Finite Group Databasebeta

← #29597512

Subgroups — #29597512

Order 15616.

894 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 894 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21449142C211yesmaximal, characteristic
2C2×#16839551C212yesmaximal, complemented
3#21445740C211yesmaximal, characteristic
4#21443936C212yesmaximal, complemented
5C22×#99×C61C211yesmaximal, characteristic
6C2×#14519758C411yescharacteristic, complemented
7C2×#14519758C2211yescharacteristic
8C22×C22⋊Dic61C411yescharacteristic, complemented
9C2×#14519694—21no—
10C2×#14519694C2212yes—
11#16839726—21no—
12#16839676—21no—
13#16839676—21no—
14#16839642C411yescharacteristic, complemented
15#16839642C2211yescharacteristic
16#16839635—21no—
17#16839618—21no—
18#16839618C411yescharacteristic, complemented
19#16839551—24no—
20C23×D4×C61C2211yescharacteristic
21C22×C22⋊C4×C61—21no—
22C2×#99×C61—21no—
23C2×#99×C61—24no—
24C2×#99×C61C2212yes—
25C23×Dic61C2×C411yescharacteristic, complemented
26C23×Dic61C2×C411yescharacteristic, complemented
27C2×#11758194—22no—
28#14519758—22no—
29#14519758—22no—
30#14519758—42no—
31C2×#11758196—21no—
32C2×#11758196—21no—
33C2×C22⋊Dic61—21no—
34C2×C22⋊Dic61—21no—
35C2×C22⋊Dic61—21no—
36C2×C22⋊Dic61—21no—
37C2×C22⋊Dic61—21no—
38C2×C22⋊Dic61—21no—
39C2×C22⋊Dic61—21no—
40C2×C22⋊Dic61—21no—
41C2×C22⋊Dic61—41no—
42C2×C22⋊Dic61—41no—
43C2×C22⋊Dic61C2×C411yescharacteristic, complemented
44C2×C22⋊Dic61C2×C411yescharacteristic, complemented
45#14519694—22no—
46#14519694—22no—
47#14519694—42no—
48C22⋊#92418—41no—
49C22⋊#92418—41no—
50#14519684—21no—
51#14519684—21no—
52C25×C61C2×C411yescharacteristic
53C25×C61D411yescharacteristic
54C22×D4×C61—22no—
55C22×D4×C61—22no—
56C22×D4×C61—41no—
57C22×D4×C61—41no—
58C22×D4×C61—42no—
59C22×D4×C61C2×C411yescharacteristic
60C22×D4×C61D411yescharacteristic
61C22×D4×C61D411yescharacteristic
62C22×D4×C61C2311yescharacteristic
63C23×C4×C61—41no—
64C23×C4×C61D411yescharacteristic
65C2×C22⋊C4×C61—24no—
66C2×C22⋊C4×C61—22no—
67C2×C22⋊C4×C61—41no—
68C2×C22⋊C4×C61—42no—
69#99×C61—24no—
70#99×C61—22no—
71#99×C61D414yes—
72C24×C61—21no—
73C24×C61—22no—
74C24×C61—21no—
75C24×C61—21no—
76C24×C61—21no—
77C24×C61—21no—
78C24×C61—21no—
79C24×C61—22no—
80C24×C61—41no—
81C24×C61—42no—
82C24×C61—42no—
83C24×C61—81no—
84C24×C61—81no—
85C24×C61C22⋊C411yescharacteristic
86C24×C61C22⋊C411yescharacteristic
87C24×C61C22⋊C411yescharacteristic
88C24×C61C22×C411yescharacteristic
89C24×C61C2×D411yescharacteristic
90C2×D4×C61—22no—
91C2×D4×C61—22no—
92C2×D4×C61—22no—
93C2×D4×C61—21no—
94C2×D4×C61—21no—
95C2×D4×C61—22no—
96C2×D4×C61—41no—
97C2×D4×C61—41no—
98C2×D4×C61—41no—
99C2×D4×C61—41no—
100C2×D4×C61—41no—
101C2×D4×C61—41no—
102C2×D4×C61—44no—
103C2×D4×C61—44no—
104C2×D4×C61—44no—
105C2×D4×C61—44no—
106C2×D4×C61C2×D412yes—
107C2×D4×C61#4112yes—
108C22×C4×C61—21no—
109C22×C4×C61—21no—
110C22×C4×C61—22no—
111C22×C4×C61—41no—
112C22×C4×C61—44no—
113C22×C4×C61—42no—
114C22×C4×C61—82no—
115C22×C4×C61—82no—
116C22×C4×C61C22⋊C411yescharacteristic
117C22×C4×C61C2×D411yescharacteristic
118C22×Dic61—21no—
119C22×Dic61—21no—
120C22×Dic61—21no—
121C22×Dic61—21no—
122C22×Dic61—22no—
123C22×Dic61—41no—
124C22×Dic61—41no—
125C22×Dic61—41no—
126C22×Dic61—81no—
127C22⋊C4×C61—24no—
128C22⋊C4×C61—44no—
129C22⋊C4×C61—42no—
130C22⋊Dic61—22no—
131C22⋊Dic61—42no—
132C22⋊Dic61—42no—
133C22⋊Dic61—41no—
134C22⋊Dic61—41no—
135C22⋊Dic61—42no—
136C22⋊Dic61—41no—
137C22⋊Dic61—41no—
138C22⋊Dic61—41no—
139C22⋊Dic61—81no—
140C22⋊Dic61—81no—
141C22⋊Dic61—81no—
142#11758196—42no—
143#11758196—42no—
144#11758194—42no—
145#11758194—42no—
146C2×#92418—42no—
147C23×C61—22no—
148C23×C61—22no—
149C23×C61—22no—
150C23×C61—22no—
151C23×C61—22no—
152C23×C61—21no—
153C23×C61—21no—
154C23×C61—21no—
155C23×C61—21no—
156C23×C61—21no—
157C23×C61—21no—
158C23×C61—21no—
159C23×C61—21no—
160C23×C61—21no—
161C23×C61—21no—
162C23×C61—21no—
163C23×C61—41no—
164C23×C61—42no—
165C23×C61—42no—
166C23×C61—42no—
167C23×C61—41no—
168C23×C61—41no—
169C23×C61—41no—
170C23×C61—41no—
171C23×C61—41no—
172C23×C61—41no—
173C23×C61—42no—
174C23×C61—41no—
175C23×C61—41no—
176C23×C61—42no—
177C23×C61—42no—
178C23×C61—81no—
179C23×C61—81no—
180C23×C61—81no—
181C23×C61—81no—
182C23×C61—84no—
183C23×C61—82no—
184C23×C61—82no—
185C23×C61—84no—
186C23×C61—84no—
187C23×C61#9911yescharacteristic
188C23×C61#9911yescharacteristic
189C23×C61#9912yes—
190C23×C61C2×C22⋊C411yescharacteristic
191C23×C61C4×D412yes—
192C23×C61#12011yescharacteristic
193C23×C61#12311yescharacteristic
194D4×C61—42no—
195D4×C61—42no—
196D4×C61—44no—
197D4×C61—44no—
198D4×C61—42no—
199D4×C61—42no—
200C2×C4×C61—21no—
201C2×C4×C61—21no—
202C2×C4×C61—21no—
203C2×C4×C61—21no—
204C2×C4×C61—21no—
205C2×C4×C61—42no—
206C2×C4×C61—42no—
207C2×C4×C61—44no—
208C2×C4×C61—88no—
209C2×C4×C61—82no—
210C2×C4×C61—82no—
211C2×C4×C61#12112yes—
212C2×Dic61—41no—
213C2×Dic61—41no—
214C2×Dic61—41no—
215C2×Dic61—41no—
216C2×Dic61—41no—
217C2×Dic61—41no—
218C2×Dic61—41no—
219C2×Dic61—41no—
220C2×Dic61—41no—
221C2×Dic61—41no—
222C2×Dic61—41no—
223C2×Dic61—41no—
224C2×Dic61—82no—
225C2×Dic61—82no—
226#92418—82no—
227#13084—611nomaximal, Sylow
228C22×C61—21no—
229C22×C61—21no—
230C22×C61—21no—
231C22×C61—21no—
232C22×C61—21no—
233C22×C61—21no—
234C22×C61—22no—
235C22×C61—21no—
236C22×C61—21no—
237C22×C61—22no—
238C22×C61—21no—
239C22×C61—42no—
240C22×C61—42no—
241C22×C61—42no—
242C22×C61—42no—
243C22×C61—41no—
244C22×C61—41no—
245C22×C61—44no—
246C22×C61—42no—
247C22×C61—44no—
248C22×C61—41no—
249C22×C61—41no—
250C22×C61—41no—
251C22×C61—41no—
252C22×C61—41no—
253C22×C61—41no—
254C22×C61—41no—
255C22×C61—41no—
256C22×C61—41no—
257C22×C61—81no—
258C22×C61—81no—
259C22×C61—84no—
260C22×C61—81no—
261C22×C61—81no—
262C22×C61—82no—
263C22×C61—82no—
264C22×C61—84no—
265C22×C61#35212yescomplemented
266C22×C61#38611yescharacteristic
267C22×C61C2×#9911yescharacteristic
268C22×C61C2×#9911yescharacteristic
269C4×C61—22no—
270C4×C61—41no—
271C4×C61—84no—
272Dic61—81no—
273Dic61—81no—
274Dic61—81no—
275Dic61—81no—
276C22×#99D6111yescharacteristic
277#2405—611no—
278C2×#352—612no—
279#1783—611no—
280#1390—612no—
281C2×C61—21no—
282C2×C61—21no—
283C2×C61—22no—
284C2×C61—41no—
285C2×C61—41no—
286C2×C61—42no—
287C2×C61—41no—
288C2×C61—42no—
289C2×C61—81no—
290C2×C61#189811yescharacteristic
291C2×C61C2×#35211yescharacteristic
292C2×C61#212111yescharacteristic
293C23×D4C2×D6111yescharacteristic
294C2×#123—611no—
295C2×#123—611no—
296C22×C22⋊C4—21no—
297C22×C22⋊C4—611no—
298C2×#100—612no—
299C2×#100—1221no—
300C2×#99—21no—
301C2×#99—24no—
302C2×#99C2×D6112yes—
303#407—1221no—
304#394—1221no—
305#394—1221no—
306#386—611no—
307#386—611no—
308#385—1221no—
309#379—611no—
310#379—1221no—
311#352—1224no—
312C61#1308411yescharacteristic, complemented, Sylow
313C25C4×D6111yescharacteristic
314C25C22⋊D6111yescharacteristic
315C22×D4—22no—
316C22×D4—22no—
317C22×D4—41no—
318C22×D4—41no—
319C22×D4—42no—
320C22×D4C4×D6111yescharacteristic
321C22×D4D24411yescharacteristic
322C22×D4C22⋊D6111yescharacteristic
323C22×D4C22×D6111yescharacteristic
324C23×C4—41no—
325C23×C4—611no—
326C23×C4—611no—
327C23×C4D24411yescharacteristic
328C2×M16—1222no—
329#123—1222no—
330#123—1222no—
331#123—2442no—
332C2×C4⋊C4—1221no—
333C2×C4⋊C4—1221no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—41no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—611no—
339C2×C22⋊C4—611no—
340C2×C22⋊C4—1221no—
341C2×C22⋊C4—1221no—
342C2×C22⋊C4—1221no—
343C2×C22⋊C4—1221no—
344C2×C22⋊C4—1221no—
345C2×C22⋊C4—1221no—
346C2×C22⋊C4—1221no—
347C2×C22⋊C4—1221no—
348C2×C22⋊C4—2441no—
349C2×C22⋊C4—2441no—
350#100—1222no—
351#100—1222no—
352#100—2442no—
353#99—24no—
354#99—22no—
355#99C22⋊D6114yes—
356C22⋊C8—2441no—
357C22⋊C8—2441no—
358#95—1221no—
359#95—1221no—
360C24—21no—
361C24—22no—
362C24—21no—
363C24—21no—
364C24—21no—
365C24—21no—
366C24—21no—
367C24—22no—
368C24—41no—
369C24—42no—
370C24—42no—
371C24—81no—
372C24—81no—
373C24#1175819811yescharacteristic
374C24#1175819811yescharacteristic
375C24#1175819811yescharacteristic
376C24C2×C4×D6111yescharacteristic
377C24C2×C22⋊D6111yescharacteristic
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—22no—
381C2×D4—21no—
382C2×D4—21no—
383C2×D4—22no—
384C2×D4—41no—
385C2×D4—41no—
386C2×D4—41no—
387C2×D4—41no—
388C2×D4—41no—
389C2×D4—41no—
390C2×D4—44no—
391C2×D4—44no—
392C2×D4—44no—
393C2×D4—44no—
394C2×D4#1175822212yes—
395C2×D4C2×C22⋊D6112yes—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—41no—
400C22×C4—44no—
401C22×C4—42no—
402C22×C4—82no—
403C22×C4—82no—
404C22×C4—1222no—
405C22×C4—1221no—
406C22×C4—1221no—
407C22×C4—1221no—
408C22×C4—1221no—
409C22×C4—4881no—
410C22×C4—2441no—
411C22×C4—2441no—
412C22×C4—2441no—
413C22×C4#1175819811yescharacteristic
414C22×C4C2×D24411yescharacteristic
415M16—2442no—
416M16—2442no—
417C2×C8—2442no—
418C4⋊C4—2442no—
419C4⋊C4—2442no—
420C22⋊C4—24no—
421C22⋊C4—44no—
422C22⋊C4—42no—
423C22⋊C4—1222no—
424C22⋊C4—4881no—
425C22⋊C4—4881no—
426C22⋊C4—4881no—
427C22⋊C4—2442no—
428C22⋊C4—2442no—
429C22⋊C4—2441no—
430C22⋊C4—2441no—
431C22⋊C4—2442no—
432C22⋊C4—2441no—
433C22⋊C4—2441no—
434C22⋊C4—2441no—
435C23—22no—
436C23—22no—
437C23—22no—
438C23—22no—
439C23—21no—
440C23—21no—
441C23—21no—
442C23—21no—
443C23—21no—
444C23—22no—
445C23—21no—
446C23—21no—
447C23—21no—
448C23—21no—
449C23—21no—
450C23—21no—
451C23—41no—
452C23—42no—
453C23—42no—
454C23—41no—
455C23—41no—
456C23—42no—
457C23—41no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23—42no—
462C23—41no—
463C23—41no—
464C23—42no—
465C23—42no—
466C23—81no—
467C23—81no—
468C23—81no—
469C23—81no—
470C23—84no—
471C23—82no—
472C23—82no—
473C23—84no—
474C23—84no—
475C23#1451969111yescharacteristic
476C23#1451969111yescharacteristic
477C23#1451969112yes—
478C23C2×#1175819811yescharacteristic
479C23C4×C22⋊D6112yes—
480C23#1451974611yescharacteristic
481C23#1451976011yescharacteristic
482D4—42no—
483D4—42no—
484D4—44no—
485D4—44no—
486D4—42no—
487D4—42no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—44no—
496C2×C4—88no—
497C2×C4—82no—
498C2×C4—82no—
499C2×C4—4882no—
500C2×C4—4882no—
501C2×C4—2441no—
502C2×C4—2441no—
503C2×C4—2441no—
504C2×C4—2441no—
505C2×C4—2441no—
506C2×C4—2441no—
507C2×C4—2441no—
508C2×C4—2441no—
509C2×C4—2441no—
510C2×C4—2441no—
511C2×C4—2441no—
512C2×C4—2441no—
513C2×C4#1451975112yes—
514C8—4882no—
515C22—21no—
516C22—21no—
517C22—21no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—22no—
524C22—22no—
525C22—21no—
526C22—42no—
527C22—42no—
528C22—42no—
529C22—42no—
530C22—41no—
531C22—41no—
532C22—44no—
533C22—42no—
534C22—44no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—81no—
545C22—81no—
546C22—84no—
547C22—81no—
548C22—81no—
549C22—82no—
550C22—82no—
551C22—84no—
552C22#1683955112yescomplemented
553C22#1683964111yescharacteristic
554C22C2×#1451969111yescharacteristic
555C22C2×#1451969111yescharacteristic
556C4—22no—
557C4—41no—
558C4—84no—
559C4—4881no—
560C4—4881no—
561C4—4881no—
562C4—4881no—
563C2—21no—
564C2—21no—
565C2—22no—
566C2—41no—
567C2—41no—
568C2—42no—
569C2—41no—
570C2—42no—
571C2—81no—
572C2#2144627211yescharacteristic
573C2C2×#1683955111yescharacteristic
574C2#2144746311yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC24×C61C22×C4
FrattiniC22×D4C22×D61
FittingC22×#99×C61C2
socleC22×C61C2×#99
prime radicalC23×D4×C61C22
cosocleC22×D4×C61C23
hypercenterC22×#99D61
hypocenterC61#13084
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C23×D4 ◁ C22×#99

Complements

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

NH ≅ G/Ntype
2. C2×#16839551C2semidirect
4. #21443936C2semidirect
6. C2×#14519758C4semidirect
8. C22×C22⋊Dic61C4semidirect
14. #16839642C4semidirect
18. #16839618C4semidirect
25. C23×Dic61C2×C4semidirect
26. C23×Dic61C2×C4semidirect
43. C2×C22⋊Dic61C2×C4semidirect
44. C2×C22⋊Dic61C2×C4semidirect
265. C22×C61#352semidirect
312. C61#13084semidirect
552. C22#16839551semidirect

Maximal subgroups

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

subgroupindex
#214491422
C2×#168395512
#214457402
#214439362
C22×#99×C612
#1308461