Finite Group Databasebeta

← #30597503

Subgroups — #30597503

Order 15616.

582 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 124 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840789C211yesmaximal, characteristic
2#21461556C212yesmaximal, complemented
3#21461057C211yesmaximal, characteristic
4#21460662C212yesmaximal, complemented
5#21445606C211yesmaximal, characteristic
6C22×D61⋊C8C411yescharacteristic, complemented
7C23×#92420C2211yescharacteristic
8#16840789—22no—
9#16840789—22no—
10C2×#14519844C411yescharacteristic, complemented
11C2×#14519834C411yescharacteristic, complemented
12C2×C22⋊#92420C2211yescharacteristic
13C2×C22⋊#92420C2212yes—
14C2×#14519832—22no—
15C2×C4×#92420C411yescharacteristic, complemented
16#16840628—22no—
17#16840608C412yescomplemented
18#16840606C412yescomplemented
19C2×#14519737C2211yescharacteristic
20C2×#14519691C412yes—
21C22⋊C4×Dic61C2212yes—
22#16839529C411yescharacteristic
23C61×#342C411yescharacteristic
24C2×D61⋊C8—21no—
25C2×D61⋊C8—21no—
26C2×D61⋊C8—42no—
27C22×#92420—22no—
28C22×#92420—42no—
29C22×#92420C2×C411yescharacteristic
30C22×#92420C2×C411yescharacteristic
31C22×#92420C2×C411yescharacteristic
32C22×#92420C2×C411yescharacteristic
33C22×#92420D412yes—
34C22×#92420D412yes—
35#14519844—22no—
36#14519834—22no—
37C22⋊#92420—22no—
38C22⋊#92420—22no—
39C22⋊#92420C2×C414yes—
40#14519832—44no—
41C4×#92420—21no—
42C4×#92420—21no—
43C22×C22⋊D61C2×C411yescharacteristic
44C23×Dic61C2311yescharacteristic
45C22×C4×D61C2×C411yescharacteristic
46#14519737—22no—
47#14519737—22no—
48C2×#11758196C2×C411yescharacteristic
49C2×C22⋊Dic61C2×C412yes—
50C2×#11758198C2×C411yescharacteristic
51C2×C4×Dic61—22no—
52C2×C4×Dic61C2×C411yescharacteristic
53#14519691—24no—
54#14519684—22no—
55C2×C22⋊C4×C61C2×C412yes—
56C2×C22⋊C4×C61C2×C411yescharacteristic
57C24×C61C22×C411yescharacteristic
58C23×D61C4211yescharacteristic
59C22×C4×C61—22no—
60C22×C4×C61C4211yescharacteristic
61C22×C4×C61C4211yescharacteristic
62C2×C22⋊D61—22no—
63C2×C22⋊D61—21no—
64C2×C22⋊D61—21no—
65C2×C22⋊D61M1614yes—
66C22×Dic61—22no—
67C22×Dic61—41no—
68C22×Dic61—41no—
69C22×Dic61C4211yescharacteristic
70C22×Dic61C22×C411yescharacteristic
71C22×Dic61C22×C411yescharacteristic
72C22×Dic61C2×D412yes—
73C22×Dic61#4112yes—
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×C4×D61—41no—
77C2×C4×D61—41no—
78C2×#92420—24no—
79C2×#92420—22no—
80C2×#92420—21no—
81C2×#92420—21no—
82C2×#92420—24no—
83C2×#92420—41no—
84C2×#92420—42no—
85C2×#92420—42no—
86C2×#92420—42no—
87C2×#92420—41no—
88C2×#92420—41no—
89C2×#92420C22⋊C411yescharacteristic
90C2×#92420C22⋊C412yes—
91C2×#92420C22⋊C411yescharacteristic
92D61⋊C8—42no—
93D61⋊C8—42no—
94C22⋊C4×C61—22no—
95C22⋊C4×C61—22no—
96C22⋊C4×C61—22no—
97C22⋊Dic61—22no—
98C22⋊Dic61—22no—
99#11758198—22no—
100#11758196—22no—
101C4×Dic61—21no—
102C4×Dic61—21no—
103C4×Dic61—42no—
104C4×Dic61—42no—
105C23×C61—41no—
106C23×C61—41no—
107C23×C61C2×C4211yescharacteristic
108C23×C61C4×D412yes—
109C23×C61C2×M1612yes—
110C23×C61#13111yescharacteristic
111C23×C61#13111yescharacteristic
112C22×D61—21no—
113C22×D61—21no—
114C22×D61—41no—
115C22×D61—41no—
116C22×D61#9712yescomplemented
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—42no—
122C2×C4×C61—42no—
123C2×C4×C61—42no—
124C22⋊D61—24no—
125C22⋊D61—24no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—22no—
129C2×Dic61—21no—
130C2×Dic61—22no—
131C2×Dic61—21no—
132C2×Dic61—41no—
133C2×Dic61—42no—
134C2×Dic61—42no—
135C2×Dic61—42no—
136C2×Dic61—42no—
137C2×Dic61#9712yescomplemented
138C2×Dic61C2×C22⋊C411yescharacteristic
139C2×Dic61#11711yescharacteristic
140C2×Dic61C4×D412yes—
141C4×D61—42no—
142C4×D61—41no—
143C4×D61—41no—
144#92420—21no—
145#92420—22no—
146#92420—44no—
147#92420—41no—
148#92420—41no—
149#92420#9912yescomplemented
150#8160—611nomaximal, Sylow
151C22×C61—22no—
152C22×C61—21no—
153C22×C61—22no—
154C22×C61—21no—
155C22×C61—42no—
156C22×C61—41no—
157C22×C61—41no—
158C22×C61C4×C22⋊C411yescharacteristic
159C22×C61C2×#9711yescharacteristic
160C22×C61#40511yescharacteristic
161C22×C61#43512yes—
162C22×C61#43512yes—
163C2×D61—22no—
164C2×D61—42no—
165C2×D61—41no—
166C2×D61—41no—
167C2×D61—42no—
168C4×C61—41no—
169C4×C61—41no—
170C4×C61—82no—
171Dic61—22no—
172Dic61—22no—
173Dic61—21no—
174Dic61—82no—
175Dic61C2×#9911yescharacteristic
176Dic61#41011yescharacteristic
177C2×C8×D4—611no—
178C4×#99—611no—
179#1752—612no—
180#1459—611no—
181#1282—612no—
182C2×C61—22no—
183C2×C61—22no—
184C2×C61—21no—
185C2×C61—21no—
186C2×C61#175211yescharacteristic
187C2×C61C4×#9911yescharacteristic
188C2×C61#175711yescharacteristic
189D61—42no—
190C23×C8—611no—
191C23×C8—611no—
192C2×C4×D4—611no—
193C8×D4—1222no—
194C8×D4—1222no—
195C2×C4⋊C8—611no—
196C2×#99—612no—
197C2×C22⋊C8—612no—
198C2×C22⋊C8—611no—
199C2×C22⋊C8—611no—
200C2×#97—1222no—
201C2×C4×C8—611no—
202C4×C22⋊C4—612no—
203#342—611no—
204#342#692311yescharacteristic
205#336—1222no—
206#324—612no—
207#323—612no—
208C61#816011yescharacteristic, complemented, Sylow
209C22×D4—611no—
210C23×C4—611no—
211C23×C4—611no—
212C22×C8—611no—
213C22×C8—612no—
214C22×C8—611no—
215C22×C8—612no—
216C22×C8—611no—
217C22×C8—611no—
218C22×C8—1221no—
219C22×C8—1221no—
220C22×C8—1222no—
221C22×C8—2442no—
222C22×C8—2442no—
223C4×D4—1222no—
224C4×D4—1222no—
225C2×C4⋊C4—611no—
226C2×C22⋊C4—611no—
227C2×C22⋊C4—612no—
228C2×C22⋊C4C2×#692312yes—
229C2×C22⋊C4C2×#692311yescharacteristic
230C2×C42—611no—
231C2×C42—1222no—
232C4⋊C8—1222no—
233#99—1224no—
234C22⋊C8—614no—
235C22⋊C8—1222no—
236C22⋊C8—1222no—
237C22⋊C8—1222no—
238#97—2444no—
239C4×C8—1221no—
240C4×C8—1221no—
241#95—1222no—
242C24—611no—
243C24C22×#692311yescharacteristic
244C2×D4—614no—
245C2×D4—1222no—
246C2×D4—1221no—
247C2×D4—1221no—
248C22×C4—22no—
249C22×C4—611no—
250C22×C4—611no—
251C22×C4—612no—
252C22×C4—611no—
253C22×C4—612no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4—1222no—
257C22×C4—2441no—
258C22×C4—2441no—
259C22×C4—2441no—
260C22×C4—2441no—
261C22×C4C4×#692311yescharacteristic
262C22×C4C4×#692311yescharacteristic
263C2×C8—611no—
264C2×C8—611no—
265C2×C8—612no—
266C2×C8—1224no—
267C2×C8—1222no—
268C2×C8—1221no—
269C2×C8—1224no—
270C2×C8—1221no—
271C2×C8—2442no—
272C2×C8—2441no—
273C2×C8—2442no—
274C2×C8—2442no—
275C2×C8—2442no—
276C2×C8—2442no—
277C2×C8—2441no—
278C2×C8—2441no—
279C4⋊C4—1222no—
280C22⋊C4—22no—
281C22⋊C4—22no—
282C22⋊C4—22no—
283C22⋊C4—1222no—
284C22⋊C4—1222no—
285C22⋊C4—1222no—
286C42—1221no—
287C42—1221no—
288C42—2442no—
289C42—2442no—
290C23—41no—
291C23—41no—
292C23—612no—
293C23—1221no—
294C23—1221no—
295C23—2441no—
296C23—2441no—
297C23C2×C4×#692311yescharacteristic
298C23D4×#692312yes—
299C23D61⋊M1612yes—
300C23#1451986411yescharacteristic
301C23#1451986511yescharacteristic
302D4—1224no—
303D4—1224no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—611no—
312C2×C4—612no—
313C2×C4—611no—
314C2×C4—612no—
315C2×C4—1222no—
316C2×C4—1222no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4—2442no—
324C2×C4—2441no—
325C2×C4—2442no—
326C2×C4—2442no—
327C2×C4—2442no—
328C2×C4—2442no—
329C8—612no—
330C8—1222no—
331C8—1221no—
332C8—2441no—
333C8—2441no—
334C8—2444no—
335C22—22no—
336C22—21no—
337C22—22no—
338C22—21no—
339C22—42no—
340C22—41no—
341C22—41no—
342C22—1222no—
343C22—2442no—
344C22—2442no—
345C22—2441no—
346C22—2441no—
347C22C22⋊C4×#692311yescharacteristic
348C22#1684072111yescharacteristic
349C22#1684072711yescharacteristic
350C22#1684079212yes—
351C22#1684079412yes—
352C4—41no—
353C4—41no—
354C4—82no—
355C4—611no—
356C4—611no—
357C4—1222no—
358C4—1222no—
359C4—1221no—
360C4—4882no—
361C2—22no—
362C2—22no—
363C2—21no—
364C2—21no—
365C2—2442no—
366C2#2146155711yescharacteristic
367C2#99×#692311yescharacteristic
368C2#2146157711yescharacteristic
subgroupG/H
centerC22C22⋊C4×#6923
commutatorC23×C61C2×C42
FrattiniC24C22×#6923
FittingC61×#342C4
socleC22×C61C4×C22⋊C4
prime radicalC22×C22⋊D61C2×C4
cosocleC23×Dic61C23
hypercenter#342#6923
hypocenterC61#8160
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
2. #21461556C2semidirect
4. #21460662C2semidirect
6. C22×D61⋊C8C4semidirect
10. C2×#14519844C4semidirect
11. C2×#14519834C4semidirect
15. C2×C4×#92420C4semidirect
17. #16840608C4semidirect
18. #16840606C4semidirect
116. C22×D61#97semidirect
137. C2×Dic61#97semidirect
149. #92420#99semidirect
208. C61#8160semidirect

Maximal subgroups

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

subgroupindex
C2×#168407892
#214615562
#214610572
#214606622
#214456062
#816061