Finite Group Databasebeta

← #30595394

Subgroups — #30595394

Order 15616.

708 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 708 conjugacy classes of subgroups — too many to draw. Only its 114 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#21461711C211yesmaximal, characteristic, complemented
2#21461480C211yesmaximal, characteristic, complemented
3#21460640C212yesmaximal, complemented
4#21460635C212yesmaximal, complemented
5#21448306C211yesmaximal, characteristic
6C22×D61⋊C8—21no—
7C2×#14519834—21no—
8#16840628—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C22×#11758224C411yescharacteristic
13C2×#14519735C411yescharacteristic
14C2×C42×D61C2211yescharacteristic
15#16839668C411yescharacteristic
16#16839667C2211yescharacteristic
17#16839665C2211yescharacteristic
18#16839638—21no—
19#16839638—21no—
20C22⋊C4×Dic61—21no—
21C22⋊C4×Dic61—21no—
22C61×#390C411yescharacteristic
23C2×D61⋊C8—24no—
24C2×D61⋊C8—42no—
25C2×D61⋊C8—42no—
26C22×#92420—22no—
27C22×#92420—22no—
28#14519834—42no—
29C2×#11758224—22no—
30C2×#11758224—42no—
31C2×#11758224—42no—
32C2×#11758224C814yescomplemented
33C22×Dic122C2×C411yescharacteristic
34C22×C22⋊D61—21no—
35C23×Dic61—21no—
36C22×C4×D61C2×C411yescharacteristic
37C22×C4×D61D411yescharacteristic
38C22×C4×D61D411yescharacteristic
39#14519735—42no—
40C2×C4⋊Dic61C2×C411yescharacteristic
41C2×C22⋊Dic61—21no—
42C2×C22⋊Dic61—21no—
43C2×#11758198—21no—
44C2×C4×Dic61—21no—
45C2×C4×Dic61D411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61C2311yescharacteristic
48C42×D61—42no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53C22×D4×C61C2×C411yescharacteristic
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C22⋊C4×C61—21no—
56C2×C22⋊C4×C61—21no—
57C2×C42×C61C2×C411yescharacteristic
58C24×C61—21no—
59C23×D61C22⋊C411yescharacteristic
60C2×D4×C61—21no—
61C2×D4×C61—41no—
62C2×D4×C61—41no—
63C2×D4×C61C2×C812yescomplemented
64C22×C4×C61—21no—
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C22×C411yescharacteristic
68C2×C22⋊D61—24no—
69C2×C22⋊D61—42no—
70C2×C22⋊D61—42no—
71C22×Dic61—21no—
72C22×Dic61—24no—
73C22×Dic61—21no—
74C22×Dic61—42no—
75C22×Dic61—42no—
76C22×Dic61C22⋊C411yescharacteristic
77C22×Dic61C2×D411yescharacteristic
78C22×Dic61C2×D411yescharacteristic
79#11758224—48no—
80#11758224—48no—
81C2×C4×D61—22no—
82C2×C4×D61—22no—
83C2×C4×D61—22no—
84C2×C4×D61—22no—
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61—22no—
88C2×C4×D61—22no—
89C2×C4×D61—41no—
90C2×C4×D61C2×C812yes—
91C2×C4×D61M1612yes—
92C2×Dic122—21no—
93C2×Dic122—41no—
94C2×Dic122—41no—
95C2×Dic122C2×C812yescomplemented
96C2×#92420—24no—
97C2×#92420—42no—
98C2×#92420—42no—
99C2×#92420—42no—
100C2×#92420—42no—
101C2×#92420—42no—
102D61⋊C8—48no—
103C4⋊C4×C61—41no—
104C22⋊C4×C61—42no—
105C22⋊C4×C61—42no—
106C42×C61—41no—
107C22⋊Dic61—42no—
108C22⋊Dic61—41no—
109C22⋊Dic61—41no—
110#11758198—42no—
111C4⋊Dic61—41no—
112C4×Dic61—41no—
113C4×Dic61—41no—
114C4×Dic61—41no—
115C4×Dic61—42no—
116C23×C61—22no—
117C23×C61—41no—
118C23×C61—41no—
119C23×C61—41no—
120C23×C61—41no—
121C23×C61—41no—
122C23×C61—41no—
123C23×C61C2×C22⋊C411yescharacteristic
124C22×D61—21no—
125C22×D61—21no—
126C22×D61—21no—
127C22×D61—21no—
128C22×D61C22⋊C812yes—
129C22×D61#9912yes—
130C22×D61#10012yes—
131D4×C61—42no—
132D4×C61—42no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61#10412yes—
144C2×C4×C61C22×C811yescharacteristic
145C2×C4×C61C2×M1611yescharacteristic
146C22⋊D61—48no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61—21no—
153C2×Dic61—22no—
154C2×Dic61—48no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61C22⋊C812yes—
161C2×Dic61#13512yes—
162C2×Dic61AGL(1,ℤ/8)11yescharacteristic
163C2×Dic61#13711yescharacteristic
164C4×D61—24no—
165C4×D61—24no—
166C4×D61—24no—
167C4×D61—24no—
168C4×D61—44no—
169Dic122—42no—
170Dic122—42no—
171#92420—44no—
172#92420—82no—
173#7578—611nomaximal, Sylow
174C22×C61—42no—
175C22×C61—42no—
176C22×C61—42no—
177C22×C61—81no—
178C22×C61—81no—
179C22×C61—81no—
180C22×C61—81no—
181C22×C61C2×C22⋊C811yescharacteristic
182C22×C61C2×#9911yescharacteristic
183C22×C61C2×#10011yescharacteristic
184C22×C61#41611yescharacteristic
185C22×C61#41711yescharacteristic
186C22×C61C2×#10411yescharacteristic
187C22×C61#42111yescharacteristic
188C2×D61—22no—
189C2×D61—22no—
190C2×D61—22no—
191C2×D61—22no—
192C2×D61—22no—
193C2×D61—22no—
194C2×D61#32314yes—
195C4×C61—21no—
196C4×C61—21no—
197C4×C61—22no—
198C4×C61—41no—
199C4×C61—81no—
200Dic61—22no—
201Dic61—21no—
202Dic61—21no—
203Dic61—22no—
204Dic61—42no—
205Dic61—81no—
206#2297—611no—
207#1817—611no—
208C2×#336—611no—
209#1272—612no—
210#1270—612no—
211C2×C61—82no—
212C2×C61C2×#32311yescharacteristic
213C2×C61#147611yescharacteristic
214C2×C61#147711yescharacteristic
215C2×C61#150411yescharacteristic
216C2×C61#151611yescharacteristic
217C2×C61#153011yescharacteristic
218C2×C61#155111yescharacteristic
219D61—24no—
220C22×#41—611no—
221C23×C8—1221no—
222C2×#117—611no—
223C22×C42—611no—
224C2×C22⋊C8—1221no—
225#391—611no—
226#391—611no—
227#390—611no—
228#390#692311yescharacteristic
229#386—1221no—
230#386—1221no—
231C4×C22⋊C4—1221no—
232C4×C22⋊C4—1221no—
233#336—612no—
234#336—612no—
235#336—1221no—
236#336—1221no—
237C61#757811yescharacteristic, complemented, Sylow
238C2×#41—614no—
239C2×#41—1222no—
240C2×#41—2442no—
241C2×#41—2442no—
242C22×Q8—611no—
243C22×D4—1221no—
244C22×D4C2×#692311yescharacteristic
245C23×C4—611no—
246C23×C4—611no—
247C23×C4—611no—
248C23×C4—1221no—
249C22×C8—1222no—
250C22×C8—1224no—
251C22×C8—1222no—
252C22×C8—2442no—
253C22×C8—2442no—
254#117—2442no—
255C2×C4⋊C4—611no—
256C2×C4⋊C4C2×#692311yescharacteristic
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—1221no—
260C2×C22⋊C4—1221no—
261C2×C22⋊C4—1221no—
262C2×C42—611no—
263C2×C42—611no—
264C2×C42—611no—
265C2×C42—1221no—
266C2×C42—2442no—
267C2×C42C2×#692311yescharacteristic
268C22⋊C8—2442no—
269#95—1221no—
270#95—1221no—
271#95—1221no—
272#95—1221no—
273C24—21no—
274C24—611no—
275#41—2448no—
276#41—2448no—
277C2×Q8—612no—
278C2×Q8—1221no—
279C2×Q8—2441no—
280C2×Q8—2441no—
281C2×D4—21no—
282C2×D4—41no—
283C2×D4—41no—
284C2×D4—1224no—
285C2×D4—2442no—
286C2×D4—2442no—
287C2×D4D61⋊C812yescomplemented
288C22×C4—21no—
289C22×C4—611no—
290C22×C4—611no—
291C22×C4—611no—
292C22×C4—612no—
293C22×C4—612no—
294C22×C4—1221no—
295C22×C4—1221no—
296C22×C4—1222no—
297C22×C4—1222no—
298C22×C4—1222no—
299C22×C4—1222no—
300C22×C4—1222no—
301C22×C4—1224no—
302C22×C4—1222no—
303C22×C4—1221no—
304C22×C4—1221no—
305C22×C4—2441no—
306C22×C4—2442no—
307C22×C4—2442no—
308C22×C4C22⋊#692311yescharacteristic
309C22×C4C22⋊#692311yescharacteristic
310C22×C4C22×#692311yescharacteristic
311C2×C8—1224no—
312C2×C8—2442no—
313C2×C8—2442no—
314C2×C8—2442no—
315C2×C8—2442no—
316C2×C8—2448no—
317C2×C8—2442no—
318C4⋊C4—41no—
319C4⋊C4—2441no—
320C22⋊C4—42no—
321C22⋊C4—42no—
322C22⋊C4—2442no—
323C22⋊C4—2442no—
324C22⋊C4—2441no—
325C22⋊C4—2441no—
326C42—41no—
327C42—2441no—
328C42—2441no—
329C42—2441no—
330C42—2442no—
331C23—22no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—612no—
339C23—612no—
340C23—612no—
341C23—1221no—
342C23—1221no—
343C23—1221no—
344C23—1221no—
345C23C2×C22⋊#692311yescharacteristic
346Q8—2442no—
347Q8—2442no—
348D4—42no—
349D4—42no—
350D4—2448no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—612no—
362C2×C4—612no—
363C2×C4—611no—
364C2×C4—611no—
365C2×C4—1224no—
366C2×C4—1224no—
367C2×C4—1224no—
368C2×C4—1224no—
369C2×C4—1221no—
370C2×C4—1221no—
371C2×C4—1221no—
372C2×C4—1221no—
373C2×C4—1221no—
374C2×C4—1221no—
375C2×C4—1222no—
376C2×C4—2444no—
377C2×C4—2448no—
378C2×C4—2441no—
379C2×C4—2441no—
380C2×C4—2441no—
381C2×C4—2441no—
382C2×C4—2441no—
383C2×C4#1451984112yes—
384C2×C4C2×D61⋊C811yescharacteristic
385C2×C4D61⋊M1611yescharacteristic
386C8—4882no—
387C8—2444no—
388C22—42no—
389C22—42no—
390C22—42no—
391C22—81no—
392C22—81no—
393C22—81no—
394C22—81no—
395C22—614no—
396C22—1222no—
397C22—1222no—
398C22—1222no—
399C22—1222no—
400C22—1222no—
401C22—1222no—
402C22D61⋊(C22⋊C8)11yescharacteristic
403C22D61⋊#9911yescharacteristic
404C22D61⋊#10011yescharacteristic
405C22#1684075211yescharacteristic
406C22#1684075311yescharacteristic
407C22C2×#1451984111yescharacteristic
408C22#1684076011yescharacteristic
409C4—21no—
410C4—21no—
411C4—22no—
412C4—41no—
413C4—81no—
414C4—1222no—
415C4—1221no—
416C4—1221no—
417C4—1222no—
418C4—4881no—
419C4—2442no—
420C2—82no—
421C2—1224no—
422C2D61⋊#32311yescharacteristic
423C2#2146111111yescharacteristic
424C2#2146111511yescharacteristic
425C2#2146120411yescharacteristic
426C2#2146124411yescharacteristic
427C2#2146128911yescharacteristic
428C2#2146133911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#390C4
socleC23×C61C2×C22⋊C4
prime radicalC22×#11758224C4
cosocleC2×C4×Dic61C23
hypercenter#390#6923
hypocenterC61#7578
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #21461711C2semidirect
2. #21461480C2semidirect
3. #21460640C2semidirect
4. #21460635C2semidirect
32. C2×#11758224C8semidirect
63. C2×D4×C61C2×C8semidirect
95. C2×Dic122C2×C8semidirect
237. C61#7578semidirect
287. C2×D4D61⋊C8semidirect

Maximal subgroups

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

subgroupindex
#214617112
#214614802
#214606402
#214606352
#214483062
#757861