Finite Group Databasebeta

← #30606423

Subgroups — #30606423

Order 15616.

466 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840725C211yesmaximal, characteristic
2#21462047C211yesmaximal, characteristic
3C2×#16840653C211yesmaximal, characteristic, complemented
4C2×#16840652C211yesmaximal, characteristic, complemented
5#21460859C211yesmaximal, characteristic, complemented
6#21460859C211yesmaximal, characteristic, complemented
7#21447428C211yesmaximal, characteristic
8C2×D61⋊M16C411yescharacteristic
9C2×#14519856C411yescharacteristic
10C2×#14519852C2211yescharacteristic
11C2×#14519852C2211yescharacteristic
12#16840725—22no—
13#16840725—22no—
14C2×#14519831C2211yescharacteristic
15C2×#14519831C2211yescharacteristic
16C2×C8×#6923C411yescharacteristic
17C2×C8×#6923C411yescharacteristic
18#16840657C412yescomplemented
19C22⋊#11758187C412yescomplemented
20#16840653—22no—
21#16840652—22no—
22C22×C8×D61C2211yescharacteristic
23C2×#14519716C2211yescharacteristic
24C2×#14519716C2211yescharacteristic
25C22⋊#11758185C411yescharacteristic, complemented
26#16839541C411yescharacteristic, complemented
27#16839541C411yescharacteristic, complemented
28C61×C22⋊C16C411yescharacteristic, complemented
29C2×#11758213—21no—
30D61⋊M16—22no—
31D61⋊M16—22no—
32C2×#11758217—21no—
33C2×D61⋊C8C2×C411yescharacteristic
34C2×D61⋊C8C2×C411yescharacteristic
35#14519856—22no—
36#14519856—22no—
37C2×C4⋊#6923—21no—
38C2×C22⋊#6923—21no—
39C2×C4×#6923C2×C411yescharacteristic
40C2×C4×#6923C2×C411yescharacteristic
41#14519852—21no—
42#14519852—21no—
43#14519852—21no—
44#14519852—21no—
45C2×#11758187C2×C412yes—
46C2×#11758187C2×C412yes—
47#14519831—21no—
48#14519831—21no—
49#14519831D412yes—
50#14519831D412yes—
51C8×#6923—22no—
52C8×#6923—22no—
53C22×C4×D61C2×C411yescharacteristic
54C22×#92418C2×C411yescharacteristic
55C2×C8×D61—21no—
56C2×C8×D61—21no—
57C2×C8×D61—21no—
58C2×C8×D61—21no—
59C2×C8×D61C2×C411yescharacteristic
60C2×C8×D61C2×C411yescharacteristic
61C2×C8×D61C2×C411yescharacteristic
62C2×C8×D61C2311yescharacteristic
63#14519716—21no—
64#14519716—21no—
65#14519716—21no—
66#14519716—21no—
67C2×#11758185C2×C411yescharacteristic
68C2×#11758185C2×C411yescharacteristic
69C22×C8×C61C2×C411yescharacteristic
70C2×C16×C61C2×C411yescharacteristic
71C2×C16×C61C2×C411yescharacteristic
72C23×D61M1611yescharacteristic
73C22×#6923—21no—
74C22×#6923—21no—
75C22×C4×C61C4211yescharacteristic
76C22×Dic61M1611yescharacteristic
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61C4211yescharacteristic
82C2×C4×D61M1611yescharacteristic
83C2×C4×D61M1611yescharacteristic
84C2×C4×D61C22×C411yescharacteristic
85C22⋊#6923—24no—
86#11758217—24no—
87C2×#92420—21no—
88C2×#92420—21no—
89C4⋊#6923—24no—
90C4×#6923—21no—
91C4×#6923—21no—
92C4×#6923C22⋊C412yes—
93C4×#6923M1612yes—
94#11758213—24no—
95D61⋊C8—21no—
96D61⋊C8—21no—
97D61⋊C8C22⋊C412yes—
98D61⋊C8M1612yes—
99C2×C8×C61—21no—
100C2×C8×C61—21no—
101C2×C8×C61C4211yescharacteristic
102C2×C8×C61C22×C411yescharacteristic
103C2×#92418—21no—
104C2×#92418—21no—
105C2×#92418C4211yescharacteristic
106C2×#92418C22×C411yescharacteristic
107C8×D61—21no—
108C8×D61—21no—
109C8×D61—21no—
110C8×D61—21no—
111C8×D61—21no—
112C8×D61—21no—
113C8×D61C2×D411yescharacteristic
114C8×D61C2×D411yescharacteristic
115C8×D61#4111yescharacteristic
116C8×D61#4111yescharacteristic
117#11758187—22no—
118#11758187—22no—
119C16×C61—21no—
120C16×C61—21no—
121#11758185—21no—
122#11758185—21no—
123C23×C61#9711yescharacteristic
124C22×D61—21no—
125C22×D61—21no—
126C22×D61—41no—
127C22×D61—41no—
128C22×D61#9711yescharacteristic
129C22×D61C2×M1611yescharacteristic
130C2×#6923—22no—
131C2×#6923—22no—
132C2×#6923—41no—
133C2×#6923—41no—
134C2×#6923—41no—
135C2×#6923—41no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61#9711yescharacteristic
139C2×C4×C61C2×C4211yescharacteristic
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61#9711yescharacteristic
143C2×Dic61C2×M1611yescharacteristic
144C4×D61—21no—
145C4×D61—21no—
146C4×D61—21no—
147C4×D61—21no—
148C4×D61—21no—
149C4×D61—21no—
150C4×D61C2×C22⋊C411yescharacteristic
151C4×D61#11711yescharacteristic
152C4×D61C2×M1611yescharacteristic
153C4×D61C2×M1611yescharacteristic
154#92420—22no—
155#92420—22no—
156C8×C61—21no—
157C8×C61C4×D411yescharacteristic
158C8×C61C4×D411yescharacteristic
159#92418—21no—
160#92418C4×D411yescharacteristic
161#92418C4×D411yescharacteristic
162#12606—611nomaximal, Sylow
163C22×C61—21no—
164C22×C61—21no—
165C22×C61—21no—
166C22×C61C2×#9711yescharacteristic
167C2×D61—21no—
168C2×D61—21no—
169C2×D61—21no—
170C2×D61—21no—
171C2×D61—21no—
172C2×D61—42no—
173C2×D61—42no—
174C2×D61#40711yescharacteristic
175C2×D61#43211yescharacteristic
176#6923—42no—
177#6923—42no—
178C4×C61—21no—
179C4×C61C4×C22⋊C411yescharacteristic
180C4×C61C4×M1611yescharacteristic
181Dic61—21no—
182Dic61#40711yescharacteristic
183Dic61#43211yescharacteristic
184C2×#405—611no—
185#2112—611no—
186#2112—611no—
187C2×#347—611no—
188C2×#347—611no—
189#1375—611no—
190#1375—611no—
191C2×C61—41no—
192C2×C61#174911yescharacteristic
193C2×C61#211011yescharacteristic
194C2×C61#211011yescharacteristic
195D61—21no—
196D61—21no—
197D61—41no—
198C22×M16—611no—
199C23×C8—611no—
200C2×#117—611no—
201C2×M32—611no—
202C2×M32—611no—
203C2×M32—611no—
204C2×M32—611no—
205#405—1222no—
206#405—1222no—
207C2×#97—611no—
208C2×#97—611no—
209C2×C4×C8—611no—
210C2×C4×C8—611no—
211C22⋊C16—612no—
212C22⋊C16—612no—
213C22⋊C16—611no—
214C22⋊C16—611no—
215C22⋊C16—611no—
216C22⋊C16#692311yescharacteristic, complemented
217#347—1222no—
218#347—1222no—
219C61#1260611yescharacteristic, complemented, Sylow
220C23×C4—611no—
221C2×M16—1222no—
222C2×M16—1222no—
223C2×M16—1221no—
224C2×M16—1221no—
225C22×C8—611no—
226C22×C8—611no—
227C22×C8—611no—
228C22×C8—611no—
229C22×C8—611no—
230C22×C8—611no—
231C22×C8—611no—
232C22×C8—1221no—
233C22×C8—1221no—
234C22×C8—1221no—
235C22×C8—1221no—
236C22×C8C2×#692311yescharacteristic
237#117—1222no—
238#117—1222no—
239C2×C4⋊C4—1221no—
240C2×C22⋊C4—1221no—
241C2×C42—611no—
242C2×C42—611no—
243M32—1221no—
244M32—1221no—
245M32—1221no—
246M32—1221no—
247M32—1221no—
248M32—1221no—
249M32—1221no—
250M32—1221no—
251C2×C16—612no—
252C2×C16—612no—
253C2×C16—611no—
254C2×C16—611no—
255C2×C16C2×#692311yescharacteristic
256C2×C16C2×#692311yescharacteristic
257#97—612no—
258#97—612no—
259#97—1221no—
260#97—1221no—
261C4×C8—1222no—
262C4×C8—1222no—
263C24—611no—
264C22×C4—611no—
265C22×C4—611no—
266C22×C4—611no—
267C22×C4—611no—
268C22×C4—611no—
269C22×C4—1221no—
270C22×C4—1221no—
271C22×C4—1221no—
272C22×C4—1221no—
273C22×C4—1221no—
274C22×C4—1221no—
275C22×C4C4×#692311yescharacteristic
276M16—1224no—
277M16—1224no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—611no—
281C2×C8—611no—
282C2×C8—611no—
283C2×C8—611no—
284C2×C8—611no—
285C2×C8—612no—
286C2×C8—612no—
287C2×C8—611no—
288C2×C8—1221no—
289C2×C8—1221no—
290C2×C8—1221no—
291C2×C8—1221no—
292C2×C8—1221no—
293C2×C8—1221no—
294C2×C8—1221no—
295C2×C8—1221no—
296C2×C8—1221no—
297C2×C8—1221no—
298C2×C8—1221no—
299C2×C8—1221no—
300C2×C8C4×#692311yescharacteristic
301C2×C8C22×#692311yescharacteristic
302C4⋊C4—1224no—
303C22⋊C4—1224no—
304C42—612no—
305C42—612no—
306C42—1221no—
307C42—1221no—
308C16—21no—
309C16—21no—
310C16—1222no—
311C16—1222no—
312C16—1221no—
313C16—1221no—
314C23—611no—
315C23—611no—
316C23—1221no—
317C23—1221no—
318C23—2441no—
319C23—2441no—
320C23#1451983111yescharacteristic
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—611no—
324C2×C4—611no—
325C2×C4—611no—
326C2×C4—611no—
327C2×C4—611no—
328C2×C4—611no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—1221no—
333C2×C4—1221no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—1222no—
338C2×C4—1222no—
339C2×C4—2441no—
340C2×C4—2441no—
341C2×C4—2441no—
342C2×C4—2441no—
343C2×C4#1451983111yescharacteristic
344C2×C4C2×C4×#692311yescharacteristic
345C8—21no—
346C8—611no—
347C8—611no—
348C8—1222no—
349C8—1222no—
350C8—1221no—
351C8D4×#692311yescharacteristic
352C8D4×#692311yescharacteristic
353C22—21no—
354C22—21no—
355C22—21no—
356C22—611no—
357C22—611no—
358C22—1221no—
359C22—1221no—
360C22—1221no—
361C22—1221no—
362C22—1221no—
363C22—2442no—
364C22—2442no—
365C22C2×#1451983111yescharacteristic
366C4—21no—
367C4—611no—
368C4—611no—
369C4—1221no—
370C4—2442no—
371C4—2442no—
372C4C22⋊C4×#692311yescharacteristic
373C4M16×#692311yescharacteristic
374C2—41no—
375C2—1221no—
376C2—1221no—
377C2—2441no—
378C2#2146154711yescharacteristic
379C2#2146203811yescharacteristic
380C2#2146203911yescharacteristic
subgroupG/H
centerC2×C4C2×C4×#6923
commutatorC2×C4×C61C2×C42
FrattiniC2×C8C22×#6923
FittingC61×C22⋊C16C4
socleC22×C61C2×#97
prime radicalC23×D61M16
cosocleC2×C8×D61C23
hypercenterC22⋊C16#6923
hypocenterC61#12606
LCSG ▷ C2×C4×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22⋊C16

Complements

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

NH ≅ G/Ntype
3. C2×#16840653C2semidirect
4. C2×#16840652C2semidirect
5. #21460859C2semidirect
6. #21460859C2semidirect
18. #16840657C4semidirect
19. C22⋊#11758187C4semidirect
25. C22⋊#11758185C4semidirect
26. #16839541C4semidirect
27. #16839541C4semidirect
28. C61×C22⋊C16C4semidirect
216. C22⋊C16#6923semidirect
219. C61#12606semidirect

Maximal subgroups

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

subgroupindex
C2×#168407252
#214620472
C2×#168406532
C2×#168406522
#214608592
#214474282
#1260661