Finite Group Databasebeta

← #30595719

Subgroups — #30595719

Order 15616.

538 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 538 conjugacy classes of subgroups — too many to draw. Only its 92 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, complemented
2C4×#14519834C211yesmaximal, characteristic, complemented
3#21460640C212yesmaximal, complemented
4#21460636C212yesmaximal, complemented
5#21454121C211yesmaximal, characteristic
6C2×#14519834—21no—
7C2×#14519834—21no—
8C2×C4×#92420—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519765C411yescharacteristic
13C2×#14519757C411yescharacteristic
14C2×#14519752C411yescharacteristic
15C2×C42×D61C2211yescharacteristic
16#16839667C2211yescharacteristic
17#16839663C2211yescharacteristic
18#16839654—21no—
19#16839654—21no—
20#16839640—21no—
21#16839640—21no—
22C61×#382C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25#14519834—24no—
26#14519834—42no—
27C4×#92420—42no—
28C22×Dic122C2×C411yescharacteristic
29C22×D244—21no—
30C22×D244C2×C411yescharacteristic
31C22×C4×D61C2×C411yescharacteristic
32C22×C4×D61D411yescharacteristic
33C22×C4×D61D411yescharacteristic
34#14519765—42no—
35#14519757—42no—
36#14519752—42no—
37C2×C4⋊Dic61—21no—
38C2×#11758198—21no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46C2×C4×Dic61C2311yescharacteristic
47C42×D61—42no—
48#14519684—21no—
49#14519684—21no—
50C2×C4⋊C4×C61C2×C411yescharacteristic
51C2×C4⋊C4×C61C2×C411yescharacteristic
52C2×C42×C61C2×C411yescharacteristic
53#95×C61—21no—
54#95×C61—21no—
55C23×D61—21no—
56C23×D61C22⋊C411yescharacteristic
57C22×C4×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61C22⋊C411yescharacteristic
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C22×C411yescharacteristic
62C22×Dic61—21no—
63C22×Dic61C22⋊C411yescharacteristic
64C22×Dic61C2×D411yescharacteristic
65C22×Dic61C2×D411yescharacteristic
66C2×D244—22no—
67C2×D244—41no—
68C2×D244—41no—
69C2×D244—42no—
70C2×D244—42no—
71C2×D244—42no—
72C2×C4×D61—22no—
73C2×C4×D61—22no—
74C2×C4×D61—22no—
75C2×C4×D61—22no—
76C2×C4×D61—22no—
77C2×C4×D61—22no—
78C2×C4×D61—41no—
79C2×C4×D61—41no—
80C2×C4×D61—41no—
81C2×Dic122—22no—
82C2×Dic122—41no—
83C2×Dic122—41no—
84C2×#92420—24no—
85C2×#92420—42no—
86C2×#92420—42no—
87C2×#92420—42no—
88C2×#92420—42no—
89C2×#92420—42no—
90C4⋊C4×C61—41no—
91C4⋊C4×C61—41no—
92C42×C61—22no—
93#11758198—42no—
94#11758198—42no—
95#11758198—42no—
96#11758198—42no—
97#11758198—42no—
98#11758198—42no—
99C4⋊Dic61—42no—
100C4×Dic61—22no—
101C4×Dic61—41no—
102C4×Dic61—41no—
103C23×C61C2×C22⋊C411yescharacteristic
104C22×D61—21no—
105C22×D61—21no—
106C22×D61—21no—
107C22×D61—21no—
108C22×D61—21no—
109C22×D61—21no—
110C22×D61—41no—
111C22×D61—41no—
112C22×D61—41no—
113C22×D61—41no—
114C22×D61—41no—
115C22×D61—41no—
116C22×D61—41no—
117C22×D61#10412yes—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61#9912yes—
132C2×C4×C61#13112yes—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61#10012yes—
143C2×Dic61#13512yes—
144C2×Dic61#13512yes—
145D244—82no—
146D244—84no—
147C4×D61—44no—
148C4×D61—44no—
149C4×D61—44no—
150Dic122—82no—
151#92420—44no—
152#92420—82no—
153#7670—611nomaximal, Sylow
154C22×C61#40811yescharacteristic
155C22×C61C2×#9911yescharacteristic
156C22×C61C2×#10011yescharacteristic
157C22×C61#41611yescharacteristic
158C22×C61#41611yescharacteristic
159C22×C61C2×#10411yescharacteristic
160C22×C61#42111yescharacteristic
161C2×D61—22no—
162C2×D61—22no—
163C2×D61—22no—
164C2×D61—41no—
165C2×D61—41no—
166C2×D61—41no—
167C2×D61—41no—
168C2×D61—81no—
169C2×D61—81no—
170C2×D61—81no—
171C2×D61—81no—
172C2×D61—81no—
173C2×D61—81no—
174C2×D61—81no—
175C4×C61—22no—
176C4×C61—22no—
177C4×C61—41no—
178C4×C61—81no—
179C4×C61—81no—
180Dic61—22no—
181Dic61—22no—
182Dic61—22no—
183Dic61—81no—
184#2850—611no—
185#1817—611no—
186C4×C22⋊C8—611no—
187#1272—612no—
188#1270—612no—
189C2×C61#147111yescharacteristic
190C2×C61#148211yescharacteristic
191C2×C61#149411yescharacteristic
192C2×C61#150111yescharacteristic
193C2×C61#151611yescharacteristic
194C2×C61#152711yescharacteristic
195C2×C61#154311yescharacteristic
196D61—42no—
197D61—161no—
198C2×#124—611no—
199C2×C22⋊Q8—611no—
200C2×#121—611no—
201C22×C42—611no—
202C2×C22⋊C8—1221no—
203C2×C22⋊C8—1221no—
204C2×C4×C8—1221no—
205#391—611no—
206#390—611no—
207#388—1221no—
208#388—1221no—
209#386—1221no—
210#386—1221no—
211#382#692311yescharacteristic
212#336—612no—
213#336—612no—
214#336—1221no—
215C61#767011yescharacteristic, complemented, Sylow
216C22×Q8—611no—
217C22×D4—611no—
218C22×D4—1221no—
219C23×C4—611no—
220C23×C4—611no—
221C23×C4—611no—
222C22×C8—1222no—
223C22×C8—1222no—
224#124—2442no—
225C22⋊Q8—2442no—
226#121—2442no—
227C2×C4⋊C4—1221no—
228C2×C4⋊C4C2×#692311yescharacteristic
229C2×C4⋊C4C2×#692311yescharacteristic
230C2×C22⋊C4—1221no—
231C2×C22⋊C4—1221no—
232C2×C22⋊C4—1221no—
233C2×C22⋊C4—1221no—
234C2×C22⋊C4—1221no—
235C2×C22⋊C4—1221no—
236C2×C42—611no—
237C2×C42—611no—
238C2×C42—611no—
239C2×C42—2442no—
240C2×C42C2×#692311yescharacteristic
241C22⋊C8—1224no—
242C22⋊C8—2442no—
243C4×C8—2442no—
244#95—21no—
245#95—21no—
246#95—1221no—
247#95—1221no—
248C24—611no—
249C24—1221no—
250C2×Q8—1222no—
251C2×Q8—2441no—
252C2×Q8—2441no—
253C2×D4—1222no—
254C2×D4—2441no—
255C2×D4—2441no—
256C2×D4—2442no—
257C2×D4—2442no—
258C2×D4—2442no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—611no—
262C22×C4—611no—
263C22×C4—611no—
264C22×C4—1222no—
265C22×C4—1222no—
266C22×C4—1222no—
267C22×C4—1222no—
268C22×C4—1222no—
269C22×C4—1222no—
270C22×C4—1221no—
271C22×C4—2441no—
272C22×C4—2441no—
273C22×C4—2441no—
274C22×C4C22⋊#692311yescharacteristic
275C22×C4C22⋊#692311yescharacteristic
276C22×C4C22×#692311yescharacteristic
277C2×C8—1224no—
278C2×C8—2442no—
279C2×C8—2442no—
280C2×C8—2442no—
281C2×C8—2442no—
282C2×C8—2442no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—2442no—
286C22⋊C4—2442no—
287C22⋊C4—2442no—
288C22⋊C4—2442no—
289C22⋊C4—2442no—
290C22⋊C4—2442no—
291C22⋊C4—2442no—
292C42—22no—
293C42—1222no—
294C42—2441no—
295C42—2441no—
296C23—612no—
297C23—1221no—
298C23—1221no—
299C23—1221no—
300C23—1221no—
301C23—1221no—
302C23—1221no—
303C23—2441no—
304C23—2441no—
305C23—2441no—
306C23—2441no—
307C23—2441no—
308C23—2441no—
309C23—2441no—
310C23C2×C22⋊#692311yescharacteristic
311Q8—4882no—
312D4—4882no—
313D4—4884no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—612no—
328C2×C4—612no—
329C2×C4—612no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—1221no—
333C2×C4—1221no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—2444no—
337C2×C4—2444no—
338C2×C4—2444no—
339C2×C4—2441no—
340C2×C4—2441no—
341C2×C4—2441no—
342C2×C4#1451983612yes—
343C2×C4#1451986512yes—
344C8—4882no—
345C8—2444no—
346C22—1222no—
347C22—1222no—
348C22—1222no—
349C22—4881no—
350C22—4881no—
351C22—4881no—
352C22—4881no—
353C22—4881no—
354C22—4881no—
355C22—4881no—
356C22—2441no—
357C22—2441no—
358C22—2441no—
359C22—2441no—
360C22#1684073711yescharacteristic
361C22C2×#1451983611yescharacteristic
362C22D61⋊#10011yescharacteristic
363C22#1684075211yescharacteristic
364C22#1684075211yescharacteristic
365C22D61⋊#10411yescharacteristic
366C22#1684075911yescharacteristic
367C4—22no—
368C4—22no—
369C4—41no—
370C4—81no—
371C4—81no—
372C4—1222no—
373C4—1222no—
374C4—1222no—
375C4—4881no—
376C2—9761no—
377C2—2442no—
378C2#2146109611yescharacteristic
379C2#2146113311yescharacteristic
380C2#2146117311yescharacteristic
381C2#2146119611yescharacteristic
382C2#2146124711yescharacteristic
383C2#2146127911yescharacteristic
384C2#2146132311yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#382C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519752C4
cosocleC2×C4×Dic61C23
hypercenter#382#6923
hypocenterC61#7670
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
1. #21461711C2semidirect
2. C4×#14519834C2semidirect
3. #21460640C2semidirect
4. #21460636C2semidirect
215. C61#7670semidirect

Maximal subgroups

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

subgroupindex
#214617112
C4×#145198342
#214606402
#214606362
#214541212
#767061