Finite Group Databasebeta

← #29590476

Subgroups — #29590476

Order 15616.

586 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 586 conjugacy classes of subgroups — too many to draw. Only its 73 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#21450088C211yesmaximal, characteristic
2#342×D61C211yesmaximal, characteristic
3#21444144C211yesmaximal, characteristic
4#21443844C211yesmaximal, characteristic, complemented
5#21443842C211yesmaximal, characteristic, complemented
6#21443819C211yesmaximal, characteristic, complemented
7C61×#1344C211yesmaximal, characteristic, complemented
8C2×#14519735C411yescharacteristic, complemented
9C2×C22⋊C4×D61—21no—
10C2×C22⋊C4×D61C2211yescharacteristic
11#16839724—21no—
12#16839699C411yescharacteristic, complemented
13#16839698C2211yescharacteristic
14#16839688C411yescharacteristic, complemented
15#16839655—21no—
16#16839651—21no—
17#16839636—21no—
18#16839624C411yescharacteristic, complemented
19#16839617—21no—
20#16839529C2211yescharacteristic
21#16839528—21no—
22#16839486C2211yescharacteristic
23#16839485—21no—
24C61×#397C2211yescharacteristic
25C61×#342C2211yescharacteristic
26C61×#323C2211yescharacteristic
27C24×D61D411yescharacteristic
28C22×C4×D61—41no—
29C22×C4×D61C2×C411yescharacteristic
30C22×C4×D61D411yescharacteristic
31C2×#11758189—41no—
32#14519735—41no—
33#14519735—41no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61C2×C411yescharacteristic, complemented
36C2×#11758196—21no—
37C2×C22⋊Dic61—21no—
38C2×C22⋊Dic61—21no—
39C2×C22⋊Dic61D411yescharacteristic
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198—41no—
45C2×#11758198C2×C411yescharacteristic
46C2×#11758198D411yescharacteristic
47C22⋊C4×D61—24no—
48C22⋊C4×D61—41no—
49C22⋊C4×D61—41no—
50C22⋊C4×D61—42no—
51C2×C4×Dic61—21no—
52C22⋊#92418—21no—
53#14519689—41no—
54#14519684—21no—
55#14519684—21no—
56#14519684C2×C411yescharacteristic, complemented
57C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
58C2×C22⋊C4×C61—21no—
59C2×C22⋊C4×C61—21no—
60C2×C22⋊C4×C61C2311yescharacteristic
61C22⋊C8×C61—21no—
62#95×C61—21no—
63#95×C61C2×C411yescharacteristic, complemented
64C24×C61C2×D411yescharacteristic
65C23×D61—21no—
66C23×D61—21no—
67C23×D61—21no—
68C23×D61—21no—
69C23×D61—22no—
70C23×D61—42no—
71C23×D61—81no—
72C23×D61C22⋊C411yescharacteristic
73C23×D61C22⋊C411yescharacteristic
74C22×C4×C61—21no—
75C22×C4×C61—21no—
76C22×C4×C61—41no—
77C22×C4×C61C22×C411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C22×Dic61—21no—
80C22×Dic61—21no—
81C22×Dic61—41no—
82C22×Dic61C22⋊C411yescharacteristic
83C22×Dic61C22⋊C411yescharacteristic
84C2×C4×D61—21no—
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×C4×D61—42no—
89C2×C4×D61—44no—
90C2×C4×D61—81no—
91C2×C4×D61—82no—
92C2×C4×D61—82no—
93C2×C8×C61—41no—
94C4⋊C4×C61—41no—
95C22⋊C4×C61—22no—
96C22⋊C4×C61—41no—
97C22⋊C4×C61—41no—
98C22⋊C4×C61—41no—
99C22⋊C4×C61—41no—
100C22⋊Dic61—22no—
101C22⋊Dic61—41no—
102C22⋊Dic61—41no—
103C22⋊Dic61—81no—
104#11758198—41no—
105#11758198—41no—
106#11758198—44no—
107#11758198—42no—
108#11758198—41no—
109#11758198—41no—
110#11758198—42no—
111#11758198—81no—
112C4⋊Dic61—41no—
113C4⋊Dic61—81no—
114#11758196—81no—
115C4×Dic61—42no—
116C2×#92418—41no—
117#11758189—82no—
118C23×C61—21no—
119C23×C61—21no—
120C23×C61—41no—
121C23×C61—41no—
122C23×C61C2×C22⋊C411yescharacteristic
123C23×C61AGL(1,ℤ/8)11yescharacteristic
124C23×C61#13711yescharacteristic
125C22×D61—22no—
126C22×D61—22no—
127C22×D61—21no—
128C22×D61—21no—
129C22×D61—21no—
130C22×D61—22no—
131C22×D61—22no—
132C22×D61—21no—
133C22×D61—22no—
134C22×D61—41no—
135C22×D61—42no—
136C22×D61—42no—
137C22×D61—41no—
138C22×D61—41no—
139C22×D61—81no—
140C22×D61—81no—
141C22×D61—84no—
142C22×D61—82no—
143C22×D61—82no—
144C22×D61#9911yescharacteristic
145C22×D61#9911yescharacteristic
146C22×D61#10412yes—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—42no—
153C2×C4×C61—41no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—81no—
159C2×C4×C61—81no—
160C2×Dic61—21no—
161C2×Dic61—21no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165C2×Dic61—41no—
166C2×Dic61—41no—
167C2×Dic61—42no—
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61—41no—
171C2×Dic61—81no—
172C2×Dic61—81no—
173C4×D61—42no—
174C4×D61—42no—
175C4×D61—42no—
176C4×D61—81no—
177C4×D61—88no—
178C8×C61—81no—
179#92418—81no—
180#11755—611nomaximal, Sylow
181C22×C61—21no—
182C22×C61—21no—
183C22×C61—21no—
184C22×C61—21no—
185C22×C61—41no—
186C22×C61—41no—
187C22×C61—41no—
188C22×C61—41no—
189C22×C61—81no—
190C22×C61C2×#9911yescharacteristic
191C22×C61#41711yescharacteristic
192C22×C61C2×#10411yescharacteristic
193C2×D61—21no—
194C2×D61—21no—
195C2×D61—21no—
196C2×D61—21no—
197C2×D61—21no—
198C2×D61—22no—
199C2×D61—42no—
200C2×D61—42no—
201C2×D61—44no—
202C2×D61—44no—
203C2×D61—41no—
204C2×D61—41no—
205C2×D61—42no—
206C2×D61—81no—
207C2×D61—82no—
208C2×D61—82no—
209C2×D61#35212yes—
210C4×C61—41no—
211C4×C61—41no—
212C4×C61—81no—
213C4×C61—82no—
214C4×C61—81no—
215Dic61—41no—
216Dic61—41no—
217Dic61—81no—
218Dic61—82no—
219Dic61—81no—
220#2482—611no—
221C2×#342—611no—
222#1462—611no—
223#1352—611no—
224#1352—611no—
225#1344—611no—
226#1344D6111yescharacteristic, complemented
227C2×C61—21no—
228C2×C61—21no—
229C2×C61—41no—
230C2×C61—41no—
231C2×C61#150411yescharacteristic
232C2×C61C2×#35211yescharacteristic
233C2×C61#212711yescharacteristic
234D61—22no—
235D61—41no—
236D61—42no—
237C2×#117—611no—
238C22×C22⋊C4—611no—
239C22×C22⋊C4—1221no—
240#407—1221no—
241#399—611no—
242#399—611no—
243#397—611no—
244#397C2×D6111yescharacteristic
245#388—1221no—
246#388—1221no—
247#385—1221no—
248#381—611no—
249#379—1221no—
250#342—611no—
251#342—1221no—
252#342C2×D6111yescharacteristic
253#323—611no—
254#323—1221no—
255#323C2×D6111yescharacteristic
256C61#1175511yescharacteristic, complemented, Sylow
257C25—611no—
258C23×C4—611no—
259C23×C4—611no—
260C23×C4—2441no—
261C2×M16—2441no—
262#117—2441no—
263#117—2441no—
264C2×C4⋊C4—611no—
265C2×C4⋊C4—1221no—
266C2×C4⋊C4—1221no—
267C2×C4⋊C4C4×D6111yescharacteristic, complemented
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—611no—
271C2×C22⋊C4—611no—
272C2×C22⋊C4—611no—
273C2×C22⋊C4—1224no—
274C2×C22⋊C4—1221no—
275C2×C22⋊C4—1221no—
276C2×C22⋊C4—1221no—
277C2×C22⋊C4—1221no—
278C2×C22⋊C4—1221no—
279C2×C22⋊C4—1221no—
280C2×C22⋊C4—2441no—
281C2×C22⋊C4—2441no—
282C2×C22⋊C4—2442no—
283C2×C22⋊C4—2441no—
284C2×C22⋊C4C22×D6111yescharacteristic
285C2×C42—1221no—
286C22⋊C8—21no—
287C22⋊C8—1221no—
288C22⋊C8—2441no—
289#95—21no—
290#95—611no—
291#95—1221no—
292#95—1221no—
293#95C4×D6111yescharacteristic, complemented
294C24—611no—
295C24—611no—
296C24—1222no—
297C24—1221no—
298C24—1221no—
299C24—1221no—
300C24—1221no—
301C24—4881no—
302C24—2442no—
303C24D4×D6111yescharacteristic
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—41no—
307C22×C4—611no—
308C22×C4—611no—
309C22×C4—1221no—
310C22×C4—1221no—
311C22×C4—1221no—
312C22×C4—1221no—
313C22×C4—1221no—
314C22×C4—1221no—
315C22×C4—4881no—
316C22×C4—4882no—
317C22×C4—4882no—
318C22×C4—2444no—
319C22×C4—2442no—
320C22×C4—2441no—
321C22×C4C2×C4×D6111yescharacteristic
322C22×C4D4×D6111yescharacteristic
323M16—4882no—
324C2×C8—41no—
325C2×C8—2441no—
326C4⋊C4—41no—
327C4⋊C4—4881no—
328C4⋊C4—4881no—
329C4⋊C4—2441no—
330C22⋊C4—22no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—1222no—
336C22⋊C4—4881no—
337C22⋊C4—4881no—
338C22⋊C4—2441no—
339C22⋊C4—2441no—
340C22⋊C4—2441no—
341C22⋊C4—2441no—
342C22⋊C4—2442no—
343C22⋊C4—2444no—
344C22⋊C4—2442no—
345C22⋊C4—2441no—
346C22⋊C4—2441no—
347C42—2442no—
348C23—21no—
349C23—21no—
350C23—41no—
351C23—41no—
352C23—611no—
353C23—611no—
354C23—612no—
355C23—1222no—
356C23—1222no—
357C23—1222no—
358C23—1222no—
359C23—1222no—
360C23—1221no—
361C23—1221no—
362C23—1221no—
363C23—1221no—
364C23—4881no—
365C23—4881no—
366C23—4882no—
367C23—4882no—
368C23—4884no—
369C23—2441no—
370C23—2441no—
371C23—2441no—
372C23—2442no—
373C23—2442no—
374C23C22⋊C4×D6111yescharacteristic
375C23#1451980111yescharacteristic
376C23#1451980611yescharacteristic
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4—1221no—
391C2×C4—1221no—
392C2×C4—4881no—
393C2×C4—4888no—
394C2×C4—4881no—
395C2×C4—4881no—
396C2×C4—2442no—
397C2×C4—2442no—
398C2×C4—2442no—
399C2×C4—2442no—
400C2×C4—2441no—
401C2×C4—2441no—
402C2×C4—2441no—
403C2×C4—2441no—
404C2×C4—2441no—
405C2×C4—2441no—
406C2×C4—2441no—
407C2×C4—2441no—
408C8—81no—
409C8—4881no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—81no—
419C22—612no—
420C22—1221no—
421C22—1221no—
422C22—1221no—
423C22—1221no—
424C22—1221no—
425C22—1222no—
426C22—4881no—
427C22—4882no—
428C22—4882no—
429C22—2442no—
430C22—2442no—
431C22—2442no—
432C22—2444no—
433C22—2444no—
434C22—2441no—
435C22—2441no—
436C22#99×D6111yescharacteristic
437C22#1683976011yescharacteristic
438C22#104×D6111yescharacteristic
439C4—41no—
440C4—41no—
441C4—81no—
442C4—82no—
443C4—81no—
444C4—4881no—
445C4—4882no—
446C4—4881no—
447C4—2441no—
448C4—2441no—
449C2—21no—
450C2—21no—
451C2—41no—
452C2—41no—
453C2—1222no—
454C2—2441no—
455C2—2442no—
456C2#2144432011yescharacteristic
457C2#352×D6111yescharacteristic
458C2#2144748711yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1344C2
socleC22×C61C2×#99
prime radicalC24×D61D4
cosocleC2×C22⋊C4×C61C23
hypercenter#1344D61
hypocenterC61#11755
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1344

Complements

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

NH ≅ G/Ntype
4. #21443844C2semidirect
5. #21443842C2semidirect
6. #21443819C2semidirect
7. C61×#1344C2semidirect
8. C2×#14519735C4semidirect
12. #16839699C4semidirect
14. #16839688C4semidirect
18. #16839624C4semidirect
35. C2×C4⋊Dic61C2×C4semidirect
56. #14519684C2×C4semidirect
57. C2×C4⋊C4×C61C2×C4semidirect
63. #95×C61C2×C4semidirect
226. #1344D61semidirect
256. C61#11755semidirect
267. C2×C4⋊C4C4×D61semidirect
293. #95C4×D61semidirect

Maximal subgroups

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

subgroupindex
#214500882
#342×D612
#214441442
#214438442
#214438422
#214438192
C61×#13442
#1175561