Finite Group Databasebeta

← #29579367

Subgroups — #29579367

Order 15616.

428 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456144C211yesmaximal, characteristic
2#21445684C211yesmaximal, characteristic, complemented
3#21444565C211yesmaximal, characteristic, complemented
4#21444318C211yesmaximal, characteristic, complemented
5#21444315C211yesmaximal, characteristic
6#21444217C211yesmaximal, characteristic
7C61×#1481C211yesmaximal, characteristic, complemented
8#16840312C2211yescharacteristic
9#16840119—21no—
10#16840119—21no—
11#16840114C411yescharacteristic, complemented
12#16840114C411yescharacteristic, complemented
13#16840110C411yescharacteristic, complemented
14#16840110C411yescharacteristic, complemented
15#16839815C2211yescharacteristic
16#16839756—21no—
17#16839756—21no—
18C2×C4×#92418C2211yescharacteristic
19C2×C8×Dic61—21no—
20C4×C4⋊Dic61C2211yescharacteristic
21#16839516—21no—
22#16839514—21no—
23#16839512—21no—
24#16839499—22no—
25#16839497—22no—
26#16839489—22no—
27C61×#533C2211yescharacteristic
28C61×#431C2211yescharacteristic
29C2×C4⋊C8×C61C2211yescharacteristic
30C61×Q8⋊C8—22no—
31C2×#11758222—21no—
32C22×#92418D411yescharacteristic
33C22×#92418D411yescharacteristic
34#14519777C2×C411yescharacteristic
35#14519774C2×C411yescharacteristic
36#14519765—21no—
37#14519751—21no—
38#14519751—21no—
39C4×D244—21no—
40C4×D244—21no—
41C2×C4⋊Dic61—21no—
42C2×C4×Dic61—21no—
43C4⋊#92418—21no—
44#14519700—21no—
45#14519700—21no—
46#14519700—21no—
47#14519700—21no—
48#14519697—21no—
49#14519697—21no—
50#14519697—21no—
51#14519697—21no—
52C22⋊#92418—21no—
53C4×#92418—21no—
54C4×#92418C2×C411yescharacteristic
55C4×#92418C2×C411yescharacteristic
56C4×#92418D411yescharacteristic
57C4×#92418D411yescharacteristic
58C8×Dic61—42no—
59#14519684D412yes—
60C22×C8×C61—21no—
61C4⋊Q8×C61C2×C411yescharacteristic
62C4⋊Q8×C61C2×C411yescharacteristic
63#125×C61—21no—
64C22⋊Q8×C61—21no—
65C22⋊Q8×C61—21no—
66C4×Q8×C61—21no—
67C4×Q8×C61—21no—
68#117×C61—21no—
69C2×C42×C61C2311yescharacteristic
70C4⋊C8×C61—21no—
71C4⋊C8×C61—21no—
72C4⋊C8×C61D412yes—
73C22⋊C8×C61—21no—
74C4×C8×C61—21no—
75C2×Q8×C61—21no—
76C2×Q8×C61—21no—
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61#4111yescharacteristic
80C2×C22⋊D61—41no—
81C22×Dic61—22no—
82#11758222—41no—
83#11758222—41no—
84#11758222—41no—
85#11758222—41no—
86C2×D244—21no—
87C2×D244—21no—
88C2×D244—21no—
89C2×C4×D61—41no—
90C2×Dic122—21no—
91C2×C8×C61—22no—
92C2×C8×C61—41no—
93C2×C8×C61—41no—
94C2×C8×C61—41no—
95C4⋊C4×C61—21no—
96C4⋊C4×C61—21no—
97C4⋊C4×C61—21no—
98C4⋊C4×C61—21no—
99C4⋊C4×C61—41no—
100C4⋊C4×C61—41no—
101C22⋊C4×C61—41no—
102C42×C61—41no—
103C42×C61C22×C411yescharacteristic
104C42×C61C2×D411yescharacteristic
105C42×C61C2×D411yescharacteristic
106C42×C61#4111yescharacteristic
107#11758198—41no—
108#11758198—41no—
109C4⋊Dic61—24no—
110C4⋊Dic61—21no—
111C4⋊Dic61—21no—
112C4×Dic61—41no—
113C4×Dic61—41no—
114C2×#92418—21no—
115C2×#92418—21no—
116C2×#92418—21no—
117C2×#92418—21no—
118C2×#92418—41no—
119C2×#92418C22⋊C411yescharacteristic
120C2×#92418C22⋊C411yescharacteristic
121C2×#92418C22⋊C411yescharacteristic
122C2×#92418C22⋊C411yescharacteristic
123C23×C61#12111yescharacteristic
124C22×D61—41no—
125Q8×C61—42no—
126Q8×C61—81no—
127C2×C4×C61—22no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61C2×C22⋊C411yescharacteristic
132C2×C4×C61C4×D411yescharacteristic
133C2×C4×C61C4×D411yescharacteristic
134C2×C4×C61#12111yescharacteristic
135C2×C4×C61#12411yescharacteristic
136C2×C4×C61#12711yescharacteristic
137C2×C4×C61#13511yescharacteristic
138C2×C4×C61#13511yescharacteristic
139C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C61#13711yescharacteristic
141C22⋊D61—81no—
142C22⋊D61—81no—
143C2×Dic61—24no—
144C2×Dic61—42no—
145C2×Dic61—42no—
146C2×Dic61—41no—
147D244—41no—
148D244—41no—
149D244—42no—
150D244—81no—
151C4×D61—81no—
152C4×D61—81no—
153Dic122—41no—
154Dic122—41no—
155C8×C61—42no—
156C8×C61—81no—
157#92418—21no—
158#92418—21no—
159#92418—21no—
160#92418—21no—
161#92418—81no—
162#9751—611nomaximal, Sylow
163C22×C61—21no—
164C22×C61—21no—
165C22×C61#39011yescharacteristic
166C22×C61#46311yescharacteristic
167C22×C61#46411yescharacteristic
168C2×D61—81no—
169C2×D61—81no—
170C2×D61—81no—
171C4×C61—21no—
172C4×C61—21no—
173C4×C61—21no—
174C4×C61—81no—
175C4×C61—81no—
176C4×C61#41611yescharacteristic
177C4×C61#41711yescharacteristic
178C4×C61#44312yes—
179C4×C61#46311yescharacteristic
180C4×C61#46411yescharacteristic
181Dic61—44no—
182Dic61—81no—
183#3131—611no—
184C8×C4⋊C4—611no—
185#1564—611no—
186#1503—611no—
187#1502—611no—
188#1481D6111yescharacteristic, complemented
189#1480—611no—
190C2×C61—21no—
191C2×C61—21no—
192C2×C61#197411yescharacteristic
193C2×C61#197611yescharacteristic
194C2×C61#198311yescharacteristic
195D61—161no—
196#533C2×D6111yescharacteristic
197#532—611no—
198#488—1221no—
199#488—1221no—
200#487—611no—
201#487—611no—
202#486—611no—
203#486—611no—
204#431—611no—
205#431C2×D6111yescharacteristic
206C2×C4⋊C8C2×D6111yescharacteristic
207#416—1221no—
208#416—1221no—
209C2×C4×C8—611no—
210C2×C4×C8—1221no—
211C4×C4⋊C4—611no—
212#336—1221no—
213#335—1221no—
214#334—1221no—
215#328—1222no—
216#327—1222no—
217Q8⋊C8—22no—
218D4⋊C8—1222no—
219C61#975111yescharacteristic, complemented, Sylow
220C2×#41—1221no—
221C22×C8—21no—
222C22×C8—611no—
223C22×C8—611no—
224C4⋊Q8—611no—
225C4⋊Q8C4×D6111yescharacteristic
226C4⋊Q8C4×D6111yescharacteristic
227#127—611no—
228#125—21no—
229#124—1221no—
230C22⋊Q8—21no—
231C22⋊Q8—21no—
232#121—1221no—
233#121—1221no—
234C4×Q8—21no—
235C4×Q8—21no—
236C4×D4—1221no—
237C4×D4—1221no—
238#117—21no—
239C2×C4⋊C4—1221no—
240C2×C42—1221no—
241C2×C42C22×D6111yescharacteristic
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—1221no—
245C4⋊C8C22⋊D6112yes—
246#103—1221no—
247#103—1221no—
248#103—1221no—
249#103—1221no—
250#102—1221no—
251#102—1221no—
252#102—1221no—
253#102—1221no—
254C22⋊C8—21no—
255C22⋊C8—1221no—
256C4×C8—21no—
257C4×C8—611no—
258C4×C8—611no—
259C4×C8—611no—
260C4×C8—611no—
261C4×C8—1221no—
262C4×C8—2442no—
263#95—612no—
264#41—2441no—
265#41—2441no—
266#41—2441no—
267#41—2441no—
268C2×Q8—21no—
269C2×Q8—21no—
270C2×Q8—1221no—
271C2×D4—1221no—
272C2×D4—1221no—
273C2×D4—1221no—
274C2×D4—2441no—
275C22×C4—1222no—
276C22×C4—2441no—
277C22×C4#1175822211yescharacteristic
278C22×C4D4×D6111yescharacteristic
279C22×C4D4×D6111yescharacteristic
280C2×C8—22no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—611no—
285C2×C8—611no—
286C2×C8—611no—
287C2×C8—611no—
288C2×C8—1221no—
289C2×C8—1221no—
290C2×C8—1221no—
291C2×C8—1221no—
292C2×C8—2441no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—1224no—
300C4⋊C4—1221no—
301C4⋊C4—1221no—
302C22⋊C4—41no—
303C22⋊C4—2441no—
304C22⋊C4—2441no—
305C42—41no—
306C42—2441no—
307C42—2441no—
308C42C2×C4×D6111yescharacteristic
309C42D4×D6111yescharacteristic
310C42#1175822411yescharacteristic
311C42C2×C22⋊D6111yescharacteristic
312C23—2441no—
313C23#1451975011yescharacteristic
314Q8—42no—
315Q8—81no—
316Q8—2441no—
317Q8—2441no—
318D4—4881no—
319D4—4881no—
320D4—4881no—
321D4—2441no—
322D4—2441no—
323D4—2442no—
324C2×C4—22no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—1224no—
329C2×C4—4881no—
330C2×C4—4881no—
331C2×C4—2441no—
332C2×C4—2442no—
333C2×C4—2442no—
334C2×C4C22⋊C4×D6111yescharacteristic
335C2×C4#1451973711yescharacteristic
336C2×C4C4×C22⋊D6111yescharacteristic
337C2×C4#1451974911yescharacteristic
338C2×C4#1451976311yescharacteristic
339C2×C4#1451977311yescharacteristic
340C2×C4#1451979811yescharacteristic
341C2×C4#1451980011yescharacteristic
342C2×C4#1451980411yescharacteristic
343C2×C4#1451980911yescharacteristic
344C8—42no—
345C8—81no—
346C8—1221no—
347C8—1221no—
348C8—1221no—
349C8—1221no—
350C8—4881no—
351C22—21no—
352C22—21no—
353C22—4881no—
354C22—4881no—
355C22—4881no—
356C22#1683966211yescharacteristic
357C22#1683998011yescharacteristic
358C22#1683998711yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—81no—
363C4—81no—
364C4—4881no—
365C4—2444no—
366C4#1683975711yescharacteristic
367C4#1683976211yescharacteristic
368C4#1683987712yes—
369C4#1683997911yescharacteristic
370C4#1683998611yescharacteristic
371C2—21no—
372C2—21no—
373C2—9761no—
374C2#2144670611yescharacteristic
375C2#2144671611yescharacteristic
376C2#2144674811yescharacteristic
subgroupG/H
centerC2×C4#14519749
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1481C2
socleC22×C61#390
prime radical#16840312C22
cosocleC2×C42×C61C23
hypercenter#1481D61
hypocenterC61#9751
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1481

Complements

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

NH ≅ G/Ntype
2. #21445684C2semidirect
3. #21444565C2semidirect
4. #21444318C2semidirect
7. C61×#1481C2semidirect
11. #16840114C4semidirect
12. #16840114C4semidirect
13. #16840110C4semidirect
14. #16840110C4semidirect
188. #1481D61semidirect
219. C61#9751semidirect

Maximal subgroups

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

subgroupindex
#214561442
#214456842
#214445652
#214443182
#214443152
#214442172
C61×#14812
#975161