Finite Group Databasebeta

← #30595476

Subgroups — #30595476

Order 15616.

504 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 110 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#21461709C211yesmaximal, characteristic
2#21461673C211yesmaximal, characteristic
3#21460640C212yesmaximal, complemented
4#21460638C212yesmaximal, complemented
5#21448347C211yesmaximal, characteristic
6C2×C4⋊#92420—21no—
7C2×C22⋊#92420—21no—
8C2×C22⋊#92420—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519756C411yescharacteristic
13C2×#14519742C411yescharacteristic
14C22×C4×Dic61C2211yescharacteristic
15#16839667C2211yescharacteristic
16#16839658C2211yescharacteristic
17#16839644—21no—
18#16839634—21no—
19C4⋊C4×Dic61C411yescharacteristic
20#16839613—21no—
21C22⋊C4×Dic61—21no—
22C61×#380C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25C4⋊#92420—42no—
26C22⋊#92420—42no—
27C22⋊#92420—42no—
28C22×Dic122C2×C411yescharacteristic
29C23×Dic61D411yescharacteristic
30C23×Dic61D411yescharacteristic
31#14519756—22no—
32#14519756C814yescomplemented
33#14519742—42no—
34C2×C4⋊Dic61C2×C411yescharacteristic
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×C22⋊Dic61—21no—
39C2×C4×Dic61—21no—
40C2×C4×Dic61—21no—
41C2×C4×Dic61—42no—
42C2×C4×Dic61C2×C411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61C2311yescharacteristic
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50C23×C4×C61C2×C411yescharacteristic
51C2×C4⋊C4×C61C2×C411yescharacteristic
52C2×C4⋊C4×C61C2×C411yescharacteristic
53C2×C22⋊C4×C61—21no—
54#95×C61—21no—
55C24×C61C22⋊C411yescharacteristic
56C22×C4×C61—21no—
57C22×C4×C61—21no—
58C22×C4×C61—41no—
59C22×C4×C61—41no—
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C2×C812yes—
62C22×C4×C61M1612yes—
63C22×C4×C61C22×C411yescharacteristic
64C22×Dic61—21no—
65C22×Dic61—21no—
66C22×Dic61—22no—
67C22×Dic61—21no—
68C22×Dic61—22no—
69C22×Dic61—21no—
70C22×Dic61—41no—
71C22×Dic61—41no—
72C22×Dic61—41no—
73C22×Dic61C22⋊C411yescharacteristic
74C22×Dic61C22⋊C411yescharacteristic
75C22×Dic61C2×D411yescharacteristic
76C22×Dic61C2×D411yescharacteristic
77C2×Dic122—21no—
78C2×Dic122—41no—
79C2×Dic122—41no—
80C2×Dic122C2×C812yes—
81C2×#92420—42no—
82C2×#92420—42no—
83C2×#92420—42no—
84C2×#92420—42no—
85C2×#92420—42no—
86C2×#92420—42no—
87C4⋊C4×C61—41no—
88C4⋊C4×C61—41no—
89C22⋊C4×C61—42no—
90C22⋊Dic61—24no—
91C4⋊Dic61—21no—
92C4⋊Dic61C2×C812yes—
93#11758196—24no—
94#11758196—42no—
95#11758196—41no—
96#11758196—41no—
97C4×Dic61—22no—
98C4×Dic61—22no—
99C4×Dic61—41no—
100C4×Dic61—41no—
101C4×Dic61—42no—
102C4×Dic61—42no—
103C23×C61—21no—
104C23×C61—21no—
105C23×C61—21no—
106C23×C61—21no—
107C23×C61—21no—
108C23×C61—21no—
109C23×C61C22⋊C812yes—
110C23×C61C2×C22⋊C411yescharacteristic
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—42no—
116C2×C4×C61—42no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61C22⋊C812yes—
124C2×C4×C61C22×C811yescharacteristic
125C2×C4×C61C2×M1611yescharacteristic
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—22no—
133C2×Dic61—22no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—44no—
138C2×Dic61—42no—
139C2×Dic61—42no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61#9912yes—
145C2×Dic61AGL(1,ℤ/8)11yescharacteristic
146C2×Dic61#13711yescharacteristic
147C2×Dic61#13712yes—
148Dic122—42no—
149Dic122—42no—
150#92420—82no—
151#92420—82no—
152#7600—611nomaximal, Sylow
153C22×C61—22no—
154C22×C61—22no—
155C22×C61—22no—
156C22×C61—41no—
157C22×C61—41no—
158C22×C61—41no—
159C22×C61—41no—
160C22×C61C2×C22⋊C811yescharacteristic
161C22×C61C2×#9911yescharacteristic
162C22×C61#41311yescharacteristic
163C22×C61#41711yescharacteristic
164C22×C61#41911yescharacteristic
165C22×C61#42111yescharacteristic
166C22×C61#42111yescharacteristic
167C4×C61—21no—
168C4×C61—21no—
169C4×C61—22no—
170C4×C61—81no—
171C4×C61—81no—
172Dic61—22no—
173Dic61—22no—
174Dic61—21no—
175Dic61—21no—
176Dic61—42no—
177Dic61—42no—
178Dic61—41no—
179C4×C22⋊Q8—611no—
180#1817—611no—
181#1797—611no—
182#1272—612no—
183#1271—612no—
184C2×C61—42no—
185C2×C61#145911yescharacteristic
186C2×C61#147711yescharacteristic
187C2×C61#147911yescharacteristic
188C2×C61#151111yescharacteristic
189C2×C61#151311yescharacteristic
190C2×C61#153511yescharacteristic
191C2×C61#155911yescharacteristic
192C2×C22⋊Q8—611no—
193C2×C4×Q8—611no—
194C22×C42—611no—
195C2×C4⋊C8—1221no—
196C2×C22⋊C8—1221no—
197C2×C22⋊C8—1221no—
198#391—611no—
199#389—611no—
200#387—1221no—
201#385—1221no—
202#380#692311yescharacteristic
203C4×C4⋊C4—611no—
204C4×C4⋊C4—1221no—
205C4×C22⋊C4—1221no—
206#336—612no—
207#336—612no—
208#336—1221no—
209C61#760011yescharacteristic, complemented, Sylow
210C22×Q8—611no—
211C23×C4—611no—
212C23×C4—611no—
213C23×C4C2×#692311yescharacteristic
214C22×C8—1222no—
215C22×C8—1222no—
216C22⋊Q8—614no—
217C22⋊Q8—1222no—
218C4×Q8—2442no—
219C2×C4⋊C4—611no—
220C2×C4⋊C4—1221no—
221C2×C4⋊C4—1221no—
222C2×C4⋊C4—1221no—
223C2×C4⋊C4C2×#692311yescharacteristic
224C2×C4⋊C4C2×#692311yescharacteristic
225C2×C22⋊C4—21no—
226C2×C22⋊C4—1221no—
227C2×C42—611no—
228C2×C42—611no—
229C2×C42—611no—
230C2×C42—611no—
231C2×C42—1221no—
232C2×C42—1221no—
233C2×C42—2442no—
234C4⋊C8—2442no—
235C22⋊C8—2442no—
236C22⋊C8—2442no—
237#95—21no—
238#95—1221no—
239#95—1221no—
240#95—1221no—
241#95—1221no—
242C24C22⋊#692311yescharacteristic
243C2×Q8—612no—
244C2×Q8—1221no—
245C2×Q8—2441no—
246C2×Q8—2441no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—611no—
252C22×C4—611no—
253C22×C4—611no—
254C22×C4—611no—
255C22×C4—1221no—
256C22×C4—1222no—
257C22×C4—1221no—
258C22×C4—1222no—
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4—2441no—
262C22×C4—2441no—
263C22×C4—2441no—
264C22×C4D61⋊C812yes—
265C22×C4#1175821312yes—
266C22×C4C22⋊#692311yescharacteristic
267C22×C4C22×#692311yescharacteristic
268C2×C8—2442no—
269C2×C8—2442no—
270C2×C8—2442no—
271C2×C8—2442no—
272C2×C8—2442no—
273C2×C8—2442no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—612no—
277C4⋊C4—1224no—
278C4⋊C4—1221no—
279C4⋊C4—2441no—
280C4⋊C4—2441no—
281C4⋊C4—2442no—
282C22⋊C4—42no—
283C22⋊C4—1224no—
284C42—1222no—
285C42—1222no—
286C42—2441no—
287C42—2441no—
288C42—2442no—
289C42—2442no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23#1451983412yes—
297C23C2×C22⋊#692311yescharacteristic
298Q8—2442no—
299Q8—2442no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—612no—
313C2×C4—611no—
314C2×C4—611no—
315C2×C4—612no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—1222no—
323C2×C4—1222no—
324C2×C4—1221no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—2444no—
328C2×C4—2442no—
329C2×C4—2442no—
330C2×C4—2441no—
331C2×C4—2441no—
332C2×C4—2441no—
333C2×C4—2441no—
334C2×C4#1451983412yes—
335C2×C4C2×D61⋊C811yescharacteristic
336C2×C4C2×#1175821311yescharacteristic
337C8—4882no—
338C8—4882no—
339C22—22no—
340C22—22no—
341C22—22no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22C2×#1451983411yescharacteristic
347C22D61⋊#9911yescharacteristic
348C22#1684074911yescharacteristic
349C22#1684075311yescharacteristic
350C22#1684075511yescharacteristic
351C22#1684075911yescharacteristic
352C22#1684076011yescharacteristic
353C4—22no—
354C4—21no—
355C4—21no—
356C4—81no—
357C4—81no—
358C4—1222no—
359C4—1222no—
360C4—1221no—
361C4—1221no—
362C4—2442no—
363C4—2442no—
364C4—2441no—
365C2—42no—
366C2#2146105711yescharacteristic
367C2#2146111611yescharacteristic
368C2#2146112311yescharacteristic
369C2#2146122811yescharacteristic
370C2#2146123511yescharacteristic
371C2#2146130411yescharacteristic
372C2#2146135511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#380C4
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#380#6923
hypocenterC61#7600
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #21460640C2semidirect
4. #21460638C2semidirect
32. #14519756C8semidirect
209. C61#7600semidirect

Maximal subgroups

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

subgroupindex
#214617092
#214616732
#214606402
#214606382
#214483472
#760061