Finite Group Databasebeta

← #30595331

Subgroups — #30595331

Order 15616.

538 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C4⋊#92420C211yesmaximal, characteristic, complemented
2#21461533C211yesmaximal, characteristic, complemented
3#21460637C212yesmaximal, complemented
4#21460635C212yesmaximal
5#21448284C211yesmaximal, characteristic
6C2×C4⋊#92420—21no—
7C2×C4×#92420—21no—
8C2×C4×#92420—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519736—21no—
13#16839665C411yescharacteristic
14#16839665C2211yescharacteristic
15#16839661C411yescharacteristic
16#16839661C2211yescharacteristic
17#16839655—21no—
18#16839655—21no—
19C4×C4⋊Dic61C411yescharacteristic
20C4×C22⋊Dic61—21no—
21C42×Dic61C2211yescharacteristic
22C2×C4×D4×C61C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25C4⋊#92420—24no—
26C4×#92420—24no—
27C4×#92420—42no—
28#14519736—42no—
29#14519736—42no—
30C2×C4⋊Dic61—21no—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61C2×C411yescharacteristic
33C2×C4⋊Dic61C2×C411yescharacteristic
34C2×C22⋊Dic61—21no—
35C2×C22⋊Dic61—21no—
36C2×C22⋊Dic61—21no—
37C2×C22⋊Dic61—21no—
38C2×C4×Dic61—21no—
39C2×C4×Dic61C2×C411yescharacteristic
40C2×C4×Dic61D411yescharacteristic
41C2×C4×Dic61D411yescharacteristic
42C2×C4×Dic61D411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61C2311yescharacteristic
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48C22×D4×C61C2×C411yescharacteristic
49C23×C4×C61—21no—
50C4×D4×C61—22no—
51C4×D4×C61C814yescomplemented
52C2×C4⋊C4×C61C2×C411yescharacteristic
53C2×C22⋊C4×C61—21no—
54C2×C42×C61C2×C411yescharacteristic
55C24×C61—21no—
56C2×D4×C61—21no—
57C2×D4×C61—41no—
58C2×D4×C61—41no—
59C2×D4×C61C2×C812yes—
60C22×C4×C61—21no—
61C22×C4×C61—24no—
62C22×C4×C61—42no—
63C22×C4×C61—42no—
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C22×C411yescharacteristic
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61C22⋊C411yescharacteristic
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61C2×D411yescharacteristic
72C22×Dic61C2×D411yescharacteristic
73C2×#92420—24no—
74C2×#92420—24no—
75C2×#92420—42no—
76C2×#92420—42no—
77C2×#92420—42no—
78C2×#92420—42no—
79C4⋊C4×C61—21no—
80C4⋊C4×C61C2×C812yes—
81C22⋊C4×C61—24no—
82C42×C61C2×C812yes—
83C42×C61M1612yes—
84C22⋊Dic61—42no—
85C22⋊Dic61—42no—
86C22⋊Dic61—41no—
87C22⋊Dic61—41no—
88C22⋊Dic61—42no—
89C4⋊Dic61—42no—
90C4⋊Dic61—41no—
91C4⋊Dic61—41no—
92C4⋊Dic61—41no—
93C4⋊Dic61—41no—
94C4×Dic61—22no—
95C4×Dic61—22no—
96C4×Dic61—22no—
97C4×Dic61—41no—
98C4×Dic61—41no—
99C4×Dic61—42no—
100C4×Dic61D812yes—
101C4×Dic61SD1612yes—
102C23×C61—22no—
103C23×C61—41no—
104C23×C61—41no—
105C23×C61—41no—
106C23×C61—41no—
107C23×C61—41no—
108C23×C61—41no—
109C23×C61C2×C22⋊C411yescharacteristic
110D4×C61—42no—
111D4×C61—42no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—22no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—48no—
120C2×C4×C61C22⋊C812yes—
121C2×C4×C61C22⋊C812yes—
122C2×C4×C61#10212yes—
123C2×C4×C61#10412yes—
124C2×C4×C61C22×C811yescharacteristic
125C2×C4×C61C2×M1611yescharacteristic
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61#10212yes—
141C2×Dic61#10412yes—
142C2×Dic61C2×D811yescharacteristic
143C2×Dic61C2×SD1611yescharacteristic
144C2×Dic61#13512yes—
145#92420—44no—
146#92420—44no—
147#7560—611nomaximal, Sylow
148C22×C61—42no—
149C22×C61—42no—
150C22×C61—42no—
151C22×C61—81no—
152C22×C61—81no—
153C22×C61—81no—
154C22×C61—81no—
155C22×C61C2×C22⋊C811yescharacteristic
156C22×C61#41011yescharacteristic
157C22×C61#41311yescharacteristic
158C22×C61C2×#10211yescharacteristic
159C22×C61#41611yescharacteristic
160C22×C61C2×#10411yescharacteristic
161C22×C61C2×#10411yescharacteristic
162C4×C61—21no—
163C4×C61—21no—
164C4×C61—22no—
165C4×C61—42no—
166C4×C61D4⋊C814yes—
167Dic61—22no—
168Dic61—22no—
169Dic61—21no—
170Dic61—21no—
171Dic61—22no—
172Dic61—81no—
173Dic61—81no—
174#2293—611no—
175C4×C4⋊C8—611no—
176#1744—611no—
177#1271—612no—
178#1270—612no—
179C2×C61—82no—
180C2×C61#145811yescharacteristic
181C2×C61C2×D4⋊C811yescharacteristic
182C2×C61#147611yescharacteristic
183C2×C61#150011yescharacteristic
184C2×C61#150211yescharacteristic
185C2×C61#152411yescharacteristic
186C2×C61#154011yescharacteristic
187C2×C4×D4#692311yescharacteristic
188C2×#117—1221no—
189C2×C4⋊C8—1221no—
190C2×C4×C8—1221no—
191C2×C4×C8—1221no—
192#390—611no—
193#390—611no—
194#389—611no—
195#389—611no—
196#388—1221no—
197#388—1221no—
198C4×C4⋊C4—611no—
199C4×C22⋊C4—1221no—
200C43—611no—
201#336—612no—
202#336—612no—
203#336—1221no—
204C61#756011yescharacteristic, complemented, Sylow
205C22×D4C2×#692311yescharacteristic
206C23×C4—21no—
207C22×C8—1222no—
208C22×C8—1222no—
209C4×D4—22no—
210C4×D4#9242014yescomplemented
211#117—2442no—
212#117—2442no—
213C2×C4⋊C4—611no—
214C2×C4⋊C4—611no—
215C2×C4⋊C4—1221no—
216C2×C4⋊C4—1221no—
217C2×C4⋊C4C2×#692311yescharacteristic
218C2×C22⋊C4—21no—
219C2×C22⋊C4—1221no—
220C2×C22⋊C4—1221no—
221C2×C22⋊C4—1221no—
222C2×C22⋊C4—1221no—
223C2×C42—611no—
224C2×C42—611no—
225C2×C42—611no—
226C2×C42—611no—
227C2×C42—611no—
228C2×C42—611no—
229C2×C42—1221no—
230C2×C42C2×#692311yescharacteristic
231C4⋊C8—1224no—
232C4×C8—1224no—
233C4×C8—2442no—
234#95—1221no—
235#95—1221no—
236#95—1221no—
237C24—21no—
238C2×D4—21no—
239C2×D4—41no—
240C2×D4—41no—
241C2×D4C2×#9242012yes—
242C22×C4—21no—
243C22×C4—24no—
244C22×C4—42no—
245C22×C4—42no—
246C22×C4—611no—
247C22×C4—611no—
248C22×C4—611no—
249C22×C4—611no—
250C22×C4—1221no—
251C22×C4—1221no—
252C22×C4C22⋊#692311yescharacteristic
253C22×C4C22⋊#692311yescharacteristic
254C22×C4C22×#692311yescharacteristic
255C2×C8—1224no—
256C2×C8—1224no—
257C2×C8—2442no—
258C2×C8—2442no—
259C2×C8—2442no—
260C2×C8—2442no—
261C4⋊C4—21no—
262C4⋊C4—2441no—
263C4⋊C4—2441no—
264C4⋊C4—2442no—
265C4⋊C4—2441no—
266C4⋊C4—2441no—
267C4⋊C4C2×#9242012yes—
268C22⋊C4—24no—
269C22⋊C4—2442no—
270C22⋊C4—2441no—
271C22⋊C4—2441no—
272C22⋊C4—2442no—
273C22⋊C4—2442no—
274C42—612no—
275C42—612no—
276C42—1222no—
277C42—1222no—
278C42—1222no—
279C42—2441no—
280C42—2441no—
281C42—2442no—
282C42C2×#9242012yes—
283C42#1175821712yes—
284C23—22no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23—41no—
291C23C2×C22⋊#692311yescharacteristic
292D4—42no—
293D4—42no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—22no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—48no—
302C2×C4—612no—
303C2×C4—611no—
304C2×C4—611no—
305C2×C4—612no—
306C2×C4—612no—
307C2×C4—1221no—
308C2×C4—1221no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—1221no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—1221no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4—2441no—
320C2×C4—2441no—
321C2×C4C22⋊#9242012yes—
322C2×C4C22⋊#9242012yes—
323C2×C4#1451983912yes—
324C2×C4#1451984112yes—
325C2×C4C22×#9242011yescharacteristic
326C2×C4C2×#1175821711yescharacteristic
327C8—2444no—
328C8—2444no—
329C22—42no—
330C22—42no—
331C22—42no—
332C22—81no—
333C22—81no—
334C22—81no—
335C22—81no—
336C22C2×C22⋊#9242011yescharacteristic
337C22#1684074111yescharacteristic
338C22#1684074811yescharacteristic
339C22C2×#1451983911yescharacteristic
340C22#1684075211yescharacteristic
341C22C2×#1451984111yescharacteristic
342C22D61⋊#10411yescharacteristic
343C4—21no—
344C4—21no—
345C4—22no—
346C4—42no—
347C4—1222no—
348C4—1222no—
349C4—1222no—
350C4—1221no—
351C4—1221no—
352C4—4881no—
353C4—4881no—
354C4D4⋊#9242014yes—
355C2—82no—
356C2#2146105011yescharacteristic
357C2C2×D4⋊#9242011yescharacteristic
358C2#2146111011yescharacteristic
359C2#2146119011yescharacteristic
360C2#2146119811yescharacteristic
361C2#2146126911yescharacteristic
362C2#2146131611yescharacteristic
subgroupG/H
centerC22×C4C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC2×C4×D4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC22×D4×C61C2×C4
cosocleC2×C4×Dic61C23
hypercenterC2×C4×D4#6923
hypocenterC61#7560
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C4×C4⋊#92420C2semidirect
2. #21461533C2semidirect
3. #21460637C2semidirect
51. C4×D4×C61C8semidirect
204. C61#7560semidirect
210. C4×D4#92420semidirect

Maximal subgroups

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

subgroupindex
C4×C4⋊#924202
#214615332
#214606372
#214606352
#214482842
#756061