Finite Group Databasebeta

← #29589477

Subgroups — #29589477

Order 15616.

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

normal subgroups only

This group has 442 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#21448484C211yesmaximal, characteristic
2#21444157C211yesmaximal, characteristic
3#21443768C212yesmaximal, complemented
4#21443748C212yesmaximal, complemented
5C61×#1466C211yesmaximal, characteristic
6C2×#14519758C411yescharacteristic
7C22×#11758196C411yescharacteristic
8#16839726—21no—
9#16839657—21no—
10#16839656—21no—
11#16839646—21no—
12#16839642C411yescharacteristic
13#16839635—21no—
14#16839634C2211yescharacteristic
15#16839623C2211yescharacteristic
16C4×C22⋊Dic61C411yescharacteristic
17#16839488—21no—
18#16839486C2212yes—
19C2×C4×D4×C61C2211yescharacteristic
20C61×#432—21no—
21C61×#323—21no—
22C61×#323C2212yes—
23C23×Dic61C2×C411yescharacteristic
24C23×Dic61C2×C411yescharacteristic
25C2×#11758194—41no—
26#14519758—22no—
27#14519758—22no—
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—21no—
36C2×C22⋊Dic61C2×C411yescharacteristic
37C2×C22⋊Dic61C2×C411yescharacteristic
38C2×C4×Dic61—21no—
39C22⋊#92418—22no—
40C22⋊#92418—41no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46C22×D4×C61C2×C411yescharacteristic
47C23×C4×C61C2×C411yescharacteristic
48C23×C4×C61D411yescharacteristic
49C4×D4×C61—41no—
50C4×D4×C61—41no—
51C2×C4⋊C4×C61D411yescharacteristic
52C2×C22⋊C4×C61D411yescharacteristic
53C2×C22⋊C4×C61C2311yescharacteristic
54C2×C42×C61D411yescharacteristic
55C4⋊C8×C61—41no—
56C22⋊C8×C61—22no—
57#97×C61—41no—
58C24×C61C22⋊C411yescharacteristic
59C24×C61C22×C411yescharacteristic
60C2×D4×C61—21no—
61C2×D4×C61—21no—
62C2×D4×C61—41no—
63C2×D4×C61—41no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—81no—
69C22×C4×C61—81no—
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61C22⋊C411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—21no—
80C22×Dic61—41no—
81C22×Dic61—41no—
82C22×Dic61—41no—
83C22×Dic61—81no—
84C22×Dic61M1612yescomplemented
85C2×C8×C61—42no—
86C4⋊C4×C61—41no—
87C22⋊C4×C61—41no—
88C22⋊C4×C61—41no—
89C42×C61—21no—
90C42×C61—21no—
91C22⋊Dic61—24no—
92C22⋊Dic61—21no—
93C22⋊Dic61—41no—
94C22⋊Dic61—81no—
95C22⋊Dic61M1612yescomplemented
96#11758196—24no—
97#11758196—42no—
98#11758196—41no—
99#11758196—41no—
100#11758196—81no—
101C4×Dic61—81no—
102#11758194—82no—
103C2×#92418—42no—
104C23×C61—21no—
105C23×C61—21no—
106C23×C61—21no—
107C23×C61—21no—
108C23×C61—21no—
109C23×C61—41no—
110C23×C61—41no—
111C23×C61—41no—
112C23×C61—41no—
113C23×C61C2×C22⋊C411yescharacteristic
114C23×C61C2×M1611yescharacteristic
115C23×C61C2×M1611yescharacteristic
116D4×C61—42no—
117D4×C61—42no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—41no—
125C2×C4×C61—42no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—81no—
130C2×C4×C61—81no—
131C2×C4×C61—81no—
132C2×C4×C61#9911yescharacteristic
133C2×C4×C61#9911yescharacteristic
134C2×Dic61—22no—
135C2×Dic61—22no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—42no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—42no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—82no—
149C8×C61—82no—
150#92418—82no—
151#11528—611nomaximal, Sylow
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—41no—
157C22×C61—41no—
158C22×C61—42no—
159C22×C61—42no—
160C22×C61—41no—
161C22×C61—41no—
162C22×C61—41no—
163C22×C61—41no—
164C22×C61—41no—
165C22×C61—81no—
166C22×C61#40711yescharacteristic
167C22×C61C2×#9911yescharacteristic
168C22×C61#41311yescharacteristic
169C4×C61—21no—
170C4×C61—21no—
171C4×C61—41no—
172C4×C61—41no—
173C4×C61—41no—
174C4×C61—41no—
175Dic61—42no—
176Dic61—42no—
177Dic61—81no—
178Dic61—81no—
179#2322—611no—
180#1466D6111yescharacteristic
181#1465—611no—
182#1326—612no—
183#1317—612no—
184C2×C61—21no—
185C2×C61—21no—
186C2×C61—41no—
187C2×C61—41no—
188C2×C61—81no—
189C2×C61#146511yescharacteristic
190C2×C61#212111yescharacteristic
191C2×C61#212311yescharacteristic
192C2×#123—611no—
193C2×C4×D4C2×D6111yescharacteristic
194C22×C4⋊C4—611no—
195#432—21no—
196#407—1221no—
197#389—1221no—
198#388—1221no—
199#387—1221no—
200#386—611no—
201#385—611no—
202#385—1221no—
203#381—611no—
204C4×C22⋊C4—611no—
205#324—1221no—
206#323—21no—
207#323—612no—
208#323C2×D6112yes—
209C61#1152811yescharacteristic, complemented, Sylow
210C22×D4C4×D6111yescharacteristic
211C23×C4—611no—
212C23×C4—611no—
213C23×C4C4×D6111yescharacteristic
214C23×C4D24411yescharacteristic
215C2×M16—2441no—
216#123—1222no—
217#123—1222no—
218C4×D4—41no—
219C4×D4—41no—
220C2×C4⋊C4—1221no—
221C2×C4⋊C4—1221no—
222C2×C4⋊C4—1221no—
223C2×C4⋊C4—1221no—
224C2×C4⋊C4—2441no—
225C2×C4⋊C4—2441no—
226C2×C4⋊C4D24411yescharacteristic
227C2×C22⋊C4—611no—
228C2×C22⋊C4—611no—
229C2×C22⋊C4—1221no—
230C2×C22⋊C4—1221no—
231C2×C22⋊C4C22⋊D6111yescharacteristic
232C2×C22⋊C4C22×D6111yescharacteristic
233C2×C42—1221no—
234C2×C42C22⋊D6111yescharacteristic
235C4⋊C8—41no—
236C22⋊C8—22no—
237C22⋊C8—1222no—
238C22⋊C8—2441no—
239#97—41no—
240#95—1221no—
241#95—1221no—
242#95—1221no—
243#95—1221no—
244#95—1221no—
245C24#1175819811yescharacteristic
246C24C2×C4×D6111yescharacteristic
247C2×D4—21no—
248C2×D4—21no—
249C2×D4—41no—
250C2×D4—41no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—81no—
256C22×C4—81no—
257C22×C4—612no—
258C22×C4—1221no—
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4—1221no—
263C22×C4—4881no—
264C22×C4—2441no—
265C22×C4—2441no—
266C22×C4—2441no—
267C22×C4#1175819811yescharacteristic
268C22×C4#1175819811yescharacteristic
269C22×C4#1175819811yescharacteristic
270C22×C4C2×D24411yescharacteristic
271C22×C4C2×C22⋊D6111yescharacteristic
272M16—4882no—
273C2×C8—42no—
274C2×C8—2442no—
275C4⋊C4—41no—
276C4⋊C4—1224no—
277C4⋊C4—4881no—
278C4⋊C4—2442no—
279C4⋊C4—2441no—
280C4⋊C4—2441no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C22⋊C4—612no—
284C22⋊C4—1224no—
285C22⋊C4—1221no—
286C22⋊C4—4881no—
287C22⋊C4—2441no—
288C42—21no—
289C42—21no—
290C42—4881no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23C2×#1175819811yescharacteristic
301C23M16×D6111yescharacteristic
302C23M16×D6111yescharacteristic
303D4—42no—
304D4—42no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—1222no—
320C2×C4—1222no—
321C2×C4—4882no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4—2441no—
326C2×C4—2441no—
327C2×C4—2441no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4—2442no—
331C2×C4—2441no—
332C2×C4—2441no—
333C2×C4—2442no—
334C2×C4#1451969111yescharacteristic
335C2×C4#1451969111yescharacteristic
336C8—82no—
337C8—4882no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—42no—
345C22—42no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—81no—
352C22#1683972511yescharacteristic
353C22C2×#1451969111yescharacteristic
354C22#1683974411yescharacteristic
355C4—21no—
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—4881no—
362C4—4881no—
363C4—2442no—
364C4—2442no—
365C2—21no—
366C2—21no—
367C2—41no—
368C2—41no—
369C2—81no—
370C2#2144415511yescharacteristic
371C2#2144746611yescharacteristic
372C2#2144747211yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC24×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1466C2
socleC22×C61C2×#99
prime radicalC22×D4×C61C2×C4
cosocleC2×C22⋊C4×C61C23
hypercenter#1466D61
hypocenterC61#11528
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1466

Complements

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

NH ≅ G/Ntype
3. #21443768C2semidirect
4. #21443748C2semidirect
84. C22×Dic61M16semidirect
95. C22⋊Dic61M16semidirect
209. C61#11528semidirect

Maximal subgroups

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

subgroupindex
#214484842
#214441572
#214437682
#214437482
C61×#14662
#1152861