Finite Group Databasebeta

← #29571437

Subgroups — #29571437

Order 15616.

1006 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840242C211yesmaximal, characteristic
2#21444215C212yesmaximal, complemented
3#21444209C212yesmaximal, complemented
4#21444133C211yesmaximal, characteristic, complemented
5C61×#1458C211yesmaximal, characteristic, complemented
6C22×#11758222C411yescharacteristic
7#16840242—24no—
8#16840242—24no—
9C2×C4×Dic122C411yescharacteristic
10C2×C4×Dic122C2211yescharacteristic
11C2×C4×D244C411yescharacteristic
12C2×C4×D244C2211yescharacteristic
13C2×#14519737—21no—
14C2×#14519737—21no—
15C2×#14519735—21no—
16C22×C4⋊Dic61C411yescharacteristic
17C2×C4⋊C4×D61—21no—
18#16839815C2212yes—
19#16839494—24no—
20#16839489—24no—
21#16839488—21no—
22#16839486—21no—
23C2×#117×C61C2211yescharacteristic
24C61×#431C2212yes—
25C61×#324—21no—
26C61×#323—21no—
27C2×#11758222—22no—
28C2×#11758222—22no—
29C2×#11758222—22no—
30C2×#11758222—22no—
31C2×#11758222—22no—
32C2×#11758222C814yescomplemented
33C22×Dic122C2×C411yescharacteristic
34C22×D244C2×C411yescharacteristic
35C22×C22⋊D61—21no—
36C23×Dic61—21no—
37C22×C4×D61—21no—
38C22×C4×D61—21no—
39C22×C4×D61—21no—
40C4×Dic122—22no—
41C4×Dic122—22no—
42C4×Dic122—22no—
43C4×Dic122D414yes—
44C4×D244—22no—
45C4×D244—22no—
46C4×D244—22no—
47C4×D244D414yes—
48#14519737—28no—
49#14519737—28no—
50#14519735—28no—
51C2×C4⋊Dic61—21no—
52C2×C4⋊Dic61—22no—
53C2×C4⋊Dic61—22no—
54C2×C4⋊Dic61C2×C411yescharacteristic
55C2×C4⋊Dic61C2×C411yescharacteristic
56C2×#11758196—21no—
57C2×#11758196—21no—
58C4⋊C4×D61—28no—
59C2×#11758198—21no—
60C2×#11758198—21no—
61C2×C4×Dic61—21no—
62C2×C4×Dic61—21no—
63C4⋊#92418—22no—
64C22⋊#92418—22no—
65C4×#92418—22no—
66C23×C4×C61C2×C411yescharacteristic
67#117×C61—22no—
68#117×C61—22no—
69C2×C4⋊C4×C61D411yescharacteristic
70C2×C4⋊C4×C61D411yescharacteristic
71C2×C22⋊C4×C61D411yescharacteristic
72C2×C22⋊C4×C61D411yescharacteristic
73C2×C42×C61C2×C411yescharacteristic
74C2×C42×C61C2311yescharacteristic
75C4⋊C8×C61—22no—
76C22⋊C8×C61—22no—
77C4×C8×C61—22no—
78C24×C61C22⋊C411yescharacteristic
79C23×D61—21no—
80C22×C4×C61—21no—
81C22×C4×C61—21no—
82C22×C4×C61—21no—
83C22×C4×C61—21no—
84C22×C4×C61C22⋊C411yescharacteristic
85C22×C4×C61C22⋊C411yescharacteristic
86C22×C4×C61C22⋊C411yescharacteristic
87C22×C4×C61C2×C812yes—
88C22×C4×C61M1612yes—
89C22×C4×C61C22×C411yescharacteristic
90C22×C4×C61C2×D411yescharacteristic
91C22×C4×C61C2×D411yescharacteristic
92C2×C22⋊D61—24no—
93C2×C22⋊D61—24no—
94C2×C22⋊D61—24no—
95C22×Dic61—21no—
96C22×Dic61—21no—
97C22×Dic61—21no—
98C22×Dic61—24no—
99C22×Dic61—82no—
100#11758222—28no—
101#11758222—28no—
102#11758222—28no—
103#11758222—28no—
104C2×D244—21no—
105C2×D244—21no—
106C2×D244—21no—
107C2×D244C22⋊C412yes—
108C2×D244C2×C812yes—
109C2×D244M1612yes—
110C2×C4×D61—24no—
111C2×C4×D61—24no—
112C2×C4×D61—24no—
113C2×C4×D61—24no—
114C2×C4×D61—24no—
115C2×C4×D61—82no—
116C2×C4×D61—82no—
117C2×Dic122—21no—
118C2×Dic122—21no—
119C2×Dic122—21no—
120C2×Dic122C22⋊C412yes—
121C2×Dic122C2×C812yes—
122C2×Dic122M1612yes—
123C2×C8×C61—42no—
124C4⋊C4×C61—22no—
125C4⋊C4×C61—22no—
126C22⋊C4×C61—22no—
127C22⋊C4×C61—22no—
128C42×C61—21no—
129C42×C61—21no—
130C42×C61C2×D412yes—
131C42×C61C2×D412yes—
132#11758198—24no—
133#11758198—24no—
134C4⋊Dic61—24no—
135C4⋊Dic61—21no—
136C4⋊Dic61—21no—
137C4⋊Dic61C22⋊C412yes—
138C4⋊Dic61C22⋊C412yes—
139#11758196—24no—
140#11758196—24no—
141C4×Dic61—24no—
142C4×Dic61—24no—
143C2×#92418—42no—
144C23×C61—21no—
145C23×C61—21no—
146C23×C61—41no—
147C23×C61—41no—
148C23×C61C22⋊C812yes—
149C23×C61C2×C22⋊C411yescharacteristic
150C22×D61—22no—
151C22×D61—22no—
152C22×D61—22no—
153C22×D61—42no—
154C22×D61—42no—
155C2×C4×C61—21no—
156C2×C4×C61—21no—
157C2×C4×C61—22no—
158C2×C4×C61—22no—
159C2×C4×C61—22no—
160C2×C4×C61—22no—
161C2×C4×C61—21no—
162C2×C4×C61—21no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61—41no—
166C2×C4×C61—41no—
167C2×C4×C61C22⋊C812yes—
168C2×C4×C61C2×C22⋊C411yescharacteristic
169C2×C4×C61C2×C22⋊C411yescharacteristic
170C2×C4×C61#12012yes—
171C2×C4×C61#12012yes—
172C2×C4×C61C22×C811yescharacteristic
173C2×C4×C61C2×M1611yescharacteristic
174C2×C4×C61C2×M1611yescharacteristic
175C2×C4×C61C2×M1611yescharacteristic
176C22⋊D61—216no—
177C2×Dic61—22no—
178C2×Dic61—22no—
179C2×Dic61—22no—
180C2×Dic61—22no—
181C2×Dic61—22no—
182C2×Dic61—42no—
183C2×Dic61—42no—
184C2×Dic61—84no—
185D244—22no—
186D244—22no—
187D244—22no—
188D244C22⋊C814yes—
189C4×D61—216no—
190C4×D61—84no—
191C4×D61—84no—
192Dic122—22no—
193Dic122—22no—
194Dic122—22no—
195Dic122C22⋊C814yes—
196C8×C61—82no—
197#92418—82no—
198#8324—611nomaximal, Sylow
199C22×C61—21no—
200C22×C61—21no—
201C22×C61—22no—
202C22×C61—42no—
203C22×C61—42no—
204C22×C61—41no—
205C22×C61—41no—
206C22×C61#37911yescharacteristic
207C22×C61C2×C22⋊C811yescharacteristic
208C22×C61#40711yescharacteristic
209C2×D61—24no—
210C2×D61—44no—
211C2×D61—44no—
212C2×D61—42no—
213C2×D61—42no—
214C4×C61—22no—
215C4×C61—22no—
216C4×C61—22no—
217C4×C61—41no—
218C4×C61—41no—
219C4×C61C2×C22⋊C811yescharacteristic
220C4×C61C2×C22⋊C811yescharacteristic
221C4×C61#40711yescharacteristic
222C4×C61#40711yescharacteristic
223Dic61—24no—
224Dic61—42no—
225Dic61—42no—
226C2×#520—611no—
227#1479—612no—
228#1478—612no—
229#1458—611no—
230#1458D6111yescharacteristic, complemented
231C2×C61—21no—
232C2×C61—21no—
233C2×C61—42no—
234C2×C61#177911yescharacteristic
235C2×C61#179511yescharacteristic
236C2×C61#179611yescharacteristic
237D61—44no—
238C22×#41—611no—
239#520—1224no—
240#520—1224no—
241C2×C4×Q8—611no—
242C2×C4×Q8—611no—
243C2×C4×D4—611no—
244C2×C4×D4—611no—
245C2×C4×D4—1221no—
246C2×C4×D4—1221no—
247C2×#117—1221no—
248C2×#117C2×D6111yescharacteristic
249C22×C4⋊C4—611no—
250C22×C4⋊C4—1221no—
251#431—612no—
252#431C2×D6112yes—
253Q8⋊C8—1224no—
254D4⋊C8—1224no—
255#324—21no—
256#324—1221no—
257#323—21no—
258#323—1221no—
259C61#832411yescharacteristic, complemented, Sylow
260C2×#41—614no—
261C2×#41—1222no—
262C2×#41—1222no—
263C2×#41—1222no—
264C2×#41—1222no—
265C2×#41—1222no—
266C22×Q8—611no—
267C22×D4—611no—
268C22×D4—1221no—
269C23×C4—1221no—
270C23×C4—1221no—
271C23×C4—1221no—
272C23×C4—1221no—
273C23×C4C4×D6111yescharacteristic
274C4×Q8—614no—
275C4×Q8—1222no—
276C4×Q8—1222no—
277C4×Q8—1222no—
278C4×D4—614no—
279C4×D4—1222no—
280C4×D4—1222no—
281C4×D4—1228no—
282C4×D4—1228no—
283C4×D4—1222no—
284#117—22no—
285#117—22no—
286#117—1228no—
287C2×C4⋊C4—611no—
288C2×C4⋊C4—611no—
289C2×C4⋊C4—1228no—
290C2×C4⋊C4—1222no—
291C2×C4⋊C4—1222no—
292C2×C4⋊C4—1221no—
293C2×C4⋊C4—1221no—
294C2×C4⋊C4—1221no—
295C2×C4⋊C4D24411yescharacteristic
296C2×C4⋊C4C22⋊D6111yescharacteristic
297C2×C22⋊C4—1221no—
298C2×C22⋊C4—1221no—
299C2×C22⋊C4D24411yescharacteristic
300C2×C22⋊C4C22⋊D6111yescharacteristic
301C2×C42—1221no—
302C2×C42—1221no—
303C2×C42C4×D6111yescharacteristic
304C2×C42C22×D6111yescharacteristic
305C4⋊C8—22no—
306C4⋊C8—1222no—
307C22⋊C8—22no—
308C22⋊C8—1222no—
309C4×C8—22no—
310C4×C8—1222no—
311C24—1221no—
312C24#1175819811yescharacteristic
313#41—1228no—
314#41—1228no—
315#41—1228no—
316#41—1228no—
317C2×Q8—612no—
318C2×Q8—612no—
319C2×Q8—612no—
320C2×Q8—1221no—
321C2×Q8—1221no—
322C2×Q8—1221no—
323C2×D4—612no—
324C2×D4—612no—
325C2×D4—612no—
326C2×D4—1224no—
327C2×D4—1224no—
328C2×D4—1224no—
329C2×D4—1221no—
330C2×D4—1221no—
331C2×D4—1221no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—1224no—
337C22×C4—1224no—
338C22×C4—1224no—
339C22×C4—1221no—
340C22×C4—1224no—
341C22×C4—1224no—
342C22×C4—1221no—
343C22×C4—1221no—
344C22×C4—1224no—
345C22×C4—4882no—
346C22×C4—4882no—
347C22×C4—4882no—
348C22×C4C8×D6112yes—
349C22×C4#1175818912yes—
350C22×C4#1175819811yescharacteristic
351C22×C4#1175819811yescharacteristic
352C22×C4#1175819811yescharacteristic
353C22×C4C2×C4×D6111yescharacteristic
354C22×C4C2×D24411yescharacteristic
355C22×C4C2×C22⋊D6111yescharacteristic
356C2×C8—42no—
357C2×C8—2442no—
358C4⋊C4—22no—
359C4⋊C4—22no—
360C4⋊C4—612no—
361C4⋊C4—612no—
362C4⋊C4—1224no—
363C4⋊C4—1224no—
364C4⋊C4—1221no—
365C4⋊C4—1221no—
366C4⋊C4—1224no—
367C22⋊C4—22no—
368C22⋊C4—22no—
369C22⋊C4—1224no—
370C22⋊C4—1224no—
371C42—21no—
372C42—21no—
373C42—1224no—
374C42—1224no—
375C42D4×D6112yes—
376C42D4×D6112yes—
377C23—21no—
378C23—21no—
379C23—41no—
380C23—41no—
381C23—1222no—
382C23—1222no—
383C23—1222no—
384C23—2442no—
385C23—2442no—
386C23#1451968912yes—
387C23C2×#1175819811yescharacteristic
388Q8—614no—
389Q8—1222no—
390Q8—1222no—
391Q8—1222no—
392D4—614no—
393D4—12216no—
394D4—1222no—
395D4—1222no—
396D4—1222no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—12216no—
410C2×C4—1222no—
411C2×C4—1222no—
412C2×C4—1222no—
413C2×C4—1222no—
414C2×C4—1222no—
415C2×C4—4884no—
416C2×C4—4884no—
417C2×C4—4884no—
418C2×C4—2442no—
419C2×C4—2442no—
420C2×C4#1451968912yes—
421C2×C4C22⋊C4×D6111yescharacteristic
422C2×C4C22⋊C4×D6111yescharacteristic
423C2×C4#1451974512yes—
424C2×C4#1451974712yes—
425C2×C4C2×C8×D6111yescharacteristic
426C2×C4M16×D6111yescharacteristic
427C2×C4M16×D6111yescharacteristic
428C2×C4C2×#1175818911yescharacteristic
429C8—82no—
430C8—4882no—
431C22—21no—
432C22—21no—
433C22—22no—
434C22—42no—
435C22—42no—
436C22—41no—
437C22—41no—
438C22—1224no—
439C22—2444no—
440C22—2444no—
441C22—2442no—
442C22—2442no—
443C22#1683961711yescharacteristic
444C22C2×#1451968911yescharacteristic
445C22#1683972511yescharacteristic
446C4—22no—
447C4—22no—
448C4—22no—
449C4—41no—
450C4—41no—
451C4—1224no—
452C4—2442no—
453C4—2442no—
454C4C22⋊C8×D6111yescharacteristic
455C4C22⋊C8×D6111yescharacteristic
456C4#1683972411yescharacteristic
457C4#1683972411yescharacteristic
458C2—21no—
459C2—21no—
460C2—42no—
461C2—2444no—
462C2#2144572811yescharacteristic
463C2#2144578711yescharacteristic
464C2#2144579511yescharacteristic
subgroupG/H
centerC22#16839617
commutatorC2×C4×C61C22×C8
FrattiniC2×C42C22×D61
FittingC61×#1458C2
socleC22×C61#379
prime radicalC22×#11758222C4
cosocleC2×C42×C61C23
hypercenter#1458D61
hypocenterC61#8324
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1458

Complements

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

NH ≅ G/Ntype
2. #21444215C2semidirect
3. #21444209C2semidirect
4. #21444133C2semidirect
5. C61×#1458C2semidirect
32. C2×#11758222C8semidirect
230. #1458D61semidirect
259. C61#8324semidirect

Maximal subgroups

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

subgroupindex
C2×#168402422
#214442152
#214442092
#214441332
C61×#14582
#832461