Finite Group Databasebeta

← #29738987

Subgroups — #29738987

Order 15616.

714 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21451058C211yesmaximal, characteristic, complemented
2#21448770C211yesmaximal, characteristic
3#21447341C212yesmaximal
4#21447208C212yesmaximal
5#21446588C212yesmaximal, complemented
6#21446535C211yesmaximal, characteristic, complemented
7#21446409C212yesmaximal, complemented
8#21445978C211yesmaximal, characteristic, complemented
9#21445820C211yesmaximal, characteristic
10C4×#14519697C211yesmaximal, characteristic
11C61×#1948C211yesmaximal, characteristic, complemented
12C2×C4×D244C2211yescharacteristic
13C2×#14519735—21no—
14C2×#14519710C2212yes—
15C2×#14519710C2212yes—
16C2×#14519706C2212yes—
17C2×#14519699C2212yes—
18C2×#14519697C2211yescharacteristic
19C2×#14519697C2211yescharacteristic
20C2×C4×#92418C2211yescharacteristic
21#16839704—22no—
22#16839663C2212yes—
23#16839660—21no—
24#16839658C2212yes—
25#16839652—22no—
26#16839632C2211yescharacteristic
27#16839628—21no—
28#16839627C2212yes—
29#16839619—21no—
30C4⋊C4×Dic61C2212yes—
31C4×C4⋊Dic61C2211yescharacteristic
32#16839525C2212yes—
33#16839524C2211yescharacteristic
34#16839524C2211yescharacteristic
35#16839516C2212yes—
36C2×#106×C61C2212yes—
37C2×C4⋊C8×C61C2211yescharacteristic
38C61×#384C2211yescharacteristic
39C4×C4⋊C4×C61C2211yescharacteristic
40C61×#340C2212yes—
41C22×D244C2311yescharacteristic
42C22×C4×D61—21no—
43C22×#92418C2311yescharacteristic
44C22×#92418C2311yescharacteristic
45C4×D244—22no—
46C4×D244Q814yes—
47#14519735—44no—
48C2×C4⋊Dic61—21no—
49C2×C4⋊Dic61—21no—
50C2×C4⋊Dic61D411yescharacteristic
51C2×C4⋊Dic61D411yescharacteristic
52C2×C4⋊Dic61C2312yes—
53C2×C4⋊Dic61C2311yescharacteristic
54C2×#11758196—22no—
55C2×#11758198—21no—
56C2×#11758198—22no—
57C2×#11758198—22no—
58C2×C4×Dic61—22no—
59C2×C4×Dic61C2312yes—
60#14519710—24no—
61#14519710—42no—
62#14519706—24no—
63#14519699—42no—
64#14519697—22no—
65#14519697—22no—
66C4×#92418—22no—
67#14519684—22no—
68#14519684—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×C61C2311yescharacteristic
76C2×C4⋊C4×C61C2312yes—
77C2×C4⋊C4×C61C2311yescharacteristic
78C2×C42×C61—21no—
79C2×C42×C61C2311yescharacteristic
80#106×C61—42no—
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—21no—
110C4⋊C4×C61—22no—
111C4⋊C4×C61—21no—
112C4⋊C4×C61—42no—
113C4⋊C4×C61—81no—
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—42no—
126C4⋊Dic61—81no—
127C4⋊Dic61C2×Q812yes—
128#11758196—82no—
129C4×Dic61—22no—
130C4×Dic61—22no—
131C4×Dic61—44no—
132C2×#92418—21no—
133C2×#92418—21no—
134C2×#92418—21no—
135C2×#92418—21no—
136C2×#92418#4112yes—
137C2×#92418#4112yes—
138C23×C61C22×D411yescharacteristic
139C22×D61—22no—
140C22×D61—41no—
141C22×D61—41no—
142C22×D61—41no—
143C22×D61—41no—
144C22×D61—41no—
145C22×D61—41no—
146C2×C4×C61—21no—
147C2×C4×C61—21no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—42no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—42no—
154C2×C4×C61—41no—
155C2×C4×C61—42no—
156C2×C4×C61—41no—
157C2×C4×C61C22⋊Q812yes—
158C2×C4×C61C22⋊Q812yes—
159C2×C4×C61#13512yes—
160C2×C4×C61AGL(1,ℤ/8)12yes—
161C2×C4×C61C22×Q811yescharacteristic
162C2×C4×C61C2×#4111yescharacteristic
163C2×C4×C61C2×#4111yescharacteristic
164C2×C4×C61C2×#4111yescharacteristic
165C2×C4×C61H(5,𝔽2)11yescharacteristic
166C2×C4×C612−1+411yescharacteristic
167C2×Dic61—22no—
168C2×Dic61—22no—
169C2×Dic61—22no—
170C2×Dic61—22no—
171C2×Dic61—22no—
172C2×Dic61—22no—
173C2×Dic61—22no—
174C2×Dic61—41no—
175C2×Dic61—41no—
176C2×Dic61—42no—
177C2×Dic61—42no—
178C2×Dic61—42no—
179D244—22no—
180D244—22no—
181D244—41no—
182D244—41no—
183C4×D61—48no—
184C8×C61—42no—
185#92418—22no—
186#92418—22no—
187#26087—611nomaximal, Sylow
188C22×C61C2×C22⋊Q811yescharacteristic
189C22×C61#54711yescharacteristic
190C22×C61#55011yescharacteristic
191C22×C61C2×#13511yescharacteristic
192C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
193C22×C61#57611yescharacteristic
194C22×C61#57811yescharacteristic
195C2×D61—42no—
196C2×D61—42no—
197C2×D61—42no—
198C2×D61—81no—
199C2×D61—81no—
200C2×D61—81no—
201C2×D61—81no—
202C4×C61—22no—
203C4×C61—81no—
204C4×C61—81no—
205C4×C61—82no—
206C4×C61#47814yes—
207C4×C61#53311yescharacteristic
208C4×C61#54411yescharacteristic
209C4×C61#55211yescharacteristic
210C4×C61#55311yescharacteristic
211Dic61—42no—
212Dic61—42no—
213Dic61—42no—
214Dic61—82no—
215#2571—611no—
216#2354—611no—
217#2092—612no—
218#2067—612no—
219#1949—612no—
220#1948D6111yescharacteristic, complemented
221#1939—611no—
222#1921—612no—
223#1845—611no—
224#1802—611no—
225C4×#102—611no—
226C2×C61#244111yescharacteristic
227C2×C61C2×#47811yescharacteristic
228C2×C61#308311yescharacteristic
229C2×C61#334111yescharacteristic
230C2×C61#335311yescharacteristic
231C2×C61#339311yescharacteristic
232C2×C61#339911yescharacteristic
233D61—82no—
234C2×C4×D4—611no—
235C2×#117—1221no—
236C2×#107—612no—
237C2×#107—612no—
238C2×#106C2×D6112yes—
239C2×C4⋊C8—612no—
240C2×C4⋊C8C2×D6111yescharacteristic
241C2×#102—611no—
242C2×#102—611no—
243C2×#102—612no—
244C2×C4×C8—611no—
245#400—1222no—
246#390—612no—
247#389—612no—
248#389—1221no—
249#388—1222no—
250#384—611no—
251#384C2×D6111yescharacteristic
252#382—612no—
253#382—1221no—
254#380—1221no—
255C4×C4⋊C4—611no—
256C4×C4⋊C4—612no—
257C4×C4⋊C4C2×D6111yescharacteristic
258#340—612no—
259#340—611no—
260#340—611no—
261#340C2×D6112yes—
262#336—612no—
263C61#2608711yescharacteristic, complemented, Sylow
264C22×D4—611no—
265C23×C4—1221no—
266C22×C8—611no—
267C22×C8—611no—
268C22×C8C22×D6112yes—
269C4×D4—614no—
270C4×D4—1222no—
271#117—2444no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—611no—
275C2×C4⋊C4—611no—
276C2×C4⋊C4—611no—
277C2×C4⋊C4—612no—
278C2×C4⋊C4—1222no—
279C2×C4⋊C4—1221no—
280C2×C4⋊C4—1221no—
281C2×C4⋊C4C22×D6111yescharacteristic
282C2×C4⋊C4C22×D6111yescharacteristic
283C2×C4⋊C4C22×D6112yes—
284C2×C22⋊C4—1221no—
285C2×C22⋊C4—1222no—
286C2×C22⋊C4—1222no—
287C2×C42—21no—
288C2×C42—612no—
289C2×C42—1222no—
290C2×C42C22×D6111yescharacteristic
291#107—1224no—
292#107—2442no—
293#106—42no—
294C4⋊C8—22no—
295C4⋊C8—1224no—
296#102—1222no—
297#102—1222no—
298#102—2442no—
299C4×C8—1222no—
300#95—21no—
301#95—612no—
302#95—1222no—
303#95—1222no—
304#95—1222no—
305#95—1222no—
306C24—1221no—
307C2×D4—612no—
308C2×D4—1221no—
309C2×D4—1221no—
310C2×D4—1221no—
311C2×D4—1221no—
312C2×D4—1221no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—22no—
316C22×C4—612no—
317C22×C4—612no—
318C22×C4—1221no—
319C22×C4—1224no—
320C22×C4—1222no—
321C22×C4—2442no—
322C22×C4—2442no—
323C22×C4D4×D6111yescharacteristic
324C22×C4D4×D6111yescharacteristic
325C22×C4C23×D6111yescharacteristic
326C2×C8—22no—
327C2×C8—22no—
328C2×C8—22no—
329C2×C8—612no—
330C2×C8—612no—
331C2×C8—1221no—
332C2×C8—1221no—
333C2×C8—1221no—
334C2×C8—1221no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—22no—
338C4⋊C4—21no—
339C4⋊C4—22no—
340C4⋊C4—21no—
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—2442no—
352C22⋊C4—1224no—
353C22⋊C4—4882no—
354C22⋊C4—2444no—
355C42—42no—
356C42—1222no—
357C42—1222no—
358C42—2444no—
359C42#1175822212yes—
360C42Q8×D6112yes—
361C23—1222no—
362C23—2441no—
363C23—2441no—
364C23—2441no—
365C23—2441no—
366C23—2441no—
367C23—2441no—
368C23C2×D4×D6111yescharacteristic
369D4—1222no—
370D4—1222no—
371D4—2441no—
372D4—2441no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—42no—
384C2×C4—1222no—
385C2×C4—1222no—
386C2×C4—1222no—
387C2×C4—1222no—
388C2×C4—1222no—
389C2×C4—1222no—
390C2×C4—1222no—
391C2×C4—2442no—
392C2×C4—2442no—
393C2×C4—2442no—
394C2×C4—2441no—
395C2×C4—2441no—
396C2×C4—2448no—
397C2×C4#1451975512yes—
398C2×C4#1451975512yes—
399C2×C4#1451979812yes—
400C2×C4#1451980412yes—
401C2×C4C2×Q8×D6111yescharacteristic
402C2×C4#41×D6111yescharacteristic
403C2×C4#41×D6111yescharacteristic
404C2×C4C2×#1175822211yescharacteristic
405C2×C4#1451982211yescharacteristic
406C2×C4#1451982511yescharacteristic
407C8—42no—
408C8—1222no—
409C8—1222no—
410C22—4881no—
411C22—4881no—
412C22—4881no—
413C22—4881no—
414C22—2442no—
415C22—2442no—
416C22—2442no—
417C22C2×#1451975511yescharacteristic
418C22#1684041411yescharacteristic
419C22#1684043011yescharacteristic
420C22C2×#1451979811yescharacteristic
421C22C2×#1451980411yescharacteristic
422C22#1684056611yescharacteristic
423C22#1684057811yescharacteristic
424C4—22no—
425C4—81no—
426C4—81no—
427C4—82no—
428C4—4882no—
429C4—2442no—
430C4—2442no—
431C4—2442no—
432C4#1684006114yes—
433C4#1684031811yescharacteristic
434C4#1684038911yescharacteristic
435C4#1684045311yescharacteristic
436C4#1684046211yescharacteristic
437C2—4882no—
438C2#2144953411yescharacteristic
439C2C2×#1684006111yescharacteristic
440C2#2145566911yescharacteristic
441C2#2145824011yescharacteristic
442C2#2145840611yescharacteristic
443C2#2145880611yescharacteristic
444C2#2145886011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1948C2
socleC23×C61C22×D4
prime radicalC22×D244C23
hypercenter#1948D61
hypocenterC61#26087
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
1. #21451058C2semidirect
5. #21446588C2semidirect
6. #21446535C2semidirect
7. #21446409C2semidirect
8. #21445978C2semidirect
11. C61×#1948C2semidirect
220. #1948D61semidirect
263. C61#26087semidirect

Maximal subgroups

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

subgroupindex
#214510582
#214487702
#214473412
#214472082
#214465882
#214465352
#214464092
#214459782
#214458202
C4×#145196972
C61×#19482
#2608761