Finite Group Databasebeta

← #29568885

Subgroups — #29568885

Order 15616.

504 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 87 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#21452190C211yesmaximal, characteristic
2#21447147C211yesmaximal, characteristic, complemented
3#21447066C211yesmaximal, characteristic, complemented
4#21446956C211yesmaximal, characteristic
5#21443641C211yesmaximal, characteristic, complemented
6#21443639C211yesmaximal, characteristic
7C61×#1271C211yesmaximal, characteristic, complemented
8C2×#14519777C2211yescharacteristic
9C2×#14519757—21no—
10C2×#14519755—21no—
11C2×#14519710—21no—
12C2×#14519702—21no—
13C2×#14519702—21no—
14C2×#14519699—21no—
15#16839684—21no—
16#16839684—21no—
17#16839683—21no—
18#16839664C2211yescharacteristic
19#16839660C2211yescharacteristic
20#16839640—21no—
21#16839525—21no—
22#16839524—21no—
23#16839517C2211yescharacteristic
24C61×#389C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×Dic122—21no—
28C22×Dic122—21no—
29C22×D244D411yescharacteristic
30C22×C4×D61—21no—
31C22×#92418—21no—
32#14519777—42no—
33#14519757—42no—
34#14519757—42no—
35#14519755—42no—
36#14519755—42no—
37C2×C4⋊Dic61—21no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61D411yescharacteristic
41C2×C4⋊Dic61D411yescharacteristic
42C2×C4⋊Dic61D411yescharacteristic
43C2×#11758196—21no—
44C2×#11758196—21no—
45C2×#11758198—21no—
46C2×#11758198—21no—
47C2×#11758198—21no—
48C2×#11758198—21no—
49C2×#11758198—21no—
50#14519710—42no—
51#14519702—42no—
52#14519702—42no—
53#14519699—42no—
54#14519684—21no—
55#14519684—21no—
56C22×C8×C61—21no—
57C22×C8×C61—21no—
58C2×C4⋊C4×C61—21no—
59C2×C4⋊C4×C61D411yescharacteristic
60C2×C4⋊C4×C61D411yescharacteristic
61C2×C42×C61C2311yescharacteristic
62#95×C61—21no—
63C23×D61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61C2×D411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61—41no—
73C2×D244—21no—
74C2×D244—41no—
75C2×D244—41no—
76C2×D244Q1612yes—
77C2×C4×D61—42no—
78C2×C4×D61—42no—
79C2×C4×D61—81no—
80C2×Dic122—22no—
81C2×Dic122—41no—
82C2×Dic122—41no—
83C2×Dic122—41no—
84C2×Dic122—41no—
85C2×Dic122—42no—
86C2×Dic122—42no—
87C2×Dic122—41no—
88C2×Dic122—81no—
89C2×C8×C61—41no—
90C2×C8×C61—41no—
91C2×C8×C61—41no—
92C2×C8×C61—41no—
93C2×C8×C61—41no—
94C2×C8×C61—41no—
95C4⋊C4×C61—21no—
96C4⋊C4×C61—41no—
97C4⋊C4×C61—41no—
98C4⋊C4×C61—41no—
99C4⋊C4×C61SD1612yes—
100C42×C61—41no—
101#11758198—42no—
102#11758198—42no—
103#11758198—41no—
104#11758198—41no—
105#11758198—41no—
106#11758198—41no—
107#11758198—81no—
108C4⋊Dic61—21no—
109C4⋊Dic61—22no—
110C4⋊Dic61—22no—
111C4⋊Dic61—42no—
112C4⋊Dic61—41no—
113C4⋊Dic61—41no—
114C4⋊Dic61—41no—
115C4⋊Dic61—41no—
116C4⋊Dic61D812yes—
117#11758196—42no—
118#11758196—41no—
119#11758196—41no—
120C2×#92418—22no—
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—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—22no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61C2×D811yescharacteristic
144C2×C4×C61C2×SD1611yescharacteristic
145C2×C4×C61C2×Q1611yescharacteristic
146C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C61#13711yescharacteristic
149C2×Dic61—22no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—42no—
158C2×Dic61—41no—
159C2×Dic61—81no—
160C2×Dic61—81no—
161D244—42no—
162D244—81no—
163C4×D61—84no—
164Dic122—42no—
165Dic122—42no—
166Dic122—84no—
167Dic122—81no—
168Dic122—81no—
169C8×C61—81no—
170C8×C61—81no—
171#92418—42no—
172#7764—611nomaximal, Sylow
173C22×C61#44711yescharacteristic
174C22×C61#45011yescharacteristic
175C22×C61#45111yescharacteristic
176C22×C61#45411yescharacteristic
177C22×C61#45511yescharacteristic
178C22×C61#45611yescharacteristic
179C22×C61B(4,𝔽2)11yescharacteristic
180C2×D61—42no—
181C2×D61—42no—
182C2×D61—42no—
183C2×D61—81no—
184C2×D61—81no—
185C2×D61—81no—
186C2×D61—81no—
187C4×C61—21no—
188C4×C61—21no—
189C4×C61—21no—
190C4×C61—21no—
191C4×C61—21no—
192C4×C61—21no—
193C4×C61—42no—
194C4×C61—81no—
195Dic61—42no—
196Dic61—82no—
197Dic61—81no—
198Dic61—81no—
199#2683—611no—
200#2057—611no—
201#2043—611no—
202#2023—611no—
203#1271—611no—
204#1271D6111yescharacteristic, complemented
205#1270—611no—
206C2×C61#159811yescharacteristic
207C2×C61#160211yescharacteristic
208C2×C61#160411yescharacteristic
209C2×C61#163711yescharacteristic
210C2×C61#163911yescharacteristic
211C2×C61#164911yescharacteristic
212C2×C61#166411yescharacteristic
213D61—82no—
214C2×C4⋊Q8—611no—
215C2×C22⋊Q8—1221no—
216C2×C22⋊Q8—1221no—
217C2×#107—1221no—
218C2×#103—1221no—
219C2×#103—1221no—
220C2×#102—1221no—
221#396—1221no—
222#396—1221no—
223#395—1221no—
224#390—611no—
225#389—611no—
226#389C2×D6111yescharacteristic
227#386—1221no—
228#340—1221no—
229#340—1221no—
230#336—611no—
231#336C2×D6111yescharacteristic
232#336C2×D6111yescharacteristic
233C61#776411yescharacteristic, complemented, Sylow
234C22×Q8—1221no—
235C22×Q8—1221no—
236C22×D4—611no—
237C23×C4—1221no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—1221no—
241C4⋊Q8—2442no—
242C22⋊Q8—2442no—
243C22⋊Q8—2442no—
244C22⋊Q8—2442no—
245C22⋊Q8—2442no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—611no—
248C2×C4⋊C4—611no—
249C2×C4⋊C4—611no—
250C2×C4⋊C4—1221no—
251C2×C4⋊C4—1221no—
252C2×C4⋊C4—1221no—
253C2×C4⋊C4—1221no—
254C2×C4⋊C4—1221no—
255C2×C4⋊C4D24411yescharacteristic
256C2×C4⋊C4D24411yescharacteristic
257C2×C22⋊C4—1221no—
258C2×C22⋊C4—1221no—
259C2×C22⋊C4—1221no—
260C2×C22⋊C4—1221no—
261C2×C22⋊C4—1221no—
262C2×C42C22×D6111yescharacteristic
263#107—2442no—
264#103—2442no—
265#103—2442no—
266#102—2442no—
267#95—21no—
268#95—1221no—
269#95—1221no—
270C24—1221no—
271C2×Q8—1222no—
272C2×Q8—4881no—
273C2×Q8—2441no—
274C2×Q8—2441no—
275C2×Q8—2442no—
276C2×Q8—2441no—
277C2×Q8—2442no—
278C2×Q8—2441no—
279C2×Q8—2441no—
280C2×D4—612no—
281C2×D4—1221no—
282C2×D4—2441no—
283C2×D4—2441no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—1221no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4—4881no—
290C22×C4—2442no—
291C22×C4—2442no—
292C22×C4—2441no—
293C22×C4C2×D24411yescharacteristic
294C22×C4D4×D6111yescharacteristic
295C22×C4D4×D6111yescharacteristic
296C2×C8—41no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—1222no—
303C2×C8—2441no—
304C2×C8—2441no—
305C4⋊C4—21no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—612no—
310C4⋊C4—1222no—
311C4⋊C4—1222no—
312C4⋊C4—1221no—
313C4⋊C4—2441no—
314C4⋊C4—2441no—
315C4⋊C4—2442no—
316C4⋊C4—2441no—
317C4⋊C4—2441no—
318C4⋊C4—2442no—
319C4⋊C4—2441no—
320C4⋊C4—2441no—
321C4⋊C4#1175819012yes—
322C22⋊C4—4881no—
323C22⋊C4—2442no—
324C22⋊C4—2442no—
325C22⋊C4—2441no—
326C22⋊C4—2441no—
327C22⋊C4—2441no—
328C22⋊C4—2441no—
329C42—41no—
330C23—1222no—
331C23—2441no—
332C23—2441no—
333C23—2441no—
334C23—2441no—
335C23—2441no—
336C23—2441no—
337C23#1451974711yescharacteristic
338Q8—4881no—
339Q8—4881no—
340Q8—4884no—
341Q8—2442no—
342Q8—2442no—
343D4—4881no—
344D4—2442no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—22no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—1222no—
358C2×C4—4884no—
359C2×C4—4881no—
360C2×C4—4881no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4—2442no—
365C2×C4—2441no—
366C2×C4—2441no—
367C2×C4—2441no—
368C2×C4—2441no—
369C2×C4—2441no—
370C2×C4D8×D6111yescharacteristic
371C2×C4C2×#1175819011yescharacteristic
372C2×C4Q16×D6111yescharacteristic
373C2×C4#1451980411yescharacteristic
374C2×C4#1451980511yescharacteristic
375C2×C4#1451980611yescharacteristic
376C8—81no—
377C8—81no—
378C8—2442no—
379C22—4881no—
380C22—4881no—
381C22—4881no—
382C22—4881no—
383C22—2442no—
384C22—2442no—
385C22—2442no—
386C22#1683989711yescharacteristic
387C22#1683991511yescharacteristic
388C22#1683991911yescharacteristic
389C22#1683993611yescharacteristic
390C22#1683994111yescharacteristic
391C22#1683994711yescharacteristic
392C22#1683995011yescharacteristic
393C4—21no—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—42no—
400C4—81no—
401C4—4881no—
402C4—4882no—
403C4—4881no—
404C4—2442no—
405C2—4882no—
406C2#2144475511yescharacteristic
407C2#2144477711yescharacteristic
408C2#2144479011yescharacteristic
409C2#2144498611yescharacteristic
410C2#2144500111yescharacteristic
411C2#2144506911yescharacteristic
412C2#2144515511yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1271C2
socleC23×C61#120
prime radicalC22×D244D4
hypercenter#1271D61
hypocenterC61#7764
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
2. #21447147C2semidirect
3. #21447066C2semidirect
5. #21443641C2semidirect
7. C61×#1271C2semidirect
204. #1271D61semidirect
233. C61#7764semidirect

Maximal subgroups

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

subgroupindex
#214521902
#214471472
#214470662
#214469562
#214436412
#214436392
C61×#12712
#776461