Finite Group Databasebeta

← #29575786

Subgroups — #29575786

Order 15616.

1024 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454101C211yesmaximal, characteristic
2C2×#16839622C211yesmaximal, characteristic, complemented
3C2×#16839497C212yesmaximal, complemented
4#21443699C212yesmaximal, complemented
5C61×#1779C211yesmaximal, characteristic, complemented
6C2×#14519751C412yescomplemented
7C2×#14519751C2211yescharacteristic
8C2×#14519746—21no—
9C22×C4⋊Dic61—21no—
10C22×C22⋊Dic61—21no—
11#16839641—22no—
12#16839641—21no—
13#16839622—24no—
14#16839622C412yescomplemented
15#16839622C2211yescharacteristic
16C2×#14519684C2212yes—
17#16839497—24no—
18C24×C4×C61C2211yescharacteristic
19C2×C22⋊C8×C61—22no—
20C2×C22⋊C8×C61C2212yes—
21C22×D244C2×C411yescharacteristic
22C22×C22⋊D61—22no—
23C22×C22⋊D61—21no—
24C23×Dic61—22no—
25#14519751—22no—
26#14519751—22no—
27#14519751—44no—
28#14519746—42no—
29#14519746—42no—
30C2×C4⋊Dic61—24no—
31C2×C4⋊Dic61—44no—
32C2×C4⋊Dic61C2×C411yescharacteristic
33C2×C4⋊Dic61C2×C412yes—
34C2×C22⋊Dic61—24no—
35C2×C22⋊Dic61—22no—
36C2×C22⋊Dic61—21no—
37C2×C22⋊Dic61—42no—
38C2×C22⋊Dic61—42no—
39C2×#11758198—22no—
40C2×#11758198—21no—
41#14519684—22no—
42#14519684—22no—
43#14519684—21no—
44#14519684D414yescomplemented
45C25×C61D411yescharacteristic
46C23×C4×C61—22no—
47C23×C4×C61—22no—
48C23×C4×C61—44no—
49C23×C4×C61C2×C412yes—
50C23×C4×C61D411yescharacteristic
51C23×C4×C61D412yes—
52C23×C4×C61C2311yescharacteristic
53C22×C8×C61—22no—
54C22⋊C8×C61—22no—
55C22⋊C8×C61—22no—
56C22⋊C8×C61—44no—
57C24×C61—21no—
58C24×C61—21no—
59C24×C61—21no—
60C24×C61—21no—
61C24×C61—42no—
62C24×C61—42no—
63C24×C61C22⋊C412yes—
64C24×C61D812yes—
65C24×C61SD1612yes—
66C24×C61C2×D411yescharacteristic
67C23×D61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—24no—
71C22×C4×C61—24no—
72C22×C4×C61—24no—
73C22×C4×C61—24no—
74C22×C4×C61—24no—
75C22×C4×C61—42no—
76C22×C4×C61—42no—
77C22×C4×C61—42no—
78C22×C4×C61—48no—
79C22×C4×C61—48no—
80C22×C4×C61C22⋊C412yes—
81C22×C4×C61C22×C411yescharacteristic
82C22×C4×C61C2×D411yescharacteristic
83C22×C4×C61C2×D412yes—
84C22×C4×C61#4112yes—
85C2×C22⋊D61—44no—
86C2×C22⋊D61—44no—
87C2×C22⋊D61—44no—
88C2×C22⋊D61—41no—
89C2×C22⋊D61—41no—
90C2×C22⋊D61—41no—
91C2×C22⋊D61—41no—
92C2×C22⋊D61—41no—
93C2×C22⋊D61—41no—
94C22×Dic61—21no—
95C22×Dic61—22no—
96C22×Dic61—24no—
97C22×Dic61—44no—
98C22×Dic61—44no—
99C22×Dic61—42no—
100C22×Dic61—42no—
101C2×D244—22no—
102C2×D244—42no—
103C2×C8×C61—44no—
104C2×C8×C61—42no—
105C22⋊Dic61—48no—
106C22⋊Dic61—44no—
107C22⋊Dic61—41no—
108C22⋊Dic61—41no—
109#11758198—44no—
110#11758198—42no—
111C4⋊Dic61—22no—
112C4⋊Dic61—48no—
113C4⋊Dic61—42no—
114C23×C61—22no—
115C23×C61—22no—
116C23×C61—22no—
117C23×C61—22no—
118C23×C61—22no—
119C23×C61—22no—
120C23×C61—22no—
121C23×C61—22no—
122C23×C61—22no—
123C23×C61—22no—
124C23×C61—22no—
125C23×C61—22no—
126C23×C61—44no—
127C23×C61—44no—
128C23×C61—42no—
129C23×C61—42no—
130C23×C61—42no—
131C23×C61—42no—
132C23×C61—44no—
133C23×C61—44no—
134C23×C61#10214yes—
135C23×C61C2×C22⋊C411yescharacteristic
136C23×C61#12011yescharacteristic
137C23×C61#12311yescharacteristic
138C23×C61C2×D811yescharacteristic
139C23×C61C2×SD1611yescharacteristic
140C23×C61AGL(1,ℤ/8)11yescharacteristic
141C23×C61#13711yescharacteristic
142C22×D61—41no—
143C22×D61—42no—
144C22×D61—41no—
145C22×D61—41no—
146C22×D61—42no—
147C2×C4×C61—24no—
148C2×C4×C61—24no—
149C2×C4×C61—22no—
150C2×C4×C61—22no—
151C2×C4×C61—22no—
152C2×C4×C61—22no—
153C2×C4×C61—42no—
154C2×C4×C61—42no—
155C2×C4×C61—48no—
156C2×C4×C61—48no—
157C2×C4×C61#9914yes—
158C2×C4×C61C4×D412yes—
159C2×C4×C61#12112yes—
160C22⋊D61—88no—
161C22⋊D61—81no—
162C22⋊D61—81no—
163C22⋊D61—81no—
164C22⋊D61—81no—
165C2×Dic61—44no—
166C2×Dic61—44no—
167C2×Dic61—41no—
168C2×Dic61—42no—
169C2×Dic61—41no—
170C2×Dic61—42no—
171C2×Dic61—41no—
172C2×Dic61—42no—
173C2×Dic61—44no—
174C2×Dic61—84no—
175C2×Dic61—84no—
176D244—82no—
177C8×C61—82no—
178#9155—611nomaximal, Sylow
179C22×C61—21no—
180C22×C61—21no—
181C22×C61—21no—
182C22×C61—21no—
183C22×C61—22no—
184C22×C61—22no—
185C22×C61—22no—
186C22×C61—22no—
187C22×C61—24no—
188C22×C61—24no—
189C22×C61—24no—
190C22×C61—44no—
191C22×C61—44no—
192C22×C61—44no—
193C22×C61—44no—
194C22×C61—42no—
195C22×C61—42no—
196C22×C61—42no—
197C22×C61—42no—
198C22×C61#38611yescharacteristic
199C22×C61C2×#9912yes—
200C22×C61C2×#10211yescharacteristic
201C22×C61#41711yescharacteristic
202C22×C61#42112yes—
203C22×C61#44711yescharacteristic
204C22×C61#44811yescharacteristic
205C22×C61#48011yescharacteristic
206C22×C61#48111yescharacteristic
207C2×D61—81no—
208C2×D61—81no—
209C2×D61—81no—
210C2×D61—82no—
211C2×D61—82no—
212C4×C61—22no—
213C4×C61—22no—
214C4×C61—24no—
215Dic61—84no—
216Dic61—81no—
217Dic61—82no—
218#2847—611no—
219C2×#380—611no—
220#1779D6111yescharacteristic, complemented
221C2×#327—612no—
222#1294—612no—
223C2×C61—21no—
224C2×C61—21no—
225C2×C61—21no—
226C2×C61—21no—
227C2×C61—44no—
228C2×C61#151312yes—
229C2×C61#151912yes—
230C2×C61#187411yescharacteristic
231C2×C61#189711yescharacteristic
232C2×C61#189811yescharacteristic
233D61—161no—
234C24×C4C2×D6111yescharacteristic
235C2×#121—611no—
236C2×#121—612no—
237C2×#120—1221no—
238C22×C4⋊C4—1221no—
239C22×C22⋊C4—1221no—
240C2×C22⋊C8—22no—
241C2×C22⋊C8C2×D6112yes—
242#386—1221no—
243#386—1222no—
244#380—612no—
245#380—611no—
246#380—1224no—
247C2×#95—612no—
248#327—1224no—
249C61#915511yescharacteristic, complemented, Sylow
250C25D24411yescharacteristic
251C22×D4—611no—
252C22×D4—1222no—
253C22×D4—1221no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—44no—
257C23×C4—1222no—
258C23×C4C4×D6112yes—
259C23×C4D24411yescharacteristic
260C23×C4C22⋊D6112yes—
261C23×C4C22×D6111yescharacteristic
262C22×C8—22no—
263#121—1222no—
264#121—1222no—
265#121—2444no—
266#120—2442no—
267#120—2442no—
268C2×C4⋊C4—611no—
269C2×C4⋊C4—612no—
270C2×C4⋊C4—1224no—
271C2×C4⋊C4—2444no—
272C2×C22⋊C4—1224no—
273C2×C22⋊C4—1222no—
274C2×C22⋊C4—1221no—
275C2×C22⋊C4—1222no—
276C2×C22⋊C4—1221no—
277C2×C22⋊C4—2442no—
278C2×C22⋊C4—2442no—
279C22⋊C8—22no—
280C22⋊C8—22no—
281C22⋊C8—44no—
282#95—614no—
283#95—1222no—
284#95—1222no—
285#95—1221no—
286C24—21no—
287C24—21no—
288C24—21no—
289C24—21no—
290C24—42no—
291C24—42no—
292C24—1221no—
293C24#1175819012yes—
294C24D48812yes—
295C24#1175819812yes—
296C24C2×D24411yescharacteristic
297C2×D4—1222no—
298C2×D4—2442no—
299C2×D4—2444no—
300C2×D4—2444no—
301C2×D4—2441no—
302C2×D4—2444no—
303C2×D4—2441no—
304C2×D4—2441no—
305C2×D4—2441no—
306C2×D4—2441no—
307C2×D4—2441no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—24no—
311C22×C4—24no—
312C22×C4—24no—
313C22×C4—24no—
314C22×C4—24no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—42no—
318C22×C4—48no—
319C22×C4—48no—
320C22×C4—1222no—
321C22×C4—1221no—
322C22×C4—1224no—
323C22×C4—2444no—
324C22×C4—2444no—
325C22×C4—2442no—
326C22×C4—2442no—
327C22×C4#1175819812yes—
328C22×C4C2×C4×D6111yescharacteristic
329C22×C4D4×D6112yes—
330C22×C4#1175822412yes—
331C22×C4C2×C22⋊D6111yescharacteristic
332C2×C8—44no—
333C2×C8—42no—
334C4⋊C4—1222no—
335C4⋊C4—2442no—
336C4⋊C4—2448no—
337C22⋊C4—2448no—
338C22⋊C4—2444no—
339C22⋊C4—2441no—
340C22⋊C4—2441no—
341C22⋊C4—2444no—
342C22⋊C4—2442no—
343C23—22no—
344C23—22no—
345C23—22no—
346C23—22no—
347C23—22no—
348C23—22no—
349C23—22no—
350C23—22no—
351C23—22no—
352C23—22no—
353C23—22no—
354C23—22no—
355C23—44no—
356C23—44no—
357C23—42no—
358C23—42no—
359C23—44no—
360C23—44no—
361C23—42no—
362C23—42no—
363C23—2442no—
364C23—2441no—
365C23—2441no—
366C23—2442no—
367C23—2441no—
368C23#1451969914yes—
369C23C2×#1175819811yescharacteristic
370C23#1451974711yescharacteristic
371C23#1451976111yescharacteristic
372C23C2×D48811yescharacteristic
373C23C2×#1175819011yescharacteristic
374C23#1451980511yescharacteristic
375C23#1451981011yescharacteristic
376D4—4882no—
377D4—4888no—
378D4—4881no—
379D4—4881no—
380D4—4881no—
381D4—4881no—
382C2×C4—24no—
383C2×C4—24no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—48no—
391C2×C4—48no—
392C2×C4—4884no—
393C2×C4—4884no—
394C2×C4—2444no—
395C2×C4—2444no—
396C2×C4—2442no—
397C2×C4—2442no—
398C2×C4—2441no—
399C2×C4—2441no—
400C2×C4—2442no—
401C2×C4—2441no—
402C2×C4—2444no—
403C2×C4#1451969114yes—
404C2×C4#1451973712yes—
405C2×C4#1451974912yes—
406C8—82no—
407C22—22no—
408C22—22no—
409C22—22no—
410C22—22no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—24no—
416C22—24no—
417C22—24no—
418C22—44no—
419C22—44no—
420C22—44no—
421C22—44no—
422C22—42no—
423C22—42no—
424C22—42no—
425C22—42no—
426C22—4882no—
427C22—4882no—
428C22—4881no—
429C22—4881no—
430C22—4881no—
431C22#1683963911yescharacteristic
432C22C2×#1451969112yes—
433C22C2×#1451969911yescharacteristic
434C22#1683976411yescharacteristic
435C22#1683977812yes—
436C22#1683989811yescharacteristic
437C22#1683990311yescharacteristic
438C22#1684007611yescharacteristic
439C22#1684008111yescharacteristic
440C4—22no—
441C4—24no—
442C4—22no—
443C4—4884no—
444C4—4882no—
445C4—4881no—
446C2—21no—
447C2—21no—
448C2—21no—
449C2—21no—
450C2—44no—
451C2—9761no—
452C2#2144436312yes—
453C2#2144438812yes—
454C2#2144613411yescharacteristic
455C2#2144626511yescharacteristic
456C2#2144627011yescharacteristic
subgroupG/H
centerC23C2×#11758198
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1779C2
socleC23×C61C2×C22⋊C4
prime radical#21454101C2
cosocleC23×C4×C61C23
hypercenter#1779D61
hypocenterC61#9155
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C24×C4 ◁ #1779

Complements

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

NH ≅ G/Ntype
2. C2×#16839622C2semidirect
3. C2×#16839497C2semidirect
4. #21443699C2semidirect
5. C61×#1779C2semidirect
6. C2×#14519751C4semidirect
14. #16839622C4semidirect
44. #14519684D4semidirect
220. #1779D61semidirect
249. C61#9155semidirect

Maximal subgroups

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

subgroupindex
#214541012
C2×#168396222
C2×#168394972
#214436992
C61×#17792
#915561