Finite Group Databasebeta

← #29662481

Subgroups — #29662481

Order 15616.

664 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#21455873C212yesmaximal, complemented
2C8×#11758222C211yesmaximal, characteristic, complemented
3#21445232C212yesmaximal, complemented
4#21445225C212yesmaximal, complemented
5#21445220C211yesmaximal, characteristic, complemented
6#21445215C211yesmaximal, characteristic, complemented
7#21445176C211yesmaximal, characteristic, complemented
8#21445171C211yesmaximal, characteristic, complemented
9#21444567C211yesmaximal, characteristic, complemented
10#21444481C212yesmaximal, complemented
11C61×#3169C211yesmaximal, characteristic, complemented
12C4×#11758222C2211yescharacteristic
13#16840083—22no—
14#16840054C2212yes—
15#16840049C2212yes—
16#16839959C2212yes—
17#16839954C2212yes—
18#16839905—22no—
19C8×Dic122C2211yescharacteristic
20C8×Dic122C2211yescharacteristic
21C4×#11758200—22no—
22C4×#11758199—22no—
23C8×D244C2211yescharacteristic
24C8×D244C2211yescharacteristic
25C8×C22⋊D61—21no—
26C8×C22⋊D61—21no—
27#16839815C2212yes—
28#16839815C2211yescharacteristic
29#16839813—21no—
30C4×C8×D61—21no—
31#16839515C2211yescharacteristic
32#16839515C2211yescharacteristic
33#16839513C2212yes—
34#16839511C2212yes—
35#16839511C2212yes—
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
48C2×#11758200—22no—
49C2×#11758199—22no—
50C2×C8×D61—21no—
51C2×C8×D61—21no—
52C4×Dic122D411yescharacteristic
53C4×Dic122C2311yescharacteristic
54C4×D244D411yescharacteristic
55C4×D244C2311yescharacteristic
56C4×C22⋊D61—21no—
57C4×C22⋊D61—21no—
58#14519736D411yescharacteristic
59#14519734—21no—
60C42×D61—21no—
61#14519710—22no—
62#14519708—22no—
63C4⋊#92418C2312yes—
64C4⋊#92418C2312yes—
65C4⋊#92418C2311yescharacteristic
66C4⋊#92418C2311yescharacteristic
67#14519706—21no—
68#14519706—21no—
69#14519700—22no—
70#14519698—22no—
71#14519698—22no—
72#14519697—22no—
73C22⋊#92418—21no—
74C22⋊#92418—22no—
75#14519689—21no—
76#14519689—21no—
77C4×#92418—21no—
78C4×#92418—22no—
79C8×Dic61—21no—
80C8×Dic61—21no—
81C2×#41×C61—22no—
82C2×D8×C61—21no—
83C2×D8×C61—21no—
84C22×C8×C61D411yescharacteristic
85C22×C8×C61D411yescharacteristic
86C4⋊Q8×C61C2312yes—
87#127×C61C2312yes—
88#124×C61—22no—
89#121×C61—22no—
90#121×C61—22no—
91C4×D4×C61—22no—
92C4×D4×C61—22no—
93C2×C42×C61C2311yescharacteristic
94#107×C61—21no—
95#107×C61—21no—
96#102×C61—22no—
97#102×C61—22no—
98C4×C8×C61D411yescharacteristic
99C4×C8×C61D411yescharacteristic
100C4×C8×C61C2311yescharacteristic
101C4×C8×C61C2311yescharacteristic
102#41×C61—84no—
103C2×Q8×C61—22no—
104C2×D4×C61—22no—
105C2×D4×C61—22no—
106C2×D4×C61—22no—
107C2×D4×C61—42no—
108C22×C4×C61—42no—
109C22×C4×C61C2×D411yescharacteristic
110C22×C4×C61C2×D411yescharacteristic
111C22×C4×C61#4111yescharacteristic
112C2×C22⋊D61—21no—
113#11758222—22no—
114#11758222—22no—
115C2×D244C2×D411yescharacteristic
116C2×C4×D61—21no—
117C2×C4×D61—21no—
118C2×C4×D61—21no—
119C2×Dic122C2×D411yescharacteristic
120D8×C61—42no—
121D8×C61—42no—
122C2×C8×C61—22no—
123C2×C8×C61—41no—
124C2×C8×C61C2×D411yescharacteristic
125C2×C8×C61C2×D411yescharacteristic
126C2×C8×C61C2×D411yescharacteristic
127C2×C8×C61C2×D411yescharacteristic
128C4⋊C4×C61—22no—
129C4⋊C4×C61—22no—
130C22⋊C4×C61—42no—
131C22⋊C4×C61—42no—
132C42×C61C2×D411yescharacteristic
133C42×C61C2×D411yescharacteristic
134C42×C61#4111yescharacteristic
135C42×C61C2411yescharacteristic
136C22⋊Dic61—21no—
137#11758200—44no—
138#11758199—44no—
139#11758198—21no—
140#11758198—21no—
141C4⋊Dic61C2×D411yescharacteristic
142C4⋊Dic61C2×D411yescharacteristic
143#11758196—21no—
144#11758196—21no—
145C4×Dic61—21no—
146C4×Dic61—21no—
147C4×Dic61—21no—
148C2×#92418—21no—
149C2×#92418—21no—
150C2×#92418—22no—
151C2×#92418—22no—
152C8×D61—42no—
153C8×D61—42no—
154C23×C61—42no—
155C23×C61#12111yescharacteristic
156C22×D61—21no—
157Q8×C61—82no—
158D4×C61—42no—
159D4×C61—42no—
160D4×C61—42no—
161D4×C61—42no—
162D4×C61—82no—
163D4×C61—84no—
164C2×C4×C61—21no—
165C2×C4×C61—21no—
166C2×C4×C61—21no—
167C2×C4×C61—21no—
168C2×C4×C61—22no—
169C2×C4×C61—42no—
170C2×C4×C61—84no—
171C2×C4×C61#12111yescharacteristic
172C2×C4×C61#12111yescharacteristic
173C2×C4×C61#12111yescharacteristic
174C2×C4×C61C22×D411yescharacteristic
175C2×C4×C61C22×D411yescharacteristic
176C2×C4×C61C2×#4111yescharacteristic
177C22⋊D61—24no—
178C2×Dic61—21no—
179C2×Dic61—21no—
180C2×Dic61—21no—
181D244—21no—
182D244#13512yes—
183C4×D61—24no—
184C4×D61—41no—
185C4×D61—41no—
186C4×D61—42no—
187Dic122—21no—
188Dic122#13512yes—
189C8×C61—21no—
190C8×C61—21no—
191C8×C61—21no—
192C8×C61#13512yes—
193#92418—41no—
194#92418—42no—
195#92418—42no—
196#92418—41no—
197#19128—611nomaximal, Sylow
198C22×C61—21no—
199C22×C61—21no—
200C22×C61—21no—
201C22×C61—82no—
202C22×C61—82no—
203C22×C61—82no—
204C22×C61C2×#12111yescharacteristic
205C2×D61—22no—
206C2×D61—41no—
207C2×D61—41no—
208C4×C61—21no—
209C4×C61—21no—
210C4×C61—21no—
211C4×C61—82no—
212C4×C61#47212yes—
213C4×C61C2×#13511yescharacteristic
214C4×C61C2×#13511yescharacteristic
215C4×C61C2×#13511yescharacteristic
216C4×C61#57511yescharacteristic
217Dic61—22no—
218Dic61—41no—
219Dic61—41no—
220#3169D6111yescharacteristic, complemented
221#3106—612no—
222C8×#41—611no—
223#1678—612no—
224#1677—612no—
225#1676—611no—
226#1675—611no—
227#1668—611no—
228#1667—611no—
229#1564—611no—
230#1543—612no—
231C2×C61—41no—
232C2×C61—162no—
233C2×C61#303511yescharacteristic
234C2×C61#305011yescharacteristic
235C2×C61C2×#47211yescharacteristic
236D61—42no—
237#532C2×D6112yes—
238C4×#41—611no—
239#500C2×D6111yescharacteristic
240#493C2×D6111yescharacteristic
241#486C2×D6112yes—
242#482—1222no—
243#477—612no—
244#476—612no—
245#466—21no—
246#466—21no—
247#460—612no—
248#459—612no—
249#449—1222no—
250C8×Q8—611no—
251C8×Q8—611no—
252C4×SD16—1222no—
253C4×D8—21no—
254C4×D8—21no—
255C4×D8—1222no—
256C8×D4—611no—
257C8×D4—611no—
258C8×D4—1221no—
259C8×D4—1221no—
260#431—611no—
261#431—612no—
262#431—1221no—
263C2×C4×C8—1221no—
264C2×C4×C8C2×D6111yescharacteristic
265#335—611no—
266#335—611no—
267#334—612no—
268#333—612no—
269#333—612no—
270#331—612no—
271#331—612no—
272C61#1912811yescharacteristic, complemented, Sylow
273C2×#41—22no—
274C2×#41—611no—
275C2×SD16—1222no—
276C2×D8—21no—
277C2×D8—21no—
278C2×D8—1222no—
279C22×C8—1221no—
280C22×C8—1221no—
281C22×C8C22⋊D6111yescharacteristic
282C22×C8C22⋊D6111yescharacteristic
283C4⋊Q8C22×D6112yes—
284#127C22×D6112yes—
285#124—22no—
286#121—22no—
287#121—22no—
288C4×Q8—611no—
289C4×Q8—611no—
290C4×D4—22no—
291C4×D4—22no—
292C4×D4—611no—
293C4×D4—611no—
294C4×D4—1221no—
295C4×D4—1221no—
296#117—611no—
297#117—1221no—
298C2×C42—1221no—
299C2×C42C22×D6111yescharacteristic
300#107—21no—
301#107—21no—
302#107—1222no—
303#106—1222no—
304C4⋊C8—611no—
305C4⋊C8—611no—
306C4⋊C8—612no—
307C4⋊C8—612no—
308C4⋊C8—1221no—
309C4⋊C8—1221no—
310#103—1222no—
311#102—22no—
312#102—22no—
313#102—1222no—
314#102—1222no—
315#102—1222no—
316C22⋊C8—1222no—
317C22⋊C8—1221no—
318C22⋊C8—1221no—
319C22⋊C8—1221no—
320C4×C8—1221no—
321C4×C8—1221no—
322C4×C8—1222no—
323C4×C8—1221no—
324C4×C8C22⋊D6111yescharacteristic
325C4×C8C22⋊D6111yescharacteristic
326C4×C8C22×D6111yescharacteristic
327C4×C8C22×D6111yescharacteristic
328#41—84no—
329#41—1222no—
330#41—1222no—
331C2×Q8—22no—
332C2×Q8—611no—
333C2×D4—22no—
334C2×D4—22no—
335C2×D4—22no—
336C2×D4—42no—
337C2×D4—611no—
338C2×D4—1221no—
339C22×C4—42no—
340C22×C4—1221no—
341C22×C4—1221no—
342C22×C4—1221no—
343C22×C4D4×D6111yescharacteristic
344C22×C4#1175822411yescharacteristic
345C22×C4C2×C22⋊D6111yescharacteristic
346SD16—2444no—
347D8—42no—
348D8—42no—
349D8—2444no—
350C2×C8—22no—
351C2×C8—41no—
352C2×C8—1222no—
353C2×C8—1222no—
354C2×C8—1221no—
355C2×C8—1221no—
356C2×C8—2442no—
357C2×C8—2442no—
358C2×C8C2×C22⋊D6111yescharacteristic
359C2×C8C2×C22⋊D6111yescharacteristic
360C2×C8C2×C22⋊D6111yescharacteristic
361C2×C8C2×C22⋊D6111yescharacteristic
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—611no—
365C4⋊C4—611no—
366C4⋊C4—1221no—
367C4⋊C4—1221no—
368C22⋊C4—42no—
369C22⋊C4—42no—
370C22⋊C4—1221no—
371C22⋊C4—1221no—
372C22⋊C4—1221no—
373C42—1221no—
374C42—1221no—
375C42—1221no—
376C42D4×D6111yescharacteristic
377C42#1175822411yescharacteristic
378C42C2×C22⋊D6111yescharacteristic
379C42C23×D6111yescharacteristic
380C23—42no—
381C23—1221no—
382C23#1451974811yescharacteristic
383Q8—82no—
384Q8—612no—
385Q8—1221no—
386D4—42no—
387D4—42no—
388D4—42no—
389D4—42no—
390D4—82no—
391D4—84no—
392D4—612no—
393D4—1224no—
394D4—1221no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—22no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—42no—
401C2×C4—84no—
402C2×C4—1224no—
403C2×C4—1221no—
404C2×C4—1221no—
405C2×C4—1221no—
406C2×C4—2442no—
407C2×C4—2441no—
408C2×C4—2441no—
409C2×C4#1451974811yescharacteristic
410C2×C4#1451974811yescharacteristic
411C2×C4#1451974811yescharacteristic
412C2×C4C2×D4×D6111yescharacteristic
413C2×C4C22×C22⋊D6111yescharacteristic
414C2×C4C2×#1175822411yescharacteristic
415C8—21no—
416C8—21no—
417C8—21no—
418C8—2442no—
419C8—2442no—
420C8—2441no—
421C8—2441no—
422C8#1451979712yes—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—82no—
427C22—82no—
428C22—82no—
429C22—1222no—
430C22—2441no—
431C22—2441no—
432C22C2×#1451974811yescharacteristic
433C4—21no—
434C4—21no—
435C4—21no—
436C4—82no—
437C4—1222no—
438C4—2441no—
439C4—2441no—
440C4#1684002912yes—
441C4#135×D6111yescharacteristic
442C4#135×D6111yescharacteristic
443C4C2×#1451979711yescharacteristic
444C4#1684056011yescharacteristic
445C2—41no—
446C2—162no—
447C2—2442no—
448C2#2145526811yescharacteristic
449C2#2145539611yescharacteristic
450C2C2×#1684002911yescharacteristic
subgroupG/H
centerC2×C4#14519748
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3169C2
socleC22×C61C2×#121
hypercenter#3169D61
hypocenterC61#19128
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. #21455873C2semidirect
2. C8×#11758222C2semidirect
3. #21445232C2semidirect
4. #21445225C2semidirect
5. #21445220C2semidirect
6. #21445215C2semidirect
7. #21445176C2semidirect
8. #21445171C2semidirect
9. #21444567C2semidirect
10. #21444481C2semidirect
11. C61×#3169C2semidirect
220. #3169D61semidirect
272. C61#19128semidirect

Maximal subgroups

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

subgroupindex
#214558732
C8×#117582222
#214452322
#214452252
#214452202
#214452152
#214451762
#214451712
#214445672
#214444812
C61×#31692
#1912861