Finite Group Databasebeta

← #30597707

Subgroups — #30597707

Order 15616.

538 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461613C211yesmaximal, characteristic, complemented
2C4×#14519839C211yesmaximal, characteristic
3D61⋊(D4⋊C8)C211yesmaximal, characteristic
4#21461015C211yesmaximal, characteristic, complemented
5#21460653C211yesmaximal, characteristic, complemented
6#21460648C211yesmaximal, characteristic, complemented
7#436×D61C211yesmaximal, characteristic
8D61⋊(C4⋊C8)C2211yescharacteristic
9C2×#14519839C412yes—
10C2×#14519831—21no—
11C4×D61⋊C8C2211yescharacteristic
12C4×D61⋊C8C2211yescharacteristic
13C4×C4⋊#6923C2211yescharacteristic
14#16840635C412yes—
15(C2×#6923)⋊C8—21no—
16#16840610C412yescomplemented
17D4⋊#92420C412yescomplemented
18#92420⋊C8—21no—
19#92420⋊C8—21no—
20C2×M16×D61—21no—
21C4×D4×D61C2211yescharacteristic
22#16839841C411yescharacteristic, complemented
23#16839840C411yescharacteristic, complemented
24#16839839C411yescharacteristic, complemented
25#16839838—21no—
26#16839837—21no—
27C4⋊C8×D61C2211yescharacteristic
28C22⋊C8×D61—21no—
29C4×C8×D61C2211yescharacteristic
30C61×#436C411yescharacteristic, complemented
31C2×D61⋊C8—21no—
32C2×D61⋊C8—21no—
33C2×D61⋊C8C2×C412yes—
34C2×C4⋊#6923C2×C412yes—
35C2×C4×#6923—21no—
36#14519844—21no—
37C4⋊#92420C2×C412yes—
38#14519839—24no—
39#14519831—42no—
40C4×#92420—21no—
41C4×#92420—21no—
42C4×#92420—21no—
43C4×#92420C2×C412yes—
44(C2×#6923)⋊C4—21no—
45C2×D4×D61C2×C411yescharacteristic
46C22×C4×D61—21no—
47C2×#11758194—21no—
48C2×#11758189—21no—
49C2×#11758189—21no—
50M16×D61—42no—
51M16×D61—42no—
52C2×C8×D61—21no—
53C2×C8×D61D411yescharacteristic
54C2×C8×D61D411yescharacteristic
55C4×D244C2×C411yescharacteristic
56D4×Dic61C2×C411yescharacteristic
57#14519739C2×C411yescharacteristic
58C4×C22⋊D61—21no—
59#14519737—21no—
60C4⋊C4×D61C2×C411yescharacteristic
61C22⋊C4×D61—21no—
62C42×D61C2311yescharacteristic
63C4⋊#92418C2×C411yescharacteristic
64#14519706—21no—
65C22⋊#92418—21no—
66#14519689—21no—
67#14519689—21no—
68C4×#92418C2×C411yescharacteristic
69C8×Dic61D411yescharacteristic
70C8×Dic61D411yescharacteristic
71C2×M16×C61—21no—
72C4×D4×C61C2×C411yescharacteristic
73C4⋊C8×C61C2×C411yescharacteristic
74C22⋊C8×C61—21no—
75C4×C8×C61C2×C411yescharacteristic
76C23×D61—21no—
77C22×#6923—22no—
78C2×D4×C61C4211yescharacteristic
79C22×C4×C61—21no—
80C2×C22⋊D61—21no—
81C22×Dic61—21no—
82D4×D61—22no—
83D4×D61—22no—
84C2×D244C4211yescharacteristic
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×C4×D61—41no—
89C2×C4×D61—41no—
90C2×C4×D61—41no—
91C2×C4×D61—41no—
92C2×C4×D61C22×C411yescharacteristic
93C2×C4×D61C2×D411yescharacteristic
94C2×C4×D61#4111yescharacteristic
95C2×#92420—22no—
96C2×#92420—22no—
97C2×#92420—22no—
98C4⋊#6923—22no—
99C4⋊#6923—22no—
100C4×#6923—41no—
101C4×#6923—41no—
102D61⋊C8—22no—
103D61⋊C8—42no—
104D61⋊C8—41no—
105D61⋊C8—41no—
106D61⋊C8M1614yescomplemented
107M16×C61—42no—
108C2×C8×C61—21no—
109C2×C8×C61C22⋊C411yescharacteristic
110C2×C8×C61C22⋊C411yescharacteristic
111C4⋊C4×C61C4211yescharacteristic
112C22⋊C4×C61—21no—
113C42×C61C22×C411yescharacteristic
114C22⋊Dic61—21no—
115#11758198—21no—
116#11758198—21no—
117C4⋊Dic61C4211yescharacteristic
118#11758196—21no—
119C4×Dic61C22×C411yescharacteristic
120C4×Dic61C2×D411yescharacteristic
121C4×Dic61#4111yescharacteristic
122#11758194—42no—
123C2×#92418—21no—
124C2×#92418C22⋊C411yescharacteristic
125C2×#92418C22⋊C411yescharacteristic
126#11758189—42no—
127#11758189—42no—
128C8×D61—21no—
129C8×D61—21no—
130C8×D61—21no—
131C8×D61—21no—
132C8×D61—41no—
133C8×D61—41no—
134C23×C61—21no—
135C22×D61—21no—
136C22×D61—42no—
137C22×D61—41no—
138C22×D61—41no—
139C22×D61—42no—
140C22×D61C4×D411yescharacteristic
141C2×#6923—42no—
142C2×#6923—42no—
143C2×#6923—42no—
144D4×C61—21no—
145D4×C61—21no—
146C2×C4×C61—21no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61C2×C4211yescharacteristic
150C2×C4×C61C2×C22⋊C411yescharacteristic
151C2×C4×C61#11711yescharacteristic
152C22⋊D61—42no—
153C2×Dic61—21no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61C4×D411yescharacteristic
157C2×Dic61C4×D411yescharacteristic
158C2×Dic61C4×D411yescharacteristic
159D244—21no—
160D244—21no—
161C4×D61—22no—
162C4×D61—41no—
163C4×D61—41no—
164C4×D61—41no—
165C4×D61—41no—
166C4×D61—41no—
167C4×D61—41no—
168C4×D61C2×M1612yes—
169C4×D61#13112yes—
170C4×D61AGL(1,ℤ/8)11yescharacteristic
171C4×D61AGL(1,ℤ/8)11yescharacteristic
172C4×D61AGL(1,ℤ/8)11yescharacteristic
173C4×D61#13711yescharacteristic
174#92420—24no—
175#92420—42no—
176#92420—42no—
177C8×C61—21no—
178C8×C61—21no—
179C8×C61—41no—
180#92418—21no—
181#92418—21no—
182#92418—41no—
183#8208—611nomaximal, Sylow
184C22×C61—41no—
185C22×C61—41no—
186C22×C61—41no—
187C22×C61C4×C22⋊C411yescharacteristic
188C2×D61—41no—
189C2×D61—41no—
190C2×D61—41no—
191C2×D61—82no—
192C2×D61—82no—
193C2×D61#43612yes—
194C2×D61#44011yescharacteristic
195C2×D61#44211yescharacteristic
196C2×D61#44412yes—
197#6923—82no—
198C4×C61—21no—
199C4×C61—41no—
200C4×C61C4×M1611yescharacteristic
201C4×C61#40511yescharacteristic
202C4×C61#41711yescharacteristic
203C4×C61#41811yescharacteristic
204Dic61—21no—
205Dic61—41no—
206Dic61#43512yes—
207Dic61#44011yescharacteristic
208Dic61#44211yescharacteristic
209C2×#436—611no—
210#1770—611no—
211C4×#102—611no—
212C2×D4⋊C8—611no—
213C2×#322—611no—
214#1279—611no—
215#1277—611no—
216C2×C61—81no—
217C2×C61#175311yescharacteristic
218C2×C61#176211yescharacteristic
219C2×C61#176511yescharacteristic
220D61—81no—
221D61#159212yes—
222D61#159412yes—
223C22×M16—1221no—
224C2×C4×D4—611no—
225#436—611no—
226#436—611no—
227#436—611no—
228#436—1221no—
229#436—1221no—
230#436#692311yescharacteristic, complemented
231C2×C4⋊C8—611no—
232C2×C4⋊C8—611no—
233C2×#102—612no—
234C2×C22⋊C8—1221no—
235C2×#97—1221no—
236C2×C4×C8—611no—
237C2×C4×C8—611no—
238C2×C4×C8—611no—
239C4×C4⋊C4—611no—
240#340—612no—
241#336—1221no—
242D4⋊C8—612no—
243D4⋊C8—612no—
244#322—1221no—
245#322—1221no—
246C61#820811yescharacteristic, complemented, Sylow
247C22×D4—611no—
248C23×C4—1221no—
249C2×M16—21no—
250C2×M16—1221no—
251C2×M16—1221no—
252C2×M16—1221no—
253C2×M16—2442no—
254C2×M16—2442no—
255C22×C8—612no—
256C22×C8—611no—
257C22×C8—611no—
258C22×C8—1221no—
259C22×C8—1221no—
260C22×C8—1221no—
261C4×D4—611no—
262C4×D4—611no—
263C4×D4—611no—
264C4×D4—1221no—
265C4×D4—1221no—
266C4×D4C2×#692311yescharacteristic
267C2×C4⋊C4—611no—
268C2×C4⋊C4—612no—
269C2×C22⋊C4—1221no—
270C2×C42—611no—
271C2×C42—1221no—
272C4⋊C8—612no—
273C4⋊C8—611no—
274C4⋊C8—1221no—
275C4⋊C8—1221no—
276C4⋊C8C2×#692311yescharacteristic
277#102—1224no—
278C22⋊C8—21no—
279C22⋊C8—1221no—
280C22⋊C8—1221no—
281C22⋊C8—1221no—
282#97—2442no—
283C4×C8—611no—
284C4×C8—611no—
285C4×C8—612no—
286C4×C8—611no—
287C4×C8—1221no—
288C4×C8—1221no—
289C4×C8—1221no—
290C4×C8C2×#692311yescharacteristic
291#95—1221no—
292C24—1221no—
293C2×D4—611no—
294C2×D4—1222no—
295C2×D4—1222no—
296C2×D4—1221no—
297C2×D4C4×#692311yescharacteristic
298C22×C4—21no—
299C22×C4—611no—
300C22×C4—611no—
301C22×C4—611no—
302C22×C4—1221no—
303C22×C4—1221no—
304C22×C4—1221no—
305C22×C4—1221no—
306C22×C4—1222no—
307C22×C4—2441no—
308C22×C4—2441no—
309C22×C4—2441no—
310C22×C4—2441no—
311M16—42no—
312M16—2442no—
313M16—2442no—
314M16—2442no—
315C2×C8—21no—
316C2×C8—614no—
317C2×C8—611no—
318C2×C8—611no—
319C2×C8—1221no—
320C2×C8—1221no—
321C2×C8—1221no—
322C2×C8—1221no—
323C2×C8—1222no—
324C2×C8—1222no—
325C2×C8—1222no—
326C2×C8—1222no—
327C2×C8—1221no—
328C2×C8—2441no—
329C2×C8—2441no—
330C2×C8—2441no—
331C2×C8—2441no—
332C2×C8—2442no—
333C2×C8C22⋊#692311yescharacteristic
334C2×C8C22⋊#692311yescharacteristic
335C4⋊C4—611no—
336C4⋊C4—1221no—
337C4⋊C4—1222no—
338C4⋊C4—1222no—
339C4⋊C4C4×#692311yescharacteristic
340C22⋊C4—21no—
341C22⋊C4—1221no—
342C22⋊C4—1221no—
343C22⋊C4—1221no—
344C42—611no—
345C42—611no—
346C42—611no—
347C42—2441no—
348C42—2441no—
349C42C22×#692311yescharacteristic
350C23—21no—
351C23—611no—
352C23—1221no—
353C23—2441no—
354C23—2441no—
355C23—2442no—
356C23—2442no—
357D4—21no—
358D4—21no—
359D4—1221no—
360D4—1221no—
361D4—2442no—
362C2×C4—21no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—611no—
366C2×C4—611no—
367C2×C4—612no—
368C2×C4—612no—
369C2×C4—611no—
370C2×C4—611no—
371C2×C4—611no—
372C2×C4—611no—
373C2×C4—611no—
374C2×C4—1222no—
375C2×C4—1221no—
376C2×C4—2441no—
377C2×C4—2441no—
378C2×C4—2441no—
379C2×C4—2441no—
380C2×C4—2441no—
381C2×C4—2441no—
382C2×C4—2442no—
383C2×C4—2442no—
384C2×C4—2442no—
385C2×C4—2441no—
386C2×C4—2441no—
387C2×C4C2×C4×#692311yescharacteristic
388C2×C4C2×C22⋊#692311yescharacteristic
389C2×C4#1451985611yescharacteristic
390C8—21no—
391C8—21no—
392C8—41no—
393C8—1224no—
394C8—1221no—
395C8—1221no—
396C8—2442no—
397C8—2442no—
398C8—2441no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—612no—
403C22—611no—
404C22—611no—
405C22—612no—
406C22—4882no—
407C22—4882no—
408C22—2441no—
409C22—2441no—
410C22—2441no—
411C22C4×C22⋊#692311yescharacteristic
412C4—21no—
413C4—41no—
414C4—612no—
415C4—611no—
416C4—611no—
417C4—1221no—
418C4—4882no—
419C4—2441no—
420C4M16×#692311yescharacteristic
421C4#1684072811yescharacteristic
422C4#1684075311yescharacteristic
423C4#1684075411yescharacteristic
424C2—81no—
425C2—612no—
426C2—612no—
427C2—4881no—
428C2#2146155911yescharacteristic
429C2#2146158911yescharacteristic
430C2#2146159711yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C2×C42
FrattiniC42C22×#6923
FittingC61×#436C4
socleC22×C61C4×C22⋊C4
prime radicalC2×D4×D61C2×C4
cosocleC42×D61C23
hypercenter#436#6923
hypocenterC61#8208
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #436

Complements

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

NH ≅ G/Ntype
1. #21461613C2semidirect
4. #21461015C2semidirect
5. #21460653C2semidirect
6. #21460648C2semidirect
16. #16840610C4semidirect
17. D4⋊#92420C4semidirect
22. #16839841C4semidirect
23. #16839840C4semidirect
24. #16839839C4semidirect
30. C61×#436C4semidirect
106. D61⋊C8M16semidirect
230. #436#6923semidirect
246. C61#8208semidirect

Maximal subgroups

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

subgroupindex
#214616132
C4×#145198392
D61⋊(D4⋊C8)2
#214610152
#214606532
#214606482
#436×D612
#820861