Finite Group Databasebeta

← #29597406

Subgroups — #29597406

Order 15616.

510 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519717C211yesmaximal, characteristic, complemented
2C2×#16839572C212yesmaximal, complemented
3#21445844C211yesmaximal, characteristic, complemented
4#21443924C212yesmaximal, complemented
5C61×#3050C211yesmaximal, characteristic
6C2×#14519717—24no—
7C2×#14519717—21no—
8C2×#14519717C2212yes—
9C22×#11758185—21no—
10C2×#14519709C2212yes—
11#16839622—21no—
12#16839572—24no—
13#16839525—21no—
14C2×#135×C61C2211yescharacteristic
15C23×C8×C61C2211yescharacteristic
16C61×#525—21no—
17C61×#467C411yescharacteristic, complemented
18C61×#467C411yescharacteristic, complemented
19C61×#466C411yescharacteristic, complemented
20C61×#466C411yescharacteristic, complemented
21C61×#465—21no—
22C61×#465—21no—
23C61×#427C2211yescharacteristic
24C61×#416—21no—
25C2×C4⋊Dic61—22no—
26C2×C22⋊Dic61—41no—
27#14519717—24no—
28#14519717—22no—
29#14519717D414yescomplemented
30C2×#11758185—24no—
31C2×#11758185—22no—
32#14519709—22no—
33#14519709—22no—
34#14519684—41no—
35C2×#41×C61—21no—
36C23×C4×C61D411yescharacteristic
37#135×C61—22no—
38#135×C61—22no—
39C2×Q16×C61C2×C411yescharacteristic
40C2×SD16×C61—21no—
41C2×D8×C61C2×C411yescharacteristic
42C22×C8×C61—22no—
43C22×C8×C61—22no—
44C22×C8×C61C2×C411yescharacteristic
45C22×C8×C61C2×C411yescharacteristic
46C22×C8×C61D411yescharacteristic
47C22×C8×C61D411yescharacteristic
48C22×C8×C61D411yescharacteristic
49C22×C8×C61C2311yescharacteristic
50#123×C61—41no—
51C22⋊Q8×C61—21no—
52C22⋊Q8×C61—21no—
53#121×C61—21no—
54#121×C61—21no—
55#120×C61—41no—
56C4×D4×C61—41no—
57C4×D4×C61—41no—
58#117×C61—21no—
59#107×C61C2×C411yescharacteristic
60#107×C61C2×C411yescharacteristic
61#106×C61—21no—
62#103×C61—21no—
63#103×C61—21no—
64#102×C61—21no—
65#102×C61—21no—
66C24×C61D811yescharacteristic
67#41×C61—42no—
68#41×C61—42no—
69C2×Q8×C61—21no—
70C2×D4×C61—21no—
71C2×D4×C61—41no—
72C2×D4×C61—41no—
73C2×D4×C61—41no—
74C22×C4×C61—22no—
75C22×C4×C61—22no—
76C22×C4×C61—41no—
77C22×C4×C61C22⋊C411yescharacteristic
78C22×C4×C61C22⋊C411yescharacteristic
79C22×C4×C61D811yescharacteristic
80C22×C4×C61SD1611yescharacteristic
81C22×C4×C61SD1611yescharacteristic
82C22×C4×C61C2×D411yescharacteristic
83C22×Dic61—42no—
84Q16×C61—22no—
85SD16×C61—41no—
86SD16×C61—41no—
87D8×C61—22no—
88C2×C8×C61—22no—
89C2×C8×C61—22no—
90C2×C8×C61—22no—
91C2×C8×C61—21no—
92C2×C8×C61—21no—
93C2×C8×C61—21no—
94C2×C8×C61—21no—
95C2×C8×C61C22⋊C411yescharacteristic
96C2×C8×C61C22⋊C411yescharacteristic
97C2×C8×C61C22×C411yescharacteristic
98C2×C8×C61C2×D412yes—
99C2×C8×C61C2×D411yescharacteristic
100C2×C8×C61#4112yes—
101C4⋊C4×C61—21no—
102C4⋊C4×C61—21no—
103C4⋊C4×C61—41no—
104C4⋊C4×C61—41no—
105C22⋊C4×C61—41no—
106C22⋊C4×C61—41no—
107C22⋊C4×C61—41no—
108C22⋊C4×C61—41no—
109C22⋊C4×C61—41no—
110C42×C61—41no—
111C22⋊Dic61—82no—
112C4⋊Dic61—42no—
113C4⋊Dic61—42no—
114#11758185—24no—
115C23×C61—22no—
116C23×C61—22no—
117C23×C61—41no—
118C23×C61—41no—
119C23×C61#10211yescharacteristic
120C23×C61#10211yescharacteristic
121C23×C61C2×D811yescharacteristic
122Q8×C61—41no—
123Q8×C61—41no—
124D4×C61—41no—
125D4×C61—41no—
126D4×C61—82no—
127D4×C61—82no—
128D4×C61—82no—
129C2×C4×C61—22no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—22no—
135C2×C4×C61—22no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—82no—
140C2×C4×C61#10211yescharacteristic
141C2×C4×C61#10211yescharacteristic
142C2×C4×C61C2×C22⋊C411yescharacteristic
143C2×C4×C61#12112yes—
144C2×C4×C61C2×SD1611yescharacteristic
145C2×C4×C61#13512yes—
146C2×Dic61—82no—
147C2×Dic61—82no—
148C2×Dic61—82no—
149C8×C61—21no—
150C8×C61—21no—
151C8×C61C4×D412yes—
152C8×C61#12011yescharacteristic
153C8×C61#12311yescharacteristic
154#13065—611nomaximal, Sylow
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—21no—
158C22×C61—21no—
159C22×C61—21no—
160C22×C61—21no—
161C22×C61—21no—
162C22×C61—44no—
163C22×C61—81no—
164C22×C61—81no—
165C22×C61—81no—
166C22×C61#36012yescomplemented
167C22×C61C2×#10211yescharacteristic
168C22×C61#46612yes—
169C4×C61—21no—
170C4×C61—21no—
171C4×C61—81no—
172C4×C61—81no—
173C4×C61—81no—
174C4×C61#38611yescharacteristic
175C4×C61#41611yescharacteristic
176C4×C61#46512yes—
177Dic61—162no—
178C22×M32—611no—
179#3050D6111yescharacteristic
180C2×#360—612no—
181#1807—611no—
182#1386—612no—
183C2×C61—22no—
184C2×C61—22no—
185C2×C61—41no—
186C2×C61—161no—
187C2×C61#189311yescharacteristic
188C2×C61C2×#36011yescharacteristic
189C2×C61#214511yescharacteristic
190C2×#135C2×D6111yescharacteristic
191C23×C8C2×D6111yescharacteristic
192#525—21no—
193C2×M32—612no—
194C2×M32—1224no—
195C2×M32—1221no—
196C22×C16—1221no—
197#467Dic6111yescharacteristic, complemented
198#467Dic6111yescharacteristic, complemented
199#466Dic6111yescharacteristic, complemented
200#466Dic6111yescharacteristic, complemented
201#465—21no—
202#465—21no—
203#427C2×D6111yescharacteristic
204C2×#106—612no—
205#416—21no—
206#380—1221no—
207#360—1224no—
208#340—1221no—
209C61#1306511yescharacteristic, complemented, Sylow
210C2×#41—21no—
211C23×C4C22⋊D6111yescharacteristic
212#135—22no—
213#135—22no—
214C2×Q16C2×Dic6111yescharacteristic
215C2×SD16—21no—
216C2×D8C2×Dic6111yescharacteristic
217C22×C8—22no—
218C22×C8—22no—
219C22×C8C2×Dic6111yescharacteristic
220C22×C8C2×Dic6111yescharacteristic
221C22×C8C22⋊D6111yescharacteristic
222C22×C8C22⋊D6111yescharacteristic
223C22×C8C22⋊D6111yescharacteristic
224C22×C8C22×D6111yescharacteristic
225#123—41no—
226C22⋊Q8—21no—
227C22⋊Q8—21no—
228#121—21no—
229#121—21no—
230#120—41no—
231C4×D4—41no—
232C4×D4—41no—
233#117—21no—
234C2×C4⋊C4—1222no—
235C2×C22⋊C4—2441no—
236M32—614no—
237M32—1224no—
238M32—1222no—
239C2×C16—1224no—
240C2×C16—1222no—
241#107C2×Dic6111yescharacteristic
242#107C2×Dic6111yescharacteristic
243#106—21no—
244#106—1222no—
245#106—1222no—
246#103—21no—
247#103—21no—
248#102—21no—
249#102—21no—
250#95—2441no—
251C24#1175819911yescharacteristic
252#41—42no—
253#41—42no—
254C2×Q8—21no—
255C2×D4—21no—
256C2×D4—41no—
257C2×D4—41no—
258C2×D4—41no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—41no—
262C22×C4—2442no—
263C22×C4#1175819911yescharacteristic
264C22×C4#1175820011yescharacteristic
265C22×C4#1175820011yescharacteristic
266C22×C4C22⋊Dic6111yescharacteristic
267C22×C4C22⋊Dic6111yescharacteristic
268C22×C4C2×C22⋊D6111yescharacteristic
269Q16—22no—
270SD16—41no—
271SD16—41no—
272D8—22no—
273C2×C8—22no—
274C2×C8—22no—
275C2×C8—22no—
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8C22⋊Dic6111yescharacteristic
281C2×C8C22⋊Dic6111yescharacteristic
282C2×C8D4×D6112yes—
283C2×C8#1175822412yes—
284C2×C8C22×Dic6111yescharacteristic
285C2×C8C2×C22⋊D6111yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—2442no—
291C4⋊C4—2442no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—4882no—
298C42—41no—
299C16—1224no—
300C23—22no—
301C23—22no—
302C23—41no—
303C23—41no—
304C23#1451969811yescharacteristic
305C23#1451969811yescharacteristic
306C23C2×#1175819911yescharacteristic
307Q8—41no—
308Q8—41no—
309D4—41no—
310D4—41no—
311D4—82no—
312D4—82no—
313D4—82no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—82no—
325C2×C4—4882no—
326C2×C4—4882no—
327C2×C4—4882no—
328C2×C4#1451969811yescharacteristic
329C2×C4#1451969811yescharacteristic
330C2×C4C2×C22⋊Dic6111yescharacteristic
331C2×C4#1451974912yes—
332C2×C4C2×#1175820011yescharacteristic
333C2×C4#1451979712yes—
334C8—21no—
335C8—21no—
336C8D4×Dic6112yes—
337C8#1451974511yescharacteristic
338C8#1451975811yescharacteristic
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—44no—
347C22—81no—
348C22—81no—
349C22—81no—
350C22#1683957212yescomplemented
351C22C2×#1451969811yescharacteristic
352C22#1683999612yes—
353C4—21no—
354C4—21no—
355C4—81no—
356C4—81no—
357C4—81no—
358C4—9762no—
359C4#1683964211yescharacteristic
360C4#1683975811yescharacteristic
361C4#1683998912yes—
362C2—22no—
363C2—22no—
364C2—41no—
365C2—161no—
366C2#2144624811yescharacteristic
367C2C2×#1683957211yescharacteristic
368C2#2144755511yescharacteristic
subgroupG/H
centerC22C2×#14519698
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
Fitting, prime radicalC61×#3050C2
socleC22×C61C2×#102
cosocleC22×C8×C61C23
hypercenter#3050D61
hypocenterC61#13065
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ #3050

Complements

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

NH ≅ G/Ntype
1. C22×#14519717C2semidirect
2. C2×#16839572C2semidirect
3. #21445844C2semidirect
4. #21443924C2semidirect
17. C61×#467C4semidirect
18. C61×#467C4semidirect
19. C61×#466C4semidirect
20. C61×#466C4semidirect
29. #14519717D4semidirect
166. C22×C61#360semidirect
197. #467Dic61semidirect
198. #467Dic61semidirect
199. #466Dic61semidirect
200. #466Dic61semidirect
209. C61#13065semidirect
350. C22#16839572semidirect

Maximal subgroups

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

subgroupindex
C22×#145197172
C2×#168395722
#214458442
#214439242
C61×#30502
#1306561