Finite Group Databasebeta

← #29568880

Subgroups — #29568880

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#21447144C211yesmaximal, characteristic, complemented
3#21446952C211yesmaximal, characteristic
4#21443643C211yesmaximal, characteristic, complemented
5#21443642C211yesmaximal, characteristic, complemented
6#21443639C211yesmaximal, characteristic
7C61×#2043C211yesmaximal, characteristic, complemented
8C2×#14519757—21no—
9C2×#14519755—21no—
10C2×#14519710—21no—
11C2×#14519697—21no—
12#16839684—21no—
13#16839684—21no—
14#16839683—21no—
15#16839664C2211yescharacteristic
16#16839660C2211yescharacteristic
17#16839640—21no—
18#16839524—21no—
19#16839524—21no—
20#16839517C2211yescharacteristic
21#16839517C2211yescharacteristic
22C2×C4⋊Q8×C61C2211yescharacteristic
23C2×#103×C61—21no—
24C2×#103×C61—21no—
25C61×#389C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×Dic122—21no—
28C22×D244D411yescharacteristic
29C22×C4×D61—21no—
30C22×#92418—21no—
31C22×#92418—21no—
32#14519757—42no—
33#14519757—42no—
34#14519755—42no—
35#14519755—42no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61D411yescharacteristic
38C2×C4⋊Dic61D411yescharacteristic
39C2×C4⋊Dic61D411yescharacteristic
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×#11758198—21no—
47#14519710—42no—
48#14519697—42no—
49#14519684—21no—
50#14519684—21no—
51C22×Q8×C61—21no—
52C22×C8×C61—21no—
53C4⋊Q8×C61—42no—
54C2×C4⋊C4×C61—21no—
55C2×C4⋊C4×C61—21no—
56C2×C4⋊C4×C61—21no—
57C2×C4⋊C4×C61D411yescharacteristic
58C2×C4⋊C4×C61D411yescharacteristic
59C2×C42×C61C2311yescharacteristic
60#103×C61—42no—
61#103×C61—42no—
62#95×C61—21no—
63C23×D61—21no—
64C2×Q8×C61—22no—
65C2×Q8×C61—41no—
66C2×Q8×C61—41no—
67C2×Q8×C61—41no—
68C2×Q8×C61—41no—
69C2×Q8×C61—41no—
70C22×C4×C61—21no—
71C22×C4×C61—21no—
72C22×C4×C61—41no—
73C22×C4×C61C2×D411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C2×D244—21no—
80C2×D244—41no—
81C2×D244—41no—
82C2×D244Q1612yes—
83C2×C4×D61—42no—
84C2×C4×D61—42no—
85C2×C4×D61—81no—
86C2×Dic122—42no—
87C2×Dic122—42no—
88C2×Dic122—81no—
89C2×C8×C61—41no—
90C2×C8×C61—41no—
91C2×C8×C61—41no—
92C4⋊C4×C61—21no—
93C4⋊C4×C61—22no—
94C4⋊C4×C61—22no—
95C4⋊C4×C61—41no—
96C4⋊C4×C61—41no—
97C4⋊C4×C61—41no—
98C4⋊C4×C61—41no—
99C4⋊C4×C61—41no—
100C4⋊C4×C61D812yes—
101C42×C61—41no—
102#11758198—42no—
103#11758198—42no—
104#11758198—41no—
105#11758198—41no—
106#11758198—41no—
107#11758198—41no—
108#11758198—81no—
109C4⋊Dic61—21no—
110C4⋊Dic61—42no—
111C4⋊Dic61—41no—
112C4⋊Dic61—41no—
113C4⋊Dic61SD1612yes—
114#11758196—42no—
115#11758196—41no—
116#11758196—41no—
117C2×#92418—22no—
118C2×#92418—41no—
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—
131Q8×C61—42no—
132Q8×C61—42no—
133Q8×C61—81no—
134Q8×C61—81no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—22no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—42no—
148C2×C4×C61—81no—
149C2×C4×C61—81no—
150C2×C4×C61C2×D811yescharacteristic
151C2×C4×C61C2×SD1611yescharacteristic
152C2×C4×C61C2×Q1611yescharacteristic
153C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C61#13711yescharacteristic
156C2×Dic61—22no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165D244—42no—
166D244—81no—
167C4×D61—84no—
168Dic122—84no—
169C8×C61—81no—
170#92418—42no—
171#92418—81no—
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—82no—
195C4×C61—81no—
196Dic61—42no—
197Dic61—81no—
198Dic61—81no—
199#2683—611no—
200#2057—611no—
201#2043D6111yescharacteristic, complemented
202#2023—611no—
203#1271—611no—
204#1271—611no—
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⋊Q8C2×D6111yescharacteristic
215C2×C22⋊Q8—1221no—
216C2×C22⋊Q8—1221no—
217C2×#107—1221no—
218C2×#103—21no—
219C2×#103—21no—
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#336—611no—
232#336C2×D6111yescharacteristic
233C61#776411yescharacteristic, complemented, Sylow
234C22×Q8—21no—
235C22×Q8—1221no—
236C22×D4—611no—
237C23×C4—1221no—
238C22×C8—21no—
239C22×C8—1221no—
240C22×C8—1221no—
241C4⋊Q8—42no—
242C22⋊Q8—2442no—
243C22⋊Q8—2442no—
244C22⋊Q8—2442no—
245C22⋊Q8—2442no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
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×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—42no—
265#103—42no—
266#102—2442no—
267#95—21no—
268#95—1221no—
269#95—1221no—
270C24—1221no—
271C2×Q8—22no—
272C2×Q8—41no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×Q8—41no—
276C2×Q8—41no—
277C2×Q8—4881no—
278C2×Q8—2442no—
279C2×Q8—2442no—
280C2×D4—612no—
281C2×D4—1221no—
282C2×D4—2441no—
283C2×D4—2441no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—41no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4—1221no—
290C22×C4—4881no—
291C22×C4—2442no—
292C22×C4—2442no—
293C22×C4D4×D6111yescharacteristic
294C22×C4D4×D6111yescharacteristic
295C22×C4C2×C22⋊D6111yescharacteristic
296C2×C8—41no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—1222no—
300C2×C8—2441no—
301C2×C8—2441no—
302C2×C8—2441no—
303C2×C8—2441no—
304C2×C8—2441no—
305C4⋊C4—21no—
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—612no—
314C4⋊C4—1221no—
315C4⋊C4—2441no—
316C4⋊C4—2441no—
317C4⋊C4—2442no—
318C4⋊C4—2442no—
319C4⋊C4—2441no—
320C4⋊C4—2441no—
321C4⋊C4#1175819912yes—
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#1451974511yescharacteristic
338Q8—42no—
339Q8—42no—
340Q8—81no—
341Q8—81no—
342Q8—4884no—
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—42no—
357C2×C4—41no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—1222no—
361C2×C4—4884no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4—2441no—
365C2×C4—2441no—
366C2×C4—2441no—
367C2×C4—2441no—
368C2×C4—2441no—
369C2×C4—2441no—
370C2×C4C2×#1175819911yescharacteristic
371C2×C4SD16×D6111yescharacteristic
372C2×C4Q16×D6111yescharacteristic
373C2×C4#1451980211yescharacteristic
374C2×C4#1451980411yescharacteristic
375C2×C4#1451980911yescharacteristic
376C8—81no—
377C8—4881no—
378C8—2442no—
379C22—4881no—
380C22—4881no—
381C22—4881no—
382C22—4881no—
383C22—2442no—
384C22—2442no—
385C22—2442no—
386C22#1683989511yescharacteristic
387C22#1683991111yescharacteristic
388C22#1683991611yescharacteristic
389C22#1683993411yescharacteristic
390C22#1683993811yescharacteristic
391C22#1683994311yescharacteristic
392C22#1683994811yescharacteristic
393C4—21no—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—42no—
400C4—82no—
401C4—81no—
402C4—4881no—
403C4—4881no—
404C4—2442no—
405C2—4882no—
406C2#2144475311yescharacteristic
407C2#2144477411yescharacteristic
408C2#2144478611yescharacteristic
409C2#2144498111yescharacteristic
410C2#2144499611yescharacteristic
411C2#2144506611yescharacteristic
412C2#2144515011yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2043C2
socleC23×C61#120
prime radicalC22×D244D4
hypercenter#2043D61
hypocenterC61#7764
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2043

Complements

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

NH ≅ G/Ntype
2. #21447144C2semidirect
4. #21443643C2semidirect
5. #21443642C2semidirect
7. C61×#2043C2semidirect
201. #2043D61semidirect
233. C61#7764semidirect

Maximal subgroups

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

subgroupindex
#214521902
#214471442
#214469522
#214436432
#214436422
#214436392
C61×#20432
#776461