Finite Group Databasebeta

← #29583858

Subgroups — #29583858

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×#16840049C211yesmaximal, characteristic
2#21446613C211yesmaximal, characteristic
3#21445816C211yesmaximal, characteristic
4C2×#16839513C211yesmaximal, characteristic, complemented
5C2×#16839511C211yesmaximal, characteristic, complemented
6#21443702C211yesmaximal, characteristic, complemented
7C61×#1990C211yesmaximal, characteristic, complemented
8C2×C4×D244C2211yescharacteristic
9#16840049—22no—
10#16840049—22no—
11C2×#14519708—21no—
12C2×C4⋊#92418C2211yescharacteristic
13C2×C4⋊#92418C2211yescharacteristic
14C2×C4⋊#92418C2211yescharacteristic
15C2×#14519697—21no—
16C2×#14519697—21no—
17C2×#14519689—21no—
18C2×#14519689—21no—
19#16839524—21no—
20#16839513—22no—
21#16839511—22no—
22C2×C4⋊Q8×C61C2211yescharacteristic
23C2×C4×C8×C61C2211yescharacteristic
24C61×#384C2211yescharacteristic
25C61×#340—21no—
26C61×#340—21no—
27C22×D244D411yescharacteristic
28C22×C4×D61—21no—
29C22×#92418—21no—
30C22×#92418—21no—
31C22×#92418—21no—
32C4×D244—21no—
33C4×D244—21no—
34C4×D244—21no—
35C4×D244—21no—
36C2×C4⋊Dic61D411yescharacteristic
37C2×#11758198—21no—
38#14519708—24no—
39C4⋊#92418—21no—
40C4⋊#92418—21no—
41C4⋊#92418—21no—
42C4⋊#92418—21no—
43C4⋊#92418—21no—
44C4⋊#92418D412yes—
45#14519697—24no—
46#14519697—42no—
47#14519689—42no—
48#14519689—42no—
49C22×Q8×C61—21no—
50C22×C8×C61D411yescharacteristic
51C22×C8×C61D411yescharacteristic
52C4⋊Q8×C61—21no—
53C4⋊Q8×C61—21no—
54C4⋊Q8×C61—21no—
55C4⋊Q8×C61D412yes—
56C2×C4⋊C4×C61—21no—
57C2×C4⋊C4×C61—21no—
58C2×C4⋊C4×C61—21no—
59C2×C4⋊C4×C61—21no—
60C2×C4⋊C4×C61—21no—
61C2×C42×C61C2311yescharacteristic
62C4×C8×C61—21no—
63C4×C8×C61—21no—
64C23×D61—21no—
65C2×Q8×C61—22no—
66C2×Q8×C61—41no—
67C2×Q8×C61—81no—
68C2×Q8×C61—81no—
69C22×C4×C61—41no—
70C22×C4×C61—41no—
71C22×C4×C61C2×D411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×C4×C61#4111yescharacteristic
74C22×Dic61—21no—
75C2×D244—21no—
76C2×D244—21no—
77C2×D244—21no—
78C2×D244—21no—
79C2×D244—21no—
80C2×D244SD1612yes—
81C2×C4×D61—41no—
82C2×C4×D61—41no—
83C2×C4×D61—41no—
84C2×C4×D61—41no—
85C2×C4×D61—41no—
86C2×C4×D61—41no—
87C2×C8×C61—21no—
88C2×C8×C61—21no—
89C2×C8×C61—21no—
90C2×C8×C61—21no—
91C2×C8×C61—21no—
92C2×C8×C61SD1612yes—
93C4⋊C4×C61—22no—
94C4⋊C4×C61—22no—
95C4⋊C4×C61—41no—
96C4⋊C4×C61—41no—
97C4⋊C4×C61—41no—
98C4⋊C4×C61—41no—
99C4⋊C4×C61—41no—
100C4⋊C4×C61—41no—
101C4⋊C4×C61—81no—
102C42×C61C2×D411yescharacteristic
103C42×C61C2×D411yescharacteristic
104C42×C61#4111yescharacteristic
105C42×C61#4111yescharacteristic
106#11758198—41no—
107#11758198—41no—
108C4⋊Dic61—21no—
109C4⋊Dic61—21no—
110C2×#92418—22no—
111C2×#92418—41no—
112C2×#92418—41no—
113C2×#92418—41no—
114C2×#92418—41no—
115C2×#92418—41no—
116C2×#92418—41no—
117C2×#92418—41no—
118C2×#92418—41no—
119C23×C61#12111yescharacteristic
120C22×D61—22no—
121C22×D61—41no—
122C22×D61—41no—
123C22×D61—41no—
124C22×D61—41no—
125C22×D61—41no—
126C22×D61—41no—
127Q8×C61—82no—
128Q8×C61—82no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—42no—
132C2×C4×C61—81no—
133C2×C4×C61—81no—
134C2×C4×C61—81no—
135C2×C4×C61—81no—
136C2×C4×C61—81no—
137C2×C4×C61#12011yescharacteristic
138C2×C4×C61#12111yescharacteristic
139C2×C4×C61#12111yescharacteristic
140C2×C4×C61#12311yescharacteristic
141C2×C4×C61#12311yescharacteristic
142C2×C4×C61#12411yescharacteristic
143C2×C4×C61C2×SD1611yescharacteristic
144C2×C4×C61C2×SD1611yescharacteristic
145C2×C4×C61#13511yescharacteristic
146C2×C4×C61#13511yescharacteristic
147C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C61#13711yescharacteristic
149C2×C4×C61#13711yescharacteristic
150C2×C4×C61#13711yescharacteristic
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154D244—22no—
155D244—22no—
156D244—41no—
157D244—41no—
158C4×D61—81no—
159C4×D61—81no—
160C4×D61—81no—
161C4×D61—81no—
162C8×C61—22no—
163C8×C61—41no—
164#92418—42no—
165#92418—81no—
166#92418—81no—
167#10480—611nomaximal, Sylow
168C22×C61#39411yescharacteristic
169C22×C61#46111yescharacteristic
170C22×C61#46311yescharacteristic
171C22×C61#46511yescharacteristic
172C22×C61#47011yescharacteristic
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—82no—
185C4×C61—161no—
186C4×C61#44811yescharacteristic
187C4×C61#45211yescharacteristic
188C4×C61#46011yescharacteristic
189C4×C61#46411yescharacteristic
190C4×C61#46511yescharacteristic
191C4×C61#46811yescharacteristic
192C4×C61#48311yescharacteristic
193C4×C61#48511yescharacteristic
194Dic61—81no—
195C2×#476—611no—
196#1990D6111yescharacteristic, complemented
197#1954—611no—
198#1802—611no—
199C2×#334—611no—
200C2×#333—611no—
201#1296—611no—
202C2×C61#167111yescharacteristic
203C2×C61#167711yescharacteristic
204C2×C61#169511yescharacteristic
205C2×C61#170311yescharacteristic
206C2×C61#203511yescharacteristic
207C2×C61#205111yescharacteristic
208C2×C61#205511yescharacteristic
209D61—82no—
210C2×C4⋊Q8C2×D6111yescharacteristic
211C2×C4×D4—611no—
212#476—1222no—
213#476—1222no—
214C2×#106—1221no—
215C2×C4⋊C8—611no—
216C2×C4⋊C8—611no—
217C2×C4⋊C8—611no—
218C2×#102—1221no—
219C2×#102—1221no—
220C2×C22⋊C8—1221no—
221C2×C22⋊C8—1221no—
222C2×C4×C8C2×D6111yescharacteristic
223#384C2×D6111yescharacteristic
224#340—21no—
225#340—21no—
226#340—1221no—
227#334—1222no—
228#333—1222no—
229C61#1048011yescharacteristic, complemented, Sylow
230C22×Q8—21no—
231C22×D4—611no—
232C23×C4—1221no—
233C22×C8—1221no—
234C22×C8—1221no—
235C22×C8—1221no—
236C22×C8C22⋊D6111yescharacteristic
237C22×C8C22⋊D6111yescharacteristic
238C4⋊Q8—21no—
239C4⋊Q8—21no—
240C4⋊Q8—21no—
241C4⋊Q8D24412yes—
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—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—611no—
252C2×C22⋊C4—1221no—
253C2×C42C22×D6111yescharacteristic
254#106—1224no—
255C4⋊C8—612no—
256C4⋊C8—1221no—
257C4⋊C8—1221no—
258C4⋊C8—1221no—
259C4⋊C8—1221no—
260C4⋊C8—1221no—
261#102—1224no—
262#102—2442no—
263C22⋊C8—2442no—
264C22⋊C8—2442no—
265C4×C8—21no—
266C4×C8—21no—
267C24—1221no—
268C2×Q8—22no—
269C2×Q8—41no—
270C2×Q8—81no—
271C2×Q8—81no—
272C2×D4—612no—
273C2×D4—1221no—
274C2×D4—1221no—
275C2×D4—1221no—
276C2×D4—1221no—
277C2×D4—1221no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—1221no—
281C22×C4—2441no—
282C22×C4—2441no—
283C22×C4—2441no—
284C22×C4—2441no—
285C22×C4—2441no—
286C22×C4—2441no—
287C22×C4D4×D6111yescharacteristic
288C22×C4#1175822411yescharacteristic
289C22×C4C2×C22⋊D6111yescharacteristic
290C2×C8—21no—
291C2×C8—21no—
292C2×C8—21no—
293C2×C8—21no—
294C2×C8—21no—
295C2×C8—1222no—
296C2×C8—2441no—
297C2×C8—2441no—
298C2×C8—2441no—
299C2×C8—2441no—
300C2×C8—2441no—
301C2×C8—2441no—
302C2×C8—2441no—
303C2×C8—2441no—
304C2×C8#1175820112yes—
305C4⋊C4—22no—
306C4⋊C4—22no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—81no—
314C4⋊C4—1221no—
315C4⋊C4—1221no—
316C22⋊C4—2441no—
317C22⋊C4—2441no—
318C42C2×D24411yescharacteristic
319C42#1175822211yescharacteristic
320C42D4×D6111yescharacteristic
321C42#1175822411yescharacteristic
322C23—1222no—
323C23—2441no—
324C23—2441no—
325C23—2441no—
326C23—2441no—
327C23—2441no—
328C23—2441no—
329C23#1451974811yescharacteristic
330Q8—82no—
331Q8—82no—
332D4—1222no—
333D4—1222no—
334D4—2441no—
335D4—2441no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—42no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—4881no—
345C2×C4—4881no—
346C2×C4—4881no—
347C2×C4—4881no—
348C2×C4—2441no—
349C2×C4—2441no—
350C2×C4—2441no—
351C2×C4#1451974711yescharacteristic
352C2×C4#1451974911yescharacteristic
353C2×C4#1451975111yescharacteristic
354C2×C4#1451975911yescharacteristic
355C2×C4#1451976111yescharacteristic
356C2×C4#1451976311yescharacteristic
357C2×C4SD16×D6111yescharacteristic
358C2×C4C2×#1175820111yescharacteristic
359C2×C4#1451979711yescharacteristic
360C2×C4#1451979811yescharacteristic
361C2×C4#1451980211yescharacteristic
362C2×C4#1451980811yescharacteristic
363C2×C4#1451980911yescharacteristic
364C2×C4#1451980911yescharacteristic
365C8—22no—
366C8—41no—
367C8—4881no—
368C8—4881no—
369C8—2442no—
370C22—4881no—
371C22—4881no—
372C22—4881no—
373C22—4881no—
374C22—2442no—
375C22—2442no—
376C22—2442no—
377C22#1683967811yescharacteristic
378C22#1683996411yescharacteristic
379C22#1683997411yescharacteristic
380C22#1683998811yescharacteristic
381C22#1684001711yescharacteristic
382C22#1684002211yescharacteristic
383C22#1684002911yescharacteristic
384C4—21no—
385C4—21no—
386C4—82no—
387C4—161no—
388C4—4881no—
389C4#1683990211yescharacteristic
390C4#1683992711yescharacteristic
391C4#1683996211yescharacteristic
392C4#1683998411yescharacteristic
393C4#1683999311yescharacteristic
394C4#1684001011yescharacteristic
395C4#1684009111yescharacteristic
396C4#1684010111yescharacteristic
397C2—4882no—
398C2#2144519111yescharacteristic
399C2#2144522511yescharacteristic
400C2#2144533911yescharacteristic
401C2#2144539111yescharacteristic
402C2#2144701411yescharacteristic
403C2#2144711211yescharacteristic
404C2#2144713411yescharacteristic
subgroupG/H
centerC23#14519748
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1990C2
socleC23×C61#121
prime radicalC22×D244D4
hypercenter#1990D61
hypocenterC61#10480
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
4. C2×#16839513C2semidirect
5. C2×#16839511C2semidirect
6. #21443702C2semidirect
7. C61×#1990C2semidirect
196. #1990D61semidirect
229. C61#10480semidirect

Maximal subgroups

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

subgroupindex
C2×#168400492
#214466132
#214458162
C2×#168395132
C2×#168395112
#214437022
C61×#19902
#1048061