Finite Group Databasebeta

← #29610758

Subgroups — #29610758

Order 15616.

1130 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839693C211yesmaximal, characteristic
2C2×#16839646C211yesmaximal, characteristic
3#21444087C211yesmaximal, characteristic
4#21444085C212yesmaximal
5#21444078C212yesmaximal
6#21444078C211yesmaximal, characteristic
7#21444077C212yesmaximal
8#21444069C211yesmaximal, characteristic
9#21444069C212yesmaximal
10#21444046C211yesmaximal, characteristic
11C2×C61×#389C211yesmaximal, characteristic
12C22×#11758196C2211yescharacteristic
13C22×#11758196C2211yescharacteristic
14C22×#11758196C2212yes—
15#16839693C418yescomplemented
16#16839646—24no—
17C2×#14519684C2211yescharacteristic
18C2×#14519684C2211yescharacteristic
19C2×#14519684C2211yescharacteristic
20C2×#14519684C2211yescharacteristic
21C2×#14519684C2211yescharacteristic
22C2×#14519684C2212yes—
23C2×#14519684C2212yes—
24C2×#14519684C2212yes—
25C2×#14519684C2212yes—
26C2×#14519684C2212yes—
27C2×#14519684C2212yes—
28C2×#14519684C2212yes—
29C2×#14519684C2212yes—
30C2×#14519684C2211yescharacteristic
31C2×#14519684C2212yes—
32C22×C4⋊C4×C61C2211yescharacteristic
33C22×C4⋊C4×C61C2211yescharacteristic
34C22×C4⋊C4×C61C2212yes—
35C22×C42×C61C2211yescharacteristic
36C61×#389—24no—
37C2×#95×C61C2212yes—
38C23×Dic61C2311yescharacteristic
39C23×Dic61C2311yescharacteristic
40C23×Dic61C2312yes—
41C23×Dic61C2311yescharacteristic
42C23×Dic61C2311yescharacteristic
43C23×Dic61C2312yes—
44C2×#11758196—22no—
45C2×#11758196—22no—
46C2×#11758196—22no—
47C2×#11758196—42no—
48C2×#11758196—42no—
49C2×#11758196—42no—
50C2×#11758196C2×C414yes—
51C2×#11758196C2×C418yes—
52#14519684—22no—
53#14519684—22no—
54#14519684—22no—
55#14519684—22no—
56#14519684—22no—
57#14519684—42no—
58#14519684—42no—
59#14519684—42no—
60#14519684—42no—
61#14519684—42no—
62#14519684—42no—
63#14519684—42no—
64#14519684—42no—
65#14519684C2×C418yes—
66#14519684C2×C414yes—
67C23×C4×C61C2312yes—
68C23×C4×C61C2312yes—
69C23×C4×C61C2311yescharacteristic
70C23×C4×C61C2311yescharacteristic
71C23×C4×C61C2311yescharacteristic
72C2×C4⋊C4×C61—22no—
73C2×C4⋊C4×C61—22no—
74C2×C4⋊C4×C61—24no—
75C2×C4⋊C4×C61—22no—
76C2×C4⋊C4×C61—42no—
77C2×C4⋊C4×C61—42no—
78C2×C4⋊C4×C61—42no—
79C2×C4⋊C4×C61C2×C414yes—
80C2×C42×C61—42no—
81C2×C42×C61D414yes—
82#95×C61—24no—
83C24×C61C2411yescharacteristic
84C22×C4×C61—22no—
85C22×C4×C61—22no—
86C22×C4×C61—22no—
87C22×C4×C61—22no—
88C22×C4×C61—22no—
89C22×C4×C61—22no—
90C22×C4×C61—21no—
91C22×C4×C61—21no—
92C22×C4×C61—22no—
93C22×C4×C61—22no—
94C22×C4×C61—21no—
95C22×C4×C61—22no—
96C22×C4×C61—22no—
97C22×C4×C61—22no—
98C22×C4×C61—22no—
99C22×C4×C61—21no—
100C22×C4×C61—22no—
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×C61C22×C414yes—
108C22×C4×C61C22×C412yes—
109C22×C4×C61C2×D412yes—
110C22×C4×C61C2×D412yes—
111C22×C4×C61C2×D412yes—
112C22×C4×C61#4112yes—
113C22×Dic61—21no—
114C22×Dic61—21no—
115C22×Dic61—21no—
116C22×Dic61—21no—
117C22×Dic61—21no—
118C22×Dic61—22no—
119C22×Dic61—22no—
120C22×Dic61—22no—
121C22×Dic61—22no—
122C22×Dic61—21no—
123C22×Dic61—21no—
124C22×Dic61—22no—
125C22×Dic61—22no—
126C22×Dic61—22no—
127C22×Dic61—21no—
128C22×Dic61—22no—
129C22×Dic61—21no—
130C22×Dic61—21no—
131C22×Dic61—22no—
132C22×Dic61—21no—
133C22×Dic61—21no—
134C22×Dic61—21no—
135C22×Dic61—22no—
136C22×Dic61—22no—
137C22×Dic61—22no—
138C22×Dic61—22no—
139C22×Dic61—22no—
140C22×Dic61—22no—
141C22×Dic61—22no—
142C22×Dic61—21no—
143C22×Dic61—22no—
144C22×Dic61—22no—
145C22×Dic61—22no—
146C22×Dic61C22×C412yes—
147C22×Dic61C22×C414yes—
148C22×Dic61C22×C412yes—
149C4⋊C4×C61—28no—
150C4⋊C4×C61—44no—
151C4⋊C4×C61—48no—
152C42×C61—44no—
153#11758196—28no—
154#11758196—48no—
155#11758196—44no—
156C23×C61C23×C411yescharacteristic
157C23×C61C22×D411yescharacteristic
158C23×C61C2×#4111yescharacteristic
159C23×C61H(5,𝔽2)11yescharacteristic
160C23×C61H(5,𝔽2)11yescharacteristic
161C23×C61H(5,𝔽2)12yes—
162C23×C61H(5,𝔽2)11yescharacteristic
163C23×C612−1+412yes—
164C23×C612−1+412yes—
165C23×C612−1+412yes—
166C23×C612−1+411yescharacteristic
167C2×C4×C61—24no—
168C2×C4×C61—22no—
169C2×C4×C61—22no—
170C2×C4×C61—24no—
171C2×C4×C61—24no—
172C2×C4×C61—24no—
173C2×C4×C61—24no—
174C2×C4×C61—22no—
175C2×C4×C61—22no—
176C2×C4×C61—22no—
177C2×C4×C61—22no—
178C2×C4×C61—22no—
179C2×C4×C61—22no—
180C2×C4×C61—42no—
181C2×C4×C61—42no—
182C2×C4×C61—42no—
183C2×C4×C61—42no—
184C2×C4×C61—42no—
185C2×C4×C61—42no—
186C2×C4×C61—42no—
187C2×C4×C61—42no—
188C2×C4×C61—42no—
189C2×C4×C61—42no—
190C2×C4×C61—42no—
191C2×C4×C61—42no—
192C2×C4×C61—42no—
193C2×C4×C61—42no—
194C2×C4×C61—42no—
195C2×C4×C61C4×D414yes—
196C2×Dic61—22no—
197C2×Dic61—22no—
198C2×Dic61—22no—
199C2×Dic61—24no—
200C2×Dic61—24no—
201C2×Dic61—24no—
202C2×Dic61—22no—
203C2×Dic61—24no—
204C2×Dic61—41no—
205C2×Dic61—41no—
206C2×Dic61—41no—
207C2×Dic61—41no—
208C2×Dic61—42no—
209C2×Dic61—41no—
210C2×Dic61—41no—
211C2×Dic61—42no—
212C2×Dic61—42no—
213C2×Dic61—42no—
214C2×Dic61—42no—
215C2×Dic61—41no—
216C2×Dic61—41no—
217C2×Dic61—41no—
218C2×Dic61—41no—
219C2×Dic61—41no—
220C2×Dic61—41no—
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—
232#14631—611nomaximal, Sylow
233C22×C61C2×C4×D411yescharacteristic
234C22×C61#51811yescharacteristic
235C22×C61#51912yes—
236C22×C61#52011yescharacteristic
237C22×C61#52012yes—
238C22×C61#53411yescharacteristic
239C22×C61#53511yescharacteristic
240C22×C61#53611yescharacteristic
241C22×C61#53611yescharacteristic
242C22×C61#53611yescharacteristic
243C22×C61#53711yescharacteristic
244C22×C61#53912yes—
245C22×C61#54011yescharacteristic
246C22×C61#54112yes—
247C22×C61#54211yescharacteristic
248C22×C61#56212yes—
249C22×C61#56212yes—
250C22×C61#56212yes—
251C22×C61#56312yes—
252C22×C61#56312yes—
253C22×C61#56312yes—
254C22×C61#56312yes—
255C22×C61#56412yes—
256C4×C61—24no—
257C4×C61—42no—
258C4×C61—44no—
259C4×C61—42no—
260C4×C61—82no—
261Dic61—42no—
262Dic61—42no—
263Dic61—44no—
264Dic61—81no—
265Dic61—82no—
266Dic61—81no—
267C2×#398—611no—
268C2×#389D6111yescharacteristic
269C2×#387—611no—
270#1445—612no—
271#1445—611no—
272#1442—612no—
273#1442—611no—
274#1442—612no—
275#1441—611no—
276#1441—612no—
277#1434—611no—
278C2×C61#232211yescharacteristic
279C2×C61#232411yescharacteristic
280C2×C61#232711yescharacteristic
281C2×C61#237812yes—
282C2×C61#238212yes—
283C2×C61#281411yescharacteristic
284C2×C61#281611yescharacteristic
285C2×C61#282111yescharacteristic
286C2×C61#282211yescharacteristic
287C2×C61#283612yes—
288C2×C61#283912yes—
289C22×C4⋊C4—611no—
290C22×C4⋊C4—612no—
291C22×C4⋊C4—611no—
292C22×C4⋊C4C2×D6111yescharacteristic
293C22×C4⋊C4C2×D6111yescharacteristic
294C22×C4⋊C4C2×D6112yes—
295C22×C42C2×D6111yescharacteristic
296#398—618no—
297#389—24no—
298#387—1224no—
299C2×#95—611no—
300C2×#95—612no—
301C2×#95—611no—
302C2×#95—611no—
303C2×#95—611no—
304C2×#95—611no—
305C2×#95—611no—
306C2×#95—612no—
307C2×#95—612no—
308C2×#95—612no—
309C2×#95—612no—
310C2×#95—612no—
311C2×#95—612no—
312C2×#95—612no—
313C2×#95—612no—
314C2×#95C2×D6112yes—
315C61#1463111yescharacteristic, complemented, Sylow
316C23×C4—611no—
317C23×C4—611no—
318C23×C4—612no—
319C23×C4—611no—
320C23×C4—611no—
321C23×C4—612no—
322C23×C4C22×D6112yes—
323C23×C4C22×D6112yes—
324C23×C4C22×D6111yescharacteristic
325C23×C4C22×D6111yescharacteristic
326C23×C4C22×D6111yescharacteristic
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—614no—
335C2×C4⋊C4—618no—
336C2×C4⋊C4—1222no—
337C2×C4⋊C4—1222no—
338C2×C4⋊C4—1222no—
339C2×C4⋊C4—2442no—
340C2×C4⋊C4—2442no—
341C2×C4⋊C4—2442no—
342C2×C4⋊C4C4×D6114yes—
343C2×C42—42no—
344C2×C42C22⋊D6114yes—
345#95—24no—
346#95—618no—
347#95—614no—
348#95—1222no—
349#95—1222no—
350#95—1222no—
351#95—1222no—
352#95—1222no—
353#95—2442no—
354#95—2442no—
355#95—2442no—
356#95—2442no—
357#95—2442no—
358#95—2442no—
359#95—2442no—
360#95—2442no—
361C24C23×D6111yescharacteristic
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—22no—
372C22×C4—21no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—21no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—612no—
386C22×C4—614no—
387C22×C4—612no—
388C22×C4—1221no—
389C22×C4—1221no—
390C22×C4—1221no—
391C22×C4—1221no—
392C22×C4—1221no—
393C22×C4—1222no—
394C22×C4—1222no—
395C22×C4—1222no—
396C22×C4—1221no—
397C22×C4—1222no—
398C22×C4—1221no—
399C22×C4—1222no—
400C22×C4—1221no—
401C22×C4—1222no—
402C22×C4—1222no—
403C22×C4—1222no—
404C22×C4—1221no—
405C22×C4—1221no—
406C22×C4—1222no—
407C22×C4—1222no—
408C22×C4—1222no—
409C22×C4—1221no—
410C22×C4—1221no—
411C22×C4—1222no—
412C22×C4—1221no—
413C22×C4—1222no—
414C22×C4—1222no—
415C22×C4—1221no—
416C22×C4—1222no—
417C22×C4—1222no—
418C22×C4—1222no—
419C22×C4—1222no—
420C22×C4—1222no—
421C22×C4C2×C4×D6114yes—
422C22×C4C2×C4×D6112yes—
423C22×C4#1175822212yes—
424C22×C4C2×C22⋊D6112yes—
425C22×C4C2×C22⋊D6112yes—
426C22×C4C2×C22⋊D6112yes—
427C4⋊C4—28no—
428C4⋊C4—44no—
429C4⋊C4—48no—
430C4⋊C4—1228no—
431C4⋊C4—2448no—
432C4⋊C4—2444no—
433C42—44no—
434C23C22×C4×D6111yescharacteristic
435C23C22×C22⋊D6111yescharacteristic
436C23C2×#1175822211yescharacteristic
437C23#1451982211yescharacteristic
438C23#1451982211yescharacteristic
439C23#1451982212yes—
440C23#1451982311yescharacteristic
441C23#1451982412yes—
442C23#1451982411yescharacteristic
443C23#1451982512yes—
444C23#1451982512yes—
445C2×C4—24no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—24no—
449C2×C4—24no—
450C2×C4—24no—
451C2×C4—24no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—1222no—
474C2×C4—1222no—
475C2×C4—1222no—
476C2×C4—1224no—
477C2×C4—1224no—
478C2×C4—1222no—
479C2×C4—1224no—
480C2×C4—1224no—
481C2×C4—2442no—
482C2×C4—2442no—
483C2×C4—2442no—
484C2×C4—2442no—
485C2×C4—2442no—
486C2×C4—2442no—
487C2×C4—2442no—
488C2×C4—2442no—
489C2×C4—2441no—
490C2×C4—2441no—
491C2×C4—2441no—
492C2×C4—2441no—
493C2×C4—2441no—
494C2×C4—2441no—
495C2×C4—2442no—
496C2×C4—2442no—
497C2×C4—2442no—
498C2×C4—2442no—
499C2×C4—2442no—
500C2×C4—2442no—
501C2×C4—2442no—
502C2×C4—2441no—
503C2×C4—2441no—
504C2×C4—2441no—
505C2×C4—2441no—
506C2×C4—2442no—
507C2×C4—2441no—
508C2×C4—2441no—
509C2×C4C4×C22⋊D6114yes—
510C22C2×C4×C22⋊D6111yescharacteristic
511C22#1684023411yescharacteristic
512C22#1684023812yes—
513C22#1684024111yescharacteristic
514C22#1684024312yes—
515C22#1684032111yescharacteristic
516C22#1684032911yescharacteristic
517C22#1684033311yescharacteristic
518C22#1684033611yescharacteristic
519C22#1684033611yescharacteristic
520C22#1684034011yescharacteristic
521C22#1684035912yes—
522C22#1684036311yescharacteristic
523C22#1684037012yes—
524C22#1684037711yescharacteristic
525C22#1684050712yes—
526C22#1684050712yes—
527C22#1684050812yes—
528C22#1684051112yes—
529C22#1684051112yes—
530C22#1684051312yes—
531C22#1684051612yes—
532C22C61⋊#56412yes—
533C4—24no—
534C4—42no—
535C4—42no—
536C4—44no—
537C4—82no—
538C4—4881no—
539C4—4881no—
540C4—4882no—
541C4—2444no—
542C4—2442no—
543C4—2442no—
544C2#2144848811yescharacteristic
545C2#2144850611yescharacteristic
546C2#2144853511yescharacteristic
547C2#2144898112yes—
548C2#2144900112yes—
549C2#2145383011yescharacteristic
550C2#2145384711yescharacteristic
551C2#2145387811yescharacteristic
552C2#2145388611yescharacteristic
553C2#2145401412yes—
554C2#2145405912yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#389C2
socle, prime radical, cosocleC24×C61C24
hypercenterC2×#389D61
hypocenterC61#14631
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
15. #16839693C4semidirect
315. C61#14631semidirect

Maximal subgroups

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

subgroupindex
C2×#168396932
C2×#168396462
#214440872
#214440852
#214440782
#214440772
#214440692
#214440462
C2×C61×#3892
#1463161