Finite Group Databasebeta

← #29595184

Subgroups — #29595184

Order 15616.

564 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 123 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#21448531C211yesmaximal, characteristic
2C2×#16839556C212yesmaximal
3C4×#14519692C211yesmaximal, characteristic
4#21443943C212yesmaximal
5C4×#99×C61C211yesmaximal, characteristic
6C2×#14519764C2211yescharacteristic
7C2×C4×Dic122C411yescharacteristic, complemented
8C2×#14519692C2212yes—
9#16839667C411yescharacteristic, complemented
10#16839665C2211yescharacteristic
11#16839650—21no—
12#16839650—21no—
13#16839635—21no—
14#16839635—21no—
15#16839631C411yescharacteristic, complemented
16C4×C22⋊Dic61—21no—
17#16839608C411yescharacteristic, complemented
18#16839556C418yescomplemented
19#16839529—21no—
20C2×C4×D4×C61C2211yescharacteristic
21C2×#99×C61C2212yes—
22C4×C22⋊C4×C61—21no—
23C61×#342—21no—
24C22×Dic122C2×C411yescharacteristic
25#14519764—22no—
26#14519764C2×C414yes—
27C4×Dic122—41no—
28C4×Dic122—41no—
29C2×C4⋊Dic61C2×C411yescharacteristic
30C2×#11758196—21no—
31C2×#11758196—21no—
32C2×#11758196—21no—
33C2×C22⋊Dic61—21no—
34C2×C22⋊Dic61—21no—
35C2×C22⋊Dic61—22no—
36C2×C22⋊Dic61—21no—
37C2×C22⋊Dic61—21no—
38C2×C4×Dic61—21no—
39C2×C4×Dic61—41no—
40C2×C4×Dic61C2×C411yescharacteristic
41C2×C4×Dic61C2×C411yescharacteristic
42#14519692—22no—
43#14519692C2×C414yes—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—41no—
49C22×D4×C61C2311yescharacteristic
50C23×C4×C61D411yescharacteristic
51C23×C4×C61D411yescharacteristic
52C4×D4×C61—41no—
53C4×D4×C61—41no—
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C22⋊C4×C61—22no—
56C2×C22⋊C4×C61D411yescharacteristic
57C2×C22⋊C4×C61D411yescharacteristic
58C2×C42×C61—41no—
59C2×C42×C61C2×C411yescharacteristic
60#99×C61—22no—
61#99×C61C2×C414yes—
62#95×C61—41no—
63C24×C61C2×D411yescharacteristic
64C24×C61C2×D411yescharacteristic
65C2×D4×C61—41no—
66C2×D4×C61—41no—
67C2×D4×C61C22×C412yes—
68C2×D4×C61#4112yes—
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61—21no—
72C22×C4×C61—21no—
73C22×C4×C61—42no—
74C22×C4×C61—81no—
75C22×C4×C61—81no—
76C22×C4×C61C22⋊C411yescharacteristic
77C22×C4×C61C22⋊C411yescharacteristic
78C22×C4×C61C22⋊C411yescharacteristic
79C22×C4×C61C22⋊C411yescharacteristic
80C22×C4×C61C22×C411yescharacteristic
81C22×Dic61—21no—
82C22×Dic61—21no—
83C22×Dic61—21no—
84C22×Dic61—21no—
85C22×Dic61—42no—
86C2×Dic122—21no—
87C2×Dic122—41no—
88C2×Dic122—41no—
89C2×Dic122C4212yescomplemented
90C4⋊C4×C61—41no—
91C22⋊C4×C61—24no—
92C22⋊C4×C61—41no—
93C22⋊C4×C61—41no—
94C22⋊C4×C61—42no—
95C42×C61—21no—
96C42×C61—21no—
97C42×C61—82no—
98C22⋊Dic61—24no—
99C22⋊Dic61—24no—
100C22⋊Dic61—24no—
101C22⋊Dic61—42no—
102C22⋊Dic61—81no—
103C22⋊Dic61—81no—
104C4⋊Dic61—41no—
105#11758196—41no—
106#11758196—41no—
107#11758196—81no—
108#11758196—81no—
109C4×Dic61—21no—
110C4×Dic61—42no—
111C4×Dic61—41no—
112C4×Dic61—82no—
113C4×Dic61C4212yescomplemented
114C23×C61—21no—
115C23×C61—21no—
116C23×C61—21no—
117C23×C61—21no—
118C23×C61—41no—
119C23×C61—41no—
120C23×C61—41no—
121C23×C61—41no—
122C23×C61C2×C22⋊C411yescharacteristic
123C23×C61C4×D412yes—
124C23×C61C4×D412yes—
125D4×C61—42no—
126D4×C61—42no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—41no—
133C2×C4×C61—42no—
134C2×C4×C61—42no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—44no—
139C2×C4×C61—81no—
140C2×C4×C61—81no—
141C2×C4×C61—82no—
142C2×C4×C61—82no—
143C2×C4×C61#9911yescharacteristic
144C2×C4×C61#9911yescharacteristic
145C2×C4×C61C2×C4211yescharacteristic
146C2×C4×C61#11711yescharacteristic
147C2×Dic61—22no—
148C2×Dic61—22no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—44no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—82no—
161C2×Dic61—82no—
162Dic122—42no—
163Dic122—42no—
164#12627—611nomaximal, Sylow
165C22×C61—21no—
166C22×C61—21no—
167C22×C61—22no—
168C22×C61—22no—
169C22×C61—42no—
170C22×C61—42no—
171C22×C61—41no—
172C22×C61—41no—
173C22×C61—41no—
174C22×C61—41no—
175C22×C61—81no—
176C22×C61—81no—
177C22×C61C4×C22⋊C411yescharacteristic
178C22×C61C2×#9911yescharacteristic
179C22×C61#41011yescharacteristic
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—21no—
183C4×C61—21no—
184C4×C61—41no—
185C4×C61—41no—
186C4×C61—41no—
187C4×C61—84no—
188Dic61—42no—
189Dic61—42no—
190Dic61—81no—
191Dic61—84no—
192Dic61—81no—
193#2326—611no—
194C2×#354—612no—
195C4×#99—611no—
196C4×#99D6111yescharacteristic
197#1393—612no—
198C2×C61—21no—
199C2×C61—21no—
200C2×C61—42no—
201C2×C61—42no—
202C2×C61C4×#9911yescharacteristic
203C2×C61#212711yescharacteristic
204C2×C61#212911yescharacteristic
205C2×#124—611no—
206C2×C4×Q8—611no—
207C2×C4×D4C2×D6111yescharacteristic
208C2×#99—612no—
209C2×#99C2×D6112yes—
210#391—611no—
211#390—611no—
212#388—1221no—
213#388—1221no—
214#385—1221no—
215#385—1221no—
216#384—611no—
217C4×C22⋊C4—21no—
218C4×C22⋊C4—1221no—
219#376—611no—
220#354—618no—
221#342—21no—
222#342—1221no—
223C61#1262711yescharacteristic, complemented, Sylow
224C22×Q8—611no—
225C22×D4C22×D6111yescharacteristic
226C23×C4D24411yescharacteristic
227C23×C4C22⋊D6111yescharacteristic
228#124—614no—
229#124—1222no—
230C4×Q8—2441no—
231C4×Q8—2441no—
232C4×D4—41no—
233C4×D4—41no—
234C2×C4⋊C4—611no—
235C2×C4⋊C4—1221no—
236C2×C4⋊C4—1221no—
237C2×C4⋊C4—1221no—
238C2×C4⋊C4C4×D6111yescharacteristic
239C2×C22⋊C4—22no—
240C2×C22⋊C4—1221no—
241C2×C22⋊C4—1221no—
242C2×C22⋊C4—1222no—
243C2×C22⋊C4—1221no—
244C2×C22⋊C4—1221no—
245C2×C22⋊C4D24411yescharacteristic
246C2×C22⋊C4C22⋊D6111yescharacteristic
247C2×C42—41no—
248C2×C42—611no—
249C2×C42—611no—
250C2×C42—1221no—
251C2×C42—2441no—
252C2×C42C4×D6111yescharacteristic
253#99—22no—
254#99—614no—
255#99—1222no—
256#99C4×D6114yes—
257#95—41no—
258#95—1221no—
259#95—1221no—
260#95—1221no—
261#95—1221no—
262#95—2441no—
263C24C2×D24411yescharacteristic
264C24C2×C22⋊D6111yescharacteristic
265C2×Q8—612no—
266C2×Q8—1221no—
267C2×Q8—2441no—
268C2×Q8—2441no—
269C2×D4—41no—
270C2×D4—41no—
271C2×D4C2×C4×D6112yes—
272C2×D4#1175822212yes—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—42no—
278C22×C4—81no—
279C22×C4—81no—
280C22×C4—1221no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4—2442no—
285C22×C4#1175819811yescharacteristic
286C22×C4#1175819811yescharacteristic
287C22×C4#1175819811yescharacteristic
288C22×C4#1175819811yescharacteristic
289C22×C4C2×C4×D6111yescharacteristic
290C4⋊C4—41no—
291C4⋊C4—4881no—
292C4⋊C4—4881no—
293C4⋊C4—2441no—
294C4⋊C4—2441no—
295C4⋊C4—2441no—
296C22⋊C4—24no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—42no—
300C22⋊C4—1224no—
301C22⋊C4—1224no—
302C22⋊C4—1224no—
303C22⋊C4—4881no—
304C22⋊C4—4881no—
305C22⋊C4—2442no—
306C42—21no—
307C42—21no—
308C42—82no—
309C42—612no—
310C42—1221no—
311C42—4882no—
312C42—2441no—
313C42—2442no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23C2×#1175819811yescharacteristic
323C23C4×C22⋊D6112yes—
324C23C4×D24412yes—
325Q8—2442no—
326Q8—2442no—
327D4—42no—
328D4—42no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—44no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—82no—
344C2×C4—82no—
345C2×C4—1222no—
346C2×C4—1222no—
347C2×C4—4882no—
348C2×C4—4882no—
349C2×C4—2444no—
350C2×C4—2441no—
351C2×C4—2441no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4—2441no—
355C2×C4—2441no—
356C2×C4—2441no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4#1451969111yescharacteristic
361C2×C4#1451969111yescharacteristic
362C2×C4C42×D6111yescharacteristic
363C2×C4#1451973411yescharacteristic
364C22—21no—
365C22—21no—
366C22—22no—
367C22—22no—
368C22—42no—
369C22—42no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—81no—
375C22—81no—
376C22C4×#1175819811yescharacteristic
377C22C2×#1451969111yescharacteristic
378C22#1683973511yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—21no—
383C4—41no—
384C4—41no—
385C4—41no—
386C4—84no—
387C4—4881no—
388C4—4884no—
389C4—4881no—
390C4—2442no—
391C4—2442no—
392C2—21no—
393C2—21no—
394C2—42no—
395C2—42no—
396C2C4×#1451969111yescharacteristic
397C2#2144748611yescharacteristic
398C2#2144749311yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC2×C4×C61C2×C42
FrattiniC22×D4C22×D61
FittingC4×#99×C61C2
socleC22×C61C2×#99
prime radical, cosocleC22×D4×C61C23
hypercenterC4×#99D61
hypocenterC61#12627
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
7. C2×C4×Dic122C4semidirect
9. #16839667C4semidirect
15. #16839631C4semidirect
17. #16839608C4semidirect
18. #16839556C4semidirect
89. C2×Dic122C42semidirect
113. C4×Dic61C42semidirect
223. C61#12627semidirect

Maximal subgroups

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

subgroupindex
#214485312
C2×#168395562
C4×#145196922
#214439432
C4×#99×C612
#1262761