Finite Group Databasebeta

← #29569019

Subgroups — #29569019

Order 15616.

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

normal subgroups only

This group has 424 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#21453772C211yesmaximal, characteristic
2#21447152C211yesmaximal, characteristic
3#21447148C211yesmaximal, characteristic
4#21446921C211yesmaximal, characteristic
5#21443644C211yesmaximal, characteristic
6#21443643C211yesmaximal, characteristic
7C61×#1271C211yesmaximal, characteristic
8C22×Dic244—21no—
9C2×#14519777C2211yescharacteristic
10C2×#14519711—21no—
11C2×#14519708—21no—
12C2×#14519702—21no—
13#16839701—21no—
14#16839701—21no—
15#16839683—21no—
16#16839668C2211yescharacteristic
17#16839661—21no—
18#16839660C2211yescharacteristic
19#16839649—21no—
20#16839648—21no—
21#16839525—21no—
22#16839524—21no—
23#16839517C2211yescharacteristic
24C61×#389C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×Dic122—21no—
28C22×Dic122D411yescharacteristic
29C2×Dic244—42no—
30C2×Dic244—42no—
31C2×Dic244—42no—
32C22×#92418—21no—
33#14519777—42no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61—21no—
38C2×C4⋊Dic61D411yescharacteristic
39C2×C4⋊Dic61D411yescharacteristic
40C2×C4⋊Dic61D411yescharacteristic
41C2×#11758196—21no—
42C2×C4×Dic61—21no—
43#14519711—42no—
44#14519708—42no—
45#14519702—42no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54C22×C8×C61—21no—
55C22×C8×C61—21no—
56C2×C4⋊C4×C61—21no—
57C2×C4⋊C4×C61D411yescharacteristic
58C2×C4⋊C4×C61D411yescharacteristic
59C2×C42×C61C2311yescharacteristic
60#95×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61C2×D411yescharacteristic
64C22×C4×C61C2×D411yescharacteristic
65C22×C4×C61C2×D411yescharacteristic
66C22×Dic61—21no—
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61—41no—
71C2×Dic122—22no—
72C2×Dic122—21no—
73C2×Dic122—21no—
74C2×Dic122—41no—
75C2×Dic122—41no—
76C2×Dic122—41no—
77C2×Dic122—41no—
78C2×Dic122—41no—
79C2×Dic122—41no—
80C2×Dic122—41no—
81C2×C8×C61—22no—
82C2×C8×C61—22no—
83C2×C8×C61—41no—
84C2×C8×C61—41no—
85C2×C8×C61—41no—
86C2×C8×C61—41no—
87C4⋊C4×C61—21no—
88C4⋊C4×C61—41no—
89C4⋊C4×C61—41no—
90C4⋊C4×C61—41no—
91C4⋊C4×C61Q1612yescomplemented
92C42×C61—41no—
93C4⋊Dic61—22no—
94C4⋊Dic61—22no—
95C4⋊Dic61—21no—
96C4⋊Dic61—21no—
97C4⋊Dic61—41no—
98C4⋊Dic61—41no—
99C4⋊Dic61—41no—
100C4⋊Dic61—41no—
101C4⋊Dic61—81no—
102C4⋊Dic61—81no—
103#11758196—41no—
104#11758196—41no—
105C4×Dic61—81no—
106C2×#92418—22no—
107C2×#92418—41no—
108C2×#92418—41no—
109Dic244—48no—
110C23×C61#12011yescharacteristic
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—22no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61C2×Q1611yescharacteristic
124C2×C4×C61#13511yescharacteristic
125C2×C4×C61#13511yescharacteristic
126C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
127C2×C4×C61#13711yescharacteristic
128C2×C4×C61#13711yescharacteristic
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—
138C2×Dic61—41no—
139C2×Dic61—42no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—81no—
143C2×Dic61—81no—
144Dic122—42no—
145Dic122—42no—
146Dic122—42no—
147Dic122—81no—
148Dic122—81no—
149Dic122—81no—
150C8×C61—42no—
151C8×C61—42no—
152#92418—42no—
153#7783—611nomaximal, Sylow
154C22×C61#44911yescharacteristic
155C22×C61#45111yescharacteristic
156C22×C61#45211yescharacteristic
157C22×C61#45311yescharacteristic
158C22×C61#45611yescharacteristic
159C22×C61#45611yescharacteristic
160C22×C61B(4,𝔽2)11yescharacteristic
161C4×C61—21no—
162C4×C61—21no—
163C4×C61—21no—
164C4×C61—21no—
165C4×C61—21no—
166C4×C61—21no—
167C4×C61—42no—
168C4×C61—81no—
169Dic61—82no—
170Dic61—81no—
171Dic61—81no—
172Dic61—81no—
173Dic61—81no—
174#2805—611no—
175#2058—611no—
176#2057—611no—
177#2016—611no—
178#1272—611no—
179#1271—611no—
180#1271D6111yescharacteristic
181C2×C61#160011yescharacteristic
182C2×C61#160311yescharacteristic
183C2×C61#160511yescharacteristic
184C2×C61#163211yescharacteristic
185C2×C61#164811yescharacteristic
186C2×C61#165211yescharacteristic
187C2×C61#166011yescharacteristic
188C22×Q16—1221no—
189C2×C4⋊Q8—611no—
190C2×#107—1221no—
191C2×#106—1221no—
192C2×#103—1221no—
193#400—1221no—
194#400—1221no—
195#395—1221no—
196#391—611no—
197#389—611no—
198#389—1221no—
199#389C2×D6111yescharacteristic
200#387—1221no—
201#387—1221no—
202#340—1221no—
203#340—1221no—
204#336—611no—
205#336C2×D6111yescharacteristic
206#336C2×D6111yescharacteristic
207C61#778311yescharacteristic, complemented, Sylow
208C22×Q8—611no—
209C22×Q8—1221no—
210C2×Q16—2442no—
211C2×Q16—2442no—
212C2×Q16—2442no—
213C22×C8—21no—
214C22×C8—21no—
215C22×C8—1221no—
216C4⋊Q8—2442no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—611no—
219C2×C4⋊C4—611no—
220C2×C4⋊C4—611no—
221C2×C4⋊C4—1221no—
222C2×C4⋊C4—1221no—
223C2×C4⋊C4—1221no—
224C2×C4⋊C4—1221no—
225C2×C4⋊C4—1221no—
226C2×C4⋊C4D24411yescharacteristic
227C2×C4⋊C4D24411yescharacteristic
228C2×C42—1221no—
229C2×C42C22×D6111yescharacteristic
230#107—2442no—
231#106—2442no—
232#103—2442no—
233#95—21no—
234#95—1221no—
235#95—1221no—
236#95—1221no—
237#95—1221no—
238#95—1221no—
239#95—1221no—
240#95—1221no—
241#95—1221no—
242C2×Q8—1222no—
243C2×Q8—1221no—
244C2×Q8—1221no—
245C2×Q8—2441no—
246C2×Q8—2441no—
247C2×Q8—2441no—
248C2×Q8—2441no—
249C2×Q8—2441no—
250C2×Q8—2441no—
251C2×Q8—2441no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4—1221no—
258C22×C4—2441no—
259C22×C4C2×D24411yescharacteristic
260C22×C4D4×D6111yescharacteristic
261C22×C4D4×D6111yescharacteristic
262Q16—2448no—
263C2×C8—22no—
264C2×C8—22no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8—1222no—
270C2×C8—2441no—
271C2×C8—2441no—
272C4⋊C4—21no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—1222no—
277C4⋊C4—1222no—
278C4⋊C4—1221no—
279C4⋊C4—1221no—
280C4⋊C4—4881no—
281C4⋊C4—4881no—
282C4⋊C4—2441no—
283C4⋊C4—2441no—
284C4⋊C4—2441no—
285C4⋊C4—2441no—
286C4⋊C4—2441no—
287C4⋊C4—2441no—
288C4⋊C4Dic24412yescomplemented
289C42—41no—
290C42—4881no—
291C23#1451974711yescharacteristic
292Q8—4881no—
293Q8—4881no—
294Q8—4881no—
295Q8—2442no—
296Q8—2442no—
297Q8—2442no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—22no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—4881no—
311C2×C4—4881no—
312C2×C4—2441no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4—2442no—
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—2441no—
325C2×C4C2×Dic24411yescharacteristic
326C2×C4#1451979611yescharacteristic
327C2×C4#1451980011yescharacteristic
328C2×C4#1451980411yescharacteristic
329C2×C4#1451980611yescharacteristic
330C2×C4#1451981011yescharacteristic
331C8—42no—
332C8—42no—
333C8—2442no—
334C22#1683991011yescharacteristic
335C22#1683992011yescharacteristic
336C22#1683992511yescharacteristic
337C22#1683993111yescharacteristic
338C22#1683994611yescharacteristic
339C22#1683994711yescharacteristic
340C22#1683995011yescharacteristic
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—42no—
348C4—81no—
349C4—4881no—
350C4—4882no—
351C4—4881no—
352C4—4881no—
353C4—4881no—
354C2#2144476811yescharacteristic
355C2#2144478311yescharacteristic
356C2#2144479511yescharacteristic
357C2#2144495511yescharacteristic
358C2#2144506411yescharacteristic
359C2#2144509011yescharacteristic
360C2#2144513211yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1271C2
socle, prime radicalC23×C61#120
hypercenter#1271D61
hypocenterC61#7783
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
91. C4⋊C4×C61Q16semidirect
207. C61#7783semidirect
288. C4⋊C4Dic244semidirect

Maximal subgroups

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

subgroupindex
#214537722
#214471522
#214471482
#214469212
#214436442
#214436432
C61×#12712
#778361