Finite Group Databasebeta

← #29569130

Subgroups — #29569130

Order 15616.

516 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 85 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#21452183C211yesmaximal, characteristic
2#21447296C211yesmaximal, characteristic, complemented
3#21447223C211yesmaximal, characteristic, complemented
4#21443643C211yesmaximal, characteristic, complemented
5#21443640C211yesmaximal, characteristic, complemented
6#21443639C211yesmaximal, characteristic, complemented
7C61×#2093C211yesmaximal, characteristic, complemented
8C2×#14519761—21no—
9C2×#14519749—21no—
10C2×#14519708—21no—
11C2×#14519697—21no—
12#16839684—21no—
13#16839678—21no—
14#16839671—21no—
15#16839664C2211yescharacteristic
16#16839660C2211yescharacteristic
17#16839637—21no—
18#16839524—21no—
19#16839524—21no—
20#16839517C2211yescharacteristic
21#16839517C2211yescharacteristic
22C2×#107×C61—21no—
23C2×#102×C61—21no—
24C61×#390C2211yescharacteristic
25C61×#384C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×D244D411yescharacteristic
28C22×C22⋊D61—21no—
29C22×C22⋊D61—21no—
30C23×Dic61—21no—
31C22×#92418—21no—
32C22×#92418—21no—
33#14519761—42no—
34#14519761—42no—
35#14519749—42no—
36#14519749—42no—
37C2×C4⋊Dic61—21no—
38C2×C4⋊Dic61D411yescharacteristic
39C2×C4⋊Dic61D411yescharacteristic
40C2×C4⋊Dic61D411yescharacteristic
41C2×#11758196—21no—
42C2×C22⋊Dic61—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×#11758198—21no—
47#14519708—42no—
48#14519697—42no—
49#14519684—21no—
50#14519684—21no—
51C22×D4×C61D411yescharacteristic
52C22×C8×C61—21no—
53C2×C4⋊C4×C61—21no—
54C2×C4⋊C4×C61—21no—
55C2×C4⋊C4×C61—21no—
56C2×C4⋊C4×C61D411yescharacteristic
57C2×C22⋊C4×C61—21no—
58C2×C22⋊C4×C61—21no—
59C2×C42×C61C2311yescharacteristic
60#107×C61—42no—
61#102×C61—42no—
62C24×C61—21no—
63C23×D61—21no—
64C2×D4×C61—21no—
65C2×D4×C61—41no—
66C2×D4×C61—41no—
67C2×D4×C61SD1612yes—
68C22×C4×C61—21no—
69C22×C4×C61—41no—
70C22×C4×C61C2×D411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C2×C22⋊D61—42no—
74C2×C22⋊D61—42no—
75C2×C22⋊D61—42no—
76C2×C22⋊D61—81no—
77C2×C22⋊D61—81no—
78C2×C22⋊D61—81no—
79C22×Dic61—21no—
80C22×Dic61—21no—
81C22×Dic61—21no—
82C22×Dic61—42no—
83C22×Dic61—42no—
84C22×Dic61—81no—
85C2×D244—21no—
86C2×D244—21no—
87C2×D244—41no—
88C2×D244—41no—
89C2×C8×C61—22no—
90C2×C8×C61—41no—
91C2×C8×C61—41no—
92C4⋊C4×C61—41no—
93C4⋊C4×C61—41no—
94C4⋊C4×C61—41no—
95C4⋊C4×C61—41no—
96C4⋊C4×C61—41no—
97C4⋊C4×C61—41no—
98C4⋊C4×C61—41no—
99C22⋊C4×C61—41no—
100C22⋊C4×C61—41no—
101C22⋊C4×C61—41no—
102C22⋊C4×C61—41no—
103C42×C61—41no—
104C22⋊Dic61—42no—
105#11758198—42no—
106#11758198—41no—
107#11758198—41no—
108#11758198—41no—
109#11758198—41no—
110#11758198—81no—
111C4⋊Dic61—21no—
112C4⋊Dic61—42no—
113C4⋊Dic61—41no—
114C4⋊Dic61—41no—
115C4⋊Dic61D812yes—
116#11758196—41no—
117#11758196—41no—
118C2×#92418—22no—
119C2×#92418—41no—
120C2×#92418—41no—
121C2×#92418—41no—
122C2×#92418—41no—
123C2×#92418—41no—
124C23×C61—22no—
125C23×C61—41no—
126C23×C61—41no—
127C23×C61—41no—
128C23×C61—41no—
129C23×C61—41no—
130C23×C61—41no—
131C23×C61#12011yescharacteristic
132C22×D61—41no—
133C22×D61—41no—
134C22×D61—41no—
135C22×D61—41no—
136C22×D61—41no—
137C22×D61—41no—
138C22×D61—41no—
139D4×C61—42no—
140D4×C61—81no—
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—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—81no—
151C2×C4×C61—81no—
152C2×C4×C61—81no—
153C2×C4×C61C2×D811yescharacteristic
154C2×C4×C61C2×SD1611yescharacteristic
155C2×C4×C61#13511yescharacteristic
156C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
159C22⋊D61—84no—
160C22⋊D61—84no—
161C2×Dic61—22no—
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—84no—
171D244—42no—
172D244—81no—
173C8×C61—42no—
174#92418—42no—
175#92418—81no—
176#7800—611nomaximal, Sylow
177C22×C61—42no—
178C22×C61—42no—
179C22×C61—42no—
180C22×C61—81no—
181C22×C61—81no—
182C22×C61—81no—
183C22×C61—81no—
184C22×C61#44711yescharacteristic
185C22×C61#44911yescharacteristic
186C22×C61#45011yescharacteristic
187C22×C61#45311yescharacteristic
188C22×C61#45511yescharacteristic
189C22×C61#45611yescharacteristic
190C22×C61#45811yescharacteristic
191C2×D61—81no—
192C2×D61—81no—
193C2×D61—81no—
194C2×D61—81no—
195C2×D61—81no—
196C2×D61—81no—
197C2×D61—81no—
198C4×C61—21no—
199C4×C61—21no—
200C4×C61—21no—
201C4×C61—21no—
202C4×C61—21no—
203C4×C61—21no—
204C4×C61—81no—
205C4×C61—161no—
206Dic61—42no—
207Dic61—81no—
208Dic61—81no—
209#2682—611no—
210#2093D6111yescharacteristic, complemented
211#2084—611no—
212#2071—611no—
213#1271—611no—
214#1270—611no—
215#1270—611no—
216C2×C61—82no—
217C2×C61#161011yescharacteristic
218C2×C61#161211yescharacteristic
219C2×C61#161311yescharacteristic
220C2×C61#162111yescharacteristic
221C2×C61#163911yescharacteristic
222C2×C61#165411yescharacteristic
223C2×C61#166111yescharacteristic
224D61—161no—
225C2×#123—1221no—
226C2×#121—1221no—
227C2×#107—21no—
228C2×#106—1221no—
229C2×#102—21no—
230C2×#102—1221no—
231#396—1221no—
232#394—1221no—
233#392—1221no—
234#390—611no—
235#390C2×D6111yescharacteristic
236#389—611no—
237#385—1221no—
238#384C2×D6111yescharacteristic
239#340—1221no—
240#340—1221no—
241#336—611no—
242#336—611no—
243#336C2×D6111yescharacteristic
244C61#780011yescharacteristic, complemented, Sylow
245C22×D4—611no—
246C22×D4—1221no—
247C22×D4—1221no—
248C22×D4C22⋊D6111yescharacteristic
249C23×C4—1221no—
250C22×C8—21no—
251C22×C8—1221no—
252C22×C8—1221no—
253#123—2442no—
254#123—2442no—
255#121—2442no—
256#121—2442no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—611no—
261C2×C4⋊C4—611no—
262C2×C4⋊C4—611no—
263C2×C4⋊C4—1221no—
264C2×C4⋊C4—1221no—
265C2×C4⋊C4C22⋊D6111yescharacteristic
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—1221no—
269C2×C22⋊C4—1221no—
270C2×C22⋊C4—1221no—
271C2×C22⋊C4—1221no—
272C2×C22⋊C4—1221no—
273C2×C42C22×D6111yescharacteristic
274#107—42no—
275#106—2442no—
276#102—42no—
277#102—2442no—
278#95—1221no—
279#95—1221no—
280C24—21no—
281C24—1221no—
282C2×D4—21no—
283C2×D4—41no—
284C2×D4—41no—
285C2×D4—1221no—
286C2×D4—1221no—
287C2×D4—4881no—
288C2×D4—4881no—
289C2×D4—4881no—
290C2×D4—2441no—
291C2×D4—2441no—
292C2×D4—2442no—
293C2×D4—2442no—
294C2×D4—2442no—
295C2×D4#1175820112yes—
296C22×C4—21no—
297C22×C4—41no—
298C22×C4—1221no—
299C22×C4—1221no—
300C22×C4—1221no—
301C22×C4—4881no—
302C22×C4—2442no—
303C22×C4—2442no—
304C22×C4D4×D6111yescharacteristic
305C22×C4D4×D6111yescharacteristic
306C22×C4C2×C22⋊D6111yescharacteristic
307C2×C8—22no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—1222no—
311C2×C8—2441no—
312C2×C8—2441no—
313C2×C8—2441no—
314C2×C8—2441no—
315C2×C8—2441no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—612no—
324C4⋊C4—1221no—
325C4⋊C4—2441no—
326C4⋊C4—2441no—
327C4⋊C4—2442no—
328C4⋊C4—2441no—
329C4⋊C4—2441no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—4881no—
335C22⋊C4—2442no—
336C22⋊C4—2442no—
337C22⋊C4—2441no—
338C22⋊C4—2441no—
339C22⋊C4—2441no—
340C22⋊C4—2441no—
341C42—41no—
342C23—22no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—2441no—
350C23—2441no—
351C23—2441no—
352C23—2441no—
353C23—2441no—
354C23—2441no—
355C23—2441no—
356C23#1451974511yescharacteristic
357D4—42no—
358D4—81no—
359D4—4881no—
360D4—4884no—
361D4—4884no—
362D4—2442no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—81no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4—1222no—
376C2×C4—4884no—
377C2×C4—2441no—
378C2×C4—2441no—
379C2×C4—2441no—
380C2×C4—2441no—
381C2×C4—2441no—
382C2×C4—2441no—
383C2×C4—2441no—
384C2×C4—2441no—
385C2×C4D8×D6111yescharacteristic
386C2×C4C2×#1175820111yescharacteristic
387C2×C4#1451979611yescharacteristic
388C2×C4#1451980111yescharacteristic
389C2×C4#1451980111yescharacteristic
390C2×C4#1451980211yescharacteristic
391C8—42no—
392C8—4881no—
393C8—2442no—
394C22—42no—
395C22—42no—
396C22—42no—
397C22—81no—
398C22—81no—
399C22—81no—
400C22—81no—
401C22—4881no—
402C22—4881no—
403C22—4881no—
404C22—4881no—
405C22—4881no—
406C22—4881no—
407C22—4881no—
408C22#1683989411yescharacteristic
409C22#1683990411yescharacteristic
410C22#1683991211yescharacteristic
411C22#1683992911yescharacteristic
412C22#1683993811yescharacteristic
413C22#1683994311yescharacteristic
414C22#1683995111yescharacteristic
415C4—21no—
416C4—21no—
417C4—21no—
418C4—21no—
419C4—21no—
420C4—21no—
421C4—81no—
422C4—161no—
423C4—4881no—
424C4—4881no—
425C4—2442no—
426C2—82no—
427C2—9761no—
428C2#2144482011yescharacteristic
429C2#2144483011yescharacteristic
430C2#2144483811yescharacteristic
431C2#2144488111yescharacteristic
432C2#2144499711yescharacteristic
433C2#2144510211yescharacteristic
434C2#2144513311yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2093C2
socleC23×C61#120
prime radical#21452183C2
hypercenter#2093D61
hypocenterC61#7800
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2093

Complements

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

NH ≅ G/Ntype
2. #21447296C2semidirect
3. #21447223C2semidirect
4. #21443643C2semidirect
5. #21443640C2semidirect
6. #21443639C2semidirect
7. C61×#2093C2semidirect
210. #2093D61semidirect
244. C61#7800semidirect

Maximal subgroups

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

subgroupindex
#214521832
#214472962
#214472232
#214436432
#214436402
#214436392
C61×#20932
#780061