Finite Group Databasebeta

← #29578317

Subgroups — #29578317

Order 15616.

446 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21446612C211yesmaximal, characteristic
2#21446535C211yesmaximal, characteristic, complemented
3C4×#14519699C211yesmaximal, characteristic
4C2×#16839489C211yesmaximal, characteristic
5C2×#16839484C211yesmaximal, characteristic, complemented
6#21443658C211yesmaximal, characteristic, complemented
7C61×#1277C211yesmaximal, characteristic, complemented
8C2×C4×D244C2211yescharacteristic
9C2×#14519706—21no—
10C2×#14519699C411yescharacteristic
11C2×#14519699C411yescharacteristic
12C2×#14519689—21no—
13C2×#14519689—21no—
14C2×C4×#92418C2211yescharacteristic
15C2×C4×#92418C2211yescharacteristic
16C4×C4⋊Dic61C2211yescharacteristic
17#16839525C411yescharacteristic
18#16839525C411yescharacteristic
19#16839516—21no—
20#16839489—22no—
21#16839484—22no—
22C2×C4⋊C8×C61C2211yescharacteristic
23C2×C4⋊C8×C61C2211yescharacteristic
24C2×C4×C8×C61C2211yescharacteristic
25C22×D244C2×C411yescharacteristic
26C22×C4×D61—21no—
27C22×#92418—21no—
28C22×#92418D411yescharacteristic
29C22×#92418D411yescharacteristic
30C4×D244—21no—
31C4×D244—21no—
32C4×D244—21no—
33C4×D244—21no—
34C2×C4⋊Dic61C2×C411yescharacteristic
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×C4⋊Dic61C2×C411yescharacteristic
37C2×#11758198—21no—
38C2×C4×Dic61—21no—
39#14519706—42no—
40#14519699—22no—
41#14519699—22no—
42#14519689—42no—
43#14519689—42no—
44C4×#92418—21no—
45C4×#92418—21no—
46C4×#92418—21no—
47C4×#92418D412yes—
48#14519684—21no—
49C22×C8×C61—21no—
50C22×C8×C61—21no—
51C22×C8×C61C2×C411yescharacteristic
52C22×C8×C61C2×C411yescharacteristic
53C2×C42×C61C2311yescharacteristic
54C4⋊C8×C61—21no—
55C4⋊C8×C61—21no—
56C4⋊C8×C61—21no—
57C4⋊C8×C61—21no—
58C4×C8×C61—21no—
59C4×C8×C61—21no—
60C23×D61—21no—
61C22×C4×C61C22×C411yescharacteristic
62C22×C4×C61C2×D411yescharacteristic
63C22×C4×C61#4111yescharacteristic
64C22×Dic61—21no—
65C22×Dic61—21no—
66C22×Dic61—21no—
67C2×D244—21no—
68C2×D244—21no—
69C2×D244—21no—
70C2×D244—21no—
71C2×D244—21no—
72C2×D244M1612yes—
73C2×C4×D61—41no—
74C2×C4×D61—41no—
75C2×C4×D61—41no—
76C2×C4×D61—41no—
77C2×C4×D61—41no—
78C2×C4×D61—41no—
79C2×C8×C61—21no—
80C2×C8×C61—21no—
81C2×C8×C61—21no—
82C2×C8×C61—21no—
83C2×C8×C61—21no—
84C2×C8×C61—21no—
85C2×C8×C61—41no—
86C2×C8×C61—41no—
87C2×C8×C61—41no—
88C2×C8×C61—41no—
89C2×C8×C61—41no—
90C2×C8×C61—41no—
91C42×C61C2×D411yescharacteristic
92C42×C61#4111yescharacteristic
93C42×C61#4111yescharacteristic
94C42×C61#4111yescharacteristic
95#11758198—41no—
96#11758198—41no—
97C4⋊Dic61—21no—
98C4⋊Dic61—21no—
99C4⋊Dic61—21no—
100C4⋊Dic61—21no—
101C4⋊Dic61—21no—
102C4⋊Dic61M1612yes—
103C4×Dic61—41no—
104C4×Dic61—41no—
105C2×#92418—22no—
106C2×#92418—22no—
107C2×#92418—22no—
108C2×#92418—21no—
109C2×#92418—21no—
110C2×#92418—21no—
111C2×#92418—21no—
112C2×#92418—21no—
113C2×#92418—21no—
114C23×C61C4×D411yescharacteristic
115C22×D61—22no—
116C22×D61—41no—
117C22×D61—41no—
118C22×D61—41no—
119C22×D61—41no—
120C22×D61—41no—
121C22×D61—41no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61#11711yescharacteristic
125C2×C4×C61C4×D411yescharacteristic
126C2×C4×C61#12111yescharacteristic
127C2×C4×C61#12311yescharacteristic
128C2×C4×C61#12411yescharacteristic
129C2×C4×C61#12611yescharacteristic
130C2×C4×C61C2×M1611yescharacteristic
131C2×C4×C61C2×M1611yescharacteristic
132C2×C4×C61#13111yescharacteristic
133C2×C4×C61#13111yescharacteristic
134C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C61#13711yescharacteristic
138C2×Dic61—22no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147D244—22no—
148D244—22no—
149D244—41no—
150D244—41no—
151C4×D61—81no—
152C4×D61—81no—
153C4×D61—81no—
154C4×D61—81no—
155C8×C61—41no—
156C8×C61—41no—
157C8×C61—81no—
158C8×C61—81no—
159#92418—24no—
160#92418—41no—
161#92418—41no—
162#9560—611nomaximal, Sylow
163C22×C61#38811yescharacteristic
164C22×C61#43511yescharacteristic
165C22×C61#43511yescharacteristic
166C22×C61#44011yescharacteristic
167C22×C61#44211yescharacteristic
168C22×C61#44311yescharacteristic
169C22×C61#44311yescharacteristic
170C2×D61—42no—
171C2×D61—42no—
172C2×D61—42no—
173C2×D61—81no—
174C2×D61—81no—
175C2×D61—81no—
176C2×D61—81no—
177C4×C61—21no—
178C4×C61—21no—
179C4×C61#43211yescharacteristic
180C4×C61#43311yescharacteristic
181C4×C61#43511yescharacteristic
182C4×C61#43611yescharacteristic
183C4×C61#46811yescharacteristic
184C4×C61#46911yescharacteristic
185C4×C61#48911yescharacteristic
186C4×C61#49011yescharacteristic
187Dic61—42no—
188Dic61—81no—
189Dic61—81no—
190#1954—611no—
191#1939—611no—
192C4×#102—611no—
193C2×D4⋊C8—611no—
194C2×#322—611no—
195#1279—611no—
196#1277D6111yescharacteristic, complemented
197C2×C61#158511yescharacteristic
198C2×C61#158611yescharacteristic
199C2×C61#158611yescharacteristic
200C2×C61#158811yescharacteristic
201C2×C61#192411yescharacteristic
202C2×C61#193611yescharacteristic
203C2×C61#193711yescharacteristic
204D61—82no—
205C2×C4×D4—611no—
206C2×C4⋊C8—1221no—
207C2×C4⋊C8C2×D6111yescharacteristic
208C2×C4⋊C8C2×D6111yescharacteristic
209C2×#102—611no—
210C2×#102—611no—
211C2×C22⋊C8—1221no—
212C2×C22⋊C8—1221no—
213C2×C4×C8—611no—
214C2×C4×C8—611no—
215C2×C4×C8C2×D6111yescharacteristic
216C4×C4⋊C4—611no—
217#340—611no—
218#340—611no—
219#336—1221no—
220D4⋊C8—1222no—
221#322—1222no—
222C61#956011yescharacteristic, complemented, Sylow
223C22×D4—611no—
224C23×C4—1221no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—611no—
228C22×C8—611no—
229C22×C8—1221no—
230C22×C8C4×D6111yescharacteristic
231C22×C8C4×D6111yescharacteristic
232C4×D4—1221no—
233C4×D4—1221no—
234C4×D4—1221no—
235C4×D4—1221no—
236C2×C4⋊C4—611no—
237C2×C4⋊C4—611no—
238C2×C4⋊C4—611no—
239C2×C22⋊C4—1221no—
240C2×C42—1221no—
241C2×C42C22×D6111yescharacteristic
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8—2442no—
247#102—1222no—
248#102—1222no—
249C22⋊C8—2442no—
250C22⋊C8—2442no—
251C4×C8—21no—
252C4×C8—21no—
253C4×C8—612no—
254C4×C8—1221no—
255C4×C8—1221no—
256C4×C8—1221no—
257#95—1221no—
258C24—1221no—
259C2×D4—612no—
260C2×D4—1221no—
261C2×D4—1221no—
262C2×D4—1221no—
263C2×D4—1221no—
264C2×D4—1221no—
265C22×C4—1221no—
266C22×C4—1221no—
267C22×C4—1221no—
268C22×C4—2441no—
269C22×C4—2441no—
270C22×C4—2441no—
271C22×C4—2441no—
272C22×C4—2441no—
273C22×C4—2441no—
274C22×C4C2×C4×D6111yescharacteristic
275C22×C4D4×D6111yescharacteristic
276C22×C4#1175822611yescharacteristic
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—1222no—
290C2×C8—1222no—
291C2×C8—1222no—
292C2×C8—1221no—
293C2×C8—1221no—
294C2×C8—1221no—
295C2×C8—1221no—
296C2×C8—1221no—
297C2×C8—1221no—
298C4⋊C4—612no—
299C4⋊C4—1221no—
300C4⋊C4—1221no—
301C4⋊C4—1221no—
302C4⋊C4—1221no—
303C4⋊C4—1221no—
304C22⋊C4—2441no—
305C22⋊C4—2441no—
306C42—2441no—
307C42—2441no—
308C42#1175822211yescharacteristic
309C42#1175822211yescharacteristic
310C42D4×D6111yescharacteristic
311C42#1175822411yescharacteristic
312C23—1222no—
313C23—2441no—
314C23—2441no—
315C23—2441no—
316C23—2441no—
317C23—2441no—
318C23—2441no—
319C23#1451973911yescharacteristic
320D4—1222no—
321D4—1222no—
322D4—2441no—
323D4—2441no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—1222no—
327C2×C4—4881no—
328C2×C4—4881no—
329C2×C4—4881no—
330C2×C4—4881no—
331C2×C4—2441no—
332C2×C4—2441no—
333C2×C4—2441no—
334C2×C4—2441no—
335C2×C4—2441no—
336C2×C4—2441no—
337C2×C4—2441no—
338C2×C4—2441no—
339C2×C4#1451973411yescharacteristic
340C2×C4#1451973711yescharacteristic
341C2×C4#1451975011yescharacteristic
342C2×C4#1451976211yescharacteristic
343C2×C4#1451976311yescharacteristic
344C2×C4#1451977211yescharacteristic
345C2×C4M16×D6111yescharacteristic
346C2×C4M16×D6111yescharacteristic
347C2×C4#1451978311yescharacteristic
348C2×C4#1451978311yescharacteristic
349C2×C4#1451980111yescharacteristic
350C2×C4#1451980411yescharacteristic
351C2×C4#1451980411yescharacteristic
352C2×C4#1451980911yescharacteristic
353C8—41no—
354C8—41no—
355C8—81no—
356C8—81no—
357C8—1224no—
358C8—2441no—
359C8—2441no—
360C22—4881no—
361C22—4881no—
362C22—4881no—
363C22—4881no—
364C22—2442no—
365C22—2442no—
366C22—2442no—
367C22#1683965111yescharacteristic
368C22#1683983211yescharacteristic
369C22#1683983211yescharacteristic
370C22#1683986111yescharacteristic
371C22#1683987311yescharacteristic
372C22#1683987811yescharacteristic
373C22#1683987811yescharacteristic
374C4—21no—
375C4—21no—
376C4—4881no—
377C4—4881no—
378C4—2442no—
379C4#1683981711yescharacteristic
380C4#1683982111yescharacteristic
381C4#1683983611yescharacteristic
382C4#1683983711yescharacteristic
383C4#1684001111yescharacteristic
384C4#1684001411yescharacteristic
385C4#1684012311yescharacteristic
386C4#1684012511yescharacteristic
387C2—4882no—
388C2#2144467511yescharacteristic
389C2#2144468211yescharacteristic
390C2#2144468211yescharacteristic
391C2#2144469611yescharacteristic
392C2#2144643011yescharacteristic
393C2#2144651411yescharacteristic
394C2#2144652111yescharacteristic
subgroupG/H
centerC22×C4D4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1277C2
socleC23×C61C4×D4
prime radicalC22×D244C2×C4
cosocleC2×C42×C61C23
hypercenter#1277D61
hypocenterC61#9560
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
2. #21446535C2semidirect
5. C2×#16839484C2semidirect
6. #21443658C2semidirect
7. C61×#1277C2semidirect
196. #1277D61semidirect
222. C61#9560semidirect

Maximal subgroups

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

subgroupindex
#214466122
#214465352
C4×#145196992
C2×#168394892
C2×#168394842
#214436582
C61×#12772
#956061