Finite Group Databasebeta

← #30598926

Subgroups — #30598926

Order 15616.

516 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461752C211yesmaximal, characteristic
2#21461752C211yesmaximal, characteristic
3C2×#16840621C212yesmaximal
4#21460697C212yesmaximal
5#21448390C211yesmaximal, characteristic
6C2×#14519844—21no—
7C2×#14519844—21no—
8C2×#14519844C2212yes—
9C2×#14519844C2212yes—
10C2×C4⋊#92420—21no—
11C2×C4⋊#92420—21no—
12#16840621—24no—
13C2×#14519776C2211yescharacteristic
14C2×#14519742—21no—
15#16839666—21no—
16#16839660C411yescharacteristic
17#16839657—21no—
18#16839631C2211yescharacteristic
19C4⋊C4×Dic61C411yescharacteristic
20C4⋊C4×Dic61C411yescharacteristic
21#16839613—21no—
22C42×Dic61C2211yescharacteristic
23C61×#389C411yescharacteristic
24C22×#92420—22no—
25C22×#92420—22no—
26#14519844—22no—
27#14519844—22no—
28#14519844—22no—
29#14519844—22no—
30#14519844—42no—
31#14519844—42no—
32C4⋊#92420—42no—
33C4⋊#92420—42no—
34C22×Dic122—21no—
35#14519776—21no—
36#14519776—21no—
37#14519776D412yes—
38#14519776Q812yes—
39#14519742—42no—
40#14519742—42no—
41C2×C4⋊Dic61C2×C411yescharacteristic
42C2×C4⋊Dic61C2×C411yescharacteristic
43C2×#11758196—21no—
44C2×#11758196—21no—
45C2×#11758196—21no—
46C2×#11758196—21no—
47C2×C4×Dic61—21no—
48C2×C4×Dic61—21no—
49C2×C4×Dic61C2×C411yescharacteristic
50C2×C4×Dic61D411yescharacteristic
51C2×C4×Dic61D411yescharacteristic
52C2×C4×Dic61D411yescharacteristic
53C2×C4×Dic61D411yescharacteristic
54C2×C4×Dic61C2311yescharacteristic
55#14519684—21no—
56#14519684—21no—
57#14519684—21no—
58C2×C4⋊C4×C61—21no—
59C2×C4⋊C4×C61C2×C411yescharacteristic
60C2×C4⋊C4×C61C2×C411yescharacteristic
61C2×C42×C61C2×C411yescharacteristic
62#95×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C22×C411yescharacteristic
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61C22⋊C411yescharacteristic
72C22×Dic61C2×D411yescharacteristic
73C22×Dic61C2×D411yescharacteristic
74C2×Dic122—22no—
75C2×Dic122—22no—
76C2×Dic122—41no—
77C2×Dic122—41no—
78C2×Dic122—41no—
79C2×Dic122—41no—
80C2×#92420—42no—
81C2×#92420—42no—
82C2×#92420—42no—
83C2×#92420—42no—
84C2×#92420—42no—
85C2×#92420—42no—
86C4⋊C4×C61—21no—
87C4⋊C4×C61—41no—
88C4⋊C4×C61—42no—
89C4⋊C4×C61C4⋊C412yes—
90C42×C61—41no—
91C4⋊Dic61—21no—
92C4⋊Dic61—41no—
93C4⋊Dic61C4⋊C412yes—
94#11758196—22no—
95#11758196—22no—
96#11758196—42no—
97#11758196—41no—
98#11758196—41no—
99#11758196—41no—
100#11758196—41no—
101C4×Dic61—22no—
102C4×Dic61—21no—
103C4×Dic61—21no—
104C4×Dic61—21no—
105C4×Dic61—21no—
106C4×Dic61—42no—
107C4×Dic61—42no—
108C4×Dic61D812yes—
109C4×Dic61SD1612yes—
110C4×Dic61SD1612yes—
111C4×Dic61Q1612yes—
112C4×Dic61C2×D411yescharacteristic
113C4×Dic61C2×Q811yescharacteristic
114C4×Dic61#4111yescharacteristic
115C4×Dic61#4111yescharacteristic
116C23×C61C2×C22⋊C411yescharacteristic
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—22no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61#10212yes—
130C2×C4×C61#10312yes—
131C2×C4×C61C2×C4⋊C411yescharacteristic
132C2×C4×C61#11711yescharacteristic
133C2×Dic61—22no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61#10112yes—
143C2×Dic61#10212yes—
144C2×Dic61#10312yes—
145C2×Dic61#12111yescharacteristic
146C2×Dic61#12111yescharacteristic
147C2×Dic61C22⋊Q811yescharacteristic
148C2×Dic61C22⋊Q811yescharacteristic
149C2×Dic61C2×D811yescharacteristic
150C2×Dic61C2×SD1611yescharacteristic
151C2×Dic61C2×SD1611yescharacteristic
152C2×Dic61C2×Q1611yescharacteristic
153C2×Dic61AGL(1,ℤ/8)11yescharacteristic
154C2×Dic61AGL(1,ℤ/8)11yescharacteristic
155C2×Dic61#13711yescharacteristic
156C2×Dic61#13711yescharacteristic
157Dic122—42no—
158Dic122—42no—
159Dic122—42no—
160Dic122—42no—
161#92420—82no—
162#92420—82no—
163#8586—611nomaximal, Sylow
164C22×C61#38011yescharacteristic
165C22×C61C2×#10111yescharacteristic
166C22×C61#41311yescharacteristic
167C22×C61C2×#10211yescharacteristic
168C22×C61C2×#10311yescharacteristic
169C22×C61#41711yescharacteristic
170C22×C61#41711yescharacteristic
171C4×C61—21no—
172C4×C61—21no—
173C4×C61—22no—
174C4×C61—22no—
175C4×C61—42no—
176C4×C61—81no—
177Dic61—42no—
178Dic61—41no—
179Dic61—81no—
180Dic61#33214yescomplemented
181Dic61#45911yescharacteristic
182Dic61#46011yescharacteristic
183Dic61#46111yescharacteristic
184Dic61#46211yescharacteristic
185Dic61#47411yescharacteristic
186Dic61#47511yescharacteristic
187Dic61#47611yescharacteristic
188Dic61#47711yescharacteristic
189C4×C4⋊Q8—611no—
190#1842—611no—
191#1842—611no—
192C2×#332—612no—
193#1296—612no—
194C2×C61C2×#33211yescharacteristic
195C2×C61#154711yescharacteristic
196C2×C61#155011yescharacteristic
197C2×C61#156111yescharacteristic
198C2×C61#180111yescharacteristic
199C2×C61#180211yescharacteristic
200C2×C61#180311yescharacteristic
201C2×C4⋊Q8—611no—
202C2×C4×Q8—1221no—
203C2×C4⋊C8—612no—
204C2×C4⋊C8—612no—
205C2×C4⋊C8—1221no—
206C2×C4⋊C8—1221no—
207C2×C4⋊C8—1221no—
208C2×C4⋊C8—1221no—
209#391—1221no—
210#389—611no—
211#389—1221no—
212#389#692311yescharacteristic
213#384—611no—
214C4×C4⋊C4—611no—
215C4×C4⋊C4—611no—
216C4×C4⋊C4—1221no—
217C43—611no—
218#332—1224no—
219C61#858611yescharacteristic, complemented, Sylow
220C22×Q8—1221no—
221C22×C8—1222no—
222C22×C8—1222no—
223C4⋊Q8—612no—
224C4⋊Q8—612no—
225C4⋊Q8—1221no—
226C4⋊Q8—1221no—
227C4×Q8—2442no—
228C4×Q8—2442no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—611no—
231C2×C4⋊C4—611no—
232C2×C4⋊C4—1221no—
233C2×C4⋊C4—1221no—
234C2×C4⋊C4—1221no—
235C2×C4⋊C4—1221no—
236C2×C4⋊C4C2×#692311yescharacteristic
237C2×C4⋊C4C2×#692311yescharacteristic
238C2×C42—611no—
239C2×C42—611no—
240C2×C42—611no—
241C2×C42—611no—
242C2×C42—611no—
243C2×C42—611no—
244C2×C42—1221no—
245C2×C42—1221no—
246C2×C42C2×#692311yescharacteristic
247C4⋊C8—1222no—
248C4⋊C8—1222no—
249C4⋊C8—1222no—
250C4⋊C8—1222no—
251C4⋊C8—2442no—
252C4⋊C8—2442no—
253C4⋊C8—2442no—
254C4⋊C8—2442no—
255#95—21no—
256#95—1221no—
257#95—1221no—
258#95—1221no—
259C2×Q8—1222no—
260C2×Q8—1222no—
261C2×Q8—2441no—
262C2×Q8—2441no—
263C2×Q8—2441no—
264C2×Q8—2441no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—611no—
268C22×C4—611no—
269C22×C4—611no—
270C22×C4—611no—
271C22×C4—1221no—
272C22×C4—1221no—
273C22×C4C22⋊#692311yescharacteristic
274C22×C4C22⋊#692311yescharacteristic
275C22×C4C22×#692311yescharacteristic
276C2×C8—2442no—
277C2×C8—2442no—
278C2×C8—2442no—
279C2×C8—2442no—
280C2×C8—2442no—
281C2×C8—2442no—
282C4⋊C4—21no—
283C4⋊C4—41no—
284C4⋊C4—42no—
285C4⋊C4—612no—
286C4⋊C4—1222no—
287C4⋊C4—1222no—
288C4⋊C4—1221no—
289C4⋊C4—2441no—
290C4⋊C4—2441no—
291C4⋊C4—2441no—
292C4⋊C4—2441no—
293C4⋊C4—2441no—
294C4⋊C4—2442no—
295C4⋊C4C4⋊#692312yes—
296C42—41no—
297C42—612no—
298C42—612no—
299C42—612no—
300C42—612no—
301C42—611no—
302C42—611no—
303C42—611no—
304C42—611no—
305C42—1221no—
306C42—1221no—
307C42—1222no—
308C42—1221no—
309C42—1221no—
310C42—2442no—
311C42—2442no—
312C23C2×C22⋊#692311yescharacteristic
313Q8—2442no—
314Q8—2442no—
315Q8—2442no—
316Q8—2442no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—22no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—611no—
330C2×C4—611no—
331C2×C4—611no—
332C2×C4—611no—
333C2×C4—612no—
334C2×C4—612no—
335C2×C4—611no—
336C2×C4—611no—
337C2×C4—612no—
338C2×C4—611no—
339C2×C4—611no—
340C2×C4—611no—
341C2×C4—611no—
342C2×C4—611no—
343C2×C4—611no—
344C2×C4—1222no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—2441no—
349C2×C4—2441no—
350C2×C4—2441no—
351C2×C4—2441no—
352C2×C4—2441no—
353C2×C4#1451983912yes—
354C2×C4#1451984012yes—
355C2×C4C2×C4⋊#692311yescharacteristic
356C2×C4#1451985611yescharacteristic
357C8—4882no—
358C8—4882no—
359C22#1684070411yescharacteristic
360C22D61⋊#10111yescharacteristic
361C22#1684074911yescharacteristic
362C22C2×#1451983911yescharacteristic
363C22C2×#1451984011yescharacteristic
364C22#1684075311yescharacteristic
365C22#1684075311yescharacteristic
366C4—22no—
367C4—22no—
368C4—21no—
369C4—21no—
370C4—42no—
371C4—81no—
372C4—614no—
373C4—611no—
374C4—611no—
375C4—611no—
376C4—611no—
377C4—611no—
378C4—611no—
379C4—611no—
380C4—611no—
381C4—4881no—
382C4—2441no—
383C4—2442no—
384C2D61⋊#33211yescharacteristic
385C2#2146133111yescharacteristic
386C2#2146133711yescharacteristic
387C2#2146135911yescharacteristic
388C2#2146168611yescharacteristic
389C2#2146168711yescharacteristic
390C2#2146168811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#389C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#389#6923
hypocenterC61#8586
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
180. Dic61#332semidirect
219. C61#8586semidirect

Maximal subgroups

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

subgroupindex
#214617522
C2×#168406212
#214606972
#214483902
#858661