Finite Group Databasebeta

← #29575363

Subgroups — #29575363

Order 15616.

606 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839813C211yesmaximal, characteristic
2C4×#14519757C211yesmaximal, characteristic
3#21445796C211yesmaximal, characteristic
4C2×#16839494C211yesmaximal, characteristic, complemented
5C2×#16839492C211yesmaximal, characteristic, complemented
6#21443660C211yesmaximal, characteristic, complemented
7C61×#1279C211yesmaximal, characteristic, complemented
8C2×#14519757C411yescharacteristic
9C2×C4×Dic122C2211yescharacteristic
10C2×C42×D61C2211yescharacteristic
11#16839813—22no—
12#16839813—22no—
13C2×C4⋊#92418C2211yescharacteristic
14C2×#14519706—21no—
15C2×#14519689—21no—
16C2×#14519689—21no—
17C2×C4×#92418C2211yescharacteristic
18#16839667C411yescharacteristic
19#16839661C411yescharacteristic
20#16839647—21no—
21#16839636—21no—
22#16839619C411yescharacteristic
23C4×C4⋊Dic61—21no—
24C4×#11758198—21no—
25#16839516—21no—
26#16839494—22no—
27#16839492—22no—
28C2×C4⋊C8×C61C2211yescharacteristic
29C2×C4×C8×C61C2211yescharacteristic
30C4×C4⋊C4×C61C2211yescharacteristic
31C22×Dic122C2×C411yescharacteristic
32C22×C4×D61C2×C411yescharacteristic
33C22×C4×D61D411yescharacteristic
34C22×C4×D61D411yescharacteristic
35C22×#92418—21no—
36C22×#92418—21no—
37#14519757—22no—
38#14519757—22no—
39C4×Dic122—21no—
40C4×Dic122—21no—
41C4×Dic122—21no—
42C4×Dic122—21no—
43C2×C4⋊Dic61—21no—
44C2×C4⋊Dic61—21no—
45C2×C4⋊Dic61C2×C411yescharacteristic
46C2×#11758196—21no—
47C2×#11758198—21no—
48C2×#11758198—21no—
49C2×C4×Dic61—21no—
50C2×C4×Dic61C2×C411yescharacteristic
51C2×C4×Dic61D411yescharacteristic
52C2×C4×Dic61D411yescharacteristic
53C42×D61—21no—
54C42×D61—21no—
55C42×D61—21no—
56C42×D61—21no—
57C4⋊#92418—21no—
58C4⋊#92418—21no—
59#14519706—24no—
60#14519689—24no—
61#14519689—42no—
62C4×#92418—21no—
63C4×#92418D412yes—
64#14519684—21no—
65#14519684—21no—
66#14519684—21no—
67#14519684—21no—
68C22×C8×C61—21no—
69C22×C8×C61—21no—
70C2×C4⋊C4×C61C2×C411yescharacteristic
71C2×C4⋊C4×C61C2×C411yescharacteristic
72C2×C42×C61—21no—
73C2×C42×C61C2311yescharacteristic
74C4⋊C8×C61—21no—
75C4⋊C8×C61—21no—
76C4×C8×C61—21no—
77C4×C8×C61D412yes—
78#95×C61—21no—
79C23×D61C22⋊C411yescharacteristic
80C22×C4×C61—21no—
81C22×C4×C61—21no—
82C22×C4×C61C22×C411yescharacteristic
83C22×C4×C61C2×D411yescharacteristic
84C22×C4×C61C2×D411yescharacteristic
85C22×Dic61—21no—
86C22×Dic61—21no—
87C22×Dic61C22⋊C411yescharacteristic
88C22×Dic61C22⋊C411yescharacteristic
89C22×Dic61C22⋊C411yescharacteristic
90C2×C4×D61—21no—
91C2×C4×D61—21no—
92C2×C4×D61—21no—
93C2×C4×D61—21no—
94C2×C4×D61—21no—
95C2×C4×D61—21no—
96C2×C4×D61—21no—
97C2×C4×D61—21no—
98C2×C4×D61—21no—
99C2×C4×D61—21no—
100C2×C4×D61—21no—
101C2×C4×D61—21no—
102C2×C4×D61—41no—
103C2×C4×D61—41no—
104C2×C4×D61SD1612yes—
105C2×C4×D61Q1612yes—
106C2×Dic122—21no—
107C2×Dic122—21no—
108C2×Dic122—21no—
109C2×Dic122—21no—
110C2×Dic122—21no—
111C2×Dic122M1612yes—
112C2×C8×C61—22no—
113C2×C8×C61—41no—
114C2×C8×C61—41no—
115C2×C8×C61—41no—
116C2×C8×C61—41no—
117C2×C8×C61—41no—
118C4⋊C4×C61—21no—
119C4⋊C4×C61—21no—
120C4⋊C4×C61—21no—
121C4⋊C4×C61M1612yes—
122C42×C61—41no—
123C42×C61—41no—
124C42×C61C2×D411yescharacteristic
125C42×C61C2×D411yescharacteristic
126C42×C61#4111yescharacteristic
127C42×C61#4111yescharacteristic
128#11758198—24no—
129#11758198—42no—
130C4⋊Dic61—24no—
131C4⋊Dic61—21no—
132C4⋊Dic61—21no—
133C4⋊Dic61—42no—
134#11758196—41no—
135#11758196—41no—
136C4×Dic61—21no—
137C4×Dic61—21no—
138C4×Dic61—21no—
139C4×Dic61—21no—
140C4×Dic61—21no—
141C4×Dic61—21no—
142C4×Dic61—41no—
143C4×Dic61—41no—
144C2×#92418—22no—
145C2×#92418—41no—
146C2×#92418—41no—
147C2×#92418—41no—
148C2×#92418—41no—
149C2×#92418—41no—
150C23×C61C2×C22⋊C411yescharacteristic
151C22×D61—21no—
152C22×D61—21no—
153C22×D61—21no—
154C22×D61—21no—
155C22×D61—21no—
156C22×D61—21no—
157C22×D61#10312yes—
158C2×C4×C61—21no—
159C2×C4×C61—21no—
160C2×C4×C61—22no—
161C2×C4×C61—41no—
162C2×C4×C61—41no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61—41no—
166C2×C4×C61C4×D411yescharacteristic
167C2×C4×C61C4×D411yescharacteristic
168C2×C4×C61#12011yescharacteristic
169C2×C4×C61#12111yescharacteristic
170C2×C4×C61#12111yescharacteristic
171C2×C4×C61#12311yescharacteristic
172C2×C4×C61C2×M1611yescharacteristic
173C2×C4×C61C2×M1611yescharacteristic
174C2×C4×C61#13111yescharacteristic
175C2×C4×C61#13111yescharacteristic
176C2×C4×C61C2×SD1611yescharacteristic
177C2×C4×C61C2×Q1611yescharacteristic
178C2×C4×C61#13511yescharacteristic
179C2×C4×C61#13511yescharacteristic
180C2×Dic61—21no—
181C2×Dic61—21no—
182C2×Dic61—21no—
183C2×Dic61—21no—
184C2×Dic61—21no—
185C2×Dic61—22no—
186C2×Dic61—21no—
187C2×Dic61—21no—
188C2×Dic61—21no—
189C2×Dic61—41no—
190C2×Dic61—41no—
191C2×Dic61—41no—
192C2×Dic61—41no—
193C2×Dic61—41no—
194C2×Dic61#10312yes—
195C4×D61—22no—
196C4×D61—22no—
197C4×D61—22no—
198C4×D61—22no—
199C4×D61—42no—
200C4×D61—42no—
201C4×D61—41no—
202C4×D61—41no—
203C4×D61—41no—
204C4×D61—41no—
205Dic122—22no—
206Dic122—22no—
207Dic122—41no—
208Dic122—41no—
209C8×C61—42no—
210C8×C61—81no—
211#92418—42no—
212#92418—81no—
213#9075—611nomaximal, Sylow
214C22×C61#38611yescharacteristic
215C22×C61#40711yescharacteristic
216C22×C61#40811yescharacteristic
217C22×C61C2×#10311yescharacteristic
218C22×C61#41611yescharacteristic
219C22×C61#42111yescharacteristic
220C22×C61#42111yescharacteristic
221C2×D61—22no—
222C2×D61—22no—
223C2×D61—22no—
224C2×D61—41no—
225C2×D61—41no—
226C2×D61—41no—
227C2×D61—41no—
228C4×C61—21no—
229C4×C61—21no—
230C4×C61—42no—
231C4×C61—81no—
232C4×C61#43511yescharacteristic
233C4×C61#43511yescharacteristic
234C4×C61#43611yescharacteristic
235C4×C61#43611yescharacteristic
236C4×C61#46511yescharacteristic
237C4×C61#46511yescharacteristic
238C4×C61#46711yescharacteristic
239C4×C61#46711yescharacteristic
240Dic61—22no—
241Dic61—42no—
242Dic61—41no—
243Dic61—41no—
244Dic61—81no—
245C2×#431—611no—
246C4×C22⋊Q8—611no—
247#1797—611no—
248C2×Q8⋊C8—611no—
249C2×Q8⋊C8—611no—
250#1279—611no—
251#1279D6111yescharacteristic, complemented
252C2×C61#148111yescharacteristic
253C2×C61#148211yescharacteristic
254C2×C61#148711yescharacteristic
255C2×C61#148811yescharacteristic
256C2×C61#187011yescharacteristic
257C2×C61#189211yescharacteristic
258C2×C61#189711yescharacteristic
259D61—42no—
260C2×C22⋊Q8—611no—
261C2×C4×Q8—611no—
262C22×C42—611no—
263#431—1222no—
264#431—1222no—
265C2×C4⋊C8—611no—
266C2×C4⋊C8—1221no—
267C2×C4⋊C8C2×D6111yescharacteristic
268C2×C22⋊C8—1221no—
269C2×C22⋊C8—1221no—
270C2×C4×C8—611no—
271C2×C4×C8C2×D6111yescharacteristic
272#391—611no—
273#389—611no—
274#387—1221no—
275#385—1221no—
276#380—611no—
277C4×C4⋊C4—1221no—
278C4×C4⋊C4C2×D6111yescharacteristic
279C4×C22⋊C4—1221no—
280#336—1221no—
281Q8⋊C8—1222no—
282Q8⋊C8—1222no—
283C61#907511yescharacteristic, complemented, Sylow
284C22×Q8—611no—
285C23×C4—611no—
286C23×C4—611no—
287C23×C4—611no—
288C22×C8—21no—
289C22×C8—21no—
290C22×C8—1221no—
291C22×C8—1221no—
292C22⋊Q8—1222no—
293C22⋊Q8—1222no—
294C4×Q8—1221no—
295C4×Q8—1221no—
296C4×Q8—1221no—
297C4×Q8—1221no—
298C2×C4⋊C4—611no—
299C2×C4⋊C4—1221no—
300C2×C4⋊C4—1221no—
301C2×C4⋊C4—1221no—
302C2×C4⋊C4C4×D6111yescharacteristic
303C2×C4⋊C4C4×D6111yescharacteristic
304C2×C22⋊C4—1221no—
305C2×C22⋊C4—1221no—
306C2×C42—21no—
307C2×C42—611no—
308C2×C42—611no—
309C2×C42—611no—
310C2×C42—1221no—
311C2×C42—1221no—
312C2×C42—1221no—
313C2×C42—1221no—
314C2×C42—1221no—
315C2×C42C22×D6111yescharacteristic
316C4⋊C8—21no—
317C4⋊C8—21no—
318C4⋊C8—1224no—
319C4⋊C8—1221no—
320C4⋊C8—1221no—
321C22⋊C8—1224no—
322C22⋊C8—2442no—
323C4×C8—21no—
324C4×C8—612no—
325C4×C8—1221no—
326C4×C8D24412yes—
327#95—21no—
328#95—1221no—
329#95—1221no—
330#95—1221no—
331#95—1221no—
332C24—611no—
333C2×Q8—612no—
334C2×Q8—1221no—
335C2×Q8—1221no—
336C2×Q8—1221no—
337C2×Q8—1221no—
338C2×Q8—1221no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—611no—
342C22×C4—612no—
343C22×C4—612no—
344C22×C4—611no—
345C22×C4—611no—
346C22×C4—1221no—
347C22×C4—1221no—
348C22×C4—1221no—
349C22×C4—1221no—
350C22×C4—1221no—
351C22×C4—1221no—
352C22×C4—1221no—
353C22×C4—1221no—
354C22×C4—1221no—
355C22×C4—1221no—
356C22×C4—1221no—
357C22×C4—1221no—
358C22×C4—1221no—
359C22×C4—1221no—
360C22×C4—2441no—
361C22×C4—2441no—
362C22×C4C2×C4×D6111yescharacteristic
363C22×C4D4×D6111yescharacteristic
364C22×C4D4×D6111yescharacteristic
365C2×C8—22no—
366C2×C8—41no—
367C2×C8—41no—
368C2×C8—41no—
369C2×C8—41no—
370C2×C8—41no—
371C2×C8—1222no—
372C2×C8—2441no—
373C2×C8—2441no—
374C2×C8—2441no—
375C2×C8—2441no—
376C2×C8—2441no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—1224no—
381C4⋊C4—1221no—
382C4⋊C4—1221no—
383C4⋊C4—2442no—
384C4⋊C4—2441no—
385C4⋊C4—2441no—
386C4⋊C4#1175818912yes—
387C22⋊C4—1224no—
388C22⋊C4—2442no—
389C42—41no—
390C42—41no—
391C42—1221no—
392C42—1221no—
393C42—1221no—
394C42—1221no—
395C42—1221no—
396C42—1221no—
397C42—2441no—
398C42—2441no—
399C42C2×D24411yescharacteristic
400C42#1175822211yescharacteristic
401C42D4×D6111yescharacteristic
402C42#1175822611yescharacteristic
403C23—612no—
404C23—1221no—
405C23—1221no—
406C23—1221no—
407C23—1221no—
408C23—1221no—
409C23—1221no—
410C23C22⋊C4×D6111yescharacteristic
411Q8—1222no—
412Q8—1222no—
413Q8—2441no—
414Q8—2441no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—22no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—612no—
424C2×C4—1221no—
425C2×C4—1221no—
426C2×C4—1222no—
427C2×C4—1222no—
428C2×C4—1222no—
429C2×C4—1222no—
430C2×C4—1222no—
431C2×C4—1221no—
432C2×C4—1221no—
433C2×C4—1221no—
434C2×C4—1221no—
435C2×C4—1221no—
436C2×C4—1221no—
437C2×C4—2442no—
438C2×C4—2442no—
439C2×C4—2441no—
440C2×C4—2441no—
441C2×C4—2441no—
442C2×C4—2441no—
443C2×C4—2441no—
444C2×C4—2441no—
445C2×C4—2441no—
446C2×C4—2441no—
447C2×C4—2441no—
448C2×C4#1451973911yescharacteristic
449C2×C4C4×D24411yescharacteristic
450C2×C4#1451974711yescharacteristic
451C2×C4#1451975011yescharacteristic
452C2×C4#1451975211yescharacteristic
453C2×C4#1451976211yescharacteristic
454C2×C4M16×D6111yescharacteristic
455C2×C4C2×#1175818911yescharacteristic
456C2×C4#1451978311yescharacteristic
457C2×C4#1451978511yescharacteristic
458C2×C4SD16×D6111yescharacteristic
459C2×C4Q16×D6111yescharacteristic
460C2×C4#1451979611yescharacteristic
461C2×C4#1451979811yescharacteristic
462C8—42no—
463C8—81no—
464C8—4881no—
465C8—2442no—
466C22—1222no—
467C22—1222no—
468C22—1222no—
469C22—2441no—
470C22—2441no—
471C22—2441no—
472C22—2441no—
473C22#1683964011yescharacteristic
474C22#1683972411yescharacteristic
475C22#1683972711yescharacteristic
476C22#103×D6111yescharacteristic
477C22#1683975511yescharacteristic
478C22#1683977711yescharacteristic
479C22#1683977711yescharacteristic
480C4—21no—
481C4—21no—
482C4—42no—
483C4—81no—
484C4—1222no—
485C4—4881no—
486C4—2441no—
487C4—2441no—
488C4—2442no—
489C4#1683983211yescharacteristic
490C4#1683983511yescharacteristic
491C4#1683983911yescharacteristic
492C4#1683984111yescharacteristic
493C4#1683999011yescharacteristic
494C4#1683999211yescharacteristic
495C4#1684000211yescharacteristic
496C4#1684000411yescharacteristic
497C2—2442no—
498C2#2144422011yescharacteristic
499C2#2144422411yescharacteristic
500C2#2144424611yescharacteristic
501C2#2144425011yescharacteristic
502C2#2144611511yescharacteristic
503C2#2144624111yescharacteristic
504C2#2144626611yescharacteristic
subgroupG/H
centerC22×C4D4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1279C2
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1279D61
hypocenterC61#9075
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
4. C2×#16839494C2semidirect
5. C2×#16839492C2semidirect
6. #21443660C2semidirect
7. C61×#1279C2semidirect
251. #1279D61semidirect
283. C61#9075semidirect

Maximal subgroups

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

subgroupindex
C2×#168398132
C4×#145197572
#214457962
C2×#168394942
C2×#168394922
#214436602
C61×#12792
#907561