Finite Group Databasebeta

← #29575752

Subgroups — #29575752

Order 15616.

800 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454151C211yesmaximal, characteristic
2C2×#16839613C211yesmaximal, characteristic, complemented
3#21445885C211yesmaximal, characteristic, complemented
4C2×#16839497C211yesmaximal, characteristic
5C2×#16839495C211yesmaximal, characteristic
6#21443697C211yesmaximal, characteristic, complemented
7C61×#1294C211yesmaximal, characteristic, complemented
8C2×#14519761—21no—
9C2×#14519751C2211yescharacteristic
10C22×#11758196—21no—
11C22×C4×Dic61—21no—
12C22×C4×Dic61C2211yescharacteristic
13C2×C22⋊#92418C2211yescharacteristic
14#16839663C412yescomplemented
15#16839661C412yescomplemented
16#16839654—22no—
17#16839639—21no—
18#16839613—22no—
19#16839613—22no—
20C2×#14519684C2211yescharacteristic
21#16839516—22no—
22#16839497—22no—
23#16839495—22no—
24C2×C22⋊C8×C61C2211yescharacteristic
25C61×#380C2211yescharacteristic
26C2×#95×C61C2211yescharacteristic
27C22×D244C2×C411yescharacteristic
28C22×C22⋊D61—21no—
29C23×Dic61—21no—
30C23×Dic61D411yescharacteristic
31C23×Dic61D411yescharacteristic
32C22×#92418—21no—
33#14519761—42no—
34#14519761—42no—
35#14519751—21no—
36#14519751—21no—
37#14519751—21no—
38#14519751—21no—
39C2×C4⋊Dic61—22no—
40C2×C4⋊Dic61C2×C411yescharacteristic
41C2×#11758196—28no—
42C2×#11758196—24no—
43C2×#11758198—21no—
44C2×#11758198—22no—
45C2×#11758198—22no—
46C2×C4×Dic61—21no—
47C2×C4×Dic61—21no—
48C2×C4×Dic61—21no—
49C2×C4×Dic61—21no—
50C2×C4×Dic61—24no—
51C2×C4×Dic61—42no—
52C2×C4×Dic61—42no—
53C2×C4×Dic61C2×C412yes—
54C2×C4×Dic61D412yes—
55C22⋊#92418—21no—
56C22⋊#92418—21no—
57#14519684—21no—
58#14519684—22no—
59#14519684D412yes—
60C23×C4×C61—21no—
61C23×C4×C61C2311yescharacteristic
62C22×C8×C61—21no—
63C2×C4⋊C4×C61C2×C412yes—
64C2×C22⋊C4×C61—21no—
65C22⋊C8×C61—21no—
66C22⋊C8×C61—21no—
67#95×C61—21no—
68#95×C61—21no—
69#95×C61D412yes—
70C24×C61C2×D411yescharacteristic
71C23×D61—21no—
72C22×C4×C61—24no—
73C22×C4×C61—22no—
74C22×C4×C61—22no—
75C22×C4×C61—42no—
76C22×C4×C61—42no—
77C22×C4×C61—41no—
78C22×C4×C61—41no—
79C22×C4×C61C22×C411yescharacteristic
80C22×C4×C61C2×D411yescharacteristic
81C22×C4×C61C2×D411yescharacteristic
82C22×C4×C61C2×D411yescharacteristic
83C22×C4×C61#4111yescharacteristic
84C22×C4×C61#4111yescharacteristic
85C2×C22⋊D61—41no—
86C2×C22⋊D61—41no—
87C2×C22⋊D61—41no—
88C2×C22⋊D61—41no—
89C2×C22⋊D61—41no—
90C2×C22⋊D61—41no—
91C22×Dic61—21no—
92C22×Dic61—21no—
93C22×Dic61—21no—
94C22×Dic61—21no—
95C22×Dic61—21no—
96C22×Dic61—21no—
97C22×Dic61—24no—
98C22×Dic61—24no—
99C22×Dic61—22no—
100C22×Dic61—21no—
101C22×Dic61—42no—
102C22×Dic61—41no—
103C22×Dic61—41no—
104C22×Dic61C22⋊C412yes—
105C22×Dic61C22⋊C412yes—
106C22×Dic61D812yes—
107C22×Dic61SD1612yes—
108C2×D244—21no—
109C2×D244—21no—
110C2×D244—42no—
111C2×C8×C61—42no—
112C2×C8×C61—41no—
113C4⋊C4×C61—42no—
114C22⋊C4×C61—41no—
115C22⋊C4×C61—41no—
116#11758198—41no—
117#11758198—41no—
118#11758198—44no—
119#11758198—44no—
120C4⋊Dic61—21no—
121C4⋊Dic61—21no—
122C4⋊Dic61—44no—
123#11758196—216no—
124C4×Dic61—22no—
125C4×Dic61—22no—
126C4×Dic61—22no—
127C4×Dic61—22no—
128C4×Dic61—48no—
129C2×#92418—42no—
130C2×#92418—41no—
131C23×C61—22no—
132C23×C61—22no—
133C23×C61C2×C22⋊C411yescharacteristic
134C23×C61#12011yescharacteristic
135C23×C61#12311yescharacteristic
136C23×C61C2×D811yescharacteristic
137C23×C61C2×SD1611yescharacteristic
138C23×C61AGL(1,ℤ/8)11yescharacteristic
139C23×C61#13711yescharacteristic
140C22×D61—41no—
141C22×D61—42no—
142C22×D61—41no—
143C22×D61—41no—
144C22×D61—42no—
145C2×C4×C61—22no—
146C2×C4×C61—22no—
147C2×C4×C61—24no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—42no—
153C2×C4×C61—44no—
154C2×C4×C61—44no—
155C2×C4×C61—42no—
156C2×C4×C61—42no—
157C2×C4×C61—42no—
158C2×C4×C61—42no—
159C2×C4×C61C4×D411yescharacteristic
160C2×C4×C61C4×D411yescharacteristic
161C2×C4×C61#12111yescharacteristic
162C2×C4×C61#12111yescharacteristic
163C22⋊D61—81no—
164C22⋊D61—81no—
165C22⋊D61—81no—
166C22⋊D61—81no—
167C2×Dic61—24no—
168C2×Dic61—24no—
169C2×Dic61—22no—
170C2×Dic61—22no—
171C2×Dic61—22no—
172C2×Dic61—22no—
173C2×Dic61—22no—
174C2×Dic61—22no—
175C2×Dic61—22no—
176C2×Dic61—22no—
177C2×Dic61—24no—
178C2×Dic61—42no—
179C2×Dic61—44no—
180C2×Dic61—44no—
181C2×Dic61—42no—
182C2×Dic61—41no—
183C2×Dic61—41no—
184C2×Dic61—41no—
185C2×Dic61#10214yes—
186C2×Dic61#10414yes—
187D244—81no—
188D244—81no—
189C8×C61—81no—
190#92418—81no—
191#9148—611nomaximal, Sylow
192C22×C61—21no—
193C22×C61—21no—
194C22×C61—21no—
195C22×C61—21no—
196C22×C61—22no—
197C22×C61—22no—
198C22×C61—22no—
199C22×C61—22no—
200C22×C61#38611yescharacteristic
201C22×C61#41012yes—
202C22×C61C2×#10211yescharacteristic
203C22×C61#41711yescharacteristic
204C22×C61C2×#10412yes—
205C22×C61#44711yescharacteristic
206C22×C61#44811yescharacteristic
207C22×C61#48011yescharacteristic
208C22×C61#48111yescharacteristic
209C2×D61—81no—
210C2×D61—81no—
211C2×D61—81no—
212C2×D61—82no—
213C2×D61—82no—
214C4×C61—21no—
215C4×C61—21no—
216C4×C61—21no—
217C4×C61—21no—
218C4×C61—44no—
219C4×C61—82no—
220Dic61—24no—
221Dic61—24no—
222Dic61—44no—
223Dic61—81no—
224#2854—611no—
225C2×C4×C4⋊C4—611no—
226#1817—611no—
227C2×#327—611no—
228C2×#327—611no—
229#1294—611no—
230#1294D6111yescharacteristic, complemented
231C2×C61—21no—
232C2×C61—21no—
233C2×C61—21no—
234C2×C61—21no—
235C2×C61#150212yes—
236C2×C61#150912yes—
237C2×C61#187411yescharacteristic
238C2×C61#189611yescharacteristic
239C2×C61#189911yescharacteristic
240D61—161no—
241C2×#123—1221no—
242C2×#121—611no—
243C22×C4⋊C4—1221no—
244C22×C42—611no—
245C22×C42—1221no—
246C2×C22⋊C8—611no—
247C2×C22⋊C8C2×D6111yescharacteristic
248#390—612no—
249#389—612no—
250#388—1222no—
251#386—1221no—
252#380C2×D6111yescharacteristic
253C4×C4⋊C4—1222no—
254C4×C4⋊C4—1222no—
255C2×#95—611no—
256C2×#95C2×D6111yescharacteristic
257#336—1222no—
258#327—1222no—
259#327—1222no—
260C61#914811yescharacteristic, complemented, Sylow
261C22×D4—611no—
262C22×D4—1221no—
263C23×C4—21no—
264C23×C4—611no—
265C23×C4—611no—
266C23×C4—1221no—
267C23×C4C22×D6111yescharacteristic
268C22×C8—21no—
269C22×C8—1221no—
270#123—2442no—
271#123—2442no—
272#121—1221no—
273#121—1221no—
274#121—1221no—
275#121—1221no—
276C2×C4⋊C4—611no—
277C2×C4⋊C4—1224no—
278C2×C4⋊C4—1228no—
279C2×C4⋊C4—1222no—
280C2×C4⋊C4C4×D6112yes—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—1222no—
283C2×C22⋊C4—1222no—
284C2×C22⋊C4—1221no—
285C2×C42—612no—
286C2×C42—612no—
287C2×C42—1221no—
288C2×C42—1221no—
289C2×C42—1221no—
290C2×C42—1221no—
291C2×C42—1224no—
292C2×C42—2442no—
293C2×C42—2442no—
294C22⋊C8—21no—
295C22⋊C8—21no—
296C22⋊C8—1221no—
297C22⋊C8—1221no—
298#95—21no—
299#95—21no—
300#95—612no—
301#95—1222no—
302#95—1221no—
303#95D24412yes—
304C24—1221no—
305C24D4×D6111yescharacteristic
306C2×D4—1221no—
307C2×D4—1221no—
308C2×D4—2442no—
309C2×D4—2441no—
310C2×D4—2441no—
311C2×D4—2441no—
312C2×D4—2441no—
313C2×D4—2441no—
314C2×D4—2441no—
315C22×C4—24no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—612no—
323C22×C4—612no—
324C22×C4—612no—
325C22×C4—612no—
326C22×C4—1224no—
327C22×C4—1221no—
328C22×C4—1221no—
329C22×C4—1221no—
330C22×C4—1221no—
331C22×C4—1221no—
332C22×C4—1221no—
333C22×C4—1224no—
334C22×C4—1222no—
335C22×C4—1221no—
336C22×C4—2442no—
337C22×C4—2441no—
338C22×C4—2441no—
339C22×C4C2×C4×D6111yescharacteristic
340C22×C4C2×D24411yescharacteristic
341C22×C4#1175822211yescharacteristic
342C22×C4D4×D6111yescharacteristic
343C22×C4D4×D6111yescharacteristic
344C22×C4#1175822611yescharacteristic
345C2×C8—42no—
346C2×C8—41no—
347C2×C8—2442no—
348C2×C8—2441no—
349C4⋊C4—42no—
350C4⋊C4—12216no—
351C4⋊C4—1221no—
352C4⋊C4—1221no—
353C4⋊C4—2444no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—2444no—
357C22⋊C4—2444no—
358C22⋊C4—2441no—
359C22⋊C4—2441no—
360C42—1222no—
361C42—1222no—
362C42—1222no—
363C42—1222no—
364C42—2448no—
365C23—22no—
366C23—22no—
367C23—2442no—
368C23—2441no—
369C23—2441no—
370C23—2442no—
371C23—2441no—
372C23C22⋊C4×D6111yescharacteristic
373C23#1451974711yescharacteristic
374C23#1451976211yescharacteristic
375C23D8×D6111yescharacteristic
376C23SD16×D6111yescharacteristic
377C23#1451980411yescharacteristic
378C23#1451980911yescharacteristic
379D4—4881no—
380D4—4881no—
381D4—4881no—
382D4—4881no—
383D4—4881no—
384D4—4881no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—24no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—42no—
393C2×C4—44no—
394C2×C4—44no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—614no—
400C2×C4—614no—
401C2×C4—1224no—
402C2×C4—1224no—
403C2×C4—1222no—
404C2×C4—1222no—
405C2×C4—1222no—
406C2×C4—1222no—
407C2×C4—1222no—
408C2×C4—1222no—
409C2×C4—1222no—
410C2×C4—1222no—
411C2×C4—1224no—
412C2×C4—2441no—
413C2×C4—2441no—
414C2×C4—2441no—
415C2×C4—2442no—
416C2×C4—2444no—
417C2×C4—2444no—
418C2×C4—2442no—
419C2×C4#1451973911yescharacteristic
420C2×C4C4×D24411yescharacteristic
421C2×C4#1451975011yescharacteristic
422C2×C4#1451975211yescharacteristic
423C8—81no—
424C8—4881no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—22no—
430C22—22no—
431C22—22no—
432C22—22no—
433C22—4881no—
434C22—4881no—
435C22—4882no—
436C22—4882no—
437C22—4881no—
438C22#1683964011yescharacteristic
439C22#1683973412yes—
440C22#102×D6111yescharacteristic
441C22#1683976211yescharacteristic
442C22#104×D6112yes—
443C22#1683989711yescharacteristic
444C22#1683990211yescharacteristic
445C22#1684007711yescharacteristic
446C22#1684008211yescharacteristic
447C4—21no—
448C4—21no—
449C4—21no—
450C4—21no—
451C4—44no—
452C4—82no—
453C4—1224no—
454C4—1224no—
455C4—4881no—
456C4—2444no—
457C2—21no—
458C2—21no—
459C2—21no—
460C2—21no—
461C2—9761no—
462C2#2144431212yes—
463C2#2144434312yes—
464C2#2144613511yescharacteristic
465C2#2144626111yescharacteristic
466C2#2144627611yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1294C2
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519751C22
cosocleC23×C4×C61C23
hypercenter#1294D61
hypocenterC61#9148
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
2. C2×#16839613C2semidirect
3. #21445885C2semidirect
6. #21443697C2semidirect
7. C61×#1294C2semidirect
14. #16839663C4semidirect
15. #16839661C4semidirect
230. #1294D61semidirect
260. C61#9148semidirect

Maximal subgroups

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

subgroupindex
#214541512
C2×#168396132
#214458852
C2×#168394972
C2×#168394952
#214436972
C61×#12942
#914861