240C22×C61C22×C22⋊C411yescharacteristic
241C22×C61C4×#4111yescharacteristic
242C22×C61C4×#4111yescharacteristic
243C22×C61#51912yes—
244C22×C61#52012yes—
245C22×C61#52512yes—
246C22×C61#53212yes—
247C22×C61#53511yescharacteristic
248C22×C61#53611yescharacteristic
249C22×C61#53611yescharacteristic
250C22×C61#53612yes—
251C22×C61#53611yescharacteristic
252C22×C61#53712yes—
253C22×C61#53912yes—
254C22×C61#53912yes—
255C22×C61#53912yes—
256C22×C61#53912yes—
257C22×C61#54112yes—
258C22×C61#54112yes—
259C22×C61#54112yes—
260C22×C61#54112yes—
261C4×C61—24no—
262C4×C61—42no—
263C4×C61—44no—
264C4×C61—42no—
265C4×C61—82no—
266Dic61—24no—
267Dic61—24no—
268Dic61—42no—
269Dic61—44no—
270Dic61—42no—
271Dic61—82no—
272C22×#125—611no—
273C2×#383—611no—
274C2×C4×C4⋊C4—611no—
275#1445—612no—
276#1445—612no—
277#1441—612no—
278#1441—612no—
279#1436—611no—
280#1436—611no—
281#1436—611no—
282#1436D6111yescharacteristic
283C2×C61#229711yescharacteristic
284C2×C61#231011yescharacteristic
285C2×C61#231111yescharacteristic
286C2×C61#233612yes—
287C2×C61#233612yes—
288C2×C61#263312yes—
289C2×C61#263412yes—
290C2×C61#266412yes—
291C2×C61#266412yes—
292C2×#125—618no—
293C2×#125—1224no—
294C2×#125—1224no—
295C22×C4⋊C4—611no—
296C22×C4⋊C4—611no—
297C22×C4⋊C4—611no—
298C22×C4⋊C4—611no—
299C22×C4⋊C4—611no—
300C22×C4⋊C4—612no—
301C22×C4⋊C4C2×D6111yescharacteristic
302C22×C42—611no—
303C22×C42—611no—
304C22×C42C2×D6111yescharacteristic
305#383—1224no—
306C4×C4⋊C4—1224no—
307C2×#95—611no—
308C2×#95—612no—
309C2×#95—612no—
310C2×#95—612no—
311C2×#95—612no—
312C2×#95—612no—
313C2×#95—612no—
314C2×#95—612no—
315C2×#95—612no—
316C2×#95—612no—
317C2×#95C2×D6111yescharacteristic
318C2×#95C2×D6112yes—
319C2×#95C2×D6112yes—
320C61#1428911yescharacteristic, complemented, Sylow
321C23×C4—611no—
322C23×C4—611no—
323C23×C4—611no—
324C23×C4—611no—
325C23×C4—612no—
326C23×C4—612no—
327C23×C4C22×D6112yes—
328C23×C4C22×D6111yescharacteristic
329C23×C4C22×D6111yescharacteristic
330C23×C4C22×D6112yes—
331C23×C4C22×D6111yescharacteristic
332#125—12232no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—614no—
336C2×C4⋊C4—614no—
337C2×C4⋊C4—614no—
338C2×C4⋊C4—614no—
339C2×C4⋊C4—614no—
340C2×C4⋊C4—1222no—
341C2×C4⋊C4—1222no—
342C2×C4⋊C4—1222no—
343C2×C4⋊C4—1222no—
344C2×C4⋊C4—1222no—
345C2×C4⋊C4—1222no—
346C2×C4⋊C4—1222no—
347C2×C4⋊C4—1222no—
348C2×C4⋊C4—1224no—
349C2×C4⋊C4—1224no—
350C2×C4⋊C4—1224no—
351C2×C4⋊C4—1222no—
352C2×C4⋊C4—1222no—
353C2×C4⋊C4C4×D6114yes—
354C2×C42—22no—
355C2×C42—42no—
356C2×C42—614no—
357C2×C42—614no—
358C2×C42—614no—
359C2×C42—1222no—
360C2×C42—2442no—
361#95—24no—
362#95—22no—
363#95—42no—
364#95—1224no—
365#95—1224no—
366#95—1224no—
367#95—1224no—
368#95—1224no—
369#95—1224no—
370#95—1222no—
371#95—2442no—
372#95—2442no—
373#95—2442no—
374C24C23×D6111yescharacteristic
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
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—22no—
397C22×C4—22no—
398C22×C4—612no—
399C22×C4—612no—
400C22×C4—612no—
401C22×C4—612no—
402C22×C4—612no—
403C22×C4—612no—
404C22×C4—612no—
405C22×C4—612no—
406C22×C4—614no—
407C22×C4—1222no—
408C22×C4—1222no—
409C22×C4—1222no—
410C22×C4—1222no—
411C22×C4—1222no—
412C22×C4—1221no—
413C22×C4—1221no—
414C22×C4—1221no—
415C22×C4—1221no—
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×C4—1222no—
425C22×C4—1222no—
426C22×C4—1222no—
427C22×C4—1222no—
428C22×C4—1222no—
429C22×C4—1222no—
430C22×C4—1222no—
431C22×C4—1222no—
432C22×C4C2×C4×D6112yes—
433C22×C4C2×C4×D6112yes—
434C22×C4C2×C4×D6112yes—
435C22×C4#1175822214yes—
436C22×C4D4×D6112yes—
437C22×C4D4×D6112yes—
438C4⋊C4—28no—
439C4⋊C4—1228no—
440C4⋊C4—1228no—
441C4⋊C4—1228no—
442C4⋊C4—1228no—
443C4⋊C4—12216no—
444C4⋊C4—1228no—
445C42—44no—
446C42—6116no—
447C42—2444no—
448C23C22×C4×D6111yescharacteristic
449C23C2×D4×D6111yescharacteristic
450C23C2×D4×D6111yescharacteristic
451C23#41×D6112yes—
452C23C2×#1175822212yes—
453C23#1451982212yes—
454C23#1451982412yes—
455C23#1451982412yes—
456C23#1451982512yes—
457C2×C4—24no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—24no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—614no—
486C2×C4—614no—
487C2×C4—1222no—
488C2×C4—1222no—
489C2×C4—1224no—
490C2×C4—1224no—
491C2×C4—1224no—
492C2×C4—1222no—
493C2×C4—1224no—
494C2×C4—1222no—
495C2×C4—1222no—
496C2×C4—1222no—
497C2×C4—1222no—
498C2×C4—1222no—
499C2×C4—1224no—
500C2×C4—1224no—
501C2×C4—1224no—
502C2×C4—1224no—
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—2441no—
514C2×C4—2441no—
515C2×C4—2442no—
516C2×C4—2442no—
517C2×C4—2442no—
518C2×C4—2442no—
519C2×C4C22⋊C4×D6114yes—
520C22C2×C22⋊C4×D6111yescharacteristic
521C22#1684023011yescharacteristic
522C22C4×#1175822211yescharacteristic
523C22#1684023812yes—
524C22#1684024112yes—
525C22#1684027112yes—
526C22#1684030912yes—
527C22#1684032711yescharacteristic
528C22#1684033211yescharacteristic
529C22#1684033411yescharacteristic
530C22#1684033512yes—
531C22#1684033711yescharacteristic
532C22#1684033912yes—
533C22#1684035412yes—
534C22#1684035512yes—
535C22#1684035812yes—
536C22#1684035912yes—
537C22#1684036912yes—
538C22#1684037012yes—
539C22#1684037112yes—
540C22#1684037412yes—
541C4—24no—
542C4—42no—
543C4—44no—
544C4—42no—
545C4—82no—
546C4—1224no—
547C4—1224no—
548C4—4882no—
549C4—2442no—
550C4—2444no—
551C4—2442no—
552C2#2144830511yescharacteristic
553C2#2144840211yescharacteristic
554C2#2144840611yescharacteristic
555C2#2144861812yes—
556C2#2144862112yes—
557C2#2145169112yes—
558C2#2145169912yes—
559C2#2145198212yes—
560C2#2145198412yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1436C2
socle, prime radical, cosocleC24×C61C24
hypercenter#1436D61
hypocenterC61#14289
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
14. C2×#14519767C4semidirect
320. C61#14289semidirect

Maximal subgroups

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

subgroupindex
C22×#145197672
C2×#168396292
C2×C4×#117581962
#214440852
#214440712
#214440702
#214440542
#214440522
#214440512
C61×#14362
#1428961