Finite Group Databasebeta

← #29579336

Subgroups — #29579336

Order 15616.

526 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840110C211yesmaximal, characteristic
2#21446746C211yesmaximal, characteristic
3#21445688C211yesmaximal, characteristic, complemented
4C2×#16839512C211yesmaximal, characteristic, complemented
5C2×#16839508C211yesmaximal, characteristic, complemented
6C2×#16839505C211yesmaximal, characteristic
7C61×#1981C211yesmaximal, characteristic, complemented
8C2×#14519774C2211yescharacteristic
9#16840110—22no—
10#16840110C414yescomplemented
11C2×C4⋊#92418C2211yescharacteristic
12C2×C4⋊#92418C2211yescharacteristic
13C2×#14519697—21no—
14C2×#14519697—21no—
15C2×#14519697—22no—
16C2×#14519688—21no—
17C2×C4×#92418C2211yescharacteristic
18#16839517—21no—
19#16839512—22no—
20#16839508—22no—
21#16839505—22no—
22C2×C4⋊Q8×C61C2211yescharacteristic
23C2×C4⋊C8×C61C2211yescharacteristic
24C2×#103×C61—22no—
25C4×C4⋊C4×C61C2211yescharacteristic
26C22×D244—21no—
27C22×D244—21no—
28C22×D244—21no—
29C22×#92418—21no—
30C22×#92418—21no—
31C22×#92418D411yescharacteristic
32C22×#92418D411yescharacteristic
33#14519774—21no—
34#14519774—21no—
35#14519774—21no—
36#14519774C2×C412yes—
37C4⋊#92418—21no—
38C4⋊#92418—21no—
39C4⋊#92418—21no—
40C4⋊#92418D412yes—
41#14519697—24no—
42#14519697—24no—
43#14519697—44no—
44#14519688—42no—
45C4×#92418C2×C412yes—
46C4×#92418D412yes—
47C22×Q8×C61—21no—
48C22×C8×C61—21no—
49C4⋊Q8×C61—21no—
50C4⋊Q8×C61—21no—
51C4⋊Q8×C61—21no—
52C4⋊Q8×C61C2×C412yes—
53C2×C4⋊C4×C61—21no—
54C2×C4⋊C4×C61—21no—
55C2×C4⋊C4×C61D412yes—
56C2×C42×C61—21no—
57C2×C42×C61C2311yescharacteristic
58C4⋊C8×C61—21no—
59C4⋊C8×C61—21no—
60#103×C61—44no—
61#95×C61—21no—
62C23×D61—41no—
63C2×Q8×C61—22no—
64C2×Q8×C61—41no—
65C2×Q8×C61—42no—
66C2×Q8×C61—42no—
67C22×C4×C61—22no—
68C22×C4×C61—41no—
69C22×C4×C61C2×D411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C22×C4×C61#4111yescharacteristic
72C2×D244—22no—
73C2×D244—22no—
74C2×D244—22no—
75C2×D244—41no—
76C2×D244—41no—
77C2×D244—41no—
78C2×D244—42no—
79C2×D244—42no—
80C2×D244—41no—
81C2×D244—41no—
82C2×D244—41no—
83C2×D244—41no—
84C2×D244—82no—
85C2×C8×C61—41no—
86C2×C8×C61—42no—
87C4⋊C4×C61—22no—
88C4⋊C4×C61—22no—
89C4⋊C4×C61—22no—
90C4⋊C4×C61—22no—
91C4⋊C4×C61—41no—
92C4⋊C4×C61—41no—
93C42×C61—41no—
94C42×C61—41no—
95C42×C61C22×C411yescharacteristic
96C42×C61C2×D411yescharacteristic
97C42×C61C2×D411yescharacteristic
98C42×C61#4111yescharacteristic
99C2×#92418—21no—
100C2×#92418—21no—
101C2×#92418—21no—
102C2×#92418—21no—
103C2×#92418—22no—
104C2×#92418—41no—
105C2×#92418—41no—
106C2×#92418—41no—
107C2×#92418—42no—
108C2×#92418C22⋊C412yes—
109C2×#92418C22⋊C412yes—
110C23×C61#12111yescharacteristic
111C22×D61—42no—
112C22×D61—81no—
113C22×D61—81no—
114C22×D61—82no—
115C22×D61—82no—
116Q8×C61—44no—
117Q8×C61—81no—
118Q8×C61—81no—
119C2×C4×C61—22no—
120C2×C4×C61—42no—
121C2×C4×C61—42no—
122C2×C4×C61—42no—
123C2×C4×C61—42no—
124C2×C4×C61—82no—
125C2×C4×C61C2×C22⋊C411yescharacteristic
126C2×C4×C61C4×D411yescharacteristic
127C2×C4×C61C4×D411yescharacteristic
128C2×C4×C61#12111yescharacteristic
129C2×C4×C61#12411yescharacteristic
130C2×C4×C61#12711yescharacteristic
131C2×C4×C61#13511yescharacteristic
132C2×C4×C61#13511yescharacteristic
133C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C61AGL(1,ℤ/8)12yes—
135C2×C4×C61AGL(1,ℤ/8)12yes—
136C2×C4×C61#13711yescharacteristic
137D244—42no—
138D244—42no—
139D244—44no—
140D244—82no—
141D244—82no—
142D244—81no—
143D244—81no—
144D244—81no—
145D244—81no—
146C8×C61—81no—
147#92418—22no—
148#92418—22no—
149#92418—42no—
150#92418—81no—
151#9746—611nomaximal, Sylow
152C22×C61#39011yescharacteristic
153C22×C61#46311yescharacteristic
154C22×C61#46411yescharacteristic
155C22×C61#46912yes—
156C22×C61#47112yes—
157C2×D61—82no—
158C2×D61—82no—
159C2×D61—82no—
160C2×D61—162no—
161C2×D61—162no—
162C4×C61—21no—
163C4×C61—21no—
164C4×C61—82no—
165C4×C61—82no—
166C4×C61#41611yescharacteristic
167C4×C61#41711yescharacteristic
168C4×C61#44212yes—
169C4×C61#46311yescharacteristic
170C4×C61#46411yescharacteristic
171C4×C61#49611yescharacteristic
172C4×C61#49611yescharacteristic
173C2×#486—611no—
174#1982—611no—
175#1981D6111yescharacteristic, complemented
176#1770—611no—
177C2×#334—611no—
178C2×#332—611no—
179C2×#331—611no—
180C2×C61#170112yes—
181C2×C61#170212yes—
182C2×C61#197211yescharacteristic
183C2×C61#197711yescharacteristic
184C2×C61#198311yescharacteristic
185D61—162no—
186C2×C4⋊Q8C2×D6111yescharacteristic
187C2×#127—611no—
188#486—614no—
189#486—1222no—
190C2×C4⋊C8—611no—
191C2×C4⋊C8—611no—
192C2×C4⋊C8C2×D6111yescharacteristic
193C2×#103—22no—
194C2×#102—1221no—
195C2×#102—1221no—
196C2×#102—1222no—
197C2×#97—1221no—
198C2×C4×C8—611no—
199C4×C4⋊C4C2×D6111yescharacteristic
200#336—1221no—
201#334—1222no—
202#332—1222no—
203#331—1222no—
204C61#974611yescharacteristic, complemented, Sylow
205C22×Q8—21no—
206C22×D4—1221no—
207C22×D4—1221no—
208C22×D4—1221no—
209C22×C8—21no—
210C22×C8—611no—
211C22×C8—611no—
212C22×C8—1221no—
213C22×C8—1221no—
214C4⋊Q8—21no—
215C4⋊Q8—21no—
216C4⋊Q8—21no—
217C4⋊Q8C4×D6112yes—
218#127—612no—
219#127—1221no—
220#127—1221no—
221#127—1221no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4C22⋊D6112yes—
225C2×C42—21no—
226C2×C42C22×D6111yescharacteristic
227C4⋊C8—21no—
228C4⋊C8—21no—
229C4⋊C8—612no—
230C4⋊C8—1221no—
231C4⋊C8—1221no—
232C4⋊C8—1221no—
233#103—44no—
234#102—1224no—
235#102—1224no—
236#102—2444no—
237#97—2442no—
238C4×C8—612no—
239C4×C8—612no—
240#95—21no—
241C24—2441no—
242C2×Q8—22no—
243C2×Q8—41no—
244C2×Q8—42no—
245C2×Q8—42no—
246C2×D4—1222no—
247C2×D4—1222no—
248C2×D4—1222no—
249C2×D4—4882no—
250C2×D4—2441no—
251C2×D4—2441no—
252C2×D4—2441no—
253C2×D4—2441no—
254C2×D4—2441no—
255C2×D4—2441no—
256C2×D4—2442no—
257C2×D4—2442no—
258C2×D4—2441no—
259C22×C4—22no—
260C22×C4—41no—
261C22×C4D4×D6111yescharacteristic
262C22×C4#1175822411yescharacteristic
263C22×C4C2×C22⋊D6111yescharacteristic
264C2×C8—41no—
265C2×C8—42no—
266C2×C8—612no—
267C2×C8—612no—
268C2×C8—1221no—
269C2×C8—1221no—
270C2×C8—1221no—
271C2×C8—1221no—
272C2×C8—1222no—
273C2×C8—2441no—
274C2×C8—2442no—
275C2×C8—2441no—
276C2×C8—2441no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—22no—
280C4⋊C4—22no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C42—41no—
284C42—41no—
285C42C2×C4×D6111yescharacteristic
286C42#1175822211yescharacteristic
287C42D4×D6111yescharacteristic
288C42D4×D6111yescharacteristic
289C23—4881no—
290C23—4881no—
291C23—4882no—
292C23—4882no—
293C23—2442no—
294C23#1451974911yescharacteristic
295Q8—44no—
296Q8—81no—
297Q8—81no—
298D4—4882no—
299D4—4882no—
300D4—4881no—
301D4—4881no—
302D4—4881no—
303D4—4881no—
304D4—2442no—
305D4—2442no—
306D4—2444no—
307C2×C4—22no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—82no—
313C2×C4C22⋊C4×D6111yescharacteristic
314C2×C4#1451973711yescharacteristic
315C2×C4C4×C22⋊D6111yescharacteristic
316C2×C4#1451975011yescharacteristic
317C2×C4#1451976311yescharacteristic
318C2×C4#1451977311yescharacteristic
319C2×C4#1451979811yescharacteristic
320C2×C4#1451980011yescharacteristic
321C2×C4#1451980212yes—
322C2×C4#1451980312yes—
323C2×C4#1451980411yescharacteristic
324C2×C4#1451980911yescharacteristic
325C8—81no—
326C8—1222no—
327C8—1222no—
328C8—4881no—
329C8—2442no—
330C22—9762no—
331C22—9762no—
332C22—4882no—
333C22—4882no—
334C22—4882no—
335C22#1683966211yescharacteristic
336C22#1683997911yescharacteristic
337C22#1683998611yescharacteristic
338C22#1684001312yes—
339C22#1684002712yes—
340C4—21no—
341C4—21no—
342C4—82no—
343C4—82no—
344C4#1683975711yescharacteristic
345C4#1683976211yescharacteristic
346C4#1683987212yes—
347C4#1683998011yescharacteristic
348C4#1683998711yescharacteristic
349C4#1684014911yescharacteristic
350C4#1684015211yescharacteristic
351C2—9762no—
352C2#2144538212yes—
353C2#2144538912yes—
354C2#2144669411yescharacteristic
355C2#2144672111yescharacteristic
356C2#2144674811yescharacteristic
subgroupG/H
centerC23#14519749
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1981C2
socleC23×C61#121
prime radicalC2×#14519774C22
cosocleC2×C42×C61C23
hypercenter#1981D61
hypocenterC61#9746
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1981

Complements

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

NH ≅ G/Ntype
3. #21445688C2semidirect
4. C2×#16839512C2semidirect
5. C2×#16839508C2semidirect
7. C61×#1981C2semidirect
10. #16840110C4semidirect
175. #1981D61semidirect
204. C61#9746semidirect

Maximal subgroups

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

subgroupindex
C2×#168401102
#214467462
#214456882
C2×#168395122
C2×#168395082
C2×#168395052
C61×#19812
#974661