Finite Group Databasebeta

← #29738153

Subgroups — #29738153

Order 15616.

734 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21450850C211yesmaximal, characteristic, complemented
2#21448770C211yesmaximal, characteristic
3#21447202C212yesmaximal
4#21446964C212yesmaximal
5#21446773C212yesmaximal, complemented
6#21446535C211yesmaximal, characteristic, complemented
7#21446413C212yesmaximal, complemented
8#21445946C211yesmaximal, characteristic, complemented
9#21445820C211yesmaximal, characteristic
10C4×#14519697C211yesmaximal, characteristic
11C61×#1947C211yesmaximal, characteristic, complemented
12C2×#14519768C2212yes—
13C2×C4×D244C2211yescharacteristic
14C2×#14519735—21no—
15C2×#14519706C2212yes—
16C2×#14519699C2212yes—
17C2×#14519697C2211yescharacteristic
18C2×#14519697C2211yescharacteristic
19C2×C4×#92418C2211yescharacteristic
20#16839694—22no—
21#16839663C2212yes—
22#16839661C2212yes—
23#16839660—21no—
24#16839652—22no—
25#16839632—21no—
26#16839632C2211yescharacteristic
27#16839619—21no—
28C4⋊C4×Dic61C2212yes—
29C4×C4⋊Dic61C2211yescharacteristic
30#16839525C2212yes—
31#16839524C2211yescharacteristic
32#16839524C2211yescharacteristic
33#16839524C2212yes—
34#16839524C2212yes—
35#16839516C2212yes—
36C2×#107×C61C2212yes—
37C2×C4⋊C8×C61C2211yescharacteristic
38C61×#384C2211yescharacteristic
39C4×C4⋊C4×C61C2211yescharacteristic
40C61×#340C2212yes—
41C22×D244C2311yescharacteristic
42C22×C4×D61—21no—
43C22×#92418C2311yescharacteristic
44C22×#92418C2311yescharacteristic
45#14519768—24no—
46#14519768—42no—
47C4×D244—22no—
48C4×D244Q814yes—
49#14519735—44no—
50C2×C4⋊Dic61—21no—
51C2×C4⋊Dic61—22no—
52C2×C4⋊Dic61—21no—
53C2×C4⋊Dic61—22no—
54C2×C4⋊Dic61D411yescharacteristic
55C2×C4⋊Dic61D411yescharacteristic
56C2×C4⋊Dic61C2312yes—
57C2×C4⋊Dic61C2311yescharacteristic
58C2×#11758196—22no—
59C2×#11758198—21no—
60C2×#11758198—22no—
61C2×#11758198—22no—
62C2×C4×Dic61—22no—
63C2×C4×Dic61C2312yes—
64#14519706—42no—
65#14519699—42no—
66#14519697—22no—
67#14519697—22no—
68C4×#92418—22no—
69#14519684—22no—
70#14519684—22no—
71#14519684D412yes—
72C22×C8×C61C2312yes—
73C2×C4⋊C4×C61—21no—
74C2×C4⋊C4×C61—21no—
75C2×C4⋊C4×C61C2312yes—
76C2×C4⋊C4×C61C2311yescharacteristic
77C2×C4⋊C4×C61C2311yescharacteristic
78C2×C42×C61—21no—
79C2×C42×C61C2311yescharacteristic
80#107×C61—24no—
81C4⋊C8×C61—22no—
82#95×C61—21no—
83C23×D61—21no—
84C22×C4×C61—21no—
85C22×C4×C61—21no—
86C22×C4×C61—22no—
87C22×C4×C61C2×D411yescharacteristic
88C22×C4×C61C2×D411yescharacteristic
89C22×C4×C61C2411yescharacteristic
90C22×Dic61—21no—
91C22×Dic61—22no—
92C22×Dic61C2×D412yes—
93C22×Dic61C2×D412yes—
94C2×D244—21no—
95C2×D244—21no—
96C2×D244—21no—
97C2×D244—21no—
98C2×D244—21no—
99C2×D244C2×Q812yes—
100C2×C4×D61—24no—
101C2×C4×D61—42no—
102C2×C4×D61—42no—
103C2×C8×C61—22no—
104C2×C8×C61—22no—
105C2×C8×C61—22no—
106C4⋊C4×C61—21no—
107C4⋊C4×C61—21no—
108C4⋊C4×C61—22no—
109C4⋊C4×C61—22no—
110C4⋊C4×C61—42no—
111C4⋊C4×C61—81no—
112C4⋊C4×C61#4112yes—
113C4⋊C4×C61#4112yes—
114C42×C61—42no—
115C42×C61C2×Q812yes—
116C42×C61#4112yes—
117#11758198—24no—
118#11758198—44no—
119#11758198—82no—
120C4⋊Dic61—22no—
121C4⋊Dic61—22no—
122C4⋊Dic61—21no—
123C4⋊Dic61—22no—
124C4⋊Dic61—22no—
125C4⋊Dic61—44no—
126C4⋊Dic61—42no—
127C4⋊Dic61—82no—
128C4⋊Dic61—81no—
129C4⋊Dic61C2×Q812yes—
130#11758196—44no—
131C4×Dic61—22no—
132C4×Dic61—22no—
133C4×Dic61—44no—
134C2×#92418—21no—
135C2×#92418—21no—
136C2×#92418—21no—
137C2×#92418—21no—
138C2×#92418—21no—
139C2×#92418—21no—
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—22no—
151C2×C4×C61—22no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61—42no—
157C2×C4×C61—42no—
158C2×C4×C61—42no—
159C2×C4×C61C22⋊Q812yes—
160C2×C4×C61C22⋊Q812yes—
161C2×C4×C61#13512yes—
162C2×C4×C61AGL(1,ℤ/8)12yes—
163C2×C4×C61C22×Q811yescharacteristic
164C2×C4×C61C2×#4111yescharacteristic
165C2×C4×C61C2×#4111yescharacteristic
166C2×C4×C61C2×#4111yescharacteristic
167C2×C4×C61H(5,𝔽2)11yescharacteristic
168C2×C4×C612−1+411yescharacteristic
169C2×Dic61—22no—
170C2×Dic61—22no—
171C2×Dic61—22no—
172C2×Dic61—22no—
173C2×Dic61—22no—
174C2×Dic61—22no—
175C2×Dic61—22no—
176C2×Dic61—41no—
177C2×Dic61—41no—
178C2×Dic61—42no—
179C2×Dic61—42no—
180C2×Dic61—42no—
181D244—22no—
182D244—22no—
183D244—41no—
184D244—41no—
185C4×D61—48no—
186C8×C61—42no—
187#92418—41no—
188#92418—41no—
189#26025—611nomaximal, Sylow
190C22×C61C2×C22⋊Q811yescharacteristic
191C22×C61#54611yescharacteristic
192C22×C61#54811yescharacteristic
193C22×C61C2×#13511yescharacteristic
194C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
195C22×C61#57611yescharacteristic
196C22×C61#57811yescharacteristic
197C2×D61—42no—
198C2×D61—42no—
199C2×D61—42no—
200C2×D61—81no—
201C2×D61—81no—
202C2×D61—81no—
203C2×D61—81no—
204C4×C61—22no—
205C4×C61—42no—
206C4×C61—42no—
207C4×C61—82no—
208C4×C61#47814yes—
209C4×C61#53311yescharacteristic
210C4×C61#54411yescharacteristic
211C4×C61#55511yescharacteristic
212C4×C61#55611yescharacteristic
213Dic61—42no—
214Dic61—42no—
215Dic61—42no—
216Dic61—82no—
217#2552—611no—
218#2354—611no—
219#2067—612no—
220#2025—612no—
221#1989—612no—
222#1947D6111yescharacteristic, complemented
223#1939—611no—
224#1921—612no—
225#1834—611no—
226#1802—611no—
227C4×#102—611no—
228C2×C61#243911yescharacteristic
229C2×C61C2×#47811yescharacteristic
230C2×C61#308311yescharacteristic
231C2×C61#330511yescharacteristic
232C2×C61#333011yescharacteristic
233C2×C61#336411yescharacteristic
234C2×C61#336611yescharacteristic
235D61—82no—
236C2×#125—612no—
237C2×C4×D4—611no—
238C2×#117—1221no—
239C2×#107C2×D6112yes—
240C2×C4⋊C8—612no—
241C2×C4⋊C8C2×D6111yescharacteristic
242C2×#102—611no—
243C2×#102—611no—
244C2×#102—612no—
245C2×C4×C8—611no—
246#398—1222no—
247#390—612no—
248#389—612no—
249#389—1221no—
250#388—1222no—
251#384—611no—
252#384—1221no—
253#384C2×D6111yescharacteristic
254#380—1221no—
255C4×C4⋊C4—611no—
256C4×C4⋊C4—612no—
257C4×C4⋊C4C2×D6111yescharacteristic
258#340—612no—
259#340—612no—
260#340—612no—
261#340—611no—
262#340—611no—
263#340C2×D6112yes—
264#336—612no—
265C61#2602511yescharacteristic, complemented, Sylow
266C22×D4—611no—
267C23×C4—1221no—
268C22×C8—611no—
269C22×C8—611no—
270C22×C8C22×D6112yes—
271#125—1224no—
272#125—2442no—
273C4×D4—614no—
274C4×D4—1222no—
275#117—2444no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—611no—
279C2×C4⋊C4—611no—
280C2×C4⋊C4—611no—
281C2×C4⋊C4—612no—
282C2×C4⋊C4—1222no—
283C2×C4⋊C4—1221no—
284C2×C4⋊C4—1222no—
285C2×C4⋊C4—1222no—
286C2×C4⋊C4—1221no—
287C2×C4⋊C4C22×D6112yes—
288C2×C4⋊C4C22×D6111yescharacteristic
289C2×C4⋊C4C22×D6111yescharacteristic
290C2×C22⋊C4—1221no—
291C2×C22⋊C4—1222no—
292C2×C22⋊C4—1222no—
293C2×C42—21no—
294C2×C42—612no—
295C2×C42—1222no—
296C2×C42C22×D6111yescharacteristic
297#107—24no—
298C4⋊C8—22no—
299C4⋊C8—2442no—
300#102—1222no—
301#102—1222no—
302#102—2442no—
303C4×C8—1222no—
304#95—21no—
305#95—612no—
306#95—1222no—
307#95—1222no—
308C24—1221no—
309C2×D4—612no—
310C2×D4—1221no—
311C2×D4—1221no—
312C2×D4—1221no—
313C2×D4—1221no—
314C2×D4—1221no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—22no—
318C22×C4—612no—
319C22×C4—612no—
320C22×C4—1221no—
321C22×C4—1224no—
322C22×C4—1222no—
323C22×C4—2442no—
324C22×C4—2442no—
325C22×C4D4×D6111yescharacteristic
326C22×C4D4×D6111yescharacteristic
327C22×C4C23×D6111yescharacteristic
328C2×C8—22no—
329C2×C8—22no—
330C2×C8—22no—
331C2×C8—1221no—
332C2×C8—1221no—
333C2×C8—1221no—
334C2×C8—1221no—
335C2×C8—1221no—
336C2×C8—1221no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—22no—
340C4⋊C4—22no—
341C4⋊C4—42no—
342C4⋊C4—81no—
343C4⋊C4—612no—
344C4⋊C4—1221no—
345C4⋊C4—1222no—
346C4⋊C4—1222no—
347C4⋊C4—1222no—
348C4⋊C4—1222no—
349C4⋊C4—4881no—
350C4⋊C4—4882no—
351C4⋊C4—2444no—
352C4⋊C4—2444no—
353C4⋊C4—2442no—
354C4⋊C4#1175822412yes—
355C4⋊C4#1175822612yes—
356C22⋊C4—1224no—
357C22⋊C4—4882no—
358C22⋊C4—2444no—
359C42—42no—
360C42—1222no—
361C42—1222no—
362C42—2444no—
363C42#1175822212yes—
364C42Q8×D6112yes—
365C23—1222no—
366C23—2441no—
367C23—2441no—
368C23—2441no—
369C23—2441no—
370C23—2441no—
371C23—2441no—
372C23C2×D4×D6111yescharacteristic
373D4—1222no—
374D4—1222no—
375D4—2441no—
376D4—2441no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—1222no—
389C2×C4—1222no—
390C2×C4—1222no—
391C2×C4—1222no—
392C2×C4—1222no—
393C2×C4—1222no—
394C2×C4—1222no—
395C2×C4—2442no—
396C2×C4—2442no—
397C2×C4—2442no—
398C2×C4—2441no—
399C2×C4—2441no—
400C2×C4—2448no—
401C2×C4#1451975512yes—
402C2×C4#1451975512yes—
403C2×C4#1451980012yes—
404C2×C4#1451980112yes—
405C2×C4C2×Q8×D6111yescharacteristic
406C2×C4C2×#1175822411yescharacteristic
407C2×C4C2×#1175822211yescharacteristic
408C2×C4C2×#1175822611yescharacteristic
409C2×C4#1451982311yescharacteristic
410C2×C4#1451982411yescharacteristic
411C8—42no—
412C8—2441no—
413C8—2441no—
414C22—4881no—
415C22—4881no—
416C22—4881no—
417C22—4881no—
418C22—2442no—
419C22—2442no—
420C22—2442no—
421C22C2×#1451975511yescharacteristic
422C22#1684040311yescharacteristic
423C22#1684041811yescharacteristic
424C22C2×#1451980011yescharacteristic
425C22C2×#1451980111yescharacteristic
426C22#1684056611yescharacteristic
427C22#1684057811yescharacteristic
428C4—22no—
429C4—42no—
430C4—42no—
431C4—82no—
432C4—4882no—
433C4—2442no—
434C4—2442no—
435C4—2442no—
436C4#1684006514yes—
437C4#1684031711yescharacteristic
438C4#1684039211yescharacteristic
439C4#1684047711yescharacteristic
440C4#1684048511yescharacteristic
441C2—4882no—
442C2#2144951211yescharacteristic
443C2C2×#1684006511yescharacteristic
444C2#2145566911yescharacteristic
445C2#2145776611yescharacteristic
446C2#2145812111yescharacteristic
447C2#2145850811yescharacteristic
448C2#2145853011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1947C2
socleC23×C61C22×D4
prime radicalC22×D244C23
hypercenter#1947D61
hypocenterC61#26025
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1947

Complements

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

NH ≅ G/Ntype
1. #21450850C2semidirect
5. #21446773C2semidirect
6. #21446535C2semidirect
7. #21446413C2semidirect
8. #21445946C2semidirect
11. C61×#1947C2semidirect
222. #1947D61semidirect
265. C61#26025semidirect

Maximal subgroups

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

subgroupindex
#214508502
#214487702
#214472022
#214469642
#214467732
#214465352
#214464132
#214459462
#214458202
C4×#145196972
C61×#19472
#2602561