Finite Group Databasebeta

← #30603983

Subgroups — #30603983

Order 15616.

548 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 90 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#21461059C211yesmaximal, characteristic, complemented
2#21461055C211yesmaximal, characteristic, complemented
3#21460764C212yesmaximal, complemented
4#21460744C212yesmaximal, complemented
5#21448482C211yesmaximal, characteristic
6#16840778—21no—
7C2×C22⋊#92420—21no—
8#16840607—21no—
9#16840605—21no—
10#16840605C2212yes—
11#16840605C2212yes—
12C2×#14519745C411yescharacteristic
13C2×D4×Dic61C2211yescharacteristic
14C22×#11758198C411yescharacteristic
15#16839662—21no—
16#16839654—21no—
17#16839651—21no—
18#16839639—21no—
19#16839635C2211yescharacteristic
20#16839617C2211yescharacteristic
21C22⋊C4×Dic61C411yescharacteristic
22C61×#386C411yescharacteristic
23C22×#92420—41no—
24C4⋊#92420—41no—
25C22⋊#92420—22no—
26C22⋊#92420—22no—
27C22⋊#92420—41no—
28C4×#92420—41no—
29C24×D61C2×C411yescharacteristic
30C22×C22⋊D61—21no—
31C23×Dic61C2×C411yescharacteristic
32C23×Dic61D411yescharacteristic
33#14519745—22no—
34#14519745C814yescomplemented
35D4×Dic61—41no—
36D4×Dic61—41no—
37C2×C4⋊Dic61D411yescharacteristic
38C2×#11758196—21no—
39C2×C22⋊Dic61C2×C411yescharacteristic
40C2×C22⋊Dic61D411yescharacteristic
41C2×C22⋊Dic61C2311yescharacteristic
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×#11758198—21no—
47C2×#11758198—41no—
48C2×#11758198—41no—
49C2×C4×Dic61—21no—
50C2×C4×Dic61D411yescharacteristic
51#14519684—21no—
52#14519684—21no—
53C22×D4×C61C2×C411yescharacteristic
54C23×C4×C61C2×C411yescharacteristic
55C2×C22⋊C4×C61—21no—
56C2×C22⋊C4×C61C2×C411yescharacteristic
57#95×C61—21no—
58C24×C61C22⋊C411yescharacteristic
59C24×C61C22×C411yescharacteristic
60C23×D61—21no—
61C23×D61—21no—
62C23×D61—41no—
63C23×D61—41no—
64C23×D61—81no—
65C23×D61—81no—
66C23×D61C2×C812yescomplemented
67C2×D4×C61—41no—
68C2×D4×C61—41no—
69C2×D4×C61C2×C812yes—
70C2×D4×C61M1612yes—
71C22×C4×C61—21no—
72C22×C4×C61—21no—
73C22×C4×C61—41no—
74C22×C4×C61—81no—
75C22×C4×C61C22⋊C411yescharacteristic
76C2×C22⋊D61—24no—
77C2×C22⋊D61—81no—
78C2×C22⋊D61—81no—
79C22×Dic61—21no—
80C22×Dic61—21no—
81C22×Dic61—21no—
82C22×Dic61—21no—
83C22×Dic61—21no—
84C22×Dic61—81no—
85C22×Dic61—81no—
86C22×Dic61C22⋊C411yescharacteristic
87C22×Dic61C22⋊C411yescharacteristic
88C22×Dic61C2×D411yescharacteristic
89C22×Dic61C2×D411yescharacteristic
90C2×#92420—42no—
91C2×#92420—42no—
92C2×#92420—82no—
93C22⋊C4×C61—41no—
94C22⋊C4×C61—81no—
95C22⋊Dic61—21no—
96C22⋊Dic61—41no—
97C22⋊Dic61—41no—
98C22⋊Dic61C2×C812yescomplemented
99#11758198—24no—
100#11758198—42no—
101#11758198—41no—
102#11758198—41no—
103#11758198—81no—
104#11758198—81no—
105C4⋊Dic61—41no—
106#11758196—81no—
107C4×Dic61—21no—
108C4×Dic61—21no—
109C4×Dic61—81no—
110C23×C61—21no—
111C23×C61—21no—
112C23×C61—21no—
113C23×C61—21no—
114C23×C61—41no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61—41no—
118C23×C61C22⋊C812yes—
119C23×C61C2×C22⋊C411yescharacteristic
120C23×C61C22×C811yescharacteristic
121C23×C61C2×M1611yescharacteristic
122C22×D61—22no—
123C22×D61—41no—
124C22×D61—41no—
125C22×D61—41no—
126C22×D61—41no—
127C22×D61—42no—
128C22×D61—41no—
129C22×D61—41no—
130C22×D61—42no—
131C22×D61—82no—
132C22×D61—82no—
133C22×D61—84no—
134C22×D61—82no—
135C22×D61—82no—
136D4×C61—42no—
137D4×C61—42no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—82no—
147C2×C4×C61C22⋊C812yes—
148C22⋊D61—84no—
149C2×Dic61—22no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61—21no—
153C2×Dic61—41no—
154C2×Dic61—42no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—81no—
161C2×Dic61—81no—
162C2×Dic61—81no—
163C2×Dic61#9911yescharacteristic
164C2×Dic61#9911yescharacteristic
165#92420—82no—
166#92420—82no—
167#11473—611nomaximal, Sylow
168C22×C61—21no—
169C22×C61—21no—
170C22×C61—21no—
171C22×C61—21no—
172C22×C61—22no—
173C22×C61—42no—
174C22×C61—41no—
175C22×C61—41no—
176C22×C61—42no—
177C22×C61—41no—
178C22×C61—41no—
179C22×C61—41no—
180C22×C61—41no—
181C22×C61—81no—
182C22×C61C2×C22⋊C811yescharacteristic
183C22×C61C2×#9911yescharacteristic
184C22×C61#41311yescharacteristic
185C2×D61—42no—
186C2×D61—42no—
187C2×D61—42no—
188C2×D61—81no—
189C2×D61—81no—
190C2×D61—84no—
191C2×D61—81no—
192C2×D61—81no—
193C2×D61—84no—
194C4×C61—22no—
195C4×C61—81no—
196C4×C61—81no—
197Dic61—21no—
198Dic61—21no—
199Dic61—42no—
200Dic61—41no—
201Dic61—41no—
202Dic61—41no—
203#2321—611no—
204#1460—611no—
205#1459—611no—
206#1326—612no—
207#1316—612no—
208C2×C61—21no—
209C2×C61—21no—
210C2×C61—41no—
211C2×C61—41no—
212C2×C61—42no—
213C2×C61#145911yescharacteristic
214C2×C61#212111yescharacteristic
215C2×C61#212211yescharacteristic
216D61—82no—
217C2×#120—611no—
218C2×C4×D4—611no—
219C22×C22⋊C4—611no—
220#431—1221no—
221C2×C22⋊C8—1221no—
222#390—1221no—
223#388—1221no—
224#388—1221no—
225#386—1221no—
226#386#692311yescharacteristic
227#385—611no—
228#379—611no—
229C4×C22⋊C4—611no—
230#324—1221no—
231#323—612no—
232#323—612no—
233#323—1221no—
234C61#1147311yescharacteristic, complemented, Sylow
235C25—611no—
236C22×D4—1221no—
237C22×D4C2×#692311yescharacteristic
238C23×C4—611no—
239C23×C4—611no—
240C23×C4C2×#692311yescharacteristic
241C22×C8—2441no—
242#120—614no—
243#120—1222no—
244C4×D4—2441no—
245C4×D4—2441no—
246C2×C4⋊C4—611no—
247C2×C4⋊C4—1221no—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—611no—
250C2×C22⋊C4—611no—
251C2×C22⋊C4—611no—
252C2×C22⋊C4—1221no—
253C2×C22⋊C4—1221no—
254C2×C22⋊C4—1221no—
255C2×C22⋊C4—1221no—
256C2×C22⋊C4—1221no—
257C2×C22⋊C4—2441no—
258C2×C22⋊C4—2441no—
259C2×C22⋊C4C2×#692311yescharacteristic
260C2×C42—611no—
261C2×C42—1221no—
262C4⋊C8—2441no—
263C22⋊C8—1222no—
264C22⋊C8—1222no—
265C22⋊C8—2441no—
266C4×C8—2441no—
267#95—21no—
268#95—1221no—
269#95—1221no—
270C24—612no—
271C24—1221no—
272C24—1221no—
273C24—4881no—
274C24—4881no—
275C24—2441no—
276C24—2441no—
277C24C22⋊#692311yescharacteristic
278C24C22×#692311yescharacteristic
279C2×D4—41no—
280C2×D4—41no—
281C2×D4—1224no—
282C2×D4—4881no—
283C2×D4—4881no—
284C2×D4D61⋊C812yes—
285C2×D4#1175821312yes—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—41no—
289C22×C4—81no—
290C22×C4—611no—
291C22×C4—611no—
292C22×C4—611no—
293C22×C4—611no—
294C22×C4—1221no—
295C22×C4—1221no—
296C22×C4—1221no—
297C22×C4—1221no—
298C22×C4—1221no—
299C22×C4—4881no—
300C22×C4—4881no—
301C22×C4C22⋊#692311yescharacteristic
302C2×C8—4882no—
303C2×C8—2442no—
304C2×C8—2442no—
305C4⋊C4—4881no—
306C4⋊C4—2441no—
307C22⋊C4—41no—
308C22⋊C4—81no—
309C22⋊C4—612no—
310C22⋊C4—1221no—
311C22⋊C4—1224no—
312C22⋊C4—4881no—
313C22⋊C4—4881no—
314C22⋊C4—2441no—
315C22⋊C4—2441no—
316C22⋊C4—2442no—
317C22⋊C4—2441no—
318C22⋊C4—2441no—
319C42—1221no—
320C42—1221no—
321C42—4881no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23—1222no—
331C23—4882no—
332C23—4882no—
333C23—4884no—
334C23—4882no—
335C23—4882no—
336C23—2442no—
337C23—2441no—
338C23—2441no—
339C23—2441no—
340C23—2441no—
341C23—2442no—
342C23—2441no—
343C23—2441no—
344C23#1451983412yes—
345C23C2×C22⋊#692311yescharacteristic
346C23C2×D61⋊C811yescharacteristic
347C23C2×#1175821311yescharacteristic
348D4—42no—
349D4—42no—
350D4—4884no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—82no—
360C2×C4—611no—
361C2×C4—611no—
362C2×C4—1222no—
363C2×C4—1221no—
364C2×C4—1221no—
365C2×C4—1221no—
366C2×C4—4881no—
367C2×C4—4881no—
368C2×C4—4881no—
369C2×C4—2441no—
370C2×C4—2442no—
371C2×C4—2441no—
372C2×C4—2441no—
373C2×C4—2441no—
374C2×C4—2441no—
375C2×C4—2441no—
376C2×C4#1451983412yes—
377C8—4882no—
378C8—4882no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—22no—
384C22—42no—
385C22—41no—
386C22—41no—
387C22—42no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—81no—
393C22—4881no—
394C22—4881no—
395C22—4884no—
396C22—4884no—
397C22—4881no—
398C22—4881no—
399C22—2442no—
400C22—2442no—
401C22—2442no—
402C22C2×#1451983411yescharacteristic
403C22D61⋊#9911yescharacteristic
404C22#1684074911yescharacteristic
405C4—22no—
406C4—81no—
407C4—81no—
408C4—1221no—
409C4—1221no—
410C4—2442no—
411C4—2441no—
412C4—2441no—
413C4—2441no—
414C2—21no—
415C2—21no—
416C2—41no—
417C2—41no—
418C2—42no—
419C2—4882no—
420C2#2146105711yescharacteristic
421C2#2146207711yescharacteristic
422C2#2146207911yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC23×C61C22×C8
FrattiniC24C22×#6923
FittingC61×#386C4
socleC22×C61C2×#99
prime radicalC2×#14519745C4
cosocleC2×C22⋊Dic61C23
hypercenter#386#6923
hypocenterC61#11473
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #386

Complements

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

NH ≅ G/Ntype
1. #21461059C2semidirect
2. #21461055C2semidirect
3. #21460764C2semidirect
4. #21460744C2semidirect
34. #14519745C8semidirect
66. C23×D61C2×C8semidirect
98. C22⋊Dic61C2×C8semidirect
234. C61#11473semidirect

Maximal subgroups

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

subgroupindex
#214610592
#214610552
#214607642
#214607442
#214484822
#1147361