Finite Group Databasebeta

← #29576118

Subgroups — #29576118

Order 15616.

510 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455276C211yesmaximal, characteristic
2#21454780C211yesmaximal, characteristic, complemented
3#21445836C211yesmaximal, characteristic, complemented
4#21444315C211yesmaximal, characteristic, complemented
5#21444269C211yesmaximal, characteristic, complemented
6#21443658C211yesmaximal, characteristic, complemented
7C61×#1301C211yesmaximal, characteristic, complemented
8C2×#14519799—21no—
9#16840312C2211yescharacteristic
10C4×#11758222C2211yescharacteristic
11#16839985—21no—
12#16839978—21no—
13#16839973C411yescharacteristic, complemented
14#16839968C411yescharacteristic, complemented
15#16839963C411yescharacteristic, complemented
16#16839958C411yescharacteristic, complemented
17#16839889—21no—
18#16839839—21no—
19#16839830—22no—
20#16839813—21no—
21C2×#14519703—21no—
22#16839759—21no—
23C4×#11758189—21no—
24C2×C4×#92418C2211yescharacteristic
25C4×C4⋊Dic61C2211yescharacteristic
26#16839523—21no—
27#16839497—22no—
28#16839489—21no—
29#16839489—21no—
30C61×#431C2211yescharacteristic
31C61×#423C2211yescharacteristic
32C2×C4⋊C8×C61C2211yescharacteristic
33C2×#11758222—21no—
34C2×#11758222D411yescharacteristic
35#14519799—42no—
36#14519799—42no—
37C2×Dic244—21no—
38C2×#11758190—21no—
39C2×#11758190—21no—
40C2×D488—21no—
41C2×#11758189—22no—
42C22×#92418—21no—
43#14519777C2×C411yescharacteristic
44#14519774C2×C411yescharacteristic
45#14519765—21no—
46#14519751—21no—
47#14519751—21no—
48C4×Dic122C2×C411yescharacteristic
49C4×Dic122D411yescharacteristic
50C4×D244—21no—
51C4×D244—21no—
52C4×D244C2×C411yescharacteristic
53C4×D244D411yescharacteristic
54C4×C22⋊D61—21no—
55C4×C22⋊D61—21no—
56#14519736D411yescharacteristic
57#14519734—21no—
58C2×C4⋊Dic61—21no—
59C2×C4×Dic61—21no—
60C42×D61—21no—
61#14519706—22no—
62#14519703—42no—
63#14519702—21no—
64#14519702—21no—
65#14519699—21no—
66#14519699—21no—
67#14519689—22no—
68#14519687—22no—
69C4×#92418—21no—
70C4×#92418D411yescharacteristic
71C4×#92418D411yescharacteristic
72#14519684—21no—
73C2×M16×C61—21no—
74C22×C8×C61—21no—
75C2×C42×C61C2311yescharacteristic
76C4⋊C8×C61—21no—
77C4⋊C8×C61—21no—
78C4⋊C8×C61—21no—
79C4⋊C8×C61—21no—
80C4⋊C8×C61C2×C411yescharacteristic
81C4⋊C8×C61C2×C411yescharacteristic
82C22⋊C8×C61D412yes—
83C4×C8×C61—21no—
84C22×C4×C61C2×D411yescharacteristic
85C22×C4×C61C2×D411yescharacteristic
86C22×C4×C61#4111yescharacteristic
87C2×C22⋊D61—21no—
88C2×C22⋊D61—41no—
89C22×Dic61—41no—
90#11758222—21no—
91#11758222—21no—
92#11758222—21no—
93#11758222—21no—
94#11758222—41no—
95#11758222—41no—
96#11758222—41no—
97#11758222—41no—
98C2×D244—21no—
99C2×D244—21no—
100C2×D244—21no—
101C2×D244C22⋊C411yescharacteristic
102C2×C4×D61—21no—
103C2×C4×D61—21no—
104C2×C4×D61—21no—
105C2×C4×D61—41no—
106C2×Dic122—21no—
107C2×Dic122C22⋊C411yescharacteristic
108M16×C61—41no—
109M16×C61—41no—
110C2×C8×C61—21no—
111C2×C8×C61—21no—
112C2×C8×C61—22no—
113C2×C8×C61—41no—
114C2×C8×C61—41no—
115C2×C8×C61—41no—
116C42×C61C22×C411yescharacteristic
117C42×C61C2×D411yescharacteristic
118C42×C61C2×D411yescharacteristic
119C42×C61#4111yescharacteristic
120C22⋊Dic61—21no—
121#11758198—21no—
122#11758198—21no—
123#11758198—41no—
124#11758198—41no—
125C4⋊Dic61—22no—
126C4⋊Dic61—21no—
127C4⋊Dic61—21no—
128C4⋊Dic61—41no—
129C4⋊Dic61C22⋊C411yescharacteristic
130C4⋊Dic61C22⋊C411yescharacteristic
131#11758196—21no—
132#11758196—21no—
133C4×Dic61—21no—
134C4×Dic61—21no—
135C4×Dic61—21no—
136C4×Dic61—41no—
137C4×Dic61—41no—
138C2×#92418—21no—
139C2×#92418—21no—
140C2×#92418—42no—
141Dic244—42no—
142D488—42no—
143#11758190—42no—
144#11758190—42no—
145#11758189—44no—
146C23×C61#12111yescharacteristic
147C22×D61—21no—
148C22×D61—41no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—41no—
152C2×C4×C61C2×C22⋊C411yescharacteristic
153C2×C4×C61C4×D411yescharacteristic
154C2×C4×C61C4×D411yescharacteristic
155C2×C4×C61#12011yescharacteristic
156C2×C4×C61#12111yescharacteristic
157C2×C4×C61#12311yescharacteristic
158C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C61#13711yescharacteristic
162C22⋊D61—41no—
163C22⋊D61—41no—
164C22⋊D61—81no—
165C22⋊D61—81no—
166C2×Dic61—21no—
167C2×Dic61—21no—
168C2×Dic61—21no—
169C2×Dic61—42no—
170C2×Dic61—41no—
171C2×Dic61—81no—
172C2×Dic61—81no—
173D244—21no—
174D244—21no—
175D244—41no—
176D244—41no—
177D244—41no—
178D244—41no—
179D244—81no—
180C4×D61—42no—
181C4×D61—41no—
182C4×D61—41no—
183C4×D61—41no—
184C4×D61—41no—
185C4×D61—81no—
186C4×D61—81no—
187Dic122—21no—
188Dic122—21no—
189Dic122—41no—
190Dic122—41no—
191C8×C61—42no—
192C8×C61—41no—
193C8×C61—41no—
194C8×C61—81no—
195#92418—22no—
196#92418—41no—
197#9210—611nomaximal, Sylow
198C22×C61—21no—
199C22×C61—21no—
200C22×C61#38611yescharacteristic
201C22×C61#46811yescharacteristic
202C22×C61#46911yescharacteristic
203C2×D61—41no—
204C2×D61—41no—
205C2×D61—41no—
206C2×D61—81no—
207C2×D61—81no—
208C2×D61—81no—
209C4×C61—21no—
210C4×C61—21no—
211C4×C61—21no—
212C4×C61#41711yescharacteristic
213C4×C61#41811yescharacteristic
214C4×C61#44311yescharacteristic
215C4×C61#44411yescharacteristic
216C4×C61#46811yescharacteristic
217C4×C61#46911yescharacteristic
218Dic61—41no—
219Dic61—41no—
220Dic61—41no—
221Dic61—82no—
222Dic61—81no—
223#3035—611no—
224#2965—611no—
225#1806—611no—
226#1502—611no—
227#1492—611no—
228#1301D6111yescharacteristic, complemented
229#1279—611no—
230C2×C61—21no—
231C2×C61—21no—
232C2×C61#187611yescharacteristic
233C2×C61#189511yescharacteristic
234C2×C61#190611yescharacteristic
235D61—81no—
236D61—161no—
237C2×#135—1221no—
238#532—611no—
239C4×#41—611no—
240#464—1221no—
241#463—1221no—
242#462—611no—
243#461—611no—
244#460—611no—
245#459—611no—
246#446—1221no—
247#436—1221no—
248#435—1222no—
249#431—1221no—
250#431C2×D6111yescharacteristic
251#423C2×D6111yescharacteristic
252C2×C4⋊C8C2×D6111yescharacteristic
253C2×#104—1221no—
254#416—1221no—
255C4×M16—1221no—
256C2×C4×C8—611no—
257C4×C4⋊C4—611no—
258#339—1221no—
259#327—1222no—
260D4⋊C8—1221no—
261D4⋊C8—1221no—
262C61#921011yescharacteristic, complemented, Sylow
263C2×#41—611no—
264C2×#41—1221no—
265#135—2442no—
266#135—2442no—
267C2×Q16—1221no—
268C2×SD16—1221no—
269C2×SD16—1221no—
270C2×D8—1221no—
271C2×M16—21no—
272C2×M16—1222no—
273C22×C8—21no—
274C22×C8—1221no—
275C4⋊Q8—611no—
276#127—611no—
277#124—1221no—
278#121—1221no—
279#121—1221no—
280C4×Q8—611no—
281C4×Q8—611no—
282C4×D4—611no—
283C4×D4—611no—
284C4×D4—1221no—
285C4×D4—1221no—
286C4×D4—1221no—
287C4×D4—1221no—
288#117—611no—
289#117—1221no—
290C2×C4⋊C4—1221no—
291C2×C42—1221no—
292C2×C42—1221no—
293C2×C42C22×D6111yescharacteristic
294C4⋊C8—21no—
295C4⋊C8—21no—
296C4⋊C8—21no—
297C4⋊C8—21no—
298C4⋊C8—1222no—
299C4⋊C8C4×D6111yescharacteristic
300C4⋊C8C4×D6111yescharacteristic
301#104—2442no—
302#103—1221no—
303#103—1221no—
304#102—1221no—
305#102—1221no—
306C22⋊C8—1222no—
307C22⋊C8D24412yes—
308#97—1222no—
309C4×C8—21no—
310C4×C8—611no—
311C4×C8—611no—
312C4×C8—1221no—
313#95—1221no—
314#41—1221no—
315#41—1221no—
316#41—1221no—
317#41—1221no—
318#41—2441no—
319#41—2441no—
320#41—2441no—
321#41—2441no—
322C2×Q8—611no—
323C2×Q8—1221no—
324C2×D4—611no—
325C2×D4—1221no—
326C2×D4—1221no—
327C2×D4—1221no—
328C2×D4—1221no—
329C2×D4—2441no—
330C22×C4—1221no—
331C22×C4—1221no—
332C22×C4—1221no—
333C22×C4—2441no—
334C22×C4—2441no—
335C22×C4C2×D24411yescharacteristic
336C22×C4D4×D6111yescharacteristic
337C22×C4#1175822611yescharacteristic
338Q16—2442no—
339SD16—2442no—
340SD16—2442no—
341D8—2442no—
342M16—41no—
343M16—41no—
344M16—2444no—
345C2×C8—21no—
346C2×C8—21no—
347C2×C8—22no—
348C2×C8—41no—
349C2×C8—41no—
350C2×C8—41no—
351C2×C8—1221no—
352C2×C8—1221no—
353C2×C8—2442no—
354C4⋊C4—611no—
355C4⋊C4—611no—
356C4⋊C4—1222no—
357C4⋊C4—1221no—
358C4⋊C4—1221no—
359C4⋊C4—1221no—
360C4⋊C4—1221no—
361C4⋊C4—2441no—
362C22⋊C4—1221no—
363C22⋊C4—1221no—
364C22⋊C4—1221no—
365C22⋊C4—2441no—
366C22⋊C4—2441no—
367C42—1221no—
368C42—1221no—
369C42—1221no—
370C42—2441no—
371C42—2441no—
372C42C2×C4×D6111yescharacteristic
373C42#1175822211yescharacteristic
374C42D4×D6111yescharacteristic
375C42D4×D6111yescharacteristic
376C23—1221no—
377C23—2441no—
378C23#1451975211yescharacteristic
379Q8—1221no—
380Q8—1221no—
381Q8—2441no—
382Q8—2441no—
383D4—1221no—
384D4—1221no—
385D4—4881no—
386D4—4881no—
387D4—4881no—
388D4—2441no—
389D4—2441no—
390D4—2441no—
391D4—2441no—
392D4—2441no—
393D4—2441no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—41no—
397C2×C4—1221no—
398C2×C4—1221no—
399C2×C4—1221no—
400C2×C4—4881no—
401C2×C4—4881no—
402C2×C4—4881no—
403C2×C4—4881no—
404C2×C4—2442no—
405C2×C4—2442no—
406C2×C4—2441no—
407C2×C4—2441no—
408C2×C4—2441no—
409C2×C4—2441no—
410C2×C4—2441no—
411C2×C4C22⋊C4×D6111yescharacteristic
412C2×C4#1451973911yescharacteristic
413C2×C4C4×D24411yescharacteristic
414C2×C4#1451974711yescharacteristic
415C2×C4#1451975011yescharacteristic
416C2×C4#1451976211yescharacteristic
417C2×C4#1451980111yescharacteristic
418C2×C4#1451980411yescharacteristic
419C2×C4#1451980411yescharacteristic
420C2×C4#1451980911yescharacteristic
421C8—42no—
422C8—41no—
423C8—41no—
424C8—81no—
425C8—1222no—
426C8—2441no—
427C22—21no—
428C22—21no—
429C22—4881no—
430C22—4881no—
431C22—4881no—
432C22—2441no—
433C22—2441no—
434C22—2441no—
435C22#1683964011yescharacteristic
436C22#1684000911yescharacteristic
437C22#1684001611yescharacteristic
438C4—21no—
439C4—21no—
440C4—21no—
441C4—4882no—
442C4—4881no—
443C4—2441no—
444C4—2441no—
445C4—2441no—
446C4#1683976211yescharacteristic
447C4#1683976511yescharacteristic
448C4#1683987811yescharacteristic
449C4#1683988311yescharacteristic
450C4#1684001111yescharacteristic
451C4#1684001411yescharacteristic
452C2—21no—
453C2—21no—
454C2—9761no—
455C2—4881no—
456C2#2144614711yescharacteristic
457C2#2144625611yescharacteristic
458C2#2144632111yescharacteristic
subgroupG/H
centerC2×C4#14519750
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1301C2
socleC22×C61#386
prime radical#21455276C2
cosocleC2×C42×C61C23
hypercenter#1301D61
hypocenterC61#9210
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1301

Complements

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

NH ≅ G/Ntype
2. #21454780C2semidirect
3. #21445836C2semidirect
4. #21444315C2semidirect
5. #21444269C2semidirect
6. #21443658C2semidirect
7. C61×#1301C2semidirect
13. #16839973C4semidirect
14. #16839968C4semidirect
15. #16839963C4semidirect
16. #16839958C4semidirect
228. #1301D61semidirect
262. C61#9210semidirect

Maximal subgroups

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

subgroupindex
#214552762
#214547802
#214458362
#214443152
#214442692
#214436582
C61×#13012
#921061