Finite Group Databasebeta

← #29583869

Subgroups — #29583869

Order 15616.

474 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840053C211yesmaximal, characteristic
2#21446779C211yesmaximal, characteristic, complemented
3#21446612C211yesmaximal, characteristic
4#21445816C211yesmaximal, characteristic
5C2×#16839514C211yesmaximal, characteristic, complemented
6C2×#16839510C211yesmaximal, characteristic, complemented
7C61×#1296C211yesmaximal, characteristic, complemented
8C2×#14519777C2211yescharacteristic
9C2×C4×D244C2211yescharacteristic
10#16840053—22no—
11#16840053—22no—
12C2×#14519709—21no—
13C2×C4⋊#92418C2211yescharacteristic
14C2×#14519699—21no—
15C2×#14519697—21no—
16C2×#14519689—21no—
17C2×#14519689—21no—
18C2×C4×#92418C2211yescharacteristic
19#16839524—21no—
20#16839524—21no—
21#16839524—21no—
22#16839514—22no—
23#16839510—22no—
24C2×C4⋊C8×C61C2211yescharacteristic
25C2×C4⋊C8×C61C2211yescharacteristic
26C61×#384C2211yescharacteristic
27C22×Dic122—21no—
28C22×D244D411yescharacteristic
29C22×C4×D61—21no—
30C22×#92418—21no—
31C22×#92418D411yescharacteristic
32C22×#92418D411yescharacteristic
33#14519777—21no—
34#14519777—21no—
35#14519777—21no—
36#14519777D412yes—
37C4×D244—21no—
38C4×D244—21no—
39C4×D244—21no—
40C4×D244—21no—
41C2×C4⋊Dic61—21no—
42C2×C4⋊Dic61—21no—
43C2×C4⋊Dic61D411yescharacteristic
44C2×#11758198—21no—
45#14519709—24no—
46C4⋊#92418—21no—
47C4⋊#92418—21no—
48#14519699—24no—
49#14519697—42no—
50#14519689—42no—
51#14519689—42no—
52C4×#92418—21no—
53C4×#92418—21no—
54C22×C8×C61—21no—
55C22×C8×C61—21no—
56C2×C4⋊C4×C61—21no—
57C2×C4⋊C4×C61—21no—
58C2×C4⋊C4×C61—21no—
59C2×C42×C61C2311yescharacteristic
60C4⋊C8×C61—21no—
61C4⋊C8×C61—21no—
62C4⋊C8×C61—21no—
63C4⋊C8×C61D412yes—
64C23×D61—21no—
65C22×C4×C61—41no—
66C22×C4×C61C2×D411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C22×C4×C61#4111yescharacteristic
69C22×Dic61—21no—
70C22×Dic61—41no—
71C2×D244—21no—
72C2×D244—21no—
73C2×D244—21no—
74C2×D244—21no—
75C2×D244—21no—
76C2×D244Q1612yes—
77C2×C4×D61—41no—
78C2×C4×D61—41no—
79C2×C4×D61—41no—
80C2×C4×D61—41no—
81C2×C4×D61—41no—
82C2×C4×D61—41no—
83C2×Dic122—22no—
84C2×Dic122—41no—
85C2×Dic122—81no—
86C2×Dic122—81no—
87C2×C8×C61—22no—
88C2×C8×C61—41no—
89C2×C8×C61—41no—
90C2×C8×C61—41no—
91C2×C8×C61—41no—
92C2×C8×C61—41no—
93C4⋊C4×C61—41no—
94C4⋊C4×C61—41no—
95C4⋊C4×C61—41no—
96C4⋊C4×C61—41no—
97C4⋊C4×C61—81no—
98C42×C61C2×D411yescharacteristic
99C42×C61C2×D411yescharacteristic
100C42×C61#4111yescharacteristic
101C42×C61#4111yescharacteristic
102#11758198—41no—
103#11758198—41no—
104C4⋊Dic61—22no—
105C4⋊Dic61—21no—
106C4⋊Dic61—22no—
107C4⋊Dic61—21no—
108C4⋊Dic61—41no—
109C4⋊Dic61—41no—
110C2×#92418—21no—
111C2×#92418—21no—
112C2×#92418—21no—
113C2×#92418—21no—
114C2×#92418—21no—
115C2×#92418—41no—
116C2×#92418—41no—
117C2×#92418—41no—
118C2×#92418SD1612yes—
119C23×C61#12111yescharacteristic
120C22×D61—22no—
121C22×D61—41no—
122C22×D61—41no—
123C22×D61—41no—
124C22×D61—41no—
125C22×D61—41no—
126C22×D61—41no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—81no—
130C2×C4×C61—81no—
131C2×C4×C61—81no—
132C2×C4×C61#12011yescharacteristic
133C2×C4×C61#12111yescharacteristic
134C2×C4×C61#12111yescharacteristic
135C2×C4×C61#12311yescharacteristic
136C2×C4×C61#12311yescharacteristic
137C2×C4×C61#12411yescharacteristic
138C2×C4×C61C2×SD1611yescharacteristic
139C2×C4×C61C2×Q1611yescharacteristic
140C2×C4×C61#13511yescharacteristic
141C2×C4×C61#13511yescharacteristic
142C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C61#13711yescharacteristic
145C2×C4×C61#13711yescharacteristic
146C2×Dic61—42no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—81no—
151C2×Dic61—81no—
152D244—22no—
153D244—22no—
154D244—41no—
155D244—41no—
156C4×D61—81no—
157C4×D61—81no—
158C4×D61—81no—
159C4×D61—81no—
160Dic122—82no—
161Dic122—82no—
162C8×C61—42no—
163C8×C61—81no—
164#92418—22no—
165#92418—41no—
166#92418—81no—
167#10481—611nomaximal, Sylow
168C22×C61#39411yescharacteristic
169C22×C61#46111yescharacteristic
170C22×C61#46311yescharacteristic
171C22×C61#46711yescharacteristic
172C22×C61#46811yescharacteristic
173C22×C61#47111yescharacteristic
174C22×C61#47211yescharacteristic
175C2×D61—42no—
176C2×D61—42no—
177C2×D61—42no—
178C2×D61—81no—
179C2×D61—81no—
180C2×D61—81no—
181C2×D61—81no—
182C4×C61—21no—
183C4×C61—21no—
184C4×C61—161no—
185C4×C61#44911yescharacteristic
186C4×C61#45111yescharacteristic
187C4×C61#46011yescharacteristic
188C4×C61#46411yescharacteristic
189C4×C61#46511yescharacteristic
190C4×C61#46811yescharacteristic
191C4×C61#48411yescharacteristic
192C4×C61#48511yescharacteristic
193Dic61—82no—
194Dic61—81no—
195C2×#476—611no—
196#1990—611no—
197#1954—611no—
198#1802—611no—
199C2×#335—611no—
200C2×#333—611no—
201#1296D6111yescharacteristic, complemented
202C2×C61#167511yescharacteristic
203C2×C61#168311yescharacteristic
204C2×C61#169111yescharacteristic
205C2×C61#169711yescharacteristic
206C2×C61#203611yescharacteristic
207C2×C61#205111yescharacteristic
208C2×C61#205511yescharacteristic
209D61—82no—
210C2×C4⋊Q8—611no—
211C2×C4×D4—611no—
212#476—1222no—
213#476—1222no—
214C2×#106—1221no—
215C2×C4⋊C8—611no—
216C2×C4⋊C8C2×D6111yescharacteristic
217C2×C4⋊C8C2×D6111yescharacteristic
218C2×#102—1221no—
219C2×#102—1221no—
220C2×C22⋊C8—1221no—
221C2×C22⋊C8—1221no—
222C2×C4×C8—611no—
223#384C2×D6111yescharacteristic
224#340—1221no—
225#340—1221no—
226#340—1221no—
227#335—1222no—
228#333—1222no—
229C61#1048111yescharacteristic, complemented, Sylow
230C22×Q8—1221no—
231C22×D4—611no—
232C23×C4—1221no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—611no—
236C22×C8—611no—
237C22×C8—1221no—
238C4⋊Q8—612no—
239C4⋊Q8—1221no—
240C4⋊Q8—1221no—
241C4⋊Q8—1221no—
242C4×D4—1221no—
243C4×D4—1221no—
244C4×D4—1221no—
245C4×D4—1221no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—611no—
250C2×C4⋊C4—1221no—
251C2×C4⋊C4—1221no—
252C2×C22⋊C4—1221no—
253C2×C42C22×D6111yescharacteristic
254#106—1224no—
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—1221no—
259C4⋊C8—1221no—
260C4⋊C8D24412yes—
261#102—1224no—
262#102—2442no—
263C22⋊C8—2442no—
264C22⋊C8—2442no—
265C4×C8—1221no—
266C4×C8—1221no—
267C24—1221no—
268C2×Q8—1222no—
269C2×Q8—4881no—
270C2×Q8—4881no—
271C2×Q8—2441no—
272C2×D4—612no—
273C2×D4—1221no—
274C2×D4—1221no—
275C2×D4—1221no—
276C2×D4—1221no—
277C2×D4—1221no—
278C22×C4—41no—
279C22×C4—1221no—
280C22×C4—2441no—
281C22×C4—2441no—
282C22×C4—2441no—
283C22×C4—2441no—
284C22×C4—2441no—
285C22×C4—2441no—
286C22×C4—2441no—
287C22×C4#1175822211yescharacteristic
288C22×C4D4×D6111yescharacteristic
289C22×C4D4×D6111yescharacteristic
290C2×C8—22no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—41no—
296C2×C8—612no—
297C2×C8—1221no—
298C2×C8—1221no—
299C2×C8—1221no—
300C2×C8—1221no—
301C2×C8—1221no—
302C2×C8—2441no—
303C2×C8—2441no—
304C2×C8—2441no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—81no—
310C4⋊C4—1222no—
311C4⋊C4—1221no—
312C4⋊C4—1222no—
313C4⋊C4—1221no—
314C4⋊C4—2441no—
315C4⋊C4—2441no—
316C22⋊C4—2441no—
317C22⋊C4—2441no—
318C42C2×D24411yescharacteristic
319C42#1175822211yescharacteristic
320C42D4×D6111yescharacteristic
321C42#1175822611yescharacteristic
322C23—1222no—
323C23—2441no—
324C23—2441no—
325C23—2441no—
326C23—2441no—
327C23—2441no—
328C23—2441no—
329C23#1451975011yescharacteristic
330Q8—4882no—
331Q8—4882no—
332D4—1222no—
333D4—1222no—
334D4—2441no—
335D4—2441no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—4881no—
342C2×C4—4881no—
343C2×C4—4881no—
344C2×C4—4881no—
345C2×C4—4881no—
346C2×C4—4881no—
347C2×C4—2441no—
348C2×C4—2442no—
349C2×C4—2441no—
350C2×C4—2441no—
351C2×C4#1451974711yescharacteristic
352C2×C4#1451975011yescharacteristic
353C2×C4#1451975211yescharacteristic
354C2×C4#1451976211yescharacteristic
355C2×C4#1451976211yescharacteristic
356C2×C4#1451976511yescharacteristic
357C2×C4SD16×D6111yescharacteristic
358C2×C4Q16×D6111yescharacteristic
359C2×C4#1451979811yescharacteristic
360C2×C4#1451979811yescharacteristic
361C2×C4#1451980111yescharacteristic
362C2×C4#1451980111yescharacteristic
363C2×C4#1451980611yescharacteristic
364C2×C4#1451980911yescharacteristic
365C8—42no—
366C8—81no—
367C8—1222no—
368C8—4881no—
369C8—2441no—
370C22—4881no—
371C22—4881no—
372C22—4881no—
373C22—4881no—
374C22—2442no—
375C22—2442no—
376C22—2442no—
377C22#1683968011yescharacteristic
378C22#1683996611yescharacteristic
379C22#1683997611yescharacteristic
380C22#1684000211yescharacteristic
381C22#1684000711yescharacteristic
382C22#1684002811yescharacteristic
383C22#1684003111yescharacteristic
384C4—21no—
385C4—21no—
386C4—161no—
387C4—4882no—
388C4—4881no—
389C4#1683990811yescharacteristic
390C4#1683991911yescharacteristic
391C4#1683996111yescharacteristic
392C4#1683998711yescharacteristic
393C4#1683999211yescharacteristic
394C4#1684000911yescharacteristic
395C4#1684009911yescharacteristic
396C4#1684010611yescharacteristic
397C2—4882no—
398C2#2144521711yescharacteristic
399C2#2144526911yescharacteristic
400C2#2144531711yescharacteristic
401C2#2144535111yescharacteristic
402C2#2144702511yescharacteristic
403C2#2144711411yescharacteristic
404C2#2144713811yescharacteristic
subgroupG/H
centerC23#14519750
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1296C2
socleC23×C61#121
prime radicalC22×D244D4
hypercenter#1296D61
hypocenterC61#10481
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
2. #21446779C2semidirect
5. C2×#16839514C2semidirect
6. C2×#16839510C2semidirect
7. C61×#1296C2semidirect
201. #1296D61semidirect
229. C61#10481semidirect

Maximal subgroups

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

subgroupindex
C2×#168400532
#214467792
#214466122
#214458162
C2×#168395142
C2×#168395102
C61×#12962
#1048161