Finite Group Databasebeta

← #29583343

Subgroups — #29583343

Order 15616.

716 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 716 conjugacy classes of subgroups — too many to draw. Only its 113 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#21451921C211yesmaximal, characteristic
2#21446134C212yesmaximal, complemented
3C2×#16839497C212yesmaximal, complemented
4#21444075C211yesmaximal, characteristic, complemented
5C61×#1280C211yesmaximal, characteristic, complemented
6C2×#14519751—21no—
7C2×#14519751—21no—
8C2×#14519751C2212yes—
9C22×C4⋊Dic61C2211yescharacteristic
10C2×#14519699—22no—
11#16839699—22no—
12#16839672—22no—
13C2×#14519684—21no—
14C2×#14519684—21no—
15C2×#14519684C2211yescharacteristic
16#16839525—22no—
17#16839497—24no—
18C2×C22⋊C8×C61C2212yes—
19C2×#95×C61C2211yescharacteristic
20C22×D244—21no—
21C22×D244—21no—
22C22×D244D412yes—
23C22×C22⋊D61—22no—
24C23×Dic61—21no—
25C23×Dic61—21no—
26#14519751—22no—
27#14519751—22no—
28#14519751—22no—
29#14519751—22no—
30#14519751—42no—
31#14519751—42no—
32#14519751—42no—
33#14519751—42no—
34C2×C4⋊Dic61—22no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61—42no—
38C2×C4⋊Dic61D412yes—
39C2×#11758198—22no—
40C2×#11758198—22no—
41C2×#11758198—22no—
42#14519699—44no—
43#14519684—21no—
44#14519684—42no—
45#14519684—42no—
46#14519684D412yescomplemented
47C23×C4×C61D411yescharacteristic
48C23×C4×C61D411yescharacteristic
49C23×C4×C61C2311yescharacteristic
50C22×C8×C61—22no—
51C22⋊C8×C61—22no—
52C22⋊C8×C61—22no—
53#95×C61—22no—
54C24×C61C2×D411yescharacteristic
55C23×D61—22no—
56C22×C4×C61—21no—
57C22×C4×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61—41no—
61C22×C4×C61—41no—
62C22×C4×C61—41no—
63C22×C4×C61—41no—
64C22×C4×C61—41no—
65C22×C4×C61—41no—
66C22×C4×C61D812yes—
67C22×C4×C61SD1612yes—
68C22×C4×C61C2×D412yes—
69C22×C4×C61C2×D411yescharacteristic
70C22×C4×C61#4112yes—
71C22×C4×C61#4111yescharacteristic
72C2×C22⋊D61—42no—
73C2×C22⋊D61—42no—
74C2×C22⋊D61—42no—
75C2×C22⋊D61—42no—
76C2×C22⋊D61—42no—
77C2×C22⋊D61—42no—
78C22×Dic61—22no—
79C22×Dic61—22no—
80C22×Dic61—22no—
81C22×Dic61—41no—
82C22×Dic61—41no—
83C22×Dic61—41no—
84C22×Dic61—41no—
85C22×Dic61—41no—
86C22×Dic61—41no—
87C22×Dic61—41no—
88C22×Dic61—41no—
89C22×Dic61—41no—
90C22×Dic61—41no—
91C22×Dic61—41no—
92C22×Dic61—41no—
93C2×D244—22no—
94C2×D244—22no—
95C2×D244—42no—
96C2×D244—42no—
97C2×D244—42no—
98C2×D244—42no—
99C2×D244—81no—
100C2×D244—81no—
101C2×D244—81no—
102C2×D244—81no—
103C2×C8×C61—42no—
104C2×C8×C61—42no—
105C2×C8×C61—42no—
106#11758198—44no—
107#11758198—44no—
108#11758198—42no—
109#11758198—42no—
110C4⋊Dic61—24no—
111C4⋊Dic61—22no—
112C4⋊Dic61—22no—
113C4⋊Dic61—42no—
114C4⋊Dic61—42no—
115C4⋊Dic61—42no—
116C23×C61—21no—
117C23×C61—21no—
118C23×C61—21no—
119C23×C61—21no—
120C23×C61#12011yescharacteristic
121C23×C61#12111yescharacteristic
122C23×C61#12411yescharacteristic
123C23×C61C2×D811yescharacteristic
124C23×C61C2×SD1611yescharacteristic
125C23×C61AGL(1,ℤ/8)11yescharacteristic
126C23×C61AGL(1,ℤ/8)11yescharacteristic
127C22×D61—42no—
128C22×D61—42no—
129C22×D61—42no—
130C22×D61—42no—
131C22×D61—42no—
132C22×D61—42no—
133C22×D61—42no—
134C2×C4×C61—22no—
135C2×C4×C61—22no—
136C2×C4×C61—22no—
137C2×C4×C61—22no—
138C2×C4×C61—41no—
139C2×C4×C61—42no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—42no—
146C2×C4×C61—42no—
147C2×C4×C61—81no—
148C2×C4×C61—81no—
149C2×C4×C61#12112yes—
150C2×C4×C61#12312yes—
151C22⋊D61—82no—
152C22⋊D61—82no—
153C22⋊D61—82no—
154C22⋊D61—82no—
155C2×Dic61—42no—
156C2×Dic61—42no—
157C2×Dic61—42no—
158C2×Dic61—42no—
159C2×Dic61—42no—
160C2×Dic61—42no—
161C2×Dic61—42no—
162C2×Dic61—42no—
163C2×Dic61—42no—
164C2×Dic61—81no—
165C2×Dic61—81no—
166C2×Dic61—81no—
167C2×Dic61—81no—
168C2×Dic61—81no—
169C2×Dic61—81no—
170C2×Dic61—81no—
171C2×Dic61—81no—
172D244—44no—
173D244—82no—
174D244—84no—
175D244—84no—
176C8×C61—82no—
177#10403—611nomaximal, Sylow
178C22×C61—21no—
179C22×C61—21no—
180C22×C61—21no—
181C22×C61—21no—
182C22×C61—21no—
183C22×C61—21no—
184C22×C61—21no—
185C22×C61—21no—
186C22×C61—21no—
187C22×C61—21no—
188C22×C61—21no—
189C22×C61—21no—
190C22×C61#39411yescharacteristic
191C22×C61#44711yescharacteristic
192C22×C61#45011yescharacteristic
193C22×C61#45411yescharacteristic
194C22×C61#45511yescharacteristic
195C22×C61B(4,𝔽2)11yescharacteristic
196C22×C61#45811yescharacteristic
197C22×C61#45911yescharacteristic
198C22×C61#46011yescharacteristic
199C22×C61#48611yescharacteristic
200C22×C61#49011yescharacteristic
201C2×D61—82no—
202C2×D61—82no—
203C2×D61—82no—
204C2×D61—82no—
205C2×D61—82no—
206C2×D61—82no—
207C2×D61—82no—
208C4×C61—22no—
209C4×C61—22no—
210C4×C61—42no—
211C4×C61—42no—
212Dic61—82no—
213Dic61—82no—
214Dic61—82no—
215#2656—611no—
216#1874—612no—
217C2×#327—612no—
218#1442—611no—
219#1280D6111yescharacteristic, complemented
220C2×C61—21no—
221C2×C61—21no—
222C2×C61—21no—
223C2×C61—21no—
224C2×C61#159811yescharacteristic
225C2×C61#160111yescharacteristic
226C2×C61#160711yescharacteristic
227C2×C61#161611yescharacteristic
228C2×C61#204011yescharacteristic
229C2×C61#204111yescharacteristic
230C2×C61#204411yescharacteristic
231D61—162no—
232C2×#121—612no—
233C2×#121—1221no—
234C2×#121—1221no—
235C22×C4⋊C4—611no—
236C2×#102—1222no—
237C2×C22⋊C8C2×D6112yes—
238#399—1222no—
239#392—1222no—
240C2×#95—611no—
241C2×#95—1221no—
242C2×#95—1221no—
243C2×#95C2×D6111yescharacteristic
244#340—1222no—
245#327—1224no—
246C61#1040311yescharacteristic, complemented, Sylow
247C22×D4—612no—
248C22×D4—1221no—
249C22×D4—1221no—
250C22×D4—1222no—
251C23×C4—1221no—
252C23×C4—1221no—
253C23×C4D24411yescharacteristic
254C23×C4D24411yescharacteristic
255C23×C4C22×D6111yescharacteristic
256C22×C8—22no—
257#121—1222no—
258#121—1222no—
259#121—1222no—
260#121—1222no—
261#121—2442no—
262#121—2442no—
263#121—2442no—
264#121—2442no—
265C2×C4⋊C4—612no—
266C2×C4⋊C4—1222no—
267C2×C4⋊C4—1221no—
268C2×C4⋊C4—1221no—
269C2×C4⋊C4—2442no—
270C2×C22⋊C4—1222no—
271C2×C22⋊C4—1222no—
272C2×C22⋊C4—1222no—
273#102—2444no—
274C22⋊C8—22no—
275C22⋊C8—22no—
276#95—22no—
277#95—612no—
278#95—1221no—
279#95—2442no—
280#95—2442no—
281C24—1222no—
282C24C2×D24411yescharacteristic
283C2×D4—1222no—
284C2×D4—1222no—
285C2×D4—4881no—
286C2×D4—4881no—
287C2×D4—4881no—
288C2×D4—4881no—
289C2×D4—2442no—
290C2×D4—2442no—
291C2×D4—2442no—
292C2×D4—2442no—
293C2×D4—2442no—
294C2×D4—2442no—
295C2×D4—2442no—
296C2×D4—2442no—
297C2×D4—2442no—
298C2×D4—2442no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—1222no—
310C22×C4—1222no—
311C22×C4—1222no—
312C22×C4—2441no—
313C22×C4—2441no—
314C22×C4—2441no—
315C22×C4—2441no—
316C22×C4—2441no—
317C22×C4—2441no—
318C22×C4—2441no—
319C22×C4—2441no—
320C22×C4—2441no—
321C22×C4—2441no—
322C22×C4—2441no—
323C22×C4—2441no—
324C22×C4#1175819012yes—
325C22×C4D48812yes—
326C22×C4#1175822212yes—
327C22×C4D4×D6112yes—
328C22×C4D4×D6111yescharacteristic
329C22×C4#1175822611yescharacteristic
330C2×C8—42no—
331C2×C8—42no—
332C2×C8—42no—
333C4⋊C4—1224no—
334C4⋊C4—1222no—
335C4⋊C4—1222no—
336C4⋊C4—2442no—
337C4⋊C4—2442no—
338C4⋊C4—2442no—
339C22⋊C4—2444no—
340C22⋊C4—2444no—
341C22⋊C4—2442no—
342C22⋊C4—2442no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—2442no—
348C23—2442no—
349C23—2442no—
350C23—2442no—
351C23—2442no—
352C23—2442no—
353C23—2442no—
354C23#1451974711yescharacteristic
355C23#1451975211yescharacteristic
356C23#1451976511yescharacteristic
357C23C2×D48811yescharacteristic
358C23C2×#1175819011yescharacteristic
359C23#1451980511yescharacteristic
360C23#1451980511yescharacteristic
361D4—4882no—
362D4—4884no—
363D4—4884no—
364D4—4882no—
365D4—4882no—
366D4—4882no—
367D4—4882no—
368D4—2444no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—42no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—4881no—
385C2×C4—4881no—
386C2×C4—4881no—
387C2×C4—4881no—
388C2×C4—4881no—
389C2×C4—4881no—
390C2×C4—4881no—
391C2×C4—4881no—
392C2×C4—2442no—
393C2×C4—2442no—
394C2×C4—2442no—
395C2×C4—2442no—
396C2×C4—2442no—
397C2×C4—2442no—
398C2×C4—2442no—
399C2×C4—2442no—
400C2×C4—2442no—
401C2×C4#1451975012yes—
402C2×C4#1451976212yes—
403C8—82no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—4882no—
417C22—4882no—
418C22—4882no—
419C22—4882no—
420C22—4882no—
421C22—4882no—
422C22—4882no—
423C22#1683968011yescharacteristic
424C22#1683989811yescharacteristic
425C22#1683991511yescharacteristic
426C22#1683993711yescharacteristic
427C22#1683994211yescharacteristic
428C22#1683995011yescharacteristic
429C22#1683995311yescharacteristic
430C22#1683995811yescharacteristic
431C22#1683996311yescharacteristic
432C22#1684010911yescharacteristic
433C22#1684012711yescharacteristic
434C4—22no—
435C4—22no—
436C4—42no—
437C4—42no—
438C4—4882no—
439C4—4882no—
440C4—4882no—
441C2—21no—
442C2—21no—
443C2—21no—
444C2—21no—
445C2—9762no—
446C2#2144475611yescharacteristic
447C2#2144477311yescharacteristic
448C2#2144480711yescharacteristic
449C2#2144485811yescharacteristic
450C2#2144704911yescharacteristic
451C2#2144705411yescharacteristic
452C2#2144707111yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#1280C2
socleC23×C61#120
prime radical#21451921C2
hypercenter#1280D61
hypocenterC61#10403
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
2. #21446134C2semidirect
3. C2×#16839497C2semidirect
4. #21444075C2semidirect
5. C61×#1280C2semidirect
46. #14519684D4semidirect
219. #1280D61semidirect
246. C61#10403semidirect

Maximal subgroups

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

subgroupindex
#214519212
#214461342
C2×#168394972
#214440752
C61×#12802
#1040361