Finite Group Databasebeta

← #29595158

Subgroups — #29595158

Order 15616.

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

normal subgroups only

This group has 548 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#21448484C211yesmaximal, characteristic
2C2×#16839553C212yesmaximal
3C4×#14519692C211yesmaximal, characteristic
4#21443938C212yesmaximal
5C4×#100×C61C211yesmaximal, characteristic
6C2×#14519758C2211yescharacteristic
7C22×#11758196C411yescharacteristic, complemented
8C2×#14519692C2212yes—
9#16839657—21no—
10#16839656—21no—
11#16839646—21no—
12#16839642C2211yescharacteristic
13#16839635—21no—
14#16839634C411yescharacteristic, complemented
15#16839623C411yescharacteristic, complemented
16C4×C22⋊Dic61—21no—
17C4×C22⋊Dic61C411yescharacteristic, complemented
18#16839553C418yescomplemented
19#16839529—21no—
20C2×C4×D4×C61C2211yescharacteristic
21C2×#100×C61C2212yes—
22C4×M16×C61—21no—
23C61×#343—21no—
24C23×Dic61C2×C411yescharacteristic
25C23×Dic61C2×C411yescharacteristic
26#14519758—22no—
27#14519758C2×C414yes—
28C2×#11758196—21no—
29C2×#11758196—21no—
30C2×#11758196—21no—
31C2×#11758196—21no—
32C2×#11758196—41no—
33C2×#11758196—41no—
34C2×C22⋊Dic61—21no—
35C2×C22⋊Dic61—22no—
36C2×C22⋊Dic61—21no—
37C2×C22⋊Dic61C2×C411yescharacteristic
38C2×C22⋊Dic61C2×C411yescharacteristic
39C2×C4×Dic61—21no—
40C2×C4×Dic61—41no—
41#14519692—22no—
42#14519692C2×C414yes—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—41no—
49C22×D4×C61C2311yescharacteristic
50C23×C4×C61C2×C411yescharacteristic
51C23×C4×C61D411yescharacteristic
52C2×M16×C61—22no—
53C4×D4×C61—41no—
54C4×D4×C61—41no—
55C2×C4⋊C4×C61D411yescharacteristic
56C2×C22⋊C4×C61C2×C411yescharacteristic
57C2×C22⋊C4×C61D411yescharacteristic
58C2×C42×C61D411yescharacteristic
59#100×C61—22no—
60#100×C61C2×C414yes—
61#97×C61—41no—
62C4×C8×C61—41no—
63C24×C61C22×C411yescharacteristic
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—81no—
74C22×C4×C61—81no—
75C22×C4×C61C22⋊C411yescharacteristic
76C22×C4×C61C22⋊C411yescharacteristic
77C22×C4×C61C22⋊C411yescharacteristic
78C22×C4×C61C22⋊C411yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C22×Dic61—21no—
81C22×Dic61—21no—
82C22×Dic61—21no—
83C22×Dic61—21no—
84C22×Dic61—21no—
85C22×Dic61—41no—
86C22×Dic61—41no—
87C22×Dic61—42no—
88C22×Dic61—41no—
89C22×Dic61—81no—
90C22×Dic61C4212yescomplemented
91M16×C61—24no—
92M16×C61—42no—
93C2×C8×C61—42no—
94C4⋊C4×C61—41no—
95C22⋊C4×C61—41no—
96C22⋊C4×C61—41no—
97C42×C61—21no—
98C42×C61—21no—
99C22⋊Dic61—21no—
100C22⋊Dic61—24no—
101C22⋊Dic61—24no—
102C22⋊Dic61—42no—
103C22⋊Dic61—41no—
104C22⋊Dic61—81no—
105C22⋊Dic61C4212yescomplemented
106#11758196—24no—
107#11758196—42no—
108#11758196—41no—
109#11758196—41no—
110#11758196—81no—
111C4×Dic61—81no—
112C4×Dic61—82no—
113C23×C61—21no—
114C23×C61—21no—
115C23×C61—21no—
116C23×C61—21no—
117C23×C61—41no—
118C23×C61—41no—
119C23×C61—41no—
120C23×C61—41no—
121C23×C61C2×C4211yescharacteristic
122C23×C61C2×C22⋊C411yescharacteristic
123C23×C61#11711yescharacteristic
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—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—81no—
138C2×C4×C61—81no—
139C2×C4×C61—81no—
140C2×C4×C61#9911yescharacteristic
141C2×C4×C61#9911yescharacteristic
142C2×C4×C61C4×D412yes—
143C2×Dic61—22no—
144C2×Dic61—22no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—42no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—42no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—44no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—82no—
159C2×Dic61—82no—
160C2×Dic61—82no—
161C8×C61—44no—
162#12621—611nomaximal, Sylow
163C22×C61—21no—
164C22×C61—21no—
165C22×C61—21no—
166C22×C61—21no—
167C22×C61—22no—
168C22×C61—41no—
169C22×C61—41no—
170C22×C61—42no—
171C22×C61—42no—
172C22×C61—41no—
173C22×C61—41no—
174C22×C61—41no—
175C22×C61—41no—
176C22×C61—81no—
177C22×C61C4×C22⋊C411yescharacteristic
178C22×C61C2×#9911yescharacteristic
179C22×C61#41011yescharacteristic
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—22no—
183C4×C61—41no—
184C4×C61—41no—
185C4×C61—41no—
186Dic61—42no—
187Dic61—42no—
188Dic61—81no—
189Dic61—84no—
190Dic61—81no—
191#2322—611no—
192C2×#352—612no—
193C4×#100D6111yescharacteristic
194C4×#99—611no—
195#1390—612no—
196C2×C61—21no—
197C2×C61—21no—
198C2×C61—42no—
199C2×C61—41no—
200C2×C61—41no—
201C2×C61C4×#9911yescharacteristic
202C2×C61#212111yescharacteristic
203C2×C61#212311yescharacteristic
204C2×#123—611no—
205C2×C4×D4C2×D6111yescharacteristic
206C22×C4⋊C4—611no—
207C2×#100C2×D6112yes—
208C2×#99—612no—
209C4×M16—21no—
210#389—1221no—
211#388—1221no—
212#387—1221no—
213#386—611no—
214#385—611no—
215#385—1221no—
216#381—611no—
217C4×C22⋊C4—611no—
218C4×C22⋊C4—1221no—
219#352—618no—
220#343—21no—
221#342—1221no—
222C61#1262111yescharacteristic, complemented, Sylow
223C22×D4C22×D6111yescharacteristic
224C23×C4—611no—
225C23×C4—611no—
226C23×C4C4×D6111yescharacteristic
227C23×C4D24411yescharacteristic
228C2×M16—22no—
229#123—614no—
230#123—1222no—
231C4×D4—41no—
232C4×D4—41no—
233C2×C4⋊C4—1221no—
234C2×C4⋊C4—1221no—
235C2×C4⋊C4—1221no—
236C2×C4⋊C4—1221no—
237C2×C4⋊C4—2441no—
238C2×C4⋊C4—2441no—
239C2×C4⋊C4C22⋊D6111yescharacteristic
240C2×C22⋊C4—611no—
241C2×C22⋊C4—611no—
242C2×C22⋊C4—1221no—
243C2×C22⋊C4—1222no—
244C2×C22⋊C4—1221no—
245C2×C22⋊C4C4×D6111yescharacteristic
246C2×C22⋊C4D24411yescharacteristic
247C2×C42—1221no—
248C2×C42—2441no—
249C2×C42C22⋊D6111yescharacteristic
250#100—22no—
251#100C4×D6114yes—
252#99—614no—
253#99—1222no—
254#97—41no—
255C4×C8—41no—
256#95—1221no—
257#95—1221no—
258#95—1221no—
259#95—1221no—
260#95—1221no—
261#95—2441no—
262C24C2×C4×D6111yescharacteristic
263C24C2×D24411yescharacteristic
264C2×D4—41no—
265C2×D4—41no—
266C2×D4C2×C4×D6112yes—
267C2×D4#1175822212yes—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—81no—
273C22×C4—81no—
274C22×C4—612no—
275C22×C4—1221no—
276C22×C4—1221no—
277C22×C4—1221no—
278C22×C4—1221no—
279C22×C4—1221no—
280C22×C4—4881no—
281C22×C4—2442no—
282C22×C4—2441no—
283C22×C4—2441no—
284C22×C4—2441no—
285C22×C4#1175819811yescharacteristic
286C22×C4#1175819811yescharacteristic
287C22×C4#1175819811yescharacteristic
288C22×C4#1175819811yescharacteristic
289C22×C4C2×C22⋊D6111yescharacteristic
290M16—24no—
291M16—42no—
292C2×C8—42no—
293C4⋊C4—41no—
294C4⋊C4—1224no—
295C4⋊C4—4881no—
296C4⋊C4—2442no—
297C4⋊C4—2441no—
298C4⋊C4—2441no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—612no—
302C22⋊C4—1221no—
303C22⋊C4—1224no—
304C22⋊C4—1224no—
305C22⋊C4—4881no—
306C22⋊C4—2442no—
307C22⋊C4—2441no—
308C42—21no—
309C42—21no—
310C42—4882no—
311C42—4881no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23C42×D6111yescharacteristic
321C23C2×#1175819811yescharacteristic
322C23#1451973411yescharacteristic
323C23C4×D24412yes—
324D4—42no—
325D4—42no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—1222no—
340C2×C4—1222no—
341C2×C4—4882no—
342C2×C4—4882no—
343C2×C4—4882no—
344C2×C4—2441no—
345C2×C4—2444no—
346C2×C4—2441no—
347C2×C4—2441no—
348C2×C4—2441no—
349C2×C4—2441no—
350C2×C4—2441no—
351C2×C4—2441no—
352C2×C4—2441no—
353C2×C4—2442no—
354C2×C4—2441no—
355C2×C4—2441no—
356C2×C4—2442no—
357C2×C4#1451969111yescharacteristic
358C2×C4#1451969111yescharacteristic
359C2×C4C4×C22⋊D6112yes—
360C8—44no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—22no—
366C22—41no—
367C22—41no—
368C22—42no—
369C22—42no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—81no—
375C22C4×#1175819811yescharacteristic
376C22C2×#1451969111yescharacteristic
377C22#1683973511yescharacteristic
378C4—21no—
379C4—21no—
380C4—22no—
381C4—41no—
382C4—41no—
383C4—41no—
384C4—4881no—
385C4—4884no—
386C4—4881no—
387C4—2442no—
388C4—2442no—
389C2—21no—
390C2—21no—
391C2—42no—
392C2—41no—
393C2—41no—
394C2C4×#1451969111yescharacteristic
395C2#2144746611yescharacteristic
396C2#2144747411yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC23×C61C2×C42
FrattiniC22×D4C22×D61
FittingC4×#100×C61C2
socleC22×C61C2×#99
prime radical, cosocleC22×D4×C61C23
hypercenterC4×#100D61
hypocenterC61#12621
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#100

Complements

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

NH ≅ G/Ntype
7. C22×#11758196C4semidirect
14. #16839634C4semidirect
15. #16839623C4semidirect
17. C4×C22⋊Dic61C4semidirect
18. #16839553C4semidirect
90. C22×Dic61C42semidirect
105. C22⋊Dic61C42semidirect
222. C61#12621semidirect

Maximal subgroups

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

subgroupindex
#214484842
C2×#168395532
C4×#145196922
#214439382
C4×#100×C612
#1262161