Finite Group Databasebeta

← #30602423

Subgroups — #30602423

Order 15616.

1510 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519856C211yesmaximal, characteristic
2C2×#16840705C211yesmaximal, characteristic
3C2×#16840640C214yesmaximal
4C2×#16839624C211yesmaximal, characteristic
5C2×#14519856—28no—
6C2×#14519856—22no—
7C2×#14519856C414yescomplemented
8C22×C4⋊#6923—21no—
9C22×C22⋊#6923C2212yes—
10C22×C22⋊#6923C2212yes—
11C22×C4×#6923—21no—
12#16840705—22no—
13#16840705C414yescomplemented
14C2×(C2×#6923)⋊C4—21no—
15C2×(C2×#6923)⋊C4—21no—
16#16840640—28no—
17C23×C4×D61C2211yescharacteristic
18C22×#11758198C2212yes—
19#16839624—21no—
20#16839624—21no—
21#16839624—21no—
22#16839624—21no—
23C2×#14519684C412yescomplemented
24C2×#14519684C411yescharacteristic, complemented
25C2×#95×C61C411yescharacteristic, complemented
26C23×#6923—22no—
27C23×#6923—22no—
28#14519856—216no—
29#14519856—216no—
30C2×C4⋊#6923—28no—
31C2×C4⋊#6923—24no—
32C2×C22⋊#6923—24no—
33C2×C22⋊#6923—22no—
34C2×C22⋊#6923—24no—
35C2×C22⋊#6923—24no—
36C2×C22⋊#6923—22no—
37C2×C22⋊#6923C2×C414yes—
38C2×C22⋊#6923C2×C414yes—
39C2×C22⋊#6923D418yes—
40C2×C4×#6923—28no—
41C2×C4×#6923—24no—
42(C2×#6923)⋊C4—24no—
43(C2×#6923)⋊C4—24no—
44C24×D61C2311yescharacteristic
45C23×Dic61C2×C411yescharacteristic
46C23×Dic61C2×C412yes—
47C22×C4×D61—24no—
48C22×C4×D61—24no—
49C22×C4×D61C2×C412yes—
50C22×C4×D61C2×C412yes—
51C22×C4×D61D412yes—
52C22×C4×D61D411yescharacteristic
53C22×C4×D61D411yescharacteristic
54C22×C4×D61D411yescharacteristic
55C22×C4×D61D411yescharacteristic
56C22×C4×D61Q812yes—
57C2×#11758198—24no—
58C2×#11758198—22no—
59C2×#11758198—22no—
60C2×#11758198—24no—
61#14519684—21no—
62#14519684—21no—
63#14519684—22no—
64#14519684—22no—
65C23×C4×C61C2×C412yes—
66C23×C4×C61C2×C411yescharacteristic
67#95×C61—21no—
68#95×C61—21no—
69C24×C61C22×C411yescharacteristic
70C23×D61—41no—
71C23×D61—42no—
72C23×D61—41no—
73C23×D61C22×C411yescharacteristic
74C23×D61C22×C411yescharacteristic
75C23×D61C2×D411yescharacteristic
76C23×D61C2×D411yescharacteristic
77C23×D61C2×D411yescharacteristic
78C23×D61C2×D414yes—
79C23×D61C2×Q811yescharacteristic
80C23×D61#4114yes—
81C22×#6923—24no—
82C22×#6923—28no—
83C22×#6923—24no—
84C22×#6923—44no—
85C22×#6923—42no—
86C22×#6923—42no—
87C22×#6923—44no—
88C22×#6923—42no—
89C22×#6923—42no—
90C22×#6923—44no—
91C22×C4×C61—24no—
92C22×C4×C61—22no—
93C22×C4×C61—24no—
94C22×C4×C61—42no—
95C22×C4×C61—42no—
96C22×C4×C61C4212yes—
97C22×C4×C61C22⋊C411yescharacteristic
98C22×C4×C61C22⋊C411yescharacteristic
99C22×C4×C61C4⋊C412yes—
100C22×Dic61—24no—
101C22×Dic61—22no—
102C22×Dic61—24no—
103C22×Dic61—42no—
104C22×Dic61—42no—
105C22×Dic61C4212yes—
106C22×Dic61C22⋊C411yescharacteristic
107C22×Dic61C22⋊C411yescharacteristic
108C22×Dic61C4⋊C412yes—
109C2×C4×D61—24no—
110C2×C4×D61—24no—
111C2×C4×D61—28no—
112C2×C4×D61—22no—
113C2×C4×D61—22no—
114C2×C4×D61—24no—
115C2×C4×D61—24no—
116C2×C4×D61—24no—
117C2×C4×D61—28no—
118C2×C4×D61—22no—
119C2×C4×D61—22no—
120C2×C4×D61—24no—
121C2×C4×D61C22⋊C412yes—
122C2×C4×D61C22⋊C412yes—
123C2×C4×D61C22⋊C412yes—
124C2×C4×D61C22⋊C412yes—
125C2×C4×D61C4⋊C412yes—
126C2×C4×D61C4⋊C412yes—
127C2×C4×D61C4⋊C412yes—
128C2×C4×D61C4⋊C412yes—
129C22⋊#6923—24no—
130C22⋊#6923—28no—
131C22⋊#6923—28no—
132C22⋊#6923—42no—
133C22⋊#6923—42no—
134C22⋊#6923C22⋊C418yes—
135C4⋊#6923—216no—
136C4×#6923—216no—
137#11758198—42no—
138#11758198—44no—
139#11758198—42no—
140C23×C61—21no—
141C23×C61—22no—
142C23×C61—21no—
143C23×C61C2×C4211yescharacteristic
144C23×C61C2×C22⋊C411yescharacteristic
145C23×C61C2×C4⋊C411yescharacteristic
146C23×C61C4×D414yes—
147C22×D61—22no—
148C22×D61—21no—
149C22×D61—21no—
150C22×D61—22no—
151C22×D61—21no—
152C22×D61—21no—
153C22×D61—41no—
154C22×D61—41no—
155C22×D61—41no—
156C22×D61—41no—
157C22×D61—44no—
158C22×D61—44no—
159C22×D61—41no—
160C22×D61—41no—
161C22×D61—41no—
162C22×D61—41no—
163C22×D61—44no—
164C22×D61—44no—
165C22×D61C2×C22⋊C411yescharacteristic
166C22×D61C2×C22⋊C411yescharacteristic
167C22×D61C2×C22⋊C412yes—
168C22×D61C2×C4⋊C411yescharacteristic
169C22×D61C2×C4⋊C411yescharacteristic
170C22×D61#11712yes—
171C22×D61C4×D414yes—
172C22×D61#12012yes—
173C22×D61#12012yes—
174C22×D61#12114yes—
175C22×D61C22⋊Q814yes—
176C22×D61#12312yes—
177C22×D61#12312yes—
178C2×#6923—28no—
179C2×#6923—48no—
180C2×#6923—48no—
181C2×#6923—44no—
182C2×#6923—44no—
183C2×#6923—44no—
184C2×#6923—44no—
185C2×#6923—44no—
186C2×#6923—84no—
187C2×#6923—84no—
188C2×C4×C61—24no—
189C2×C4×C61—24no—
190C2×C4×C61—22no—
191C2×C4×C61—22no—
192C2×C4×C61—42no—
193C2×C4×C61—42no—
194C2×C4×C61—42no—
195C2×C4×C61—84no—
196C2×C4×C61#9512yes—
197C2×C4×C61#9512yes—
198C2×Dic61—24no—
199C2×Dic61—24no—
200C2×Dic61—22no—
201C2×Dic61—22no—
202C2×Dic61—42no—
203C2×Dic61—42no—
204C2×Dic61—42no—
205C2×Dic61—84no—
206C2×Dic61#9512yes—
207C2×Dic61#9512yes—
208C4×D61—22no—
209C4×D61—22no—
210C4×D61—24no—
211C4×D61—24no—
212C4×D61—22no—
213C4×D61—22no—
214C4×D61—24no—
215C4×D61—24no—
216C4×D61—24no—
217C4×D61—24no—
218#10736—611nomaximal, Sylow
219C22×C61—24no—
220C22×C61—24no—
221C22×C61—21no—
222C22×C61—21no—
223C22×C61—21no—
224C22×C61—21no—
225C22×C61C2×#9511yescharacteristic
226C22×C61C4×C22⋊C412yes—
227C22×C61#38512yes—
228C22×C61#38612yes—
229C22×C61#41012yes—
230C22×C61#41011yescharacteristic
231C22×C61#41011yescharacteristic
232C2×D61—22no—
233C2×D61—22no—
234C2×D61—24no—
235C2×D61—24no—
236C2×D61—22no—
237C2×D61—22no—
238C2×D61—21no—
239C2×D61—21no—
240C2×D61—21no—
241C2×D61—21no—
242C2×D61—21no—
243C2×D61—21no—
244C2×D61—21no—
245C2×D61—21no—
246C2×D61—42no—
247C2×D61—42no—
248C2×D61—44no—
249C2×D61—42no—
250C2×D61—44no—
251C2×D61—42no—
252C2×D61#37911yescharacteristic
253C2×D61#38012yes—
254C2×D61#38111yescharacteristic
255C2×D61#38512yes—
256C2×D61#38612yes—
257#6923—48no—
258#6923—84no—
259C4×C61—22no—
260C4×C61—22no—
261C4×C61—82no—
262Dic61—22no—
263Dic61—22no—
264Dic61—82no—
265C22×#117—611no—
266C2×#381—611no—
267C2×#381—611no—
268C2×#342—614no—
269C2×C61—22no—
270C2×C61—22no—
271C2×C61C22⋊#9511yescharacteristic
272C2×C61#174011yescharacteristic
273C2×C61#174011yescharacteristic
274C2×C61#189912yes—
275C2×C61#189912yes—
276D61—21no—
277D61—22no—
278D61—22no—
279D61—21no—
280D61—22no—
281C24×C4—611no—
282C2×#117—614no—
283C2×#117—1228no—
284C2×#117—1222no—
285C22×C4⋊C4—1221no—
286C22×C22⋊C4—612no—
287C22×C22⋊C4—612no—
288C22×C22⋊C4—612no—
289C22×C42—1221no—
290#381—614no—
291#381—1221no—
292#381—1221no—
293#381—1221no—
294#381—1221no—
295#381—1222no—
296C2×#95—612no—
297C2×#95—611no—
298C2×#95—1221no—
299C2×#95—1221no—
300C2×#95#692311yescharacteristic, complemented
301#342—1228no—
302C61#1073611yescharacteristic, complemented, Sylow
303C25—611no—
304C23×C4—611no—
305C23×C4—612no—
306C23×C4—612no—
307C23×C4—612no—
308C23×C4—612no—
309C23×C4—611no—
310C23×C4—611no—
311C23×C4—611no—
312C23×C4—611no—
313C23×C4—612no—
314C23×C4—1224no—
315C23×C4—1224no—
316C23×C4—1222no—
317C23×C4—1222no—
318C23×C4C2×#692312yes—
319C23×C4C2×#692311yescharacteristic
320#117—12216no—
321#117—12216no—
322C2×C4⋊C4—1224no—
323C2×C4⋊C4—1228no—
324C2×C22⋊C4—614no—
325C2×C22⋊C4—618no—
326C2×C22⋊C4—614no—
327C2×C22⋊C4—1222no—
328C2×C22⋊C4—1224no—
329C2×C22⋊C4—1224no—
330C2×C22⋊C4—1224no—
331C2×C22⋊C4—1224no—
332C2×C22⋊C4—1222no—
333C2×C22⋊C4—1222no—
334C2×C22⋊C4—1224no—
335C2×C22⋊C4—1222no—
336C2×C42—1224no—
337C2×C42—1228no—
338#95—21no—
339#95—21no—
340#95—1222no—
341#95—1222no—
342#95—1224no—
343#95—1224no—
344#95—1221no—
345#95—1221no—
346C24—611no—
347C24—611no—
348C24—611no—
349C24—611no—
350C24—611no—
351C24—611no—
352C24—614no—
353C24—614no—
354C24—2442no—
355C24—2441no—
356C24—2441no—
357C24C22×#692311yescharacteristic
358C22×C4—24no—
359C22×C4—22no—
360C22×C4—24no—
361C22×C4—42no—
362C22×C4—42no—
363C22×C4—612no—
364C22×C4—611no—
365C22×C4—611no—
366C22×C4—612no—
367C22×C4—612no—
368C22×C4—612no—
369C22×C4—612no—
370C22×C4—612no—
371C22×C4—612no—
372C22×C4—612no—
373C22×C4—612no—
374C22×C4—612no—
375C22×C4—1222no—
376C22×C4—1222no—
377C22×C4—1224no—
378C22×C4—1224no—
379C22×C4—1228no—
380C22×C4—1224no—
381C22×C4—1224no—
382C22×C4—1224no—
383C22×C4—1222no—
384C22×C4—1222no—
385C22×C4—1224no—
386C22×C4—1228no—
387C22×C4—1224no—
388C22×C4—1228no—
389C22×C4—1224no—
390C22×C4—1224no—
391C22×C4—1224no—
392C22×C4—1222no—
393C22×C4—2444no—
394C22×C4—2444no—
395C22×C4—2442no—
396C22×C4—2442no—
397C22×C4—2442no—
398C22×C4—2442no—
399C22×C4—2444no—
400C22×C4—2442no—
401C22×C4—2442no—
402C22×C4C4×#692312yes—
403C22×C4C4⋊#692312yes—
404C22×C4C22⋊#692311yescharacteristic
405C22×C4C22⋊#692311yescharacteristic
406C4⋊C4—12216no—
407C22⋊C4—618no—
408C22⋊C4—1228no—
409C22⋊C4—1224no—
410C22⋊C4—1228no—
411C22⋊C4—2442no—
412C22⋊C4—2444no—
413C22⋊C4—2442no—
414C22⋊C4—2442no—
415C22⋊C4—2442no—
416C42—12216no—
417C23—22no—
418C23—21no—
419C23—21no—
420C23—612no—
421C23—614no—
422C23—612no—
423C23—611no—
424C23—611no—
425C23—611no—
426C23—611no—
427C23—612no—
428C23—614no—
429C23—612no—
430C23—612no—
431C23—612no—
432C23—614no—
433C23—1222no—
434C23—1222no—
435C23—1221no—
436C23—1221no—
437C23—1221no—
438C23—1221no—
439C23—2441no—
440C23—2441no—
441C23—2441no—
442C23—2441no—
443C23—2441no—
444C23—2441no—
445C23—2441no—
446C23—2441no—
447C23—2444no—
448C23—2444no—
449C23—2444no—
450C23—2444no—
451C23C2×C4×#692311yescharacteristic
452C23C2×C22⋊#692311yescharacteristic
453C23C2×C4⋊#692311yescharacteristic
454C23D4×#692314yes—
455C2×C4—24no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—24no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—84no—
463C2×C4—612no—
464C2×C4—612no—
465C2×C4—1222no—
466C2×C4—1222no—
467C2×C4—1224no—
468C2×C4—1224no—
469C2×C4—1224no—
470C2×C4—1224no—
471C2×C4—1222no—
472C2×C4—1222no—
473C2×C4—1224no—
474C2×C4—1224no—
475C2×C4—1224no—
476C2×C4—1222no—
477C2×C4—1222no—
478C2×C4—1224no—
479C2×C4—1228no—
480C2×C4—4884no—
481C2×C4—4884no—
482C2×C4—4884no—
483C2×C4—2444no—
484C2×C4—2444no—
485C2×C4—2444no—
486C2×C4—2442no—
487C2×C4—2442no—
488C2×C4—2442no—
489C2×C4—2444no—
490C2×C4—2444no—
491C2×C4—2448no—
492C2×C4—2448no—
493C2×C4(C2×#6923)⋊C412yes—
494C2×C4(C2×#6923)⋊C412yes—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—21no—
499C22—24no—
500C22—24no—
501C22—611no—
502C22—612no—
503C22—612no—
504C22—611no—
505C22—612no—
506C22—1221no—
507C22—1221no—
508C22—1221no—
509C22—1221no—
510C22—1221no—
511C22—1221no—
512C22—1221no—
513C22—1221no—
514C22—1224no—
515C22—1222no—
516C22—1222no—
517C22—1224no—
518C22—1222no—
519C22—1222no—
520C22—2442no—
521C22—2442no—
522C22—2444no—
523C22—2444no—
524C22—2442no—
525C22—2442no—
526C22C2×(C2×#6923)⋊C411yescharacteristic
527C22C22⋊C4×#692312yes—
528C22#1684070912yes—
529C22#1684071012yes—
530C22#1684074112yes—
531C22#1684074211yescharacteristic
532C22#1684074311yescharacteristic
533C4—22no—
534C4—22no—
535C4—82no—
536C4—1222no—
537C4—1222no—
538C4—4884no—
539C4—4882no—
540C4—2448no—
541C2—22no—
542C2—22no—
543C2—1222no—
544C2—1221no—
545C2—1222no—
546C2—1221no—
547C2—1222no—
548C2#2146099211yescharacteristic
549C2#2146151811yescharacteristic
550C2#2146151911yescharacteristic
551C2#2146184212yes—
552C2#2146184312yes—
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC23×C61C2×C42
FrattiniC24C22×#6923
FittingC2×#95×C61C4
socleC23×C61C2×C22⋊C4
prime radical, cosocleC24×D61C23
hypercenterC2×#95#6923
hypocenterC61#10736
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
7. C2×#14519856C4semidirect
13. #16840705C4semidirect
23. C2×#14519684C4semidirect
24. C2×#14519684C4semidirect
25. C2×#95×C61C4semidirect
300. C2×#95#6923semidirect
302. C61#10736semidirect

Maximal subgroups

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

subgroupindex
C22×#145198562
C2×#168407052
C2×#168406402
C2×#168396242
#1073661