Finite Group Databasebeta

← #29583003

Subgroups — #29583003

Order 15616.

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

normal subgroups only

This group has 856 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#21451789C211yesmaximal, characteristic, complemented
2#21445750C212yesmaximal
3#21443698C212yesmaximal, complemented
4#21443662C211yesmaximal, characteristic, complemented
5C61×#1438C211yesmaximal, characteristic
6C2×#14519698—22no—
7C2×#14519698—22no—
8C2×C22⋊#92418C2212yes—
9#16839704—22no—
10#16839696—22no—
11#16839635—22no—
12#16839622C2212yes—
13C23×D4×C61C2211yescharacteristic
14C22×C22⋊C4×C61—22no—
15C2×#95×C61C2211yescharacteristic
16C2×#95×C61C2211yescharacteristic
17C22×#92418—22no—
18C2×C4⋊Dic61D412yes—
19C2×C4⋊Dic61D412yes—
20C2×#11758196—22no—
21C2×#11758196—22no—
22C2×C22⋊Dic61—22no—
23#14519698—44no—
24#14519698—44no—
25C22⋊#92418—22no—
26C22⋊#92418—22no—
27#14519684—22no—
28#14519684—22no—
29#14519684—22no—
30C25×C61—21no—
31C22×D4×C61—22no—
32C22×D4×C61—22no—
33C22×D4×C61—21no—
34C22×D4×C61—44no—
35C22×D4×C61Q812yes—
36C23×C4×C61—21no—
37C23×C4×C61D412yes—
38C23×C4×C61C2311yescharacteristic
39C2×C22⋊C4×C61—44no—
40C2×C22⋊C4×C61—44no—
41C2×C22⋊C4×C61—44no—
42#95×C61—22no—
43#95×C61—22no—
44C24×C61—24no—
45C24×C61—22no—
46C24×C61—42no—
47C24×C61—42no—
48C24×C61—42no—
49C24×C61—41no—
50C24×C61—41no—
51C24×C61—42no—
52C24×C61—42no—
53C24×C61C2×D411yescharacteristic
54C2×D4×C61—24no—
55C2×D4×C61—24no—
56C2×D4×C61—24no—
57C2×D4×C61—42no—
58C2×D4×C61—42no—
59C2×D4×C61—44no—
60C2×D4×C61—48no—
61C2×D4×C61—44no—
62C2×D4×C61—42no—
63C22×C4×C61—22no—
64C22×C4×C61—22no—
65C22×C4×C61—22no—
66C22×C4×C61—22no—
67C22×C4×C61—42no—
68C22×C4×C61—42no—
69C22×C4×C61—42no—
70C22×C4×C61—42no—
71C22×C4×C61—41no—
72C22×C4×C61—41no—
73C22×C4×C61—42no—
74C22×C4×C61C2×D412yes—
75C22×C4×C61C2×Q811yescharacteristic
76C22×C4×C61#4112yes—
77C22×C4×C61#4111yescharacteristic
78C22×Dic61—22no—
79C22×Dic61—22no—
80C22⋊C4×C61—416no—
81C22⋊Dic61—42no—
82C22⋊Dic61—42no—
83C4⋊Dic61—42no—
84C4⋊Dic61—42no—
85#11758196—82no—
86#11758196—82no—
87C2×#92418—42no—
88C2×#92418—42no—
89C2×#92418—42no—
90C23×C61—21no—
91C23×C61—21no—
92C23×C61—22no—
93C23×C61—24no—
94C23×C61—44no—
95C23×C61—44no—
96C23×C61—42no—
97C23×C61—44no—
98C23×C61—44no—
99C23×C61—44no—
100C23×C61—44no—
101C23×C61—42no—
102C23×C61—44no—
103C23×C61—44no—
104C23×C61—82no—
105C23×C61—82no—
106C23×C61—82no—
107C23×C61—82no—
108C23×C61—82no—
109C23×C61—82no—
110C23×C61—81no—
111C23×C61—81no—
112C23×C61—81no—
113C23×C61—81no—
114C23×C61#12011yescharacteristic
115C23×C61C22⋊Q811yescharacteristic
116C23×C61#12411yescharacteristic
117C23×C61#13512yes—
118C23×C61AGL(1,ℤ/8)12yes—
119D4×C61—28no—
120D4×C61—44no—
121D4×C61—44no—
122D4×C61—44no—
123C2×C4×C61—22no—
124C2×C4×C61—22no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—42no—
128C2×C4×C61—44no—
129C2×C4×C61—44no—
130C2×C4×C61—42no—
131C2×C4×C61—42no—
132C2×C4×C61—42no—
133C2×C4×C61—42no—
134C2×C4×C61—82no—
135C2×C4×C61—81no—
136C2×C4×C61—81no—
137C2×C4×C61—82no—
138C2×C4×C61C22⋊Q812yes—
139C2×C4×C61#12412yes—
140C2×Dic61—42no—
141C2×Dic61—42no—
142C2×Dic61—42no—
143C2×Dic61—42no—
144C2×Dic61—42no—
145C2×Dic61—42no—
146#92418—82no—
147#10344—611nomaximal, Sylow
148C22×C61—22no—
149C22×C61—22no—
150C22×C61—22no—
151C22×C61—22no—
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—48no—
157C22×C61—44no—
158C22×C61—84no—
159C22×C61—84no—
160C22×C61—84no—
161C22×C61—84no—
162C22×C61—84no—
163C22×C61—82no—
164C22×C61—82no—
165C22×C61#39311yescharacteristic
166C22×C61#44912yes—
167C22×C61#45311yescharacteristic
168C22×C61#45411yescharacteristic
169C22×C61B(4,𝔽2)12yes—
170C22×C61#47812yes—
171C22×C61#48811yescharacteristic
172C22×C61#49011yescharacteristic
173C4×C61—22no—
174C4×C61—22no—
175C4×C61—82no—
176C4×C61—82no—
177Dic61—82no—
178Dic61—82no—
179#2646—611no—
180#1786—612no—
181#1438D6111yescharacteristic
182#1294—612no—
183#1280—611no—
184C2×C61—21no—
185C2×C61—22no—
186C2×C61—21no—
187C2×C61—84no—
188C2×C61#159712yes—
189C2×C61#160012yes—
190C2×C61#202511yescharacteristic
191C2×C61#202711yescharacteristic
192C2×C61#202911yescharacteristic
193C23×D4C2×D6111yescharacteristic
194C22×C22⋊C4—22no—
195C2×#102—1222no—
196C2×#102—1222no—
197C2×C22⋊C8—612no—
198#400—1222no—
199#398—1222no—
200#385—1222no—
201#380—612no—
202C2×#95C2×D6111yescharacteristic
203C2×#95C2×D6111yescharacteristic
204C61#1034411yescharacteristic, complemented, Sylow
205C25—21no—
206C22×D4—21no—
207C22×D4—22no—
208C22×D4—22no—
209C22×D4—44no—
210C22×D4Dic12212yes—
211C23×C4—21no—
212C23×C4C22⋊D6112yes—
213C23×C4C22×D6111yescharacteristic
214C22×C8—1222no—
215C2×C4⋊C4—612no—
216C2×C4⋊C4—612no—
217C2×C4⋊C4—1222no—
218C2×C4⋊C4—1222no—
219C2×C22⋊C4—44no—
220C2×C22⋊C4—44no—
221C2×C22⋊C4—44no—
222C2×C22⋊C4—1222no—
223#102—2444no—
224#102—2444no—
225C22⋊C8—1222no—
226C22⋊C8—1222no—
227#95—22no—
228#95—22no—
229#95—1222no—
230#95—1222no—
231#95—1222no—
232C24—24no—
233C24—22no—
234C24—42no—
235C24—42no—
236C24—42no—
237C24—41no—
238C24—41no—
239C24—42no—
240C24—42no—
241C24C2×C22⋊D6111yescharacteristic
242C2×D4—24no—
243C2×D4—24no—
244C2×D4—24no—
245C2×D4—42no—
246C2×D4—42no—
247C2×D4—44no—
248C2×D4—48no—
249C2×D4—44no—
250C2×D4—42no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—42no—
256C22×C4—42no—
257C22×C4—42no—
258C22×C4—42no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—42no—
262C22×C4—1222no—
263C22×C4—1222no—
264C22×C4C2×Dic12211yescharacteristic
265C22×C4#1175822211yescharacteristic
266C22×C4D4×D6112yes—
267C22×C4#1175822412yes—
268C2×C8—2442no—
269C2×C8—2442no—
270C2×C8—2442no—
271C4⋊C4—4882no—
272C4⋊C4—4882no—
273C4⋊C4—2442no—
274C4⋊C4—2442no—
275C22⋊C4—416no—
276C22⋊C4—2442no—
277C22⋊C4—2442no—
278C23—22no—
279C23—21no—
280C23—21no—
281C23—24no—
282C23—44no—
283C23—44no—
284C23—42no—
285C23—44no—
286C23—44no—
287C23—44no—
288C23—44no—
289C23—44no—
290C23—44no—
291C23—42no—
292C23—82no—
293C23—82no—
294C23—82no—
295C23—82no—
296C23—82no—
297C23—81no—
298C23—81no—
299C23—82no—
300C23—81no—
301C23—81no—
302C23#1451974511yescharacteristic
303C23#1451975611yescharacteristic
304C23#1451976411yescharacteristic
305C23#1451979712yes—
306C23#1451980312yes—
307D4—28no—
308D4—44no—
309D4—44no—
310D4—44no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—42no—
316C2×C4—44no—
317C2×C4—44no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—81no—
323C2×C4—82no—
324C2×C4—81no—
325C2×C4—82no—
326C2×C4—2442no—
327C2×C4—2442no—
328C2×C4—2442no—
329C2×C4—2442no—
330C2×C4—2442no—
331C2×C4—2442no—
332C2×C4#1451975412yes—
333C2×C4#1451976312yes—
334C8—4882no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—22no—
340C22—22no—
341C22—22no—
342C22—22no—
343C22—48no—
344C22—44no—
345C22—84no—
346C22—84no—
347C22—84no—
348C22—82no—
349C22—82no—
350C22—84no—
351C22—84no—
352C22#1683967411yescharacteristic
353C22#1683990512yes—
354C22#1683992911yescharacteristic
355C22#1683993411yescharacteristic
356C22#1683994812yes—
357C22#1684006212yes—
358C22#1684011611yescharacteristic
359C22#1684012611yescharacteristic
360C4—22no—
361C4—22no—
362C4—82no—
363C4—82no—
364C4—4882no—
365C4—4882no—
366C2—21no—
367C2—22no—
368C2—21no—
369C2—84no—
370C2#2144474612yes—
371C2#2144476312yes—
372C2#2144696511yescharacteristic
373C2#2144697511yescharacteristic
374C2#2144698311yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#1438C2
socleC23×C61#120
prime radicalC23×D4×C61C22
hypercenter#1438D61
hypocenterC61#10344
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1438

Complements

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

NH ≅ G/Ntype
1. #21451789C2semidirect
3. #21443698C2semidirect
4. #21443662C2semidirect
204. C61#10344semidirect

Maximal subgroups

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

subgroupindex
#214517892
#214457502
#214436982
#214436622
C61×#14382
#1034461