Finite Group Databasebeta

← #29590616

Subgroups — #29590616

Order 15616.

460 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 83 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#21451173C211yesmaximal, characteristic
2#21444157C211yesmaximal, characteristic
3#21443842C212yesmaximal, complemented
4#21443839C212yesmaximal, complemented
5C4×#99×C61C211yesmaximal, characteristic
6C2×C4×Dic122C411yescharacteristic, complemented
7#16839726—21no—
8#16839698C411yescharacteristic, complemented
9#16839698C2211yescharacteristic
10#16839674C411yescharacteristic, complemented
11#16839674C2211yescharacteristic
12#16839665—21no—
13#16839658—21no—
14#16839635—21no—
15#16839635—21no—
16#16839628C411yescharacteristic, complemented
17#16839488—21no—
18#16839486C2212yes—
19C2×C4×D4×C61C2211yescharacteristic
20C2×#99×C61—21no—
21C4×C22⋊C4×C61—21no—
22C61×#342C2212yes—
23C22×Dic122C2×C411yescharacteristic
24C2×#11758194—41no—
25C4×Dic122—41no—
26C4×Dic122—41no—
27C2×C4⋊Dic61—21no—
28C2×C4⋊Dic61C2×C411yescharacteristic
29C2×#11758196—21no—
30C2×#11758196—21no—
31C2×#11758196—21no—
32C2×C22⋊Dic61—21no—
33C2×C22⋊Dic61—21no—
34C2×C22⋊Dic61—21no—
35C2×C22⋊Dic61—21no—
36C2×C4×Dic61—21no—
37C22⋊#92418—22no—
38C22⋊#92418—41no—
39#14519684—21no—
40#14519684—21no—
41#14519684—21no—
42#14519684C2×C411yescharacteristic
43#14519684C2×C411yescharacteristic
44C22×D4×C61D411yescharacteristic
45C23×C4×C61D411yescharacteristic
46C23×C4×C61D411yescharacteristic
47C4×D4×C61—41no—
48C4×D4×C61—41no—
49C2×C4⋊C4×C61D411yescharacteristic
50C2×C22⋊C4×C61—22no—
51C2×C22⋊C4×C61C2×C411yescharacteristic
52C2×C22⋊C4×C61C2311yescharacteristic
53C2×C42×C61—41no—
54C2×C42×C61C2×C411yescharacteristic
55#99×C61—24no—
56#95×C61—41no—
57C24×C61C22⋊C411yescharacteristic
58C24×C61C2×D411yescharacteristic
59C2×D4×C61—22no—
60C2×D4×C61—22no—
61C2×D4×C61—41no—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—42no—
67C22×C4×C61—81no—
68C22×C4×C61—81no—
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61C22×C411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C2×Dic122—41no—
79C2×Dic122—42no—
80C4⋊C4×C61—41no—
81C22⋊C4×C61—24no—
82C22⋊C4×C61—41no—
83C22⋊C4×C61—41no—
84C22⋊C4×C61—42no—
85C42×C61—21no—
86C42×C61—21no—
87C42×C61—82no—
88C22⋊Dic61—42no—
89C22⋊Dic61—42no—
90C22⋊Dic61—81no—
91C22⋊Dic61—81no—
92C4⋊Dic61—42no—
93C4⋊Dic61—41no—
94#11758196—41no—
95#11758196—41no—
96#11758196—81no—
97#11758196—81no—
98C4×Dic61—42no—
99#11758194—82no—
100C2×#92418—42no—
101C23×C61—21no—
102C23×C61—21no—
103C23×C61—21no—
104C23×C61—21no—
105C23×C61—21no—
106C23×C61—41no—
107C23×C61—41no—
108C23×C61—41no—
109C23×C61—41no—
110C23×C61C2×C22⋊C411yescharacteristic
111C23×C61#13712yes—
112D4×C61—44no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—41no—
119C2×C4×C61—42no—
120C2×C4×C61—42no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—44no—
125C2×C4×C61—81no—
126C2×C4×C61—81no—
127C2×C4×C61—82no—
128C2×C4×C61—82no—
129C2×C4×C61#9911yescharacteristic
130C2×C4×C61#9911yescharacteristic
131C2×C4×C61#10412yes—
132C2×Dic61—22no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144Dic122—42no—
145Dic122—42no—
146#92418—82no—
147#11784—611nomaximal, Sylow
148C22×C61—21no—
149C22×C61—21no—
150C22×C61—22no—
151C22×C61—42no—
152C22×C61—42no—
153C22×C61—41no—
154C22×C61—41no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61—41no—
158C22×C61—81no—
159C22×C61—81no—
160C22×C61C2×#9911yescharacteristic
161C22×C61#41911yescharacteristic
162C22×C61C2×#10411yescharacteristic
163C4×C61—21no—
164C4×C61—21no—
165C4×C61—22no—
166C4×C61—41no—
167C4×C61—41no—
168C4×C61—41no—
169C4×C61—84no—
170Dic61—42no—
171Dic61—81no—
172Dic61—81no—
173Dic61—81no—
174#2580—611no—
175C4×#99D6111yescharacteristic
176#1465—611no—
177#1352—612no—
178#1351—612no—
179C2×C61—21no—
180C2×C61—21no—
181C2×C61—42no—
182C2×C61—81no—
183C2×C61#150811yescharacteristic
184C2×C61#212011yescharacteristic
185C2×C61#212711yescharacteristic
186C2×C4×Q8—611no—
187C2×C4×D4C2×D6111yescharacteristic
188C2×#99—21no—
189#407—1221no—
190#399—611no—
191#399—611no—
192#393—611no—
193#393—611no—
194#390—1221no—
195#389—1221no—
196#385—1221no—
197#385—1221no—
198#382—611no—
199C4×C22⋊C4—21no—
200#342C2×D6112yes—
201#324—1221no—
202#323—612no—
203C61#1178411yescharacteristic, complemented, Sylow
204C22×Q8—611no—
205C22×D4C22⋊D6111yescharacteristic
206C23×C4D24411yescharacteristic
207C23×C4C22⋊D6111yescharacteristic
208C2×M16—2441no—
209C4×Q8—2441no—
210C4×Q8—2441no—
211C4×D4—41no—
212C4×D4—41no—
213C2×C4⋊C4—611no—
214C2×C4⋊C4—1221no—
215C2×C4⋊C4—1221no—
216C2×C4⋊C4—1221no—
217C2×C4⋊C4—1221no—
218C2×C4⋊C4D24411yescharacteristic
219C2×C22⋊C4—22no—
220C2×C22⋊C4—1221no—
221C2×C22⋊C4—1221no—
222C2×C22⋊C4—1221no—
223C2×C22⋊C4—1221no—
224C2×C22⋊C4C4×D6111yescharacteristic
225C2×C22⋊C4C22×D6111yescharacteristic
226C2×C42—41no—
227C2×C42—1221no—
228C2×C42C4×D6111yescharacteristic
229#99—24no—
230C22⋊C8—1222no—
231C22⋊C8—2441no—
232#95—41no—
233#95—611no—
234#95—611no—
235#95—1221no—
236#95—1221no—
237#95—1221no—
238C24#1175819811yescharacteristic
239C24C2×C22⋊D6111yescharacteristic
240C2×Q8—2441no—
241C2×Q8—2442no—
242C2×D4—22no—
243C2×D4—22no—
244C2×D4—41no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—42no—
250C22×C4—81no—
251C22×C4—81no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4#1175819811yescharacteristic
257C22×C4#1175819811yescharacteristic
258C22×C4#1175819811yescharacteristic
259C22×C4C2×C4×D6111yescharacteristic
260C22×C4C2×D24411yescharacteristic
261M16—4882no—
262C2×C8—2442no—
263C4⋊C4—41no—
264C4⋊C4—4881no—
265C4⋊C4—4881no—
266C4⋊C4—2441no—
267C4⋊C4—2441no—
268C4⋊C4—2441no—
269C4⋊C4—2442no—
270C22⋊C4—24no—
271C22⋊C4—41no—
272C22⋊C4—41no—
273C22⋊C4—42no—
274C22⋊C4—4881no—
275C22⋊C4—4881no—
276C22⋊C4—2442no—
277C22⋊C4—2442no—
278C42—21no—
279C42—21no—
280C42—82no—
281C42—2442no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23—41no—
291C23C2×#1175819811yescharacteristic
292C23#1451980712yes—
293Q8—2442no—
294Q8—2442no—
295D4—44no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—41no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—44no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4—82no—
311C2×C4—82no—
312C2×C4—1222no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4—2441no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4#1451969111yescharacteristic
325C2×C4#1451969111yescharacteristic
326C2×C4#1451970512yes—
327C8—4882no—
328C22—21no—
329C22—21no—
330C22—22no—
331C22—42no—
332C22—42no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—81no—
339C22—81no—
340C22C2×#1451969111yescharacteristic
341C22#1683977011yescharacteristic
342C22C2×#1451970511yescharacteristic
343C4—21no—
344C4—21no—
345C4—22no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—84no—
350C4—4881no—
351C4—4881no—
352C4—4881no—
353C4—2442no—
354C2—21no—
355C2—21no—
356C2—42no—
357C2—81no—
358C2#2144433811yescharacteristic
359C2#2144745811yescharacteristic
360C2#2144748611yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC4×#99×C61C2
socleC22×C61C2×#99
prime radicalC22×D4×C61D4
cosocleC2×C22⋊C4×C61C23
hypercenterC4×#99D61
hypocenterC61#11784
LCSG ▷ C22×C4×C61 ▷ C23×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
3. #21443842C2semidirect
4. #21443839C2semidirect
6. C2×C4×Dic122C4semidirect
8. #16839698C4semidirect
10. #16839674C4semidirect
16. #16839628C4semidirect
203. C61#11784semidirect

Maximal subgroups

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

subgroupindex
#214511732
#214441572
#214438422
#214438392
C4×#99×C612
#1178461