Finite Group Databasebeta

← #29574254

Subgroups — #29574254

Order 15616.

602 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448719C211yesmaximal, characteristic
2#21446580C211yesmaximal, characteristic, complemented
3#21445816C211yesmaximal, characteristic
4C2×#16839491C211yesmaximal, characteristic
5#21443702C211yesmaximal, characteristic, complemented
6#21443659C211yesmaximal, characteristic, complemented
7C61×#1834C211yesmaximal, characteristic, complemented
8C2×C4×D244C2211yescharacteristic
9C2×#14519739—21no—
10C2×C4⋊C4×D61—21no—
11C2×#14519708—21no—
12C2×C4⋊#92418C2211yescharacteristic
13C2×C4⋊#92418C2211yescharacteristic
14C2×#14519697—21no—
15#16839658—21no—
16#16839633—22no—
17#16839619—21no—
18C4×C4⋊Dic61C2211yescharacteristic
19#16839524—21no—
20#16839524—21no—
21#16839491C414yescomplemented
22C2×C4×C8×C61C2211yescharacteristic
23C61×#384C2211yescharacteristic
24C61×#384C2211yescharacteristic
25C61×#340—22no—
26C22×D244D411yescharacteristic
27C22×C4×D61—21no—
28C22×C4×D61—22no—
29C22×#92418—21no—
30C22×#92418—21no—
31C4×D244—21no—
32C4×D244—21no—
33C4×D244C2×C412yes—
34C4×D244Q812yes—
35#14519739—42no—
36#14519739—42no—
37C2×C4⋊Dic61D411yescharacteristic
38C2×C4⋊Dic61D411yescharacteristic
39C2×C4⋊Dic61D411yescharacteristic
40C2×#11758196—22no—
41C4⋊C4×D61—42no—
42C4⋊C4×D61—42no—
43C2×#11758198—21no—
44C2×#11758198—22no—
45C2×C4×Dic61—21no—
46#14519708—42no—
47C4⋊#92418—21no—
48C4⋊#92418—21no—
49C4⋊#92418—21no—
50C4⋊#92418C2×C412yescomplemented
51#14519697—42no—
52#14519684—22no—
53#14519684—21no—
54C22×C8×C61—21no—
55C2×C4⋊C4×C61—21no—
56C2×C4⋊C4×C61—21no—
57C2×C4⋊C4×C61—21no—
58C2×C4⋊C4×C61—21no—
59C2×C4⋊C4×C61—21no—
60C2×C4⋊C4×C61D412yes—
61C2×C42×C61C2311yescharacteristic
62C4×C8×C61—21no—
63C4×C8×C61C2×C412yescomplemented
64C23×D61—21no—
65C22×C4×C61—22no—
66C22×C4×C61—41no—
67C22×C4×C61C2×D411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61—21no—
73C2×D244—21no—
74C2×D244—21no—
75C2×D244—21no—
76C2×D244C4⋊C412yes—
77C2×D244SD1612yes—
78C2×D244SD1612yes—
79C2×C4×D61—22no—
80C2×C4×D61—22no—
81C2×C4×D61—41no—
82C2×C4×D61—41no—
83C2×C4×D61—41no—
84C2×C4×D61—41no—
85C2×C4×D61—44no—
86C2×C4×D61—44no—
87C2×C4×D61—82no—
88C2×C8×C61—22no—
89C2×C8×C61—41no—
90C2×C8×C61—41no—
91C4⋊C4×C61—42no—
92C4⋊C4×C61—42no—
93C4⋊C4×C61—41no—
94C4⋊C4×C61—41no—
95C4⋊C4×C61—41no—
96C4⋊C4×C61—41no—
97C4⋊C4×C61—41no—
98C4⋊C4×C61—41no—
99C4⋊C4×C61—41no—
100C4⋊C4×C61—41no—
101C42×C61C22×C411yescharacteristic
102C42×C61C2×Q811yescharacteristic
103C42×C61#4111yescharacteristic
104C42×C61#4111yescharacteristic
105#11758198—22no—
106#11758198—22no—
107#11758198—44no—
108C4⋊Dic61—21no—
109C4⋊Dic61—21no—
110C4⋊Dic61—21no—
111C4⋊Dic61—21no—
112C4⋊Dic61C4⋊C412yes—
113C4⋊Dic61D812yes—
114#11758196—44no—
115C4×Dic61—41no—
116C4×Dic61—41no—
117C2×#92418—22no—
118C2×#92418—41no—
119C2×#92418—41no—
120C2×#92418—41no—
121C2×#92418—41no—
122C2×#92418—41no—
123C23×C61#12011yescharacteristic
124C22×D61—22no—
125C22×D61—22no—
126C22×D61—22no—
127C22×D61—41no—
128C22×D61—41no—
129C22×D61—41no—
130C22×D61—41no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—42no—
134C2×C4×C61—42no—
135C2×C4×C61—42no—
136C2×C4×C61—81no—
137C2×C4×C61—81no—
138C2×C4×C61—81no—
139C2×C4×C61C2×C4⋊C411yescharacteristic
140C2×C4×C61C4×D411yescharacteristic
141C2×C4×C61C4×D411yescharacteristic
142C2×C4×C61C22⋊Q811yescharacteristic
143C2×C4×C61C22⋊Q811yescharacteristic
144C2×C4×C61#12311yescharacteristic
145C2×C4×C61C2×D811yescharacteristic
146C2×C4×C61C2×SD1611yescharacteristic
147C2×C4×C61C2×SD1611yescharacteristic
148C2×C4×C61#13511yescharacteristic
149C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C61#13711yescharacteristic
152C2×C4×C61#13711yescharacteristic
153C2×Dic61—22no—
154C2×Dic61—22no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162D244—22no—
163D244—22no—
164D244—22no—
165D244#10614yescomplemented
166C4×D61—42no—
167C4×D61—42no—
168C4×D61—42no—
169C4×D61—42no—
170C4×D61—88no—
171C8×C61—42no—
172#92418—42no—
173#92418—81no—
174#8894—611nomaximal, Sylow
175C22×C61#38511yescharacteristic
176C22×C61#44711yescharacteristic
177C22×C61#44811yescharacteristic
178C22×C61#45011yescharacteristic
179C22×C61#45211yescharacteristic
180C22×C61#45411yescharacteristic
181C22×C61#45511yescharacteristic
182C2×D61—24no—
183C2×D61—42no—
184C2×D61—42no—
185C2×D61—42no—
186C2×D61—42no—
187C2×D61—42no—
188C2×D61—42no—
189C4×C61—21no—
190C4×C61—21no—
191C4×C61—82no—
192C4×C61—161no—
193C4×C61C2×#10611yescharacteristic
194C4×C61#42811yescharacteristic
195C4×C61C4×D811yescharacteristic
196C4×C61#44011yescharacteristic
197C4×C61#47411yescharacteristic
198C4×C61#47811yescharacteristic
199C4×C61#48111yescharacteristic
200C4×C61#48311yescharacteristic
201Dic61—42no—
202Dic61—42no—
203Dic61—81no—
204D4×C4⋊C4—611no—
205#1948—611no—
206#1834D6111yescharacteristic, complemented
207#1802—611no—
208C2×D4⋊C8—611no—
209#1296—611no—
210#1279—611no—
211C2×C61#162711yescharacteristic
212C2×C61#163511yescharacteristic
213C2×C61#163911yescharacteristic
214C2×C61#164311yescharacteristic
215C2×C61#185311yescharacteristic
216C2×C61#186011yescharacteristic
217C2×C61#186211yescharacteristic
218D61—44no—
219C2×C4×D4—611no—
220C2×C4×D4—1221no—
221C22×C4⋊C4—1221no—
222C2×#106—1221no—
223C2×C4⋊C8—611no—
224C2×C4⋊C8—611no—
225C2×#102—1221no—
226C2×C4×C8C2×D6111yescharacteristic
227#389—1221no—
228#385—1222no—
229#384C2×D6111yescharacteristic
230#384C2×D6111yescharacteristic
231#380—1221no—
232C4×C4⋊C4—611no—
233#340—22no—
234#340—1221no—
235#340—1221no—
236D4⋊C8—614no—
237C61#889411yescharacteristic, complemented, Sylow
238C22×D4—611no—
239C23×C4—1222no—
240C23×C4—1221no—
241C22×C8—21no—
242C22×C8—1221no—
243C22×C8—1221no—
244C4×D4—612no—
245C4×D4—612no—
246C4×D4—1221no—
247C4×D4—1221no—
248C4×D4—2442no—
249C4×D4—2442no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—611no—
256C2×C4⋊C4—611no—
257C2×C4⋊C4—611no—
258C2×C4⋊C4—1222no—
259C2×C4⋊C4—2442no—
260C2×C4⋊C4—2442no—
261C2×C4⋊C4C22⋊D6112yes—
262C2×C22⋊C4—1221no—
263C2×C22⋊C4—1222no—
264C2×C42—1221no—
265C2×C42C22×D6111yescharacteristic
266#106—2442no—
267C4⋊C8—612no—
268C4⋊C8—1221no—
269C4⋊C8—1221no—
270C4⋊C8—1221no—
271#102—2442no—
272C4×C8—21no—
273C4×C8C4×D6112yescomplemented
274#95—1222no—
275#95—1221no—
276C24—1221no—
277C2×D4—612no—
278C2×D4—612no—
279C2×D4—612no—
280C2×D4—1221no—
281C2×D4—1221no—
282C2×D4—1221no—
283C22×C4—22no—
284C22×C4—41no—
285C22×C4—1221no—
286C22×C4—1221no—
287C22×C4—1222no—
288C22×C4—1222no—
289C22×C4—1221no—
290C22×C4—4882no—
291C22×C4—2444no—
292C22×C4—2444no—
293C22×C4—2441no—
294C22×C4—2441no—
295C22×C4—2441no—
296C22×C4—2441no—
297C22×C4D4×D6111yescharacteristic
298C22×C4D4×D6111yescharacteristic
299C22×C4C2×C22⋊D6111yescharacteristic
300C2×C8—22no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—1222no—
304C2×C8—2441no—
305C2×C8—2441no—
306C2×C8—2441no—
307C2×C8—2441no—
308C2×C8—2441no—
309C4⋊C4—42no—
310C4⋊C4—42no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—612no—
320C4⋊C4—612no—
321C4⋊C4—1221no—
322C4⋊C4—1221no—
323C4⋊C4—1221no—
324C4⋊C4—1221no—
325C4⋊C4—2444no—
326C22⋊C4—1222no—
327C22⋊C4—1222no—
328C22⋊C4—2444no—
329C42—2441no—
330C42—2441no—
331C42C2×C4×D6111yescharacteristic
332C42#1175822211yescharacteristic
333C42Q8×D6111yescharacteristic
334C42#1175822611yescharacteristic
335C23—1222no—
336C23—1222no—
337C23—1222no—
338C23—2441no—
339C23—2441no—
340C23—2441no—
341C23—2441no—
342C23#1451974511yescharacteristic
343D4—614no—
344D4—1222no—
345D4—1222no—
346D4—1222no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—81no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—1222no—
356C2×C4—1222no—
357C2×C4—4888no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4—2441no—
365C2×C4—2442no—
366C2×C4—2442no—
367C2×C4—2442no—
368C2×C4—2442no—
369C2×C4C4⋊C4×D6111yescharacteristic
370C2×C4C4×C22⋊D6111yescharacteristic
371C2×C4#1451973911yescharacteristic
372C2×C4#1451975311yescharacteristic
373C2×C4#1451975511yescharacteristic
374C2×C4#1451976211yescharacteristic
375C2×C4D8×D6111yescharacteristic
376C2×C4SD16×D6111yescharacteristic
377C2×C4SD16×D6111yescharacteristic
378C2×C4#1451980011yescharacteristic
379C2×C4#1451980111yescharacteristic
380C2×C4#1451980411yescharacteristic
381C2×C4#1451980611yescharacteristic
382C2×C4#1451980911yescharacteristic
383C8—42no—
384C8—4881no—
385C8—2442no—
386C22—1224no—
387C22—2442no—
388C22—2442no—
389C22—2442no—
390C22—2442no—
391C22—2442no—
392C22—2442no—
393C22#1683963311yescharacteristic
394C22#1683989411yescharacteristic
395C22#1683989911yescharacteristic
396C22#1683991111yescharacteristic
397C22#1683992311yescharacteristic
398C22#1683993411yescharacteristic
399C22#1683993911yescharacteristic
400C4—21no—
401C4—21no—
402C4—82no—
403C4—161no—
404C4—4881no—
405C4—2442no—
406C4—2442no—
407C4#106×D6111yescharacteristic
408C4#1683980111yescharacteristic
409C4#1683984411yescharacteristic
410C4#1683986111yescharacteristic
411C4#1684004111yescharacteristic
412C4#1684006511yescharacteristic
413C4#1684008211yescharacteristic
414C4#1684009411yescharacteristic
415C2—2444no—
416C2#2144491911yescharacteristic
417C2#2144496711yescharacteristic
418C2#2144499511yescharacteristic
419C2#2144502311yescharacteristic
420C2#2144601011yescharacteristic
421C2#2144605111yescharacteristic
422C2#2144606311yescharacteristic
subgroupG/H
centerC23#14519745
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1834C2
socleC23×C61#120
prime radicalC22×D244D4
cosocleC2×C42×C61C23
hypercenter#1834D61
hypocenterC61#8894
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1834

Complements

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

NH ≅ G/Ntype
2. #21446580C2semidirect
5. #21443702C2semidirect
6. #21443659C2semidirect
7. C61×#1834C2semidirect
21. #16839491C4semidirect
50. C4⋊#92418C2×C4semidirect
63. C4×C8×C61C2×C4semidirect
165. D244#106semidirect
206. #1834D61semidirect
237. C61#8894semidirect
273. C4×C8C4×D61semidirect

Maximal subgroups

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

subgroupindex
#214487192
#214465802
#214458162
C2×#168394912
#214437022
#214436592
C61×#18342
#889461