Finite Group Databasebeta

← #29590317

Subgroups — #29590317

Order 15616.

452 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 107 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#21449087C211yesmaximal, characteristic
2#21444133C211yesmaximal, characteristic
3#21443848C212yesmaximal, complemented
4#21443845C212yesmaximal, complemented
5C61×#1742C211yesmaximal, characteristic
6C2×C4×Dic122C411yescharacteristic
7#16839815—21no—
8#16839701C2211yescharacteristic
9#16839698C411yescharacteristic
10#16839695—21no—
11#16839685—21no—
12#16839682C2211yescharacteristic
13#16839674C411yescharacteristic
14C4×#11758196—21no—
15C4×C4⋊Dic61C411yescharacteristic
16C4×C22⋊Dic61—21no—
17#16839488C2212yes—
18#16839486—21no—
19C22×M16×C61—21no—
20C2×#117×C61C2211yescharacteristic
21C61×#343—21no—
22C61×#343C2212yes—
23C22×Dic122C2×C411yescharacteristic
24C4×Dic122—41no—
25C4×Dic122—41no—
26C2×C4⋊Dic61—21no—
27C2×C4⋊Dic61C2×C411yescharacteristic
28C2×#11758196—21no—
29C2×#11758196—21no—
30C2×#11758196—21no—
31C2×C22⋊Dic61—21no—
32C2×C22⋊Dic61—21no—
33C2×C4×Dic61—21no—
34C2×C4×Dic61—21no—
35C4⋊#92418—41no—
36C22⋊#92418—22no—
37C4×#92418—41no—
38#14519684—21no—
39#14519684—21no—
40#14519684—21no—
41#14519684—21no—
42#14519684C2×C411yescharacteristic
43#14519684C2×C411yescharacteristic
44C23×C4×C61D411yescharacteristic
45C2×M16×C61—24no—
46C2×M16×C61—22no—
47C2×M16×C61—41no—
48C2×M16×C61—42no—
49C22×C8×C61—41no—
50#117×C61—41no—
51#117×C61—41no—
52C2×C4⋊C4×C61D411yescharacteristic
53C2×C4⋊C4×C61C2311yescharacteristic
54C2×C22⋊C4×C61C2×C411yescharacteristic
55C2×C22⋊C4×C61D411yescharacteristic
56C2×C42×C61C2×C411yescharacteristic
57C2×C42×C61D411yescharacteristic
58C24×C61C22⋊C411yescharacteristic
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—22no—
62C22×C4×C61C22⋊C411yescharacteristic
63C22×C4×C61C22⋊C411yescharacteristic
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61SD1612yes—
66C22×C4×C61Q1612yes—
67C22×C4×C61C22×C411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74C2×Dic122—41no—
75C2×Dic122—42no—
76M16×C61—24no—
77M16×C61—44no—
78M16×C61—42no—
79C2×C8×C61—42no—
80C2×C8×C61—44no—
81C4⋊C4×C61—41no—
82C4⋊C4×C61—41no—
83C22⋊C4×C61—41no—
84C22⋊C4×C61—41no—
85C42×C61—21no—
86C42×C61—21no—
87C42×C61—21no—
88C42×C61—21no—
89C22⋊Dic61—42no—
90C22⋊Dic61—42no—
91C4⋊Dic61—42no—
92C4⋊Dic61—41no—
93#11758196—42no—
94#11758196—42no—
95#11758196—42no—
96C4×Dic61—41no—
97C4×Dic61—41no—
98C4×Dic61—42no—
99C2×#92418—42no—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61—41no—
103C23×C61—41no—
104C23×C61#10312yes—
105C23×C61C2×C22⋊C411yescharacteristic
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—22no—
109C2×C4×C61—22no—
110C2×C4×C61—22no—
111C2×C4×C61—22no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61#9911yescharacteristic
121C2×C4×C61#9911yescharacteristic
122C2×C4×C61#10312yes—
123C2×C4×C61#10412yes—
124C2×C4×C61C2×SD1611yescharacteristic
125C2×C4×C61C2×Q1611yescharacteristic
126C2×Dic61—22no—
127C2×Dic61—22no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138Dic122—42no—
139Dic122—42no—
140C8×C61—44no—
141#92418—82no—
142#11721—611nomaximal, Sylow
143C22×C61—21no—
144C22×C61—21no—
145C22×C61—22no—
146C22×C61—42no—
147C22×C61—41no—
148C22×C61—41no—
149C22×C61—81no—
150C22×C61C2×#9911yescharacteristic
151C22×C61C2×#10311yescharacteristic
152C22×C61C2×#10411yescharacteristic
153C4×C61—21no—
154C4×C61—21no—
155C4×C61—41no—
156C4×C61—41no—
157C4×C61—41no—
158C4×C61—41no—
159C4×C61#32812yes—
160C4×C61#32812yes—
161Dic61—42no—
162Dic61—42no—
163Dic61—81no—
164Dic61—81no—
165#2396—611no—
166#1742D6111yescharacteristic
167#1458—611no—
168#1354—612no—
169#1353—612no—
170C2×C61—21no—
171C2×C61—21no—
172C2×C61—42no—
173C2×C61C2×#32811yescharacteristic
174C2×C61#212011yescharacteristic
175C2×C61#213211yescharacteristic
176C22×M16—21no—
177C2×C4×Q8—611no—
178C2×#117C2×D6111yescharacteristic
179#431—1221no—
180#400—611no—
181#399—611no—
182#398—1221no—
183#396—1221no—
184#395—611no—
185#393—611no—
186C4×C4⋊C4—611no—
187C4×C4⋊C4—1221no—
188C4×C22⋊C4—1221no—
189#343—21no—
190#343C2×D6112yes—
191#324—612no—
192#323—1221no—
193C61#1172111yescharacteristic, complemented, Sylow
194C22×Q8—611no—
195C23×C4C22⋊D6111yescharacteristic
196C2×M16—24no—
197C2×M16—22no—
198C2×M16—41no—
199C2×M16—42no—
200C22×C8—41no—
201C4×Q8—2441no—
202C4×Q8—2441no—
203#117—41no—
204#117—41no—
205C2×C4⋊C4—611no—
206C2×C4⋊C4—1221no—
207C2×C4⋊C4—1221no—
208C2×C4⋊C4—1221no—
209C2×C4⋊C4—1221no—
210C2×C4⋊C4C22⋊D6111yescharacteristic
211C2×C4⋊C4C22×D6111yescharacteristic
212C2×C22⋊C4—1221no—
213C2×C22⋊C4—1221no—
214C2×C22⋊C4C4×D6111yescharacteristic
215C2×C22⋊C4D24411yescharacteristic
216C2×C42—1221no—
217C2×C42—1221no—
218C2×C42C4×D6111yescharacteristic
219C2×C42D24411yescharacteristic
220C4⋊C8—2441no—
221C22⋊C8—1222no—
222C4×C8—2441no—
223#95—611no—
224#95—611no—
225#95—1221no—
226#95—1221no—
227#95—1221no—
228#95—1221no—
229C24#1175819811yescharacteristic
230C2×Q8—2441no—
231C2×Q8—2442no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—22no—
235C22×C4—1221no—
236C22×C4—1221no—
237C22×C4—1221no—
238C22×C4—1221no—
239C22×C4#1175819811yescharacteristic
240C22×C4#1175819811yescharacteristic
241C22×C4#1175819811yescharacteristic
242C22×C4#1175820012yes—
243C22×C4#1175820212yes—
244C22×C4C2×C4×D6111yescharacteristic
245C22×C4C2×D24411yescharacteristic
246C22×C4C2×C22⋊D6111yescharacteristic
247M16—24no—
248M16—44no—
249M16—42no—
250C2×C8—42no—
251C2×C8—44no—
252C2×C8—2442no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—2441no—
256C4⋊C4—2442no—
257C4⋊C4—2442no—
258C4⋊C4—2442no—
259C4⋊C4—2442no—
260C22⋊C4—41no—
261C22⋊C4—41no—
262C22⋊C4—2442no—
263C22⋊C4—2442no—
264C42—21no—
265C42—21no—
266C42—21no—
267C42—21no—
268C42—2441no—
269C42—2441no—
270C42—2442no—
271C23—21no—
272C23—21no—
273C23—41no—
274C23—41no—
275C23#1451970012yes—
276C23C2×#1175819811yescharacteristic
277Q8—2442no—
278Q8—2442no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—1222no—
294C2×C4—1222no—
295C2×C4—2441no—
296C2×C4—2441no—
297C2×C4—2441no—
298C2×C4—2441no—
299C2×C4—2441no—
300C2×C4—2441no—
301C2×C4—2441no—
302C2×C4—2441no—
303C2×C4—2441no—
304C2×C4—2441no—
305C2×C4#1451969111yescharacteristic
306C2×C4#1451969111yescharacteristic
307C2×C4#1451970012yes—
308C2×C4#1451970512yes—
309C2×C4C2×#1175820011yescharacteristic
310C2×C4C2×#1175820211yescharacteristic
311C8—44no—
312C8—4882no—
313C22—21no—
314C22—21no—
315C22—22no—
316C22—42no—
317C22—41no—
318C22—41no—
319C22—81no—
320C22C2×#1451969111yescharacteristic
321C22C2×#1451970011yescharacteristic
322C22C2×#1451970511yescharacteristic
323C4—21no—
324C4—21no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—4881no—
330C4—4881no—
331C4—2442no—
332C4—2442no—
333C4#1683949812yes—
334C4#1683949812yes—
335C2—21no—
336C2—21no—
337C2—42no—
338C2C2×#1683949811yescharacteristic
339C2#2144746111yescharacteristic
340C2#2144750211yescharacteristic
subgroupG/H
centerC2×C4#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1742C2
socleC22×C61C2×#99
prime radicalC24×C61C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1742D61
hypocenterC61#11721
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#117 ◁ #1742

Complements

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

NH ≅ G/Ntype
3. #21443848C2semidirect
4. #21443845C2semidirect
193. C61#11721semidirect

Maximal subgroups

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

subgroupindex
#214490872
#214441332
#214438482
#214438452
C61×#17422
#1172161