Finite Group Databasebeta

← #30595718

Subgroups — #30595718

Order 15616.

538 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 538 conjugacy classes of subgroups — too many to draw. Only its 94 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#21461710C211yesmaximal, characteristic, complemented
2C4×C22⋊#92420C211yesmaximal, characteristic, complemented
3#21460640C212yesmaximal, complemented
4#21460635C212yesmaximal, complemented
5#21454118C211yesmaximal, characteristic
6C2×C22⋊#92420—21no—
7C2×C22⋊#92420—21no—
8C2×C4×#92420—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519764C411yescharacteristic
13C2×#14519756C411yescharacteristic
14C22×C4×Dic61C2211yescharacteristic
15#16839667C2211yescharacteristic
16#16839665C2211yescharacteristic
17#16839656—21no—
18#16839656—21no—
19#16839642—21no—
20#16839642—21no—
21#16839627C411yescharacteristic
22C2×#121×C61C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25C22⋊#92420—24no—
26C22⋊#92420—42no—
27C4×#92420—42no—
28C22×Dic122C2×C411yescharacteristic
29C23×Dic61D411yescharacteristic
30C23×Dic61D411yescharacteristic
31#14519764—42no—
32#14519756—42no—
33C2×C4⋊Dic61C2×C411yescharacteristic
34C2×#11758196—21no—
35C2×C22⋊Dic61—21no—
36C2×C22⋊Dic61—21no—
37C2×C22⋊Dic61—21no—
38C2×C22⋊Dic61—21no—
39C2×C22⋊Dic61—21no—
40C2×C4×Dic61—42no—
41C2×C4×Dic61C2×C411yescharacteristic
42C2×C4×Dic61D411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61C2311yescharacteristic
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49C22×D4×C61—21no—
50C22×D4×C61C2×C411yescharacteristic
51C23×C4×C61C2×C411yescharacteristic
52#121×C61—42no—
53C2×C4⋊C4×C61C2×C411yescharacteristic
54C2×C22⋊C4×C61—21no—
55C24×C61—21no—
56C24×C61C22⋊C411yescharacteristic
57C2×D4×C61—22no—
58C2×D4×C61—41no—
59C2×D4×C61—41no—
60C2×D4×C61—42no—
61C2×D4×C61—42no—
62C2×D4×C61—42no—
63C22×C4×C61—22no—
64C22×C4×C61—22no—
65C22×C4×C61—21no—
66C22×C4×C61—41no—
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C22×C411yescharacteristic
69C22×Dic61—22no—
70C22×Dic61—22no—
71C22×Dic61—22no—
72C22×Dic61—22no—
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61—41no—
76C22×Dic61—41no—
77C22×Dic61C22⋊C411yescharacteristic
78C22×Dic61C22⋊C411yescharacteristic
79C22×Dic61C2×D411yescharacteristic
80C22×Dic61C2×D411yescharacteristic
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—
91C22⋊C4×C61—42no—
92C22⋊Dic61—42no—
93C22⋊Dic61—42no—
94C22⋊Dic61—42no—
95C22⋊Dic61—42no—
96C22⋊Dic61—42no—
97C4⋊Dic61—41no—
98#11758196—42no—
99C4×Dic61—22no—
100C4×Dic61—22no—
101C4×Dic61—41no—
102C4×Dic61—41no—
103C23×C61—21no—
104C23×C61—21no—
105C23×C61—21no—
106C23×C61—21no—
107C23×C61—21no—
108C23×C61—21no—
109C23×C61—41no—
110C23×C61—41no—
111C23×C61—41no—
112C23×C61—41no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61—41no—
116C23×C61#10412yes—
117C23×C61C2×C22⋊C411yescharacteristic
118D4×C61—82no—
119D4×C61—84no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—44no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61#10012yes—
129C2×C4×C61#13112yes—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—44no—
140C2×Dic61—44no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61#9912yes—
148C2×Dic61#13512yes—
149C2×Dic61#13512yes—
150Dic122—82no—
151#92420—44no—
152#92420—82no—
153#7670—611nomaximal, Sylow
154C22×C61—22no—
155C22×C61—22no—
156C22×C61—22no—
157C22×C61—41no—
158C22×C61—41no—
159C22×C61—41no—
160C22×C61—41no—
161C22×C61—81no—
162C22×C61—81no—
163C22×C61—81no—
164C22×C61—81no—
165C22×C61—81no—
166C22×C61—81no—
167C22×C61—81no—
168C22×C61#40811yescharacteristic
169C22×C61C2×#9911yescharacteristic
170C22×C61C2×#10011yescharacteristic
171C22×C61#41611yescharacteristic
172C22×C61#41611yescharacteristic
173C22×C61C2×#10411yescharacteristic
174C22×C61#42111yescharacteristic
175C4×C61—22no—
176C4×C61—22no—
177C4×C61—81no—
178Dic61—22no—
179Dic61—22no—
180Dic61—22no—
181Dic61—41no—
182Dic61—81no—
183Dic61—81no—
184#2850—611no—
185#1817—611no—
186C4×C22⋊C8—611no—
187#1272—612no—
188#1270—612no—
189C2×C61—42no—
190C2×C61—161no—
191C2×C61#147111yescharacteristic
192C2×C61#148211yescharacteristic
193C2×C61#149411yescharacteristic
194C2×C61#150111yescharacteristic
195C2×C61#151611yescharacteristic
196C2×C61#152711yescharacteristic
197C2×C61#154311yescharacteristic
198C2×#124—611no—
199C2×C22⋊Q8—611no—
200C2×#121#692311yescharacteristic
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—611no—
212#336—612no—
213#336—612no—
214#336—1221no—
215C61#767011yescharacteristic, complemented, Sylow
216C22×Q8—611no—
217C22×D4—21no—
218C22×D4C2×#692311yescharacteristic
219C23×C4—611no—
220C23×C4—611no—
221C23×C4C2×#692311yescharacteristic
222C22×C8—1222no—
223C22×C8—1222no—
224#124—2442no—
225C22⋊Q8—2442no—
226#121—42no—
227C2×C4⋊C4—611no—
228C2×C4⋊C4—1221no—
229C2×C4⋊C4C2×#692311yescharacteristic
230C2×C22⋊C4—21no—
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—611no—
240C2×C42—2442no—
241C22⋊C8—1224no—
242C22⋊C8—2442no—
243C4×C8—2442no—
244#95—1221no—
245#95—1221no—
246#95—1221no—
247#95—1221no—
248C24—21no—
249C24C22⋊#692311yescharacteristic
250C2×Q8—1222no—
251C2×Q8—2441no—
252C2×Q8—2441no—
253C2×D4—22no—
254C2×D4—41no—
255C2×D4—41no—
256C2×D4—42no—
257C2×D4—42no—
258C2×D4—42no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—21no—
262C22×C4—41no—
263C22×C4—611no—
264C22×C4—611no—
265C22×C4—611no—
266C22×C4—611no—
267C22×C4—1222no—
268C22×C4—1222no—
269C22×C4—1222no—
270C22×C4—1222no—
271C22×C4—1221no—
272C22×C4—1221no—
273C22×C4—2441no—
274C22×C4—2441no—
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—2441no—
285C4⋊C4—2442no—
286C22⋊C4—42no—
287C22⋊C4—2442no—
288C22⋊C4—2442no—
289C22⋊C4—2442no—
290C22⋊C4—2442no—
291C22⋊C4—2442no—
292C42—1222no—
293C42—1222no—
294C42—2441no—
295C42—2441no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23#1451984112yes—
310C23C2×C22⋊#692311yescharacteristic
311Q8—4882no—
312D4—82no—
313D4—84no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—44no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—612no—
323C2×C4—612no—
324C2×C4—612no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—1221no—
328C2×C4—1221no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—1221no—
333C2×C4—1221no—
334C2×C4—2444no—
335C2×C4—2444no—
336C2×C4—2441no—
337C2×C4—2441no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4—2441no—
341C2×C4—2441no—
342C2×C4#1451983712yes—
343C2×C4#1451986412yes—
344C8—4882no—
345C8—2444no—
346C22—22no—
347C22—22no—
348C22—22no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22#1684073511yescharacteristic
361C22D61⋊#9911yescharacteristic
362C22C2×#1451983711yescharacteristic
363C22#1684075211yescharacteristic
364C22#1684075211yescharacteristic
365C22C2×#1451984111yescharacteristic
366C22#1684076011yescharacteristic
367C4—22no—
368C4—22no—
369C4—81no—
370C4—1222no—
371C4—1222no—
372C4—1222no—
373C4—4881no—
374C4—4881no—
375C4—2441no—
376C2—42no—
377C2—161no—
378C2#2146109511yescharacteristic
379C2#2146113011yescharacteristic
380C2#2146117011yescharacteristic
381C2#2146119511yescharacteristic
382C2#2146124411yescharacteristic
383C2#2146127811yescharacteristic
384C2#2146132211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
Fitting, prime radicalC2×#121×C61C4
socleC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×#121#6923
hypocenterC61#7670
LCSG ▷ C22×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. #21461710C2semidirect
2. C4×C22⋊#92420C2semidirect
3. #21460640C2semidirect
4. #21460635C2semidirect
215. C61#7670semidirect

Maximal subgroups

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

subgroupindex
#214617102
C4×C22⋊#924202
#214606402
#214606352
#214541182
#767061