Finite Group Databasebeta

← #29582364

Subgroups — #29582364

Order 15616.

628 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840058C211yesmaximal, characteristic, complemented
2C2×#16840053C211yesmaximal, characteristic
3#21450742C211yesmaximal, characteristic
4#21446620C211yesmaximal, characteristic, complemented
5C2×#16839492C211yesmaximal, characteristic, complemented
6C2×#16839489C211yesmaximal, characteristic
7C61×#1296C211yesmaximal, characteristic, complemented
8C2×#14519777C2211yescharacteristic
9C2×#14519757—21no—
10C2×C4×Dic122C2211yescharacteristic
11C2×C4×D244C2211yescharacteristic
12#16840058—22no—
13#16840058—22no—
14#16840053—22no—
15#16840053—22no—
16C2×#14519711—21no—
17C2×#14519709—21no—
18C2×#14519702—21no—
19C2×#14519700—22no—
20C2×#14519699—21no—
21C2×C4×#92418C2211yescharacteristic
22#16839684—22no—
23#16839663—21no—
24#16839661—21no—
25#16839619—21no—
26#16839492—22no—
27#16839489—22no—
28C2×C4⋊C8×C61C2211yescharacteristic
29C2×C4⋊C8×C61C2211yescharacteristic
30C61×#384C2211yescharacteristic
31C22×Dic122—21no—
32C22×Dic122D411yescharacteristic
33C22×D244D411yescharacteristic
34C22×C4×D61—21no—
35C22×#92418—21no—
36#14519777—21no—
37#14519777—21no—
38#14519777—21no—
39#14519777D412yes—
40#14519757—42no—
41#14519757—42no—
42C4×Dic122—21no—
43C4×Dic122—21no—
44C4×Dic122—21no—
45C4×Dic122—21no—
46C4×D244—21no—
47C4×D244—21no—
48C4×D244—21no—
49C4×D244—21no—
50C2×C4⋊Dic61—21no—
51C2×C4⋊Dic61—21no—
52C2×C4⋊Dic61—22no—
53C2×C4⋊Dic61D411yescharacteristic
54C2×C4⋊Dic61D411yescharacteristic
55C2×#11758196—21no—
56C2×#11758198—22no—
57C2×#11758198—21no—
58C2×#11758198—22no—
59C2×C4×Dic61—21no—
60#14519711—24no—
61#14519709—24no—
62#14519702—24no—
63#14519700—44no—
64#14519699—24no—
65C4×#92418—21no—
66C4×#92418—21no—
67#14519684—22no—
68C22×C8×C61—21no—
69C22×C8×C61—21no—
70C2×C4⋊C4×C61—21no—
71C2×C4⋊C4×C61—21no—
72C2×C4⋊C4×C61D412yes—
73C2×C42×C61C2311yescharacteristic
74C4⋊C8×C61—21no—
75C4⋊C8×C61—21no—
76C4⋊C8×C61D412yes—
77C4⋊C8×C61D412yes—
78C23×D61—21no—
79C22×C4×C61—22no—
80C22×C4×C61C2×D411yescharacteristic
81C22×C4×C61C2×D411yescharacteristic
82C22×C4×C61C2×D411yescharacteristic
83C22×Dic61—21no—
84C22×Dic61—21no—
85C22×Dic61—21no—
86C22×Dic61—41no—
87C2×D244—21no—
88C2×D244—21no—
89C2×D244—21no—
90C2×D244—21no—
91C2×D244—21no—
92C2×D244Q1612yes—
93C2×C4×D61—41no—
94C2×C4×D61—41no—
95C2×C4×D61—41no—
96C2×C4×D61—41no—
97C2×C4×D61—41no—
98C2×C4×D61—41no—
99C2×Dic122—21no—
100C2×Dic122—21no—
101C2×Dic122—21no—
102C2×Dic122—21no—
103C2×Dic122—21no—
104C2×Dic122—22no—
105C2×Dic122—42no—
106C2×Dic122—42no—
107C2×Dic122—41no—
108C2×Dic122SD1612yes—
109C2×C8×C61—22no—
110C2×C8×C61—22no—
111C2×C8×C61—41no—
112C2×C8×C61—41no—
113C2×C8×C61—41no—
114C2×C8×C61—41no—
115C4⋊C4×C61—42no—
116C4⋊C4×C61—41no—
117C4⋊C4×C61—41no—
118C4⋊C4×C61—41no—
119C4⋊C4×C61—41no—
120C42×C61C2×D411yescharacteristic
121C42×C61C2×D411yescharacteristic
122C42×C61C2×D411yescharacteristic
123C42×C61#4111yescharacteristic
124#11758198—44no—
125#11758198—41no—
126#11758198—41no—
127#11758198—82no—
128C4⋊Dic61—22no—
129C4⋊Dic61—22no—
130C4⋊Dic61—21no—
131C4⋊Dic61—21no—
132C4⋊Dic61—21no—
133C4⋊Dic61—21no—
134C4⋊Dic61—44no—
135C4⋊Dic61—41no—
136C4⋊Dic61—41no—
137#11758196—41no—
138#11758196—41no—
139C4×Dic61—41no—
140C4×Dic61—41no—
141C2×#92418—22no—
142C2×#92418—41no—
143C2×#92418—41no—
144C23×C61#12011yescharacteristic
145C22×D61—22no—
146C22×D61—41no—
147C22×D61—41no—
148C22×D61—41no—
149C22×D61—41no—
150C22×D61—41no—
151C22×D61—41no—
152C2×C4×C61—21no—
153C2×C4×C61—21no—
154C2×C4×C61—42no—
155C2×C4×C61—42no—
156C2×C4×C61—42no—
157C2×C4×C61#12011yescharacteristic
158C2×C4×C61#12011yescharacteristic
159C2×C4×C61#12111yescharacteristic
160C2×C4×C61#12111yescharacteristic
161C2×C4×C61#12111yescharacteristic
162C2×C4×C61#12711yescharacteristic
163C2×C4×C61C2×SD1611yescharacteristic
164C2×C4×C61C2×Q1611yescharacteristic
165C2×C4×C61#13511yescharacteristic
166C2×C4×C61#13511yescharacteristic
167C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C61#13711yescharacteristic
169C2×C4×C61#13711yescharacteristic
170C2×C4×C61#13711yescharacteristic
171C2×Dic61—22no—
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61—41no—
175C2×Dic61—42no—
176C2×Dic61—41no—
177C2×Dic61—41no—
178C2×Dic61—41no—
179C2×Dic61—41no—
180C2×Dic61—41no—
181C2×Dic61—81no—
182C2×Dic61—81no—
183D244—22no—
184D244—22no—
185D244—41no—
186D244—41no—
187C4×D61—81no—
188C4×D61—81no—
189C4×D61—81no—
190C4×D61—81no—
191Dic122—22no—
192Dic122—22no—
193Dic122—41no—
194Dic122—41no—
195Dic122—44no—
196Dic122—82no—
197C8×C61—42no—
198C8×C61—42no—
199#92418—42no—
200#10236—611nomaximal, Sylow
201C22×C61#39211yescharacteristic
202C22×C61#45011yescharacteristic
203C22×C61#45111yescharacteristic
204C22×C61#45211yescharacteristic
205C22×C61#45211yescharacteristic
206C22×C61#45311yescharacteristic
207C22×C61#45411yescharacteristic
208C2×D61—42no—
209C2×D61—42no—
210C2×D61—42no—
211C2×D61—81no—
212C2×D61—81no—
213C2×D61—81no—
214C2×D61—81no—
215C4×C61—21no—
216C4×C61—21no—
217C4×C61—82no—
218C4×C61#44811yescharacteristic
219C4×C61#44911yescharacteristic
220C4×C61#45111yescharacteristic
221C4×C61#45211yescharacteristic
222C4×C61#46511yescharacteristic
223C4×C61#46711yescharacteristic
224C4×C61#46811yescharacteristic
225C4×C61#47011yescharacteristic
226Dic61—42no—
227Dic61—81no—
228Dic61—82no—
229Dic61—81no—
230C2×#477—611no—
231C2×#476—611no—
232#2538—611no—
233#1956—611no—
234C2×Q8⋊C8—611no—
235C2×D4⋊C8—611no—
236#1296D6111yescharacteristic, complemented
237C2×C61#163111yescharacteristic
238C2×C61#163211yescharacteristic
239C2×C61#163711yescharacteristic
240C2×C61#163811yescharacteristic
241C2×C61#200011yescharacteristic
242C2×C61#200111yescharacteristic
243C2×C61#200611yescharacteristic
244D61—82no—
245C2×C4⋊Q8—611no—
246C2×C22⋊Q8—1221no—
247C2×C4×Q8—611no—
248C2×C4×D4—611no—
249#477—1222no—
250#477—1222no—
251#476—1222no—
252#476—1222no—
253C2×#107—1221no—
254C2×#106—1221no—
255C2×C4⋊C8C2×D6111yescharacteristic
256C2×C4⋊C8C2×D6111yescharacteristic
257C2×#103—1221no—
258C2×#103—1222no—
259C2×#102—1221no—
260C2×C4×C8—611no—
261#396—1222no—
262#390—1221no—
263#389—1221no—
264#384C2×D6111yescharacteristic
265#380—1221no—
266Q8⋊C8—1222no—
267D4⋊C8—1222no—
268C61#1023611yescharacteristic, complemented, Sylow
269C22×Q8—611no—
270C22×Q8—1221no—
271C22×D4—611no—
272C23×C4—1221no—
273C22×C8—21no—
274C22×C8—21no—
275C22×C8—1221no—
276C4⋊Q8—612no—
277C4⋊Q8—1221no—
278C4⋊Q8—1221no—
279C4⋊Q8—1221no—
280C22⋊Q8—2442no—
281C22⋊Q8—2442no—
282C4×Q8—1221no—
283C4×Q8—1221no—
284C4×Q8—1221no—
285C4×Q8—1221no—
286C4×D4—1221no—
287C4×D4—1221no—
288C4×D4—1221no—
289C4×D4—1221no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—611no—
293C2×C4⋊C4—611no—
294C2×C4⋊C4—1221no—
295C2×C4⋊C4—1221no—
296C2×C4⋊C4—1222no—
297C2×C4⋊C4—1221no—
298C2×C4⋊C4D24412yes—
299C2×C22⋊C4—1222no—
300C2×C22⋊C4—1222no—
301C2×C22⋊C4—1221no—
302C2×C42—1221no—
303C2×C42C22×D6111yescharacteristic
304#107—1224no—
305#106—1224no—
306C4⋊C8—21no—
307C4⋊C8—21no—
308C4⋊C8D24412yes—
309C4⋊C8D24412yes—
310#103—1224no—
311#103—2444no—
312#102—1224no—
313C4×C8—1221no—
314C4×C8—1221no—
315#95—1222no—
316C24—1221no—
317C2×Q8—612no—
318C2×Q8—1221no—
319C2×Q8—1221no—
320C2×Q8—1221no—
321C2×Q8—1221no—
322C2×Q8—1222no—
323C2×Q8—1221no—
324C2×Q8—2442no—
325C2×Q8—2442no—
326C2×Q8—2441no—
327C2×D4—612no—
328C2×D4—1221no—
329C2×D4—1221no—
330C2×D4—1221no—
331C2×D4—1221no—
332C2×D4—1221no—
333C22×C4—22no—
334C22×C4—1221no—
335C22×C4—1221no—
336C22×C4—1221no—
337C22×C4—2441no—
338C22×C4—2441no—
339C22×C4—2441no—
340C22×C4—2441no—
341C22×C4—2441no—
342C22×C4—2441no—
343C22×C4—2441no—
344C22×C4C2×D24411yescharacteristic
345C22×C4D4×D6111yescharacteristic
346C22×C4D4×D6111yescharacteristic
347C2×C8—22no—
348C2×C8—22no—
349C2×C8—41no—
350C2×C8—41no—
351C2×C8—41no—
352C2×C8—41no—
353C2×C8—1222no—
354C2×C8—2441no—
355C2×C8—2441no—
356C4⋊C4—42no—
357C4⋊C4—41no—
358C4⋊C4—41no—
359C4⋊C4—41no—
360C4⋊C4—41no—
361C4⋊C4—1222no—
362C4⋊C4—1222no—
363C4⋊C4—1221no—
364C4⋊C4—1221no—
365C4⋊C4—1221no—
366C4⋊C4—1221no—
367C4⋊C4—2444no—
368C4⋊C4—2441no—
369C4⋊C4—2441no—
370C4⋊C4—2441no—
371C4⋊C4—2441no—
372C22⋊C4—4882no—
373C22⋊C4—2444no—
374C22⋊C4—2441no—
375C22⋊C4—2441no—
376C42—2441no—
377C42—2441no—
378C42C2×D24411yescharacteristic
379C42C2×D24411yescharacteristic
380C42D4×D6111yescharacteristic
381C42#1175822611yescharacteristic
382C23—1222no—
383C23—2441no—
384C23—2441no—
385C23—2441no—
386C23—2441no—
387C23—2441no—
388C23—2441no—
389C23#1451974711yescharacteristic
390Q8—1222no—
391Q8—1222no—
392Q8—4882no—
393Q8—2444no—
394Q8—2441no—
395Q8—2441no—
396D4—1222no—
397D4—1222no—
398D4—2441no—
399D4—2441no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—1222no—
406C2×C4—4881no—
407C2×C4—4881no—
408C2×C4—4881no—
409C2×C4—4881no—
410C2×C4—4881no—
411C2×C4—4881no—
412C2×C4—2441no—
413C2×C4—2441no—
414C2×C4—2441no—
415C2×C4—2441no—
416C2×C4—2441no—
417C2×C4—2442no—
418C2×C4—2441no—
419C2×C4—2441no—
420C2×C4—2441no—
421C2×C4#1451974711yescharacteristic
422C2×C4#1451974711yescharacteristic
423C2×C4#1451975211yescharacteristic
424C2×C4#1451975211yescharacteristic
425C2×C4#1451975211yescharacteristic
426C2×C4#1451977411yescharacteristic
427C2×C4SD16×D6111yescharacteristic
428C2×C4Q16×D6111yescharacteristic
429C2×C4#1451979611yescharacteristic
430C2×C4#1451979811yescharacteristic
431C2×C4#1451980111yescharacteristic
432C2×C4#1451980611yescharacteristic
433C2×C4#1451980611yescharacteristic
434C2×C4#1451980911yescharacteristic
435C8—42no—
436C8—42no—
437C8—2442no—
438C22—4881no—
439C22—4881no—
440C22—4881no—
441C22—4881no—
442C22—2442no—
443C22—2442no—
444C22—2442no—
445C22#1683967211yescharacteristic
446C22#1683991411yescharacteristic
447C22#1683991911yescharacteristic
448C22#1683992511yescharacteristic
449C22#1683992711yescharacteristic
450C22#1683993211yescharacteristic
451C22#1683993711yescharacteristic
452C4—21no—
453C4—21no—
454C4—82no—
455C4—4881no—
456C4—4882no—
457C4—4881no—
458C4—2442no—
459C4#1683990211yescharacteristic
460C4#1683990811yescharacteristic
461C4#1683991911yescharacteristic
462C4#1683992511yescharacteristic
463C4#1683999211yescharacteristic
464C4#1684000411yescharacteristic
465C4#1684000911yescharacteristic
466C4#1684002111yescharacteristic
467C2—4882no—
468C2#2144494711yescharacteristic
469C2#2144495411yescharacteristic
470C2#2144498511yescharacteristic
471C2#2144499211yescharacteristic
472C2#2144682511yescharacteristic
473C2#2144683011yescharacteristic
474C2#2144686311yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1296C2
socleC23×C61#120
prime radicalC22×D244D4
hypercenter#1296D61
hypocenterC61#10236
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
1. C2×#16840058C2semidirect
4. #21446620C2semidirect
5. C2×#16839492C2semidirect
7. C61×#1296C2semidirect
236. #1296D61semidirect
268. C61#10236semidirect

Maximal subgroups

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

subgroupindex
C2×#168400582
C2×#168400532
#214507422
#214466202
C2×#168394922
C2×#168394892
C61×#12962
#1023661