Finite Group Databasebeta

← #29590720

Subgroups — #29590720

Order 15616.

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

normal subgroups only

This group has 680 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
1C2×#16839674C211yesmaximal, characteristic
2#21444146C211yesmaximal, characteristic
3#21443839C214yesmaximal, complemented
4C61×#1819C211yesmaximal, characteristic
5C23×Dic122C411yescharacteristic, complemented
6C22×C22⋊Dic61—21no—
7#16839726—21no—
8#16839674—21no—
9#16839674—21no—
10#16839674C412yescomplemented
11#16839674C2212yes—
12C2×#14519684—21no—
13C2×#14519684C411yescharacteristic, complemented
14#16839486—21no—
15#16839486C2212yes—
16C22×C22⋊C4×C61C2211yescharacteristic
17C61×#379—21no—
18C61×#342—21no—
19C61×#342C2212yes—
20C22×Dic122—21no—
21C22×Dic122—41no—
22C22×Dic122—41no—
23C22×Dic122—44no—
24C22×Dic122C2×C412yes—
25C23×Dic61—21no—
26C23×Dic61—21no—
27C2×#11758194—41no—
28C2×C22⋊Dic61—22no—
29C2×C22⋊Dic61—22no—
30C2×C22⋊Dic61—44no—
31C22⋊#92418—22no—
32C22⋊#92418—41no—
33#14519684—22no—
34#14519684—21no—
35#14519684—22no—
36#14519684C2×C412yes—
37C25×C61D411yescharacteristic
38C23×C4×C61C2×C411yescharacteristic
39C23×C4×C61D411yescharacteristic
40C2×C22⋊C4×C61—22no—
41C2×C22⋊C4×C61—41no—
42C2×C22⋊C4×C61—41no—
43C2×C22⋊C4×C61—41no—
44C2×C22⋊C4×C61—41no—
45C2×C22⋊C4×C61C2×C411yescharacteristic
46C2×C22⋊C4×C61D411yescharacteristic
47C2×C22⋊C4×C61D411yescharacteristic
48C2×C22⋊C4×C61C2311yescharacteristic
49C24×C61—22no—
50C24×C61—21no—
51C24×C61—21no—
52C24×C61—41no—
53C24×C61—42no—
54C24×C61—42no—
55C24×C61C22⋊C411yescharacteristic
56C24×C61C22⋊C411yescharacteristic
57C24×C61C2×D411yescharacteristic
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—42no—
63C22×C4×C61—42no—
64C22×C4×C61—42no—
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C22×C411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×Dic61—24no—
70C22×Dic61—22no—
71C22×Dic61—22no—
72C22×Dic61—42no—
73C22×Dic61—41no—
74C22×Dic61—41no—
75C22×Dic61—42no—
76C22×Dic61—42no—
77C22×Dic61—42no—
78C2×Dic122—44no—
79C2×Dic122—42no—
80C2×Dic122—44no—
81C2×Dic122—48no—
82C2×Dic122—42no—
83C2×Dic122—44no—
84C2×Dic122—44no—
85C22⋊C4×C61—41no—
86C22⋊C4×C61—41no—
87C22⋊C4×C61—41no—
88C22⋊C4×C61—41no—
89C22⋊C4×C61—42no—
90C22⋊C4×C61—42no—
91C22⋊C4×C61—82no—
92C22⋊C4×C61—82no—
93C22⋊Dic61—44no—
94C22⋊Dic61—44no—
95#11758194—82no—
96C2×#92418—42no—
97C23×C61—22no—
98C23×C61—22no—
99C23×C61—21no—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61—21no—
103C23×C61—21no—
104C23×C61—21no—
105C23×C61—21no—
106C23×C61—42no—
107C23×C61—42no—
108C23×C61—41no—
109C23×C61—41no—
110C23×C61—41no—
111C23×C61—41no—
112C23×C61—48no—
113C23×C61—42no—
114C23×C61—42no—
115C23×C61—81no—
116C23×C61—81no—
117C23×C61—84no—
118C23×C61#9911yescharacteristic
119C23×C61#9911yescharacteristic
120C23×C61C2×C22⋊C411yescharacteristic
121C23×C61#13712yes—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—42no—
127C2×C4×C61—42no—
128C2×C4×C61—42no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—81no—
134C2×C4×C61—82no—
135C2×C4×C61—82no—
136C2×C4×C61—82no—
137C2×Dic61—24no—
138C2×Dic61—42no—
139C2×Dic61—44no—
140C2×Dic61—44no—
141C2×Dic61—42no—
142C2×Dic61—42no—
143C2×Dic61—42no—
144C2×Dic61—42no—
145C2×Dic61—84no—
146Dic122—48no—
147Dic122—44no—
148Dic122—44no—
149#92418—82no—
150#11808—611nomaximal, Sylow
151C22×C61—24no—
152C22×C61—24no—
153C22×C61—21no—
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—21no—
158C22×C61—21no—
159C22×C61—22no—
160C22×C61—42no—
161C22×C61—42no—
162C22×C61—41no—
163C22×C61—41no—
164C22×C61—41no—
165C22×C61—41no—
166C22×C61—41no—
167C22×C61—81no—
168C22×C61—84no—
169C22×C61—84no—
170C22×C61—81no—
171C22×C61AΣL(1,𝔽16)12yes—
172C22×C61#35412yes—
173C22×C61C2×#9911yescharacteristic
174C22×C61#41911yescharacteristic
175C22×C61#42111yescharacteristic
176C4×C61—41no—
177C4×C61—41no—
178C4×C61—41no—
179C4×C61—41no—
180C4×C61—162no—
181Dic61—44no—
182Dic61—82no—
183C2×#393—611no—
184#1819D6111yescharacteristic
185#1462—611no—
186#1351—614no—
187C2×C61—21no—
188C2×C61—21no—
189C2×C61—22no—
190C2×C61—22no—
191C2×C61—42no—
192C2×C61—81no—
193C2×C61#151111yescharacteristic
194C2×C61C2×AΣL(1,𝔽16)11yescharacteristic
195C2×C61C2×#35411yescharacteristic
196C23×Q8—611no—
197C22×C22⋊C4—1221no—
198C22×C22⋊C4C2×D6111yescharacteristic
199#407—1221no—
200#393—612no—
201#393—612no—
202#393—1221no—
203#393—1221no—
204#379—21no—
205C2×#95—611no—
206C2×#95—1221no—
207#342—21no—
208#342C2×D6112yes—
209#323—612no—
210#323—1221no—
211C61#1180811yescharacteristic, complemented, Sylow
212C25C22⋊D6111yescharacteristic
213C22×Q8—612no—
214C22×Q8—1221no—
215C22×Q8—2441no—
216C22×Q8—2441no—
217C22×Q8—2444no—
218C23×C4—1221no—
219C23×C4—1221no—
220C23×C4C4×D6111yescharacteristic
221C23×C4D24411yescharacteristic
222C2×M16—2441no—
223C2×C22⋊C4—22no—
224C2×C22⋊C4—41no—
225C2×C22⋊C4—41no—
226C2×C22⋊C4—41no—
227C2×C22⋊C4—41no—
228C2×C22⋊C4—1222no—
229C2×C22⋊C4—1222no—
230C2×C22⋊C4—2444no—
231C2×C22⋊C4C4×D6111yescharacteristic
232C2×C22⋊C4D24411yescharacteristic
233C2×C22⋊C4C22⋊D6111yescharacteristic
234C2×C22⋊C4C22×D6111yescharacteristic
235C22⋊C8—1222no—
236C22⋊C8—2441no—
237#95—612no—
238#95—1221no—
239#95—1222no—
240#95—1222no—
241C24—22no—
242C24—21no—
243C24—21no—
244C24—41no—
245C24—42no—
246C24—42no—
247C24#1175819811yescharacteristic
248C24#1175819811yescharacteristic
249C24C2×C22⋊D6111yescharacteristic
250C2×Q8—2442no—
251C2×Q8—2442no—
252C2×Q8—2444no—
253C2×Q8—2444no—
254C2×Q8—2448no—
255C2×Q8—2444no—
256C2×Q8—2444no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—42no—
262C22×C4—42no—
263C22×C4—42no—
264C22×C4—1224no—
265C22×C4—1222no—
266C22×C4—1222no—
267C22×C4—2442no—
268C22×C4—2442no—
269C22×C4—2442no—
270C22×C4—2442no—
271C22×C4—2441no—
272C22×C4—2441no—
273C22×C4#1175819811yescharacteristic
274C22×C4#1175819811yescharacteristic
275C22×C4C2×C4×D6111yescharacteristic
276C22×C4C2×D24411yescharacteristic
277M16—4882no—
278C2×C8—2442no—
279C22⋊C4—41no—
280C22⋊C4—41no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C22⋊C4—42no—
284C22⋊C4—42no—
285C22⋊C4—82no—
286C22⋊C4—82no—
287C22⋊C4—2444no—
288C22⋊C4—2444no—
289C23—21no—
290C23—21no—
291C23—22no—
292C23—22no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23—42no—
299C23—42no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23—48no—
305C23—42no—
306C23—42no—
307C23—81no—
308C23—81no—
309C23—84no—
310C23#1451969111yescharacteristic
311C23#1451969111yescharacteristic
312C23C2×#1175819811yescharacteristic
313C23#1451980712yes—
314Q8—2444no—
315Q8—2448no—
316Q8—2444no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—81no—
329C2×C4—82no—
330C2×C4—82no—
331C2×C4—82no—
332C2×C4—1224no—
333C2×C4—4884no—
334C2×C4—2442no—
335C2×C4—2442no—
336C2×C4—2442no—
337C2×C4—2442no—
338C2×C4—2444no—
339C2×C4—2442no—
340C2×C4—2444no—
341C8—4882no—
342C22—24no—
343C22—24no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—22no—
351C22—42no—
352C22—42no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—81no—
359C22—84no—
360C22—84no—
361C22—81no—
362C22#1683954812yes—
363C22#1683955612yes—
364C22C2×#1451969111yescharacteristic
365C22#1683977011yescharacteristic
366C22#1683978011yescharacteristic
367C4—41no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—162no—
372C4—4882no—
373C4—2444no—
374C2—21no—
375C2—21no—
376C2—22no—
377C2—22no—
378C2—42no—
379C2—81no—
380C2#2144435111yescharacteristic
381C2C2×#1683954811yescharacteristic
382C2C2×#1683955611yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1819C2
socleC22×C61C2×#99
prime radicalC25×C61D4
cosocleC2×C22⋊C4×C61C23
hypercenter#1819D61
hypocenterC61#11808
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ #1819

Complements

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

NH ≅ G/Ntype
3. #21443839C2semidirect
5. C23×Dic122C4semidirect
10. #16839674C4semidirect
13. C2×#14519684C4semidirect
211. C61#11808semidirect

Maximal subgroups

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

subgroupindex
C2×#168396742
#214441462
#214438392
C61×#18192
#1180861