Finite Group Databasebeta

← #29645860

Subgroups — #29645860

Order 15616.

1322 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519733C211yesmaximal, characteristic
2#21454448C212yesmaximal, complemented
3#21444150C214yesmaximal, complemented
4#21444148C212yesmaximal, complemented
5#21444146C211yesmaximal, characteristic
6#21444130C214yesmaximal, complemented
7C61×#1462C211yesmaximal, characteristic
8C24×Dic61C411yescharacteristic
9C2×#14519733—22no—
10C2×#14519733—22no—
11C2×#14519733—22no—
12C2×#14519733—22no—
13C2×#14519733C412yes—
14C2×#14519733C412yes—
15C2×#14519733C2212yes—
16C2×#14519733C2212yes—
17C22×#11758196C411yescharacteristic
18C22×#11758196C2211yescharacteristic
19C22×C22⋊Dic61C411yescharacteristic
20C22×C4×Dic61C411yescharacteristic
21C22×C4×Dic61C2211yescharacteristic
22#16839816—22no—
23#16839816C2214yescomplemented
24#16839812—22no—
25#16839812C2214yescomplemented
26#16839785—22no—
27#16839726C2212yes—
28M16×Dic61—22no—
29#16839487C2218yescomplemented
30#16839486C2214yes—
31C22×C22⋊C4×C61C2211yescharacteristic
32C61×#407C2212yes—
33C61×#323C2214yes—
34C23×Dic61—21no—
35C23×Dic61—21no—
36C23×Dic61—21no—
37C23×Dic61—21no—
38C23×Dic61—28no—
39C23×Dic61C2×C411yescharacteristic
40C23×Dic61C2×C412yes—
41C23×Dic61C2×C411yescharacteristic
42C23×Dic61C2×C412yes—
43C23×Dic61C2×C411yescharacteristic
44C23×Dic61C2×C411yescharacteristic
45C2×#11758194—22no—
46#14519733—24no—
47#14519733—24no—
48#14519733—24no—
49#14519733—24no—
50#14519733—24no—
51#14519733—24no—
52#14519733—24no—
53#14519733—24no—
54C2×#11758196—22no—
55C2×#11758196—22no—
56C2×#11758196—22no—
57C2×#11758196—22no—
58C2×#11758196C2×C412yes—
59C2×#11758196C2×C412yes—
60C2×#11758196C2×C412yes—
61C2×#11758196C2312yes—
62C2×C22⋊Dic61—22no—
63C2×C22⋊Dic61—22no—
64C2×C22⋊Dic61C2×C412yes—
65C2×C22⋊Dic61C2×C412yes—
66C2×C4×Dic61—21no—
67C2×C4×Dic61—21no—
68C2×C4×Dic61—21no—
69C2×C4×Dic61—21no—
70C2×C4×Dic61C2×C412yes—
71C2×C4×Dic61C2×C412yes—
72C2×C4×Dic61C2×C411yescharacteristic
73C2×C4×Dic61C2×C411yescharacteristic
74C2×C4×Dic61D412yes—
75C2×C4×Dic61D412yes—
76C2×C4×Dic61D412yes—
77C2×C4×Dic61D412yes—
78C2×C4×Dic61C2311yescharacteristic
79C2×C4×Dic61C2311yescharacteristic
80#14519706—24no—
81#14519706—24no—
82C22⋊#92418—22no—
83C22⋊#92418C2314yes—
84#14519687—24no—
85C8×Dic61—24no—
86C25×C61C2×C411yescharacteristic
87C23×C4×C61C2×C411yescharacteristic
88C23×C4×C61C2311yescharacteristic
89C2×M16×C61—22no—
90C2×C22⋊C4×C61—22no—
91C2×C22⋊C4×C61—22no—
92C2×C22⋊C4×C61C2×C412yes—
93C2×C22⋊C4×C61C2312yes—
94C22⋊C8×C61—22no—
95C22⋊C8×C61C2314yes—
96C24×C61—21no—
97C24×C61—21no—
98C24×C61—24no—
99C24×C61—42no—
100C24×C61—42no—
101C24×C61C22×C411yescharacteristic
102C24×C61C22×C412yes—
103C22×C4×C61—21no—
104C22×C4×C61—21no—
105C22×C4×C61—42no—
106C22×C4×C61—42no—
107C22×C4×C61C22×C412yes—
108C22×C4×C61C22×C411yescharacteristic
109C22×C4×C61C2×D412yes—
110C22×C4×C61C2×D412yes—
111C22×C4×C61C2411yescharacteristic
112C22×Dic61—28no—
113C22×Dic61—28no—
114C22×Dic61—28no—
115C22×Dic61—28no—
116C22×Dic61—21no—
117C22×Dic61—21no—
118C22×Dic61—24no—
119C22×Dic61—22no—
120C22×Dic61—22no—
121C22×Dic61—22no—
122C22×Dic61—22no—
123C22×Dic61—24no—
124C22×Dic61—24no—
125C22×Dic61—24no—
126C22×Dic61—24no—
127C22×Dic61—21no—
128C22×Dic61—21no—
129C22×Dic61—42no—
130C22×Dic61—42no—
131C22×Dic61C22⋊C411yescharacteristic
132C22×Dic61C22⋊C411yescharacteristic
133C22×Dic61C22⋊C411yescharacteristic
134C22×Dic61C22⋊C411yescharacteristic
135C22×Dic61C22⋊C412yes—
136C22×Dic61C22⋊C412yes—
137C22×Dic61M1618yescomplemented
138C22×Dic61C22×C411yescharacteristic
139C22×Dic61C22×C412yes—
140C22×Dic61C22×C412yes—
141C22×Dic61C22×C411yescharacteristic
142C22×Dic61C22×C411yescharacteristic
143C22×Dic61C22×C411yescharacteristic
144M16×C61—44no—
145C2×C8×C61—24no—
146C22⋊C4×C61—24no—
147C22⋊C4×C61—24no—
148C22⋊Dic61—24no—
149C22⋊Dic61—24no—
150#11758196—24no—
151#11758196—24no—
152#11758196—24no—
153#11758196—24no—
154C4×Dic61—22no—
155C4×Dic61—22no—
156C4×Dic61—22no—
157C4×Dic61—22no—
158C4×Dic61C22⋊C412yes—
159C4×Dic61C22⋊C412yes—
160C4×Dic61C22⋊C412yes—
161C4×Dic61C22⋊C412yes—
162C4×Dic61C2×D412yes—
163C4×Dic61C2×D412yes—
164C4×Dic61C2×D412yes—
165C4×Dic61C2×D412yes—
166#11758194—44no—
167C2×#92418—24no—
168C23×C61—22no—
169C23×C61—22no—
170C23×C61—22no—
171C23×C61—24no—
172C23×C61—24no—
173C23×C61—22no—
174C23×C61—22no—
175C23×C61—416no—
176C23×C61—42no—
177C23×C61—42no—
178C23×C61—42no—
179C23×C61—42no—
180C23×C61—42no—
181C23×C61—42no—
182C23×C61C2×C22⋊C411yescharacteristic
183C23×C61C2×C22⋊C411yescharacteristic
184C23×C61C2×M1614yes—
185C23×C61C23×C411yescharacteristic
186C2×C4×C61—24no—
187C2×C4×C61—22no—
188C2×C4×C61—41no—
189C2×C4×C61—42no—
190C2×C4×C61—41no—
191C2×C4×C61—42no—
192C2×C4×C61—42no—
193C2×C4×C61—42no—
194C2×C4×C61C2×C22⋊C412yes—
195C2×C4×C61C22×D412yes—
196C2×Dic61—28no—
197C2×Dic61—28no—
198C2×Dic61—24no—
199C2×Dic61—24no—
200C2×Dic61—22no—
201C2×Dic61—22no—
202C2×Dic61—22no—
203C2×Dic61—24no—
204C2×Dic61—22no—
205C2×Dic61—22no—
206C2×Dic61—22no—
207C2×Dic61—22no—
208C2×Dic61—28no—
209C2×Dic61—28no—
210C2×Dic61—22no—
211C2×Dic61—42no—
212C2×Dic61—41no—
213C2×Dic61—41no—
214C2×Dic61—42no—
215C2×Dic61—42no—
216C2×Dic61—42no—
217C2×Dic61C2×C22⋊C411yescharacteristic
218C2×Dic61C2×C22⋊C411yescharacteristic
219C2×Dic61C2×C22⋊C412yes—
220C2×Dic61C2×C22⋊C412yes—
221C2×Dic61C2×C22⋊C411yescharacteristic
222C2×Dic61C2×C22⋊C411yescharacteristic
223C2×Dic61C2×M1614yes—
224C2×Dic61C2×M1614yes—
225C8×C61—44no—
226#92418—44no—
227#17357—611nomaximal, Sylow
228C22×C61—28no—
229C22×C61—21no—
230C22×C61—21no—
231C22×C61—21no—
232C22×C61—21no—
233C22×C61—21no—
234C22×C61—21no—
235C22×C61—24no—
236C22×C61—44no—
237C22×C61—44no—
238C22×C61—48no—
239C22×C61—48no—
240C22×C61—42no—
241C22×C61—42no—
242C22×C61#41012yes—
243C22×C61#41312yes—
244C22×C61C22×C22⋊C411yescharacteristic
245C22×C61C22×M1612yes—
246C4×C61—22no—
247C4×C61—22no—
248C4×C61—42no—
249Dic61—21no—
250Dic61—21no—
251Dic61—24no—
252Dic61—22no—
253Dic61—22no—
254Dic61—42no—
255Dic61#40712yes—
256Dic61#40712yes—
257C22×#117—611no—
258#2920—612no—
259#1464—614no—
260#1463—612no—
261#1462—611no—
262#1462D6111yescharacteristic
263#1458—614no—
264C2×C61—22no—
265C2×C61—22no—
266C2×C61—22no—
267C2×C61—44no—
268C2×C61C2×#40711yescharacteristic
269C2×C61C2×#41011yescharacteristic
270C2×C61C2×#41311yescharacteristic
271C24×C4—611no—
272C2×#117—612no—
273C2×#117—612no—
274C2×#117—612no—
275C2×#117—612no—
276C2×#117—1222no—
277C2×#117—1222no—
278C2×#117—1222no—
279C2×#117—1222no—
280C22×C4⋊C4—611no—
281C22×C4⋊C4—611no—
282C22×C22⋊C4—611no—
283C22×C22⋊C4C2×D6111yescharacteristic
284C22×C42—611no—
285C22×C42—611no—
286#432—614no—
287#432—1222no—
288#431—614no—
289#431—1222no—
290#423—1222no—
291#407—612no—
292#407C2×D6112yes—
293C4×M16—1222no—
294#324—618no—
295#323—614no—
296#323C2×D6114yes—
297C61#1735711yescharacteristic, complemented, Sylow
298C25C4×D6111yescharacteristic
299C23×C4—612no—
300C23×C4—611no—
301C23×C4—611no—
302C23×C4—611no—
303C23×C4—612no—
304C23×C4—611no—
305C23×C4—1221no—
306C23×C4—1221no—
307C23×C4—1221no—
308C23×C4—1221no—
309C23×C4—1228no—
310C23×C4C4×D6111yescharacteristic
311C23×C4C22×D6111yescharacteristic
312C2×M16—22no—
313C2×M16—1222no—
314#117—1224no—
315#117—1224no—
316#117—1224no—
317#117—1224no—
318#117—1224no—
319#117—1224no—
320#117—1224no—
321#117—1224no—
322C2×C4⋊C4—612no—
323C2×C4⋊C4—612no—
324C2×C4⋊C4—612no—
325C2×C4⋊C4—612no—
326C2×C4⋊C4—1222no—
327C2×C4⋊C4—1222no—
328C2×C4⋊C4—1222no—
329C2×C4⋊C4—1222no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—612no—
333C2×C22⋊C4—612no—
334C2×C22⋊C4—1222no—
335C2×C22⋊C4—1222no—
336C2×C22⋊C4C4×D6112yes—
337C2×C22⋊C4C22×D6112yes—
338C2×C42—611no—
339C2×C42—611no—
340C2×C42—612no—
341C2×C42—612no—
342C2×C42—612no—
343C2×C42—612no—
344C2×C42—611no—
345C2×C42—611no—
346C2×C42—612no—
347C2×C42—612no—
348C2×C42—1221no—
349C2×C42—1221no—
350C2×C42—1221no—
351C2×C42—1221no—
352C4⋊C8—1224no—
353C4⋊C8—1224no—
354C22⋊C8—22no—
355C22⋊C8—614no—
356C22⋊C8—1222no—
357C22⋊C8C22×D6114yes—
358#97—1224no—
359C4×C8—1224no—
360C24—21no—
361C24—21no—
362C24—24no—
363C24—42no—
364C24—42no—
365C24C2×C4×D6111yescharacteristic
366C24C2×C4×D6112yes—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—42no—
370C22×C4—42no—
371C22×C4—611no—
372C22×C4—611no—
373C22×C4—612no—
374C22×C4—611no—
375C22×C4—611no—
376C22×C4—611no—
377C22×C4—611no—
378C22×C4—612no—
379C22×C4—618no—
380C22×C4—611no—
381C22×C4—611no—
382C22×C4—612no—
383C22×C4—612no—
384C22×C4—1222no—
385C22×C4—1222no—
386C22×C4—1222no—
387C22×C4—1222no—
388C22×C4—1224no—
389C22×C4—1224no—
390C22×C4—1224no—
391C22×C4—1224no—
392C22×C4—1228no—
393C22×C4—1228no—
394C22×C4—1228no—
395C22×C4—1228no—
396C22×C4—1221no—
397C22×C4—1221no—
398C22×C4—1224no—
399C22×C4—1221no—
400C22×C4—1221no—
401C22×C4—2442no—
402C22×C4—2442no—
403C22×C4C2×C4×D6112yes—
404C22×C4C2×C4×D6111yescharacteristic
405C22×C4D4×D6112yes—
406C22×C4D4×D6112yes—
407C22×C4C23×D6111yescharacteristic
408M16—44no—
409M16—2444no—
410C2×C8—24no—
411C2×C8—1224no—
412C4⋊C4—1224no—
413C4⋊C4—1224no—
414C4⋊C4—1224no—
415C4⋊C4—1224no—
416C22⋊C4—24no—
417C22⋊C4—24no—
418C22⋊C4—1224no—
419C22⋊C4—1224no—
420C42—612no—
421C42—612no—
422C42—612no—
423C42—612no—
424C42—612no—
425C42—612no—
426C42—612no—
427C42—612no—
428C42—1222no—
429C42—1222no—
430C42—1222no—
431C42—1222no—
432C23—22no—
433C23—22no—
434C23—22no—
435C23—24no—
436C23—24no—
437C23—22no—
438C23—22no—
439C23—42no—
440C23—42no—
441C23—416no—
442C23—42no—
443C23—42no—
444C23—42no—
445C23—42no—
446C23C22⋊C4×D6111yescharacteristic
447C23C22⋊C4×D6111yescharacteristic
448C23M16×D6114yes—
449C23C22×C4×D6111yescharacteristic
450C2×C4—24no—
451C2×C4—22no—
452C2×C4—41no—
453C2×C4—42no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—611no—
459C2×C4—611no—
460C2×C4—614no—
461C2×C4—611no—
462C2×C4—611no—
463C2×C4—612no—
464C2×C4—612no—
465C2×C4—614no—
466C2×C4—1222no—
467C2×C4—1222no—
468C2×C4—1222no—
469C2×C4—1222no—
470C2×C4—1228no—
471C2×C4—1228no—
472C2×C4—1224no—
473C2×C4—1224no—
474C2×C4—1228no—
475C2×C4—1228no—
476C2×C4—1222no—
477C2×C4—1224no—
478C2×C4—1222no—
479C2×C4—1222no—
480C2×C4—1222no—
481C2×C4—2441no—
482C2×C4—2441no—
483C2×C4—2442no—
484C2×C4—2442no—
485C2×C4—2442no—
486C2×C4—2442no—
487C2×C4C22⋊C4×D6112yes—
488C2×C4C2×D4×D6112yes—
489C8—44no—
490C8—2444no—
491C22—28no—
492C22—21no—
493C22—21no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—24no—
499C22—44no—
500C22—48no—
501C22—48no—
502C22—44no—
503C22—42no—
504C22—42no—
505C22#1683973412yes—
506C22#1683974312yes—
507C22C2×C22⋊C4×D6111yescharacteristic
508C22C2×M16×D6112yes—
509C4—22no—
510C4—22no—
511C4—42no—
512C4—612no—
513C4—612no—
514C4—1221no—
515C4—1221no—
516C4—1224no—
517C4—1222no—
518C4—1222no—
519C4—2442no—
520C2—22no—
521C2—22no—
522C2—22no—
523C2—44no—
524C2#407×D6111yescharacteristic
525C2C2×#1683973411yescharacteristic
526C2C2×#1683974311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1462C2
socleC22×C61C22×C22⋊C4
prime radicalC25×C61C2×C4
cosocleC22×C4×C61C24
hypercenter#1462D61
hypocenterC61#17357
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1462

Complements

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

NH ≅ G/Ntype
2. #21454448C2semidirect
3. #21444150C2semidirect
4. #21444148C2semidirect
6. #21444130C2semidirect
23. #16839816C22semidirect
25. #16839812C22semidirect
29. #16839487C22semidirect
137. C22×Dic61M16semidirect
297. C61#17357semidirect

Maximal subgroups

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

subgroupindex
C22×#145197332
#214544482
#214441502
#214441482
#214441462
#214441302
C61×#14622
#1735761