Finite Group Databasebeta

← #30600804

Subgroups — #30600804

Order 15616.

470 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462716C211yesmaximal, characteristic, complemented
2#21461690C211yesmaximal, characteristic, complemented
3#21461248C211yesmaximal, characteristic
4#21461125C211yesmaximal, characteristic
5#21460709C211yesmaximal, characteristic, complemented
6#21460674C211yesmaximal, characteristic, complemented
7#21455286C211yesmaximal, characteristic
8#16840814—22no—
9#16840813—21no—
10#16840812—21no—
11#16840785—21no—
12#16840784—21no—
13#16840781C2211yescharacteristic
14#16840780C2211yescharacteristic
15D61⋊(C4⋊C8)C2211yescharacteristic
16C2×#14519840—21no—
17#16840706C2211yescharacteristic
18#16840635—21no—
19#16840613—21no—
20#16840613—21no—
21D4⋊#92420—22no—
22C2×#14519806—21no—
23#16840310C2211yescharacteristic
24C4×Q8×D61C2211yescharacteristic
25#16839983—21no—
26#16839982—21no—
27#16839973C411yescharacteristic, complemented
28#16839972C411yescharacteristic, complemented
29#16839959C411yescharacteristic, complemented
30#16839784C2211yescharacteristic
31#16839760—21no—
32C61×#460C411yescharacteristic, complemented
33C2×D61⋊C8—21no—
34C2×C4⋊#6923—21no—
35#14519844—22no—
36#14519844—21no—
37#14519844—21no—
38C4⋊#92420—22no—
39C4⋊#92420—21no—
40C4⋊#92420—21no—
41#14519840—42no—
42#14519834—21no—
43#14519834D411yescharacteristic
44#14519834D411yescharacteristic
45#14519832—22no—
46#14519832—22no—
47C4×#92420—21no—
48C4×#92420D412yes—
49(C2×#6923)⋊C4—21no—
50(C2×#6923)⋊C4—21no—
51C2×#11758224—21no—
52C2×Q8×D61D411yescharacteristic
53#14519806—42no—
54#14519806—42no—
55C2×Dic244—21no—
56C2×#11758202—21no—
57C2×#11758200—21no—
58C2×#11758189—21no—
59#14519777C2×C411yescharacteristic
60#14519764—21no—
61#14519748—21no—
62#14519748—21no—
63Q8×Dic61D411yescharacteristic
64C4×Dic122—21no—
65C4×Dic122C2×C411yescharacteristic
66#14519742—21no—
67#14519742D411yescharacteristic
68D4×Dic61—21no—
69D4×Dic61—21no—
70C4⋊C4×D61—21no—
71C4⋊C4×D61D411yescharacteristic
72C42×D61—21no—
73C42×D61C2311yescharacteristic
74C4⋊#92418C2×C411yescharacteristic
75#14519706—21no—
76#14519702—21no—
77#14519700—21no—
78#14519698—21no—
79C2×SD16×C61—21no—
80#127×C61C2×C411yescharacteristic
81C4×Q8×C61C2×C411yescharacteristic
82C4⋊C8×C61C2×C411yescharacteristic
83#102×C61—21no—
84C22×#6923—41no—
85C2×Q8×C61C22⋊C411yescharacteristic
86C2×D4×C61—21no—
87C2×D4×C61—21no—
88C2×D4×C61—21no—
89C2×C22⋊D61—41no—
90C22×Dic61—41no—
91Q8×D61—21no—
92Q8×D61—21no—
93Q8×D61—21no—
94Q8×D61—21no—
95#11758224—41no—
96#11758224—41no—
97#11758224—41no—
98#11758224—41no—
99C2×C4×D61—21no—
100C2×C4×D61—21no—
101C2×C4×D61C2×D411yescharacteristic
102C2×C4×D61C2×D411yescharacteristic
103C2×C4×D61#4111yescharacteristic
104C2×Dic122—21no—
105C2×Dic122—21no—
106C2×Dic122C22⋊C411yescharacteristic
107C2×#92420—21no—
108C2×#92420—21no—
109C2×#92420—22no—
110C2×#92420—41no—
111C4⋊#6923—41no—
112C4⋊#6923—41no—
113D61⋊C8—41no—
114D61⋊C8—41no—
115SD16×C61—42no—
116C2×C8×C61—21no—
117C4⋊C4×C61—21no—
118C4⋊C4×C61C22⋊C411yescharacteristic
119C42×C61—21no—
120C42×C61C22×C411yescharacteristic
121C22⋊Dic61—41no—
122C22⋊Dic61—41no—
123#11758202—42no—
124#11758200—42no—
125C4⋊Dic61—21no—
126C4⋊Dic61—21no—
127C4⋊Dic61—21no—
128C4⋊Dic61C22⋊C411yescharacteristic
129#11758196—21no—
130#11758196—21no—
131#11758196—21no—
132C4×Dic61—21no—
133C4×Dic61—21no—
134C4×Dic61—21no—
135C4×Dic61C2×D411yescharacteristic
136C4×Dic61C2×D411yescharacteristic
137C4×Dic61#4111yescharacteristic
138C2×#92418—21no—
139Dic244—42no—
140#11758189—41no—
141#11758189—41no—
142C23×C61—41no—
143C22×D61#12111yescharacteristic
144C2×#6923—81no—
145C2×#6923—81no—
146C2×#6923—81no—
147Q8×C61—21no—
148Q8×C61—21no—
149D4×C61—42no—
150D4×C61—41no—
151D4×C61—41no—
152D4×C61—81no—
153C2×C4×C61—21no—
154C2×C4×C61—21no—
155C2×C4×C61C2×C22⋊C411yescharacteristic
156C2×C4×C61C4×D411yescharacteristic
157C2×C4×C61C4×D411yescharacteristic
158C22⋊D61—81no—
159C22⋊D61—81no—
160C2×Dic61—21no—
161C2×Dic61—21no—
162C2×Dic61—41no—
163C2×Dic61—81no—
164C2×Dic61—81no—
165C2×Dic61#12011yescharacteristic
166C2×Dic61#12111yescharacteristic
167C2×Dic61#12311yescharacteristic
168C4×D61—41no—
169C4×D61—41no—
170C4×D61—41no—
171C4×D61—41no—
172C4×D61—81no—
173C4×D61AGL(1,ℤ/8)11yescharacteristic
174C4×D61AGL(1,ℤ/8)11yescharacteristic
175C4×D61AGL(1,ℤ/8)11yescharacteristic
176C4×D61#13711yescharacteristic
177Dic122—21no—
178Dic122—21no—
179Dic122—41no—
180Dic122—41no—
181Dic122—41no—
182Dic122—41no—
183#92420—41no—
184#92420—41no—
185#92420—42no—
186#92420—81no—
187C8×C61—41no—
188#92418—41no—
189#9310—611nomaximal, Sylow
190C22×C61—81no—
191C22×C61—81no—
192C22×C61—81no—
193C22×C61#38611yescharacteristic
194C2×D61—21no—
195C2×D61—21no—
196C2×D61#46811yescharacteristic
197C2×D61#46911yescharacteristic
198#6923—161no—
199C4×C61—21no—
200C4×C61—21no—
201C4×C61—41no—
202C4×C61—41no—
203C4×C61#41711yescharacteristic
204C4×C61#41811yescharacteristic
205Dic61—21no—
206Dic61—21no—
207Dic61—41no—
208Dic61—41no—
209Dic61—81no—
210Dic61#46811yescharacteristic
211Dic61#46911yescharacteristic
212#3037—611no—
213#2983—611no—
214#1805—611no—
215#1517—611no—
216#1480—611no—
217#1301—611no—
218#1286—611no—
219C2×C61—161no—
220C2×C61#188111yescharacteristic
221C2×C61#189511yescharacteristic
222C2×C61#190511yescharacteristic
223D61—21no—
224D61—21no—
225C2×#137—1221no—
226#532—611no—
227C2×C4×Q8—611no—
228#464—1221no—
229#464—1221no—
230#462—611no—
231#462—611no—
232#460—611no—
233#460#692311yescharacteristic, complemented
234#446—1222no—
235#446—1221no—
236#446—1221no—
237#432—1221no—
238#432—1221no—
239#431—611no—
240#431—611no—
241#423—611no—
242C2×C4⋊C8—611no—
243#417—1221no—
244C2×#103—1221no—
245#382—611no—
246#340—1221no—
247#327—1221no—
248#327—1221no—
249D4⋊C8—1222no—
250C61#931011yescharacteristic, complemented, Sylow
251C2×#41—1221no—
252C22×Q8—611no—
253#137—2442no—
254#137—2442no—
255C2×Q16—1221no—
256C2×Q16—1221no—
257C2×SD16—21no—
258C2×SD16—1221no—
259C2×M16—1221no—
260C22×C8—1221no—
261C4⋊Q8—611no—
262#127C2×#692311yescharacteristic
263#124—1221no—
264#121—1221no—
265#121—1221no—
266C4×Q8—611no—
267C4×Q8—611no—
268C4×Q8—611no—
269C4×Q8—1221no—
270C4×Q8—1221no—
271C4×Q8C2×#692311yescharacteristic
272C4×D4—1221no—
273C4×D4—1221no—
274C2×C4⋊C4—611no—
275C2×C4⋊C4—1221no—
276C2×C4⋊C4—1221no—
277C2×C42—611no—
278C2×C42—1221no—
279C4⋊C8—611no—
280C4⋊C8—1221no—
281C4⋊C8—1221no—
282C4⋊C8—1221no—
283C4⋊C8—1221no—
284C4⋊C8—1221no—
285C4⋊C8—1222no—
286C4⋊C8—1222no—
287C4⋊C8C2×#692311yescharacteristic
288#103—1221no—
289#103—1221no—
290#103—2442no—
291#102—21no—
292#102—1221no—
293C22⋊C8—611no—
294C22⋊C8—611no—
295C22⋊C8—1221no—
296#97—1222no—
297#97—1222no—
298C4×C8—612no—
299C4×C8—1221no—
300#95—1221no—
301#95—1221no—
302#41—2441no—
303#41—2441no—
304#41—2441no—
305#41—2441no—
306C2×Q8—611no—
307C2×Q8—1221no—
308C2×Q8—1221no—
309C2×Q8—1221no—
310C2×Q8—1221no—
311C2×Q8—1221no—
312C2×Q8—1221no—
313C2×Q8C22⋊#692311yescharacteristic
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—2441no—
318C22×C4—611no—
319C22×C4—611no—
320C22×C4—611no—
321C22×C4—1221no—
322C22×C4—1221no—
323C22×C4—2441no—
324C22×C4—2441no—
325Q16—2442no—
326Q16—2442no—
327SD16—42no—
328SD16—2442no—
329M16—2441no—
330M16—2441no—
331C2×C8—21no—
332C2×C8—1222no—
333C2×C8—1221no—
334C2×C8—1221no—
335C2×C8—1221no—
336C2×C8—2441no—
337C2×C8—2441no—
338C2×C8—2441no—
339C4⋊C4—21no—
340C4⋊C4—611no—
341C4⋊C4—1221no—
342C4⋊C4—1221no—
343C4⋊C4—1221no—
344C4⋊C4—1221no—
345C4⋊C4—1221no—
346C4⋊C4—1221no—
347C4⋊C4—2441no—
348C4⋊C4—2441no—
349C4⋊C4C22⋊#692311yescharacteristic
350C22⋊C4—2441no—
351C22⋊C4—2441no—
352C42—21no—
353C42—611no—
354C42—611no—
355C42—611no—
356C42—1221no—
357C42—1221no—
358C42—1221no—
359C42C22×#692311yescharacteristic
360C23—41no—
361C23—611no—
362Q8—21no—
363Q8—21no—
364Q8—1221no—
365Q8—1221no—
366Q8—2441no—
367Q8—2441no—
368Q8—2441no—
369Q8—2441no—
370D4—42no—
371D4—41no—
372D4—41no—
373D4—81no—
374D4—4881no—
375D4—4881no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—611no—
379C2×C4—611no—
380C2×C4—611no—
381C2×C4—611no—
382C2×C4—611no—
383C2×C4—611no—
384C2×C4—611no—
385C2×C4—1221no—
386C2×C4—1221no—
387C2×C4—4881no—
388C2×C4—4881no—
389C2×C4—4881no—
390C2×C4—4881no—
391C2×C4—4881no—
392C2×C4—4881no—
393C2×C4—2441no—
394C2×C4—2441no—
395C2×C4—2441no—
396C2×C4—2441no—
397C2×C4—2441no—
398C2×C4C2×C22⋊#692311yescharacteristic
399C2×C4D4×#692311yescharacteristic
400C2×C4D4×#692311yescharacteristic
401C8—41no—
402C8—4881no—
403C8—2442no—
404C8—2441no—
405C8—2441no—
406C8—2441no—
407C22—81no—
408C22—81no—
409C22—81no—
410C22—611no—
411C22—611no—
412C22—1221no—
413C22—1221no—
414C22#1684071011yescharacteristic
415C4—21no—
416C4—21no—
417C4—41no—
418C4—41no—
419C4—611no—
420C4—611no—
421C4—1221no—
422C4—1221no—
423C4—9761no—
424C4—4881no—
425C4—2441no—
426C4—2441no—
427C4#1684075311yescharacteristic
428C4#1684075411yescharacteristic
429C2—161no—
430C2—1221no—
431C2—1221no—
432C2#2146181711yescharacteristic
433C2#2146183511yescharacteristic
434C2#2146185511yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#460C4
socleC22×C61#386
prime radical#16840310C22
cosocleC42×D61C23
hypercenter#460#6923
hypocenterC61#9310
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #21462716C2semidirect
2. #21461690C2semidirect
5. #21460709C2semidirect
6. #21460674C2semidirect
27. #16839973C4semidirect
28. #16839972C4semidirect
29. #16839959C4semidirect
32. C61×#460C4semidirect
233. #460#6923semidirect
250. C61#9310semidirect

Maximal subgroups

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

subgroupindex
#214627162
#214616902
#214612482
#214611252
#214607092
#214606742
#214552862
#931061