Finite Group Databasebeta

← #29574504

Subgroups — #29574504

Order 15616.

426 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454565C211yesmaximal, characteristic
2#21446594C211yesmaximal, characteristic, complemented
3#21444590C211yesmaximal, characteristic, complemented
4#21444466C211yesmaximal, characteristic
5#21444271C211yesmaximal, characteristic
6#21443654C211yesmaximal, characteristic, complemented
7C61×#1278C211yesmaximal, characteristic, complemented
8C2×#14519785—21no—
9#16840312C2211yescharacteristic
10#16839841—21no—
11#16839835—22no—
12C8×D244—21no—
13C2×#14519712—21no—
14#16839786C2211yescharacteristic
15C2×C4⋊#92418C2211yescharacteristic
16C2×C4⋊#92418C2211yescharacteristic
17#16839730—21no—
18#16839526—21no—
19#16839513—21no—
20#16839513—21no—
21#16839507C411yescharacteristic
22#16839507C411yescharacteristic
23#16839505C411yescharacteristic
24#16839505C411yescharacteristic
25#16839491—22no—
26C61×#431C2211yescharacteristic
27C4×M16×C61C2211yescharacteristic
28C2×C4×C8×C61C2211yescharacteristic
29C2×#11758222—21no—
30#14519785—42no—
31#14519785—42no—
32C2×#11758194—21no—
33C2×#11758189—22no—
34C22×#92418—21no—
35C22×#92418—21no—
36C2×C8×D61—22no—
37#14519777C2×C411yescharacteristic
38#14519774C2×C411yescharacteristic
39#14519765—21no—
40#14519751—21no—
41#14519751Q812yes—
42C4×D244—21no—
43C4×D244D412yes—
44#14519712—42no—
45C4⋊#92418—21no—
46C4⋊#92418—21no—
47C4⋊#92418—21no—
48C4⋊#92418—21no—
49C4⋊#92418C2×C411yescharacteristic
50C4⋊#92418C2×C411yescharacteristic
51C4⋊#92418D411yescharacteristic
52C4⋊#92418D411yescharacteristic
53#14519689—22no—
54#14519689—22no—
55C2×M16×C61D411yescharacteristic
56C2×M16×C61D411yescharacteristic
57C22×C8×C61—21no—
58C2×C42×C61C2311yescharacteristic
59C4⋊C8×C61C2×C411yescharacteristic
60C4⋊C8×C61C2×C411yescharacteristic
61C22⋊C8×C61—21no—
62#97×C61—21no—
63C4×C8×C61—21no—
64C4×C8×C61—21no—
65C4×C8×C61—21no—
66C4×C8×C61—21no—
67C22×C4×C61C2×D411yescharacteristic
68C22×C4×C61C2×Q811yescharacteristic
69C22×C4×C61#4111yescharacteristic
70C2×C22⋊D61—22no—
71#11758222—41no—
72#11758222—41no—
73#11758222—41no—
74#11758222—41no—
75C2×D244—21no—
76C2×D244—21no—
77C2×D244C4⋊C412yes—
78C2×C4×D61—22no—
79C2×Dic122—21no—
80M16×C61—21no—
81M16×C61—21no—
82M16×C61—21no—
83M16×C61SD1612yes—
84C2×C8×C61—21no—
85C2×C8×C61—22no—
86C2×C8×C61—21no—
87C2×C8×C61—21no—
88C2×C8×C61—21no—
89C2×C8×C61—41no—
90C2×C8×C61—41no—
91C42×C61C22×C411yescharacteristic
92C42×C61C2×D411yescharacteristic
93C42×C61C2×D411yescharacteristic
94C42×C61#4111yescharacteristic
95#11758198—22no—
96#11758198—22no—
97C4⋊Dic61—21no—
98C4⋊Dic61C4⋊C412yes—
99#11758194—41no—
100#11758194—41no—
101C2×#92418—21no—
102C2×#92418—21no—
103C2×#92418—21no—
104C2×#92418—21no—
105C2×#92418—41no—
106C2×#92418—41no—
107C2×#92418—41no—
108C2×#92418—41no—
109C2×#92418—41no—
110#11758189—44no—
111C8×D61—44no—
112C23×C61C22⋊Q811yescharacteristic
113C22×D61—22no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—41no—
117C2×C4×C61C2×C4⋊C411yescharacteristic
118C2×C4×C61C4×D411yescharacteristic
119C2×C4×C61C4×D411yescharacteristic
120C2×C4×C61#12011yescharacteristic
121C2×C4×C61C22⋊Q811yescharacteristic
122C2×C4×C61#12311yescharacteristic
123C2×C4×C61C2×SD1611yescharacteristic
124C2×C4×C61#13511yescharacteristic
125C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
126C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
127C22⋊D61—42no—
128C22⋊D61—42no—
129C2×Dic61—22no—
130D244—42no—
131D244—41no—
132D244—41no—
133D244—41no—
134D244—41no—
135C4×D61—42no—
136C4×D61—42no—
137Dic122—41no—
138Dic122—41no—
139C8×C61—22no—
140C8×C61—42no—
141C8×C61—41no—
142C8×C61—41no—
143C8×C61—41no—
144#92418—41no—
145#92418—41no—
146#92418—41no—
147#92418—41no—
148#92418—81no—
149#8932—611nomaximal, Sylow
150C22×C61—21no—
151C22×C61—21no—
152C22×C61#38511yescharacteristic
153C22×C61#47611yescharacteristic
154C22×C61#47811yescharacteristic
155C2×D61—42no—
156C2×D61—42no—
157C2×D61—42no—
158C4×C61—21no—
159C4×C61—21no—
160C4×C61—21no—
161C4×C61C4×SD1611yescharacteristic
162C4×C61#44211yescharacteristic
163C4×C61#44311yescharacteristic
164C4×C61#44411yescharacteristic
165C4×C61#44911yescharacteristic
166C4×C61#45011yescharacteristic
167Dic61—42no—
168#2935—611no—
169#1950—611no—
170#1570—611no—
171#1540—611no—
172#1492—611no—
173#1278D6111yescharacteristic, complemented
174#1277—611no—
175C2×C61—21no—
176C2×C61—21no—
177C2×C61#185811yescharacteristic
178C2×C61#186411yescharacteristic
179C2×C61#186611yescharacteristic
180D61—82no—
181C2×#131—1221no—
182#532—611no—
183#436—1221no—
184#435—1222no—
185C8×D4—1221no—
186#431C2×D6111yescharacteristic
187C2×#108—1221no—
188#423—611no—
189C2×C4⋊C8—611no—
190C2×C4⋊C8—611no—
191#408—1221no—
192C4×M16C2×D6111yescharacteristic
193C2×C4×C8C2×D6111yescharacteristic
194#341—1221no—
195#334—1221no—
196#334—1221no—
197#332—611no—
198#332—611no—
199#331—611no—
200#331—611no—
201D4⋊C8—1222no—
202C61#893211yescharacteristic, complemented, Sylow
203C2×#41—1221no—
204#131—2442no—
205#131—2442no—
206C2×M16—1222no—
207C2×M16—1221no—
208C2×M16D24411yescharacteristic
209C2×M16D24411yescharacteristic
210C22×C8—21no—
211C22×C8—1222no—
212C22×C8—1221no—
213C22×C8—1221no—
214C4⋊Q8—611no—
215#127—611no—
216#124—1221no—
217#121—612no—
218#121—1221no—
219C4×D4—612no—
220C4×D4—1221no—
221C2×C42C22×D6111yescharacteristic
222#108—2442no—
223C4⋊C8—611no—
224C4⋊C8—611no—
225C4⋊C8—611no—
226C4⋊C8—611no—
227C4⋊C8—1221no—
228C4⋊C8—1221no—
229C4⋊C8—1221no—
230C4⋊C8—1221no—
231C4⋊C8C4×D6111yescharacteristic
232C4⋊C8C4×D6111yescharacteristic
233C22⋊C8—21no—
234C22⋊C8—1222no—
235C22⋊C8—1222no—
236#97—21no—
237C4×C8—21no—
238C4×C8—21no—
239C4×C8—21no—
240C4×C8—21no—
241#41—2441no—
242#41—2441no—
243#41—2441no—
244#41—2441no—
245C2×Q8—1221no—
246C2×D4—612no—
247C2×D4—1222no—
248C2×D4—1221no—
249C2×D4—1221no—
250C22×C4—1222no—
251C22×C4C2×D24411yescharacteristic
252C22×C4#1175822411yescharacteristic
253C22×C4Q8×D6111yescharacteristic
254M16—21no—
255M16—21no—
256M16—21no—
257M16—2444no—
258M16—2441no—
259M16—2441no—
260M16#1175819012yes—
261C2×C8—21no—
262C2×C8—22no—
263C2×C8—21no—
264C2×C8—21no—
265C2×C8—21no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8—1221no—
269C2×C8—1221no—
270C2×C8—1221no—
271C2×C8—1221no—
272C2×C8—2444no—
273C2×C8—2441no—
274C2×C8—2441no—
275C2×C8—2441no—
276C2×C8—2441no—
277C2×C8—2441no—
278C4⋊C4—612no—
279C4⋊C4—1221no—
280C22⋊C4—1222no—
281C22⋊C4—1222no—
282C42C2×C4×D6111yescharacteristic
283C42#1175822211yescharacteristic
284C42D4×D6111yescharacteristic
285C42D4×D6111yescharacteristic
286C23—1222no—
287C23#1451975711yescharacteristic
288Q8—2441no—
289Q8—2441no—
290D4—2442no—
291D4—2442no—
292D4—2442no—
293D4—2441no—
294D4—2441no—
295D4—2441no—
296D4—2441no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—41no—
300C2×C4—1222no—
301C2×C4—2442no—
302C2×C4—2442no—
303C2×C4C4⋊C4×D6111yescharacteristic
304C2×C4#1451973711yescharacteristic
305C2×C4C4×D24411yescharacteristic
306C2×C4#1451974711yescharacteristic
307C2×C4#1451975511yescharacteristic
308C2×C4#1451975911yescharacteristic
309C2×C4C2×#1175819011yescharacteristic
310C2×C4#1451979911yescharacteristic
311C2×C4#1451980511yescharacteristic
312C2×C4#1451980511yescharacteristic
313C8—22no—
314C8—42no—
315C8—41no—
316C8—41no—
317C8—41no—
318C8—4881no—
319C8—2441no—
320C8—2441no—
321C8—2441no—
322C8—2441no—
323C22—21no—
324C22—21no—
325C22—2442no—
326C22—2442no—
327C22—2442no—
328C22#1683963611yescharacteristic
329C22#1684005311yescharacteristic
330C22#1684006311yescharacteristic
331C4—21no—
332C4—21no—
333C4—21no—
334C4—2442no—
335C4C4×#1175819011yescharacteristic
336C4#1683987511yescharacteristic
337C4#1683987611yescharacteristic
338C4#1683988111yescharacteristic
339C4#1683990911yescharacteristic
340C4#1683991511yescharacteristic
341C2—21no—
342C2—21no—
343C2—4882no—
344C2#2144604011yescharacteristic
345C2#2144608311yescharacteristic
346C2#2144609511yescharacteristic
subgroupG/H
centerC2×C4#14519747
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1278C2
socleC22×C61#385
prime radical#16840312C22
cosocleC2×C42×C61C23
hypercenter#1278D61
hypocenterC61#8932
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1278

Complements

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

NH ≅ G/Ntype
2. #21446594C2semidirect
3. #21444590C2semidirect
6. #21443654C2semidirect
7. C61×#1278C2semidirect
173. #1278D61semidirect
202. C61#8932semidirect

Maximal subgroups

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

subgroupindex
#214545652
#214465942
#214445902
#214444662
#214442712
#214436542
C61×#12782
#893261