Finite Group Databasebeta

← #29589610

Subgroups — #29589610

Order 15616.

446 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 73 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#21450126C211yesmaximal, characteristic
2#21444158C211yesmaximal, characteristic
3#21444134C211yesmaximal, characteristic
4#21443749C211yesmaximal, characteristic, complemented
5#21443748C211yesmaximal, characteristic, complemented
6#21443748C211yesmaximal, characteristic, complemented
7C61×#1317C211yesmaximal, characteristic, complemented
8C2×#14519761C411yescharacteristic
9C2×#14519760C411yescharacteristic
10C2×#14519737C2211yescharacteristic
11C22×#11758196C411yescharacteristic
12#16839816—21no—
13C22⋊C8×D61—21no—
14#16839696—21no—
15#16839691—21no—
16#16839659—21no—
17#16839623C2211yescharacteristic
18#16839621—21no—
19#16839620C411yescharacteristic
20#16839487—21no—
21#16839486C2211yescharacteristic
22#16839486C2211yescharacteristic
23#16839485—21no—
24C61×#381C2211yescharacteristic
25C61×#323C2211yescharacteristic
26C61×#323C2211yescharacteristic
27C22×C22⋊D61C2×C411yescharacteristic
28C23×Dic61C2×C411yescharacteristic
29C23×Dic61C2×C411yescharacteristic
30C22×C4×D61D411yescharacteristic
31C2×C8×D61—41no—
32#14519761—42no—
33#14519760—42no—
34#14519737—41no—
35#14519737—41no—
36C2×C4⋊Dic61—21no—
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×#11758196—41no—
42C2×#11758196—41no—
43C2×#11758196D411yescharacteristic
44C2×C22⋊Dic61C2×C411yescharacteristic
45C2×#11758198—21no—
46C2×#11758198—21no—
47C2×#11758198D411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49#14519706—41no—
50C22⋊#92418—21no—
51C22⋊#92418—21no—
52#14519689—41no—
53#14519687—41no—
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57C23×C4×C61C2×C411yescharacteristic
58C2×C22⋊C4×C61C2×C411yescharacteristic
59C2×C22⋊C4×C61C2311yescharacteristic
60C22⋊C8×C61—21no—
61C22⋊C8×C61—21no—
62#95×C61—21no—
63#95×C61—21no—
64C24×C61C22×C411yescharacteristic
65C23×D61C22⋊C411yescharacteristic
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—41no—
71C22×C4×C61—41no—
72C22×C4×C61C2×D411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C2×C22⋊D61—21no—
75C2×C22⋊D61—21no—
76C2×C22⋊D61—22no—
77C2×C22⋊D61—41no—
78C22×Dic61—21no—
79C22×Dic61—21no—
80C22×Dic61—21no—
81C22×Dic61—21no—
82C22×Dic61—21no—
83C22×Dic61—21no—
84C22×Dic61—42no—
85C22×Dic61—41no—
86C22×Dic61—41no—
87C22×Dic61C22⋊C411yescharacteristic
88C22×Dic61C22⋊C411yescharacteristic
89C22×Dic61C22⋊C411yescharacteristic
90C2×C4×D61—21no—
91C2×C4×D61—21no—
92C2×C4×D61—42no—
93C2×C8×C61—41no—
94C2×C8×C61—41no—
95C22⋊C4×C61—41no—
96C22⋊C4×C61—41no—
97C22⋊Dic61—41no—
98#11758198—41no—
99#11758198—42no—
100#11758198—42no—
101C4⋊Dic61—42no—
102#11758196—41no—
103#11758196—42no—
104#11758196—42no—
105#11758196—42no—
106#11758196—41no—
107#11758196—41no—
108C4×Dic61—21no—
109C4×Dic61—21no—
110C2×#92418—41no—
111C2×#92418—41no—
112C8×D61—82no—
113C23×C61—21no—
114C23×C61—21no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61C2×C22⋊C411yescharacteristic
118C23×C61#13111yescharacteristic
119C23×C61#13111yescharacteristic
120C22×D61—21no—
121C22×D61—21no—
122C22×D61—41no—
123C22×D61—41no—
124C22×D61#10012yes—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—81no—
136C2×C4×C61—81no—
137C22⋊D61—42no—
138C22⋊D61—42no—
139C2×Dic61—22no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—42no—
145C2×Dic61—42no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—81no—
154C2×Dic61—81no—
155C2×Dic61#9911yescharacteristic
156C2×Dic61#9911yescharacteristic
157C4×D61—42no—
158C4×D61—81no—
159C8×C61—81no—
160C8×C61—81no—
161#92418—81no—
162#92418—81no—
163#11558—611nomaximal, Sylow
164C22×C61—21no—
165C22×C61—21no—
166C22×C61—21no—
167C22×C61—21no—
168C22×C61—41no—
169C22×C61—41no—
170C22×C61—42no—
171C22×C61—41no—
172C22×C61—41no—
173C22×C61#40811yescharacteristic
174C22×C61C2×#9911yescharacteristic
175C22×C61C2×#10011yescharacteristic
176C2×D61—22no—
177C2×D61—41no—
178C2×D61—41no—
179C2×D61—42no—
180C2×D61—81no—
181C4×C61—41no—
182C4×C61—41no—
183C4×C61—81no—
184C4×C61—81no—
185Dic61—21no—
186Dic61—41no—
187Dic61—41no—
188Dic61—81no—
189Dic61—81no—
190Dic61#35212yes—
191#2486—611no—
192#1466—611no—
193#1459—611no—
194#1317—611no—
195#1317—611no—
196#1317—611no—
197#1317D6111yescharacteristic, complemented
198C2×C61—21no—
199C2×C61—21no—
200C2×C61—41no—
201C2×C61—41no—
202C2×C61#147111yescharacteristic
203C2×C61C2×#35211yescharacteristic
204C2×C61#212311yescharacteristic
205D61—42no—
206C2×#123—611no—
207C2×#123—611no—
208C2×C4×D4—611no—
209C22×C4⋊C4—611no—
210#432—1221no—
211C2×C22⋊C8—1221no—
212#398—1221no—
213#397—1221no—
214#389—1221no—
215#381—611no—
216#381C2×D6111yescharacteristic
217#380—611no—
218#380—1221no—
219#324—1221no—
220#323—611no—
221#323—611no—
222#323—1221no—
223#323C2×D6111yescharacteristic
224#323C2×D6111yescharacteristic
225C61#1155811yescharacteristic, complemented, Sylow
226C22×D4—611no—
227C23×C4—611no—
228C23×C4—611no—
229C23×C4—611no—
230C23×C4C4×D6111yescharacteristic
231C22×C8—2441no—
232#123—2442no—
233#123—2442no—
234C4×D4—2441no—
235C4×D4—2441no—
236C2×C4⋊C4—611no—
237C2×C4⋊C4—1221no—
238C2×C4⋊C4—1221no—
239C2×C4⋊C4—1221no—
240C2×C4⋊C4—1221no—
241C2×C4⋊C4—1221no—
242C2×C4⋊C4—2441no—
243C2×C4⋊C4—2441no—
244C2×C22⋊C4—611no—
245C2×C22⋊C4—611no—
246C2×C22⋊C4—1221no—
247C2×C22⋊C4—1221no—
248C2×C22⋊C4C4×D6111yescharacteristic
249C2×C22⋊C4C22×D6111yescharacteristic
250C2×C42—611no—
251C4⋊C8—2441no—
252C22⋊C8—21no—
253C22⋊C8—21no—
254C22⋊C8—1221no—
255C22⋊C8—1221no—
256C22⋊C8—2441no—
257#97—2441no—
258#95—21no—
259#95—21no—
260#95—1221no—
261#95—1221no—
262#95—1221no—
263C24—611no—
264C24C2×C4×D6111yescharacteristic
265C2×D4—1222no—
266C2×D4—1221no—
267C2×D4—1221no—
268C2×D4—2441no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—611no—
276C22×C4—611no—
277C22×C4—611no—
278C22×C4—1221no—
279C22×C4—1221no—
280C22×C4—1221no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4—1221no—
285C22×C4—1221no—
286C22×C4—2442no—
287C22×C4—2442no—
288C22×C4—2441no—
289C22×C4—2441no—
290C22×C4D4×D6111yescharacteristic
291C22×C4D4×D6111yescharacteristic
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—4882no—
295C2×C8—2441no—
296C2×C8—2441no—
297C4⋊C4—2441no—
298C4⋊C4—2441no—
299C4⋊C4—2441no—
300C4⋊C4—2442no—
301C4⋊C4—2442no—
302C4⋊C4—2442no—
303C4⋊C4—2442no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—2441no—
307C22⋊C4—2442no—
308C22⋊C4—2442no—
309C22⋊C4—2441no—
310C42—1221no—
311C42—1221no—
312C23—21no—
313C23—21no—
314C23—41no—
315C23—41no—
316C23—612no—
317C23—1221no—
318C23—1221no—
319C23—2441no—
320C23—2441no—
321C23C22⋊C4×D6111yescharacteristic
322C23#1451978311yescharacteristic
323C23#1451978511yescharacteristic
324D4—2442no—
325D4—2442no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—611no—
339C2×C4—611no—
340C2×C4—1222no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—1221no—
344C2×C4—1221no—
345C2×C4—4881no—
346C2×C4—4881no—
347C2×C4—4881no—
348C2×C4—2442no—
349C2×C4—2442no—
350C2×C4—2442no—
351C2×C4—2441no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4—2441no—
355C2×C4—2441no—
356C2×C4—2441no—
357C2×C4—2441no—
358C8—81no—
359C8—81no—
360C8—4881no—
361C8—4881no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—41no—
367C22—41no—
368C22—42no—
369C22—41no—
370C22—41no—
371C22—1222no—
372C22—4881no—
373C22—2442no—
374C22—2441no—
375C22—2441no—
376C22#1683972711yescharacteristic
377C22#99×D6111yescharacteristic
378C22#100×D6111yescharacteristic
379C4—41no—
380C4—41no—
381C4—81no—
382C4—81no—
383C4—612no—
384C4—1221no—
385C4—4881no—
386C4—4881no—
387C4—2441no—
388C4—2441no—
389C2—21no—
390C2—21no—
391C2—41no—
392C2—41no—
393C2—2442no—
394C2#2144417711yescharacteristic
395C2#352×D6111yescharacteristic
396C2#2144747111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC24×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1317C2
socleC22×C61C2×#99
prime radicalC22×C22⋊D61C2×C4
cosocleC2×C22⋊C4×C61C23
hypercenter#1317D61
hypocenterC61#11558
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1317

Complements

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

NH ≅ G/Ntype
4. #21443749C2semidirect
5. #21443748C2semidirect
6. #21443748C2semidirect
7. C61×#1317C2semidirect
197. #1317D61semidirect
225. C61#11558semidirect

Maximal subgroups

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

subgroupindex
#214501262
#214441582
#214441342
#214437492
#214437482
C61×#13172
#1155861