Finite Group Databasebeta

← #29583366

Subgroups — #29583366

Order 15616.

576 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 115 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#21451933C211yesmaximal, characteristic
2#21446126C212yesmaximal
3C2×#16839498C212yesmaximal
4#21443662C211yesmaximal, characteristic
5C61×#1442C211yesmaximal, characteristic
6C2×#14519756C2212yes—
7C2×#14519700—22no—
8C2×C22⋊#92418C2212yes—
9#16839694—22no—
10#16839683—22no—
11#16839622—21no—
12#16839622—21no—
13#16839524—22no—
14#16839498—24no—
15C22×C4⋊C4×C61C2211yescharacteristic
16C2×#95×C61—21no—
17C2×#95×C61—21no—
18C2×#95×C61C2211yescharacteristic
19C2×#95×C61C2211yescharacteristic
20C22×Dic122D412yes—
21C22×#92418—22no—
22#14519756—22no—
23#14519756—22no—
24#14519756—22no—
25#14519756—22no—
26C2×C4⋊Dic61—21no—
27C2×C4⋊Dic61—21no—
28C2×C4⋊Dic61—21no—
29C2×C4⋊Dic61—21no—
30C2×C4⋊Dic61D412yes—
31C2×#11758196—22no—
32C2×C22⋊Dic61—22no—
33#14519700—44no—
34C22⋊#92418—22no—
35C22⋊#92418—22no—
36#14519684—22no—
37#14519684—22no—
38C23×C4×C61—21no—
39C23×C4×C61—21no—
40C23×C4×C61D411yescharacteristic
41C23×C4×C61D411yescharacteristic
42C23×C4×C61C2311yescharacteristic
43C2×C4⋊C4×C61—22no—
44C2×C4⋊C4×C61—42no—
45#95×C61—22no—
46#95×C61—21no—
47#95×C61—42no—
48#95×C61—42no—
49#95×C61D412yes—
50C24×C61C2×D411yescharacteristic
51C22×C4×C61—21no—
52C22×C4×C61—21no—
53C22×C4×C61—21no—
54C22×C4×C61—21no—
55C22×C4×C61—22no—
56C22×C4×C61—22no—
57C22×C4×C61—41no—
58C22×C4×C61—41no—
59C22×C4×C61—41no—
60C22×C4×C61—41no—
61C22×C4×C61—41no—
62C22×C4×C61—41no—
63C22×C4×C61—41no—
64C22×C4×C61—41no—
65C22×C4×C61—41no—
66C22×C4×C61—41no—
67C22×C4×C61—41no—
68C22×C4×C61—41no—
69C22×C4×C61—41no—
70C22×C4×C61—41no—
71C22×C4×C61—41no—
72C22×C4×C61—41no—
73C22×C4×C61—41no—
74C22×C4×C61—41no—
75C22×C4×C61SD1612yes—
76C22×C4×C61Q1612yes—
77C22×C4×C61C2×D412yes—
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61#4112yes—
80C22×C4×C61#4111yescharacteristic
81C22×Dic61—22no—
82C22×Dic61—22no—
83C2×Dic122—22no—
84C2×Dic122—22no—
85C2×Dic122—42no—
86C2×Dic122—42no—
87C4⋊C4×C61—24no—
88C4⋊C4×C61—42no—
89C22⋊Dic61—42no—
90C22⋊Dic61—42no—
91C4⋊Dic61—22no—
92C4⋊Dic61—22no—
93C4⋊Dic61—81no—
94C4⋊Dic61—81no—
95C4⋊Dic61—81no—
96C4⋊Dic61—81no—
97#11758196—42no—
98#11758196—42no—
99C2×#92418—42no—
100C2×#92418—42no—
101C2×#92418—42no—
102C23×C61—21no—
103C23×C61—21no—
104C23×C61—21no—
105C23×C61—21no—
106C23×C61#12011yescharacteristic
107C23×C61#12111yescharacteristic
108C23×C61#12411yescharacteristic
109C23×C61C2×SD1611yescharacteristic
110C23×C61C2×Q1611yescharacteristic
111C23×C61#13711yescharacteristic
112C23×C61#13711yescharacteristic
113C2×C4×C61—22no—
114C2×C4×C61—22no—
115C2×C4×C61—22no—
116C2×C4×C61—22no—
117C2×C4×C61—41no—
118C2×C4×C61—42no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—42no—
125C2×C4×C61—42no—
126C2×C4×C61—42no—
127C2×C4×C61—42no—
128C2×C4×C61—42no—
129C2×C4×C61—42no—
130C2×C4×C61—42no—
131C2×C4×C61—42no—
132C2×C4×C61—81no—
133C2×C4×C61—81no—
134C2×C4×C61—81no—
135C2×C4×C61—81no—
136C2×C4×C61—81no—
137C2×C4×C61—81no—
138C2×C4×C61—81no—
139C2×C4×C61—81no—
140C2×C4×C61—81no—
141C2×C4×C61—81no—
142C2×C4×C61#12112yes—
143C2×C4×C61#12312yes—
144C2×Dic61—42no—
145C2×Dic61—42no—
146C2×Dic61—42no—
147C2×Dic61—42no—
148C2×Dic61—42no—
149C2×Dic61—42no—
150Dic122—44no—
151Dic122—82no—
152#92418—82no—
153#10407—611nomaximal, Sylow
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—21no—
158C22×C61—21no—
159C22×C61—21no—
160C22×C61—21no—
161C22×C61—21no—
162C22×C61—21no—
163C22×C61—21no—
164C22×C61—21no—
165C22×C61—21no—
166C22×C61#39411yescharacteristic
167C22×C61#44811yescharacteristic
168C22×C61#45111yescharacteristic
169C22×C61#45411yescharacteristic
170C22×C61#45511yescharacteristic
171C22×C61B(4,𝔽2)11yescharacteristic
172C22×C61#45811yescharacteristic
173C22×C61#46111yescharacteristic
174C22×C61#46211yescharacteristic
175C22×C61#48711yescharacteristic
176C22×C61#49111yescharacteristic
177C4×C61—22no—
178C4×C61—22no—
179C4×C61—42no—
180C4×C61—42no—
181C4×C61—82no—
182C4×C61—82no—
183Dic61—82no—
184Dic61—82no—
185#2659—611no—
186#1872—612no—
187C2×#328—612no—
188#1442D6111yescharacteristic
189#1280—611no—
190C2×C61—21no—
191C2×C61—21no—
192C2×C61—21no—
193C2×C61—21no—
194C2×C61#159911yescharacteristic
195C2×C61#160211yescharacteristic
196C2×C61#160811yescharacteristic
197C2×C61#161711yescharacteristic
198C2×C61#204011yescharacteristic
199C2×C61#204311yescharacteristic
200C2×C61#204411yescharacteristic
201C2×C22⋊Q8—612no—
202C22×C4⋊C4C2×D6111yescharacteristic
203C2×#103—1222no—
204C2×C22⋊C8—612no—
205#398—1222no—
206#395—1222no—
207#380—1221no—
208#380—1221no—
209C2×#95—21no—
210C2×#95—21no—
211C2×#95C2×D6111yescharacteristic
212C2×#95C2×D6111yescharacteristic
213#340—1222no—
214#328—1224no—
215C61#1040711yescharacteristic, complemented, Sylow
216C22×Q8—612no—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4C22⋊D6111yescharacteristic
220C23×C4C22⋊D6111yescharacteristic
221C23×C4C22×D6111yescharacteristic
222C22×C8—1222no—
223C22⋊Q8—1222no—
224C22⋊Q8—1222no—
225C22⋊Q8—1222no—
226C22⋊Q8—1222no—
227C2×C4⋊C4—22no—
228C2×C4⋊C4—42no—
229C2×C4⋊C4—612no—
230C2×C4⋊C4—1221no—
231C2×C4⋊C4—1221no—
232C2×C4⋊C4—1221no—
233C2×C4⋊C4—1221no—
234C2×C4⋊C4—1222no—
235C2×C22⋊C4—1222no—
236#103—2444no—
237C22⋊C8—1222no—
238C22⋊C8—1222no—
239#95—21no—
240#95—22no—
241#95—42no—
242#95—42no—
243#95—1222no—
244#95—1222no—
245#95D24412yes—
246C24C2×C22⋊D6111yescharacteristic
247C2×Q8—1222no—
248C2×Q8—1222no—
249C2×Q8—2442no—
250C2×Q8—2442no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—1222no—
276C22×C4—1222no—
277C22×C4#1175820012yes—
278C22×C4#1175820212yes—
279C22×C4C2×D24411yescharacteristic
280C22×C4#1175822211yescharacteristic
281C22×C4D4×D6112yes—
282C22×C4#1175822612yes—
283C2×C8—2442no—
284C2×C8—2442no—
285C2×C8—2442no—
286C4⋊C4—24no—
287C4⋊C4—42no—
288C4⋊C4—1222no—
289C4⋊C4—1222no—
290C4⋊C4—4881no—
291C4⋊C4—4881no—
292C4⋊C4—4881no—
293C4⋊C4—4881no—
294C4⋊C4—2442no—
295C4⋊C4—2442no—
296C22⋊C4—2442no—
297C22⋊C4—2442no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23#1451974511yescharacteristic
303C23#1451975111yescharacteristic
304C23#1451976611yescharacteristic
305C23C2×#1175820011yescharacteristic
306C23C2×#1175820211yescharacteristic
307C23#1451980711yescharacteristic
308C23#1451980711yescharacteristic
309Q8—4882no—
310Q8—2444no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—2442no—
341C2×C4—2442no—
342C2×C4—2442no—
343C2×C4—2442no—
344C2×C4—2442no—
345C2×C4—2442no—
346C2×C4#1451975212yes—
347C2×C4#1451976212yes—
348C8—4882no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22#1683967911yescharacteristic
362C22#1683990011yescharacteristic
363C22#1683991711yescharacteristic
364C22#1683993411yescharacteristic
365C22#1683993911yescharacteristic
366C22#1683994811yescharacteristic
367C22#1683995111yescharacteristic
368C22#1683996711yescharacteristic
369C22#1683997211yescharacteristic
370C22#1684011411yescharacteristic
371C22#1684013211yescharacteristic
372C4—22no—
373C4—22no—
374C4—42no—
375C4—42no—
376C4—82no—
377C4—82no—
378C4—4882no—
379C4—4882no—
380C2—21no—
381C2—21no—
382C2—21no—
383C2—21no—
384C2#2144475811yescharacteristic
385C2#2144477511yescharacteristic
386C2#2144480911yescharacteristic
387C2#2144486011yescharacteristic
388C2#2144704811yescharacteristic
389C2#2144706511yescharacteristic
390C2#2144707011yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#1442C2
socleC23×C61#120
prime radicalC24×C61C2×D4
hypercenter#1442D61
hypocenterC61#10407
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1442

Complements

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

NH ≅ G/Ntype
215. C61#10407semidirect

Maximal subgroups

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

subgroupindex
#214519332
#214461262
C2×#168394982
#214436622
C61×#14422
#1040761