Finite Group Databasebeta

← #29647743

Subgroups — #29647743

Order 15616.

918 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459686C211yesmaximal, characteristic
2#21454899C211yesmaximal, characteristic, complemented
3#21448782C211yesmaximal, characteristic, complemented
4#21444395C214yesmaximal, complemented
5#21444383C211yesmaximal, characteristic, complemented
6#21444380C211yesmaximal, characteristic
7#21444313C211yesmaximal, characteristic
8#21444304C214yesmaximal, complemented
9C61×#1503C211yesmaximal, characteristic, complemented
10#16840497C412yescomplemented
11#16840491C412yescomplemented
12#16840486C412yescomplemented
13#16840485—22no—
14#16840473C412yescomplemented
15#16840450—22no—
16#16840361—22no—
17#16840338—21no—
18#16840312C2211yescharacteristic
19#16840298C2214yes—
20#16840242—21no—
21C2×C4×Dic122C2211yescharacteristic
22C8×Dic122—22no—
23#16839886—22no—
24#16839815C2211yescharacteristic
25#16839812C2214yes—
26#16839668—21no—
27#16839643—22no—
28#16839629C2212yes—
29#16839628C2211yescharacteristic
30C4×C4⋊Dic61—21no—
31#16839607C2212yes—
32#16839499C2214yes—
33#16839497C2214yes—
34#16839495C2212yes—
35#16839495C2212yes—
36C61×#533C2211yescharacteristic
37C61×#431C2211yescharacteristic
38C4×C4⋊C4×C61C2211yescharacteristic
39C61×#328C2212yes—
40C61×#328C2212yes—
41C2×#11758222—21no—
42C22×Dic122D411yescharacteristic
43#14519777—22no—
44#14519777C2×C411yescharacteristic
45#14519774C2×C411yescharacteristic
46#14519772—24no—
47#14519772—24no—
48#14519768—24no—
49#14519768C2×C414yes—
50#14519766C2×C414yes—
51#14519765—22no—
52#14519765—21no—
53#14519762—24no—
54#14519761—24no—
55#14519757—22no—
56#14519757—22no—
57#14519753—24no—
58#14519751—21no—
59#14519751C2312yes—
60Q8×Dic61C2×C414yes—
61C4×Dic122—22no—
62C4×Dic122C2×C412yes—
63C4×Dic122C2×C412yes—
64C4×Dic122D412yes—
65C4×Dic122D412yes—
66C4×D244—21no—
67C4×D244—22no—
68C4×D244C2×C412yes—
69#14519739C2×C414yes—
70#14519737—24no—
71#14519735—22no—
72#14519735—24no—
73C2×C4⋊Dic61—21no—
74C2×C4⋊Dic61D411yescharacteristic
75C2×#11758196D412yes—
76C4⋊C4×D61—22no—
77C2×C4×Dic61—22no—
78C2×C4×Dic61C2312yes—
79C4⋊#92418—21no—
80#14519706—24no—
81C22⋊#92418C2312yes—
82C4×#92418—21no—
83C8×Dic61—24no—
84#14519684—21no—
85#14519684—22no—
86#14519684—22no—
87#14519684—22no—
88#14519684C2312yes—
89C4⋊Q8×C61C2×C411yescharacteristic
90C4⋊Q8×C61C2×C411yescharacteristic
91#125×C61—21no—
92C22⋊Q8×C61—21no—
93C22⋊Q8×C61C2312yes—
94C4×Q8×C61—21no—
95C4×Q8×C61C2×C412yes—
96#117×C61—21no—
97C2×C4⋊C4×C61—21no—
98C2×C42×C61—21no—
99C2×C42×C61C2311yescharacteristic
100C4⋊C8×C61—21no—
101C22⋊C8×C61C2312yes—
102C4×C8×C61—21no—
103#95×C61C2311yescharacteristic
104#95×C61C2311yescharacteristic
105C2×Q8×C61—21no—
106C2×Q8×C61C22×C412yes—
107C22×C4×C61—21no—
108C22×C4×C61—21no—
109C22×C4×C61C2×D411yescharacteristic
110C22×C4×C61C2×D411yescharacteristic
111C22×C4×C61C2411yescharacteristic
112C2×C22⋊D61—22no—
113C22×Dic61—22no—
114C22×Dic61C2×D412yes—
115C22×Dic61C2×D412yes—
116#11758222—42no—
117#11758222—42no—
118C2×D244—21no—
119C2×D244—21no—
120C2×D244C22×C412yes—
121C2×C4×D61—22no—
122C2×C4×D61—24no—
123C2×Dic122—22no—
124C2×Dic122—22no—
125C2×Dic122—21no—
126C2×Dic122C22⋊C412yes—
127C2×Dic122C22⋊C412yes—
128C2×C8×C61—22no—
129C4⋊C4×C61—21no—
130C4⋊C4×C61—21no—
131C4⋊C4×C61—21no—
132C4⋊C4×C61—22no—
133C4⋊C4×C61—22no—
134C4⋊C4×C61—42no—
135C4⋊C4×C61C22×C412yes—
136C22⋊C4×C61—22no—
137C42×C61—22no—
138C42×C61—42no—
139C42×C61C22×C411yescharacteristic
140C42×C61C22×C411yescharacteristic
141C42×C61C2×D411yescharacteristic
142C42×C61C2×D411yescharacteristic
143#11758198—22no—
144#11758198—22no—
145#11758198—24no—
146#11758198—24no—
147#11758198—24no—
148C4⋊Dic61—21no—
149C4⋊Dic61—24no—
150C4⋊Dic61—24no—
151C4⋊Dic61—42no—
152C4⋊Dic61C22⋊C412yes—
153C4⋊Dic61C22⋊C412yes—
154C4⋊Dic61C22×C412yes—
155#11758196—24no—
156#11758196C22⋊C414yes—
157#11758196C22⋊C414yes—
158C4×Dic61—24no—
159C4×Dic61—44no—
160C4×Dic61C22×C414yes—
161C4×Dic61C2×D414yes—
162C2×#92418—22no—
163C23×C61C22×D411yescharacteristic
164C22×D61—22no—
165Q8×C61—42no—
166Q8×C61—81no—
167C2×C4×C61—22no—
168C2×C4×C61—22no—
169C2×C4×C61—22no—
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×C61—41no—
177C2×C4×C61C2×C22⋊C411yescharacteristic
178C2×C4×C61C2×C22⋊C411yescharacteristic
179C2×C4×C61C2×C22⋊C411yescharacteristic
180C2×C4×C61C2×C22⋊C411yescharacteristic
181C2×C4×C61#13512yes—
182C2×C4×C61#13512yes—
183C2×C4×C61C23×C411yescharacteristic
184C2×C4×C61C22×D411yescharacteristic
185C22⋊D61—42no—
186C22⋊D61—42no—
187C2×Dic61—22no—
188C2×Dic61—22no—
189C2×Dic61—22no—
190C2×Dic61—42no—
191C2×Dic61—42no—
192C2×Dic61—42no—
193C2×Dic61—42no—
194C2×Dic61C2×C22⋊C414yes—
195C2×Dic61C2×C22⋊C414yes—
196D244—42no—
197D244—42no—
198D244—81no—
199C4×D61—44no—
200C4×D61—84no—
201Dic122—24no—
202Dic122—24no—
203Dic122—42no—
204C8×C61—42no—
205#92418—42no—
206#17616—611nomaximal, Sylow
207C22×C61—21no—
208C22×C61—21no—
209C22×C61C22×C22⋊C411yescharacteristic
210C22×C61C2×#13511yescharacteristic
211C22×C61C2×#13511yescharacteristic
212C2×D61—42no—
213C2×D61—42no—
214C2×D61—42no—
215C4×C61—21no—
216C4×C61—21no—
217C4×C61—21no—
218C4×C61—21no—
219C4×C61—42no—
220C4×C61—42no—
221C4×C61—42no—
222C4×C61—81no—
223C4×C61#41612yes—
224C4×C61#41612yes—
225Dic61—24no—
226Dic61—24no—
227Dic61—42no—
228Dic61—82no—
229#3507—611no—
230#2982—611no—
231#2356—611no—
232#1521—614no—
233#1518—611no—
234#1517—611no—
235#1503D6111yescharacteristic, complemented
236#1502—611no—
237#1500—614no—
238C2×C61—21no—
239C2×C61—21no—
240C2×C61#288411yescharacteristic
241C2×C61C2×#41611yescharacteristic
242C2×C61#290111yescharacteristic
243D61—82no—
244#559—612no—
245#557—612no—
246#556—612no—
247#556—1222no—
248#554—612no—
249#552—1222no—
250#539—1222no—
251#536—1221no—
252#533C2×D6111yescharacteristic
253#532—611no—
254#529—614no—
255#520—1221no—
256C2×C4×Q8—611no—
257C8×Q8—1222no—
258C8×Q8—1222no—
259#431—611no—
260#431—614no—
261#431C2×D6111yescharacteristic
262#391—1221no—
263#387—1222no—
264#383—612no—
265#382—611no—
266C4×C4⋊C4—1221no—
267C4×C4⋊C4C2×D6111yescharacteristic
268#376—612no—
269#328—614no—
270#328C2×D6112yes—
271#328C2×D6112yes—
272#327—614no—
273#327—612no—
274#327—612no—
275C61#1761611yescharacteristic, complemented, Sylow
276C2×#41—1221no—
277C22×Q8—611no—
278C4⋊Q8—611no—
279C4⋊Q8—1222no—
280C4⋊Q8C4×D6111yescharacteristic
281C4⋊Q8C4×D6111yescharacteristic
282#127—611no—
283#126—1224no—
284#126—1224no—
285#125—21no—
286#125—614no—
287#125—1224no—
288#124—614no—
289#124—1222no—
290#124—1221no—
291#123—1224no—
292#123—1224no—
293C22⋊Q8—21no—
294C22⋊Q8—1222no—
295C22⋊Q8—1222no—
296C22⋊Q8—1224no—
297C22⋊Q8C22×D6112yes—
298#121—612no—
299#121—1221no—
300C4×Q8—21no—
301C4×Q8—612no—
302C4×Q8—612no—
303C4×Q8—612no—
304C4×Q8—612no—
305C4×Q8—614no—
306C4×Q8—1222no—
307C4×Q8C4×D6112yes—
308C4×D4—614no—
309C4×D4—612no—
310C4×D4—1222no—
311C4×D4—1224no—
312C4×D4—1221no—
313#117—21no—
314#117—1224no—
315#117—1222no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—611no—
318C2×C4⋊C4—612no—
319C2×C4⋊C4—1222no—
320C2×C4⋊C4—1221no—
321C2×C42—21no—
322C2×C42—612no—
323C2×C42—1222no—
324C2×C42C22×D6111yescharacteristic
325C4⋊C8—21no—
326C4⋊C8—1224no—
327C4⋊C8—1221no—
328C22⋊C8—612no—
329C22⋊C8C22×D6112yes—
330C4×C8—21no—
331C4×C8—1224no—
332C4×C8—1221no—
333#95—612no—
334#95—1222no—
335#95—1222no—
336#95—1222no—
337#95—1221no—
338#95C22×D6111yescharacteristic
339#95C22×D6111yescharacteristic
340#41—2442no—
341#41—2442no—
342C2×Q8—21no—
343C2×Q8—612no—
344C2×Q8—612no—
345C2×Q8—1221no—
346C2×Q8—1222no—
347C2×Q8—1222no—
348C2×Q8C2×C4×D6112yes—
349C2×D4—612no—
350C2×D4—1222no—
351C2×D4—1221no—
352C2×D4—1221no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—612no—
356C22×C4—612no—
357C22×C4—1224no—
358C22×C4—1222no—
359C22×C4—1222no—
360C22×C4D4×D6111yescharacteristic
361C22×C4D4×D6111yescharacteristic
362C22×C4C23×D6111yescharacteristic
363C2×C8—22no—
364C2×C8—1222no—
365C4⋊C4—22no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—22no—
370C4⋊C4—42no—
371C4⋊C4—612no—
372C4⋊C4—614no—
373C4⋊C4—614no—
374C4⋊C4—612no—
375C4⋊C4—612no—
376C4⋊C4—1224no—
377C4⋊C4—1224no—
378C4⋊C4—1224no—
379C4⋊C4—1221no—
380C4⋊C4—2442no—
381C4⋊C4C2×C4×D6112yes—
382C22⋊C4—22no—
383C22⋊C4—1224no—
384C22⋊C4—1224no—
385C22⋊C4—1224no—
386C22⋊C4—1222no—
387C22⋊C4—1222no—
388C42—22no—
389C42—42no—
390C42—614no—
391C42—614no—
392C42—1224no—
393C42—2444no—
394C42C2×C4×D6111yescharacteristic
395C42C2×C4×D6111yescharacteristic
396C42D4×D6111yescharacteristic
397C42D4×D6111yescharacteristic
398C23—1222no—
399C23C2×D4×D6111yescharacteristic
400Q8—42no—
401Q8—81no—
402Q8—1224no—
403Q8—1224no—
404Q8—2442no—
405D4—4881no—
406D4—2442no—
407D4—2442no—
408D4—2442no—
409D4—2442no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—614no—
421C2×C4—614no—
422C2×C4—1222no—
423C2×C4—1222no—
424C2×C4—1222no—
425C2×C4—4884no—
426C2×C4—2442no—
427C2×C4—2442no—
428C2×C4—2442no—
429C2×C4—2442no—
430C2×C4—2444no—
431C2×C4C22⋊C4×D6111yescharacteristic
432C2×C4C22⋊C4×D6111yescharacteristic
433C2×C4C22⋊C4×D6111yescharacteristic
434C2×C4C22⋊C4×D6111yescharacteristic
435C2×C4#1451979812yes—
436C2×C4#1451980012yes—
437C2×C4C22×C4×D6111yescharacteristic
438C2×C4C2×D4×D6111yescharacteristic
439C8—42no—
440C8—2442no—
441C22—21no—
442C22—21no—
443C22—2442no—
444C22—2442no—
445C22—2442no—
446C22C2×C22⋊C4×D6111yescharacteristic
447C22C2×#1451979811yescharacteristic
448C22C2×#1451980011yescharacteristic
449C4—21no—
450C4—21no—
451C4—21no—
452C4—21no—
453C4—42no—
454C4—42no—
455C4—42no—
456C4—81no—
457C4—1224no—
458C4—1224no—
459C4—4882no—
460C4—2442no—
461C4#1683975712yes—
462C4#1683975712yes—
463C2—21no—
464C2—21no—
465C2—4882no—
466C2#2145428111yescharacteristic
467C2C2×#1683975711yescharacteristic
468C2#2145436311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1503C2
socleC22×C61C22×C22⋊C4
prime radical#16840312C22
cosocleC22×C4×C61C24
hypercenter#1503D61
hypocenterC61#17616
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1503

Complements

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

NH ≅ G/Ntype
2. #21454899C2semidirect
3. #21448782C2semidirect
4. #21444395C2semidirect
5. #21444383C2semidirect
8. #21444304C2semidirect
9. C61×#1503C2semidirect
10. #16840497C4semidirect
11. #16840491C4semidirect
12. #16840486C4semidirect
14. #16840473C4semidirect
235. #1503D61semidirect
275. C61#17616semidirect

Maximal subgroups

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

subgroupindex
#214596862
#214548992
#214487822
#214443952
#214443832
#214443802
#214443132
#214443042
C61×#15032
#1761661