Finite Group Databasebeta

← #29575554

Subgroups — #29575554

Order 15616.

586 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454843C211yesmaximal, characteristic
2#21444137C211yesmaximal, characteristic
3C2×#16839488C212yesmaximal, complemented
4#21443667C212yesmaximal, complemented
5C61×#2322C211yesmaximal, characteristic
6D4×#92418—24no—
7#16839815—21no—
8C2×C22⋊#92418—21no—
9C2×C22⋊#92418C2212yes—
10C2×C22⋊#92418C2212yes—
11#16839488—24no—
12#16839488—21no—
13#16839486—21no—
14C2×#123×C61C411yescharacteristic
15C2×C4×D4×C61C2211yescharacteristic
16C22×C4⋊C4×C61C2211yescharacteristic
17C61×#389—21no—
18C61×#388—21no—
19C61×#387—21no—
20C61×#386C411yescharacteristic
21C61×#385—21no—
22C61×#385C411yescharacteristic
23C61×#381C411yescharacteristic
24C4×C22⋊C4×C61C2211yescharacteristic
25C22×#92418—22no—
26C22×#92418—22no—
27C22×#92418—22no—
28C4⋊#92418—22no—
29C22⋊#92418—22no—
30C22⋊#92418—22no—
31C22⋊#92418—22no—
32C22⋊#92418—22no—
33C22⋊#92418D414yes—
34C4×#92418—22no—
35C22×D4×C61C2×C411yescharacteristic
36C23×C4×C61C2×C411yescharacteristic
37C23×C4×C61C2×C411yescharacteristic
38C23×C4×C61D411yescharacteristic
39C23×C4×C61C2311yescharacteristic
40#123×C61—22no—
41#123×C61C814yescomplemented
42C4×D4×C61—22no—
43C4×D4×C61—22no—
44C2×C4⋊C4×C61—21no—
45C2×C4⋊C4×C61—22no—
46C2×C4⋊C4×C61—21no—
47C2×C4⋊C4×C61—21no—
48C2×C4⋊C4×C61—22no—
49C2×C4⋊C4×C61—21no—
50C2×C4⋊C4×C61D411yescharacteristic
51C2×C22⋊C4×C61—21no—
52C2×C22⋊C4×C61—21no—
53C2×C22⋊C4×C61C2×C411yescharacteristic
54C2×C22⋊C4×C61C2×C411yescharacteristic
55C2×C22⋊C4×C61C2×C411yescharacteristic
56C2×C22⋊C4×C61D411yescharacteristic
57C2×C42×C61—21no—
58C2×C42×C61D411yescharacteristic
59#95×C61—21no—
60#95×C61—21no—
61#95×C61—21no—
62#95×C61—21no—
63#95×C61—21no—
64C24×C61C22⋊C411yescharacteristic
65C24×C61C22×C411yescharacteristic
66C2×D4×C61—22no—
67C2×D4×C61—22no—
68C2×D4×C61C2×C812yes—
69C2×D4×C61M1612yes—
70C22×C4×C61—21no—
71C22×C4×C61—21no—
72C22×C4×C61—22no—
73C22×C4×C61—21no—
74C22×C4×C61—22no—
75C22×C4×C61—21no—
76C22×C4×C61—21no—
77C22×C4×C61—21no—
78C22×C4×C61—21no—
79C22×C4×C61—22no—
80C22×C4×C61—81no—
81C22×C4×C61—81no—
82C22×C4×C61—81no—
83C22×C4×C61C22⋊C411yescharacteristic
84C22×C4×C61C22⋊C411yescharacteristic
85C22×C4×C61C22⋊C411yescharacteristic
86C22×C4×C61C2×C812yescomplemented
87C22×C4×C61C2×D412yes—
88C22×C4×C61C2×D411yescharacteristic
89C22×C4×C61C2×D411yescharacteristic
90C22×C4×C61#4112yes—
91C4⋊C4×C61—24no—
92C4⋊C4×C61—22no—
93C4⋊C4×C61—41no—
94C4⋊C4×C61—42no—
95C4⋊C4×C61—41no—
96C4⋊C4×C61—81no—
97C22⋊C4×C61—24no—
98C22⋊C4×C61—22no—
99C22⋊C4×C61—21no—
100C22⋊C4×C61—22no—
101C22⋊C4×C61—22no—
102C22⋊C4×C61—81no—
103C22⋊C4×C61C2×C812yescomplemented
104C42×C61—21no—
105C42×C61—21no—
106C42×C61—81no—
107C2×#92418—24no—
108C2×#92418—42no—
109C2×#92418—82no—
110C2×#92418—82no—
111C2×#92418—82no—
112C23×C61—21no—
113C23×C61—21no—
114C23×C61—41no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61—41no—
118C23×C61C22⋊C812yes—
119C23×C61C2×C22⋊C411yescharacteristic
120C23×C61C4×D412yes—
121C23×C61C22×C811yescharacteristic
122C23×C61C2×M1611yescharacteristic
123C23×C61#13112yes—
124D4×C61—24no—
125D4×C61—24no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—22no—
131C2×C4×C61—22no—
132C2×C4×C61—24no—
133C2×C4×C61—42no—
134C2×C4×C61—42no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—42no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—42no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—81no—
152C2×C4×C61—82no—
153C2×C4×C61C22⋊C812yes—
154C2×C4×C61#12011yescharacteristic
155C2×C4×C61#12112yes—
156C2×C4×C61#12311yescharacteristic
157#92418—44no—
158#92418—82no—
159#9108—611nomaximal, Sylow
160C22×C61—21no—
161C22×C61—22no—
162C22×C61—21no—
163C22×C61—22no—
164C22×C61—22no—
165C22×C61—41no—
166C22×C61—41no—
167C22×C61—42no—
168C22×C61—42no—
169C22×C61—41no—
170C22×C61—41no—
171C22×C61—81no—
172C22×C61#38611yescharacteristic
173C22×C61C2×C22⋊C811yescharacteristic
174C22×C61#40811yescharacteristic
175C22×C61C8×D412yes—
176C22×C61#43512yes—
177C4×C61—22no—
178C4×C61—21no—
179C4×C61—22no—
180C4×C61—21no—
181C4×C61—42no—
182C4×C61—42no—
183C4×C61—41no—
184C4×C61—41no—
185C4×C61—81no—
186C4×C61—81no—
187#2972—611no—
188#2322D6111yescharacteristic
189#1459—611no—
190C2×#324—612no—
191#1282—612no—
192C2×C61—21no—
193C2×C61—21no—
194C2×C61—22no—
195C2×C61—22no—
196C2×C61—42no—
197C2×C61#186911yescharacteristic
198C2×C61#191311yescharacteristic
199C2×C61#191511yescharacteristic
200C2×#123Dic6111yescharacteristic
201C2×C4×D4C2×D6111yescharacteristic
202C22×C4⋊C4C2×D6111yescharacteristic
203C8×D4—1224no—
204#431—1221no—
205C2×C22⋊C8—612no—
206C2×C22⋊C8—612no—
207C2×C22⋊C8—1221no—
208#389—21no—
209#388—21no—
210#387—21no—
211#386Dic6111yescharacteristic
212#385—21no—
213#385Dic6111yescharacteristic
214#381Dic6111yescharacteristic
215C4×C22⋊C4C2×D6111yescharacteristic
216#324—1224no—
217#324—1221no—
218#323—1221no—
219C61#910811yescharacteristic, complemented, Sylow
220C22×D4C2×Dic6111yescharacteristic
221C23×C4C2×Dic6111yescharacteristic
222C23×C4C2×Dic6111yescharacteristic
223C23×C4C22⋊D6111yescharacteristic
224C23×C4C22×D6111yescharacteristic
225C22×C8—1222no—
226C22×C8—1222no—
227C22×C8—1222no—
228#123—22no—
229#123#9241814yescomplemented
230C4×D4—22no—
231C4×D4—22no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—22no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4C22⋊D6111yescharacteristic
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4C2×Dic6111yescharacteristic
242C2×C22⋊C4C2×Dic6111yescharacteristic
243C2×C22⋊C4C2×Dic6111yescharacteristic
244C2×C22⋊C4C22⋊D6111yescharacteristic
245C2×C42—21no—
246C2×C42C22⋊D6111yescharacteristic
247C4⋊C8—1222no—
248C22⋊C8—614no—
249C22⋊C8—1222no—
250C22⋊C8—1222no—
251C22⋊C8—1222no—
252C22⋊C8—1222no—
253C4×C8—1222no—
254#95—21no—
255#95—21no—
256#95—21no—
257#95—21no—
258#95—21no—
259C24C22⋊Dic6111yescharacteristic
260C24C22×Dic6111yescharacteristic
261C2×D4—22no—
262C2×D4—22no—
263C2×D4C2×#9241812yes—
264C2×D4#1175819412yes—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—22no—
268C22×C4—21no—
269C22×C4—22no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—22no—
275C22×C4—81no—
276C22×C4—81no—
277C22×C4—81no—
278C22×C4C2×#9241812yescomplemented
279C22×C4C22⋊Dic6111yescharacteristic
280C22×C4C22⋊Dic6111yescharacteristic
281C22×C4C22⋊Dic6111yescharacteristic
282C22×C4D4×D6112yes—
283C22×C4#1175822412yes—
284C22×C4C2×C22⋊D6111yescharacteristic
285C22×C4C2×C22⋊D6111yescharacteristic
286C2×C8—1224no—
287C2×C8—4882no—
288C2×C8—4882no—
289C2×C8—4882no—
290C2×C8—2442no—
291C4⋊C4—24no—
292C4⋊C4—22no—
293C4⋊C4—41no—
294C4⋊C4—42no—
295C4⋊C4—41no—
296C4⋊C4—81no—
297C22⋊C4—24no—
298C22⋊C4—22no—
299C22⋊C4—21no—
300C22⋊C4—22no—
301C22⋊C4—22no—
302C22⋊C4—81no—
303C22⋊C4C2×#9241812yescomplemented
304C42—21no—
305C42—21no—
306C42—81no—
307C23—21no—
308C23—21no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23C22⋊#9241812yes—
314C23C2×C22⋊Dic6111yescharacteristic
315C23D4×Dic6112yes—
316C23C22×#9241811yescharacteristic
317C23C2×#1175819411yescharacteristic
318C23#1451978412yes—
319D4—24no—
320D4—24no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—24no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—41no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—81no—
347C2×C4—82no—
348C2×C4C22⋊#9241812yes—
349C2×C4#1451974511yescharacteristic
350C2×C4#1451974912yes—
351C2×C4#1451975811yescharacteristic
352C8—4882no—
353C8—2444no—
354C22—21no—
355C22—22no—
356C22—21no—
357C22—22no—
358C22—22no—
359C22—41no—
360C22—41no—
361C22—42no—
362C22—42no—
363C22—41no—
364C22—41no—
365C22—81no—
366C22#1683964211yescharacteristic
367C22C2×C22⋊#9241811yescharacteristic
368C22#1683972911yescharacteristic
369C22D4×#9241812yes—
370C22#1683983412yes—
371C4—22no—
372C4—21no—
373C4—21no—
374C4—22no—
375C4—42no—
376C4—41no—
377C4—42no—
378C4—41no—
379C4—81no—
380C4—81no—
381C2—21no—
382C2—21no—
383C2—22no—
384C2—22no—
385C2—42no—
386C2#2144611211yescharacteristic
387C2#2144636211yescharacteristic
388C2#2144637211yescharacteristic
subgroupG/H
centerC22#16839642
commutatorC23×C61C22×C8
FrattiniC23×C4C22×D61
FittingC61×#2322C2
socleC22×C61#386
prime radicalC22×D4×C61C2×C4
cosocleC23×C4×C61C23
hypercenter#2322D61
hypocenterC61#9108
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2322

Complements

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

NH ≅ G/Ntype
3. C2×#16839488C2semidirect
4. #21443667C2semidirect
41. #123×C61C8semidirect
86. C22×C4×C61C2×C8semidirect
103. C22⋊C4×C61C2×C8semidirect
219. C61#9108semidirect
229. #123#92418semidirect
278. C22×C4C2×#92418semidirect
303. C22⋊C4C2×#92418semidirect

Maximal subgroups

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

subgroupindex
#214548432
#214441372
C2×#168394882
#214436672
C61×#23222
#910861