Finite Group Databasebeta

← #29590705

Subgroups — #29590705

Order 15616.

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

normal subgroups only

This group has 472 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#21449055C211yesmaximal, characteristic
2#21445902C211yesmaximal, characteristic, complemented
3#21443826C212yesmaximal, complemented
4#21443823C212yesmaximal, complemented
5C61×#1464C211yesmaximal, characteristic, complemented
6C2×C4×D244C411yescharacteristic
7C2×C4×C22⋊D61—21no—
8#16839726—21no—
9#16839692C2211yescharacteristic
10#16839687C411yescharacteristic
11#16839684—21no—
12#16839679C2211yescharacteristic
13#16839678—21no—
14#16839671C411yescharacteristic
15C4×C4⋊Dic61C411yescharacteristic
16C4×#11758198—21no—
17#16839531—21no—
18#16839531C2212yes—
19C2×#117×C61C2211yescharacteristic
20C61×#432—21no—
21C61×#324C2212yes—
22C61×#323—21no—
23C22×D244C2×C411yescharacteristic
24C22×C22⋊D61—21no—
25C22×C4×D61—21no—
26C2×#11758194—22no—
27C4×D244—41no—
28C4×D244—41no—
29C4×C22⋊D61—44no—
30C2×C4⋊Dic61—21no—
31C2×C4⋊Dic61C2×C411yescharacteristic
32C2×#11758196—21no—
33C2×C22⋊Dic61—21no—
34C2×#11758198—21no—
35C2×#11758198—21no—
36C2×#11758198—21no—
37C2×#11758198—21no—
38C2×C4×Dic61—21no—
39C22⋊#92418—41no—
40C22⋊#92418—41no—
41#14519684—21no—
42#14519684—21no—
43#14519684C2×C411yescharacteristic
44#14519684C2×C411yescharacteristic
45C23×C4×C61D411yescharacteristic
46#117×C61—41no—
47#117×C61—41no—
48C2×C4⋊C4×C61D411yescharacteristic
49C2×C4⋊C4×C61C2311yescharacteristic
50C2×C22⋊C4×C61C2×C411yescharacteristic
51C2×C22⋊C4×C61D411yescharacteristic
52C2×C42×C61C2×C411yescharacteristic
53C2×C42×C61D411yescharacteristic
54C4⋊C8×C61—41no—
55C22⋊C8×C61—22no—
56#97×C61—41no—
57C24×C61C22⋊C411yescharacteristic
58C23×D61—21no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—22no—
62C22×C4×C61—41no—
63C22×C4×C61C22⋊C411yescharacteristic
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C22×C411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C2×C22⋊D61—42no—
70C2×C22⋊D61—42no—
71C2×C22⋊D61—42no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—21no—
75C2×D244—41no—
76C2×D244—42no—
77C2×C4×D61—42no—
78C2×C4×D61—42no—
79C2×C4×D61—41no—
80C2×C4×D61—41no—
81C2×C8×C61—42no—
82C4⋊C4×C61—41no—
83C4⋊C4×C61—41no—
84C22⋊C4×C61—41no—
85C22⋊C4×C61—41no—
86C42×C61—21no—
87C42×C61—21no—
88C42×C61—21no—
89C42×C61—21no—
90C22⋊Dic61—42no—
91#11758198—42no—
92#11758198—42no—
93#11758198—42no—
94#11758198—42no—
95C4⋊Dic61—42no—
96C4⋊Dic61—41no—
97#11758196—42no—
98C4×Dic61—42no—
99#11758194—42no—
100#11758194—42no—
101C2×#92418—42no—
102C23×C61—21no—
103C23×C61—21no—
104C23×C61—21no—
105C23×C61—41no—
106C23×C61—41no—
107C23×C61C2×C22⋊C411yescharacteristic
108C22×D61—22no—
109C22×D61—41no—
110C22×D61—41no—
111C22×D61—41no—
112C22×D61—41no—
113C22×D61—41no—
114C22×D61—41no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
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—42no—
124C2×C4×C61—42no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61#9911yescharacteristic
130C2×C4×C61#9911yescharacteristic
131C2×C4×C61AGL(1,ℤ/8)12yes—
132C22⋊D61—48no—
133C2×Dic61—22no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142D244—42no—
143D244—42no—
144C4×D61—82no—
145C4×D61—82no—
146C8×C61—82no—
147#92418—82no—
148#11804—611nomaximal, Sylow
149C22×C61—21no—
150C22×C61—21no—
151C22×C61—42no—
152C22×C61—41no—
153C22×C61—41no—
154C22×C61—41no—
155C22×C61—81no—
156C22×C61C2×#9911yescharacteristic
157C22×C61#41811yescharacteristic
158C22×C61#42111yescharacteristic
159C2×D61—42no—
160C2×D61—42no—
161C2×D61—42no—
162C2×D61—81no—
163C2×D61—81no—
164C2×D61—81no—
165C2×D61—81no—
166C4×C61—22no—
167C4×C61—21no—
168C4×C61—21no—
169C4×C61—41no—
170C4×C61—41no—
171C4×C61—41no—
172C4×C61—41no—
173Dic61—42no—
174Dic61—81no—
175Dic61—81no—
176#2392—611no—
177#1822—611no—
178#1464D6111yescharacteristic, complemented
179#1346—612no—
180#1345—612no—
181C2×C61—21no—
182C2×C61—21no—
183C2×C61—81no—
184C2×C61#151011yescharacteristic
185C2×C61#212011yescharacteristic
186C2×C61#213211yescharacteristic
187D61—82no—
188C2×C4×D4—611no—
189C2×C4×D4—1221no—
190C2×#117C2×D6111yescharacteristic
191#432—21no—
192#407—1221no—
193#398—611no—
194#397—611no—
195#396—1221no—
196#394—611no—
197#394—1221no—
198#392—611no—
199C4×C4⋊C4—611no—
200C4×C22⋊C4—1221no—
201#343—612no—
202#343—1221no—
203#324C2×D6112yes—
204#323—21no—
205C61#1180411yescharacteristic, complemented, Sylow
206C22×D4—611no—
207C22×D4—1221no—
208C23×C4—1221no—
209C23×C4D24411yescharacteristic
210C2×M16—1222no—
211C4×D4—2441no—
212C4×D4—2441no—
213C4×D4—2444no—
214#117—41no—
215#117—41no—
216C2×C4⋊C4—611no—
217C2×C4⋊C4—1221no—
218C2×C4⋊C4—1221no—
219C2×C4⋊C4D24411yescharacteristic
220C2×C4⋊C4C22×D6111yescharacteristic
221C2×C22⋊C4—1221no—
222C2×C22⋊C4—1221no—
223C2×C22⋊C4—1221no—
224C2×C22⋊C4—1221no—
225C2×C22⋊C4—1221no—
226C2×C22⋊C4C4×D6111yescharacteristic
227C2×C22⋊C4C22⋊D6111yescharacteristic
228C2×C42—1221no—
229C2×C42C4×D6111yescharacteristic
230C2×C42C22⋊D6111yescharacteristic
231C4⋊C8—41no—
232C22⋊C8—22no—
233C22⋊C8—2441no—
234C22⋊C8—2441no—
235#97—41no—
236#95—611no—
237#95—611no—
238#95—1221no—
239#95—1221no—
240C24—1221no—
241C24#1175819811yescharacteristic
242C2×D4—2441no—
243C2×D4—2442no—
244C2×D4—2442no—
245C2×D4—2442no—
246C2×D4—2442no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—22no—
250C22×C4—41no—
251C22×C4—1221no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4—2442no—
255C22×C4—2442no—
256C22×C4—2441no—
257C22×C4—2441no—
258C22×C4#1175819811yescharacteristic
259C22×C4#1175819811yescharacteristic
260C22×C4#1175819811yescharacteristic
261C22×C4C2×C4×D6111yescharacteristic
262C22×C4C2×D24411yescharacteristic
263C22×C4C2×C22⋊D6111yescharacteristic
264M16—2442no—
265M16—2442no—
266C2×C8—42no—
267C2×C8—2442no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—2441no—
271C4⋊C4—2442no—
272C4⋊C4—2442no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—2442no—
276C22⋊C4—2442no—
277C22⋊C4—2442no—
278C22⋊C4—2442no—
279C22⋊C4—2442no—
280C42—21no—
281C42—21no—
282C42—21no—
283C42—21no—
284C42—2442no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—41no—
289C23—41no—
290C23—1222no—
291C23—2441no—
292C23—2441no—
293C23—2441no—
294C23—2441no—
295C23—2441no—
296C23—2441no—
297C23C2×#1175819811yescharacteristic
298D4—2442no—
299D4—2442no—
300D4—2448no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—1222no—
316C2×C4—4882no—
317C2×C4—4882no—
318C2×C4—2441no—
319C2×C4—2441no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4—2441no—
326C2×C4#1451969111yescharacteristic
327C2×C4#1451969111yescharacteristic
328C2×C4#1451980512yes—
329C8—82no—
330C8—4882no—
331C22—21no—
332C22—21no—
333C22—42no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—81no—
338C22—4881no—
339C22—4881no—
340C22—4881no—
341C22—4881no—
342C22—2442no—
343C22—2442no—
344C22—2442no—
345C22C2×#1451969111yescharacteristic
346C22#1683976811yescharacteristic
347C22#1683977811yescharacteristic
348C4—22no—
349C4—21no—
350C4—21no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—4881no—
356C4—4881no—
357C4—2442no—
358C2—21no—
359C2—21no—
360C2—81no—
361C2—4882no—
362C2#2144434911yescharacteristic
363C2#2144745811yescharacteristic
364C2#2144750211yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1464C2
socleC22×C61C2×#99
prime radical#16839671C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1464D61
hypocenterC61#11804
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

Complements

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

NH ≅ G/Ntype
2. #21445902C2semidirect
3. #21443826C2semidirect
4. #21443823C2semidirect
5. C61×#1464C2semidirect
178. #1464D61semidirect
205. C61#11804semidirect

Maximal subgroups

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

subgroupindex
#214490552
#214459022
#214438262
#214438232
C61×#14642
#1180461