Finite Group Databasebeta

← #29586626

Subgroups — #29586626

Order 15616.

1658 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×#14519758C211yesmaximal, characteristic
2#21448397C211yesmaximal, characteristic
3C2×#16839623C212yesmaximal, complemented
4C2×#16839528C212yesmaximal, complemented
5C22×#99×C61C211yesmaximal, characteristic
6C24×Dic61C2211yescharacteristic
7C2×#14519758—24no—
8C2×#14519758—22no—
9C2×#14519758—24no—
10C2×#14519758C414yescomplemented
11C22×#11758196—21no—
12C22×C22⋊Dic61—21no—
13C22×C22⋊Dic61C2211yescharacteristic
14C22×C22⋊Dic61C2212yes—
15#16839642—24no—
16#16839625—21no—
17#16839623—24no—
18#16839623—24no—
19#16839618—21no—
20C2×#14519684—24no—
21#16839528—24no—
22C23×D4×C61C2211yescharacteristic
23C22×C22⋊C4×C61C2212yes—
24C2×#99×C61—22no—
25C2×#99×C61—24no—
26C23×Dic61—21no—
27C23×Dic61—21no—
28C23×Dic61—22no—
29C23×Dic61—21no—
30C23×Dic61—22no—
31C23×Dic61—22no—
32C23×Dic61—22no—
33C23×Dic61—22no—
34C23×Dic61C2×C412yes—
35C23×Dic61D414yes—
36C23×Dic61D414yes—
37#14519758—216no—
38#14519758—28no—
39#14519758—28no—
40C2×#11758196—28no—
41C2×#11758196—24no—
42C2×C22⋊Dic61—28no—
43C2×C22⋊Dic61—24no—
44C2×C22⋊Dic61—22no—
45C2×C22⋊Dic61—21no—
46C2×C22⋊Dic61—22no—
47C2×C22⋊Dic61—22no—
48C2×C22⋊Dic61—22no—
49C2×C22⋊Dic61—22no—
50C2×C22⋊Dic61—22no—
51C2×C22⋊Dic61—22no—
52C2×C22⋊Dic61—24no—
53C2×C22⋊Dic61C2×C412yes—
54C2×C22⋊Dic61D414yes—
55#14519684—216no—
56#14519684—24no—
57C25×C61D411yescharacteristic
58C25×C61C2311yescharacteristic
59C22×D4×C61—22no—
60C22×D4×C61—22no—
61C22×D4×C61—22no—
62C22×D4×C61—22no—
63C22×D4×C61—22no—
64C22×D4×C61—22no—
65C22×D4×C61C2×C412yes—
66C22×D4×C61D412yes—
67C23×C4×C61—22no—
68C23×C4×C61D411yescharacteristic
69C2×C22⋊C4×C61—22no—
70C2×C22⋊C4×C61—22no—
71C2×C22⋊C4×C61—22no—
72C2×C22⋊C4×C61—22no—
73C2×C22⋊C4×C61—22no—
74C2×C22⋊C4×C61D414yes—
75#99×C61—28no—
76C24×C61—22no—
77C24×C61—21no—
78C24×C61—22no—
79C24×C61—21no—
80C24×C61—44no—
81C24×C61—44no—
82C24×C61C22⋊C412yes—
83C24×C61C22×C411yescharacteristic
84C24×C61C2×D411yescharacteristic
85C24×C61C2×D412yes—
86C24×C61C2×D412yes—
87C24×C61C2×D411yescharacteristic
88C24×C61C2×D412yes—
89C24×C61C2×D412yes—
90C24×C61#4112yes—
91C24×C61#4112yes—
92C2×D4×C61—22no—
93C2×D4×C61—22no—
94C2×D4×C61—24no—
95C2×D4×C61—24no—
96C2×D4×C61—22no—
97C2×D4×C61—24no—
98C2×D4×C61—24no—
99C2×D4×C61—22no—
100C2×D4×C61—42no—
101C2×D4×C61—42no—
102C2×D4×C61—42no—
103C2×D4×C61—42no—
104C2×D4×C61—42no—
105C2×D4×C61—42no—
106C2×D4×C61—42no—
107C2×D4×C61—42no—
108C22×C4×C61—21no—
109C22×C4×C61—22no—
110C22×C4×C61—22no—
111C22×C4×C61—21no—
112C22×C4×C61—24no—
113C22×C4×C61—48no—
114C22×C4×C61—42no—
115C22×C4×C61—42no—
116C22×C4×C61C22⋊C412yes—
117C22×Dic61—22no—
118C22×Dic61—22no—
119C22×Dic61—22no—
120C22×Dic61—24no—
121C22×Dic61—24no—
122C22×Dic61—24no—
123C22×Dic61—24no—
124C22×Dic61—24no—
125C22×Dic61—24no—
126C22×Dic61—24no—
127C22×Dic61—24no—
128C22×Dic61—24no—
129C22×Dic61—24no—
130C22×Dic61—24no—
131C22×Dic61—24no—
132C22×Dic61—44no—
133C22×Dic61—41no—
134C22×Dic61—41no—
135C22×Dic61—42no—
136C22×Dic61—42no—
137C22×Dic61—42no—
138C22×Dic61—42no—
139C22×Dic61—41no—
140C22×Dic61—41no—
141C22×Dic61—42no—
142C22×Dic61—42no—
143C22×Dic61—48no—
144C22×Dic61C22⋊C414yescomplemented
145C22⋊C4×C61—24no—
146C22⋊C4×C61—24no—
147C22⋊C4×C61—42no—
148C22⋊C4×C61—42no—
149C22⋊Dic61—216no—
150C22⋊Dic61—22no—
151C22⋊Dic61—24no—
152C22⋊Dic61—42no—
153C22⋊Dic61—42no—
154C22⋊Dic61—42no—
155C22⋊Dic61—42no—
156C22⋊Dic61—84no—
157C22⋊Dic61C22⋊C414yescomplemented
158#11758196—216no—
159C23×C61—28no—
160C23×C61—24no—
161C23×C61—22no—
162C23×C61—22no—
163C23×C61—22no—
164C23×C61—42no—
165C23×C61—42no—
166C23×C61—44no—
167C23×C61—44no—
168C23×C61—44no—
169C23×C61—44no—
170C23×C61—44no—
171C23×C61—44no—
172C23×C61—48no—
173C23×C61—42no—
174C23×C61—42no—
175C23×C61—44no—
176C23×C61—82no—
177C23×C61—84no—
178C23×C61C2×C22⋊C411yescharacteristic
179C23×C61C2×C22⋊C411yescharacteristic
180C23×C61C2×C22⋊C411yescharacteristic
181C23×C61C4×D412yes—
182C23×C61C4×D412yes—
183C23×C61#12012yes—
184C23×C61#12012yes—
185C23×C61#12012yes—
186C23×C61#12011yescharacteristic
187C23×C61#12011yescharacteristic
188C23×C61#12112yes—
189C23×C61#12112yes—
190C23×C61#12112yes—
191C23×C61#12112yes—
192C23×C61#12112yes—
193C23×C61#12112yes—
194C23×C61#12311yescharacteristic
195C23×C61#12312yes—
196C23×C61#12311yescharacteristic
197C23×C61#12412yes—
198C23×C61#12712yes—
199D4×C61—44no—
200D4×C61—44no—
201D4×C61—44no—
202D4×C61—44no—
203C2×C4×C61—22no—
204C2×C4×C61—22no—
205C2×C4×C61—22no—
206C2×C4×C61—42no—
207C2×C4×C61—42no—
208C2×C4×C61—48no—
209C2×C4×C61—44no—
210C2×C4×C61—84no—
211C2×C4×C61—84no—
212C2×Dic61—24no—
213C2×Dic61—24no—
214C2×Dic61—28no—
215C2×Dic61—44no—
216C2×Dic61—48no—
217C2×Dic61—42no—
218C2×Dic61—42no—
219C2×Dic61—44no—
220C2×Dic61—44no—
221C2×Dic61—44no—
222C2×Dic61—44no—
223C2×Dic61—44no—
224C2×Dic61—48no—
225C2×Dic61—44no—
226C2×Dic61—48no—
227C2×Dic61—84no—
228#10992—611nomaximal, Sylow
229C22×C61—22no—
230C22×C61—24no—
231C22×C61—22no—
232C22×C61—24no—
233C22×C61—24no—
234C22×C61—24no—
235C22×C61—24no—
236C22×C61—24no—
237C22×C61—24no—
238C22×C61—24no—
239C22×C61—41no—
240C22×C61—41no—
241C22×C61—42no—
242C22×C61—42no—
243C22×C61—41no—
244C22×C61—42no—
245C22×C61—42no—
246C22×C61—42no—
247C22×C61—41no—
248C22×C61—42no—
249C22×C61—44no—
250C22×C61—44no—
251C22×C61—42no—
252C22×C61—82no—
253C22×C61—84no—
254C22×C61—84no—
255C22×C61#37911yescharacteristic
256C22×C61#38612yes—
257C22×C61#38611yescharacteristic
258C22×C61#38611yescharacteristic
259C22×C61#39012yes—
260C22×C61#39212yes—
261C22×C61#39212yes—
262C22×C61#39412yes—
263C22×C61#39412yes—
264C22×C61#45814yes—
265C4×C61—42no—
266C4×C61—84no—
267Dic61—44no—
268Dic61—44no—
269Dic61—84no—
270C22×#123—611no—
271C22×#99D6111yescharacteristic
272#2308—611no—
273C2×#381—612no—
274C2×#342—612no—
275C2×C61—21no—
276C2×C61—22no—
277C2×C61—21no—
278C2×C61—22no—
279C2×C61—22no—
280C2×C61—22no—
281C2×C61—22no—
282C2×C61—82no—
283C2×C61#143811yescharacteristic
284C2×C61#189012yes—
285C2×C61#202214yes—
286C23×D4C2×D6111yescharacteristic
287C24×C4—611no—
288C2×#123—614no—
289C2×#123—1224no—
290C2×#123—1224no—
291C2×#123—1222no—
292C22×C4⋊C4—1221no—
293C22×C22⋊C4—611no—
294C22×C22⋊C4—612no—
295C22×C22⋊C4—1221no—
296C22×C22⋊C4C2×D6112yes—
297C2×#99—22no—
298C2×#99—24no—
299#386—1224no—
300#381—1224no—
301#381—1221no—
302#381—1224no—
303#379—1221no—
304C2×#95—1224no—
305#342—1224no—
306C61#1099211yescharacteristic, complemented, Sylow
307C25D24411yescharacteristic
308C25C22×D6111yescharacteristic
309C22×D4—22no—
310C22×D4—22no—
311C22×D4—22no—
312C22×D4—22no—
313C22×D4—22no—
314C22×D4—22no—
315C22×D4C4×D6112yes—
316C22×D4C22⋊D6112yes—
317C23×C4—22no—
318C23×C4—612no—
319C23×C4—614no—
320C23×C4—614no—
321C23×C4—1221no—
322C23×C4—1221no—
323C23×C4—1222no—
324C23×C4—1222no—
325C23×C4—1222no—
326C23×C4—1222no—
327C23×C4—1221no—
328C23×C4—1222no—
329C23×C4D24411yescharacteristic
330#123—1228no—
331#123—1228no—
332#123—12216no—
333C2×C4⋊C4—1228no—
334C2×C4⋊C4—1224no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—612no—
341C2×C22⋊C4—614no—
342C2×C22⋊C4—1228no—
343C2×C22⋊C4—1224no—
344C2×C22⋊C4—1222no—
345C2×C22⋊C4—1221no—
346C2×C22⋊C4—1224no—
347C2×C22⋊C4—1222no—
348C2×C22⋊C4—1222no—
349C2×C22⋊C4—1222no—
350C2×C22⋊C4—1222no—
351C2×C22⋊C4—1222no—
352C2×C22⋊C4—1222no—
353C2×C22⋊C4C22⋊D6114yes—
354#99—28no—
355#95—12216no—
356#95—1224no—
357C24—22no—
358C24—21no—
359C24—22no—
360C24—21no—
361C24—44no—
362C24—44no—
363C24#1175819812yes—
364C24C2×C4×D6111yescharacteristic
365C24C2×D24411yescharacteristic
366C24#1175822212yes—
367C24D4×D6112yes—
368C24D4×D6112yes—
369C24D4×D6112yes—
370C24#1175822412yes—
371C24C2×C22⋊D6111yescharacteristic
372C24C2×C22⋊D6112yes—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—24no—
376C2×D4—24no—
377C2×D4—24no—
378C2×D4—22no—
379C2×D4—24no—
380C2×D4—22no—
381C2×D4—42no—
382C2×D4—42no—
383C2×D4—42no—
384C2×D4—42no—
385C2×D4—42no—
386C2×D4—42no—
387C2×D4—42no—
388C2×D4—42no—
389C22×C4—22no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—24no—
394C22×C4—48no—
395C22×C4—42no—
396C22×C4—42no—
397C22×C4—614no—
398C22×C4—1222no—
399C22×C4—1222no—
400C22×C4—1222no—
401C22×C4—1224no—
402C22×C4—1224no—
403C22×C4—1224no—
404C22×C4—1224no—
405C22×C4—1224no—
406C22×C4—1224no—
407C22×C4—1224no—
408C22×C4—1224no—
409C22×C4—1224no—
410C22×C4—1224no—
411C22×C4—1224no—
412C22×C4—1224no—
413C22×C4—2448no—
414C22×C4—2444no—
415C22×C4—2441no—
416C22×C4—2441no—
417C22×C4—2442no—
418C22×C4—2442no—
419C22×C4—2442no—
420C22×C4—2442no—
421C22×C4—2441no—
422C22×C4—2441no—
423C22×C4—2442no—
424C22×C4—2442no—
425C22×C4#1175819812yes—
426C4⋊C4—12216no—
427C22⋊C4—24no—
428C22⋊C4—24no—
429C22⋊C4—42no—
430C22⋊C4—42no—
431C22⋊C4—614no—
432C22⋊C4—12216no—
433C22⋊C4—1222no—
434C22⋊C4—1224no—
435C22⋊C4—4884no—
436C22⋊C4—2442no—
437C22⋊C4—2442no—
438C22⋊C4—2442no—
439C22⋊C4—2442no—
440C23—28no—
441C23—24no—
442C23—22no—
443C23—22no—
444C23—22no—
445C23—42no—
446C23—44no—
447C23—44no—
448C23—44no—
449C23—44no—
450C23—44no—
451C23—42no—
452C23—44no—
453C23—48no—
454C23—44no—
455C23—42no—
456C23—42no—
457C23—82no—
458C23—84no—
459C23C22⋊C4×D6111yescharacteristic
460C23C22⋊C4×D6111yescharacteristic
461C23C2×#1175819811yescharacteristic
462C23#1451973712yes—
463C23C4×C22⋊D6112yes—
464C23#1451974512yes—
465C23#1451974512yes—
466C23#1451974611yescharacteristic
467C23#1451974712yes—
468C23#1451974711yescharacteristic
469C23#1451974812yes—
470C23#1451974912yes—
471C23#1451974912yes—
472C23#1451975012yes—
473C23#1451975012yes—
474C23#1451975112yes—
475C23#1451975912yes—
476C23#1451976011yescharacteristic
477C23#1451976111yescharacteristic
478C23#1451976312yes—
479C23#1451977312yes—
480D4—44no—
481D4—44no—
482D4—44no—
483D4—44no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—48no—
490C2×C4—44no—
491C2×C4—84no—
492C2×C4—84no—
493C2×C4—1224no—
494C2×C4—1224no—
495C2×C4—1228no—
496C2×C4—4884no—
497C2×C4—2448no—
498C2×C4—2448no—
499C2×C4—2444no—
500C2×C4—2448no—
501C2×C4—2444no—
502C2×C4—2442no—
503C2×C4—2442no—
504C2×C4—2444no—
505C2×C4—2444no—
506C2×C4—2444no—
507C2×C4—2444no—
508C2×C4—2444no—
509C22—24no—
510C22—24no—
511C22—24no—
512C22—24no—
513C22—24no—
514C22—24no—
515C22—24no—
516C22—22no—
517C22—22no—
518C22—24no—
519C22—41no—
520C22—41no—
521C22—42no—
522C22—42no—
523C22—41no—
524C22—42no—
525C22—42no—
526C22—42no—
527C22—41no—
528C22—42no—
529C22—44no—
530C22—44no—
531C22—42no—
532C22—82no—
533C22—84no—
534C22—84no—
535C22#1683961711yescharacteristic
536C22#1683963812yes—
537C22#1683963911yescharacteristic
538C22#1683964111yescharacteristic
539C22#1683966212yes—
540C22#1683967012yes—
541C22#1683967112yes—
542C22#1683967712yes—
543C22#1683967812yes—
544C22#1683995314yes—
545C4—42no—
546C4—84no—
547C4—4884no—
548C4—2444no—
549C4—2444no—
550C2—22no—
551C2—21no—
552C2—21no—
553C2—22no—
554C2—22no—
555C2—22no—
556C2—22no—
557C2—82no—
558C2#2144405811yescharacteristic
559C2#2144623012yes—
560C2#2144694914yes—
subgroupG/H
centerC23#14519747
commutatorC24×C61C22×C4
FrattiniC25C22×D61
FittingC22×#99×C61C2
socleC23×C61#120
prime radicalC23×D4×C61C22
cosocleC25×C61C23
hypercenterC22×#99D61
hypocenterC61#10992
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C25 ◁ C22×#99

Complements

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

NH ≅ G/Ntype
3. C2×#16839623C2semidirect
4. C2×#16839528C2semidirect
10. C2×#14519758C4semidirect
144. C22×Dic61C22⋊C4semidirect
157. C22⋊Dic61C22⋊C4semidirect
306. C61#10992semidirect

Maximal subgroups

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

subgroupindex
C22×#145197582
#214483972
C2×#168396232
C2×#168395282
C22×#99×C612
#1099261