Finite Group Databasebeta

← #29575239

Subgroups — #29575239

Order 15616.

470 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456379C211yesmaximal, characteristic
2#21454768C211yesmaximal, characteristic, complemented
3#21446737C211yesmaximal, characteristic
4#21444219C211yesmaximal, characteristic
5#21443660C211yesmaximal, characteristic, complemented
6#21443655C211yesmaximal, characteristic, complemented
7C61×#1503C211yesmaximal, characteristic, complemented
8#16840312C2211yescharacteristic
9#16840158C411yescharacteristic, complemented
10#16840136C411yescharacteristic, complemented
11#16840112C411yescharacteristic, complemented
12#16840110C411yescharacteristic, complemented
13#16839993—22no—
14#16839893—21no—
15#16839893—22no—
16Q8×#92418—21no—
17C4×#11758201—22no—
18#16839789—21no—
19C2×C4⋊#92418C2211yescharacteristic
20C2×#14519705—21no—
21C2×#14519705—21no—
22#16839718—21no—
23C4×#11758194C2211yescharacteristic
24C2×C4×#92418C2211yescharacteristic
25#16839491—21no—
26#16839491—21no—
27C61×#533C2211yescharacteristic
28C61×#431C2211yescharacteristic
29C4×C4⋊C4×C61C2211yescharacteristic
30C61×#328—22no—
31C2×#11758222—21no—
32C2×#11758201—22no—
33C2×#11758194D411yescharacteristic
34C2×#11758194D411yescharacteristic
35C22×#92418—21no—
36C22×#92418—21no—
37#14519777C2×C411yescharacteristic
38#14519774C2×C411yescharacteristic
39#14519765—21no—
40#14519751—21no—
41#14519751—21no—
42C4×D244—21no—
43C4×D244—21no—
44#14519708—22no—
45C4⋊#92418—22no—
46C4⋊#92418—22no—
47C4⋊#92418—21no—
48C4⋊#92418D411yescharacteristic
49C4⋊#92418D411yescharacteristic
50#14519705—42no—
51#14519705—42no—
52#14519701—22no—
53#14519697—22no—
54#14519688—22no—
55#14519688—21no—
56C4×#92418—22no—
57C4×#92418—21no—
58C4×#92418—21no—
59C4×#92418C2×C411yescharacteristic
60C4×#92418C2×C411yescharacteristic
61C4⋊Q8×C61C2×C411yescharacteristic
62C4⋊Q8×C61C2×C411yescharacteristic
63#125×C61—21no—
64C22⋊Q8×C61—21no—
65C22⋊Q8×C61D412yes—
66C4×Q8×C61—21no—
67C4×Q8×C61D412yes—
68#117×C61—21no—
69C2×C4⋊C4×C61—21no—
70C2×C42×C61—21no—
71C2×C42×C61C2311yescharacteristic
72C4⋊C8×C61—21no—
73C22⋊C8×C61—21no—
74C4×C8×C61—21no—
75#95×C61—21no—
76C2×Q8×C61—21no—
77C2×Q8×C61C22⋊C412yes—
78C22×C4×C61—41no—
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61C2×D411yescharacteristic
81C22×C4×C61#4111yescharacteristic
82C2×C22⋊D61—41no—
83#11758222—41no—
84#11758222—41no—
85#11758222—41no—
86#11758222—41no—
87C2×D244—21no—
88C2×D244—21no—
89C2×D244—21no—
90C2×C4×D61—41no—
91C2×Dic122—21no—
92C2×C8×C61—41no—
93C4⋊C4×C61—21no—
94C4⋊C4×C61—21no—
95C4⋊C4×C61—21no—
96C4⋊C4×C61—22no—
97C4⋊C4×C61—22no—
98C4⋊C4×C61—22no—
99C4⋊C4×C61—41no—
100C4⋊C4×C61C22⋊C412yes—
101C22⋊C4×C61—22no—
102C42×C61—22no—
103C42×C61—41no—
104C42×C61—41no—
105C42×C61C22×C411yescharacteristic
106C42×C61C2×D411yescharacteristic
107C42×C61C2×D411yescharacteristic
108C42×C61#4111yescharacteristic
109#11758201—44no—
110#11758198—41no—
111#11758198—41no—
112C4⋊Dic61—21no—
113C4⋊Dic61—21no—
114#11758194—21no—
115#11758194—21no—
116#11758194—21no—
117#11758194SD1612yescomplemented
118C2×#92418—21no—
119C2×#92418—21no—
120C2×#92418—21no—
121C2×#92418—21no—
122C2×#92418—21no—
123C2×#92418—21no—
124C2×#92418—42no—
125C2×#92418—41no—
126C2×#92418—41no—
127C23×C61#12111yescharacteristic
128C22×D61—41no—
129Q8×C61—42no—
130Q8×C61—41no—
131Q8×C61—41no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—22no—
135C2×C4×C61—22no—
136C2×C4×C61—41no—
137C2×C4×C61—42no—
138C2×C4×C61—81no—
139C2×C4×C61—81no—
140C2×C4×C61C2×C22⋊C411yescharacteristic
141C2×C4×C61C4×D411yescharacteristic
142C2×C4×C61C4×D411yescharacteristic
143C2×C4×C61#12011yescharacteristic
144C2×C4×C61#12111yescharacteristic
145C2×C4×C61#12311yescharacteristic
146C2×C4×C61C2×SD1611yescharacteristic
147C2×C4×C61#13511yescharacteristic
148C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C61#13711yescharacteristic
150C22⋊D61—81no—
151C22⋊D61—81no—
152C2×Dic61—41no—
153D244—42no—
154D244—41no—
155D244—41no—
156D244—41no—
157D244—41no—
158C4×D61—81no—
159C4×D61—81no—
160Dic122—41no—
161Dic122—41no—
162C8×C61—81no—
163#92418—22no—
164#92418—22no—
165#92418—41no—
166#92418—41no—
167#92418—41no—
168#92418—41no—
169#9054—611nomaximal, Sylow
170C22×C61—21no—
171C22×C61—21no—
172C22×C61#38611yescharacteristic
173C22×C61#46011yescharacteristic
174C22×C61#46411yescharacteristic
175C2×D61—81no—
176C2×D61—81no—
177C2×D61—81no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—42no—
182C4×C61—42no—
183C4×C61—82no—
184C4×C61C4×SD1611yescharacteristic
185C4×C61#44011yescharacteristic
186C4×C61#44311yescharacteristic
187C4×C61#44411yescharacteristic
188C4×C61#44811yescharacteristic
189C4×C61#44911yescharacteristic
190Dic61—81no—
191#3167—611no—
192#2962—611no—
193#1980—611no—
194#1503D6111yescharacteristic, complemented
195#1480—611no—
196#1279—611no—
197#1278—611no—
198C2×C61—21no—
199C2×C61—21no—
200C2×C61#187611yescharacteristic
201C2×C61#188011yescharacteristic
202C2×C61#188411yescharacteristic
203D61—161no—
204#533C2×D6111yescharacteristic
205#532—611no—
206#498—611no—
207#492—611no—
208#487—611no—
209#486—611no—
210#465—1222no—
211#446—1221no—
212#446—1222no—
213C8×Q8—1221no—
214C4×SD16—1222no—
215#431C2×D6111yescharacteristic
216#424—1221no—
217C2×C4⋊C8—611no—
218C2×#104—1221no—
219C2×#104—1221no—
220#405—1221no—
221C4×M16—611no—
222C2×C4×C8—611no—
223C4×C4⋊C4C2×D6111yescharacteristic
224#328—22no—
225D4⋊C8—1221no—
226D4⋊C8—1221no—
227C61#905411yescharacteristic, complemented, Sylow
228C2×#41—1221no—
229C2×SD16—1222no—
230C2×M16—611no—
231C2×M16—611no—
232C22×C8—1221no—
233C22×C8—1221no—
234C4⋊Q8—611no—
235C4⋊Q8C4×D6111yescharacteristic
236C4⋊Q8C4×D6111yescharacteristic
237#127—611no—
238#125—21no—
239#124—1221no—
240C22⋊Q8—21no—
241C22⋊Q8C22⋊D6112yes—
242#121—1221no—
243#121—1221no—
244C4×Q8—21no—
245C4×Q8D24412yes—
246C4×D4—1221no—
247C4×D4—1221no—
248#117—21no—
249C2×C4⋊C4—21no—
250C2×C42—21no—
251C2×C42C22×D6111yescharacteristic
252#106—1222no—
253C4⋊C8—21no—
254C4⋊C8—611no—
255C4⋊C8—611no—
256C4⋊C8—1222no—
257C4⋊C8—1222no—
258C4⋊C8—1221no—
259#104—2442no—
260#104—2442no—
261#103—1222no—
262#102—1222no—
263C22⋊C8—21no—
264#97—1222no—
265#97—1221no—
266C4×C8—21no—
267C4×C8—611no—
268C4×C8—611no—
269C4×C8—1222no—
270C4×C8—1221no—
271C4×C8—1221no—
272#95—21no—
273#41—2441no—
274#41—2441no—
275#41—2441no—
276#41—2441no—
277C2×Q8—21no—
278C2×Q8—1221no—
279C2×Q8#1175819812yes—
280C2×D4—1221no—
281C2×D4—1221no—
282C2×D4—1221no—
283C2×D4—2441no—
284C22×C4—41no—
285C22×C4—2441no—
286C22×C4D4×D6111yescharacteristic
287C22×C4#1175822411yescharacteristic
288C22×C4C2×C22⋊D6111yescharacteristic
289SD16—2444no—
290M16—612no—
291M16—1221no—
292M16—1221no—
293M16—1221no—
294C2×C8—41no—
295C2×C8—1221no—
296C2×C8—1221no—
297C2×C8—1221no—
298C2×C8—1221no—
299C2×C8—1221no—
300C2×C8—1221no—
301C2×C8—2442no—
302C2×C8—2441no—
303C2×C8—2441no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—22no—
310C4⋊C4—41no—
311C4⋊C4—1221no—
312C4⋊C4—1221no—
313C4⋊C4#1175819812yes—
314C22⋊C4—22no—
315C22⋊C4—2441no—
316C22⋊C4—2441no—
317C42—22no—
318C42—41no—
319C42—41no—
320C42C2×C4×D6111yescharacteristic
321C42C2×D24411yescharacteristic
322C42D4×D6111yescharacteristic
323C42#1175822411yescharacteristic
324C23—2441no—
325C23#1451974911yescharacteristic
326Q8—42no—
327Q8—41no—
328Q8—41no—
329Q8—2441no—
330Q8—2441no—
331D4—4881no—
332D4—4881no—
333D4—2442no—
334D4—2441no—
335D4—2441no—
336D4—2441no—
337D4—2441no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—4881no—
347C2×C4—4881no—
348C2×C4—2441no—
349C2×C4C2×#1175819811yescharacteristic
350C2×C4#1451973711yescharacteristic
351C2×C4#1451973711yescharacteristic
352C2×C4#1451974711yescharacteristic
353C2×C4#1451974911yescharacteristic
354C2×C4#1451976111yescharacteristic
355C2×C4SD16×D6111yescharacteristic
356C2×C4#1451980011yescharacteristic
357C2×C4#1451980411yescharacteristic
358C2×C4#1451980911yescharacteristic
359C8—81no—
360C8—1222no—
361C8—1222no—
362C8—2441no—
363C8—2441no—
364C8—2441no—
365C8—2441no—
366C22—21no—
367C22—21no—
368C22—4881no—
369C22—4881no—
370C22—4881no—
371C22#1683963911yescharacteristic
372C22#1683996011yescharacteristic
373C22#1683998611yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—42no—
378C4—42no—
379C4—82no—
380C4—4881no—
381C4#1683984711yescharacteristic
382C4#1683986511yescharacteristic
383C4#1683987611yescharacteristic
384C4#1683988111yescharacteristic
385C4#1683990211yescharacteristic
386C4#1683991011yescharacteristic
387C2—21no—
388C2—21no—
389C2—9761no—
390C2#2144614411yescharacteristic
391C2#2144617211yescharacteristic
392C2#2144620011yescharacteristic
subgroupG/H
centerC2×C4#14519747
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1503C2
socleC22×C61#386
prime radical#16840312C22
cosocleC2×C42×C61C23
hypercenter#1503D61
hypocenterC61#9054
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. #21454768C2semidirect
5. #21443660C2semidirect
6. #21443655C2semidirect
7. C61×#1503C2semidirect
9. #16840158C4semidirect
10. #16840136C4semidirect
11. #16840112C4semidirect
12. #16840110C4semidirect
117. #11758194SD16semidirect
194. #1503D61semidirect
227. C61#9054semidirect

Maximal subgroups

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

subgroupindex
#214563792
#214547682
#214467372
#214442192
#214436602
#214436552
C61×#15032
#905461