Finite Group Databasebeta

← #29576276

Subgroups — #29576276

Order 15616.

724 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455819C211yesmaximal, characteristic
2C4×D4×Dic61C211yesmaximal, characteristic, complemented
3#21446646C211yesmaximal, characteristic, complemented
4#21444315C211yesmaximal, characteristic, complemented
5#21443720C211yesmaximal, characteristic, complemented
6#21443651C211yesmaximal, characteristic, complemented
7C61×#1486C211yesmaximal, characteristic, complemented
8#16840312C2211yescharacteristic
9C2×D4×Dic61—21no—
10C22×C4×Dic61—21no—
11#16840075—21no—
12#16840042C412yescomplemented
13#16839957C412yescomplemented
14#16839896—21no—
15C4×#11758199—22no—
16#16839815C2211yescharacteristic
17C2×#14519703—21no—
18C2×#14519703—21no—
19C4⋊C4×Dic61—21no—
20C4×C4⋊Dic61C2211yescharacteristic
21C22⋊C4×Dic61—22no—
22C4×C22⋊Dic61—21no—
23C42×Dic61C2211yescharacteristic
24#16839497—22no—
25C2×C4×D4×C61C2211yescharacteristic
26C61×#431C2211yescharacteristic
27C61×#423C2211yescharacteristic
28C61×D4⋊C8—22no—
29C2×#11758222—21no—
30C23×Dic61—22no—
31C2×#11758199—22no—
32#14519777C2×C411yescharacteristic, complemented
33#14519774C2×C411yescharacteristic, complemented
34#14519765—21no—
35#14519751—21no—
36#14519751—21no—
37C4×D244—21no—
38C4×D244—21no—
39D4×Dic61—28no—
40C2×C4⋊Dic61—21no—
41C2×C22⋊Dic61—22no—
42C2×C4×Dic61—21no—
43C2×C4×Dic61—22no—
44C2×C4×Dic61—21no—
45C2×C4×Dic61—21no—
46C2×C4×Dic61—42no—
47C2×C4×Dic61—42no—
48C2×C4×Dic61D411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50#14519710—22no—
51C4⋊#92418C2×C412yescomplemented
52#14519703—42no—
53#14519703—42no—
54#14519698—22no—
55#14519697—22no—
56C22⋊#92418—21no—
57C4×#92418—21no—
58#14519684—22no—
59#14519684D412yes—
60C22×D4×C61D411yescharacteristic
61C23×C4×C61—21no—
62C2×M16×C61—21no—
63C4×D4×C61—21no—
64C4×D4×C61—21no—
65C4×D4×C61C2×C412yes—
66C4×D4×C61D412yes—
67C2×C4⋊C4×C61D411yescharacteristic
68C2×C22⋊C4×C61—21no—
69C2×C42×C61C2311yescharacteristic
70C4⋊C8×C61—21no—
71C4⋊C8×C61—21no—
72C4⋊C8×C61—21no—
73C22⋊C8×C61—21no—
74C4×C8×C61—21no—
75C24×C61—21no—
76C2×D4×C61—24no—
77C2×D4×C61—21no—
78C2×D4×C61C22⋊C412yes—
79C22×C4×C61—21no—
80C22×C4×C61—22no—
81C22×C4×C61—22no—
82C22×C4×C61—41no—
83C22×C4×C61—41no—
84C22×C4×C61—41no—
85C22×C4×C61—41no—
86C22×C4×C61C2×D411yescharacteristic
87C22×C4×C61C2×D411yescharacteristic
88C22×C4×C61C2×D411yescharacteristic
89C2×C22⋊D61—41no—
90C22×Dic61—21no—
91C22×Dic61—28no—
92C22×Dic61—22no—
93C22×Dic61—21no—
94C22×Dic61—44no—
95C22×Dic61—44no—
96#11758222—41no—
97#11758222—41no—
98#11758222—41no—
99#11758222—41no—
100C2×D244—21no—
101C2×D244—21no—
102C2×D244—21no—
103C2×C4×D61—41no—
104C2×Dic122—21no—
105M16×C61—41no—
106M16×C61—41no—
107C2×C8×C61—41no—
108C2×C8×C61—41no—
109C4⋊C4×C61—21no—
110C4⋊C4×C61C22⋊C412yes—
111C22⋊C4×C61—22no—
112C22⋊C4×C61—22no—
113C42×C61C22×C411yescharacteristic
114C42×C61C2×D411yescharacteristic
115C42×C61#4111yescharacteristic
116C42×C61#4111yescharacteristic
117C22⋊Dic61—28no—
118#11758199—44no—
119#11758198—41no—
120#11758198—41no—
121C4⋊Dic61—24no—
122C4⋊Dic61—21no—
123C4⋊Dic61—21no—
124C4×Dic61—24no—
125C4×Dic61—21no—
126C4×Dic61—21no—
127C4×Dic61—21no—
128C4×Dic61—42no—
129C4×Dic61—44no—
130C4×Dic61—41no—
131C4×Dic61—41no—
132C4×Dic61D812yescomplemented
133C2×#92418—22no—
134C23×C61—24no—
135C23×C61—22no—
136C23×C61—42no—
137C23×C61—41no—
138C23×C61—41no—
139C23×C61#12011yescharacteristic
140C22×D61—41no—
141D4×C61—24no—
142D4×C61—22no—
143D4×C61#10414yescomplemented
144C2×C4×C61—22no—
145C2×C4×C61—22no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—42no—
150C2×C4×C61—42no—
151C2×C4×C61—42no—
152C2×C4×C61—42no—
153C2×C4×C61C2×C22⋊C411yescharacteristic
154C2×C4×C61C4×D411yescharacteristic
155C2×C4×C61C4×D411yescharacteristic
156C2×C4×C61#12111yescharacteristic
157C2×C4×C61#12111yescharacteristic
158C2×C4×C61#12311yescharacteristic
159C2×C4×C61C2×D811yescharacteristic
160C2×C4×C61#13511yescharacteristic
161C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
163C22⋊D61—81no—
164C22⋊D61—81no—
165C2×Dic61—22no—
166C2×Dic61—22no—
167C2×Dic61—22no—
168C2×Dic61—22no—
169C2×Dic61—24no—
170C2×Dic61—416no—
171C2×Dic61—41no—
172C2×Dic61—42no—
173C2×Dic61—42no—
174C2×Dic61—41no—
175C2×Dic61—41no—
176D244—42no—
177D244—41no—
178D244—41no—
179D244—81no—
180C4×D61—81no—
181C4×D61—81no—
182Dic122—41no—
183Dic122—41no—
184C8×C61—81no—
185C8×C61—81no—
186#92418—42no—
187#9233—611nomaximal, Sylow
188C22×C61—21no—
189C22×C61—21no—
190C22×C61—24no—
191C22×C61—44no—
192C22×C61—44no—
193C22×C61—42no—
194C22×C61—42no—
195C22×C61#38611yescharacteristic
196C22×C61#44711yescharacteristic
197C22×C61#44911yescharacteristic
198C2×D61—81no—
199C2×D61—81no—
200C2×D61—81no—
201C4×C61—21no—
202C4×C61—21no—
203C4×C61—21no—
204C4×C61—42no—
205C4×C61C2×#10412yes—
206C4×C61C4×D811yescharacteristic
207C4×C61#44211yescharacteristic
208C4×C61#45911yescharacteristic
209C4×C61#46311yescharacteristic
210Dic61—24no—
211Dic61—42no—
212Dic61—44no—
213Dic61—81no—
214#3100—611no—
215C42×D4—611no—
216#1962—611no—
217#1502—611no—
218#1486D6111yescharacteristic, complemented
219#1303—611no—
220#1276—611no—
221C2×C61—21no—
222C2×C61—21no—
223C2×C61—44no—
224C2×C61#187911yescharacteristic
225C2×C61#189611yescharacteristic
226C2×C61#190611yescharacteristic
227D61—161no—
228#532—611no—
229C2×C4×D4—1221no—
230C2×C4×D4C2×D6111yescharacteristic
231C22×C42—1221no—
232#480—1221no—
233#474—612no—
234#459—612no—
235#447—1221no—
236C4×D8—1222no—
237#431—611no—
238#431C2×D6111yescharacteristic
239#423C2×D6111yescharacteristic
240C2×#104—1221no—
241C2×#104—1221no—
242C4×C4⋊C4—611no—
243C4×C4⋊C4—1221no—
244C4×C22⋊C4—1222no—
245C4×C22⋊C4—1221no—
246C43—611no—
247#327—1222no—
248D4⋊C8—22no—
249C61#923311yescharacteristic, complemented, Sylow
250C2×#41—1221no—
251C22×D4D24411yescharacteristic
252C23×C4—21no—
253C23×C4—1222no—
254C2×D8—1222no—
255C2×M16—21no—
256C4⋊Q8—611no—
257#127—611no—
258#124—1221no—
259#121—1221no—
260#121—1221no—
261C4×D4—21no—
262C4×D4—21no—
263C4×D4—1228no—
264C4×D4—1221no—
265C4×D4—1221no—
266C4×D4C4×D6112yes—
267C4×D4C22⋊D6112yes—
268C2×C4⋊C4—1221no—
269C2×C4⋊C4D24411yescharacteristic
270C2×C22⋊C4—21no—
271C2×C22⋊C4—1222no—
272C2×C42—611no—
273C2×C42—611no—
274C2×C42—1221no—
275C2×C42—1222no—
276C2×C42—1221no—
277C2×C42—1221no—
278C2×C42—2442no—
279C2×C42—2442no—
280C2×C42C22×D6111yescharacteristic
281#107—1222no—
282C4⋊C8—21no—
283C4⋊C8—21no—
284C4⋊C8—21no—
285C4⋊C8—612no—
286#104—2442no—
287#104—2442no—
288#102—1222no—
289#102—1222no—
290C22⋊C8—21no—
291C22⋊C8—1221no—
292C4×C8—21no—
293C4×C8—1221no—
294#95—612no—
295#95—1222no—
296C24—21no—
297#41—2441no—
298#41—2441no—
299#41—2441no—
300#41—2441no—
301C2×Q8—1221no—
302C2×D4—24no—
303C2×D4—21no—
304C2×D4—1221no—
305C2×D4—1221no—
306C2×D4—1221no—
307C2×D4—2441no—
308C2×D4#1175819812yes—
309C22×C4—21no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—1221no—
317C22×C4—1228no—
318C22×C4—1222no—
319C22×C4—1221no—
320C22×C4—2444no—
321C22×C4—2444no—
322C22×C4—2441no—
323C22×C4C2×D24411yescharacteristic
324C22×C4D4×D6111yescharacteristic
325C22×C4D4×D6111yescharacteristic
326D8—2444no—
327M16—41no—
328M16—41no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8—1222no—
332C4⋊C4—21no—
333C4⋊C4—1224no—
334C4⋊C4—1221no—
335C4⋊C4—1221no—
336C4⋊C4#1175819812yes—
337C22⋊C4—22no—
338C22⋊C4—22no—
339C22⋊C4—1228no—
340C22⋊C4—2441no—
341C22⋊C4—2441no—
342C42—612no—
343C42—1224no—
344C42—1221no—
345C42—1221no—
346C42—1221no—
347C42—2444no—
348C42—2442no—
349C42—2441no—
350C42—2441no—
351C42C2×C4×D6111yescharacteristic
352C42#1175822411yescharacteristic
353C42#1175822411yescharacteristic
354C42C2×C22⋊D6111yescharacteristic
355C23—24no—
356C23—22no—
357C23—42no—
358C23—41no—
359C23—41no—
360C23—2441no—
361C23#1451974711yescharacteristic
362Q8—2441no—
363Q8—2441no—
364D4—24no—
365D4—22no—
366D4—4881no—
367D4—4881no—
368D4—4881no—
369D4—2442no—
370D4—2441no—
371D4—2441no—
372D4#1451970314yescomplemented
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—1222no—
383C2×C4—1222no—
384C2×C4—1222no—
385C2×C4—1222no—
386C2×C4—1224no—
387C2×C4—4881no—
388C2×C4—4881no—
389C2×C4—24416no—
390C2×C4—2441no—
391C2×C4—2441no—
392C2×C4—2442no—
393C2×C4—2442no—
394C2×C4—2441no—
395C2×C4C2×#1175819811yescharacteristic
396C2×C4#1451973711yescharacteristic
397C2×C4#1451973711yescharacteristic
398C2×C4#1451974911yescharacteristic
399C2×C4#1451974911yescharacteristic
400C2×C4#1451976111yescharacteristic
401C2×C4D8×D6111yescharacteristic
402C2×C4#1451979811yescharacteristic
403C2×C4#1451980111yescharacteristic
404C2×C4#1451980411yescharacteristic
405C8—81no—
406C8—81no—
407C8—2442no—
408C22—21no—
409C22—21no—
410C22—24no—
411C22—44no—
412C22—44no—
413C22—42no—
414C22—42no—
415C22—4881no—
416C22—4881no—
417C22—4881no—
418C22#1683963911yescharacteristic
419C22#1683989711yescharacteristic
420C22#1683990811yescharacteristic
421C4—21no—
422C4—21no—
423C4—21no—
424C4—42no—
425C4—1224no—
426C4—4881no—
427C4—2442no—
428C4—2444no—
429C4C2×#1451970312yes—
430C4#1683984211yescharacteristic
431C4#1683987111yescharacteristic
432C4#1683995511yescharacteristic
433C4#1683997911yescharacteristic
434C2—21no—
435C2—21no—
436C2—44no—
437C2—9761no—
438C2#2144616511yescharacteristic
439C2#2144626011yescharacteristic
440C2#2144631811yescharacteristic
subgroupG/H
centerC2×C4#14519749
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1486C2
socleC22×C61#386
prime radical#21455819C2
cosocleC2×C42×C61C23
hypercenter#1486D61
hypocenterC61#9233
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1486

Complements

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

NH ≅ G/Ntype
2. C4×D4×Dic61C2semidirect
3. #21446646C2semidirect
4. #21444315C2semidirect
5. #21443720C2semidirect
6. #21443651C2semidirect
7. C61×#1486C2semidirect
12. #16840042C4semidirect
13. #16839957C4semidirect
32. #14519777C2×C4semidirect
33. #14519774C2×C4semidirect
51. C4⋊#92418C2×C4semidirect
132. C4×Dic61D8semidirect
143. D4×C61#104semidirect
218. #1486D61semidirect
249. C61#9233semidirect
372. D4#14519703semidirect

Maximal subgroups

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

subgroupindex
#214558192
C4×D4×Dic612
#214466462
#214443152
#214437202
#214436512
C61×#14862
#923361