Finite Group Databasebeta

← #30602154

Subgroups — #30602154

Order 15616.

506 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461751C211yesmaximal, characteristic
2#21461534C211yesmaximal, characteristic
3#21460655C212yesmaximal
4#21460655C212yesmaximal
5#21448390C211yesmaximal, characteristic
6C2×C4⋊#92420—21no—
7C2×C4⋊#92420—21no—
8C2×C4⋊#92420C2212yes—
9C2×C4×#92420C2212yes—
10#16840628—21no—
11#16840628—21no—
12C2×#14519776C411yescharacteristic
13C2×#14519742—21no—
14#16839666—21no—
15#16839660C411yescharacteristic
16#16839657—21no—
17#16839631C411yescharacteristic
18C4⋊C4×Dic61C2211yescharacteristic
19C4⋊C4×Dic61C2211yescharacteristic
20#16839613—21no—
21C42×Dic61C2211yescharacteristic
22C61×#389C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25C4⋊#92420—24no—
26C4⋊#92420—42no—
27C4⋊#92420—42no—
28C4×#92420—22no—
29C4×#92420Q814yescomplemented
30C22×Dic122—21no—
31#14519776—22no—
32#14519776—22no—
33#14519742—42no—
34#14519742—42no—
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×C4⋊Dic61C2×C411yescharacteristic
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×C4×Dic61—21no—
42C2×C4×Dic61—21no—
43C2×C4×Dic61C2×C411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48C2×C4×Dic61C2311yescharacteristic
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52C2×C4⋊C4×C61—21no—
53C2×C4⋊C4×C61C2×C411yescharacteristic
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C42×C61C2×C411yescharacteristic
56#95×C61—21no—
57C22×C4×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61C22⋊C411yescharacteristic
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C22×C411yescharacteristic
62C22×Dic61—21no—
63C22×Dic61—21no—
64C22×Dic61C22⋊C411yescharacteristic
65C22×Dic61C22⋊C411yescharacteristic
66C22×Dic61C2×D411yescharacteristic
67C22×Dic61C2×D411yescharacteristic
68C2×Dic122—24no—
69C2×Dic122—42no—
70C2×Dic122—42no—
71C2×#92420—24no—
72C2×#92420—42no—
73C2×#92420—42no—
74C2×#92420—42no—
75C2×#92420—42no—
76C2×#92420—42no—
77C4⋊C4×C61—21no—
78C4⋊C4×C61—22no—
79C4⋊C4×C61—42no—
80C4⋊C4×C61M1612yes—
81C42×C61—22no—
82C4⋊Dic61—21no—
83C4⋊Dic61—22no—
84C4⋊Dic61M1612yes—
85#11758196—24no—
86#11758196—42no—
87#11758196—42no—
88#11758196—42no—
89C4×Dic61—21no—
90C4×Dic61—21no—
91C4×Dic61—41no—
92C4×Dic61—41no—
93C4×Dic61—41no—
94C4×Dic61—41no—
95C4×Dic61—41no—
96C4×Dic61—41no—
97C4×Dic61D812yes—
98C4×Dic61SD1612yes—
99C4×Dic61SD1612yes—
100C4×Dic61Q1612yes—
101C4×Dic61C2×Q812yes—
102C4×Dic61#4112yes—
103C23×C61C2×C22⋊C411yescharacteristic
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—22no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61#10212yes—
115C2×C4×C61#10312yes—
116C2×C4×C61C4×Q812yes—
117C2×C4×C61C2×M1611yescharacteristic
118C2×C4×C61C2×M1611yescharacteristic
119C2×C4×C61#13112yes—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—22no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61#10212yes—
133C2×Dic61#10312yes—
134C2×Dic61C22⋊Q812yes—
135C2×Dic61#12411yescharacteristic
136C2×Dic61C4⋊Q811yescharacteristic
137C2×Dic61C2×D811yescharacteristic
138C2×Dic61C2×SD1611yescharacteristic
139C2×Dic61C2×SD1611yescharacteristic
140C2×Dic61C2×Q1611yescharacteristic
141Dic122—48no—
142#92420—44no—
143#92420—82no—
144#9874—611nomaximal, Sylow
145C22×C61#39111yescharacteristic
146C22×C61#40711yescharacteristic
147C22×C61#40811yescharacteristic
148C22×C61C2×#10211yescharacteristic
149C22×C61C2×#10311yescharacteristic
150C22×C61#42111yescharacteristic
151C22×C61#42111yescharacteristic
152C4×C61—22no—
153C4×C61—22no—
154C4×C61—42no—
155C4×C61—81no—
156C4×C61#44612yes—
157C4×C61#44612yes—
158Dic61—22no—
159Dic61—22no—
160Dic61—22no—
161Dic61—42no—
162Dic61—81no—
163Dic61#48611yescharacteristic
164Dic61#48711yescharacteristic
165Dic61#49811yescharacteristic
166Dic61#50011yescharacteristic
167C4×C4⋊Q8—611no—
168#1842—611no—
169#1744—611no—
170#1279—612no—
171#1279—612no—
172C2×C61#148011yescharacteristic
173C2×C61#148111yescharacteristic
174C2×C61#148611yescharacteristic
175C2×C61#148711yescharacteristic
176C2×C61#198511yescharacteristic
177C2×C61#199011yescharacteristic
178C2×C61#199511yescharacteristic
179C2×C4⋊Q8—611no—
180C2×C4×Q8—1221no—
181C2×C4⋊C8—612no—
182C2×C4⋊C8—1221no—
183C2×C4⋊C8—1221no—
184C2×C4×C8—612no—
185#391—1221no—
186#389—611no—
187#389—1221no—
188#389#692311yescharacteristic
189#384—611no—
190C4×C4⋊C4—611no—
191C4×C4⋊C4—611no—
192C4×C4⋊C4—1221no—
193C43—611no—
194#336—1221no—
195#336—1221no—
196C61#987411yescharacteristic, complemented, Sylow
197C22×Q8—1221no—
198C22×C8—1222no—
199C22×C8—1222no—
200C4⋊Q8—1222no—
201C4⋊Q8—1222no—
202C4×Q8—2442no—
203C4×Q8—2442no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—611no—
206C2×C4⋊C4—611no—
207C2×C4⋊C4—1221no—
208C2×C4⋊C4—1221no—
209C2×C4⋊C4—1221no—
210C2×C4⋊C4—1221no—
211C2×C4⋊C4C2×#692311yescharacteristic
212C2×C4⋊C4C2×#692311yescharacteristic
213C2×C42—611no—
214C2×C42—611no—
215C2×C42—611no—
216C2×C42—611no—
217C2×C42—611no—
218C2×C42—611no—
219C2×C42—1221no—
220C2×C42—1221no—
221C2×C42C2×#692311yescharacteristic
222C4⋊C8—1224no—
223C4⋊C8—2442no—
224C4⋊C8—2442no—
225C4×C8—614no—
226C4×C8—1222no—
227#95—21no—
228#95—1221no—
229#95—1221no—
230#95—1221no—
231C2×Q8—1224no—
232C2×Q8—2442no—
233C2×Q8—2442no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—611no—
237C22×C4—611no—
238C22×C4—611no—
239C22×C4—611no—
240C22×C4—1221no—
241C22×C4—1221no—
242C22×C4C22⋊#692311yescharacteristic
243C22×C4C22⋊#692311yescharacteristic
244C22×C4C22×#692311yescharacteristic
245C2×C8—1224no—
246C2×C8—2442no—
247C2×C8—2442no—
248C2×C8—2442no—
249C2×C8—2442no—
250C2×C8—2442no—
251C4⋊C4—21no—
252C4⋊C4—22no—
253C4⋊C4—42no—
254C4⋊C4—612no—
255C4⋊C4—1224no—
256C4⋊C4—1221no—
257C4⋊C4—1222no—
258C4⋊C4—2442no—
259C4⋊C4—2442no—
260C4⋊C4—2442no—
261C4⋊C4#1175821312yes—
262C42—22no—
263C42—612no—
264C42—612no—
265C42—612no—
266C42—612no—
267C42—612no—
268C42—612no—
269C42—1221no—
270C42—1221no—
271C42—2441no—
272C42—2441no—
273C42—2441no—
274C42—2441no—
275C42—2441no—
276C42—2441no—
277C23C2×C22⋊#692311yescharacteristic
278Q8—2448no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—22no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—611no—
290C2×C4—611no—
291C2×C4—611no—
292C2×C4—611no—
293C2×C4—611no—
294C2×C4—611no—
295C2×C4—612no—
296C2×C4—612no—
297C2×C4—612no—
298C2×C4—1221no—
299C2×C4—1221no—
300C2×C4—1221no—
301C2×C4—1221no—
302C2×C4—1221no—
303C2×C4—1221no—
304C2×C4—1222no—
305C2×C4—2441no—
306C2×C4—2441no—
307C2×C4—2441no—
308C2×C4—2441no—
309C2×C4—2441no—
310C2×C4#1451983912yes—
311C2×C4#1451984012yes—
312C2×C4Q8×#692312yes—
313C2×C4D61⋊M1611yescharacteristic
314C2×C4C2×#1175821311yescharacteristic
315C2×C4#1451986412yes—
316C8—4882no—
317C8—2444no—
318C22(C2×#6923)⋊Q811yescharacteristic
319C22#1684073311yescharacteristic
320C22#1684073511yescharacteristic
321C22C2×#1451983911yescharacteristic
322C22C2×#1451984011yescharacteristic
323C22#1684075911yescharacteristic
324C22#1684075911yescharacteristic
325C4—22no—
326C4—22no—
327C4—42no—
328C4—81no—
329C4—611no—
330C4—611no—
331C4—611no—
332C4—611no—
333C4—1222no—
334C4—1222no—
335C4—1222no—
336C4—4881no—
337C4—2442no—
338C4#1684081212yes—
339C4#1684081412yes—
340C2#2146112411yescharacteristic
341C2#2146112711yescharacteristic
342C2#2146114511yescharacteristic
343C2#2146114811yescharacteristic
344C2#2146199211yescharacteristic
345C2#2146200011yescharacteristic
346C2#2146200611yescharacteristic
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#9874
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
29. C4×#92420Q8semidirect
196. C61#9874semidirect

Maximal subgroups

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

subgroupindex
#214617512
#214615342
#214606552
#214483902
#987461