Finite Group Databasebeta

← #30600045

Subgroups — #30600045

Order 15616.

768 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 768 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462298C211yesmaximal, characteristic
2#21461722C212yesmaximal, complemented
3D61⋊#323C211yesmaximal, characteristic
4#21460693C212yesmaximal, complemented
5#397×D61C211yesmaximal, characteristic
6C22×C22⋊#6923—21no—
7D61⋊(C22⋊C8)C2212yes—
8#16840709—24no—
9#16840704—21no—
10#16840704C2212yes—
11#16840635—24no—
12#16840606—21no—
13#16840605—21no—
14C2×C4⋊C4×D61C2211yescharacteristic
15C2×C22⋊C4×D61—21no—
16C2×C22⋊C4×D61C2211yescharacteristic
17#16839691—21no—
18#16839690—21no—
19#16839689C411yescharacteristic, complemented
20#16839688C411yescharacteristic, complemented
21#16839687C411yescharacteristic, complemented
22#95×D61—21no—
23#95×D61C2211yescharacteristic
24C61×#397C411yescharacteristic, complemented
25C23×#6923—22no—
26C2×D61⋊C8—22no—
27C2×C4⋊#6923—22no—
28C2×C4⋊#6923D414yes—
29C2×C22⋊#6923—22no—
30C2×C22⋊#6923—22no—
31C2×C22⋊#6923—42no—
32C2×C22⋊#6923—42no—
33#14519834—22no—
34C22⋊#92420—22no—
35(C2×#6923)⋊C4—22no—
36(C2×#6923)⋊C4—22no—
37C24×D61D411yescharacteristic
38C22×C4×D61—21no—
39C22×C4×D61—21no—
40C22×C4×D61D411yescharacteristic
41C22×C4×D61C2311yescharacteristic
42C2×C4⋊Dic61C2×C411yescharacteristic, complemented
43C2×#11758196—21no—
44C4⋊C4×D61—22no—
45C4⋊C4×D61—22no—
46C2×C22⋊Dic61—21no—
47C2×C22⋊Dic61D411yescharacteristic
48C2×#11758198—21no—
49C2×#11758198—21no—
50C2×#11758198C2×C411yescharacteristic
51C2×#11758198D411yescharacteristic
52C22⋊C4×D61—22no—
53C22⋊C4×D61—22no—
54C22⋊C4×D61—42no—
55C22⋊C4×D61—42no—
56#14519684—21no—
57#14519684—21no—
58#14519684—21no—
59#14519684—21no—
60#14519684C2×C411yescharacteristic, complemented
61C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
62C2×C22⋊C4×C61—21no—
63C2×C22⋊C4×C61C2×C411yescharacteristic
64#95×C61—21no—
65#95×C61C2×C411yescharacteristic, complemented
66C24×C61C22⋊C411yescharacteristic
67C23×D61—21no—
68C23×D61—21no—
69C23×D61—21no—
70C23×D61—21no—
71C23×D61—42no—
72C23×D61—42no—
73C23×D61C22⋊C411yescharacteristic
74C23×D61D812yes—
75C23×D61SD1612yes—
76C23×D61C2×D411yescharacteristic
77C22×#6923—24no—
78C22×#6923—44no—
79C22×#6923—82no—
80C22×#6923—82no—
81C22×C4×C61—21no—
82C22×C4×C61—21no—
83C22×C4×C61C22⋊C411yescharacteristic
84C22×C4×C61C22×C411yescharacteristic
85C22×Dic61—21no—
86C22×Dic61—21no—
87C22×Dic61C22⋊C411yescharacteristic
88C22×Dic61C2×D411yescharacteristic
89C2×C4×D61—21no—
90C2×C4×D61—21no—
91C2×C4×D61—42no—
92C2×C4×D61—42no—
93C2×C4×D61—42no—
94C2×C4×D61—42no—
95C2×C4×D61—41no—
96C2×C4×D61—41no—
97C2×C4×D61—41no—
98C2×C4×D61—41no—
99C2×C4×D61—41no—
100C2×C4×D61—41no—
101C2×C4×D61—41no—
102C2×C4×D61—41no—
103C2×C4×D61C2×D412yes—
104C2×C4×D61#4112yes—
105C22⋊#6923—44no—
106C22⋊#6923—42no—
107C22⋊#6923—42no—
108C2×#92420—42no—
109C4⋊#6923—44no—
110C4⋊#6923—82no—
111D61⋊C8—44no—
112C4⋊C4×C61—22no—
113C22⋊C4×C61—22no—
114C22⋊C4×C61—42no—
115C22⋊Dic61—22no—
116C22⋊Dic61—42no—
117#11758198—22no—
118#11758198—22no—
119#11758198—42no—
120#11758198—42no—
121C4⋊Dic61—22no—
122#11758196—42no—
123C23×C61—21no—
124C23×C61—21no—
125C23×C61—41no—
126C23×C61—41no—
127C23×C61#10212yes—
128C23×C61C2×C22⋊C411yescharacteristic
129C22×D61—22no—
130C22×D61—22no—
131C22×D61—21no—
132C22×D61—21no—
133C22×D61—22no—
134C22×D61—22no—
135C22×D61—22no—
136C22×D61—22no—
137C22×D61—44no—
138C22×D61—44no—
139C22×D61—42no—
140C22×D61—42no—
141C22×D61—41no—
142C22×D61—41no—
143C22×D61—82no—
144C22×D61—82no—
145C22×D61—81no—
146C22×D61—81no—
147C22×D61#10212yes—
148C22×D61#12011yescharacteristic
149C22×D61#12311yescharacteristic
150C22×D61C2×D811yescharacteristic
151C22×D61C2×SD1611yescharacteristic
152C22×D61AGL(1,ℤ/8)11yescharacteristic
153C22×D61#13711yescharacteristic
154C2×#6923—44no—
155C2×#6923—44no—
156C2×#6923—44no—
157C2×#6923—88no—
158C2×C4×C61—21no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61—41no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61—41no—
166C2×C4×C61—41no—
167C2×C4×C61C4×D412yes—
168C2×Dic61—21no—
169C2×Dic61—41no—
170C2×Dic61—41no—
171C2×Dic61—41no—
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61—41no—
175C2×Dic61—41no—
176C2×Dic61—41no—
177C2×Dic61#12112yes—
178C4×D61—24no—
179C4×D61—42no—
180C4×D61—42no—
181C4×D61—81no—
182C4×D61—82no—
183C4×D61—82no—
184C4×D61—81no—
185C4×D61—81no—
186C4×D61—81no—
187C4×D61—81no—
188#92420—82no—
189#9025—611nomaximal, Sylow
190C22×C61—21no—
191C22×C61—21no—
192C22×C61—22no—
193C22×C61—42no—
194C22×C61—41no—
195C22×C61—41no—
196C22×C61—81no—
197C22×C61#38611yescharacteristic
198C22×C61C2×#10211yescharacteristic
199C22×C61#41711yescharacteristic
200C2×D61—21no—
201C2×D61—21no—
202C2×D61—22no—
203C2×D61—22no—
204C2×D61—22no—
205C2×D61—22no—
206C2×D61—22no—
207C2×D61—41no—
208C2×D61—41no—
209C2×D61—44no—
210C2×D61—44no—
211C2×D61—42no—
212C2×D61—82no—
213C2×D61—82no—
214C2×D61—81no—
215C2×D61#44711yescharacteristic
216C2×D61#44811yescharacteristic
217C2×D61#45512yes—
218C2×D61#45812yes—
219C2×D61#48011yescharacteristic
220C2×D61#48111yescharacteristic
221#6923—84no—
222C4×C61—22no—
223C4×C61—41no—
224C4×C61—81no—
225C4×C61—81no—
226Dic61—22no—
227Dic61—41no—
228Dic61—81no—
229Dic61—81no—
230C2×#397—611no—
231#2315—611no—
232#1823—612no—
233C2×#323—611no—
234#1294—612no—
235C2×C61—21no—
236C2×C61—21no—
237C2×C61—42no—
238C2×C61#187411yescharacteristic
239C2×C61#188511yescharacteristic
240C2×C61#189011yescharacteristic
241D61—21no—
242D61—21no—
243D61—42no—
244D61#160712yes—
245D61#160812yes—
246C22×C4⋊C4—611no—
247C22×C22⋊C4—611no—
248C22×C22⋊C4—1221no—
249C22×C22⋊C4—1221no—
250C2×C22⋊C8—612no—
251#397—611no—
252#397—611no—
253#397—611no—
254#397—1221no—
255#397—1221no—
256#397#692311yescharacteristic, complemented
257#385—1224no—
258#380—612no—
259#380—1221no—
260C2×#95—611no—
261C2×#95—1221no—
262#340—1224no—
263#323—1221no—
264#323—1221no—
265C61#902511yescharacteristic, complemented, Sylow
266C25—611no—
267C23×C4—611no—
268C23×C4—611no—
269C23×C4—1221no—
270C23×C4—1221no—
271C23×C4—1222no—
272C22×C8—1222no—
273C2×C4⋊C4—611no—
274C2×C4⋊C4—614no—
275C2×C4⋊C4—1222no—
276C2×C4⋊C4—1222no—
277C2×C4⋊C4—1222no—
278C2×C4⋊C4—1221no—
279C2×C4⋊C4C2×#692311yescharacteristic, complemented
280C2×C22⋊C4—21no—
281C2×C22⋊C4—611no—
282C2×C22⋊C4—611no—
283C2×C22⋊C4—611no—
284C2×C22⋊C4—1222no—
285C2×C22⋊C4—1222no—
286C2×C22⋊C4—1221no—
287C2×C22⋊C4—1221no—
288C2×C22⋊C4—1222no—
289C2×C22⋊C4—1222no—
290C2×C22⋊C4—1221no—
291C2×C22⋊C4—2442no—
292C2×C22⋊C4—2442no—
293C2×C22⋊C4—2442no—
294C2×C22⋊C4—2442no—
295C2×C22⋊C4C2×#692311yescharacteristic
296C22⋊C8—1222no—
297C22⋊C8—1222no—
298#95—21no—
299#95—611no—
300#95—1221no—
301#95—1221no—
302#95—1221no—
303#95—1222no—
304#95—1222no—
305#95—1221no—
306#95C2×#692311yescharacteristic, complemented
307C24—611no—
308C24—612no—
309C24—612no—
310C24—611no—
311C24—1221no—
312C24—1221no—
313C24—1221no—
314C24—1221no—
315C24—2442no—
316C24—2442no—
317C24C22⋊#692311yescharacteristic
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—611no—
321C22×C4—612no—
322C22×C4—612no—
323C22×C4—611no—
324C22×C4—1221no—
325C22×C4—1221no—
326C22×C4—1224no—
327C22×C4—1221no—
328C22×C4—1221no—
329C22×C4—4882no—
330C22×C4—4882no—
331C22×C4—2442no—
332C22×C4—2441no—
333C22×C4—2441no—
334C22×C4—2441no—
335C22×C4—2441no—
336C22×C4—2441no—
337C22×C4—2441no—
338C22×C4—2441no—
339C22×C4—2441no—
340C22×C4—2442no—
341C22×C4—2442no—
342C22×C4—2442no—
343C22×C4—2444no—
344C22×C4C22⋊#692311yescharacteristic
345C22×C4C22×#692311yescharacteristic
346C2×C8—2442no—
347C2×C8—2444no—
348C4⋊C4—22no—
349C4⋊C4—1222no—
350C4⋊C4—4882no—
351C4⋊C4—2442no—
352C4⋊C4—2444no—
353C22⋊C4—22no—
354C22⋊C4—42no—
355C22⋊C4—1222no—
356C22⋊C4—1222no—
357C22⋊C4—1222no—
358C22⋊C4—2442no—
359C22⋊C4—2442no—
360C22⋊C4—2442no—
361C22⋊C4—2442no—
362C22⋊C4—2444no—
363C22⋊C4—2442no—
364C23—21no—
365C23—21no—
366C23—41no—
367C23—41no—
368C23—611no—
369C23—611no—
370C23—611no—
371C23—611no—
372C23—611no—
373C23—611no—
374C23—612no—
375C23—1222no—
376C23—1222no—
377C23—1222no—
378C23—1222no—
379C23—1222no—
380C23—1222no—
381C23—1221no—
382C23—1221no—
383C23—4881no—
384C23—4881no—
385C23—4882no—
386C23—4882no—
387C23—2441no—
388C23—2441no—
389C23—2442no—
390C23—2442no—
391C23—2444no—
392C23—2444no—
393C23#1451983912yes—
394C23C2×C22⋊#692311yescharacteristic
395C2×C4—21no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—612no—
405C2×C4—1224no—
406C2×C4—1221no—
407C2×C4—4881no—
408C2×C4—4881no—
409C2×C4—4881no—
410C2×C4—4881no—
411C2×C4—4881no—
412C2×C4—4882no—
413C2×C4—4882no—
414C2×C4—4888no—
415C2×C4—2442no—
416C2×C4—2442no—
417C2×C4—2441no—
418C2×C4—2441no—
419C2×C4—2441no—
420C2×C4—2444no—
421C2×C4—2444no—
422C2×C4—2444no—
423C2×C4—2441no—
424C2×C4—2441no—
425C2×C4—2441no—
426C2×C4—2441no—
427C2×C4—2441no—
428C2×C4D4×#692312yes—
429C8—4882no—
430C22—21no—
431C22—21no—
432C22—22no—
433C22—42no—
434C22—41no—
435C22—41no—
436C22—81no—
437C22—611no—
438C22—611no—
439C22—612no—
440C22—612no—
441C22—611no—
442C22—611no—
443C22—1222no—
444C22—1222no—
445C22—1222no—
446C22—1222no—
447C22—1221no—
448C22—1221no—
449C22—1222no—
450C22—4881no—
451C22—4882no—
452C22—4882no—
453C22—2442no—
454C22—2444no—
455C22—2444no—
456C22—2441no—
457C22—2441no—
458C22#1684071011yescharacteristic
459C22C2×#1451983911yescharacteristic
460C22#1684075311yescharacteristic
461C4—22no—
462C4—41no—
463C4—81no—
464C4—81no—
465C4—1222no—
466C4—4881no—
467C4—4884no—
468C4—4881no—
469C4—2441no—
470C2—21no—
471C2—21no—
472C2—42no—
473C2—612no—
474C2—612no—
475C2—1221no—
476C2—1221no—
477C2—2442no—
478C2#2146180611yescharacteristic
479C2#2146182411yescharacteristic
480C2#2146182911yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#397C4
socleC22×C61#386
prime radicalC24×D61D4
cosocleC22×C4×D61C23
hypercenter#397#6923
hypocenterC61#9025
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #397

Complements

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

NH ≅ G/Ntype
2. #21461722C2semidirect
4. #21460693C2semidirect
19. #16839689C4semidirect
20. #16839688C4semidirect
21. #16839687C4semidirect
24. C61×#397C4semidirect
42. C2×C4⋊Dic61C2×C4semidirect
60. #14519684C2×C4semidirect
61. C2×C4⋊C4×C61C2×C4semidirect
65. #95×C61C2×C4semidirect
256. #397#6923semidirect
265. C61#9025semidirect
279. C2×C4⋊C4C2×#6923semidirect
306. #95C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214622982
#214617222
D61⋊#3232
#214606932
#397×D612
#902561