Finite Group Databasebeta

← #29568782

Subgroups — #29568782

Order 15616.

492 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 81 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#21453769C211yesmaximal, characteristic, complemented
2#21447050C211yesmaximal, characteristic
3#21446907C211yesmaximal, characteristic
4#21443644C211yesmaximal, characteristic, complemented
5#21443643C211yesmaximal, characteristic, complemented
6#21443642C211yesmaximal, characteristic, complemented
7C61×#2041C211yesmaximal, characteristic
8C22×#11758200—21no—
9C2×#14519698—21no—
10C2×#14519698—21no—
11C2×#14519698—21no—
12#16839704—21no—
13#16839700—21no—
14#16839682—21no—
15#16839668C2211yescharacteristic
16#16839660C2211yescharacteristic
17#16839657—21no—
18#16839648—21no—
19#16839647—21no—
20#16839517C2211yescharacteristic
21#16839517C2211yescharacteristic
22C2×#127×C61C2211yescharacteristic
23C2×#102×C61—21no—
24C2×#102×C61—21no—
25C61×#389C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×Dic122D411yescharacteristic
28C2×#11758200—42no—
29C2×#11758200—42no—
30C2×#11758200—42no—
31C22×#92418—21no—
32C22×#92418—21no—
33C2×C4⋊Dic61D411yescharacteristic
34C2×C4⋊Dic61D411yescharacteristic
35C2×C4⋊Dic61D411yescharacteristic
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×C4×Dic61—21no—
40#14519698—42no—
41#14519698—42no—
42#14519698—42no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51C22×D4×C61—21no—
52C22×D4×C61—21no—
53C22×D4×C61—21no—
54C22×C8×C61—21no—
55#127×C61—42no—
56C2×C4⋊C4×C61—21no—
57C2×C4⋊C4×C61D411yescharacteristic
58C2×C4⋊C4×C61D411yescharacteristic
59C2×C42×C61C2311yescharacteristic
60#102×C61—42no—
61#102×C61—42no—
62#95×C61—21no—
63C24×C61—41no—
64C2×D4×C61—22no—
65C2×D4×C61—22no—
66C2×D4×C61—22no—
67C2×D4×C61—41no—
68C2×D4×C61—41no—
69C2×D4×C61—41no—
70C2×D4×C61—41no—
71C2×D4×C61—41no—
72C2×D4×C61—41no—
73C2×D4×C61—41no—
74C2×D4×C61—41no—
75C2×D4×C61—41no—
76C2×D4×C61—41no—
77C2×D4×C61—41no—
78C2×D4×C61—41no—
79C2×D4×C61—41no—
80C2×D4×C61—41no—
81C2×D4×C61—41no—
82C22×C4×C61—21no—
83C22×C4×C61—21no—
84C22×C4×C61C2×D411yescharacteristic
85C22×C4×C61C2×D411yescharacteristic
86C22×C4×C61C2×D411yescharacteristic
87C22×Dic61—21no—
88C22×Dic61—21no—
89C22×Dic61—21no—
90C22×Dic61—21no—
91C2×Dic122—21no—
92C2×Dic122—21no—
93C2×Dic122—41no—
94C2×Dic122—41no—
95C2×C8×C61—41no—
96C2×C8×C61—41no—
97C2×C8×C61—41no—
98C4⋊C4×C61—21no—
99C4⋊C4×C61—21no—
100C4⋊C4×C61—41no—
101C4⋊C4×C61—41no—
102C4⋊C4×C61—41no—
103C42×C61—41no—
104#11758200—48no—
105C4⋊Dic61—21no—
106C4⋊Dic61—41no—
107C4⋊Dic61—41no—
108C4⋊Dic61SD1612yescomplemented
109#11758196—41no—
110#11758196—41no—
111#11758196—81no—
112#11758196—81no—
113C4×Dic61—81no—
114C2×#92418—22no—
115C2×#92418—41no—
116C2×#92418—41no—
117C2×#92418—41no—
118C2×#92418—41no—
119C2×#92418—41no—
120C23×C61—42no—
121C23×C61—81no—
122C23×C61—81no—
123C23×C61—81no—
124C23×C61—81no—
125C23×C61—81no—
126C23×C61—81no—
127C23×C61#12011yescharacteristic
128D4×C61—42no—
129D4×C61—42no—
130D4×C61—42no—
131D4×C61—42no—
132D4×C61—42no—
133D4×C61—42no—
134D4×C61—81no—
135D4×C61—81no—
136D4×C61—81no—
137D4×C61—81no—
138D4×C61—81no—
139D4×C61—81no—
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—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61C2×SD1611yescharacteristic
153C2×C4×C61#13511yescharacteristic
154C2×C4×C61#13511yescharacteristic
155C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C61#13711yescharacteristic
158C2×Dic61—22no—
159C2×Dic61—41no—
160C2×Dic61—41no—
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—
170Dic122—42no—
171Dic122—81no—
172C8×C61—81no—
173#92418—42no—
174#92418—81no—
175#7747—611nomaximal, Sylow
176C22×C61—82no—
177C22×C61—82no—
178C22×C61—82no—
179C22×C61—161no—
180C22×C61—161no—
181C22×C61—161no—
182C22×C61—161no—
183C22×C61#44811yescharacteristic
184C22×C61#44911yescharacteristic
185C22×C61#44911yescharacteristic
186C22×C61#45311yescharacteristic
187C22×C61#45411yescharacteristic
188C22×C61#45411yescharacteristic
189C22×C61B(4,𝔽2)11yescharacteristic
190C4×C61—21no—
191C4×C61—21no—
192C4×C61—21no—
193C4×C61—21no—
194C4×C61—21no—
195C4×C61—21no—
196C4×C61—81no—
197C4×C61—81no—
198Dic61—42no—
199Dic61—81no—
200Dic61—81no—
201Dic61—81no—
202#2805—611no—
203#2041—611no—
204#2041D6111yescharacteristic
205#2014—611no—
206#1272—611no—
207#1271—611no—
208#1271—611no—
209C2×C61—162no—
210C2×C61#159711yescharacteristic
211C2×C61#159911yescharacteristic
212C2×C61#160011yescharacteristic
213C2×C61#162211yescharacteristic
214C2×C61#162611yescharacteristic
215C2×C61#162811yescharacteristic
216C2×C61#165711yescharacteristic
217C22×SD16—1221no—
218C2×#127C2×D6111yescharacteristic
219C2×#102—21no—
220C2×#102—21no—
221C2×#102—1221no—
222C2×#102—1221no—
223C2×#102—1221no—
224#400—1221no—
225#400—1221no—
226#395—1221no—
227#391—611no—
228#389—611no—
229#389—1221no—
230#389C2×D6111yescharacteristic
231#387—1221no—
232#387—1221no—
233#336—611no—
234#336—611no—
235#336C2×D6111yescharacteristic
236C61#774711yescharacteristic, complemented, Sylow
237C22×Q8—611no—
238C22×D4—21no—
239C22×D4—21no—
240C22×D4—21no—
241C2×SD16—2442no—
242C2×SD16—2442no—
243C2×SD16—2442no—
244C22×C8—21no—
245C22×C8—1221no—
246C22×C8—1221no—
247#127—42no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—611no—
250C2×C4⋊C4—611no—
251C2×C4⋊C4—611no—
252C2×C4⋊C4—1221no—
253C2×C4⋊C4—1221no—
254C2×C4⋊C4—1221no—
255C2×C4⋊C4C22⋊D6111yescharacteristic
256C2×C4⋊C4C22⋊D6111yescharacteristic
257C2×C42—1221no—
258C2×C42C22×D6111yescharacteristic
259#102—42no—
260#102—42no—
261#102—2442no—
262#102—2442no—
263#102—2442no—
264#95—21no—
265#95—1221no—
266#95—1221no—
267#95—1221no—
268#95—1221no—
269#95—1221no—
270#95—1221no—
271#95—1221no—
272#95—1221no—
273C24—41no—
274C2×Q8—1221no—
275C2×Q8—1221no—
276C2×Q8—2441no—
277C2×Q8—2441no—
278C2×D4—22no—
279C2×D4—22no—
280C2×D4—22no—
281C2×D4—41no—
282C2×D4—41no—
283C2×D4—41no—
284C2×D4—41no—
285C2×D4—41no—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—41no—
289C2×D4—41no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—41no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—1221no—
299C22×C4—1221no—
300C22×C4—1221no—
301C22×C4—1221no—
302C22×C4D4×D6111yescharacteristic
303C22×C4D4×D6111yescharacteristic
304C22×C4C2×C22⋊D6111yescharacteristic
305SD16—2448no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—1222no—
310C2×C8—2441no—
311C2×C8—2441no—
312C2×C8—2441no—
313C2×C8—2441no—
314C2×C8—2441no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—612no—
321C4⋊C4—1221no—
322C4⋊C4—4881no—
323C4⋊C4—4881no—
324C4⋊C4—2441no—
325C4⋊C4—2441no—
326C4⋊C4—2441no—
327C4⋊C4—2441no—
328C42—41no—
329C42—4881no—
330C23—42no—
331C23—81no—
332C23—81no—
333C23—81no—
334C23—81no—
335C23—81no—
336C23—81no—
337C23#1451974511yescharacteristic
338Q8—4881no—
339Q8—2442no—
340D4—42no—
341D4—42no—
342D4—42no—
343D4—42no—
344D4—42no—
345D4—42no—
346D4—81no—
347D4—81no—
348D4—81no—
349D4—81no—
350D4—81no—
351D4—81no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—1222no—
365C2×C4—2441no—
366C2×C4—2441no—
367C2×C4—2441no—
368C2×C4—2441no—
369C2×C4—2441no—
370C2×C4—2441no—
371C2×C4—2441no—
372C2×C4—2441no—
373C2×C4—2441no—
374C2×C4—2441no—
375C2×C4—2441no—
376C2×C4SD16×D6111yescharacteristic
377C2×C4#1451979611yescharacteristic
378C2×C4#1451979711yescharacteristic
379C2×C4#1451980111yescharacteristic
380C2×C4#1451980311yescharacteristic
381C2×C4#1451980611yescharacteristic
382C8—81no—
383C8—4881no—
384C8—2442no—
385C22—82no—
386C22—82no—
387C22—82no—
388C22—161no—
389C22—161no—
390C22—161no—
391C22—161no—
392C22#1683989911yescharacteristic
393C22#1683990411yescharacteristic
394C22#1683990511yescharacteristic
395C22#1683992811yescharacteristic
396C22#1683993311yescharacteristic
397C22#1683993411yescharacteristic
398C22#1683994811yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—21no—
404C4—21no—
405C4—81no—
406C4—81no—
407C4—4881no—
408C4—4881no—
409C4—4881no—
410C4—2442no—
411C2—162no—
412C2#2144474611yescharacteristic
413C2#2144475711yescharacteristic
414C2#2144476211yescharacteristic
415C2#2144489011yescharacteristic
416C2#2144491211yescharacteristic
417C2#2144492711yescharacteristic
418C2#2144511611yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2041C2
socleC23×C61#120
prime radicalC2×#127×C61C22
hypercenter#2041D61
hypocenterC61#7747
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2041

Complements

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

NH ≅ G/Ntype
1. #21453769C2semidirect
4. #21443644C2semidirect
5. #21443643C2semidirect
6. #21443642C2semidirect
108. C4⋊Dic61SD16semidirect
236. C61#7747semidirect

Maximal subgroups

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

subgroupindex
#214537692
#214470502
#214469072
#214436442
#214436432
#214436422
C61×#20412
#774761