Finite Group Databasebeta

← #29590710

Subgroups — #29590710

Order 15616.

448 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 79 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#21451561C211yesmaximal, characteristic
2#21445899C211yesmaximal, characteristic, complemented
3#21443826C212yesmaximal, complemented
4#21443823C212yesmaximal, complemented
5C61×#1463C211yesmaximal, characteristic, complemented
6C2×#14519760—21no—
7C2×#14519751C411yescharacteristic
8#16839726—21no—
9#16839692C411yescharacteristic
10#16839692C2211yescharacteristic
11#16839684—21no—
12#16839684—21no—
13#16839679C411yescharacteristic
14#16839679C2211yescharacteristic
15#16839641—21no—
16#16839622C411yescharacteristic
17#16839531—21no—
18#16839531C2212yes—
19C22×C4⋊C4×C61C2211yescharacteristic
20C61×#407—21no—
21C61×#324—21no—
22C61×#324C2212yes—
23C22×D244C2×C411yescharacteristic
24C22×C22⋊D61—21no—
25C2×#11758194—22no—
26#14519760—44no—
27#14519751—41no—
28#14519751—41no—
29C2×C4⋊Dic61—21no—
30C2×C4⋊Dic61C2×C411yescharacteristic
31C2×#11758196—21no—
32C2×#11758196—21no—
33C2×C22⋊Dic61—21no—
34C2×#11758198—21no—
35C2×#11758198—21no—
36C2×#11758198—21no—
37C2×#11758198—21no—
38C2×#11758198—21no—
39C22⋊#92418—41no—
40C22⋊#92418—41no—
41#14519684—21no—
42#14519684—21no—
43#14519684C2×C411yescharacteristic
44#14519684C2×C411yescharacteristic
45C23×C4×C61C2×C411yescharacteristic
46C23×C4×C61D411yescharacteristic
47C23×C4×C61D411yescharacteristic
48C2×M16×C61—41no—
49C2×C4⋊C4×C61—41no—
50C2×C4⋊C4×C61—41no—
51C2×C4⋊C4×C61C2×C411yescharacteristic
52C2×C4⋊C4×C61D411yescharacteristic
53C2×C4⋊C4×C61D411yescharacteristic
54C2×C4⋊C4×C61C2311yescharacteristic
55C22⋊C8×C61—22no—
56C22⋊C8×C61—41no—
57C24×C61C22⋊C411yescharacteristic
58C23×D61—21no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—22no—
66C22×C4×C61—41no—
67C22×C4×C61—81no—
68C22×C4×C61—81no—
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61C22×C411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C2×C22⋊D61—42no—
76C2×C22⋊D61—42no—
77C2×C22⋊D61—41no—
78C2×C22⋊D61—41no—
79C22×Dic61—21no—
80C22×Dic61—21no—
81C22×Dic61—21no—
82C2×D244—41no—
83C2×D244—81no—
84M16×C61—82no—
85C2×C8×C61—42no—
86C4⋊C4×C61—41no—
87C4⋊C4×C61—41no—
88C4⋊C4×C61—41no—
89C4⋊C4×C61—41no—
90C22⋊Dic61—42no—
91#11758198—42no—
92#11758198—42no—
93#11758198—42no—
94#11758198—81no—
95#11758198—81no—
96C4⋊Dic61—41no—
97C4⋊Dic61—81no—
98#11758196—42no—
99#11758196—42no—
100#11758194—42no—
101#11758194—42no—
102C2×#92418—42no—
103C23×C61—21no—
104C23×C61—21no—
105C23×C61—41no—
106C23×C61—41no—
107C23×C61#9911yescharacteristic
108C23×C61#9911yescharacteristic
109C23×C61C2×C22⋊C411yescharacteristic
110C22×D61—41no—
111C22×D61—41no—
112C22×D61—41no—
113C22×D61—41no—
114C22×D61—41no—
115C22×D61—41no—
116C22×D61—41no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—42no—
127C2×C4×C61—42no—
128C2×C4×C61—42no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—81no—
134C2×C4×C61—81no—
135C2×C4×C61—81no—
136C2×C4×C61AGL(1,ℤ/8)12yes—
137C22⋊D61—82no—
138C22⋊D61—82no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148D244—82no—
149C8×C61—82no—
150#92418—82no—
151#11805—611nomaximal, Sylow
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—21no—
158C22×C61—21no—
159C22×C61—21no—
160C22×C61—42no—
161C22×C61—42no—
162C22×C61C2×#9911yescharacteristic
163C22×C61#41811yescharacteristic
164C22×C61#42111yescharacteristic
165C2×D61—81no—
166C2×D61—81no—
167C2×D61—81no—
168C2×D61—81no—
169C2×D61—81no—
170C2×D61—81no—
171C2×D61—81no—
172C4×C61—22no—
173C4×C61—41no—
174C4×C61—41no—
175C4×C61—41no—
176C4×C61—41no—
177C4×C61—41no—
178Dic61—81no—
179Dic61—81no—
180Dic61—81no—
181#2618—611no—
182#1821—611no—
183#1463D6111yescharacteristic, complemented
184#1346—612no—
185#1345—612no—
186C2×C61—21no—
187C2×C61—21no—
188C2×C61—41no—
189C2×C61—41no—
190C2×C61#151011yescharacteristic
191C2×C61#212111yescharacteristic
192C2×C61#213311yescharacteristic
193D61—161no—
194C2×#123—1221no—
195C2×#121—611no—
196C22×C4⋊C4C2×D6111yescharacteristic
197#407—21no—
198#407—1221no—
199#398—611no—
200#398—611no—
201#396—1221no—
202#396—1221no—
203#394—611no—
204#394—611no—
205#386—1221no—
206#380—611no—
207#343—612no—
208#343—1221no—
209#324—21no—
210#324C2×D6112yes—
211C61#1180511yescharacteristic, complemented, Sylow
212C22×D4—611no—
213C22×D4—1221no—
214C23×C4C4×D6111yescharacteristic
215C23×C4D24411yescharacteristic
216C23×C4C22⋊D6111yescharacteristic
217C2×M16—41no—
218C2×M16—1222no—
219#123—2444no—
220#121—2441no—
221#121—2441no—
222C2×C4⋊C4—41no—
223C2×C4⋊C4—41no—
224C2×C4⋊C4—611no—
225C2×C4⋊C4—1221no—
226C2×C4⋊C4—1221no—
227C2×C4⋊C4—1221no—
228C2×C4⋊C4C4×D6111yescharacteristic
229C2×C4⋊C4D24411yescharacteristic
230C2×C4⋊C4C22⋊D6111yescharacteristic
231C2×C4⋊C4C22×D6111yescharacteristic
232C2×C22⋊C4—1221no—
233C2×C22⋊C4—1221no—
234C2×C22⋊C4—1221no—
235C2×C22⋊C4—1221no—
236C2×C22⋊C4—1221no—
237C2×C22⋊C4—1221no—
238C22⋊C8—22no—
239C22⋊C8—41no—
240C22⋊C8—2441no—
241C22⋊C8—2441no—
242#95—611no—
243#95—611no—
244#95—1221no—
245#95—1221no—
246C24—1221no—
247C24#1175819811yescharacteristic
248C2×D4—4881no—
249C2×D4—2441no—
250C2×D4—2442no—
251C2×D4—2442no—
252C2×D4—2441no—
253C2×D4—2441no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—22no—
261C22×C4—41no—
262C22×C4—81no—
263C22×C4—81no—
264C22×C4—1221no—
265C22×C4—1221no—
266C22×C4—1221no—
267C22×C4#1175819811yescharacteristic
268C22×C4#1175819811yescharacteristic
269C22×C4#1175819811yescharacteristic
270C22×C4C2×C4×D6111yescharacteristic
271C22×C4C2×D24411yescharacteristic
272C22×C4C2×C22⋊D6111yescharacteristic
273M16—82no—
274M16—2442no—
275M16—2442no—
276C2×C8—42no—
277C2×C8—2442no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—4881no—
283C4⋊C4—2441no—
284C4⋊C4—2442no—
285C4⋊C4—2442no—
286C22⋊C4—4881no—
287C22⋊C4—4881no—
288C22⋊C4—2442no—
289C22⋊C4—2442no—
290C22⋊C4—2442no—
291C22⋊C4—2442no—
292C23—21no—
293C23—21no—
294C23—41no—
295C23—41no—
296C23—2441no—
297C23—2441no—
298C23—2441no—
299C23—2441no—
300C23—2441no—
301C23—2441no—
302C23—2441no—
303C23#1451969111yescharacteristic
304C23#1451969111yescharacteristic
305C23C2×#1175819811yescharacteristic
306D4—4882no—
307D4—4882no—
308D4—4882no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4—2441no—
332C2×C4—2441no—
333C2×C4—2441no—
334C2×C4—2441no—
335C2×C4—2441no—
336C2×C4—2441no—
337C2×C4#1451980512yes—
338C8—82no—
339C8—4882no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—42no—
349C22—42no—
350C22—4881no—
351C22—4881no—
352C22—4881no—
353C22—4881no—
354C22—4881no—
355C22—4881no—
356C22—4881no—
357C22C2×#1451969111yescharacteristic
358C22#1683976811yescharacteristic
359C22#1683977811yescharacteristic
360C4—22no—
361C4—41no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—4881no—
367C4—4881no—
368C4—4881no—
369C2—21no—
370C2—21no—
371C2—41no—
372C2—41no—
373C2—9761no—
374C2#2144434911yescharacteristic
375C2#2144746311yescharacteristic
376C2#2144750611yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1463C2
socleC22×C61C2×#99
prime radicalC2×#14519751C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1463D61
hypocenterC61#11805
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
2. #21445899C2semidirect
3. #21443826C2semidirect
4. #21443823C2semidirect
5. C61×#1463C2semidirect
183. #1463D61semidirect
211. C61#11805semidirect

Maximal subgroups

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

subgroupindex
#214515612
#214458992
#214438262
#214438232
C61×#14632
#1180561