Finite Group Databasebeta

← #29575607

Subgroups — #29575607

Order 15616.

696 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#97×D61C211yesmaximal, characteristic, complemented
2#21454121C211yesmaximal, characteristic
3#21445582C211yesmaximal, characteristic, complemented
4C2×#16839501C211yesmaximal, characteristic, complemented
5C2×#16839501C211yesmaximal, characteristic, complemented
6#21443700C211yesmaximal, characteristic, complemented
7C61×#1295C211yesmaximal, characteristic, complemented
8C22×C8×D61—21no—
9C2×#14519765C2211yescharacteristic
10C2×#14519757C411yescharacteristic
11C2×#14519752C411yescharacteristic
12C2×C42×D61C2211yescharacteristic
13C2×#14519689—21no—
14C2×#14519688C2211yescharacteristic
15C2×#14519688C2211yescharacteristic
16C2×#14519687—21no—
17#97×D61—22no—
18#97×D61—22no—
19#16839667C411yescharacteristic
20#16839663C411yescharacteristic
21#16839654—21no—
22#16839654—21no—
23#16839640—21no—
24#16839640—21no—
25#16839516—21no—
26#16839501—22no—
27#16839501—22no—
28C2×#97×C61C2211yescharacteristic
29C2×#97×C61C2211yescharacteristic
30C61×#382C2211yescharacteristic
31C22×Dic122C2×C411yescharacteristic
32C22×D244—21no—
33C22×D244C2×C411yescharacteristic
34C22×C4×D61C2×C411yescharacteristic
35C22×C4×D61D411yescharacteristic
36C22×C4×D61D411yescharacteristic
37C22×#92418—21no—
38C22×#92418—21no—
39C2×C8×D61—24no—
40C2×C8×D61—24no—
41C2×C8×D61—24no—
42#14519765—21no—
43#14519765—21no—
44#14519765—21no—
45#14519765—21no—
46#14519757—42no—
47#14519752—42no—
48C2×C4⋊Dic61—21no—
49C2×#11758198—21no—
50C2×#11758198—21no—
51C2×#11758198—21no—
52C2×#11758198—21no—
53C2×#11758198—21no—
54C2×#11758198—21no—
55C2×C4×Dic61C2×C411yescharacteristic
56C2×C4×Dic61D411yescharacteristic
57C2×C4×Dic61D411yescharacteristic
58C42×D61—21no—
59C42×D61—21no—
60C42×D61—21no—
61C42×D61—21no—
62#14519689—24no—
63#14519688—21no—
64#14519688—21no—
65#14519688—21no—
66#14519688D412yescomplemented
67#14519687—24no—
68#14519684—21no—
69#14519684—21no—
70C22×C8×C61—21no—
71C22×C8×C61—21no—
72C2×C4⋊C4×C61C2×C411yescharacteristic
73C2×C4⋊C4×C61C2×C411yescharacteristic
74C2×C42×C61C2311yescharacteristic
75#97×C61—21no—
76#97×C61—21no—
77#97×C61—21no—
78#97×C61D412yescomplemented
79#95×C61—21no—
80#95×C61—21no—
81C23×D61—21no—
82C23×D61C22⋊C411yescharacteristic
83C22×C4×C61—21no—
84C22×C4×C61—21no—
85C22×C4×C61C22×C411yescharacteristic
86C22×C4×C61C2×D411yescharacteristic
87C22×C4×C61C2×D411yescharacteristic
88C22×Dic61—21no—
89C22×Dic61C22⋊C411yescharacteristic
90C22×Dic61C22⋊C411yescharacteristic
91C22×Dic61C22⋊C411yescharacteristic
92C2×D244—21no—
93C2×D244—21no—
94C2×D244—41no—
95C2×D244—41no—
96C2×D244—42no—
97C2×D244—42no—
98C2×D244—42no—
99C2×C4×D61—22no—
100C2×C4×D61—21no—
101C2×C4×D61—21no—
102C2×C4×D61—22no—
103C2×C4×D61—22no—
104C2×C4×D61—22no—
105C2×C4×D61—21no—
106C2×C4×D61—21no—
107C2×C4×D61—21no—
108C2×C4×D61—21no—
109C2×C4×D61—41no—
110C2×C4×D61—41no—
111C2×Dic122—21no—
112C2×Dic122—21no—
113C2×Dic122—41no—
114C2×Dic122—41no—
115C2×C8×C61—22no—
116C2×C8×C61—22no—
117C2×C8×C61—22no—
118C2×C8×C61—22no—
119C2×C8×C61—41no—
120C2×C8×C61—41no—
121C4⋊C4×C61—41no—
122C4⋊C4×C61—41no—
123C42×C61C2×D411yescharacteristic
124C42×C61C2×D411yescharacteristic
125C42×C61#4111yescharacteristic
126C42×C61#4111yescharacteristic
127#11758198—42no—
128#11758198—42no—
129#11758198—42no—
130#11758198—41no—
131#11758198—41no—
132#11758198—41no—
133#11758198—41no—
134#11758198—42no—
135C4⋊Dic61—42no—
136C4×Dic61—21no—
137C4×Dic61—21no—
138C4×Dic61—21no—
139C4×Dic61—21no—
140C4×Dic61—21no—
141C4×Dic61—21no—
142C2×#92418—22no—
143C2×#92418—22no—
144C2×#92418—22no—
145C2×#92418—22no—
146C2×#92418—41no—
147C2×#92418—41no—
148C8×D61—216no—
149C23×C61C2×C22⋊C411yescharacteristic
150C22×D61—21no—
151C22×D61—21no—
152C22×D61—21no—
153C22×D61—21no—
154C22×D61—41no—
155C22×D61—41no—
156C22×D61—41no—
157C22×D61—41no—
158C22×D61—41no—
159C22×D61—41no—
160C22×D61—41no—
161C22×D61#10012yes—
162C22×D61#10412yes—
163C22×D61#10412yes—
164C2×C4×C61—21no—
165C2×C4×C61—21no—
166C2×C4×C61—21no—
167C2×C4×C61—21no—
168C2×C4×C61—21no—
169C2×C4×C61—21no—
170C2×C4×C61—41no—
171C2×C4×C61—41no—
172C2×C4×C61—41no—
173C2×C4×C61—41no—
174C2×C4×C61—41no—
175C2×C4×C61—41no—
176C2×C4×C61C4×D411yescharacteristic
177C2×C4×C61C4×D411yescharacteristic
178C2×C4×C61#12011yescharacteristic
179C2×C4×C61#12111yescharacteristic
180C2×C4×C61#12111yescharacteristic
181C2×C4×C61#12311yescharacteristic
182C2×Dic61—21no—
183C2×Dic61—21no—
184C2×Dic61—21no—
185C2×Dic61—21no—
186C2×Dic61—21no—
187C2×Dic61—21no—
188C2×Dic61—21no—
189C2×Dic61—21no—
190C2×Dic61—41no—
191C2×Dic61—41no—
192C2×Dic61—41no—
193C2×Dic61#10412yes—
194D244—81no—
195D244—81no—
196D244—84no—
197C4×D61—24no—
198C4×D61—24no—
199C4×D61—42no—
200C4×D61—42no—
201C4×D61—42no—
202C4×D61—42no—
203Dic122—81no—
204Dic122—81no—
205C8×C61—24no—
206C8×C61—42no—
207#92418—24no—
208#92418—42no—
209#9119—611nomaximal, Sylow
210C22×C61#38611yescharacteristic
211C22×C61C2×#10011yescharacteristic
212C22×C61#41311yescharacteristic
213C22×C61C2×#10411yescharacteristic
214C22×C61C2×#10411yescharacteristic
215C22×C61C2×#10411yescharacteristic
216C22×C61#42111yescharacteristic
217C2×D61—22no—
218C2×D61—22no—
219C2×D61—22no—
220C2×D61—22no—
221C2×D61—22no—
222C2×D61—22no—
223C2×D61—81no—
224C2×D61—81no—
225C2×D61—81no—
226C2×D61—81no—
227C2×D61—81no—
228C2×D61—81no—
229C2×D61—81no—
230C2×D61#32914yescomplemented
231C4×C61—21no—
232C4×C61—21no—
233C4×C61—21no—
234C4×C61—21no—
235C4×C61—21no—
236C4×C61—21no—
237C4×C61—81no—
238C4×C61—81no—
239Dic61—22no—
240Dic61—41no—
241Dic61—41no—
242Dic61—81no—
243C22×#97—611no—
244#2850—611no—
245#1749—611no—
246C2×#329—611no—
247C2×#329—611no—
248#1295—611no—
249#1295D6111yescharacteristic, complemented
250C2×C61C2×#32911yescharacteristic
251C2×C61#152411yescharacteristic
252C2×C61#153011yescharacteristic
253C2×C61#153211yescharacteristic
254C2×C61#187111yescharacteristic
255C2×C61#189611yescharacteristic
256C2×C61#190011yescharacteristic
257D61—24no—
258D61—161no—
259C23×C8—1221no—
260C2×#124—611no—
261C2×C22⋊Q8—611no—
262C2×#121—611no—
263C22×C42—611no—
264C2×C22⋊C8—1221no—
265C2×#97—611no—
266C2×#97—611no—
267C2×#97—1222no—
268C2×#97—1221no—
269C2×#97—1222no—
270C2×#97C2×D6111yescharacteristic
271C2×#97C2×D6111yescharacteristic
272#391—611no—
273#390—611no—
274#388—1221no—
275#388—1221no—
276#386—1221no—
277#386—1221no—
278#382C2×D6111yescharacteristic
279#336—1221no—
280#329—1222no—
281#329—1222no—
282C61#911911yescharacteristic, complemented, Sylow
283C22×Q8—611no—
284C22×D4—611no—
285C22×D4—1221no—
286C23×C4—611no—
287C23×C4—611no—
288C23×C4—611no—
289C22×C8—21no—
290C22×C8—21no—
291C22×C8—1224no—
292C22×C8—1224no—
293C22×C8—1224no—
294C22×C8—1221no—
295C22×C8—1221no—
296#124—1221no—
297#124—1221no—
298#124—1221no—
299#124—1221no—
300C22⋊Q8—2442no—
301#121—2442no—
302C2×C4⋊C4—1221no—
303C2×C4⋊C4C4×D6111yescharacteristic
304C2×C4⋊C4C4×D6111yescharacteristic
305C2×C22⋊C4—1221no—
306C2×C22⋊C4—1221no—
307C2×C22⋊C4—1221no—
308C2×C22⋊C4—1221no—
309C2×C22⋊C4—1221no—
310C2×C22⋊C4—1221no—
311C2×C42—611no—
312C2×C42—611no—
313C2×C42—611no—
314C2×C42—1221no—
315C2×C42—1221no—
316C2×C42—1221no—
317C2×C42—1221no—
318C2×C42C22×D6111yescharacteristic
319C22⋊C8—1224no—
320#97—21no—
321#97—21no—
322#97—21no—
323#97—612no—
324#97—1224no—
325#97—1221no—
326#97—1221no—
327#97—1221no—
328#97D24412yescomplemented
329#95—21no—
330#95—21no—
331#95—1221no—
332#95—1221no—
333C24—611no—
334C24—1221no—
335C2×Q8—1221no—
336C2×Q8—1221no—
337C2×Q8—2441no—
338C2×Q8—2441no—
339C2×D4—1221no—
340C2×D4—1221no—
341C2×D4—2441no—
342C2×D4—2441no—
343C2×D4—2442no—
344C2×D4—2442no—
345C2×D4—2442no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—611no—
349C22×C4—611no—
350C22×C4—611no—
351C22×C4—1222no—
352C22×C4—1222no—
353C22×C4—1222no—
354C22×C4—1222no—
355C22×C4—1221no—
356C22×C4—1221no—
357C22×C4—1221no—
358C22×C4—1221no—
359C22×C4—1221no—
360C22×C4—1221no—
361C22×C4—1221no—
362C22×C4—2441no—
363C22×C4—2441no—
364C22×C4C2×C4×D6111yescharacteristic
365C22×C4D4×D6111yescharacteristic
366C22×C4D4×D6111yescharacteristic
367C2×C8—22no—
368C2×C8—22no—
369C2×C8—22no—
370C2×C8—22no—
371C2×C8—41no—
372C2×C8—41no—
373C2×C8—12216no—
374C2×C8—1222no—
375C2×C8—1222no—
376C2×C8—1222no—
377C2×C8—1222no—
378C2×C8—2441no—
379C2×C8—2441no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C4⋊C4—2442no—
383C22⋊C4—2442no—
384C22⋊C4—2442no—
385C22⋊C4—2442no—
386C22⋊C4—2442no—
387C22⋊C4—2441no—
388C22⋊C4—2441no—
389C22⋊C4—2441no—
390C22⋊C4—2441no—
391C42—1221no—
392C42—1221no—
393C42—1221no—
394C42—1221no—
395C42—1221no—
396C42—1221no—
397C42C2×D24411yescharacteristic
398C42#1175822211yescharacteristic
399C42D4×D6111yescharacteristic
400C42#1175822611yescharacteristic
401C23—612no—
402C23—612no—
403C23—612no—
404C23—1221no—
405C23—1221no—
406C23—1221no—
407C23—1221no—
408C23—2441no—
409C23—2441no—
410C23—2441no—
411C23—2441no—
412C23—2441no—
413C23—2441no—
414C23—2441no—
415C23C22⋊C4×D6111yescharacteristic
416Q8—4881no—
417Q8—4881no—
418D4—4881no—
419D4—4881no—
420D4—4884no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—612no—
434C2×C4—1224no—
435C2×C4—1224no—
436C2×C4—1221no—
437C2×C4—1221no—
438C2×C4—1221no—
439C2×C4—1221no—
440C2×C4—1221no—
441C2×C4—1221no—
442C2×C4—1221no—
443C2×C4—1221no—
444C2×C4—2442no—
445C2×C4—2442no—
446C2×C4—2442no—
447C2×C4—2442no—
448C2×C4—2441no—
449C2×C4—2441no—
450C2×C4—2441no—
451C2×C4#1451973911yescharacteristic
452C2×C4C4×D24411yescharacteristic
453C2×C4#1451974711yescharacteristic
454C2×C4#1451975011yescharacteristic
455C2×C4#1451975211yescharacteristic
456C2×C4#1451976211yescharacteristic
457C8—24no—
458C8—42no—
459C8—1224no—
460C8—2442no—
461C22—614no—
462C22—1222no—
463C22—1222no—
464C22—1222no—
465C22—1222no—
466C22—1222no—
467C22—1222no—
468C22—4881no—
469C22—4881no—
470C22—4881no—
471C22—4881no—
472C22—4881no—
473C22—4881no—
474C22—4881no—
475C22#1683964011yescharacteristic
476C22#100×D6111yescharacteristic
477C22#1683974511yescharacteristic
478C22#104×D6111yescharacteristic
479C22#104×D6111yescharacteristic
480C22#104×D6111yescharacteristic
481C22#1683977711yescharacteristic
482C4—21no—
483C4—21no—
484C4—21no—
485C4—21no—
486C4—21no—
487C4—21no—
488C4—81no—
489C4—81no—
490C4—1222no—
491C4—4881no—
492C4—2441no—
493C4—2441no—
494C2—1224no—
495C2—9761no—
496C2#329×D6111yescharacteristic
497C2#2144440611yescharacteristic
498C2#2144442811yescharacteristic
499C2#2144443811yescharacteristic
500C2#2144612011yescharacteristic
501C2#2144626111yescharacteristic
502C2#2144628111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1295C2
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519752C4
cosocleC2×C42×C61C23
hypercenter#1295D61
hypocenterC61#9119
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
1. C2×#97×D61C2semidirect
3. #21445582C2semidirect
4. C2×#16839501C2semidirect
5. C2×#16839501C2semidirect
6. #21443700C2semidirect
7. C61×#1295C2semidirect
66. #14519688D4semidirect
78. #97×C61D4semidirect
230. C2×D61#329semidirect
249. #1295D61semidirect
282. C61#9119semidirect
328. #97D244semidirect

Maximal subgroups

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

subgroupindex
C2×#97×D612
#214541212
#214455822
C2×#168395012
#214437002
C61×#12952
#911961