Finite Group Databasebeta

← #30595769

Subgroups — #30595769

Order 15616.

702 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 702 conjugacy classes of subgroups — too many to draw. Only its 116 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
1C4×#14519834C211yesmaximal, characteristic, complemented
2#21461483C211yesmaximal, characteristic, complemented
3#21460635C214yesmaximal, complemented
4#21454161C211yesmaximal, characteristic
5C22×#11758213—21no—
6C2×#14519834—21no—
7C2×C4×#92420—21no—
8#16840628—21no—
9#16840628C2212yes—
10#16840628C2212yes—
11C2×#14519748—21no—
12C2×#14519748—21no—
13C2×#14519748C412yes—
14C2×C42×D61C2211yescharacteristic
15#16839665—21no—
16#16839665—21no—
17#16839665C2212yes—
18#16839632C411yescharacteristic
19C2×#127×C61C411yescharacteristic
20C2×#11758213—24no—
21C2×#11758213—42no—
22C2×#11758213—42no—
23C22×#92420—22no—
24C22×#92420—22no—
25#14519834—24no—
26C4×#92420—42no—
27C22×C22⋊D61—22no—
28C22×C4×D61C2×C411yescharacteristic
29C22×C4×D61D411yescharacteristic
30C22×C4×D61D411yescharacteristic
31#14519748—44no—
32#14519748—42no—
33#14519748—42no—
34#14519748—44no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61C2×C412yes—
38C2×C22⋊Dic61—22no—
39C2×C22⋊Dic61—22no—
40C2×C22⋊Dic61—22no—
41C2×C4×Dic61D411yescharacteristic
42C2×C4×Dic61D411yescharacteristic
43C2×C4×Dic61C2311yescharacteristic
44C42×D61—42no—
45C22×D4×C61—21no—
46C22×D4×C61—21no—
47C22×D4×C61C2×C412yes—
48#127×C61—42no—
49C2×C42×C61C2×C411yescharacteristic
50C24×C61—22no—
51C23×D61C22⋊C411yescharacteristic
52C2×D4×C61—24no—
53C2×D4×C61—42no—
54C2×D4×C61—42no—
55C2×D4×C61—42no—
56C2×D4×C61—42no—
57C2×D4×C61—42no—
58C2×D4×C61—42no—
59C2×D4×C61—42no—
60C2×D4×C61—42no—
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22⋊C411yescharacteristic
63C22×C4×C61C22×C411yescharacteristic
64C2×C22⋊D61—44no—
65C2×C22⋊D61—44no—
66C2×C22⋊D61—44no—
67C22×Dic61—22no—
68C22×Dic61C22⋊C411yescharacteristic
69C22×Dic61C2×D411yescharacteristic
70C22×Dic61C2×D411yescharacteristic
71C2×C4×D61—22no—
72C2×C4×D61—22no—
73C2×C4×D61—22no—
74C2×C4×D61—22no—
75C2×C4×D61—22no—
76C2×C4×D61—22no—
77C2×C4×D61—41no—
78C2×C4×D61—41no—
79C2×C4×D61D812yes—
80C2×C4×D61SD1612yes—
81C2×#92420—24no—
82C2×#92420—24no—
83C2×#92420—42no—
84C2×#92420—42no—
85C2×#92420—42no—
86C2×#92420—42no—
87#11758213—48no—
88C42×C61—22no—
89C22⋊Dic61—44no—
90C22⋊Dic61—42no—
91C22⋊Dic61—42no—
92C22⋊Dic61—44no—
93C4⋊Dic61—42no—
94C4⋊Dic61—42no—
95C4⋊Dic61—42no—
96C4×Dic61—22no—
97C4×Dic61—41no—
98C4×Dic61—41no—
99C23×C61—42no—
100C23×C61—42no—
101C23×C61—42no—
102C23×C61—42no—
103C23×C61—42no—
104C23×C61—42no—
105C23×C61—42no—
106C23×C61C2×C22⋊C411yescharacteristic
107C22×D61—21no—
108C22×D61—21no—
109C22×D61—21no—
110C22×D61—21no—
111C22×D61—21no—
112C22×D61—21no—
113C22×D61#10212yes—
114D4×C61—84no—
115D4×C61—84no—
116D4×C61—84no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61#9912yes—
122C2×C4×C61#10212yes—
123C2×C4×C61#10412yes—
124C2×C4×C61#10412yes—
125C2×C4×C61#13112yes—
126C22⋊D61—88no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—42no—
134C2×Dic61—42no—
135C2×Dic61—42no—
136C2×Dic61#10012yes—
137C2×Dic61C2×D811yescharacteristic
138C2×Dic61C2×SD1611yescharacteristic
139C2×Dic61AGL(1,ℤ/8)12yes—
140C4×D61—24no—
141C4×D61—24no—
142C4×D61—44no—
143C4×D61—44no—
144#92420—44no—
145#92420—44no—
146#7684—611nomaximal, Sylow
147C22×C61—82no—
148C22×C61—82no—
149C22×C61—82no—
150C22×C61—82no—
151C22×C61—82no—
152C22×C61—82no—
153C22×C61—82no—
154C22×C61#40811yescharacteristic
155C22×C61C2×#9911yescharacteristic
156C22×C61C2×#10011yescharacteristic
157C22×C61C2×#10211yescharacteristic
158C22×C61#41811yescharacteristic
159C22×C61C2×#10411yescharacteristic
160C22×C61C2×#10411yescharacteristic
161C2×D61—22no—
162C2×D61—22no—
163C2×D61—22no—
164C2×D61—41no—
165C2×D61—41no—
166C2×D61—41no—
167C2×D61—41no—
168C4×C61—22no—
169C4×C61—22no—
170C4×C61#32714yes—
171Dic61—22no—
172Dic61—21no—
173Dic61—21no—
174Dic61—22no—
175Dic61—82no—
176#2856—611no—
177C4×C22⋊C8—611no—
178#1728—611no—
179#1270—614no—
180C2×C61—162no—
181C2×C61#147111yescharacteristic
182C2×C61#148411yescharacteristic
183C2×C61#149211yescharacteristic
184C2×C61C2×#32711yescharacteristic
185C2×C61#150711yescharacteristic
186C2×C61#152511yescharacteristic
187C2×C61#154511yescharacteristic
188D61—42no—
189C22×M16—1221no—
190C2×#127#692311yescharacteristic
191C2×#121—612no—
192C2×#121—1221no—
193C2×#121—1221no—
194C22×C42—611no—
195C2×C22⋊C8—1221no—
196C2×C4×C8—1221no—
197#390—612no—
198#390—1221no—
199#390—1221no—
200#384—611no—
201#336—612no—
202#336—612no—
203#336—1221no—
204C61#768411yescharacteristic, complemented, Sylow
205C22×D4—21no—
206C22×D4—21no—
207C22×D4—1222no—
208C22×D4C2×#692312yes—
209C23×C4—611no—
210C23×C4—611no—
211C23×C4—611no—
212C2×M16—1224no—
213C2×M16—2442no—
214C2×M16—2442no—
215C22×C8—1222no—
216C22×C8—1222no—
217#127—42no—
218#121—2442no—
219#121—2442no—
220#121—2444no—
221#121—2444no—
222C2×C4⋊C4—612no—
223C2×C4⋊C4—1221no—
224C2×C4⋊C4—1221no—
225C2×C22⋊C4—1222no—
226C2×C22⋊C4—1222no—
227C2×C22⋊C4—1222no—
228C2×C42—611no—
229C2×C42—611no—
230C2×C42—611no—
231C2×C42—2442no—
232C2×C42C2×#692311yescharacteristic
233C22⋊C8—1224no—
234C4×C8—2442no—
235C24—22no—
236C24—611no—
237C2×D4—24no—
238C2×D4—42no—
239C2×D4—42no—
240C2×D4—42no—
241C2×D4—42no—
242C2×D4—42no—
243C2×D4—42no—
244C2×D4—42no—
245C2×D4—42no—
246C2×D4—2444no—
247C2×D4—2444no—
248C2×D4—2444no—
249C22×C4—611no—
250C22×C4—611no—
251C22×C4—611no—
252C22×C4—612no—
253C22×C4—612no—
254C22×C4—1222no—
255C22×C4—1222no—
256C22×C4—1222no—
257C22×C4—1222no—
258C22×C4—1222no—
259C22×C4—1222no—
260C22×C4—1222no—
261C22×C4—2441no—
262C22×C4—2441no—
263C22×C4C22⋊#692311yescharacteristic
264C22×C4C22⋊#692311yescharacteristic
265C22×C4C22×#692311yescharacteristic
266M16—2448no—
267C2×C8—1224no—
268C2×C8—1224no—
269C2×C8—2442no—
270C2×C8—2442no—
271C2×C8—2442no—
272C2×C8—2442no—
273C4⋊C4—2442no—
274C4⋊C4—2442no—
275C4⋊C4—2442no—
276C22⋊C4—2442no—
277C22⋊C4—2442no—
278C22⋊C4—2444no—
279C22⋊C4—2444no—
280C42—22no—
281C42—1222no—
282C42—2441no—
283C42—2441no—
284C23—42no—
285C23—42no—
286C23—42no—
287C23—42no—
288C23—42no—
289C23—42no—
290C23—42no—
291C23—612no—
292C23—1221no—
293C23—1221no—
294C23—1221no—
295C23—1221no—
296C23—1221no—
297C23—1221no—
298C23C2×C22⋊#692311yescharacteristic
299D4—84no—
300D4—84no—
301D4—84no—
302D4—4888no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—612no—
308C2×C4—611no—
309C2×C4—611no—
310C2×C4—612no—
311C2×C4—1221no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—1221no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—1224no—
318C2×C4—1224no—
319C2×C4—2444no—
320C2×C4—2444no—
321C2×C4—2442no—
322C2×C4—2442no—
323C2×C4—2442no—
324C2×C4#1451983512yes—
325C2×C4#1451983912yes—
326C2×C4#1451984112yes—
327C2×C4#1451984112yes—
328C2×C4#1451986412yes—
329C8—2444no—
330C8—2444no—
331C22—82no—
332C22—82no—
333C22—82no—
334C22—82no—
335C22—82no—
336C22—82no—
337C22—82no—
338C22—1222no—
339C22—1222no—
340C22—1222no—
341C22—2441no—
342C22—2441no—
343C22—2441no—
344C22—2441no—
345C22#1684073611yescharacteristic
346C22C2×#1451983511yescharacteristic
347C22D61⋊#10011yescharacteristic
348C22C2×#1451983911yescharacteristic
349C22#1684075411yescharacteristic
350C22C2×#1451984111yescharacteristic
351C22C2×#1451984111yescharacteristic
352C4—22no—
353C4—22no—
354C4—1222no—
355C4—1221no—
356C4—1221no—
357C4—1222no—
358C4—4882no—
359C4#1684061314yes—
360C2—162no—
361C2—2442no—
362C2#2146109411yescharacteristic
363C2#2146113911yescharacteristic
364C2#2146116511yescharacteristic
365C2C2×#1684061311yescharacteristic
366C2#2146121511yescharacteristic
367C2#2146127411yescharacteristic
368C2#2146132711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#127×C61C4
socleC23×C61C2×C22⋊C4
prime radical#21454161C2
cosocleC2×C4×Dic61C23
hypercenterC2×#127#6923
hypocenterC61#7684
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C4×#14519834C2semidirect
2. #21461483C2semidirect
3. #21460635C2semidirect
204. C61#7684semidirect

Maximal subgroups

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

subgroupindex
C4×#145198342
#214614832
#214606352
#214541612
#768461