Finite Group Databasebeta

← #29580995

Subgroups — #29580995

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#21456167C211yesmaximal, characteristic
2#21455854C211yesmaximal, characteristic, complemented
3#21455851C211yesmaximal, characteristic
4#21446758C211yesmaximal, characteristic, complemented
5#21444217C211yesmaximal, characteristic
6#21443649C211yesmaximal, characteristic, complemented
7C61×#1481C211yesmaximal, characteristic, complemented
8#16840312C2211yescharacteristic
9C2×C4×Dic122C2211yescharacteristic
10#16840132—21no—
11#16840128—21no—
12#16840124—21no—
13#16840124—21no—
14#16840095—21no—
15#16840081—21no—
16#16840054—21no—
17#16840048—21no—
18#16839969—21no—
19#16839963—21no—
20#16839917—21no—
21#16839903—21no—
22C4×#11758202—22no—
23C4×#11758190—22no—
24#16839815C2211yescharacteristic
25#16839756—22no—
26C2×#14519688C2211yescharacteristic
27#16839516—22no—
28#16839489—22no—
29C61×#533C2211yescharacteristic
30C61×#431C2211yescharacteristic
31C2×C4⋊C8×C61C2211yescharacteristic
32C61×Q8⋊C8—22no—
33C2×#11758222—21no—
34C22×Dic122D411yescharacteristic
35C2×#11758202—22no—
36C2×#11758190—22no—
37C22×#92418D412yes—
38#14519777D411yescharacteristic
39#14519774D411yescharacteristic
40#14519765—21no—
41#14519751—21no—
42#14519751—21no—
43C4×Dic122—21no—
44C4×Dic122—21no—
45C4×Dic122—21no—
46C4×Dic122—21no—
47C4×D244—21no—
48C4×D244—21no—
49C2×C4⋊Dic61D411yescharacteristic
50C2×#11758196—21no—
51C2×C4×Dic61—21no—
52#14519710—22no—
53#14519709—22no—
54C4⋊#92418—21no—
55#14519702—22no—
56#14519701—22no—
57#14519700—22no—
58#14519700—22no—
59#14519700—22no—
60#14519699—22no—
61#14519697—22no—
62#14519697—22no—
63C22⋊#92418—21no—
64#14519688—21no—
65#14519688—21no—
66C4×#92418D412yes—
67C22×C8×C61—21no—
68C4⋊Q8×C61D411yescharacteristic
69C4⋊Q8×C61D411yescharacteristic
70#125×C61—21no—
71C22⋊Q8×C61—21no—
72C22⋊Q8×C61—21no—
73C4×Q8×C61—21no—
74C4×Q8×C61—21no—
75#117×C61—21no—
76C2×C42×C61C2311yescharacteristic
77C4⋊C8×C61—21no—
78C4⋊C8×C61—21no—
79C4⋊C8×C61—21no—
80C22⋊C8×C61—21no—
81C4×C8×C61D412yes—
82C2×Q8×C61—21no—
83C2×Q8×C61—21no—
84C22×C4×C61C2×D411yescharacteristic
85C22×C4×C61C2×D411yescharacteristic
86C22×C4×C61#4111yescharacteristic
87C2×C22⋊D61—41no—
88C22×Dic61—21no—
89C22×Dic61—21no—
90#11758222—42no—
91#11758222—42no—
92C2×D244—21no—
93C2×D244—21no—
94C2×D244—21no—
95C2×C4×D61—41no—
96C2×Dic122—21no—
97C2×Dic122—21no—
98C2×Dic122—21no—
99C2×Dic122—42no—
100C2×C8×C61—22no—
101C2×C8×C61—41no—
102C2×C8×C61—42no—
103C4⋊C4×C61—21no—
104C4⋊C4×C61—21no—
105C4⋊C4×C61—21no—
106C4⋊C4×C61—21no—
107C4⋊C4×C61—41no—
108C4⋊C4×C61—41no—
109C22⋊C4×C61—41no—
110C42×C61—41no—
111C42×C61C2×D411yescharacteristic
112C42×C61C2×D411yescharacteristic
113C42×C61C2×D411yescharacteristic
114C42×C61C2×D411yescharacteristic
115#11758202—44no—
116#11758198—41no—
117#11758198—41no—
118C4⋊Dic61—21no—
119C4⋊Dic61—21no—
120C4⋊Dic61—21no—
121C4⋊Dic61—21no—
122#11758196—41no—
123#11758196—41no—
124C4×Dic61—41no—
125C4×Dic61—41no—
126C2×#92418—22no—
127C2×#92418—22no—
128C2×#92418—22no—
129C2×#92418—22no—
130#11758190—44no—
131C23×C61#12111yescharacteristic
132C22×D61—41no—
133Q8×C61—42no—
134Q8×C61—42no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61#12011yescharacteristic
140C2×C4×C61#12011yescharacteristic
141C2×C4×C61#12011yescharacteristic
142C2×C4×C61#12111yescharacteristic
143C2×C4×C61#12111yescharacteristic
144C2×C4×C61#12711yescharacteristic
145C2×C4×C61#13512yes—
146C2×C4×C61#13712yes—
147C22⋊D61—82no—
148C2×Dic61—22no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—42no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154D244—42no—
155D244—42no—
156D244—42no—
157C4×D61—81no—
158C4×D61—81no—
159Dic122—22no—
160Dic122—22no—
161Dic122—41no—
162Dic122—41no—
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—81no—
181C4×C61—81no—
182C4×C61#45212yes—
183C4×C61#49511yescharacteristic
184C4×C61#49711yescharacteristic
185Dic61—42no—
186Dic61—81no—
187Dic61—81no—
188#3135—611no—
189#3104—611no—
190#3103—611no—
191#1985—611no—
192#1481D6111yescharacteristic, complemented
193#1480—611no—
194#1275—611no—
195C2×C61—22no—
196C2×C61#201011yescharacteristic
197C2×C61#201511yescharacteristic
198C2×C61#201711yescharacteristic
199D61—161no—
200#533C2×D6111yescharacteristic
201#532—611no—
202C2×C4×Q8—611no—
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#431C2×D6111yescharacteristic
219C2×C4⋊C8C2×D6111yescharacteristic
220#416—1222no—
221C2×#97—611no—
222#336—1222no—
223Q8⋊C8—22no—
224D4⋊C8—1222no—
225C61#1003511yescharacteristic, complemented, Sylow
226C2×#41—1221no—
227C22×Q8—611no—
228C2×Q16—1222no—
229C2×SD16—1222no—
230C22×C8—21no—
231C22×C8—612no—
232C4⋊Q8—611no—
233C4⋊Q8D24411yescharacteristic
234C4⋊Q8D24411yescharacteristic
235#127—611no—
236#125—21no—
237#124—1221no—
238C22⋊Q8—21no—
239C22⋊Q8—21no—
240#121—1221no—
241#121—1221no—
242C4×Q8—21no—
243C4×Q8—21no—
244C4×Q8—1221no—
245C4×Q8—1221no—
246C4×Q8—1221no—
247C4×Q8—1221no—
248C4×D4—1221no—
249C4×D4—1221no—
250#117—21no—
251C2×C4⋊C4—611no—
252C2×C4⋊C4—1221no—
253C2×C42—1221no—
254C2×C42C22×D6111yescharacteristic
255#107—1222no—
256#106—1222no—
257C4⋊C8—21no—
258C4⋊C8—21no—
259C4⋊C8—21no—
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—21no—
270C22⋊C8—1221no—
271#97—1221no—
272#97—1221no—
273C4×C8—612no—
274C4×C8C22⋊D6112yes—
275#41—2442no—
276#41—2442no—
277C2×Q8—21no—
278C2×Q8—21no—
279C2×Q8—1221no—
280C2×Q8—1221no—
281C2×Q8—1221no—
282C2×Q8—2442no—
283C2×D4—1221no—
284C2×D4—1221no—
285C2×D4—1221no—
286C2×D4—2441no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4—2441no—
290C22×C4#1175822211yescharacteristic
291C22×C4D4×D6111yescharacteristic
292C22×C4D4×D6111yescharacteristic
293Q16—2444no—
294SD16—2444no—
295C2×C8—22no—
296C2×C8—41no—
297C2×C8—42no—
298C2×C8—1222no—
299C2×C8—1222no—
300C2×C8—1222no—
301C2×C8—1222no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—1221no—
309C4⋊C4—1221no—
310C4⋊C4—1221no—
311C4⋊C4—1221no—
312C4⋊C4—2441no—
313C4⋊C4—2441no—
314C22⋊C4—41no—
315C22⋊C4—2441no—
316C22⋊C4—2441no—
317C42—41no—
318C42—2441no—
319C42—2441no—
320C42C2×D24411yescharacteristic
321C42D4×D6111yescharacteristic
322C42D4×D6111yescharacteristic
323C42C2×C22⋊D6111yescharacteristic
324C23—2441no—
325C23#1451975011yescharacteristic
326Q8—42no—
327Q8—42no—
328Q8—1222no—
329Q8—1222no—
330Q8—2441no—
331Q8—2441no—
332Q8—2442no—
333D4—4882no—
334D4—2442no—
335D4—2442no—
336D4—2442no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—1222no—
342C2×C4—4881no—
343C2×C4—4881no—
344C2×C4—2442no—
345C2×C4—2441no—
346C2×C4—2441no—
347C2×C4—2441no—
348C2×C4—2441no—
349C2×C4#1451974511yescharacteristic
350C2×C4#1451974711yescharacteristic
351C2×C4#1451974711yescharacteristic
352C2×C4#1451975011yescharacteristic
353C2×C4#1451975111yescharacteristic
354C2×C4#1451977311yescharacteristic
355C2×C4#1451979812yes—
356C2×C4#1451980912yes—
357C8—42no—
358C8—81no—
359C8—2442no—
360C8—2442no—
361C22—21no—
362C22—21no—
363C22—4881no—
364C22—4881no—
365C22—4881no—
366C22#1683967111yescharacteristic
367C22#1683998712yes—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—81no—
373C4—81no—
374C4—4881no—
375C4—4881no—
376C4—2442no—
377C4#1683992712yes—
378C4#1684014311yescharacteristic
379C4#1684015511yescharacteristic
380C2—22no—
381C2—9761no—
382C2#2144688511yescharacteristic
383C2#2144691411yescharacteristic
384C2#2144692311yescharacteristic
subgroupG/H
centerC2×C4#14519773
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1481C2
socleC22×C61#392
prime radical#16840312C22
hypercenter#1481D61
hypocenterC61#10035
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1481

Complements

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

NH ≅ G/Ntype
2. #21455854C2semidirect
4. #21446758C2semidirect
6. #21443649C2semidirect
7. C61×#1481C2semidirect
192. #1481D61semidirect
225. C61#10035semidirect

Maximal subgroups

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

subgroupindex
#214561672
#214558542
#214558512
#214467582
#214442172
#214436492
C61×#14812
#1003561