Finite Group Databasebeta

← #29662716

Subgroups — #29662716

Order 15616.

704 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455268C212yesmaximal, complemented
2#21454785C211yesmaximal, characteristic, complemented
3#21445384C212yesmaximal, complemented
4#21445377C212yesmaximal, complemented
5#21445334C211yesmaximal, characteristic, complemented
6#21445329C211yesmaximal, characteristic, complemented
7#21445300C211yesmaximal, characteristic, complemented
8#21445295C211yesmaximal, characteristic, complemented
9C2×#16839513C211yesmaximal, characteristic, complemented
10#21444468C212yesmaximal, complemented
11C61×#3169C211yesmaximal, characteristic, complemented
12C2×#14519797—22no—
13C4×#11758222C2211yescharacteristic
14#16839981—22no—
15#16839974—22no—
16#16839969C2212yes—
17#16839964C2212yes—
18#16839959C2212yes—
19#16839954C2212yes—
20#16839892C2211yescharacteristic
21#16839892C2211yescharacteristic
22#16839841C2211yescharacteristic
23#16839841C2211yescharacteristic
24#16839833—21no—
25#16839833—21no—
26#16839815C2211yescharacteristic
27#16839813—21no—
28C2×C4⋊#92418C2212yes—
29#16839758—22no—
30C4×#11758189—21no—
31#16839513C2212yes—
32#16839513C2211yescharacteristic
33#16839513C2211yescharacteristic
34#16839508C2212yes—
35#16839508C2212yes—
36#16839506C2212yes—
37#16839506C2212yes—
38C61×#532C2212yes—
39C61×#500C2211yescharacteristic
40C61×#493C2211yescharacteristic
41C61×#486C2212yes—
42C61×#466—21no—
43C61×#466—21no—
44C4×D8×C61—21no—
45C4×D8×C61—21no—
46C2×C4×C8×C61C2211yescharacteristic
47C2×#11758222D411yescharacteristic
48#14519797—48no—
49C2×#11758202—22no—
50C2×#11758200—22no—
51C2×#11758201—22no—
52C2×#11758199—22no—
53C2×#11758189—21no—
54C2×#11758189—21no—
55C22×#92418—22no—
56C4×Dic122D411yescharacteristic
57C4×Dic122C2311yescharacteristic
58C4×D244D411yescharacteristic
59C4×D244C2311yescharacteristic
60C4×C22⋊D61—21no—
61C4×C22⋊D61—21no—
62#14519736D411yescharacteristic
63#14519734—21no—
64C42×D61—21no—
65C4⋊#92418—22no—
66C4⋊#92418C2312yes—
67C4⋊#92418C2312yes—
68C4⋊#92418C2311yescharacteristic
69C4⋊#92418C2311yescharacteristic
70#14519706—21no—
71#14519706—21no—
72#14519701—22no—
73#14519701—22no—
74#14519698—22no—
75#14519698—22no—
76C22⋊#92418—21no—
77#14519689—21no—
78#14519689—21no—
79#14519687—21no—
80#14519687—21no—
81C4×#92418—21no—
82C2×#41×C61—22no—
83C2×D8×C61—21no—
84C2×D8×C61—21no—
85C22×C8×C61D411yescharacteristic
86C22×C8×C61D411yescharacteristic
87C4⋊Q8×C61C2312yes—
88#127×C61C2312yes—
89#124×C61—22no—
90#121×C61—22no—
91#121×C61—22no—
92C4×D4×C61—22no—
93C4×D4×C61—22no—
94C2×C42×C61C2311yescharacteristic
95#107×C61—21no—
96#107×C61—21no—
97#102×C61—22no—
98#102×C61—22no—
99C4×C8×C61D411yescharacteristic
100C4×C8×C61D411yescharacteristic
101C4×C8×C61C2311yescharacteristic
102C4×C8×C61C2311yescharacteristic
103#41×C61—44no—
104#41×C61—44no—
105C2×Q8×C61—22no—
106C2×D4×C61—22no—
107C2×D4×C61—22no—
108C2×D4×C61—22no—
109C2×D4×C61—42no—
110C22×C4×C61—42no—
111C22×C4×C61C2×D411yescharacteristic
112C22×C4×C61C2×D411yescharacteristic
113C22×C4×C61#4111yescharacteristic
114C2×C22⋊D61—21no—
115#11758222—24no—
116C2×D244C2×D411yescharacteristic
117C2×C4×D61—21no—
118C2×C4×D61—21no—
119C2×C4×D61—21no—
120C2×Dic122C2×D411yescharacteristic
121D8×C61—42no—
122D8×C61—42no—
123C2×C8×C61—22no—
124C2×C8×C61—41no—
125C2×C8×C61C2×D411yescharacteristic
126C2×C8×C61C2×D411yescharacteristic
127C2×C8×C61C2×D411yescharacteristic
128C2×C8×C61C2×D411yescharacteristic
129C4⋊C4×C61—22no—
130C4⋊C4×C61—22no—
131C22⋊C4×C61—42no—
132C22⋊C4×C61—42no—
133C42×C61C2×D411yescharacteristic
134C42×C61C2×D411yescharacteristic
135C42×C61#4111yescharacteristic
136C42×C61C2411yescharacteristic
137C22⋊Dic61—21no—
138#11758202—44no—
139#11758201—44no—
140#11758200—44no—
141#11758199—44no—
142#11758198—21no—
143#11758198—21no—
144C4⋊Dic61C2×D411yescharacteristic
145C4⋊Dic61C2×D411yescharacteristic
146#11758196—21no—
147#11758196—21no—
148C4×Dic61—21no—
149C4×Dic61—21no—
150C4×Dic61—21no—
151C2×#92418—21no—
152C2×#92418—21no—
153C2×#92418—22no—
154C2×#92418—22no—
155C2×#92418—44no—
156#11758189—42no—
157#11758189—42no—
158C23×C61—42no—
159C23×C61#12111yescharacteristic
160C22×D61—21no—
161Q8×C61—42no—
162Q8×C61—42no—
163D4×C61—42no—
164D4×C61—42no—
165D4×C61—42no—
166D4×C61—42no—
167D4×C61—82no—
168D4×C61—84no—
169C2×C4×C61—21no—
170C2×C4×C61—21no—
171C2×C4×C61—41no—
172C2×C4×C61—42no—
173C2×C4×C61—84no—
174C2×C4×C61#12111yescharacteristic
175C2×C4×C61#12111yescharacteristic
176C2×C4×C61#12111yescharacteristic
177C2×C4×C61AGL(1,ℤ/8)14yes—
178C2×C4×C61C22×D411yescharacteristic
179C2×C4×C61C22×D411yescharacteristic
180C2×C4×C61C2×#4111yescharacteristic
181C22⋊D61—42no—
182C2×Dic61—21no—
183C2×Dic61—21no—
184C2×Dic61—21no—
185D244—22no—
186C4×D61—42no—
187C4×D61—41no—
188C4×D61—41no—
189C4×D61—42no—
190Dic122—22no—
191C8×C61—21no—
192C8×C61—21no—
193C8×C61—21no—
194C8×C61#13512yescomplemented
195#92418—41no—
196#92418—42no—
197#92418—42no—
198#92418—41no—
199#19157—611nomaximal, Sylow
200C22×C61—21no—
201C22×C61—21no—
202C22×C61—82no—
203C22×C61—82no—
204C22×C61—82no—
205C22×C61#46912yes—
206C22×C61C2×#12111yescharacteristic
207C2×D61—41no—
208C2×D61—41no—
209C2×D61—41no—
210C4×C61—21no—
211C4×C61—21no—
212C4×C61—21no—
213C4×C61—82no—
214C4×C61#46912yes—
215C4×C61C2×#13511yescharacteristic
216C4×C61C2×AGL(1,ℤ/8)12yes—
217C4×C61#57511yescharacteristic
218Dic61—41no—
219Dic61—41no—
220Dic61—41no—
221#3169D6111yescharacteristic, complemented
222#3035—612no—
223#2965—611no—
224#1702—612no—
225#1701—612no—
226#1694—611no—
227#1693—611no—
228#1688—611no—
229#1687—611no—
230C2×#334—611no—
231#1540—612no—
232C2×C61—22no—
233C2×C61—162no—
234C2×C61#303511yescharacteristic
235C2×C61C2×#46911yescharacteristic
236C2×C61#306711yescharacteristic
237D61—81no—
238C2×#135—1222no—
239#532C2×D6112yes—
240C4×#41—611no—
241#500C2×D6111yescharacteristic
242#493C2×D6111yescharacteristic
243#486C2×D6112yes—
244#466—21no—
245#466—21no—
246#464—1222no—
247#463—1222no—
248#462—612no—
249#461—612no—
250#460—612no—
251#459—612no—
252#446—611no—
253#446—611no—
254C4×D8—21no—
255C4×D8—21no—
256#436—611no—
257#436—611no—
258#435—1221no—
259#435—1221no—
260#431—611no—
261#431—1221no—
262C2×C4⋊C8—612no—
263#416—1222no—
264C4×M16—1221no—
265C2×C4×C8C2×D6111yescharacteristic
266#334—611no—
267#334—611no—
268#334—612no—
269#332—612no—
270#332—612no—
271#331—612no—
272#331—612no—
273C61#1915711yescharacteristic, complemented, Sylow
274C2×#41—22no—
275C2×#41—611no—
276#135—2448no—
277C2×Q16—1222no—
278C2×SD16—1222no—
279C2×SD16—1222no—
280C2×D8—21no—
281C2×D8—21no—
282C2×D8—1222no—
283C2×M16—1221no—
284C2×M16—1221no—
285C22×C8—1222no—
286C22×C8C22⋊D6111yescharacteristic
287C22×C8C22⋊D6111yescharacteristic
288C4⋊Q8C22×D6112yes—
289#127C22×D6112yes—
290#124—22no—
291#121—22no—
292#121—22no—
293C4×Q8—611no—
294C4×Q8—611no—
295C4×D4—22no—
296C4×D4—22no—
297C4×D4—611no—
298C4×D4—611no—
299C4×D4—1221no—
300C4×D4—1221no—
301#117—611no—
302#117—1221no—
303C2×C42—1221no—
304C2×C42C22×D6111yescharacteristic
305#107—21no—
306#107—21no—
307C4⋊C8—611no—
308C4⋊C8—611no—
309C4⋊C8—612no—
310C4⋊C8—612no—
311C4⋊C8—1221no—
312C4⋊C8—1221no—
313C4⋊C8—1222no—
314#103—1222no—
315#103—1222no—
316#102—22no—
317#102—22no—
318#102—1222no—
319#102—1222no—
320C22⋊C8—1221no—
321C22⋊C8—1221no—
322C22⋊C8—1221no—
323#97—1221no—
324#97—1221no—
325C4×C8—1221no—
326C4×C8C22⋊D6111yescharacteristic
327C4×C8C22⋊D6111yescharacteristic
328C4×C8C22×D6111yescharacteristic
329C4×C8C22×D6111yescharacteristic
330#41—44no—
331#41—44no—
332#41—1224no—
333C2×Q8—22no—
334C2×Q8—611no—
335C2×D4—22no—
336C2×D4—22no—
337C2×D4—22no—
338C2×D4—42no—
339C2×D4—611no—
340C2×D4—1221no—
341C22×C4—42no—
342C22×C4—1221no—
343C22×C4—1221no—
344C22×C4—1221no—
345C22×C4D4×D6111yescharacteristic
346C22×C4#1175822411yescharacteristic
347C22×C4C2×C22⋊D6111yescharacteristic
348Q16—2444no—
349SD16—2444no—
350SD16—2444no—
351D8—42no—
352D8—42no—
353D8—2444no—
354M16—2442no—
355M16—2442no—
356C2×C8—22no—
357C2×C8—41no—
358C2×C8—1222no—
359C2×C8—1222no—
360C2×C8—1221no—
361C2×C8—1221no—
362C2×C8—2444no—
363C2×C8C2×C22⋊D6111yescharacteristic
364C2×C8C2×C22⋊D6111yescharacteristic
365C2×C8C2×C22⋊D6111yescharacteristic
366C2×C8C2×C22⋊D6111yescharacteristic
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—611no—
370C4⋊C4—611no—
371C4⋊C4—1221no—
372C4⋊C4—1221no—
373C22⋊C4—42no—
374C22⋊C4—42no—
375C22⋊C4—1221no—
376C22⋊C4—1221no—
377C22⋊C4—1221no—
378C42—1221no—
379C42—1221no—
380C42—1221no—
381C42D4×D6111yescharacteristic
382C42#1175822411yescharacteristic
383C42C2×C22⋊D6111yescharacteristic
384C42C23×D6111yescharacteristic
385C23—42no—
386C23—1221no—
387C23#1451974811yescharacteristic
388Q8—42no—
389Q8—42no—
390Q8—1222no—
391D4—42no—
392D4—42no—
393D4—42no—
394D4—42no—
395D4—82no—
396D4—84no—
397D4—1222no—
398D4—2442no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—41no—
402C2×C4—42no—
403C2×C4—84no—
404C2×C4—1221no—
405C2×C4—1221no—
406C2×C4—1221no—
407C2×C4—2442no—
408C2×C4—2442no—
409C2×C4—2441no—
410C2×C4—2441no—
411C2×C4#1451974811yescharacteristic
412C2×C4#1451974811yescharacteristic
413C2×C4#1451974811yescharacteristic
414C2×C4#1451980114yes—
415C2×C4C2×D4×D6111yescharacteristic
416C2×C4C22×C22⋊D6111yescharacteristic
417C2×C4C2×#1175822411yescharacteristic
418C8—21no—
419C8—21no—
420C8—21no—
421C8—2441no—
422C8—2442no—
423C8—2442no—
424C8—2441no—
425C8#1451979712yescomplemented
426C22—21no—
427C22—21no—
428C22—82no—
429C22—82no—
430C22—82no—
431C22—2441no—
432C22—2441no—
433C22—2441no—
434C22#1684001212yes—
435C22C2×#1451974811yescharacteristic
436C4—21no—
437C4—21no—
438C4—21no—
439C4—82no—
440C4—2441no—
441C4—2441no—
442C4—2441no—
443C4#1684001212yes—
444C4C2×#1451979711yescharacteristic
445C4C2×#1451980112yes—
446C4#1684056011yescharacteristic
447C2—22no—
448C2—162no—
449C2—4881no—
450C2#2145526811yescharacteristic
451C2C2×#1684001211yescharacteristic
452C2#2145553511yescharacteristic
subgroupG/H
centerC2×C4#14519748
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3169C2
socleC22×C61C2×#121
hypercenter#3169D61
hypocenterC61#19157
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3169

Complements

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

NH ≅ G/Ntype
1. #21455268C2semidirect
2. #21454785C2semidirect
3. #21445384C2semidirect
4. #21445377C2semidirect
5. #21445334C2semidirect
6. #21445329C2semidirect
7. #21445300C2semidirect
8. #21445295C2semidirect
9. C2×#16839513C2semidirect
10. #21444468C2semidirect
11. C61×#3169C2semidirect
194. C8×C61#135semidirect
221. #3169D61semidirect
273. C61#19157semidirect
425. C8#14519797semidirect

Maximal subgroups

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

subgroupindex
#214552682
#214547852
#214453842
#214453772
#214453342
#214453292
#214453002
#214452952
C2×#168395132
#214444682
C61×#31692
#1915761