Finite Group Databasebeta

← #29581077

Subgroups — #29581077

Order 15616.

802 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840138C211yesmaximal, characteristic
2C2×#16839963C211yesmaximal, characteristic, complemented
3#21450822C211yesmaximal, characteristic, complemented
4#21446745C211yesmaximal, characteristic, complemented
5C2×#16839492C211yesmaximal, characteristic, complemented
6#21443658C211yesmaximal, characteristic, complemented
7C2×C61×#331C211yesmaximal, characteristic, complemented
8C22×#11758190—21no—
9C22×#11758199—22no—
10C2×#14519774C2211yescharacteristic
11C2×#14519764—21no—
12C2×C4×Dic122C2211yescharacteristic
13#16840138—22no—
14#16840138—22no—
15#16839963—22no—
16#16839963—22no—
17C2×#14519699—21no—
18C2×#14519699—22no—
19C2×C4×#92418C2211yescharacteristic
20#16839676—22no—
21#16839665—21no—
22#16839665—22no—
23C4×C4⋊Dic61C2211yescharacteristic
24#16839492—22no—
25C2×#127×C61C2211yescharacteristic
26C2×C4⋊C8×C61C2211yescharacteristic
27C2×C4⋊C8×C61C2211yescharacteristic
28C61×#331—22no—
29C22×Dic122D411yescharacteristic
30C22×D244—21no—
31C22×D244—21no—
32C22×D244—21no—
33C2×#11758190—24no—
34C2×#11758190—42no—
35C2×#11758190—42no—
36C2×#11758199—28no—
37C2×#11758199—48no—
38C22×#92418—21no—
39#14519774—21no—
40#14519774—21no—
41#14519774—21no—
42#14519774D412yes—
43#14519764—42no—
44#14519764—42no—
45C4×Dic122—21no—
46C4×Dic122—21no—
47C4×Dic122—21no—
48C4×Dic122—21no—
49C2×C4⋊Dic61D411yescharacteristic
50C2×C4⋊Dic61D412yes—
51C2×#11758196—21no—
52C2×C22⋊Dic61—24no—
53C2×C22⋊Dic61—24no—
54C2×C4×Dic61—21no—
55C2×C4×Dic61—21no—
56#14519699—24no—
57#14519699—44no—
58C4×#92418—21no—
59C4×#92418D412yes—
60#14519684—21no—
61C22×D4×C61—21no—
62C22×D4×C61—21no—
63C22×D4×C61D412yes—
64C22×C8×C61—21no—
65C22×C8×C61—21no—
66#127×C61—21no—
67#127×C61—21no—
68#127×C61—21no—
69#127×C61—21no—
70C2×C42×C61C2311yescharacteristic
71C4⋊C8×C61—21no—
72C4⋊C8×C61—21no—
73C4⋊C8×C61—21no—
74C4⋊C8×C61D412yes—
75C24×C61—22no—
76C23×D61—41no—
77C2×D4×C61—22no—
78C2×D4×C61—22no—
79C2×D4×C61—44no—
80C2×D4×C61—41no—
81C2×D4×C61—41no—
82C2×D4×C61—41no—
83C2×D4×C61—41no—
84C2×D4×C61—41no—
85C2×D4×C61—41no—
86C2×D4×C61—42no—
87C2×D4×C61—41no—
88C2×D4×C61—42no—
89C2×D4×C61—41no—
90C22×C4×C61C2×D411yescharacteristic
91C22×C4×C61C2×D411yescharacteristic
92C22×C4×C61C2×D411yescharacteristic
93C22×Dic61—21no—
94C22×Dic61—22no—
95C22×Dic61—21no—
96C2×D244—22no—
97C2×D244—22no—
98C2×D244—22no—
99C2×D244—44no—
100C2×D244—41no—
101C2×D244—41no—
102C2×D244—42no—
103C2×D244—41no—
104C2×D244—42no—
105C2×D244—41no—
106C2×D244—41no—
107C2×D244—41no—
108C2×D244—41no—
109C2×Dic122—21no—
110C2×Dic122—21no—
111C2×Dic122—21no—
112C2×Dic122—21no—
113C2×Dic122—21no—
114C2×Dic122D812yescomplemented
115C2×C8×C61—22no—
116C2×C8×C61—41no—
117C2×C8×C61—41no—
118C2×C8×C61—41no—
119C2×C8×C61—42no—
120C42×C61C2×D411yescharacteristic
121C42×C61C2×D411yescharacteristic
122C42×C61C2×D411yescharacteristic
123C42×C61#4111yescharacteristic
124C22⋊Dic61—48no—
125C22⋊Dic61—84no—
126#11758199—416no—
127C4⋊Dic61—21no—
128C4⋊Dic61—21no—
129C4⋊Dic61—22no—
130C4⋊Dic61—22no—
131#11758196—41no—
132#11758196—41no—
133C4×Dic61—41no—
134C4×Dic61—41no—
135C4×Dic61—41no—
136C4×Dic61—41no—
137C2×#92418—24no—
138C2×#92418—22no—
139#11758190—48no—
140C23×C61—42no—
141C23×C61—42no—
142C23×C61—42no—
143C23×C61—44no—
144C23×C61—44no—
145C23×C61#12011yescharacteristic
146C22×D61—42no—
147C22×D61—81no—
148C22×D61—81no—
149C22×D61—82no—
150C22×D61—82no—
151D4×C61—44no—
152D4×C61—82no—
153D4×C61—81no—
154D4×C61—81no—
155D4×C61—82no—
156D4×C61—81no—
157D4×C61—81no—
158D4×C61—81no—
159D4×C61—81no—
160C2×C4×C61—22no—
161C2×C4×C61#12011yescharacteristic
162C2×C4×C61#12011yescharacteristic
163C2×C4×C61#12111yescharacteristic
164C2×C4×C61#12111yescharacteristic
165C2×C4×C61#12111yescharacteristic
166C2×C4×C61#12711yescharacteristic
167C2×C4×C61C2×D811yescharacteristic
168C2×C4×C61#13511yescharacteristic
169C2×C4×C61#13512yes—
170C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C61AGL(1,ℤ/8)12yes—
173C2×Dic61—22no—
174C2×Dic61—41no—
175C2×Dic61—41no—
176C2×Dic61—41no—
177C2×Dic61—42no—
178C2×Dic61—42no—
179C2×Dic61—42no—
180C2×Dic61—42no—
181D244—44no—
182D244—42no—
183D244—42no—
184D244—44no—
185D244—82no—
186D244—81no—
187D244—81no—
188D244—81no—
189D244—81no—
190Dic122—22no—
191Dic122—22no—
192Dic122—41no—
193Dic122—41no—
194C8×C61—42no—
195C8×C61—81no—
196#92418—24no—
197#10047—611nomaximal, Sylow
198C22×C61—84no—
199C22×C61—84no—
200C22×C61—82no—
201C22×C61—82no—
202C22×C61—82no—
203C22×C61#39211yescharacteristic
204C22×C61#44711yescharacteristic
205C22×C61#44911yescharacteristic
206C22×C61#44912yes—
207C22×C61#45312yes—
208C2×D61—82no—
209C2×D61—82no—
210C2×D61—82no—
211C2×D61—162no—
212C2×D61—162no—
213C4×C61—21no—
214C4×C61—21no—
215C4×C61#44711yescharacteristic
216C4×C61#44911yescharacteristic
217C4×C61#46312yes—
218C4×C61#46611yescharacteristic
219C4×C61#46911yescharacteristic
220C4×C61#49511yescharacteristic
221C4×C61#49611yescharacteristic
222Dic61—42no—
223Dic61—82no—
224Dic61—81no—
225C2×#493—611no—
226C2×#460—611no—
227#2548—611no—
228#1982—611no—
229C2×#331D6111yescharacteristic, complemented
230C2×Q8⋊C8—611no—
231#1279—611no—
232C2×C61—162no—
233C2×C61#162012yes—
234C2×C61#162112yes—
235C2×C61#199911yescharacteristic
236C2×C61#200211yescharacteristic
237C2×C61#201211yescharacteristic
238D61—162no—
239C22×SD16—1221no—
240C22×D8—1222no—
241C2×#127—611no—
242C2×#127C2×D6111yescharacteristic
243C2×#124—1221no—
244C2×C4×Q8—611no—
245#493—1222no—
246#493—1222no—
247#460—1222no—
248#460—1222no—
249C2×C4⋊C8C2×D6111yescharacteristic
250C2×C4⋊C8C2×D6111yescharacteristic
251C2×#102—1221no—
252C2×#102—1222no—
253C2×C4×C8—611no—
254#394—1222no—
255#390—1222no—
256#390—1221no—
257C4×C4⋊C4—611no—
258#331—22no—
259Q8⋊C8—1222no—
260C61#1004711yescharacteristic, complemented, Sylow
261C22×Q8—611no—
262C22×D4—21no—
263C22×D4—21no—
264C22×D4—1221no—
265C22×D4—1221no—
266C22×D4—1221no—
267C22×D4D24412yes—
268C2×SD16—1224no—
269C2×SD16—2442no—
270C2×SD16—2442no—
271C2×D8—1228no—
272C2×D8—2448no—
273C22×C8—21no—
274C22×C8—21no—
275C22×C8—1221no—
276#127—21no—
277#127—21no—
278#127—21no—
279#127—21no—
280#127—612no—
281#127—1221no—
282#127—1221no—
283#127—1221no—
284#124—2442no—
285#124—2442no—
286C4×Q8—1221no—
287C4×Q8—1221no—
288C4×Q8—1221no—
289C4×Q8—1221no—
290C2×C4⋊C4—611no—
291C2×C4⋊C4—612no—
292C2×C4⋊C4—1221no—
293C2×C22⋊C4—1224no—
294C2×C22⋊C4—1224no—
295C2×C42—1221no—
296C2×C42—1221no—
297C2×C42C22×D6111yescharacteristic
298C4⋊C8—21no—
299C4⋊C8—21no—
300C4⋊C8—21no—
301C4⋊C8C22⋊D6112yes—
302#102—1224no—
303#102—2444no—
304C4×C8—612no—
305C4×C8—1221no—
306#95—1221no—
307C24—22no—
308C24—2441no—
309C2×Q8—612no—
310C2×Q8—1221no—
311C2×Q8—1221no—
312C2×Q8—1221no—
313C2×Q8—1221no—
314C2×Q8—1221no—
315C2×D4—22no—
316C2×D4—22no—
317C2×D4—44no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4—42no—
324C2×D4—41no—
325C2×D4—42no—
326C2×D4—41no—
327C2×D4—41no—
328C2×D4—1222no—
329C2×D4—1222no—
330C2×D4—1222no—
331C2×D4—2444no—
332C2×D4—2441no—
333C2×D4—2441no—
334C2×D4—2441no—
335C2×D4—2441no—
336C2×D4—2442no—
337C2×D4—2441no—
338C2×D4—2442no—
339C2×D4—2441no—
340C2×D4—2441no—
341C22×C4—1221no—
342C22×C4—1222no—
343C22×C4—1221no—
344C22×C4C2×D24411yescharacteristic
345C22×C4D4×D6111yescharacteristic
346C22×C4D4×D6111yescharacteristic
347SD16—2448no—
348D8—24416no—
349C2×C8—22no—
350C2×C8—41no—
351C2×C8—41no—
352C2×C8—41no—
353C2×C8—42no—
354C2×C8—1224no—
355C2×C8—1222no—
356C4⋊C4—1221no—
357C4⋊C4—1221no—
358C4⋊C4—1222no—
359C4⋊C4—1222no—
360C4⋊C4—2441no—
361C4⋊C4—2441no—
362C22⋊C4—4884no—
363C22⋊C4—2448no—
364C42—2441no—
365C42—2441no—
366C42—2441no—
367C42—2441no—
368C42#1175822211yescharacteristic
369C42D4×D6111yescharacteristic
370C42D4×D6111yescharacteristic
371C42C2×C22⋊D6111yescharacteristic
372C23—42no—
373C23—42no—
374C23—44no—
375C23—42no—
376C23—44no—
377C23—4881no—
378C23—4881no—
379C23—4882no—
380C23—4882no—
381C23—2442no—
382C23#1451974711yescharacteristic
383Q8—1222no—
384Q8—1222no—
385Q8—2441no—
386Q8—2441no—
387D4—44no—
388D4—82no—
389D4—82no—
390D4—81no—
391D4—81no—
392D4—81no—
393D4—81no—
394D4—81no—
395D4—81no—
396D4—4882no—
397D4—4881no—
398D4—4881no—
399D4—4881no—
400D4—4881no—
401D4—2444no—
402D4—2444no—
403D4—2442no—
404D4—2442no—
405C2×C4—22no—
406C2×C4—1222no—
407C2×C4—2442no—
408C2×C4—2442no—
409C2×C4—2441no—
410C2×C4—2442no—
411C2×C4—2442no—
412C2×C4—2441no—
413C2×C4—2441no—
414C2×C4#1451974511yescharacteristic
415C2×C4#1451974711yescharacteristic
416C2×C4#1451975011yescharacteristic
417C2×C4#1451975011yescharacteristic
418C2×C4#1451975111yescharacteristic
419C2×C4#1451977311yescharacteristic
420C2×C4D8×D6111yescharacteristic
421C2×C4#1451979812yes—
422C2×C4#1451979811yescharacteristic
423C2×C4#1451980112yes—
424C2×C4#1451980111yescharacteristic
425C2×C4#1451980411yescharacteristic
426C8—42no—
427C8—81no—
428C8—1224no—
429C22—84no—
430C22—84no—
431C22—82no—
432C22—82no—
433C22—82no—
434C22—9762no—
435C22—9762no—
436C22—4882no—
437C22—4882no—
438C22—4882no—
439C22#1683967111yescharacteristic
440C22#1683989711yescharacteristic
441C22#1683990811yescharacteristic
442C22#1683990812yes—
443C22#1683993212yes—
444C4—21no—
445C4—21no—
446C4—4882no—
447C4—4881no—
448C4—2442no—
449C4#1683989411yescharacteristic
450C4#1683990611yescharacteristic
451C4#1683997612yes—
452C4#1683999711yescharacteristic
453C4#1684001411yescharacteristic
454C4#1684014311yescharacteristic
455C4#1684015011yescharacteristic
456C2—162no—
457C2—9762no—
458C2#2144487912yes—
459C2#2144488512yes—
460C2#2144681611yescharacteristic
461C2#2144683611yescharacteristic
462C2#2144689811yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC2×C61×#331C2
socleC23×C61#120
prime radicalC2×#16840138C2
hypercenterC2×#331D61
hypocenterC61#10047
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#331

Complements

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

NH ≅ G/Ntype
2. C2×#16839963C2semidirect
3. #21450822C2semidirect
4. #21446745C2semidirect
5. C2×#16839492C2semidirect
6. #21443658C2semidirect
7. C2×C61×#331C2semidirect
114. C2×Dic122D8semidirect
229. C2×#331D61semidirect
260. C61#10047semidirect

Maximal subgroups

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

subgroupindex
C2×#168401382
C2×#168399632
#214508222
#214467452
C2×#168394922
#214436582
C2×C61×#3312
#1004761