Finite Group Databasebeta

← #30607649

Subgroups — #30607649

Order 15616.

484 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 98 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
1C22×#14519852C211yesmaximal, characteristic
2C2×#16840681C212yesmaximal, complemented
3#21461698C211yesmaximal, characteristic
4#21460893C212yesmaximal, complemented
5#467×D61C211yesmaximal, characteristic
6C2×#14519852—21no—
7C2×#14519852—24no—
8C2×#14519852C2212yes—
9C22×#11758187—21no—
10C2×#14519847C2212yes—
11#16840733—21no—
12#16840681—24no—
13#16840638—21no—
14C2×Q16×D61C2211yescharacteristic
15C22×C8×D61C2211yescharacteristic
16C22⋊Q8×D61—21no—
17#16840004C411yescharacteristic
18#16840003C411yescharacteristic
19#16840002—21no—
20#16840001—21no—
21#16840000C411yescharacteristic
22#107×D61C2211yescharacteristic
23#103×D61—21no—
24C61×#467C411yescharacteristic
25C2×#11758213—22no—
26#14519852—24no—
27#14519852—22no—
28#14519852D414yes—
29C2×#11758187—24no—
30C2×#11758187—22no—
31#14519847—22no—
32#14519847—22no—
33#14519834—41no—
34C22⋊#92420—41no—
35C2×Q8×D61—21no—
36C22×C4×D61D411yescharacteristic
37C2×Dic244C2×C411yescharacteristic
38C2×#11758202—21no—
39Q16×D61—22no—
40Q16×D61—22no—
41C22×#92418D411yescharacteristic
42C2×C8×D61—22no—
43C2×C8×D61—22no—
44C2×C8×D61C2×C411yescharacteristic
45C2×C8×D61D411yescharacteristic
46C2×C8×D61D411yescharacteristic
47C2×C8×D61C2311yescharacteristic
48#14519757—21no—
49#14519756—21no—
50#14519755—41no—
51#14519754—41no—
52#14519753—21no—
53C4⋊C4×D61—21no—
54C4⋊C4×D61—41no—
55C22⋊C4×D61—41no—
56#14519711C2×C411yescharacteristic
57#14519710—21no—
58#14519702—21no—
59#14519701—21no—
60#14519700—21no—
61C2×Q16×C61C2×C411yescharacteristic
62C22×C8×C61C2×C411yescharacteristic
63C22⋊Q8×C61—21no—
64#107×C61C2×C411yescharacteristic
65#103×C61—21no—
66C23×D61SD1611yescharacteristic
67C2×Q8×C61—21no—
68C22×C4×C61C22⋊C411yescharacteristic
69C22×Dic61D811yescharacteristic
70Q8×D61—42no—
71Q8×D61—42no—
72C2×C4×D61—22no—
73C2×C4×D61—22no—
74C2×C4×D61—41no—
75C2×C4×D61—41no—
76C2×C4×D61C22⋊C411yescharacteristic
77C2×C4×D61D811yescharacteristic
78C2×C4×D61SD1611yescharacteristic
79C2×C4×D61C2×D411yescharacteristic
80C2×Dic122—21no—
81C2×Dic122—41no—
82C2×#92420—42no—
83#11758213—42no—
84#11758213—42no—
85Q16×C61—22no—
86C2×C8×C61—22no—
87C2×C8×C61C22⋊C411yescharacteristic
88C2×C8×C61C22×C411yescharacteristic
89C4⋊C4×C61—21no—
90C4⋊C4×C61—41no—
91C22⋊C4×C61—41no—
92C22⋊Dic61—41no—
93#11758202—41no—
94#11758202—41no—
95#11758198—41no—
96#11758198—41no—
97C4⋊Dic61—21no—
98C4⋊Dic61—41no—
99#11758196—41no—
100#11758196—41no—
101#11758196—41no—
102C2×#92418—21no—
103C2×#92418—21no—
104C2×#92418C22⋊C411yescharacteristic
105C2×#92418C2×D411yescharacteristic
106Dic244—22no—
107C8×D61—22no—
108C8×D61—22no—
109C8×D61—21no—
110C8×D61—21no—
111C8×D61C2×D412yes—
112C8×D61#4112yes—
113#11758187—24no—
114C23×C61#10211yescharacteristic
115C22×D61—22no—
116C22×D61—22no—
117C22×D61—41no—
118C22×D61#10211yescharacteristic
119C22×D61C2×SD1611yescharacteristic
120Q8×C61—41no—
121Q8×C61—41no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61#10211yescharacteristic
127C2×C4×C61C2×C22⋊C411yescharacteristic
128C2×Dic61—22no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61#10211yescharacteristic
132C2×Dic61C2×D811yescharacteristic
133C4×D61—22no—
134C4×D61—21no—
135C4×D61—21no—
136C4×D61—22no—
137C4×D61—82no—
138C4×D61—82no—
139C4×D61#12112yes—
140C4×D61#13512yes—
141Dic122—41no—
142Dic122—41no—
143Dic122—82no—
144#92420—82no—
145C8×C61—21no—
146C8×C61C4×D412yes—
147#92418—21no—
148#92418#12011yescharacteristic
149#92418#12311yescharacteristic
150#13066—611nomaximal, Sylow
151C22×C61—21no—
152C22×C61—21no—
153C22×C61#36212yescomplemented
154C22×C61C2×#10211yescharacteristic
155C2×D61—21no—
156C2×D61—21no—
157C2×D61—21no—
158C2×D61—21no—
159C2×D61—21no—
160C2×D61—44no—
161C2×D61#46512yes—
162C4×C61—21no—
163C4×C61—81no—
164C4×C61—81no—
165C4×C61#38611yescharacteristic
166C4×C61#41611yescharacteristic
167Dic61—21no—
168Dic61—81no—
169Dic61—81no—
170Dic61#46612yes—
171C22×M32—611no—
172C2×#467—611no—
173C2×#362—612no—
174#1810—611no—
175#1387—612no—
176C2×C61—22no—
177C2×C61#189311yescharacteristic
178C2×C61C2×#36211yescharacteristic
179C2×C61#214811yescharacteristic
180D61—22no—
181D61—41no—
182C22×Q16—611no—
183C23×C8—611no—
184C2×C22⋊Q8—1221no—
185C2×M32—612no—
186C2×M32—1224no—
187C2×M32—1221no—
188C22×C16—1221no—
189#467—611no—
190#467—611no—
191#467—611no—
192#467—1221no—
193#467—1221no—
194#467#692311yescharacteristic
195C2×#108—612no—
196C2×#107—611no—
197C2×#103—1221no—
198#407—1221no—
199#362—1224no—
200#341—1221no—
201C61#1306611yescharacteristic, complemented, Sylow
202C22×Q8—1221no—
203C23×C4—611no—
204C2×Q16—611no—
205C2×Q16—1222no—
206C2×Q16—1222no—
207C2×Q16—1221no—
208C2×Q16C2×#692311yescharacteristic
209C2×M16—1222no—
210C22×C8—611no—
211C22×C8—611no—
212C22×C8—611no—
213C22×C8—611no—
214C22×C8—611no—
215C22×C8—1222no—
216C22×C8—1222no—
217C22×C8C2×#692311yescharacteristic
218C22⋊Q8—21no—
219C22⋊Q8—1221no—
220C22⋊Q8—1221no—
221C22⋊Q8—1221no—
222C22⋊Q8—2441no—
223C22⋊Q8—2441no—
224C2×C4⋊C4—1221no—
225C2×C4⋊C4—2441no—
226C2×C22⋊C4—2441no—
227M32—614no—
228M32—1222no—
229M32—1224no—
230C2×C16—1222no—
231C2×C16—1224no—
232#108—1222no—
233#108—1222no—
234#107—611no—
235#107—1221no—
236#107C2×#692311yescharacteristic
237#103—21no—
238#103—1221no—
239#103—1221no—
240#103—1221no—
241C22⋊C8—2441no—
242C22⋊C8—2441no—
243C24—611no—
244C2×Q8—21no—
245C2×Q8—1221no—
246C2×Q8—2441no—
247C2×Q8—2442no—
248C2×Q8—2442no—
249C22×C4—611no—
250C22×C4—611no—
251C22×C4—611no—
252C22×C4—611no—
253C22×C4—611no—
254C22×C4—1222no—
255C22×C4—1222no—
256C22×C4—2441no—
257C22×C4—2441no—
258C22×C4C22⋊#692311yescharacteristic
259Q16—22no—
260Q16—1222no—
261Q16—2441no—
262Q16—2441no—
263M16—2442no—
264M16—2442no—
265C2×C8—22no—
266C2×C8—611no—
267C2×C8—612no—
268C2×C8—612no—
269C2×C8—611no—
270C2×C8—1221no—
271C2×C8—1221no—
272C2×C8—1222no—
273C2×C8—1221no—
274C2×C8—1221no—
275C2×C8—1222no—
276C2×C8—2442no—
277C2×C8C22⋊#692311yescharacteristic
278C2×C8C22×#692311yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—41no—
281C4⋊C4—1221no—
282C4⋊C4—2441no—
283C4⋊C4—2441no—
284C4⋊C4—2441no—
285C4⋊C4—2441no—
286C22⋊C4—41no—
287C22⋊C4—2441no—
288C22⋊C4—2441no—
289C22⋊C4—2441no—
290C16—1224no—
291C23—611no—
292C23—611no—
293C23—1222no—
294C23—1222no—
295C23—2441no—
296C23#1451983911yescharacteristic
297Q8—41no—
298Q8—41no—
299Q8—4882no—
300Q8—2441no—
301Q8—2441no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—611no—
307C2×C4—612no—
308C2×C4—612no—
309C2×C4—611no—
310C2×C4—1222no—
311C2×C4—1222no—
312C2×C4—1222no—
313C2×C4—1221no—
314C2×C4—1221no—
315C2×C4—4882no—
316C2×C4—4882no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4#1451983911yescharacteristic
320C2×C4C2×C22⋊#692311yescharacteristic
321C8—21no—
322C8—611no—
323C8—611no—
324C8—1221no—
325C8—4882no—
326C8D4×#692312yes—
327C22—21no—
328C22—21no—
329C22—612no—
330C22—1221no—
331C22—1221no—
332C22—1221no—
333C22—1221no—
334C22—1221no—
335C22—2444no—
336C22#1684068112yescomplemented
337C22C2×#1451983911yescharacteristic
338C4—21no—
339C4—81no—
340C4—81no—
341C4—612no—
342C4—1221no—
343C4—4881no—
344C4—4881no—
345C4#1684071011yescharacteristic
346C4#1684075211yescharacteristic
347C2—22no—
348C2—1222no—
349C2—2441no—
350C2#2146183311yescharacteristic
351C2C2×#1684068111yescharacteristic
352C2#2146214611yescharacteristic
subgroupG/H
centerC22C2×#14519839
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#467C4
socleC22×C61C2×#102
prime radicalC23×D61SD16
cosocleC2×C8×D61C23
hypercenter#467#6923
hypocenterC61#13066
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #467

Complements

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

NH ≅ G/Ntype
2. C2×#16840681C2semidirect
4. #21460893C2semidirect
153. C22×C61#362semidirect
201. C61#13066semidirect
336. C22#16840681semidirect

Maximal subgroups

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

subgroupindex
C22×#145198522
C2×#168406812
#214616982
#214608932
#467×D612
#1306661