Finite Group Databasebeta

← #29575742

Subgroups — #29575742

Order 15616.

1010 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454107C211yesmaximal, characteristic
2C2×#16839609C211yesmaximal, characteristic
3#21445728C211yesmaximal, characteristic
4C2×#16839500C211yesmaximal, characteristic, complemented
5C2×#16839498C211yesmaximal, characteristic, complemented
6#21443697C211yesmaximal, characteristic, complemented
7C61×#1294C211yesmaximal, characteristic, complemented
8C23×C4×D61C2211yescharacteristic
9C2×#14519757C412yescomplemented
10C2×#14519756C2211yescharacteristic
11C22×#11758198—21no—
12C22×C4×Dic61—21no—
13C2×C22⋊#92418C2211yescharacteristic
14C2×#14519689—22no—
15#16839637—21no—
16#16839636—22no—
17#16839619C412yescomplemented
18#16839617—21no—
19#16839609—22no—
20#16839609—22no—
21C2×#14519684C2211yescharacteristic
22#16839500—22no—
23#16839498—22no—
24C2×C22⋊C8×C61C2211yescharacteristic
25C61×#380C2211yescharacteristic
26C2×#95×C61C2211yescharacteristic
27C24×D61D411yescharacteristic
28C22×Dic122C2×C411yescharacteristic
29C23×Dic61—21no—
30C23×Dic61D411yescharacteristic
31C22×C4×D61—21no—
32C22×C4×D61—21no—
33C22×C4×D61—21no—
34C22×C4×D61—21no—
35C22×C4×D61—44no—
36C22×C4×D61C2×C412yes—
37C22×C4×D61D412yes—
38C22×#92418—21no—
39#14519757—44no—
40#14519756—21no—
41#14519756—21no—
42#14519756—21no—
43#14519756—21no—
44C2×C4⋊Dic61—22no—
45C2×C4⋊Dic61C2×C411yescharacteristic
46C2×#11758196—21no—
47C2×C22⋊Dic61—21no—
48C2×#11758198—28no—
49C2×#11758198—24no—
50C2×#11758198—22no—
51C2×#11758198—22no—
52C2×C4×Dic61—24no—
53C2×C4×Dic61—44no—
54C22⋊#92418—21no—
55C22⋊#92418—21no—
56#14519689—44no—
57#14519684—21no—
58#14519684—22no—
59#14519684D412yes—
60C23×C4×C61—21no—
61C23×C4×C61C2311yescharacteristic
62C22×C8×C61—21no—
63C2×C4⋊C4×C61C2×C412yes—
64C2×C22⋊C4×C61—21no—
65C22⋊C8×C61—21no—
66C22⋊C8×C61—21no—
67#95×C61—21no—
68#95×C61—21no—
69#95×C61D412yes—
70C24×C61C2×D411yescharacteristic
71C23×D61—21no—
72C23×D61—21no—
73C23×D61—24no—
74C23×D61—21no—
75C23×D61—21no—
76C23×D61—21no—
77C23×D61—21no—
78C23×D61—42no—
79C23×D61C22⋊C412yes—
80C22×C4×C61—24no—
81C22×C4×C61—22no—
82C22×C4×C61—22no—
83C22×C4×C61—42no—
84C22×C4×C61—42no—
85C22×C4×C61—41no—
86C22×C4×C61—41no—
87C22×C4×C61C22×C411yescharacteristic
88C22×C4×C61C2×D411yescharacteristic
89C22×C4×C61C2×D411yescharacteristic
90C22×C4×C61C2×D411yescharacteristic
91C22×C4×C61#4111yescharacteristic
92C22×C4×C61#4111yescharacteristic
93C22×Dic61—21no—
94C22×Dic61—21no—
95C22×Dic61—24no—
96C22×Dic61—24no—
97C22×Dic61—22no—
98C22×Dic61—21no—
99C22×Dic61—21no—
100C22×Dic61—42no—
101C22×Dic61—41no—
102C22×Dic61—41no—
103C22×Dic61C22⋊C412yes—
104C2×C4×D61—22no—
105C2×C4×D61—22no—
106C2×C4×D61—22no—
107C2×C4×D61—22no—
108C2×C4×D61—24no—
109C2×C4×D61—24no—
110C2×C4×D61—42no—
111C2×C4×D61—42no—
112C2×C4×D61—44no—
113C2×C4×D61—44no—
114C2×C4×D61—44no—
115C2×C4×D61—44no—
116C2×Dic122—21no—
117C2×Dic122—21no—
118C2×Dic122—42no—
119C2×C8×C61—42no—
120C2×C8×C61—41no—
121C4⋊C4×C61—42no—
122C22⋊C4×C61—41no—
123C22⋊C4×C61—41no—
124C22⋊Dic61—41no—
125C22⋊Dic61—41no—
126#11758198—216no—
127#11758198—44no—
128#11758198—44no—
129C4⋊Dic61—21no—
130C4⋊Dic61—21no—
131C4⋊Dic61—44no—
132#11758196—41no—
133#11758196—41no—
134C4×Dic61—48no—
135C2×#92418—42no—
136C2×#92418—41no—
137C23×C61—22no—
138C23×C61—22no—
139C23×C61C2×C22⋊C411yescharacteristic
140C23×C61#12011yescharacteristic
141C23×C61#12311yescharacteristic
142C23×C61#13511yescharacteristic
143C23×C61#13511yescharacteristic
144C23×C61#13711yescharacteristic
145C23×C61#13711yescharacteristic
146C22×D61—24no—
147C22×D61—24no—
148C22×D61—22no—
149C22×D61—22no—
150C22×D61—22no—
151C22×D61—22no—
152C22×D61—22no—
153C22×D61—22no—
154C22×D61—44no—
155C22×D61—44no—
156C22×D61—44no—
157C22×D61—44no—
158C22×D61—42no—
159C22×D61—42no—
160C22×D61—41no—
161C22×D61—41no—
162C22×D61—41no—
163C22×D61—41no—
164C22×D61#10414yes—
165C2×C4×C61—22no—
166C2×C4×C61—22no—
167C2×C4×C61—24no—
168C2×C4×C61—41no—
169C2×C4×C61—41no—
170C2×C4×C61—41no—
171C2×C4×C61—41no—
172C2×C4×C61—42no—
173C2×C4×C61—44no—
174C2×C4×C61—44no—
175C2×C4×C61—42no—
176C2×C4×C61—42no—
177C2×C4×C61—42no—
178C2×C4×C61—42no—
179C2×C4×C61C4×D411yescharacteristic
180C2×C4×C61C4×D411yescharacteristic
181C2×C4×C61#12111yescharacteristic
182C2×C4×C61#12111yescharacteristic
183C2×Dic61—24no—
184C2×Dic61—24no—
185C2×Dic61—22no—
186C2×Dic61—22no—
187C2×Dic61—24no—
188C2×Dic61—42no—
189C2×Dic61—44no—
190C2×Dic61—44no—
191C2×Dic61—42no—
192C2×Dic61—41no—
193C2×Dic61—41no—
194C2×Dic61—42no—
195C2×Dic61—42no—
196C2×Dic61#9914yes—
197C4×D61—44no—
198C4×D61—44no—
199C4×D61—44no—
200C4×D61—44no—
201Dic122—81no—
202Dic122—81no—
203C8×C61—81no—
204#92418—81no—
205#9146—611nomaximal, Sylow
206C22×C61—21no—
207C22×C61—21no—
208C22×C61—21no—
209C22×C61—21no—
210C22×C61—22no—
211C22×C61—22no—
212C22×C61—22no—
213C22×C61—22no—
214C22×C61#38611yescharacteristic
215C22×C61C2×#9912yes—
216C22×C61#41611yescharacteristic
217C22×C61#41911yescharacteristic
218C22×C61C2×#10412yes—
219C22×C61#45211yescharacteristic
220C22×C61#45211yescharacteristic
221C22×C61#48511yescharacteristic
222C22×C61#48511yescharacteristic
223C2×D61—24no—
224C2×D61—24no—
225C2×D61—24no—
226C2×D61—44no—
227C2×D61—44no—
228C2×D61—44no—
229C2×D61—44no—
230C2×D61—42no—
231C2×D61—42no—
232C2×D61—42no—
233C2×D61—42no—
234C4×C61—21no—
235C4×C61—21no—
236C4×C61—21no—
237C4×C61—21no—
238C4×C61—44no—
239C4×C61—82no—
240Dic61—24no—
241Dic61—44no—
242Dic61—81no—
243Dic61—81no—
244#2848—611no—
245C2×C4×C22⋊C4—611no—
246#1779—611no—
247C2×#328—611no—
248C2×#328—611no—
249#1294—611no—
250#1294D6111yescharacteristic, complemented
251C2×C61—21no—
252C2×C61—21no—
253C2×C61—21no—
254C2×C61—21no—
255C2×C61#150112yes—
256C2×C61#150812yes—
257C2×C61#187311yescharacteristic
258C2×C61#189611yescharacteristic
259C2×C61#189811yescharacteristic
260D61—44no—
261C24×C4—611no—
262C2×C22⋊Q8—611no—
263C2×C22⋊Q8—612no—
264C22×C22⋊C4—1221no—
265C22×C42—1221no—
266C2×C22⋊C8—611no—
267C2×C22⋊C8—1222no—
268C2×C22⋊C8C2×D6111yescharacteristic
269#385—1222no—
270#385—1221no—
271#380—612no—
272#380C2×D6111yescharacteristic
273#379—1221no—
274C4×C22⋊C4—1222no—
275C4×C22⋊C4—1222no—
276C2×#95—611no—
277C2×#95C2×D6111yescharacteristic
278#328—1222no—
279#328—1222no—
280C61#914611yescharacteristic, complemented, Sylow
281C25—611no—
282C22×Q8—611no—
283C23×C4—21no—
284C23×C4—611no—
285C23×C4—612no—
286C23×C4—612no—
287C23×C4—1221no—
288C23×C4—1221no—
289C23×C4—1221no—
290C23×C4—1221no—
291C23×C4—1221no—
292C23×C4—2444no—
293C23×C4C22×D6111yescharacteristic
294C22×C8—21no—
295C22×C8—1221no—
296C22⋊Q8—1221no—
297C22⋊Q8—1221no—
298C22⋊Q8—1221no—
299C22⋊Q8—1221no—
300C22⋊Q8—2444no—
301C2×C4⋊C4—611no—
302C2×C4⋊C4—1222no—
303C2×C4⋊C4—1221no—
304C2×C4⋊C4C4×D6112yes—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—1224no—
307C2×C22⋊C4—1228no—
308C2×C22⋊C4—1222no—
309C2×C22⋊C4—1222no—
310C2×C22⋊C4—1221no—
311C2×C42—1224no—
312C2×C42—2444no—
313C22⋊C8—21no—
314C22⋊C8—21no—
315C22⋊C8—1221no—
316C22⋊C8—1221no—
317C22⋊C8—2444no—
318#95—21no—
319#95—21no—
320#95—612no—
321#95—1222no—
322#95—1221no—
323#95D24412yes—
324C24—612no—
325C24—1224no—
326C24—1221no—
327C24—1221no—
328C24—1221no—
329C24—1221no—
330C24—1221no—
331C24—1221no—
332C24—2442no—
333C24D4×D6111yescharacteristic
334C2×Q8—1221no—
335C2×Q8—1221no—
336C2×Q8—2442no—
337C22×C4—24no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—42no—
341C22×C4—42no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4—612no—
345C22×C4—1224no—
346C22×C4—1224no—
347C22×C4—1224no—
348C22×C4—1221no—
349C22×C4—1221no—
350C22×C4—1224no—
351C22×C4—1222no—
352C22×C4—1222no—
353C22×C4—1222no—
354C22×C4—1222no—
355C22×C4—1222no—
356C22×C4—1221no—
357C22×C4—1221no—
358C22×C4—2442no—
359C22×C4—2442no—
360C22×C4—2444no—
361C22×C4—2444no—
362C22×C4—2444no—
363C22×C4—2444no—
364C22×C4—2442no—
365C22×C4—2441no—
366C22×C4—2441no—
367C22×C4C2×C4×D6111yescharacteristic
368C22×C4C2×D24411yescharacteristic
369C22×C4#1175822211yescharacteristic
370C22×C4D4×D6111yescharacteristic
371C22×C4D4×D6111yescharacteristic
372C22×C4#1175822611yescharacteristic
373C2×C8—42no—
374C2×C8—41no—
375C2×C8—2442no—
376C2×C8—2441no—
377C4⋊C4—42no—
378C4⋊C4—1221no—
379C4⋊C4—1221no—
380C4⋊C4—2444no—
381C4⋊C4—2441no—
382C4⋊C4—2441no—
383C22⋊C4—41no—
384C22⋊C4—41no—
385C22⋊C4—12216no—
386C22⋊C4—2444no—
387C22⋊C4—2444no—
388C22⋊C4—2441no—
389C22⋊C4—2441no—
390C42—2448no—
391C23—22no—
392C23—22no—
393C23—614no—
394C23—1224no—
395C23—1224no—
396C23—1222no—
397C23—1222no—
398C23—1222no—
399C23—1222no—
400C23—1222no—
401C23—1222no—
402C23—2444no—
403C23—2444no—
404C23—2444no—
405C23—2444no—
406C23—2442no—
407C23—2442no—
408C23—2441no—
409C23—2441no—
410C23—2441no—
411C23—2441no—
412C23C22⋊C4×D6111yescharacteristic
413C23#1451974711yescharacteristic
414C23#1451976211yescharacteristic
415C23#1451979611yescharacteristic
416C23#1451979811yescharacteristic
417C23#1451980611yescharacteristic
418C23#1451980911yescharacteristic
419Q8—4881no—
420Q8—4881no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—24no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—44no—
430C2×C4—44no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—614no—
436C2×C4—1224no—
437C2×C4—1224no—
438C2×C4—1222no—
439C2×C4—1222no—
440C2×C4—1224no—
441C2×C4—2444no—
442C2×C4—2444no—
443C2×C4—2444no—
444C2×C4—2444no—
445C2×C4—2442no—
446C2×C4—2442no—
447C2×C4—2441no—
448C2×C4—2441no—
449C2×C4—2442no—
450C2×C4—2444no—
451C2×C4—2444no—
452C2×C4—2442no—
453C2×C4#1451973911yescharacteristic
454C2×C4C4×D24411yescharacteristic
455C2×C4#1451975011yescharacteristic
456C2×C4#1451975211yescharacteristic
457C8—81no—
458C8—4881no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—22no—
464C22—22no—
465C22—22no—
466C22—22no—
467C22—1224no—
468C22—1224no—
469C22—1224no—
470C22—2444no—
471C22—2444no—
472C22—2444no—
473C22—2444no—
474C22—2442no—
475C22—2442no—
476C22—2442no—
477C22—2442no—
478C22#1683964011yescharacteristic
479C22#99×D6112yes—
480C22#1683975511yescharacteristic
481C22#1683976911yescharacteristic
482C22#104×D6112yes—
483C22#1683992511yescharacteristic
484C22#1683992711yescharacteristic
485C22#1684010511yescharacteristic
486C22#1684010611yescharacteristic
487C4—21no—
488C4—21no—
489C4—21no—
490C4—21no—
491C4—44no—
492C4—82no—
493C4—1224no—
494C4—4881no—
495C4—4881no—
496C4—2444no—
497C2—21no—
498C2—21no—
499C2—21no—
500C2—21no—
501C2—2444no—
502C2#2144430712yes—
503C2#2144433712yes—
504C2#2144613011yescharacteristic
505C2#2144626111yescharacteristic
506C2#2144627111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1294C2
socleC23×C61C2×C22⋊C4
prime radicalC24×D61D4
cosocleC23×C4×C61C23
hypercenter#1294D61
hypocenterC61#9146
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
4. C2×#16839500C2semidirect
5. C2×#16839498C2semidirect
6. #21443697C2semidirect
7. C61×#1294C2semidirect
9. C2×#14519757C4semidirect
17. #16839619C4semidirect
250. #1294D61semidirect
280. C61#9146semidirect

Maximal subgroups

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

subgroupindex
#214541072
C2×#168396092
#214457282
C2×#168395002
C2×#168394982
#214436972
C61×#12942
#914661