Finite Group Databasebeta

← #29575627

Subgroups — #29575627

Order 15616.

600 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839817C211yesmaximal, 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
8C2×#14519765C2211yescharacteristic
9C2×#14519757C411yescharacteristic
10C2×#14519752C411yescharacteristic
11C2×C42×D61C2211yescharacteristic
12#16839817—22no—
13#16839817—22no—
14C2×#14519706—21no—
15C2×#14519689—21no—
16C2×#14519689—21no—
17C2×#14519688C2211yescharacteristic
18C2×#14519688C2211yescharacteristic
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—
39#14519765—21no—
40#14519765—21no—
41#14519765—21no—
42#14519765—21no—
43#14519757—42no—
44#14519752—42no—
45C2×C4⋊Dic61—21no—
46C2×#11758198—21no—
47C2×#11758198—21no—
48C2×#11758198—21no—
49C2×#11758198—21no—
50C2×#11758198—21no—
51C2×#11758198—21no—
52C2×C4×Dic61C2×C411yescharacteristic
53C2×C4×Dic61D411yescharacteristic
54C2×C4×Dic61D411yescharacteristic
55C42×D61—21no—
56C42×D61—21no—
57C42×D61—21no—
58C42×D61—21no—
59#14519706—24no—
60#14519689—24no—
61#14519689—24no—
62#14519688—21no—
63#14519688—21no—
64#14519688—21no—
65#14519688D412yescomplemented
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×C61C2311yescharacteristic
73#97×C61—21no—
74#97×C61—21no—
75#97×C61—21no—
76#97×C61D412yescomplemented
77#95×C61—21no—
78#95×C61—21no—
79C23×D61—21no—
80C23×D61C22⋊C411yescharacteristic
81C22×C4×C61—21no—
82C22×C4×C61—21no—
83C22×C4×C61C22×C411yescharacteristic
84C22×C4×C61C2×D411yescharacteristic
85C22×C4×C61C2×D411yescharacteristic
86C22×Dic61—21no—
87C22×Dic61C22⋊C411yescharacteristic
88C22×Dic61C22⋊C411yescharacteristic
89C22×Dic61C22⋊C411yescharacteristic
90C2×D244—21no—
91C2×D244—21no—
92C2×D244—41no—
93C2×D244—41no—
94C2×D244—42no—
95C2×D244—42no—
96C2×D244—42no—
97C2×C4×D61—22no—
98C2×C4×D61—21no—
99C2×C4×D61—21no—
100C2×C4×D61—21no—
101C2×C4×D61—21no—
102C2×C4×D61—21no—
103C2×C4×D61—21no—
104C2×C4×D61—22no—
105C2×C4×D61—41no—
106C2×C4×D61—41no—
107C2×C4×D61—41no—
108C2×C4×D61—41no—
109C2×Dic122—21no—
110C2×Dic122—21no—
111C2×Dic122—41no—
112C2×Dic122—41no—
113C2×C8×C61—22no—
114C2×C8×C61—22no—
115C2×C8×C61—41no—
116C2×C8×C61—41no—
117C2×C8×C61—41no—
118C2×C8×C61—41no—
119C4⋊C4×C61—41no—
120C4⋊C4×C61—41no—
121C42×C61C2×D411yescharacteristic
122C42×C61C2×D411yescharacteristic
123C42×C61#4111yescharacteristic
124C42×C61#4111yescharacteristic
125#11758198—42no—
126#11758198—42no—
127#11758198—42no—
128#11758198—41no—
129#11758198—41no—
130#11758198—41no—
131#11758198—41no—
132#11758198—42no—
133C4⋊Dic61—42no—
134C4×Dic61—21no—
135C4×Dic61—21no—
136C4×Dic61—21no—
137C4×Dic61—21no—
138C4×Dic61—21no—
139C4×Dic61—21no—
140C2×#92418—22no—
141C2×#92418—22no—
142C2×#92418—41no—
143C2×#92418—41no—
144C2×#92418—41no—
145C2×#92418—41no—
146C23×C61C2×C22⋊C411yescharacteristic
147C22×D61—21no—
148C22×D61—21no—
149C22×D61—21no—
150C22×D61—21no—
151C22×D61—21no—
152C22×D61—21no—
153C22×D61—41no—
154C22×D61—41no—
155C22×D61—41no—
156C22×D61—41no—
157C22×D61—41no—
158C22×D61—41no—
159C22×D61—41no—
160C22×D61#10412yes—
161C2×C4×C61—21no—
162C2×C4×C61—21no—
163C2×C4×C61—21no—
164C2×C4×C61—21no—
165C2×C4×C61—21no—
166C2×C4×C61—21no—
167C2×C4×C61—41no—
168C2×C4×C61—41no—
169C2×C4×C61—41no—
170C2×C4×C61—41no—
171C2×C4×C61—41no—
172C2×C4×C61—41no—
173C2×C4×C61C4×D411yescharacteristic
174C2×C4×C61C4×D411yescharacteristic
175C2×C4×C61#12011yescharacteristic
176C2×C4×C61#12111yescharacteristic
177C2×C4×C61#12111yescharacteristic
178C2×C4×C61#12311yescharacteristic
179C2×Dic61—21no—
180C2×Dic61—21no—
181C2×Dic61—21no—
182C2×Dic61—21no—
183C2×Dic61—21no—
184C2×Dic61—21no—
185C2×Dic61—21no—
186C2×Dic61—21no—
187C2×Dic61—41no—
188C2×Dic61—41no—
189C2×Dic61—41no—
190C2×Dic61#10012yes—
191D244—81no—
192D244—81no—
193D244—84no—
194C4×D61—42no—
195C4×D61—42no—
196C4×D61—42no—
197C4×D61—42no—
198C4×D61—42no—
199C4×D61—42no—
200Dic122—81no—
201Dic122—81no—
202C8×C61—42no—
203C8×C61—42no—
204#92418—42no—
205#92418—42no—
206#9123—611nomaximal, Sylow
207C22×C61#38611yescharacteristic
208C22×C61C2×#10011yescharacteristic
209C22×C61#41311yescharacteristic
210C22×C61C2×#10411yescharacteristic
211C22×C61#42111yescharacteristic
212C22×C61#42111yescharacteristic
213C22×C61#42111yescharacteristic
214C2×D61—22no—
215C2×D61—22no—
216C2×D61—22no—
217C2×D61—41no—
218C2×D61—41no—
219C2×D61—41no—
220C2×D61—41no—
221C2×D61—81no—
222C2×D61—81no—
223C2×D61—81no—
224C2×D61—81no—
225C2×D61—81no—
226C2×D61—81no—
227C2×D61—81no—
228C4×C61—21no—
229C4×C61—21no—
230C4×C61—21no—
231C4×C61—21no—
232C4×C61—21no—
233C4×C61—21no—
234C4×C61—81no—
235C4×C61—81no—
236Dic61—22no—
237Dic61—41no—
238Dic61—41no—
239Dic61—81no—
240C2×#432—611no—
241#2850—611no—
242#1749—611no—
243C2×#329—611no—
244C2×#329—611no—
245#1295—611no—
246#1295D6111yescharacteristic, complemented
247C2×C61#152711yescharacteristic
248C2×C61#153211yescharacteristic
249C2×C61#153511yescharacteristic
250C2×C61#153611yescharacteristic
251C2×C61#187111yescharacteristic
252C2×C61#189711yescharacteristic
253C2×C61#190011yescharacteristic
254D61—42no—
255D61—161no—
256C2×#124—611no—
257C2×C22⋊Q8—611no—
258C2×#121—611no—
259C22×C42—611no—
260#432—1222no—
261#432—1222no—
262C2×C4⋊C8—1221no—
263C2×C22⋊C8—1221no—
264C2×C22⋊C8—1221no—
265C2×#97—611no—
266C2×#97—611no—
267C2×#97C2×D6111yescharacteristic
268C2×#97C2×D6111yescharacteristic
269#391—611no—
270#390—611no—
271#388—1221no—
272#388—1221no—
273#386—1221no—
274#386—1221no—
275#382C2×D6111yescharacteristic
276#336—1221no—
277#329—1222no—
278#329—1222no—
279C61#912311yescharacteristic, complemented, Sylow
280C22×Q8—611no—
281C22×D4—611no—
282C22×D4—1221no—
283C23×C4—611no—
284C23×C4—611no—
285C23×C4—611no—
286C22×C8—21no—
287C22×C8—21no—
288C22×C8—1221no—
289C22×C8—1221no—
290#124—1221no—
291#124—1221no—
292#124—1221no—
293#124—1221no—
294C22⋊Q8—2442no—
295#121—2442no—
296C2×C4⋊C4—1221no—
297C2×C4⋊C4C4×D6111yescharacteristic
298C2×C4⋊C4C4×D6111yescharacteristic
299C2×C22⋊C4—1221no—
300C2×C22⋊C4—1221no—
301C2×C22⋊C4—1221no—
302C2×C22⋊C4—1221no—
303C2×C22⋊C4—1221no—
304C2×C22⋊C4—1221no—
305C2×C42—611no—
306C2×C42—611no—
307C2×C42—611no—
308C2×C42—1221no—
309C2×C42—1221no—
310C2×C42—1221no—
311C2×C42—1221no—
312C2×C42C22×D6111yescharacteristic
313C4⋊C8—1224no—
314C22⋊C8—1224no—
315C22⋊C8—1224no—
316#97—21no—
317#97—21no—
318#97—21no—
319#97—612no—
320#97—1221no—
321#97—1221no—
322#97—1221no—
323#97D24412yescomplemented
324#95—21no—
325#95—21no—
326#95—1221no—
327#95—1221no—
328C24—611no—
329C24—1221no—
330C2×Q8—1221no—
331C2×Q8—1221no—
332C2×Q8—2441no—
333C2×Q8—2441no—
334C2×D4—1221no—
335C2×D4—1221no—
336C2×D4—2441no—
337C2×D4—2441no—
338C2×D4—2442no—
339C2×D4—2442no—
340C2×D4—2442no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—611no—
344C22×C4—611no—
345C22×C4—611no—
346C22×C4—1222no—
347C22×C4—1222no—
348C22×C4—1221no—
349C22×C4—1221no—
350C22×C4—1221no—
351C22×C4—1221no—
352C22×C4—1221no—
353C22×C4—1221no—
354C22×C4—1221no—
355C22×C4—2441no—
356C22×C4—2441no—
357C22×C4—2441no—
358C22×C4—2441no—
359C22×C4C2×C4×D6111yescharacteristic
360C22×C4D4×D6111yescharacteristic
361C22×C4D4×D6111yescharacteristic
362C2×C8—22no—
363C2×C8—22no—
364C2×C8—41no—
365C2×C8—41no—
366C2×C8—41no—
367C2×C8—41no—
368C2×C8—1222no—
369C2×C8—1222no—
370C2×C8—2441no—
371C2×C8—2441no—
372C2×C8—2441no—
373C2×C8—2441no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—2442no—
377C22⋊C4—2442no—
378C22⋊C4—2442no—
379C22⋊C4—2442no—
380C22⋊C4—2442no—
381C22⋊C4—2441no—
382C22⋊C4—2441no—
383C22⋊C4—2441no—
384C22⋊C4—2441no—
385C42—1221no—
386C42—1221no—
387C42—1221no—
388C42—1221no—
389C42—1221no—
390C42—1221no—
391C42C2×D24411yescharacteristic
392C42#1175822211yescharacteristic
393C42D4×D6111yescharacteristic
394C42#1175822611yescharacteristic
395C23—612no—
396C23—1221no—
397C23—1221no—
398C23—1221no—
399C23—1221no—
400C23—1221no—
401C23—1221no—
402C23—2441no—
403C23—2441no—
404C23—2441no—
405C23—2441no—
406C23—2441no—
407C23—2441no—
408C23—2441no—
409C23C22⋊C4×D6111yescharacteristic
410Q8—4881no—
411Q8—4881no—
412D4—4881no—
413D4—4881no—
414D4—4884no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—612no—
428C2×C4—1221no—
429C2×C4—1221no—
430C2×C4—1221no—
431C2×C4—1221no—
432C2×C4—1221no—
433C2×C4—1221no—
434C2×C4—1221no—
435C2×C4—1221no—
436C2×C4—2442no—
437C2×C4—2442no—
438C2×C4—2442no—
439C2×C4—2442no—
440C2×C4—2442no—
441C2×C4—2442no—
442C2×C4—2441no—
443C2×C4—2441no—
444C2×C4—2441no—
445C2×C4#1451973911yescharacteristic
446C2×C4C4×D24411yescharacteristic
447C2×C4#1451974711yescharacteristic
448C2×C4#1451975011yescharacteristic
449C2×C4#1451975211yescharacteristic
450C2×C4#1451976211yescharacteristic
451C8—42no—
452C8—42no—
453C8—2442no—
454C8—2442no—
455C22—1222no—
456C22—1222no—
457C22—1222no—
458C22—4881no—
459C22—4881no—
460C22—4881no—
461C22—4881no—
462C22—4881no—
463C22—4881no—
464C22—4881no—
465C22—2441no—
466C22—2441no—
467C22—2441no—
468C22—2441no—
469C22#1683964011yescharacteristic
470C22#100×D6111yescharacteristic
471C22#1683974511yescharacteristic
472C22#104×D6111yescharacteristic
473C22#1683977711yescharacteristic
474C22#1683977711yescharacteristic
475C22#1683977711yescharacteristic
476C4—21no—
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—21no—
482C4—81no—
483C4—81no—
484C4—1222no—
485C4—4881no—
486C4—2441no—
487C4—2441no—
488C2—9761no—
489C2—2442no—
490C2#2144441511yescharacteristic
491C2#2144443811yescharacteristic
492C2#2144444911yescharacteristic
493C2#2144445211yescharacteristic
494C2#2144612011yescharacteristic
495C2#2144626611yescharacteristic
496C2#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#9123
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×#16839817C2semidirect
3. #21445582C2semidirect
4. C2×#16839501C2semidirect
5. C2×#16839501C2semidirect
6. #21443700C2semidirect
7. C61×#1295C2semidirect
65. #14519688D4semidirect
76. #97×C61D4semidirect
246. #1295D61semidirect
279. C61#9123semidirect
323. #97D244semidirect

Maximal subgroups

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

subgroupindex
C2×#168398172
#214541212
#214455822
C2×#168395012
#214437002
C61×#12952
#912361