Finite Group Databasebeta

← #30596767

Subgroups — #30596767

Order 15616.

612 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462495C211yesmaximal, characteristic
2C2×#16840765C211yesmaximal, characteristic
3#21460689C214yesmaximal, complemented
4C2×#16839785C211yesmaximal, characteristic
5C22×#11758217—21no—
6#16840783—21no—
7#16840782C412yes—
8#16840779C412yes—
9#16840778—21no—
10#16840765—21no—
11#16840765—21no—
12#16840765C412yes—
13#16840765C2212yes—
14#16840765C2212yes—
15C2×#14519844C412yes—
16C2×C4⋊#92420—21no—
17#16840732—21no—
18C4×#11758217—21no—
19C22×#11758194C411yescharacteristic
20C22×C4×Dic61C2211yescharacteristic
21#16839785—21no—
22#16839785—21no—
23#16839785—21no—
24#16839785—21no—
25C2×#14519706C412yes—
26C2×#14519706C2212yes—
27C22×M16×C61C411yescharacteristic
28C2×#11758217—22no—
29C2×#11758217—22no—
30C2×#11758217—22no—
31C2×#11758217—44no—
32C22×#92420—22no—
33#14519844—22no—
34#14519844C2×C414yes—
35#14519844C2×C414yes—
36C4⋊#92420—22no—
37C4⋊#92420—22no—
38C4⋊#92420—22no—
39C22⋊#92420—22no—
40C22⋊#92420—22no—
41#14519832—22no—
42C4×#92420—22no—
43C23×Dic61D411yescharacteristic
44C23×Dic61Q811yescharacteristic
45C2×#11758194—21no—
46C2×#11758194—21no—
47C2×#11758194—42no—
48C22×#92418C2×C412yes—
49C2×C4×Dic61C2×C411yescharacteristic
50C2×C4×Dic61C2×C411yescharacteristic
51C2×C4×Dic61C2×C411yescharacteristic
52C2×C4×Dic61C2×C411yescharacteristic
53C2×C4×Dic61C2×C411yescharacteristic
54C2×C4×Dic61D411yescharacteristic
55C2×C4×Dic61D411yescharacteristic
56C2×C4×Dic61D411yescharacteristic
57C2×C4×Dic61D411yescharacteristic
58C2×C4×Dic61D411yescharacteristic
59C2×C4×Dic61Q811yescharacteristic
60C2×C4×Dic61C2311yescharacteristic
61#14519706—22no—
62#14519706—22no—
63#14519706—22no—
64#14519706—22no—
65C23×C4×C61C2×C411yescharacteristic
66C2×M16×C61—21no—
67C2×M16×C61—21no—
68C2×M16×C61—42no—
69C22×C8×C61C2×C412yes—
70C24×C61C4⋊C411yescharacteristic
71C22×C4×C61—22no—
72C22×C4×C61—22no—
73C22×C4×C61C4211yescharacteristic
74C22×C4×C61C4211yescharacteristic
75C22×C4×C61C22⋊C411yescharacteristic
76C22×C4×C61C22⋊C411yescharacteristic
77C22×C4×C61C4⋊C411yescharacteristic
78C22×C4×C61C22×C411yescharacteristic
79C22×Dic61—22no—
80C22×Dic61—22no—
81C22×Dic61—42no—
82C22×Dic61C22⋊C411yescharacteristic
83C22×Dic61C22⋊C411yescharacteristic
84C22×Dic61C22⋊C411yescharacteristic
85C22×Dic61C22⋊C411yescharacteristic
86C22×Dic61C4⋊C411yescharacteristic
87C22×Dic61C4⋊C411yescharacteristic
88C22×Dic61C4⋊C411yescharacteristic
89C22×Dic61C4⋊C411yescharacteristic
90C22×Dic61C4⋊C411yescharacteristic
91C22×Dic61C4⋊C411yescharacteristic
92C22×Dic61C2×D411yescharacteristic
93C22×Dic61C2×Q811yescharacteristic
94#11758217—44no—
95#11758217—42no—
96#11758217—44no—
97#11758217—42no—
98C2×#92420—24no—
99C2×#92420—24no—
100C2×#92420—44no—
101M16×C61—42no—
102M16×C61—42no—
103C2×C8×C61—22no—
104C2×C8×C61—42no—
105C4×Dic61C4211yescharacteristic
106C4×Dic61C4211yescharacteristic
107C4×Dic61C22⋊C411yescharacteristic
108C4×Dic61C22⋊C411yescharacteristic
109C4×Dic61C22⋊C411yescharacteristic
110C4×Dic61C22⋊C411yescharacteristic
111C4×Dic61C22⋊C411yescharacteristic
112C4×Dic61C22⋊C411yescharacteristic
113C4×Dic61C4⋊C411yescharacteristic
114C4×Dic61C4⋊C411yescharacteristic
115C4×Dic61C4⋊C411yescharacteristic
116C4×Dic61C4⋊C411yescharacteristic
117C4×Dic61C22×C411yescharacteristic
118C4×Dic61C22×C411yescharacteristic
119C4×Dic61C2×D411yescharacteristic
120C4×Dic61C2×D411yescharacteristic
121#11758194—42no—
122#11758194—42no—
123C2×#92418—22no—
124C2×#92418—42no—
125C23×C61—22no—
126C23×C61—22no—
127C23×C61—41no—
128C23×C61#9511yescharacteristic
129C23×C61#9511yescharacteristic
130C23×C61C2×C4⋊C411yescharacteristic
131C2×C4×C61—22no—
132C2×C4×C61—22no—
133C2×C4×C61—22no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61#9511yescharacteristic
139C2×C4×C61#9511yescharacteristic
140C2×C4×C61#10012yes—
141C2×C4×C61#10112yes—
142C2×C4×C61C2×C4211yescharacteristic
143C2×C4×C61C2×C22⋊C411yescharacteristic
144C2×Dic61—22no—
145C2×Dic61—22no—
146C2×Dic61—22no—
147C2×Dic61—22no—
148C2×Dic61—22no—
149C2×Dic61—22no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61#9511yescharacteristic
158C2×Dic61#9511yescharacteristic
159C2×Dic61#9511yescharacteristic
160C2×Dic61#9511yescharacteristic
161C2×Dic61C2×C22⋊C411yescharacteristic
162C2×Dic61C2×C22⋊C411yescharacteristic
163C2×Dic61C2×C4⋊C411yescharacteristic
164C2×Dic61C2×C4⋊C411yescharacteristic
165C2×Dic61AGL(1,ℤ/8)12yes—
166C2×Dic61#13712yes—
167#92420—44no—
168#92420—44no—
169C8×C61—42no—
170#92418—42no—
171#8004—611nomaximal, Sylow
172C22×C61—21no—
173C22×C61—21no—
174C22×C61—21no—
175C22×C61—21no—
176C22×C61—21no—
177C22×C61—21no—
178C22×C61—21no—
179C22×C61—44no—
180C22×C61#34312yes—
181C22×C61C2×#9511yescharacteristic
182C22×C61#42812yes—
183C4×C61—21no—
184C4×C61—21no—
185C4×C61#34312yes—
186C4×C61C2×#10011yescharacteristic
187C4×C61C2×#10111yescharacteristic
188Dic61—21no—
189Dic61—21no—
190Dic61—21no—
191Dic61—21no—
192Dic61—21no—
193Dic61#33812yes—
194Dic61#41712yes—
195Dic61#41811yescharacteristic
196Dic61#41911yescharacteristic
197#2920—611no—
198C2×#423—611no—
199C2×#423—611no—
200#1292—614no—
201C2×C61—22no—
202C2×C61—22no—
203C2×C61—41no—
204C2×C61C2×#33811yescharacteristic
205C2×C61#173611yescharacteristic
206C2×C61C2×#34311yescharacteristic
207C22×M16—611no—
208C22×M16—1221no—
209C22×M16#692311yescharacteristic
210C22×C42—611no—
211#432—612no—
212#432—1221no—
213#431—612no—
214#431—1221no—
215#423—612no—
216#423—612no—
217#423—612no—
218#423—1221no—
219#423—1221no—
220#423—1221no—
221#423—1221no—
222#423—1221no—
223#423—1221no—
224C2×C4⋊C8—612no—
225C2×C4⋊C8—612no—
226C2×C4⋊C8—612no—
227C2×C4⋊C8—1221no—
228#407—1221no—
229C4×M16—1221no—
230C61#800411yescharacteristic, complemented, Sylow
231C23×C4—611no—
232C23×C4—611no—
233C23×C4C2×#692311yescharacteristic
234C2×M16—21no—
235C2×M16—21no—
236C2×M16—42no—
237C2×M16—1222no—
238C2×M16—1222no—
239C2×M16—1222no—
240C2×M16—1221no—
241C2×M16—1221no—
242C2×M16—2444no—
243C2×M16—2442no—
244C22×C8—612no—
245C22×C8—1222no—
246C22×C8C2×#692312yes—
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×C42—611no—
256C2×C42—611no—
257C2×C42—611no—
258C2×C42—611no—
259C4⋊C8—614no—
260C4⋊C8—614no—
261C4⋊C8—1222no—
262C4⋊C8—1222no—
263C4⋊C8—1222no—
264C4⋊C8—1222no—
265C4⋊C8—1222no—
266C4⋊C8—1222no—
267C4⋊C8—1222no—
268C4⋊C8—1222no—
269C22⋊C8—1222no—
270C22⋊C8—1222no—
271#97—1222no—
272C4×C8—1222no—
273C24C4⋊#692311yescharacteristic
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—611no—
277C22×C4—611no—
278C22×C4—611no—
279C22×C4—611no—
280C22×C4—611no—
281C22×C4—611no—
282C22×C4—611no—
283C22×C4—611no—
284C22×C4—611no—
285C22×C4—611no—
286C22×C4—611no—
287C22×C4—611no—
288C22×C4—1222no—
289C22×C4—1222no—
290C22×C4—2442no—
291C22×C4C4×#692311yescharacteristic
292C22×C4C4×#692311yescharacteristic
293C22×C4C4⋊#692311yescharacteristic
294C22×C4C22⋊#692311yescharacteristic
295C22×C4C22⋊#692311yescharacteristic
296C22×C4C22×#692311yescharacteristic
297M16—42no—
298M16—42no—
299M16—2442no—
300M16—2444no—
301M16—2442no—
302M16—2442no—
303M16—2444no—
304M16—2442no—
305C2×C8—22no—
306C2×C8—42no—
307C2×C8—1224no—
308C2×C8—1224no—
309C2×C8—1222no—
310C2×C8—2444no—
311C2×C8—2442no—
312C42—611no—
313C42—611no—
314C42—611no—
315C42—611no—
316C42—611no—
317C42—611no—
318C42—611no—
319C42—611no—
320C42—611no—
321C42—611no—
322C42—611no—
323C42—611no—
324C42—611no—
325C42—611no—
326C42—611no—
327C42—611no—
328C23—22no—
329C23—22no—
330C23—41no—
331C23(C2×#6923)⋊C411yescharacteristic
332C23(C2×#6923)⋊C411yescharacteristic
333C23C2×C4⋊#692311yescharacteristic
334C2×C4—22no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—612no—
342C2×C4—612no—
343C2×C4—611no—
344C2×C4—611no—
345C2×C4—611no—
346C2×C4—611no—
347C2×C4—611no—
348C2×C4—611no—
349C2×C4—611no—
350C2×C4—611no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—1222no—
354C2×C4—1222no—
355C2×C4—1221no—
356C2×C4—1221no—
357C2×C4—1222no—
358C2×C4—1222no—
359C2×C4—1222no—
360C2×C4—1222no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4(C2×#6923)⋊C411yescharacteristic
365C2×C4(C2×#6923)⋊C411yescharacteristic
366C2×C4#1451983712yes—
367C2×C4#1451983812yes—
368C2×C4C2×C4×#692311yescharacteristic
369C2×C4C2×C22⋊#692311yescharacteristic
370C8—42no—
371C8—2444no—
372C8—2444no—
373C8—2442no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—44no—
382C22#1684064212yes—
383C22C2×(C2×#6923)⋊C411yescharacteristic
384C22#1684077312yes—
385C4—21no—
386C4—21no—
387C4—612no—
388C4—611no—
389C4—611no—
390C4—612no—
391C4—1221no—
392C4—1221no—
393C4—1221no—
394C4—1221no—
395C4—1221no—
396C4#1684064212yes—
397C4C2×#1451983711yescharacteristic
398C4C2×#1451983811yescharacteristic
399C2—22no—
400C2—22no—
401C2—41no—
402C2D61⋊#33811yescharacteristic
403C2#2146150711yescharacteristic
404C2C2×#1684064211yescharacteristic
subgroupG/H
centerC22C2×(C2×#6923)⋊C4
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC22×M16×C61C4
socleC22×C61C2×#95
prime radicalC24×C61C4⋊C4
cosocleC2×C4×Dic61C23
hypercenterC22×M16#6923
hypocenterC61#8004
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
3. #21460689C2semidirect
230. C61#8004semidirect

Maximal subgroups

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

subgroupindex
#214624952
C2×#168407652
#214606892
C2×#168397852
#800461