Finite Group Databasebeta

← #29576950

Subgroups — #29576950

Order 15616.

530 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 103 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#21455910C211yesmaximal, characteristic
2#21446737C211yesmaximal, characteristic, complemented
3#21444326C211yesmaximal, characteristic, complemented
4#21444262C211yesmaximal, characteristic, complemented
5#21443712C211yesmaximal, characteristic, complemented
6#21443675C211yesmaximal, characteristic, complemented
7C61×#2319C211yesmaximal, characteristic, complemented
8#16840312C2211yescharacteristic
9#16840080—21no—
10#16840052C412yescomplemented
11#16839957C412yescomplemented
12#16839896—21no—
13#16839872—22no—
14#16839819C2211yescharacteristic
15#16839819C2211yescharacteristic
16C2×#14519705—22no—
17C4×#11758194C2211yescharacteristic
18#16839495—21no—
19#16839495—21no—
20D4⋊#92418—22no—
21C2×C4×D4×C61C2211yescharacteristic
22C61×#390—21no—
23C61×#389—21no—
24C61×#388—22no—
25C61×#381—21no—
26C61×#380—21no—
27C4×C4⋊C4×C61C2211yescharacteristic
28C61×#376C2211yescharacteristic
29C2×#11758222—21no—
30C2×#11758199—22no—
31C2×#11758194—21no—
32#14519777C2×C411yescharacteristic
33#14519774C2×C411yescharacteristic
34#14519765—21no—
35#14519751—21no—
36#14519751—21no—
37C4×D244—21no—
38C4×D244—21no—
39#14519708—22no—
40C4⋊#92418—21no—
41C4⋊#92418C2×C412yes—
42#14519705—44no—
43#14519698—22no—
44#14519697—22no—
45C22⋊#92418—21no—
46C22⋊#92418—21no—
47#14519688—21no—
48#14519688—21no—
49#14519688—21no—
50C4×#92418—21no—
51C22×D4×C61D411yescharacteristic
52C23×C4×C61—21no—
53C4×D4×C61—21no—
54C4×D4×C61—21no—
55C4×D4×C61C2×C412yes—
56C4×D4×C61D412yes—
57C2×C4⋊C4×C61—21no—
58C2×C4⋊C4×C61—22no—
59C2×C4⋊C4×C61D411yescharacteristic
60C2×C22⋊C4×C61—21no—
61C2×C22⋊C4×C61—22no—
62C2×C22⋊C4×C61—22no—
63C2×C42×C61—21no—
64C2×C42×C61D412yes—
65C2×C42×C61C2311yescharacteristic
66#95×C61—22no—
67#95×C61—21no—
68#95×C61—21no—
69#95×C61D411yescharacteristic
70#95×C61D411yescharacteristic
71C24×C61—21no—
72C2×D4×C61—21no—
73C2×D4×C61—42no—
74C2×D4×C61C22⋊C412yes—
75C22×C4×C61—21no—
76C22×C4×C61—22no—
77C22×C4×C61—22no—
78C22×C4×C61—21no—
79C22×C4×C61—22no—
80C22×C4×C61—21no—
81C22×C4×C61—82no—
82C22×C4×C61C2×D411yescharacteristic
83C22×C4×C61C2×D411yescharacteristic
84C22×C4×C61C2×D411yescharacteristic
85C2×C22⋊D61—41no—
86#11758222—42no—
87#11758222—42no—
88C2×D244—21no—
89C2×D244—21no—
90C2×D244—21no—
91C2×C4×D61—41no—
92C2×Dic122—21no—
93C4⋊C4×C61—21no—
94C4⋊C4×C61—42no—
95C4⋊C4×C61—82no—
96C4⋊C4×C61C22⋊C412yes—
97C22⋊C4×C61—22no—
98C22⋊C4×C61—22no—
99C22⋊C4×C61—82no—
100C22⋊C4×C61—82no—
101C42×C61—42no—
102C42×C61—42no—
103C42×C61C22×C411yescharacteristic
104C42×C61C2×D411yescharacteristic
105C42×C61#4111yescharacteristic
106C42×C61#4111yescharacteristic
107#11758199—44no—
108#11758198—41no—
109#11758198—41no—
110C4⋊Dic61—21no—
111C4⋊Dic61—21no—
112#11758194—22no—
113#11758194—41no—
114C2×#92418—22no—
115C2×#92418—41no—
116C2×#92418—41no—
117C23×C61—22no—
118C23×C61—42no—
119C23×C61—42no—
120C23×C61—41no—
121C23×C61—41no—
122C23×C61#12011yescharacteristic
123C22×D61—41no—
124D4×C61—22no—
125D4×C61—22no—
126D4×C61—42no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—22no—
130C2×C4×C61—22no—
131C2×C4×C61—41no—
132C2×C4×C61—42no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—42no—
137C2×C4×C61—42no—
138C2×C4×C61—41no—
139C2×C4×C61—42no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—82no—
143C2×C4×C61—82no—
144C2×C4×C61C2×C22⋊C411yescharacteristic
145C2×C4×C61C4×D411yescharacteristic
146C2×C4×C61C4×D411yescharacteristic
147C2×C4×C61#12111yescharacteristic
148C2×C4×C61#12111yescharacteristic
149C2×C4×C61#12311yescharacteristic
150C22⋊D61—81no—
151C22⋊D61—81no—
152C2×Dic61—41no—
153D244—42no—
154D244—42no—
155D244—81no—
156C4×D61—82no—
157Dic122—42no—
158#92418—42no—
159#92418—42no—
160#92418—81no—
161#9329—611nomaximal, Sylow
162C22×C61—21no—
163C22×C61—21no—
164C22×C61—42no—
165C22×C61—42no—
166C22×C61—42no—
167C22×C61—82no—
168C22×C61—82no—
169C22×C61#38611yescharacteristic
170C22×C61#45311yescharacteristic
171C22×C61#45411yescharacteristic
172C2×D61—81no—
173C2×D61—81no—
174C2×D61—81no—
175C4×C61—21no—
176C4×C61—21no—
177C4×C61—21no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—42no—
181C4×C61—81no—
182C4×C61—82no—
183C4×C61—81no—
184C4×C61#42112yes—
185Dic61—81no—
186#3109—611no—
187#2319D6111yescharacteristic, complemented
188#1980—611no—
189#1505—611no—
190#1490—611no—
191#1300—611no—
192#1285—611no—
193C2×C61—21no—
194C2×C61—21no—
195C2×C61—82no—
196C2×C61#188311yescharacteristic
197C2×C61#189711yescharacteristic
198C2×C61#190411yescharacteristic
199D61—161no—
200#532—611no—
201C2×C4×D4C2×D6111yescharacteristic
202#481—1221no—
203#476—612no—
204#459—612no—
205#447—1221no—
206#442—1222no—
207#432—611no—
208#432—611no—
209C2×#104—1222no—
210C4×M16—611no—
211#390—21no—
212#389—21no—
213#388—22no—
214#381—21no—
215#380—21no—
216C4×C4⋊C4C2×D6111yescharacteristic
217#376C2×D6111yescharacteristic
218#327—1221no—
219#327—1221no—
220D4⋊C8—1222no—
221C61#932911yescharacteristic, complemented, Sylow
222C2×#41—1221no—
223C22×D4C22⋊D6111yescharacteristic
224C23×C4—21no—
225C2×D8—1222no—
226C2×M16—1221no—
227C4⋊Q8—611no—
228#127—611no—
229#124—1221no—
230#121—1221no—
231#121—1221no—
232C4×D4—21no—
233C4×D4—21no—
234C4×D4—1221no—
235C4×D4—1221no—
236C4×D4C4×D6112yes—
237C4×D4D24412yes—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—22no—
240C2×C4⋊C4C22⋊D6111yescharacteristic
241C2×C22⋊C4—21no—
242C2×C22⋊C4—22no—
243C2×C22⋊C4—22no—
244C2×C42—21no—
245C2×C42C22⋊D6112yes—
246C2×C42C22×D6111yescharacteristic
247#106—1222no—
248C4⋊C8—612no—
249C4⋊C8—1221no—
250#104—2444no—
251#102—1222no—
252#102—1222no—
253C22⋊C8—1221no—
254C22⋊C8—1221no—
255#97—1221no—
256#97—1221no—
257#97—1221no—
258C4×C8—1221no—
259#95—22no—
260#95—21no—
261#95—21no—
262#95C22⋊D6111yescharacteristic
263#95C22⋊D6111yescharacteristic
264C24—21no—
265#41—2442no—
266#41—2442no—
267C2×Q8—1221no—
268C2×D4—21no—
269C2×D4—42no—
270C2×D4—1221no—
271C2×D4—1221no—
272C2×D4—1221no—
273C2×D4—2441no—
274C2×D4#1175819812yes—
275C22×C4—21no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—21no—
279C22×C4—22no—
280C22×C4—21no—
281C22×C4—82no—
282C22×C4—2441no—
283C22×C4C2×C22⋊D6111yescharacteristic
284C22×C4C2×C22⋊D6111yescharacteristic
285C22×C4C2×C22⋊D6111yescharacteristic
286D8—2444no—
287M16—1222no—
288M16—2441no—
289C2×C8—1222no—
290C2×C8—2441no—
291C2×C8—2441no—
292C4⋊C4—21no—
293C4⋊C4—42no—
294C4⋊C4—82no—
295C4⋊C4—1221no—
296C4⋊C4—1221no—
297C4⋊C4#1175819812yes—
298C22⋊C4—22no—
299C22⋊C4—22no—
300C22⋊C4—82no—
301C22⋊C4—82no—
302C22⋊C4—2441no—
303C22⋊C4—2441no—
304C42—42no—
305C42—42no—
306C42C2×C4×D6111yescharacteristic
307C42C2×D24411yescharacteristic
308C42#1175822211yescharacteristic
309C42#1175822211yescharacteristic
310C23—22no—
311C23—42no—
312C23—42no—
313C23—41no—
314C23—41no—
315C23—2441no—
316C23#1451974611yescharacteristic
317Q8—2442no—
318D4—22no—
319D4—22no—
320D4—42no—
321D4—4881no—
322D4—4881no—
323D4—4881no—
324D4—2442no—
325D4—2442no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—82no—
342C2×C4—82no—
343C2×C4—4882no—
344C2×C4—2441no—
345C2×C4C2×#1175819811yescharacteristic
346C2×C4C4×C22⋊D6111yescharacteristic
347C2×C4C4×C22⋊D6111yescharacteristic
348C2×C4#1451975111yescharacteristic
349C2×C4#1451975111yescharacteristic
350C2×C4#1451976011yescharacteristic
351C8—4881no—
352C8—2442no—
353C8—2442no—
354C22—21no—
355C22—21no—
356C22—42no—
357C22—42no—
358C22—42no—
359C22—82no—
360C22—82no—
361C22—4881no—
362C22—4881no—
363C22—4881no—
364C22#1683964111yescharacteristic
365C22#1683993011yescharacteristic
366C22#1683993511yescharacteristic
367C4—21no—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—42no—
373C4—81no—
374C4—82no—
375C4—81no—
376C4—4881no—
377C4#1683978012yes—
378C2—21no—
379C2—21no—
380C2—82no—
381C2—9761no—
382C2#2144619511yescharacteristic
383C2#2144626711yescharacteristic
384C2#2144630611yescharacteristic
subgroupG/H
centerC22#16839641
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#2319C2
socleC22×C61#386
prime radical#21455910C2
cosocleC2×C42×C61C23
hypercenter#2319D61
hypocenterC61#9329
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2319

Complements

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

NH ≅ G/Ntype
2. #21446737C2semidirect
3. #21444326C2semidirect
4. #21444262C2semidirect
5. #21443712C2semidirect
6. #21443675C2semidirect
7. C61×#2319C2semidirect
10. #16840052C4semidirect
11. #16839957C4semidirect
187. #2319D61semidirect
221. C61#9329semidirect

Maximal subgroups

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

subgroupindex
#214559102
#214467372
#214443262
#214442622
#214437122
#214436752
C61×#23192
#932961