Finite Group Databasebeta

← #29577691

Subgroups — #29577691

Order 15616.

518 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 518 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#21454847C211yesmaximal, characteristic
2#21450814C211yesmaximal, characteristic
3#21444544C211yesmaximal, characteristic, complemented
4#21444544C211yesmaximal, characteristic, complemented
5#21444159C211yesmaximal, characteristic
6#21443675C211yesmaximal, characteristic, complemented
7C61×#1285C211yesmaximal, characteristic, complemented
8C2×#14519777C2211yescharacteristic
9C2×#14519765C412yes—
10C2×C4×D244C2211yescharacteristic
11#16839835—22no—
12#16839832—22no—
13#16839819C2211yescharacteristic
14#16839819C2211yescharacteristic
15#16839724—21no—
16C22⋊C8×D61—21no—
17#16839689—21no—
18#16839689—21no—
19#16839668C412yes—
20#16839619—21no—
21#16839619—21no—
22#16839510—22no—
23#16839510—22no—
24#16839485—21no—
25#16839485—21no—
26C61×#432C2211yescharacteristic
27C61×#432C2211yescharacteristic
28C4×C4⋊C4×C61C2211yescharacteristic
29C22×Dic122C2×C412yes—
30C22×D244C2×C411yescharacteristic
31C22×C4×D61D411yescharacteristic
32C22×C4×D61D411yescharacteristic
33C2×#11758189—22no—
34C2×C8×D61—22no—
35#14519777—21no—
36#14519777—21no—
37#14519777—21no—
38#14519777—21no—
39#14519765—44no—
40C4×D244—21no—
41C4×D244—21no—
42C4×D244—21no—
43C4×D244—21no—
44C2×C4⋊Dic61—21no—
45C2×C4⋊Dic61—21no—
46C2×C4⋊Dic61C2×C411yescharacteristic
47C2×#11758198—22no—
48C2×#11758198—22no—
49C2×#11758198D411yescharacteristic
50C2×#11758198D411yescharacteristic
51C4⋊#92418—21no—
52C4⋊#92418D412yes—
53C22⋊#92418—21no—
54C22⋊#92418—21no—
55#14519689—22no—
56#14519689—22no—
57#14519688—21no—
58#14519688—21no—
59#14519684—22no—
60#14519684—22no—
61C2×C4⋊C4×C61—21no—
62C2×C42×C61C2×C412yes—
63C2×C42×C61C2311yescharacteristic
64C4⋊C8×C61—21no—
65C4⋊C8×C61D412yes—
66C22⋊C8×C61—21no—
67C22⋊C8×C61—21no—
68#97×C61—21no—
69#97×C61—21no—
70#95×C61—21no—
71C23×D61C22⋊C411yescharacteristic
72C23×D61C22⋊C411yescharacteristic
73C22×C4×C61—22no—
74C22×C4×C61C22×C411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C22×Dic61—22no—
78C22×Dic61C22⋊C411yescharacteristic
79C22×Dic61C22⋊C411yescharacteristic
80C2×D244—22no—
81C2×D244—21no—
82C2×D244—21no—
83C2×D244—41no—
84C2×C4×D61—21no—
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×C4×D61—42no—
89C2×C4×D61—42no—
90C2×Dic122—22no—
91C2×Dic122—22no—
92C2×Dic122—42no—
93C2×Dic122—42no—
94C2×C8×C61—22no—
95C2×C8×C61—41no—
96C4⋊C4×C61—42no—
97C42×C61—42no—
98C42×C61C2×D411yescharacteristic
99C42×C61C2×D411yescharacteristic
100C42×C61#4111yescharacteristic
101C42×C61#4111yescharacteristic
102#11758198—21no—
103#11758198—21no—
104#11758198—21no—
105#11758198—21no—
106#11758198—44no—
107#11758198—44no—
108C4⋊Dic61—21no—
109C4⋊Dic61—21no—
110C4⋊Dic61—41no—
111C4⋊Dic61—41no—
112C4⋊Dic61—41no—
113C4⋊Dic61—41no—
114C2×#92418—22no—
115C2×#92418—41no—
116#11758189—82no—
117C8×D61—82no—
118C23×C61C2×C22⋊C411yescharacteristic
119C22×D61—21no—
120C22×D61—21no—
121C22×D61—21no—
122C22×D61—21no—
123C22×D61—21no—
124C22×D61—41no—
125C22×D61—41no—
126C22×D61—41no—
127C22×D61—41no—
128C22×D61#10012yes—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—22no—
132C2×C4×C61—41no—
133C2×C4×C61—42no—
134C2×C4×C61—42no—
135C2×C4×C61—42no—
136C2×C4×C61C4×D411yescharacteristic
137C2×C4×C61C4×D411yescharacteristic
138C2×C4×C61#12011yescharacteristic
139C2×C4×C61#12111yescharacteristic
140C2×C4×C61#12111yescharacteristic
141C2×C4×C61#12311yescharacteristic
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—42no—
147C2×Dic61—42no—
148C2×Dic61—42no—
149D244—42no—
150D244—42no—
151C4×D61—42no—
152C4×D61—42no—
153C4×D61—81no—
154C4×D61—81no—
155Dic122—82no—
156Dic122—82no—
157C8×C61—42no—
158C8×C61—81no—
159#92418—42no—
160#92418—81no—
161#9451—611nomaximal, Sylow
162C22×C61—21no—
163C22×C61—21no—
164C22×C61#38611yescharacteristic
165C22×C61C2×#10011yescharacteristic
166C22×C61#41311yescharacteristic
167C2×D61—22no—
168C2×D61—41no—
169C2×D61—41no—
170C2×D61—42no—
171C2×D61—42no—
172C2×D61—41no—
173C2×D61—41no—
174C2×D61—41no—
175C2×D61—81no—
176C2×D61—81no—
177C4×C61—21no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—82no—
183C4×C61#45512yes—
184Dic61—41no—
185Dic61—41no—
186Dic61—82no—
187#2973—611no—
188#2547—611no—
189#1558—611no—
190#1558—611no—
191#1466—611no—
192#1285—611no—
193#1285D6111yescharacteristic, complemented
194C2×C61—21no—
195C2×C61—21no—
196C2×C61#188511yescharacteristic
197C2×C61#190011yescharacteristic
198C2×C61#190911yescharacteristic
199D61—42no—
200D61—81no—
201C2×C4⋊Q8—611no—
202C2×#124—612no—
203C2×C4×D4—611no—
204#435—1222no—
205#435—1222no—
206#432—611no—
207#432—611no—
208#432C2×D6111yescharacteristic
209#432C2×D6111yescharacteristic
210#407—1221no—
211C2×C22⋊C8—1221no—
212#397—1221no—
213#397—1221no—
214#391—612no—
215#380—1221no—
216#380—1221no—
217C4×C4⋊C4C2×D6111yescharacteristic
218#333—1222no—
219#333—1222no—
220#323—1221no—
221#323—1221no—
222C61#945111yescharacteristic, complemented, Sylow
223C22×Q8—612no—
224C22×D4—611no—
225C23×C4—611no—
226C23×C4—611no—
227C2×M16—1222no—
228C22×C8—1222no—
229C4⋊Q8—1221no—
230C4⋊Q8—1221no—
231C4⋊Q8—1221no—
232C4⋊Q8—1221no—
233#124—2444no—
234C4×D4—1221no—
235C4×D4—1221no—
236C4×D4—1221no—
237C4×D4—1221no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—611no—
240C2×C4⋊C4—1221no—
241C2×C4⋊C4—1221no—
242C2×C22⋊C4—611no—
243C2×C22⋊C4—611no—
244C2×C22⋊C4—1222no—
245C2×C22⋊C4—1222no—
246C2×C42C4×D6112yes—
247C2×C42C22×D6111yescharacteristic
248C4⋊C8—21no—
249C4⋊C8—612no—
250C4⋊C8—1221no—
251C4⋊C8D24412yes—
252C22⋊C8—21no—
253C22⋊C8—21no—
254C22⋊C8—1222no—
255C22⋊C8—1222no—
256C22⋊C8—1221no—
257C22⋊C8—1221no—
258#97—21no—
259#97—21no—
260#97—1221no—
261#97—1221no—
262#95—21no—
263#95—1222no—
264#95—1222no—
265C24—611no—
266C24—611no—
267C2×Q8—1222no—
268C2×Q8—1222no—
269C2×Q8—2442no—
270C2×Q8—2442no—
271C2×D4—1222no—
272C2×D4—1221no—
273C2×D4—1221no—
274C2×D4—2441no—
275C22×C4—22no—
276C22×C4—611no—
277C22×C4—611no—
278C22×C4—1221no—
279C22×C4—1221no—
280C22×C4—1221no—
281C22×C4—1221no—
282C22×C4—1222no—
283C22×C4—2442no—
284C22×C4—2442no—
285C22×C4C2×C4×D6111yescharacteristic
286C22×C4D4×D6111yescharacteristic
287C22×C4D4×D6111yescharacteristic
288M16—4882no—
289C2×C8—22no—
290C2×C8—41no—
291C2×C8—1222no—
292C2×C8—4882no—
293C2×C8—2441no—
294C4⋊C4—42no—
295C4⋊C4—1221no—
296C4⋊C4—1221no—
297C4⋊C4—2441no—
298C4⋊C4—2441no—
299C4⋊C4—2441no—
300C4⋊C4—2441no—
301C22⋊C4—1221no—
302C22⋊C4—1221no—
303C22⋊C4—1221no—
304C22⋊C4—1221no—
305C22⋊C4—2444no—
306C22⋊C4—2444no—
307C42—42no—
308C42C2×D24411yescharacteristic
309C42#1175822211yescharacteristic
310C42D4×D6111yescharacteristic
311C42#1175822611yescharacteristic
312C23—612no—
313C23—1221no—
314C23—1221no—
315C23—1221no—
316C23—1221no—
317C23—1221no—
318C23—2441no—
319C23—2441no—
320C23—2441no—
321C23—2441no—
322C23C22⋊C4×D6111yescharacteristic
323Q8—4882no—
324Q8—4882no—
325D4—2442no—
326D4—2442no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—4881no—
337C2×C4—4881no—
338C2×C4—2442no—
339C2×C4—2442no—
340C2×C4—2442no—
341C2×C4—2442no—
342C2×C4—2442no—
343C2×C4—2441no—
344C2×C4—2441no—
345C2×C4#1451973911yescharacteristic
346C2×C4C4×D24411yescharacteristic
347C2×C4#1451974711yescharacteristic
348C2×C4#1451975011yescharacteristic
349C2×C4#1451975211yescharacteristic
350C2×C4#1451976211yescharacteristic
351C8—42no—
352C8—81no—
353C8—4881no—
354C8—2442no—
355C22—21no—
356C22—21no—
357C22—1222no—
358C22—4881no—
359C22—4881no—
360C22—2442no—
361C22—2442no—
362C22—2441no—
363C22—2441no—
364C22—2441no—
365C22—2441no—
366C22—2441no—
367C22#1683964011yescharacteristic
368C22#100×D6111yescharacteristic
369C22#1683974511yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—82no—
376C4—4882no—
377C4—2441no—
378C4—2441no—
379C4#1683994112yes—
380C2—21no—
381C2—21no—
382C2—4881no—
383C2—2442no—
384C2#2144620611yescharacteristic
385C2#2144628111yescharacteristic
386C2#2144634011yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1285C2
socleC22×C61#386
prime radicalC22×D244C2×C4
cosocleC2×C42×C61C23
hypercenter#1285D61
hypocenterC61#9451
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1285

Complements

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

NH ≅ G/Ntype
3. #21444544C2semidirect
4. #21444544C2semidirect
6. #21443675C2semidirect
7. C61×#1285C2semidirect
193. #1285D61semidirect
222. C61#9451semidirect

Maximal subgroups

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

subgroupindex
#214548472
#214508142
#214445442
#214441592
#214436752
C61×#12852
#945161