Finite Group Databasebeta

← #29834274

Subgroups — #29834274

Order 15616.

718 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840192C212yesmaximal, complemented
2C4×#14519799C211yesmaximal, characteristic, complemented
3#21447878C212yesmaximal, complemented
4#21447871C212yesmaximal, complemented
5#21447866C211yesmaximal, characteristic, complemented
6#21447861C211yesmaximal, characteristic, complemented
7#21447856C211yesmaximal, characteristic, complemented
8#21447851C211yesmaximal, characteristic, complemented
9C2×C4⋊#11758185C211yesmaximal, characteristic, complemented
10#21447526C212yesmaximal, complemented
11C61×#3147C211yesmaximal, characteristic, complemented
12C2×#14519799C2211yescharacteristic
13C4×#11758222—21no—
14#16840192—28no—
15C2×#14519723C2212yes—
16C2×#14519721C2212yes—
17C2×#14519720C2212yes—
18C2×#14519718C2212yes—
19C22×#11758185C2212yes—
20C4×Dic244C2211yescharacteristic
21C4×Dic244C2211yescharacteristic
22C4×#11758190—21no—
23C4×#11758190—21no—
24C4×D488C2211yescharacteristic
25C4×D488C2211yescharacteristic
26#16839800C2211yescharacteristic
27#16839759—21no—
28C4⋊#11758185C2211yescharacteristic
29C4⋊#11758185C2211yescharacteristic
30C4⋊#11758185C2212yes—
31#16839566C2212yes—
32#16839566C2212yes—
33#16839563C2212yes—
34#16839563C2212yes—
35C2×#135×C61—21no—
36C2×#135×C61C2212yes—
37C61×#532—21no—
38C61×#495—21no—
39C61×#495C2212yes—
40C61×#494C2211yescharacteristic
41C61×#493C2211yescharacteristic
42C61×#492—21no—
43C2×C4×C8×C61C2211yescharacteristic
44C2×#11758222—21no—
45#14519799—22no—
46#14519799D414yescomplemented
47C2×Dic244C2311yescharacteristic
48C2×#11758190—21no—
49C2×D488C2311yescharacteristic
50C4×Dic122—21no—
51C4×Dic122—21no—
52C4×D244—21no—
53C4×D244—21no—
54C4×C22⋊D61—41no—
55C4×C22⋊D61—41no—
56#14519736—21no—
57#14519734—41no—
58C42×D61—41no—
59#14519723—24no—
60#14519721—24no—
61#14519720—24no—
62#14519718—24no—
63C2×#11758185—24no—
64C2×#11758185C2312yes—
65C2×#11758185C2312yes—
66#14519711C2311yescharacteristic
67#14519711C2311yescharacteristic
68#14519709—21no—
69#14519702—21no—
70#14519702—21no—
71#14519699—21no—
72#14519699—21no—
73C2×#41×C61—22no—
74#135×C61—24no—
75#135×C61—24no—
76#135×C61—44no—
77C2×Q16×C61—21no—
78C2×Q16×C61C2312yes—
79C2×SD16×C61—22no—
80C2×SD16×C61—22no—
81C2×D8×C61—21no—
82C2×D8×C61C2312yes—
83C22×C8×C61D411yescharacteristic
84C22×C8×C61C2311yescharacteristic
85C4⋊Q8×C61—21no—
86#127×C61—21no—
87#124×C61—22no—
88#121×C61—41no—
89#121×C61—41no—
90C4×D4×C61—41no—
91C4×D4×C61—41no—
92C2×C42×C61D411yescharacteristic
93C4×C8×C61D411yescharacteristic
94C4×C8×C61D411yescharacteristic
95C4×C8×C61C2311yescharacteristic
96C4×C8×C61C2311yescharacteristic
97#41×C61—44no—
98#41×C61—44no—
99C2×Q8×C61—22no—
100C2×D4×C61—22no—
101C2×D4×C61—42no—
102C2×D4×C61—41no—
103C2×D4×C61—41no—
104C22×C4×C61—42no—
105C22×C4×C61D811yescharacteristic
106C22×C4×C61D811yescharacteristic
107C22×C4×C61C2×D411yescharacteristic
108C2×C22⋊D61—41no—
109#11758222—24no—
110#11758222—42no—
111C2×D244—21no—
112C2×C4×D61—41no—
113C2×C4×D61—41no—
114C2×C4×D61—41no—
115C2×Dic122—21no—
116Q16×C61—22no—
117Q16×C61—22no—
118Q16×C61—42no—
119SD16×C61—44no—
120SD16×C61—44no—
121D8×C61—22no—
122D8×C61—22no—
123D8×C61—42no—
124C2×C8×C61—22no—
125C2×C8×C61C2×D411yescharacteristic
126C2×C8×C61C2×D411yescharacteristic
127C2×C8×C61C2×D411yescharacteristic
128C2×C8×C61C2×D412yes—
129C2×C8×C61#4112yes—
130C2×C8×C61C2411yescharacteristic
131C4⋊C4×C61—41no—
132C4⋊C4×C61—41no—
133C22⋊C4×C61—42no—
134C22⋊C4×C61—42no—
135C42×C61D811yescharacteristic
136C42×C61D811yescharacteristic
137C42×C61C2×D411yescharacteristic
138C42×C61C2×D411yescharacteristic
139C22⋊Dic61—41no—
140#11758198—41no—
141#11758198—41no—
142C4⋊Dic61—21no—
143C4⋊Dic61—21no—
144#11758196—41no—
145#11758196—41no—
146C4×Dic61—41no—
147C4×Dic61—41no—
148C4×Dic61—41no—
149Dic244—21no—
150Dic244C2×D412yes—
151D488—21no—
152D488C2×D412yes—
153#11758190—24no—
154#11758185—22no—
155#11758185—22no—
156C23×C61—42no—
157C23×C61C2×D811yescharacteristic
158C22×D61—41no—
159Q8×C61—42no—
160Q8×C61—42no—
161D4×C61—42no—
162D4×C61—42no—
163D4×C61—82no—
164D4×C61—84no—
165D4×C61—82no—
166C2×C4×C61—22no—
167C2×C4×C61—41no—
168C2×C4×C61—42no—
169C2×C4×C61—84no—
170C2×C4×C61#12112yes—
171C2×C4×C61C2×D811yescharacteristic
172C2×C4×C61C2×D811yescharacteristic
173C2×C4×C61C2×D811yescharacteristic
174C2×C4×C61C2×D811yescharacteristic
175C2×C4×C61C2×D811yescharacteristic
176C2×C4×C61AGL(1,ℤ/8)12yes—
177C2×C4×C61C22×D411yescharacteristic
178C22⋊D61—44no—
179C2×Dic61—41no—
180C2×Dic61—41no—
181C2×Dic61—41no—
182D244—22no—
183D244—41no—
184C4×D61—44no—
185C4×D61—82no—
186C4×D61—82no—
187Dic122—22no—
188Dic122—41no—
189C8×C61—21no—
190C8×C61—21no—
191C8×C61#12112yes—
192C8×C61C22×D411yescharacteristic
193C8×C61C2×#4111yescharacteristic
194#33579—611nomaximal, Sylow
195C22×C61—21no—
196C22×C61—21no—
197C22×C61—82no—
198C22×C61—82no—
199C22×C61—82no—
200C22×C61#45912yes—
201C22×C61C22×D811yescharacteristic
202C2×D61—42no—
203C2×D61—81no—
204C2×D61—81no—
205C4×C61—21no—
206C4×C61—21no—
207C4×C61—21no—
208C4×C61—82no—
209C4×C61#45912yes—
210C4×C61#50812yescomplemented
211C4×C61C2×#12111yescharacteristic
212C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
213Dic61—42no—
214Dic61—81no—
215Dic61—81no—
216C2×#508—612no—
217#3147D6111yescharacteristic, complemented
218C4×#135—611no—
219#2211—612no—
220#2210—612no—
221#2209—611no—
222#2208—611no—
223#2207—611no—
224#2206—611no—
225C2×C4⋊C16—611no—
226#2138—612no—
227C2×C61—22no—
228C2×C61—162no—
229C2×C61C2×#45911yescharacteristic
230C2×C61C2×#50811yescharacteristic
231C2×C61#341411yescharacteristic
232D61—82no—
233C2×#135—21no—
234C2×#135—611no—
235C2×#135C2×D6112yes—
236#532—21no—
237C4×#41—1221no—
238#508—1228no—
239C2×Q32—612no—
240C2×SD32—612no—
241C2×SD32—612no—
242C2×D16—612no—
243C22×C16—612no—
244#495—21no—
245#495C2×D6112yes—
246#494C2×D6111yescharacteristic
247#493C2×D6111yescharacteristic
248#492—21no—
249C4×Q16—611no—
250C4×Q16—611no—
251C4×SD16—1221no—
252C4×SD16—1221no—
253C4×D8—611no—
254C4×D8—611no—
255#427—611no—
256#416—1221no—
257C2×C4×C8C2×D6111yescharacteristic
258C4⋊C16—611no—
259C4⋊C16—611no—
260C4⋊C16—612no—
261#358—612no—
262#358—612no—
263#357—612no—
264#357—612no—
265C61#3357911yescharacteristic, complemented, Sylow
266C2×#41—22no—
267C2×#41—1221no—
268#135—24no—
269#135—24no—
270#135—44no—
271#135—614no—
272#135—1222no—
273C2×Q16—21no—
274C2×Q16—611no—
275C2×Q16C22×D6112yes—
276C2×SD16—22no—
277C2×SD16—22no—
278C2×SD16—1221no—
279C2×D8—21no—
280C2×D8—611no—
281C2×D8C22×D6112yes—
282C22×C8C22⋊D6111yescharacteristic
283C22×C8C22×D6111yescharacteristic
284C4⋊Q8—21no—
285#127—21no—
286#124—22no—
287#121—41no—
288#121—41no—
289C4×Q8—1221no—
290C4×Q8—1221no—
291C4×D4—41no—
292C4×D4—41no—
293C4×D4—1221no—
294C4×D4—1221no—
295C4×D4—2441no—
296C4×D4—2441no—
297#117—1221no—
298#117—2441no—
299C2×C42—2441no—
300C2×C42C22⋊D6111yescharacteristic
301Q32—1224no—
302SD32—1224no—
303SD32—1224no—
304D16—1224no—
305C2×C16—612no—
306C2×C16—612no—
307C2×C16—1224no—
308#107—611no—
309#107—611no—
310#106—1221no—
311#103—1221no—
312#103—1221no—
313#102—1221no—
314#102—1221no—
315C4×C8C22⋊D6111yescharacteristic
316C4×C8C22⋊D6111yescharacteristic
317C4×C8C22×D6111yescharacteristic
318C4×C8C22×D6111yescharacteristic
319#41—44no—
320#41—44no—
321#41—1224no—
322#41—2442no—
323C2×Q8—22no—
324C2×Q8—1221no—
325C2×D4—22no—
326C2×D4—42no—
327C2×D4—41no—
328C2×D4—41no—
329C2×D4—1221no—
330C2×D4—2441no—
331C22×C4—42no—
332C22×C4—2441no—
333C22×C4—2441no—
334C22×C4—2441no—
335C22×C4#1175819911yescharacteristic
336C22×C4#1175819911yescharacteristic
337C22×C4C2×C22⋊D6111yescharacteristic
338Q16—22no—
339Q16—22no—
340Q16—42no—
341Q16—612no—
342Q16—1221no—
343SD16—44no—
344SD16—44no—
345SD16—1224no—
346D8—22no—
347D8—22no—
348D8—42no—
349D8—612no—
350D8—1221no—
351C2×C8—22no—
352C2×C8D4×D6112yes—
353C2×C8#1175822412yes—
354C2×C8C2×C22⋊D6111yescharacteristic
355C2×C8C2×C22⋊D6111yescharacteristic
356C2×C8C2×C22⋊D6111yescharacteristic
357C2×C8C23×D6111yescharacteristic
358C4⋊C4—41no—
359C4⋊C4—41no—
360C4⋊C4—1221no—
361C4⋊C4—1221no—
362C4⋊C4—2441no—
363C4⋊C4—2441no—
364C22⋊C4—42no—
365C22⋊C4—42no—
366C22⋊C4—2441no—
367C22⋊C4—2441no—
368C22⋊C4—2441no—
369C42—2441no—
370C42—2441no—
371C42—2441no—
372C42#1175819911yescharacteristic
373C42#1175819911yescharacteristic
374C42C2×C22⋊D6111yescharacteristic
375C42C2×C22⋊D6111yescharacteristic
376C16—1222no—
377C16—1222no—
378C23—42no—
379C23—2441no—
380C23C2×#1175819911yescharacteristic
381Q8—42no—
382Q8—42no—
383Q8—1222no—
384Q8—2441no—
385D4—42no—
386D4—42no—
387D4—82no—
388D4—84no—
389D4—82no—
390D4—1222no—
391D4—2444no—
392D4—2441no—
393C2×C4—22no—
394C2×C4—41no—
395C2×C4—42no—
396C2×C4—84no—
397C2×C4—4882no—
398C2×C4—4882no—
399C2×C4—2441no—
400C2×C4—2441no—
401C2×C4—2441no—
402C2×C4—2444no—
403C2×C4#1451974812yes—
404C2×C4C2×#1175819911yescharacteristic
405C2×C4C2×#1175819911yescharacteristic
406C2×C4C2×#1175819911yescharacteristic
407C2×C4C2×#1175819911yescharacteristic
408C2×C4C2×#1175819911yescharacteristic
409C2×C4#1451980312yes—
410C2×C4C22×C22⋊D6111yescharacteristic
411C8—21no—
412C8—21no—
413C8#1451974812yes—
414C8C2×D4×D6111yescharacteristic
415C8C2×#1175822411yescharacteristic
416C22—21no—
417C22—21no—
418C22—82no—
419C22—82no—
420C22—82no—
421C22—4881no—
422C22—4881no—
423C22—2442no—
424C22#1683995412yes—
425C22C22×#1175819911yescharacteristic
426C4—21no—
427C4—21no—
428C4—21no—
429C4—82no—
430C4—4881no—
431C4—4881no—
432C4—2442no—
433C4#1683995412yes—
434C4#1684019212yescomplemented
435C4C2×#1451974811yescharacteristic
436C4C2×#1451980311yescharacteristic
437C2—22no—
438C2—162no—
439C2—4882no—
440C2C2×#1683995411yescharacteristic
441C2C2×#1684019211yescharacteristic
442C2#2145895311yescharacteristic
subgroupG/H
centerC2×C4C2×#11758199
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#3147C2
socleC22×C61C22×D8
hypercenter#3147D61
hypocenterC61#33579
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3147

Complements

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

NH ≅ G/Ntype
1. C2×#16840192C2semidirect
2. C4×#14519799C2semidirect
3. #21447878C2semidirect
4. #21447871C2semidirect
5. #21447866C2semidirect
6. #21447861C2semidirect
7. #21447856C2semidirect
8. #21447851C2semidirect
9. C2×C4⋊#11758185C2semidirect
10. #21447526C2semidirect
11. C61×#3147C2semidirect
46. #14519799D4semidirect
210. C4×C61#508semidirect
217. #3147D61semidirect
265. C61#33579semidirect
434. C4#16840192semidirect

Maximal subgroups

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

subgroupindex
C2×#168401922
C4×#145197992
#214478782
#214478712
#214478662
#214478612
#214478562
#214478512
C2×C4⋊#117581852
#214475262
C61×#31472
#3357961