Finite Group Databasebeta

← #29597453

Subgroups — #29597453

Order 15616.

478 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840179C211yesmaximal, characteristic, complemented
2C2×#16840032C211yesmaximal, characteristic
3C2×#16839574C211yesmaximal, characteristic, complemented
4C2×#16839562C211yesmaximal, characteristic, complemented
5#21443927C211yesmaximal, characteristic, complemented
6#21443912C211yesmaximal, characteristic, complemented
7C61×#1816C211yesmaximal, characteristic, complemented
8C2×#14519802—21no—
9C22×D488C2211yescharacteristic
10#16840179—22no—
11#16840179—22no—
12C2×#14519717—21no—
13C2×#14519717C2211yescharacteristic
14C22×#11758185—21no—
15C22×#11758185C2211yescharacteristic
16#16840032—22no—
17#16840032C414yescomplemented
18C2×#14519713C2211yescharacteristic
19C2×#14519693—21no—
20#16839574—22no—
21#16839562—21no—
22#16839562—21no—
23C2×#131×C61C2211yescharacteristic
24C2×#108×C61C2211yescharacteristic
25C2×#107×C61C2211yescharacteristic
26C61×#417—21no—
27C61×#343—21no—
28C22×D244—21no—
29#14519802—24no—
30#14519802—42no—
31C2×#11758201—41no—
32C2×D488—21no—
33C2×D488—21no—
34C2×D488—21no—
35C2×D488—21no—
36C2×D488—21no—
37C2×D488C2×C412yes—
38C2×#11758199—41no—
39C2×#11758194—21no—
40#14519717—24no—
41#14519717—21no—
42#14519717D412yes—
43C2×#11758185—24no—
44C2×#11758185—21no—
45C2×#11758185—21no—
46C2×#11758185—21no—
47C2×#11758185D411yescharacteristic
48C2×#11758185D411yescharacteristic
49#14519713—21no—
50#14519713C2×C412yes—
51#14519693—24no—
52C2×#41×C61D411yescharacteristic
53#131×C61—21no—
54#131×C61—21no—
55#131×C61C2×C412yes—
56#131×C61D412yes—
57C2×M16×C61—21no—
58C2×M16×C61—21no—
59C2×M16×C61D411yescharacteristic
60C22×C8×C61—21no—
61C22×C8×C61C2311yescharacteristic
62C2×C4⋊C4×C61—21no—
63#108×C61—21no—
64#108×C61—21no—
65#107×C61—21no—
66#107×C61—21no—
67#103×C61—41no—
68#102×C61—41no—
69C23×D61—41no—
70#41×C61—21no—
71#41×C61—21no—
72#41×C61C22⋊C412yes—
73#41×C61SD1612yes—
74C2×Q8×C61D811yescharacteristic
75C2×D4×C61—21no—
76C2×D4×C61D811yescharacteristic
77C22×C4×C61—21no—
78C22×C4×C61—41no—
79C22×C4×C61C2×D411yescharacteristic
80C2×D244—22no—
81C2×D244—41no—
82C2×D244—41no—
83C2×D244—41no—
84C2×D244—41no—
85C2×D244—41no—
86M16×C61—21no—
87M16×C61—22no—
88M16×C61—22no—
89M16×C61—41no—
90M16×C61—41no—
91M16×C61C22⋊C412yes—
92C2×C8×C61—21no—
93C2×C8×C61—22no—
94C2×C8×C61—22no—
95C2×C8×C61—41no—
96C2×C8×C61C22×C411yescharacteristic
97C2×C8×C61C2×D411yescharacteristic
98C2×C8×C61C2×D411yescharacteristic
99C2×C8×C61C2×D411yescharacteristic
100C2×C8×C61#4111yescharacteristic
101C2×C8×C61#4111yescharacteristic
102C4⋊C4×C61—41no—
103C4⋊C4×C61—41no—
104#11758201—44no—
105#11758199—44no—
106#11758194—22no—
107#11758194—41no—
108C2×#92418—41no—
109D488—22no—
110D488—22no—
111D488—41no—
112D488—41no—
113#11758185—21no—
114#11758185—22no—
115#11758185—21no—
116C23×C61—21no—
117C23×C61#13511yescharacteristic
118C22×D61—42no—
119C22×D61—81no—
120C22×D61—81no—
121C22×D61—161no—
122C22×D61—161no—
123Q8×C61—21no—
124Q8×C61#10212yes—
125D4×C61—22no—
126D4×C61—22no—
127D4×C61—21no—
128D4×C61#10212yes—
129C2×C4×C61—21no—
130C2×C4×C61—22no—
131C2×C4×C61—22no—
132C2×C4×C61—81no—
133C2×C4×C61—161no—
134C2×C4×C61C2×C22⋊C411yescharacteristic
135C2×C4×C61#12111yescharacteristic
136C2×C4×C61#12111yescharacteristic
137C2×C4×C61C2×D811yescharacteristic
138C2×C4×C61C2×SD1611yescharacteristic
139C2×C4×C61#13511yescharacteristic
140D244—42no—
141D244—42no—
142D244—81no—
143D244—81no—
144C8×C61—22no—
145C8×C61—81no—
146C8×C61C4×D411yescharacteristic
147C8×C61C4×D411yescharacteristic
148C8×C61#12011yescharacteristic
149C8×C61#12311yescharacteristic
150#92418—42no—
151#13073—611nomaximal, Sylow
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—22no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61#41611yescharacteristic
158C22×C61#46511yescharacteristic
159C22×C61#46611yescharacteristic
160C2×D61—82no—
161C2×D61—162no—
162C2×D61—161no—
163C2×D61—161no—
164C2×D61—162no—
165C4×C61—22no—
166C4×C61—161no—
167C4×C61#38611yescharacteristic
168C4×C61C2×#10211yescharacteristic
169C4×C61#46511yescharacteristic
170C4×C61#46611yescharacteristic
171C2×#504—611no—
172C2×#472—611no—
173C2×#361—611no—
174C2×#357—611no—
175#1816D6111yescharacteristic, complemented
176#1387—611no—
177#1381—611no—
178C2×C61—21no—
179C2×C61—21no—
180C2×C61—42no—
181C2×C61#189311yescharacteristic
182C2×C61#222111yescharacteristic
183C2×C61#222311yescharacteristic
184D61—162no—
185C2×AGL(1,ℤ/8)—1221no—
186C22×D8—611no—
187C2×#131C2×D6111yescharacteristic
188#504—1222no—
189#504—1222no—
190C2×M32—611no—
191C2×M32—1221no—
192C22×C16—611no—
193C22×C16—1221no—
194#472—614no—
195#472—1222no—
196C2×#108—611no—
197C2×#108C2×D6111yescharacteristic
198C2×#107C2×D6111yescharacteristic
199#417—21no—
200C2×#100—1221no—
201#361—1222no—
202#357—1221no—
203#357—1221no—
204#343—21no—
205C61#1307311yescharacteristic, complemented, Sylow
206C2×#41C22⋊D6111yescharacteristic
207C22×D4—1221no—
208AGL(1,ℤ/8)—1224no—
209AGL(1,ℤ/8)—2442no—
210C2×SD16—2441no—
211C2×D8—612no—
212C2×D8—1221no—
213C2×D8—1221no—
214C2×D8—1221no—
215C2×D8—1221no—
216C2×D8—1221no—
217C2×D8—2441no—
218#131—21no—
219#131—21no—
220#131C4×D6112yes—
221#131D24412yes—
222C2×M16—21no—
223C2×M16—21no—
224C2×M16—1221no—
225C2×M16C22⋊D6111yescharacteristic
226C22×C8—21no—
227C22×C8C22×D6111yescharacteristic
228C2×C4⋊C4—21no—
229M32—612no—
230M32—1224no—
231M32—1221no—
232C2×C16—611no—
233C2×C16—611no—
234C2×C16—1224no—
235C2×C16—1221no—
236C2×C16—1221no—
237C2×C16—1221no—
238#108—21no—
239#108—21no—
240#108—612no—
241#108—1221no—
242#107—21no—
243#107—21no—
244#103—41no—
245#102—41no—
246#100—1224no—
247C24—2441no—
248#41—21no—
249#41—21no—
250#41#1175819812yes—
251#41#1175820112yes—
252C2×Q8#1175819911yescharacteristic
253C2×D4—21no—
254C2×D4—1222no—
255C2×D4—2441no—
256C2×D4—2441no—
257C2×D4—2441no—
258C2×D4—2441no—
259C2×D4—2441no—
260C2×D4#1175819911yescharacteristic
261C22×C4—21no—
262C22×C4—41no—
263C22×C4C2×C22⋊D6111yescharacteristic
264SD16—2444no—
265D8—1222no—
266D8—1222no—
267D8—2444no—
268D8—2441no—
269D8—2441no—
270M16—21no—
271M16—22no—
272M16—22no—
273M16—41no—
274M16—41no—
275M16—1222no—
276M16—2441no—
277M16#1175819812yes—
278C2×C8—21no—
279C2×C8—22no—
280C2×C8—22no—
281C2×C8—41no—
282C2×C8—2441no—
283C2×C8C2×C4×D6111yescharacteristic
284C2×C8C2×D24411yescharacteristic
285C2×C8D4×D6111yescharacteristic
286C2×C8D4×D6111yescharacteristic
287C2×C8#1175822411yescharacteristic
288C2×C8#1175822411yescharacteristic
289C4⋊C4—41no—
290C4⋊C4—41no—
291C16—1221no—
292C16—1221no—
293C16—1222no—
294C23—21no—
295C23—9761no—
296C23—9761no—
297C23—4881no—
298C23—4881no—
299C23—2442no—
300C23#1451979711yescharacteristic
301Q8—21no—
302Q8#1451969712yes—
303D4—22no—
304D4—22no—
305D4—21no—
306D4—4881no—
307D4—4881no—
308D4—2442no—
309D4—2442no—
310D4#1451969712yes—
311C2×C4—21no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—81no—
315C2×C4—161no—
316C2×C4C2×#1175819811yescharacteristic
317C2×C4#1451974911yescharacteristic
318C2×C4#1451974911yescharacteristic
319C2×C4C2×#1175819911yescharacteristic
320C2×C4C2×#1175820111yescharacteristic
321C2×C4#1451979711yescharacteristic
322C8—22no—
323C8—81no—
324C8—2442no—
325C8#1451973711yescharacteristic
326C8#1451973711yescharacteristic
327C8#1451974711yescharacteristic
328C8#1451976111yescharacteristic
329C22—21no—
330C22—21no—
331C22—22no—
332C22—41no—
333C22—41no—
334C22—9762no—
335C22—9762no—
336C22—9761no—
337C22—9761no—
338C22—4882no—
339C22#1683975611yescharacteristic
340C22#1683999311yescharacteristic
341C22#1683999611yescharacteristic
342C4—22no—
343C4—161no—
344C4#1683963911yescharacteristic
345C4C2×#1451969711yescharacteristic
346C4#1683999311yescharacteristic
347C4#1683999611yescharacteristic
348C2—21no—
349C2—21no—
350C2—42no—
351C2—9762no—
352C2#2144624511yescharacteristic
353C2#2144793711yescharacteristic
354C2#2144795111yescharacteristic
subgroupG/H
centerC22#16839996
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC61×#1816C2
socleC22×C61#466
prime radicalC2×#16840032C2
cosocleC22×C8×C61C23
hypercenter#1816D61
hypocenterC61#13073
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131 ◁ #1816

Complements

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

NH ≅ G/Ntype
1. C2×#16840179C2semidirect
3. C2×#16839574C2semidirect
4. C2×#16839562C2semidirect
5. #21443927C2semidirect
6. #21443912C2semidirect
7. C61×#1816C2semidirect
17. #16840032C4semidirect
175. #1816D61semidirect
205. C61#13073semidirect

Maximal subgroups

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

subgroupindex
C2×#168401792
C2×#168400322
C2×#168395742
C2×#168395622
#214439272
#214439122
C61×#18162
#1307361