Finite Group Databasebeta

← #30607410

Subgroups — #30607410

Order 15616.

414 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 94 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×#16840772C211yesmaximal, characteristic
2C2×#16840687C211yesmaximal, characteristic, complemented
3C2×#16840686C211yesmaximal, characteristic, complemented
4#21461698C211yesmaximal, characteristic
5#21460884C211yesmaximal, characteristic, complemented
6#21460884C211yesmaximal, characteristic, complemented
7#21447428C211yesmaximal, characteristic
8C2×#14519856—21no—
9C2×#14519847C2211yescharacteristic
10C2×#14519847C2211yescharacteristic
11#16840772—22no—
12#16840772—22no—
13C2×#14519846—21no—
14C2×#14519845C2211yescharacteristic
15C2×#14519845C2211yescharacteristic
16#16840733—21no—
17#16840687—22no—
18#16840686—22no—
19#16840638—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—
29#14519856—24no—
30#14519856—42no—
31C2×C4⋊#6923—21no—
32C2×C4⋊#6923—21no—
33C2×C22⋊#6923—41no—
34C2×C4×#6923—41no—
35#14519847—21no—
36#14519847—21no—
37#14519847—21no—
38#14519847—21no—
39#14519846—24no—
40#14519845—21no—
41#14519845—21no—
42#14519845D412yes—
43#14519845D412yes—
44#14519834—41no—
45C22⋊#92420—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—44no—
79C2×#92420—41no—
80C2×#92420—41no—
81C4⋊#6923—22no—
82C4⋊#6923—22no—
83C4⋊#6923—41no—
84C4⋊#6923—41no—
85C4×#6923—44no—
86#11758213—41no—
87#11758213—41no—
88#11758213—41no—
89#11758213—41no—
90C2×C8×C61—21no—
91C2×C8×C61—21no—
92C2×C8×C61C4⋊C411yescharacteristic
93C2×C8×C61C22×C411yescharacteristic
94C2×#92418—21no—
95C2×#92418—21no—
96C2×#92418C4⋊C411yescharacteristic
97C2×#92418C2×Q811yescharacteristic
98C8×D61—21no—
99C8×D61—21no—
100C8×D61—21no—
101C8×D61—21no—
102C8×D61—21no—
103C8×D61—21no—
104C8×D61C2×D411yescharacteristic
105C8×D61C2×D411yescharacteristic
106C8×D61#4111yescharacteristic
107C8×D61#4111yescharacteristic
108C16×C61—21no—
109C16×C61—21no—
110#11758185—21no—
111#11758185—21no—
112C23×C61#10611yescharacteristic
113C22×D61—21no—
114C22×D61—21no—
115C22×D61—41no—
116C22×D61—41no—
117C22×D61#10611yescharacteristic
118C22×D61C2×SD1611yescharacteristic
119C2×#6923—42no—
120C2×#6923—42no—
121C2×#6923—81no—
122C2×#6923—81no—
123C2×#6923—81no—
124C2×#6923—81no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61#10611yescharacteristic
128C2×C4×C61C2×C4⋊C411yescharacteristic
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61#10611yescharacteristic
132C2×Dic61C2×SD1611yescharacteristic
133C4×D61—21no—
134C4×D61—21no—
135C4×D61—21no—
136C4×D61—21no—
137C4×D61—21no—
138C4×D61—21no—
139C4×D61#12011yescharacteristic
140C4×D61#12311yescharacteristic
141C4×D61AGL(1,ℤ/8)11yescharacteristic
142C4×D61#13711yescharacteristic
143#92420—81no—
144#92420—81no—
145C8×C61—21no—
146C8×C61C4×D411yescharacteristic
147C8×C61C4×D411yescharacteristic
148#92418—21no—
149#92418C22⋊Q811yescharacteristic
150#92418C22⋊Q811yescharacteristic
151#12930—611nomaximal, Sylow
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—21no—
155C22×C61C2×#10611yescharacteristic
156C2×D61—21no—
157C2×D61—21no—
158C2×D61—21no—
159C2×D61—21no—
160C2×D61—21no—
161C2×D61—42no—
162C2×D61—42no—
163C2×D61#45011yescharacteristic
164C2×D61#48311yescharacteristic
165#6923—82no—
166#6923—82no—
167C4×C61—21no—
168C4×C61#38511yescharacteristic
169C4×C61#42811yescharacteristic
170Dic61—21no—
171Dic61#44811yescharacteristic
172Dic61#48111yescharacteristic
173C2×#427—611no—
174C2×#365—611no—
175C2×#365—611no—
176#2112—611no—
177#1810—611no—
178#1383—611no—
179#1383—611no—
180C2×C61—41no—
181C2×C61#185311yescharacteristic
182C2×C61#215511yescharacteristic
183C2×C61#215511yescharacteristic
184D61—21no—
185D61—21no—
186D61—41no—
187C23×C8—611no—
188C2×#117—1221no—
189C2×M32—611no—
190C2×M32—611no—
191C2×#108—611no—
192C2×#108—611no—
193#427—1222no—
194#427—1222no—
195C2×#107—1221no—
196C2×#106—611no—
197C2×#106—611no—
198#407—1221no—
199#365—1222no—
200#365—1222no—
201C22⋊C16—611no—
202C22⋊C16—611no—
203C22⋊C16—611no—
204C22⋊C16#692311yescharacteristic, complemented
205#341—1221no—
206C61#1293011yescharacteristic, complemented, Sylow
207C23×C4—611no—
208C2×M16—1221no—
209C2×M16—1221no—
210C22×C8—611no—
211C22×C8—611no—
212C22×C8—611no—
213C22×C8—611no—
214C22×C8—611no—
215C22×C8—1221no—
216C22×C8—1221no—
217C22×C8—1221no—
218C22×C8—1221no—
219C22×C8C2×#692311yescharacteristic
220#117—1224no—
221#117—2442no—
222C2×C4⋊C4—1221no—
223C2×C4⋊C4—1221no—
224C2×C22⋊C4—2441no—
225C2×C42—2441no—
226M32—1221no—
227M32—1221no—
228M32—1221no—
229M32—1221no—
230C2×C16—611no—
231C2×C16—611no—
232C2×C16C2×#692311yescharacteristic
233C2×C16C2×#692311yescharacteristic
234#108—1221no—
235#108—1221no—
236#108—1221no—
237#108—1221no—
238#107—1224no—
239#106—612no—
240#106—612no—
241#106—1221no—
242#106—1221no—
243C22⋊C8—2441no—
244C22⋊C8—2441no—
245C24—611no—
246C22×C4—611no—
247C22×C4—611no—
248C22×C4—611no—
249C22×C4—611no—
250C22×C4—611no—
251C22×C4—1221no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4—2441no—
256C22×C4—2441no—
257C22×C4C4⋊#692311yescharacteristic
258M16—2441no—
259M16—2441no—
260M16—2441no—
261M16—2441no—
262C2×C8—21no—
263C2×C8—21no—
264C2×C8—611no—
265C2×C8—611no—
266C2×C8—611no—
267C2×C8—611no—
268C2×C8—611no—
269C2×C8—611no—
270C2×C8—1221no—
271C2×C8—1221no—
272C2×C8—1221no—
273C2×C8—1221no—
274C2×C8—1221no—
275C2×C8—1221no—
276C2×C8—1221no—
277C2×C8—1221no—
278C2×C8—2441no—
279C2×C8—2441no—
280C2×C8C4⋊#692311yescharacteristic
281C2×C8C22×#692311yescharacteristic
282C4⋊C4—1222no—
283C4⋊C4—1222no—
284C4⋊C4—2441no—
285C4⋊C4—2441no—
286C22⋊C4—2444no—
287C42—2444no—
288C16—21no—
289C16—21no—
290C16—1221no—
291C16—1221no—
292C23—611no—
293C23—611no—
294C23—1221no—
295C23—1221no—
296C23—2441no—
297C23—2441no—
298C23#1451984511yescharacteristic
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—611no—
302C2×C4—611no—
303C2×C4—611no—
304C2×C4—611no—
305C2×C4—611no—
306C2×C4—611no—
307C2×C4—1221no—
308C2×C4—1221no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—1221no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—1221no—
315C2×C4—4881no—
316C2×C4—4881no—
317C2×C4—4881no—
318C2×C4—4881no—
319C2×C4—2442no—
320C2×C4—2442no—
321C2×C4#1451984511yescharacteristic
322C2×C4C2×C4⋊#692311yescharacteristic
323C8—21no—
324C8—611no—
325C8—611no—
326C8—1221no—
327C8—4881no—
328C8—4881no—
329C8D4×#692311yescharacteristic
330C8D4×#692311yescharacteristic
331C22—21no—
332C22—21no—
333C22—21no—
334C22—611no—
335C22—611no—
336C22—1221no—
337C22—1221no—
338C22—1221no—
339C22—1221no—
340C22—1221no—
341C22—2442no—
342C22—2442no—
343C22C2×#1451984511yescharacteristic
344C4—21no—
345C4—611no—
346C4—611no—
347C4—1221no—
348C4—4882no—
349C4—4882no—
350C4#1684070911yescharacteristic
351C4#1684077311yescharacteristic
352C2—41no—
353C2—1221no—
354C2—1221no—
355C2—2441no—
356C2#2146176911yescharacteristic
357C2#2146216611yescharacteristic
358C2#2146216711yescharacteristic
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#12930
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
204. C22⋊C16#6923semidirect
206. C61#12930semidirect

Maximal subgroups

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

subgroupindex
C2×#168407722
C2×#168406872
C2×#168406862
#214616982
#214608842
#214474282
#1293061