Finite Group Databasebeta

← #29575100

Subgroups — #29575100

Order 15616.

528 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454383C211yesmaximal, characteristic
2#21449087C211yesmaximal, characteristic
3#21444249C212yesmaximal, complemented
4#21443721C212yesmaximal, complemented
5C61×#1458C211yesmaximal, characteristic
6C22×#11758194—21no—
7C2×C4×Dic122C2211yescharacteristic
8#16839789—24no—
9#16839786—21no—
10#16839786C2212yes—
11#16839701C411yescharacteristic
12#16839698C411yescharacteristic
13#16839695—21no—
14#16839685—21no—
15#16839682C411yescharacteristic
16#16839674C411yescharacteristic
17C4×#11758196—21no—
18C4×C4⋊Dic61C2211yescharacteristic
19C4×C22⋊Dic61—21no—
20#16839494—24no—
21C2×#117×C61C2211yescharacteristic
22C61×#431C2212yes—
23C61×#324—21no—
24C61×#323—21no—
25C22×Dic122C2×C411yescharacteristic
26C2×#11758194—22no—
27C2×#11758194—22no—
28C2×#11758194—42no—
29C2×#11758194—42no—
30C22×#92418—22no—
31C4×Dic122—22no—
32C4×Dic122—22no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61C2×C411yescharacteristic
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×C22⋊Dic61—21no—
39C2×C22⋊Dic61—21no—
40C2×C4×Dic61—21no—
41C2×C4×Dic61—21no—
42C4⋊#92418—24no—
43C4⋊#92418—22no—
44C4⋊#92418D414yes—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684C2×C411yescharacteristic
50#14519684C2×C411yescharacteristic
51C23×C4×C61D411yescharacteristic
52#117×C61—22no—
53#117×C61—22no—
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C4⋊C4×C61D411yescharacteristic
56C2×C22⋊C4×C61C2×C411yescharacteristic
57C2×C22⋊C4×C61D411yescharacteristic
58C2×C42×C61D411yescharacteristic
59C2×C42×C61C2311yescharacteristic
60C4⋊C8×C61—22no—
61C22⋊C8×C61—22no—
62C4×C8×C61—22no—
63C24×C61C22⋊C411yescharacteristic
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61SD1612yes—
72C22×C4×C61Q1612yes—
73C22×C4×C61C22×C411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—21no—
80C2×Dic122—22no—
81C2×Dic122—42no—
82C2×C8×C61—42no—
83C4⋊C4×C61—22no—
84C4⋊C4×C61—22no—
85C22⋊C4×C61—22no—
86C22⋊C4×C61—22no—
87C42×C61—21no—
88C42×C61—21no—
89C42×C61C2×D412yes—
90C42×C61#4112yes—
91C22⋊Dic61—42no—
92C22⋊Dic61—42no—
93C4⋊Dic61—22no—
94C4⋊Dic61—42no—
95#11758196—42no—
96#11758196—42no—
97#11758196—42no—
98C4×Dic61—41no—
99C4×Dic61—41no—
100C4×Dic61—41no—
101C4×Dic61—41no—
102#11758194—44no—
103#11758194—42no—
104#11758194—42no—
105C2×#92418—24no—
106C2×#92418—44no—
107C23×C61—21no—
108C23×C61—21no—
109C23×C61—41no—
110C23×C61—41no—
111C23×C61#10312yes—
112C23×C61C2×C22⋊C411yescharacteristic
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—22no—
116C2×C4×C61—22no—
117C2×C4×C61—22no—
118C2×C4×C61—22no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61#10312yes—
126C2×C4×C61C4×D412yes—
127C2×C4×C61#12011yescharacteristic
128C2×C4×C61#12112yes—
129C2×C4×C61#12311yescharacteristic
130C2×C4×C61C2×SD1611yescharacteristic
131C2×C4×C61C2×Q1611yescharacteristic
132C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C61#13711yescharacteristic
134C2×Dic61—22no—
135C2×Dic61—22no—
136C2×Dic61—41no—
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—
146Dic122—24no—
147Dic122—42no—
148C8×C61—82no—
149#92418—44no—
150#9033—611nomaximal, Sylow
151C22×C61—21no—
152C22×C61—21no—
153C22×C61—22no—
154C22×C61—42no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61—81no—
158C22×C61#38611yescharacteristic
159C22×C61C2×#10311yescharacteristic
160C22×C61#41711yescharacteristic
161C4×C61—22no—
162C4×C61—22no—
163C4×C61—22no—
164C4×C61—41no—
165C4×C61—41no—
166C4×C61#45011yescharacteristic
167C4×C61#45111yescharacteristic
168C4×C61#48311yescharacteristic
169C4×C61#48411yescharacteristic
170Dic61—42no—
171Dic61—42no—
172Dic61—81no—
173Dic61—81no—
174#2905—611no—
175#2396—611no—
176#1487—612no—
177#1458D6111yescharacteristic
178#1303—612no—
179C2×C61—21no—
180C2×C61—21no—
181C2×C61—42no—
182C2×C61#187211yescharacteristic
183C2×C61#188411yescharacteristic
184C2×C61#189111yescharacteristic
185C22×M16—1221no—
186C2×C4×Q8—611no—
187C2×#117C2×D6111yescharacteristic
188#431C2×D6112yes—
189#424—1224no—
190#423—612no—
191#423—1221no—
192#400—611no—
193#399—611no—
194#398—1221no—
195#396—1221no—
196#395—611no—
197#393—611no—
198C4×C4⋊C4—611no—
199C4×C4⋊C4—1221no—
200C4×C22⋊C4—1221no—
201Q8⋊C8—1224no—
202#324—21no—
203#323—21no—
204C61#903311yescharacteristic, complemented, Sylow
205C22×Q8—611no—
206C23×C4D24411yescharacteristic
207C2×M16—1222no—
208C2×M16—1222no—
209C2×M16—2442no—
210C2×M16—2442no—
211C22×C8—1222no—
212C4×Q8—1222no—
213C4×Q8—1222no—
214#117—22no—
215#117—22no—
216C2×C4⋊C4—611no—
217C2×C4⋊C4—1221no—
218C2×C4⋊C4—1221no—
219C2×C4⋊C4—1221no—
220C2×C4⋊C4—1221no—
221C2×C4⋊C4C4×D6111yescharacteristic
222C2×C4⋊C4C22⋊D6111yescharacteristic
223C2×C22⋊C4—1221no—
224C2×C22⋊C4—1221no—
225C2×C22⋊C4C4×D6111yescharacteristic
226C2×C22⋊C4C22⋊D6111yescharacteristic
227C2×C42—1221no—
228C2×C42—1221no—
229C2×C42D24411yescharacteristic
230C2×C42C22×D6111yescharacteristic
231C4⋊C8—22no—
232C4⋊C8—614no—
233C4⋊C8—1224no—
234C4⋊C8—1222no—
235C22⋊C8—22no—
236C4×C8—22no—
237#95—611no—
238#95—611no—
239#95—1221no—
240#95—1221no—
241#95—1221no—
242#95—1221no—
243C24#1175819811yescharacteristic
244C2×Q8—1222no—
245C2×Q8—2442no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—1221no—
251C22×C4—1221no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4#1175819012yes—
255C22×C4Dic24412yes—
256C22×C4#1175819811yescharacteristic
257C22×C4#1175819811yescharacteristic
258C22×C4#1175819811yescharacteristic
259C22×C4C2×C4×D6111yescharacteristic
260C22×C4C2×D24411yescharacteristic
261C22×C4C2×C22⋊D6111yescharacteristic
262M16—2444no—
263M16—2442no—
264M16—2442no—
265C2×C8—42no—
266C2×C8—1224no—
267C2×C8—2444no—
268C4⋊C4—22no—
269C4⋊C4—22no—
270C4⋊C4—1222no—
271C4⋊C4—2442no—
272C4⋊C4—2442no—
273C4⋊C4—2442no—
274C4⋊C4—2442no—
275C22⋊C4—22no—
276C22⋊C4—22no—
277C22⋊C4—2442no—
278C22⋊C4—2442no—
279C42—21no—
280C42—21no—
281C42—2441no—
282C42—2441no—
283C42—2441no—
284C42—2441no—
285C42D4×D6112yes—
286C42#1175822412yes—
287C23—21no—
288C23—21no—
289C23—41no—
290C23—41no—
291C23#1451970212yes—
292C23C2×#1175819811yescharacteristic
293Q8—1224no—
294Q8—2442no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—1222no—
308C2×C4—1222no—
309C2×C4—2441no—
310C2×C4—2441no—
311C2×C4—2441no—
312C2×C4—2441no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4#1451970212yes—
320C2×C4#1451973712yes—
321C2×C4#1451974711yescharacteristic
322C2×C4#1451974912yes—
323C2×C4#1451976111yescharacteristic
324C2×C4C2×#1175819011yescharacteristic
325C2×C4C2×Dic24411yescharacteristic
326C2×C4#1451980511yescharacteristic
327C2×C4#1451981011yescharacteristic
328C8—82no—
329C8—2444no—
330C22—21no—
331C22—21no—
332C22—22no—
333C22—42no—
334C22—41no—
335C22—41no—
336C22—81no—
337C22#1683963911yescharacteristic
338C22C2×#1451970211yescharacteristic
339C22#1683976411yescharacteristic
340C4—22no—
341C4—22no—
342C4—22no—
343C4—41no—
344C4—41no—
345C4—4881no—
346C4—4881no—
347C4—2442no—
348C4—2442no—
349C4#1683991511yescharacteristic
350C4#1683992011yescharacteristic
351C4#1684009311yescharacteristic
352C4#1684009811yescharacteristic
353C2—21no—
354C2—21no—
355C2—42no—
356C2#2144612411yescharacteristic
357C2#2144620011yescharacteristic
358C2#2144623511yescharacteristic
subgroupG/H
centerC2×C4#14519747
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1458C2
socleC22×C61#386
prime radicalC24×C61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1458D61
hypocenterC61#9033
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1458

Complements

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

NH ≅ G/Ntype
3. #21444249C2semidirect
4. #21443721C2semidirect
204. C61#9033semidirect

Maximal subgroups

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

subgroupindex
#214543832
#214490872
#214442492
#214437212
C61×#14582
#903361