Finite Group Databasebeta

← #29579378

Subgroups — #29579378

Order 15616.

416 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#21445688C211yesmaximal, characteristic, complemented
3#21444565C211yesmaximal, characteristic, complemented
4#21444313C211yesmaximal, characteristic
5#21444222C211yesmaximal, characteristic, complemented
6#21444219C211yesmaximal, characteristic
7C61×#1503C211yesmaximal, characteristic, complemented
8#16840312C2211yescharacteristic
9#16840119—21no—
10#16840119—21no—
11#16840114C411yescharacteristic, complemented
12#16840114C411yescharacteristic, complemented
13#16840110C411yescharacteristic, complemented
14#16840110C411yescharacteristic, complemented
15#16839815C2211yescharacteristic
16C2×C4⋊#92418C2211yescharacteristic
17#16839756—21no—
18#16839756—21no—
19C2×#14519688—21no—
20C2×C4×#92418C2211yescharacteristic
21#16839517—21no—
22#16839514—21no—
23#16839512—21no—
24#16839495—22no—
25Q8⋊#92418—22no—
26#16839491—22no—
27C61×#533C2211yescharacteristic
28C61×#431C2211yescharacteristic
29C4×C4⋊C4×C61C2211yescharacteristic
30C61×#328—22no—
31C2×#11758222—21no—
32C22×#92418—21no—
33C22×#92418D411yescharacteristic
34C22×#92418D411yescharacteristic
35#14519777C2×C411yescharacteristic
36#14519774C2×C411yescharacteristic
37#14519765—21no—
38#14519751—21no—
39#14519751—21no—
40C4×D244—21no—
41C4×D244—21no—
42C4⋊#92418—21no—
43C4⋊#92418—21no—
44C4⋊#92418D412yes—
45#14519700—21no—
46#14519700—21no—
47#14519700—21no—
48#14519700—21no—
49#14519697—21no—
50#14519697—21no—
51#14519697—21no—
52#14519697—21no—
53C22⋊#92418—21no—
54#14519688—42no—
55C4×#92418—21no—
56C4×#92418C2×C411yescharacteristic
57C4×#92418C2×C411yescharacteristic
58C4×#92418D411yescharacteristic
59C4×#92418D411yescharacteristic
60C4⋊Q8×C61C2×C411yescharacteristic
61C4⋊Q8×C61C2×C411yescharacteristic
62#125×C61—21no—
63C22⋊Q8×C61—21no—
64C22⋊Q8×C61—21no—
65C4×Q8×C61—21no—
66C4×Q8×C61—21no—
67#117×C61—21no—
68C2×C4⋊C4×C61—21no—
69C2×C42×C61—21no—
70C2×C42×C61C2311yescharacteristic
71C4⋊C8×C61—21no—
72C22⋊C8×C61—21no—
73C4×C8×C61—21no—
74#95×C61D412yes—
75C2×Q8×C61—21no—
76C2×Q8×C61—21no—
77C22×C4×C61—22no—
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61#4111yescharacteristic
81C2×C22⋊D61—41no—
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—41no—
92C4⋊C4×C61—21no—
93C4⋊C4×C61—21no—
94C4⋊C4×C61—21no—
95C4⋊C4×C61—21no—
96C4⋊C4×C61—42no—
97C4⋊C4×C61—41no—
98C4⋊C4×C61—41no—
99C22⋊C4×C61—41no—
100C42×C61—41no—
101C42×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—21no—
110C4⋊Dic61—21no—
111C2×#92418—21no—
112C2×#92418—21no—
113C2×#92418—21no—
114C2×#92418—21no—
115C2×#92418—22no—
116C2×#92418—41no—
117C2×#92418—41no—
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—42no—
130C2×C4×C61—42no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—42no—
134C2×C4×C61C2×C22⋊C411yescharacteristic
135C2×C4×C61C4×D411yescharacteristic
136C2×C4×C61C4×D411yescharacteristic
137C2×C4×C61#12111yescharacteristic
138C2×C4×C61#12411yescharacteristic
139C2×C4×C61#12711yescharacteristic
140C2×C4×C61#13511yescharacteristic
141C2×C4×C61#13511yescharacteristic
142C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C61#13711yescharacteristic
144C22⋊D61—81no—
145C22⋊D61—81no—
146C2×Dic61—41no—
147D244—41no—
148D244—41no—
149D244—42no—
150D244—81no—
151C4×D61—81no—
152C4×D61—81no—
153Dic122—41no—
154Dic122—41no—
155C8×C61—81no—
156#92418—21no—
157#92418—21no—
158#92418—21no—
159#92418—21no—
160#92418—42no—
161#92418—81no—
162#9754—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—82no—
175C4×C61—81no—
176C4×C61—81no—
177C4×C61#41611yescharacteristic
178C4×C61#41711yescharacteristic
179C4×C61#44412yes—
180C4×C61#46311yescharacteristic
181C4×C61#46411yescharacteristic
182Dic61—81no—
183#3131—611no—
184#1770—611no—
185#1564—611no—
186#1503D6111yescharacteristic, complemented
187#1502—611no—
188#1481—611no—
189#1480—611no—
190C2×C61—21no—
191C2×C61—21no—
192C2×C61#197511yescharacteristic
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⋊C8—611no—
207#416—1221no—
208#416—1221no—
209C2×#97—1221no—
210C2×C4×C8—611no—
211C4×C4⋊C4C2×D6111yescharacteristic
212#336—1221no—
213#335—1221no—
214#334—1221no—
215#328—22no—
216#327—1222no—
217Q8⋊C8—1222no—
218D4⋊C8—1222no—
219C61#975411yescharacteristic, complemented, Sylow
220C2×#41—1221no—
221C22×C8—611no—
222C22×C8—611no—
223C22×C8—1221no—
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—21no—
240C2×C42—21no—
241C2×C42C22×D6111yescharacteristic
242C4⋊C8—21no—
243C4⋊C8—612no—
244C4⋊C8—1221no—
245C4⋊C8—1221no—
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—
256#97—2442no—
257C4×C8—21no—
258C4×C8—611no—
259C4×C8—611no—
260C4×C8—611no—
261C4×C8—611no—
262C4×C8—1221no—
263#95C22⋊D6112yes—
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—22no—
276C22×C4—2441no—
277C22×C4D4×D6111yescharacteristic
278C22×C4#1175822411yescharacteristic
279C22×C4C2×C22⋊D6111yescharacteristic
280C2×C8—41no—
281C2×C8—611no—
282C2×C8—611no—
283C2×C8—611no—
284C2×C8—611no—
285C2×C8—1221no—
286C2×C8—1221no—
287C2×C8—1221no—
288C2×C8—1221no—
289C2×C8—1222no—
290C2×C8—2441no—
291C2×C8—2441no—
292C2×C8—2441no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—42no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—1221no—
301C4⋊C4—1221no—
302C22⋊C4—41no—
303C22⋊C4—2441no—
304C22⋊C4—2441no—
305C42—41no—
306C42—41no—
307C42—41no—
308C42C2×C4×D6111yescharacteristic
309C42#1175822211yescharacteristic
310C42D4×D6111yescharacteristic
311C42D4×D6111yescharacteristic
312C23—2441no—
313C23#1451974911yescharacteristic
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—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—4881no—
332C2×C4—4881no—
333C2×C4—2441no—
334C2×C4C22⋊C4×D6111yescharacteristic
335C2×C4#1451973711yescharacteristic
336C2×C4C4×C22⋊D6111yescharacteristic
337C2×C4#1451975011yescharacteristic
338C2×C4#1451976311yescharacteristic
339C2×C4#1451977311yescharacteristic
340C2×C4#1451979811yescharacteristic
341C2×C4#1451980011yescharacteristic
342C2×C4#1451980411yescharacteristic
343C2×C4#1451980911yescharacteristic
344C8—81no—
345C8—1221no—
346C8—1221no—
347C8—1221no—
348C8—1221no—
349C8—4881no—
350C8—2442no—
351C22—21no—
352C22—21no—
353C22—4881no—
354C22—4881no—
355C22—4881no—
356C22#1683966211yescharacteristic
357C22#1683997911yescharacteristic
358C22#1683998611yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—82no—
363C4—81no—
364C4—81no—
365C4—4881no—
366C4#1683975711yescharacteristic
367C4#1683976211yescharacteristic
368C4#1683988112yes—
369C4#1683998011yescharacteristic
370C4#1683998711yescharacteristic
371C2—21no—
372C2—21no—
373C2—9761no—
374C2#2144670911yescharacteristic
375C2#2144671411yescharacteristic
376C2#2144674811yescharacteristic
subgroupG/H
centerC2×C4#14519750
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1503C2
socleC22×C61#390
prime radical#16840312C22
cosocleC2×C42×C61C23
hypercenter#1503D61
hypocenterC61#9754
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1503

Complements

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

NH ≅ G/Ntype
2. #21445688C2semidirect
3. #21444565C2semidirect
5. #21444222C2semidirect
7. C61×#1503C2semidirect
11. #16840114C4semidirect
12. #16840114C4semidirect
13. #16840110C4semidirect
14. #16840110C4semidirect
186. #1503D61semidirect
219. C61#9754semidirect

Maximal subgroups

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

subgroupindex
#214561442
#214456882
#214445652
#214443132
#214442222
#214442192
C61×#15032
#975461