Finite Group Databasebeta

← #29584738

Subgroups — #29584738

Order 15616.

418 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21446612C211yesmaximal, characteristic
2#21445975C211yesmaximal, characteristic, complemented
3#21445820C211yesmaximal, characteristic
4#21445816C211yesmaximal, characteristic
5#21443703C211yesmaximal, characteristic, complemented
6#21443653C211yesmaximal, characteristic, complemented
7C61×#1296C211yesmaximal, characteristic, complemented
8C2×C4×D244C2211yescharacteristic
9C2×#14519708—21no—
10C2×#14519708—21no—
11C2×C4⋊#92418C2211yescharacteristic
12C2×#14519699—21no—
13C2×#14519697—21no—
14C2×#14519689—21no—
15C2×#14519689—21no—
16C2×C4×#92418C2211yescharacteristic
17#16839632C2211yescharacteristic
18#16839525—21no—
19#16839524—21no—
20C2×C4⋊C8×C61C2211yescharacteristic
21C2×C4⋊C8×C61C2211yescharacteristic
22C61×#384C2211yescharacteristic
23C22×D244D411yescharacteristic
24C22×C4×D61—21no—
25C22×#92418—21no—
26C22×#92418D411yescharacteristic
27C22×#92418D411yescharacteristic
28C4×D244—21no—
29C4×D244—21no—
30C4×D244—21no—
31C4×D244—21no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61D411yescharacteristic
36C2×#11758198—21no—
37#14519708—42no—
38#14519708—42no—
39C4⋊#92418—21no—
40C4⋊#92418—21no—
41#14519699—42no—
42#14519697—42no—
43#14519689—42no—
44#14519689—42no—
45C4×#92418—21no—
46C4×#92418—21no—
47C22×C8×C61—21no—
48C22×C8×C61—21no—
49C2×C4⋊C4×C61—21no—
50C2×C4⋊C4×C61—21no—
51C2×C4⋊C4×C61—21no—
52C2×C42×C61C2311yescharacteristic
53C4⋊C8×C61—21no—
54C4⋊C8×C61—21no—
55C4⋊C8×C61—21no—
56C4⋊C8×C61—21no—
57C23×D61—21no—
58C22×C4×C61—41no—
59C22×C4×C61C2×D411yescharacteristic
60C22×C4×C61C2×D411yescharacteristic
61C22×C4×C61#4111yescharacteristic
62C22×Dic61—21no—
63C22×Dic61—41no—
64C2×D244—21no—
65C2×D244—21no—
66C2×D244—21no—
67C2×D244—21no—
68C2×D244—21no—
69C2×D244SD1612yes—
70C2×C4×D61—41no—
71C2×C4×D61—41no—
72C2×C4×D61—41no—
73C2×C4×D61—41no—
74C2×C4×D61—41no—
75C2×C4×D61—41no—
76C2×C8×C61—41no—
77C2×C8×C61—41no—
78C2×C8×C61—41no—
79C2×C8×C61—41no—
80C2×C8×C61—41no—
81C2×C8×C61—41no—
82C4⋊C4×C61—41no—
83C4⋊C4×C61—41no—
84C4⋊C4×C61—41no—
85C4⋊C4×C61—41no—
86C4⋊C4×C61—81no—
87C42×C61#4111yescharacteristic
88C42×C61#4111yescharacteristic
89C42×C61#4111yescharacteristic
90C42×C61#4111yescharacteristic
91#11758198—41no—
92#11758198—41no—
93C4⋊Dic61—21no—
94C4⋊Dic61—21no—
95C4⋊Dic61—41no—
96C4⋊Dic61—41no—
97C4⋊Dic61—41no—
98C4⋊Dic61—41no—
99C4⋊Dic61—81no—
100C2×#92418—21no—
101C2×#92418—21no—
102C2×#92418—21no—
103C2×#92418—21no—
104C2×#92418—41no—
105C2×#92418—41no—
106C2×#92418—41no—
107C2×#92418D812yes—
108C2×#92418SD1612yes—
109C23×C61#12111yescharacteristic
110C22×D61—22no—
111C22×D61—41no—
112C22×D61—41no—
113C22×D61—41no—
114C22×D61—41no—
115C22×D61—41no—
116C22×D61—41no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—81no—
120C2×C4×C61—81no—
121C2×C4×C61—81no—
122C2×C4×C61#12311yescharacteristic
123C2×C4×C61#12311yescharacteristic
124C2×C4×C61#12311yescharacteristic
125C2×C4×C61#12411yescharacteristic
126C2×C4×C61#12611yescharacteristic
127C2×C4×C61#12611yescharacteristic
128C2×C4×C61C2×D811yescharacteristic
129C2×C4×C61C2×SD1611yescharacteristic
130C2×C4×C61C2×SD1611yescharacteristic
131C2×C4×C61#13511yescharacteristic
132C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C61#13711yescharacteristic
135C2×C4×C61#13711yescharacteristic
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—81no—
140C2×Dic61—81no—
141C2×Dic61—81no—
142D244—22no—
143D244—22no—
144D244—41no—
145D244—41no—
146C4×D61—81no—
147C4×D61—81no—
148C4×D61—81no—
149C4×D61—81no—
150C8×C61—81no—
151C8×C61—81no—
152#92418—22no—
153#92418—22no—
154#92418—81no—
155#10619—611nomaximal, Sylow
156C22×C61#39711yescharacteristic
157C22×C61#45911yescharacteristic
158C22×C61#46111yescharacteristic
159C22×C61#46511yescharacteristic
160C22×C61#46811yescharacteristic
161C22×C61#47111yescharacteristic
162C22×C61#47111yescharacteristic
163C2×D61—42no—
164C2×D61—42no—
165C2×D61—42no—
166C2×D61—81no—
167C2×D61—81no—
168C2×D61—81no—
169C2×D61—81no—
170C4×C61—21no—
171C4×C61—21no—
172C4×C61—161no—
173C4×C61#48011yescharacteristic
174C4×C61#48111yescharacteristic
175C4×C61#48111yescharacteristic
176C4×C61#48211yescharacteristic
177C4×C61#48311yescharacteristic
178C4×C61#48511yescharacteristic
179C4×C61#48611yescharacteristic
180C4×C61#48911yescharacteristic
181Dic61—81no—
182Dic61—161no—
183#1954—611no—
184#1844—611no—
185#1802—611no—
186#1802—611no—
187#1296—611no—
188#1296D6111yescharacteristic, complemented
189#1277—611no—
190C2×C61#166511yescharacteristic
191C2×C61#167111yescharacteristic
192C2×C61#168511yescharacteristic
193C2×C61#169111yescharacteristic
194C2×C61#207111yescharacteristic
195C2×C61#207711yescharacteristic
196C2×C61#207911yescharacteristic
197D61—82no—
198C2×C4×D4—611no—
199C2×#106—1221no—
200C2×#106—1221no—
201C2×C4⋊C8—611no—
202C2×C4⋊C8C2×D6111yescharacteristic
203C2×C4⋊C8C2×D6111yescharacteristic
204C2×#102—1221no—
205C2×#102—1221no—
206C2×C22⋊C8—1221no—
207C2×C22⋊C8—1221no—
208C2×C4×C8—611no—
209#384—611no—
210#384C2×D6111yescharacteristic
211#340—1221no—
212#340—1221no—
213C61#1061911yescharacteristic, complemented, Sylow
214C22×D4—611no—
215C23×C4—1221no—
216C22×C8—21no—
217C22×C8—21no—
218C22×C8—611no—
219C22×C8—611no—
220C22×C8—1221no—
221C4×D4—1221no—
222C4×D4—1221no—
223C4×D4—1221no—
224C4×D4—1221no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—611no—
229C2×C4⋊C4—1221no—
230C2×C4⋊C4—1221no—
231C2×C4⋊C4—1221no—
232C2×C22⋊C4—1221no—
233C2×C42C22×D6111yescharacteristic
234#106—2442no—
235#106—2442no—
236C4⋊C8—21no—
237C4⋊C8—21no—
238C4⋊C8—21no—
239C4⋊C8—21no—
240C4⋊C8—1221no—
241C4⋊C8—1221no—
242#102—2442no—
243#102—2442no—
244C22⋊C8—2442no—
245C22⋊C8—2442no—
246C4×C8—1221no—
247C4×C8—1221no—
248C24—1221no—
249C2×D4—612no—
250C2×D4—1221no—
251C2×D4—1221no—
252C2×D4—1221no—
253C2×D4—1221no—
254C2×D4—1221no—
255C22×C4—41no—
256C22×C4—1221no—
257C22×C4—2441no—
258C22×C4—2441no—
259C22×C4—2441no—
260C22×C4—2441no—
261C22×C4—2441no—
262C22×C4—2441no—
263C22×C4—2441no—
264C22×C4#1175822211yescharacteristic
265C22×C4D4×D6111yescharacteristic
266C22×C4D4×D6111yescharacteristic
267C2×C8—41no—
268C2×C8—41no—
269C2×C8—41no—
270C2×C8—41no—
271C2×C8—41no—
272C2×C8—41no—
273C2×C8—612no—
274C2×C8—612no—
275C2×C8—1221no—
276C2×C8—1221no—
277C2×C8—1221no—
278C2×C8—1221no—
279C2×C8—2441no—
280C2×C8—2441no—
281C2×C8—2441no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—81no—
287C4⋊C4—1221no—
288C4⋊C4—1221no—
289C4⋊C4—4881no—
290C4⋊C4—2441no—
291C4⋊C4—2441no—
292C4⋊C4—2441no—
293C4⋊C4—2441no—
294C22⋊C4—2441no—
295C22⋊C4—2441no—
296C42#1175822211yescharacteristic
297C42#1175822211yescharacteristic
298C42#1175822411yescharacteristic
299C42#1175822611yescharacteristic
300C23—1222no—
301C23—2441no—
302C23—2441no—
303C23—2441no—
304C23—2441no—
305C23—2441no—
306C23—2441no—
307C23#1451975011yescharacteristic
308D4—1222no—
309D4—1222no—
310D4—2441no—
311D4—2441no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—4881no—
318C2×C4—4881no—
319C2×C4—4881no—
320C2×C4—4881no—
321C2×C4—4881no—
322C2×C4—4881no—
323C2×C4—4881no—
324C2×C4—2441no—
325C2×C4—2441no—
326C2×C4—2441no—
327C2×C4#1451975911yescharacteristic
328C2×C4#1451976211yescharacteristic
329C2×C4#1451976211yescharacteristic
330C2×C4#1451976311yescharacteristic
331C2×C4#1451977111yescharacteristic
332C2×C4#1451977211yescharacteristic
333C2×C4D8×D6111yescharacteristic
334C2×C4SD16×D6111yescharacteristic
335C2×C4SD16×D6111yescharacteristic
336C2×C4#1451979611yescharacteristic
337C2×C4#1451980411yescharacteristic
338C2×C4#1451980411yescharacteristic
339C2×C4#1451980911yescharacteristic
340C2×C4#1451980911yescharacteristic
341C8—81no—
342C8—81no—
343C8—1222no—
344C8—1222no—
345C8—4881no—
346C22—4881no—
347C22—4881no—
348C22—4881no—
349C22—4881no—
350C22—2442no—
351C22—2442no—
352C22—2442no—
353C22#1683969111yescharacteristic
354C22#1683995611yescharacteristic
355C22#1683996611yescharacteristic
356C22#1683999011yescharacteristic
357C22#1684001111yescharacteristic
358C22#1684002411yescharacteristic
359C22#1684002811yescharacteristic
360C4—21no—
361C4—21no—
362C4—161no—
363C4—9761no—
364C4—4881no—
365C4#1684007711yescharacteristic
366C4#1684008211yescharacteristic
367C4#1684008211yescharacteristic
368C4#1684008411yescharacteristic
369C4#1684009111yescharacteristic
370C4#1684010511yescharacteristic
371C4#1684010711yescharacteristic
372C4#1684012311yescharacteristic
373C2—4882no—
374C2#2144515911yescharacteristic
375C2#2144519311yescharacteristic
376C2#2144528711yescharacteristic
377C2#2144532111yescharacteristic
378C2#2144722611yescharacteristic
379C2#2144725711yescharacteristic
380C2#2144726811yescharacteristic
subgroupG/H
centerC23#14519750
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1296C2
socleC23×C61#121
prime radicalC22×D244D4
hypercenter#1296D61
hypocenterC61#10619
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
2. #21445975C2semidirect
5. #21443703C2semidirect
6. #21443653C2semidirect
7. C61×#1296C2semidirect
188. #1296D61semidirect
213. C61#10619semidirect

Maximal subgroups

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

subgroupindex
#214466122
#214459752
#214458202
#214458162
#214437032
#214436532
C61×#12962
#1061961