Finite Group Databasebeta

← #29590510

Subgroups — #29590510

Order 15616.

484 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 83 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#21451385C211yesmaximal, characteristic
2#21445558C211yesmaximal, characteristic, complemented
3#21443847C212yesmaximal, complemented
4#21443823C212yesmaximal, complemented
5C61×#1464C211yesmaximal, characteristic, complemented
6C22×#11758194—21no—
7C2×C4×D244C411yescharacteristic
8#16839701C2211yescharacteristic
9#16839698C411yescharacteristic
10#16839679C2211yescharacteristic
11#16839671C411yescharacteristic
12#16839653—21no—
13#16839641—21no—
14#16839638—21no—
15#16839633—21no—
16#16839630C411yescharacteristic
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—24no—
27C2×#11758194—22no—
28C2×#11758194—41no—
29C2×#11758194—42no—
30C22×#92418—41no—
31C4×D244—41no—
32C4×D244—41no—
33C2×C4⋊Dic61C2×C411yescharacteristic
34C2×#11758196—21no—
35C2×C22⋊Dic61—21no—
36C2×#11758198—21no—
37C2×#11758198—21no—
38C2×#11758198—21no—
39C2×#11758198—21no—
40#14519684—21no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684C2×C411yescharacteristic
45#14519684C2×C411yescharacteristic
46C23×C4×C61D411yescharacteristic
47#117×C61—41no—
48#117×C61—41no—
49C2×C4⋊C4×C61D411yescharacteristic
50C2×C4⋊C4×C61C2311yescharacteristic
51C2×C22⋊C4×C61C2×C411yescharacteristic
52C2×C22⋊C4×C61D411yescharacteristic
53C2×C42×C61C2×C411yescharacteristic
54C2×C42×C61D411yescharacteristic
55C4⋊C8×C61—41no—
56C22⋊C8×C61—22no—
57#97×C61—41no—
58C24×C61C22⋊C411yescharacteristic
59C23×D61—21no—
60C22×C4×C61—22no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C22×C411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C2×C22⋊D61—42no—
72C2×C22⋊D61—42no—
73C2×C22⋊D61—81no—
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77C2×D244—41no—
78C2×D244—42no—
79C2×C4×D61—42no—
80C2×C4×D61—81no—
81C2×C4×D61—81no—
82C2×C8×C61—42no—
83C4⋊C4×C61—41no—
84C4⋊C4×C61—41no—
85C22⋊C4×C61—41no—
86C22⋊C4×C61—41no—
87C42×C61—21no—
88C42×C61—21no—
89C42×C61—21no—
90C42×C61—21no—
91C22⋊Dic61—81no—
92#11758198—42no—
93#11758198—41no—
94#11758198—41no—
95#11758198—41no—
96#11758198—41no—
97#11758198—81no—
98C4⋊Dic61—41no—
99#11758196—81no—
100#11758194—24no—
101#11758194—44no—
102#11758194—42no—
103C2×#92418—44no—
104C2×#92418—42no—
105C23×C61—21no—
106C23×C61—21no—
107C23×C61—41no—
108C23×C61—41no—
109C23×C61#10412yes—
110C23×C61C2×C22⋊C411yescharacteristic
111C22×D61—22no—
112C22×D61—41no—
113C22×D61—41no—
114C22×D61—41no—
115C22×D61—41no—
116C22×D61—41no—
117C22×D61—41no—
118C2×C4×C61—22no—
119C2×C4×C61—22no—
120C2×C4×C61—22no—
121C2×C4×C61—22no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
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—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61#9911yescharacteristic
135C2×C4×C61#9911yescharacteristic
136C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C61#13711yescharacteristic
138C22⋊D61—84no—
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—42no—
149D244—42no—
150C4×D61—84no—
151C8×C61—82no—
152#92418—44no—
153#11761—611nomaximal, Sylow
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—22no—
157C22×C61—42no—
158C22×C61—41no—
159C22×C61—41no—
160C22×C61—81no—
161C22×C61C2×#9911yescharacteristic
162C22×C61#41711yescharacteristic
163C22×C61C2×#10411yescharacteristic
164C2×D61—42no—
165C2×D61—42no—
166C2×D61—42no—
167C2×D61—81no—
168C2×D61—81no—
169C2×D61—81no—
170C2×D61—81no—
171C4×C61—21no—
172C4×C61—21no—
173C4×C61—21no—
174C4×C61—21no—
175C4×C61—41no—
176C4×C61—41no—
177C4×C61—41no—
178C4×C61—41no—
179Dic61—81no—
180Dic61—81no—
181Dic61—81no—
182#2598—611no—
183#1742—611no—
184#1464D6111yescharacteristic, complemented
185#1353—612no—
186#1345—612no—
187C2×C61—21no—
188C2×C61—21no—
189C2×C61—42no—
190C2×C61#150411yescharacteristic
191C2×C61#212011yescharacteristic
192C2×C61#213411yescharacteristic
193D61—82no—
194C22×M16—1221no—
195C2×C4×D4—611no—
196C2×#117C2×D6111yescharacteristic
197#432—21no—
198#400—611no—
199#399—611no—
200#394—611no—
201#392—611no—
202#388—1221no—
203#386—1221no—
204#386—1221no—
205#385—1221no—
206#383—611no—
207#343—612no—
208#343—1221no—
209#324C2×D6112yes—
210#323—21no—
211C61#1176111yescharacteristic, complemented, Sylow
212C22×D4—611no—
213C22×D4—1221no—
214C23×C4—1221no—
215C23×C4D24411yescharacteristic
216C2×M16—1224no—
217C2×M16—1222no—
218C2×M16—2441no—
219C2×M16—2442no—
220C22×C8—2441no—
221C4×D4—2441no—
222C4×D4—2441no—
223#117—41no—
224#117—41no—
225C2×C4⋊C4—611no—
226C2×C4⋊C4—1221no—
227C2×C4⋊C4D24411yescharacteristic
228C2×C4⋊C4C22×D6111yescharacteristic
229C2×C22⋊C4—1221no—
230C2×C22⋊C4—1221no—
231C2×C22⋊C4—1221no—
232C2×C22⋊C4—1221no—
233C2×C22⋊C4—1221no—
234C2×C22⋊C4C4×D6111yescharacteristic
235C2×C22⋊C4C22⋊D6111yescharacteristic
236C2×C42C4×D6111yescharacteristic
237C2×C42C22⋊D6111yescharacteristic
238C4⋊C8—41no—
239C22⋊C8—22no—
240#97—41no—
241#95—611no—
242#95—611no—
243#95—1221no—
244#95—1221no—
245#95—1221no—
246#95—1221no—
247C24—1221no—
248C24#1175819811yescharacteristic
249C2×D4—4881no—
250C2×D4—2441no—
251C2×D4—2442no—
252C2×D4—2442no—
253C2×D4—2442no—
254C22×C4—22no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4—4881no—
263C22×C4—4881no—
264C22×C4—2442no—
265C22×C4#1175819811yescharacteristic
266C22×C4#1175819811yescharacteristic
267C22×C4#1175819811yescharacteristic
268C22×C4C2×C4×D6111yescharacteristic
269C22×C4C2×D24411yescharacteristic
270C22×C4C2×C22⋊D6111yescharacteristic
271M16—1224no—
272M16—2444no—
273M16—2442no—
274C2×C8—42no—
275C2×C8—2444no—
276C2×C8—2442no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—4881no—
280C4⋊C4—2441no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C22⋊C4—4881no—
284C22⋊C4—4881no—
285C22⋊C4—2442no—
286C22⋊C4—2441no—
287C22⋊C4—2441no—
288C22⋊C4—2441no—
289C22⋊C4—2441no—
290C42—21no—
291C42—21no—
292C42—21no—
293C42—21no—
294C23—21no—
295C23—21no—
296C23—41no—
297C23—41no—
298C23—1222no—
299C23—2441no—
300C23—2441no—
301C23—2441no—
302C23—2441no—
303C23—2441no—
304C23—2441no—
305C23#1451970312yes—
306C23C2×#1175819811yescharacteristic
307D4—4884no—
308D4—2442no—
309D4—2442no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—4884no—
327C2×C4—2441no—
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#1451969111yescharacteristic
337C2×C4#1451969111yescharacteristic
338C2×C4#1451980511yescharacteristic
339C2×C4#1451981011yescharacteristic
340C8—82no—
341C8—2444no—
342C22—21no—
343C22—21no—
344C22—22no—
345C22—42no—
346C22—41no—
347C22—41no—
348C22—81no—
349C22—4881no—
350C22—4881no—
351C22—4881no—
352C22—4881no—
353C22—2442no—
354C22—2442no—
355C22—2442no—
356C22C2×#1451969111yescharacteristic
357C22#1683976411yescharacteristic
358C22C2×#1451970311yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—4881no—
368C4—4881no—
369C4—4881no—
370C2—21no—
371C2—21no—
372C2—42no—
373C2—4882no—
374C2#2144432411yescharacteristic
375C2#2144745811yescharacteristic
376C2#2144751011yescharacteristic
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#11761
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. #21445558C2semidirect
3. #21443847C2semidirect
4. #21443823C2semidirect
5. C61×#1464C2semidirect
184. #1464D61semidirect
211. C61#11761semidirect

Maximal subgroups

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

subgroupindex
#214513852
#214455582
#214438472
#214438232
C61×#14642
#1176161