Finite Group Databasebeta

← #29574450

Subgroups — #29574450

Order 15616.

644 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448883C211yesmaximal, characteristic
2#21446624C211yesmaximal, characteristic
3#21446580C211yesmaximal, characteristic, complemented
4C2×#16839505C211yesmaximal, characteristic
5#21443660C211yesmaximal, characteristic, complemented
6#21443658C211yesmaximal, characteristic, complemented
7C61×#1948C211yesmaximal, characteristic, complemented
8C2×#14519774C2211yescharacteristic
9C2×C4×D244—21no—
10C2×#14519739—21no—
11C2×#14519708—21no—
12C2×C4⋊#92418C2211yescharacteristic
13C2×#14519697—22no—
14C2×C4×#92418C2211yescharacteristic
15#16839664—21no—
16#16839663—21no—
17#16839640—22no—
18C4×C4⋊Dic61C2211yescharacteristic
19#16839524—21no—
20#16839505C414yescomplemented
21C2×#106×C61—21no—
22C2×C4⋊C8×C61C2211yescharacteristic
23C61×#384C2211yescharacteristic
24C4×C4⋊C4×C61C2211yescharacteristic
25C61×#340—21no—
26C22×D244—21no—
27C22×D244—21no—
28C22×D244D412yes—
29C22×C4×D61—22no—
30C22×#92418—21no—
31C22×#92418—21no—
32#14519774—21no—
33#14519774—21no—
34#14519774C2×C412yes—
35#14519774Q812yes—
36C4×D244—42no—
37C4×D244—42no—
38#14519739—42no—
39#14519739—42no—
40C2×C4⋊Dic61D411yescharacteristic
41C2×C4⋊Dic61D411yescharacteristic
42C2×#11758198—22no—
43C2×#11758198—22no—
44C2×#11758198—22no—
45C2×C4×Dic61—21no—
46#14519708—42no—
47C4⋊#92418—21no—
48C4⋊#92418C2×C412yescomplemented
49#14519697—44no—
50C4×#92418—21no—
51C4×#92418—21no—
52#14519684—21no—
53C22×C8×C61—21no—
54C2×C4⋊C4×C61—21no—
55C2×C4⋊C4×C61—21no—
56C2×C4⋊C4×C61—21no—
57C2×C4⋊C4×C61D411yescharacteristic
58C2×C4⋊C4×C61D411yescharacteristic
59C2×C42×C61—21no—
60C2×C42×C61C2311yescharacteristic
61#106×C61—42no—
62C4⋊C8×C61—21no—
63C4⋊C8×C61C2×C412yescomplemented
64#95×C61—21no—
65C23×D61—22no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—41no—
69C22×C4×C61C2×D411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×Dic61—21no—
73C22×Dic61—21no—
74C2×D244—22no—
75C2×D244—22no—
76C2×D244—22no—
77C2×D244—22no—
78C2×D244—22no—
79C2×D244—41no—
80C2×D244—41no—
81C2×D244—41no—
82C2×D244—41no—
83C2×D244—41no—
84C2×D244—41no—
85C2×D244—41no—
86C2×D244—41no—
87C2×D244—42no—
88C2×D244—42no—
89C2×D244C4⋊C414yes—
90C2×C4×D61—44no—
91C2×C4×D61—44no—
92C2×C4×D61—82no—
93C2×C8×C61—22no—
94C2×C8×C61—41no—
95C2×C8×C61—41no—
96C4⋊C4×C61—21no—
97C4⋊C4×C61—21no—
98C4⋊C4×C61—21no—
99C4⋊C4×C61—42no—
100C4⋊C4×C61—41no—
101C4⋊C4×C61—41no—
102C4⋊C4×C61—41no—
103C4⋊C4×C61—41no—
104C4⋊C4×C61SD1612yes—
105C42×C61—41no—
106C42×C61—41no—
107C42×C61C22×C411yescharacteristic
108C42×C61C2×Q811yescharacteristic
109C42×C61#4111yescharacteristic
110C42×C61#4111yescharacteristic
111#11758198—44no—
112#11758198—44no—
113#11758198—82no—
114C4⋊Dic61—21no—
115C4⋊Dic61—21no—
116C4⋊Dic61—21no—
117C4⋊Dic61SD1612yes—
118C4×Dic61—41no—
119C4×Dic61—41no—
120C2×#92418—22no—
121C2×#92418—22no—
122C2×#92418—41no—
123C2×#92418—41no—
124C2×#92418—41no—
125C2×#92418—41no—
126C23×C61#12011yescharacteristic
127C22×D61—24no—
128C22×D61—42no—
129C22×D61—42no—
130C22×D61—42no—
131C22×D61—42no—
132C22×D61—42no—
133C22×D61—42no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—22no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—81no—
143C2×C4×C61—81no—
144C2×C4×C61—81no—
145C2×C4×C61C2×C4⋊C411yescharacteristic
146C2×C4×C61C4×D411yescharacteristic
147C2×C4×C61C4×D411yescharacteristic
148C2×C4×C61C22⋊Q811yescharacteristic
149C2×C4×C61C22⋊Q811yescharacteristic
150C2×C4×C61#12311yescharacteristic
151C2×C4×C61C2×SD1611yescharacteristic
152C2×C4×C61C2×SD1611yescharacteristic
153C2×C4×C61#13511yescharacteristic
154C2×C4×C61#13511yescharacteristic
155C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
159C2×Dic61—22no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165D244—44no—
166D244—42no—
167D244—42no—
168D244—42no—
169D244—42no—
170D244—42no—
171D244—42no—
172D244—42no—
173D244—42no—
174D244—82no—
175C4×D61—88no—
176C8×C61—42no—
177#92418—42no—
178#92418—42no—
179#8924—611nomaximal, Sylow
180C22×C61#38511yescharacteristic
181C22×C61#44911yescharacteristic
182C22×C61#44911yescharacteristic
183C22×C61#45011yescharacteristic
184C22×C61#45011yescharacteristic
185C22×C61#45311yescharacteristic
186C22×C61#45511yescharacteristic
187C2×D61—44no—
188C2×D61—44no—
189C2×D61—44no—
190C2×D61—82no—
191C2×D61—82no—
192C2×D61—82no—
193C2×D61—82no—
194C4×C61—21no—
195C4×C61—21no—
196C4×C61—42no—
197C4×C61—81no—
198C4×C61—161no—
199C4×C61C4×SD1611yescharacteristic
200C4×C61C4×SD1611yescharacteristic
201C4×C61#44211yescharacteristic
202C4×C61#44211yescharacteristic
203C4×C61#47611yescharacteristic
204C4×C61#47611yescharacteristic
205C4×C61#47811yescharacteristic
206C4×C61#47811yescharacteristic
207Dic61—42no—
208Dic61—81no—
209#2366—611no—
210#1957—611no—
211#1948—611no—
212#1948D6111yescharacteristic, complemented
213C2×#331—611no—
214#1279—611no—
215#1279—611no—
216C2×C61#162011yescharacteristic
217C2×C61#162911yescharacteristic
218C2×C61#164211yescharacteristic
219C2×C61#164211yescharacteristic
220C2×C61#185611yescharacteristic
221C2×C61#186411yescharacteristic
222C2×C61#186411yescharacteristic
223D61—84no—
224C2×#127—611no—
225C2×C4×D4—1221no—
226C2×C4×D4—1221no—
227C2×#106—21no—
228C2×#106—1221no—
229C2×C4⋊C8—611no—
230C2×C4⋊C8C2×D6111yescharacteristic
231C2×#102—1222no—
232C2×C4×C8—611no—
233#390—1221no—
234#390—1221no—
235#386—1222no—
236#384C2×D6111yescharacteristic
237C4×C4⋊C4—611no—
238C4×C4⋊C4C2×D6111yescharacteristic
239#340—21no—
240#340—1221no—
241#331—614no—
242C61#892411yescharacteristic, complemented, Sylow
243C22×D4—612no—
244C22×D4—1221no—
245C22×D4—1221no—
246C23×C4—1222no—
247C22×C8—21no—
248C22×C8—1221no—
249C22×C8—1221no—
250#127—612no—
251#127—612no—
252#127—1221no—
253#127—1221no—
254C4×D4—2442no—
255C4×D4—2442no—
256C4×D4—2442no—
257C4×D4—2442no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—611no—
262C2×C4⋊C4—611no—
263C2×C4⋊C4C22⋊D6111yescharacteristic
264C2×C4⋊C4C22⋊D6111yescharacteristic
265C2×C22⋊C4—1222no—
266C2×C22⋊C4—1222no—
267C2×C22⋊C4—1222no—
268C2×C42—21no—
269C2×C42—1221no—
270C2×C42C22×D6111yescharacteristic
271#106—42no—
272#106—2442no—
273C4⋊C8—21no—
274C4⋊C8—612no—
275C4⋊C8—1221no—
276C4⋊C8C4×D6112yescomplemented
277#102—2444no—
278C4×C8—1221no—
279C4×C8—1221no—
280#95—21no—
281#95—1221no—
282C24—1222no—
283C2×D4—614no—
284C2×D4—1222no—
285C2×D4—1222no—
286C2×D4—1222no—
287C2×D4—1222no—
288C2×D4—1222no—
289C2×D4—2442no—
290C2×D4—2442no—
291C2×D4—2441no—
292C2×D4—2441no—
293C2×D4—2441no—
294C2×D4—2441no—
295C2×D4—2441no—
296C2×D4—2441no—
297C2×D4—2441no—
298C2×D4—2441no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—41no—
302C22×C4—1221no—
303C22×C4—1221no—
304C22×C4—4882no—
305C22×C4—2444no—
306C22×C4—2444no—
307C22×C4D4×D6111yescharacteristic
308C22×C4D4×D6111yescharacteristic
309C22×C4C2×C22⋊D6111yescharacteristic
310C2×C8—22no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—1222no—
314C2×C8—1222no—
315C2×C8—2441no—
316C2×C8—2441no—
317C2×C8—2441no—
318C2×C8—2441no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—42no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—612no—
328C4⋊C4—1221no—
329C4⋊C4—1221no—
330C4⋊C4—1221no—
331C4⋊C4#1175820112yes—
332C22⋊C4—4882no—
333C22⋊C4—2444no—
334C22⋊C4—2444no—
335C42—41no—
336C42—41no—
337C42—2441no—
338C42—2441no—
339C42C2×C4×D6111yescharacteristic
340C42#1175822211yescharacteristic
341C42Q8×D6111yescharacteristic
342C42#1175822611yescharacteristic
343C23—1224no—
344C23—2442no—
345C23—2442no—
346C23—2442no—
347C23—2442no—
348C23—2442no—
349C23—2442no—
350C23#1451974511yescharacteristic
351D4—4882no—
352D4—2444no—
353D4—2442no—
354D4—2442no—
355D4—2442no—
356D4—2442no—
357D4—2442no—
358D4—2442no—
359D4—2442no—
360D4—2442no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—22no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—81no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—1222no—
373C2×C4—4888no—
374C2×C4—2441no—
375C2×C4—2441no—
376C2×C4—2441no—
377C2×C4—2441no—
378C2×C4—2441no—
379C2×C4C4⋊C4×D6111yescharacteristic
380C2×C4C4×C22⋊D6111yescharacteristic
381C2×C4#1451973911yescharacteristic
382C2×C4#1451975311yescharacteristic
383C2×C4#1451975511yescharacteristic
384C2×C4#1451976211yescharacteristic
385C2×C4SD16×D6111yescharacteristic
386C2×C4C2×#1175820111yescharacteristic
387C2×C4#1451979711yescharacteristic
388C2×C4#1451979811yescharacteristic
389C2×C4#1451980211yescharacteristic
390C2×C4#1451980311yescharacteristic
391C2×C4#1451980411yescharacteristic
392C2×C4#1451980411yescharacteristic
393C8—42no—
394C8—2442no—
395C8—2442no—
396C22—4882no—
397C22—4882no—
398C22—4882no—
399C22—4882no—
400C22—2444no—
401C22—2444no—
402C22—2444no—
403C22#1683963311yescharacteristic
404C22#1683990511yescharacteristic
405C22#1683990611yescharacteristic
406C22#1683991111yescharacteristic
407C22#1683991211yescharacteristic
408C22#1683992811yescharacteristic
409C22#1683993811yescharacteristic
410C4—21no—
411C4—21no—
412C4—42no—
413C4—81no—
414C4—161no—
415C4—4881no—
416C4—2442no—
417C4#1683984911yescharacteristic
418C4C4×#1175820111yescharacteristic
419C4#1683987211yescharacteristic
420C4#1683987311yescharacteristic
421C4#1684004911yescharacteristic
422C4#1684005111yescharacteristic
423C4#1684005911yescharacteristic
424C4#1684006111yescharacteristic
425C2—4884no—
426C2#2144487711yescharacteristic
427C2#2144493411yescharacteristic
428C2#2144501711yescharacteristic
429C2#2144501811yescharacteristic
430C2#2144602711yescharacteristic
431C2#2144607711yescharacteristic
432C2#2144607911yescharacteristic
subgroupG/H
centerC23#14519745
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1948C2
socleC23×C61#120
prime radicalC2×#14519774C22
cosocleC2×C42×C61C23
hypercenter#1948D61
hypocenterC61#8924
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
3. #21446580C2semidirect
5. #21443660C2semidirect
6. #21443658C2semidirect
7. C61×#1948C2semidirect
20. #16839505C4semidirect
48. C4⋊#92418C2×C4semidirect
63. C4⋊C8×C61C2×C4semidirect
212. #1948D61semidirect
242. C61#8924semidirect
276. C4⋊C8C4×D61semidirect

Maximal subgroups

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

subgroupindex
#214488832
#214466242
#214465802
C2×#168395052
#214436602
#214436582
C61×#19482
#892461