Finite Group Databasebeta

← #29567975

Subgroups — #29567975

Order 15616.

596 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14519756C211yesmaximal, characteristic
2C4×C22⋊#92418C211yesmaximal, characteristic
3#21443644C212yesmaximal, complemented
4#21443641C212yesmaximal, complemented
5C2×C61×#336C211yesmaximal, characteristic
6C2×#14519756C411yescharacteristic
7C2×C4×Dic122C411yescharacteristic
8C2×C22⋊#92418—21no—
9C2×C4×#92418—21no—
10#16839668C2211yescharacteristic
11#16839660C2211yescharacteristic
12#16839646—21no—
13#16839635—21no—
14#16839622C411yescharacteristic
15C4×#11758196—21no—
16C4×C4⋊Dic61C411yescharacteristic
17C4×C22⋊Dic61—21no—
18#16839517C2212yes—
19C23×C8×C61—21no—
20C22×C42×C61C2211yescharacteristic
21C61×#336—21no—
22C61×#336C2212yes—
23C22×Dic122C2×C411yescharacteristic
24C22×#92418—22no—
25#14519756—22no—
26#14519756C814yescomplemented
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—24no—
39C4×#92418—42no—
40#14519684—21no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45C23×C4×C61C2×C411yescharacteristic
46C23×C4×C61D411yescharacteristic
47C23×C4×C61D411yescharacteristic
48C22×C8×C61—24no—
49C22×C8×C61—22no—
50C22×C8×C61—42no—
51C22×C8×C61—42no—
52C2×C42×C61—42no—
53C2×C42×C61C2×C411yescharacteristic
54C2×C42×C61D411yescharacteristic
55C2×C42×C61D411yescharacteristic
56C2×C42×C61C2311yescharacteristic
57C24×C61C22⋊C411yescharacteristic
58C22×C4×C61—22no—
59C22×C4×C61—22no—
60C22×C4×C61—22no—
61C22×C4×C61—22no—
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×C61C2×C812yes—
69C22×C4×C61M1612yes—
70C22×C4×C61SD1612yes—
71C22×C4×C61Q1612yes—
72C22×C4×C61C22×C411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C2×Dic122—21no—
80C2×Dic122—41no—
81C2×Dic122—41no—
82C2×Dic122C2×C812yescomplemented
83C2×C8×C61—24no—
84C2×C8×C61—42no—
85C2×C8×C61—48no—
86C2×C8×C61—42no—
87C42×C61—22no—
88C42×C61—22no—
89C42×C61—41no—
90C42×C61—41no—
91C22⋊Dic61—24no—
92C22⋊Dic61—42no—
93C4⋊Dic61—21no—
94C4⋊Dic61—41no—
95C4⋊Dic61—41no—
96C4⋊Dic61C2×C812yescomplemented
97#11758196—24no—
98#11758196—42no—
99#11758196—42no—
100C4×Dic61—42no—
101C4×Dic61—42no—
102C2×#92418—24no—
103C2×#92418—42no—
104C2×#92418—42no—
105C23×C61—21no—
106C23×C61—21no—
107C23×C61—21no—
108C23×C61—21no—
109C23×C61C22⋊C812yes—
110C23×C61#10312yes—
111C23×C61#10412yes—
112C23×C61C2×C22⋊C411yescharacteristic
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—24no—
122C2×C4×C61—24no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—42no—
127C2×C4×C61—42no—
128C2×C4×C61—44no—
129C2×C4×C61C22⋊C812yes—
130C2×C4×C61#9912yes—
131C2×C4×C61#10312yes—
132C2×C4×C61#10412yes—
133C2×C4×C61C22×C811yescharacteristic
134C2×C4×C61C2×M1611yescharacteristic
135C2×C4×C61C2×SD1611yescharacteristic
136C2×C4×C61C2×Q1611yescharacteristic
137C2×C4×C61#13512yes—
138C2×Dic61—22no—
139C2×Dic61—22no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150Dic122—42no—
151Dic122—42no—
152C8×C61—44no—
153#92418—44no—
154#7566—611nomaximal, Sylow
155C22×C61—22no—
156C22×C61—22no—
157C22×C61—22no—
158C22×C61—22no—
159C22×C61—22no—
160C22×C61—22no—
161C22×C61Q8⋊C814yes—
162C22×C61C2×C22⋊C811yescharacteristic
163C22×C61C2×#9911yescharacteristic
164C22×C61#41311yescharacteristic
165C22×C61C2×#10311yescharacteristic
166C22×C61#41611yescharacteristic
167C22×C61C2×#10411yescharacteristic
168C22×C61C2×#10411yescharacteristic
169C4×C61—21no—
170C4×C61—21no—
171C4×C61—22no—
172C4×C61—21no—
173C4×C61—21no—
174C4×C61—22no—
175C4×C61—41no—
176C4×C61#32814yes—
177Dic61—42no—
178Dic61—42no—
179Dic61—81no—
180Dic61—81no—
181C4×C22⋊Q8—611no—
182C4×C22⋊C8—611no—
183C2×#336D6111yescharacteristic
184#1272—612no—
185#1271—612no—
186C2×C61—24no—
187C2×C61#145911yescharacteristic
188C2×C61C2×Q8⋊C811yescharacteristic
189C2×C61#147611yescharacteristic
190C2×C61C2×#32811yescharacteristic
191C2×C61#150111yescharacteristic
192C2×C61#152411yescharacteristic
193C2×C61#154211yescharacteristic
194C23×C8—21no—
195C2×C22⋊Q8—611no—
196C2×C4×Q8—611no—
197C22×C42C2×D6111yescharacteristic
198C2×C22⋊C8—1221no—
199C2×C4×C8—1221no—
200#391—611no—
201#389—611no—
202#387—1221no—
203#385—1221no—
204#380—611no—
205C4×C4⋊C4—611no—
206C4×C4⋊C4—1221no—
207C4×C22⋊C4—1221no—
208#336—21no—
209#336—612no—
210#336C2×D6112yes—
211C61#756611yescharacteristic, complemented, Sylow
212C22×Q8—611no—
213C23×C4C4×D6111yescharacteristic
214C23×C4D24411yescharacteristic
215C23×C4C22⋊D6111yescharacteristic
216C22×C8—24no—
217C22×C8—22no—
218C22×C8—42no—
219C22×C8—42no—
220C22×C8—1222no—
221C22⋊Q8—614no—
222C22⋊Q8—1222no—
223C4×Q8—2442no—
224C2×C4⋊C4—611no—
225C2×C4⋊C4—611no—
226C2×C4⋊C4—611no—
227C2×C4⋊C4—1221no—
228C2×C4⋊C4—1221no—
229C2×C4⋊C4—1221no—
230C2×C22⋊C4—1221no—
231C2×C22⋊C4—1221no—
232C2×C42—42no—
233C2×C42—1221no—
234C2×C42—1221no—
235C2×C42C4×D6111yescharacteristic
236C2×C42D24411yescharacteristic
237C2×C42C22⋊D6111yescharacteristic
238C2×C42C22×D6111yescharacteristic
239C22⋊C8—1224no—
240C4×C8—2442no—
241#95—1221no—
242#95—1221no—
243#95—1221no—
244#95—1221no—
245#95—1221no—
246C24#1175819811yescharacteristic
247C2×Q8—612no—
248C2×Q8—1221no—
249C2×Q8—2441no—
250C2×Q8—2441no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—1221no—
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4C8×D6112yes—
263C22×C4#1175818912yes—
264C22×C4#1175819811yescharacteristic
265C22×C4#1175819811yescharacteristic
266C22×C4#1175819811yescharacteristic
267C22×C4#1175820012yes—
268C22×C4#1175820212yes—
269C22×C4C2×C4×D6111yescharacteristic
270C22×C4C2×D24411yescharacteristic
271C22×C4C2×C22⋊D6111yescharacteristic
272C2×C8—24no—
273C2×C8—42no—
274C2×C8—48no—
275C2×C8—42no—
276C2×C8—1224no—
277C2×C8—2442no—
278C2×C8—2442no—
279C4⋊C4—612no—
280C4⋊C4—1224no—
281C4⋊C4—1221no—
282C4⋊C4—2441no—
283C4⋊C4—2441no—
284C4⋊C4—2442no—
285C4⋊C4—2442no—
286C22⋊C4—1224no—
287C22⋊C4—2442no—
288C42—22no—
289C42—22no—
290C42—41no—
291C42—41no—
292C42—2442no—
293C42—2442no—
294C23—21no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23#1451968912yes—
299C23#1451970012yes—
300C23#1451970312yes—
301C23C2×#1175819811yescharacteristic
302Q8—2442no—
303Q8—2442no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—24no—
313C2×C4—24no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—44no—
320C2×C4—1222no—
321C2×C4—1222no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4—2441no—
326C2×C4—2441no—
327C2×C4—2441no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4—2441no—
332C2×C4#1451968912yes—
333C2×C4#1451969112yes—
334C2×C4#1451970012yes—
335C2×C4#1451970512yes—
336C2×C4C2×C8×D6111yescharacteristic
337C2×C4C2×#1175818911yescharacteristic
338C2×C4C2×#1175820011yescharacteristic
339C2×C4C2×#1175820211yescharacteristic
340C2×C4#1451979912yes—
341C8—44no—
342C8—2444no—
343C22—22no—
344C22—22no—
345C22—22no—
346C22—22no—
347C22—22no—
348C22—22no—
349C22#1683949214yes—
350C22C2×#1451968911yescharacteristic
351C22C2×#1451969111yescharacteristic
352C22#1683974411yescharacteristic
353C22C2×#1451970011yescharacteristic
354C22#1683975911yescharacteristic
355C22C2×#1451970311yescharacteristic
356C22C2×#1451970511yescharacteristic
357C4—22no—
358C4—21no—
359C4—21no—
360C4—21no—
361C4—21no—
362C4—22no—
363C4—41no—
364C4—4881no—
365C4—4881no—
366C4—2442no—
367C4—2442no—
368C4#1683949814yes—
369C2—24no—
370C2#2144413511yescharacteristic
371C2C2×#1683949211yescharacteristic
372C2#2144420211yescharacteristic
373C2C2×#1683949811yescharacteristic
374C2#2144431111yescharacteristic
375C2#2144440511yescharacteristic
376C2#2144447711yescharacteristic
subgroupG/H
centerC22×C4#11758198
commutatorC2×C4×C61C22×C8
FrattiniC2×C42C22×D61
FittingC2×C61×#336C2
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C42×C61C23
hypercenterC2×#336D61
hypocenterC61#7566
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×#336

Complements

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

NH ≅ G/Ntype
3. #21443644C2semidirect
4. #21443641C2semidirect
26. #14519756C8semidirect
82. C2×Dic122C2×C8semidirect
96. C4⋊Dic61C2×C8semidirect
211. C61#7566semidirect

Maximal subgroups

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

subgroupindex
C4×#145197562
C4×C22⋊#924182
#214436442
#214436412
C2×C61×#3362
#756661