Finite Group Databasebeta

← #29571375

Subgroups — #29571375

Order 15616.

874 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 874 conjugacy classes of subgroups — too many to draw. Only its 139 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
1C22×#14519771C211yesmaximal, characteristic
2#21445887C211yesmaximal, characteristic, complemented
3C2×#16839487C212yesmaximal, complemented
4C2×#16839485C212yesmaximal
5C61×#1817C211yesmaximal, characteristic, complemented
6C2×#14519771—24no—
7C2×#14519771—24no—
8C2×#14519771—22no—
9C2×#14519771—22no—
10C22×#11758196C411yescharacteristic
11C22×#11758196C411yescharacteristic
12C22×#11758196C2211yescharacteristic
13C22×#11758198C411yescharacteristic
14C22×#11758198C411yescharacteristic
15C22×#11758198C2211yescharacteristic
16C2×C22⋊#92418C2212yes—
17#16839517—22no—
18#16839487—24no—
19#16839485—24no—
20C22×C42×C61C2211yescharacteristic
21C2×C22⋊C8×C61C2212yes—
22C61×#336—22no—
23C24×D61C2×C411yescharacteristic
24C23×Dic61C2×C411yescharacteristic
25C23×Dic61C2×C411yescharacteristic
26C23×Dic61C2×C411yescharacteristic
27C22×#92418—22no—
28#14519771—216no—
29#14519771—216no—
30C2×#11758196—22no—
31C2×#11758196—22no—
32C2×#11758196—21no—
33C2×#11758196—22no—
34C2×#11758196—21no—
35C2×#11758196—22no—
36C2×#11758196—22no—
37C2×#11758196—22no—
38C2×#11758196—22no—
39C2×#11758196D414yes—
40C2×#11758198—22no—
41C2×#11758198—22no—
42C2×#11758198—22no—
43C2×#11758198—22no—
44C2×#11758198—21no—
45C2×#11758198—22no—
46C2×#11758198—21no—
47C2×#11758198—22no—
48C2×#11758198—22no—
49C2×#11758198D414yes—
50C22⋊#92418—22no—
51C22⋊#92418—22no—
52C23×C4×C61C2×C411yescharacteristic
53C23×C4×C61C2×C411yescharacteristic
54C23×C4×C61C2311yescharacteristic
55C22×C8×C61—22no—
56C2×C42×C61—22no—
57C2×C42×C61—22no—
58C2×C42×C61D412yes—
59C2×C42×C61D412yes—
60C22⋊C8×C61—22no—
61C22⋊C8×C61—22no—
62C24×C61C22×C411yescharacteristic
63C23×D61—21no—
64C23×D61—21no—
65C23×D61—22no—
66C23×D61—22no—
67C23×D61—42no—
68C23×D61—42no—
69C23×D61C22⋊C412yes—
70C22×C4×C61—21no—
71C22×C4×C61—21no—
72C22×C4×C61—21no—
73C22×C4×C61—21no—
74C22×C4×C61—22no—
75C22×C4×C61—22no—
76C22×C4×C61—42no—
77C22×C4×C61—42no—
78C22×C4×C61C22⋊C412yes—
79C22×C4×C61C22⋊C412yes—
80C22×C4×C61C2×D411yescharacteristic
81C22×C4×C61C2×D411yescharacteristic
82C22×C4×C61C2×D412yes—
83C22×C4×C61C2×D412yes—
84C22×Dic61—21no—
85C22×Dic61—21no—
86C22×Dic61—21no—
87C22×Dic61—21no—
88C22×Dic61—21no—
89C22×Dic61—21no—
90C22×Dic61—22no—
91C22×Dic61—22no—
92C22×Dic61—42no—
93C22×Dic61—42no—
94C22×Dic61C22⋊C412yes—
95C22×Dic61C22⋊C412yes—
96C22×Dic61C22⋊C412yes—
97C2×C8×C61—44no—
98C2×C8×C61—42no—
99C42×C61—24no—
100C42×C61—24no—
101#11758198—28no—
102#11758198—28no—
103#11758198—24no—
104#11758198—24no—
105#11758196—28no—
106#11758196—28no—
107#11758196—24no—
108#11758196—24no—
109C2×#92418—44no—
110C2×#92418—42no—
111C23×C61—22no—
112C23×C61—22no—
113C23×C61C2×C22⋊C411yescharacteristic
114C23×C61C2×C22⋊C411yescharacteristic
115C23×C61C2×C22⋊C411yescharacteristic
116C23×C61#13112yes—
117C23×C61#13112yes—
118C22×D61—22no—
119C22×D61—24no—
120C22×D61—42no—
121C22×D61—42no—
122C22×D61—42no—
123C22×D61—41no—
124C22×D61—41no—
125C22×D61—42no—
126C22×D61—42no—
127C22×D61—42no—
128C22×D61—42no—
129C22×D61—84no—
130C22×D61—84no—
131C2×C4×C61—22no—
132C2×C4×C61—22no—
133C2×C4×C61—22no—
134C2×C4×C61—22no—
135C2×C4×C61—22no—
136C2×C4×C61—22no—
137C2×C4×C61—24no—
138C2×C4×C61—42no—
139C2×C4×C61—42no—
140C2×C4×C61—42no—
141C2×C4×C61—42no—
142C2×C4×C61—42no—
143C2×C4×C61—42no—
144C2×C4×C61#12012yes—
145C2×C4×C61#12012yes—
146C2×Dic61—22no—
147C2×Dic61—22no—
148C2×Dic61—22no—
149C2×Dic61—24no—
150C2×Dic61—42no—
151C2×Dic61—42no—
152C2×Dic61—42no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—42no—
156C2×Dic61—42no—
157C2×Dic61—42no—
158C2×Dic61—42no—
159C8×C61—82no—
160#92418—82no—
161#8309—611nomaximal, Sylow
162C22×C61—24no—
163C22×C61—24no—
164C22×C61—21no—
165C22×C61—21no—
166C22×C61—21no—
167C22×C61—21no—
168C22×C61#37911yescharacteristic
169C22×C61#40812yes—
170C22×C61#40812yes—
171C22×C61#40811yescharacteristic
172C22×C61#40811yescharacteristic
173C22×C61#41012yes—
174C22×C61#41312yes—
175C2×D61—42no—
176C2×D61—42no—
177C2×D61—42no—
178C2×D61—84no—
179C2×D61—82no—
180C2×D61—82no—
181C2×D61—84no—
182C4×C61—22no—
183C4×C61—22no—
184C4×C61—42no—
185C4×C61—42no—
186Dic61—42no—
187Dic61—42no—
188Dic61—42no—
189C22×#126—611no—
190#1817—611no—
191#1817D6111yescharacteristic, complemented
192C2×#324—612no—
193C2×#323—612no—
194C2×C61—22no—
195C2×C61—22no—
196C2×C61#147312yes—
197C2×C61#147312yes—
198C2×C61#178011yescharacteristic
199C2×C61#178211yescharacteristic
200C2×C61#178511yescharacteristic
201D61—82no—
202C2×#126—1224no—
203C2×#126—1224no—
204C2×#126—1222no—
205C2×#126—1222no—
206C22×C4⋊C4—611no—
207C22×C4⋊C4—611no—
208C22×C4⋊C4—611no—
209C22×C22⋊C4—611no—
210C22×C22⋊C4—611no—
211C22×C22⋊C4—611no—
212C22×C42C2×D6111yescharacteristic
213C2×C22⋊C8—612no—
214C2×C22⋊C8C2×D6112yes—
215#336—22no—
216#336—1222no—
217#324—1224no—
218#323—1224no—
219C61#830911yescharacteristic, complemented, Sylow
220C25—611no—
221C23×C4—611no—
222C23×C4—611no—
223C23×C4—611no—
224C23×C4C4×D6111yescharacteristic
225C23×C4C4×D6111yescharacteristic
226C23×C4C22×D6111yescharacteristic
227C22×C8—22no—
228C22×C8—1222no—
229#126—12216no—
230#126—12216no—
231C2×C4⋊C4—614no—
232C2×C4⋊C4—1222no—
233C2×C4⋊C4—1222no—
234C2×C4⋊C4—1222no—
235C2×C4⋊C4—1222no—
236C2×C4⋊C4—1222no—
237C2×C4⋊C4—1222no—
238C2×C4⋊C4—1221no—
239C2×C4⋊C4—1222no—
240C2×C4⋊C4—1221no—
241C2×C22⋊C4—614no—
242C2×C22⋊C4—1222no—
243C2×C22⋊C4—1222no—
244C2×C22⋊C4—1222no—
245C2×C22⋊C4—1222no—
246C2×C22⋊C4—1222no—
247C2×C22⋊C4—1222no—
248C2×C22⋊C4—1221no—
249C2×C22⋊C4—1222no—
250C2×C22⋊C4—1221no—
251C2×C42—22no—
252C2×C42—22no—
253C2×C42D24412yes—
254C2×C42C22⋊D6112yes—
255C22⋊C8—22no—
256C22⋊C8—22no—
257C22⋊C8—1222no—
258C22⋊C8—1222no—
259C24—612no—
260C24—1222no—
261C24—1222no—
262C24—1221no—
263C24—1221no—
264C24—2442no—
265C24—2442no—
266C24C2×C4×D6111yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—42no—
274C22×C4—42no—
275C22×C4—612no—
276C22×C4—612no—
277C22×C4—612no—
278C22×C4—1221no—
279C22×C4—1221no—
280C22×C4—1221no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4—1222no—
285C22×C4—1222no—
286C22×C4—2442no—
287C22×C4—2442no—
288C22×C4#1175819812yes—
289C22×C4#1175819812yes—
290C22×C4C2×D24411yescharacteristic
291C22×C4D4×D6112yes—
292C22×C4D4×D6112yes—
293C22×C4C2×C22⋊D6111yescharacteristic
294C2×C8—44no—
295C2×C8—42no—
296C2×C8—2444no—
297C2×C8—2442no—
298C4⋊C4—1228no—
299C4⋊C4—1228no—
300C4⋊C4—1224no—
301C4⋊C4—1224no—
302C22⋊C4—1228no—
303C22⋊C4—1228no—
304C22⋊C4—1224no—
305C22⋊C4—1224no—
306C42—24no—
307C42—24no—
308C23—22no—
309C23—22no—
310C23—1224no—
311C23—1222no—
312C23—4884no—
313C23—4884no—
314C23—2442no—
315C23—2442no—
316C23—2442no—
317C23—2442no—
318C23—2442no—
319C23—2441no—
320C23—2441no—
321C23—2442no—
322C23—2442no—
323C23C22⋊C4×D6111yescharacteristic
324C23C22⋊C4×D6111yescharacteristic
325C23C2×#1175819811yescharacteristic
326C23#1451978312yes—
327C23#1451978512yes—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—24no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—1224no—
342C2×C4—1222no—
343C2×C4—1222no—
344C2×C4—1222no—
345C2×C4—2442no—
346C2×C4—2442no—
347C2×C4—2442no—
348C2×C4—2441no—
349C2×C4—2441no—
350C2×C4—2442no—
351C2×C4—2442no—
352C2×C4—2442no—
353C2×C4—2442no—
354C2×C4#1451974512yes—
355C2×C4#1451974712yes—
356C8—82no—
357C8—4882no—
358C22—24no—
359C22—24no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—4884no—
365C22—4884no—
366C22—4882no—
367C22—4882no—
368C22—2442no—
369C22—2442no—
370C22—2442no—
371C22#1683961711yescharacteristic
372C22#1683972712yes—
373C22#1683972712yes—
374C22#1683972811yescharacteristic
375C22#1683973011yescharacteristic
376C22#1683973512yes—
377C22#1683974412yes—
378C4—22no—
379C4—22no—
380C4—42no—
381C4—42no—
382C4—2442no—
383C4—2442no—
384C4—2442no—
385C2—22no—
386C2—22no—
387C2—4882no—
388C2#2144418612yes—
389C2#2144418912yes—
390C2#2144573011yescharacteristic
391C2#2144573611yescharacteristic
392C2#2144574511yescharacteristic
subgroupG/H
centerC23C2×#11758198
commutatorC24×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1817C2
socleC23×C61C2×C22⋊C4
prime radicalC24×D61C2×C4
cosocleC23×C4×C61C23
hypercenter#1817D61
hypocenterC61#8309
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1817

Complements

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

NH ≅ G/Ntype
2. #21445887C2semidirect
3. C2×#16839487C2semidirect
5. C61×#1817C2semidirect
191. #1817D61semidirect
219. C61#8309semidirect

Maximal subgroups

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

subgroupindex
C22×#145197712
#214458872
C2×#168394872
C2×#168394852
C61×#18172
#830961