Finite Group Databasebeta

← #29569285

Subgroups — #29569285

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#21452181C211yesmaximal, characteristic
2#21447353C211yesmaximal, characteristic, complemented
3#21447353C211yesmaximal, characteristic, complemented
4#21443642C211yesmaximal, characteristic, complemented
5#21443639C211yesmaximal, characteristic, complemented
6#21443639C211yesmaximal, characteristic, complemented
7C61×#2100C211yesmaximal, characteristic, complemented
8C2×#14519762—21no—
9C2×#14519752—21no—
10C2×#14519708—21no—
11C2×#14519708—21no—
12C2×#14519697—21no—
13C2×#14519697—21no—
14#16839684—21no—
15#16839679—21no—
16#16839672—21no—
17#16839664C2211yescharacteristic
18#16839664C2211yescharacteristic
19#16839636—21no—
20#16839517C2211yescharacteristic
21#16839517C2211yescharacteristic
22C61×#389C2211yescharacteristic
23C61×#384C2211yescharacteristic
24C61×#340—21no—
25C61×#340—21no—
26C61×#336C2211yescharacteristic
27C22×D244—21no—
28C22×D244—21no—
29C22×D244D411yescharacteristic
30C22×D244D411yescharacteristic
31C22×C4×D61—21no—
32C22×#92418—21no—
33C22×#92418—21no—
34#14519762—42no—
35#14519762—42no—
36#14519752—42no—
37#14519752—42no—
38C2×C4⋊Dic61D411yescharacteristic
39C2×C4⋊Dic61D411yescharacteristic
40C2×#11758196—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×#11758198—21no—
47C2×#11758198—21no—
48#14519708—42no—
49#14519708—42no—
50#14519697—42no—
51#14519697—42no—
52#14519684—21no—
53C22×C8×C61—21no—
54C2×C4⋊C4×C61—21no—
55C2×C4⋊C4×C61—21no—
56C2×C4⋊C4×C61—21no—
57C2×C4⋊C4×C61—21no—
58C2×C4⋊C4×C61D411yescharacteristic
59C2×C4⋊C4×C61D411yescharacteristic
60C2×C42×C61C2311yescharacteristic
61#95×C61—21no—
62C23×D61—21no—
63C23×D61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—41no—
67C22×C4×C61C2×D411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×Dic61—21no—
71C22×Dic61—21no—
72C2×D244—21no—
73C2×D244—21no—
74C2×D244—21no—
75C2×D244—41no—
76C2×D244—41no—
77C2×D244—41no—
78C2×D244—41no—
79C2×D244—42no—
80C2×D244—42no—
81C2×D244—42no—
82C2×D244—81no—
83C2×D244—81no—
84C2×D244—81no—
85C2×D244SD1612yes—
86C2×C4×D61—42no—
87C2×C4×D61—42no—
88C2×C4×D61—81no—
89C2×C8×C61—41no—
90C2×C8×C61—41no—
91C2×C8×C61—41no—
92C4⋊C4×C61—21no—
93C4⋊C4×C61—41no—
94C4⋊C4×C61—42no—
95C4⋊C4×C61—41no—
96C4⋊C4×C61—41no—
97C4⋊C4×C61—41no—
98C4⋊C4×C61—41no—
99C4⋊C4×C61—41no—
100C4⋊C4×C61—41no—
101C4⋊C4×C61SD1612yes—
102C42×C61—41no—
103#11758198—42no—
104#11758198—42no—
105#11758198—41no—
106#11758198—41no—
107#11758198—41no—
108#11758198—41no—
109#11758198—41no—
110#11758198—41no—
111#11758198—41no—
112#11758198—41no—
113#11758198—81no—
114C4⋊Dic61—41no—
115C4⋊Dic61—41no—
116#11758196—42no—
117C2×#92418—22no—
118C2×#92418—22no—
119C2×#92418—41no—
120C2×#92418—41no—
121C2×#92418—41no—
122C2×#92418—41no—
123C23×C61#12011yescharacteristic
124C22×D61—22no—
125C22×D61—41no—
126C22×D61—41no—
127C22×D61—41no—
128C22×D61—41no—
129C22×D61—41no—
130C22×D61—41no—
131C22×D61—41no—
132C22×D61—41no—
133C22×D61—41no—
134C22×D61—41no—
135C22×D61—41no—
136C22×D61—41no—
137C22×D61—41no—
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—22no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
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×SD1611yescharacteristic
154C2×C4×C61C2×SD1611yescharacteristic
155C2×C4×C61#13511yescharacteristic
156C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C61#13711yescharacteristic
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165D244—42no—
166D244—42no—
167D244—81no—
168D244—81no—
169D244—84no—
170D244—84no—
171C4×D61—84no—
172C8×C61—81no—
173#92418—42no—
174#92418—42no—
175#7825—611nomaximal, Sylow
176C22×C61#45011yescharacteristic
177C22×C61#45011yescharacteristic
178C22×C61#45211yescharacteristic
179C22×C61#45311yescharacteristic
180C22×C61#45311yescharacteristic
181C22×C61#45411yescharacteristic
182C22×C61#45811yescharacteristic
183C2×D61—42no—
184C2×D61—42no—
185C2×D61—42no—
186C2×D61—81no—
187C2×D61—81no—
188C2×D61—81no—
189C2×D61—81no—
190C2×D61—81no—
191C2×D61—81no—
192C2×D61—81no—
193C2×D61—81no—
194C2×D61—81no—
195C2×D61—81no—
196C2×D61—81no—
197C4×C61—21no—
198C4×C61—21no—
199C4×C61—21no—
200C4×C61—21no—
201C4×C61—21no—
202C4×C61—21no—
203C4×C61—42no—
204C4×C61—81no—
205C4×C61—161no—
206Dic61—81no—
207Dic61—81no—
208#2682—611no—
209#2100D6111yescharacteristic, complemented
210#2094—611no—
211#2094—611no—
212#1271—611no—
213#1270—611no—
214#1270—611no—
215C2×C61#161311yescharacteristic
216C2×C61#161611yescharacteristic
217C2×C61#161811yescharacteristic
218C2×C61#162911yescharacteristic
219C2×C61#163111yescharacteristic
220C2×C61#163511yescharacteristic
221C2×C61#165611yescharacteristic
222D61—82no—
223D61—161no—
224C2×#123—1221no—
225C2×#121—1221no—
226C2×#106—1221no—
227C2×#106—1221no—
228C2×#102—1221no—
229C2×#102—1221no—
230#396—1221no—
231#394—1221no—
232#392—1221no—
233#390—611no—
234#390—611no—
235#389C2×D6111yescharacteristic
236#385—1221no—
237#384C2×D6111yescharacteristic
238#340—21no—
239#340—21no—
240#336—611no—
241#336—611no—
242#336C2×D6111yescharacteristic
243C61#782511yescharacteristic, complemented, Sylow
244C22×D4—611no—
245C22×D4—611no—
246C22×D4—1221no—
247C22×D4—1221no—
248C23×C4—1221no—
249C22×C8—21no—
250C22×C8—1221no—
251C22×C8—1221no—
252#123—2442no—
253#123—2442no—
254#121—2442no—
255#121—2442no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—611no—
261C2×C4⋊C4—611no—
262C2×C4⋊C4—1221no—
263C2×C4⋊C4C22⋊D6111yescharacteristic
264C2×C4⋊C4C22⋊D6111yescharacteristic
265C2×C22⋊C4—1221no—
266C2×C22⋊C4—1221no—
267C2×C22⋊C4—1221no—
268C2×C22⋊C4—1221no—
269C2×C22⋊C4—1221no—
270C2×C22⋊C4—1221no—
271C2×C22⋊C4—1221no—
272C2×C42C22×D6111yescharacteristic
273#106—2442no—
274#106—2442no—
275#102—2442no—
276#102—2442no—
277#95—21no—
278#95—1221no—
279C24—1221no—
280C24—1221no—
281C2×D4—612no—
282C2×D4—1221no—
283C2×D4—1221no—
284C2×D4—1221no—
285C2×D4—4881no—
286C2×D4—4881no—
287C2×D4—4881no—
288C2×D4—2442no—
289C2×D4—2441no—
290C2×D4—2441no—
291C2×D4—2441no—
292C2×D4—2441no—
293C2×D4—2442no—
294C2×D4—2442no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—41no—
298C22×C4—1221no—
299C22×C4—1221no—
300C22×C4—4881no—
301C22×C4—2442no—
302C22×C4—2442no—
303C22×C4D4×D6111yescharacteristic
304C22×C4D4×D6111yescharacteristic
305C22×C4C2×C22⋊D6111yescharacteristic
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—1222no—
310C2×C8—1222no—
311C2×C8—2441no—
312C2×C8—2441no—
313C2×C8—2441no—
314C2×C8—2441no—
315C4⋊C4—21no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—42no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—2441no—
325C4⋊C4—2441no—
326C4⋊C4—2442no—
327C4⋊C4#1175820112yes—
328C22⋊C4—4881no—
329C22⋊C4—2442no—
330C22⋊C4—2442no—
331C22⋊C4—2441no—
332C22⋊C4—2441no—
333C22⋊C4—2441no—
334C22⋊C4—2441no—
335C22⋊C4—2441no—
336C22⋊C4—2441no—
337C22⋊C4—2441no—
338C22⋊C4—2441no—
339C42—41no—
340C23—1222no—
341C23—2441no—
342C23—2441no—
343C23—2441no—
344C23—2441no—
345C23—2441no—
346C23—2441no—
347C23—2441no—
348C23—2441no—
349C23—2441no—
350C23—2441no—
351C23—2441no—
352C23—2441no—
353C23—2441no—
354C23#1451974511yescharacteristic
355D4—4881no—
356D4—4881no—
357D4—4884no—
358D4—4884no—
359D4—2442no—
360D4—2442no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—22no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4—81no—
376C2×C4—4884no—
377C2×C4—2441no—
378C2×C4—2441no—
379C2×C4—2441no—
380C2×C4—2441no—
381C2×C4—2441no—
382C2×C4—2441no—
383C2×C4SD16×D6111yescharacteristic
384C2×C4C2×#1175820111yescharacteristic
385C2×C4#1451980011yescharacteristic
386C2×C4#1451980211yescharacteristic
387C2×C4#1451980411yescharacteristic
388C2×C4#1451980911yescharacteristic
389C8—81no—
390C8—2442no—
391C8—2442no—
392C22—4881no—
393C22—4881no—
394C22—4881no—
395C22—4881no—
396C22—4881no—
397C22—4881no—
398C22—4881no—
399C22—4881no—
400C22—4881no—
401C22—4881no—
402C22—4881no—
403C22—2442no—
404C22—2442no—
405C22—2442no—
406C22#1683991111yescharacteristic
407C22#1683991211yescharacteristic
408C22#1683992311yescharacteristic
409C22#1683992811yescharacteristic
410C22#1683992811yescharacteristic
411C22#1683993411yescharacteristic
412C22#1683995111yescharacteristic
413C4—21no—
414C4—21no—
415C4—21no—
416C4—21no—
417C4—21no—
418C4—21no—
419C4—42no—
420C4—81no—
421C4—161no—
422C4—4881no—
423C4—4881no—
424C2—9761no—
425C2—4882no—
426C2#2144483711yescharacteristic
427C2#2144485511yescharacteristic
428C2#2144486611yescharacteristic
429C2#2144493411yescharacteristic
430C2#2144494411yescharacteristic
431C2#2144496711yescharacteristic
432C2#2144511111yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2100C2
socleC23×C61#120
prime radical#21452181C2
hypercenter#2100D61
hypocenterC61#7825
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2100

Complements

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

NH ≅ G/Ntype
2. #21447353C2semidirect
3. #21447353C2semidirect
4. #21443642C2semidirect
5. #21443639C2semidirect
6. #21443639C2semidirect
7. C61×#2100C2semidirect
209. #2100D61semidirect
243. C61#7825semidirect

Maximal subgroups

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

subgroupindex
#214521812
#214473532
#214436422
#214436392
C61×#21002
#782561