Finite Group Databasebeta

← #29589468

Subgroups — #29589468

Order 15616.

530 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 75 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#21448474C211yesmaximal, characteristic
2#21444158C211yesmaximal, characteristic, complemented
3#21444154C211yesmaximal, characteristic, complemented
4#21443768C211yesmaximal, characteristic, complemented
5#21443766C211yesmaximal, characteristic, complemented
6#21443747C211yesmaximal, characteristic, complemented
7C61×#1316C211yesmaximal, characteristic, complemented
8C2×#14519746C411yescharacteristic
9C2×#14519737C2211yescharacteristic
10C22×C22⋊Dic61C411yescharacteristic
11#16839816—21no—
12#16839724—21no—
13#16839662—21no—
14#16839656—21no—
15#16839650—21no—
16#16839639C411yescharacteristic
17#16839638—21no—
18#16839634C2211yescharacteristic
19C22⋊C4×Dic61C411yescharacteristic
20#16839487—21no—
21#16839486C2211yescharacteristic
22#16839486C2211yescharacteristic
23#16839485—21no—
24C61×#379C2211yescharacteristic
25C61×#323C2211yescharacteristic
26C61×#323C2211yescharacteristic
27C22×C22⋊D61—21no—
28C22×C22⋊D61C2×C411yescharacteristic
29C23×Dic61C2×C411yescharacteristic
30C23×Dic61C2×C411yescharacteristic
31C22×C4×D61D411yescharacteristic
32C2×#11758189—41no—
33#14519746—22no—
34#14519746—22no—
35#14519737—41no—
36#14519737—41no—
37C2×#11758196—21no—
38C2×#11758196D411yescharacteristic
39C2×C22⋊Dic61—21no—
40C2×C22⋊Dic61—21no—
41C2×C22⋊Dic61—21no—
42C2×C22⋊Dic61—41no—
43C2×C22⋊Dic61—41no—
44C2×C22⋊Dic61C2×C411yescharacteristic
45C2×#11758198—21no—
46C2×#11758198D411yescharacteristic
47C2×C4×Dic61—21no—
48C2×C4×Dic61D411yescharacteristic
49#14519706—41no—
50C22⋊#92418—21no—
51C22⋊#92418—21no—
52#14519689—41no—
53#14519687—41no—
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57C25×C61C2×C411yescharacteristic
58C2×C22⋊C4×C61—21no—
59C2×C22⋊C4×C61—21no—
60C2×C22⋊C4×C61C2×C411yescharacteristic
61C2×C22⋊C4×C61C2311yescharacteristic
62C22⋊C8×C61—21no—
63C22⋊C8×C61—21no—
64C24×C61—21no—
65C24×C61—21no—
66C24×C61—41no—
67C24×C61—41no—
68C24×C61—81no—
69C24×C61—81no—
70C24×C61M1612yescomplemented
71C24×C61C22×C411yescharacteristic
72C23×D61C22⋊C411yescharacteristic
73C22×C4×C61—21no—
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C2×C22⋊D61—21no—
77C2×C22⋊D61—21no—
78C2×C22⋊D61—24no—
79C2×C22⋊D61—41no—
80C2×C22⋊D61—41no—
81C2×C22⋊D61—81no—
82C2×C22⋊D61—81no—
83C22×Dic61—21no—
84C22×Dic61—21no—
85C22×Dic61—21no—
86C22×Dic61—21no—
87C22×Dic61—41no—
88C22×Dic61—81no—
89C22×Dic61—81no—
90C22×Dic61C22⋊C411yescharacteristic
91C22×Dic61C22⋊C411yescharacteristic
92C22×Dic61C22⋊C411yescharacteristic
93C2×C4×D61—21no—
94C2×C4×D61—21no—
95C2×C4×D61—81no—
96C2×C8×C61—41no—
97C2×C8×C61—41no—
98C22⋊C4×C61—41no—
99C22⋊C4×C61—41no—
100C22⋊C4×C61—81no—
101C22⋊C4×C61—81no—
102C22⋊Dic61—24no—
103C22⋊Dic61—21no—
104C22⋊Dic61—42no—
105C22⋊Dic61—41no—
106C22⋊Dic61—41no—
107C22⋊Dic61M1612yescomplemented
108#11758198—41no—
109#11758198—81no—
110#11758196—41no—
111#11758196—81no—
112C4×Dic61—21no—
113C4×Dic61—21no—
114C4×Dic61—81no—
115C2×#92418—41no—
116C2×#92418—41no—
117#11758189—82no—
118C23×C61—21no—
119C23×C61—21no—
120C23×C61—22no—
121C23×C61—41no—
122C23×C61—41no—
123C23×C61—41no—
124C23×C61—41no—
125C23×C61—41no—
126C23×C61—41no—
127C23×C61—42no—
128C23×C61—42no—
129C23×C61—41no—
130C23×C61—41no—
131C23×C61—82no—
132C23×C61—82no—
133C23×C61—84no—
134C23×C61—82no—
135C23×C61—82no—
136C23×C61C2×C22⋊C411yescharacteristic
137C23×C61C2×M1611yescharacteristic
138C23×C61C2×M1611yescharacteristic
139C22×D61—21no—
140C22×D61—21no—
141C22×D61—21no—
142C22×D61—41no—
143C22×D61—41no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C22⋊D61—42no—
152C22⋊D61—42no—
153C22⋊D61—84no—
154C2×Dic61—21no—
155C2×Dic61—22no—
156C2×Dic61—21no—
157C2×Dic61—21no—
158C2×Dic61—21no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165C2×Dic61—41no—
166C2×Dic61—81no—
167C2×Dic61—81no—
168C2×Dic61—82no—
169C2×Dic61#9911yescharacteristic
170C2×Dic61#9911yescharacteristic
171C4×D61—42no—
172C4×D61—81no—
173C8×C61—81no—
174C8×C61—81no—
175#92418—81no—
176#92418—81no—
177#11527—611nomaximal, Sylow
178C22×C61—21no—
179C22×C61—21no—
180C22×C61—21no—
181C22×C61—21no—
182C22×C61—41no—
183C22×C61—41no—
184C22×C61—42no—
185C22×C61—42no—
186C22×C61—42no—
187C22×C61—41no—
188C22×C61—41no—
189C22×C61—42no—
190C22×C61—81no—
191C22×C61—81no—
192C22×C61—84no—
193C22×C61—84no—
194C22×C61—81no—
195C22×C61—81no—
196C22×C61#40711yescharacteristic
197C22×C61C2×#9911yescharacteristic
198C22×C61#41311yescharacteristic
199C2×D61—42no—
200C2×D61—41no—
201C2×D61—41no—
202C2×D61—41no—
203C2×D61—81no—
204C4×C61—41no—
205C4×C61—41no—
206C4×C61—81no—
207Dic61—21no—
208Dic61—21no—
209Dic61—42no—
210Dic61—41no—
211Dic61—41no—
212Dic61—81no—
213#2321—611no—
214#1466—611no—
215#1465—611no—
216#1326—611no—
217#1326—611no—
218#1316—611no—
219#1316D6111yescharacteristic, complemented
220C2×C61—21no—
221C2×C61—21no—
222C2×C61—41no—
223C2×C61—41no—
224C2×C61—82no—
225C2×C61#146511yescharacteristic
226C2×C61#212111yescharacteristic
227C2×C61#212211yescharacteristic
228D61—81no—
229C2×#120—611no—
230C2×C4×D4—611no—
231C22×C22⋊C4—611no—
232#432—1221no—
233#407—1221no—
234#390—1221no—
235#388—1221no—
236#388—1221no—
237#386—611no—
238#386—1221no—
239#385—611no—
240#379C2×D6111yescharacteristic
241C4×C22⋊C4—611no—
242#324—1221no—
243#323—611no—
244#323—611no—
245#323—1221no—
246#323C2×D6111yescharacteristic
247#323C2×D6111yescharacteristic
248C61#1152711yescharacteristic, complemented, Sylow
249C25C4×D6111yescharacteristic
250C22×D4—611no—
251C22×D4—1221no—
252C23×C4—611no—
253C23×C4—611no—
254C23×C4—611no—
255C2×M16—2441no—
256#120—1222no—
257#120—1222no—
258C4×D4—2441no—
259C4×D4—2441no—
260C2×C4⋊C4—611no—
261C2×C4⋊C4—1221no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—611no—
265C2×C22⋊C4—611no—
266C2×C22⋊C4—1221no—
267C2×C22⋊C4—1221no—
268C2×C22⋊C4—1221no—
269C2×C22⋊C4—1221no—
270C2×C22⋊C4—2441no—
271C2×C22⋊C4—2441no—
272C2×C22⋊C4C4×D6111yescharacteristic
273C2×C22⋊C4C22×D6111yescharacteristic
274C2×C42—611no—
275C2×C42—1221no—
276C4⋊C8—2441no—
277C22⋊C8—21no—
278C22⋊C8—21no—
279C22⋊C8—1221no—
280C22⋊C8—1221no—
281C22⋊C8—2441no—
282#97—2441no—
283#95—1221no—
284#95—1221no—
285#95—1221no—
286C24—21no—
287C24—21no—
288C24—41no—
289C24—41no—
290C24—81no—
291C24—81no—
292C24—611no—
293C24#1175818912yescomplemented
294C24C2×C4×D6111yescharacteristic
295C2×D4—1224no—
296C2×D4—1221no—
297C2×D4—1221no—
298C2×D4—4881no—
299C2×D4—4881no—
300C2×D4—2441no—
301C2×D4—2441no—
302C22×C4—21no—
303C22×C4—611no—
304C22×C4—611no—
305C22×C4—611no—
306C22×C4—1221no—
307C22×C4—1221no—
308C22×C4—1221no—
309C22×C4—1221no—
310C22×C4—1221no—
311C22×C4—1221no—
312C22×C4—4881no—
313C22×C4—4881no—
314C22×C4—4881no—
315C22×C4—2441no—
316C22×C4D4×D6111yescharacteristic
317C22×C4D4×D6111yescharacteristic
318M16—4882no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—2441no—
322C2×C8—2441no—
323C4⋊C4—4881no—
324C4⋊C4—2441no—
325C22⋊C4—41no—
326C22⋊C4—41no—
327C22⋊C4—81no—
328C22⋊C4—81no—
329C22⋊C4—612no—
330C22⋊C4—1224no—
331C22⋊C4—1221no—
332C22⋊C4—4881no—
333C22⋊C4—2441no—
334C22⋊C4—2441no—
335C22⋊C4—2441no—
336C22⋊C4—2442no—
337C42—1221no—
338C42—1221no—
339C42—4881no—
340C23—21no—
341C23—21no—
342C23—22no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—42no—
350C23—42no—
351C23—41no—
352C23—41no—
353C23—82no—
354C23—82no—
355C23—82no—
356C23—82no—
357C23—84no—
358C23—1221no—
359C23—1221no—
360C23—1221no—
361C23—2441no—
362C23—2441no—
363C23C22⋊C4×D6111yescharacteristic
364C23M16×D6111yescharacteristic
365C23C2×#1175818911yescharacteristic
366D4—4884no—
367D4—2442no—
368D4—2442no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—611no—
377C2×C4—611no—
378C2×C4—1222no—
379C2×C4—1221no—
380C2×C4—1221no—
381C2×C4—1221no—
382C2×C4—1221no—
383C2×C4—4881no—
384C2×C4—4881no—
385C2×C4—4881no—
386C2×C4—4882no—
387C2×C4—2442no—
388C2×C4—2441no—
389C2×C4—2441no—
390C2×C4—2441no—
391C2×C4—2441no—
392C2×C4—2441no—
393C2×C4—2441no—
394C2×C4—2441no—
395C8—81no—
396C8—81no—
397C8—4881no—
398C8—4881no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—41no—
404C22—41no—
405C22—42no—
406C22—42no—
407C22—42no—
408C22—41no—
409C22—41no—
410C22—42no—
411C22—81no—
412C22—81no—
413C22—84no—
414C22—84no—
415C22—81no—
416C22—81no—
417C22—4881no—
418C22—2442no—
419C22—2441no—
420C22—2441no—
421C22—2441no—
422C22#1683972411yescharacteristic
423C22#99×D6111yescharacteristic
424C22#1683974311yescharacteristic
425C4—41no—
426C4—41no—
427C4—81no—
428C4—1221no—
429C4—1221no—
430C4—4881no—
431C4—2442no—
432C4—2441no—
433C4—2441no—
434C2—21no—
435C2—21no—
436C2—41no—
437C2—41no—
438C2—82no—
439C2—4881no—
440C2#2144415411yescharacteristic
441C2#2144746211yescharacteristic
442C2#2144746711yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC24×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1316C2
socleC22×C61C2×#99
prime radicalC2×#14519746C4
cosocleC2×C22⋊C4×C61C23
hypercenter#1316D61
hypocenterC61#11527
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1316

Complements

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

NH ≅ G/Ntype
2. #21444158C2semidirect
3. #21444154C2semidirect
4. #21443768C2semidirect
5. #21443766C2semidirect
6. #21443747C2semidirect
7. C61×#1316C2semidirect
70. C24×C61M16semidirect
107. C22⋊Dic61M16semidirect
219. #1316D61semidirect
248. C61#11527semidirect
293. C24#11758189semidirect

Maximal subgroups

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

subgroupindex
#214484742
#214441582
#214441542
#214437682
#214437662
#214437472
C61×#13162
#1152761