Finite Group Databasebeta

← #29579000

Subgroups — #29579000

Order 15616.

668 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454120C211yesmaximal, characteristic
2C2×#16839500C212yesmaximal, complemented
3C2×#16839497C212yesmaximal
4#21444046C211yesmaximal, characteristic, complemented
5C4×C22⋊C8×C61C211yesmaximal, characteristic, complemented
6C2×#14519765C411yescharacteristic, complemented
7C2×#14519756C2211yescharacteristic
8C2×#14519751C2211yescharacteristic
9#16839668C411yescharacteristic, complemented
10#16839664C411yescharacteristic, complemented
11#16839653—21no—
12#16839653—21no—
13#16839641—21no—
14#16839641—21no—
15#16839628C411yescharacteristic, complemented
16C2×#14519684—21no—
17C2×#14519684—21no—
18C2×#14519684C2212yes—
19#16839500—24no—
20#16839497—24no—
21C22×C42×C61C2211yescharacteristic
22C2×C22⋊C8×C61C2212yes—
23C2×C4×C8×C61—21no—
24C61×#336—21no—
25C22×Dic122C2×C411yescharacteristic
26C22×D244C2×C411yescharacteristic
27C22×C22⋊D61—21no—
28C23×Dic61—22no—
29#14519765—42no—
30#14519756—22no—
31#14519756—22no—
32#14519751—22no—
33#14519751—22no—
34C2×C4⋊Dic61C2×C411yescharacteristic
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×#11758196—21no—
37C2×C22⋊Dic61—21no—
38C2×#11758198—21no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43#14519684—24no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—22no—
49#14519684—22no—
50#14519684—42no—
51C23×C4×C61D411yescharacteristic
52C23×C4×C61D411yescharacteristic
53C23×C4×C61C2311yescharacteristic
54C22×C8×C61—22no—
55C2×C42×C61—42no—
56C2×C42×C61C2×C411yescharacteristic
57C2×C42×C61C2×C411yescharacteristic
58C2×C42×C61D411yescharacteristic
59C2×C42×C61D411yescharacteristic
60C22⋊C8×C61—22no—
61C22⋊C8×C61D414yes—
62C4×C8×C61—42no—
63C24×C61C2×D411yescharacteristic
64C23×D61—21no—
65C22×C4×C61—22no—
66C22×C4×C61—22no—
67C22×C4×C61—22no—
68C22×C4×C61—22no—
69C22×C4×C61—41no—
70C22×C4×C61—41no—
71C22×C4×C61—41no—
72C22×C4×C61—41no—
73C22×C4×C61C22⋊C411yescharacteristic
74C22×C4×C61C22⋊C411yescharacteristic
75C22×C4×C61C22⋊C411yescharacteristic
76C22×C4×C61C22⋊C411yescharacteristic
77C22×C4×C61C22×C411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61C2×D412yes—
80C22×C4×C61#4112yes—
81C2×C22⋊D61—41no—
82C2×C22⋊D61—41no—
83C2×C22⋊D61—42no—
84C2×C22⋊D61—42no—
85C22×Dic61—24no—
86C22×Dic61—21no—
87C22×Dic61—21no—
88C22×Dic61—21no—
89C22×Dic61—42no—
90C22×Dic61—42no—
91C22×Dic61—42no—
92C22×Dic61—42no—
93C22×Dic61—42no—
94C22×Dic61—42no—
95C2×D244—22no—
96C2×D244—41no—
97C2×D244—41no—
98C2×Dic122—22no—
99C2×Dic122—41no—
100C2×Dic122—41no—
101C2×C8×C61—24no—
102C2×C8×C61—42no—
103C2×C8×C61—42no—
104C42×C61—22no—
105C42×C61—22no—
106C42×C61—41no—
107C42×C61—41no—
108C22⋊Dic61—41no—
109C22⋊Dic61—41no—
110#11758198—42no—
111#11758198—42no—
112#11758198—42no—
113#11758198—42no—
114#11758198—42no—
115C4⋊Dic61—22no—
116C4⋊Dic61—22no—
117#11758196—42no—
118C23×C61—21no—
119C23×C61—21no—
120C23×C61—21no—
121C23×C61—21no—
122C23×C61C2×C22⋊C411yescharacteristic
123C23×C61#12411yescharacteristic
124C23×C61#12711yescharacteristic
125C23×C61#13512yes—
126C23×C61#13512yes—
127C22×D61—41no—
128C22×D61—41no—
129C22×D61—41no—
130C22×D61—41no—
131C22×D61—41no—
132C22×D61—41no—
133C22×D61—41no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—21no—
147C2×C4×C61—21no—
148C2×C4×C61—42no—
149C2×C4×C61—42no—
150C2×C4×C61—44no—
151C2×C4×C61—44no—
152C2×C4×C61#9912yes—
153C2×C4×C61#10412yes—
154C2×C4×C61C4×D412yes—
155C2×C4×C61#12112yes—
156C22⋊D61—82no—
157C22⋊D61—82no—
158C2×Dic61—44no—
159C2×Dic61—44no—
160C2×Dic61—44no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165C2×Dic61—41no—
166C2×Dic61—41no—
167C2×Dic61—41no—
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61—82no—
171C2×Dic61—82no—
172C2×Dic61—82no—
173C2×Dic61—82no—
174D244—82no—
175Dic122—82no—
176C8×C61—44no—
177#9681—611nomaximal, Sylow
178C22×C61—21no—
179C22×C61—21no—
180C22×C61—21no—
181C22×C61—21no—
182C22×C61—22no—
183C22×C61—22no—
184C22×C61—22no—
185C22×C61—22no—
186C22×C61#39011yescharacteristic
187C22×C61C2×#9911yescharacteristic
188C22×C61#41011yescharacteristic
189C22×C61#41611yescharacteristic
190C22×C61#41611yescharacteristic
191C22×C61C2×#10411yescharacteristic
192C22×C61#42111yescharacteristic
193C22×C61#48812yes—
194C22×C61#49512yes—
195C2×D61—81no—
196C2×D61—81no—
197C2×D61—81no—
198C2×D61—81no—
199C2×D61—81no—
200C2×D61—81no—
201C2×D61—81no—
202C4×C61—22no—
203C4×C61—22no—
204C4×C61—22no—
205C4×C61—22no—
206C4×C61—41no—
207C4×C61—41no—
208Dic61—84no—
209Dic61—81no—
210Dic61—81no—
211Dic61—81no—
212#2850—611no—
213C4×C22⋊C8D6111yescharacteristic, complemented
214C2×#328—612no—
215C2×#327—612no—
216#1434—611no—
217C2×C61—22no—
218C2×C61—22no—
219C2×C61#150011yescharacteristic
220C2×C61#150111yescharacteristic
221C2×C61#151611yescharacteristic
222C2×C61#152111yescharacteristic
223C2×C61#195811yescharacteristic
224C2×C61#196411yescharacteristic
225C2×C61#198011yescharacteristic
226D61—161no—
227C2×#124—611no—
228C2×C22⋊Q8—611no—
229C2×#121—611no—
230C22×C42C2×D6111yescharacteristic
231C2×C22⋊C8C2×D6112yes—
232C2×C4×C8—21no—
233#391—611no—
234#390—611no—
235#388—1221no—
236#388—1221no—
237#386—1221no—
238#386—1221no—
239#382—611no—
240C2×#95—612no—
241C2×#95—1221no—
242C2×#95—1221no—
243#336—21no—
244#328—1224no—
245#327—1224no—
246C61#968111yescharacteristic, complemented, Sylow
247C22×Q8—611no—
248C22×D4—611no—
249C22×D4—1221no—
250C23×C4—1222no—
251C23×C4D24411yescharacteristic
252C23×C4D24411yescharacteristic
253C23×C4C22×D6111yescharacteristic
254C22×C8—22no—
255#124—2442no—
256C22⋊Q8—1222no—
257C22⋊Q8—1222no—
258#121—1222no—
259#121—1222no—
260C2×C4⋊C4—611no—
261C2×C4⋊C4—611no—
262C2×C4⋊C4—1221no—
263C2×C22⋊C4—1221no—
264C2×C22⋊C4—1221no—
265C2×C22⋊C4—1221no—
266C2×C22⋊C4—1221no—
267C2×C22⋊C4—1221no—
268C2×C22⋊C4—1221no—
269C2×C42—42no—
270C2×C42C4×D6111yescharacteristic
271C2×C42C4×D6111yescharacteristic
272C2×C42C22⋊D6111yescharacteristic
273C2×C42C22⋊D6111yescharacteristic
274C22⋊C8—22no—
275C22⋊C8D24414yes—
276C4×C8—42no—
277#95—1224no—
278#95—1221no—
279#95—1221no—
280#95—1221no—
281#95—1221no—
282#95—1222no—
283#95—1222no—
284#95—2442no—
285C24—1221no—
286C24C2×D24411yescharacteristic
287C2×Q8—1222no—
288C2×Q8—2441no—
289C2×Q8—2441no—
290C2×D4—1222no—
291C2×D4—2441no—
292C2×D4—2441no—
293C2×D4—2441no—
294C2×D4—2441no—
295C2×D4—2442no—
296C2×D4—2442no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—1224no—
306C22×C4—1221no—
307C22×C4—1221no—
308C22×C4—1221no—
309C22×C4—2442no—
310C22×C4—2442no—
311C22×C4—2442no—
312C22×C4—2442no—
313C22×C4—2442no—
314C22×C4—2442no—
315C22×C4#1175819811yescharacteristic
316C22×C4#1175819811yescharacteristic
317C22×C4#1175819811yescharacteristic
318C22×C4#1175819811yescharacteristic
319C22×C4C2×C4×D6111yescharacteristic
320C22×C4C2×D24412yes—
321C22×C4#1175822212yes—
322C22×C4C2×C22⋊D6111yescharacteristic
323C2×C8—24no—
324C2×C8—42no—
325C2×C8—42no—
326C4⋊C4—1222no—
327C4⋊C4—1222no—
328C4⋊C4—2442no—
329C22⋊C4—2442no—
330C22⋊C4—2442no—
331C22⋊C4—2441no—
332C22⋊C4—2441no—
333C22⋊C4—2442no—
334C22⋊C4—2442no—
335C22⋊C4—2442no—
336C42—22no—
337C42—22no—
338C42—41no—
339C42—41no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—2441no—
345C23—2441no—
346C23—2441no—
347C23—2441no—
348C23—2441no—
349C23—2441no—
350C23—2441no—
351C23C2×#1175819811yescharacteristic
352C23#1451976511yescharacteristic
353C23#1451977411yescharacteristic
354C23#1451979912yes—
355C23#1451979912yes—
356Q8—4882no—
357D4—4882no—
358D4—4882no—
359D4—4882no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—44no—
377C2×C4—44no—
378C2×C4—4882no—
379C2×C4—4882no—
380C2×C4—4882no—
381C2×C4—4882no—
382C2×C4—2444no—
383C2×C4—2444no—
384C2×C4—2444no—
385C2×C4—2441no—
386C2×C4—2441no—
387C2×C4—2441no—
388C2×C4—2441no—
389C2×C4—2441no—
390C2×C4—2441no—
391C2×C4—2441no—
392C2×C4—2441no—
393C2×C4—2441no—
394C2×C4#1451969112yes—
395C2×C4#1451970312yes—
396C2×C4C4×D24412yes—
397C2×C4#1451975112yes—
398C8—44no—
399C22—22no—
400C22—22no—
401C22—21no—
402C22—21no—
403C22—22no—
404C22—22no—
405C22—21no—
406C22—21no—
407C22—4881no—
408C22—4881no—
409C22—4881no—
410C22—4881no—
411C22—4881no—
412C22—4881no—
413C22—4881no—
414C22#1683966411yescharacteristic
415C22C2×#1451969111yescharacteristic
416C22#1683973511yescharacteristic
417C22#1683975911yescharacteristic
418C22#1683975911yescharacteristic
419C22C2×#1451970311yescharacteristic
420C22#1683977811yescharacteristic
421C22#1684011712yes—
422C22#1684014612yes—
423C4—22no—
424C4—22no—
425C4—22no—
426C4—22no—
427C4—41no—
428C4—41no—
429C4—4884no—
430C4—4881no—
431C4—4881no—
432C4—4881no—
433C2—22no—
434C2—22no—
435C2—9761no—
436C2#2144430611yescharacteristic
437C2#2144431111yescharacteristic
438C2#2144437611yescharacteristic
439C2#2144439711yescharacteristic
440C2#2144663011yescharacteristic
441C2#2144665511yescharacteristic
442C2#2144673811yescharacteristic
subgroupG/H
centerC23C2×#11758198
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC4×C22⋊C8×C61C2
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519751C22
cosocleC23×C4×C61C23
hypercenterC4×C22⋊C8D61
hypocenterC61#9681
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#16839500C2semidirect
4. #21444046C2semidirect
5. C4×C22⋊C8×C61C2semidirect
6. C2×#14519765C4semidirect
9. #16839668C4semidirect
10. #16839664C4semidirect
15. #16839628C4semidirect
213. C4×C22⋊C8D61semidirect
246. C61#9681semidirect

Maximal subgroups

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

subgroupindex
#214541202
C2×#168395002
C2×#168394972
#214440462
C4×C22⋊C8×C612
#968161