Finite Group Databasebeta

← #30595437

Subgroups — #30595437

Order 15616.

578 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 122 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#21461676C211yesmaximal, characteristic
2#21461480C211yesmaximal, characteristic
3#21460640C212yesmaximal, complemented
4#21460637C212yesmaximal, complemented
5C4×#14519757C211yesmaximal, characteristic
6C22×D61⋊C8—21no—
7C2×#14519844—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
23C2×D61⋊C8—24no—
24C2×D61⋊C8—42no—
25C2×D61⋊C8—42no—
26C22×#92420—22no—
27C22×#92420—22no—
28#14519844—42no—
29#14519834—42no—
30C22×Dic122C2×C411yescharacteristic
31C22×C4×D61C2×C411yescharacteristic
32C22×C4×D61D411yescharacteristic
33C22×C4×D61D411yescharacteristic
34#14519757—22no—
35#14519757C814yescomplemented
36C4×Dic122—42no—
37C2×C4⋊Dic61—21no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61C2×C411yescharacteristic
40C2×#11758196—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×C4×Dic61—21no—
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46C2×C4×Dic61C2311yescharacteristic
47C42×D61—42no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52C2×C4⋊C4×C61C2×C411yescharacteristic
53C2×C4⋊C4×C61C2×C411yescharacteristic
54C2×C42×C61—21no—
55C2×C42×C61C2×C411yescharacteristic
56#95×C61—21no—
57C23×D61C22⋊C411yescharacteristic
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22×C411yescharacteristic
63C22×Dic61—21no—
64C22×Dic61—21no—
65C22×Dic61C22⋊C411yescharacteristic
66C22×Dic61C2×D411yescharacteristic
67C22×Dic61C2×D411yescharacteristic
68C2×C4×D61—22no—
69C2×C4×D61—22no—
70C2×C4×D61—21no—
71C2×C4×D61—21no—
72C2×C4×D61—41no—
73C2×C4×D61—41no—
74C2×C4×D61—41no—
75C2×C4×D61—41no—
76C2×C4×D61C2×C812yes—
77C2×C4×D61M1612yes—
78C2×C4×D61SD1612yes—
79C2×C4×D61Q1612yes—
80C2×Dic122—21no—
81C2×Dic122—41no—
82C2×Dic122—41no—
83C2×Dic122C2×C812yescomplemented
84C2×#92420—24no—
85C2×#92420—42no—
86C2×#92420—42no—
87C2×#92420—42no—
88C2×#92420—42no—
89C2×#92420—42no—
90D61⋊C8—48no—
91C4⋊C4×C61—21no—
92C4⋊C4×C61—41no—
93C4⋊C4×C61C2×C812yescomplemented
94C42×C61—22no—
95C42×C61—42no—
96#11758198—24no—
97#11758198—42no—
98C4⋊Dic61—24no—
99C4⋊Dic61—41no—
100C4⋊Dic61—41no—
101C4⋊Dic61—41no—
102#11758196—42no—
103C4×Dic61—22no—
104C4×Dic61—41no—
105C4×Dic61—41no—
106C4×Dic61—42no—
107C23×C61C2×C22⋊C411yescharacteristic
108C22×D61—21no—
109C22×D61—21no—
110C22×D61—21no—
111C22×D61—21no—
112C22×D61C22⋊C812yes—
113C22×D61#10312yes—
114C22×D61#10412yes—
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—22no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61#9912yes—
128C2×C4×C61#10312yes—
129C2×C4×C61C22×C811yescharacteristic
130C2×C4×C61C2×M1611yescharacteristic
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—22no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61C22⋊C812yes—
144C2×Dic61C2×SD1611yescharacteristic
145C2×Dic61C2×Q1611yescharacteristic
146C2×Dic61AGL(1,ℤ/8)11yescharacteristic
147C2×Dic61#13711yescharacteristic
148C4×D61—24no—
149C4×D61—24no—
150C4×D61—42no—
151C4×D61—42no—
152C4×D61—42no—
153C4×D61—42no—
154Dic122—42no—
155Dic122—42no—
156#92420—44no—
157#92420—82no—
158#7589—611nomaximal, Sylow
159C22×C61C2×C22⋊C811yescharacteristic
160C22×C61C2×#9911yescharacteristic
161C22×C61#41311yescharacteristic
162C22×C61C2×#10311yescharacteristic
163C22×C61#41711yescharacteristic
164C22×C61C2×#10411yescharacteristic
165C22×C61#42111yescharacteristic
166C2×D61—22no—
167C2×D61—22no—
168C2×D61—22no—
169C2×D61—22no—
170C2×D61—22no—
171C2×D61—22no—
172C2×D61Q8⋊C814yes—
173C4×C61—21no—
174C4×C61—21no—
175C4×C61—22no—
176C4×C61—22no—
177C4×C61—42no—
178C4×C61—81no—
179Dic61—22no—
180Dic61—21no—
181Dic61—21no—
182Dic61—21no—
183Dic61—21no—
184Dic61—42no—
185Dic61—81no—
186C4×C22⋊Q8—611no—
187#1797—611no—
188C2×#336—611no—
189#1272—612no—
190#1271—612no—
191C2×C61#145911yescharacteristic
192C2×C61C2×Q8⋊C811yescharacteristic
193C2×C61#147711yescharacteristic
194C2×C61#150411yescharacteristic
195C2×C61#152011yescharacteristic
196C2×C61#153211yescharacteristic
197C2×C61#155011yescharacteristic
198D61—24no—
199C23×C8—1221no—
200C2×C22⋊Q8—611no—
201C2×C4×Q8—611no—
202C22×C42—611no—
203C2×C4⋊C8—1221no—
204C2×C22⋊C8—1221no—
205#391—611no—
206#389—611no—
207#387—1221no—
208#385—1221no—
209#380—611no—
210C4×C4⋊C4—1221no—
211C4×C4⋊C4#692311yescharacteristic
212C4×C22⋊C4—1221no—
213#336—612no—
214#336—612no—
215#336—1221no—
216C61#758911yescharacteristic, complemented, Sylow
217C22×Q8—611no—
218C23×C4—611no—
219C23×C4—611no—
220C23×C4—611no—
221C22×C8—1222no—
222C22×C8—1224no—
223C22×C8—1222no—
224C22×C8—2442no—
225C22×C8—2442no—
226C22⋊Q8—614no—
227C22⋊Q8—1222no—
228C4×Q8—2442no—
229C2×C4⋊C4—611no—
230C2×C4⋊C4—1221no—
231C2×C4⋊C4—1221no—
232C2×C4⋊C4—1221no—
233C2×C4⋊C4C2×#692311yescharacteristic
234C2×C4⋊C4C2×#692311yescharacteristic
235C2×C22⋊C4—1221no—
236C2×C22⋊C4—1221no—
237C2×C42—21no—
238C2×C42—611no—
239C2×C42—611no—
240C2×C42—611no—
241C2×C42—1221no—
242C2×C42—2442no—
243C2×C42C2×#692311yescharacteristic
244C4⋊C8—2442no—
245C22⋊C8—2442no—
246#95—21no—
247#95—1221no—
248#95—1221no—
249#95—1221no—
250#95—1221no—
251C24—611no—
252C2×Q8—612no—
253C2×Q8—1221no—
254C2×Q8—2441no—
255C2×Q8—2441no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—611no—
259C22×C4—611no—
260C22×C4—611no—
261C22×C4—612no—
262C22×C4—612no—
263C22×C4—612no—
264C22×C4—612no—
265C22×C4—1221no—
266C22×C4—1221no—
267C22×C4—1222no—
268C22×C4—1222no—
269C22×C4—1221no—
270C22×C4—1221no—
271C22×C4—2441no—
272C22×C4—2441no—
273C22×C4—2441no—
274C22×C4—2441no—
275C22×C4C22⋊#692311yescharacteristic
276C22×C4C22⋊#692311yescharacteristic
277C22×C4C22×#692311yescharacteristic
278C2×C8—1224no—
279C2×C8—2442no—
280C2×C8—2442no—
281C2×C8—2442no—
282C2×C8—2442no—
283C2×C8—2448no—
284C2×C8—2442no—
285C4⋊C4—21no—
286C4⋊C4—41no—
287C4⋊C4—1224no—
288C4⋊C4—2441no—
289C4⋊C4—2441no—
290C4⋊C4—2441no—
291C4⋊C4—2442no—
292C4⋊C4D61⋊C812yescomplemented
293C22⋊C4—1224no—
294C22⋊C4—2442no—
295C42—22no—
296C42—42no—
297C42—1222no—
298C42—2441no—
299C42—2441no—
300C42—2442no—
301C23—612no—
302C23—612no—
303C23—612no—
304C23—1221no—
305C23—1221no—
306C23—1221no—
307C23—1221no—
308C23C2×C22⋊#692311yescharacteristic
309Q8—2442no—
310Q8—2442no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—22no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—612no—
324C2×C4—611no—
325C2×C4—611no—
326C2×C4—611no—
327C2×C4—611no—
328C2×C4—1224no—
329C2×C4—1224no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—1221no—
333C2×C4—1221no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—1222no—
337C2×C4—2442no—
338C2×C4—2442no—
339C2×C4—2442no—
340C2×C4—2442no—
341C2×C4—2441no—
342C2×C4—2441no—
343C2×C4—2441no—
344C2×C4—2441no—
345C2×C4—2441no—
346C2×C4#1451983612yes—
347C2×C4#1451984012yes—
348C2×C4C2×D61⋊C811yescharacteristic
349C2×C4D61⋊M1611yescharacteristic
350C8—4882no—
351C8—2444no—
352C22—614no—
353C22—1222no—
354C22—1222no—
355C22—1222no—
356C22—1222no—
357C22—1222no—
358C22—1222no—
359C22D61⋊(C22⋊C8)11yescharacteristic
360C22C2×#1451983611yescharacteristic
361C22#1684074811yescharacteristic
362C22C2×#1451984011yescharacteristic
363C22#1684075311yescharacteristic
364C22D61⋊#10411yescharacteristic
365C22#1684076011yescharacteristic
366C4—22no—
367C4—21no—
368C4—21no—
369C4—22no—
370C4—42no—
371C4—81no—
372C4—1221no—
373C4—1221no—
374C4—1222no—
375C4—1221no—
376C4—1221no—
377C4—4881no—
378C4—2442no—
379C2—1224no—
380C2#2146105611yescharacteristic
381C2D61⋊(Q8⋊C8)11yescharacteristic
382C2#2146111511yescharacteristic
383C2#2146120711yescharacteristic
384C2#2146125811yescharacteristic
385C2#2146129411yescharacteristic
386C2#2146133611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC4×C4⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC4×C4⋊C4#6923
hypocenterC61#7589
LCSG ▷ C2×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
35. #14519757C8semidirect
83. C2×Dic122C2×C8semidirect
93. C4⋊C4×C61C2×C8semidirect
216. C61#7589semidirect
292. C4⋊C4D61⋊C8semidirect

Maximal subgroups

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

subgroupindex
#214616762
#214614802
#214606402
#214606372
C4×#145197572
#758961