Finite Group Databasebeta

← #29590347

Subgroups — #29590347

Order 15616.

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

normal subgroups only

This group has 456 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×#14519692C211yesmaximal, characteristic
2#21444140C211yesmaximal, characteristic
3#21443843C212yesmaximal, complemented
4#21443819C212yesmaximal, complemented
5C61×#2395C211yesmaximal, characteristic
6#16839815—21no—
7C2×#14519692—21no—
8C4×C22⋊Dic61—21no—
9#16839529C2212yes—
10#16839486—21no—
11#16839486C2212yes—
12C2×C4×D4×C61C2211yescharacteristic
13C2×#117×C61C411yescharacteristic, complemented
14C61×#400C411yescharacteristic, complemented
15C61×#399C2211yescharacteristic
16C61×#398C411yescharacteristic, complemented
17C61×#397—21no—
18C61×#397C2211yescharacteristic
19C61×#394—21no—
20C4×C4⋊C4×C61—21no—
21C4×C22⋊C4×C61—21no—
22C4×C22⋊C4×C61C411yescharacteristic, complemented
23C2×C22⋊Dic61—22no—
24C2×C4×Dic61—41no—
25C4⋊#92418—41no—
26#14519692—24no—
27C22⋊#92418—22no—
28C4×#92418—41no—
29#14519684—41no—
30C22×D4×C61D411yescharacteristic
31C23×C4×C61C2×C411yescharacteristic
32C23×C4×C61D411yescharacteristic
33C4×D4×C61—41no—
34C4×D4×C61—41no—
35#117×C61—41no—
36#117×C61—41no—
37C2×C4⋊C4×C61—21no—
38C2×C4⋊C4×C61—21no—
39C2×C4⋊C4×C61C2×C411yescharacteristic
40C2×C4⋊C4×C61C2×C411yescharacteristic
41C2×C4⋊C4×C61C2×C411yescharacteristic
42C2×C22⋊C4×C61—21no—
43C2×C22⋊C4×C61—21no—
44C2×C22⋊C4×C61—21no—
45C2×C22⋊C4×C61—21no—
46C2×C22⋊C4×C61D411yescharacteristic
47C2×C22⋊C4×C61C2311yescharacteristic
48C2×C42×C61—21no—
49C2×C42×C61—21no—
50C2×C42×C61D411yescharacteristic
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×C61C22⋊C411yescharacteristic
58C24×C61C2×D411yescharacteristic
59C2×D4×C61—22no—
60C2×D4×C61—22no—
61C2×D4×C61—41no—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—42no—
71C22×C4×C61—42no—
72C22×C4×C61C22⋊C411yescharacteristic
73C22×C4×C61C22⋊C411yescharacteristic
74C22×C4×C61C22⋊C411yescharacteristic
75C22×C4×C61C22×C411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C22×Dic61—42no—
78C4⋊C4×C61—41no—
79C4⋊C4×C61—42no—
80C4⋊C4×C61—41no—
81C4⋊C4×C61—41no—
82C4⋊C4×C61—42no—
83C22⋊C4×C61—41no—
84C22⋊C4×C61—41no—
85C22⋊C4×C61—42no—
86C22⋊C4×C61—42no—
87C22⋊C4×C61—42no—
88C22⋊C4×C61—42no—
89C42×C61—21no—
90C42×C61—21no—
91C42×C61—42no—
92C42×C61—41no—
93C42×C61—41no—
94C22⋊Dic61—24no—
95C22⋊Dic61—42no—
96C4×Dic61—82no—
97C2×#92418—42no—
98C23×C61—21no—
99C23×C61—21no—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61—21no—
103C23×C61—41no—
104C23×C61—41no—
105C23×C61—41no—
106C23×C61—41no—
107C23×C61C2×C22⋊C411yescharacteristic
108C23×C61#13512yes—
109D4×C61—44no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—22no—
113C2×C4×C61—22no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—42no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—42no—
121C2×C4×C61—42no—
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—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—81no—
135C2×C4×C61#9911yescharacteristic
136C2×C4×C61#9911yescharacteristic
137C2×C4×C61#10412yes—
138C2×Dic61—44no—
139C2×Dic61—82no—
140C2×Dic61—82no—
141#92418—82no—
142#11727—611nomaximal, Sylow
143C22×C61—21no—
144C22×C61—21no—
145C22×C61—22no—
146C22×C61—42no—
147C22×C61—41no—
148C22×C61—41no—
149C22×C61—41no—
150C22×C61—41no—
151C22×C61—41no—
152C22×C61—81no—
153C22×C61—81no—
154C22×C61—81no—
155C22×C61C2×#9911yescharacteristic
156C22×C61#41611yescharacteristic
157C22×C61C2×#10411yescharacteristic
158C4×C61—21no—
159C4×C61—22no—
160C4×C61—42no—
161C4×C61—41no—
162C4×C61—41no—
163C4×C61—41no—
164C4×C61—81no—
165C4×C61—81no—
166C4×C61—81no—
167C4×C61#35212yes—
168Dic61—84no—
169#2395D6111yescharacteristic
170C4×#99—611no—
171#1460—611no—
172#1352—612no—
173#1344—612no—
174C2×C61—21no—
175C2×C61—21no—
176C2×C61—42no—
177C2×C61—81no—
178C2×C61#150111yescharacteristic
179C2×C61C2×#35211yescharacteristic
180C2×C61#212611yescharacteristic
181C2×C4×D4C2×D6111yescharacteristic
182C2×#117Dic6111yescharacteristic, complemented
183#431—1221no—
184C2×#99—1221no—
185#400Dic6111yescharacteristic, complemented
186#399C2×D6111yescharacteristic
187#398Dic6111yescharacteristic, complemented
188#397—21no—
189#397C2×D6111yescharacteristic
190#394—21no—
191C4×C4⋊C4—21no—
192C4×C22⋊C4—21no—
193C4×C22⋊C4—1221no—
194C4×C22⋊C4Dic6111yescharacteristic, complemented
195#342—612no—
196#323—612no—
197#323—1221no—
198C61#1172711yescharacteristic, complemented, Sylow
199C22×D4C22⋊D6111yescharacteristic
200C23×C4C2×Dic6111yescharacteristic
201C23×C4C22⋊D6111yescharacteristic
202C4×D4—41no—
203C4×D4—41no—
204#117—41no—
205#117—41no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4C2×Dic6111yescharacteristic
209C2×C4⋊C4C2×Dic6111yescharacteristic
210C2×C4⋊C4C2×Dic6111yescharacteristic
211C2×C22⋊C4—21no—
212C2×C22⋊C4—21no—
213C2×C22⋊C4—21no—
214C2×C22⋊C4—21no—
215C2×C22⋊C4—1222no—
216C2×C22⋊C4C22⋊D6111yescharacteristic
217C2×C22⋊C4C22×D6111yescharacteristic
218C2×C42—21no—
219C2×C42—21no—
220C2×C42—2441no—
221C2×C42C22⋊D6111yescharacteristic
222C4⋊C8—2441no—
223#99—1224no—
224C22⋊C8—1222no—
225C4×C8—2441no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95—21no—
230#95—2441no—
231#95C2×Dic6111yescharacteristic
232#95C2×Dic6111yescharacteristic
233C24C22⋊Dic6111yescharacteristic
234C24C2×C22⋊D6111yescharacteristic
235C2×D4—22no—
236C2×D4—22no—
237C2×D4—41no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4—2442no—
249C22×C4C22⋊Dic6111yescharacteristic
250C22×C4C22⋊Dic6111yescharacteristic
251C22×C4C22⋊Dic6111yescharacteristic
252C22×C4C22×Dic6111yescharacteristic
253C22×C4C2×C22⋊D6111yescharacteristic
254C2×C8—2442no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—42no—
259C4⋊C4—42no—
260C22⋊C4—41no—
261C22⋊C4—41no—
262C22⋊C4—42no—
263C22⋊C4—42no—
264C22⋊C4—42no—
265C22⋊C4—42no—
266C22⋊C4—1224no—
267C22⋊C4—2442no—
268C42—21no—
269C42—21no—
270C42—42no—
271C42—41no—
272C42—41no—
273C42—4882no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23—41no—
283C23C2×C22⋊Dic6111yescharacteristic
284C23#1451979712yes—
285D4—44no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—42no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—81no—
311C2×C4—4882no—
312C2×C4—4882no—
313C2×C4—2444no—
314C2×C4#1451969211yescharacteristic
315C2×C4#1451969211yescharacteristic
316C2×C4#1451970412yes—
317C8—4882no—
318C22—21no—
319C22—21no—
320C22—22no—
321C22—42no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—81no—
328C22—81no—
329C22—81no—
330C22C2×#1451969211yescharacteristic
331C22#1683975811yescharacteristic
332C22C2×#1451970411yescharacteristic
333C4—21no—
334C4—22no—
335C4—42no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—81no—
340C4—81no—
341C4—81no—
342C4—4884no—
343C4#1683955212yes—
344C2—21no—
345C2—21no—
346C2—42no—
347C2—81no—
348C2#2144431011yescharacteristic
349C2C2×#1683955211yescharacteristic
350C2#2144748411yescharacteristic
subgroupG/H
centerC2×C4#14519692
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#2395C2
socleC22×C61C2×#99
prime radicalC22×D4×C61D4
cosocleC2×C22⋊C4×C61C23
hypercenter#2395D61
hypocenterC61#11727
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2395

Complements

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

NH ≅ G/Ntype
3. #21443843C2semidirect
4. #21443819C2semidirect
13. C2×#117×C61C4semidirect
14. C61×#400C4semidirect
16. C61×#398C4semidirect
22. C4×C22⋊C4×C61C4semidirect
182. C2×#117Dic61semidirect
185. #400Dic61semidirect
187. #398Dic61semidirect
194. C4×C22⋊C4Dic61semidirect
198. C61#11727semidirect

Maximal subgroups

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

subgroupindex
C4×#145196922
#214441402
#214438432
#214438192
C61×#23952
#1172761