Finite Group Databasebeta

← #29589609

Subgroups — #29589609

Order 15616.

750 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 750 conjugacy classes of subgroups — too many to draw. Only its 87 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#21449175C211yesmaximal, characteristic
2#21444137C211yesmaximal, characteristic, complemented
3#21443746C214yesmaximal, complemented
4C61×#1466C211yesmaximal, characteristic, complemented
5C23×D244C411yescharacteristic
6C2×#14519751—21no—
7C2×#14519745C412yes—
8C2×C22⋊#92418—21no—
9#16839679—21no—
10#16839671—21no—
11#16839664—21no—
12#16839622C411yescharacteristic
13#16839617C2212yes—
14#16839488—21no—
15#16839486C2212yes—
16C2×C4×D4×C61C2211yescharacteristic
17C61×#432—21no—
18C61×#323—21no—
19C61×#323C2212yes—
20C24×D61C2×C412yes—
21C22×D244—21no—
22C22×D244—21no—
23C22×D244—44no—
24C22×D244—41no—
25C22×D244—41no—
26C22×C22⋊D61—22no—
27C22×#92418—41no—
28#14519751—44no—
29#14519745—44no—
30C2×C4⋊Dic61—21no—
31C2×C22⋊Dic61C2×C412yes—
32C2×#11758198—22no—
33C2×#11758198—22no—
34C2×#11758198—22no—
35C22⋊#92418—22no—
36C22⋊#92418—41no—
37#14519684—21no—
38C22×D4×C61C2×C411yescharacteristic
39C23×C4×C61C2×C411yescharacteristic
40C23×C4×C61D411yescharacteristic
41C4×D4×C61—41no—
42C4×D4×C61—41no—
43C2×C4⋊C4×C61D411yescharacteristic
44C2×C22⋊C4×C61D411yescharacteristic
45C2×C22⋊C4×C61C2311yescharacteristic
46C2×C42×C61D411yescharacteristic
47C4⋊C8×C61—41no—
48C22⋊C8×C61—22no—
49#97×C61—41no—
50C24×C61C22⋊C411yescharacteristic
51C24×C61C22×C411yescharacteristic
52C23×D61—22no—
53C23×D61—24no—
54C23×D61—44no—
55C23×D61—42no—
56C23×D61—42no—
57C23×D61—82no—
58C2×D4×C61—22no—
59C2×D4×C61—22no—
60C2×D4×C61—41no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—42no—
66C22×C4×C61—42no—
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C2×C22⋊D61—44no—
73C2×C22⋊D61—44no—
74C2×C22⋊D61—82no—
75C22×Dic61—22no—
76C2×D244—24no—
77C2×D244—42no—
78C2×D244—42no—
79C2×D244—44no—
80C2×D244—48no—
81C2×D244—44no—
82C2×D244—41no—
83C2×D244—41no—
84C2×D244—44no—
85C2×C8×C61—42no—
86C4⋊C4×C61—41no—
87C22⋊C4×C61—41no—
88C22⋊C4×C61—41no—
89C42×C61—21no—
90C42×C61—21no—
91C22⋊Dic61—42no—
92#11758198—44no—
93#11758198—44no—
94#11758198—82no—
95C4⋊Dic61—42no—
96C2×#92418—42no—
97C2×#92418—82no—
98C23×C61—21no—
99C23×C61—21no—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61—41no—
103C23×C61—41no—
104C23×C61—41no—
105C23×C61—41no—
106C23×C61#10012yes—
107C23×C61C2×C22⋊C411yescharacteristic
108C23×C61#13112yes—
109C22×D61—24no—
110C22×D61—42no—
111C22×D61—42no—
112C22×D61—42no—
113C22×D61—44no—
114C22×D61—42no—
115C22×D61—42no—
116C22×D61—42no—
117C22×D61—44no—
118C22×D61—88no—
119C22×D61—88no—
120C22×D61—84no—
121C22×D61—84no—
122D4×C61—44no—
123C2×C4×C61—22no—
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—42no—
131C2×C4×C61—42no—
132C2×C4×C61—42no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—81no—
137C2×C4×C61#9911yescharacteristic
138C2×C4×C61#9911yescharacteristic
139C22⋊D61—88no—
140C2×Dic61—42no—
141C2×Dic61—42no—
142C2×Dic61—42no—
143D244—44no—
144D244—48no—
145D244—44no—
146C8×C61—82no—
147#92418—82no—
148#11557—611nomaximal, Sylow
149C22×C61—21no—
150C22×C61—21no—
151C22×C61—22no—
152C22×C61—22no—
153C22×C61—42no—
154C22×C61—42no—
155C22×C61—42no—
156C22×C61—41no—
157C22×C61—41no—
158C22×C61—41no—
159C22×C61—41no—
160C22×C61—81no—
161C22×C61#40811yescharacteristic
162C22×C61C2×#9911yescharacteristic
163C22×C61C2×#10011yescharacteristic
164C2×D61—44no—
165C2×D61—44no—
166C2×D61—44no—
167C2×D61—82no—
168C2×D61—82no—
169C2×D61—88no—
170C2×D61—82no—
171C2×D61—82no—
172C2×D61—88no—
173C4×C61—21no—
174C4×C61—41no—
175C4×C61—41no—
176C4×C61—41no—
177C4×C61—41no—
178C4×C61AΣL(1,𝔽16)12yes—
179Dic61—82no—
180#2408—611no—
181#1466D6111yescharacteristic, complemented
182#1459—611no—
183#1316—614no—
184C2×C61—21no—
185C2×C61—21no—
186C2×C61—42no—
187C2×C61—42no—
188C2×C61#147111yescharacteristic
189C2×C61C2×AΣL(1,𝔽16)11yescharacteristic
190C2×C61#212211yescharacteristic
191D61—84no—
192C23×D4—611no—
193C2×#121—1221no—
194C2×#120—612no—
195C2×C4×D4C2×D6111yescharacteristic
196#432—21no—
197C2×C22⋊C8—1221no—
198#394—1221no—
199#392—1221no—
200#390—1221no—
201#380—611no—
202#379—612no—
203#324—1221no—
204#323—21no—
205#323—612no—
206#323C2×D6112yes—
207C61#1155711yescharacteristic, complemented, Sylow
208C25—612no—
209C22×D4—1222no—
210C22×D4—1221no—
211C22×D4—1221no—
212C22×D4—2441no—
213C22×D4—2441no—
214C22×D4—2444no—
215C22×D4C4×D6111yescharacteristic
216C23×C4C4×D6111yescharacteristic
217C23×C4D24411yescharacteristic
218C22×C8—2441no—
219#121—2444no—
220#120—2444no—
221C4×D4—41no—
222C4×D4—41no—
223C2×C4⋊C4—1221no—
224C2×C4⋊C4D24411yescharacteristic
225C2×C22⋊C4—612no—
226C2×C22⋊C4—1222no—
227C2×C22⋊C4—1222no—
228C2×C22⋊C4—1222no—
229C2×C22⋊C4C22⋊D6111yescharacteristic
230C2×C22⋊C4C22×D6111yescharacteristic
231C2×C42C22⋊D6111yescharacteristic
232C4⋊C8—41no—
233C22⋊C8—22no—
234C22⋊C8—1222no—
235C22⋊C8—2441no—
236#97—41no—
237#95—1221no—
238C24—1222no—
239C24—1224no—
240C24—4882no—
241C24—2442no—
242C24—2442no—
243C24—2444no—
244C24#1175819811yescharacteristic
245C24C2×C4×D6111yescharacteristic
246C2×D4—22no—
247C2×D4—22no—
248C2×D4—41no—
249C2×D4—1224no—
250C2×D4—4882no—
251C2×D4—2442no—
252C2×D4—2442no—
253C2×D4—2444no—
254C2×D4—2448no—
255C2×D4—2444no—
256C2×D4—2444no—
257C2×D4—2444no—
258C2×D4—2444no—
259C2×D4—2441no—
260C2×D4—2441no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—42no—
266C22×C4—42no—
267C22×C4—1222no—
268C22×C4#1175819811yescharacteristic
269C22×C4#1175819811yescharacteristic
270C22×C4#1175819811yescharacteristic
271C22×C4C2×D24411yescharacteristic
272C22×C4C2×C22⋊D6111yescharacteristic
273C2×C8—42no—
274C2×C8—4882no—
275C2×C8—2442no—
276C4⋊C4—41no—
277C4⋊C4—2442no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C22⋊C4—4882no—
281C22⋊C4—2444no—
282C22⋊C4—2444no—
283C22⋊C4—2442no—
284C42—21no—
285C42—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23—1224no—
295C23—4884no—
296C23—4884no—
297C23—4888no—
298C23—4888no—
299C23—2442no—
300C23—2442no—
301C23—2442no—
302C23—2444no—
303C23—2444no—
304C23—2442no—
305C23—2442no—
306C23—2442no—
307C23#1451969312yes—
308C23C2×#1175819811yescharacteristic
309C23#1451978512yes—
310D4—44no—
311D4—4888no—
312D4—2444no—
313D4—2448no—
314D4—2444no—
315C2×C4—22no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—81no—
329C2×C4—2442no—
330C2×C4—2442no—
331C2×C4—2442no—
332C2×C4#1451969111yescharacteristic
333C2×C4#1451969111yescharacteristic
334C8—82no—
335C8—4882no—
336C22—21no—
337C22—21no—
338C22—22no—
339C22—22no—
340C22—42no—
341C22—42no—
342C22—42no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—81no—
348C22—4882no—
349C22—4882no—
350C22—4888no—
351C22—4888no—
352C22—4882no—
353C22—4882no—
354C22—2444no—
355C22—2444no—
356C22—2444no—
357C22#1683973011yescharacteristic
358C22C2×#1451969111yescharacteristic
359C22C2×#1451969311yescharacteristic
360C4—21no—
361C4—41no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—4882no—
366C4#1683955012yes—
367C2—21no—
368C2—21no—
369C2—42no—
370C2—42no—
371C2—4884no—
372C2#2144418011yescharacteristic
373C2C2×#1683955011yescharacteristic
374C2#2144746811yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC24×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1466C2
socleC22×C61C2×#99
prime radical#21449175C2
cosocleC2×C22⋊C4×C61C23
hypercenter#1466D61
hypocenterC61#11557
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1466

Complements

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

NH ≅ G/Ntype
2. #21444137C2semidirect
3. #21443746C2semidirect
4. C61×#1466C2semidirect
181. #1466D61semidirect
207. C61#11557semidirect

Maximal subgroups

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

subgroupindex
#214491752
#214441372
#214437462
C61×#14662
#1155761