Finite Group Databasebeta

← #30606777

Subgroups — #30606777

Order 15616.

1038 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840659C212yesmaximal, complemented
2C2×#16840658C212yesmaximal, complemented
3#21462048C212yesmaximal, complemented
4C22×M16×D61C211yesmaximal, characteristic
5C2×#14519851C2214yescomplemented
6#16840659—24no—
7#16840658—24no—
8#16840657—24no—
9C23×C4×D61C411yescharacteristic
10C22×#11758194C2211yescharacteristic
11C22×#11758189C411yescharacteristic
12C22×#11758189C2211yescharacteristic
13C2×M16×D61—24no—
14C2×M16×D61—24no—
15C2×M16×D61—24no—
16C22×C8×D61C411yescharacteristic
17C22×C8×D61C2211yescharacteristic
18C22×M16×C61C411yescharacteristic
19#14519851—24no—
20#14519851—24no—
21C2×#11758187—24no—
22C24×D61C811yescharacteristic
23C23×Dic61C811yescharacteristic
24C22×C4×D61—22no—
25C22×C4×D61—22no—
26C22×C4×D61—22no—
27C22×C4×D61—22no—
28C22×C4×D61—22no—
29C22×C4×D61—22no—
30C22×C4×D61C811yescharacteristic
31C22×C4×D61C811yescharacteristic
32C22×C4×D61C2×C411yescharacteristic
33C22×C4×D61C2×C411yescharacteristic
34C2×#11758194—22no—
35C2×#11758194—22no—
36C2×#11758194D414yes—
37C2×#11758189—22no—
38C2×#11758189—22no—
39C2×#11758189—22no—
40C2×#11758189—22no—
41C2×#11758189—22no—
42C2×#11758189D414yes—
43M16×D61—232no—
44C22×#92418C2×C411yescharacteristic
45C22×#92418C2311yescharacteristic
46C2×C8×D61—22no—
47C2×C8×D61—22no—
48C2×C8×D61—22no—
49C2×C8×D61—22no—
50C2×C8×D61—22no—
51C2×C8×D61D414yes—
52C23×C4×C61C2×C411yescharacteristic
53C2×M16×C61—22no—
54C2×M16×C61—22no—
55C2×M16×C61—22no—
56C22×C8×C61C2×C411yescharacteristic
57C22×C8×C61C2×C411yescharacteristic
58C24×C61C2×C811yescharacteristic
59C23×D61—22no—
60C23×D61—22no—
61C23×D61—22no—
62C23×D61—44no—
63C23×D61C2×C811yescharacteristic
64C23×D61C2×C811yescharacteristic
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61C22⋊C412yes—
70C22×C4×C61C2×C811yescharacteristic
71C22×C4×C61M1612yes—
72C22×C4×C61C22×C411yescharacteristic
73C22×Dic61—22no—
74C22×Dic61—22no—
75C22×Dic61—22no—
76C22×Dic61C2×C811yescharacteristic
77C22×Dic61C2×C811yescharacteristic
78C2×C4×D61—28no—
79C2×C4×D61—28no—
80C2×C4×D61—28no—
81C2×C4×D61—28no—
82C2×C4×D61—22no—
83C2×C4×D61—22no—
84C2×C4×D61—22no—
85C2×C4×D61—22no—
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×C4×D61—21no—
89C2×C4×D61—21no—
90C2×C4×D61—21no—
91C2×C4×D61—21no—
92C2×C4×D61—21no—
93C2×C4×D61—21no—
94C2×C4×D61—22no—
95C2×C4×D61—22no—
96C2×C4×D61C22⋊C412yes—
97C2×C4×D61C22⋊C412yes—
98C2×C4×D61M1612yes—
99C2×C4×D61M1612yes—
100M16×C61—28no—
101C2×C8×C61—21no—
102C2×C8×C61—21no—
103C2×C8×C61—21no—
104C2×C8×C61—21no—
105C2×C8×C61C22⋊C412yes—
106C2×C8×C61C22⋊C412yes—
107#11758194—28no—
108C2×#92418—21no—
109C2×#92418—21no—
110C2×#92418C22⋊C412yes—
111C2×#92418C2×D412yes—
112C2×#92418C2×D412yes—
113C2×#92418C2×D412yes—
114#11758189—28no—
115#11758189—28no—
116C8×D61—28no—
117C8×D61—28no—
118#11758187—44no—
119C23×C61—21no—
120C23×C61—21no—
121C23×C61—42no—
122C23×C61C22⋊C812yes—
123C23×C61C22×C811yescharacteristic
124C22×D61—21no—
125C22×D61—21no—
126C22×D61—24no—
127C22×D61—28no—
128C22×D61—21no—
129C22×D61—21no—
130C22×D61—48no—
131C22×D61—48no—
132C22×D61—44no—
133C22×D61—44no—
134C22×D61—42no—
135C22×D61C22⋊C812yes—
136C22×D61C22⋊C812yes—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—22no—
140C2×C4×C61—22no—
141C2×C4×C61—22no—
142C2×C4×C61—22no—
143C2×C4×C61C22⋊C812yes—
144C2×C4×C61C2×C22⋊C411yescharacteristic
145C2×C4×C61C2×C22⋊C411yescharacteristic
146C2×C4×C61C2×C22⋊C411yescharacteristic
147C2×C4×C61C2×M1611yescharacteristic
148C2×C4×C61C2×M1611yescharacteristic
149C2×C4×C61C2×M1611yescharacteristic
150C2×Dic61—28no—
151C2×Dic61—21no—
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61C22⋊C812yes—
156C2×Dic61C22⋊C812yes—
157C4×D61—28no—
158C4×D61—28no—
159C4×D61—22no—
160C4×D61—22no—
161C4×D61—22no—
162C4×D61—22no—
163C4×D61—22no—
164C4×D61—22no—
165C4×D61—22no—
166C4×D61—22no—
167C8×C61—22no—
168C8×C61—22no—
169#92418—22no—
170#92418#12014yes—
171#12681—611nomaximal, Sylow
172C22×C61—22no—
173C22×C61—22no—
174C22×C61—42no—
175C22×C61—42no—
176C22×C61—42no—
177C22×C61C2×C22⋊C811yescharacteristic
178C22×C61C2×C22⋊C811yescharacteristic
179C22×C61C2×C22⋊C811yescharacteristic
180C2×D61—24no—
181C2×D61—24no—
182C2×D61—22no—
183C2×D61—22no—
184C2×D61—22no—
185C2×D61—416no—
186C2×D61—42no—
187C2×D61—42no—
188C2×D61—42no—
189C2×D61#34914yescomplemented
190C4×C61—22no—
191C4×C61#37911yescharacteristic
192C4×C61#40711yescharacteristic
193C4×C61#40711yescharacteristic
194C4×C61#40711yescharacteristic
195Dic61—22no—
196Dic61—22no—
197C23×M16—611no—
198C2×#349—612no—
199C2×#349—612no—
200#2112—612no—
201C2×C61—21no—
202C2×C61—21no—
203C2×C61—42no—
204C2×C61#177911yescharacteristic
205C2×C61C2×#34912yes—
206D61—24no—
207D61—42no—
208C24×C4—611no—
209C22×M16—611no—
210C22×M16—611no—
211C22×M16—611no—
212C22×M16—1224no—
213C22×M16—1224no—
214C22×M16—1224no—
215C22×M16#692311yescharacteristic
216C23×C8—611no—
217C23×C8—611no—
218C2×M32—614no—
219#349—1224no—
220#349—1224no—
221C22⋊C16—1224no—
222C61#1268111yescharacteristic, complemented, Sylow
223C25—611no—
224C23×C4—611no—
225C23×C4—611no—
226C23×C4—611no—
227C23×C4—611no—
228C23×C4—611no—
229C23×C4—1222no—
230C23×C4—1222no—
231C23×C4—1222no—
232C23×C4—1222no—
233C23×C4—1222no—
234C23×C4—1222no—
235C23×C4C2×#692311yescharacteristic
236C2×M16—22no—
237C2×M16—22no—
238C2×M16—22no—
239C2×M16—614no—
240C2×M16—614no—
241C2×M16—1222no—
242C2×M16—1222no—
243C2×M16—1222no—
244C2×M16—1222no—
245C2×M16—1222no—
246C2×M16—1222no—
247C2×M16—12232no—
248C2×M16—1222no—
249C22×C8—611no—
250C22×C8—611no—
251C22×C8—614no—
252C22×C8—1222no—
253C22×C8—1222no—
254C22×C8—1222no—
255C22×C8—1222no—
256C22×C8—1222no—
257C22×C8C2×#692311yescharacteristic
258C22×C8C2×#692311yescharacteristic
259M32—1224no—
260M32—1224no—
261C2×C16—1224no—
262C24—611no—
263C24—611no—
264C24—1222no—
265C24—1222no—
266C24—1222no—
267C24—2444no—
268C24D61⋊C811yescharacteristic
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—611no—
274C22×C4—611no—
275C22×C4—612no—
276C22×C4—612no—
277C22×C4—612no—
278C22×C4—612no—
279C22×C4—1222no—
280C22×C4—1222no—
281C22×C4—1222no—
282C22×C4—1222no—
283C22×C4—1228no—
284C22×C4—1228no—
285C22×C4—1228no—
286C22×C4—1228no—
287C22×C4—1222no—
288C22×C4—1222no—
289C22×C4—1222no—
290C22×C4—1222no—
291C22×C4—1222no—
292C22×C4—1221no—
293C22×C4—1221no—
294C22×C4—1221no—
295C22×C4—1221no—
296C22×C4—1221no—
297C22×C4—1221no—
298C22×C4—1221no—
299C22×C4—1221no—
300C22×C4D61⋊C811yescharacteristic
301C22×C4#1175821312yes—
302C22×C4C22⋊#692312yes—
303C22×C4C22×#692311yescharacteristic
304M16—28no—
305M16—1228no—
306M16—1228no—
307M16—1228no—
308C2×C8—21no—
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—612no—
313C2×C8—612no—
314C2×C8—612no—
315C2×C8—612no—
316C2×C8—1228no—
317C2×C8—1228no—
318C2×C8—1221no—
319C2×C8—1221no—
320C2×C8C22⋊#692312yes—
321C2×C8C22⋊#692312yes—
322C16—2444no—
323C23—21no—
324C23—21no—
325C23—42no—
326C23—612no—
327C23—612no—
328C23—1224no—
329C23—1228no—
330C23—1221no—
331C23—1221no—
332C23—1221no—
333C23—1221no—
334C23—2442no—
335C23—2444no—
336C23—2448no—
337C23—2448no—
338C23—2444no—
339C23#1451983412yes—
340C23C2×D61⋊C811yescharacteristic
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—612no—
348C2×C4—612no—
349C2×C4—1228no—
350C2×C4—1228no—
351C2×C4—1228no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—1221no—
355C2×C4—1221no—
356C2×C4—1222no—
357C2×C4—1222no—
358C2×C4—1222no—
359C2×C4—1222no—
360C2×C4—1222no—
361C2×C4—1222no—
362C2×C4—1222no—
363C2×C4—1222no—
364C2×C4#1451983412yes—
365C2×C4C2×C22⋊#692311yescharacteristic
366C2×C4C2×C22⋊#692311yescharacteristic
367C2×C4C2×C22⋊#692311yescharacteristic
368C2×C4D61⋊M1611yescharacteristic
369C2×C4D61⋊M1611yescharacteristic
370C2×C4C2×#1175821311yescharacteristic
371C8—22no—
372C8—22no—
373C8—614no—
374C8—1222no—
375C22—22no—
376C22—22no—
377C22—42no—
378C22—42no—
379C22—42no—
380C22—614no—
381C22—1224no—
382C22—1224no—
383C22—1222no—
384C22—1222no—
385C22—1222no—
386C22—2442no—
387C22—2442no—
388C22—24416no—
389C22—2442no—
390C22D61⋊(C22⋊C8)11yescharacteristic
391C22D61⋊(C22⋊C8)11yescharacteristic
392C22C2×#1451983411yescharacteristic
393C4—22no—
394C4—1222no—
395C4—1222no—
396C4#1684070311yescharacteristic
397C4#1684073311yescharacteristic
398C4#1684073311yescharacteristic
399C4#1684073411yescharacteristic
400C2—21no—
401C2—21no—
402C2—42no—
403C2—1224no—
404C2—2442no—
405C2#2146164211yescharacteristic
406C2D61⋊#34912yes—
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC23×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC22×M16×C61C4
socleC22×C61C2×C22⋊C8
prime radicalC24×D61C8
cosocleC22×#92418C23
hypercenterC22×M16#6923
hypocenterC61#12681
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
1. C2×#16840659C2semidirect
2. C2×#16840658C2semidirect
3. #21462048C2semidirect
5. C2×#14519851C22semidirect
189. C2×D61#349semidirect
222. C61#12681semidirect

Maximal subgroups

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

subgroupindex
C2×#168406592
C2×#168406582
#214620482
C22×M16×D612
#1268161