Finite Group Databasebeta

← #30598247

Subgroups — #30598247

Order 15616.

1030 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
1#21461675C211yesmaximal, characteristic
2#21461675C211yesmaximal, characteristic
3C2×#16840621C214yesmaximal, complemented
4C22×#14519776C211yesmaximal, characteristic
5C2×#14519844C2212yes—
6C2×#14519844C2212yes—
7C2×C22⋊#92420—21no—
8C2×C22⋊#92420—21no—
9#16840628—21no—
10#16840628—21no—
11#16840621—28no—
12C23×Dic122—21no—
13C2×#14519776—28no—
14C2×#14519776—21no—
15C2×#14519776—21no—
16C2×#14519776C412yes—
17C2×#14519776C2212yes—
18C22×C4⋊Dic61C411yescharacteristic
19C22×#11758196—21no—
20C22×C4×Dic61C2211yescharacteristic
21C22×C4⋊C4×C61C411yescharacteristic
22C22×#92420—22no—
23C22×#92420—22no—
24#14519844—24no—
25#14519844—24no—
26C22⋊#92420—42no—
27C22⋊#92420—42no—
28C22×Dic122—28no—
29C22×Dic122—22no—
30C22×Dic122—22no—
31C22×Dic122—44no—
32C22×Dic122—42no—
33C22×Dic122—42no—
34C23×Dic61—21no—
35C23×Dic61D411yescharacteristic
36C23×Dic61D411yescharacteristic
37#14519776—28no—
38#14519776—28no—
39#14519776—24no—
40#14519776—24no—
41#14519776—24no—
42#14519776D418yes—
43C2×C4⋊Dic61—21no—
44C2×C4⋊Dic61—24no—
45C2×C4⋊Dic61C2×C412yes—
46C2×#11758196—28no—
47C2×#11758196—22no—
48C2×#11758196—22no—
49C2×C4×Dic61—24no—
50C2×C4×Dic61C2×C411yescharacteristic
51C2×C4×Dic61D411yescharacteristic
52C2×C4×Dic61D411yescharacteristic
53C2×C4×Dic61C2311yescharacteristic
54C23×C4×C61—21no—
55C23×C4×C61C2×C411yescharacteristic
56C2×C4⋊C4×C61—21no—
57C2×C4⋊C4×C61—24no—
58C2×C4⋊C4×C61C2×C412yes—
59C24×C61C22⋊C411yescharacteristic
60C22×C4×C61—22no—
61C22×C4×C61—22no—
62C22×C4×C61—22no—
63C22×C4×C61—24no—
64C22×C4×C61—22no—
65C22×C4×C61—42no—
66C22×C4×C61—42no—
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C22×C411yescharacteristic
69C22×Dic61—22no—
70C22×Dic61—22no—
71C22×Dic61—22no—
72C22×Dic61—22no—
73C22×Dic61—24no—
74C22×Dic61—22no—
75C22×Dic61—42no—
76C22×Dic61—42no—
77C22×Dic61C22⋊C411yescharacteristic
78C22×Dic61C22⋊C411yescharacteristic
79C22×Dic61D812yes—
80C22×Dic61SD1612yes—
81C22×Dic61SD1612yes—
82C22×Dic61Q1612yes—
83C22×Dic61C2×D411yescharacteristic
84C22×Dic61C2×D411yescharacteristic
85C2×Dic122—28no—
86C2×Dic122—28no—
87C2×Dic122—44no—
88C2×Dic122—416no—
89C2×Dic122—416no—
90C2×Dic122—44no—
91C2×Dic122—42no—
92C2×Dic122—42no—
93C2×Dic122—44no—
94C2×#92420—42no—
95C2×#92420—42no—
96C2×#92420—42no—
97C2×#92420—42no—
98C2×#92420—42no—
99C2×#92420—42no—
100C4⋊C4×C61—24no—
101C4⋊C4×C61—22no—
102C4⋊C4×C61C22⋊C414yes—
103C4⋊Dic61—24no—
104C4⋊Dic61—22no—
105C4⋊Dic61C22⋊C414yes—
106#11758196—28no—
107#11758196—28no—
108C4×Dic61—22no—
109C4×Dic61—22no—
110C4×Dic61—22no—
111C4×Dic61C2×D414yes—
112C23×C61—21no—
113C23×C61—21no—
114C23×C61—21no—
115C23×C61—21no—
116C23×C61#10112yes—
117C23×C61#10212yes—
118C23×C61#10312yes—
119C23×C61C2×C22⋊C411yescharacteristic
120C2×C4×C61—28no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—24no—
126C2×C4×C61—48no—
127C2×C4×C61—42no—
128C2×C4×C61—42no—
129C2×C4×C61#10112yes—
130C2×C4×C61C2×C22⋊C412yes—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—24no—
136C2×Dic61—24no—
137C2×Dic61—24no—
138C2×Dic61—24no—
139C2×Dic61—24no—
140C2×Dic61—48no—
141C2×Dic61—42no—
142C2×Dic61—42no—
143C2×Dic61#10212yes—
144C2×Dic61#10312yes—
145C2×Dic61#12012yes—
146C2×Dic61#12012yes—
147C2×Dic61C2×D811yescharacteristic
148C2×Dic61C2×SD1611yescharacteristic
149C2×Dic61C2×SD1611yescharacteristic
150C2×Dic61C2×Q1611yescharacteristic
151C2×Dic61AGL(1,ℤ/8)12yes—
152C2×Dic61#13712yes—
153Dic122—416no—
154Dic122—48no—
155Dic122—48no—
156#92420—82no—
157#92420—82no—
158#8340—611nomaximal, Sylow
159C22×C61—22no—
160C22×C61—22no—
161C22×C61—22no—
162C22×C61—22no—
163C22×C61—22no—
164C22×C61—22no—
165C22×C61#33214yescomplemented
166C22×C61#37911yescharacteristic
167C22×C61C2×#10111yescharacteristic
168C22×C61C2×#10111yescharacteristic
169C22×C61C2×#10211yescharacteristic
170C22×C61C2×#10311yescharacteristic
171C22×C61#41811yescharacteristic
172C22×C61#41911yescharacteristic
173C4×C61—22no—
174C4×C61—22no—
175C4×C61—44no—
176Dic61—22no—
177Dic61—22no—
178Dic61—44no—
179Dic61#44712yes—
180Dic61#44812yes—
181Dic61#45012yes—
182Dic61#45112yes—
183C22×C4⋊Q8—611no—
184#1797—611no—
185#1797—611no—
186C2×#332—614no—
187C2×C61—24no—
188C2×C61C2×#33211yescharacteristic
189C2×C61#154611yescharacteristic
190C2×C61#154911yescharacteristic
191C2×C61#155611yescharacteristic
192C2×C61#178411yescharacteristic
193C2×C61#178611yescharacteristic
194C2×C61#178711yescharacteristic
195C23×Q8—1221no—
196C2×C4⋊Q8—612no—
197C2×C4⋊Q8—612no—
198C2×C4⋊Q8—1221no—
199C2×C4⋊Q8—1221no—
200C2×C4⋊Q8—1228no—
201C22×C4⋊C4—611no—
202C22×C4⋊C4—1221no—
203C22×C4⋊C4#692311yescharacteristic
204C22×C42—611no—
205C2×C4⋊C8—612no—
206C2×C4⋊C8—612no—
207C2×C22⋊C8—1221no—
208C2×C22⋊C8—1221no—
209#336—1221no—
210#336—1221no—
211#332—1228no—
212C61#834011yescharacteristic, complemented, Sylow
213C22×Q8—1222no—
214C22×Q8—1222no—
215C22×Q8—1228no—
216C22×Q8—2442no—
217C22×Q8—2442no—
218C22×Q8—2444no—
219C23×C4—21no—
220C23×C4—611no—
221C23×C4—611no—
222C23×C4—1221no—
223C23×C4C2×#692311yescharacteristic
224C22×C8—1222no—
225C22×C8—1222no—
226C4⋊Q8—618no—
227C4⋊Q8—1224no—
228C4⋊Q8—1224no—
229C4⋊Q8—1228no—
230C4⋊Q8—1228no—
231C4⋊Q8—1224no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—24no—
234C2×C4⋊C4—612no—
235C2×C4⋊C4—1224no—
236C2×C4⋊C4—1222no—
237C2×C4⋊C4—1222no—
238C2×C4⋊C4—1228no—
239C2×C4⋊C4—1221no—
240C2×C4⋊C4C2×#692312yes—
241C2×C42—611no—
242C2×C42—611no—
243C2×C42—611no—
244C2×C42—611no—
245C2×C42—1224no—
246C4⋊C8—1224no—
247C4⋊C8—1224no—
248C22⋊C8—2442no—
249C22⋊C8—2442no—
250C24C22⋊#692311yescharacteristic
251C2×Q8—1228no—
252C2×Q8—1228no—
253C2×Q8—2442no—
254C2×Q8—2442no—
255C2×Q8—2444no—
256C2×Q8—2444no—
257C2×Q8—24416no—
258C2×Q8—24416no—
259C2×Q8—2444no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—24no—
264C22×C4—22no—
265C22×C4—42no—
266C22×C4—42no—
267C22×C4—611no—
268C22×C4—611no—
269C22×C4—612no—
270C22×C4—612no—
271C22×C4—612no—
272C22×C4—612no—
273C22×C4—611no—
274C22×C4—611no—
275C22×C4—1222no—
276C22×C4—1222no—
277C22×C4—1222no—
278C22×C4—1222no—
279C22×C4—1224no—
280C22×C4—1222no—
281C22×C4—2442no—
282C22×C4—2442no—
283C22×C4C22⋊#692311yescharacteristic
284C22×C4C22×#692311yescharacteristic
285C2×C8—2442no—
286C2×C8—2442no—
287C2×C8—2442no—
288C2×C8—2442no—
289C2×C8—2442no—
290C2×C8—2442no—
291C4⋊C4—24no—
292C4⋊C4—22no—
293C4⋊C4—614no—
294C4⋊C4—1228no—
295C4⋊C4—1228no—
296C4⋊C4—1224no—
297C4⋊C4—1222no—
298C4⋊C4C22⋊#692314yes—
299C42—614no—
300C42—1222no—
301C42—1222no—
302C42—1222no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23#1451983812yes—
308C23#1451983912yes—
309C23#1451984012yes—
310C23C2×C22⋊#692311yescharacteristic
311Q8—2448no—
312Q8—2448no—
313Q8—24416no—
314C2×C4—28no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—24no—
320C2×C4—48no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—611no—
324C2×C4—611no—
325C2×C4—611no—
326C2×C4—611no—
327C2×C4—612no—
328C2×C4—612no—
329C2×C4—612no—
330C2×C4—612no—
331C2×C4—612no—
332C2×C4—612no—
333C2×C4—1224no—
334C2×C4—1224no—
335C2×C4—1224no—
336C2×C4—1224no—
337C2×C4—1221no—
338C2×C4—1221no—
339C2×C4—1221no—
340C2×C4—1221no—
341C2×C4—1224no—
342C2×C4—2448no—
343C2×C4—2442no—
344C2×C4—2442no—
345C2×C4#1451983812yes—
346C2×C4C2×C22⋊#692312yes—
347C8—4882no—
348C8—4882no—
349C22—22no—
350C22—22no—
351C22—22no—
352C22—22no—
353C22—22no—
354C22—22no—
355C22#1684062114yescomplemented
356C22#1684070311yescharacteristic
357C22C2×#1451983811yescharacteristic
358C22C2×#1451983811yescharacteristic
359C22C2×#1451983911yescharacteristic
360C22C2×#1451984011yescharacteristic
361C22#1684075411yescharacteristic
362C22#1684075511yescharacteristic
363C4—22no—
364C4—22no—
365C4—44no—
366C4—612no—
367C4—612no—
368C4—612no—
369C4—612no—
370C4—1222no—
371C4—1222no—
372C4—2444no—
373C2—24no—
374C2C2×#1684062111yescharacteristic
375C2#2146132811yescharacteristic
376C2#2146133411yescharacteristic
377C2#2146134811yescharacteristic
378C2#2146165311yescharacteristic
379C2#2146165711yescharacteristic
380C2#2146165811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC22×C4⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC22×C4⋊C4#6923
hypocenterC61#8340
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#16840621C2semidirect
165. C22×C61#332semidirect
212. C61#8340semidirect
355. C22#16840621semidirect

Maximal subgroups

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

subgroupindex
#214616752
C2×#168406212
C22×#145197762
#834061