Finite Group Databasebeta

← #29574852

Subgroups — #29574852

Order 15616.

608 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839968C211yesmaximal, characteristic
2#21448770C211yesmaximal, characteristic
3#21446779C211yesmaximal, characteristic, complemented
4#21446770C211yesmaximal, characteristic, complemented
5C2×#16839489C211yesmaximal, characteristic
6#21443658C211yesmaximal, characteristic, complemented
7C61×#1296C211yesmaximal, characteristic, complemented
8C22×#11758190—21no—
9C2×#14519777C2211yescharacteristic
10C2×C4×D244C2211yescharacteristic
11C2×#14519735—21no—
12#16839968—22no—
13#16839968C414yescomplemented
14C2×#14519702—21no—
15C2×C4×#92418C2211yescharacteristic
16#16839663—21no—
17#16839652—22no—
18#16839619—21no—
19C4⋊C4×Dic61—21no—
20C4×C4⋊Dic61C2211yescharacteristic
21#16839525—21no—
22#16839525—21no—
23#16839524—22no—
24#16839489—22no—
25C2×C4⋊C8×C61C2211yescharacteristic
26C2×C4⋊C8×C61C2211yescharacteristic
27C61×#384C2211yescharacteristic
28C22×Dic122—21no—
29C22×D244D411yescharacteristic
30C22×C4×D61—21no—
31C2×#11758190—24no—
32C2×#11758190—42no—
33C2×#11758190—42no—
34C22×#92418—21no—
35#14519777—21no—
36#14519777—21no—
37#14519777—21no—
38#14519777C2×C412yes—
39C4×D244—21no—
40C4×D244—21no—
41C4×D244C2×C412yes—
42C4×D244D412yes—
43#14519735—42no—
44#14519735—42no—
45C2×C4⋊Dic61—21no—
46C2×C4⋊Dic61—21no—
47C2×C4⋊Dic61D411yescharacteristic
48C2×C4⋊Dic61D411yescharacteristic
49C2×C4⋊Dic61D411yescharacteristic
50C2×#11758198—21no—
51C2×#11758198—22no—
52C2×#11758198—22no—
53C2×C4×Dic61—22no—
54C2×C4×Dic61—21no—
55#14519702—24no—
56C4×#92418—21no—
57C4×#92418—21no—
58#14519684—22no—
59#14519684—21no—
60C22×C8×C61—21no—
61C22×C8×C61—21no—
62C2×C4⋊C4×C61—21no—
63C2×C4⋊C4×C61—21no—
64C2×C4⋊C4×C61D412yes—
65C2×C42×C61C2311yescharacteristic
66C4⋊C8×C61—21no—
67C4⋊C8×C61—21no—
68C4⋊C8×C61—21no—
69C4⋊C8×C61C2×C412yes—
70C23×D61—21no—
71C22×C4×C61—22no—
72C22×C4×C61C2×D411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—41no—
79C2×D244—21no—
80C2×D244—21no—
81C2×D244—21no—
82C2×D244—21no—
83C2×D244—21no—
84C2×D244C22⋊C412yes—
85C2×C4×D61—22no—
86C2×C4×D61—22no—
87C2×C4×D61—41no—
88C2×C4×D61—41no—
89C2×C4×D61—41no—
90C2×C4×D61—41no—
91C2×Dic122—22no—
92C2×Dic122—41no—
93C2×Dic122—41no—
94C2×Dic122—41no—
95C2×Dic122—41no—
96C2×Dic122—41no—
97C2×C8×C61—22no—
98C2×C8×C61—41no—
99C2×C8×C61—41no—
100C2×C8×C61—41no—
101C2×C8×C61—41no—
102C2×C8×C61—41no—
103C4⋊C4×C61—42no—
104C4⋊C4×C61—41no—
105C4⋊C4×C61—41no—
106C4⋊C4×C61—41no—
107C4⋊C4×C61—41no—
108C42×C61C22×C411yescharacteristic
109C42×C61C2×D411yescharacteristic
110C42×C61#4111yescharacteristic
111C42×C61#4111yescharacteristic
112#11758198—22no—
113#11758198—22no—
114#11758198—44no—
115#11758198—82no—
116C4⋊Dic61—21no—
117C4⋊Dic61—21no—
118C4⋊Dic61—22no—
119C4⋊Dic61—22no—
120C4⋊Dic61—21no—
121C4⋊Dic61—21no—
122C4⋊Dic61—41no—
123C4⋊Dic61—41no—
124C4⋊Dic61C22⋊C412yes—
125C4⋊Dic61SD1612yescomplemented
126C4×Dic61—44no—
127C4×Dic61—41no—
128C4×Dic61—41no—
129C2×#92418—22no—
130C2×#92418—41no—
131C2×#92418—41no—
132#11758190—48no—
133C23×C61#12011yescharacteristic
134C22×D61—22no—
135C22×D61—41no—
136C22×D61—41no—
137C22×D61—41no—
138C22×D61—41no—
139C22×D61—41no—
140C22×D61—41no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—42no—
144C2×C4×C61—42no—
145C2×C4×C61—42no—
146C2×C4×C61C2×C22⋊C411yescharacteristic
147C2×C4×C61C4×D411yescharacteristic
148C2×C4×C61C4×D411yescharacteristic
149C2×C4×C61#12111yescharacteristic
150C2×C4×C61#12111yescharacteristic
151C2×C4×C61#12311yescharacteristic
152C2×C4×C61C2×SD1611yescharacteristic
153C2×C4×C61#13511yescharacteristic
154C2×C4×C61#13511yescharacteristic
155C2×C4×C61#13511yescharacteristic
156C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C61#13711yescharacteristic
160C2×Dic61—22no—
161C2×Dic61—22no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165C2×Dic61—41no—
166C2×Dic61—42no—
167C2×Dic61—41no—
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61—81no—
171C2×Dic61—81no—
172D244—22no—
173D244—22no—
174D244—41no—
175D244—41no—
176C4×D61—42no—
177C4×D61—42no—
178C4×D61—42no—
179C4×D61—42no—
180Dic122—42no—
181Dic122—42no—
182Dic122—81no—
183Dic122—81no—
184C8×C61—42no—
185C8×C61—81no—
186#92418—42no—
187#8988—611nomaximal, Sylow
188C22×C61#38611yescharacteristic
189C22×C61#44911yescharacteristic
190C22×C61#44911yescharacteristic
191C22×C61#45011yescharacteristic
192C22×C61#45211yescharacteristic
193C22×C61#45511yescharacteristic
194C22×C61#45611yescharacteristic
195C2×D61—42no—
196C2×D61—42no—
197C2×D61—42no—
198C2×D61—81no—
199C2×D61—81no—
200C2×D61—81no—
201C2×D61—81no—
202C4×C61—21no—
203C4×C61—21no—
204C4×C61—82no—
205C4×C61#41611yescharacteristic
206C4×C61#41811yescharacteristic
207C4×C61C4×SD1611yescharacteristic
208C4×C61#44011yescharacteristic
209C4×C61#46111yescharacteristic
210C4×C61#46311yescharacteristic
211C4×C61#48211yescharacteristic
212C4×C61#48211yescharacteristic
213Dic61—42no—
214Dic61—42no—
215Dic61—82no—
216Dic61—81no—
217C2×#461—611no—
218#2354—611no—
219#1990—611no—
220#1988—611no—
221C2×D4⋊C8—611no—
222#1296D6111yescharacteristic, complemented
223#1279—611no—
224C2×C61#164211yescharacteristic
225C2×C61#164611yescharacteristic
226C2×C61#165011yescharacteristic
227C2×C61#165411yescharacteristic
228C2×C61#187511yescharacteristic
229C2×C61#187711yescharacteristic
230C2×C61#188211yescharacteristic
231D61—82no—
232C22×SD16—1221no—
233C2×C4⋊Q8—611no—
234C2×C4×D4—611no—
235C2×#117—1221no—
236#461—614no—
237#461—1222no—
238C2×C4⋊C8C2×D6111yescharacteristic
239C2×C4⋊C8C2×D6111yescharacteristic
240C2×#103—1221no—
241C2×C4×C8—611no—
242#390—1221no—
243#388—1222no—
244#384C2×D6111yescharacteristic
245#380—1221no—
246C4×C4⋊C4—611no—
247C4×C4⋊C4—1221no—
248#340—1221no—
249#340—1221no—
250#340—1222no—
251D4⋊C8—1222no—
252C61#898811yescharacteristic, complemented, Sylow
253C22×Q8—1221no—
254C22×D4—611no—
255C23×C4—1221no—
256C2×SD16—1224no—
257C2×SD16—2442no—
258C2×SD16—2442no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—1221no—
262C4⋊Q8—612no—
263C4⋊Q8—1221no—
264C4⋊Q8—1221no—
265C4⋊Q8—1221no—
266C4×D4—612no—
267C4×D4—612no—
268C4×D4—1221no—
269C4×D4—1221no—
270#117—2442no—
271#117—2442no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—611no—
275C2×C4⋊C4—611no—
276C2×C4⋊C4—611no—
277C2×C4⋊C4—1221no—
278C2×C4⋊C4—1221no—
279C2×C4⋊C4D24412yes—
280C2×C22⋊C4—1221no—
281C2×C22⋊C4—1222no—
282C2×C22⋊C4—1222no—
283C2×C42—1222no—
284C2×C42—1221no—
285C2×C42C22×D6111yescharacteristic
286C4⋊C8—21no—
287C4⋊C8—21no—
288C4⋊C8—21no—
289C4⋊C8C4×D6112yes—
290#103—1224no—
291C4×C8—1221no—
292C4×C8—1221no—
293#95—1222no—
294#95—1221no—
295C24—1221no—
296C2×Q8—1222no—
297C2×Q8—2441no—
298C2×Q8—2441no—
299C2×Q8—2441no—
300C2×Q8—2441no—
301C2×Q8—2441no—
302C2×D4—612no—
303C2×D4—1221no—
304C2×D4—1221no—
305C2×D4—1221no—
306C2×D4—1221no—
307C2×D4—1221no—
308C22×C4—22no—
309C22×C4—1221no—
310C22×C4—1221no—
311C22×C4—1222no—
312C22×C4—1222no—
313C22×C4—1221no—
314C22×C4—2441no—
315C22×C4—2441no—
316C22×C4—2441no—
317C22×C4—2441no—
318C22×C4—2441no—
319C22×C4C2×D24411yescharacteristic
320C22×C4D4×D6111yescharacteristic
321C22×C4D4×D6111yescharacteristic
322SD16—2448no—
323C2×C8—22no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—41no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—1222no—
330C2×C8—2441no—
331C2×C8—2441no—
332C4⋊C4—42no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—612no—
338C4⋊C4—612no—
339C4⋊C4—1221no—
340C4⋊C4—1221no—
341C4⋊C4—1221no—
342C4⋊C4—1222no—
343C4⋊C4—1222no—
344C4⋊C4—1221no—
345C4⋊C4—2441no—
346C4⋊C4—2441no—
347C22⋊C4—1222no—
348C22⋊C4—1222no—
349C22⋊C4—4882no—
350C22⋊C4—2444no—
351C42—2444no—
352C42—2441no—
353C42—2441no—
354C42C2×C4×D6111yescharacteristic
355C42#1175822211yescharacteristic
356C42D4×D6111yescharacteristic
357C42#1175822611yescharacteristic
358C23—1222no—
359C23—2441no—
360C23—2441no—
361C23—2441no—
362C23—2441no—
363C23—2441no—
364C23—2441no—
365C23#1451974711yescharacteristic
366Q8—4881no—
367Q8—4881no—
368Q8—2442no—
369Q8—2442no—
370D4—1222no—
371D4—1222no—
372D4—2441no—
373D4—2441no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—1222no—
380C2×C4—1222no—
381C2×C4—4881no—
382C2×C4—4881no—
383C2×C4—2441no—
384C2×C4—2442no—
385C2×C4—2441no—
386C2×C4—2441no—
387C2×C4—2441no—
388C2×C4—2441no—
389C2×C4—2441no—
390C2×C4—2441no—
391C2×C4—2442no—
392C2×C4—2442no—
393C2×C4—2442no—
394C2×C4—2442no—
395C2×C4C22⋊C4×D6111yescharacteristic
396C2×C4#1451973911yescharacteristic
397C2×C4C4×D24411yescharacteristic
398C2×C4#1451975011yescharacteristic
399C2×C4#1451975211yescharacteristic
400C2×C4#1451976211yescharacteristic
401C2×C4SD16×D6111yescharacteristic
402C2×C4#1451979811yescharacteristic
403C2×C4#1451979811yescharacteristic
404C2×C4#1451980011yescharacteristic
405C2×C4#1451980111yescharacteristic
406C2×C4#1451980111yescharacteristic
407C2×C4#1451980411yescharacteristic
408C2×C4#1451980911yescharacteristic
409C8—42no—
410C8—81no—
411C8—2442no—
412C22—4881no—
413C22—4881no—
414C22—4881no—
415C22—4881no—
416C22—2442no—
417C22—2442no—
418C22—2442no—
419C22#1683964011yescharacteristic
420C22#1683990811yescharacteristic
421C22#1683991011yescharacteristic
422C22#1683991411yescharacteristic
423C22#1683992711yescharacteristic
424C22#1683994211yescharacteristic
425C22#1683994711yescharacteristic
426C4—21no—
427C4—21no—
428C4—82no—
429C4—4881no—
430C4—4882no—
431C4—2442no—
432C4—2442no—
433C4#1683975711yescharacteristic
434C4#1683976511yescharacteristic
435C4#1683984911yescharacteristic
436C4#1683986111yescharacteristic
437C4#1683996611yescharacteristic
438C4#1683997611yescharacteristic
439C4#1684008811yescharacteristic
440C4#1684008911yescharacteristic
441C2—4882no—
442C2#2144502011yescharacteristic
443C2#2144504811yescharacteristic
444C2#2144507611yescharacteristic
445C2#2144510411yescharacteristic
446C2#2144614011yescharacteristic
447C2#2144615411yescharacteristic
448C2#2144618711yescharacteristic
subgroupG/H
centerC23#14519747
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1296C2
socleC23×C61#120
prime radicalC22×D244D4
cosocleC2×C42×C61C23
hypercenter#1296D61
hypocenterC61#8988
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
3. #21446779C2semidirect
4. #21446770C2semidirect
6. #21443658C2semidirect
7. C61×#1296C2semidirect
13. #16839968C4semidirect
125. C4⋊Dic61SD16semidirect
222. #1296D61semidirect
252. C61#8988semidirect

Maximal subgroups

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

subgroupindex
C2×#168399682
#214487702
#214467792
#214467702
C2×#168394892
#214436582
C61×#12962
#898861