Finite Group Databasebeta

← #29725174

Subgroups — #29725174

Order 15616.

706 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21450742C211yesmaximal, characteristic
2#21448778C211yesmaximal, characteristic, complemented
3#21447392C212yesmaximal, complemented
4#21447236C212yesmaximal
5#21446755C211yesmaximal, characteristic, complemented
6#21446580C211yesmaximal, characteristic, complemented
7#21446444C212yesmaximal
8#21446407C212yesmaximal, complemented
9#21445816C211yesmaximal, characteristic
10C4×#14519699C211yesmaximal, characteristic
11C61×#1834C211yesmaximal, characteristic, complemented
12C2×#14519757—21no—
13C2×C4×Dic122C2211yescharacteristic
14C2×C4×D244C2211yescharacteristic
15C2×#14519708C2212yes—
16C2×C4⋊#92418C2211yescharacteristic
17C2×#14519699C2211yescharacteristic
18C2×#14519699C2211yescharacteristic
19C2×#14519697C2212yes—
20#16839684—22no—
21#16839667—21no—
22#16839663C2212yes—
23#16839661C2212yes—
24#16839643—22no—
25#16839627C2212yes—
26#16839619—21no—
27C4⋊C4×Dic61—21no—
28C4⋊C4×Dic61C2212yes—
29C4×C4⋊Dic61C2211yescharacteristic
30#16839525C2211yescharacteristic
31#16839525C2211yescharacteristic
32#16839524C2212yes—
33#16839524C2212yes—
34#16839516C2212yes—
35#16839516C2212yes—
36C2×C4×C8×C61C2211yescharacteristic
37C61×#384C2211yescharacteristic
38C61×#384C2211yescharacteristic
39C61×#340C2212yes—
40C61×#340C2212yes—
41C22×Dic122D411yescharacteristic
42C22×D244C2311yescharacteristic
43C22×C4×D61—21no—
44C22×#92418C2312yes—
45#14519757—44no—
46C4×Dic122—22no—
47C4×Dic122—22no—
48C4×D244—22no—
49C4×D244—22no—
50C2×C4⋊Dic61—22no—
51C2×C4⋊Dic61D411yescharacteristic
52C2×C4⋊Dic61C2311yescharacteristic
53C2×C4⋊Dic61C2311yescharacteristic
54C2×C4⋊Dic61C2311yescharacteristic
55C2×#11758196D412yes—
56C2×#11758198—21no—
57C2×#11758198—22no—
58C2×#11758198—22no—
59C2×C4×Dic61—21no—
60C2×C4×Dic61—22no—
61C2×C4×Dic61C2312yes—
62#14519708—24no—
63C4⋊#92418—22no—
64#14519699—22no—
65#14519699—22no—
66#14519697—24no—
67#14519684—21no—
68#14519684—22no—
69#14519684—22no—
70#14519684—22no—
71#14519684—22no—
72C22×C8×C61C2311yescharacteristic
73C22×C8×C61C2311yescharacteristic
74C2×C4⋊C4×C61—21no—
75C2×C4⋊C4×C61—21no—
76C2×C4⋊C4×C61—21no—
77C2×C4⋊C4×C61—21no—
78C2×C4⋊C4×C61C2312yes—
79C2×C4⋊C4×C61C2312yes—
80C2×C42×C61C2311yescharacteristic
81C4×C8×C61—22no—
82C23×D61—21no—
83C22×C4×C61—22no—
84C22×C4×C61—22no—
85C22×C4×C61C2×D411yescharacteristic
86C22×C4×C61C2×D411yescharacteristic
87C22×C4×C61C2411yescharacteristic
88C22×Dic61—21no—
89C22×Dic61—21no—
90C22×Dic61—21no—
91C22×Dic61C2×D412yes—
92C22×Dic61C2×D412yes—
93C2×D244—21no—
94C2×D244—21no—
95C2×D244—21no—
96C2×D244—21no—
97C2×D244—21no—
98C2×D244#4112yes—
99C2×C4×D61—42no—
100C2×C4×D61—42no—
101C2×C4×D61—42no—
102C2×Dic122—22no—
103C2×Dic122—22no—
104C2×Dic122—22no—
105C2×C8×C61—21no—
106C2×C8×C61—21no—
107C2×C8×C61—21no—
108C2×C8×C61—21no—
109C2×C8×C61—21no—
110C2×C8×C61—21no—
111C4⋊C4×C61—22no—
112C4⋊C4×C61—22no—
113C4⋊C4×C61—22no—
114C4⋊C4×C61—22no—
115C4⋊C4×C61—42no—
116C4⋊C4×C61—42no—
117C4⋊C4×C61—81no—
118C4⋊C4×C61—81no—
119C42×C61#4112yes—
120C42×C61#4112yes—
121#11758198—44no—
122#11758198—42no—
123#11758198—82no—
124C4⋊Dic61—22no—
125C4⋊Dic61—21no—
126C4⋊Dic61—21no—
127C4⋊Dic61—21no—
128C4⋊Dic61—21no—
129C4⋊Dic61—21no—
130C4⋊Dic61—44no—
131C4⋊Dic61#4112yes—
132#11758196—24no—
133C4×Dic61—22no—
134C4×Dic61—22no—
135C4×Dic61—42no—
136C4×Dic61—82no—
137C2×#92418—22no—
138C2×#92418—22no—
139C2×#92418—22no—
140C23×C61C22×D411yescharacteristic
141C22×D61—22no—
142C22×D61—41no—
143C22×D61—41no—
144C22×D61—41no—
145C22×D61—41no—
146C22×D61—41no—
147C22×D61—41no—
148C2×C4×C61—21no—
149C2×C4×C61—21no—
150C2×C4×C61—42no—
151C2×C4×C61—42no—
152C2×C4×C61—42no—
153C2×C4×C61—42no—
154C2×C4×C61—42no—
155C2×C4×C61—42no—
156C2×C4×C61#12312yes—
157C2×C4×C61#12312yes—
158C2×C4×C61#13512yes—
159C2×C4×C61AGL(1,ℤ/8)12yes—
160C2×C4×C61C2×#4111yescharacteristic
161C2×C4×C61C2×#4111yescharacteristic
162C2×C4×C61C2×#4111yescharacteristic
163C2×C4×C61C2×#4111yescharacteristic
164C2×C4×C612−1+411yescharacteristic
165C2×C4×C612−1+411yescharacteristic
166C2×Dic61—22no—
167C2×Dic61—22no—
168C2×Dic61—22no—
169C2×Dic61—22no—
170C2×Dic61—22no—
171C2×Dic61—22no—
172C2×Dic61—22no—
173C2×Dic61—41no—
174C2×Dic61—41no—
175C2×Dic61—41no—
176C2×Dic61—41no—
177C2×Dic61—41no—
178C2×Dic61—41no—
179C2×Dic61—41no—
180C2×Dic61—41no—
181D244—22no—
182D244—22no—
183D244—41no—
184D244—41no—
185C4×D61—84no—
186Dic122—44no—
187C8×C61—41no—
188C8×C61—41no—
189#92418—42no—
190#24991—611nomaximal, Sylow
191C22×C61C2×#12311yescharacteristic
192C22×C61#54811yescharacteristic
193C22×C61#54811yescharacteristic
194C22×C61C2×#13511yescharacteristic
195C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
196C22×C61#57711yescharacteristic
197C22×C61#57711yescharacteristic
198C2×D61—42no—
199C2×D61—42no—
200C2×D61—42no—
201C2×D61—81no—
202C2×D61—81no—
203C2×D61—81no—
204C2×D61—81no—
205C4×C61—22no—
206C4×C61—82no—
207C4×C61—82no—
208C4×C61#48214yes—
209C4×C61#52911yescharacteristic
210C4×C61#54111yescharacteristic
211C4×C61#55211yescharacteristic
212C4×C61#55611yescharacteristic
213Dic61—42no—
214Dic61—42no—
215Dic61—42no—
216Dic61—81no—
217Dic61—81no—
218#2538—611no—
219#2355—611no—
220#2101—612no—
221#2073—612no—
222#1984—611no—
223#1948—611no—
224#1926—612no—
225#1920—612no—
226#1834D6111yescharacteristic, complemented
227#1802—611no—
228C4×#102—611no—
229C2×C61#242111yescharacteristic
230C2×C61C2×#48211yescharacteristic
231C2×C61#309911yescharacteristic
232C2×C61#336011yescharacteristic
233C2×C61#336011yescharacteristic
234C2×C61#336811yescharacteristic
235C2×C61#337311yescharacteristic
236D61—82no—
237C2×C22⋊Q8—1221no—
238C2×C4×Q8—611no—
239C2×C4×D4—611no—
240C2×#106—612no—
241C2×C4⋊C8—611no—
242C2×#102—611no—
243C2×#102—611no—
244C2×#102—612no—
245C2×C4×C8C2×D6111yescharacteristic
246#396—1222no—
247#391—1221no—
248#390—612no—
249#389—612no—
250#387—1222no—
251#384C2×D6111yescharacteristic
252#384C2×D6111yescharacteristic
253#382—612no—
254#380—1221no—
255C4×C4⋊C4—612no—
256C4×C4⋊C4—611no—
257C4×C4⋊C4—1221no—
258#340—611no—
259#340—611no—
260#340—612no—
261#340—612no—
262#340C2×D6112yes—
263#340C2×D6112yes—
264#336—612no—
265#336—612no—
266C61#2499111yescharacteristic, complemented, Sylow
267C22×Q8—611no—
268C22×D4—611no—
269C23×C4—1221no—
270C22×C8—612no—
271C22×C8C22×D6111yescharacteristic
272C22×C8C22×D6111yescharacteristic
273C22⋊Q8—2444no—
274C4×Q8—1222no—
275C4×Q8—1222no—
276C4×D4—1222no—
277C4×D4—1222no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—611no—
283C2×C4⋊C4—611no—
284C2×C4⋊C4—612no—
285C2×C4⋊C4—611no—
286C2×C4⋊C4—611no—
287C2×C4⋊C4—1222no—
288C2×C4⋊C4C22×D6112yes—
289C2×C4⋊C4C22×D6112yes—
290C2×C22⋊C4—1222no—
291C2×C22⋊C4—1222no—
292C2×C22⋊C4—1221no—
293C2×C42—612no—
294C2×C42—1222no—
295C2×C42—1221no—
296C2×C42C22×D6111yescharacteristic
297#106—1224no—
298C4⋊C8—1222no—
299#102—1224no—
300#102—1222no—
301#102—1222no—
302C4×C8—22no—
303#95—1222no—
304#95—1222no—
305#95—1222no—
306#95—1222no—
307#95—1221no—
308C24—1221no—
309C2×Q8—1222no—
310C2×Q8—1222no—
311C2×Q8—1222no—
312C2×D4—612no—
313C2×D4—1221no—
314C2×D4—1221no—
315C2×D4—1221no—
316C2×D4—1221no—
317C2×D4—1221no—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—612no—
321C22×C4—612no—
322C22×C4—1221no—
323C22×C4—1221no—
324C22×C4—1221no—
325C22×C4—2442no—
326C22×C4—2442no—
327C22×C4—2442no—
328C22×C4D4×D6111yescharacteristic
329C22×C4D4×D6111yescharacteristic
330C22×C4C23×D6111yescharacteristic
331C2×C8—21no—
332C2×C8—21no—
333C2×C8—21no—
334C2×C8—21no—
335C2×C8—21no—
336C2×C8—21no—
337C2×C8—1222no—
338C2×C8—1222no—
339C2×C8—1222no—
340C4⋊C4—22no—
341C4⋊C4—22no—
342C4⋊C4—22no—
343C4⋊C4—22no—
344C4⋊C4—42no—
345C4⋊C4—42no—
346C4⋊C4—81no—
347C4⋊C4—81no—
348C4⋊C4—612no—
349C4⋊C4—1221no—
350C4⋊C4—1224no—
351C4⋊C4—1222no—
352C4⋊C4—1221no—
353C4⋊C4—1221no—
354C4⋊C4—1221no—
355C4⋊C4—1221no—
356C4⋊C4—2444no—
357C22⋊C4—4882no—
358C22⋊C4—2444no—
359C22⋊C4—2442no—
360C42—1222no—
361C42—1222no—
362C42—4882no—
363C42—2442no—
364C42#1175822212yes—
365C42#1175822612yes—
366C23—1222no—
367C23—2441no—
368C23—2441no—
369C23—2441no—
370C23—2441no—
371C23—2441no—
372C23—2441no—
373C23C2×D4×D6111yescharacteristic
374Q8—2444no—
375D4—1222no—
376D4—1222no—
377D4—2441no—
378D4—2441no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—1222no—
388C2×C4—1222no—
389C2×C4—1222no—
390C2×C4—1222no—
391C2×C4—1222no—
392C2×C4—1222no—
393C2×C4—1222no—
394C2×C4—4884no—
395C2×C4—2441no—
396C2×C4—2441no—
397C2×C4—2441no—
398C2×C4—2441no—
399C2×C4—2441no—
400C2×C4—2441no—
401C2×C4—2441no—
402C2×C4—2441no—
403C2×C4#1451976212yes—
404C2×C4#1451976212yes—
405C2×C4#1451980012yes—
406C2×C4#1451980112yes—
407C2×C4#41×D6111yescharacteristic
408C2×C4#41×D6111yescharacteristic
409C2×C4C2×#1175822211yescharacteristic
410C2×C4C2×#1175822611yescharacteristic
411C2×C4#1451982411yescharacteristic
412C2×C4#1451982411yescharacteristic
413C8—41no—
414C8—41no—
415C8—2442no—
416C22—4881no—
417C22—4881no—
418C22—4881no—
419C22—4881no—
420C22—2442no—
421C22—2442no—
422C22—2442no—
423C22C2×#1451976211yescharacteristic
424C22#1684042011yescharacteristic
425C22#1684042011yescharacteristic
426C22C2×#1451980011yescharacteristic
427C22C2×#1451980111yescharacteristic
428C22#1684056811yescharacteristic
429C22#1684056811yescharacteristic
430C4—22no—
431C4—82no—
432C4—82no—
433C4—4881no—
434C4—4881no—
435C4—2442no—
436C4—2442no—
437C4—2442no—
438C4#1684008914yes—
439C4#1684029711yescharacteristic
440C4#1684037511yescharacteristic
441C4#1684045111yescharacteristic
442C4#1684048011yescharacteristic
443C2—4882no—
444C2#2144932511yescharacteristic
445C2C2×#1684008911yescharacteristic
446C2#2145581311yescharacteristic
447C2#2145847311yescharacteristic
448C2#2145847311yescharacteristic
449C2#2145855311yescharacteristic
450C2#2145861611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1834C2
socleC23×C61C22×D4
prime radicalC22×D244C23
hypercenter#1834D61
hypocenterC61#24991
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1834

Complements

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

NH ≅ G/Ntype
2. #21448778C2semidirect
3. #21447392C2semidirect
5. #21446755C2semidirect
6. #21446580C2semidirect
8. #21446407C2semidirect
11. C61×#1834C2semidirect
226. #1834D61semidirect
266. C61#24991semidirect

Maximal subgroups

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

subgroupindex
#214507422
#214487782
#214473922
#214472362
#214467552
#214465802
#214464442
#214464072
#214458162
C4×#145196992
C61×#18342
#2499161