Finite Group Databasebeta

← #29574654

Subgroups — #29574654

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#21454937C211yesmaximal, characteristic, complemented
2C4×#14519803C211yesmaximal, characteristic
3#21444210C211yesmaximal, characteristic, complemented
4#21444202C211yesmaximal, characteristic, complemented
5#21443669C211yesmaximal, characteristic, complemented
6#21443656C211yesmaximal, characteristic, complemented
7C61×#1954C211yesmaximal, characteristic, complemented
8C2×#14519803C411yescharacteristic
9C4×#11758222C2211yescharacteristic
10#16839889—21no—
11#16839872—21no—
12#16839862—21no—
13C4×#11758200—21no—
14C4×#11758199—21no—
15#16839839—21no—
16#16839833—22no—
17#16839818—21no—
18#16839815C2211yescharacteristic
19#16839815C2211yescharacteristic
20#16839802C411yescharacteristic
21#16839784—21no—
22#16839767C411yescharacteristic
23#16839761C411yescharacteristic
24C4×#11758194C2211yescharacteristic
25#16839494—21no—
26#16839491—21no—
27D4⋊#92418—21no—
28D4⋊#92418—21no—
29C2×C4×D4×C61C2211yescharacteristic
30C2×C4⋊C8×C61C2211yescharacteristic
31C2×C22⋊C8×C61—22no—
32C2×C4×C8×C61C2211yescharacteristic
33C2×#11758222C2×C411yescharacteristic
34#14519803—22no—
35#14519803—22no—
36C2×#11758200—21no—
37C2×#11758199—21no—
38C2×#11758194C2×C411yescharacteristic
39C2×#11758194C2×C411yescharacteristic
40C2×#11758189—22no—
41C4×Dic122D411yescharacteristic
42C4×Dic122D411yescharacteristic
43C4×D244D411yescharacteristic
44C4×D244D411yescharacteristic
45C4×C22⋊D61—21no—
46C4×C22⋊D61—21no—
47#14519736C2×C411yescharacteristic
48#14519734—21no—
49C42×D61—21no—
50#14519710—21no—
51#14519708—21no—
52C4⋊#92418—21no—
53C4⋊#92418D411yescharacteristic
54C4⋊#92418D411yescharacteristic
55#14519706—22no—
56#14519700—21no—
57#14519698—21no—
58#14519698—21no—
59#14519697—21no—
60C22⋊#92418—21no—
61C22⋊#92418—21no—
62#14519689—22no—
63#14519688—21no—
64#14519687—22no—
65C4×#92418—21no—
66C4×#92418—21no—
67C4×#92418—21no—
68C22×D4×C61C2×C411yescharacteristic
69C23×C4×C61—21no—
70C22×C8×C61—21no—
71C22×C8×C61D412yes—
72C4×D4×C61—21no—
73C4×D4×C61—21no—
74C4×D4×C61—21no—
75C4×D4×C61—21no—
76C2×C4⋊C4×C61C2×C411yescharacteristic
77C2×C22⋊C4×C61—21no—
78C2×C42×C61C2311yescharacteristic
79C4⋊C8×C61—21no—
80C4⋊C8×C61—21no—
81C22⋊C8×C61—44no—
82C4×C8×C61—21no—
83C4×C8×C61—21no—
84C24×C61—21no—
85C2×D4×C61—21no—
86C2×D4×C61—21no—
87C2×D4×C61—21no—
88C2×D4×C61—21no—
89C2×D4×C61—21no—
90C2×D4×C61M1612yescomplemented
91C22×C4×C61—21no—
92C22×C4×C61—42no—
93C22×C4×C61—42no—
94C22×C4×C61—41no—
95C22×C4×C61—41no—
96C22×C4×C61C22×C411yescharacteristic
97C22×C4×C61C2×D411yescharacteristic
98C22×C4×C61#4111yescharacteristic
99C2×C22⋊D61—21no—
100#11758222—21no—
101#11758222—21no—
102#11758222—21no—
103#11758222—21no—
104C2×D244C22⋊C411yescharacteristic
105C2×C4×D61—21no—
106C2×C4×D61—21no—
107C2×C4×D61—21no—
108C2×Dic122C22⋊C411yescharacteristic
109C2×C8×C61—22no—
110C2×C8×C61—22no—
111C2×C8×C61—41no—
112C2×C8×C61—41no—
113C2×C8×C61—42no—
114C4⋊C4×C61—21no—
115C4⋊C4×C61—21no—
116C22⋊C4×C61—41no—
117C22⋊C4×C61—41no—
118C42×C61C2×D411yescharacteristic
119C42×C61C2×D411yescharacteristic
120C42×C61C2×D411yescharacteristic
121C42×C61#4111yescharacteristic
122C22⋊Dic61—21no—
123#11758200—24no—
124#11758199—24no—
125#11758198—21no—
126#11758198—21no—
127C4⋊Dic61C22⋊C411yescharacteristic
128C4⋊Dic61C22⋊C411yescharacteristic
129#11758196—21no—
130#11758196—21no—
131C4×Dic61—21no—
132C4×Dic61—21no—
133C4×Dic61—21no—
134#11758194—21no—
135#11758194—21no—
136#11758194—21no—
137#11758194M1612yescomplemented
138C2×#92418—21no—
139C2×#92418—21no—
140C2×#92418—21no—
141C2×#92418—21no—
142C2×#92418—41no—
143#11758189—82no—
144C23×C61—22no—
145C23×C61—42no—
146C23×C61—42no—
147C23×C61—41no—
148C23×C61—41no—
149C23×C61C4×D411yescharacteristic
150C22×D61—21no—
151D4×C61—22no—
152D4×C61—22no—
153D4×C61—41no—
154D4×C61—41no—
155C2×C4×C61—21no—
156C2×C4×C61—21no—
157C2×C4×C61—41no—
158C2×C4×C61—42no—
159C2×C4×C61—41no—
160C2×C4×C61—82no—
161C2×C4×C61—81no—
162C2×C4×C61—81no—
163C2×C4×C61C2×C22⋊C411yescharacteristic
164C2×C4×C61C4×D411yescharacteristic
165C2×C4×C61#12011yescharacteristic
166C2×C4×C61#12111yescharacteristic
167C2×C4×C61#12111yescharacteristic
168C2×C4×C61#12311yescharacteristic
169C2×C4×C61C2×M1611yescharacteristic
170C2×C4×C61C2×M1611yescharacteristic
171C2×C4×C61#13111yescharacteristic
172C2×C4×C61#13111yescharacteristic
173C22⋊D61—41no—
174C22⋊D61—41no—
175C2×Dic61—21no—
176C2×Dic61—21no—
177C2×Dic61—21no—
178D244—21no—
179D244—21no—
180C4×D61—41no—
181C4×D61—41no—
182C4×D61—41no—
183C4×D61—41no—
184C4×D61—81no—
185Dic122—21no—
186Dic122—21no—
187C8×C61—42no—
188C8×C61—42no—
189#92418—22no—
190#92418—41no—
191#92418—41no—
192#92418—41no—
193#92418—81no—
194#8956—611nomaximal, Sylow
195C22×C61—21no—
196C22×C61—21no—
197C22×C61—44no—
198C22×C61—42no—
199C22×C61—82no—
200C22×C61—81no—
201C22×C61—81no—
202C22×C61#38611yescharacteristic
203C22×C61#43511yescharacteristic
204C22×C61#43611yescharacteristic
205C2×D61—41no—
206C2×D61—41no—
207C2×D61—41no—
208C4×C61—21no—
209C4×C61—21no—
210C4×C61—21no—
211C4×C61—81no—
212C4×C61#40711yescharacteristic
213C4×C61#40811yescharacteristic
214C4×C61#43511yescharacteristic
215C4×C61#43611yescharacteristic
216C4×C61#45311yescharacteristic
217C4×C61#45411yescharacteristic
218Dic61—41no—
219Dic61—41no—
220Dic61—41no—
221#2989—611no—
222C4×AGL(1,ℤ/8)—611no—
223#1954D6111yescharacteristic, complemented
224#1478—611no—
225#1476—611no—
226#1283—611no—
227#1278—611no—
228C2×C61—21no—
229C2×C61—21no—
230C2×C61—82no—
231C2×C61#187011yescharacteristic
232C2×C61#188111yescharacteristic
233C2×C61#188311yescharacteristic
234D61—81no—
235C2×AGL(1,ℤ/8)—611no—
236C4×#41—611no—
237C2×C4×D4C2×D6111yescharacteristic
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#431—611no—
248#428—611no—
249#423—1221no—
250C2×C4⋊C8C2×D6111yescharacteristic
251#418—611no—
252#417—611no—
253C2×C22⋊C8—22no—
254C4×M16—611no—
255C2×C4×C8C2×D6111yescharacteristic
256Q8⋊C8—1221no—
257D4⋊C8—1221no—
258D4⋊C8—1221no—
259D4⋊C8—1221no—
260C61#895611yescharacteristic, complemented, Sylow
261C2×#41—611no—
262C22×D4C4×D6111yescharacteristic
263C23×C4—21no—
264AGL(1,ℤ/8)—1222no—
265AGL(1,ℤ/8)—1222no—
266C2×SD16—1221no—
267C2×D8—1221no—
268C2×M16—611no—
269C2×M16—611no—
270C2×M16—1222no—
271C22×C8—21no—
272C22×C8C22⋊D6112yes—
273C4×Q8—611no—
274C4×Q8—611no—
275C4×D4—21no—
276C4×D4—21no—
277C4×D4—21no—
278C4×D4—21no—
279C4×D4—611no—
280C4×D4—611no—
281C4×D4—1221no—
282C4×D4—1221no—
283#117—611no—
284#117—1221no—
285C2×C4⋊C4C4×D6111yescharacteristic
286C2×C22⋊C4—21no—
287C2×C42—1221no—
288C2×C42C22×D6111yescharacteristic
289#107—1221no—
290#106—1221no—
291C4⋊C8—21no—
292C4⋊C8—21no—
293C4⋊C8—611no—
294C4⋊C8—611no—
295C4⋊C8—1222no—
296C4⋊C8—1221no—
297#103—1221no—
298#102—1221no—
299#102—1221no—
300#102—1221no—
301C22⋊C8—44no—
302C22⋊C8—1222no—
303C22⋊C8—1221no—
304C22⋊C8—1221no—
305#97—1222no—
306#97—1221no—
307C4×C8—21no—
308C4×C8—21no—
309C4×C8—1221no—
310C4×C8—1221no—
311C4×C8—1221no—
312C24—21no—
313#41—1221no—
314#41—1221no—
315#41—1221no—
316#41—1221no—
317C2×Q8—611no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—611no—
324C2×D4—1221no—
325C2×D4#1175818912yescomplemented
326C22×C4—21no—
327C22×C4—42no—
328C22×C4—42no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—1221no—
332C22×C4—1221no—
333C22×C4—1221no—
334C22×C4C2×C4×D6111yescharacteristic
335C22×C4#1175822211yescharacteristic
336C22×C4C2×C22⋊D6111yescharacteristic
337SD16—1224no—
338D8—1224no—
339M16—612no—
340M16—1221no—
341M16—1221no—
342M16—1221no—
343M16—4882no—
344C2×C8—22no—
345C2×C8—22no—
346C2×C8—41no—
347C2×C8—41no—
348C2×C8—42no—
349C2×C8—1221no—
350C2×C8—1221no—
351C2×C8—1221no—
352C2×C8—1221no—
353C2×C8—2441no—
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—611no—
357C4⋊C4—611no—
358C4⋊C4—1221no—
359C4⋊C4—1221no—
360C22⋊C4—41no—
361C22⋊C4—41no—
362C22⋊C4—1221no—
363C22⋊C4—1221no—
364C22⋊C4—1221no—
365C42—1221no—
366C42—1221no—
367C42—1221no—
368C42D4×D6111yescharacteristic
369C42D4×D6111yescharacteristic
370C42D4×D6111yescharacteristic
371C42#1175822411yescharacteristic
372C23—22no—
373C23—42no—
374C23—42no—
375C23—41no—
376C23—41no—
377C23—1221no—
378C23C4×C22⋊D6111yescharacteristic
379Q8—1221no—
380Q8—1221no—
381D4—22no—
382D4—22no—
383D4—41no—
384D4—41no—
385D4—1221no—
386D4—1221no—
387D4—2441no—
388D4—2441no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—41no—
392C2×C4—42no—
393C2×C4—41no—
394C2×C4—82no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4—1221no—
398C2×C4—1221no—
399C2×C4—1221no—
400C2×C4—4881no—
401C2×C4—2441no—
402C2×C4—2441no—
403C2×C4—2441no—
404C2×C4—2441no—
405C2×C4C22⋊C4×D6111yescharacteristic
406C2×C4#1451973711yescharacteristic
407C2×C4#1451974511yescharacteristic
408C2×C4#1451974811yescharacteristic
409C2×C4#1451975011yescharacteristic
410C2×C4#1451975911yescharacteristic
411C2×C4M16×D6111yescharacteristic
412C2×C4C2×#1175818911yescharacteristic
413C2×C4#1451978311yescharacteristic
414C2×C4#1451978511yescharacteristic
415C8—42no—
416C8—42no—
417C8—1222no—
418C8—4881no—
419C8—2441no—
420C8—2441no—
421C8—2441no—
422C22—21no—
423C22—21no—
424C22—44no—
425C22—42no—
426C22—82no—
427C22—81no—
428C22—81no—
429C22—2441no—
430C22—2441no—
431C22—2441no—
432C22#1683963811yescharacteristic
433C22#1683983311yescharacteristic
434C22#1683983811yescharacteristic
435C4—21no—
436C4—21no—
437C4—21no—
438C4—81no—
439C4—2441no—
440C4—2441no—
441C4—2441no—
442C4#1683972411yescharacteristic
443C4#1683972711yescharacteristic
444C4#1683983011yescharacteristic
445C4#1683983711yescharacteristic
446C4#1683992911yescharacteristic
447C4#1683993411yescharacteristic
448C2—21no—
449C2—21no—
450C2—82no—
451C2—4881no—
452C2#2144611311yescharacteristic
453C2#2144618411yescharacteristic
454C2#2144619811yescharacteristic
subgroupG/H
centerC2×C4#14519745
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1954C2
socleC22×C61#386
prime radicalC2×#14519803C4
cosocleC2×C42×C61C23
hypercenter#1954D61
hypocenterC61#8956
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1954

Complements

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

NH ≅ G/Ntype
1. #21454937C2semidirect
3. #21444210C2semidirect
4. #21444202C2semidirect
5. #21443669C2semidirect
6. #21443656C2semidirect
7. C61×#1954C2semidirect
90. C2×D4×C61M16semidirect
137. #11758194M16semidirect
223. #1954D61semidirect
260. C61#8956semidirect
325. C2×D4#11758189semidirect

Maximal subgroups

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

subgroupindex
#214549372
C4×#145198032
#214442102
#214442022
#214436692
#214436562
C61×#19542
#895661