Finite Group Databasebeta

← #29571764

Subgroups — #29571764

Order 15616.

998 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 998 conjugacy classes of subgroups — too many to draw. Only its 131 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×#16840417C211yesmaximal, characteristic
2#21445811C211yesmaximal, characteristic, complemented
3#21444499C212yesmaximal, complemented
4#21444245C212yesmaximal, complemented
5C61×#1460C211yesmaximal, characteristic, complemented
6C22×#11758222C412yes—
7#16840417—24no—
8#16840417—24no—
9C2×#14519777C2211yescharacteristic
10C2×#14519759—22no—
11C2×#14519756C412yes—
12C2×#14519748—21no—
13C2×C4×D244C2211yescharacteristic
14C2×C4⋊C4×D61—21no—
15#16839786C2212yes—
16C2×#14519694—21no—
17#16839531—21no—
18#16839510—24no—
19#16839491—24no—
20C2×C4×D4×C61C2211yescharacteristic
21C61×#431C2212yes—
22C61×#323—22no—
23C2×#11758222—24no—
24C2×#11758222—24no—
25C2×#11758222—48no—
26C22×Dic122C2×C412yes—
27C22×D244C2×C411yescharacteristic
28C22×C22⋊D61—22no—
29C22×C4×D61—22no—
30C22×C4×D61—21no—
31C2×#11758194—22no—
32#14519777—22no—
33#14519777D414yes—
34#14519759—216no—
35#14519756—24no—
36#14519756—24no—
37#14519748—28no—
38C4×D244—22no—
39C4×D244D414yes—
40C2×C4⋊Dic61—21no—
41C2×C4⋊Dic61—21no—
42C2×C4⋊Dic61C2×C411yescharacteristic
43C2×#11758196—22no—
44C4⋊C4×D61—28no—
45C2×C22⋊Dic61—22no—
46C2×#11758198—21no—
47C4⋊#92418—22no—
48C4⋊#92418—22no—
49#14519694—42no—
50C22×D4×C61D411yescharacteristic
51C23×C4×C61C2×C412yes—
52C4×D4×C61—22no—
53C4×D4×C61—22no—
54C2×C4⋊C4×C61D411yescharacteristic
55C2×C22⋊C4×C61D412yes—
56C2×C42×C61C2311yescharacteristic
57C4⋊C8×C61—22no—
58C22⋊C8×C61—22no—
59C4×C8×C61—22no—
60C24×C61C22⋊C412yes—
61C23×D61—21no—
62C2×D4×C61—22no—
63C2×D4×C61—22no—
64C2×D4×C61—21no—
65C2×D4×C61—21no—
66C22×C4×C61—22no—
67C22×C4×C61—22no—
68C22×C4×C61—44no—
69C22×C4×C61C22⋊C412yes—
70C22×C4×C61C22×C411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C2×C22⋊D61—28no—
74C2×C22⋊D61—48no—
75C22×Dic61—22no—
76C22×Dic61—21no—
77#11758222—48no—
78#11758222—416no—
79#11758222—48no—
80C2×D244—21no—
81C2×D244—24no—
82C2×D244C22⋊C412yes—
83C2×C4×D61—28no—
84C2×C4×D61—24no—
85C2×C4×D61—48no—
86C2×C4×D61—42no—
87C2×C4×D61—41no—
88C2×C4×D61—41no—
89C2×Dic122—22no—
90C2×Dic122—44no—
91C2×Dic122C22⋊C414yes—
92C2×C8×C61—42no—
93C4⋊C4×C61—22no—
94C22⋊C4×C61—24no—
95C42×C61C2×D412yes—
96C42×C61C2×D412yes—
97C22⋊Dic61—28no—
98#11758198—24no—
99C4⋊Dic61—21no—
100C4⋊Dic61—24no—
101C4⋊Dic61—24no—
102C4⋊Dic61C22⋊C412yes—
103#11758196—28no—
104#11758194—42no—
105#11758194—42no—
106C2×#92418—42no—
107C23×C61—22no—
108C23×C61—22no—
109C23×C61—22no—
110C23×C61—42no—
111C23×C61—42no—
112C23×C61C2×C22⋊C411yescharacteristic
113C22×D61—24no—
114C22×D61—22no—
115C22×D61—42no—
116C22×D61—41no—
117C22×D61—41no—
118D4×C61—42no—
119D4×C61—42no—
120C2×C4×C61—22no—
121C2×C4×C61—22no—
122C2×C4×C61—41no—
123C2×C4×C61—44no—
124C2×C4×C61—44no—
125C2×C4×C61—42no—
126C2×C4×C61C2×C22⋊C411yescharacteristic
127C2×C4×C61C2×C22⋊C411yescharacteristic
128C2×C4×C61#12012yes—
129C2×C4×C61#12012yes—
130C2×C4×C61#13512yes—
131C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C61#13711yescharacteristic
133C22⋊D61—416no—
134C2×Dic61—22no—
135C2×Dic61—24no—
136C2×Dic61—44no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139D244—24no—
140D244—22no—
141D244#10014yescomplemented
142C4×D61—416no—
143C4×D61—44no—
144C4×D61—44no—
145Dic122—44no—
146Dic122—44no—
147C8×C61—82no—
148#92418—82no—
149#8393—611nomaximal, Sylow
150C22×C61—21no—
151C22×C61—21no—
152C22×C61—42no—
153C22×C61—42no—
154C22×C61—42no—
155C22×C61—82no—
156C22×C61—82no—
157C22×C61#37911yescharacteristic
158C22×C61#41611yescharacteristic
159C22×C61#41711yescharacteristic
160C2×D61—24no—
161C2×D61—44no—
162C2×D61—44no—
163C2×D61—42no—
164C2×D61—42no—
165C4×C61—22no—
166C4×C61—21no—
167C4×C61—42no—
168C4×C61C2×#10012yes—
169C4×C61#44912yes—
170C4×C61#45212yes—
171Dic61—44no—
172Dic61—42no—
173C2×#547—611no—
174#1800—611no—
175#1548—612no—
176#1486—612no—
177#1460D6111yescharacteristic, complemented
178C2×C61—21no—
179C2×C61—21no—
180C2×C61—82no—
181C2×C61#178311yescharacteristic
182C2×C61#178811yescharacteristic
183C2×C61#179611yescharacteristic
184D61—44no—
185C22×#41—612no—
186#547—1224no—
187#547—1224no—
188C2×C4⋊Q8—611no—
189C2×#123—1222no—
190C2×C22⋊Q8—612no—
191C2×#121—1221no—
192C2×C4×D4—611no—
193C2×C4×D4C2×D6111yescharacteristic
194C22×C4⋊C4—1221no—
195#431C2×D6112yes—
196#423—612no—
197C2×#100—1221no—
198#343—1221no—
199#333—1224no—
200D4⋊C8—1224no—
201#323—22no—
202C61#839311yescharacteristic, complemented, Sylow
203C2×#41—1224no—
204C2×#41—1224no—
205C2×#41—2448no—
206C22×Q8—612no—
207C22×D4—611no—
208C22×D4—1222no—
209C22×D4D24411yescharacteristic
210C23×C4—1222no—
211C23×C4—1221no—
212C23×C4C4×D6112yes—
213C2×M16—1222no—
214C4⋊Q8—614no—
215C4⋊Q8—1222no—
216#123—12216no—
217C22⋊Q8—1224no—
218C22⋊Q8—1224no—
219#121—1228no—
220C4×D4—22no—
221C4×D4—22no—
222C4×D4—614no—
223C4×D4—1222no—
224C2×C4⋊C4—611no—
225C2×C4⋊C4—1228no—
226C2×C4⋊C4—1222no—
227C2×C4⋊C4—1221no—
228C2×C4⋊C4—1221no—
229C2×C4⋊C4D24411yescharacteristic
230C2×C22⋊C4—1222no—
231C2×C22⋊C4—1221no—
232C2×C22⋊C4C22⋊D6112yes—
233C2×C42C22×D6111yescharacteristic
234C4⋊C8—22no—
235C4⋊C8—1222no—
236C4⋊C8—1222no—
237#100—2442no—
238C22⋊C8—22no—
239C4×C8—22no—
240C24—1221no—
241C24#1175819812yes—
242#41—2448no—
243#41—24416no—
244#41—2448no—
245C2×Q8—614no—
246C2×Q8—1222no—
247C2×Q8—2444no—
248C2×D4—21no—
249C2×D4—22no—
250C2×D4—22no—
251C2×D4—21no—
252C2×D4—612no—
253C2×D4—1224no—
254C2×D4—1228no—
255C2×D4—1221no—
256C2×D4—2448no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—44no—
260C22×C4—1228no—
261C22×C4—1221no—
262C22×C4—1222no—
263C22×C4—1224no—
264C22×C4—2448no—
265C22×C4—2441no—
266C22×C4—2442no—
267C22×C4—2441no—
268C22×C4#1175819812yes—
269C22×C4C2×C4×D6111yescharacteristic
270C22×C4C2×D24411yescharacteristic
271C22×C4C2×C22⋊D6111yescharacteristic
272M16—2442no—
273M16—2442no—
274C2×C8—42no—
275C2×C8—2442no—
276C4⋊C4—22no—
277C4⋊C4—612no—
278C4⋊C4—1228no—
279C4⋊C4—1221no—
280C4⋊C4—1224no—
281C4⋊C4—1224no—
282C22⋊C4—24no—
283C22⋊C4—1228no—
284C22⋊C4—1224no—
285C42D4×D6112yes—
286C42D4×D6112yes—
287C23—22no—
288C23—22no—
289C23—22no—
290C23—42no—
291C23—42no—
292C23—1224no—
293C23—1222no—
294C23—2442no—
295C23—2441no—
296C23—2441no—
297C23C2×#1175819811yescharacteristic
298Q8—2444no—
299Q8—2444no—
300D4—42no—
301D4—42no—
302D4—614no—
303D4—1224no—
304D4—1222no—
305D4—24416no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—41no—
309C2×C4—44no—
310C2×C4—44no—
311C2×C4—42no—
312C2×C4—1222no—
313C2×C4—1224no—
314C2×C4—24416no—
315C2×C4—2444no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4—2444no—
319C2×C4—2444no—
320C2×C4C22⋊C4×D6111yescharacteristic
321C2×C4C22⋊C4×D6111yescharacteristic
322C2×C4#1451974512yes—
323C2×C4#1451974712yes—
324C2×C4#1451979912yes—
325C2×C4#1451980511yescharacteristic
326C2×C4#1451981011yescharacteristic
327C8—82no—
328C8—4882no—
329C22—21no—
330C22—21no—
331C22—42no—
332C22—42no—
333C22—42no—
334C22—82no—
335C22—82no—
336C22—1224no—
337C22—2444no—
338C22—2444no—
339C22—2442no—
340C22—2442no—
341C22#1683961711yescharacteristic
342C22#1683975911yescharacteristic
343C22#1683976411yescharacteristic
344C4—21no—
345C4—22no—
346C4—42no—
347C4—2444no—
348C4—2442no—
349C4#100×D6112yes—
350C4#1683990912yes—
351C4#1683992612yes—
352C2—21no—
353C2—21no—
354C2—82no—
355C2—2444no—
356C2#2144573811yescharacteristic
357C2#2144576011yescharacteristic
358C2#2144579211yescharacteristic
subgroupG/H
centerC22#16839617
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1460C2
socleC22×C61#379
prime radicalC2×#16840417C2
cosocleC2×C42×C61C23
hypercenter#1460D61
hypocenterC61#8393
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1460

Complements

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

NH ≅ G/Ntype
2. #21445811C2semidirect
3. #21444499C2semidirect
4. #21444245C2semidirect
5. C61×#1460C2semidirect
141. D244#100semidirect
177. #1460D61semidirect
202. C61#8393semidirect

Maximal subgroups

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

subgroupindex
C2×#168404172
#214458112
#214444992
#214442452
C61×#14602
#839361