Finite Group Databasebeta

← #30607407

Subgroups — #30607407

Order 15616.

420 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D61⋊#108C211yesmaximal, characteristic
2C2×#16840687C211yesmaximal, characteristic, complemented
3C2×#16840686C211yesmaximal, characteristic, complemented
4#21461695C211yesmaximal, characteristic
5#21460884C211yesmaximal, characteristic, complemented
6#21460884C211yesmaximal, characteristic, complemented
7#21447428C211yesmaximal, characteristic
8C2×D61⋊M16—21no—
9C2×#14519848—21no—
10D61⋊#108—22no—
11D61⋊#108—22no—
12C2×#14519847C2211yescharacteristic
13C2×#14519847C2211yescharacteristic
14C2×#14519845C2211yescharacteristic
15C2×#14519845C2211yescharacteristic
16#16840704—21no—
17#16840687—22no—
18#16840686—22no—
19#16840636—21no—
20C22×C8×D61C2211yescharacteristic
21C2×#14519716C2211yescharacteristic
22C2×#14519716C2211yescharacteristic
23C22⋊#11758185C411yescharacteristic, complemented
24#16839541C411yescharacteristic, complemented
25#16839541C411yescharacteristic, complemented
26C61×C22⋊C16C411yescharacteristic, complemented
27C2×#11758213—21no—
28C2×#11758213—21no—
29D61⋊M16—24no—
30D61⋊M16—42no—
31C2×#11758217—41no—
32C2×D61⋊C8—41no—
33C2×C4⋊#6923—21no—
34C2×C4⋊#6923—21no—
35C2×C22⋊#6923—41no—
36#14519848—24no—
37#14519847—21no—
38#14519847—21no—
39#14519847D412yes—
40#14519847D412yes—
41#14519845—21no—
42#14519845—21no—
43#14519845—21no—
44#14519845—21no—
45(C2×#6923)⋊C4—41no—
46C22×C4×D61D411yescharacteristic
47C22×#92418Q811yescharacteristic
48C2×C8×D61—21no—
49C2×C8×D61—21no—
50C2×C8×D61—21no—
51C2×C8×D61—21no—
52C2×C8×D61C2×C411yescharacteristic
53C2×C8×D61D411yescharacteristic
54C2×C8×D61Q811yescharacteristic
55C2×C8×D61C2311yescharacteristic
56#14519716—21no—
57#14519716—21no—
58#14519716—21no—
59#14519716—21no—
60C2×#11758185C2×C411yescharacteristic
61C2×#11758185C2×C411yescharacteristic
62C22×C8×C61C2×C411yescharacteristic
63C2×C16×C61C2×C411yescharacteristic
64C2×C16×C61C2×C411yescharacteristic
65C23×D61SD1611yescharacteristic
66C22×#6923—41no—
67C22×#6923—41no—
68C22×C4×C61C4⋊C411yescharacteristic
69C22×Dic61SD1611yescharacteristic
70C2×C4×D61—21no—
71C2×C4×D61—21no—
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×C4×D61C4⋊C411yescharacteristic
75C2×C4×D61SD1611yescharacteristic
76C2×C4×D61SD1611yescharacteristic
77C2×C4×D61C2×D411yescharacteristic
78C22⋊#6923—82no—
79#11758217—44no—
80C2×#92420—41no—
81C2×#92420—41no—
82C4⋊#6923—41no—
83C4⋊#6923—41no—
84C4⋊#6923—41no—
85C4⋊#6923—41no—
86#11758213—22no—
87#11758213—22no—
88#11758213—41no—
89#11758213—41no—
90D61⋊C8—44no—
91C2×C8×C61—21no—
92C2×C8×C61—21no—
93C2×C8×C61C4⋊C411yescharacteristic
94C2×C8×C61C22×C411yescharacteristic
95C2×#92418—21no—
96C2×#92418—21no—
97C2×#92418C4⋊C411yescharacteristic
98C2×#92418C2×Q811yescharacteristic
99C8×D61—21no—
100C8×D61—21no—
101C8×D61—21no—
102C8×D61—21no—
103C8×D61—21no—
104C8×D61—21no—
105C8×D61C2×D411yescharacteristic
106C8×D61C2×D411yescharacteristic
107C8×D61#4111yescharacteristic
108C8×D61#4111yescharacteristic
109C16×C61—21no—
110C16×C61—21no—
111#11758185—21no—
112#11758185—21no—
113C23×C61#10611yescharacteristic
114C22×D61—22no—
115C22×D61—21no—
116C22×D61—21no—
117C22×D61—41no—
118C22×D61#10611yescharacteristic
119C22×D61C2×SD1611yescharacteristic
120C2×#6923—81no—
121C2×#6923—81no—
122C2×#6923—81no—
123C2×#6923—81no—
124C2×#6923—81no—
125C2×#6923—81no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61#10611yescharacteristic
129C2×C4×C61C2×C4⋊C411yescharacteristic
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61#10611yescharacteristic
133C2×Dic61C2×SD1611yescharacteristic
134C4×D61—21no—
135C4×D61—21no—
136C4×D61—21no—
137C4×D61—21no—
138C4×D61—21no—
139C4×D61—21no—
140C4×D61#12011yescharacteristic
141C4×D61#12311yescharacteristic
142C4×D61AGL(1,ℤ/8)11yescharacteristic
143C4×D61#13711yescharacteristic
144#92420—42no—
145#92420—42no—
146C8×C61—21no—
147C8×C61C4×D411yescharacteristic
148C8×C61C4×D411yescharacteristic
149#92418—21no—
150#92418C22⋊Q811yescharacteristic
151#92418C22⋊Q811yescharacteristic
152#12928—611nomaximal, Sylow
153C22×C61—21no—
154C22×C61—21no—
155C22×C61—21no—
156C22×C61C2×#10611yescharacteristic
157C2×D61—21no—
158C2×D61—21no—
159C2×D61—21no—
160C2×D61—21no—
161C2×D61—42no—
162C2×D61—42no—
163C2×D61#36512yescomplemented
164C2×D61#44811yescharacteristic
165C2×D61#48111yescharacteristic
166#6923—161no—
167#6923—161no—
168C4×C61—21no—
169C4×C61#38511yescharacteristic
170C4×C61#42811yescharacteristic
171Dic61—21no—
172Dic61#45011yescharacteristic
173Dic61#48311yescharacteristic
174C22×#108—611no—
175C2×#365—611no—
176C2×#365—611no—
177#2112—611no—
178#1807—611no—
179#1383—611no—
180#1383—611no—
181C2×C61—41no—
182C2×C61#185311yescharacteristic
183C2×C61C2×#36511yescharacteristic
184C2×C61#215511yescharacteristic
185D61—21no—
186D61—21no—
187D61—22no—
188C22×M16—1221no—
189C23×C8—611no—
190C2×M32—611no—
191C2×M32—611no—
192C2×#108—611no—
193C2×#108—611no—
194C2×#108—1222no—
195C2×#108—1222no—
196C2×#108—1221no—
197C2×#106—611no—
198C2×#106—611no—
199#380—1221no—
200#365—1222no—
201#365—1222no—
202C22⋊C16—611no—
203C22⋊C16—611no—
204C22⋊C16—611no—
205C22⋊C16#692311yescharacteristic, complemented
206#340—1221no—
207C61#1292811yescharacteristic, complemented, Sylow
208C23×C4—611no—
209C2×M16—1221no—
210C2×M16—1221no—
211C2×M16—1224no—
212C2×M16—2441no—
213C2×M16—2442no—
214C22×C8—611no—
215C22×C8—611no—
216C22×C8—611no—
217C22×C8—611no—
218C22×C8—611no—
219C22×C8—1221no—
220C22×C8—1221no—
221C22×C8—1221no—
222C22×C8—1221no—
223C22×C8—2441no—
224C22×C8C2×#692311yescharacteristic
225C2×C4⋊C4—1221no—
226C2×C4⋊C4—1221no—
227C2×C22⋊C4—2441no—
228M32—1221no—
229M32—1221no—
230M32—1221no—
231M32—1221no—
232C2×C16—611no—
233C2×C16—611no—
234C2×C16C2×#692311yescharacteristic
235C2×C16C2×#692311yescharacteristic
236#108—612no—
237#108—612no—
238#108—1221no—
239#108—1221no—
240#108—1224no—
241#106—1221no—
242#106—1221no—
243#106—1221no—
244#106—1221no—
245#95—2441no—
246C24—611no—
247C22×C4—611no—
248C22×C4—611no—
249C22×C4—611no—
250C22×C4—611no—
251C22×C4—611no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4—2441no—
257C22×C4—2441no—
258C22×C4C4⋊#692311yescharacteristic
259M16—1222no—
260M16—1222no—
261M16—2441no—
262M16—2441no—
263M16—2444no—
264C2×C8—21no—
265C2×C8—21no—
266C2×C8—611no—
267C2×C8—611no—
268C2×C8—611no—
269C2×C8—611no—
270C2×C8—611no—
271C2×C8—611no—
272C2×C8—1221no—
273C2×C8—1221no—
274C2×C8—1221no—
275C2×C8—1221no—
276C2×C8—1221no—
277C2×C8—1221no—
278C2×C8—1221no—
279C2×C8—1221no—
280C2×C8—2441no—
281C2×C8—2441no—
282C2×C8—2444no—
283C2×C8C4⋊#692311yescharacteristic
284C2×C8C22×#692311yescharacteristic
285C4⋊C4—2441no—
286C4⋊C4—2441no—
287C4⋊C4—2441no—
288C4⋊C4—2441no—
289C22⋊C4—4882no—
290C16—21no—
291C16—21no—
292C16—1221no—
293C16—1221no—
294C23—611no—
295C23—611no—
296C23—1222no—
297C23—1221no—
298C23—1221no—
299C23—2441no—
300C23#1451984511yescharacteristic
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—611no—
304C2×C4—611no—
305C2×C4—611no—
306C2×C4—611no—
307C2×C4—611no—
308C2×C4—611no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—1221no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—1221no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—4881no—
318C2×C4—4881no—
319C2×C4—4881no—
320C2×C4—4881no—
321C2×C4—4881no—
322C2×C4—4881no—
323C2×C4#1451984511yescharacteristic
324C2×C4C2×C4⋊#692311yescharacteristic
325C8—21no—
326C8—611no—
327C8—611no—
328C8—1221no—
329C8—2442no—
330C8—2442no—
331C8D4×#692311yescharacteristic
332C8D4×#692311yescharacteristic
333C22—21no—
334C22—21no—
335C22—21no—
336C22—611no—
337C22—611no—
338C22—612no—
339C22—1221no—
340C22—1221no—
341C22—1221no—
342C22—1221no—
343C22—2442no—
344C22—2442no—
345C22C2×#1451984511yescharacteristic
346C4—21no—
347C4—611no—
348C4—611no—
349C4—1221no—
350C4—9761no—
351C4—9761no—
352C4#1684070911yescharacteristic
353C4#1684077311yescharacteristic
354C2—41no—
355C2—1221no—
356C2—1221no—
357C2—1222no—
358C2#2146176911yescharacteristic
359C2D61⋊#36511yescharacteristic
360C2#2146216611yescharacteristic
subgroupG/H
centerC22C2×#14519845
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×C22⋊C16C4
socleC22×C61C2×#106
prime radicalC23×D61SD16
cosocleC2×C8×D61C23
hypercenterC22⋊C16#6923
hypocenterC61#12928
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22⋊C16

Complements

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

NH ≅ G/Ntype
2. C2×#16840687C2semidirect
3. C2×#16840686C2semidirect
5. #21460884C2semidirect
6. #21460884C2semidirect
23. C22⋊#11758185C4semidirect
24. #16839541C4semidirect
25. #16839541C4semidirect
26. C61×C22⋊C16C4semidirect
163. C2×D61#365semidirect
205. C22⋊C16#6923semidirect
207. C61#12928semidirect

Maximal subgroups

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

subgroupindex
C2×D61⋊#1082
C2×#168406872
C2×#168406862
#214616952
#214608842
#214474282
#1292861