Finite Group Databasebeta

← #29590522

Subgroups — #29590522

Order 15616.

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

normal subgroups only

This group has 446 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#21450106C211yesmaximal, characteristic
2#21444149C211yesmaximal, characteristic
3#21443845C212yesmaximal, complemented
4#21443824C212yesmaximal, complemented
5C2×C61×#343C211yesmaximal, characteristic
6C2×#14519736C411yescharacteristic
7#16839726—21no—
8#16839701C411yescharacteristic
9#16839701C2211yescharacteristic
10#16839692C411yescharacteristic
11#16839692C2211yescharacteristic
12#16839643—21no—
13#16839643—21no—
14#16839635—21no—
15#16839625—21no—
16#16839625C411yescharacteristic
17#16839488—21no—
18#16839488C2212yes—
19C22×M16×C61—21no—
20C22×C4⋊C4×C61C2211yescharacteristic
21C61×#343—21no—
22C61×#343C2212yes—
23C2×#11758194—41no—
24#14519736—41no—
25#14519736—41no—
26C2×C4⋊Dic61C2×C411yescharacteristic
27C2×C4⋊Dic61C2×C411yescharacteristic
28C2×#11758196—21no—
29C2×#11758196—21no—
30C2×C22⋊Dic61—21no—
31C2×C22⋊Dic61—21no—
32C2×C4×Dic61—21no—
33C22⋊#92418—22no—
34C22⋊#92418—41no—
35#14519684—21no—
36#14519684—21no—
37#14519684—21no—
38#14519684—21no—
39#14519684—21no—
40#14519684—21no—
41#14519684—21no—
42#14519684C2×C411yescharacteristic
43#14519684C2×C411yescharacteristic
44C23×C4×C61C2×C411yescharacteristic
45C23×C4×C61D411yescharacteristic
46C23×C4×C61D411yescharacteristic
47C2×M16×C61—24no—
48C2×M16×C61—22no—
49C2×M16×C61—41no—
50C2×M16×C61—42no—
51C22×C8×C61—41no—
52C2×C4⋊C4×C61—41no—
53C2×C4⋊C4×C61—41no—
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C4⋊C4×C61D411yescharacteristic
56C2×C4⋊C4×C61D411yescharacteristic
57C2×C4⋊C4×C61C2311yescharacteristic
58C24×C61C22⋊C411yescharacteristic
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—22no—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—42no—
69C22×C4×C61—42no—
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61C22⋊C411yescharacteristic
73C22×C4×C61C22×C411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—21no—
80M16×C61—24no—
81M16×C61—44no—
82M16×C61—42no—
83C2×C8×C61—44no—
84C2×C8×C61—42no—
85C4⋊C4×C61—41no—
86C4⋊C4×C61—41no—
87C4⋊C4×C61—41no—
88C4⋊C4×C61—41no—
89C22⋊Dic61—42no—
90C22⋊Dic61—41no—
91C22⋊Dic61—41no—
92C4⋊Dic61—41no—
93C4⋊Dic61—41no—
94#11758196—42no—
95#11758196—41no—
96#11758196—41no—
97C4×Dic61—42no—
98#11758194—82no—
99C2×#92418—42no—
100C23×C61—22no—
101C23×C61—21no—
102C23×C61—21no—
103C23×C61—41no—
104C23×C61#9911yescharacteristic
105C23×C61#9911yescharacteristic
106C23×C61C2×C22⋊C411yescharacteristic
107C2×C4×C61—22no—
108C2×C4×C61—22no—
109C2×C4×C61—22no—
110C2×C4×C61—22no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—42no—
120C2×C4×C61—42no—
121C2×C4×C61—42no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—81no—
127C2×C4×C61#10412yes—
128C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C61#13711yescharacteristic
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—42no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C8×C61—44no—
142#92418—82no—
143#11764—611nomaximal, Sylow
144C22×C61—21no—
145C22×C61—21no—
146C22×C61—21no—
147C22×C61—21no—
148C22×C61—21no—
149C22×C61—21no—
150C22×C61—21no—
151C22×C61—42no—
152C22×C61—42no—
153C22×C61#35212yes—
154C22×C61C2×#9911yescharacteristic
155C22×C61#41711yescharacteristic
156C22×C61C2×#10411yescharacteristic
157C4×C61—21no—
158C4×C61—22no—
159C4×C61—21no—
160C4×C61—41no—
161C4×C61—41no—
162C4×C61—41no—
163C4×C61—41no—
164Dic61—81no—
165Dic61—81no—
166Dic61—81no—
167Dic61—81no—
168#2484—611no—
169C2×#343D6111yescharacteristic
170#1463—611no—
171#1353—612no—
172#1346—612no—
173C2×C61—21no—
174C2×C61—21no—
175C2×C61—22no—
176C2×C61—41no—
177C2×C61#150411yescharacteristic
178C2×C61C2×#35211yescharacteristic
179C2×C61#213311yescharacteristic
180C22×M16—21no—
181C2×#117—611no—
182C22×C4⋊C4C2×D6111yescharacteristic
183#407—1221no—
184#400—611no—
185#400—611no—
186#398—611no—
187#398—611no—
188#387—1221no—
189#387—1221no—
190#385—1221no—
191#381—611no—
192#381—1221no—
193#343—21no—
194#343C2×D6112yes—
195#324—612no—
196#324—1221no—
197C61#1176411yescharacteristic, complemented, Sylow
198C23×C4C4×D6111yescharacteristic
199C23×C4D24411yescharacteristic
200C23×C4C22⋊D6111yescharacteristic
201C2×M16—24no—
202C2×M16—22no—
203C2×M16—41no—
204C2×M16—42no—
205C2×M16—2441no—
206C22×C8—41no—
207#117—2441no—
208#117—2441no—
209C2×C4⋊C4—41no—
210C2×C4⋊C4—41no—
211C2×C4⋊C4—611no—
212C2×C4⋊C4—611no—
213C2×C4⋊C4—1221no—
214C2×C4⋊C4—1221no—
215C2×C4⋊C4C4×D6111yescharacteristic
216C2×C4⋊C4D24411yescharacteristic
217C2×C4⋊C4C22⋊D6111yescharacteristic
218C2×C4⋊C4C22×D6111yescharacteristic
219C2×C22⋊C4—1221no—
220C2×C22⋊C4—1221no—
221C2×C42—1221no—
222C22⋊C8—1222no—
223C22⋊C8—2441no—
224#95—611no—
225#95—611no—
226#95—1221no—
227#95—1221no—
228#95—1221no—
229#95—1221no—
230#95—1221no—
231#95—1221no—
232#95—1221no—
233C24#1175819811yescharacteristic
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—22no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4—1221no—
246C22×C4—1221no—
247C22×C4—1221no—
248C22×C4—1221no—
249C22×C4#1175819811yescharacteristic
250C22×C4#1175819811yescharacteristic
251C22×C4#1175819811yescharacteristic
252C22×C4C2×C4×D6111yescharacteristic
253C22×C4C2×D24411yescharacteristic
254C22×C4C2×C22⋊D6111yescharacteristic
255M16—24no—
256M16—44no—
257M16—42no—
258M16—4882no—
259C2×C8—44no—
260C2×C8—42no—
261C2×C8—2442no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—2441no—
267C4⋊C4—2441no—
268C4⋊C4—2441no—
269C4⋊C4—2442no—
270C4⋊C4—2441no—
271C22⋊C4—2442no—
272C22⋊C4—2441no—
273C22⋊C4—2441no—
274C42—2442no—
275C23—21no—
276C23—21no—
277C23—22no—
278C23—41no—
279C23#1451969111yescharacteristic
280C23#1451969111yescharacteristic
281C23C2×#1175819811yescharacteristic
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—81no—
302C2×C4—2441no—
303C2×C4—2441no—
304C2×C4—2441no—
305C2×C4—2441no—
306C2×C4—2442no—
307C2×C4—2441no—
308C2×C4—2441no—
309C2×C4—2441no—
310C2×C4—2441no—
311C2×C4—2441no—
312C2×C4—2441no—
313C2×C4#1451970512yes—
314C2×C4#1451980311yescharacteristic
315C2×C4#1451980811yescharacteristic
316C8—44no—
317C8—4882no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—42no—
326C22—42no—
327C22#1683955312yes—
328C22C2×#1451969111yescharacteristic
329C22#1683976111yescharacteristic
330C22C2×#1451970511yescharacteristic
331C4—21no—
332C4—21no—
333C4—22no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—4881no—
339C4—4881no—
340C4—4881no—
341C4—4881no—
342C2—21no—
343C2—21no—
344C2—22no—
345C2—41no—
346C2#2144432111yescharacteristic
347C2C2×#1683955311yescharacteristic
348C2#2144750611yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC2×C61×#343C2
socleC22×C61C2×#99
prime radicalC24×C61C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenterC2×#343D61
hypocenterC61#11764
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ C2×#343

Complements

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

NH ≅ G/Ntype
3. #21443845C2semidirect
4. #21443824C2semidirect
197. C61#11764semidirect

Maximal subgroups

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

subgroupindex
#214501062
#214441492
#214438452
#214438242
C2×C61×#3432
#1176461