Finite Group Databasebeta

← #29573367

Subgroups — #29573367

Order 15616.

592 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14519735C211yesmaximal, characteristic
2#21445796C211yesmaximal, characteristic
3C4×#14519689C211yesmaximal, characteristic
4#21443660C211yesmaximal, characteristic, complemented
5#21443659C211yesmaximal, characteristic, complemented
6#21443658C211yesmaximal, characteristic, complemented
7C61×#1279C211yesmaximal, characteristic, complemented
8C2×#14519735C411yescharacteristic
9C2×#14519735C411yescharacteristic
10C2×C42×D61C2211yescharacteristic
11C2×C4⋊#92418C2211yescharacteristic
12C2×#14519689—21no—
13C2×#14519689—21no—
14C2×C4×#92418C2211yescharacteristic
15C4⋊C4×Dic61C411yescharacteristic
16C4⋊C4×Dic61C411yescharacteristic
17C4×C4⋊Dic61C2211yescharacteristic
18C4×#11758198—21no—
19#16839609—21no—
20#16839607—21no—
21C42×Dic61—21no—
22#16839516—21no—
23#16839516—21no—
24C2×C4⋊C8×C61C2211yescharacteristic
25C2×C4×C8×C61C2211yescharacteristic
26C4×C4⋊C4×C61C2211yescharacteristic
27C22×C4×D61C2×C411yescharacteristic
28C22×C4×D61D411yescharacteristic
29C22×C4×D61D411yescharacteristic
30C22×#92418—21no—
31C22×#92418—21no—
32#14519735—22no—
33#14519735—22no—
34#14519735—22no—
35#14519735C814yescomplemented
36C2×C4⋊Dic61C2×C411yescharacteristic
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×#11758198—21no—
39C2×#11758198—21no—
40C2×C4×Dic61—21no—
41C2×C4×Dic61—21no—
42C2×C4×Dic61—21no—
43C2×C4×Dic61—21no—
44C2×C4×Dic61—21no—
45C2×C4×Dic61C2×C411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48C42×D61—21no—
49C42×D61—21no—
50C42×D61—21no—
51C42×D61—21no—
52C4⋊#92418—21no—
53C4⋊#92418—21no—
54#14519689—24no—
55#14519689—42no—
56C4×#92418—21no—
57C4×#92418—21no—
58#14519684—21no—
59#14519684—21no—
60#14519684—21no—
61C22×C8×C61—21no—
62C22×C8×C61—21no—
63C2×C4⋊C4×C61C2×C411yescharacteristic
64C2×C4⋊C4×C61C2×C411yescharacteristic
65C2×C42×C61—21no—
66C2×C42×C61C2311yescharacteristic
67C4⋊C8×C61—21no—
68C4⋊C8×C61—21no—
69C4×C8×C61—21no—
70C4×C8×C61—21no—
71#95×C61—21no—
72C23×D61C22⋊C411yescharacteristic
73C22×C4×C61—21no—
74C22×C4×C61—21no—
75C22×C4×C61C22×C411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C22×Dic61—21no—
79C22×Dic61—21no—
80C22×Dic61C22⋊C411yescharacteristic
81C22×Dic61C22⋊C411yescharacteristic
82C22×Dic61C22⋊C411yescharacteristic
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×C4×D61—21no—
89C2×C4×D61—21no—
90C2×C4×D61—21no—
91C2×C4×D61—21no—
92C2×C4×D61—21no—
93C2×C4×D61—21no—
94C2×C4×D61—21no—
95C2×C4×D61—22no—
96C2×C4×D61—41no—
97C2×C4×D61C2×C812yes—
98C2×C4×D61M1612yes—
99C2×C8×C61—22no—
100C2×C8×C61—41no—
101C2×C8×C61—41no—
102C2×C8×C61—41no—
103C2×C8×C61—41no—
104C2×C8×C61—41no—
105C4⋊C4×C61—21no—
106C4⋊C4×C61—21no—
107C4⋊C4×C61C2×C812yes—
108C4⋊C4×C61M1612yes—
109C42×C61—41no—
110C42×C61—41no—
111C42×C61#4111yescharacteristic
112C42×C61#4111yescharacteristic
113C42×C61#4111yescharacteristic
114C42×C61#4111yescharacteristic
115#11758198—24no—
116#11758198—24no—
117C4⋊Dic61—21no—
118C4⋊Dic61—21no—
119C4⋊Dic61C2×C812yes—
120C4⋊Dic61M1612yes—
121C4×Dic61—24no—
122C4×Dic61—21no—
123C4×Dic61—21no—
124C4×Dic61—21no—
125C4×Dic61—21no—
126C4×Dic61—21no—
127C4×Dic61—21no—
128C4×Dic61—24no—
129C4×Dic61—42no—
130C4×Dic61—41no—
131C4×Dic61—41no—
132C4×Dic61—42no—
133C2×#92418—22no—
134C2×#92418—41no—
135C2×#92418—41no—
136C2×#92418—41no—
137C2×#92418—41no—
138C2×#92418—41no—
139C23×C61C2×C22⋊C411yescharacteristic
140C22×D61—21no—
141C22×D61—21no—
142C22×D61—21no—
143C22×D61—21no—
144C22×D61—21no—
145C22×D61—21no—
146C22×D61C22⋊C812yes—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—22no—
150C2×C4×C61—22no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61—41no—
155C2×C4×C61#11711yescharacteristic
156C2×C4×C61#11711yescharacteristic
157C2×C4×C61#12311yescharacteristic
158C2×C4×C61#12311yescharacteristic
159C2×C4×C61#12311yescharacteristic
160C2×C4×C61#12311yescharacteristic
161C2×C4×C61C22×C811yescharacteristic
162C2×C4×C61C2×M1611yescharacteristic
163C2×C4×C61C2×M1611yescharacteristic
164C2×C4×C61C2×M1611yescharacteristic
165C2×C4×C61#13511yescharacteristic
166C2×C4×C61#13511yescharacteristic
167C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C61#13711yescharacteristic
169C2×Dic61—21no—
170C2×Dic61—21no—
171C2×Dic61—21no—
172C2×Dic61—21no—
173C2×Dic61—21no—
174C2×Dic61—22no—
175C2×Dic61—22no—
176C2×Dic61—21no—
177C2×Dic61—21no—
178C2×Dic61—41no—
179C2×Dic61—41no—
180C2×Dic61—41no—
181C2×Dic61—41no—
182C2×Dic61C22⋊C812yes—
183C2×Dic61#10412yes—
184C4×D61—22no—
185C4×D61—22no—
186C4×D61—22no—
187C4×D61—22no—
188C4×D61—42no—
189C4×D61—42no—
190C4×D61—41no—
191C4×D61—41no—
192C4×D61—41no—
193C4×D61—41no—
194C8×C61—42no—
195C8×C61—81no—
196#92418—42no—
197#92418—81no—
198#8708—611nomaximal, Sylow
199C22×C61#38111yescharacteristic
200C22×C61C2×C22⋊C811yescharacteristic
201C22×C61#40711yescharacteristic
202C22×C61#41611yescharacteristic
203C22×C61#41711yescharacteristic
204C22×C61C2×#10411yescharacteristic
205C22×C61#42111yescharacteristic
206C2×D61—22no—
207C2×D61—22no—
208C2×D61—22no—
209C2×D61—41no—
210C2×D61—41no—
211C2×D61—41no—
212C2×D61—41no—
213C4×C61—21no—
214C4×C61—21no—
215C4×C61—42no—
216C4×C61—42no—
217C4×C61#43111yescharacteristic
218C4×C61#43111yescharacteristic
219C4×C61#43211yescharacteristic
220C4×C61#43211yescharacteristic
221C4×C61#48211yescharacteristic
222C4×C61#48211yescharacteristic
223C4×C61#48511yescharacteristic
224C4×C61#48511yescharacteristic
225Dic61—22no—
226Dic61—22no—
227Dic61—41no—
228Dic61—42no—
229Dic61—42no—
230C4×#117—611no—
231#1797—611no—
232C4×C22⋊C8—611no—
233#1279—611no—
234#1279—611no—
235#1279—611no—
236#1279D6111yescharacteristic, complemented
237C2×C61#147611yescharacteristic
238C2×C61#147711yescharacteristic
239C2×C61#148811yescharacteristic
240C2×C61#148911yescharacteristic
241C2×C61#181711yescharacteristic
242C2×C61#182511yescharacteristic
243C2×C61#182611yescharacteristic
244D61—42no—
245C2×#117—611no—
246C2×#117—611no—
247C22×C42—611no—
248C2×C4⋊C8—611no—
249C2×C4⋊C8C2×D6111yescharacteristic
250C2×C22⋊C8—1221no—
251C2×C22⋊C8—1221no—
252C2×C4×C8—611no—
253C2×C4×C8C2×D6111yescharacteristic
254C4×C4⋊C4—611no—
255C4×C4⋊C4—611no—
256C4×C4⋊C4—611no—
257C4×C4⋊C4C2×D6111yescharacteristic
258C4×C22⋊C4—1221no—
259C4×C22⋊C4—1221no—
260#376—1221no—
261C43—1221no—
262#336—1221no—
263#336—1221no—
264C61#870811yescharacteristic, complemented, Sylow
265C23×C4—611no—
266C23×C4—611no—
267C23×C4—611no—
268C22×C8—21no—
269C22×C8—21no—
270C22×C8—1221no—
271C22×C8—1221no—
272#117—614no—
273#117—1222no—
274#117—1222no—
275#117—1222no—
276C2×C4⋊C4—611no—
277C2×C4⋊C4—611no—
278C2×C4⋊C4C4×D6111yescharacteristic
279C2×C4⋊C4C4×D6111yescharacteristic
280C2×C22⋊C4—1221no—
281C2×C22⋊C4—1221no—
282C2×C42—21no—
283C2×C42—611no—
284C2×C42—611no—
285C2×C42—611no—
286C2×C42—1221no—
287C2×C42—1221no—
288C2×C42—1221no—
289C2×C42—1221no—
290C2×C42—1221no—
291C2×C42—1221no—
292C2×C42—1221no—
293C2×C42—1221no—
294C2×C42—1221no—
295C2×C42C22×D6111yescharacteristic
296C4⋊C8—21no—
297C4⋊C8—21no—
298C4⋊C8—1221no—
299C4⋊C8—1221no—
300C22⋊C8—1224no—
301C22⋊C8—2442no—
302C4×C8—21no—
303C4×C8—21no—
304C4×C8—1221no—
305C4×C8—1221no—
306#95—21no—
307#95—1221no—
308#95—1221no—
309#95—1221no—
310C24—611no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—611no—
314C22×C4—611no—
315C22×C4—612no—
316C22×C4—612no—
317C22×C4—611no—
318C22×C4—1222no—
319C22×C4—1221no—
320C22×C4—1221no—
321C22×C4—1221no—
322C22×C4—1221no—
323C22×C4—1221no—
324C22×C4—1221no—
325C22×C4—1221no—
326C22×C4—1221no—
327C22×C4—1221no—
328C22×C4—1221no—
329C22×C4—1221no—
330C22×C4—1221no—
331C22×C4—1221no—
332C22×C4—1221no—
333C22×C4—2441no—
334C22×C4C2×C4×D6111yescharacteristic
335C22×C4D4×D6111yescharacteristic
336C22×C4D4×D6111yescharacteristic
337C2×C8—22no—
338C2×C8—41no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8—41no—
342C2×C8—41no—
343C2×C8—1222no—
344C2×C8—2441no—
345C2×C8—2441no—
346C2×C8—2441no—
347C2×C8—2441no—
348C2×C8—2441no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—612no—
352C4⋊C4—612no—
353C4⋊C4—1221no—
354C4⋊C4—1221no—
355C4⋊C4C8×D6112yes—
356C4⋊C4#1175818912yes—
357C22⋊C4—1224no—
358C22⋊C4—1224no—
359C42—41no—
360C42—41no—
361C42—1224no—
362C42—1224no—
363C42—1221no—
364C42—1221no—
365C42—1221no—
366C42—1221no—
367C42—1221no—
368C42—1221no—
369C42—2442no—
370C42—2442no—
371C42—2441no—
372C42—2441no—
373C42#1175822211yescharacteristic
374C42#1175822211yescharacteristic
375C42#1175822411yescharacteristic
376C42#1175822611yescharacteristic
377C23—612no—
378C23—1221no—
379C23—1221no—
380C23—1221no—
381C23—1221no—
382C23—1221no—
383C23—1221no—
384C23C22⋊C4×D6111yescharacteristic
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—612no—
394C2×C4—612no—
395C2×C4—1221no—
396C2×C4—1221no—
397C2×C4—1221no—
398C2×C4—1221no—
399C2×C4—1222no—
400C2×C4—1222no—
401C2×C4—1222no—
402C2×C4—1222no—
403C2×C4—1222no—
404C2×C4—1222no—
405C2×C4—1221no—
406C2×C4—1221no—
407C2×C4—1221no—
408C2×C4—2442no—
409C2×C4—2442no—
410C2×C4—2441no—
411C2×C4—2441no—
412C2×C4—2441no—
413C2×C4—2441no—
414C2×C4—2441no—
415C2×C4—2441no—
416C2×C4—2441no—
417C2×C4—2441no—
418C2×C4#1451973411yescharacteristic
419C2×C4#1451973511yescharacteristic
420C2×C4#1451975911yescharacteristic
421C2×C4#1451975911yescharacteristic
422C2×C4#1451976211yescharacteristic
423C2×C4#1451976211yescharacteristic
424C2×C4C2×C8×D6111yescharacteristic
425C2×C4M16×D6111yescharacteristic
426C2×C4M16×D6111yescharacteristic
427C2×C4C2×#1175818911yescharacteristic
428C2×C4#1451979611yescharacteristic
429C2×C4#1451979811yescharacteristic
430C2×C4#1451980411yescharacteristic
431C2×C4#1451980911yescharacteristic
432C8—42no—
433C8—81no—
434C8—4881no—
435C8—2442no—
436C22—1222no—
437C22—1222no—
438C22—1222no—
439C22—2441no—
440C22—2441no—
441C22—2441no—
442C22—2441no—
443C22#1683962411yescharacteristic
444C22C22⋊C8×D6111yescharacteristic
445C22#1683972411yescharacteristic
446C22#1683975511yescharacteristic
447C22#1683976211yescharacteristic
448C22#104×D6111yescharacteristic
449C22#1683977711yescharacteristic
450C4—21no—
451C4—21no—
452C4—42no—
453C4—42no—
454C4—1222no—
455C4—1222no—
456C4—2441no—
457C4—2442no—
458C4—2442no—
459C4#1683981311yescharacteristic
460C4#1683981411yescharacteristic
461C4#1683981711yescharacteristic
462C4#1683981811yescharacteristic
463C4#1684008411yescharacteristic
464C4#1684008811yescharacteristic
465C4#1684010111yescharacteristic
466C4#1684010511yescharacteristic
467C2—2442no—
468C2#2144419811yescharacteristic
469C2#2144420511yescharacteristic
470C2#2144425011yescharacteristic
471C2#2144425711yescharacteristic
472C2#2144588611yescharacteristic
473C2#2144591211yescharacteristic
474C2#2144591711yescharacteristic
subgroupG/H
centerC22×C4D4×D61
commutatorC2×C4×C61C22×C8
FrattiniC2×C42C22×D61
FittingC61×#1279C2
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1279D61
hypocenterC61#8708
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
4. #21443660C2semidirect
5. #21443659C2semidirect
6. #21443658C2semidirect
7. C61×#1279C2semidirect
35. #14519735C8semidirect
236. #1279D61semidirect
264. C61#8708semidirect

Maximal subgroups

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

subgroupindex
C4×#145197352
#214457962
C4×#145196892
#214436602
#214436592
#214436582
C61×#12792
#870861