Finite Group Databasebeta

← #29574749

Subgroups — #29574749

Order 15616.

664 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840049C211yesmaximal, characteristic
2C4⋊C4×D244C211yesmaximal, characteristic
3#21446622C211yesmaximal, characteristic, complemented
4C2×#16839489C211yesmaximal, characteristic
5#21443703C211yesmaximal, characteristic, complemented
6#21443660C211yesmaximal, characteristic, complemented
7C61×#1987C211yesmaximal, characteristic, complemented
8C2×C4×D244—21no—
9C2×C4×D244C2211yescharacteristic
10C2×C4⋊C4×D61—21no—
11#16840049—22no—
12#16840049C414yescomplemented
13C2×#14519708—21no—
14C2×C4⋊#92418C2211yescharacteristic
15C2×#14519701—22no—
16C2×#14519697—21no—
17C2×C4×#92418C2211yescharacteristic
18#16839660—21no—
19#16839636—22no—
20#16839632C2211yescharacteristic
21#16839619—21no—
22#16839489—22no—
23C2×C4⋊Q8×C61C2211yescharacteristic
24C2×C4⋊C8×C61C2211yescharacteristic
25C4×C4⋊C4×C61C2211yescharacteristic
26C61×#340—21no—
27C61×#340—21no—
28C22×D244D411yescharacteristic
29C22×C4×D61—21no—
30C22×C4×D61—22no—
31C22×#92418—21no—
32C22×#92418—21no—
33C4×D244—21no—
34C4×D244—21no—
35C4×D244—42no—
36C4×D244—42no—
37C4×D244C2×C412yes—
38C4×D244D412yes—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61—21no—
41C2×C4⋊Dic61D411yescharacteristic
42C2×C4⋊Dic61D412yes—
43C2×#11758196—22no—
44C4⋊C4×D61—42no—
45C4⋊C4×D61—42no—
46C2×#11758198—21no—
47C2×#11758198—22no—
48#14519708—24no—
49C4⋊#92418—21no—
50C4⋊#92418C2×C412yescomplemented
51#14519701—44no—
52#14519697—24no—
53C4×#92418—21no—
54C4×#92418—21no—
55#14519684—22no—
56C22×Q8×C61—21no—
57C22×C8×C61—21no—
58C4⋊Q8×C61—21no—
59C4⋊Q8×C61—21no—
60C4⋊Q8×C61—21no—
61C4⋊Q8×C61C2×C412yescomplemented
62C2×C4⋊C4×C61—21no—
63C2×C4⋊C4×C61—21no—
64C2×C4⋊C4×C61D411yescharacteristic
65C2×C4⋊C4×C61D411yescharacteristic
66C2×C42×C61—21no—
67C2×C42×C61C2311yescharacteristic
68C4⋊C8×C61—21no—
69C4⋊C8×C61—21no—
70#95×C61—21no—
71C23×D61—21no—
72C2×Q8×C61—22no—
73C2×Q8×C61—42no—
74C2×Q8×C61—42no—
75C2×Q8×C61—41no—
76C22×C4×C61—21no—
77C22×C4×C61—21no—
78C22×C4×C61—41no—
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61C2×D411yescharacteristic
81C22×C4×C61C2×D411yescharacteristic
82C22×Dic61—21no—
83C22×Dic61—22no—
84C2×D244—21no—
85C2×D244—21no—
86C2×D244—21no—
87C2×D244C22⋊C412yes—
88C2×D244SD1612yes—
89C2×D244Q1612yes—
90C2×C4×D61—22no—
91C2×C4×D61—22no—
92C2×C4×D61—41no—
93C2×C4×D61—41no—
94C2×C4×D61—41no—
95C2×C4×D61—41no—
96C2×C4×D61—44no—
97C2×C4×D61—44no—
98C2×C4×D61—82no—
99C2×C8×C61—41no—
100C2×C8×C61—41no—
101C2×C8×C61—41no—
102C4⋊C4×C61—21no—
103C4⋊C4×C61—22no—
104C4⋊C4×C61—22no—
105C4⋊C4×C61—21no—
106C4⋊C4×C61—21no—
107C4⋊C4×C61—41no—
108C4⋊C4×C61—41no—
109C4⋊C4×C61SD1612yes—
110C42×C61—41no—
111C42×C61—41no—
112C42×C61C22×C411yescharacteristic
113C42×C61C2×D411yescharacteristic
114C42×C61#4111yescharacteristic
115C42×C61#4111yescharacteristic
116#11758198—22no—
117#11758198—22no—
118#11758198—44no—
119C4⋊Dic61—21no—
120C4⋊Dic61—41no—
121C4⋊Dic61—41no—
122C4⋊Dic61—41no—
123C4⋊Dic61—41no—
124C4⋊Dic61—42no—
125C4⋊Dic61C22⋊C412yes—
126#11758196—44no—
127C2×#92418—22no—
128C2×#92418—22no—
129C2×#92418—41no—
130C2×#92418—41no—
131C2×#92418—41no—
132C2×#92418—41no—
133C23×C61#12011yescharacteristic
134C22×D61—22no—
135C22×D61—22no—
136C22×D61—22no—
137C22×D61—41no—
138C22×D61—41no—
139C22×D61—41no—
140C22×D61—41no—
141Q8×C61—44no—
142Q8×C61—82no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—22no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—42no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—81no—
153C2×C4×C61—81no—
154C2×C4×C61C2×C22⋊C411yescharacteristic
155C2×C4×C61C4×D411yescharacteristic
156C2×C4×C61C4×D411yescharacteristic
157C2×C4×C61#12111yescharacteristic
158C2×C4×C61#12111yescharacteristic
159C2×C4×C61#12311yescharacteristic
160C2×C4×C61C2×SD1611yescharacteristic
161C2×C4×C61C2×SD1611yescharacteristic
162C2×C4×C61C2×Q1611yescharacteristic
163C2×C4×C61#13511yescharacteristic
164C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C61#13711yescharacteristic
167C2×C4×C61#13711yescharacteristic
168C2×Dic61—22no—
169C2×Dic61—41no—
170C2×Dic61—41no—
171C2×Dic61—42no—
172C2×Dic61—42no—
173C2×Dic61—42no—
174D244—22no—
175D244—22no—
176D244—22no—
177D244#10314yescomplemented
178C4×D61—42no—
179C4×D61—42no—
180C4×D61—42no—
181C4×D61—42no—
182C4×D61—88no—
183C8×C61—81no—
184#92418—42no—
185#92418—42no—
186#8973—611nomaximal, Sylow
187C22×C61#38611yescharacteristic
188C22×C61#45011yescharacteristic
189C22×C61#45011yescharacteristic
190C22×C61#45111yescharacteristic
191C22×C61#45211yescharacteristic
192C22×C61#45311yescharacteristic
193C22×C61#45411yescharacteristic
194C2×D61—24no—
195C2×D61—42no—
196C2×D61—42no—
197C2×D61—42no—
198C2×D61—42no—
199C2×D61—42no—
200C2×D61—42no—
201C4×C61—21no—
202C4×C61—21no—
203C4×C61—42no—
204C4×C61—82no—
205C4×C61—81no—
206C4×C61C2×#10311yescharacteristic
207C4×C61#41711yescharacteristic
208C4×C61C4×SD1611yescharacteristic
209C4×C61#44011yescharacteristic
210C4×C61#46111yescharacteristic
211C4×C61#46311yescharacteristic
212C4×C61#48311yescharacteristic
213C4×C61#48411yescharacteristic
214Dic61—42no—
215Dic61—82no—
216C2×#476—611no—
217D4×C4⋊C4—611no—
218#1987D6111yescharacteristic, complemented
219#1956—611no—
220C2×D4⋊C8—611no—
221#1296—611no—
222#1279—611no—
223C2×C61#162911yescharacteristic
224C2×C61#163211yescharacteristic
225C2×C61#163511yescharacteristic
226C2×C61#163711yescharacteristic
227C2×C61#187211yescharacteristic
228C2×C61#187711yescharacteristic
229C2×C61#188311yescharacteristic
230D61—44no—
231C2×C4⋊Q8C2×D6111yescharacteristic
232C2×C4×D4—611no—
233C2×C4×D4—1221no—
234C22×C4⋊C4—1221no—
235#476—614no—
236#476—1222no—
237C2×#106—1221no—
238C2×C4⋊C8—611no—
239C2×C4⋊C8C2×D6111yescharacteristic
240C2×#103—1222no—
241C2×#102—1221no—
242C2×C4×C8—611no—
243#389—1221no—
244#385—1222no—
245#384—611no—
246#380—1221no—
247C4×C4⋊C4C2×D6111yescharacteristic
248#340—21no—
249#340—21no—
250D4⋊C8—1222no—
251C61#897311yescharacteristic, complemented, Sylow
252C22×Q8—21no—
253C22×D4—611no—
254C23×C4—1222no—
255C23×C4—1221no—
256C22×C8—21no—
257C22×C8—1221no—
258C22×C8—1221no—
259C4⋊Q8—21no—
260C4⋊Q8—21no—
261C4⋊Q8—21no—
262C4⋊Q8C4×D6112yescomplemented
263C4×D4—612no—
264C4×D4—612no—
265C4×D4—1221no—
266C4×D4—1221no—
267C4×D4—2442no—
268C4×D4—2442no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—611no—
272C2×C4⋊C4—612no—
273C2×C4⋊C4—1222no—
274C2×C4⋊C4—1221no—
275C2×C4⋊C4—1221no—
276C2×C4⋊C4—2442no—
277C2×C4⋊C4—2442no—
278C2×C4⋊C4C22⋊D6111yescharacteristic
279C2×C4⋊C4C22⋊D6111yescharacteristic
280C2×C22⋊C4—1221no—
281C2×C22⋊C4—1222no—
282C2×C42—21no—
283C2×C42C22×D6111yescharacteristic
284#106—1224no—
285C4⋊C8—21no—
286C4⋊C8—21no—
287C4⋊C8—612no—
288C4⋊C8—1221no—
289#103—2444no—
290#102—1224no—
291C4×C8—1221no—
292C4×C8—1221no—
293#95—21no—
294#95—1222no—
295C24—1221no—
296C2×Q8—22no—
297C2×Q8—42no—
298C2×Q8—42no—
299C2×Q8—41no—
300C2×D4—612no—
301C2×D4—612no—
302C2×D4—612no—
303C2×D4—1221no—
304C2×D4—1221no—
305C2×D4—1221no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—41no—
309C22×C4—1221no—
310C22×C4—1222no—
311C22×C4—1222no—
312C22×C4—1222no—
313C22×C4—4882no—
314C22×C4—2444no—
315C22×C4—2444no—
316C22×C4—2441no—
317C22×C4—2441no—
318C22×C4—2441no—
319C22×C4—2441no—
320C22×C4D4×D6111yescharacteristic
321C22×C4D4×D6111yescharacteristic
322C22×C4C2×C22⋊D6111yescharacteristic
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—1222no—
327C2×C8—1222no—
328C2×C8—2441no—
329C2×C8—2441no—
330C2×C8—2441no—
331C2×C8—2441no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—22no—
335C4⋊C4—22no—
336C4⋊C4—21no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—612no—
340C4⋊C4—1221no—
341C4⋊C4—2442no—
342C4⋊C4—2444no—
343C4⋊C4—2441no—
344C4⋊C4—2441no—
345C4⋊C4—2441no—
346C4⋊C4—2441no—
347C4⋊C4#1175820112yes—
348C22⋊C4—1222no—
349C22⋊C4—1222no—
350C22⋊C4—2444no—
351C42—41no—
352C42—41no—
353C42C2×C4×D6111yescharacteristic
354C42#1175822211yescharacteristic
355C42D4×D6111yescharacteristic
356C42#1175822411yescharacteristic
357C23—1222no—
358C23—1222no—
359C23—1222no—
360C23—2441no—
361C23—2441no—
362C23—2441no—
363C23—2441no—
364C23#1451974511yescharacteristic
365Q8—44no—
366Q8—82no—
367D4—614no—
368D4—1222no—
369D4—1222no—
370D4—1222no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—22no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—81no—
381C2×C4—81no—
382C2×C4—1222no—
383C2×C4—4888no—
384C2×C4—2442no—
385C2×C4—2442no—
386C2×C4—2442no—
387C2×C4—2441no—
388C2×C4—2441no—
389C2×C4—2442no—
390C2×C4—2442no—
391C2×C4—2442no—
392C2×C4—2442no—
393C2×C4C22⋊C4×D6111yescharacteristic
394C2×C4#1451973711yescharacteristic
395C2×C4C4×C22⋊D6111yescharacteristic
396C2×C4#1451974811yescharacteristic
397C2×C4#1451975011yescharacteristic
398C2×C4#1451975911yescharacteristic
399C2×C4SD16×D6111yescharacteristic
400C2×C4C2×#1175820111yescharacteristic
401C2×C4Q16×D6111yescharacteristic
402C2×C4#1451979711yescharacteristic
403C2×C4#1451980211yescharacteristic
404C2×C4#1451980411yescharacteristic
405C2×C4#1451980811yescharacteristic
406C2×C4#1451980911yescharacteristic
407C8—81no—
408C8—2442no—
409C8—2442no—
410C22—1224no—
411C22—2442no—
412C22—2442no—
413C22—2442no—
414C22—2442no—
415C22—2442no—
416C22—2442no—
417C22#1683963811yescharacteristic
418C22#1683991111yescharacteristic
419C22#1683991211yescharacteristic
420C22#1683991611yescharacteristic
421C22#1683992211yescharacteristic
422C22#1683992811yescharacteristic
423C22#1683993311yescharacteristic
424C4—21no—
425C4—21no—
426C4—42no—
427C4—82no—
428C4—81no—
429C4—4882no—
430C4—2442no—
431C4#103×D6111yescharacteristic
432C4#1683976211yescharacteristic
433C4C4×#1175820111yescharacteristic
434C4#1683986011yescharacteristic
435C4#1683996411yescharacteristic
436C4#1683997411yescharacteristic
437C4#1684009111yescharacteristic
438C4#1684009611yescharacteristic
439C2—2444no—
440C2#2144493411yescharacteristic
441C2#2144495211yescharacteristic
442C2#2144496911yescharacteristic
443C2#2144498211yescharacteristic
444C2#2144612311yescharacteristic
445C2#2144615611yescharacteristic
446C2#2144619211yescharacteristic
subgroupG/H
centerC23#14519745
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1987C2
socleC23×C61#120
prime radicalC22×D244D4
cosocleC2×C42×C61C23
hypercenter#1987D61
hypocenterC61#8973
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1987

Complements

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

NH ≅ G/Ntype
3. #21446622C2semidirect
5. #21443703C2semidirect
6. #21443660C2semidirect
7. C61×#1987C2semidirect
12. #16840049C4semidirect
50. C4⋊#92418C2×C4semidirect
61. C4⋊Q8×C61C2×C4semidirect
177. D244#103semidirect
218. #1987D61semidirect
251. C61#8973semidirect
262. C4⋊Q8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168400492
C4⋊C4×D2442
#214466222
C2×#168394892
#214437032
#214436602
C61×#19872
#897361