Finite Group Databasebeta

← #30597272

Subgroups — #30597272

Order 15616.

914 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840733C211yesmaximal, characteristic
2#21462263C211yesmaximal, characteristic
3#21460719C214yesmaximal, complemented
4C2×#16839725C211yesmaximal, characteristic
5C22×#11758213—21no—
6C2×#14519856—21no—
7#16840733—21no—
8#16840733—21no—
9#16840733C412yescomplemented
10#16840733C2212yes—
11C2×#14519834—21no—
12C2×C22⋊#92420C412yescomplemented
13#16840705—21no—
14#16840704—21no—
15#16840704C2212yes—
16#16840703C412yes—
17C4×C22⋊#6923—21no—
18C4×C22⋊#6923C412yes—
19C23×C4×D61C2211yescharacteristic
20C22×#11758194C411yescharacteristic, complemented
21#16839725—21no—
22#16839725—21no—
23#16839725C412yescomplemented
24#16839725C2212yes—
25C2×#14519689—21no—
26C2×#14519689—21no—
27C22×M16×C61C411yescharacteristic, complemented
28C2×#11758213—22no—
29C2×#11758213—22no—
30C2×#11758213—42no—
31C2×#11758213—42no—
32C22×#92420—22no—
33#14519856—42no—
34#14519856—42no—
35C2×C4⋊#6923—22no—
36C2×C22⋊#6923—22no—
37C2×C22⋊#6923—22no—
38C2×C22⋊#6923C2×C414yes—
39C2×C4×#6923—22no—
40#14519834—22no—
41#14519834—22no—
42C22⋊#92420—22no—
43C22⋊#92420C2×C414yes—
44(C2×#6923)⋊C4—22no—
45(C2×#6923)⋊C4—22no—
46C24×D61C2×C411yescharacteristic
47C23×Dic61C2×C411yescharacteristic
48C22×C4×D61—42no—
49C22×C4×D61—42no—
50C22×C4×D61C2×C411yescharacteristic
51C22×C4×D61C2×C411yescharacteristic
52C22×C4×D61C2×C411yescharacteristic
53C22×C4×D61D411yescharacteristic
54C22×C4×D61D411yescharacteristic
55C22×C4×D61D411yescharacteristic
56C22×C4×D61D411yescharacteristic
57C22×C4×D61D411yescharacteristic
58C22×C4×D61D411yescharacteristic
59C22×C4×D61Q811yescharacteristic
60C22×C4×D61Q811yescharacteristic
61C22×C4×D61C2311yescharacteristic
62C2×#11758194—21no—
63C2×#11758194—42no—
64C2×#11758194C2×C412yes—
65C22×#92418—21no—
66#14519689—22no—
67#14519689—22no—
68#14519689—22no—
69#14519689—22no—
70C23×C4×C61C2×C411yescharacteristic
71C2×M16×C61—21no—
72C2×M16×C61—42no—
73C2×M16×C61C2×C412yes—
74C22×C8×C61—21no—
75C24×C61C4211yescharacteristic
76C23×D61—42no—
77C23×D61—42no—
78C23×D61—42no—
79C23×D61C4211yescharacteristic
80C23×D61C22⋊C411yescharacteristic
81C23×D61C22⋊C411yescharacteristic
82C23×D61C4⋊C411yescharacteristic
83C23×D61C4⋊C411yescharacteristic
84C23×D61C22×C411yescharacteristic
85C22×#6923—24no—
86C22×C4×C61—22no—
87C22×C4×C61—22no—
88C22×C4×C61C4211yescharacteristic
89C22×C4×C61C22⋊C411yescharacteristic
90C22×C4×C61C22⋊C411yescharacteristic
91C22×C4×C61C4⋊C411yescharacteristic
92C22×C4×C61C4⋊C411yescharacteristic
93C22×C4×C61C22×C411yescharacteristic
94C22×Dic61—42no—
95C22×Dic61C4211yescharacteristic
96C22×Dic61C22⋊C411yescharacteristic
97C22×Dic61C22⋊C411yescharacteristic
98C22×Dic61C4⋊C411yescharacteristic
99C22×Dic61C4⋊C411yescharacteristic
100C22×Dic61C22×C411yescharacteristic
101C2×C4×D61—22no—
102C2×C4×D61—22no—
103C2×C4×D61—22no—
104C2×C4×D61—22no—
105C2×C4×D61—42no—
106C2×C4×D61—42no—
107C2×C4×D61—41no—
108C2×C4×D61—41no—
109C2×C4×D61—42no—
110C2×C4×D61—41no—
111C2×C4×D61—41no—
112C2×C4×D61—41no—
113C2×C4×D61—41no—
114C2×C4×D61—42no—
115C2×C4×D61—41no—
116C2×C4×D61—41no—
117C2×C4×D61—42no—
118C2×C4×D61—42no—
119C2×C4×D61C22⋊C411yescharacteristic
120C2×C4×D61C22⋊C411yescharacteristic
121C2×C4×D61C22⋊C411yescharacteristic
122C2×C4×D61C22⋊C411yescharacteristic
123C2×C4×D61C22⋊C411yescharacteristic
124C2×C4×D61C22⋊C411yescharacteristic
125C2×C4×D61C4⋊C411yescharacteristic
126C2×C4×D61C4⋊C411yescharacteristic
127C2×C4×D61C4⋊C411yescharacteristic
128C2×C4×D61C4⋊C411yescharacteristic
129C2×C4×D61C4⋊C411yescharacteristic
130C2×C4×D61C4⋊C411yescharacteristic
131C2×C4×D61C2×D411yescharacteristic
132C2×C4×D61C2×D411yescharacteristic
133C2×C4×D61C2×D411yescharacteristic
134C2×C4×D61C2×Q811yescharacteristic
135C22⋊#6923—44no—
136C22⋊#6923—44no—
137C22⋊#6923—44no—
138C2×#92420—24no—
139C2×#92420—44no—
140C4⋊#6923—42no—
141C4⋊#6923—42no—
142C4×#6923—44no—
143#11758213—44no—
144#11758213—42no—
145#11758213—42no—
146M16×C61—42no—
147M16×C61—42no—
148C2×C8×C61—22no—
149C2×C8×C61—42no—
150#11758194—42no—
151#11758194—42no—
152C2×#92418—22no—
153C2×#92418—42no—
154C23×C61—22no—
155C23×C61—22no—
156C23×C61—41no—
157C23×C61#9511yescharacteristic
158C23×C61#9511yescharacteristic
159C23×C61C2×C4211yescharacteristic
160C22×D61—22no—
161C22×D61—22no—
162C22×D61—22no—
163C22×D61—22no—
164C22×D61—22no—
165C22×D61—22no—
166C22×D61—22no—
167C22×D61—41no—
168C22×D61—41no—
169C22×D61—41no—
170C22×D61—41no—
171C22×D61—41no—
172C22×D61—41no—
173C22×D61—41no—
174C22×D61—41no—
175C22×D61—41no—
176C22×D61—41no—
177C22×D61—41no—
178C22×D61—416no—
179C22×D61#9511yescharacteristic
180C22×D61#9511yescharacteristic
181C22×D61C2×C22⋊C411yescharacteristic
182C22×D61C2×C4⋊C411yescharacteristic
183C2×#6923—44no—
184C2×#6923—44no—
185C2×#6923—44no—
186C2×C4×C61—22no—
187C2×C4×C61—22no—
188C2×C4×C61—22no—
189C2×C4×C61—21no—
190C2×C4×C61—21no—
191C2×C4×C61—21no—
192C2×C4×C61—21no—
193C2×C4×C61#9511yescharacteristic
194C2×C4×C61#9511yescharacteristic
195C2×C4×C61#9912yes—
196C2×C4×C61#9912yes—
197C2×C4×C61C2×C22⋊C411yescharacteristic
198C2×C4×C61C2×C4⋊C411yescharacteristic
199C2×Dic61—22no—
200C2×Dic61—22no—
201C2×Dic61—41no—
202C2×Dic61—41no—
203C2×Dic61—41no—
204C2×Dic61—41no—
205C2×Dic61#9511yescharacteristic
206C2×Dic61#9511yescharacteristic
207C2×Dic61C2×C22⋊C411yescharacteristic
208C2×Dic61C2×C4⋊C411yescharacteristic
209C4×D61—22no—
210C4×D61—22no—
211C4×D61—22no—
212C4×D61—22no—
213C4×D61—21no—
214C4×D61—21no—
215C4×D61—21no—
216C4×D61—21no—
217C4×D61—21no—
218C4×D61—21no—
219C4×D61—21no—
220C4×D61—21no—
221C4×D61—41no—
222C4×D61—41no—
223C4×D61—41no—
224C4×D61—41no—
225C4×D61—41no—
226C4×D61—41no—
227C4×D61—41no—
228C4×D61—41no—
229#92420—44no—
230C8×C61—42no—
231#92418—42no—
232#8108—611nomaximal, Sylow
233C22×C61—21no—
234C22×C61—21no—
235C22×C61—21no—
236C22×C61—21no—
237C22×C61—21no—
238C22×C61—21no—
239C22×C61—21no—
240C22×C61—44no—
241C22×C61#34212yes—
242C22×C61#34412yes—
243C22×C61C2×#9511yescharacteristic
244C2×D61—21no—
245C2×D61—21no—
246C2×D61—21no—
247C2×D61—21no—
248C2×D61—21no—
249C2×D61—21no—
250C2×D61—21no—
251C2×D61—21no—
252C2×D61—21no—
253C2×D61—21no—
254C2×D61—21no—
255C2×D61—44no—
256C2×D61—44no—
257C2×D61—44no—
258C2×D61—44no—
259C2×D61—44no—
260C2×D61—44no—
261C2×D61#41312yes—
262#6923—84no—
263C4×C61—21no—
264C4×C61—21no—
265C4×C61#34212yes—
266C4×C61C2×#9911yescharacteristic
267C4×C61C2×#9911yescharacteristic
268Dic61—21no—
269Dic61—21no—
270Dic61—21no—
271Dic61—21no—
272C2×#407—611no—
273C2×#407—611no—
274#2280—611no—
275#1305—614no—
276C2×C61—22no—
277C2×C61—22no—
278C2×C61—41no—
279C2×C61C2×#34211yescharacteristic
280C2×C61#174211yescharacteristic
281C2×C61C2×#34411yescharacteristic
282D61—22no—
283D61—41no—
284D61—41no—
285D61—41no—
286C24×C4—611no—
287C22×M16—611no—
288C22×M16—1221no—
289C22×M16#692311yescharacteristic, complemented
290C2×#117—1221no—
291#407—612no—
292#407—612no—
293#407—612no—
294#407—612no—
295#407—1221no—
296#407—1221no—
297#407—1221no—
298#407—1221no—
299C2×C22⋊C8—612no—
300C2×C22⋊C8—1221no—
301C2×C22⋊C8—1221no—
302C2×C22⋊C8—1221no—
303#381—1221no—
304#380—612no—
305#380—1221no—
306#379—612no—
307C4×C22⋊C4—612no—
308C4×C22⋊C4—1221no—
309C61#810811yescharacteristic, complemented, Sylow
310C25—611no—
311C23×C4—611no—
312C23×C4—611no—
313C23×C4—611no—
314C23×C4—611no—
315C23×C4—611no—
316C23×C4—611no—
317C23×C4—611no—
318C23×C4—611no—
319C23×C4—611no—
320C23×C4—611no—
321C23×C4—611no—
322C23×C4—611no—
323C23×C4—611no—
324C23×C4—2442no—
325C23×C4—2442no—
326C23×C4C2×#692311yescharacteristic
327C2×M16—21no—
328C2×M16—42no—
329C2×M16—612no—
330C2×M16—1222no—
331C2×M16—1222no—
332C2×M16—1221no—
333C2×M16—2442no—
334C2×M16—2442no—
335C2×M16—2442no—
336C2×M16C2×#692312yes—
337C22×C8—21no—
338C22×C8—1222no—
339C22×C8—1221no—
340#117—2442no—
341#117—2442no—
342C2×C4⋊C4—1222no—
343C2×C22⋊C4—614no—
344C2×C22⋊C4—1222no—
345C2×C22⋊C4—1222no—
346C2×C42—1222no—
347C22⋊C8—614no—
348C22⋊C8—1222no—
349C22⋊C8—1222no—
350C22⋊C8—1222no—
351C22⋊C8—1222no—
352C22⋊C8—1222no—
353C22⋊C8—1222no—
354C22⋊C8—1222no—
355#95—1222no—
356#95—1222no—
357C24—611no—
358C24—611no—
359C24—611no—
360C24—611no—
361C24—611no—
362C24—611no—
363C24—2442no—
364C24—2442no—
365C24—2442no—
366C24C4×#692311yescharacteristic
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—611no—
370C22×C4—611no—
371C22×C4—611no—
372C22×C4—611no—
373C22×C4—611no—
374C22×C4—611no—
375C22×C4—611no—
376C22×C4—611no—
377C22×C4—611no—
378C22×C4—611no—
379C22×C4—611no—
380C22×C4—611no—
381C22×C4—611no—
382C22×C4—611no—
383C22×C4—611no—
384C22×C4—611no—
385C22×C4—611no—
386C22×C4—611no—
387C22×C4—611no—
388C22×C4—611no—
389C22×C4—611no—
390C22×C4—611no—
391C22×C4—1222no—
392C22×C4—1222no—
393C22×C4—1222no—
394C22×C4—1222no—
395C22×C4—1224no—
396C22×C4—2441no—
397C22×C4—2441no—
398C22×C4—2441no—
399C22×C4—2441no—
400C22×C4—2441no—
401C22×C4—2441no—
402C22×C4—2441no—
403C22×C4—2441no—
404C22×C4—2442no—
405C22×C4—2442no—
406C22×C4—2442no—
407C22×C4—2442no—
408C22×C4—2442no—
409C22×C4—2442no—
410C22×C4—2442no—
411C22×C4C4×#692311yescharacteristic
412C22×C4C4⋊#692311yescharacteristic
413C22×C4C4⋊#692311yescharacteristic
414C22×C4C22⋊#692311yescharacteristic
415C22×C4C22⋊#692311yescharacteristic
416C22×C4C22×#692311yescharacteristic
417M16—42no—
418M16—42no—
419M16—2442no—
420M16—2442no—
421M16—2444no—
422M16—2442no—
423M16—2442no—
424C2×C8—22no—
425C2×C8—42no—
426C2×C8—1224no—
427C2×C8—1222no—
428C2×C8—2442no—
429C2×C8—2444no—
430C4⋊C4—2442no—
431C4⋊C4—2442no—
432C22⋊C4—2444no—
433C22⋊C4—2444no—
434C22⋊C4—2444no—
435C42—2444no—
436C23—22no—
437C23—22no—
438C23—41no—
439C23—611no—
440C23—611no—
441C23—611no—
442C23—611no—
443C23—1222no—
444C23—1222no—
445C23—1222no—
446C23—1222no—
447C23—1222no—
448C23—1222no—
449C23—1222no—
450C23—2441no—
451C23—2441no—
452C23—2441no—
453C23—2441no—
454C23—2441no—
455C23—2441no—
456C23—2441no—
457C23—2441no—
458C23—2441no—
459C23—2441no—
460C23—2441no—
461C23—24416no—
462C23(C2×#6923)⋊C411yescharacteristic
463C23(C2×#6923)⋊C411yescharacteristic
464C23C2×C4×#692311yescharacteristic
465C2×C4—22no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—611no—
473C2×C4—611no—
474C2×C4—611no—
475C2×C4—611no—
476C2×C4—1222no—
477C2×C4—1222no—
478C2×C4—1221no—
479C2×C4—1221no—
480C2×C4—1221no—
481C2×C4—1221no—
482C2×C4—1221no—
483C2×C4—1221no—
484C2×C4—1221no—
485C2×C4—1221no—
486C2×C4—1222no—
487C2×C4—1222no—
488C2×C4—1222no—
489C2×C4—1222no—
490C2×C4—2441no—
491C2×C4—2441no—
492C2×C4—2441no—
493C2×C4—2441no—
494C2×C4—2441no—
495C2×C4—2441no—
496C2×C4—2441no—
497C2×C4—2441no—
498C2×C4—2441no—
499C2×C4—2441no—
500C2×C4—2441no—
501C2×C4—2441no—
502C2×C4—2444no—
503C2×C4—2444no—
504C2×C4—2444no—
505C2×C4(C2×#6923)⋊C411yescharacteristic
506C2×C4(C2×#6923)⋊C411yescharacteristic
507C2×C4#1451983512yes—
508C2×C4#1451983612yes—
509C2×C4C2×C22⋊#692311yescharacteristic
510C2×C4C2×C4⋊#692311yescharacteristic
511C8—42no—
512C8—2444no—
513C8—2442no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—21no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—44no—
522C22—612no—
523C22—1221no—
524C22—1221no—
525C22—1221no—
526C22—1221no—
527C22—1221no—
528C22—1221no—
529C22—1221no—
530C22—1221no—
531C22—1221no—
532C22—1221no—
533C22—1221no—
534C22—2444no—
535C22—2444no—
536C22—2444no—
537C22—2444no—
538C22—2444no—
539C22—2444no—
540C22#1684064012yes—
541C22#1684064512yes—
542C22C2×(C2×#6923)⋊C411yescharacteristic
543C4—21no—
544C4—21no—
545C4—1221no—
546C4—1221no—
547C4—1221no—
548C4—1221no—
549C4—4884no—
550C4#1684064012yes—
551C4C2×#1451983511yescharacteristic
552C4C2×#1451983611yescharacteristic
553C2—22no—
554C2—22no—
555C2—41no—
556C2—1222no—
557C2—2441no—
558C2—2441no—
559C2—2441no—
560C2C2×#1684064011yescharacteristic
561C2#2146152311yescharacteristic
562C2C2×#1684064511yescharacteristic
subgroupG/H
centerC22C2×(C2×#6923)⋊C4
commutatorC23×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC22×M16×C61C4
socleC22×C61C2×#95
prime radicalC24×D61C2×C4
cosocleC22×C4×D61C23
hypercenterC22×M16#6923
hypocenterC61#8108
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
3. #21460719C2semidirect
9. #16840733C4semidirect
12. C2×C22⋊#92420C4semidirect
20. C22×#11758194C4semidirect
23. #16839725C4semidirect
27. C22×M16×C61C4semidirect
289. C22×M16#6923semidirect
309. C61#8108semidirect

Maximal subgroups

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

subgroupindex
C2×#168407332
#214622632
#214607192
C2×#168397252
#810861