Finite Group Databasebeta

← #29590382

Subgroups — #29590382

Order 15616.

434 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C4×#14519696C211yesmaximal, characteristic, complemented
2#21444143C211yesmaximal, characteristic, complemented
3#21443846C212yesmaximal, complemented
4#21443822C212yesmaximal
5C61×#2398C211yesmaximal, characteristic
6#16839815—21no—
7C2×#14519696—21no—
8C4×#11758194—21no—
9#16839531C2212yes—
10#16839488—21no—
11#16839488C2212yes—
12C2×C4×Q8×C61C2211yescharacteristic
13C2×C4×D4×C61C411yescharacteristic
14C61×#400C411yescharacteristic
15C61×#400C2211yescharacteristic
16C61×#397—21no—
17C61×#394C411yescharacteristic
18C61×#394C2211yescharacteristic
19C61×#393—21no—
20C4×C22⋊C4×C61—21no—
21C4×C22⋊C4×C61—21no—
22C61×#376C411yescharacteristic
23C2×#11758194—22no—
24C4⋊#92418—41no—
25#14519696—24no—
26C22⋊#92418—22no—
27#14519688—41no—
28C4×#92418—41no—
29C4×#92418—41no—
30C22×Q8×C61D411yescharacteristic
31C22×D4×C61C2×C411yescharacteristic
32C23×C4×C61—21no—
33C4×Q8×C61—41no—
34C4×Q8×C61—41no—
35C4×D4×C61—41no—
36C4×D4×C61—41no—
37C2×C4⋊C4×C61C2×C411yescharacteristic
38C2×C4⋊C4×C61C2×C411yescharacteristic
39C2×C4⋊C4×C61D411yescharacteristic
40C2×C4⋊C4×C61C2311yescharacteristic
41C2×C22⋊C4×C61—21no—
42C2×C22⋊C4×C61—21no—
43C2×C22⋊C4×C61—21no—
44C2×C22⋊C4×C61—21no—
45C2×C22⋊C4×C61—21no—
46C2×C42×C61—21no—
47C2×C42×C61C2×C411yescharacteristic
48C2×C42×C61D411yescharacteristic
49C2×C42×C61D411yescharacteristic
50#95×C61—21no—
51#95×C61—21no—
52#95×C61—21no—
53#95×C61—21no—
54#95×C61—21no—
55#95×C61C2×C411yescharacteristic
56#95×C61C2×C411yescharacteristic
57C24×C61—21no—
58C2×Q8×C61—22no—
59C2×Q8×C61—22no—
60C2×Q8×C61—41no—
61C2×D4×C61—41no—
62C2×D4×C61—42no—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—42no—
67C22×C4×C61—42no—
68C22×C4×C61—41no—
69C22×C4×C61—41no—
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61C22⋊C411yescharacteristic
73C22×C4×C61C22⋊C411yescharacteristic
74C22×C4×C61C22×C411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C4⋊C4×C61—41no—
78C4⋊C4×C61—41no—
79C4⋊C4×C61—41no—
80C4⋊C4×C61—41no—
81C22⋊C4×C61—42no—
82C22⋊C4×C61—42no—
83C22⋊C4×C61—42no—
84C22⋊C4×C61—42no—
85C22⋊C4×C61—42no—
86C42×C61—21no—
87C42×C61—21no—
88C42×C61—21no—
89C42×C61—21no—
90C42×C61—21no—
91C42×C61—21no—
92C42×C61—42no—
93#11758194—24no—
94#11758194—42no—
95C2×#92418—42no—
96C2×#92418—42no—
97C23×C61—22no—
98C23×C61—41no—
99C23×C61—41no—
100C23×C61—41no—
101C23×C61—41no—
102C23×C61—41no—
103C23×C61—41no—
104C23×C61C2×C22⋊C411yescharacteristic
105Q8×C61—44no—
106D4×C61—42no—
107D4×C61—42no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—22no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—82no—
132C2×C4×C61—82no—
133C2×C4×C61#9911yescharacteristic
134C2×C4×C61#9911yescharacteristic
135C2×C4×C61#10412yes—
136C2×C4×C61#13512yes—
137#92418—44no—
138#92418—82no—
139#11734—611nomaximal, Sylow
140C22×C61—21no—
141C22×C61—21no—
142C22×C61—42no—
143C22×C61—42no—
144C22×C61—42no—
145C22×C61—81no—
146C22×C61—81no—
147C22×C61—81no—
148C22×C61—81no—
149C22×C61C2×#9911yescharacteristic
150C22×C61#41611yescharacteristic
151C22×C61C2×#10411yescharacteristic
152C4×C61—21no—
153C4×C61—22no—
154C4×C61—22no—
155C4×C61—41no—
156C4×C61—41no—
157C4×C61—41no—
158C4×C61—41no—
159C4×C61—81no—
160C4×C61—81no—
161C4×C61—81no—
162C4×C61#35512yes—
163#2398D6111yescharacteristic
164C4×#101—611no—
165#1461—611no—
166#1353—612no—
167#1345—612no—
168C2×C61—21no—
169C2×C61—21no—
170C2×C61—82no—
171C2×C61#150111yescharacteristic
172C2×C61#212011yescharacteristic
173C2×C61C2×#35511yescharacteristic
174C2×C4×Q8C2×D6111yescharacteristic
175C2×C4×D4Dic6111yescharacteristic
176#431—1221no—
177C2×#101—1221no—
178C4×M16—1221no—
179#400Dic6111yescharacteristic
180#400C2×D6111yescharacteristic
181#397—21no—
182#394Dic6111yescharacteristic
183#394C2×D6111yescharacteristic
184#393—21no—
185C4×C22⋊C4—21no—
186C4×C22⋊C4—21no—
187#376Dic6111yescharacteristic
188#343—612no—
189#324—612no—
190#324—1221no—
191C61#1173411yescharacteristic, complemented, Sylow
192C22×Q8C22⋊D6111yescharacteristic
193C22×D4C2×Dic6111yescharacteristic
194C23×C4—21no—
195C2×M16—1222no—
196C4×Q8—41no—
197C4×Q8—41no—
198C4×D4—41no—
199C4×D4—41no—
200C2×C4⋊C4C2×Dic6111yescharacteristic
201C2×C4⋊C4C2×Dic6111yescharacteristic
202C2×C4⋊C4C22⋊D6111yescharacteristic
203C2×C4⋊C4C22×D6111yescharacteristic
204C2×C22⋊C4—21no—
205C2×C22⋊C4—21no—
206C2×C22⋊C4—21no—
207C2×C22⋊C4—21no—
208C2×C22⋊C4—21no—
209C2×C42—21no—
210C2×C42C2×Dic6111yescharacteristic
211C2×C42C22⋊D6111yescharacteristic
212C2×C42C22⋊D6111yescharacteristic
213C4⋊C8—2441no—
214#101—1224no—
215C22⋊C8—1222no—
216#97—2441no—
217C4×C8—2441no—
218C4×C8—2441no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95C2×Dic6111yescharacteristic
225#95C2×Dic6111yescharacteristic
226C24—21no—
227C2×Q8—22no—
228C2×Q8—22no—
229C2×Q8—41no—
230C2×D4—41no—
231C2×D4—42no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4—41no—
238C22×C4—41no—
239C22×C4C22⋊Dic6111yescharacteristic
240C22×C4C22⋊Dic6111yescharacteristic
241C22×C4C22⋊Dic6111yescharacteristic
242C22×C4C22⋊Dic6111yescharacteristic
243C22×C4C22×Dic6111yescharacteristic
244C22×C4C2×C22⋊D6111yescharacteristic
245C22×C4C2×C22⋊D6111yescharacteristic
246M16—1224no—
247M16—2442no—
248C2×C8—2442no—
249C2×C8—2442no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C22⋊C4—42no—
255C22⋊C4—42no—
256C22⋊C4—42no—
257C22⋊C4—42no—
258C22⋊C4—42no—
259C42—21no—
260C42—21no—
261C42—21no—
262C42—21no—
263C42—21no—
264C42—21no—
265C42—42no—
266C23—22no—
267C23—41no—
268C23—41no—
269C23—41no—
270C23—41no—
271C23—41no—
272C23—41no—
273C23C2×C22⋊Dic6111yescharacteristic
274Q8—44no—
275D4—42no—
276D4—42no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—22no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—82no—
301C2×C4—82no—
302C2×C4#1451969211yescharacteristic
303C2×C4#1451969211yescharacteristic
304C2×C4#1451970412yes—
305C2×C4#1451979712yes—
306C8—4882no—
307C8—2444no—
308C22—21no—
309C22—21no—
310C22—42no—
311C22—42no—
312C22—42no—
313C22—81no—
314C22—81no—
315C22—81no—
316C22—81no—
317C22C2×#1451969211yescharacteristic
318C22#1683975811yescharacteristic
319C22C2×#1451970411yescharacteristic
320C4—21no—
321C4—22no—
322C4—22no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—81no—
328C4—81no—
329C4—81no—
330C4#1683955912yes—
331C2—21no—
332C2—21no—
333C2—82no—
334C2#2144431011yescharacteristic
335C2#2144746011yescharacteristic
336C2C2×#1683955911yescharacteristic
subgroupG/H
centerC2×C4#14519692
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#2398C2
socleC22×C61C2×#99
prime radicalC22×D4×C61C2×C4
cosocleC2×C4⋊C4×C61C23
hypercenter#2398D61
hypocenterC61#11734
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2398

Complements

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

NH ≅ G/Ntype
1. C4×#14519696C2semidirect
2. #21444143C2semidirect
3. #21443846C2semidirect
191. C61#11734semidirect

Maximal subgroups

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

subgroupindex
C4×#145196962
#214441432
#214438462
#214438222
C61×#23982
#1173461