Finite Group Databasebeta

← #29580757

Subgroups — #29580757

Order 15616.

602 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455850C211yesmaximal, characteristic, complemented
2#21455283C211yesmaximal, characteristic
3#21444378C211yesmaximal, characteristic, complemented
4#21444248C211yesmaximal, characteristic, complemented
5#21444210C211yesmaximal, characteristic, complemented
6#21443677C211yesmaximal, characteristic, complemented
7C61×#2580C211yesmaximal, characteristic, complemented
8C2×#14519803—21no—
9#16840312C2211yescharacteristic
10#16840080—21no—
11#16840047—21no—
12#16839977—22no—
13#16839967—21no—
14#16839962—21no—
15#16839957—21no—
16#16839901—21no—
17C4×#11758201—22no—
18#16839815C2211yescharacteristic
19#16839815C2211yescharacteristic
20#16839786C2211yescharacteristic
21#16839761—21no—
22#16839495—22no—
23Q8⋊#92418—22no—
24D4⋊#92418—22no—
25C2×C4×Q8×C61C2211yescharacteristic
26C2×C4×D4×C61C2211yescharacteristic
27C61×#399—21no—
28C61×#393—21no—
29C61×#390—21no—
30C61×#389—21no—
31C61×#385—22no—
32C61×#382C2211yescharacteristic
33C2×#11758222—21no—
34#14519803—42no—
35#14519803—42no—
36C2×#11758200—22no—
37C2×#11758201—22no—
38C2×#11758199—22no—
39C2×#11758194—21no—
40#14519777D411yescharacteristic
41#14519774D411yescharacteristic
42#14519765—21no—
43#14519751—21no—
44#14519751—21no—
45C4×D244—21no—
46C4×D244—21no—
47#14519708—22no—
48C4⋊#92418—21no—
49C4⋊#92418—21no—
50C4⋊#92418—21no—
51C4⋊#92418D412yes—
52#14519701—22no—
53#14519700—22no—
54#14519697—22no—
55#14519697—22no—
56C22⋊#92418—21no—
57C22⋊#92418—21no—
58C4×#92418—21no—
59C4×#92418D412yes—
60C22×Q8×C61D411yescharacteristic
61C22×D4×C61D411yescharacteristic
62C23×C4×C61—21no—
63C4×Q8×C61—21no—
64C4×Q8×C61—21no—
65C4×Q8×C61—21no—
66C4×Q8×C61—21no—
67C4×D4×C61—21no—
68C4×D4×C61—21no—
69C4×D4×C61—21no—
70C4×D4×C61—21no—
71C2×C4⋊C4×C61—21no—
72C2×C4⋊C4×C61—21no—
73C2×C4⋊C4×C61—22no—
74C2×C4⋊C4×C61D411yescharacteristic
75C2×C4⋊C4×C61D411yescharacteristic
76C2×C22⋊C4×C61—22no—
77C2×C22⋊C4×C61—21no—
78C2×C22⋊C4×C61—22no—
79C2×C42×C61—21no—
80C2×C42×C61C2311yescharacteristic
81#95×C61—22no—
82#95×C61—21no—
83#95×C61D412yes—
84C24×C61—21no—
85C2×Q8×C61—21no—
86C2×Q8×C61—21no—
87C2×Q8×C61—42no—
88C2×D4×C61—21no—
89C2×D4×C61—21no—
90C2×D4×C61—21no—
91C2×D4×C61—21no—
92C2×D4×C61—21no—
93C2×D4×C61SD1612yescomplemented
94C22×C4×C61—21no—
95C22×C4×C61—22no—
96C22×C4×C61—21no—
97C22×C4×C61—21no—
98C22×C4×C61—41no—
99C22×C4×C61—41no—
100C22×C4×C61—82no—
101C22×C4×C61C2×D411yescharacteristic
102C22×C4×C61C2×D411yescharacteristic
103C22×C4×C61C2×D411yescharacteristic
104C2×C22⋊D61—41no—
105#11758222—41no—
106#11758222—41no—
107#11758222—41no—
108#11758222—41no—
109C2×D244—21no—
110C2×D244—21no—
111C2×D244—21no—
112C2×C4×D61—41no—
113C2×Dic122—21no—
114C4⋊C4×C61—21no—
115C4⋊C4×C61—21no—
116C4⋊C4×C61—21no—
117C4⋊C4×C61—21no—
118C4⋊C4×C61—41no—
119C4⋊C4×C61—41no—
120C4⋊C4×C61—41no—
121C4⋊C4×C61—41no—
122C4⋊C4×C61—82no—
123C22⋊C4×C61—44no—
124C22⋊C4×C61—41no—
125C22⋊C4×C61—41no—
126C22⋊C4×C61—82no—
127C42×C61—41no—
128C42×C61—41no—
129C42×C61C2×D411yescharacteristic
130C42×C61C2×D411yescharacteristic
131C42×C61C2×D411yescharacteristic
132C42×C61#4111yescharacteristic
133#11758201—44no—
134#11758200—44no—
135#11758199—44no—
136#11758198—41no—
137#11758198—41no—
138C4⋊Dic61—21no—
139C4⋊Dic61—21no—
140#11758194—41no—
141#11758194—41no—
142C2×#92418—22no—
143C2×#92418—22no—
144C2×#92418—41no—
145C23×C61—22no—
146C23×C61—42no—
147C23×C61—42no—
148C23×C61—41no—
149C23×C61—41no—
150C23×C61#12011yescharacteristic
151C22×D61—41no—
152Q8×C61—22no—
153Q8×C61—22no—
154Q8×C61—41no—
155Q8×C61—41no—
156D4×C61—22no—
157D4×C61—22no—
158D4×C61—41no—
159D4×C61—41no—
160C2×C4×C61—22no—
161C2×C4×C61—41no—
162C2×C4×C61—41no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61—42no—
166C2×C4×C61—41no—
167C2×C4×C61—42no—
168C2×C4×C61—41no—
169C2×C4×C61—42no—
170C2×C4×C61—41no—
171C2×C4×C61—41no—
172C2×C4×C61—42no—
173C2×C4×C61—82no—
174C2×C4×C61—82no—
175C2×C4×C61#12011yescharacteristic
176C2×C4×C61#12011yescharacteristic
177C2×C4×C61#12111yescharacteristic
178C2×C4×C61#12111yescharacteristic
179C2×C4×C61#12111yescharacteristic
180C2×C4×C61#12711yescharacteristic
181C2×C4×C61C2×SD1611yescharacteristic
182C2×C4×C61#13511yescharacteristic
183C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
184C2×C4×C61#13711yescharacteristic
185C22⋊D61—81no—
186C22⋊D61—81no—
187C2×Dic61—41no—
188D244—42no—
189D244—41no—
190D244—41no—
191D244—81no—
192C4×D61—81no—
193C4×D61—81no—
194Dic122—41no—
195Dic122—41no—
196#92418—42no—
197#92418—42no—
198#92418—81no—
199#9998—611nomaximal, Sylow
200C22×C61—21no—
201C22×C61—21no—
202C22×C61—44no—
203C22×C61—42no—
204C22×C61—82no—
205C22×C61—81no—
206C22×C61—81no—
207C22×C61#39211yescharacteristic
208C22×C61#44811yescharacteristic
209C22×C61#44911yescharacteristic
210C2×D61—81no—
211C2×D61—81no—
212C2×D61—81no—
213C4×C61—21no—
214C4×C61—21no—
215C4×C61—21no—
216C4×C61—21no—
217C4×C61—42no—
218C4×C61—82no—
219C4×C61—81no—
220C4×C61—81no—
221C4×C61#45011yescharacteristic
222C4×C61#45211yescharacteristic
223C4×C61#46511yescharacteristic
224C4×C61#46811yescharacteristic
225Dic61—81no—
226#3103—611no—
227#3036—611no—
228#2580D6111yescharacteristic, complemented
229#1517—611no—
230#1487—611no—
231#1478—611no—
232#1286—611no—
233C2×C61—21no—
234C2×C61—21no—
235C2×C61—82no—
236C2×C61#200011yescharacteristic
237C2×C61#200811yescharacteristic
238C2×C61#201011yescharacteristic
239D61—161no—
240C2×AGL(1,ℤ/8)—1221no—
241#532—611no—
242C2×C4×Q8C2×D6111yescharacteristic
243C2×C4×D4C2×D6111yescharacteristic
244#481—1221no—
245#475—1221no—
246#463—1222no—
247#461—1221no—
248#460—1221no—
249#459—1221no—
250#448—1221no—
251C4×SD16—1222no—
252#431—611no—
253#431—611no—
254#423—611no—
255#417—1221no—
256#399—21no—
257#393—21no—
258#390—21no—
259#389—21no—
260#385—22no—
261#382C2×D6111yescharacteristic
262#327—1222no—
263Q8⋊C8—1222no—
264D4⋊C8—1222no—
265C61#999811yescharacteristic, complemented, Sylow
266C2×#41—1221no—
267C22×Q8C22⋊D6111yescharacteristic
268C22×D4C22⋊D6111yescharacteristic
269C23×C4—21no—
270AGL(1,ℤ/8)—2442no—
271AGL(1,ℤ/8)—2442no—
272C2×SD16—1222no—
273C2×SD16—1222no—
274C2×D8—1222no—
275C2×M16—1221no—
276C4⋊Q8—611no—
277#127—611no—
278#124—1221no—
279#121—1221no—
280#121—1221no—
281C4×Q8—21no—
282C4×Q8—21no—
283C4×Q8—21no—
284C4×Q8—21no—
285C4×D4—21no—
286C4×D4—21no—
287C4×D4—21no—
288C4×D4—21no—
289C4×D4—1221no—
290C4×D4—1221no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4C22⋊D6111yescharacteristic
295C2×C4⋊C4C22⋊D6111yescharacteristic
296C2×C22⋊C4—22no—
297C2×C22⋊C4—21no—
298C2×C22⋊C4—22no—
299C2×C42—21no—
300C2×C42C22×D6111yescharacteristic
301#106—1222no—
302C4⋊C8—612no—
303C4⋊C8—1221no—
304C4⋊C8—1221no—
305C4⋊C8—1221no—
306#103—1222no—
307#103—1222no—
308#102—1222no—
309#102—1222no—
310C22⋊C8—1221no—
311C22⋊C8—1221no—
312C4×C8—612no—
313C4×C8—1221no—
314#95—22no—
315#95—21no—
316#95C22⋊D6112yes—
317C24—21no—
318#41—2441no—
319#41—2441no—
320#41—2441no—
321#41—2441no—
322C2×Q8—21no—
323C2×Q8—21no—
324C2×Q8—42no—
325C2×Q8—1221no—
326C2×D4—21no—
327C2×D4—21no—
328C2×D4—21no—
329C2×D4—21no—
330C2×D4—21no—
331C2×D4—1221no—
332C2×D4—1221no—
333C2×D4—1221no—
334C2×D4—2441no—
335C2×D4#1175820112yescomplemented
336C22×C4—21no—
337C22×C4—22no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—82no—
343C22×C4—2441no—
344C22×C4C2×C22⋊D6111yescharacteristic
345C22×C4C2×C22⋊D6111yescharacteristic
346C22×C4C2×C22⋊D6111yescharacteristic
347SD16—2444no—
348SD16—2444no—
349D8—2444no—
350M16—2441no—
351M16—2441no—
352C2×C8—1222no—
353C2×C8—1222no—
354C2×C8—2441no—
355C4⋊C4—21no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—41no—
360C4⋊C4—41no—
361C4⋊C4—41no—
362C4⋊C4—41no—
363C4⋊C4—82no—
364C4⋊C4—1221no—
365C4⋊C4—1221no—
366C22⋊C4—44no—
367C22⋊C4—41no—
368C22⋊C4—41no—
369C22⋊C4—82no—
370C22⋊C4—2441no—
371C22⋊C4—2441no—
372C42—41no—
373C42—41no—
374C42D4×D6111yescharacteristic
375C42D4×D6111yescharacteristic
376C42D4×D6111yescharacteristic
377C42#1175822411yescharacteristic
378C23—22no—
379C23—42no—
380C23—42no—
381C23—41no—
382C23—41no—
383C23—2441no—
384C23#1451974611yescharacteristic
385Q8—22no—
386Q8—22no—
387Q8—41no—
388Q8—41no—
389Q8—2441no—
390Q8—2441no—
391D4—22no—
392D4—22no—
393D4—41no—
394D4—41no—
395D4—4881no—
396D4—4881no—
397D4—4881no—
398D4—2442no—
399D4—2441no—
400D4—2441no—
401C2×C4—22no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—42no—
407C2×C4—41no—
408C2×C4—42no—
409C2×C4—41no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—82no—
415C2×C4—82no—
416C2×C4—4881no—
417C2×C4—4881no—
418C2×C4—2441no—
419C2×C4#1451974511yescharacteristic
420C2×C4#1451974511yescharacteristic
421C2×C4#1451974811yescharacteristic
422C2×C4#1451974911yescharacteristic
423C2×C4#1451974911yescharacteristic
424C2×C4#1451977311yescharacteristic
425C2×C4C2×#1175820111yescharacteristic
426C2×C4#1451979711yescharacteristic
427C2×C4#1451980211yescharacteristic
428C2×C4#1451980811yescharacteristic
429C8—4881no—
430C8—2442no—
431C8—2442no—
432C22—21no—
433C22—21no—
434C22—44no—
435C22—42no—
436C22—82no—
437C22—81no—
438C22—81no—
439C22—4881no—
440C22—4881no—
441C22—4881no—
442C22#1683967011yescharacteristic
443C22#1683990111yescharacteristic
444C22#1683990711yescharacteristic
445C4—21no—
446C4—21no—
447C4—21no—
448C4—21no—
449C4—42no—
450C4—82no—
451C4—81no—
452C4—81no—
453C4—4881no—
454C4#1683991211yescharacteristic
455C4#1683992211yescharacteristic
456C4#1683999311yescharacteristic
457C4#1684001011yescharacteristic
458C2—21no—
459C2—21no—
460C2—82no—
461C2—9761no—
462C2#2144682011yescharacteristic
463C2#2144687211yescharacteristic
464C2#2144688411yescharacteristic
subgroupG/H
centerC22#16839670
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2580C2
socleC22×C61#392
prime radical#21455283C2
hypercenter#2580D61
hypocenterC61#9998
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2580

Complements

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

NH ≅ G/Ntype
1. #21455850C2semidirect
3. #21444378C2semidirect
4. #21444248C2semidirect
5. #21444210C2semidirect
6. #21443677C2semidirect
7. C61×#2580C2semidirect
93. C2×D4×C61SD16semidirect
228. #2580D61semidirect
265. C61#9998semidirect
335. C2×D4#11758201semidirect

Maximal subgroups

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

subgroupindex
#214558502
#214552832
#214443782
#214442482
#214442102
#214436772
C61×#25802
#999861