Finite Group Databasebeta

← #30595355

Subgroups — #30595355

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×#14519834C211yesmaximal, characteristic
2#21461480C211yesmaximal, characteristic
3#21460639C212yesmaximal, complemented
4#21460638C212yesmaximal, complemented
5C4×#14519753C211yesmaximal, characteristic
6C22×D61⋊C8—21no—
7C2×#14519834—21no—
8C2×C4×#92420—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519753C411yescharacteristic
13C2×C42×D61C2211yescharacteristic
14#16839669C2211yescharacteristic
15#16839658C2211yescharacteristic
16#16839643—21no—
17#16839633—21no—
18#16839619C411yescharacteristic
19C4×#11758196—21no—
20C4×C4⋊Dic61C411yescharacteristic
21C4×#11758198—21no—
22C2×C4×Q8×C61C411yescharacteristic
23C2×D61⋊C8—24no—
24C2×D61⋊C8—42no—
25C2×D61⋊C8—42no—
26C22×#92420—22no—
27C22×#92420—22no—
28#14519834—24no—
29C4×#92420—42no—
30C22×C4×D61C2×C411yescharacteristic
31C22×C4×D61D411yescharacteristic
32C22×C4×D61D411yescharacteristic
33#14519753—22no—
34#14519753C814yescomplemented
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×C4⋊Dic61C2×C411yescharacteristic
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×C4×Dic61—21no—
42C2×C4×Dic61D411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61C2311yescharacteristic
45C42×D61—42no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51C22×Q8×C61C2×C411yescharacteristic
52C4×Q8×C61—42no—
53C2×C4⋊C4×C61—21no—
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C42×C61—21no—
56C2×C42×C61C2×C411yescharacteristic
57C23×D61C22⋊C411yescharacteristic
58C2×Q8×C61—21no—
59C2×Q8×C61—41no—
60C2×Q8×C61—41no—
61C2×Q8×C61C2×C812yescomplemented
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C22×C411yescharacteristic
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61C22⋊C411yescharacteristic
70C22×Dic61C2×D411yescharacteristic
71C22×Dic61C2×D411yescharacteristic
72C2×C4×D61—22no—
73C2×C4×D61—22no—
74C2×C4×D61—22no—
75C2×C4×D61—22no—
76C2×C4×D61—41no—
77C2×C4×D61—41no—
78C2×C4×D61—41no—
79C2×C4×D61C2×C812yes—
80C2×C4×D61M1612yes—
81C2×C4×D61SD1612yes—
82C2×C4×D61Q1612yes—
83C2×#92420—24no—
84C2×#92420—24no—
85C2×#92420—42no—
86C2×#92420—42no—
87C2×#92420—42no—
88C2×#92420—42no—
89D61⋊C8—48no—
90C4⋊C4×C61—42no—
91C4⋊C4×C61—41no—
92C42×C61—22no—
93C42×C61—42no—
94#11758198—24no—
95#11758198—42no—
96C4⋊Dic61—21no—
97C4⋊Dic61—41no—
98C4⋊Dic61C2×C812yescomplemented
99#11758196—24no—
100#11758196—42no—
101C4×Dic61—22no—
102C4×Dic61—41no—
103C4×Dic61—41no—
104C4×Dic61—42no—
105C23×C61C2×C22⋊C411yescharacteristic
106C22×D61—21no—
107C22×D61—21no—
108C22×D61—21no—
109C22×D61—21no—
110C22×D61C22⋊C812yes—
111C22×D61#10312yes—
112C22×D61#10412yes—
113Q8×C61—42no—
114Q8×C61—42no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—22no—
118C2×C4×C61—21no—
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—41no—
126C2×C4×C61#9912yes—
127C2×C4×C61#10312yes—
128C2×C4×C61#10412yes—
129C2×C4×C61C22×C811yescharacteristic
130C2×C4×C61C2×M1611yescharacteristic
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—22no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61C22⋊C812yes—
144C2×Dic61C2×SD1611yescharacteristic
145C2×Dic61C2×Q1611yescharacteristic
146C2×Dic61#13512yes—
147C4×D61—24no—
148C4×D61—24no—
149C4×D61—42no—
150C4×D61—42no—
151C4×D61—44no—
152#92420—44no—
153#92420—44no—
154#7566—611nomaximal, Sylow
155C22×C61C2×C22⋊C811yescharacteristic
156C22×C61C2×#9911yescharacteristic
157C22×C61#41311yescharacteristic
158C22×C61C2×#10311yescharacteristic
159C22×C61#41611yescharacteristic
160C22×C61C2×#10411yescharacteristic
161C22×C61C2×#10411yescharacteristic
162C2×D61—22no—
163C2×D61—22no—
164C2×D61—22no—
165C2×D61—22no—
166C2×D61—22no—
167C2×D61—22no—
168C2×D61Q8⋊C814yes—
169C4×C61—21no—
170C4×C61—21no—
171C4×C61—42no—
172C4×C61—41no—
173C4×C61—81no—
174C4×C61#32814yes—
175Dic61—22no—
176Dic61—21no—
177Dic61—21no—
178Dic61—22no—
179Dic61—42no—
180Dic61—81no—
181C4×C22⋊Q8—611no—
182C4×C22⋊C8—611no—
183C2×#336—611no—
184#1272—612no—
185#1271—612no—
186C2×C61#145911yescharacteristic
187C2×C61C2×Q8⋊C811yescharacteristic
188C2×C61#147611yescharacteristic
189C2×C61C2×#32811yescharacteristic
190C2×C61#150111yescharacteristic
191C2×C61#152411yescharacteristic
192C2×C61#154211yescharacteristic
193D61—24no—
194C23×C8—1221no—
195C2×C22⋊Q8—611no—
196C2×C4×Q8#692311yescharacteristic
197C22×C42—611no—
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—612no—
209#336—612no—
210#336—1221no—
211C61#756611yescharacteristic, complemented, Sylow
212C22×Q8C2×#692311yescharacteristic
213C23×C4—611no—
214C23×C4—611no—
215C23×C4—611no—
216C22×C8—1222no—
217C22×C8—1222no—
218C22×C8—1224no—
219C22×C8—2442no—
220C22×C8—2442no—
221C22⋊Q8—614no—
222C22⋊Q8—1222no—
223C4×Q8—42no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—611no—
226C2×C4⋊C4—611no—
227C2×C4⋊C4—1221no—
228C2×C4⋊C4—1221no—
229C2×C4⋊C4C2×#692311yescharacteristic
230C2×C22⋊C4—1221no—
231C2×C22⋊C4—1221no—
232C2×C42—21no—
233C2×C42—611no—
234C2×C42—611no—
235C2×C42—611no—
236C2×C42—1221no—
237C2×C42—2442no—
238C2×C42C2×#692311yescharacteristic
239C22⋊C8—1224no—
240C4×C8—2442no—
241#95—1221no—
242#95—1221no—
243#95—1221no—
244#95—1221no—
245#95—1221no—
246C24—611no—
247C2×Q8—21no—
248C2×Q8—41no—
249C2×Q8—41no—
250C2×Q8D61⋊C812yescomplemented
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—611no—
254C22×C4—611no—
255C22×C4—611no—
256C22×C4—612no—
257C22×C4—612no—
258C22×C4—612no—
259C22×C4—612no—
260C22×C4—1222no—
261C22×C4—1222no—
262C22×C4—1222no—
263C22×C4—1222no—
264C22×C4—1221no—
265C22×C4—1221no—
266C22×C4—2441no—
267C22×C4—2441no—
268C22×C4—2441no—
269C22×C4C22⋊#692311yescharacteristic
270C22×C4C22⋊#692311yescharacteristic
271C22×C4C22×#692311yescharacteristic
272C2×C8—1224no—
273C2×C8—1224no—
274C2×C8—2442no—
275C2×C8—2442no—
276C2×C8—2442no—
277C2×C8—2448no—
278C2×C8—2442no—
279C4⋊C4—41no—
280C4⋊C4—42no—
281C4⋊C4—612no—
282C4⋊C4—1224no—
283C4⋊C4—1221no—
284C4⋊C4—2441no—
285C4⋊C4—2442no—
286C22⋊C4—1224no—
287C22⋊C4—2442no—
288C42—22no—
289C42—42no—
290C42—1222no—
291C42—2441no—
292C42—2441no—
293C42—2442no—
294C23—612no—
295C23—612no—
296C23—612no—
297C23—1221no—
298C23—1221no—
299C23—1221no—
300C23—1221no—
301C23C2×C22⋊#692311yescharacteristic
302Q8—42no—
303Q8—42no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—22no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—612no—
316C2×C4—611no—
317C2×C4—611no—
318C2×C4—612no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4—1221no—
324C2×C4—1221no—
325C2×C4—1224no—
326C2×C4—1224no—
327C2×C4—1222no—
328C2×C4—2442no—
329C2×C4—2442no—
330C2×C4—2444no—
331C2×C4—2441no—
332C2×C4—2441no—
333C2×C4—2441no—
334C2×C4—2441no—
335C2×C4—2441no—
336C2×C4#1451983512yes—
337C2×C4#1451984012yes—
338C2×C4#1451984212yes—
339C2×C4C2×D61⋊C811yescharacteristic
340C2×C4D61⋊M1611yescharacteristic
341C8—2444no—
342C8—2444no—
343C22—614no—
344C22—1222no—
345C22—1222no—
346C22—1222no—
347C22—1222no—
348C22—1222no—
349C22—1222no—
350C22D61⋊(C22⋊C8)11yescharacteristic
351C22C2×#1451983511yescharacteristic
352C22#1684074811yescharacteristic
353C22C2×#1451984011yescharacteristic
354C22#1684075211yescharacteristic
355C22D61⋊#10411yescharacteristic
356C22C2×#1451984211yescharacteristic
357C4—21no—
358C4—21no—
359C4—42no—
360C4—41no—
361C4—81no—
362C4—1222no—
363C4—1221no—
364C4—1221no—
365C4—1222no—
366C4—4881no—
367C4—2442no—
368C4#1684061614yes—
369C2—1224no—
370C2#2146105411yescharacteristic
371C2D61⋊(Q8⋊C8)11yescharacteristic
372C2#2146111311yescharacteristic
373C2C2×#1684061611yescharacteristic
374C2#2146119411yescharacteristic
375C2#2146127111yescharacteristic
376C2#2146132011yescharacteristic
subgroupG/H
centerC22×C4C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC2×C4×Q8×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×C4×Q8#6923
hypocenterC61#7566
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
3. #21460639C2semidirect
4. #21460638C2semidirect
34. #14519753C8semidirect
61. C2×Q8×C61C2×C8semidirect
98. C4⋊Dic61C2×C8semidirect
211. C61#7566semidirect
250. C2×Q8D61⋊C8semidirect

Maximal subgroups

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

subgroupindex
C4×#145198342
#214614802
#214606392
#214606382
C4×#145197532
#756661