Finite Group Databasebeta

← #30595470

Subgroups — #30595470

Order 15616.

588 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 118 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, complemented
2#21461673C211yesmaximal, characteristic, complemented
3#21460637C212yesmaximal, complemented
4#21460635C212yesmaximal, complemented
5#121×Dic61C211yesmaximal, characteristic
6C2×C4⋊#92420—21no—
7C2×C22⋊#92420—21no—
8C2×C22⋊#92420—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×D4×Dic61—21no—
13C2×D4×Dic61C411yescharacteristic
14C22×C4×Dic61C2211yescharacteristic
15#16839665C2211yescharacteristic
16#16839661C2211yescharacteristic
17#16839655—21no—
18#16839642—21no—
19#16839622C411yescharacteristic
20C4⋊C4×Dic61C411yescharacteristic
21C22⋊C4×Dic61—21no—
22C2×#121×C61C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25C4⋊#92420—42no—
26C22⋊#92420—42no—
27C22⋊#92420—42no—
28C23×Dic61—21no—
29C23×Dic61D411yescharacteristic
30C23×Dic61D411yescharacteristic
31D4×Dic61—42no—
32D4×Dic61—44no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61C2×C411yescharacteristic
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×C22⋊Dic61—21no—
37C2×C22⋊Dic61—21no—
38C2×C22⋊Dic61—21no—
39C2×C22⋊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—
49C22×D4×C61—21no—
50C22×D4×C61C2×C411yescharacteristic
51C23×C4×C61C2×C411yescharacteristic
52#121×C61—22no—
53#121×C61C814yescomplemented
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C22⋊C4×C61—21no—
56C24×C61—21no—
57C24×C61C22⋊C411yescharacteristic
58C2×D4×C61—24no—
59C2×D4×C61—21no—
60C2×D4×C61—41no—
61C2×D4×C61—41no—
62C2×D4×C61—42no—
63C2×D4×C61—42no—
64C2×D4×C61C2×C812yes—
65C22×C4×C61—21no—
66C22×C4×C61—41no—
67C22×C4×C61—41no—
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C2×C812yes—
70C22×C4×C61M1612yes—
71C22×C4×C61C22×C411yescharacteristic
72C22×Dic61—22no—
73C22×Dic61—21no—
74C22×Dic61—22no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—41no—
79C22×Dic61—41no—
80C22×Dic61—41no—
81C22×Dic61—42no—
82C22×Dic61—42no—
83C22×Dic61—42no—
84C22×Dic61C22⋊C411yescharacteristic
85C22×Dic61C22⋊C411yescharacteristic
86C22×Dic61C2×D411yescharacteristic
87C22×Dic61C2×D411yescharacteristic
88C2×#92420—42no—
89C2×#92420—42no—
90C2×#92420—42no—
91C2×#92420—42no—
92C2×#92420—42no—
93C2×#92420—42no—
94C4⋊C4×C61—21no—
95C4⋊C4×C61C2×C812yes—
96C22⋊C4×C61—24no—
97C22⋊Dic61—42no—
98C22⋊Dic61—42no—
99C22⋊Dic61—41no—
100C22⋊Dic61—42no—
101C22⋊Dic61—41no—
102C4⋊Dic61—42no—
103C4⋊Dic61—41no—
104C4⋊Dic61—41no—
105C4×Dic61—22no—
106C4×Dic61—22no—
107C4×Dic61—41no—
108C4×Dic61—41no—
109C4×Dic61—42no—
110C23×C61—21no—
111C23×C61—21no—
112C23×C61—21no—
113C23×C61—21no—
114C23×C61—21no—
115C23×C61—21no—
116C23×C61—22no—
117C23×C61—41no—
118C23×C61—41no—
119C23×C61—41no—
120C23×C61—41no—
121C23×C61—41no—
122C23×C61—41no—
123C23×C61C22⋊C812yes—
124C23×C61C2×C22⋊C411yescharacteristic
125D4×C61—42no—
126D4×C61—42no—
127D4×C61—48no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—22no—
133C2×C4×C61—42no—
134C2×C4×C61—42no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61C22⋊C812yes—
138C2×C4×C61C22×C811yescharacteristic
139C2×C4×C61C2×M1611yescharacteristic
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—44no—
150C2×Dic61—42no—
151C2×Dic61—42no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—84no—
159C2×Dic61#9912yes—
160C2×Dic61AGL(1,ℤ/8)11yescharacteristic
161C2×Dic61AGL(1,ℤ/8)12yes—
162C2×Dic61#13711yescharacteristic
163#92420—82no—
164#92420—82no—
165#7599—611nomaximal, Sylow
166C22×C61—22no—
167C22×C61—22no—
168C22×C61—22no—
169C22×C61—41no—
170C22×C61—41no—
171C22×C61—41no—
172C22×C61—41no—
173C22×C61—42no—
174C22×C61—42no—
175C22×C61—42no—
176C22×C61—81no—
177C22×C61—81no—
178C22×C61—81no—
179C22×C61—81no—
180C22×C61C2×C22⋊C811yescharacteristic
181C22×C61C2×#9911yescharacteristic
182C22×C61#41311yescharacteristic
183C22×C61#41711yescharacteristic
184C22×C61#41811yescharacteristic
185C22×C61#42111yescharacteristic
186C22×C61#42111yescharacteristic
187C4×C61—22no—
188C4×C61—21no—
189C4×C61—21no—
190C4×C61—42no—
191Dic61—22no—
192Dic61—22no—
193Dic61—21no—
194Dic61—21no—
195Dic61—41no—
196Dic61—81no—
197Dic61—81no—
198C4×#121—611no—
199#1817—611no—
200#1797—611no—
201#1271—612no—
202#1270—612no—
203C2×C61—42no—
204C2×C61—82no—
205C2×C61#145911yescharacteristic
206C2×C61#147711yescharacteristic
207C2×C61#147811yescharacteristic
208C2×C61#151011yescharacteristic
209C2×C61#151311yescharacteristic
210C2×C61#153511yescharacteristic
211C2×C61#155711yescharacteristic
212C2×#121#692311yescharacteristic
213C2×C4×D4—611no—
214C2×C4×D4—1221no—
215C22×C42—611no—
216C2×C4⋊C8—1221no—
217C2×C22⋊C8—1221no—
218C2×C22⋊C8—1221no—
219#390—611no—
220#389—611no—
221#388—1221no—
222#386—1221no—
223#380—611no—
224C4×C4⋊C4—611no—
225C4×C22⋊C4—1221no—
226#336—612no—
227#336—612no—
228#336—1221no—
229C61#759911yescharacteristic, complemented, Sylow
230C22×D4—21no—
231C22×D4C2×#692311yescharacteristic
232C23×C4—611no—
233C23×C4—611no—
234C23×C4—1221no—
235C23×C4C2×#692311yescharacteristic
236C22×C8—1222no—
237C22×C8—1222no—
238#121—22no—
239#121#9242014yescomplemented
240C4×D4—2442no—
241C4×D4—2444no—
242C2×C4⋊C4—611no—
243C2×C4⋊C4—611no—
244C2×C4⋊C4—1221no—
245C2×C4⋊C4C2×#692311yescharacteristic
246C2×C22⋊C4—21no—
247C2×C22⋊C4—1221no—
248C2×C22⋊C4—1221no—
249C2×C22⋊C4—1221no—
250C2×C22⋊C4—1221no—
251C2×C42—611no—
252C2×C42—611no—
253C2×C42—611no—
254C2×C42—611no—
255C2×C42—1221no—
256C2×C42—2442no—
257C4⋊C8—2442no—
258C22⋊C8—2442no—
259C22⋊C8—2442no—
260#95—1221no—
261#95—1221no—
262#95—1221no—
263C24—21no—
264C24C22⋊#692311yescharacteristic
265C2×D4—24no—
266C2×D4—21no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—42no—
270C2×D4—42no—
271C2×D4C2×#9242012yes—
272C22×C4—21no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—611no—
276C22×C4—611no—
277C22×C4—611no—
278C22×C4—611no—
279C22×C4—1221no—
280C22×C4—1222no—
281C22×C4—1222no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4—1221no—
285C22×C4—2442no—
286C22×C4—2441no—
287C22×C4—2441no—
288C22×C4—2441no—
289C22×C4—2442no—
290C22×C4—2442no—
291C22×C4C2×#9242012yes—
292C22×C4#1175821712yes—
293C22×C4C22⋊#692311yescharacteristic
294C22×C4C22×#692311yescharacteristic
295C2×C8—2442no—
296C2×C8—2442no—
297C2×C8—2442no—
298C2×C8—2442no—
299C2×C8—2442no—
300C2×C8—2442no—
301C4⋊C4—21no—
302C4⋊C4—2441no—
303C4⋊C4—2441no—
304C4⋊C4—2442no—
305C4⋊C4C2×#9242012yes—
306C22⋊C4—24no—
307C22⋊C4—2442no—
308C22⋊C4—2441no—
309C22⋊C4—2441no—
310C22⋊C4—2442no—
311C22⋊C4—2442no—
312C42—1222no—
313C42—1222no—
314C42—2441no—
315C42—2441no—
316C42—2442no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—21no—
323C23—22no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23C22⋊#9242012yes—
331C23C2×C22⋊#692311yescharacteristic
332D4—42no—
333D4—42no—
334D4—48no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—22no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—612no—
345C2×C4—611no—
346C2×C4—611no—
347C2×C4—612no—
348C2×C4—1221no—
349C2×C4—1221no—
350C2×C4—1221no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—1221no—
355C2×C4—1221no—
356C2×C4—1221no—
357C2×C4—4884no—
358C2×C4—2444no—
359C2×C4—2442no—
360C2×C4—2442no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4—2441no—
365C2×C4—2441no—
366C2×C4—2441no—
367C2×C4C22⋊#9242012yes—
368C2×C4C22×#9242011yescharacteristic
369C2×C4C2×#1175821711yescharacteristic
370C8—4882no—
371C8—4882no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—42no—
380C22—42no—
381C22—42no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22—81no—
386C22C2×C22⋊#9242011yescharacteristic
387C22D61⋊#9911yescharacteristic
388C22#1684074911yescharacteristic
389C22#1684075311yescharacteristic
390C22#1684075411yescharacteristic
391C22#1684075911yescharacteristic
392C22#1684076011yescharacteristic
393C4—22no—
394C4—21no—
395C4—21no—
396C4—42no—
397C4—1222no—
398C4—1222no—
399C4—1221no—
400C4—1221no—
401C4—4881no—
402C4—4881no—
403C4—2441no—
404C2—42no—
405C2—82no—
406C2#2146105511yescharacteristic
407C2#2146111411yescharacteristic
408C2#2146111811yescharacteristic
409C2#2146122511yescharacteristic
410C2#2146123511yescharacteristic
411C2#2146130411yescharacteristic
412C2#2146135111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
Fitting, prime radicalC2×#121×C61C4
socleC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×#121#6923
hypocenterC61#7599
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. #21461709C2semidirect
2. #21461673C2semidirect
3. #21460637C2semidirect
4. #21460635C2semidirect
53. #121×C61C8semidirect
229. C61#7599semidirect
239. #121#92420semidirect

Maximal subgroups

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

subgroupindex
#214617092
#214616732
#214606372
#214606352
#121×Dic612
#759961