Finite Group Databasebeta

← #30595538

Subgroups — #30595538

Order 15616.

494 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 96 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
1#21461735C211yesmaximal, characteristic, complemented
2#21461536C211yesmaximal, characteristic, complemented
3#21460639C212yesmaximal, complemented
4#21460635C212yesmaximal
5#124×Dic61C211yesmaximal, characteristic
6C2×#14519844—21no—
7C2×#14519832—21no—
8#16840628—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×Q8×Dic61C411yescharacteristic
13C2×D4×Dic61C411yescharacteristic
14#16839669C2211yescharacteristic
15#16839665C2211yescharacteristic
16#16839655—21no—
17#16839655—21no—
18#16839628C411yescharacteristic
19C22⋊C4×Dic61—21no—
20C22⋊C4×Dic61—21no—
21C42×Dic61C2211yescharacteristic
22C2×#124×C61C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25#14519844—42no—
26#14519832—24no—
27C23×Dic61—21no—
28Q8×Dic61—42no—
29D4×Dic61—42no—
30C2×C4⋊Dic61—21no—
31C2×C4⋊Dic61C2×C411yescharacteristic
32C2×C4⋊Dic61C2×C411yescharacteristic
33C2×C22⋊Dic61—21no—
34C2×C22⋊Dic61—21no—
35C2×C22⋊Dic61—21no—
36C2×C4×Dic61—21no—
37C2×C4×Dic61C2×C411yescharacteristic
38C2×C4×Dic61D411yescharacteristic
39C2×C4×Dic61D411yescharacteristic
40C2×C4×Dic61D411yescharacteristic
41C2×C4×Dic61D411yescharacteristic
42C2×C4×Dic61C2311yescharacteristic
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47C22×Q8×C61C2×C411yescharacteristic
48C22×D4×C61C2×C411yescharacteristic
49#124×C61—22no—
50#124×C61—22no—
51C2×C22⋊C4×C61—21no—
52C2×C22⋊C4×C61—21no—
53C2×C42×C61C2×C411yescharacteristic
54C24×C61—21no—
55C2×Q8×C61—21no—
56C2×Q8×C61—41no—
57C2×Q8×C61—41no—
58C2×Q8×C61M1612yes—
59C2×D4×C61—21no—
60C2×D4×C61—41no—
61C2×D4×C61—41no—
62C2×D4×C61M1612yes—
63C22×C4×C61—21no—
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C22×C411yescharacteristic
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61—42no—
70C22×Dic61—42no—
71C22×Dic61—42no—
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61C22⋊C411yescharacteristic
74C22×Dic61C2×D411yescharacteristic
75C22×Dic61C2×D411yescharacteristic
76C2×#92420—24no—
77C2×#92420—42no—
78C2×#92420—42no—
79C2×#92420—42no—
80C2×#92420—42no—
81C2×#92420—42no—
82C22⋊C4×C61—24no—
83C22⋊C4×C61—24no—
84C42×C61—21no—
85C42×C61—21no—
86C22⋊Dic61—42no—
87C22⋊Dic61—42no—
88C22⋊Dic61—41no—
89C22⋊Dic61—41no—
90C4⋊Dic61—42no—
91C4⋊Dic61—41no—
92C4⋊Dic61—41no—
93C4×Dic61—22no—
94C4×Dic61—22no—
95C4×Dic61—22no—
96C4×Dic61—21no—
97C4×Dic61—21no—
98C4×Dic61—41no—
99C4×Dic61—41no—
100C4×Dic61—42no—
101C23×C61—22no—
102C23×C61—41no—
103C23×C61—41no—
104C23×C61—41no—
105C23×C61—41no—
106C23×C61—41no—
107C23×C61—41no—
108C23×C61C2×C22⋊C411yescharacteristic
109Q8×C61—42no—
110Q8×C61—42no—
111D4×C61—42no—
112D4×C61—42no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
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—21no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61C2×M1611yescharacteristic
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—84no—
141C2×Dic61#10012yes—
142C2×Dic61#10412yes—
143C2×Dic61#13512yes—
144C2×Dic61AGL(1,ℤ/8)11yescharacteristic
145C2×Dic61#13711yescharacteristic
146#92420—44no—
147#92420—82no—
148#7618—611nomaximal, Sylow
149C22×C61—42no—
150C22×C61—42no—
151C22×C61—42no—
152C22×C61—81no—
153C22×C61—81no—
154C22×C61—81no—
155C22×C61—81no—
156C22×C61#40711yescharacteristic
157C22×C61#41011yescharacteristic
158C22×C61C2×#10011yescharacteristic
159C22×C61#41611yescharacteristic
160C22×C61#41711yescharacteristic
161C22×C61C2×#10411yescharacteristic
162C22×C61#42111yescharacteristic
163C4×C61—21no—
164C4×C61—21no—
165C4×C61—42no—
166C4×C61—41no—
167C4×C61—41no—
168Dic61—22no—
169Dic61—22no—
170Dic61—21no—
171Dic61—21no—
172Dic61—22no—
173Dic61—81no—
174Dic61—81no—
175C4×#124—611no—
176#1831—611no—
177#1745—611no—
178#1272—612no—
179#1270—612no—
180C2×C61—82no—
181C2×C61#146611yescharacteristic
182C2×C61#148811yescharacteristic
183C2×C61#148911yescharacteristic
184C2×C61#150011yescharacteristic
185C2×C61#151211yescharacteristic
186C2×C61#152711yescharacteristic
187C2×C61#155111yescharacteristic
188C2×#124#692311yescharacteristic
189C2×C4×Q8—611no—
190C2×C4×D4—611no—
191C2×C4⋊C8—1221no—
192C2×#97—1221no—
193#391—611no—
194#390—611no—
195#388—1221no—
196#388—1221no—
197#382—611no—
198C4×C22⋊C4—1221no—
199C4×C22⋊C4—1221no—
200C43—611no—
201#336—612no—
202#336—612no—
203#336—1221no—
204#336—1221no—
205C61#761811yescharacteristic, complemented, Sylow
206C22×Q8C2×#692311yescharacteristic
207C22×D4C2×#692311yescharacteristic
208C23×C4—1221no—
209C22×C8—1222no—
210C22×C8—1222no—
211#124—22no—
212#124—22no—
213C4×Q8—2442no—
214C4×D4—2442no—
215C2×C4⋊C4—611no—
216C2×C4⋊C4—611no—
217C2×C4⋊C4—1221no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
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—2442no—
232#97—1224no—
233#95—1221no—
234#95—1221no—
235#95—1221no—
236#95—1221no—
237C24—21no—
238C2×Q8—21no—
239C2×Q8—41no—
240C2×Q8—41no—
241C2×Q8#1175821712yes—
242C2×D4—21no—
243C2×D4—41no—
244C2×D4—41no—
245C2×D4#1175821712yes—
246C22×C4—21no—
247C22×C4—611no—
248C22×C4—611no—
249C22×C4—611no—
250C22×C4—611no—
251C22×C4—1221no—
252C22×C4—1221no—
253C22×C4—2442no—
254C22×C4—2442no—
255C22×C4—2442no—
256C22×C4C22⋊#692311yescharacteristic
257C22×C4C22⋊#692311yescharacteristic
258C22×C4C22×#692311yescharacteristic
259C2×C8—1224no—
260C2×C8—2442no—
261C2×C8—2442no—
262C2×C8—2442no—
263C2×C8—2442no—
264C2×C8—2442no—
265C4⋊C4—2441no—
266C4⋊C4—2441no—
267C4⋊C4—2442no—
268C22⋊C4—24no—
269C22⋊C4—24no—
270C22⋊C4—2442no—
271C22⋊C4—2442no—
272C22⋊C4—2441no—
273C22⋊C4—2441no—
274C42—21no—
275C42—21no—
276C42—1222no—
277C42—1221no—
278C42—1222no—
279C42—1221no—
280C42—1222no—
281C42—2441no—
282C42—2441no—
283C42—2442no—
284C23—22no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23—41no—
291C23C2×C22⋊#692311yescharacteristic
292Q8—42no—
293Q8—42no—
294D4—42no—
295D4—42no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—22no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—612no—
308C2×C4—612no—
309C2×C4—611no—
310C2×C4—611no—
311C2×C4—612no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—1221no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—4884no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4—2441no—
326C2×C4—2441no—
327C2×C4C2×#1175821711yescharacteristic
328C2×C4C2×#1175821711yescharacteristic
329C8—4882no—
330C8—2444no—
331C22—42no—
332C22—42no—
333C22—42no—
334C22—81no—
335C22—81no—
336C22—81no—
337C22—81no—
338C22#1684073211yescharacteristic
339C22#1684074211yescharacteristic
340C22D61⋊#10011yescharacteristic
341C22#1684075211yescharacteristic
342C22#1684075311yescharacteristic
343C22D61⋊#10411yescharacteristic
344C22#1684075911yescharacteristic
345C4—21no—
346C4—21no—
347C4—42no—
348C4—41no—
349C4—41no—
350C4—1222no—
351C4—1222no—
352C4—1222no—
353C4—1221no—
354C4—1221no—
355C4—4881no—
356C4—4881no—
357C2—82no—
358C2#2146107911yescharacteristic
359C2#2146115011yescharacteristic
360C2#2146115411yescharacteristic
361C2#2146119111yescharacteristic
362C2#2146123111yescharacteristic
363C2#2146127911yescharacteristic
364C2#2146133911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#124×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC22×D4×C61C2×C4
cosocleC2×C4×Dic61C23
hypercenterC2×#124#6923
hypocenterC61#7618
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. #21461735C2semidirect
2. #21461536C2semidirect
3. #21460639C2semidirect
205. C61#7618semidirect

Maximal subgroups

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

subgroupindex
#214617352
#214615362
#214606392
#214606352
#124×Dic612
#761861