Finite Group Databasebeta

← #29574652

Subgroups — #29574652

Order 15616.

540 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454932C211yesmaximal, characteristic, complemented
2C4×#14519805C211yesmaximal, characteristic
3#21446613C211yesmaximal, characteristic, complemented
4#21444209C211yesmaximal, characteristic, complemented
5#21444202C211yesmaximal, characteristic, complemented
6#21443670C211yesmaximal, characteristic, complemented
7C61×#1278C211yesmaximal, characteristic, complemented
8C2×#14519805C411yescharacteristic
9C4×#11758222C2211yescharacteristic
10C2×C4×D244C2211yescharacteristic
11#16839892—21no—
12#16839875—21no—
13#16839864—21no—
14C4×#11758190—21no—
15C4×D488—21no—
16#16839841—21no—
17#16839830—22no—
18#16839818—21no—
19#16839815C2211yescharacteristic
20#16839804C411yescharacteristic
21#16839784—21no—
22C2×C4⋊#92418C2211yescharacteristic
23#16839768C411yescharacteristic
24#16839764C411yescharacteristic
25C2×#14519689—22no—
26#16839494—21no—
27#16839491—21no—
28#16839489—21no—
29#16839489—21no—
30C61×#431C2211yescharacteristic
31C4×M16×C61C2211yescharacteristic
32C2×C4×C8×C61C2211yescharacteristic
33C2×#11758222C2×C411yescharacteristic
34C22×D244C2×C411yescharacteristic
35C22×C4×D61—21no—
36#14519805—22no—
37#14519805—22no—
38C2×#11758190—21no—
39C2×D488—21no—
40C2×#11758189—22no—
41C22×#92418D412yes—
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—
60C4⋊#92418—21no—
61C4⋊#92418—21no—
62#14519706—22no—
63#14519702—21no—
64#14519699—21no—
65#14519699—21no—
66#14519699—21no—
67C22⋊#92418—21no—
68#14519689—22no—
69#14519689—44no—
70#14519687—22no—
71C4×#92418—21no—
72C2×M16×C61C2×C411yescharacteristic
73C2×M16×C61C2×C411yescharacteristic
74C22×C8×C61—21no—
75C2×C42×C61C2311yescharacteristic
76C4⋊C8×C61D411yescharacteristic
77C4⋊C8×C61D411yescharacteristic
78C22⋊C8×C61—21no—
79#97×C61—21no—
80C4×C8×C61—21no—
81C4×C8×C61—21no—
82C4×C8×C61—21no—
83C4×C8×C61—21no—
84C23×D61—21no—
85C22×C4×C61C22×C411yescharacteristic
86C22×C4×C61C2×D411yescharacteristic
87C22×C4×C61#4111yescharacteristic
88C2×C22⋊D61—21no—
89C22×Dic61—21no—
90#11758222—21no—
91#11758222—21no—
92#11758222—21no—
93#11758222—21no—
94C2×D244—21no—
95C2×D244—21no—
96C2×D244—21no—
97C2×D244—21no—
98C2×D244—21no—
99C2×D244C22⋊C411yescharacteristic
100C2×D244M1612yescomplemented
101C2×C4×D61—21no—
102C2×C4×D61—21no—
103C2×C4×D61—21no—
104C2×C4×D61—42no—
105C2×C4×D61—42no—
106C2×C4×D61—41no—
107C2×C4×D61—41no—
108C2×Dic122C22⋊C411yescharacteristic
109M16×C61—21no—
110M16×C61—21no—
111M16×C61—21no—
112M16×C61M1612yescomplemented
113C2×C8×C61—21no—
114C2×C8×C61—22no—
115C2×C8×C61—21no—
116C2×C8×C61—21no—
117C2×C8×C61—21no—
118C2×C8×C61—41no—
119C2×C8×C61—41no—
120C42×C61C2×D411yescharacteristic
121C42×C61C2×D411yescharacteristic
122C42×C61C2×D411yescharacteristic
123C42×C61#4111yescharacteristic
124C22⋊Dic61—21no—
125#11758198—21no—
126#11758198—21no—
127#11758198—41no—
128#11758198—41no—
129C4⋊Dic61—21no—
130C4⋊Dic61—21no—
131C4⋊Dic61C22⋊C411yescharacteristic
132C4⋊Dic61C22⋊C411yescharacteristic
133#11758196—21no—
134#11758196—21no—
135C4×Dic61—21no—
136C4×Dic61—21no—
137C4×Dic61—21no—
138C2×#92418—22no—
139C2×#92418—42no—
140C2×#92418—41no—
141D488—24no—
142#11758190—24no—
143#11758189—82no—
144C23×C61C4×D411yescharacteristic
145C22×D61—21no—
146C22×D61—22no—
147C22×D61—42no—
148C22×D61—42no—
149C22×D61—41no—
150C22×D61—41no—
151C2×C4×C61—21no—
152C2×C4×C61—21no—
153C2×C4×C61—41no—
154C2×C4×C61C2×C22⋊C411yescharacteristic
155C2×C4×C61C4×D411yescharacteristic
156C2×C4×C61#12011yescharacteristic
157C2×C4×C61#12111yescharacteristic
158C2×C4×C61#12111yescharacteristic
159C2×C4×C61#12311yescharacteristic
160C2×C4×C61C2×M1611yescharacteristic
161C2×C4×C61C2×M1611yescharacteristic
162C2×C4×C61#13111yescharacteristic
163C2×C4×C61#13111yescharacteristic
164C22⋊D61—41no—
165C22⋊D61—41no—
166C2×Dic61—21no—
167C2×Dic61—21no—
168C2×Dic61—21no—
169C2×Dic61—42no—
170C2×Dic61—41no—
171D244—22no—
172D244—21no—
173D244—21no—
174D244—22no—
175D244—41no—
176D244—41no—
177C4×D61—41no—
178C4×D61—41no—
179C4×D61—41no—
180C4×D61—41no—
181C4×D61—81no—
182C4×D61—82no—
183C4×D61—81no—
184C4×D61—81no—
185Dic122—21no—
186Dic122—21no—
187C8×C61—22no—
188C8×C61—42no—
189C8×C61—41no—
190C8×C61—41no—
191C8×C61—41no—
192#92418—42no—
193#92418—81no—
194#8956—611nomaximal, Sylow
195C22×C61—21no—
196C22×C61—21no—
197C22×C61#38611yescharacteristic
198C22×C61#43511yescharacteristic
199C22×C61#43611yescharacteristic
200C2×D61—44no—
201C2×D61—41no—
202C2×D61—42no—
203C2×D61—41no—
204C2×D61—41no—
205C2×D61—82no—
206C2×D61—81no—
207C2×D61—81no—
208C4×C61—21no—
209C4×C61—21no—
210C4×C61—21no—
211C4×C61#40711yescharacteristic
212C4×C61#40811yescharacteristic
213C4×C61#43511yescharacteristic
214C4×C61#43611yescharacteristic
215C4×C61#45311yescharacteristic
216C4×C61#45411yescharacteristic
217Dic61—41no—
218Dic61—41no—
219Dic61—41no—
220Dic61—81no—
221#2989—611no—
222C4×AGL(1,ℤ/8)—611no—
223#1954—611no—
224#1478—611no—
225#1476—611no—
226#1283—611no—
227#1278D6111yescharacteristic, complemented
228C2×C61—21no—
229C2×C61—21no—
230C2×C61#187011yescharacteristic
231C2×C61#188111yescharacteristic
232C2×C61#188311yescharacteristic
233D61—81no—
234D61—82no—
235C2×AGL(1,ℤ/8)—611no—
236C4×#41—611no—
237C2×C4×D4—611no—
238#446—1221no—
239#442—1221no—
240#440—1221no—
241C4×SD16—1221no—
242C4×D8—1221no—
243#436—1221no—
244#435—1222no—
245#432—1221no—
246#431—611no—
247#431C2×D6111yescharacteristic
248#428—611no—
249#423—1221no—
250C2×C4⋊C8—611no—
251#418—611no—
252#417—611no—
253C2×C22⋊C8—1222no—
254C4×M16C2×D6111yescharacteristic
255C2×C4×C8C2×D6111yescharacteristic
256Q8⋊C8—1221no—
257D4⋊C8—1221no—
258D4⋊C8—1221no—
259D4⋊C8—1221no—
260C61#895611yescharacteristic, complemented, Sylow
261C2×#41—611no—
262C22×D4—611no—
263C23×C4—1221no—
264AGL(1,ℤ/8)—1222no—
265AGL(1,ℤ/8)—1222no—
266C2×SD16—1221no—
267C2×D8—1221no—
268C2×M16—1222no—
269C2×M16C4×D6111yescharacteristic
270C2×M16C4×D6111yescharacteristic
271C22×C8—21no—
272C22×C8—612no—
273C4×Q8—611no—
274C4×Q8—611no—
275C4×D4—611no—
276C4×D4—611no—
277C4×D4—1221no—
278C4×D4—1221no—
279C4×D4—1221no—
280C4×D4—1221no—
281C4×D4—1221no—
282C4×D4—1221no—
283#117—611no—
284#117—1221no—
285C2×C4⋊C4—611no—
286C2×C22⋊C4—1221no—
287C2×C42—1221no—
288C2×C42C22×D6111yescharacteristic
289#107—1221no—
290#106—1221no—
291C4⋊C8—1222no—
292C4⋊C8—1221no—
293C4⋊C8—1221no—
294C4⋊C8—1221no—
295C4⋊C8D24411yescharacteristic
296C4⋊C8D24411yescharacteristic
297#103—1221no—
298#102—1221no—
299#102—1221no—
300#102—1221no—
301C22⋊C8—21no—
302C22⋊C8—1222no—
303C22⋊C8—1221no—
304C22⋊C8—2444no—
305#97—21no—
306#97—1222no—
307C4×C8—21no—
308C4×C8—21no—
309C4×C8—21no—
310C4×C8—21no—
311C4×C8—1221no—
312C24—1221no—
313#41—1221no—
314#41—1221no—
315#41—1221no—
316#41—1221no—
317C2×Q8—611no—
318C2×D4—611no—
319C2×D4—612no—
320C2×D4—1221no—
321C2×D4—1221no—
322C2×D4—1221no—
323C2×D4—1221no—
324C2×D4—1221no—
325C2×D4—1221no—
326C22×C4—1221no—
327C22×C4—1221no—
328C22×C4—1221no—
329C22×C4—1221no—
330C22×C4—2442no—
331C22×C4—2442no—
332C22×C4—2441no—
333C22×C4—2441no—
334C22×C4C2×C4×D6111yescharacteristic
335C22×C4D4×D6111yescharacteristic
336C22×C4#1175822611yescharacteristic
337SD16—1224no—
338D8—1224no—
339M16—21no—
340M16—21no—
341M16—21no—
342M16—4882no—
343M16#1175818912yescomplemented
344C2×C8—21no—
345C2×C8—22no—
346C2×C8—21no—
347C2×C8—21no—
348C2×C8—21no—
349C2×C8—41no—
350C2×C8—41no—
351C2×C8—1222no—
352C2×C8—2441no—
353C2×C8—2442no—
354C4⋊C4—611no—
355C4⋊C4—611no—
356C4⋊C4—1221no—
357C4⋊C4—1221no—
358C4⋊C4—1221no—
359C4⋊C4—1221no—
360C22⋊C4—1221no—
361C22⋊C4—1221no—
362C22⋊C4—1221no—
363C22⋊C4—2441no—
364C22⋊C4—2441no—
365C42—1221no—
366C42—1221no—
367C42—1221no—
368C42C2×D24411yescharacteristic
369C42#1175822211yescharacteristic
370C42D4×D6111yescharacteristic
371C42D4×D6111yescharacteristic
372C23—1222no—
373C23—1221no—
374C23—2442no—
375C23—2442no—
376C23—2441no—
377C23—2441no—
378C23#1451973911yescharacteristic
379Q8—1221no—
380Q8—1221no—
381D4—1221no—
382D4—1222no—
383D4—1221no—
384D4—1222no—
385D4—2441no—
386D4—2441no—
387D4—2441no—
388D4—2441no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—41no—
392C2×C4—1221no—
393C2×C4—1221no—
394C2×C4—1221no—
395C2×C4—4882no—
396C2×C4—4881no—
397C2×C4—4881no—
398C2×C4—4881no—
399C2×C4—2442no—
400C2×C4—2441no—
401C2×C4—2441no—
402C2×C4—2441no—
403C2×C4—2441no—
404C2×C4—2441no—
405C2×C4C22⋊C4×D6111yescharacteristic
406C2×C4C4×D24411yescharacteristic
407C2×C4#1451974711yescharacteristic
408C2×C4#1451975011yescharacteristic
409C2×C4#1451975211yescharacteristic
410C2×C4#1451976211yescharacteristic
411C2×C4M16×D6111yescharacteristic
412C2×C4C2×#1175818911yescharacteristic
413C2×C4#1451978311yescharacteristic
414C2×C4#1451978511yescharacteristic
415C8—22no—
416C8—42no—
417C8—41no—
418C8—41no—
419C8—41no—
420C8—4881no—
421C8—2442no—
422C22—21no—
423C22—21no—
424C22—4882no—
425C22—4881no—
426C22—4881no—
427C22—2444no—
428C22—2441no—
429C22—2441no—
430C22—2441no—
431C22—2442no—
432C22#1683964011yescharacteristic
433C22#1683983211yescharacteristic
434C22#1683983911yescharacteristic
435C4—21no—
436C4—21no—
437C4—21no—
438C4—4881no—
439C4—2441no—
440C4—2441no—
441C4—2441no—
442C4#1683972411yescharacteristic
443C4#1683972711yescharacteristic
444C4#1683983511yescharacteristic
445C4#1683984111yescharacteristic
446C4#1683993111yescharacteristic
447C4#1683993611yescharacteristic
448C2—21no—
449C2—21no—
450C2—4882no—
451C2—4881no—
452C2#2144611511yescharacteristic
453C2#2144618211yescharacteristic
454C2#2144619611yescharacteristic
subgroupG/H
centerC2×C4#14519747
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1278C2
socleC22×C61#386
prime radicalC2×#14519805C4
cosocleC2×C42×C61C23
hypercenter#1278D61
hypocenterC61#8956
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1278

Complements

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

NH ≅ G/Ntype
1. #21454932C2semidirect
3. #21446613C2semidirect
4. #21444209C2semidirect
5. #21444202C2semidirect
6. #21443670C2semidirect
7. C61×#1278C2semidirect
100. C2×D244M16semidirect
112. M16×C61M16semidirect
227. #1278D61semidirect
260. C61#8956semidirect
343. M16#11758189semidirect

Maximal subgroups

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

subgroupindex
#214549322
C4×#145198052
#214466132
#214442092
#214442022
#214436702
C61×#12782
#895661