Finite Group Databasebeta

← #29590872

Subgroups — #29590872

Order 15616.

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

normal subgroups only

This group has 698 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#21449138C211yesmaximal, characteristic
2#21445893C211yesmaximal, characteristic, complemented
3#21443841C212yesmaximal, complemented
4#21443817C212yesmaximal, complemented
5C2×C61×#323C211yesmaximal, characteristic, complemented
6C22×#11758222C411yescharacteristic, complemented
7C2×#14519746—21no—
8#16839674C411yescharacteristic, complemented
9#16839674C2211yescharacteristic
10#16839671C411yescharacteristic, complemented
11#16839671C2211yescharacteristic
12#16839641—21no—
13#16839638—21no—
14#16839638—21no—
15#16839625C411yescharacteristic, complemented
16#16839618—21no—
17#16839529—21no—
18#16839529C2212yes—
19C22×C22⋊C4×C61C2211yescharacteristic
20C2×C22⋊C8×C61—21no—
21C61×#323—21no—
22C61×#323C2212yes—
23C2×#11758222—41no—
24C2×#11758222—41no—
25C2×#11758222—44no—
26C22×Dic122C2×C411yescharacteristic
27C22×D244C2×C411yescharacteristic
28C22×C22⋊D61—21no—
29C22×C22⋊D61—21no—
30C22×C22⋊D61—21no—
31C22×C4×D61—21no—
32#14519746—44no—
33C2×C22⋊Dic61—21no—
34C2×C22⋊Dic61—21no—
35C2×C22⋊Dic61—21no—
36C2×C22⋊Dic61—22no—
37C2×C22⋊Dic61—41no—
38C2×C22⋊Dic61—41no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684C2×C411yescharacteristic
45#14519684C2×C411yescharacteristic
46C25×C61D411yescharacteristic
47C23×C4×C61C2×C411yescharacteristic
48C23×C4×C61D411yescharacteristic
49C22×C8×C61—41no—
50C2×C22⋊C4×C61—41no—
51C2×C22⋊C4×C61—41no—
52C2×C22⋊C4×C61C2×C411yescharacteristic
53C2×C22⋊C4×C61D411yescharacteristic
54C2×C22⋊C4×C61D411yescharacteristic
55C2×C22⋊C4×C61C2311yescharacteristic
56C22⋊C8×C61—22no—
57C22⋊C8×C61—41no—
58C24×C61—21no—
59C24×C61—21no—
60C24×C61—22no—
61C24×C61—41no—
62C24×C61—42no—
63C24×C61—81no—
64C24×C61C22⋊C411yescharacteristic
65C24×C61C22⋊C411yescharacteristic
66C24×C61C2×D411yescharacteristic
67C23×D61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61—21no—
72C22×C4×C61—42no—
73C22×C4×C61—81no—
74C22×C4×C61C22⋊C411yescharacteristic
75C22×C4×C61C22⋊C411yescharacteristic
76C22×C4×C61C22×C411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C2×C22⋊D61—24no—
79C2×C22⋊D61—42no—
80C2×C22⋊D61—41no—
81C2×C22⋊D61—41no—
82C2×C22⋊D61—42no—
83C2×C22⋊D61—42no—
84C2×C22⋊D61—42no—
85C2×C22⋊D61—42no—
86C2×C22⋊D61—81no—
87C2×C22⋊D61—81no—
88C22×Dic61—21no—
89C22×Dic61—21no—
90C22×Dic61—21no—
91C22×Dic61—42no—
92#11758222—44no—
93#11758222—44no—
94#11758222—44no—
95#11758222—44no—
96C2×D244—41no—
97C2×D244—42no—
98C2×C4×D61—42no—
99C2×C4×D61—42no—
100C2×C4×D61—42no—
101C2×Dic122—41no—
102C2×Dic122—42no—
103C2×C8×C61—42no—
104C2×C8×C61—82no—
105C22⋊C4×C61—41no—
106C22⋊C4×C61—41no—
107C22⋊C4×C61—41no—
108C22⋊C4×C61—41no—
109C22⋊Dic61—42no—
110C22⋊Dic61—42no—
111C22⋊Dic61—42no—
112C22⋊Dic61—42no—
113C22⋊Dic61—42no—
114C22⋊Dic61—82no—
115C22⋊Dic61—82no—
116#11758198—81no—
117#11758198—81no—
118C23×C61—22no—
119C23×C61—21no—
120C23×C61—21no—
121C23×C61—21no—
122C23×C61—21no—
123C23×C61—21no—
124C23×C61—21no—
125C23×C61—21no—
126C23×C61—41no—
127C23×C61—42no—
128C23×C61—42no—
129C23×C61—41no—
130C23×C61—41no—
131C23×C61—41no—
132C23×C61—41no—
133C23×C61—42no—
134C23×C61—42no—
135C23×C61—81no—
136C23×C61—81no—
137C23×C61—84no—
138C23×C61—84no—
139C23×C61#9911yescharacteristic
140C23×C61#9911yescharacteristic
141C23×C61C2×C22⋊C411yescharacteristic
142C23×C61#13512yes—
143C22×D61—22no—
144C22×D61—41no—
145C22×D61—41no—
146C22×D61—41no—
147C22×D61—41no—
148C22×D61—41no—
149C22×D61—41no—
150C2×C4×C61—21no—
151C2×C4×C61—21no—
152C2×C4×C61—21no—
153C2×C4×C61—21no—
154C2×C4×C61—42no—
155C2×C4×C61—42no—
156C2×C4×C61—42no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61—81no—
162C22⋊D61—44no—
163C22⋊D61—44no—
164C22⋊D61—84no—
165C22⋊D61—84no—
166C2×Dic61—22no—
167C2×Dic61—41no—
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61—41no—
171C2×Dic61—41no—
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61—41no—
175C2×Dic61—82no—
176C2×Dic61—82no—
177C2×Dic61—82no—
178D244—42no—
179D244—42no—
180C4×D61—48no—
181Dic122—42no—
182Dic122—42no—
183C8×C61—82no—
184#11839—611nomaximal, Sylow
185C22×C61—21no—
186C22×C61—21no—
187C22×C61—21no—
188C22×C61—21no—
189C22×C61—21no—
190C22×C61—21no—
191C22×C61—22no—
192C22×C61—21no—
193C22×C61—42no—
194C22×C61—42no—
195C22×C61—42no—
196C22×C61—42no—
197C22×C61—41no—
198C22×C61—41no—
199C22×C61—41no—
200C22×C61—41no—
201C22×C61—41no—
202C22×C61—81no—
203C22×C61—84no—
204C22×C61—81no—
205C22×C61—84no—
206C22×C61AΣL(1,𝔽16)12yes—
207C22×C61C2×#9911yescharacteristic
208C22×C61#41611yescharacteristic
209C22×C61#42111yescharacteristic
210C2×D61—42no—
211C2×D61—42no—
212C2×D61—42no—
213C2×D61—81no—
214C2×D61—81no—
215C2×D61—81no—
216C2×D61—81no—
217C4×C61—41no—
218C4×C61—41no—
219C4×C61—41no—
220C4×C61—41no—
221Dic61—42no—
222Dic61—81no—
223Dic61—81no—
224Dic61—162no—
225#2404—611no—
226#1819—611no—
227C2×#323D6111yescharacteristic, complemented
228#1351—612no—
229#1343—612no—
230C2×C61—21no—
231C2×C61—21no—
232C2×C61—22no—
233C2×C61—42no—
234C2×C61—41no—
235C2×C61—81no—
236C2×C61#151611yescharacteristic
237C2×C61C2×AΣL(1,𝔽16)11yescharacteristic
238C2×C61#212711yescharacteristic
239D61—82no—
240C22×#41—611no—
241C2×#120—1221no—
242C22×C22⋊C4C2×D6111yescharacteristic
243C2×C22⋊C8—21no—
244#393—611no—
245#393—611no—
246#392—611no—
247#392—611no—
248#386—1221no—
249#386—1221no—
250#386—1221no—
251#381—611no—
252#379—1221no—
253#342—612no—
254#342—1221no—
255#323—21no—
256#323C2×D6112yes—
257C61#1183911yescharacteristic, complemented, Sylow
258C25D24411yescharacteristic
259C2×#41—2441no—
260C2×#41—2441no—
261C2×#41—2444no—
262C22×Q8—611no—
263C22×D4—611no—
264C22×D4—1221no—
265C22×D4—1221no—
266C22×D4—1221no—
267C23×C4—1221no—
268C23×C4C4×D6111yescharacteristic
269C23×C4C22⋊D6111yescharacteristic
270C22×C8—41no—
271#120—2444no—
272C2×C22⋊C4—41no—
273C2×C22⋊C4—41no—
274C2×C22⋊C4—1221no—
275C2×C22⋊C4—1221no—
276C2×C22⋊C4—1221no—
277C2×C22⋊C4—1221no—
278C2×C22⋊C4—1221no—
279C2×C22⋊C4—1222no—
280C2×C22⋊C4—2441no—
281C2×C22⋊C4—2441no—
282C2×C22⋊C4C4×D6111yescharacteristic
283C2×C22⋊C4D24411yescharacteristic
284C2×C22⋊C4C22⋊D6111yescharacteristic
285C2×C22⋊C4C22×D6111yescharacteristic
286C22⋊C8—22no—
287C22⋊C8—41no—
288#95—611no—
289#95—611no—
290#95—1221no—
291#95—1221no—
292#95—1221no—
293C24—21no—
294C24—21no—
295C24—22no—
296C24—41no—
297C24—42no—
298C24—81no—
299C24—1221no—
300C24#1175819811yescharacteristic
301C24#1175819811yescharacteristic
302C24C2×D24411yescharacteristic
303#41—2444no—
304#41—2444no—
305#41—2444no—
306#41—2444no—
307C2×Q8—2441no—
308C2×Q8—2442no—
309C2×D4—1224no—
310C2×D4—4881no—
311C2×D4—4881no—
312C2×D4—2441no—
313C2×D4—2442no—
314C2×D4—2442no—
315C2×D4—2442no—
316C2×D4—2442no—
317C2×D4—2442no—
318C2×D4—2442no—
319C2×D4—2441no—
320C2×D4—2441no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—42no—
326C22×C4—81no—
327C22×C4—1221no—
328C22×C4—1221no—
329C22×C4—1221no—
330C22×C4—2442no—
331C22×C4—2442no—
332C22×C4—2442no—
333C22×C4—2442no—
334C22×C4#1175819811yescharacteristic
335C22×C4#1175819811yescharacteristic
336C22×C4C2×C4×D6111yescharacteristic
337C22×C4C2×C22⋊D6111yescharacteristic
338C2×C8—42no—
339C2×C8—82no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C22⋊C4—4881no—
345C22⋊C4—4881no—
346C22⋊C4—4882no—
347C22⋊C4—4882no—
348C22⋊C4—2442no—
349C22⋊C4—2442no—
350C22⋊C4—2442no—
351C22⋊C4—2442no—
352C22⋊C4—2442no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—22no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—41no—
362C23—42no—
363C23—42no—
364C23—41no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23—42no—
369C23—42no—
370C23—81no—
371C23—81no—
372C23—84no—
373C23—84no—
374C23—1222no—
375C23—2441no—
376C23—2441no—
377C23—2441no—
378C23—2441no—
379C23—2441no—
380C23—2441no—
381C23#1451969111yescharacteristic
382C23#1451969111yescharacteristic
383C23C2×#1175819811yescharacteristic
384C23#1451979912yes—
385Q8—2442no—
386Q8—2442no—
387D4—4884no—
388D4—4884no—
389D4—2442no—
390D4—2442no—
391D4—2444no—
392D4—2444no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—81no—
405C2×C4—1222no—
406C2×C4—4882no—
407C2×C4—4882no—
408C2×C4—4882no—
409C2×C4—2448no—
410C2×C4—2441no—
411C2×C4—2441no—
412C2×C4—2441no—
413C2×C4—2441no—
414C2×C4—2441no—
415C2×C4—2441no—
416C2×C4—2441no—
417C2×C4—2441no—
418C8—82no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—22no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—42no—
428C22—42no—
429C22—42no—
430C22—42no—
431C22—41no—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—81no—
437C22—84no—
438C22—81no—
439C22—84no—
440C22—4881no—
441C22—4881no—
442C22—4881no—
443C22—4881no—
444C22—2442no—
445C22—2442no—
446C22—2442no—
447C22#1683955012yes—
448C22C2×#1451969111yescharacteristic
449C22#1683975911yescharacteristic
450C22#1683977811yescharacteristic
451C4—41no—
452C4—41no—
453C4—41no—
454C4—41no—
455C4—9762no—
456C4—4881no—
457C4—4881no—
458C4—2442no—
459C2—21no—
460C2—21no—
461C2—22no—
462C2—42no—
463C2—41no—
464C2—81no—
465C2—4882no—
466C2#2144437611yescharacteristic
467C2C2×#1683955011yescharacteristic
468C2#2144748611yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC2×C61×#323C2
socleC22×C61C2×#99
prime radical#21449138C2
cosocleC2×C22⋊C4×C61C23
hypercenterC2×#323D61
hypocenterC61#11839
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ C2×#323

Complements

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

NH ≅ G/Ntype
2. #21445893C2semidirect
3. #21443841C2semidirect
4. #21443817C2semidirect
5. C2×C61×#323C2semidirect
6. C22×#11758222C4semidirect
8. #16839674C4semidirect
10. #16839671C4semidirect
15. #16839625C4semidirect
227. C2×#323D61semidirect
257. C61#11839semidirect

Maximal subgroups

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

subgroupindex
#214491382
#214458932
#214438412
#214438172
C2×C61×#3232
#1183961