Finite Group Databasebeta

← #29598271

Subgroups — #29598271

Order 15616.

574 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840137C211yesmaximal, characteristic
2C2×#16839576C211yesmaximal, characteristic, complemented
3C2×#16839575C211yesmaximal, characteristic, complemented
4C2×#16839574C211yesmaximal, characteristic, complemented
5M32×Dic61C211yesmaximal, characteristic, complemented
6#21445989C211yesmaximal, characteristic, complemented
7C2×C61×#361C211yesmaximal, characteristic, complemented
8C22×D488C2211yescharacteristic
9C22×#11758199—21no—
10C2×#14519773—21no—
11C2×#14519717C2211yescharacteristic
12#16840137—21no—
13#16840137—21no—
14#16840137C412yes—
15#16840137C412yes—
16C2×#14519713C2211yescharacteristic
17C2×#14519712—21no—
18#16839785—21no—
19C2×C8×Dic61C2211yescharacteristic
20#16839576—22no—
21#16839575—22no—
22#16839574—22no—
23#16839537—21no—
24C16×Dic61—21no—
25C22×D8×C61C2211yescharacteristic
26C2×M32×C61C2211yescharacteristic
27C2×#108×C61C2211yescharacteristic
28C61×#361—22no—
29C22×D244—21no—
30C22×C22⋊D61—42no—
31C2×D488—21no—
32C2×D488—21no—
33C2×D488—21no—
34C2×D488—21no—
35C2×D488—21no—
36C2×D488C2×C412yes—
37C2×#11758199—22no—
38C2×#11758199—22no—
39C2×#11758199—42no—
40C2×#11758199—42no—
41C2×#11758194—21no—
42C22×#92418D411yescharacteristic
43#14519773—22no—
44#14519773—22no—
45#14519773—42no—
46C2×C4×Dic61D411yescharacteristic
47#14519717—21no—
48#14519717D412yescomplemented
49C2×#11758185—21no—
50#14519713—21no—
51#14519713—21no—
52#14519712—42no—
53#14519706—42no—
54C8×Dic61C2×C411yescharacteristic
55C8×Dic61C2×C411yescharacteristic
56C8×Dic61D411yescharacteristic
57C8×Dic61D411yescharacteristic
58C22×D4×C61—21no—
59C2×D8×C61—21no—
60C2×D8×C61—21no—
61C2×D8×C61—21no—
62C2×D8×C61—21no—
63C2×D8×C61—21no—
64C2×D8×C61C2×C412yes—
65C2×M16×C61—21no—
66C22×C8×C61C2311yescharacteristic
67M32×C61—21no—
68M32×C61D412yescomplemented
69C2×C16×C61—21no—
70#108×C61—21no—
71#108×C61—21no—
72C24×C61—41no—
73C23×D61—41no—
74C2×D4×C61—22no—
75C2×D4×C61—41no—
76C2×D4×C61—41no—
77C2×D4×C61—41no—
78C2×D4×C61—41no—
79C2×D4×C61—41no—
80C22×C4×C61C2×D411yescharacteristic
81C2×C22⋊D61—44no—
82C2×C22⋊D61—44no—
83C2×C22⋊D61—88no—
84C22×Dic61SD1612yes—
85C2×D244—22no—
86C2×D244—41no—
87C2×D244—41no—
88C2×D244—41no—
89C2×D244—41no—
90C2×D244—41no—
91D8×C61—22no—
92D8×C61—22no—
93D8×C61—41no—
94D8×C61—41no—
95M16×C61—41no—
96M16×C61—41no—
97C2×C8×C61—41no—
98C2×C8×C61C22×C411yescharacteristic
99C2×C8×C61C2×D411yescharacteristic
100C2×C8×C61C2×D411yescharacteristic
101C2×C8×C61C2×D411yescharacteristic
102C2×C8×C61#4111yescharacteristic
103C2×C8×C61#4111yescharacteristic
104#11758199—44no—
105#11758199—44no—
106C4×Dic61C22⋊C411yescharacteristic
107C4×Dic61C22⋊C411yescharacteristic
108C4×Dic61D812yes—
109#11758194—41no—
110#11758194—41no—
111C2×#92418—41no—
112C2×#92418C22⋊C411yescharacteristic
113C2×#92418C22⋊C411yescharacteristic
114C2×#92418D812yes—
115C2×#92418SD1612yes—
116D488—22no—
117D488—22no—
118D488—41no—
119D488—41no—
120C16×C61—22no—
121#11758185—22no—
122C23×C61—42no—
123C23×C61—84no—
124C23×C61—81no—
125C23×C61—81no—
126C23×C61C2×SD1611yescharacteristic
127C22×D61—42no—
128C22×D61—84no—
129C22×D61—81no—
130C22×D61—81no—
131D4×C61—42no—
132D4×C61—42no—
133D4×C61—81no—
134D4×C61—81no—
135C2×C4×C61C2×C22⋊C411yescharacteristic
136C2×C4×C61#12411yescharacteristic
137C2×C4×C61#12711yescharacteristic
138C2×C4×C61C2×D811yescharacteristic
139C2×C4×C61C2×D811yescharacteristic
140C2×C4×C61C2×SD1611yescharacteristic
141C22⋊D61—88no—
142C22⋊D61—88no—
143C2×Dic61—24no—
144C2×Dic61#10212yes—
145C2×Dic61#10212yes—
146D244—42no—
147D244—42no—
148D244—81no—
149D244—81no—
150C8×C61—81no—
151C8×C61C4×D411yescharacteristic
152C8×C61C4×D411yescharacteristic
153C8×C61#12111yescharacteristic
154C8×C61#12111yescharacteristic
155#92418—81no—
156#92418#10212yes—
157#92418#10212yes—
158#13213—611nomaximal, Sylow
159C22×C61—22no—
160C22×C61—84no—
161C22×C61—82no—
162C22×C61—162no—
163C22×C61—162no—
164C22×C61C2×#10211yescharacteristic
165C22×C61#48611yescharacteristic
166C22×C61#49211yescharacteristic
167C2×D61—84no—
168C2×D61—82no—
169C2×D61—162no—
170C2×D61—162no—
171C4×C61#39011yescharacteristic
172C4×C61C2×#10211yescharacteristic
173C4×C61#48611yescharacteristic
174C4×C61#49311yescharacteristic
175Dic61—22no—
176Dic61#36114yescomplemented
177C2×#493—611no—
178C2×#361—611no—
179C2×#361—611no—
180C2×#361—611no—
181C2×#361D6111yescharacteristic, complemented
182C4×M32—611no—
183#1848—611no—
184C2×C61—21no—
185C2×C61—21no—
186C2×C61—162no—
187C2×C61#195711yescharacteristic
188C2×C61C2×#36112yes—
189D61—162no—
190C22×D8—611no—
191C22×D8—1221no—
192C22×D8C2×D6111yescharacteristic
193C2×#127—1221no—
194C2×M32—611no—
195C2×M32C2×D6111yescharacteristic
196#493—612no—
197#493—612no—
198#493—1221no—
199#493—1221no—
200C2×#108—611no—
201C2×#108—1221no—
202C2×#108C2×D6111yescharacteristic
203#423—1221no—
204C2×C4×C8—611no—
205#361—22no—
206#361—1222no—
207#361—1222no—
208#361—1222no—
209#346—1221no—
210C4×C16—1221no—
211C61#1321311yescharacteristic, complemented, Sylow
212C22×D4—21no—
213C22×D4—1221no—
214C22×D4—2442no—
215C2×D8—21no—
216C2×D8—21no—
217C2×D8—21no—
218C2×D8—21no—
219C2×D8—21no—
220C2×D8—612no—
221C2×D8—1222no—
222C2×D8—1222no—
223C2×D8—1221no—
224C2×D8—1221no—
225C2×D8—1221no—
226C2×D8—1221no—
227C2×D8—1221no—
228C2×D8—2442no—
229C2×D8—2442no—
230C2×D8C4×D6112yes—
231C2×M16—21no—
232C2×M16—1221no—
233C22×C8—611no—
234C22×C8C22×D6111yescharacteristic
235#127—1222no—
236#127—1222no—
237#127—2442no—
238C2×C42—611no—
239M32—21no—
240M32—612no—
241M32—1221no—
242M32C22⋊D6112yescomplemented
243C2×C16—21no—
244C2×C16—1221no—
245#108—21no—
246#108—21no—
247#108—1221no—
248#108—1221no—
249#108—2442no—
250C4⋊C8—2442no—
251C4×C8—611no—
252C4×C8—611no—
253C4×C8—611no—
254C4×C8—611no—
255C24—41no—
256C24—2441no—
257C2×D4—22no—
258C2×D4—41no—
259C2×D4—41no—
260C2×D4—41no—
261C2×D4—41no—
262C2×D4—41no—
263C2×D4—1222no—
264C2×D4—4888no—
265C2×D4—2444no—
266C2×D4—2444no—
267C2×D4—2441no—
268C2×D4—2441no—
269C2×D4—2441no—
270C2×D4—2441no—
271C2×D4—2441no—
272C22×C4—612no—
273C22×C4D4×D6111yescharacteristic
274D8—22no—
275D8—22no—
276D8—41no—
277D8—41no—
278D8—1222no—
279D8—1222no—
280D8—2444no—
281D8—2444no—
282D8—2441no—
283D8—2441no—
284M16—41no—
285M16—41no—
286M16—2441no—
287M16—2441no—
288C2×C8—41no—
289C2×C8—611no—
290C2×C8—611no—
291C2×C8—612no—
292C2×C8—612no—
293C2×C8—2441no—
294C2×C8C2×C4×D6111yescharacteristic
295C2×C8#1175822211yescharacteristic
296C2×C8D4×D6111yescharacteristic
297C2×C8D4×D6111yescharacteristic
298C2×C8#1175822411yescharacteristic
299C2×C8C2×C22⋊D6111yescharacteristic
300C42—611no—
301C42—611no—
302C42—612no—
303C16—22no—
304C16—1222no—
305C23—42no—
306C23—84no—
307C23—81no—
308C23—81no—
309C23—4884no—
310C23—4881no—
311C23—4881no—
312C23—2442no—
313C23SD16×D6111yescharacteristic
314D4—42no—
315D4—42no—
316D4—81no—
317D4—81no—
318D4—4888no—
319D4—4888no—
320D4—4881no—
321D4—4881no—
322D4—2442no—
323D4—2442no—
324C2×C4—612no—
325C2×C4—612no—
326C2×C4—1224no—
327C2×C4C22⋊C4×D6111yescharacteristic
328C2×C4#1451976311yescharacteristic
329C2×C4#1451977311yescharacteristic
330C2×C4D8×D6111yescharacteristic
331C2×C4D8×D6111yescharacteristic
332C2×C4SD16×D6111yescharacteristic
333C8—81no—
334C8—612no—
335C8—612no—
336C8—4881no—
337C8#1451973711yescharacteristic
338C8C4×C22⋊D6111yescharacteristic
339C8#1451974911yescharacteristic
340C8#1451975011yescharacteristic
341C22—22no—
342C22—84no—
343C22—82no—
344C22—162no—
345C22—162no—
346C22—9762no—
347C22—9762no—
348C22—4884no—
349C22—4882no—
350C22#102×D6111yescharacteristic
351C22#1684010711yescharacteristic
352C22#1684013311yescharacteristic
353C4—614no—
354C4—1222no—
355C4#1683966211yescharacteristic
356C4#102×D6111yescharacteristic
357C4#1684010711yescharacteristic
358C4#1684013711yescharacteristic
359C2—21no—
360C2—21no—
361C2—162no—
362C2—9762no—
363C2#2144662311yescharacteristic
364C2#361×D6112yes—
subgroupG/H
centerC22#102×D61
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC2×C61×#361C2
socleC22×C61C2×#102
prime radicalC2×#16840137C2
cosocleC22×C8×C61C23
hypercenterC2×#361D61
hypocenterC61#13213
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#361

Complements

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

NH ≅ G/Ntype
2. C2×#16839576C2semidirect
3. C2×#16839575C2semidirect
4. C2×#16839574C2semidirect
5. M32×Dic61C2semidirect
6. #21445989C2semidirect
7. C2×C61×#361C2semidirect
48. #14519717D4semidirect
68. M32×C61D4semidirect
176. Dic61#361semidirect
181. C2×#361D61semidirect
211. C61#13213semidirect
242. M32C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168401372
C2×#168395762
C2×#168395752
C2×#168395742
M32×Dic612
#214459892
C2×C61×#3612
#1321361