Finite Group Databasebeta

← #29568095

Subgroups — #29568095

Order 15616.

482 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 109 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#21448281C211yesmaximal, characteristic
2#21445961C211yesmaximal, characteristic, complemented
3#21445934C211yesmaximal, characteristic, complemented
4#21443643C211yesmaximal, characteristic, complemented
5#21443641C211yesmaximal, characteristic, complemented
6#21443640C211yesmaximal, characteristic
7C61×#1270C211yesmaximal, characteristic
8C2×D4×Dic61C411yescharacteristic
9C2×#14519733—21no—
10C2×#14519706—21no—
11#16839665C411yescharacteristic
12#16839660C2211yescharacteristic
13#16839658C411yescharacteristic
14#16839656—21no—
15#16839650—21no—
16C4⋊C4×Dic61C411yescharacteristic
17C22⋊C4×Dic61—21no—
18C42×Dic61C2211yescharacteristic
19#16839517C2211yescharacteristic
20#16839517C2211yescharacteristic
21#16839516—21no—
22#16839516—21no—
23#16839516—21no—
24C61×#390C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C23×Dic61—21no—
28C22×#92418—21no—
29C22×#92418—21no—
30D4×Dic61—22no—
31D4×Dic61C814yescomplemented
32#14519733—42no—
33#14519733—42no—
34C2×C4⋊Dic61C2×C411yescharacteristic
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×C22⋊Dic61—21no—
39C2×C22⋊Dic61—21no—
40C2×C22⋊Dic61—21no—
41C2×C4×Dic61—21no—
42C2×C4×Dic61C2×C411yescharacteristic
43C2×C4×Dic61C2×C411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48#14519706—42no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52C22×D4×C61C2×C411yescharacteristic
53C22×C8×C61—21no—
54C22×C8×C61—21no—
55C2×C4⋊C4×C61C2×C411yescharacteristic
56C2×C22⋊C4×C61—21no—
57C2×C22⋊C4×C61—21no—
58C2×C42×C61C2311yescharacteristic
59C24×C61—21no—
60C2×D4×C61—21no—
61C2×D4×C61—41no—
62C2×D4×C61—41no—
63C2×D4×C61C2×C812yes—
64C22×C4×C61—21no—
65C22×C4×C61C22×C411yescharacteristic
66C22×C4×C61C2×D411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C22×Dic61—21no—
69C22×Dic61—24no—
70C22×Dic61—21no—
71C22×Dic61—42no—
72C22×Dic61—42no—
73C22×Dic61C22⋊C411yescharacteristic
74C22×Dic61C22⋊C411yescharacteristic
75C22×Dic61C22⋊C411yescharacteristic
76C22×Dic61C22⋊C411yescharacteristic
77C2×C8×C61—41no—
78C2×C8×C61—41no—
79C2×C8×C61—41no—
80C2×C8×C61—41no—
81C2×C8×C61—41no—
82C2×C8×C61—41no—
83C4⋊C4×C61—41no—
84C22⋊C4×C61—41no—
85C22⋊C4×C61—41no—
86C22⋊C4×C61—41no—
87C22⋊C4×C61—41no—
88C42×C61—41no—
89C22⋊Dic61—24no—
90C22⋊Dic61—42no—
91C22⋊Dic61—42no—
92C4⋊Dic61—21no—
93C4⋊Dic61—41no—
94C4⋊Dic61C2×C812yes—
95#11758196—42no—
96#11758196—41no—
97#11758196—41no—
98C4×Dic61—21no—
99C4×Dic61—21no—
100C4×Dic61—21no—
101C4×Dic61—21no—
102C4×Dic61—41no—
103C4×Dic61—41no—
104C4×Dic61—41no—
105C4×Dic61—42no—
106C4×Dic61C2×C812yes—
107C4×Dic61M1612yes—
108C2×#92418—41no—
109C2×#92418—41no—
110C2×#92418—41no—
111C2×#92418—41no—
112C2×#92418—41no—
113C2×#92418—41no—
114C23×C61—22no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61—41no—
118C23×C61—41no—
119C23×C61—41no—
120C23×C61—41no—
121C23×C61C2×C22⋊C411yescharacteristic
122D4×C61—42no—
123D4×C61—42no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61C22×C811yescharacteristic
134C2×C4×C61C2×M1611yescharacteristic
135C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C61#13711yescharacteristic
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—22no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—48no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61C22⋊C812yes—
157C2×Dic61C22⋊C812yes—
158C8×C61—81no—
159C8×C61—81no—
160#92418—81no—
161#92418—81no—
162#7594—611nomaximal, Sylow
163C22×C61—42no—
164C22×C61—42no—
165C22×C61—42no—
166C22×C61—81no—
167C22×C61—81no—
168C22×C61—81no—
169C22×C61—81no—
170C22×C61C2×C22⋊C811yescharacteristic
171C22×C61#41011yescharacteristic
172C22×C61#41311yescharacteristic
173C22×C61#41711yescharacteristic
174C22×C61#41811yescharacteristic
175C22×C61#42111yescharacteristic
176C22×C61#42111yescharacteristic
177C4×C61—21no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—21no—
183C4×C61—81no—
184Dic61—22no—
185Dic61—22no—
186Dic61—41no—
187Dic61—42no—
188Dic61—41no—
189Dic61—81no—
190#2293—611no—
191#1839—611no—
192#1831—611no—
193#1271—611no—
194#1271—611no—
195#1270—611no—
196#1270D6111yescharacteristic
197C2×C61—82no—
198C2×C61#145811yescharacteristic
199C2×C61#147711yescharacteristic
200C2×C61#147811yescharacteristic
201C2×C61#151211yescharacteristic
202C2×C61#151411yescharacteristic
203C2×C61#153511yescharacteristic
204C2×C61#155711yescharacteristic
205C2×C4×D4—611no—
206C2×#117—1221no—
207C2×C4⋊C8—1221no—
208#390—611no—
209#390C2×D6111yescharacteristic
210#389—611no—
211#389—611no—
212#388—1221no—
213#388—1221no—
214C4×C4⋊C4—611no—
215C4×C22⋊C4—1221no—
216C43—611no—
217#336—611no—
218#336—611no—
219#336—1221no—
220#336—1221no—
221#336—1221no—
222#336C2×D6111yescharacteristic
223#336C2×D6111yescharacteristic
224C61#759411yescharacteristic, complemented, Sylow
225C22×D4C4×D6111yescharacteristic
226C23×C4—1221no—
227C22×C8—21no—
228C22×C8—21no—
229C22×C8—1221no—
230C22×C8—1221no—
231C4×D4—614no—
232C4×D4—1222no—
233#117—2442no—
234#117—2442no—
235C2×C4⋊C4—611no—
236C2×C4⋊C4—611no—
237C2×C4⋊C4—1221no—
238C2×C4⋊C4—1221no—
239C2×C4⋊C4C4×D6111yescharacteristic
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—1221no—
243C2×C22⋊C4—1221no—
244C2×C22⋊C4—1221no—
245C2×C42—611no—
246C2×C42—611no—
247C2×C42—611no—
248C2×C42—611no—
249C2×C42—611no—
250C2×C42—611no—
251C2×C42—1221no—
252C2×C42C22×D6111yescharacteristic
253C4⋊C8—2442no—
254#95—1221no—
255#95—1221no—
256#95—1221no—
257C24—21no—
258C2×D4—21no—
259C2×D4—41no—
260C2×D4—41no—
261C2×D4C8×D6112yes—
262C22×C4—21no—
263C22×C4—611no—
264C22×C4—611no—
265C22×C4—611no—
266C22×C4—611no—
267C22×C4—1224no—
268C22×C4—1221no—
269C22×C4—1221no—
270C22×C4—2442no—
271C22×C4—2442no—
272C22×C4C2×C4×D6111yescharacteristic
273C22×C4D4×D6111yescharacteristic
274C22×C4D4×D6111yescharacteristic
275C2×C8—41no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—2441no—
282C2×C8—2441no—
283C2×C8—2441no—
284C2×C8—2441no—
285C2×C8—2441no—
286C2×C8—2441no—
287C4⋊C4—41no—
288C4⋊C4—612no—
289C4⋊C4—1221no—
290C4⋊C4—2441no—
291C4⋊C4—2442no—
292C4⋊C4—2441no—
293C4⋊C4—2441no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—1224no—
299C22⋊C4—2442no—
300C22⋊C4—2442no—
301C42—41no—
302C42—612no—
303C42—612no—
304C42—1221no—
305C42—1221no—
306C42—1221no—
307C42—1221no—
308C42—2441no—
309C42—2441no—
310C42—2441no—
311C42—2442no—
312C23—22no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23C22⋊C4×D6111yescharacteristic
320D4—42no—
321D4—42no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—612no—
332C2×C4—612no—
333C2×C4—1221no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—1222no—
338C2×C4—1221no—
339C2×C4—1221no—
340C2×C4—1221no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—1221no—
344C2×C4—2448no—
345C2×C4—2441no—
346C2×C4—2441no—
347C2×C4—2441no—
348C2×C4—2441no—
349C2×C4—2441no—
350C2×C4C2×C8×D6111yescharacteristic
351C2×C4M16×D6111yescharacteristic
352C2×C4#1451980111yescharacteristic
353C2×C4#1451980111yescharacteristic
354C2×C4#1451980411yescharacteristic
355C2×C4#1451980611yescharacteristic
356C8—81no—
357C8—81no—
358C8—4881no—
359C8—4881no—
360C22—42no—
361C22—42no—
362C22—42no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22C22⋊C8×D6111yescharacteristic
368C22#1683973411yescharacteristic
369C22#1683974311yescharacteristic
370C22#1683976011yescharacteristic
371C22#1683976511yescharacteristic
372C22#1683977711yescharacteristic
373C22#1683977711yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—81no—
381C4—1222no—
382C4—1222no—
383C4—4881no—
384C4—2441no—
385C4—2442no—
386C4—2441no—
387C2—82no—
388C2#2144413011yescharacteristic
389C2#2144420311yescharacteristic
390C2#2144420811yescharacteristic
391C2#2144435411yescharacteristic
392C2#2144436411yescharacteristic
393C2#2144444711yescharacteristic
394C2#2144453811yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC2×C4×C61C22×C8
FrattiniC2×C42C22×D61
FittingC61×#1270C2
socleC23×C61C2×C22⋊C4
prime radicalC22×D4×C61C2×C4
cosocleC2×C42×C61C23
hypercenter#1270D61
hypocenterC61#7594
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #21445961C2semidirect
3. #21445934C2semidirect
4. #21443643C2semidirect
5. #21443641C2semidirect
31. D4×Dic61C8semidirect
224. C61#7594semidirect

Maximal subgroups

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

subgroupindex
#214482812
#214459612
#214459342
#214436432
#214436412
#214436402
C61×#12702
#759461