Finite Group Databasebeta

← #29834974

Subgroups — #29834974

Order 15616.

546 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456402C211yesmaximal, characteristic
2C4×Q16×D61C211yesmaximal, characteristic
3#21448023C211yesmaximal, characteristic
4#21448020C211yesmaximal, characteristic
5#21447970C211yesmaximal, characteristic, complemented
6#21447969C211yesmaximal, characteristic, complemented
7#21447868C211yesmaximal, characteristic, complemented
8#21447867C211yesmaximal, characteristic, complemented
9#21447754C211yesmaximal, characteristic
10#21447751C211yesmaximal, characteristic
11C4×Dic488C211yesmaximal, characteristic, complemented
12C4×#14519723C211yesmaximal, characteristic, complemented
13C4×#14519723C211yesmaximal, characteristic, complemented
14#21447616C211yesmaximal, characteristic
15C4×Q32×C61C211yesmaximal, characteristic, complemented
16C2×Q16×D61C2211yescharacteristic
17#16840316—21no—
18C4×Q8×D61—21no—
19C2×Dic488C2211yescharacteristic
20C2×#14519723C2211yescharacteristic
21C2×#14519723C2211yescharacteristic
22#16840166C2211yescharacteristic
23#16840140C2211yescharacteristic
24#16840111—21no—
25#16840004C2211yescharacteristic
26#16840002—21no—
27#16840000C2211yescharacteristic
28C4×Dic244C2211yescharacteristic
29C4×Dic244C2211yescharacteristic
30Q16×Dic61C2211yescharacteristic
31#16839856C2211yescharacteristic
32C4×#11758202—21no—
33C4×#11758202—21no—
34#16839854—21no—
35#107×D61C2211yescharacteristic
36#103×D61—21no—
37C4×C8×D61C2211yescharacteristic
38#16839588C2211yescharacteristic
39#16839587C2211yescharacteristic
40#16839587C2211yescharacteristic
41#16839580C2211yescharacteristic
42#16839580C2211yescharacteristic
43#16839567C2211yescharacteristic
44#16839567C2211yescharacteristic
45#16839566C2211yescharacteristic
46#16839566C2211yescharacteristic
47#16839565C2211yescharacteristic
48#16839565C2211yescharacteristic
49#16839541C2211yescharacteristic
50#16839541C2211yescharacteristic
51C4×#11758185C2211yescharacteristic
52C2×Q32×C61C2211yescharacteristic
53C4×Q16×C61C2211yescharacteristic
54C4×Q16×C61C2211yescharacteristic
55C61×#366C2211yescharacteristic
56C61×#358C2211yescharacteristic
57C61×#358C2211yescharacteristic
58C4×C16×C61C2211yescharacteristic
59C2×Q8×D61—21no—
60C2×Dic244C2311yescharacteristic
61C2×Dic244C2311yescharacteristic
62C2×#11758202—21no—
63C2×#11758202—21no—
64Q16×D61—22no—
65Q16×D61—22no—
66C2×C8×D61D411yescharacteristic
67C2×C8×D61C2311yescharacteristic
68#14519776—21no—
69#14519775—21no—
70#14519767—41no—
71#14519757—21no—
72#14519755—41no—
73#14519753—21no—
74Q8×Dic61—21no—
75C4×Dic122—21no—
76C4×Dic122—21no—
77C4×Dic122—41no—
78C4×Dic122—41no—
79#14519742—21no—
80#14519742—41no—
81#14519734—41no—
82C4⋊C4×D61—21no—
83C4⋊C4×D61—41no—
84C42×D61—41no—
85C42×D61D411yescharacteristic
86Dic488—22no—
87#14519723—22no—
88#14519723—22no—
89C2×#11758185C2311yescharacteristic
90C2×#11758185C2311yescharacteristic
91#14519711C2311yescharacteristic
92#14519711C2311yescharacteristic
93#14519710—21no—
94#14519710—21no—
95#14519702—21no—
96#14519702—21no—
97#14519701—21no—
98#14519701—21no—
99#14519700—21no—
100#14519700—21no—
101C4×#92418D411yescharacteristic
102C8×Dic61D411yescharacteristic
103C8×Dic61C2311yescharacteristic
104C2×Q16×C61C2311yescharacteristic
105C2×Q16×C61C2311yescharacteristic
106C4×Q8×C61—21no—
107C4×Q8×C61—21no—
108Q32×C61—22no—
109C2×C16×C61C2311yescharacteristic
110C2×C16×C61C2311yescharacteristic
111#107×C61C2311yescharacteristic
112#107×C61C2311yescharacteristic
113#103×C61—21no—
114#103×C61—21no—
115C4×C8×C61C2311yescharacteristic
116C2×Q8×C61—21no—
117C2×Q8×C61—21no—
118Q8×D61—24no—
119Q8×D61—42no—
120C2×C4×D61—41no—
121C2×C4×D61—41no—
122C2×C4×D61D811yescharacteristic
123C2×C4×D61D811yescharacteristic
124C2×C4×D61C2×D411yescharacteristic
125C2×Dic122—21no—
126C2×Dic122—21no—
127C2×Dic122—41no—
128C2×Dic122—41no—
129Q16×C61—21no—
130Q16×C61—21no—
131Q16×C61—21no—
132Q16×C61#4112yes—
133C2×C8×C61C2×D411yescharacteristic
134C2×C8×C61C2411yescharacteristic
135C4⋊C4×C61—21no—
136C4⋊C4×C61—21no—
137C4⋊C4×C61—41no—
138C4⋊C4×C61—41no—
139C42×C61—41no—
140C42×C61—41no—
141C42×C61C2×D411yescharacteristic
142#11758202—24no—
143#11758202—42no—
144#11758198—41no—
145#11758198—41no—
146C4⋊Dic61—21no—
147C4⋊Dic61—21no—
148C4⋊Dic61—41no—
149C4⋊Dic61—41no—
150#11758196—41no—
151#11758196—41no—
152#11758196—41no—
153#11758196—41no—
154#11758196—41no—
155#11758196—41no—
156#11758196—41no—
157#11758196—41no—
158C4×Dic61—41no—
159C4×Dic61—41no—
160C4×Dic61—41no—
161C4×Dic61—41no—
162C4×Dic61D811yescharacteristic
163C4×Dic61D811yescharacteristic
164C4×Dic61C2×D411yescharacteristic
165C2×#92418C2×D411yescharacteristic
166C2×#92418C2×D411yescharacteristic
167Dic244—21no—
168Dic244—21no—
169Dic244—21no—
170Dic244#4112yes—
171C8×D61—21no—
172C8×D61—21no—
173C8×D61—41no—
174C16×C61—21no—
175C16×C61—21no—
176#11758185—21no—
177#11758185—21no—
178C22×D61C2×D811yescharacteristic
179Q8×C61—22no—
180Q8×C61—41no—
181Q8×C61—41no—
182Q8×C61—41no—
183C2×C4×C61—41no—
184C2×C4×C61—41no—
185C2×C4×C61—41no—
186C2×C4×C61—41no—
187C2×C4×C61C2×D811yescharacteristic
188C2×C4×C61C2×D811yescharacteristic
189C2×C4×C61C22×D411yescharacteristic
190C2×Dic61—41no—
191C2×Dic61—41no—
192C2×Dic61—41no—
193C2×Dic61—41no—
194C2×Dic61C2×D811yescharacteristic
195C2×Dic61C2×D811yescharacteristic
196C2×Dic61C2×D811yescharacteristic
197C4×D61—21no—
198C4×D61—21no—
199C4×D61—41no—
200C4×D61—44no—
201C4×D61—82no—
202C4×D61Q3214yescomplemented
203Dic122—22no—
204Dic122—44no—
205Dic122—41no—
206Dic122—41no—
207Dic122—41no—
208Dic122—82no—
209C8×C61—21no—
210C8×C61C2×#4111yescharacteristic
211C8×C61C2×#4111yescharacteristic
212#92418—21no—
213#92418—21no—
214#33664—611nomaximal, Sylow
215C22×C61C22×D811yescharacteristic
216C2×D61—21no—
217C2×D61—21no—
218C2×D61C2×Q3212yes—
219C4×C61—21no—
220C4×C61—42no—
221C4×C61—81no—
222C4×C61—81no—
223C4×C61—81no—
224C4×C61C2×Q3212yes—
225C4×C61#52511yescharacteristic
226C4×C61#57511yescharacteristic
227Dic61—21no—
228Dic61—21no—
229Dic61—42no—
230Dic61—81no—
231Dic61—81no—
232Dic61—81no—
233Dic61C2×Q3212yes—
234#3170—611no—
235C2×C4×Q16—611no—
236#2236—611no—
237#2236—611no—
238#2227—611no—
239#2227—611no—
240#2209—611no—
241#2209—611no—
242#2188—611no—
243#2188—611no—
244C4×Q32—611no—
245C4×Q32—611no—
246C4×Q32—611no—
247C4×Q32D6111yescharacteristic, complemented
248#2162—611no—
249C2×C61#310011yescharacteristic
250C2×C61C22×Q3211yescharacteristic
251C2×C61#341411yescharacteristic
252D61—22no—
253C22×Q16—611no—
254#533—1221no—
255C2×C4×Q8—1221no—
256C2×Q32—611no—
257C2×Q32—611no—
258C2×Q32—611no—
259C2×Q32C2×D6111yescharacteristic
260#500—611no—
261#494—611no—
262#487—1221no—
263#467—611no—
264#467—611no—
265#467—1221no—
266C4×Q16—611no—
267C4×Q16—611no—
268C4×Q16—611no—
269C4×Q16—611no—
270C4×Q16—1221no—
271C4×Q16—1221no—
272C4×Q16—1221no—
273C4×Q16C2×D6111yescharacteristic
274C4×Q16C2×D6111yescharacteristic
275C2×#107—611no—
276C2×#103—1221no—
277C2×C4×C8—611no—
278#366—611no—
279#366—611no—
280#366—611no—
281#366C2×D6111yescharacteristic
282C4⋊C16—611no—
283C4⋊C16—611no—
284#358—611no—
285#358—611no—
286#358—611no—
287#358—611no—
288#358—611no—
289#358—611no—
290#358C2×D6111yescharacteristic
291#358C2×D6111yescharacteristic
292C22⋊C16—611no—
293C22⋊C16—611no—
294C4×C16—611no—
295C4×C16C2×D6111yescharacteristic
296C61#3366411yescharacteristic, complemented, Sylow
297C22×Q8—1221no—
298C2×Q16—611no—
299C2×Q16—611no—
300C2×Q16—1221no—
301C2×Q16—1221no—
302C2×Q16—1222no—
303C2×Q16—1222no—
304C2×Q16C22×D6111yescharacteristic
305C2×Q16C22×D6111yescharacteristic
306C22×C8—611no—
307C22×C8—611no—
308C4⋊Q8—1221no—
309C4⋊Q8—1221no—
310#125—2441no—
311C22⋊Q8—1221no—
312C22⋊Q8—1221no—
313C22⋊Q8—2441no—
314C4×Q8—21no—
315C4×Q8—21no—
316C4×Q8—1221no—
317C4×Q8—1221no—
318C4×Q8—1221no—
319C4×Q8—1221no—
320C4×Q8—2441no—
321C4×Q8—2441no—
322C4×Q8—2441no—
323#117—2441no—
324C2×C4⋊C4—1221no—
325C2×C4⋊C4—2441no—
326C2×C42—611no—
327C2×C42—2441no—
328Q32—22no—
329Q32—1222no—
330Q32—1222no—
331Q32—1222no—
332C2×C16—611no—
333C2×C16—611no—
334C2×C16C22×D6111yescharacteristic
335C2×C16C22×D6111yescharacteristic
336#107—611no—
337#107—611no—
338#107—1221no—
339#107—1221no—
340#107C22×D6111yescharacteristic
341#107C22×D6111yescharacteristic
342#103—21no—
343#103—21no—
344#103—1221no—
345#103—1221no—
346#103—1221no—
347#103—1221no—
348#103—1221no—
349#103—1221no—
350C4×C8—611no—
351C4×C8—611no—
352C4×C8—611no—
353C4×C8C22×D6111yescharacteristic
354C2×Q8—21no—
355C2×Q8—21no—
356C2×Q8—1224no—
357C2×Q8—1221no—
358C2×Q8—1221no—
359C2×Q8—2441no—
360C2×Q8—2441no—
361C2×Q8—2442no—
362C22×C4—611no—
363C22×C4—611no—
364C22×C4—611no—
365C22×C4—2441no—
366C22×C4—2441no—
367Q16—21no—
368Q16—21no—
369Q16—21no—
370Q16—612no—
371Q16—1224no—
372Q16—1221no—
373Q16—1221no—
374Q16—1221no—
375Q16—2442no—
376Q16#1175822212yes—
377C2×C8—611no—
378C2×C8—611no—
379C2×C8—1221no—
380C2×C8—1221no—
381C2×C8—2441no—
382C2×C8D4×D6111yescharacteristic
383C2×C8C23×D6111yescharacteristic
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—41no—
387C4⋊C4—41no—
388C4⋊C4—1221no—
389C4⋊C4—1221no—
390C4⋊C4—2441no—
391C4⋊C4—2441no—
392C4⋊C4—2441no—
393C4⋊C4—2441no—
394C4⋊C4—2441no—
395C4⋊C4—2441no—
396C4⋊C4—2441no—
397C4⋊C4—2441no—
398C4⋊C4—2441no—
399C4⋊C4—2441no—
400C22⋊C4—2441no—
401C22⋊C4—2441no—
402C42—41no—
403C42—41no—
404C42—611no—
405C42—611no—
406C42—611no—
407C42—2441no—
408C42—2441no—
409C42—2441no—
410C42—2441no—
411C42D4×D6111yescharacteristic
412C16—21no—
413C16—21no—
414C16—1221no—
415C16—1221no—
416C23—611no—
417Q8—22no—
418Q8—41no—
419Q8—41no—
420Q8—41no—
421Q8—1222no—
422Q8—4882no—
423Q8—2444no—
424Q8—2441no—
425Q8—2441no—
426Q8—2441no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—611no—
432C2×C4—614no—
433C2×C4—611no—
434C2×C4—611no—
435C2×C4—1221no—
436C2×C4—1221no—
437C2×C4—4882no—
438C2×C4—2441no—
439C2×C4—2444no—
440C2×C4—2441no—
441C2×C4—2441no—
442C2×C4—2441no—
443C2×C4—2441no—
444C2×C4D8×D6111yescharacteristic
445C2×C4D8×D6111yescharacteristic
446C2×C4C2×D4×D6111yescharacteristic
447C8—21no—
448C8—1221no—
449C8—1221no—
450C8#41×D6111yescharacteristic
451C8C2×#1175822211yescharacteristic
452C22—612no—
453C22—1221no—
454C22—1221no—
455C22C2×D8×D6111yescharacteristic
456C4—21no—
457C4—42no—
458C4—81no—
459C4—81no—
460C4—81no—
461C4—612no—
462C4—1221no—
463C4—1221no—
464C4—4881no—
465C4—4881no—
466C4—4881no—
467C4—2442no—
468C4Q32×D6112yes—
469C4#1684027111yescharacteristic
470C4#1684055911yescharacteristic
471C2—1222no—
472C2#2145581711yescharacteristic
473C2C2×Q32×D6111yescharacteristic
474C2#2145895211yescharacteristic
subgroupG/H
centerC2×C4D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC4×Q32×C61C2
socleC22×C61C22×D8
prime radicalC22×D61C2×D8
hypercenterC4×Q32D61
hypocenterC61#33664
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ C4×Q32

Complements

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

NH ≅ G/Ntype
5. #21447970C2semidirect
6. #21447969C2semidirect
7. #21447868C2semidirect
8. #21447867C2semidirect
11. C4×Dic488C2semidirect
12. C4×#14519723C2semidirect
13. C4×#14519723C2semidirect
15. C4×Q32×C61C2semidirect
202. C4×D61Q32semidirect
247. C4×Q32D61semidirect
296. C61#33664semidirect

Maximal subgroups

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

subgroupindex
#214564022
C4×Q16×D612
#214480232
#214480202
#214479702
#214479692
#214478682
#214478672
#214477542
#214477512
C4×Dic4882
C4×#145197232
#214476162
C4×Q32×C612
#3366461