Finite Group Databasebeta

← #29834488

Subgroups — #29834488

Order 15616.

738 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840198C211yesmaximal, characteristic, complemented
2C2×M32×D61C211yesmaximal, characteristic, complemented
3#21455401C211yesmaximal, characteristic, complemented
4C2×#16839995C211yesmaximal, characteristic, complemented
5#21447931C212yesmaximal, complemented
6#21447921C212yesmaximal, complemented
7#21447914C212yesmaximal, complemented
8#21447904C212yesmaximal, complemented
9#21447608C211yesmaximal, characteristic, complemented
10#21447532C211yesmaximal, characteristic, complemented
11C61×#2140C211yesmaximal, characteristic, complemented
12C2×#14519799C2211yescharacteristic
13C22×C8×D61C2211yescharacteristic
14#16840274—21no—
15C2×#14519748—21no—
16#16840198—24no—
17C2×#14519721C2212yescomplemented
18C2×#14519718C2212yescomplemented
19C2×#14519717C2211yescharacteristic
20C2×#14519716C2212yescomplemented
21M32×D61—24no—
22C2×C16×D61C2212yescomplemented
23#16840004C2211yescharacteristic, complemented
24#16840004C2211yescharacteristic, complemented
25#16839999C2211yescharacteristic, complemented
26#16839999C2211yescharacteristic, complemented
27#16839995—21no—
28#16839995—21no—
29#16839995C2212yes—
30#16839995C2212yes—
31#16839992—21no—
32#16839992—21no—
33C2×#14519711C2211yescharacteristic
34#16839756—21no—
35C2×#14519698—21no—
36#16839589C2212yescomplemented
37#16839587C2212yescomplemented
38#16839567C2212yescomplemented
39#16839564C2212yescomplemented
40C22×D8×C61C2211yescharacteristic
41C2×M32×C61C2211yescharacteristic
42C61×#427C2211yescharacteristic
43C61×#357C2212yescomplemented
44C61×#357C2212yescomplemented
45C2×#11758222—21no—
46C22×C22⋊D61—41no—
47C22×C4×D61D411yescharacteristic
48#14519799—22no—
49#14519799—22no—
50C2×Dic244C2311yescharacteristic
51C2×#11758190—21no—
52C2×D488C2311yescharacteristic
53C22×#92418D411yescharacteristic
54C2×C8×D61—22no—
55C2×C8×D61—22no—
56C2×C8×D61D411yescharacteristic
57C2×C8×D61D411yescharacteristic
58C2×C8×D61C2311yescharacteristic
59C2×C8×D61C2311yescharacteristic
60#14519761—41no—
61#14519757—21no—
62#14519757—21no—
63#14519752—21no—
64#14519752—21no—
65#14519748—22no—
66#14519748—22no—
67#14519748—41no—
68#14519748—41no—
69#14519747—41no—
70C4×D244—41no—
71C4×D244—41no—
72C2×C4⋊Dic61—21no—
73C2×C22⋊Dic61—41no—
74#14519721—24no—
75#14519718—24no—
76#14519717D414yescomplemented
77#14519716—24no—
78C2×#11758185C2312yes—
79C16×D61—24no—
80#14519711—21no—
81#14519711C2312yes—
82#14519700—21no—
83#14519700—21no—
84#14519698—22no—
85#14519698—22no—
86#14519697—21no—
87#14519697—21no—
88C22×D4×C61—21no—
89C2×D8×C61—22no—
90C2×D8×C61—21no—
91C2×D8×C61—22no—
92C2×D8×C61C2312yes—
93C22×C8×C61C2311yescharacteristic
94#117×C61—21no—
95M32×C61—22no—
96C2×C16×C61C2312yes—
97#107×C61C2311yescharacteristic
98#107×C61C2311yescharacteristic
99#106×C61—21no—
100C24×C61—41no—
101C23×D61D811yescharacteristic
102C2×D4×C61—22no—
103C2×D4×C61—42no—
104C2×D4×C61—41no—
105C2×D4×C61—42no—
106C22×C4×C61C2×D411yescharacteristic
107C2×C22⋊D61—41no—
108C2×C22⋊D61—42no—
109C2×C22⋊D61—42no—
110C2×C22⋊D61—84no—
111C22×Dic61—41no—
112C22×Dic61D811yescharacteristic
113#11758222—42no—
114#11758222—42no—
115C2×D244—21no—
116C2×D244—41no—
117C2×D244—41no—
118C2×C4×D61—22no—
119C2×C4×D61—22no—
120C2×C4×D61—41no—
121C2×C4×D61D811yescharacteristic
122C2×C4×D61D811yescharacteristic
123C2×C4×D61C2×D411yescharacteristic
124C2×C4×D61C2×D411yescharacteristic
125C2×Dic122—21no—
126D8×C61—22no—
127D8×C61—22no—
128D8×C61—42no—
129C2×C8×C61C2×D411yescharacteristic
130C2×C8×C61C2×D412yes—
131C2×C8×C61#4112yes—
132C2×C8×C61C2411yescharacteristic
133C4⋊C4×C61—21no—
134C4⋊C4×C61—21no—
135C22⋊C4×C61—41no—
136C42×C61—41no—
137C22⋊Dic61—42no—
138C22⋊Dic61—42no—
139#11758198—41no—
140#11758198—41no—
141#11758198—41no—
142#11758198—41no—
143C4⋊Dic61—22no—
144C4⋊Dic61—41no—
145C4⋊Dic61—41no—
146C4⋊Dic61—41no—
147C2×#92418—22no—
148C2×#92418C2×D411yescharacteristic
149C2×#92418C2×D411yescharacteristic
150Dic244—21no—
151Dic244—21no—
152D488—21no—
153D488—21no—
154#11758190—42no—
155C8×D61—22no—
156C8×D61—22no—
157C8×D61—21no—
158C8×D61—21no—
159C8×D61—21no—
160C8×D61—21no—
161C16×C61—22no—
162#11758185C2×D414yescomplemented
163C23×C61—42no—
164C23×C61—82no—
165C23×C61—82no—
166C23×C61—82no—
167C23×C61C2×D811yescharacteristic
168C22×D61—22no—
169C22×D61—22no—
170C22×D61—41no—
171C22×D61—41no—
172C22×D61C2×D811yescharacteristic
173C22×D61C2×D811yescharacteristic
174D4×C61—42no—
175D4×C61—42no—
176D4×C61—82no—
177C2×C4×C61—41no—
178C2×C4×C61—41no—
179C2×C4×C61#12112yes—
180C2×C4×C61C2×D811yescharacteristic
181C2×C4×C61#13512yes—
182C2×C4×C61C22×D411yescharacteristic
183C22⋊D61—84no—
184C22⋊D61—82no—
185C22⋊D61—84no—
186C2×Dic61—22no—
187C2×Dic61—42no—
188C2×Dic61—41no—
189C2×Dic61—82no—
190C2×Dic61C2×D811yescharacteristic
191C2×Dic61C2×D811yescharacteristic
192D244—41no—
193D244—41no—
194D244—82no—
195D244—82no—
196C4×D61—21no—
197C4×D61—21no—
198C4×D61—21no—
199C4×D61—21no—
200C4×D61—22no—
201C4×D61—22no—
202C4×D61—82no—
203Dic122—41no—
204Dic122—41no—
205C8×C61#12112yes—
206C8×C61C22×D411yescharacteristic
207C8×C61C2×#4111yescharacteristic
208#92418—21no—
209#92418—21no—
210#33605—611nomaximal, Sylow
211C22×C61—21no—
212C22×C61—21no—
213C22×C61—82no—
214C22×C61—82no—
215C22×C61—82no—
216C22×C61—164no—
217C22×C61#46612yes—
218C22×C61C22×D811yescharacteristic
219C2×D61—21no—
220C2×D61—21no—
221C2×D61—21no—
222C2×D61—21no—
223C2×D61—21no—
224C2×D61—44no—
225C2×D61—81no—
226C2×D61—81no—
227C2×D61—81no—
228C2×D61#50912yescomplemented
229C4×C61—81no—
230C4×C61—81no—
231C4×C61#46612yes—
232C4×C61C2×#12111yescharacteristic
233C4×C61C2×#13511yescharacteristic
234Dic61—21no—
235Dic61—21no—
236Dic61—82no—
237Dic61—81no—
238C2×#509—611no—
239C22×M32—611no—
240#3050—611no—
241C2×#466—611no—
242#2220—612no—
243#2218—612no—
244#2217—612no—
245#2215—612no—
246#2159—611no—
247#2140D6111yescharacteristic, complemented
248#2139—611no—
249C2×C61—22no—
250C2×C61—162no—
251C2×C61C2×#46611yescharacteristic
252C2×C61C2×#50911yescharacteristic
253C2×C61#341411yescharacteristic
254D61—22no—
255D61—41no—
256D61—161no—
257C2×#135—611no—
258C22×D8C2×D6111yescharacteristic
259C23×C8—611no—
260#525—1221no—
261C2×#121—1221no—
262#509—1224no—
263C2×SD32—612no—
264C2×D16—612no—
265C2×M32—611no—
266C2×M32—612no—
267C2×M32—1224no—
268C2×M32C2×D6111yescharacteristic
269C22×C16—612no—
270#467—611no—
271#467—611no—
272#466—612no—
273#466—612no—
274#466—611no—
275#466—611no—
276#466—1221no—
277#466—1221no—
278#465—1221no—
279#465—1221no—
280#427C2×D6111yescharacteristic
281C2×#107—611no—
282#416—1221no—
283C2×#102—1221no—
284#367—612no—
285#366—612no—
286#358—612no—
287#357—612no—
288#357C2×D6112yescomplemented
289#357C2×D6112yescomplemented
290C61#3360511yescharacteristic, complemented, Sylow
291C2×#41—1221no—
292C22×D4—21no—
293C22×D4—2441no—
294C23×C4—611no—
295#135—1222no—
296#135—1222no—
297C2×Q16—611no—
298C2×SD16—1221no—
299C2×D8—22no—
300C2×D8—22no—
301C2×D8—21no—
302C2×D8—611no—
303C2×D8C22×D6112yes—
304C22×C8—611no—
305C22×C8—611no—
306C22×C8—611no—
307C22×C8—611no—
308C22×C8—611no—
309C22×C8—1222no—
310C22×C8—1222no—
311C22×C8C22×D6111yescharacteristic
312#123—2441no—
313C22⋊Q8—1221no—
314C22⋊Q8—1221no—
315#121—1221no—
316#121—1221no—
317#121—1222no—
318#121—1222no—
319#121—2441no—
320#121—2441no—
321#120—2441no—
322C4×D4—2441no—
323C4×D4—2441no—
324#117—21no—
325C2×C4⋊C4—1221no—
326C2×C22⋊C4—2441no—
327SD32—1224no—
328D16—1224no—
329M32—22no—
330M32—614no—
331M32—1224no—
332C2×C16—612no—
333C2×C16—1224no—
334C2×C16C22×D6112yes—
335#107—612no—
336#107—1221no—
337#107C22×D6111yescharacteristic
338#107C22×D6111yescharacteristic
339#106—21no—
340#103—1221no—
341#103—1221no—
342#102—1221no—
343#102—1221no—
344#102—1222no—
345#102—1222no—
346C24—41no—
347C24—611no—
348#41—2442no—
349#41—2442no—
350C2×Q8—1221no—
351C2×D4—22no—
352C2×D4—42no—
353C2×D4—41no—
354C2×D4—42no—
355C2×D4—1221no—
356C2×D4—4884no—
357C2×D4—2441no—
358C2×D4—2441no—
359C2×D4—2442no—
360C2×D4—2442no—
361C2×D4—2441no—
362C22×C4—611no—
363C22×C4—611no—
364C22×C4—611no—
365C22×C4—611no—
366C22×C4—611no—
367C22×C4—1222no—
368C22×C4—1222no—
369C22×C4—2441no—
370C22×C4—2441no—
371C22×C4D4×D6111yescharacteristic
372Q16—1221no—
373Q16—1221no—
374SD16—2442no—
375D8—22no—
376D8—22no—
377D8—42no—
378D8—1221no—
379D8—1221no—
380C2×C8—611no—
381C2×C8—611no—
382C2×C8—1222no—
383C2×C8—1221no—
384C2×C8—1221no—
385C2×C8—1221no—
386C2×C8—1221no—
387C2×C8—1222no—
388C2×C8—1222no—
389C2×C8#1175822212yes—
390C2×C8D4×D6112yes—
391C2×C8D4×D6111yescharacteristic
392C2×C8C23×D6111yescharacteristic
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—1222no—
396C4⋊C4—2441no—
397C4⋊C4—2441no—
398C4⋊C4—2441no—
399C22⋊C4—41no—
400C22⋊C4—2441no—
401C22⋊C4—2441no—
402C22⋊C4—2441no—
403C22⋊C4—2441no—
404C22⋊C4—2442no—
405C22⋊C4—2442no—
406C42—41no—
407C16—22no—
408C16—614no—
409C23—42no—
410C23—82no—
411C23—82no—
412C23—82no—
413C23—611no—
414C23—611no—
415C23—1222no—
416C23—1222no—
417C23—2441no—
418C23—2441no—
419C23D8×D6111yescharacteristic
420Q8—2441no—
421Q8—2441no—
422D4—42no—
423D4—42no—
424D4—82no—
425D4—4882no—
426D4—4882no—
427D4—4884no—
428D4—4884no—
429D4—4882no—
430D4—2441no—
431D4—2441no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—611no—
435C2×C4—611no—
436C2×C4—1222no—
437C2×C4—1222no—
438C2×C4—1222no—
439C2×C4—1221no—
440C2×C4—1221no—
441C2×C4—1221no—
442C2×C4—1221no—
443C2×C4—4882no—
444C2×C4—4882no—
445C2×C4—2442no—
446C2×C4—2441no—
447C2×C4#1451975012yes—
448C2×C4D8×D6111yescharacteristic
449C2×C4#1451979812yes—
450C2×C4C2×D4×D6111yescharacteristic
451C8—1221no—
452C8—1221no—
453C8#1451975012yes—
454C8C2×D4×D6111yescharacteristic
455C8C2×#1175822211yescharacteristic
456C22—21no—
457C22—21no—
458C22—82no—
459C22—82no—
460C22—82no—
461C22—164no—
462C22—612no—
463C22—1221no—
464C22—1221no—
465C22—1221no—
466C22—1221no—
467C22—1221no—
468C22—4881no—
469C22—4881no—
470C22—4881no—
471C22—2444no—
472C22#1683999712yes—
473C22C2×D8×D6111yescharacteristic
474C4—81no—
475C4—81no—
476C4—1221no—
477C4—1221no—
478C4—4881no—
479C4—4882no—
480C4#1683999712yes—
481C4C2×#1451975011yescharacteristic
482C4C2×#1451979811yescharacteristic
483C2—22no—
484C2—162no—
485C2—1222no—
486C2—9761no—
487C2—2441no—
488C2C2×#1683999711yescharacteristic
489C2#509×D6111yescharacteristic
490C2#2145895111yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2140C2
socleC22×C61C22×D8
hypercenter#2140D61
hypocenterC61#33605
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2140

Complements

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

NH ≅ G/Ntype
1. C2×#16840198C2semidirect
2. C2×M32×D61C2semidirect
3. #21455401C2semidirect
4. C2×#16839995C2semidirect
5. #21447931C2semidirect
6. #21447921C2semidirect
7. #21447914C2semidirect
8. #21447904C2semidirect
9. #21447608C2semidirect
10. #21447532C2semidirect
11. C61×#2140C2semidirect
17. C2×#14519721C22semidirect
18. C2×#14519718C22semidirect
20. C2×#14519716C22semidirect
22. C2×C16×D61C22semidirect
23. #16840004C22semidirect
24. #16840004C22semidirect
25. #16839999C22semidirect
26. #16839999C22semidirect
36. #16839589C22semidirect
37. #16839587C22semidirect
38. #16839567C22semidirect
39. #16839564C22semidirect
43. C61×#357C22semidirect
44. C61×#357C22semidirect
76. #14519717D4semidirect
162. #11758185C2×D4semidirect
228. C2×D61#509semidirect
247. #2140D61semidirect
288. #357C2×D61semidirect
289. #357C2×D61semidirect
290. C61#33605semidirect

Maximal subgroups

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

subgroupindex
C2×#168401982
C2×M32×D612
#214554012
C2×#168399952
#214479312
#214479212
#214479142
#214479042
#214476082
#214475322
C61×#21402
#3360561