Finite Group Databasebeta

← #29579876

Subgroups — #29579876

Order 15616.

626 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×#16840134C211yesmaximal, characteristic
2#21446780C211yesmaximal, characteristic, complemented
3#21446779C211yesmaximal, characteristic, complemented
4#21446626C211yesmaximal, characteristic
5#21445978C211yesmaximal, characteristic, complemented
6C2×#16839484C211yesmaximal, characteristic, complemented
7C61×#1957C211yesmaximal, characteristic
8C22×#11758200—22no—
9C2×#14519777C2211yescharacteristic
10#16840134—22no—
11#16840134C414yescomplemented
12C2×#14519710—22no—
13C2×#14519698—22no—
14C2×C4×#92418C2211yescharacteristic
15C2×C4×#92418C2211yescharacteristic
16#16839632C2211yescharacteristic
17#16839525—22no—
18#16839524—22no—
19#16839484—22no—
20C2×#127×C61C2211yescharacteristic
21C2×#102×C61—22no—
22C2×C4×C8×C61C2211yescharacteristic
23C61×#384C2211yescharacteristic
24C22×Dic122—21no—
25C2×#11758200—28no—
26C2×#11758200—44no—
27C2×#11758200—44no—
28C22×#92418D412yes—
29C22×#92418D412yes—
30#14519777—21no—
31#14519777—21no—
32#14519777—21no—
33#14519777C2×C412yes—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61—21no—
38C2×C4⋊Dic61—21no—
39#14519710—44no—
40#14519698—44no—
41C4×#92418—21no—
42C4×#92418—21no—
43C4×#92418C2×C412yes—
44C4×#92418D412yes—
45C22×D4×C61—21no—
46C22×D4×C61—21no—
47C22×D4×C61—21no—
48C22×C8×C61D412yes—
49#127×C61—21no—
50#127×C61—21no—
51#127×C61—21no—
52#127×C61C2×C412yes—
53C2×C4⋊C4×C61—21no—
54C2×C4⋊C4×C61—21no—
55C2×C4⋊C4×C61—21no—
56C2×C42×C61C2311yescharacteristic
57#102×C61—44no—
58C4×C8×C61—21no—
59C4×C8×C61—21no—
60C24×C61—41no—
61C2×D4×C61—22no—
62C2×D4×C61—22no—
63C2×D4×C61—22no—
64C2×D4×C61—41no—
65C2×D4×C61—41no—
66C2×D4×C61—41no—
67C2×D4×C61—42no—
68C2×D4×C61—42no—
69C2×D4×C61—42no—
70C2×D4×C61—42no—
71C2×D4×C61—42no—
72C2×D4×C61—42no—
73C22×C4×C61—41no—
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C22×Dic61—41no—
78C22×Dic61—41no—
79C2×Dic122—22no—
80C2×Dic122—42no—
81C2×Dic122—42no—
82C2×Dic122—41no—
83C2×C8×C61—22no—
84C2×C8×C61—22no—
85C2×C8×C61—22no—
86C4⋊C4×C61—42no—
87C4⋊C4×C61—42no—
88C4⋊C4×C61—42no—
89C42×C61C22×C411yescharacteristic
90C42×C61C2×D411yescharacteristic
91C42×C61#4111yescharacteristic
92C42×C61#4111yescharacteristic
93#11758200—416no—
94C4⋊Dic61—22no—
95C4⋊Dic61—22no—
96C4⋊Dic61—41no—
97C4⋊Dic61—41no—
98C4⋊Dic61—42no—
99C4⋊Dic61—42no—
100C4⋊Dic61—42no—
101C2×#92418—22no—
102C2×#92418—22no—
103C2×#92418—22no—
104C2×#92418C22⋊C414yes—
105C2×#92418D814yes—
106C2×#92418SD1614yes—
107C23×C61—42no—
108C23×C61—81no—
109C23×C61—81no—
110C23×C61—81no—
111C23×C61—81no—
112C23×C61—81no—
113C23×C61—81no—
114C23×C61#12711yescharacteristic
115D4×C61—44no—
116D4×C61—44no—
117D4×C61—44no—
118D4×C61—82no—
119D4×C61—82no—
120D4×C61—82no—
121C2×C4×C61—81no—
122C2×C4×C61—81no—
123C2×C4×C61—81no—
124C2×C4×C61C2×C22⋊C411yescharacteristic
125C2×C4×C61C4×D411yescharacteristic
126C2×C4×C61C4×D411yescharacteristic
127C2×C4×C61#12111yescharacteristic
128C2×C4×C61#12111yescharacteristic
129C2×C4×C61#12411yescharacteristic
130C2×C4×C61C2×D812yes—
131C2×C4×C61C2×SD1612yes—
132C2×C4×C61AGL(1,ℤ/8)12yes—
133C2×C4×C61AGL(1,ℤ/8)12yes—
134C2×C4×C61#13712yes—
135C2×C4×C61#13712yes—
136C2×Dic61—42no—
137C2×Dic61—81no—
138C2×Dic61—81no—
139C2×Dic61—81no—
140C2×Dic61—81no—
141C2×Dic61—81no—
142Dic122—44no—
143Dic122—82no—
144C8×C61—42no—
145#92418—42no—
146#92418#10218yescomplemented
147#9842—611nomaximal, Sylow
148C22×C61—82no—
149C22×C61—82no—
150C22×C61—82no—
151C22×C61—161no—
152C22×C61—161no—
153C22×C61—161no—
154C22×C61—161no—
155C22×C61#39011yescharacteristic
156C22×C61#49211yescharacteristic
157C22×C61#49311yescharacteristic
158C22×C61#49611yescharacteristic
159C22×C61#49611yescharacteristic
160C22×C61#49711yescharacteristic
161C22×C61#49711yescharacteristic
162C4×C61—161no—
163C4×C61C2×#10212yes—
164C4×C61#44012yes—
165C4×C61#44012yes—
166C4×C61#46812yes—
167C4×C61#46812yes—
168C4×C61#48612yes—
169Dic61—82no—
170Dic61—161no—
171C2×#492—611no—
172#1990—611no—
173#1990—611no—
174#1957—611no—
175#1957D6111yescharacteristic
176#1845—611no—
177C2×#322—611no—
178C2×C61—162no—
179C2×C61#171411yescharacteristic
180C2×C61#171411yescharacteristic
181C2×C61#172111yescharacteristic
182C2×C61#172211yescharacteristic
183C2×C61#195711yescharacteristic
184C2×C61#197311yescharacteristic
185C2×C61#197311yescharacteristic
186C22×SD16—1222no—
187C2×C4⋊Q8—611no—
188C2×#127C2×D6111yescharacteristic
189#492—614no—
190#492—1222no—
191C2×#107—1222no—
192C2×#102—22no—
193C2×#102—1222no—
194C2×C4×C8—611no—
195C2×C4×C8—611no—
196C2×C4×C8C2×D6111yescharacteristic
197#384—611no—
198#384C2×D6111yescharacteristic
199#340—1222no—
200#340—1222no—
201#322—1222no—
202C61#984211yescharacteristic, complemented, Sylow
203C22×Q8—1221no—
204C22×D4—21no—
205C22×D4—21no—
206C22×D4—21no—
207C2×SD16—1228no—
208C2×SD16—2444no—
209C2×SD16—2444no—
210C22×C8—612no—
211C22×C8—612no—
212C22×C8C22⋊D6112yes—
213C4⋊Q8—612no—
214C4⋊Q8—1221no—
215C4⋊Q8—1221no—
216C4⋊Q8—1221no—
217#127—21no—
218#127—21no—
219#127—21no—
220#127C4×D6112yes—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—1221no—
225C2×C4⋊C4—1221no—
226C2×C4⋊C4—1221no—
227C2×C4⋊C4—1221no—
228C2×C4⋊C4—1221no—
229C2×C42C22×D6111yescharacteristic
230#107—2444no—
231#102—44no—
232#102—2444no—
233C4×C8—21no—
234C4×C8—21no—
235C4×C8—612no—
236C4×C8—612no—
237C4×C8—1221no—
238C4×C8—1221no—
239C24—41no—
240C2×Q8—1222no—
241C2×Q8—2442no—
242C2×Q8—2442no—
243C2×Q8—2441no—
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—22no—
247C2×D4—41no—
248C2×D4—41no—
249C2×D4—41no—
250C2×D4—42no—
251C2×D4—42no—
252C2×D4—42no—
253C2×D4—42no—
254C2×D4—42no—
255C2×D4—42no—
256C22×C4—41no—
257C22×C4—2441no—
258C22×C4—2441no—
259C22×C4D4×D6111yescharacteristic
260C22×C4D4×D6111yescharacteristic
261C22×C4C2×C22⋊D6111yescharacteristic
262SD16—24416no—
263C2×C8—22no—
264C2×C8—22no—
265C2×C8—22no—
266C2×C8—614no—
267C2×C8—614no—
268C2×C8—614no—
269C2×C8—1222no—
270C2×C8—1222no—
271C2×C8—1222no—
272C4⋊C4—42no—
273C4⋊C4—42no—
274C4⋊C4—42no—
275C4⋊C4—1222no—
276C4⋊C4—1222no—
277C4⋊C4—2442no—
278C4⋊C4—2442no—
279C4⋊C4—2442no—
280C4⋊C4—2441no—
281C4⋊C4—2441no—
282C42C2×C4×D6111yescharacteristic
283C42#1175822211yescharacteristic
284C42D4×D6111yescharacteristic
285C42#1175822411yescharacteristic
286C23—42no—
287C23—81no—
288C23—81no—
289C23—81no—
290C23—81no—
291C23—81no—
292C23—81no—
293C23#1451977311yescharacteristic
294Q8—4882no—
295Q8—2444no—
296D4—44no—
297D4—44no—
298D4—44no—
299D4—82no—
300D4—82no—
301D4—82no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—4881no—
306C2×C4—4881no—
307C2×C4—4881no—
308C2×C4—4881no—
309C2×C4—4881no—
310C2×C4—2442no—
311C2×C4C22⋊C4×D6111yescharacteristic
312C2×C4#1451973711yescharacteristic
313C2×C4C4×C22⋊D6111yescharacteristic
314C2×C4#1451974911yescharacteristic
315C2×C4#1451975011yescharacteristic
316C2×C4#1451976311yescharacteristic
317C2×C4D8×D6112yes—
318C2×C4SD16×D6112yes—
319C2×C4#1451980112yes—
320C2×C4#1451980312yes—
321C2×C4#1451980612yes—
322C2×C4#1451980712yes—
323C8—42no—
324C8—618no—
325C8—2442no—
326C22—82no—
327C22—82no—
328C22—82no—
329C22—161no—
330C22—161no—
331C22—161no—
332C22—161no—
333C22#1683966211yescharacteristic
334C22#1684013311yescharacteristic
335C22#1684013711yescharacteristic
336C22#1684014911yescharacteristic
337C22#1684015011yescharacteristic
338C22#1684015311yescharacteristic
339C22#1684015711yescharacteristic
340C4—161no—
341C4—9761no—
342C4—4882no—
343C4#102×D6112yes—
344C4#1683985912yes—
345C4#1683986212yes—
346C4#1684000612yes—
347C4#1684000712yes—
348C4#1684010712yes—
349C2—162no—
350C2#2144543911yescharacteristic
351C2#2144544011yescharacteristic
352C2#2144548411yescharacteristic
353C2#2144549211yescharacteristic
354C2#2144662311yescharacteristic
355C2#2144669911yescharacteristic
356C2#2144670111yescharacteristic
subgroupG/H
centerC23#14519773
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1957C2
socleC23×C61#127
prime radicalC2×#127×C61C22
cosocleC2×C42×C61C23
hypercenter#1957D61
hypocenterC61#9842
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1957

Complements

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

NH ≅ G/Ntype
2. #21446780C2semidirect
3. #21446779C2semidirect
5. #21445978C2semidirect
6. C2×#16839484C2semidirect
11. #16840134C4semidirect
146. #92418#102semidirect
202. C61#9842semidirect

Maximal subgroups

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

subgroupindex
C2×#168401342
#214467802
#214467792
#214466262
#214459782
C2×#168394842
C61×#19572
#984261