Finite Group Databasebeta

← #29569935

Subgroups — #29569935

Order 15616.

608 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454449C211yesmaximal, characteristic
2#432×D61C211yesmaximal, characteristic
3C4×M16×D61C211yesmaximal, characteristic
4#21443692C211yesmaximal, characteristic, complemented
5#21443691C211yesmaximal, characteristic, complemented
6#21443690C211yesmaximal, characteristic, complemented
7C61×#1291C211yesmaximal, characteristic, complemented
8C2×M16×D61—21no—
9C2×C42×D61C2211yescharacteristic
10#16839819C2211yescharacteristic
11#16839819C2211yescharacteristic
12#16839818—21no—
13#16839817—21no—
14#16839817—21no—
15#16839816C412yes—
16#16839814C412yes—
17#16839812—21no—
18#16839784C412yes—
19C4⋊C8×D61—21no—
20#16839724—21no—
21C22⋊C8×D61C412yes—
22C4×#11758194C2211yescharacteristic
23#16839714—21no—
24#16839714—21no—
25M16×Dic61—21no—
26C4×#11758189C412yes—
27#97×D61—21no—
28#97×D61—21no—
29C4×C8×D61C412yes—
30C61×#432C2211yescharacteristic
31C61×#432C2211yescharacteristic
32C4×M16×C61C2211yescharacteristic
33C22×C4×D61C2×C411yescharacteristic
34C22×C4×D61D411yescharacteristic
35C22×C4×D61Q811yescharacteristic
36C2×#11758194—21no—
37C2×#11758189—22no—
38C2×#11758189—22no—
39M16×D61—28no—
40C2×C8×D61—22no—
41C2×C8×D61—22no—
42C2×C4×Dic61C2×C411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61Q811yescharacteristic
45C42×D61C2×C411yescharacteristic
46C42×D61C2×C411yescharacteristic
47C42×D61C2×C411yescharacteristic
48C42×D61C2×C411yescharacteristic
49C42×D61D411yescharacteristic
50C42×D61D411yescharacteristic
51C42×D61D411yescharacteristic
52C42×D61D411yescharacteristic
53C4⋊#92418—21no—
54C4⋊#92418C2×C412yes—
55#14519706—22no—
56#14519706—22no—
57C22⋊#92418—21no—
58C22⋊#92418C2×C412yes—
59#14519689—22no—
60#14519689—22no—
61#14519688—21no—
62#14519688—21no—
63#14519688—21no—
64#14519687—22no—
65#14519687—22no—
66C4×#92418C2×C412yes—
67C8×Dic61—22no—
68C8×Dic61—22no—
69C2×M16×C61—21no—
70C2×C42×C61C2311yescharacteristic
71C4⋊C8×C61—21no—
72C4⋊C8×C61C2×C412yes—
73C22⋊C8×C61—21no—
74C22⋊C8×C61C2×C412yes—
75#97×C61—21no—
76#97×C61—21no—
77#97×C61—21no—
78C4×C8×C61C2×C412yes—
79C23×D61C4⋊C411yescharacteristic
80C22×C4×C61C22×C411yescharacteristic
81C22×C4×C61C2×D411yescharacteristic
82C22×C4×C61C2×Q811yescharacteristic
83C22×Dic61C4⋊C411yescharacteristic
84C22×Dic61C4⋊C411yescharacteristic
85C22×Dic61C4⋊C411yescharacteristic
86C2×C4×D61—24no—
87C2×C4×D61—42no—
88C2×C4×D61—42no—
89C2×C4×D61C4211yescharacteristic
90C2×C4×D61C4211yescharacteristic
91C2×C4×D61C22⋊C411yescharacteristic
92C2×C4×D61C22⋊C411yescharacteristic
93C2×C4×D61C22⋊C411yescharacteristic
94C2×C4×D61C22⋊C411yescharacteristic
95C2×C4×D61C22⋊C411yescharacteristic
96C2×C4×D61C22⋊C411yescharacteristic
97C2×C4×D61C4⋊C411yescharacteristic
98C2×C4×D61C4⋊C411yescharacteristic
99C2×C4×D61C4⋊C411yescharacteristic
100C2×C4×D61C4⋊C411yescharacteristic
101M16×C61—24no—
102C2×C8×C61—22no—
103C2×C8×C61—22no—
104C2×C8×C61—22no—
105C42×C61C22×C411yescharacteristic
106C42×C61C22×C411yescharacteristic
107C42×C61C2×D411yescharacteristic
108C42×C61C2×D411yescharacteristic
109C4×Dic61C4211yescharacteristic
110C4×Dic61C4211yescharacteristic
111C4×Dic61C22⋊C411yescharacteristic
112C4×Dic61C22⋊C411yescharacteristic
113C4×Dic61C22⋊C411yescharacteristic
114C4×Dic61C22⋊C411yescharacteristic
115C4×Dic61C22⋊C411yescharacteristic
116C4×Dic61C22⋊C411yescharacteristic
117C4×Dic61C4⋊C411yescharacteristic
118C4×Dic61C4⋊C411yescharacteristic
119C4×Dic61C4⋊C411yescharacteristic
120C4×Dic61C4⋊C411yescharacteristic
121#11758194—24no—
122C2×#92418—22no—
123C2×#92418—22no—
124C2×#92418—22no—
125#11758189—28no—
126#11758189—44no—
127C8×D61—28no—
128C8×D61—44no—
129C23×C61C2×C4⋊C411yescharacteristic
130C22×D61—22no—
131C22×D61—22no—
132C22×D61—41no—
133C22×D61#9511yescharacteristic
134C22×D61#9511yescharacteristic
135C2×C4×C61—22no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61C2×C4211yescharacteristic
139C2×C4×C61C2×C22⋊C411yescharacteristic
140C2×C4×C61C2×C22⋊C411yescharacteristic
141C2×C4×C61C2×C22⋊C411yescharacteristic
142C2×C4×C61C2×C4⋊C411yescharacteristic
143C2×C4×C61C2×C4⋊C411yescharacteristic
144C2×Dic61—22no—
145C2×Dic61—22no—
146C2×Dic61—41no—
147C2×Dic61#9511yescharacteristic
148C2×Dic61#9511yescharacteristic
149C2×Dic61#9511yescharacteristic
150C2×Dic61#9511yescharacteristic
151C2×Dic61#9511yescharacteristic
152C2×Dic61#9511yescharacteristic
153C4×D61—22no—
154C4×D61—22no—
155C4×D61—22no—
156C4×D61—22no—
157C4×D61—22no—
158C4×D61—22no—
159C4×D61—22no—
160C4×D61—41no—
161C4×D61—41no—
162C4×D61—41no—
163C4×D61—41no—
164C4×D61#10414yes—
165C8×C61—24no—
166C8×C61—42no—
167C8×C61—42no—
168#92418—24no—
169#92418—42no—
170#92418—42no—
171#7994—611nomaximal, Sylow
172C22×C61—21no—
173C22×C61—21no—
174C22×C61—21no—
175C22×C61C2×#9511yescharacteristic
176C2×D61—21no—
177C2×D61—21no—
178C2×D61—21no—
179C2×D61—21no—
180C2×D61—44no—
181C2×D61#33812yes—
182C2×D61#33912yes—
183C4×C61—21no—
184C4×C61—21no—
185C4×C61—21no—
186C4×C61—21no—
187C4×C61—21no—
188C4×C61C2×#10412yes—
189Dic61—21no—
190Dic61—21no—
191Dic61—21no—
192Dic61—21no—
193Dic61#33912yes—
194Dic61#34412yes—
195#2920—611no—
196C2×#432—611no—
197C2×C4×M16—611no—
198#1291—611no—
199#1291—611no—
200#1291—611no—
201#1291D6111yescharacteristic, complemented
202C2×C61—41no—
203C2×C61C2×#33811yescharacteristic
204C2×C61C2×#33911yescharacteristic
205C2×C61C2×#34411yescharacteristic
206D61—22no—
207D61—22no—
208C22×M16—1221no—
209C22×C42—611no—
210#432—611no—
211#432—612no—
212#432—611no—
213#432—1221no—
214#432—1221no—
215#432—1221no—
216#432C2×D6111yescharacteristic
217#432C2×D6111yescharacteristic
218#431—612no—
219#431—1221no—
220#423—612no—
221C2×C4⋊C8—1221no—
222#407—1221no—
223C2×C22⋊C8—612no—
224C4×M16—611no—
225C4×M16—612no—
226C4×M16—1221no—
227C4×M16—1221no—
228C4×M16—1221no—
229C4×M16C2×D6111yescharacteristic
230C2×#97—1221no—
231C2×#97—1221no—
232C2×C4×C8—612no—
233C61#799411yescharacteristic, complemented, Sylow
234C23×C4—611no—
235C23×C4—611no—
236C23×C4—611no—
237C2×M16—21no—
238C2×M16—1222no—
239C2×M16—1222no—
240C2×M16—1228no—
241C2×M16—1221no—
242C22×C8—1222no—
243C22×C8—1222no—
244C2×C42—611no—
245C2×C42—611no—
246C2×C42—611no—
247C2×C42—611no—
248C2×C42—611no—
249C2×C42—611no—
250C2×C42—611no—
251C2×C42—611no—
252C2×C42—611no—
253C2×C42—611no—
254C2×C42—611no—
255C2×C42C22×D6111yescharacteristic
256C4⋊C8—21no—
257C4⋊C8—612no—
258C4⋊C8—1222no—
259C4⋊C8—1222no—
260C4⋊C8—1221no—
261C4⋊C8C4×D6112yes—
262C22⋊C8—21no—
263C22⋊C8—612no—
264C22⋊C8—1222no—
265C22⋊C8—1222no—
266C22⋊C8—1221no—
267C22⋊C8C4×D6112yes—
268#97—21no—
269#97—21no—
270#97—21no—
271#97—1222no—
272#97—1222no—
273#97—1221no—
274#97—1221no—
275#97—1221no—
276C4×C8—612no—
277C4×C8—1222no—
278C4×C8—1222no—
279C4×C8C4×D6112yes—
280C24—611no—
281C22×C4—611no—
282C22×C4—611no—
283C22×C4—611no—
284C22×C4—611no—
285C22×C4—611no—
286C22×C4—611no—
287C22×C4—611no—
288C22×C4—611no—
289C22×C4—611no—
290C22×C4—611no—
291C22×C4—611no—
292C22×C4—611no—
293C22×C4—611no—
294C22×C4—611no—
295C22×C4—611no—
296C22×C4—1224no—
297C22×C4—2442no—
298C22×C4—2442no—
299C22×C4C2×C4×D6111yescharacteristic
300C22×C4D4×D6111yescharacteristic
301C22×C4Q8×D6111yescharacteristic
302M16—24no—
303M16—1228no—
304M16—1224no—
305M16—2444no—
306C2×C8—22no—
307C2×C8—22no—
308C2×C8—22no—
309C2×C8—1228no—
310C2×C8—1222no—
311C2×C8—1222no—
312C2×C8—1222no—
313C2×C8—2444no—
314C42—611no—
315C42—611no—
316C42—611no—
317C42—611no—
318C42—611no—
319C42—611no—
320C42—611no—
321C42—611no—
322C42—611no—
323C42—611no—
324C42—611no—
325C42—611no—
326C42C2×C4×D6111yescharacteristic
327C42C2×C4×D6111yescharacteristic
328C42D4×D6111yescharacteristic
329C42D4×D6111yescharacteristic
330C23—611no—
331C23—611no—
332C23—1222no—
333C23—1222no—
334C23—2441no—
335C23C4⋊C4×D6111yescharacteristic
336C2×C4—22no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—611no—
340C2×C4—611no—
341C2×C4—614no—
342C2×C4—611no—
343C2×C4—611no—
344C2×C4—611no—
345C2×C4—611no—
346C2×C4—1222no—
347C2×C4—1222no—
348C2×C4—1222no—
349C2×C4—1222no—
350C2×C4—1222no—
351C2×C4—1222no—
352C2×C4—1222no—
353C2×C4—1222no—
354C2×C4—1222no—
355C2×C4—2441no—
356C2×C4—2441no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4C42×D6111yescharacteristic
361C2×C4C22⋊C4×D6111yescharacteristic
362C2×C4C22⋊C4×D6111yescharacteristic
363C2×C4C22⋊C4×D6111yescharacteristic
364C2×C4C4⋊C4×D6111yescharacteristic
365C2×C4C4⋊C4×D6111yescharacteristic
366C8—24no—
367C8—42no—
368C8—42no—
369C8—1224no—
370C8—2442no—
371C8—2442no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—612no—
376C22—612no—
377C22—1221no—
378C22—1221no—
379C22—1221no—
380C22—1221no—
381C22—2444no—
382C22#95×D6111yescharacteristic
383C4—21no—
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—612no—
389C4—612no—
390C4—1221no—
391C4—1221no—
392C4—1221no—
393C4—1221no—
394C4#104×D6112yes—
395C2—41no—
396C2—1222no—
397C2—1222no—
398C2#338×D6111yescharacteristic
399C2#339×D6111yescharacteristic
400C2#344×D6111yescharacteristic
subgroupG/H
centerC22#95×D61
commutatorC2×C4×C61C2×C42
FrattiniC2×C42C22×D61
FittingC61×#1291C2
socleC22×C61C2×#95
prime radicalC23×D61C4⋊C4
cosocleC2×C42×C61C23
hypercenter#1291D61
hypocenterC61#7994
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1291

Complements

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

NH ≅ G/Ntype
4. #21443692C2semidirect
5. #21443691C2semidirect
6. #21443690C2semidirect
7. C61×#1291C2semidirect
201. #1291D61semidirect
233. C61#7994semidirect

Maximal subgroups

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

subgroupindex
#214544492
#432×D612
C4×M16×D612
#214436922
#214436912
#214436902
C61×#12912
#799461