Finite Group Databasebeta

← #29590487

Subgroups — #29590487

Order 15616.

700 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 700 conjugacy classes of subgroups — too many to draw. Only its 87 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#21450750C211yesmaximal, characteristic
2#21444146C211yesmaximal, characteristic, complemented
3#21443842C212yesmaximal, complemented
4#21443815C212yesmaximal, complemented
5C2×C61×#342C211yesmaximal, characteristic, complemented
6C2×#14519760—21no—
7C2×#14519751C411yescharacteristic, complemented
8C2×#14519746—21no—
9#16839726—21no—
10#16839698C411yescharacteristic, complemented
11#16839698C2211yescharacteristic
12#16839671C411yescharacteristic, complemented
13#16839671C2211yescharacteristic
14#16839662—21no—
15#16839662—21no—
16C4×C22⋊Dic61C411yescharacteristic, complemented
17#16839486—21no—
18#16839486C2212yes—
19C22×C22⋊C4×C61—21no—
20C22×C22⋊C4×C61C2211yescharacteristic
21C61×#342—21no—
22C61×#342C2212yes—
23C22×D244C2×C411yescharacteristic, complemented
24C22×C22⋊D61—21no—
25C22×C22⋊D61—21no—
26C22×C22⋊D61—21no—
27C2×#11758194—41no—
28#14519760—44no—
29#14519751—41no—
30#14519751—41no—
31#14519746—44no—
32C2×C4⋊Dic61C2×C411yescharacteristic, complemented
33C2×#11758196—21no—
34C2×#11758196—21no—
35C2×C22⋊Dic61—21no—
36C2×C22⋊Dic61—21no—
37C2×C22⋊Dic61—21no—
38C2×#11758198—21no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×C4×Dic61—21no—
42C22⋊#92418—22no—
43C22⋊#92418—41no—
44#14519684C2×C411yescharacteristic, complemented
45#14519684C2×C411yescharacteristic, complemented
46C25×C61D411yescharacteristic
47C23×C4×C61—41no—
48C23×C4×C61C2×C411yescharacteristic
49C23×C4×C61D411yescharacteristic
50C2×C22⋊C4×C61—24no—
51C2×C22⋊C4×C61—22no—
52C2×C22⋊C4×C61—41no—
53C2×C22⋊C4×C61—41no—
54C2×C22⋊C4×C61—41no—
55C2×C22⋊C4×C61—42no—
56C2×C22⋊C4×C61C2×C411yescharacteristic
57C2×C22⋊C4×C61D411yescharacteristic
58C2×C22⋊C4×C61D411yescharacteristic
59C2×C22⋊C4×C61C2311yescharacteristic
60C24×C61—21no—
61C24×C61—21no—
62C24×C61—22no—
63C24×C61—21no—
64C24×C61—21no—
65C24×C61—42no—
66C24×C61—81no—
67C24×C61C22⋊C411yescharacteristic
68C24×C61C22⋊C411yescharacteristic
69C24×C61C2×D411yescharacteristic
70C23×D61—21no—
71C22×C4×C61—21no—
72C22×C4×C61—21no—
73C22×C4×C61—21no—
74C22×C4×C61—21no—
75C22×C4×C61—42no—
76C22×C4×C61—44no—
77C22×C4×C61—42no—
78C22×C4×C61—81no—
79C22×C4×C61—82no—
80C22×C4×C61—82no—
81C22×C4×C61C22⋊C411yescharacteristic
82C22×C4×C61C22⋊C411yescharacteristic
83C22×C4×C61C22×C411yescharacteristic
84C22×C4×C61C2×D411yescharacteristic
85C2×C22⋊D61—42no—
86C2×C22⋊D61—42no—
87C2×C22⋊D61—42no—
88C2×C22⋊D61—42no—
89C2×C22⋊D61—41no—
90C2×C22⋊D61—41no—
91C2×C22⋊D61—42no—
92C2×C22⋊D61—41no—
93C2×C22⋊D61—41no—
94C2×C22⋊D61—81no—
95C2×C22⋊D61—81no—
96C22×Dic61—21no—
97C22×Dic61—21no—
98C22×Dic61—21no—
99C2×D244—41no—
100C2×D244—81no—
101C22⋊C4×C61—24no—
102C22⋊C4×C61—41no—
103C22⋊C4×C61—41no—
104C22⋊C4×C61—41no—
105C22⋊C4×C61—41no—
106C22⋊C4×C61—44no—
107C22⋊C4×C61—42no—
108C22⋊Dic61—24no—
109C22⋊Dic61—42no—
110C22⋊Dic61—42no—
111#11758198—42no—
112#11758198—42no—
113#11758198—42no—
114C4⋊Dic61—41no—
115#11758196—42no—
116#11758196—42no—
117C4×Dic61—81no—
118#11758194—82no—
119C2×#92418—42no—
120C23×C61—22no—
121C23×C61—22no—
122C23×C61—22no—
123C23×C61—22no—
124C23×C61—22no—
125C23×C61—21no—
126C23×C61—21no—
127C23×C61—21no—
128C23×C61—21no—
129C23×C61—21no—
130C23×C61—21no—
131C23×C61—41no—
132C23×C61—42no—
133C23×C61—41no—
134C23×C61—41no—
135C23×C61—41no—
136C23×C61—41no—
137C23×C61—42no—
138C23×C61—81no—
139C23×C61—81no—
140C23×C61—84no—
141C23×C61—82no—
142C23×C61—82no—
143C23×C61#9911yescharacteristic
144C23×C61#9911yescharacteristic
145C23×C61#10412yes—
146C23×C61C2×C22⋊C411yescharacteristic
147C23×C61AGL(1,ℤ/8)11yescharacteristic
148C23×C61#13711yescharacteristic
149C22×D61—41no—
150C22×D61—41no—
151C22×D61—41no—
152C22×D61—41no—
153C22×D61—41no—
154C22×D61—41no—
155C22×D61—41no—
156C2×C4×C61—21no—
157C2×C4×C61—21no—
158C2×C4×C61—21no—
159C2×C4×C61—21no—
160C2×C4×C61—42no—
161C2×C4×C61—41no—
162C2×C4×C61—41no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61—44no—
166C2×C4×C61—81no—
167C2×C4×C61—81no—
168C2×C4×C61—81no—
169C2×C4×C61—88no—
170C2×C4×C61—82no—
171C2×C4×C61—82no—
172C22⋊D61—84no—
173C22⋊D61—82no—
174C22⋊D61—82no—
175C22⋊D61—82no—
176C22⋊D61—82no—
177C2×Dic61—22no—
178C2×Dic61—22no—
179C2×Dic61—41no—
180C2×Dic61—41no—
181C2×Dic61—41no—
182C2×Dic61—41no—
183C2×Dic61—41no—
184C2×Dic61—41no—
185C2×Dic61—41no—
186D244—82no—
187#92418—82no—
188#11757—611nomaximal, Sylow
189C22×C61—21no—
190C22×C61—21no—
191C22×C61—21no—
192C22×C61—21no—
193C22×C61—21no—
194C22×C61—21no—
195C22×C61—21no—
196C22×C61—21no—
197C22×C61—22no—
198C22×C61—21no—
199C22×C61—42no—
200C22×C61—42no—
201C22×C61—42no—
202C22×C61—41no—
203C22×C61—41no—
204C22×C61—44no—
205C22×C61—44no—
206C22×C61—41no—
207C22×C61—41no—
208C22×C61—41no—
209C22×C61—41no—
210C22×C61—81no—
211C22×C61—81no—
212C22×C61—82no—
213C22×C61—82no—
214C22×C61#35312yes—
215C22×C61C2×#9911yescharacteristic
216C22×C61#41711yescharacteristic
217C22×C61C2×#10411yescharacteristic
218C2×D61—81no—
219C2×D61—81no—
220C2×D61—81no—
221C2×D61—81no—
222C2×D61—81no—
223C2×D61—81no—
224C2×D61—81no—
225C4×C61—41no—
226C4×C61—41no—
227C4×C61—41no—
228C4×C61—41no—
229C4×C61—84no—
230Dic61—42no—
231Dic61—42no—
232Dic61—81no—
233#2539—611no—
234C2×#342D6111yescharacteristic, complemented
235#1462—611no—
236#1352—612no—
237#1343—612no—
238C2×C61—21no—
239C2×C61—21no—
240C2×C61—22no—
241C2×C61—41no—
242C2×C61—41no—
243C2×C61—42no—
244C2×C61—41no—
245C2×C61#150411yescharacteristic
246C2×C61#212111yescharacteristic
247C2×C61C2×#35311yescharacteristic
248D61—161no—
249C2×#123—1221no—
250C2×#121—611no—
251C2×#120—1221no—
252C22×C22⋊C4—21no—
253C22×C22⋊C4C2×D6111yescharacteristic
254#407—1221no—
255#399—611no—
256#399—611no—
257#392—611no—
258#392—611no—
259#390—1221no—
260#390—1221no—
261C4×C22⋊C4—611no—
262#342—21no—
263#342C2×D6112yes—
264#323—612no—
265#323—1221no—
266C61#1175711yescharacteristic, complemented, Sylow
267C25C22⋊D6111yescharacteristic
268C22×D4—611no—
269C22×D4—1221no—
270C22×D4—1221no—
271C22×D4—1221no—
272C23×C4—41no—
273C23×C4C4×D6111yescharacteristic
274C23×C4D24411yescharacteristic
275C2×M16—2441no—
276#123—2444no—
277#121—2441no—
278#121—2441no—
279#120—2444no—
280C2×C4⋊C4—611no—
281C2×C4⋊C4—1221no—
282C2×C4⋊C4—1221no—
283C2×C22⋊C4—24no—
284C2×C22⋊C4—22no—
285C2×C22⋊C4—41no—
286C2×C22⋊C4—41no—
287C2×C22⋊C4—41no—
288C2×C22⋊C4—42no—
289C2×C22⋊C4—1221no—
290C2×C22⋊C4—1221no—
291C2×C22⋊C4—1221no—
292C2×C22⋊C4—1221no—
293C2×C22⋊C4—1221no—
294C2×C22⋊C4—1221no—
295C2×C22⋊C4C4×D6111yescharacteristic
296C2×C22⋊C4D24411yescharacteristic
297C2×C22⋊C4C22⋊D6111yescharacteristic
298C2×C22⋊C4C22×D6111yescharacteristic
299C2×C42—1221no—
300C22⋊C8—1222no—
301C22⋊C8—2441no—
302#95—611no—
303#95—611no—
304C24—21no—
305C24—21no—
306C24—21no—
307C24—22no—
308C24—21no—
309C24—42no—
310C24—81no—
311C24—1221no—
312C24#1175819811yescharacteristic
313C24#1175819811yescharacteristic
314C24C2×C22⋊D6111yescharacteristic
315C2×D4—4881no—
316C2×D4—4881no—
317C2×D4—4881no—
318C2×D4—2441no—
319C2×D4—2442no—
320C2×D4—2442no—
321C2×D4—2442no—
322C2×D4—2442no—
323C2×D4—2441no—
324C2×D4—2441no—
325C2×D4—2441no—
326C2×D4—2442no—
327C2×D4—2441no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—42no—
333C22×C4—44no—
334C22×C4—42no—
335C22×C4—81no—
336C22×C4—82no—
337C22×C4—82no—
338C22×C4—1221no—
339C22×C4—1221no—
340C22×C4—1221no—
341C22×C4#1175819811yescharacteristic
342C22×C4#1175819811yescharacteristic
343C22×C4C2×C4×D6111yescharacteristic
344C22×C4C2×D24411yescharacteristic
345M16—4882no—
346C2×C8—2442no—
347C4⋊C4—2441no—
348C4⋊C4—2442no—
349C4⋊C4—2442no—
350C22⋊C4—24no—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—44no—
356C22⋊C4—42no—
357C22⋊C4—1224no—
358C22⋊C4—2442no—
359C22⋊C4—2442no—
360C22⋊C4—2442no—
361C22⋊C4—2442no—
362C22⋊C4—2442no—
363C42—4881no—
364C23—22no—
365C23—22no—
366C23—22no—
367C23—22no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—22no—
373C23—21no—
374C23—21no—
375C23—41no—
376C23—42no—
377C23—41no—
378C23—41no—
379C23—41no—
380C23—41no—
381C23—42no—
382C23—81no—
383C23—81no—
384C23—82no—
385C23—84no—
386C23—82no—
387C23—2441no—
388C23—2441no—
389C23—2441no—
390C23—2441no—
391C23—2441no—
392C23—2441no—
393C23—2441no—
394C23#1451969111yescharacteristic
395C23#1451969111yescharacteristic
396C23#1451970512yes—
397C23C2×#1175819811yescharacteristic
398C23#1451980311yescharacteristic
399C23#1451980811yescharacteristic
400D4—4882no—
401D4—4882no—
402D4—4882no—
403D4—4882no—
404D4—4884no—
405D4—4882no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—42no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—44no—
416C2×C4—81no—
417C2×C4—81no—
418C2×C4—81no—
419C2×C4—88no—
420C2×C4—82no—
421C2×C4—82no—
422C2×C4—1222no—
423C2×C4—1222no—
424C2×C4—2441no—
425C2×C4—2441no—
426C2×C4—2441no—
427C2×C4—2441no—
428C2×C4—2441no—
429C2×C4—2441no—
430C2×C4—2441no—
431C8—4882no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—22no—
442C22—42no—
443C22—42no—
444C22—41no—
445C22—42no—
446C22—41no—
447C22—44no—
448C22—44no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—81no—
454C22—81no—
455C22—82no—
456C22—82no—
457C22—4881no—
458C22—4881no—
459C22—4881no—
460C22—4881no—
461C22—4881no—
462C22—4881no—
463C22—4881no—
464C22#1683955412yes—
465C22C2×#1451969111yescharacteristic
466C22#1683976111yescharacteristic
467C22C2×#1451970511yescharacteristic
468C4—41no—
469C4—41no—
470C4—41no—
471C4—41no—
472C4—84no—
473C4—4881no—
474C4—2442no—
475C4—2442no—
476C2—21no—
477C2—21no—
478C2—22no—
479C2—41no—
480C2—41no—
481C2—41no—
482C2—42no—
483C2—9761no—
484C2#2144432111yescharacteristic
485C2#2144746311yescharacteristic
486C2C2×#1683955411yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC2×C61×#342C2
socleC22×C61C2×#99
prime radical#21450750C2
cosocleC2×C22⋊C4×C61C23
hypercenterC2×#342D61
hypocenterC61#11757
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
2. #21444146C2semidirect
3. #21443842C2semidirect
4. #21443815C2semidirect
5. C2×C61×#342C2semidirect
7. C2×#14519751C4semidirect
10. #16839698C4semidirect
12. #16839671C4semidirect
16. C4×C22⋊Dic61C4semidirect
23. C22×D244C2×C4semidirect
32. C2×C4⋊Dic61C2×C4semidirect
44. #14519684C2×C4semidirect
45. #14519684C2×C4semidirect
234. C2×#342D61semidirect
266. C61#11757semidirect

Maximal subgroups

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

subgroupindex
#214507502
#214441462
#214438422
#214438152
C2×C61×#3422
#1175761