Finite Group Databasebeta

← #29576155

Subgroups — #29576155

Order 15616.

578 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840049C211yesmaximal, characteristic
2C2×C8×D244C211yesmaximal, characteristic
3#21445816C211yesmaximal, characteristic
4C2×#16839511C211yesmaximal, characteristic, complemented
5#21443702C211yesmaximal, characteristic, complemented
6#21443654C211yesmaximal, characteristic, complemented
7C61×#1990C211yesmaximal, characteristic, complemented
8C22×C8×D61—21no—
9C2×C4×D244C2211yescharacteristic
10#16840049—22no—
11#16840049C414yescomplemented
12C8×D244—22no—
13C8×D244—22no—
14C2×#14519708—21no—
15C2×C4⋊#92418C2211yescharacteristic
16C2×C4⋊#92418C2211yescharacteristic
17C2×C4⋊#92418C2211yescharacteristic
18C2×#14519697—21no—
19C2×#14519697—21no—
20C2×#14519689—21no—
21#16839524—21no—
22#16839511—22no—
23C2×C4⋊Q8×C61C2211yescharacteristic
24C2×C4×C8×C61C2211yescharacteristic
25C61×#384C2211yescharacteristic
26C61×#340—21no—
27C61×#340—21no—
28C22×D244D411yescharacteristic
29C22×C4×D61—21no—
30C22×#92418—21no—
31C22×#92418—21no—
32C22×#92418—21no—
33C2×C8×D61—24no—
34C2×C8×D61—42no—
35C2×C8×D61—42no—
36C4×D244—21no—
37C4×D244—21no—
38C4×D244C2×C412yes—
39C4×D244D412yes—
40C2×C4⋊Dic61D411yescharacteristic
41C2×#11758198—21no—
42#14519708—24no—
43C4⋊#92418—21no—
44C4⋊#92418—21no—
45C4⋊#92418—21no—
46C4⋊#92418—21no—
47C4⋊#92418C2×C412yes—
48C4⋊#92418D412yes—
49#14519697—24no—
50#14519697—42no—
51#14519689—24no—
52C22×Q8×C61—21no—
53C22×C8×C61D411yescharacteristic
54C22×C8×C61D411yescharacteristic
55C4⋊Q8×C61—21no—
56C4⋊Q8×C61—21no—
57C4⋊Q8×C61—21no—
58C4⋊Q8×C61C2×C412yes—
59C2×C4⋊C4×C61—21no—
60C2×C4⋊C4×C61—21no—
61C2×C4⋊C4×C61—21no—
62C2×C4⋊C4×C61—21no—
63C2×C4⋊C4×C61—21no—
64C2×C42×C61C2311yescharacteristic
65C4×C8×C61—21no—
66C4×C8×C61—21no—
67C23×D61—21no—
68C2×Q8×C61—22no—
69C2×Q8×C61—41no—
70C2×Q8×C61—81no—
71C2×Q8×C61—81no—
72C22×C4×C61—41no—
73C22×C4×C61—41no—
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61#4111yescharacteristic
77C22×Dic61—21no—
78C2×D244—21no—
79C2×D244—21no—
80C2×D244—21no—
81C2×D244C22⋊C412yes—
82C2×D244SD1612yes—
83C2×D244Q1612yes—
84C2×C4×D61—22no—
85C2×C4×D61—22no—
86C2×C4×D61—41no—
87C2×C4×D61—41no—
88C2×C4×D61—41no—
89C2×C4×D61—41no—
90C2×C8×C61—21no—
91C2×C8×C61—21no—
92C2×C8×C61—21no—
93C2×C8×C61—21no—
94C2×C8×C61—21no—
95C2×C8×C61SD1612yes—
96C4⋊C4×C61—22no—
97C4⋊C4×C61—22no—
98C4⋊C4×C61—41no—
99C4⋊C4×C61—41no—
100C4⋊C4×C61—41no—
101C4⋊C4×C61—41no—
102C4⋊C4×C61—41no—
103C4⋊C4×C61—41no—
104C4⋊C4×C61—81no—
105C42×C61C22×C411yescharacteristic
106C42×C61C2×D411yescharacteristic
107C42×C61C2×D411yescharacteristic
108C42×C61#4111yescharacteristic
109#11758198—22no—
110#11758198—22no—
111C4⋊Dic61—21no—
112C4⋊Dic61C22⋊C412yes—
113C2×#92418—22no—
114C2×#92418—22no—
115C2×#92418—41no—
116C2×#92418—41no—
117C2×#92418—41no—
118C2×#92418—41no—
119C2×#92418—41no—
120C2×#92418—41no—
121C2×#92418—41no—
122C8×D61—48no—
123C23×C61#12111yescharacteristic
124C22×D61—22no—
125C22×D61—22no—
126C22×D61—22no—
127C22×D61—41no—
128C22×D61—41no—
129C22×D61—41no—
130C22×D61—41no—
131Q8×C61—82no—
132Q8×C61—82no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—42no—
136C2×C4×C61—81no—
137C2×C4×C61—81no—
138C2×C4×C61—81no—
139C2×C4×C61—81no—
140C2×C4×C61—81no—
141C2×C4×C61C2×C22⋊C411yescharacteristic
142C2×C4×C61C4×D411yescharacteristic
143C2×C4×C61C4×D411yescharacteristic
144C2×C4×C61#12011yescharacteristic
145C2×C4×C61#12111yescharacteristic
146C2×C4×C61#12311yescharacteristic
147C2×C4×C61C2×SD1611yescharacteristic
148C2×C4×C61C2×SD1611yescharacteristic
149C2×C4×C61C2×Q1611yescharacteristic
150C2×C4×C61#13511yescharacteristic
151C2×C4×C61#13511yescharacteristic
152C2×C4×C61#13511yescharacteristic
153C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C61#13711yescharacteristic
155C2×Dic61—22no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158D244—22no—
159D244—22no—
160D244—22no—
161D244#10314yes—
162C4×D61—42no—
163C4×D61—42no—
164C4×D61—42no—
165C4×D61—42no—
166C8×C61—22no—
167C8×C61—41no—
168#92418—42no—
169#92418—42no—
170#92418—81no—
171#9215—611nomaximal, Sylow
172C22×C61#38611yescharacteristic
173C22×C61#46111yescharacteristic
174C22×C61#46311yescharacteristic
175C22×C61#46511yescharacteristic
176C22×C61#46711yescharacteristic
177C22×C61#47111yescharacteristic
178C22×C61#47211yescharacteristic
179C2×D61—24no—
180C2×D61—42no—
181C2×D61—42no—
182C2×D61—42no—
183C2×D61—42no—
184C2×D61—42no—
185C2×D61—42no—
186C4×C61—21no—
187C4×C61—21no—
188C4×C61—82no—
189C4×C61—161no—
190C4×C61C2×#10311yescharacteristic
191C4×C61#41611yescharacteristic
192C4×C61C4×SD1611yescharacteristic
193C4×C61#44011yescharacteristic
194C4×C61#45011yescharacteristic
195C4×C61#45211yescharacteristic
196C4×C61#46511yescharacteristic
197C4×C61#46711yescharacteristic
198Dic61—42no—
199C2×#476—611no—
200C2×C8×D4—611no—
201#1990D6111yescharacteristic, complemented
202#1802—611no—
203C2×#333—611no—
204#1296—611no—
205#1277—611no—
206C2×C61#167111yescharacteristic
207C2×C61#167511yescharacteristic
208C2×C61#167711yescharacteristic
209C2×C61#168311yescharacteristic
210C2×C61#187711yescharacteristic
211C2×C61#189211yescharacteristic
212C2×C61#190711yescharacteristic
213D61—44no—
214C23×C8—1221no—
215C2×C4⋊Q8C2×D6111yescharacteristic
216C2×C4×D4—611no—
217#476—614no—
218#476—1222no—
219C8×D4—1222no—
220C8×D4—1222no—
221C2×#106—1221no—
222C2×C4⋊C8—611no—
223C2×C4⋊C8—611no—
224C2×C4⋊C8—611no—
225C2×#102—1221no—
226C2×#102—1221no—
227C2×C22⋊C8—1221no—
228C2×C4×C8C2×D6111yescharacteristic
229#384C2×D6111yescharacteristic
230#340—21no—
231#340—21no—
232#340—1221no—
233#333—1222no—
234C61#921511yescharacteristic, complemented, Sylow
235C22×Q8—21no—
236C22×D4—611no—
237C23×C4—1221no—
238C22×C8—1224no—
239C22×C8—1221no—
240C22×C8—1221no—
241C22×C8—1221no—
242C22×C8—2442no—
243C22×C8—2442no—
244C22×C8C22⋊D6111yescharacteristic
245C22×C8C22⋊D6111yescharacteristic
246C4⋊Q8—21no—
247C4⋊Q8—21no—
248C4⋊Q8—21no—
249C4⋊Q8C4×D6112yes—
250C4×D4—612no—
251C4×D4—612no—
252C4×D4—1221no—
253C4×D4—1221no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—611no—
260C2×C22⋊C4—1221no—
261C2×C42C22×D6111yescharacteristic
262#106—1224no—
263C4⋊C8—612no—
264C4⋊C8—612no—
265C4⋊C8—1221no—
266C4⋊C8—1221no—
267C4⋊C8—1221no—
268C4⋊C8—1221no—
269#102—1224no—
270#102—2442no—
271C22⋊C8—1224no—
272C4×C8—21no—
273C4×C8—21no—
274C24—1221no—
275C2×Q8—22no—
276C2×Q8—41no—
277C2×Q8—81no—
278C2×Q8—81no—
279C2×D4—612no—
280C2×D4—612no—
281C2×D4—612no—
282C2×D4—1221no—
283C2×D4—1221no—
284C2×D4—1221no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—1221no—
288C22×C4—1222no—
289C22×C4—1222no—
290C22×C4—2441no—
291C22×C4—2441no—
292C22×C4—2441no—
293C22×C4—2441no—
294C22×C4D4×D6111yescharacteristic
295C22×C4#1175822411yescharacteristic
296C22×C4C2×C22⋊D6111yescharacteristic
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—21no—
300C2×C8—21no—
301C2×C8—21no—
302C2×C8—1222no—
303C2×C8—1222no—
304C2×C8—2448no—
305C2×C8—2441no—
306C2×C8—2441no—
307C2×C8—2441no—
308C2×C8—2441no—
309C2×C8—2441no—
310C2×C8—2441no—
311C2×C8—2441no—
312C2×C8#1175820112yes—
313C4⋊C4—22no—
314C4⋊C4—22no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—81no—
322C4⋊C4—612no—
323C4⋊C4—1221no—
324C22⋊C4—1222no—
325C22⋊C4—1222no—
326C42C2×C4×D6111yescharacteristic
327C42#1175822211yescharacteristic
328C42D4×D6111yescharacteristic
329C42D4×D6111yescharacteristic
330C23—1222no—
331C23—1222no—
332C23—1222no—
333C23—2441no—
334C23—2441no—
335C23—2441no—
336C23—2441no—
337C23#1451974811yescharacteristic
338Q8—82no—
339Q8—82no—
340D4—614no—
341D4—1222no—
342D4—1222no—
343D4—1222no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—42no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—1222no—
353C2×C4—2441no—
354C2×C4—2441no—
355C2×C4—2442no—
356C2×C4—2442no—
357C2×C4—2442no—
358C2×C4—2442no—
359C2×C4C22⋊C4×D6111yescharacteristic
360C2×C4#1451973711yescharacteristic
361C2×C4C4×C22⋊D6111yescharacteristic
362C2×C4#1451974511yescharacteristic
363C2×C4#1451975011yescharacteristic
364C2×C4#1451975911yescharacteristic
365C2×C4SD16×D6111yescharacteristic
366C2×C4C2×#1175820111yescharacteristic
367C2×C4Q16×D6111yescharacteristic
368C2×C4#1451979711yescharacteristic
369C2×C4#1451979811yescharacteristic
370C2×C4#1451980011yescharacteristic
371C2×C4#1451980211yescharacteristic
372C2×C4#1451980811yescharacteristic
373C8—22no—
374C8—41no—
375C8—4881no—
376C8—2442no—
377C8—2442no—
378C22—1224no—
379C22—2442no—
380C22—2442no—
381C22—2442no—
382C22—2442no—
383C22—2442no—
384C22—2442no—
385C22#1683963811yescharacteristic
386C22#1683996411yescharacteristic
387C22#1683997411yescharacteristic
388C22#1683998811yescharacteristic
389C22#1684000011yescharacteristic
390C22#1684002211yescharacteristic
391C22#1684002911yescharacteristic
392C4—21no—
393C4—21no—
394C4—82no—
395C4—161no—
396C4—2442no—
397C4#103×D6111yescharacteristic
398C4#1683975711yescharacteristic
399C4C4×#1175820111yescharacteristic
400C4#1683986011yescharacteristic
401C4#1683991211yescharacteristic
402C4#1683992211yescharacteristic
403C4#1683999411yescharacteristic
404C4#1684000211yescharacteristic
405C2—2444no—
406C2#2144519111yescharacteristic
407C2#2144521511yescharacteristic
408C2#2144522511yescharacteristic
409C2#2144526711yescharacteristic
410C2#2144615611yescharacteristic
411C2#2144623911yescharacteristic
412C2#2144633011yescharacteristic
subgroupG/H
centerC23#14519748
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1990C2
socleC23×C61#121
prime radicalC22×D244D4
cosocleC2×C42×C61C23
hypercenter#1990D61
hypocenterC61#9215
LCSG ▷ 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×#16839511C2semidirect
5. #21443702C2semidirect
6. #21443654C2semidirect
7. C61×#1990C2semidirect
11. #16840049C4semidirect
201. #1990D61semidirect
234. C61#9215semidirect

Maximal subgroups

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

subgroupindex
C2×#168400492
C2×C8×D2442
#214458162
C2×#168395112
#214437022
#214436542
C61×#19902
#921561