Finite Group Databasebeta

← #29599680

Subgroups — #29599680

Order 15616.

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

normal subgroups only

This group has 540 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#21446099C212yesmaximal
2#21446028C211yesmaximal, characteristic
3#21443944C211yesmaximal, characteristic
4#21443937C212yesmaximal
5C61×#2683C211yesmaximal, characteristic
6#16840237C2211yescharacteristic
7#16839802—21no—
8C2×#14519694C2211yescharacteristic
9C2×#14519692C2212yes—
10#16839635—22no—
11#16839528—22no—
12#16839522—21no—
13C2×C22⋊Q8×C61—22no—
14C61×#396—22no—
15C61×#395—21no—
16C61×#390C2211yescharacteristic
17C61×#389—21no—
18C61×#386C2212yes—
19C2×#11758194—21no—
20D4×Dic61—41no—
21D4×Dic61—41no—
22#14519736—21no—
23C2×#11758196—42no—
24C2×C22⋊Dic61—22no—
25C2×C22⋊Dic61—22no—
26#14519710—41no—
27#14519708—41no—
28#14519694—21no—
29#14519694Q812yescomplemented
30#14519692—22no—
31#14519692Q814yescomplemented
32#14519684—42no—
33C22×Q8×C61—21no—
34C22×D4×C61C2311yescharacteristic
35C23×C4×C61D412yes—
36C22⋊Q8×C61—48no—
37C2×C4⋊C4×C61—21no—
38C2×C4⋊C4×C61—22no—
39C2×C4⋊C4×C61—22no—
40C2×C4⋊C4×C61—21no—
41C2×C4⋊C4×C61D411yescharacteristic
42C2×C22⋊C4×C61—22no—
43C2×C22⋊C4×C61—22no—
44C2×C22⋊C4×C61D412yes—
45C2×C42×C61D411yescharacteristic
46#95×C61—21no—
47#95×C61—22no—
48C24×C61C2×D412yes—
49C2×Q8×C61—44no—
50C2×Q8×C61—81no—
51C2×D4×C61—41no—
52C2×D4×C61—41no—
53C2×D4×C61C2×Q811yescharacteristic
54C2×D4×C61C2×Q812yes—
55C2×D4×C61#4111yescharacteristic
56C22×C4×C61—22no—
57C22×C4×C61—21no—
58C22×C4×C61—22no—
59C22×C4×C61—21no—
60C22×C4×C61—44no—
61C22×C4×C61—42no—
62C22×C4×C61C2×D411yescharacteristic
63C22×Dic61—22no—
64C22×Dic61—22no—
65C22×Dic61—42no—
66C4⋊C4×C61—24no—
67C4⋊C4×C61—44no—
68C4⋊C4×C61—44no—
69C4⋊C4×C61—41no—
70C4⋊C4×C61—81no—
71C22⋊C4×C61—44no—
72C22⋊C4×C61—44no—
73C22⋊C4×C61—42no—
74C42×C61—41no—
75C22⋊Dic61—24no—
76C22⋊Dic61—42no—
77C22⋊Dic61—42no—
78C22⋊Dic61—41no—
79C4⋊Dic61—21no—
80C4⋊Dic61—21no—
81#11758196—84no—
82C4×Dic61—41no—
83#11758194—22no—
84#11758194—41no—
85C2×#92418—41no—
86C23×C61—22no—
87C23×C61—22no—
88C23×C61—42no—
89C23×C61—42no—
90C23×C61#12011yescharacteristic
91C23×C61C22⋊Q812yes—
92C23×C61C4⋊Q812yes—
93Q8×C61—84no—
94D4×C61—41no—
95D4×C61—42no—
96D4×C61—41no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—22no—
100C2×C4×C61—24no—
101C2×C4×C61—42no—
102C2×C4×C61—41no—
103C2×C4×C61—42no—
104C2×C4×C61—41no—
105C2×C4×C61—44no—
106C2×C4×C61—42no—
107C2×C4×C61—42no—
108C2×C4×C61—42no—
109C2×C4×C61—41no—
110C2×C4×C61—42no—
111C2×C4×C61—82no—
112C2×C4×C61C22⋊Q811yescharacteristic
113C2×C4×C61C4⋊Q811yescharacteristic
114C2×Dic61—44no—
115C2×Dic61—41no—
116C2×Dic61—41no—
117C2×Dic61—82no—
118C2×Dic61—82no—
119C2×Dic61—82no—
120C2×Dic61—82no—
121#92418—42no—
122#13461—611nomaximal, Sylow
123C22×C61—21no—
124C22×C61—21no—
125C22×C61—22no—
126C22×C61—22no—
127C22×C61—42no—
128C22×C61—42no—
129C22×C61—42no—
130C22×C61—42no—
131C22×C61—82no—
132C22×C61#39511yescharacteristic
133C22×C61B(4,𝔽2)11yescharacteristic
134C22×C61#45811yescharacteristic
135C4×C61—21no—
136C4×C61—21no—
137C4×C61—42no—
138C4×C61—44no—
139C4×C61—82no—
140C4×C61—81no—
141Dic61—84no—
142Dic61—81no—
143Dic61—81no—
144#2683D6111yescharacteristic
145#1867—612no—
146#1856—611no—
147#1393—611no—
148#1390—612no—
149C2×C61—21no—
150C2×C61—21no—
151C2×C61—42no—
152C2×C61—42no—
153C2×C61#206211yescharacteristic
154C2×C61#219611yescharacteristic
155C2×C61#220111yescharacteristic
156C2×C22⋊Q8—22no—
157#518—611no—
158#428—1221no—
159C2×#100—611no—
160C2×#99—612no—
161#396—22no—
162#395—21no—
163#390C2×D6111yescharacteristic
164#389—21no—
165#386C2×D6112yes—
166#385—1222no—
167#342—1222no—
168#339—1221no—
169C61#1346111yescharacteristic, complemented, Sylow
170C22×Q8—21no—
171C22×D4C22×D6111yescharacteristic
172C23×C4C22⋊D6112yes—
173C2×M16—1221no—
174C22⋊Q8—48no—
175C4×D4—2441no—
176C4×D4—2441no—
177#117—1221no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—2442no—
183C2×C4⋊C4C22⋊D6111yescharacteristic
184C2×C22⋊C4—22no—
185C2×C22⋊C4—22no—
186C2×C22⋊C4—1222no—
187C2×C22⋊C4—1222no—
188C2×C22⋊C4C22⋊D6112yes—
189C2×C42C22⋊D6111yescharacteristic
190#107—2441no—
191#106—2441no—
192#100—612no—
193#100—1221no—
194#99—614no—
195#99—1222no—
196#95—21no—
197#95—22no—
198#95—2442no—
199C24C2×C22⋊D6112yes—
200C2×Q8—44no—
201C2×Q8—81no—
202C2×D4—41no—
203C2×D4—41no—
204C2×D4Q8×D6111yescharacteristic
205C2×D4Q8×D6112yes—
206C2×D4#1175822611yescharacteristic
207C22×C4—22no—
208C22×C4—21no—
209C22×C4—22no—
210C22×C4—21no—
211C22×C4—44no—
212C22×C4—42no—
213C22×C4—1222no—
214C22×C4—1222no—
215C22×C4—2442no—
216C22×C4C2×C22⋊D6111yescharacteristic
217M16—1222no—
218M16—2441no—
219C2×C8—2441no—
220C4⋊C4—24no—
221C4⋊C4—41no—
222C4⋊C4—44no—
223C4⋊C4—44no—
224C4⋊C4—81no—
225C4⋊C4—1221no—
226C4⋊C4—1221no—
227C4⋊C4—4884no—
228C22⋊C4—44no—
229C22⋊C4—44no—
230C22⋊C4—42no—
231C22⋊C4—1224no—
232C22⋊C4—2442no—
233C22⋊C4—2442no—
234C22⋊C4—2441no—
235C42—41no—
236C42—2441no—
237C23—22no—
238C23—22no—
239C23—42no—
240C23—42no—
241C23#1451974611yescharacteristic
242C23#1451975312yes—
243C23#1451977512yes—
244Q8—84no—
245D4—41no—
246D4—42no—
247D4—41no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—22no—
251C2×C4—24no—
252C2×C4—42no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—41no—
256C2×C4—44no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—41no—
261C2×C4—42no—
262C2×C4—82no—
263C2×C4—4882no—
264C2×C4—4882no—
265C2×C4—4882no—
266C2×C4—4882no—
267C2×C4—2444no—
268C2×C4—2441no—
269C2×C4—2441no—
270C2×C4#1451975311yescharacteristic
271C2×C4#1451977511yescharacteristic
272C8—2442no—
273C22—21no—
274C22—21no—
275C22—22no—
276C22—22no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—42no—
281C22—82no—
282C22#1683968111yescharacteristic
283C22#1683994911yescharacteristic
284C22#1683995211yescharacteristic
285C4—21no—
286C4—21no—
287C4—42no—
288C4—44no—
289C4—82no—
290C4—81no—
291C4—4884no—
292C4—4881no—
293C4—4881no—
294C2—21no—
295C2—21no—
296C2—42no—
297C2—42no—
298C2#2144717111yescharacteristic
299C2#2144780311yescharacteristic
300C2#2144783211yescharacteristic
subgroupG/H
centerC22#16839949
commutator, prime radical, cosocleC22×D4×C61C23
FrattiniC22×D4C22×D61
FittingC61×#2683C2
socleC22×C61B(4,𝔽2)
hypercenter#2683D61
hypocenterC61#13461
LCSG ▷ C22×D4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #2683

Complements

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

NH ≅ G/Ntype
29. #14519694Q8semidirect
31. #14519692Q8semidirect
169. C61#13461semidirect

Maximal subgroups

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

subgroupindex
#214460992
#214460282
#214439442
#214439372
C61×#26832
#1346161