Finite Group Databasebeta

← #29575481

Subgroups — #29575481

Order 15616.

546 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454775C211yesmaximal, characteristic, complemented
2C4×#14519805C211yesmaximal, characteristic
3#21444204C211yesmaximal, characteristic, complemented
4C2×#16839489C211yesmaximal, characteristic, complemented
5#21444139C211yesmaximal, characteristic, complemented
6#21443657C211yesmaximal, characteristic, complemented
7C61×#1283C211yesmaximal, characteristic, complemented
8C2×#14519805C411yescharacteristic
9C4×#11758222C2211yescharacteristic
10C2×C4×D244C2211yescharacteristic
11#16839886—21no—
12#16839875—21no—
13#16839864—21no—
14C4×#11758190—21no—
15C4×D488—21no—
16#16839827—21no—
17#16839825—22no—
18#16839815C2211yescharacteristic
19#16839813—21no—
20#16839804C411yescharacteristic
21#16839768C411yescharacteristic
22#16839764C411yescharacteristic
23C2×C4×#92418C2211yescharacteristic
24C4×C8×D61—21no—
25#16839492—21no—
26#16839489—21no—
27#16839489—21no—
28#16839489—21no—
29#16839485—22no—
30C61×#431C2211yescharacteristic
31C2×C4⋊C8×C61C2211yescharacteristic
32C4×M16×C61C2211yescharacteristic
33C2×#11758222C2×C411yescharacteristic
34C22×D244C2×C411yescharacteristic
35C22×C4×D61—21no—
36#14519805—22no—
37#14519805C814yescomplemented
38C2×#11758190—21no—
39C2×D488—21no—
40C22×#92418—21no—
41C2×C8×D61—22no—
42C4×Dic122D411yescharacteristic
43C4×Dic122D411yescharacteristic
44C4×D244—21no—
45C4×D244—21no—
46C4×D244—21no—
47C4×D244—21no—
48C4×D244D411yescharacteristic
49C4×D244D411yescharacteristic
50C4×C22⋊D61—21no—
51C4×C22⋊D61—21no—
52#14519736C2×C411yescharacteristic
53#14519734—21no—
54C2×C4⋊Dic61C2×C411yescharacteristic
55C2×#11758198—21no—
56C42×D61—21no—
57#14519711—21no—
58#14519709—21no—
59C4⋊#92418—21no—
60#14519706—22no—
61#14519702—21no—
62#14519699—21no—
63#14519699—21no—
64#14519699—21no—
65C22⋊#92418—21no—
66#14519689—22no—
67C4×#92418—21no—
68C4×#92418—21no—
69C4×#92418D411yescharacteristic
70C4×#92418D411yescharacteristic
71C8×Dic61—22no—
72C2×M16×C61C2×C411yescharacteristic
73C2×M16×C61C2×C411yescharacteristic
74C22×C8×C61—21no—
75C2×C42×C61C2311yescharacteristic
76C4⋊C8×C61—21no—
77C4⋊C8×C61—21no—
78C4⋊C8×C61—21no—
79C22⋊C8×C61D412yes—
80#97×C61—21no—
81C4×C8×C61—21no—
82C4×C8×C61—21no—
83C23×D61—21no—
84C22×C4×C61C22×C411yescharacteristic
85C22×C4×C61C2×D411yescharacteristic
86C22×C4×C61#4111yescharacteristic
87C2×C22⋊D61—21no—
88C22×Dic61—21no—
89#11758222—21no—
90#11758222—21no—
91#11758222C2×C812yes—
92#11758222M1612yes—
93C2×D244—21no—
94C2×D244—21no—
95C2×D244—21no—
96C2×D244—21no—
97C2×D244—21no—
98C2×D244C22⋊C411yescharacteristic
99C2×D244C2×C812yescomplemented
100C2×C4×D61—21no—
101C2×C4×D61—21no—
102C2×C4×D61—21no—
103C2×C4×D61—41no—
104C2×C4×D61—41no—
105C2×C4×D61—81no—
106C2×C4×D61—81no—
107C2×Dic122C22⋊C411yescharacteristic
108M16×C61—21no—
109M16×C61—21no—
110M16×C61—21no—
111M16×C61C2×C812yescomplemented
112C2×C8×C61—21no—
113C2×C8×C61—21no—
114C2×C8×C61—22no—
115C2×C8×C61—41no—
116C2×C8×C61—81no—
117C42×C61C2×D411yescharacteristic
118C42×C61C2×D411yescharacteristic
119C42×C61C2×D411yescharacteristic
120C42×C61#4111yescharacteristic
121C22⋊Dic61—21no—
122#11758198—21no—
123#11758198—21no—
124#11758198—41no—
125#11758198—41no—
126C4⋊Dic61—21no—
127C4⋊Dic61—21no—
128C4⋊Dic61C22⋊C411yescharacteristic
129C4⋊Dic61C22⋊C411yescharacteristic
130#11758196—21no—
131#11758196—21no—
132C4×Dic61—21no—
133C4×Dic61—21no—
134C4×Dic61—21no—
135C2×#92418—21no—
136C2×#92418—21no—
137C2×#92418—42no—
138C2×#92418—41no—
139D488—24no—
140#11758190—24no—
141C8×D61—44no—
142C23×C61C4×D411yescharacteristic
143C22×D61—21no—
144C22×D61—22no—
145C22×D61—41no—
146C22×D61—41no—
147C22×D61—81no—
148C22×D61—81no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—41no—
152C2×C4×C61C2×C22⋊C411yescharacteristic
153C2×C4×C61C4×D411yescharacteristic
154C2×C4×C61#12011yescharacteristic
155C2×C4×C61#12111yescharacteristic
156C2×C4×C61#12111yescharacteristic
157C2×C4×C61#12311yescharacteristic
158C2×C4×C61C22×C811yescharacteristic
159C2×C4×C61C2×M1611yescharacteristic
160C2×C4×C61#13111yescharacteristic
161C2×C4×C61#13111yescharacteristic
162C22⋊D61—22no—
163C22⋊D61—22no—
164C2×Dic61—21no—
165C2×Dic61—21no—
166C2×Dic61—21no—
167C2×Dic61—41no—
168C2×Dic61—81no—
169D244—22no—
170D244—21no—
171D244—22no—
172D244—41no—
173D244—41no—
174D244C22⋊C812yes—
175C4×D61—22no—
176C4×D61—22no—
177C4×D61—42no—
178C4×D61—41no—
179C4×D61—41no—
180C4×D61—82no—
181C4×D61—81no—
182C4×D61—81no—
183Dic122—21no—
184Dic122C22⋊C812yes—
185C8×C61—22no—
186C8×C61—42no—
187C8×C61—41no—
188C8×C61—81no—
189#92418—22no—
190#92418—41no—
191#92418—81no—
192#9095—611nomaximal, Sylow
193C22×C61—21no—
194C22×C61—21no—
195C22×C61#38611yescharacteristic
196C22×C61C8×D411yescharacteristic
197C22×C61#43511yescharacteristic
198C2×D61—22no—
199C2×D61—41no—
200C2×D61—41no—
201C2×D61—42no—
202C2×D61—82no—
203C2×D61—81no—
204C2×D61—81no—
205C2×D61—82no—
206C4×C61—21no—
207C4×C61—21no—
208C4×C61—21no—
209C4×C61C2×C22⋊C811yescharacteristic
210C4×C61#40811yescharacteristic
211C4×C61C8×D411yescharacteristic
212C4×C61#43511yescharacteristic
213C4×C61#47111yescharacteristic
214C4×C61#47211yescharacteristic
215Dic61—22no—
216Dic61—41no—
217Dic61—41no—
218Dic61—81no—
219C8×#41—611no—
220C4×AGL(1,ℤ/8)—611no—
221#1477—611no—
222C2×D4⋊C8—611no—
223#1460—611no—
224#1283D6111yescharacteristic, complemented
225#1278—611no—
226C2×C61—21no—
227C2×C61—21no—
228C2×C61#186911yescharacteristic
229C2×C61#190611yescharacteristic
230C2×C61#190711yescharacteristic
231D61—42no—
232D61—82no—
233C2×AGL(1,ℤ/8)—611no—
234C4×#41—611no—
235C2×C4×D4—611no—
236C8×Q8—1221no—
237#442—1221no—
238#440—1221no—
239C4×SD16—1221no—
240C4×D8—1221no—
241C8×D4—1221no—
242C8×D4—1222no—
243#431—611no—
244#431—1221no—
245#431C2×D6111yescharacteristic
246#428—611no—
247C2×C4⋊C8C2×D6111yescharacteristic
248#418—611no—
249#417—611no—
250C4×M16C2×D6111yescharacteristic
251C2×C4×C8—611no—
252C2×C4×C8—1221no—
253Q8⋊C8—1221no—
254D4⋊C8—1221no—
255D4⋊C8—1221no—
256D4⋊C8—1221no—
257#323—1222no—
258C61#909511yescharacteristic, complemented, Sylow
259C2×#41—611no—
260C22×D4—611no—
261C23×C4—1221no—
262AGL(1,ℤ/8)—614no—
263AGL(1,ℤ/8)—1222no—
264C2×SD16—1221no—
265C2×D8—1221no—
266C2×M16C4×D6111yescharacteristic
267C2×M16C4×D6111yescharacteristic
268C22×C8—21no—
269C22×C8—1222no—
270C22×C8—1221no—
271C4×Q8—611no—
272C4×Q8—611no—
273C4×D4—611no—
274C4×D4—611no—
275C4×D4—1221no—
276C4×D4—1221no—
277C4×D4—1221no—
278C4×D4—1221no—
279C4×D4—1221no—
280C4×D4—1221no—
281#117—611no—
282#117—1221no—
283C2×C4⋊C4—611no—
284C2×C22⋊C4—1221no—
285C2×C42—1221no—
286C2×C42C22×D6111yescharacteristic
287#107—1221no—
288#106—1221no—
289C4⋊C8—21no—
290C4⋊C8—21no—
291C4⋊C8—21no—
292C4⋊C8—1222no—
293C4⋊C8—1221no—
294#103—1221no—
295#102—1221no—
296#102—1221no—
297#102—1221no—
298C22⋊C8—1222no—
299C22⋊C8—1221no—
300C22⋊C8D24412yes—
301#97—21no—
302C4×C8—21no—
303C4×C8—21no—
304C4×C8—611no—
305C4×C8—611no—
306C4×C8—1222no—
307C4×C8—1221no—
308C4×C8—1221no—
309C24—1221no—
310#41—612no—
311#41—612no—
312#41—1221no—
313#41—1221no—
314C2×Q8—611no—
315C2×D4—611no—
316C2×D4—612no—
317C2×D4—1221no—
318C2×D4—1221no—
319C2×D4—1221no—
320C2×D4—1221no—
321C2×D4—1221no—
322C2×D4—1221no—
323C22×C4—1221no—
324C22×C4—1221no—
325C22×C4—1221no—
326C22×C4—1221no—
327C22×C4—4881no—
328C22×C4—4881no—
329C22×C4—2441no—
330C22×C4—2441no—
331C22×C4C2×C4×D6111yescharacteristic
332C22×C4C2×D24411yescharacteristic
333C22×C4#1175822211yescharacteristic
334SD16—1224no—
335D8—1224no—
336M16—21no—
337M16—21no—
338M16—21no—
339M16C8×D6112yescomplemented
340C2×C8—21no—
341C2×C8—21no—
342C2×C8—22no—
343C2×C8—41no—
344C2×C8—81no—
345C2×C8—1221no—
346C2×C8—1221no—
347C2×C8—2444no—
348C2×C8—2442no—
349C2×C8—2441no—
350C4⋊C4—611no—
351C4⋊C4—611no—
352C4⋊C4—1221no—
353C4⋊C4—1221no—
354C4⋊C4—1221no—
355C4⋊C4—1221no—
356C22⋊C4—1221no—
357C22⋊C4—1221no—
358C22⋊C4—1221no—
359C22⋊C4—2441no—
360C22⋊C4—2441no—
361C42—1221no—
362C42—1221no—
363C42—1221no—
364C42D4×D6111yescharacteristic
365C42D4×D6111yescharacteristic
366C42D4×D6111yescharacteristic
367C42#1175822611yescharacteristic
368C23—1221no—
369C23—1222no—
370C23—4881no—
371C23—4881no—
372C23—2441no—
373C23—2441no—
374C23C4×D24411yescharacteristic
375Q8—612no—
376Q8—1221no—
377D4—612no—
378D4—1222no—
379D4—1222no—
380D4—1222no—
381D4—1221no—
382D4—1222no—
383D4—2441no—
384D4—2441no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—41no—
388C2×C4—1221no—
389C2×C4—1222no—
390C2×C4—1222no—
391C2×C4—1221no—
392C2×C4—1221no—
393C2×C4—4882no—
394C2×C4—4881no—
395C2×C4—4881no—
396C2×C4—4881no—
397C2×C4—2442no—
398C2×C4—2441no—
399C2×C4—2441no—
400C2×C4—2441no—
401C2×C4C22⋊C4×D6111yescharacteristic
402C2×C4#1451973911yescharacteristic
403C2×C4#1451974711yescharacteristic
404C2×C4#1451975011yescharacteristic
405C2×C4#1451975211yescharacteristic
406C2×C4#1451976211yescharacteristic
407C2×C4C2×C8×D6111yescharacteristic
408C2×C4M16×D6111yescharacteristic
409C2×C4#1451978311yescharacteristic
410C2×C4#1451978511yescharacteristic
411C8—22no—
412C8—42no—
413C8—41no—
414C8—81no—
415C8—1222no—
416C8—4881no—
417C8—2441no—
418C22—21no—
419C22—21no—
420C22—1222no—
421C22—4882no—
422C22—4882no—
423C22—4881no—
424C22—4881no—
425C22—2442no—
426C22—2441no—
427C22—2441no—
428C22#1683964011yescharacteristic
429C22C8×D24411yescharacteristic
430C22#1683983511yescharacteristic
431C4—21no—
432C4—21no—
433C4—21no—
434C4—1222no—
435C4—4881no—
436C4—2441no—
437C4—2441no—
438C4C22⋊C8×D6111yescharacteristic
439C4#1683972711yescharacteristic
440C4#1683982711yescharacteristic
441C4#1683983211yescharacteristic
442C4#1684002811yescharacteristic
443C4#1684003111yescharacteristic
444C2—21no—
445C2—21no—
446C2—4882no—
447C2—2442no—
448C2#2144611011yescharacteristic
449C2#2144632111yescharacteristic
450C2#2144632811yescharacteristic
subgroupG/H
centerC2×C4#14519750
commutatorC2×C4×C61C22×C8
FrattiniC2×C42C22×D61
FittingC61×#1283C2
socleC22×C61#386
prime radicalC2×#14519805C4
cosocleC2×C42×C61C23
hypercenter#1283D61
hypocenterC61#9095
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1283

Complements

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

NH ≅ G/Ntype
1. #21454775C2semidirect
3. #21444204C2semidirect
4. C2×#16839489C2semidirect
5. #21444139C2semidirect
6. #21443657C2semidirect
7. C61×#1283C2semidirect
37. #14519805C8semidirect
99. C2×D244C2×C8semidirect
111. M16×C61C2×C8semidirect
224. #1283D61semidirect
258. C61#9095semidirect
339. M16C8×D61semidirect

Maximal subgroups

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

subgroupindex
#214547752
C4×#145198052
#214442042
C2×#168394892
#214441392
#214436572
C61×#12832
#909561