Finite Group Databasebeta

← #29580997

Subgroups — #29580997

Order 15616.

498 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 95 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
1#21456165C211yesmaximal, characteristic
2#21455858C211yesmaximal, characteristic, complemented
3#21455850C211yesmaximal, characteristic
4#21444221C211yesmaximal, characteristic, complemented
5#21444217C211yesmaximal, characteristic
6#21443650C211yesmaximal, characteristic, complemented
7C61×#1985C211yesmaximal, characteristic, complemented
8#16840319C2211yescharacteristic
9#16840312C2211yescharacteristic
10#16840131—21no—
11#16840127—21no—
12#16840122—21no—
13#16840122—21no—
14#16840097—21no—
15#16840080—21no—
16#16840057—21no—
17#16840047—21no—
18#16839972—21no—
19#16839962—21no—
20#16839918—21no—
21#16839901—21no—
22C4×#11758202—22no—
23C4×#11758201—22no—
24#16839815C2211yescharacteristic
25#16839815C2211yescharacteristic
26#16839759—22no—
27#16839492—22no—
28#16839489—22no—
29C2×C4×Q8×C61C2211yescharacteristic
30C2×C4⋊C8×C61C2211yescharacteristic
31C2×#97×C61C2211yescharacteristic
32C61×#336—22no—
33C2×#11758222—21no—
34C2×#11758202—22no—
35C2×#11758201—22no—
36#14519777D411yescharacteristic
37#14519777D411yescharacteristic
38#14519777D411yescharacteristic
39#14519774D411yescharacteristic
40#14519769—21no—
41#14519765—21no—
42#14519756—21no—
43#14519756—21no—
44#14519751—21no—
45#14519751—21no—
46C4×Dic122—21no—
47C4×Dic122—21no—
48C4×D244—21no—
49C4×D244—21no—
50#14519736—21no—
51#14519710—22no—
52#14519708—22no—
53C4⋊#92418—21no—
54C4⋊#92418—21no—
55#14519702—22no—
56#14519702—22no—
57#14519701—22no—
58#14519701—22no—
59#14519700—22no—
60#14519699—22no—
61#14519699—22no—
62#14519697—22no—
63C22⋊#92418—21no—
64C22⋊#92418—21no—
65C4×#92418D412yes—
66C4×#92418D412yes—
67C22×Q8×C61D411yescharacteristic
68C22×C8×C61—21no—
69C22×C8×C61D412yes—
70C4×Q8×C61—21no—
71C4×Q8×C61—21no—
72C4×Q8×C61—21no—
73C4×Q8×C61—21no—
74C2×C4⋊C4×C61—21no—
75C2×C4⋊C4×C61D411yescharacteristic
76C2×C42×C61—21no—
77C2×C42×C61C2311yescharacteristic
78C4⋊C8×C61—21no—
79C4⋊C8×C61—21no—
80#97×C61—21no—
81#97×C61—21no—
82C2×Q8×C61—21no—
83C2×Q8×C61—21no—
84C2×Q8×C61—42no—
85C22×C4×C61—21no—
86C22×C4×C61—21no—
87C22×C4×C61C2×D411yescharacteristic
88C22×C4×C61C2×D411yescharacteristic
89C22×C4×C61#4111yescharacteristic
90C2×C22⋊D61—41no—
91#11758222—42no—
92#11758222—42no—
93C2×D244—21no—
94C2×D244—21no—
95C2×D244—21no—
96C2×C4×D61—41no—
97C2×Dic122—21no—
98C2×Dic122—21no—
99C2×Dic122—21no—
100C2×C8×C61—22no—
101C2×C8×C61—22no—
102C2×C8×C61—22no—
103C2×C8×C61—41no—
104C2×C8×C61—42no—
105C4⋊C4×C61—21no—
106C4⋊C4×C61—21no—
107C4⋊C4×C61—41no—
108C4⋊C4×C61—41no—
109C42×C61—41no—
110C42×C61—41no—
111C42×C61C2×D411yescharacteristic
112C42×C61C2×D411yescharacteristic
113C42×C61C2×D411yescharacteristic
114C42×C61C2×D411yescharacteristic
115C22⋊Dic61—41no—
116#11758202—44no—
117#11758201—44no—
118#11758198—41no—
119#11758198—41no—
120C4⋊Dic61—21no—
121C4⋊Dic61—21no—
122C4⋊Dic61—21no—
123C4⋊Dic61—21no—
124C4⋊Dic61—21no—
125C4⋊Dic61—21no—
126#11758196—41no—
127#11758196—41no—
128C4×Dic61—41no—
129C2×#92418—22no—
130C2×#92418—22no—
131C23×C61#12111yescharacteristic
132C22×D61—41no—
133Q8×C61—22no—
134Q8×C61—22no—
135Q8×C61—41no—
136Q8×C61—41no—
137C2×C4×C61—22no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—42no—
143C2×C4×C61—41no—
144C2×C4×C61#12011yescharacteristic
145C2×C4×C61#12011yescharacteristic
146C2×C4×C61#12011yescharacteristic
147C2×C4×C61#12111yescharacteristic
148C2×C4×C61#12111yescharacteristic
149C2×C4×C61#12711yescharacteristic
150C2×C4×C61#13512yes—
151C2×C4×C61#13712yes—
152C22⋊D61—82no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156D244—42no—
157D244—42no—
158D244—42no—
159C4×D61—81no—
160C4×D61—81no—
161Dic122—42no—
162Dic122—42no—
163Dic122—42no—
164C8×C61—42no—
165C8×C61—81no—
166#92418—42no—
167#92418—42no—
168#10035—611nomaximal, Sylow
169C22×C61—21no—
170C22×C61—21no—
171C22×C61#39211yescharacteristic
172C22×C61#46412yes—
173C2×D61—81no—
174C2×D61—81no—
175C2×D61—81no—
176C4×C61—21no—
177C4×C61—21no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—42no—
181C4×C61—81no—
182C4×C61#45212yes—
183C4×C61#49511yescharacteristic
184C4×C61#49711yescharacteristic
185Dic61—81no—
186Dic61—81no—
187Dic61—81no—
188#3135—611no—
189#3104—611no—
190#3103—611no—
191#1985D6111yescharacteristic, complemented
192#1481—611no—
193#1480—611no—
194#1275—611no—
195C2×C61—22no—
196C2×C61#201011yescharacteristic
197C2×C61#201511yescharacteristic
198C2×C61#201711yescharacteristic
199D61—161no—
200#533—611no—
201#532—611no—
202C2×C4×Q8C2×D6111yescharacteristic
203#491—1221no—
204#490—1221no—
205#489—1221no—
206#489—1221no—
207#484—1221no—
208#481—1221no—
209#477—1221no—
210#475—1221no—
211#462—1221no—
212#460—1221no—
213#451—1221no—
214#448—1221no—
215C4×Q16—1222no—
216C4×SD16—1222no—
217#431—611no—
218#431—611no—
219C2×C4⋊C8C2×D6111yescharacteristic
220#416—1222no—
221C2×#97C2×D6111yescharacteristic
222#336—22no—
223Q8⋊C8—1222no—
224D4⋊C8—1222no—
225C61#1003511yescharacteristic, complemented, Sylow
226C2×#41—1221no—
227C22×Q8D24411yescharacteristic
228C2×Q16—1222no—
229C2×SD16—1222no—
230C22×C8—21no—
231C22×C8C22⋊D6112yes—
232C4⋊Q8—611no—
233C4⋊Q8—611no—
234C4⋊Q8—611no—
235#127—611no—
236#125—1221no—
237#124—1221no—
238C22⋊Q8—1221no—
239C22⋊Q8—1221no—
240#121—1221no—
241#121—1221no—
242C4×Q8—21no—
243C4×Q8—21no—
244C4×Q8—21no—
245C4×Q8—21no—
246C4×Q8—1221no—
247C4×Q8—1221no—
248C4×D4—1221no—
249C4×D4—1221no—
250#117—1221no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4D24411yescharacteristic
253C2×C42—21no—
254C2×C42C22×D6111yescharacteristic
255#107—1222no—
256#106—1222no—
257C4⋊C8—21no—
258C4⋊C8—21no—
259C4⋊C8—1221no—
260C4⋊C8—1221no—
261#103—1222no—
262#103—1222no—
263#103—1222no—
264#103—1222no—
265#103—1222no—
266#102—1222no—
267#102—1222no—
268#102—1222no—
269C22⋊C8—1221no—
270C22⋊C8—1221no—
271#97—21no—
272#97—21no—
273C4×C8—612no—
274C4×C8—612no—
275#41—2442no—
276#41—2442no—
277C2×Q8—21no—
278C2×Q8—21no—
279C2×Q8—42no—
280C2×Q8—1221no—
281C2×Q8—1221no—
282C2×Q8—1221no—
283C2×D4—1221no—
284C2×D4—1221no—
285C2×D4—1221no—
286C2×D4—2441no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—2441no—
290C22×C4C2×D24411yescharacteristic
291C22×C4#1175822211yescharacteristic
292C22×C4C2×C22⋊D6111yescharacteristic
293Q16—2444no—
294SD16—2444no—
295C2×C8—22no—
296C2×C8—22no—
297C2×C8—22no—
298C2×C8—41no—
299C2×C8—42no—
300C2×C8—1222no—
301C2×C8—1222no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—1221no—
307C4⋊C4—1221no—
308C4⋊C4—1221no—
309C4⋊C4—1221no—
310C4⋊C4—1221no—
311C4⋊C4—1221no—
312C4⋊C4—2441no—
313C4⋊C4—2441no—
314C22⋊C4—2441no—
315C22⋊C4—2441no—
316C22⋊C4—2441no—
317C42—41no—
318C42—41no—
319C42—2441no—
320C42D4×D6111yescharacteristic
321C42D4×D6111yescharacteristic
322C42D4×D6111yescharacteristic
323C42D4×D6111yescharacteristic
324C23—2441no—
325C23#1451975111yescharacteristic
326Q8—22no—
327Q8—22no—
328Q8—41no—
329Q8—41no—
330Q8—2442no—
331Q8—2442no—
332Q8—2442no—
333D4—4882no—
334D4—2442no—
335D4—2442no—
336D4—2442no—
337C2×C4—22no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—4881no—
345C2×C4—4881no—
346C2×C4—2441no—
347C2×C4—2441no—
348C2×C4—2441no—
349C2×C4#1451974511yescharacteristic
350C2×C4#1451974711yescharacteristic
351C2×C4#1451974711yescharacteristic
352C2×C4#1451975011yescharacteristic
353C2×C4#1451975011yescharacteristic
354C2×C4#1451977311yescharacteristic
355C2×C4#1451979712yes—
356C2×C4#1451980812yes—
357C8—42no—
358C8—81no—
359C8—2442no—
360C8—2442no—
361C22—21no—
362C22—21no—
363C22—4881no—
364C22—4881no—
365C22—4881no—
366C22#1683967111yescharacteristic
367C22#1683998412yes—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—42no—
373C4—81no—
374C4—4881no—
375C4—4881no—
376C4—4881no—
377C4#1683992212yes—
378C4#1684014411yescharacteristic
379C4#1684015411yescharacteristic
380C2—22no—
381C2—9761no—
382C2#2144688611yescharacteristic
383C2#2144691211yescharacteristic
384C2#2144692311yescharacteristic
subgroupG/H
centerC2×C4#14519773
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1985C2
socleC22×C61#392
prime radical#16840312C22
hypercenter#1985D61
hypocenterC61#10035
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1985

Complements

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

NH ≅ G/Ntype
2. #21455858C2semidirect
4. #21444221C2semidirect
6. #21443650C2semidirect
7. C61×#1985C2semidirect
191. #1985D61semidirect
225. C61#10035semidirect

Maximal subgroups

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

subgroupindex
#214561652
#214558582
#214558502
#214442212
#214442172
#214436502
C61×#19852
#1003561