Finite Group Databasebeta

← #29568321

Subgroups — #29568321

Order 15616.

500 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14519756C211yesmaximal, characteristic
2#21445887C211yesmaximal, characteristic
3#21443644C212yesmaximal, complemented
4#21443641C212yesmaximal, complemented
5C61×#1797C211yesmaximal, characteristic
6C2×#14519756C411yescharacteristic
7C2×C4×Dic122C411yescharacteristic
8C2×C22⋊#92418—21no—
9#16839668C2211yescharacteristic
10#16839660C2211yescharacteristic
11#16839646—21no—
12#16839635—21no—
13#16839622C411yescharacteristic
14C4×#11758196—21no—
15C4×C4⋊Dic61C411yescharacteristic
16C4×C22⋊Dic61—21no—
17#16839517—21no—
18#16839517C2212yes—
19C22×C42×C61C2211yescharacteristic
20C2×C4⋊C8×C61—21no—
21C2×C22⋊C8×C61—21no—
22C61×#336C2212yes—
23C22×Dic122C2×C411yescharacteristic
24C22×#92418—22no—
25#14519756—22no—
26#14519756—22no—
27C4×Dic122—42no—
28C2×C4⋊Dic61C2×C411yescharacteristic
29C2×C4⋊Dic61C2×C411yescharacteristic
30C2×C4⋊Dic61C2×C411yescharacteristic
31C2×#11758196—21no—
32C2×#11758196—21no—
33C2×#11758196—21no—
34C2×C22⋊Dic61—21no—
35C2×C22⋊Dic61—21no—
36C2×C4×Dic61—21no—
37C2×C4×Dic61—21no—
38C22⋊#92418—42no—
39#14519684—21no—
40#14519684—21no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44C23×C4×C61C2×C411yescharacteristic
45C23×C4×C61D411yescharacteristic
46C23×C4×C61D411yescharacteristic
47C22×C8×C61—22no—
48C2×C42×C61—42no—
49C2×C42×C61C2×C411yescharacteristic
50C2×C42×C61D411yescharacteristic
51C2×C42×C61D411yescharacteristic
52C2×C42×C61C2311yescharacteristic
53C4⋊C8×C61—42no—
54C22⋊C8×C61—42no—
55C24×C61C22⋊C411yescharacteristic
56C22×C4×C61—22no—
57C22×C4×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61—22no—
60C22×C4×C61—41no—
61C22×C4×C61—41no—
62C22×C4×C61—41no—
63C22×C4×C61—41no—
64C22×C4×C61—41no—
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61SD1612yes—
69C22×C4×C61Q1612yes—
70C22×C4×C61C22×C411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77C2×Dic122—21no—
78C2×Dic122—41no—
79C2×Dic122—41no—
80C2×Dic122M1612yes—
81C2×C8×C61—42no—
82C2×C8×C61—42no—
83C2×C8×C61—42no—
84C42×C61—22no—
85C42×C61—22no—
86C42×C61—41no—
87C42×C61—41no—
88C22⋊Dic61—24no—
89C22⋊Dic61—42no—
90C4⋊Dic61—21no—
91C4⋊Dic61—41no—
92C4⋊Dic61—41no—
93C4⋊Dic61M1612yes—
94#11758196—24no—
95#11758196—42no—
96#11758196—42no—
97C4×Dic61—42no—
98C4×Dic61—42no—
99C2×#92418—42no—
100C2×#92418—42no—
101C2×#92418—42no—
102C23×C61—21no—
103C23×C61—21no—
104C23×C61—21no—
105C23×C61—21no—
106C23×C61—21no—
107C23×C61—21no—
108C23×C61#10312yes—
109C23×C61C2×C22⋊C411yescharacteristic
110C2×C4×C61—21no—
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—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—42no—
124C2×C4×C61—42no—
125C2×C4×C61—44no—
126C2×C4×C61—42no—
127C2×C4×C61—42no—
128C2×C4×C61#9912yes—
129C2×C4×C61#10312yes—
130C2×C4×C61C2×M1611yescharacteristic
131C2×C4×C61C2×M1611yescharacteristic
132C2×C4×C61C2×SD1611yescharacteristic
133C2×C4×C61C2×Q1611yescharacteristic
134C2×C4×C61#13512yes—
135C2×Dic61—22no—
136C2×Dic61—22no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147Dic122—42no—
148Dic122—42no—
149C8×C61—82no—
150#92418—82no—
151#7648—611nomaximal, Sylow
152C22×C61—22no—
153C22×C61—22no—
154C22×C61—22no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61—41no—
158C22×C61—41no—
159C22×C61#40711yescharacteristic
160C22×C61C2×#9911yescharacteristic
161C22×C61#41311yescharacteristic
162C22×C61C2×#10311yescharacteristic
163C22×C61#41611yescharacteristic
164C22×C61#42111yescharacteristic
165C22×C61#42111yescharacteristic
166C4×C61—21no—
167C4×C61—21no—
168C4×C61—22no—
169C4×C61—22no—
170C4×C61—21no—
171C4×C61—22no—
172C4×C61—21no—
173C4×C61—41no—
174Dic61—42no—
175Dic61—42no—
176Dic61—81no—
177Dic61—81no—
178C4×C22⋊Q8—611no—
179#1817—611no—
180#1797D6111yescharacteristic
181#1272—612no—
182#1271—612no—
183C2×C61—42no—
184C2×C61#146511yescharacteristic
185C2×C61#148711yescharacteristic
186C2×C61#148811yescharacteristic
187C2×C61#151611yescharacteristic
188C2×C61#152011yescharacteristic
189C2×C61#153511yescharacteristic
190C2×C61#154211yescharacteristic
191C2×C22⋊Q8—611no—
192C2×C4×Q8—611no—
193C22×C42C2×D6111yescharacteristic
194C2×C4⋊C8—21no—
195C2×C22⋊C8—21no—
196C2×C22⋊C8—1221no—
197#391—611no—
198#389—611no—
199#387—1221no—
200#385—1221no—
201#380—611no—
202C4×C4⋊C4—611no—
203C4×C4⋊C4—1221no—
204C4×C22⋊C4—1221no—
205#336—612no—
206#336—1221no—
207#336C2×D6112yes—
208C61#764811yescharacteristic, complemented, Sylow
209C22×Q8—611no—
210C23×C4C4×D6111yescharacteristic
211C23×C4D24411yescharacteristic
212C23×C4C22⋊D6111yescharacteristic
213C22×C8—22no—
214C22×C8—1222no—
215C22⋊Q8—1222no—
216C22⋊Q8—1222no—
217C4×Q8—2442no—
218C2×C4⋊C4—611no—
219C2×C4⋊C4—611no—
220C2×C4⋊C4—611no—
221C2×C4⋊C4—1221no—
222C2×C4⋊C4—1221no—
223C2×C4⋊C4—1221no—
224C2×C22⋊C4—1221no—
225C2×C22⋊C4—1221no—
226C2×C42—42no—
227C2×C42—1221no—
228C2×C42—1221no—
229C2×C42C4×D6111yescharacteristic
230C2×C42D24411yescharacteristic
231C2×C42C22⋊D6111yescharacteristic
232C2×C42C22×D6111yescharacteristic
233C4⋊C8—42no—
234C22⋊C8—42no—
235C22⋊C8—2442no—
236#95—1221no—
237#95—1221no—
238#95—1221no—
239#95—1221no—
240#95—1221no—
241C24#1175819811yescharacteristic
242C2×Q8—612no—
243C2×Q8—1221no—
244C2×Q8—2441no—
245C2×Q8—2441no—
246C22×C4—22no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—22no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4—1221no—
258C22×C4—1221no—
259C22×C4#1175819811yescharacteristic
260C22×C4#1175819811yescharacteristic
261C22×C4#1175819811yescharacteristic
262C22×C4#1175820012yes—
263C22×C4#1175820212yes—
264C22×C4C2×C4×D6111yescharacteristic
265C22×C4C2×D24411yescharacteristic
266C22×C4C2×C22⋊D6111yescharacteristic
267C2×C8—42no—
268C2×C8—42no—
269C2×C8—42no—
270C2×C8—2442no—
271C2×C8—2442no—
272C2×C8—2442no—
273C4⋊C4—612no—
274C4⋊C4—1224no—
275C4⋊C4—1221no—
276C4⋊C4—2441no—
277C4⋊C4—2441no—
278C4⋊C4—2442no—
279C4⋊C4—2442no—
280C22⋊C4—1224no—
281C22⋊C4—2442no—
282C42—22no—
283C42—22no—
284C42—41no—
285C42—41no—
286C42—2442no—
287C42—2442no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23#1451970012yes—
295C23C2×#1175819811yescharacteristic
296Q8—2442no—
297Q8—2442no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—44no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—1222no—
317C2×C4—1222no—
318C2×C4—2441no—
319C2×C4—2441no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4—2441no—
326C2×C4—2441no—
327C2×C4—2441no—
328C2×C4#1451969112yes—
329C2×C4#1451970012yes—
330C2×C4M16×D6111yescharacteristic
331C2×C4M16×D6111yescharacteristic
332C2×C4C2×#1175820011yescharacteristic
333C2×C4C2×#1175820211yescharacteristic
334C2×C4#1451979912yes—
335C8—82no—
336C8—4882no—
337C22—22no—
338C22—22no—
339C22—22no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22#1683972511yescharacteristic
345C22C2×#1451969111yescharacteristic
346C22#1683974411yescharacteristic
347C22C2×#1451970011yescharacteristic
348C22#1683975911yescharacteristic
349C22#1683977811yescharacteristic
350C22#1683978011yescharacteristic
351C4—22no—
352C4—22no—
353C4—21no—
354C4—22no—
355C4—21no—
356C4—21no—
357C4—21no—
358C4—41no—
359C4—4881no—
360C4—4881no—
361C4—2442no—
362C4—2442no—
363C2—42no—
364C2#2144415511yescharacteristic
365C2#2144424711yescharacteristic
366C2#2144425411yescharacteristic
367C2#2144437611yescharacteristic
368C2#2144439011yescharacteristic
369C2#2144444811yescharacteristic
370C2#2144447711yescharacteristic
subgroupG/H
centerC23C2×#11758198
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1797C2
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1797D61
hypocenterC61#7648
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
3. #21443644C2semidirect
4. #21443641C2semidirect
208. C61#7648semidirect

Maximal subgroups

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

subgroupindex
C4×#145197562
#214458872
#214436442
#214436412
C61×#17972
#764861