Finite Group Databasebeta

← #29568112

Subgroups — #29568112

Order 15616.

514 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448300C211yesmaximal, characteristic
2#21445798C211yesmaximal, characteristic
3#21445798C211yesmaximal, characteristic
4#21443643C211yesmaximal, characteristic, complemented
5#21443642C211yesmaximal, characteristic, complemented
6#21443641C211yesmaximal, characteristic, complemented
7C61×#1271C211yesmaximal, characteristic, complemented
8C2×#14519735C411yescharacteristic
9C2×#14519735C411yescharacteristic
10C2×C42×D61C2211yescharacteristic
11C2×#14519706—21no—
12C2×#14519706—21no—
13C2×#14519689—21no—
14C2×#14519689—21no—
15#16839661C411yescharacteristic
16#16839660C2211yescharacteristic
17#16839658C411yescharacteristic
18#16839636—21no—
19#16839633—21no—
20C4⋊C4×Dic61—21no—
21#16839613—21no—
22#16839517C2211yescharacteristic
23#16839517C2211yescharacteristic
24C61×#389C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×C4×D61C2×C411yescharacteristic
28C22×C4×D61D411yescharacteristic
29C22×C4×D61D411yescharacteristic
30C22×#92418—21no—
31C22×#92418—21no—
32#14519735—22no—
33#14519735—42no—
34#14519735C814yescomplemented
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61C2×C411yescharacteristic
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×C4×Dic61—21no—
43C2×C4×Dic61—21no—
44C2×C4×Dic61C2×C411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C42×D61—42no—
48#14519706—42no—
49#14519706—42no—
50#14519689—42no—
51#14519689—42no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55C22×C8×C61—21no—
56C22×C8×C61—21no—
57C2×C4⋊C4×C61—21no—
58C2×C4⋊C4×C61C2×C411yescharacteristic
59C2×C4⋊C4×C61C2×C411yescharacteristic
60C2×C42×C61C2311yescharacteristic
61#95×C61—21no—
62C23×D61C22⋊C411yescharacteristic
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61C22×C411yescharacteristic
66C22×C4×C61C2×D411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61C22⋊C411yescharacteristic
72C22×Dic61C22⋊C411yescharacteristic
73C2×C4×D61—22no—
74C2×C4×D61—22no—
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61—41no—
80C2×C4×D61—41no—
81C2×C4×D61—41no—
82C2×C4×D61—41no—
83C2×C4×D61C2×C812yes—
84C2×C4×D61M1612yes—
85C2×C8×C61—41no—
86C2×C8×C61—41no—
87C2×C8×C61—41no—
88C2×C8×C61—41no—
89C2×C8×C61—41no—
90C2×C8×C61—41no—
91C4⋊C4×C61—21no—
92C4⋊C4×C61—41no—
93C4⋊C4×C61—41no—
94C4⋊C4×C61—41no—
95C4⋊C4×C61C2×C812yes—
96C42×C61—41no—
97#11758198—24no—
98#11758198—42no—
99C4⋊Dic61—21no—
100C4⋊Dic61—42no—
101C4⋊Dic61—41no—
102C4⋊Dic61C2×C812yes—
103#11758196—42no—
104#11758196—41no—
105#11758196—41no—
106C4×Dic61—24no—
107C4×Dic61—22no—
108C4×Dic61—22no—
109C4×Dic61—41no—
110C4×Dic61—42no—
111C2×#92418—41no—
112C2×#92418—41no—
113C2×#92418—41no—
114C2×#92418—41no—
115C2×#92418—41no—
116C2×#92418—41no—
117C23×C61C2×C22⋊C411yescharacteristic
118C22×D61—21no—
119C22×D61—21no—
120C22×D61—21no—
121C22×D61—21no—
122C22×D61—21no—
123C22×D61—21no—
124C22×D61C22⋊C812yes—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—22no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61C22×C811yescharacteristic
138C2×C4×C61C2×M1611yescharacteristic
139C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C61#13711yescharacteristic
142C2×C4×C61#13711yescharacteristic
143C2×Dic61—22no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61C22⋊C812yes—
156C2×Dic61#9912yes—
157C2×Dic61#10112yes—
158C4×D61—24no—
159C4×D61—24no—
160C4×D61—42no—
161C4×D61—42no—
162C4×D61—42no—
163C4×D61—42no—
164C8×C61—81no—
165C8×C61—81no—
166#92418—81no—
167#92418—81no—
168#7598—611nomaximal, Sylow
169C22×C61C2×C22⋊C811yescharacteristic
170C22×C61C2×#9911yescharacteristic
171C22×C61C2×#10111yescharacteristic
172C22×C61#41711yescharacteristic
173C22×C61#41711yescharacteristic
174C22×C61#42111yescharacteristic
175C22×C61#42111yescharacteristic
176C2×D61—22no—
177C2×D61—22no—
178C2×D61—22no—
179C2×D61—41no—
180C2×D61—41no—
181C2×D61—41no—
182C2×D61—41no—
183C4×C61—21no—
184C4×C61—21no—
185C4×C61—21no—
186C4×C61—21no—
187C4×C61—21no—
188C4×C61—21no—
189C4×C61—42no—
190C4×C61—81no—
191Dic61—42no—
192Dic61—41no—
193Dic61—41no—
194Dic61—81no—
195Dic61#32414yes—
196#2296—611no—
197#1797—611no—
198#1797—611no—
199#1271—611no—
200#1271—611no—
201#1271—611no—
202#1271D6111yescharacteristic, complemented
203C2×C61C2×#32411yescharacteristic
204C2×C61#147711yescharacteristic
205C2×C61#147711yescharacteristic
206C2×C61#151311yescharacteristic
207C2×C61#151311yescharacteristic
208C2×C61#153711yescharacteristic
209C2×C61#156111yescharacteristic
210D61—42no—
211C2×#117—611no—
212C2×#117—611no—
213C22×C42—611no—
214C2×C4⋊C8—1221no—
215C2×C4⋊C8—1221no—
216C2×C22⋊C8—1221no—
217C2×C22⋊C8—1221no—
218#389—611no—
219#389—611no—
220#389—611no—
221#389C2×D6111yescharacteristic
222#385—1221no—
223#385—1221no—
224C4×C4⋊C4—1221no—
225C4×C4⋊C4—1221no—
226#336—611no—
227#336—611no—
228#336C2×D6111yescharacteristic
229#336C2×D6111yescharacteristic
230C61#759811yescharacteristic, complemented, Sylow
231C23×C4—611no—
232C23×C4—611no—
233C23×C4—611no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—1221no—
237C22×C8—1221no—
238#117—614no—
239#117—1222no—
240#117—2442no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—611no—
243C2×C4⋊C4—611no—
244C2×C4⋊C4—1221no—
245C2×C4⋊C4—1221no—
246C2×C4⋊C4—1221no—
247C2×C4⋊C4C4×D6111yescharacteristic
248C2×C4⋊C4C4×D6111yescharacteristic
249C2×C22⋊C4—1221no—
250C2×C22⋊C4—1221no—
251C2×C42—611no—
252C2×C42—611no—
253C2×C42—611no—
254C2×C42—1221no—
255C2×C42—1221no—
256C2×C42—2442no—
257C2×C42C22×D6111yescharacteristic
258C4⋊C8—2442no—
259C4⋊C8—2442no—
260C22⋊C8—2442no—
261C22⋊C8—2442no—
262#95—21no—
263#95—1221no—
264#95—1221no—
265#95—1221no—
266C24—611no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—611no—
270C22×C4—612no—
271C22×C4—612no—
272C22×C4—611no—
273C22×C4—611no—
274C22×C4—1222no—
275C22×C4—1222no—
276C22×C4—1221no—
277C22×C4—1221no—
278C22×C4—1221no—
279C22×C4—1221no—
280C22×C4—1221no—
281C22×C4—1221no—
282C22×C4—2441no—
283C22×C4—2441no—
284C22×C4—2441no—
285C22×C4—2441no—
286C22×C4C2×C4×D6111yescharacteristic
287C22×C4D4×D6111yescharacteristic
288C22×C4D4×D6111yescharacteristic
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—2441no—
296C2×C8—2441no—
297C2×C8—2441no—
298C2×C8—2441no—
299C2×C8—2441no—
300C2×C8—2441no—
301C4⋊C4—21no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—612no—
306C4⋊C4—1221no—
307C4⋊C4—2441no—
308C4⋊C4—2442no—
309C4⋊C4—2442no—
310C4⋊C4—2441no—
311C4⋊C4—2441no—
312C4⋊C4C8×D6112yes—
313C22⋊C4—1224no—
314C22⋊C4—2442no—
315C42—41no—
316C42—1222no—
317C42—1222no—
318C42—1224no—
319C42—2441no—
320C42—2442no—
321C23—612no—
322C23—1221no—
323C23—1221no—
324C23—1221no—
325C23—1221no—
326C23—1221no—
327C23—1221no—
328C23C22⋊C4×D6111yescharacteristic
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—22no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—612no—
342C2×C4—612no—
343C2×C4—612no—
344C2×C4—1224no—
345C2×C4—1224no—
346C2×C4—1222no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—1221no—
350C2×C4—1221no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—2442no—
354C2×C4—2442no—
355C2×C4—2442no—
356C2×C4—2442no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4C2×C8×D6111yescharacteristic
363C2×C4M16×D6111yescharacteristic
364C2×C4#1451980111yescharacteristic
365C2×C4#1451980411yescharacteristic
366C2×C4#1451980611yescharacteristic
367C2×C4#1451980911yescharacteristic
368C8—81no—
369C8—81no—
370C8—4881no—
371C8—4881no—
372C22—1222no—
373C22—1222no—
374C22—1222no—
375C22—2441no—
376C22—2441no—
377C22—2441no—
378C22—2441no—
379C22C22⋊C8×D6111yescharacteristic
380C22#99×D6111yescharacteristic
381C22#101×D6111yescharacteristic
382C22#1683976011yescharacteristic
383C22#1683976211yescharacteristic
384C22#1683977711yescharacteristic
385C22#1683977711yescharacteristic
386C4—21no—
387C4—21no—
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—42no—
393C4—81no—
394C4—614no—
395C4—4881no—
396C4—2441no—
397C4—2441no—
398C4—2442no—
399C2—2442no—
400C2#324×D6111yescharacteristic
401C2#2144420311yescharacteristic
402C2#2144420511yescharacteristic
403C2#2144435911yescharacteristic
404C2#2144436111yescharacteristic
405C2#2144445511yescharacteristic
406C2#2144455511yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC2×C4×C61C22×C8
FrattiniC2×C42C22×D61
FittingC61×#1271C2
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1271D61
hypocenterC61#7598
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
4. #21443643C2semidirect
5. #21443642C2semidirect
6. #21443641C2semidirect
7. C61×#1271C2semidirect
34. #14519735C8semidirect
202. #1271D61semidirect
230. C61#7598semidirect

Maximal subgroups

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

subgroupindex
#214483002
#214457982
#214436432
#214436422
#214436412
C61×#12712
#759861