Finite Group Databasebeta

← #29568843

Subgroups — #29568843

Order 15616.

468 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 87 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#21452850C211yesmaximal, characteristic
2#21447148C211yesmaximal, characteristic
3#21447147C211yesmaximal, characteristic
4#21446921C211yesmaximal, characteristic
5#21443644C211yesmaximal, characteristic
6#21443643C211yesmaximal, characteristic
7C61×#1271C211yesmaximal, characteristic
8C22×Dic244—21no—
9C2×#14519777C2211yescharacteristic
10C2×#14519776—21no—
11C2×#14519711—21no—
12C2×#14519710—21no—
13C2×#14519702—21no—
14#16839695—21no—
15#16839683—21no—
16#16839682—21no—
17#16839668C2211yescharacteristic
18#16839660C2211yescharacteristic
19#16839648—21no—
20#16839645—21no—
21#16839525—21no—
22#16839524—21no—
23#16839517C2211yescharacteristic
24C61×#389C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×Dic122—21no—
28C22×Dic122—21no—
29C22×Dic122D411yescharacteristic
30C2×Dic244—42no—
31C2×Dic244—42no—
32C2×Dic244—42no—
33C22×#92418—21no—
34#14519777—42no—
35#14519776—42no—
36#14519776—42no—
37C2×C4⋊Dic61—21no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61D411yescharacteristic
41C2×C4⋊Dic61D411yescharacteristic
42C2×C4⋊Dic61D411yescharacteristic
43C2×#11758196—21no—
44C2×#11758196—21no—
45C2×#11758196—21no—
46C2×C4×Dic61—21no—
47#14519711—42no—
48#14519710—42no—
49#14519702—42no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56C22×C8×C61—21no—
57C22×C8×C61—21no—
58C2×C4⋊C4×C61—21no—
59C2×C4⋊C4×C61D411yescharacteristic
60C2×C4⋊C4×C61D411yescharacteristic
61C2×C42×C61C2311yescharacteristic
62#95×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61C2×D411yescharacteristic
66C22×C4×C61C2×D411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61—41no—
73C2×Dic122—22no—
74C2×Dic122—21no—
75C2×Dic122—41no—
76C2×Dic122—41no—
77C2×Dic122—41no—
78C2×Dic122—41no—
79C2×Dic122—41no—
80C2×Dic122—41no—
81C2×Dic122—42no—
82C2×Dic122—41no—
83C2×Dic122—81no—
84C2×Dic122—81no—
85C2×Dic122D812yes—
86C2×C8×C61—22no—
87C2×C8×C61—22no—
88C2×C8×C61—41no—
89C2×C8×C61—41no—
90C2×C8×C61—41no—
91C2×C8×C61—41no—
92C4⋊C4×C61—21no—
93C4⋊C4×C61—41no—
94C4⋊C4×C61—41no—
95C4⋊C4×C61—41no—
96C4⋊C4×C61Q1612yescomplemented
97C42×C61—41no—
98C4⋊Dic61—21no—
99C4⋊Dic61—22no—
100C4⋊Dic61—22no—
101C4⋊Dic61—42no—
102C4⋊Dic61—41no—
103C4⋊Dic61—41no—
104C4⋊Dic61—41no—
105C4⋊Dic61—41no—
106C4⋊Dic61Q1612yescomplemented
107#11758196—42no—
108#11758196—41no—
109#11758196—41no—
110#11758196—81no—
111C4×Dic61—42no—
112C2×#92418—22no—
113C2×#92418—41no—
114C2×#92418—41no—
115Dic244—48no—
116C23×C61#12011yescharacteristic
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—22no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61C2×D811yescharacteristic
130C2×C4×C61C2×Q1611yescharacteristic
131C2×C4×C61C2×Q1611yescharacteristic
132C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C61#13711yescharacteristic
134C2×C4×C61#13711yescharacteristic
135C2×Dic61—22no—
136C2×Dic61—22no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—42no—
147C2×Dic61—41no—
148C2×Dic61—81no—
149C2×Dic61—81no—
150Dic122—42no—
151Dic122—42no—
152Dic122—42no—
153Dic122—81no—
154Dic122—84no—
155Dic122—81no—
156Dic122—81no—
157C8×C61—42no—
158C8×C61—42no—
159#92418—42no—
160#7757—611nomaximal, Sylow
161C22×C61#44711yescharacteristic
162C22×C61#45111yescharacteristic
163C22×C61#45111yescharacteristic
164C22×C61#45311yescharacteristic
165C22×C61#45611yescharacteristic
166C22×C61#45611yescharacteristic
167C22×C61B(4,𝔽2)11yescharacteristic
168C4×C61—21no—
169C4×C61—21no—
170C4×C61—21no—
171C4×C61—21no—
172C4×C61—21no—
173C4×C61—21no—
174C4×C61—42no—
175C4×C61—81no—
176Dic61—42no—
177Dic61—42no—
178Dic61—82no—
179Dic61—81no—
180Dic61—81no—
181#2734—611no—
182#2057—611no—
183#2057—611no—
184#2016—611no—
185#1272—611no—
186#1271—611no—
187#1271D6111yescharacteristic
188C2×C61#159511yescharacteristic
189C2×C61#160511yescharacteristic
190C2×C61#160511yescharacteristic
191C2×C61#163311yescharacteristic
192C2×C61#164911yescharacteristic
193C2×C61#164911yescharacteristic
194C2×C61#166011yescharacteristic
195C22×Q16—1221no—
196C2×C4⋊Q8—611no—
197C2×C4⋊Q8—1221no—
198C2×#107—1221no—
199C2×#107—1221no—
200C2×#103—1221no—
201#398—1221no—
202#395—1221no—
203#395—1221no—
204#391—611no—
205#389—611no—
206#389C2×D6111yescharacteristic
207#387—1221no—
208#387—1221no—
209#340—1221no—
210#340—1221no—
211#336—611no—
212#336C2×D6111yescharacteristic
213#336C2×D6111yescharacteristic
214C61#775711yescharacteristic, complemented, Sylow
215C22×Q8—611no—
216C22×Q8—1221no—
217C22×Q8—1221no—
218C2×Q16—2442no—
219C2×Q16—2442no—
220C2×Q16—2442no—
221C22×C8—21no—
222C22×C8—21no—
223C22×C8—1221no—
224C4⋊Q8—2442no—
225C4⋊Q8—2442no—
226C4⋊Q8—2442no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—611no—
229C2×C4⋊C4—611no—
230C2×C4⋊C4—611no—
231C2×C4⋊C4—1221no—
232C2×C4⋊C4—1221no—
233C2×C4⋊C4—1221no—
234C2×C4⋊C4—1221no—
235C2×C4⋊C4—1221no—
236C2×C4⋊C4—1221no—
237C2×C4⋊C4D24411yescharacteristic
238C2×C4⋊C4D24411yescharacteristic
239C2×C42—1221no—
240C2×C42C22×D6111yescharacteristic
241#107—2442no—
242#107—2442no—
243#103—2442no—
244#95—21no—
245#95—1221no—
246#95—1221no—
247#95—1221no—
248#95—1221no—
249#95—1221no—
250#95—1221no—
251C2×Q8—612no—
252C2×Q8—1222no—
253C2×Q8—1221no—
254C2×Q8—4881no—
255C2×Q8—4881no—
256C2×Q8—2441no—
257C2×Q8—2441no—
258C2×Q8—2441no—
259C2×Q8—2441no—
260C2×Q8—2441no—
261C2×Q8—2442no—
262C2×Q8—2441no—
263C2×Q8—2441no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—1221no—
267C22×C4—1221no—
268C22×C4—1221no—
269C22×C4—1221no—
270C22×C4—2441no—
271C22×C4C2×D24411yescharacteristic
272C22×C4D4×D6111yescharacteristic
273C22×C4D4×D6111yescharacteristic
274Q16—2448no—
275C2×C8—22no—
276C2×C8—22no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—1222no—
282C2×C8—2441no—
283C2×C8—2441no—
284C4⋊C4—21no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—612no—
289C4⋊C4—1222no—
290C4⋊C4—1222no—
291C4⋊C4—1221no—
292C4⋊C4—4881no—
293C4⋊C4—2441no—
294C4⋊C4—2441no—
295C4⋊C4—2441no—
296C4⋊C4—2441no—
297C4⋊C4—2442no—
298C4⋊C4—2442no—
299C4⋊C4—2441no—
300C4⋊C4—2441no—
301C4⋊C4Dic24412yescomplemented
302C42—41no—
303C42—2442no—
304C23#1451974711yescharacteristic
305Q8—4881no—
306Q8—4881no—
307Q8—4881no—
308Q8—4884no—
309Q8—2442no—
310Q8—2442no—
311Q8—2442no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—22no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—1222no—
325C2×C4—1222no—
326C2×C4—4881no—
327C2×C4—4881no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4—2442no—
331C2×C4—2441no—
332C2×C4—2441no—
333C2×C4—2441no—
334C2×C4—2441no—
335C2×C4—2441no—
336C2×C4—2441no—
337C2×C4—2441no—
338C2×C4—2441no—
339C2×C4D8×D6111yescharacteristic
340C2×C4Q16×D6111yescharacteristic
341C2×C4C2×Dic24411yescharacteristic
342C2×C4#1451980411yescharacteristic
343C2×C4#1451980611yescharacteristic
344C2×C4#1451981011yescharacteristic
345C8—42no—
346C8—42no—
347C8—2442no—
348C22#1683989711yescharacteristic
349C22#1683991911yescharacteristic
350C22#1683992011yescharacteristic
351C22#1683993111yescharacteristic
352C22#1683994611yescharacteristic
353C22#1683994711yescharacteristic
354C22#1683995011yescharacteristic
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—21no—
361C4—42no—
362C4—81no—
363C4—4881no—
364C4—4882no—
365C4—4881no—
366C4—2442no—
367C4—2442no—
368C2#2144473811yescharacteristic
369C2#2144479411yescharacteristic
370C2#2144479511yescharacteristic
371C2#2144496111yescharacteristic
372C2#2144506911yescharacteristic
373C2#2144507111yescharacteristic
374C2#2144513211yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1271C2
socle, prime radicalC23×C61#120
hypercenter#1271D61
hypocenterC61#7757
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
96. C4⋊C4×C61Q16semidirect
106. C4⋊Dic61Q16semidirect
214. C61#7757semidirect
301. C4⋊C4Dic244semidirect

Maximal subgroups

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

subgroupindex
#214528502
#214471482
#214471472
#214469212
#214436442
#214436432
C61×#12712
#775761