Finite Group Databasebeta

← #29711984

Subgroups — #29711984

Order 15616.

1206 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839922C212yesmaximal
2#21448407C211yesmaximal, characteristic
3#21446967C211yesmaximal, characteristic, complemented
4#21446962C211yesmaximal, characteristic, complemented
5#21446919C211yesmaximal, characteristic, complemented
6#21446902C211yesmaximal, characteristic, complemented
7#21446174C212yesmaximal, complemented
8#21446160C212yesmaximal, complemented
9#21446127C212yesmaximal, complemented
10#21445890C211yesmaximal, characteristic, complemented
11C2×C61×#541C211yesmaximal, characteristic, complemented
12C22×#11758222C2211yescharacteristic
13C22×#11758202C2212yes—
14C22×#11758201C2212yes—
15C22×C4⋊Dic61C2211yescharacteristic
16#16839922—28no—
17C2×#14519701C2212yes—
18C2×#14519701C2212yes—
19C2×#14519700C2212yes—
20C2×#14519697C2212yes—
21C2×C22⋊#92418C2212yes—
22#16839668C2211yescharacteristic
23#16839668C2211yescharacteristic
24#16839664C2211yescharacteristic
25#16839664C2211yescharacteristic
26#16839639—22no—
27#16839619—22no—
28#16839524C2212yes—
29#16839524C2212yes—
30#16839517C2211yescharacteristic
31#16839517C2212yes—
32#16839517C2211yescharacteristic
33C61×#541—28no—
34C2×C4⋊Q8×C61C2211yescharacteristic
35C2×#126×C61—22no—
36C2×#125×C61—22no—
37C2×#125×C61C2211yescharacteristic
38C2×C22⋊Q8×C61C2212yes—
39C2×C4×Q8×C61C2212yes—
40C2×#117×C61C2211yescharacteristic
41C2×#11758222—22no—
42C2×#11758222—24no—
43C2×#11758222—22no—
44C2×#11758222—42no—
45C22×Dic122C2311yescharacteristic
46C22×D244C2311yescharacteristic
47C22×C22⋊D61—21no—
48C23×Dic61—21no—
49C22×C4×D61—21no—
50C2×#11758202—24no—
51C2×#11758202—24no—
52C2×#11758202—42no—
53C2×#11758201—24no—
54C2×#11758201—24no—
55C2×#11758201—42no—
56C22×#92418C2312yes—
57C22×#92418C2312yes—
58C2×C4⋊Dic61—21no—
59C2×C4⋊Dic61—42no—
60C2×C4⋊Dic61C2311yescharacteristic
61C2×C4⋊Dic61C2311yescharacteristic
62C2×#11758198—22no—
63C2×#11758198—22no—
64#14519701—42no—
65#14519701—42no—
66#14519700—24no—
67#14519697—24no—
68C22⋊#92418—24no—
69#14519684—22no—
70#14519684—22no—
71C22×Q8×C61C2312yes—
72C23×C4×C61C2311yescharacteristic
73C4⋊Q8×C61—24no—
74#126×C61—216no—
75#125×C61—216no—
76#125×C61—24no—
77C22⋊Q8×C61—24no—
78C22⋊Q8×C61D418yes—
79C4×Q8×C61—24no—
80C4×Q8×C61—24no—
81#117×C61—24no—
82C2×C4⋊C4×C61—22no—
83C2×C4⋊C4×C61—22no—
84C2×C4⋊C4×C61—22no—
85C2×C4⋊C4×C61—22no—
86C2×C4⋊C4×C61D412yes—
87C2×C4⋊C4×C61C2312yes—
88C2×C22⋊C4×C61—22no—
89C2×C22⋊C4×C61D412yes—
90C2×C42×C61—22no—
91C2×C42×C61C2311yescharacteristic
92C2×C42×C61C2311yescharacteristic
93C24×C61C2×D411yescharacteristic
94C23×D61—21no—
95C2×Q8×C61—22no—
96C2×Q8×C61—22no—
97C2×Q8×C61—22no—
98C2×Q8×C61—22no—
99C2×Q8×C61—22no—
100C2×Q8×C61C2×D414yes—
101C22×C4×C61—21no—
102C22×C4×C61—21no—
103C22×C4×C61—22no—
104C22×C4×C61—22no—
105C22×C4×C61—22no—
106C22×C4×C61C2×D412yes—
107C22×C4×C61C2×D412yes—
108C22×C4×C61C2×D411yescharacteristic
109C22×C4×C61C2×D414yes—
110C22×C4×C61C2411yescharacteristic
111C2×C22⋊D61—24no—
112C2×C22⋊D61—42no—
113C2×C22⋊D61—42no—
114C22×Dic61—21no—
115C22×Dic61—21no—
116C22×Dic61—21no—
117C22×Dic61—42no—
118C22×Dic61—82no—
119#11758222—48no—
120#11758222—48no—
121C2×D244—22no—
122C2×D244—22no—
123C2×D244—21no—
124C2×D244#4112yes—
125C2×C4×D61—24no—
126C2×C4×D61—42no—
127C2×C4×D61—42no—
128C2×Dic122—22no—
129C2×Dic122—22no—
130C2×Dic122—21no—
131C2×Dic122#4112yes—
132C4⋊C4×C61—28no—
133C4⋊C4×C61—28no—
134C4⋊C4×C61—28no—
135C4⋊C4×C61—28no—
136C4⋊C4×C61—24no—
137C4⋊C4×C61—22no—
138C4⋊C4×C61C2×D414yes—
139C22⋊C4×C61—28no—
140C22⋊C4×C61—24no—
141C42×C61—28no—
142C42×C61—22no—
143C42×C61—22no—
144#11758202—48no—
145#11758201—48no—
146#11758198—82no—
147#11758198—82no—
148C4⋊Dic61—22no—
149C4⋊Dic61—22no—
150C4⋊Dic61—42no—
151C2×#92418—22no—
152C2×#92418—22no—
153C2×#92418—22no—
154C2×#92418—22no—
155C2×#92418—22no—
156C2×#92418—22no—
157C23×C61—21no—
158C23×C61—21no—
159C23×C61—22no—
160C23×C61—22no—
161C23×C61#12012yes—
162C23×C61C22×D411yescharacteristic
163C22×D61—22no—
164C22×D61—41no—
165C22×D61—41no—
166C22×D61—42no—
167C22×D61—42no—
168Q8×C61—24no—
169Q8×C61—24no—
170Q8×C61—42no—
171Q8×C61—42no—
172C2×C4×C61—21no—
173C2×C4×C61—21no—
174C2×C4×C61—24no—
175C2×C4×C61—24no—
176C2×C4×C61—22no—
177C2×C4×C61—22no—
178C2×C4×C61—24no—
179C2×C4×C61—24no—
180C2×C4×C61—22no—
181C2×C4×C61—22no—
182C2×C4×C61—22no—
183C2×C4×C61—22no—
184C2×C4×C61—42no—
185C2×C4×C61—42no—
186C2×C4×C61—42no—
187C2×C4×C61—42no—
188C2×C4×C61#12012yes—
189C2×C4×C61C22×D412yes—
190C2×C4×C61C2×#4111yescharacteristic
191C2×C4×C61C2×#4111yescharacteristic
192C2×C4×C61H(5,𝔽2)12yes—
193C22⋊D61—48no—
194C2×Dic61—22no—
195C2×Dic61—41no—
196C2×Dic61—41no—
197C2×Dic61—41no—
198C2×Dic61—41no—
199C2×Dic61—42no—
200C2×Dic61—42no—
201C2×Dic61—84no—
202D244—24no—
203D244—42no—
204C4×D61—48no—
205Dic122—24no—
206Dic122—42no—
207#92418—42no—
208#92418—42no—
209#23944—611nomaximal, Sylow
210C22×C61—22no—
211C22×C61—24no—
212C22×C61—42no—
213C22×C61—41no—
214C22×C61—41no—
215C22×C61C2×#12011yescharacteristic
216C22×C61#52511yescharacteristic
217C22×C61#53511yescharacteristic
218C22×C61#57712yes—
219C22×C61#57812yes—
220C2×D61—44no—
221C2×D61—42no—
222C2×D61—81no—
223C2×D61—81no—
224C2×D61—82no—
225C4×C61—22no—
226C4×C61—44no—
227C4×C61—42no—
228C4×C61—42no—
229C4×C61—44no—
230C4×C61#54612yes—
231C4×C61#54612yes—
232Dic61—42no—
233Dic61—81no—
234Dic61—81no—
235C2×#541D6111yescharacteristic, complemented
236C2×#452—612no—
237#2311—611no—
238#2026—611no—
239#2025—611no—
240#2016—611no—
241#2013—611no—
242#1880—612no—
243#1878—612no—
244#1872—612no—
245#1818—611no—
246C2×C61—42no—
247C2×C61#240411yescharacteristic
248C2×C61#301312yes—
249C2×C61#312012yes—
250C2×C61#322211yescharacteristic
251C2×C61#322311yescharacteristic
252D61—82no—
253C22×#41—611no—
254C22×Q16—612no—
255C22×SD16—612no—
256#541—28no—
257C2×C4⋊Q8C2×D6111yescharacteristic
258C2×#126—22no—
259C2×#125—22no—
260C2×#125C2×D6111yescharacteristic
261C2×C22⋊Q8C2×D6112yes—
262C2×C4×Q8C2×D6112yes—
263C2×#117C2×D6111yescharacteristic
264C22×C4⋊C4—611no—
265#452—1228no—
266C2×#103—612no—
267C2×#103—612no—
268C2×#103—612no—
269C2×#102—612no—
270C2×C22⋊C8—612no—
271#391—611no—
272#391—611no—
273#390—611no—
274#390—611no—
275#386—1222no—
276#380—1222no—
277#340—612no—
278#340—612no—
279#336—612no—
280#336—611no—
281#336—611no—
282C61#2394411yescharacteristic, complemented, Sylow
283C2×#41—1222no—
284C2×#41—1222no—
285C2×#41—1224no—
286C2×#41—2442no—
287C22×Q8—611no—
288C22×Q8C22×D6112yes—
289C22×D4—611no—
290C22×D4—1221no—
291C23×C4—1221no—
292C23×C4—1221no—
293C23×C4C22×D6111yescharacteristic
294C2×Q16—1224no—
295C2×Q16—1224no—
296C2×Q16—2442no—
297C2×SD16—1224no—
298C2×SD16—1224no—
299C2×SD16—2442no—
300C22×C8—612no—
301C22×C8—612no—
302C4⋊Q8—24no—
303#126—216no—
304#125—216no—
305#125—24no—
306C22⋊Q8—24no—
307C22⋊Q8C22⋊D6118yes—
308C4×Q8—24no—
309C4×Q8—24no—
310#117—24no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—611no—
316C2×C4⋊C4—611no—
317C2×C4⋊C4—1221no—
318C2×C4⋊C4—2442no—
319C2×C4⋊C4C22⋊D6112yes—
320C2×C4⋊C4C22×D6112yes—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—1222no—
323C2×C22⋊C4—1222no—
324C2×C22⋊C4C22⋊D6112yes—
325C2×C42—22no—
326C2×C42C22×D6111yescharacteristic
327C2×C42C22×D6111yescharacteristic
328#103—1224no—
329#103—2442no—
330#103—2442no—
331#102—1224no—
332C22⋊C8—1224no—
333#95—1222no—
334#95—1222no—
335C24—1221no—
336C24C2×C22⋊D6111yescharacteristic
337#41—2448no—
338#41—2448no—
339C2×Q8—22no—
340C2×Q8—22no—
341C2×Q8—22no—
342C2×Q8—22no—
343C2×Q8—22no—
344C2×Q8—612no—
345C2×Q8—1221no—
346C2×Q8—1222no—
347C2×Q8—1222no—
348C2×Q8C2×C22⋊D6114yes—
349C2×D4—612no—
350C2×D4—1224no—
351C2×D4—1222no—
352C2×D4—1221no—
353C2×D4—1222no—
354C2×D4—2442no—
355C2×D4—2442no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—1224no—
362C22×C4—1221no—
363C22×C4—1221no—
364C22×C4—1221no—
365C22×C4—4882no—
366C22×C4—2442no—
367C22×C4—2442no—
368C22×C4—2442no—
369C22×C4C2×C22⋊D6112yes—
370C22×C4C2×C22⋊D6112yes—
371C22×C4C2×C22⋊D6114yes—
372C22×C4C2×C22⋊D6111yescharacteristic
373C22×C4C23×D6111yescharacteristic
374Q16—2448no—
375SD16—2448no—
376C2×C8—1222no—
377C2×C8—1222no—
378C2×C8—1222no—
379C2×C8—1222no—
380C2×C8—1222no—
381C2×C8—1222no—
382C4⋊C4—28no—
383C4⋊C4—28no—
384C4⋊C4—28no—
385C4⋊C4—22no—
386C4⋊C4—28no—
387C4⋊C4—24no—
388C4⋊C4—1222no—
389C4⋊C4—1222no—
390C4⋊C4—2442no—
391C4⋊C4C2×C22⋊D6114yes—
392C22⋊C4—28no—
393C22⋊C4—24no—
394C22⋊C4—4882no—
395C22⋊C4—4882no—
396C42—28no—
397C42—22no—
398C42—22no—
399C23—21no—
400C23—22no—
401C23—22no—
402C23—21no—
403C23—1222no—
404C23—2441no—
405C23—2442no—
406C23—2442no—
407C23—2441no—
408C23#1451974612yes—
409C23C22×C22⋊D6111yescharacteristic
410Q8—24no—
411Q8—24no—
412Q8—42no—
413Q8—42no—
414Q8—1224no—
415Q8—2442no—
416D4—1224no—
417D4—2448no—
418D4—2442no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—24no—
422C2×C4—24no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—24no—
426C2×C4—24no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—1222no—
436C2×C4—4884no—
437C2×C4—2448no—
438C2×C4—2442no—
439C2×C4—2442no—
440C2×C4—2441no—
441C2×C4—2441no—
442C2×C4—2441no—
443C2×C4—2441no—
444C2×C4#1451974612yes—
445C2×C4C22×C22⋊D6112yes—
446C2×C4#41×D6111yescharacteristic
447C2×C4#41×D6111yescharacteristic
448C2×C4#1451982312yes—
449C8—2442no—
450C8—2442no—
451C22—24no—
452C22—22no—
453C22—41no—
454C22—42no—
455C22—41no—
456C22—4881no—
457C22—4882no—
458C22—4881no—
459C22—2444no—
460C22—2442no—
461C22C2×#1451974611yescharacteristic
462C22#1684026911yescharacteristic
463C22#1684032611yescharacteristic
464C22#1684057012yes—
465C22#1684057712yes—
466C4—22no—
467C4—42no—
468C4—42no—
469C4—44no—
470C4—44no—
471C4—4881no—
472C4—4881no—
473C4—2442no—
474C4#1684040012yes—
475C4#1684040012yes—
476C2—42no—
477C2—4882no—
478C2#2144913411yescharacteristic
479C2#2145513412yes—
480C2#2145602712yes—
481C2#2145688511yescharacteristic
482C2#2145689611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#541C2
socleC23×C61C22×D4
prime radicalC22×#11758222C22
hypercenterC2×#541D61
hypocenterC61#23944
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
3. #21446967C2semidirect
4. #21446962C2semidirect
5. #21446919C2semidirect
6. #21446902C2semidirect
7. #21446174C2semidirect
8. #21446160C2semidirect
9. #21446127C2semidirect
10. #21445890C2semidirect
11. C2×C61×#541C2semidirect
235. C2×#541D61semidirect
282. C61#23944semidirect

Maximal subgroups

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

subgroupindex
C2×#168399222
#214484072
#214469672
#214469622
#214469192
#214469022
#214461742
#214461602
#214461272
#214458902
C2×C61×#5412
#2394461