Finite Group Databasebeta

← #30595641

Subgroups — #30595641

Order 15616.

500 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 104 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#21461711C211yesmaximal, characteristic
2#21461674C211yesmaximal, characteristic
3#21460640C212yesmaximal, complemented
4#21460637C212yesmaximal, complemented
5C4×#14519757C211yesmaximal, characteristic
6C2×C4⋊#92420—21no—
7C2×#14519834—21no—
8C2×#14519834—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519757C411yescharacteristic
13C2×C4×Dic122C411yescharacteristic
14C2×C42×D61C2211yescharacteristic
15#16839667C2211yescharacteristic
16#16839661C2211yescharacteristic
17#16839647—21no—
18#16839636—21no—
19#16839619C411yescharacteristic
20C4×C4⋊Dic61—21no—
21C4×#11758198—21no—
22C4×C4⋊C4×C61C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25C4⋊#92420—42no—
26#14519834—42no—
27#14519834—42no—
28C22×Dic122C2×C411yescharacteristic
29C22×C4×D61C2×C411yescharacteristic
30C22×C4×D61D411yescharacteristic
31C22×C4×D61D411yescharacteristic
32#14519757—22no—
33#14519757—22no—
34C4×Dic122—42no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×#11758196—21no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×C4×Dic61—21no—
42C2×C4×Dic61D411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61C2311yescharacteristic
45C42×D61—42no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50C2×C4⋊C4×C61C2×C411yescharacteristic
51C2×C4⋊C4×C61C2×C411yescharacteristic
52C2×C42×C61—21no—
53C2×C42×C61C2×C411yescharacteristic
54#95×C61—21no—
55C23×D61C22⋊C411yescharacteristic
56C22×C4×C61—21no—
57C22×C4×C61—21no—
58C22×C4×C61C22⋊C411yescharacteristic
59C22×C4×C61C22⋊C411yescharacteristic
60C22×C4×C61C22×C411yescharacteristic
61C22×Dic61—21no—
62C22×Dic61—21no—
63C22×Dic61C22⋊C411yescharacteristic
64C22×Dic61C2×D411yescharacteristic
65C22×Dic61C2×D411yescharacteristic
66C2×C4×D61—22no—
67C2×C4×D61—21no—
68C2×C4×D61—21no—
69C2×C4×D61—22no—
70C2×C4×D61—41no—
71C2×C4×D61—41no—
72C2×C4×D61—41no—
73C2×C4×D61—41no—
74C2×C4×D61—41no—
75C2×C4×D61SD1612yes—
76C2×C4×D61Q1612yes—
77C2×Dic122—21no—
78C2×Dic122—41no—
79C2×Dic122—41no—
80C2×Dic122M1612yes—
81C2×#92420—42no—
82C2×#92420—42no—
83C2×#92420—42no—
84C2×#92420—42no—
85C2×#92420—42no—
86C2×#92420—42no—
87C4⋊C4×C61—21no—
88C4⋊C4×C61—41no—
89C4⋊C4×C61M1612yes—
90C42×C61—22no—
91C42×C61—42no—
92#11758198—24no—
93#11758198—42no—
94C4⋊Dic61—24no—
95C4⋊Dic61—42no—
96C4⋊Dic61—41no—
97#11758196—42no—
98C4×Dic61—22no—
99C4×Dic61—41no—
100C4×Dic61—41no—
101C4×Dic61—42no—
102C23×C61C2×C22⋊C411yescharacteristic
103C22×D61—21no—
104C22×D61—21no—
105C22×D61—21no—
106C22×D61—21no—
107C22×D61—21no—
108C22×D61—21no—
109C22×D61#10312yes—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—22no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61#9912yes—
123C2×C4×C61#10312yes—
124C2×C4×C61C2×M1611yescharacteristic
125C2×C4×C61C2×M1611yescharacteristic
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—22no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61C2×SD1611yescharacteristic
140C2×Dic61C2×Q1611yescharacteristic
141C2×Dic61#13512yes—
142C4×D61—42no—
143C4×D61—42no—
144C4×D61—44no—
145C4×D61—42no—
146C4×D61—42no—
147Dic122—42no—
148Dic122—42no—
149#92420—82no—
150#92420—82no—
151#7648—611nomaximal, Sylow
152C22×C61#40711yescharacteristic
153C22×C61C2×#9911yescharacteristic
154C22×C61#41311yescharacteristic
155C22×C61C2×#10311yescharacteristic
156C22×C61#41611yescharacteristic
157C22×C61#42111yescharacteristic
158C22×C61#42111yescharacteristic
159C2×D61—22no—
160C2×D61—22no—
161C2×D61—22no—
162C2×D61—41no—
163C2×D61—41no—
164C2×D61—41no—
165C2×D61—41no—
166C4×C61—21no—
167C4×C61—21no—
168C4×C61—22no—
169C4×C61—22no—
170C4×C61—42no—
171C4×C61—81no—
172Dic61—22no—
173Dic61—21no—
174Dic61—21no—
175Dic61—42no—
176Dic61—41no—
177Dic61—81no—
178C4×C22⋊Q8—611no—
179#1817—611no—
180#1797—611no—
181#1272—612no—
182#1271—612no—
183C2×C61#146511yescharacteristic
184C2×C61#148711yescharacteristic
185C2×C61#148811yescharacteristic
186C2×C61#151611yescharacteristic
187C2×C61#152011yescharacteristic
188C2×C61#153511yescharacteristic
189C2×C61#154211yescharacteristic
190D61—42no—
191C2×C22⋊Q8—611no—
192C2×C4×Q8—611no—
193C22×C42—611no—
194C2×C4⋊C8—1221no—
195C2×C22⋊C8—1221no—
196C2×C22⋊C8—1221no—
197#391—611no—
198#389—611no—
199#387—1221no—
200#385—1221no—
201#380—611no—
202C4×C4⋊C4—1221no—
203C4×C4⋊C4#692311yescharacteristic
204C4×C22⋊C4—1221no—
205#336—612no—
206#336—612no—
207#336—1221no—
208C61#764811yescharacteristic, complemented, Sylow
209C22×Q8—611no—
210C23×C4—611no—
211C23×C4—611no—
212C23×C4—611no—
213C22×C8—1222no—
214C22×C8—1222no—
215C22⋊Q8—1222no—
216C22⋊Q8—1222no—
217C4×Q8—2442no—
218C2×C4⋊C4—611no—
219C2×C4⋊C4—1221no—
220C2×C4⋊C4—1221no—
221C2×C4⋊C4—1221no—
222C2×C4⋊C4C2×#692311yescharacteristic
223C2×C4⋊C4C2×#692311yescharacteristic
224C2×C22⋊C4—1221no—
225C2×C22⋊C4—1221no—
226C2×C42—21no—
227C2×C42—611no—
228C2×C42—611no—
229C2×C42—611no—
230C2×C42—1221no—
231C2×C42—2442no—
232C2×C42C2×#692311yescharacteristic
233C4⋊C8—2442no—
234C22⋊C8—2442no—
235C22⋊C8—2442no—
236#95—21no—
237#95—1221no—
238#95—1221no—
239#95—1221no—
240#95—1221no—
241C24—611no—
242C2×Q8—612no—
243C2×Q8—1221no—
244C2×Q8—2441no—
245C2×Q8—2441no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—611no—
249C22×C4—611no—
250C22×C4—612no—
251C22×C4—612no—
252C22×C4—611no—
253C22×C4—1222no—
254C22×C4—1221no—
255C22×C4—1222no—
256C22×C4—1221no—
257C22×C4—1221no—
258C22×C4—1221no—
259C22×C4—2441no—
260C22×C4—2441no—
261C22×C4—2441no—
262C22×C4—2441no—
263C22×C4—2441no—
264C22×C4C22⋊#692311yescharacteristic
265C22×C4C22⋊#692311yescharacteristic
266C22×C4C22×#692311yescharacteristic
267C2×C8—2442no—
268C2×C8—2442no—
269C2×C8—2442no—
270C2×C8—2442no—
271C2×C8—2442no—
272C2×C8—2442no—
273C4⋊C4—21no—
274C4⋊C4—41no—
275C4⋊C4—1224no—
276C4⋊C4—2441no—
277C4⋊C4—2442no—
278C4⋊C4—2442no—
279C4⋊C4#1175821312yes—
280C22⋊C4—1224no—
281C22⋊C4—2442no—
282C42—22no—
283C42—42no—
284C42—1222no—
285C42—2441no—
286C42—2441no—
287C42—2442no—
288C23—612no—
289C23—1221no—
290C23—1221no—
291C23—1221no—
292C23—1221no—
293C23—1221no—
294C23—1221no—
295C23C2×C22⋊#692311yescharacteristic
296Q8—2442no—
297Q8—2442no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—22no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—611no—
311C2×C4—611no—
312C2×C4—612no—
313C2×C4—1221no—
314C2×C4—1221no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—1222no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—2442no—
322C2×C4—2442no—
323C2×C4—2444no—
324C2×C4—2442no—
325C2×C4—2442no—
326C2×C4—2441no—
327C2×C4—2441no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4#1451983612yes—
332C2×C4#1451984012yes—
333C2×C4D61⋊M1611yescharacteristic
334C2×C4C2×#1175821311yescharacteristic
335C8—4882no—
336C8—4882no—
337C22—1222no—
338C22—1222no—
339C22—1222no—
340C22—2441no—
341C22—2441no—
342C22—2441no—
343C22—2441no—
344C22#1684073311yescharacteristic
345C22C2×#1451983611yescharacteristic
346C22#1684074811yescharacteristic
347C22C2×#1451984011yescharacteristic
348C22#1684075211yescharacteristic
349C22#1684075911yescharacteristic
350C22#1684076011yescharacteristic
351C4—22no—
352C4—21no—
353C4—21no—
354C4—22no—
355C4—42no—
356C4—81no—
357C4—1221no—
358C4—1221no—
359C4—1222no—
360C4—4881no—
361C4—2441no—
362C4—2442no—
363C2—2442no—
364C2#2146107611yescharacteristic
365C2#2146114811yescharacteristic
366C2#2146115111yescharacteristic
367C2#2146124711yescharacteristic
368C2#2146125811yescharacteristic
369C2#2146130311yescharacteristic
370C2#2146132011yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC4×C4⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC4×C4⋊C4#6923
hypocenterC61#7648
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #21460640C2semidirect
4. #21460637C2semidirect
208. C61#7648semidirect

Maximal subgroups

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

subgroupindex
#214617112
#214616742
#214606402
#214606372
C4×#145197572
#764861