Finite Group Databasebeta

← #29575657

Subgroups — #29575657

Order 15616.

644 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×C4⋊C8×D61C211yesmaximal, characteristic
2#21454172C211yesmaximal, characteristic
3#21445796C211yesmaximal, characteristic
4C2×#16839509C211yesmaximal, characteristic, complemented
5C2×#16839507C211yesmaximal, characteristic, complemented
6#21443702C211yesmaximal, characteristic, complemented
7C61×#1296C211yesmaximal, characteristic, complemented
8C22×C8×D61—21no—
9C2×#14519777C2211yescharacteristic
10C2×#14519757—21no—
11C2×C42×D61C2211yescharacteristic
12C2×C4⋊#92418C2211yescharacteristic
13C2×C4⋊#92418C2211yescharacteristic
14C2×#14519706—21no—
15C4⋊C8×D61—22no—
16C4⋊C8×D61—22no—
17C2×#14519689—21no—
18#16839667—21no—
19#16839661—21no—
20#16839661C412yes—
21#16839619—21no—
22#16839619C412yes—
23#16839516—21no—
24#16839509—22no—
25#16839507—22no—
26C2×C4⋊C8×C61C2211yescharacteristic
27C2×C4⋊C8×C61C2211yescharacteristic
28C61×#384C2211yescharacteristic
29C22×Dic122—21no—
30C22×C4×D61C2×C411yescharacteristic
31C22×C4×D61D411yescharacteristic
32C22×C4×D61D411yescharacteristic
33C22×#92418—21no—
34C22×#92418—21no—
35C2×C8×D61—24no—
36C2×C8×D61—42no—
37C2×C8×D61—42no—
38#14519777—21no—
39#14519777—21no—
40#14519777—21no—
41#14519777—21no—
42#14519757—42no—
43#14519757—42no—
44C2×C4⋊Dic61—21no—
45C2×C4⋊Dic61—22no—
46C2×C4⋊Dic61C2×C412yes—
47C2×#11758198—22no—
48C2×C4×Dic61C2×C411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50C2×C4×Dic61D411yescharacteristic
51C42×D61—21no—
52C42×D61—21no—
53C42×D61—21no—
54C42×D61—21no—
55C4⋊#92418—21no—
56C4⋊#92418—21no—
57C4⋊#92418—21no—
58C4⋊#92418D412yes—
59#14519706—24no—
60#14519689—42no—
61#14519684—22no—
62#14519684—22no—
63C22×C8×C61—21no—
64C22×C8×C61—21no—
65C2×C4⋊C4×C61—21no—
66C2×C4⋊C4×C61—21no—
67C2×C4⋊C4×C61C2×C412yes—
68C2×C42×C61C2311yescharacteristic
69C4⋊C8×C61—21no—
70C4⋊C8×C61—21no—
71C4⋊C8×C61—21no—
72C4⋊C8×C61D412yes—
73C23×D61C22⋊C411yescharacteristic
74C22×C4×C61—22no—
75C22×C4×C61C22×C411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C22×Dic61—22no—
79C22×Dic61C22⋊C411yescharacteristic
80C22×Dic61C22⋊C411yescharacteristic
81C22×Dic61C22⋊C411yescharacteristic
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×C4×D61—21no—
89C2×C4×D61—21no—
90C2×C4×D61—22no—
91C2×C4×D61—21no—
92C2×C4×D61—21no—
93C2×C4×D61—41no—
94C2×C4×D61D812yes—
95C2×C4×D61SD1612yes—
96C2×C4×D61SD1612yes—
97C2×C4×D61Q1612yes—
98C2×Dic122—41no—
99C2×Dic122—41no—
100C2×Dic122—41no—
101C2×Dic122—41no—
102C2×Dic122—41no—
103C2×Dic122—41no—
104C2×C8×C61—22no—
105C2×C8×C61—41no—
106C2×C8×C61—41no—
107C2×C8×C61—41no—
108C2×C8×C61—41no—
109C2×C8×C61—41no—
110C4⋊C4×C61—42no—
111C4⋊C4×C61—41no—
112C4⋊C4×C61—41no—
113C4⋊C4×C61—41no—
114C4⋊C4×C61—41no—
115C42×C61C2×D411yescharacteristic
116C42×C61C2×D411yescharacteristic
117C42×C61#4111yescharacteristic
118C42×C61#4111yescharacteristic
119#11758198—44no—
120C4⋊Dic61—22no—
121C4⋊Dic61—22no—
122C4⋊Dic61—41no—
123C4⋊Dic61—41no—
124C4⋊Dic61—44no—
125C4×Dic61—21no—
126C4×Dic61—21no—
127C4×Dic61—21no—
128C4×Dic61—21no—
129C4×Dic61—21no—
130C4×Dic61—21no—
131C2×#92418—22no—
132C2×#92418—41no—
133C2×#92418—41no—
134C2×#92418—41no—
135C2×#92418—41no—
136C2×#92418—41no—
137C8×D61—48no—
138C23×C61C2×C22⋊C411yescharacteristic
139C22×D61—21no—
140C22×D61—21no—
141C22×D61—21no—
142C22×D61—21no—
143C22×D61#10112yes—
144C22×D61#10212yes—
145C22×D61#10312yes—
146C2×C4×C61—21no—
147C2×C4×C61—21no—
148C2×C4×C61—42no—
149C2×C4×C61—42no—
150C2×C4×C61—42no—
151C2×C4×C61C4×D411yescharacteristic
152C2×C4×C61C4×D411yescharacteristic
153C2×C4×C61#12011yescharacteristic
154C2×C4×C61#12111yescharacteristic
155C2×C4×C61#12111yescharacteristic
156C2×C4×C61#12311yescharacteristic
157C2×C4×C61C2×D811yescharacteristic
158C2×C4×C61C2×SD1611yescharacteristic
159C2×C4×C61C2×SD1611yescharacteristic
160C2×C4×C61C2×Q1611yescharacteristic
161C2×C4×C61#13511yescharacteristic
162C2×C4×C61#13511yescharacteristic
163C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C61#13711yescharacteristic
165C2×Dic61—21no—
166C2×Dic61—21no—
167C2×Dic61—21no—
168C2×Dic61—21no—
169C2×Dic61—21no—
170C2×Dic61—21no—
171C2×Dic61—21no—
172C2×Dic61—42no—
173C2×Dic61—42no—
174C2×Dic61—42no—
175C2×Dic61#10212yes—
176C2×Dic61#10312yes—
177C4×D61—22no—
178C4×D61—22no—
179C4×D61—22no—
180C4×D61—22no—
181C4×D61—22no—
182C4×D61—22no—
183C4×D61—22no—
184C4×D61—22no—
185C4×D61—42no—
186C4×D61—42no—
187Dic122—81no—
188Dic122—81no—
189Dic122—81no—
190Dic122—81no—
191C8×C61—42no—
192C8×C61—81no—
193#92418—42no—
194#92418—81no—
195#9129—611nomaximal, Sylow
196C22×C61#38611yescharacteristic
197C22×C61C2×#10111yescharacteristic
198C22×C61#41311yescharacteristic
199C22×C61C2×#10211yescharacteristic
200C22×C61C2×#10311yescharacteristic
201C22×C61#41611yescharacteristic
202C22×C61#41711yescharacteristic
203C2×D61—22no—
204C2×D61—22no—
205C2×D61—22no—
206C2×D61—22no—
207C2×D61—22no—
208C2×D61—22no—
209C2×D61#33214yescomplemented
210C4×C61—21no—
211C4×C61—21no—
212C4×C61—82no—
213C4×C61#45011yescharacteristic
214C4×C61#45111yescharacteristic
215C4×C61#46511yescharacteristic
216C4×C61#46511yescharacteristic
217C4×C61#46611yescharacteristic
218C4×C61#46611yescharacteristic
219C4×C61#48311yescharacteristic
220C4×C61#48411yescharacteristic
221Dic61—22no—
222Dic61—22no—
223Dic61—41no—
224Dic61—82no—
225C22×C4⋊C8—611no—
226#2857—611no—
227#1797—611no—
228C2×#332—611no—
229C2×#332—611no—
230#1296—611no—
231#1296D6111yescharacteristic, complemented
232C2×C61C2×#33211yescharacteristic
233C2×C61#154211yescharacteristic
234C2×C61#154711yescharacteristic
235C2×C61#155211yescharacteristic
236C2×C61#187211yescharacteristic
237C2×C61#189311yescharacteristic
238C2×C61#190111yescharacteristic
239D61—24no—
240C23×C8—1221no—
241C2×C4⋊Q8—611no—
242C2×C22⋊Q8—1221no—
243C22×C42—611no—
244C2×C4⋊C8—611no—
245C2×C4⋊C8—611no—
246C2×C4⋊C8—1222no—
247C2×C4⋊C8—1221no—
248C2×C4⋊C8—1222no—
249C2×C4⋊C8C2×D6111yescharacteristic
250C2×C4⋊C8C2×D6111yescharacteristic
251C2×C22⋊C8—1221no—
252#391—1221no—
253#389—612no—
254#389—1221no—
255#384C2×D6111yescharacteristic
256#380—612no—
257#380—1221no—
258#336—1221no—
259#332—1222no—
260#332—1222no—
261C61#912911yescharacteristic, complemented, Sylow
262C22×Q8—1221no—
263C23×C4—611no—
264C23×C4—611no—
265C23×C4—611no—
266C22×C8—21no—
267C22×C8—21no—
268C22×C8—1224no—
269C22×C8—1221no—
270C22×C8—1221no—
271C22×C8—2442no—
272C22×C8—2442no—
273C4⋊Q8—1221no—
274C4⋊Q8—1221no—
275C4⋊Q8—1221no—
276C4⋊Q8—1221no—
277C22⋊Q8—2442no—
278C22⋊Q8—2442no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—612no—
282C2×C4⋊C4—1222no—
283C2×C4⋊C4—1221no—
284C2×C4⋊C4C4×D6112yes—
285C2×C22⋊C4—1222no—
286C2×C42—611no—
287C2×C42—611no—
288C2×C42—611no—
289C2×C42—1221no—
290C2×C42—1221no—
291C2×C42—1221no—
292C2×C42—1221no—
293C2×C42C22×D6111yescharacteristic
294C4⋊C8—21no—
295C4⋊C8—21no—
296C4⋊C8—21no—
297C4⋊C8—612no—
298C4⋊C8—1224no—
299C4⋊C8—1221no—
300C4⋊C8—1221no—
301C4⋊C8—1221no—
302C4⋊C8D24412yes—
303C22⋊C8—2442no—
304#95—1222no—
305#95—1222no—
306C24—611no—
307C2×Q8—2441no—
308C2×Q8—2441no—
309C2×Q8—2441no—
310C2×Q8—2441no—
311C2×Q8—2441no—
312C2×Q8—2441no—
313C22×C4—22no—
314C22×C4—611no—
315C22×C4—611no—
316C22×C4—612no—
317C22×C4—612no—
318C22×C4—612no—
319C22×C4—612no—
320C22×C4—611no—
321C22×C4—1222no—
322C22×C4—1221no—
323C22×C4—1221no—
324C22×C4—1221no—
325C22×C4—1221no—
326C22×C4—1221no—
327C22×C4—1221no—
328C22×C4—1221no—
329C22×C4—1221no—
330C22×C4—1221no—
331C22×C4—1221no—
332C22×C4—1222no—
333C22×C4—2441no—
334C22×C4C2×C4×D6111yescharacteristic
335C22×C4D4×D6111yescharacteristic
336C22×C4D4×D6111yescharacteristic
337C2×C8—22no—
338C2×C8—41no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8—41no—
342C2×C8—41no—
343C2×C8—1222no—
344C2×C8—2448no—
345C2×C8—2441no—
346C2×C8—2441no—
347C2×C8—2441no—
348C2×C8—2441no—
349C2×C8—2441no—
350C4⋊C4—42no—
351C4⋊C4—41no—
352C4⋊C4—41no—
353C4⋊C4—41no—
354C4⋊C4—41no—
355C4⋊C4—1222no—
356C4⋊C4—1222no—
357C4⋊C4—2444no—
358C4⋊C4—2441no—
359C4⋊C4—2441no—
360C22⋊C4—2444no—
361C42—1221no—
362C42—1221no—
363C42—1221no—
364C42—1221no—
365C42—1221no—
366C42—1221no—
367C42C2×D24411yescharacteristic
368C42#1175822211yescharacteristic
369C42D4×D6111yescharacteristic
370C42#1175822611yescharacteristic
371C23—612no—
372C23—612no—
373C23—612no—
374C23—1221no—
375C23—1221no—
376C23—1221no—
377C23—1221no—
378C23C22⋊C4×D6111yescharacteristic
379Q8—4881no—
380Q8—4881no—
381Q8—4881no—
382Q8—4881no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—612no—
389C2×C4—612no—
390C2×C4—1221no—
391C2×C4—1221no—
392C2×C4—1221no—
393C2×C4—1221no—
394C2×C4—1222no—
395C2×C4—1222no—
396C2×C4—1222no—
397C2×C4—1222no—
398C2×C4—1222no—
399C2×C4—1222no—
400C2×C4—1222no—
401C2×C4—1222no—
402C2×C4—1221no—
403C2×C4—1221no—
404C2×C4—1221no—
405C2×C4—2442no—
406C2×C4—2442no—
407C2×C4—2442no—
408C2×C4—2442no—
409C2×C4—2442no—
410C2×C4#1451973911yescharacteristic
411C2×C4C4×D24411yescharacteristic
412C2×C4#1451974711yescharacteristic
413C2×C4#1451975011yescharacteristic
414C2×C4#1451975211yescharacteristic
415C2×C4#1451976211yescharacteristic
416C2×C4D8×D6111yescharacteristic
417C2×C4SD16×D6111yescharacteristic
418C2×C4SD16×D6111yescharacteristic
419C2×C4Q16×D6111yescharacteristic
420C2×C4#1451979811yescharacteristic
421C2×C4#1451980011yescharacteristic
422C2×C4#1451980111yescharacteristic
423C2×C4#1451980611yescharacteristic
424C8—42no—
425C8—81no—
426C8—4881no—
427C8—2442no—
428C22—614no—
429C22—1222no—
430C22—1222no—
431C22—1222no—
432C22—1222no—
433C22—1222no—
434C22—1222no—
435C22#1683964011yescharacteristic
436C22#101×D6111yescharacteristic
437C22#1683974311yescharacteristic
438C22#102×D6111yescharacteristic
439C22#103×D6111yescharacteristic
440C22#1683975711yescharacteristic
441C22#1683976011yescharacteristic
442C4—21no—
443C4—21no—
444C4—82no—
445C4—1222no—
446C4—1222no—
447C4—4882no—
448C4—2441no—
449C4#1683991411yescharacteristic
450C4#1683991911yescharacteristic
451C4#1683999211yescharacteristic
452C4#1683999411yescharacteristic
453C4#1683999711yescharacteristic
454C4#1683999911yescharacteristic
455C4#1684009411yescharacteristic
456C4#1684009911yescharacteristic
457C2—1224no—
458C2#332×D6111yescharacteristic
459C2#2144447311yescharacteristic
460C2#2144449311yescharacteristic
461C2#2144451811yescharacteristic
462C2#2144612511yescharacteristic
463C2#2144624611yescharacteristic
464C2#2144628611yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1296C2
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1296D61
hypocenterC61#9129
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
4. C2×#16839509C2semidirect
5. C2×#16839507C2semidirect
6. #21443702C2semidirect
7. C61×#1296C2semidirect
209. C2×D61#332semidirect
231. #1296D61semidirect
261. C61#9129semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C8×D612
#214541722
#214457962
C2×#168395092
C2×#168395072
#214437022
C61×#12962
#912961