Finite Group Databasebeta

← #30601530

Subgroups — #30601530

Order 15616.

404 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461752C211yesmaximal, characteristic
2C4×C4⋊#92420C211yesmaximal, characteristic
3C2×#16840624C211yesmaximal, characteristic
4C2×#16840623C211yesmaximal, characteristic
5#21460649C211yesmaximal, characteristic
6#21460649C211yesmaximal, characteristic
7#21445667C211yesmaximal, characteristic
8C2×#14519844—21no—
9C2×#14519844—21no—
10C2×C4⋊#92420C2211yescharacteristic
11C2×C4⋊#92420C2211yescharacteristic
12C2×C4⋊#92420C2211yescharacteristic
13C2×C4⋊#92420C2211yescharacteristic
14C2×C4×#92420—21no—
15#16840628—21no—
16#16840624—22no—
17#16840623—22no—
18C2×#14519706C411yescharacteristic
19C2×#14519706C411yescharacteristic
20C2×C8×Dic61C2211yescharacteristic
21C2×C8×Dic61C2211yescharacteristic
22C42×Dic61C2211yescharacteristic
23#16839517C411yescharacteristic
24C61×#336C411yescharacteristic
25C22×#92420—21no—
26C22×#92420—21no—
27C22×#92420—21no—
28C22×#92420—21no—
29#14519844—42no—
30#14519844—42no—
31C4⋊#92420—21no—
32C4⋊#92420—21no—
33C4⋊#92420—21no—
34C4⋊#92420—21no—
35C4⋊#92420—21no—
36C4⋊#92420—21no—
37C4⋊#92420D412yes—
38C4⋊#92420Q812yes—
39C4×#92420—42no—
40C22×#92418C2×C411yescharacteristic
41C22×#92418C2×C411yescharacteristic
42C2×C4×Dic61C2×C411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61Q811yescharacteristic
46C2×C4×Dic61Q811yescharacteristic
47C2×C4×Dic61C2311yescharacteristic
48#14519706—22no—
49#14519706C814yescomplemented
50C8×Dic61—21no—
51C8×Dic61—21no—
52C8×Dic61—21no—
53C8×Dic61—21no—
54C22×C8×C61C2×C411yescharacteristic
55C22×C8×C61C2×C411yescharacteristic
56C2×C42×C61C2×C411yescharacteristic
57C22×C4×C61C4⋊C411yescharacteristic
58C22×C4×C61C4⋊C411yescharacteristic
59C22×C4×C61C22×C411yescharacteristic
60C22×Dic61C4⋊C411yescharacteristic
61C22×Dic61C4⋊C411yescharacteristic
62C22×Dic61C2×D411yescharacteristic
63C22×Dic61C2×Q811yescharacteristic
64C2×#92420—22no—
65C2×#92420—22no—
66C2×#92420—41no—
67C2×#92420—41no—
68C2×#92420—41no—
69C2×#92420—41no—
70C2×#92420—41no—
71C2×#92420—41no—
72C2×#92420—41no—
73C2×#92420—41no—
74C2×#92420—41no—
75C2×#92420—41no—
76C2×C8×C61—21no—
77C2×C8×C61—21no—
78C2×C8×C61—21no—
79C2×C8×C61—21no—
80C2×C8×C61—21no—
81C2×C8×C61C2×C812yes—
82C42×C61—21no—
83C42×C61—21no—
84C4×Dic61—22no—
85C4×Dic61—21no—
86C4×Dic61—21no—
87C4×Dic61—41no—
88C4×Dic61C2×C812yes—
89C4×Dic61M1612yes—
90C4×Dic61SD1612yes—
91C4×Dic61SD1612yes—
92C4×Dic61C2×D411yescharacteristic
93C4×Dic61C2×Q811yescharacteristic
94C4×Dic61#4111yescharacteristic
95C4×Dic61#4111yescharacteristic
96C2×#92418—21no—
97C2×#92418—21no—
98C2×#92418—21no—
99C2×#92418—21no—
100C2×#92418—21no—
101C2×#92418C2×C812yes—
102C23×C61C2×C4⋊C411yescharacteristic
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61#10612yes—
109C2×C4×C61C4×D411yescharacteristic
110C2×C4×C61C4×Q811yescharacteristic
111C2×C4×C61C22×C811yescharacteristic
112C2×C4×C61C2×M1611yescharacteristic
113C2×C4×C61#13111yescharacteristic
114C2×C4×C61#13111yescharacteristic
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61C4⋊C812yes—
120C2×Dic61C4⋊C812yes—
121C2×Dic61#10612yes—
122C2×Dic61#10812yes—
123C2×Dic61#12111yescharacteristic
124C2×Dic61C22⋊Q811yescharacteristic
125C2×Dic61#12511yescharacteristic
126C2×Dic61C4⋊Q811yescharacteristic
127C2×Dic61C2×SD1611yescharacteristic
128C2×Dic61C2×SD1611yescharacteristic
129C2×Dic61AGL(1,ℤ/8)11yescharacteristic
130C2×Dic61#13711yescharacteristic
131#92420—42no—
132#92420—42no—
133#92420—81no—
134#92420—81no—
135C8×C61—22no—
136C8×C61—41no—
137#92418—22no—
138#92418—41no—
139#9602—611nomaximal, Sylow
140C22×C61#38911yescharacteristic
141C22×C61C2×C4⋊C811yescharacteristic
142C22×C61#42411yescharacteristic
143C22×C61C2×#10611yescharacteristic
144C22×C61#42811yescharacteristic
145C22×C61C2×#10811yescharacteristic
146C22×C61#43011yescharacteristic
147C4×C61—22no—
148C4×C61—41no—
149C4×C61C8×D411yescharacteristic
150C4×C61#43611yescharacteristic
151C4×C61C8×Q811yescharacteristic
152C4×C61#44611yescharacteristic
153Dic61—22no—
154Dic61—21no—
155Dic61—21no—
156Dic61#33414yescomplemented
157Dic61#46011yescharacteristic
158Dic61#46111yescharacteristic
159Dic61#47511yescharacteristic
160Dic61#47611yescharacteristic
161#1842—611no—
162C4×C4⋊C8—611no—
163C4×C4⋊C8—611no—
164C2×#334—611no—
165C2×#334—611no—
166#1277—611no—
167#1277—611no—
168C2×C61C2×#33411yescharacteristic
169C2×C61#156511yescharacteristic
170C2×C61#157011yescharacteristic
171C2×C61#157411yescharacteristic
172C2×C61#193911yescharacteristic
173C2×C61#194811yescharacteristic
174C2×C61#195011yescharacteristic
175C2×C4⋊C8—611no—
176C2×C4⋊C8—611no—
177C2×C4⋊C8—611no—
178C2×C4⋊C8—611no—
179C2×C4⋊C8—611no—
180C2×C4⋊C8—611no—
181C2×C4⋊C8—1221no—
182C2×C4⋊C8—1221no—
183C2×C4×C8—611no—
184C2×C4×C8—611no—
185C2×C4×C8—1221no—
186C43—611no—
187#336—611no—
188#336—1221no—
189#336#692311yescharacteristic
190#334—1222no—
191#334—1222no—
192C61#960211yescharacteristic, complemented, Sylow
193C22×C8—611no—
194C22×C8—611no—
195C22×C8—1221no—
196C22×C8—1221no—
197C22×C8—1221no—
198C22×C8—1221no—
199C22×C8C2×#692311yescharacteristic
200C22×C8C2×#692311yescharacteristic
201C2×C42—611no—
202C2×C42—611no—
203C2×C42—611no—
204C2×C42—611no—
205C2×C42—611no—
206C2×C42—611no—
207C2×C42C2×#692311yescharacteristic
208C4⋊C8—614no—
209C4⋊C8—612no—
210C4⋊C8—612no—
211C4⋊C8—1222no—
212C4⋊C8—1221no—
213C4⋊C8—1221no—
214C4⋊C8—1221no—
215C4⋊C8—1221no—
216C4⋊C8—1221no—
217C4⋊C8—1221no—
218C4⋊C8—2442no—
219C4⋊C8—2442no—
220C4×C8—1221no—
221C4×C8—1221no—
222C4×C8—1221no—
223C4×C8—1221no—
224C4×C8—2442no—
225C22×C4—611no—
226C22×C4—611no—
227C22×C4—611no—
228C22×C4—611no—
229C22×C4C4⋊#692311yescharacteristic
230C22×C4C4⋊#692311yescharacteristic
231C22×C4C22×#692311yescharacteristic
232C2×C8—21no—
233C2×C8—21no—
234C2×C8—21no—
235C2×C8—21no—
236C2×C8—21no—
237C2×C8—612no—
238C2×C8—1221no—
239C2×C8—1221no—
240C2×C8—1222no—
241C2×C8—1222no—
242C2×C8—1221no—
243C2×C8—1221no—
244C2×C8—1221no—
245C2×C8—2441no—
246C2×C8—2441no—
247C2×C8—2441no—
248C2×C8—2441no—
249C2×C8—2441no—
250C2×C8—2441no—
251C2×C8—2441no—
252C2×C8—2441no—
253C2×C8—2441no—
254C2×C8—2441no—
255C2×C8D61⋊C812yes—
256C42—21no—
257C42—21no—
258C42—612no—
259C42—612no—
260C42—611no—
261C42—611no—
262C42—611no—
263C42—611no—
264C42—612no—
265C42—612no—
266C42—1221no—
267C42—1221no—
268C42—1222no—
269C42—2441no—
270C23C2×C4⋊#692311yescharacteristic
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—611no—
277C2×C4—611no—
278C2×C4—612no—
279C2×C4—612no—
280C2×C4—611no—
281C2×C4—611no—
282C2×C4—611no—
283C2×C4—611no—
284C2×C4—612no—
285C2×C4—611no—
286C2×C4—611no—
287C2×C4—612no—
288C2×C4—1221no—
289C2×C4—1221no—
290C2×C4—1221no—
291C2×C4—1221no—
292C2×C4#1451984512yes—
293C2×C4D4×#692311yescharacteristic
294C2×C4Q8×#692311yescharacteristic
295C2×C4C2×D61⋊C811yescharacteristic
296C2×C4D61⋊M1611yescharacteristic
297C2×C4#1451986411yescharacteristic
298C2×C4#1451986411yescharacteristic
299C8—22no—
300C8—41no—
301C8—1222no—
302C8—4881no—
303C8—4881no—
304C8—2442no—
305C8—2442no—
306C8—2441no—
307C22#1684071311yescharacteristic
308C22D61⋊(C4⋊C8)11yescharacteristic
309C22#1684076811yescharacteristic
310C22C2×#1451984511yescharacteristic
311C22#1684077311yescharacteristic
312C22D61⋊#10811yescharacteristic
313C22#1684077711yescharacteristic
314C4—22no—
315C4—41no—
316C4—614no—
317C4—611no—
318C4—611no—
319C4—611no—
320C4—611no—
321C4—1222no—
322C4—1221no—
323C4—1221no—
324C4#1684078911yescharacteristic
325C4#1684079511yescharacteristic
326C4#1684081111yescharacteristic
327C4#1684081411yescharacteristic
328C2D61⋊#33411yescharacteristic
329C2#2146137111yescharacteristic
330C2#2146138611yescharacteristic
331C2#2146139511yescharacteristic
332C2#2146191811yescharacteristic
333C2#2146193111yescharacteristic
334C2#2146193511yescharacteristic
subgroupG/H
centerC23C2×C4⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#336C4
socle, prime radicalC23×C61C2×C4⋊C4
cosocleC2×C4×Dic61C23
hypercenter#336#6923
hypocenterC61#9602
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #336

Complements

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

NH ≅ G/Ntype
49. #14519706C8semidirect
156. Dic61#334semidirect
192. C61#9602semidirect

Maximal subgroups

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

subgroupindex
#214617522
C4×C4⋊#924202
C2×#168406242
C2×#168406232
#214606492
#214456672
#960261