Finite Group Databasebeta

← #29590196

Subgroups — #29590196

Order 15616.

568 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 83 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#21451568C211yesmaximal, characteristic
2#21445550C211yesmaximal, characteristic, complemented
3#21444130C211yesmaximal, characteristic, complemented
4#21443817C211yesmaximal, characteristic, complemented
5#21443816C211yesmaximal, characteristic, complemented
6#21443815C211yesmaximal, characteristic, complemented
7C61×#1343C211yesmaximal, characteristic, complemented
8C2×#14519773C411yescharacteristic, complemented
9C2×#14519749—21no—
10C2×#14519733—21no—
11C2×#14519733C2211yescharacteristic
12#16839812—21no—
13#16839680C411yescharacteristic, complemented
14#16839677—21no—
15#16839676C411yescharacteristic, complemented
16#16839671C2211yescharacteristic
17#16839670—21no—
18#16839662—21no—
19#16839626C411yescharacteristic, complemented
20#16839529C2211yescharacteristic
21#16839528—21no—
22#16839487—21no—
23#16839486C2211yescharacteristic
24C61×#392C2211yescharacteristic
25C61×#342C2211yescharacteristic
26C61×#323C2211yescharacteristic
27C22×D244C2×C411yescharacteristic
28C22×C22⋊D61—21no—
29C22×C22⋊D61—21no—
30C22×C22⋊D61—21no—
31C23×Dic61D411yescharacteristic
32#14519773—41no—
33#14519773—41no—
34#14519749—42no—
35#14519749—42no—
36#14519733—24no—
37#14519733—41no—
38#14519733—41no—
39#14519733—42no—
40C2×#11758196—21no—
41C2×#11758196—41no—
42C2×#11758196C2×C411yescharacteristic
43C2×#11758196D411yescharacteristic
44C2×C22⋊Dic61—21no—
45C2×C22⋊Dic61—21no—
46C2×C22⋊Dic61—21no—
47C2×C22⋊Dic61D411yescharacteristic
48C2×#11758198—21no—
49C2×#11758198—21no—
50C2×#11758198—21no—
51C2×C4×Dic61—41no—
52C2×C4×Dic61C2×C411yescharacteristic
53C2×C4×Dic61D411yescharacteristic
54#14519706—41no—
55C22⋊#92418—21no—
56C8×Dic61—41no—
57#14519684—21no—
58#14519684C2×C411yescharacteristic
59C22×D4×C61—21no—
60C22×D4×C61C2×C411yescharacteristic
61C2×C22⋊C4×C61—21no—
62C2×C22⋊C4×C61—21no—
63C2×C22⋊C4×C61C2311yescharacteristic
64C22⋊C8×C61—21no—
65#95×C61C2×C411yescharacteristic
66C24×C61—21no—
67C24×C61C2×D411yescharacteristic
68C23×D61—21no—
69C2×D4×C61—41no—
70C2×D4×C61—41no—
71C2×D4×C61—41no—
72C2×D4×C61—81no—
73C2×D4×C61—81no—
74C2×D4×C61—81no—
75C22×C4×C61—21no—
76C22×C4×C61—41no—
77C22×C4×C61C22×C411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C2×C22⋊D61—42no—
80C2×C22⋊D61—41no—
81C2×C22⋊D61—41no—
82C2×C22⋊D61—41no—
83C2×C22⋊D61—41no—
84C2×C22⋊D61—42no—
85C2×C22⋊D61—42no—
86C2×C22⋊D61—81no—
87C2×C22⋊D61—81no—
88C2×C22⋊D61—81no—
89C2×C22⋊D61—81no—
90C22×Dic61—21no—
91C22×Dic61—21no—
92C22×Dic61—22no—
93C22×Dic61—21no—
94C22×Dic61—41no—
95C22×Dic61C22⋊C411yescharacteristic
96C22×Dic61C22⋊C411yescharacteristic
97C22×Dic61C22⋊C411yescharacteristic
98C22×Dic61C22⋊C411yescharacteristic
99C22×Dic61D812yes—
100C22×Dic61SD1612yes—
101C2×D244—41no—
102C2×D244—81no—
103C2×C8×C61—41no—
104C22⋊C4×C61—22no—
105C22⋊C4×C61—41no—
106C22⋊C4×C61—41no—
107C22⋊C4×C61—81no—
108C22⋊Dic61—22no—
109C22⋊Dic61—41no—
110C22⋊Dic61—41no—
111C22⋊Dic61—42no—
112C22⋊Dic61—81no—
113#11758198—42no—
114#11758198—81no—
115#11758198—81no—
116#11758196—41no—
117#11758196—41no—
118#11758196—44no—
119#11758196—42no—
120C4×Dic61—21no—
121C4×Dic61—21no—
122C4×Dic61—21no—
123C4×Dic61—21no—
124C4×Dic61—44no—
125C2×#92418—41no—
126C23×C61—21no—
127C23×C61—21no—
128C23×C61—41no—
129C23×C61—41no—
130C23×C61—41no—
131C23×C61—41no—
132C23×C61—41no—
133C23×C61—41no—
134C23×C61—41no—
135C23×C61—41no—
136C23×C61—41no—
137C23×C61C2×C22⋊C411yescharacteristic
138C23×C61C2×D811yescharacteristic
139C23×C61C2×SD1611yescharacteristic
140C22×D61—41no—
141C22×D61—41no—
142C22×D61—41no—
143C22×D61—41no—
144C22×D61—41no—
145C22×D61—41no—
146C22×D61—41no—
147D4×C61—82no—
148D4×C61—82no—
149D4×C61—82no—
150C2×C4×C61—21no—
151C2×C4×C61—21no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61—42no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—81no—
159C2×C4×C61—81no—
160C22⋊D61—84no—
161C22⋊D61—82no—
162C22⋊D61—82no—
163C22⋊D61—82no—
164C22⋊D61—82no—
165C2×Dic61—21no—
166C2×Dic61—21no—
167C2×Dic61—22no—
168C2×Dic61—22no—
169C2×Dic61—22no—
170C2×Dic61—22no—
171C2×Dic61—21no—
172C2×Dic61—21no—
173C2×Dic61—41no—
174C2×Dic61—41no—
175C2×Dic61—42no—
176C2×Dic61—41no—
177C2×Dic61—41no—
178C2×Dic61—41no—
179C2×Dic61—81no—
180C2×Dic61—81no—
181C2×Dic61#9911yescharacteristic
182C2×Dic61#9911yescharacteristic
183C2×Dic61#10212yes—
184C2×Dic61#10212yes—
185C2×Dic61#10412yes—
186D244—82no—
187C8×C61—81no—
188#92418—81no—
189#11693—611nomaximal, Sylow
190C22×C61—21no—
191C22×C61—21no—
192C22×C61—21no—
193C22×C61—21no—
194C22×C61—41no—
195C22×C61—41no—
196C22×C61—41no—
197C22×C61—41no—
198C22×C61—81no—
199C22×C61—81no—
200C22×C61—81no—
201C22×C61—81no—
202C22×C61—81no—
203C22×C61—81no—
204C22×C61—81no—
205C22×C61—81no—
206C22×C61C2×#9911yescharacteristic
207C22×C61C2×#10211yescharacteristic
208C22×C61C2×#10411yescharacteristic
209C2×D61—81no—
210C2×D61—81no—
211C2×D61—81no—
212C2×D61—81no—
213C2×D61—81no—
214C2×D61—81no—
215C2×D61—81no—
216C4×C61—41no—
217C4×C61—41no—
218C4×C61—81no—
219C4×C61—82no—
220Dic61—22no—
221Dic61—41no—
222Dic61—41no—
223Dic61—81no—
224Dic61—82no—
225Dic61#32712yes—
226Dic61#32712yes—
227#2619—611no—
228#1740—611no—
229#1458—611no—
230#1343—611no—
231#1343—611no—
232#1343—611no—
233#1343D6111yescharacteristic, complemented
234C2×C61—21no—
235C2×C61—21no—
236C2×C61—41no—
237C2×C61—41no—
238C2×C61—161no—
239C2×C61C2×#32711yescharacteristic
240C2×C61#212211yescharacteristic
241C2×C61#212811yescharacteristic
242D61—161no—
243C2×#127—611no—
244C2×#121—1221no—
245C2×#117—611no—
246C2×#117—1221no—
247#431—1221no—
248#394—611no—
249#394—611no—
250#394—1221no—
251#392—611no—
252#392—1221no—
253#392C2×D6111yescharacteristic
254#390—1221no—
255#382—611no—
256#342—611no—
257#342—1221no—
258#342C2×D6111yescharacteristic
259#324—1221no—
260#323—611no—
261#323C2×D6111yescharacteristic
262C61#1169311yescharacteristic, complemented, Sylow
263C22×D4—21no—
264C22×D4—611no—
265C22×D4—1221no—
266C22×D4—1221no—
267C22×D4—1221no—
268C22×D4C4×D6111yescharacteristic
269C23×C4—611no—
270#127—2441no—
271#127—2441no—
272#121—2442no—
273#121—2442no—
274#117—1224no—
275#117—2441no—
276#117—2441no—
277#117—2442no—
278C2×C4⋊C4—611no—
279C2×C4⋊C4—611no—
280C2×C4⋊C4—1221no—
281C2×C4⋊C4—2441no—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—611no—
285C2×C22⋊C4—1221no—
286C2×C22⋊C4—1221no—
287C2×C22⋊C4—1221no—
288C2×C22⋊C4—1221no—
289C2×C22⋊C4—1221no—
290C2×C22⋊C4—1221no—
291C2×C22⋊C4C22×D6111yescharacteristic
292C2×C42—611no—
293C2×C42—611no—
294C2×C42—2441no—
295C4⋊C8—2441no—
296C22⋊C8—21no—
297C22⋊C8—1221no—
298C4×C8—2441no—
299#95—611no—
300#95—1221no—
301#95C4×D6111yescharacteristic
302C24—21no—
303C24—1221no—
304C24D4×D6111yescharacteristic
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—81no—
309C2×D4—81no—
310C2×D4—81no—
311C2×D4—4881no—
312C2×D4—4881no—
313C2×D4—4881no—
314C2×D4—4881no—
315C2×D4—4881no—
316C2×D4—2441no—
317C2×D4—2442no—
318C2×D4—2441no—
319C2×D4—2441no—
320C2×D4—2442no—
321C2×D4—2442no—
322C2×D4—2441no—
323C2×D4—2441no—
324C22×C4—21no—
325C22×C4—41no—
326C22×C4—611no—
327C22×C4—611no—
328C22×C4—612no—
329C22×C4—612no—
330C22×C4—611no—
331C22×C4—611no—
332C22×C4—1221no—
333C22×C4—1221no—
334C22×C4—1222no—
335C22×C4—1221no—
336C22×C4—2441no—
337C22×C4C2×C4×D6111yescharacteristic
338C22×C4D4×D6111yescharacteristic
339C2×C8—41no—
340C2×C8—2441no—
341C4⋊C4—2441no—
342C4⋊C4—2441no—
343C4⋊C4—2442no—
344C4⋊C4—2444no—
345C22⋊C4—22no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4—81no—
349C22⋊C4—1222no—
350C22⋊C4—4881no—
351C22⋊C4—4881no—
352C22⋊C4—4881no—
353C22⋊C4—2442no—
354C22⋊C4—2442no—
355C22⋊C4—2441no—
356C22⋊C4—2441no—
357C42—1221no—
358C42—1221no—
359C42—1221no—
360C42—1221no—
361C42—2444no—
362C23—21no—
363C23—21no—
364C23—41no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23—2441no—
374C23—2441no—
375C23—2441no—
376C23—2441no—
377C23—2441no—
378C23—2441no—
379C23—2441no—
380C23C22⋊C4×D6111yescharacteristic
381C23D8×D6111yescharacteristic
382C23SD16×D6111yescharacteristic
383D4—82no—
384D4—82no—
385D4—82no—
386D4—4882no—
387D4—4882no—
388D4—4882no—
389D4—4882no—
390D4—4882no—
391D4—4884no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—42no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—81no—
401C2×C4—81no—
402C2×C4—611no—
403C2×C4—611no—
404C2×C4—612no—
405C2×C4—612no—
406C2×C4—612no—
407C2×C4—1222no—
408C2×C4—1222no—
409C2×C4—1222no—
410C2×C4—1222no—
411C2×C4—1221no—
412C2×C4—1221no—
413C2×C4—1221no—
414C2×C4—1221no—
415C2×C4—4881no—
416C2×C4—4881no—
417C2×C4—2442no—
418C2×C4—2441no—
419C2×C4—2441no—
420C2×C4—2441no—
421C2×C4—2441no—
422C2×C4—2441no—
423C8—81no—
424C8—4881no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—41no—
433C22—81no—
434C22—81no—
435C22—81no—
436C22—81no—
437C22—81no—
438C22—81no—
439C22—81no—
440C22—81no—
441C22—4881no—
442C22—4881no—
443C22—4881no—
444C22—4881no—
445C22—4881no—
446C22—4881no—
447C22—4881no—
448C22#99×D6111yescharacteristic
449C22#102×D6111yescharacteristic
450C22#104×D6111yescharacteristic
451C4—41no—
452C4—41no—
453C4—81no—
454C4—82no—
455C4—612no—
456C4—612no—
457C4—1222no—
458C4—4881no—
459C4—4882no—
460C4—2441no—
461C4—2441no—
462C2—21no—
463C2—21no—
464C2—41no—
465C2—41no—
466C2—161no—
467C2—9761no—
468C2#327×D6111yescharacteristic
469C2#2144746711yescharacteristic
470C2#2144748911yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1343C2
socleC22×C61C2×#99
prime radical#21451568C2
cosocleC2×C22⋊C4×C61C23
hypercenter#1343D61
hypocenterC61#11693
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1343

Complements

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

NH ≅ G/Ntype
2. #21445550C2semidirect
3. #21444130C2semidirect
4. #21443817C2semidirect
5. #21443816C2semidirect
6. #21443815C2semidirect
7. C61×#1343C2semidirect
8. C2×#14519773C4semidirect
13. #16839680C4semidirect
15. #16839676C4semidirect
19. #16839626C4semidirect
233. #1343D61semidirect
262. C61#11693semidirect

Maximal subgroups

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

subgroupindex
#214515682
#214455502
#214441302
#214438172
#214438162
#214438152
C61×#13432
#1169361