Finite Group Databasebeta

← #29598225

Subgroups — #29598225

Order 15616.

614 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840137C211yesmaximal, characteristic
2C2×#16839564C211yesmaximal, characteristic, complemented
3C2×#16839563C211yesmaximal, characteristic, complemented
4C2×#16839562C211yesmaximal, characteristic, complemented
5C2×C16×Dic61C211yesmaximal, characteristic, complemented
6#21445977C211yesmaximal, characteristic, complemented
7C2×C61×#357C211yesmaximal, characteristic, complemented
8C22×D488C2211yescharacteristic
9C22×#11758199—21no—
10C2×#14519773—21no—
11C22×#11758185C2211yescharacteristic
12#16840137—22no—
13#16840137C414yescomplemented
14C2×#14519711C2211yescharacteristic
15C2×#14519710—21no—
16C2×C8×Dic61C2211yescharacteristic
17#16839631—21no—
18#16839564—22no—
19#16839563—22no—
20#16839562—22no—
21C16×Dic61—22no—
22C22×D8×C61C2211yescharacteristic
23C22×C16×C61C2211yescharacteristic
24C2×#107×C61C2211yescharacteristic
25C61×#357—22no—
26C22×D244—21no—
27C22×C22⋊D61—42no—
28C2×D488—21no—
29C2×D488—21no—
30C2×D488—21no—
31C2×D488—21no—
32C2×D488—21no—
33C2×D488C2×C412yes—
34C2×#11758199—24no—
35C2×#11758199—42no—
36C2×#11758199—42no—
37C22×#92418D411yescharacteristic
38#14519773—24no—
39#14519773—42no—
40C2×C4⋊Dic61—21no—
41C2×#11758196—42no—
42C2×C4×Dic61D411yescharacteristic
43C2×#11758185—21no—
44C2×#11758185—21no—
45C2×#11758185D412yescomplemented
46#14519711—21no—
47#14519711—21no—
48#14519710—42no—
49C8×Dic61C2×C412yes—
50C8×Dic61D412yes—
51C22×D4×C61—21no—
52C2×D8×C61—21no—
53C2×D8×C61—21no—
54C2×D8×C61—21no—
55C2×D8×C61—21no—
56C2×D8×C61—21no—
57C2×D8×C61C2×C412yes—
58C22×C8×C61C2311yescharacteristic
59C2×C4⋊C4×C61—21no—
60C2×C16×C61—21no—
61C2×C16×C61—21no—
62C2×C16×C61D412yescomplemented
63#107×C61—21no—
64#107×C61—21no—
65C24×C61—41no—
66C23×D61—41no—
67C2×D4×C61—22no—
68C2×D4×C61—41no—
69C2×D4×C61—41no—
70C2×D4×C61—41no—
71C2×D4×C61—41no—
72C2×D4×C61—41no—
73C22×C4×C61—41no—
74C22×C4×C61C2×D411yescharacteristic
75C2×C22⋊D61—48no—
76C2×C22⋊D61—84no—
77C2×C22⋊D61—84no—
78C22×Dic61—41no—
79C22×Dic61D812yes—
80C2×D244—22no—
81C2×D244—41no—
82C2×D244—41no—
83C2×D244—41no—
84C2×D244—41no—
85C2×D244—41no—
86D8×C61—22no—
87D8×C61—22no—
88D8×C61—41no—
89D8×C61—41no—
90C2×C8×C61C22×C411yescharacteristic
91C2×C8×C61C2×D411yescharacteristic
92C2×C8×C61C2×D411yescharacteristic
93C2×C8×C61C2×D411yescharacteristic
94C2×C8×C61#4111yescharacteristic
95C2×C8×C61#4111yescharacteristic
96C4⋊C4×C61—41no—
97C4⋊C4×C61—41no—
98#11758199—48no—
99C4⋊Dic61—41no—
100C4⋊Dic61—41no—
101#11758196—84no—
102C4×Dic61C22⋊C412yes—
103C4×Dic61SD1612yes—
104C2×#92418C22⋊C412yes—
105C2×#92418D812yes—
106C2×#92418SD1612yes—
107D488—22no—
108D488—22no—
109D488—41no—
110D488—41no—
111C16×C61—22no—
112#11758185—22no—
113C23×C61—42no—
114C23×C61—81no—
115C23×C61—81no—
116C23×C61—82no—
117C23×C61—82no—
118C23×C61C2×D811yescharacteristic
119C22×D61—42no—
120C22×D61—81no—
121C22×D61—81no—
122C22×D61—82no—
123C22×D61—82no—
124D4×C61—42no—
125D4×C61—42no—
126D4×C61—81no—
127D4×C61—81no—
128C2×C4×C61—81no—
129C2×C4×C61—82no—
130C2×C4×C61C2×C22⋊C411yescharacteristic
131C2×C4×C61#12411yescharacteristic
132C2×C4×C61#12711yescharacteristic
133C2×C4×C61C2×D811yescharacteristic
134C2×C4×C61C2×SD1611yescharacteristic
135C2×C4×C61C2×SD1611yescharacteristic
136C22⋊D61—816no—
137C2×Dic61—81no—
138C2×Dic61—82no—
139C2×Dic61#10214yes—
140C2×Dic61D1614yes—
141C2×Dic61SD3214yes—
142D244—42no—
143D244—42no—
144D244—81no—
145D244—81no—
146C8×C61C4×D411yescharacteristic
147C8×C61C4×D411yescharacteristic
148C8×C61#12111yescharacteristic
149C8×C61#12111yescharacteristic
150#92418#10214yes—
151#13202—611nomaximal, Sylow
152C22×C61—84no—
153C22×C61—82no—
154C22×C61—162no—
155C22×C61—161no—
156C22×C61—161no—
157C22×C61C2×#10211yescharacteristic
158C22×C61#48611yescharacteristic
159C22×C61#49311yescharacteristic
160C22×C61C2×D1612yes—
161C22×C61C2×SD3212yes—
162C2×D61—84no—
163C2×D61—82no—
164C2×D61—162no—
165C2×D61—161no—
166C2×D61—161no—
167C4×C61—161no—
168C4×C61#39011yescharacteristic
169C4×C61C2×#10211yescharacteristic
170C4×C61#48611yescharacteristic
171C4×C61#49211yescharacteristic
172Dic61—161no—
173Dic61#35718yescomplemented
174C2×#493—611no—
175C2×#357—611no—
176C2×#357—611no—
177C2×#357—611no—
178C2×#357D6111yescharacteristic, complemented
179C2×C4×C16—611no—
180#1845—611no—
181C2×C61—162no—
182C2×C61#195711yescharacteristic
183C2×C61C2×#35712yes—
184C2×C61#224012yes—
185C2×C61#224611yescharacteristic
186C2×C61#224811yescharacteristic
187D61—162no—
188C22×D8—611no—
189C22×D8—1221no—
190C22×D8C2×D6111yescharacteristic
191C2×#127—1221no—
192C22×C16—611no—
193C22×C16C2×D6111yescharacteristic
194#493—614no—
195#493—1222no—
196C2×#107—611no—
197C2×#107—1221no—
198C2×#107C2×D6111yescharacteristic
199C2×C4×C8—611no—
200#384—1221no—
201#357—22no—
202#357—1222no—
203#357—1222no—
204#357—1222no—
205C4×C16—1222no—
206C61#1320211yescharacteristic, complemented, Sylow
207C22×D4—21no—
208C22×D4—1221no—
209C22×D4—2442no—
210C2×D8—21no—
211C2×D8—21no—
212C2×D8—21no—
213C2×D8—21no—
214C2×D8—21no—
215C2×D8—612no—
216C2×D8—1224no—
217C2×D8—1221no—
218C2×D8—1221no—
219C2×D8—1221no—
220C2×D8—1221no—
221C2×D8—1221no—
222C2×D8—2442no—
223C2×D8—2442no—
224C2×D8C4×D6112yes—
225C22×C8—611no—
226C22×C8C22×D6111yescharacteristic
227#127—1224no—
228#127—2442no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—1221no—
231C2×C4⋊C4—2442no—
232C2×C42—611no—
233C2×C16—21no—
234C2×C16—21no—
235C2×C16—612no—
236C2×C16—1221no—
237C2×C16—1221no—
238C2×C16C22⋊D6112yescomplemented
239#107—21no—
240#107—21no—
241#107—1221no—
242#107—1221no—
243#107—2442no—
244C4×C8—612no—
245C4×C8—612no—
246C24—41no—
247C24—2441no—
248C2×D4—22no—
249C2×D4—41no—
250C2×D4—41no—
251C2×D4—41no—
252C2×D4—41no—
253C2×D4—41no—
254C2×D4—1222no—
255C2×D4—4884no—
256C2×D4—4884no—
257C2×D4—2448no—
258C2×D4—2441no—
259C2×D4—2441no—
260C2×D4—2441no—
261C2×D4—2441no—
262C2×D4—2441no—
263C22×C4—41no—
264C22×C4—612no—
265C22×C4—2441no—
266C22×C4D4×D6111yescharacteristic
267D8—22no—
268D8—22no—
269D8—41no—
270D8—41no—
271D8—1222no—
272D8—1222no—
273D8—2448no—
274D8—2441no—
275D8—2441no—
276C2×C8—612no—
277C2×C8—612no—
278C2×C8—612no—
279C2×C8C2×C4×D6111yescharacteristic
280C2×C8#1175822211yescharacteristic
281C2×C8D4×D6111yescharacteristic
282C2×C8D4×D6111yescharacteristic
283C2×C8#1175822411yescharacteristic
284C2×C8C2×C22⋊D6111yescharacteristic
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—4884no—
288C4⋊C4—2441no—
289C4⋊C4—2441no—
290C42—612no—
291C42—612no—
292C16—22no—
293C16—1222no—
294C23—42no—
295C23—81no—
296C23—81no—
297C23—82no—
298C23—82no—
299C23—4881no—
300C23—4881no—
301C23—4882no—
302C23—4882no—
303C23—2442no—
304C23D8×D6111yescharacteristic
305D4—42no—
306D4—42no—
307D4—81no—
308D4—81no—
309D4—48816no—
310D4—4881no—
311D4—4881no—
312D4—2442no—
313D4—2442no—
314C2×C4—81no—
315C2×C4—82no—
316C2×C4—614no—
317C2×C4—614no—
318C2×C4—614no—
319C2×C4—4881no—
320C2×C4—4882no—
321C2×C4C22⋊C4×D6111yescharacteristic
322C2×C4#1451976311yescharacteristic
323C2×C4#1451977311yescharacteristic
324C2×C4D8×D6111yescharacteristic
325C2×C4SD16×D6111yescharacteristic
326C2×C4SD16×D6111yescharacteristic
327C8—614no—
328C8#1451973711yescharacteristic
329C8C4×C22⋊D6111yescharacteristic
330C8#1451974911yescharacteristic
331C8#1451975011yescharacteristic
332C22—84no—
333C22—82no—
334C22—162no—
335C22—161no—
336C22—161no—
337C22—9762no—
338C22—9761no—
339C22—9761no—
340C22—4884no—
341C22—4882no—
342C22#102×D6111yescharacteristic
343C22#1684010711yescharacteristic
344C22#1684013711yescharacteristic
345C22D16×D6112yes—
346C22SD32×D6112yes—
347C4—161no—
348C4—618no—
349C4—9761no—
350C4#1683966211yescharacteristic
351C4#102×D6111yescharacteristic
352C4#1684010711yescharacteristic
353C4#1684013311yescharacteristic
354C2—162no—
355C2—9762no—
356C2#2144662311yescharacteristic
357C2#357×D6112yes—
358C2#2144804112yes—
359C2#2144806711yescharacteristic
360C2#2144807311yescharacteristic
subgroupG/H
centerC23D8×D61
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC2×C61×#357C2
socleC23×C61C2×D8
prime radicalC2×#16840137C2
cosocleC22×C8×C61C23
hypercenterC2×#357D61
hypocenterC61#13202
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

Complements

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

NH ≅ G/Ntype
2. C2×#16839564C2semidirect
3. C2×#16839563C2semidirect
4. C2×#16839562C2semidirect
5. C2×C16×Dic61C2semidirect
6. #21445977C2semidirect
7. C2×C61×#357C2semidirect
13. #16840137C4semidirect
45. C2×#11758185D4semidirect
62. C2×C16×C61D4semidirect
173. Dic61#357semidirect
178. C2×#357D61semidirect
206. C61#13202semidirect
238. C2×C16C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168401372
C2×#168395642
C2×#168395632
C2×#168395622
C2×C16×Dic612
#214459772
C2×C61×#3572
#1320261