Finite Group Databasebeta

← #29575732

Subgroups — #29575732

Order 15616.

738 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454159C211yesmaximal, characteristic
2C2×#16839613C211yesmaximal, characteristic
3#21445885C211yesmaximal, characteristic
4C2×#16839500C211yesmaximal, characteristic
5C2×#16839498C211yesmaximal, characteristic
6#21443697C211yesmaximal, characteristic
7C61×#1294C211yesmaximal, characteristic
8C2×#14519756C2211yescharacteristic
9C22×#11758196—21no—
10C22×C4×Dic61—21no—
11C22×C4×Dic61C2211yescharacteristic
12C2×C22⋊#92418C2211yescharacteristic
13#16839667C412yescomplemented
14#16839661C412yescomplemented
15#16839647—22no—
16#16839637—21no—
17#16839623—21no—
18#16839613—22no—
19#16839613—22no—
20C2×#14519684C2211yescharacteristic
21#16839516—22no—
22#16839500—22no—
23#16839498—22no—
24C2×C22⋊C8×C61C2211yescharacteristic
25C61×#380C2211yescharacteristic
26C2×#95×C61C2211yescharacteristic
27C22×Dic122C2×C411yescharacteristic
28C23×Dic61—21no—
29C23×Dic61D411yescharacteristic
30C23×Dic61D411yescharacteristic
31C22×#92418—21no—
32#14519756—21no—
33#14519756—21no—
34#14519756—21no—
35#14519756—21no—
36C2×C4⋊Dic61—22no—
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×#11758196—28no—
39C2×#11758196—24no—
40C2×#11758196—21no—
41C2×C22⋊Dic61—21no—
42C2×C4×Dic61—21no—
43C2×C4×Dic61—21no—
44C2×C4×Dic61—21no—
45C2×C4×Dic61—21no—
46C2×C4×Dic61—24no—
47C2×C4×Dic61—42no—
48C2×C4×Dic61—42no—
49C2×C4×Dic61C2×C412yes—
50C2×C4×Dic61D412yes—
51C22⋊#92418—21no—
52C22⋊#92418—21no—
53#14519684—21no—
54#14519684—22no—
55#14519684—22no—
56#14519684—22no—
57#14519684D412yes—
58C23×C4×C61—21no—
59C23×C4×C61C2311yescharacteristic
60C22×C8×C61—21no—
61C2×C4⋊C4×C61C2×C412yes—
62C2×C22⋊C4×C61—21no—
63C22⋊C8×C61—21no—
64C22⋊C8×C61—21no—
65#95×C61—21no—
66#95×C61—21no—
67#95×C61D412yes—
68C24×C61C2×D411yescharacteristic
69C22×C4×C61—24no—
70C22×C4×C61—22no—
71C22×C4×C61—22no—
72C22×C4×C61—42no—
73C22×C4×C61—42no—
74C22×C4×C61—41no—
75C22×C4×C61—41no—
76C22×C4×C61C22×C411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61#4111yescharacteristic
81C22×C4×C61#4111yescharacteristic
82C22×Dic61—21no—
83C22×Dic61—21no—
84C22×Dic61—21no—
85C22×Dic61—21no—
86C22×Dic61—21no—
87C22×Dic61—21no—
88C22×Dic61—24no—
89C22×Dic61—24no—
90C22×Dic61—22no—
91C22×Dic61—21no—
92C22×Dic61—21no—
93C22×Dic61—42no—
94C22×Dic61—41no—
95C22×Dic61—41no—
96C22×Dic61C22⋊C412yes—
97C22×Dic61C22⋊C412yes—
98C22×Dic61SD1612yes—
99C22×Dic61Q1612yes—
100C2×Dic122—21no—
101C2×Dic122—21no—
102C2×Dic122—42no—
103C2×C8×C61—42no—
104C2×C8×C61—41no—
105C4⋊C4×C61—42no—
106C22⋊C4×C61—41no—
107C22⋊C4×C61—41no—
108C22⋊Dic61—41no—
109C22⋊Dic61—41no—
110C4⋊Dic61—21no—
111C4⋊Dic61—21no—
112C4⋊Dic61—44no—
113#11758196—216no—
114#11758196—41no—
115#11758196—41no—
116C4×Dic61—22no—
117C4×Dic61—22no—
118C4×Dic61—22no—
119C4×Dic61—22no—
120C4×Dic61—48no—
121C2×#92418—42no—
122C2×#92418—41no—
123C23×C61—22no—
124C23×C61—22no—
125C23×C61C2×C22⋊C411yescharacteristic
126C23×C61#12011yescharacteristic
127C23×C61#12311yescharacteristic
128C23×C61C2×SD1611yescharacteristic
129C23×C61C2×Q1611yescharacteristic
130C23×C61AGL(1,ℤ/8)11yescharacteristic
131C23×C61#13711yescharacteristic
132C2×C4×C61—22no—
133C2×C4×C61—22no—
134C2×C4×C61—24no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—42no—
140C2×C4×C61—44no—
141C2×C4×C61—44no—
142C2×C4×C61—42no—
143C2×C4×C61—42no—
144C2×C4×C61—42no—
145C2×C4×C61—42no—
146C2×C4×C61C4×D411yescharacteristic
147C2×C4×C61C4×D411yescharacteristic
148C2×C4×C61#12111yescharacteristic
149C2×C4×C61#12111yescharacteristic
150C2×Dic61—24no—
151C2×Dic61—24no—
152C2×Dic61—22no—
153C2×Dic61—22no—
154C2×Dic61—22no—
155C2×Dic61—22no—
156C2×Dic61—22no—
157C2×Dic61—22no—
158C2×Dic61—22no—
159C2×Dic61—22no—
160C2×Dic61—24no—
161C2×Dic61—42no—
162C2×Dic61—44no—
163C2×Dic61—44no—
164C2×Dic61—42no—
165C2×Dic61—41no—
166C2×Dic61—41no—
167C2×Dic61—42no—
168C2×Dic61—42no—
169C2×Dic61#10314yes—
170C2×Dic61#10414yes—
171Dic122—81no—
172Dic122—81no—
173C8×C61—81no—
174#92418—81no—
175#9144—611nomaximal, Sylow
176C22×C61—21no—
177C22×C61—21no—
178C22×C61—21no—
179C22×C61—21no—
180C22×C61—22no—
181C22×C61—22no—
182C22×C61—22no—
183C22×C61—22no—
184C22×C61#38611yescharacteristic
185C22×C61#41012yes—
186C22×C61C2×#10311yescharacteristic
187C22×C61#41711yescharacteristic
188C22×C61C2×#10412yes—
189C22×C61#45011yescharacteristic
190C22×C61#45111yescharacteristic
191C22×C61#48311yescharacteristic
192C22×C61#48411yescharacteristic
193C4×C61—21no—
194C4×C61—21no—
195C4×C61—21no—
196C4×C61—21no—
197C4×C61—44no—
198C4×C61—82no—
199Dic61—24no—
200Dic61—24no—
201Dic61—44no—
202Dic61—81no—
203Dic61—81no—
204#2855—611no—
205C2×C4×C4⋊C4—611no—
206#1817—611no—
207C2×#328—611no—
208C2×#328—611no—
209#1294—611no—
210#1294D6111yescharacteristic
211C2×C61—21no—
212C2×C61—21no—
213C2×C61—21no—
214C2×C61—21no—
215C2×C61#150312yes—
216C2×C61#150912yes—
217C2×C61#187211yescharacteristic
218C2×C61#189611yescharacteristic
219C2×C61#189911yescharacteristic
220C2×C22⋊Q8—611no—
221C22×C4⋊C4—1221no—
222C22×C42—611no—
223C22×C42—1221no—
224C2×C22⋊C8—611no—
225C2×C22⋊C8C2×D6111yescharacteristic
226#391—612no—
227#389—612no—
228#387—1222no—
229#385—1221no—
230#381—1221no—
231#380C2×D6111yescharacteristic
232C4×C4⋊C4—1222no—
233C4×C4⋊C4—1222no—
234C2×#95—611no—
235C2×#95C2×D6111yescharacteristic
236#336—1222no—
237#328—1222no—
238#328—1222no—
239C61#914411yescharacteristic, complemented, Sylow
240C22×Q8—611no—
241C23×C4—21no—
242C23×C4—611no—
243C23×C4—611no—
244C23×C4—1221no—
245C23×C4C22×D6111yescharacteristic
246C22×C8—21no—
247C22×C8—1221no—
248C22⋊Q8—1221no—
249C22⋊Q8—1221no—
250C22⋊Q8—1221no—
251C22⋊Q8—1221no—
252C2×C4⋊C4—611no—
253C2×C4⋊C4—1224no—
254C2×C4⋊C4—1228no—
255C2×C4⋊C4—1222no—
256C2×C4⋊C4—1221no—
257C2×C4⋊C4C4×D6112yes—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—1221no—
260C2×C42—612no—
261C2×C42—612no—
262C2×C42—1221no—
263C2×C42—1221no—
264C2×C42—1221no—
265C2×C42—1221no—
266C2×C42—1224no—
267C2×C42—2442no—
268C2×C42—2442no—
269C22⋊C8—21no—
270C22⋊C8—21no—
271C22⋊C8—1221no—
272C22⋊C8—1221no—
273#95—21no—
274#95—21no—
275#95—612no—
276#95—1222no—
277#95—1222no—
278#95—1222no—
279#95—1221no—
280#95D24412yes—
281C24D4×D6111yescharacteristic
282C2×Q8—1221no—
283C2×Q8—1221no—
284C2×Q8—2442no—
285C22×C4—24no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—612no—
293C22×C4—612no—
294C22×C4—612no—
295C22×C4—612no—
296C22×C4—1224no—
297C22×C4—1221no—
298C22×C4—1221no—
299C22×C4—1221no—
300C22×C4—1221no—
301C22×C4—1221no—
302C22×C4—1221no—
303C22×C4—1224no—
304C22×C4—1222no—
305C22×C4—1221no—
306C22×C4—1221no—
307C22×C4—2442no—
308C22×C4—2441no—
309C22×C4—2441no—
310C22×C4C2×C4×D6111yescharacteristic
311C22×C4C2×D24411yescharacteristic
312C22×C4#1175822211yescharacteristic
313C22×C4D4×D6111yescharacteristic
314C22×C4D4×D6111yescharacteristic
315C22×C4#1175822611yescharacteristic
316C2×C8—42no—
317C2×C8—41no—
318C2×C8—2442no—
319C2×C8—2441no—
320C4⋊C4—42no—
321C4⋊C4—12216no—
322C4⋊C4—1221no—
323C4⋊C4—1221no—
324C4⋊C4—2444no—
325C4⋊C4—2441no—
326C4⋊C4—2441no—
327C22⋊C4—41no—
328C22⋊C4—41no—
329C22⋊C4—2441no—
330C22⋊C4—2441no—
331C42—1222no—
332C42—1222no—
333C42—1222no—
334C42—1222no—
335C42—2448no—
336C23—22no—
337C23—22no—
338C23C22⋊C4×D6111yescharacteristic
339C23#1451974711yescharacteristic
340C23#1451976211yescharacteristic
341C23SD16×D6111yescharacteristic
342C23Q16×D6111yescharacteristic
343C23#1451980111yescharacteristic
344C23#1451980611yescharacteristic
345Q8—4881no—
346Q8—4881no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—24no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—42no—
355C2×C4—44no—
356C2×C4—44no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—614no—
362C2×C4—614no—
363C2×C4—1224no—
364C2×C4—1224no—
365C2×C4—1222no—
366C2×C4—1222no—
367C2×C4—1222no—
368C2×C4—1222no—
369C2×C4—1222no—
370C2×C4—1222no—
371C2×C4—1222no—
372C2×C4—1222no—
373C2×C4—1224no—
374C2×C4—2442no—
375C2×C4—2442no—
376C2×C4—2441no—
377C2×C4—2441no—
378C2×C4—2442no—
379C2×C4—2444no—
380C2×C4—2444no—
381C2×C4—2442no—
382C2×C4#1451973911yescharacteristic
383C2×C4C4×D24411yescharacteristic
384C2×C4#1451975011yescharacteristic
385C2×C4#1451975211yescharacteristic
386C8—81no—
387C8—4881no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—22no—
393C22—22no—
394C22—22no—
395C22—22no—
396C22#1683964011yescharacteristic
397C22#1683973412yes—
398C22#103×D6111yescharacteristic
399C22#1683976011yescharacteristic
400C22#104×D6112yes—
401C22#1683991411yescharacteristic
402C22#1683991911yescharacteristic
403C22#1684009411yescharacteristic
404C22#1684009911yescharacteristic
405C4—21no—
406C4—21no—
407C4—21no—
408C4—21no—
409C4—44no—
410C4—82no—
411C4—1224no—
412C4—1224no—
413C4—4881no—
414C4—4881no—
415C4—2444no—
416C2—21no—
417C2—21no—
418C2—21no—
419C2—21no—
420C2#2144431612yes—
421C2#2144434112yes—
422C2#2144612511yescharacteristic
423C2#2144626111yescharacteristic
424C2#2144627611yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1294C2
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C2×D4
cosocleC23×C4×C61C23
hypercenter#1294D61
hypocenterC61#9144
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
13. #16839667C4semidirect
14. #16839661C4semidirect
239. C61#9144semidirect

Maximal subgroups

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

subgroupindex
#214541592
C2×#168396132
#214458852
C2×#168395002
C2×#168394982
#214436972
C61×#12942
#914461