Finite Group Databasebeta

← #29592104

Subgroups — #29592104

Order 15616.

442 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 59 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#21452851C211yesmaximal, characteristic, complemented
2#21444822C212yesmaximal
3#21443824C212yesmaximal, complemented
4#21443753C211yesmaximal, characteristic, complemented
5C61×#2007C211yesmaximal, characteristic
6C2×#14519775—21no—
7#16840073—22no—
8#16839692C2212yes—
9#16839683—22no—
10#16839660—21no—
11#16839647—22no—
12#16839496—22no—
13#16839488C2212yes—
14C2×#137×C61—21no—
15C61×#537C2211yescharacteristic
16C2×#104×C61—21no—
17C61×#391C2211yescharacteristic
18C61×#343C2211yescharacteristic
19C22×Dic122—21no—
20#14519775—42no—
21#14519775—42no—
22C2×C4⋊Dic61—21no—
23C2×C4⋊Dic61—21no—
24C2×C4⋊Dic61D412yes—
25C2×#11758196—22no—
26C2×#11758196—22no—
27C2×C4×Dic61—21no—
28#14519710—42no—
29#14519698—42no—
30C22⋊#92418—22no—
31#14519684—22no—
32#14519684—22no—
33#14519684D412yes—
34C2×#41×C61—21no—
35C22×Q8×C61D411yescharacteristic
36#137×C61—42no—
37#137×C61—42no—
38C2×Q16×C61—41no—
39C2×SD16×C61—41no—
40C2×M16×C61—21no—
41C22⋊Q8×C61—41no—
42#121×C61—22no—
43#121×C61—41no—
44C2×C4⋊C4×C61C2311yescharacteristic
45C2×C42×C61D411yescharacteristic
46#104×C61—42no—
47#95×C61—22no—
48#41×C61—41no—
49#41×C61—41no—
50#41×C61—41no—
51#41×C61—41no—
52C2×Q8×C61—21no—
53C2×Q8×C61—21no—
54C2×Q8×C61—41no—
55C2×Q8×C61—41no—
56C2×Q8×C61D812yes—
57C2×D4×C61—21no—
58C2×D4×C61—22no—
59C2×D4×C61—41no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—41no—
63C22×C4×C61C2×D411yescharacteristic
64C22×C4×C61C2×D412yes—
65C22×Dic61—22no—
66C22×Dic61—22no—
67C2×Dic122—42no—
68C2×Dic122—81no—
69C2×Dic122—81no—
70Q16×C61—44no—
71SD16×C61—44no—
72M16×C61—22no—
73M16×C61—41no—
74C2×C8×C61—41no—
75C4⋊C4×C61—22no—
76C4⋊C4×C61—41no—
77C22⋊C4×C61—42no—
78C42×C61—41no—
79C4⋊Dic61—24no—
80C4⋊Dic61—42no—
81C4⋊Dic61—81no—
82#11758196—44no—
83#11758196—42no—
84#11758196—42no—
85C4×Dic61—42no—
86C2×#92418—42no—
87C23×C61—41no—
88C23×C61#12011yescharacteristic
89Q8×C61—42no—
90Q8×C61—41no—
91Q8×C61—41no—
92Q8×C61—81no—
93D4×C61—41no—
94D4×C61—41no—
95D4×C61—82no—
96D4×C61—81no—
97D4×C61—81no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—22no—
101C2×C4×C61—22no—
102C2×C4×C61—22no—
103C2×C4×C61—41no—
104C2×C4×C61—41no—
105C2×C4×C61—41no—
106C2×C4×C61—41no—
107C2×C4×C61—42no—
108C2×C4×C61—41no—
109C2×C4×C61—81no—
110C2×C4×C61—81no—
111C2×C4×C61C2×D811yescharacteristic
112C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
113C2×Dic61—24no—
114C2×Dic61—42no—
115C2×Dic61—42no—
116C2×Dic61—42no—
117C2×Dic61—42no—
118C2×Dic61—42no—
119Dic122—84no—
120C8×C61—42no—
121#92418—82no—
122#12101—611nomaximal, Sylow
123C22×C61—21no—
124C22×C61—21no—
125C22×C61—81no—
126C22×C61—81no—
127C22×C61—81no—
128C22×C61#44711yescharacteristic
129C22×C61#45311yescharacteristic
130C22×C61B(4,𝔽2)11yescharacteristic
131C4×C61—21no—
132C4×C61—21no—
133C4×C61—42no—
134C4×C61—42no—
135C4×C61—42no—
136C4×C61—81no—
137Dic61—44no—
138Dic61—82no—
139#2734—611no—
140#2007D6111yescharacteristic
141#1610—612no—
142#1346—612no—
143#1319—611no—
144C2×C61—21no—
145C2×C61—21no—
146C2×C61—161no—
147C2×C61#159511yescharacteristic
148C2×C61#220111yescharacteristic
149C2×C61#220511yescharacteristic
150C2×#137—21no—
151#537C2×D6111yescharacteristic
152C2×C4⋊Q8—1221no—
153#480—1222no—
154C2×#104—21no—
155#398—612no—
156#395—1222no—
157#391C2×D6111yescharacteristic
158#389—1221no—
159#387—1222no—
160#343C2×D6111yescharacteristic
161#327—1222no—
162#324—612no—
163C61#1210111yescharacteristic, complemented, Sylow
164C2×#41—21no—
165C22×Q8—1221no—
166C22×Q8C22⋊D6111yescharacteristic
167#137—42no—
168#137—42no—
169C2×Q16—41no—
170C2×SD16—41no—
171C2×M16—21no—
172C4⋊Q8—2442no—
173C4⋊Q8—2442no—
174C22⋊Q8—41no—
175#121—22no—
176#121—41no—
177C2×C4⋊C4—612no—
178C2×C4⋊C4—1221no—
179C2×C4⋊C4—1221no—
180C2×C4⋊C4—1222no—
181C2×C4⋊C4—1222no—
182C2×C4⋊C4C22×D6111yescharacteristic
183C2×C42—1221no—
184C2×C42C22⋊D6111yescharacteristic
185#107—2442no—
186#104—42no—
187#102—2442no—
188C22⋊C8—1222no—
189#95—22no—
190#95—612no—
191#95—1222no—
192#95—1222no—
193#41—41no—
194#41—41no—
195#41—41no—
196#41—41no—
197C2×Q8—21no—
198C2×Q8—21no—
199C2×Q8—41no—
200C2×Q8—41no—
201C2×Q8—4881no—
202C2×Q8—4881no—
203C2×Q8—2442no—
204C2×Q8#1175819912yes—
205C2×D4—21no—
206C2×D4—22no—
207C2×D4—41no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—41no—
211C22×C4—1222no—
212C22×C4—1222no—
213C22×C4D4×D6112yes—
214C22×C4C2×C22⋊D6111yescharacteristic
215Q16—44no—
216SD16—44no—
217M16—22no—
218M16—41no—
219C2×C8—41no—
220C2×C8—2442no—
221C4⋊C4—22no—
222C4⋊C4—41no—
223C4⋊C4—1224no—
224C4⋊C4—4881no—
225C4⋊C4—2442no—
226C4⋊C4—2444no—
227C4⋊C4—2442no—
228C4⋊C4—2442no—
229C22⋊C4—42no—
230C42—41no—
231C42—2442no—
232C23—41no—
233C23#1451974511yescharacteristic
234Q8—42no—
235Q8—41no—
236Q8—41no—
237Q8—81no—
238Q8—4884no—
239D4—41no—
240D4—41no—
241D4—82no—
242D4—81no—
243D4—81no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—42no—
254C2×C4—41no—
255C2×C4—81no—
256C2×C4—81no—
257C2×C4—1224no—
258C2×C4—2442no—
259C2×C4—2442no—
260C2×C4—2442no—
261C2×C4—2442no—
262C2×C4—2442no—
263C2×C4C2×#1175819911yescharacteristic
264C2×C4#1451980211yescharacteristic
265C8—42no—
266C8—4882no—
267C22—21no—
268C22—21no—
269C22—81no—
270C22—81no—
271C22—81no—
272C22#1683989511yescharacteristic
273C22#1683992911yescharacteristic
274C22#1683994811yescharacteristic
275C4—21no—
276C4—21no—
277C4—42no—
278C4—42no—
279C4—42no—
280C4—81no—
281C4—4882no—
282C4—2444no—
283C2—21no—
284C2—21no—
285C2—161no—
286C2#2144473611yescharacteristic
287C2#2144783111yescharacteristic
288C2#2144784811yescharacteristic
subgroupG/H
centerC22#16839948
commutator, cosocleC2×C4⋊C4×C61C23
FrattiniC2×C4⋊C4C22×D61
FittingC61×#2007C2
socleC22×C61B(4,𝔽2)
prime radicalC61×#537C22
hypercenter#2007D61
hypocenterC61#12101
LCSG ▷ C2×C4⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2007

Complements

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

NH ≅ G/Ntype
1. #21452851C2semidirect
3. #21443824C2semidirect
4. #21443753C2semidirect
163. C61#12101semidirect

Maximal subgroups

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

subgroupindex
#214528512
#214448222
#214438242
#214437532
C61×#20072
#1210161