Finite Group Databasebeta

← #29580896

Subgroups — #29580896

Order 15616.

540 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 81 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#21456222C211yesmaximal, characteristic, complemented
2#21455910C211yesmaximal, characteristic
3#21444446C211yesmaximal, characteristic, complemented
4#21444365C211yesmaximal, characteristic, complemented
5#21444262C211yesmaximal, characteristic, complemented
6#21443683C211yesmaximal, characteristic, complemented
7C61×#2633C211yesmaximal, characteristic, complemented
8#16840312C2211yescharacteristic
9#16840132—21no—
10#16840128—21no—
11#16840119—22no—
12#16840080—21no—
13#16840052—21no—
14#16839957—21no—
15#16839896—21no—
16#16839872—22no—
17#16839819C2211yescharacteristic
18#16839819C2211yescharacteristic
19#16839761—21no—
20#16839761—21no—
21C4×#11758194C2211yescharacteristic
22#16839504—22no—
23#16839495—22no—
24D4⋊#92418—22no—
25C2×#125×C61C2211yescharacteristic
26C2×C4×D4×C61C2211yescharacteristic
27C61×#399—21no—
28C61×#398—21no—
29C61×#397—21no—
30C61×#394—21no—
31C61×#385—22no—
32C61×#383C2211yescharacteristic
33C2×#11758222—21no—
34C2×#11758199—22no—
35C2×#11758194—21no—
36#14519777D411yescharacteristic
37#14519774D411yescharacteristic
38#14519765—21no—
39#14519751—21no—
40#14519751—21no—
41C4×D244—21no—
42C4×D244—21no—
43#14519708—22no—
44C4⋊#92418—21no—
45C4⋊#92418—21no—
46#14519700—22no—
47#14519700—22no—
48#14519698—22no—
49#14519697—22no—
50#14519697—22no—
51#14519697—22no—
52C22⋊#92418—21no—
53C22⋊#92418—21no—
54#14519688—21no—
55#14519688—21no—
56#14519688D412yes—
57C4×#92418D412yes—
58C22×D4×C61D411yescharacteristic
59C23×C4×C61—21no—
60#125×C61—21no—
61#125×C61—21no—
62#125×C61—21no—
63#125×C61—21no—
64C4×D4×C61—21no—
65C4×D4×C61—21no—
66C4×D4×C61—21no—
67C4×D4×C61—21no—
68C2×C4⋊C4×C61—21no—
69C2×C4⋊C4×C61—21no—
70C2×C4⋊C4×C61—22no—
71C2×C4⋊C4×C61D411yescharacteristic
72C2×C4⋊C4×C61D411yescharacteristic
73C2×C4⋊C4×C61D411yescharacteristic
74C2×C22⋊C4×C61—22no—
75C2×C22⋊C4×C61—21no—
76C2×C22⋊C4×C61—22no—
77C2×C42×C61C2311yescharacteristic
78#95×C61—22no—
79#95×C61—21no—
80#95×C61—21no—
81#95×C61D412yes—
82C24×C61—21no—
83C2×D4×C61—21no—
84C2×D4×C61—21no—
85C2×D4×C61—42no—
86C22×C4×C61—22no—
87C22×C4×C61—21no—
88C22×C4×C61—21no—
89C22×C4×C61—21no—
90C22×C4×C61—41no—
91C22×C4×C61—41no—
92C22×C4×C61—82no—
93C22×C4×C61C2×D411yescharacteristic
94C22×C4×C61C2×D411yescharacteristic
95C22×C4×C61C2×D411yescharacteristic
96C2×C22⋊D61—41no—
97#11758222—44no—
98C2×D244—21no—
99C2×D244—21no—
100C2×D244—21no—
101C2×C4×D61—41no—
102C2×Dic122—21no—
103C4⋊C4×C61—21no—
104C4⋊C4×C61—21no—
105C4⋊C4×C61—21no—
106C4⋊C4×C61—21no—
107C4⋊C4×C61—21no—
108C4⋊C4×C61—21no—
109C4⋊C4×C61—41no—
110C4⋊C4×C61—41no—
111C4⋊C4×C61—41no—
112C4⋊C4×C61—41no—
113C4⋊C4×C61—82no—
114C22⋊C4×C61—44no—
115C22⋊C4×C61—41no—
116C22⋊C4×C61—41no—
117C22⋊C4×C61—82no—
118C42×C61C2×D411yescharacteristic
119C42×C61C2×D411yescharacteristic
120C42×C61C2×D411yescharacteristic
121C42×C61#4111yescharacteristic
122#11758199—44no—
123#11758198—41no—
124#11758198—41no—
125C4⋊Dic61—21no—
126C4⋊Dic61—21no—
127#11758194—42no—
128C2×#92418—22no—
129C2×#92418—22no—
130C2×#92418—41no—
131C23×C61—22no—
132C23×C61—42no—
133C23×C61—41no—
134C23×C61—41no—
135C23×C61—42no—
136C23×C61#12011yescharacteristic
137C22×D61—41no—
138D4×C61—22no—
139D4×C61—22no—
140D4×C61—41no—
141D4×C61—41no—
142C2×C4×C61—22no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—42no—
146C2×C4×C61—42no—
147C2×C4×C61—41no—
148C2×C4×C61—42no—
149C2×C4×C61—41no—
150C2×C4×C61—42no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61—42no—
155C2×C4×C61—82no—
156C2×C4×C61—82no—
157C2×C4×C61#12011yescharacteristic
158C2×C4×C61#12011yescharacteristic
159C2×C4×C61#12111yescharacteristic
160C2×C4×C61#12111yescharacteristic
161C2×C4×C61#12111yescharacteristic
162C2×C4×C61#12711yescharacteristic
163C22⋊D61—82no—
164C2×Dic61—41no—
165D244—42no—
166D244—42no—
167D244—81no—
168C4×D61—82no—
169Dic122—42no—
170#92418—42no—
171#92418—42no—
172#92418—81no—
173#10019—611nomaximal, Sylow
174C22×C61—21no—
175C22×C61—21no—
176C22×C61—44no—
177C22×C61—42no—
178C22×C61—82no—
179C22×C61—81no—
180C22×C61—81no—
181C22×C61#39211yescharacteristic
182C22×C61#45412yes—
183C2×D61—81no—
184C2×D61—81no—
185C2×D61—81no—
186C4×C61—21no—
187C4×C61—21no—
188C4×C61—21no—
189C4×C61—21no—
190C4×C61—21no—
191C4×C61—21no—
192C4×C61—82no—
193C4×C61—81no—
194C4×C61—81no—
195C4×C61—81no—
196Dic61—81no—
197#3142—611no—
198#3109—611no—
199#2633D6111yescharacteristic, complemented
200#1534—611no—
201#1514—611no—
202#1490—611no—
203#1288—611no—
204C2×C61—22no—
205C2×C61—82no—
206C2×C61#200311yescharacteristic
207C2×C61#200811yescharacteristic
208C2×C61#201011yescharacteristic
209D61—161no—
210#532—611no—
211C2×#125C2×D6111yescharacteristic
212C2×C4×D4C2×D6111yescharacteristic
213#491—1221no—
214#490—1221no—
215#488—1222no—
216#481—1221no—
217#476—1221no—
218#459—1221no—
219#447—1221no—
220#442—1222no—
221#432—611no—
222#432—611no—
223#417—1221no—
224#417—1221no—
225C4×M16—611no—
226#399—21no—
227#398—21no—
228#397—21no—
229#394—21no—
230#385—22no—
231#383C2×D6111yescharacteristic
232#330—1222no—
233#327—1222no—
234D4⋊C8—1222no—
235C61#1001911yescharacteristic, complemented, Sylow
236C2×#41—1221no—
237C22×D4C22⋊D6111yescharacteristic
238C23×C4—21no—
239C2×D8—1222no—
240C2×M16—1221no—
241C4⋊Q8—611no—
242#127—611no—
243#125—21no—
244#125—21no—
245#125—21no—
246#125—21no—
247#124—1221no—
248#121—1221no—
249#121—1221no—
250C4×D4—21no—
251C4×D4—21no—
252C4×D4—21no—
253C4×D4—21no—
254C4×D4—1221no—
255C4×D4—1221no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4C22⋊D6111yescharacteristic
260C2×C4⋊C4C22⋊D6111yescharacteristic
261C2×C4⋊C4C22⋊D6111yescharacteristic
262C2×C22⋊C4—22no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—22no—
265C2×C42C22×D6111yescharacteristic
266#106—1222no—
267C4⋊C8—1221no—
268C4⋊C8—1221no—
269#103—1222no—
270#103—1222no—
271#102—1222no—
272#102—1222no—
273#102—1222no—
274#102—1222no—
275C22⋊C8—1221no—
276C22⋊C8—1221no—
277#97—612no—
278#97—1221no—
279#97—1221no—
280C4×C8—612no—
281#95—22no—
282#95—21no—
283#95—21no—
284#95C22⋊D6112yes—
285C24—21no—
286#41—2444no—
287C2×Q8—1221no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—42no—
291C2×D4—1221no—
292C2×D4—1221no—
293C2×D4—1221no—
294C2×D4—2441no—
295C22×C4—22no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—82no—
302C22×C4—2441no—
303C22×C4C2×C22⋊D6111yescharacteristic
304C22×C4C2×C22⋊D6111yescharacteristic
305C22×C4C2×C22⋊D6111yescharacteristic
306D8—2444no—
307M16—2442no—
308C2×C8—1222no—
309C2×C8—1222no—
310C2×C8—2441no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—82no—
322C4⋊C4—1221no—
323C4⋊C4—1221no—
324C22⋊C4—44no—
325C22⋊C4—41no—
326C22⋊C4—41no—
327C22⋊C4—82no—
328C22⋊C4—2441no—
329C22⋊C4—2441no—
330C42D4×D6111yescharacteristic
331C42D4×D6111yescharacteristic
332C42D4×D6111yescharacteristic
333C42#1175822411yescharacteristic
334C23—22no—
335C23—42no—
336C23—41no—
337C23—41no—
338C23—42no—
339C23—2441no—
340C23#1451974611yescharacteristic
341Q8—2442no—
342D4—22no—
343D4—22no—
344D4—41no—
345D4—41no—
346D4—4881no—
347D4—4882no—
348D4—2442no—
349D4—2442no—
350C2×C4—22no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—82no—
364C2×C4—82no—
365C2×C4—4882no—
366C2×C4—2441no—
367C2×C4#1451974511yescharacteristic
368C2×C4#1451974511yescharacteristic
369C2×C4#1451974811yescharacteristic
370C2×C4#1451974911yescharacteristic
371C2×C4#1451974911yescharacteristic
372C2×C4#1451977311yescharacteristic
373C8—4881no—
374C8—2442no—
375C8—2442no—
376C22—21no—
377C22—21no—
378C22—44no—
379C22—42no—
380C22—82no—
381C22—81no—
382C22—81no—
383C22—4881no—
384C22—4881no—
385C22—4881no—
386C22#1683967011yescharacteristic
387C22#1683993512yes—
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—82no—
395C4—81no—
396C4—81no—
397C4—81no—
398C4—4881no—
399C2—22no—
400C2—82no—
401C2—9761no—
402C2#2144683911yescharacteristic
403C2#2144687211yescharacteristic
404C2#2144688411yescharacteristic
subgroupG/H
centerC22#16839670
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2633C2
socleC22×C61#392
prime radical#21455910C2
hypercenter#2633D61
hypocenterC61#10019
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2633

Complements

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

NH ≅ G/Ntype
1. #21456222C2semidirect
3. #21444446C2semidirect
4. #21444365C2semidirect
5. #21444262C2semidirect
6. #21443683C2semidirect
7. C61×#2633C2semidirect
199. #2633D61semidirect
235. C61#10019semidirect

Maximal subgroups

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

subgroupindex
#214562222
#214559102
#214444462
#214443652
#214442622
#214436832
C61×#26332
#1001961